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ON THE USE OF A REGIONAL-SCALE NUMERICAL
CLIMATE MODEL IN WIND ENERGY APPLICATIONS

presented by

KARSTEN ALEXANDER SHEIN

has been accepted towards fulﬁllment
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Doctoral Geography

 

 

 

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ON THE USE OF A REGIONAL-SCALE NUMERICAL CLIMATE MODEL IN
WIND ENERGY APPLICATIONS

By

Karsten Alexander Shein

A DISSERTATION
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Geography

2005

ABSTRACT

ON THE USE OF A REGIONAL-SCALE NUMERICAL CLIMATE MODEL IN
WIND ENERGY APPLICATIONS

By

Karsten Alexander Shein

This research explores the performance of a regional scale numerical climate model
(MMS) with respect to the estimation of the wind resource over the Great Lakes region of
North America. Three model domain resolutions (36 km, 12 km and 4 km) are evaluated
for accuracy. Additionally, the ability of the model to accurately estimate the wind
resource distribution at speciﬁc locations is investigated by employing various spatial

aggregation schemes over the model domain.

The results of this evaluation of the MMS model indicated that a coarser resolution
domain provides the most reliable estimates of the wind resource over the region.
Furthermore, only the nearest grid point appears to be a necessary estimator of the wind
regime at a particular location. Using this information, the MMS model estimates were
compared with estimates produced by three statistical models, a joint probabilistic model,
a measure-correlate—predict model, and a Krige model, all of which have been used with
prior success in wind resource estimation. Of the three statistical models, the joint
probabilistic and measure-correlate—predict models provided the best estimates over the

region and were thus compared with the MM5 estimates.

It was determined that none of the three models signiﬁcantly outperformed the others,
even at relatively remote locations within the study area. However, it also was noted that
the MMS model contained a much higher systematic proportion of total estimative bias,
and that it might be possible to improve the estimates. A multiple linear regression based
upon Latitude was ﬁt to the estimated Weibull parameters from the MMS model and a
signiﬁcant improvement was noted. However, the improvement failed to cause the MMS
to signiﬁcantly outperform the other models. Thus, this research concludes that in its
present state and relative complexity of implementation relative to established statistical

models, MMS would not be a logical choice for estimating the wind resources of the

Great Lakes region.

Keywords: wind resource analysis, numerical climate model, Great Lakes

Copyright by
KARSTEN ALEXANDER SHEIN
2005

For my wife, soul mate and media naranja, Walli Ann.

ACKNOWLEDGEMENTS

I am indebted to my principal adviser, Dr. Jeffrey A. Andresen for his guidance
and council throughout my graduate work at Michigan State University. I also am
grateﬁtl to the members of my doctoral committee, Drs. Julie Winkler, Jay Harman, Jean
Palutikof, Bill Northcott, and Fred Numberger. Their instruction, comments and council

throughout this endeavor has proven invaluable.

Additionally, I am deeply thankful to the United States Forest Service North
Central Research Station for providing the MMS data needed to complete this research.
In particular, I wish to thank Drs. Warren E. Heilman, Joseph J. (Jay) Charney, Brian E.
Potter, and especially Xindi Bian for their implementation of the MMS regional climate
model, for helping me to understand the way in which the model was set up, and for
assisting me greatly in assembling the model output. Without the efforts of these ﬁne
people, this project would not have been possible. Furthermore, the material presented
herein is based upon work supported by the National Science Foundation under Grant

No. 0302469.

Finally, I wish to acknowledge my lovely wife, Dr. Walli Ann Wisniewski. It
was she who ultimately gave me the drive and desire to keep pushing ahead when there
seemed to be no light at the end of the tunnel. Her encouragement and love were without

measure.

vi

 

TABLE OF CONTENTS

List of Tables .................................................................................................................... ix
List of Figures ................................................................................................................... xi
Key to Symbols or Abbreviations ................................................................................ xviii
1. Introduction .................................................................................................................... l
1.1 Statement of Purpose ..................................................................................... 11

2. Literature Review ......................................................................................................... 16
2.1 Wind Resource Identiﬁcation and Analysis .................................................. 17

2.1.1 Properties of the wind ﬁeld ............................................................ 18

2.1.1.1 Statistical measures .......................................................... 19

2.1.1.2 Wind speed distributions ................................................. 20

2.1.1.3 Data collection ................................................................. 23

2.1.1.4 Serial correlation and stationarity .................................... 27

2.1.1.5 Resource variability ......................................................... 30

2.2 Statistical Wind Field Modeling .................................................................... 34
2.2.1 Stochastic models ............................................................................ 34

2.2.2 Probabilistic models ........................................................................ 40

2.3 Dynamical Models ......................................................................................... 44

2.4 Model Comparison and Validation ................................................................ 48

3. Study Area, Data and Methods .................................................................................... 50
3.1 Study Area ..................................................................................................... 50
3.2 Observational Data Types and Sources ......................................................... 52
3.2.1 ASOS/AWOS wind sensors and siting ........................................... 55

3.2.2 ASOS/AWOS wind observation and reporting .............................. 59

3.3 Observational Data Quality Control .............................................................. 62
3.3.1 Data homogenization and aggregation ........................................... 69

3.3.2 Representativeness of A808 data .................................................. 74

3.4 Spatial and Temporal Behavior of Observational Data ................................. 91
3.4.1 Non-seasonal assessment ................................................................ 91

3.4.2 Seasonal assessment ..................................................................... 112

3.5 FSMMS Model and Wind Estimates ........................................................... 125
3.5.1 Model implementation and domains ............................................ 125

3.5.2 Model output ................................................................................. 129

3.5.3 FSMM5 wind estimates ................................................................ 131

3.6 Statistical Model Identiﬁcation and Construction ....................................... 135
3.6.1 Measure-Correlate-Predict ............................................................ 136
3.6.2 Krige model .................................................................................. 139

vii

 

3.6.3 Joint probabilistic model ............................................................... 146

3.7 Model Evaluation ......................................................................................... 149

3.7.1 Probabilistic evaluative statistics .................................................. 150

3.7.2 Deterministic evaluative statistics ................................................ 155

3.7.3 Spatial analysis of model evaluation ............................................ 163

3.7.3.1 Trend surface analysis .................................................... 164

3.7.3.2 Isopach analysis ............................................................. 166

4. Results ........................................................................................................................ 167

4.1 MMS Model performance ............................................................................ 167

4.1.1 Performance based on grid resolution .......................................... 174

4.1.2 Performance based on spatial aggregation resolution ................... 192

4.2 Model Comparison ...................................................................................... 197

4.2.1 Statistical model performance ....................................................... 197

4.2.2 Comparison ofFSMMS to statistical models ................................ 200

4.3 Accounting for spatial bias in F SMMS ........................................................ 206

5. Discussion .................................................................................................................. 211
5.1 Summary of Research .................................................................................. 213

5.2 Conclusions and Discussion ........................................................................ 215

5.3 Future Directions ......................................................................................... 220
Appendix A. Automated Reporting Stations Used ........................................................ 223
Appendix B. Raw METAR Report File ........................................................................ 227
Appendix C. Selected Statistics ﬁ'om ASOS Stations ................................................... 228
Appendix D. ASOS 10-m Wind Observations .............................................................. 231
References ...................................................................................................................... 273

viii

LIST OF TABLES

Table 3.1 Statistics of the counts (and percentages) of non-missing values
(out of 14,617 possible observations) from series constructed with top-of-
the-hour observations and with hourly averaged values. ................................................. 71

Table 3.2 20 First-order weather stations that existed in the study area

prior to the ASOS transition during the mid-19903. Each station

corresponds to an ASOS station used in this study and is used to compare

the study period data to the long-term (1961-1990) wind climate at the

station. Mean wind speeds (u) and standard deviations (s) are based on

wind speeds (including zeros) given in m s'1 .................................................................... 75

Table 3.3 Wind data distribution and goodness-of-ﬁt statistics for 20

ASOS stations in the study area with long-term (1961-1990) wind records.

Weibull shape (k) and scale (c) parameters are given for short (ASOS) and

long-term (SAMSON) speeds. Average Anderson-Darling (A?) test

statistics based on 100 trials of 100 observations are given for the ASOS

data. ................................................................................................................................... 89

Table 4.1 Evaluative statistics of F SMMS model performance obtained

from wind estimates of 15 variations (X) of the model over the period of

record . The -0.11 value for minimum r is the lowest negative correlation

obtained (0.00 was the lowest absolute correlation obtained). ....................................... 169

Table 4.2 Evaluative statistics of FSMM5 model performance obtained

from wind estimates of 15 variations (X.) of the model over the period of

record. The mean error statistics are given in bin counts and the numbers

in parentheses in the mean error rows are the percentage of total n. k and

c are Weibull shape and scale parameters respectively. ................................................. 170

Table 4.3 Evaluative statistics of FSMM5 model performance obtained

from the 5 variants (X) of the model within each of the 3 model domains

over the period of record. The mean error statistics are given in bin counts

and are followed by the percentage of total 11. k and c are Weibull shape

and scale parameters respectively. .................................................................................. 175

Table 4.4 Evaluative statistics of 5 spatial aggregation schemes applied to

the F SMMS 36 km domain wind speed estimates over the period of

record. Percentage values in the error statistic cells are the error (bin

frequency) as a percentage of the overall number of estimates. Bold

values are statistically signiﬁcant improvements over the next higher

model (11,099). .................................................................................................................. 193

ix

Table 4.5 Evaluative statistics over the period of record for three

statistical wind resource models, a joint probabilistic model (JP), a
measure-correlate-predict model (MCP), and a Krige model (Krige). Error

values are in bin count differences (It), and the percentages are relative to

overall record length. ...................................................................................................... 198

Table 4.6 Evaluative statistics for the performance of three wind resource

estimation models, joint probabilistic (JP), measure-correlate-predict

(MCP), and F SMMS running on a 36 km domain and utilizing the one

nearest neighbor scheme over the period 11/02 to 6/04. Error measures

are given in bin count differences and the percentages are relative to

overall record length. ...................................................................................................... 200

Table 4.7 Evaluative statistics for the performance of three wind

forecasting models, joint probabilistic (JP), measure-correlate-predict

(MCP), and FSMM5 running on a 36 km domain and utilizing the one

nearest neighbor scheme for the period 11/02 to 6/04 .................................................... 201

Table 4.8 Evaluative statistics for model estimates of the wind resource at
Chapleau Airport, Ontario (CLYD). The models are joint probabilistic
(JP), measure-correlate-predict (MCP), and the 36 km domain, one nearest
neighbor variant of FSMM5 (F SMMS) for the period 11/02 to 6/04. Error
values are given in bin count differences and percentages are relative to

the length of record. ........................................................................................................ 203
Appendix A. Automated Reporting Stations Used ........................................................ 223
Appendix C. Selected Statistics from ASOS Stations ................................................... 228
Appendix D. ASOS 10-m Wind Observations .............................................................. 231

LIST OF FIGURES

Figure 1.1 An idealized wind turbine power curve, derived from the
Bonus 2 MW wind turbine (data sources: http://www.middlegrunden.dk

and http://www.bonus.dk). ................................................................................................. 5
Figure 1.2 Wind power potential for the United States, from the Wind

Energy Atlas of the United States (Elliott et al., 1987). ..................................................... 7
Figure 1.3 The study area; the Great Lakes region of North America. ........................... 13

Figure 3.1 A map of the study area, which includes the majority of the
Great Lakes region of North America. The dots represent the
ASOS/AWOS stations used in this study. ........................................................................ 52

Figure 3.2 ASOS/AWOS stations used in this research. Each number
corresponds to the list of stations in Appendix A. Stations may also be
referenced by their geographic coordinates, also in Appendix A. .................................... 53

Figure 3.3 An ASOS wind sensor array (from NOAA, 2000). ....................................... 57

Figure 3.4 Histograms of the number of non-missing observations at the

stations in the study region. Top-of-the-hour observations were those

taken within 10 minutes of the top of the hour, while hourly averaged

observations included an average of all observations from within 30

minutes of the top of the hour. .......................................................................................... 72

Figure 3.5 A comparison of observed mean wind speeds when using only
the observation closest to the top of the hour (x) or the average of all
observations for that hour (y). .......................................................................................... 73

Figure 3.6 A wind speed distribution (with calms removed) from KP59

(Copper Harbor, MI). While the distribution may vary from one station to

another, all stations in the study exhibit a similar distribution shape,

supporting the use of a Weibull distribution for wind speed description. ........................ 78

Figure 3.7 Wind speed frequency distribution (r) and cumulative
frequency distribution (1) at Rochester, NY (KROC) for ASOS data.
Theoretical Weibull distributions are shown as solid lines. ............................................. 81

Figure 3.8 Wind speed frequency distribution (r) and cumulative

frequency distribution (1) at Traverse City, MI (KTVC) for ASOS data.
Theoretical Weibull distributions are shown as solid lines. ............................................. 82

xi

Figure 3.9 Weibull pdf (r) and cdf (1) (solid lines) at Grand Rapids, MI

(KGRR) derived from 30-year hourly data (1961 - l 990) applied against the

ASOS observed (1 1/2002 - 6/2004) wind speed distribution [bars (I) and +

(r)]. .................................................................................................................................... 84

Figure 3.10 The distribution of Anderson-Darling (A2) test values from

100 random samples of 100 ASOS wind speed observations at Muskegon,

MI (MKG). The critical value (dashed) of 1.943 is shown, as is the mean

test statistic (solid) and 95% conﬁdence intervals (dotted). This station

accepted the p0pu1ation Weibull distribution 66/ 100 times. ............................................ 90

Figure 3.11 Average wind power map (at 50-m) of the contiguous United

States from Elliott et al., (1987). Values are based upon wind speed

observations from lower heights, and many of the over-water estimates are

of low conﬁdence due to limited data availability. A substantial portion of

the over-land parts of the study area are listed as category 2, or very low

wind speed potential. ........................................................................................................ 92

Figure 3.12 Annual mean wind speeds (in m s") for the period of record
across the study region. Negative values are invalid byproducts of
interpolation and should be ignored. ................................................................................ 93

Figure 3.13 Standard deviations (m 5") about mean annual wind speeds
over the study region for the period of record. ................................................................. 95

Figure 3.14 Prevailing wind directions (arrows are scaled by mean speed)
at the stations used in this study. Prevailing winds are derived from all
available data from all seasons in the period of record. ................................................... 96

Figure 3.15 Annual wind roses at four stations across the study area [(a)

Chapleau, ON, (b) Bellaire, MI, (0) Sault Ste. Marie, MI, and (d) Buffalo,

NY]. Wind regimes over the study region are very diverse over the period

of record (see Appendix D). ............................................................................................. 97

Figure 3.16 Temporal autocorrelation of non-seasonal wind speeds at
Toronto, ON (CYYZ) over the period of record. This autocorrelation
behavior is typical of wind speeds across the Great Lakes. ............................................. 98

Figure 3.17 First order (lag l) autocorrelation coefﬁcients over the study

area for the period of record. Although all stations are strongly

autocorrelated, the highest autocorrelations appear to occur at stations

most isolated from major land regions. .......................................................................... 100

xii

Figure 3.18 A 24-hour moving average time series of wind speeds at

Benton Harbor, MI (KBEH) over the period of record. Lowest wind

speeds are found during the summer months, while strongest winds are

experienced in winter. All seasons appear to exhibit substantial variability

about the station mean. ................................................................................................... 101

Figure 3.19 Power spectrum of wind speed at Ludington, MI (a coastal
location) ﬁom 11/02 to 6/04. The diurnal cycle near 0.04 cycles/hr is
dominant, accounting for 5% of the explained variance in the data ............................... 102

Figure 3.20 Power spectrum of wind speed at Lansing, MI (an inland
location) from 11/02 to 6/04. The diurnal cycle near 0.04 cycles/hr is
dominant, accounting for 7% of the explained variance in the data. .............................. 103

Figure 3.21 Annual Weibull PDF shape parameters over the study area for
the period of record. Highest values indicate highest probabilities of
winds near the mean wind speed. ................................................................................... 104

Figure 3.22 The inﬂuence on a Weibull PDF when the shape parameter is

varied. A shape value of 1 is an exponential distribution, 2 is a Raleigh

distribution, and 3.7 approximates a normal distribution. Below a shape

value of 3.7, the distribution is right skewed, and above it left skewed. ........................ 105

Figure 3.23 Non-seasonal (all data) Weibull PDF scale (c) parameters
over the study area. It is clear that as with the shape, the distribution
parameters cannot be considered regionally constant. ................................................... 106

Figure 3.24 Variations in the Weibull scale parameter result in a
stretching or squeezing of the distribution and reﬂect the behavior of the
mean and standard deviation of the wind speed distribution .......................................... 107

Figure 3.25 Schematic plots of non-seasonal wind speed distributions at 6

stations [(a) Goderich, ON, (b) Alpena, MI, (c) Muskegon, MI, ((1) Gary,

IN, (e) Niagara Falls, NY, and (t) Mackinaw Island, M1] for the period of

record. Most of the variability appears to be not in the main body (IQR)

of the distribution, but rather in the presence of high wind speed outliers.

This information likely skews both the mean and standard deviation of the

distributions toward higher values. See Appendix D for plots for all

stations. ........................................................................................................................... 109

Figure 3.26 Percent time at rated power (TARP) over the study area for

the period of record. This is a ratio of the total time a wind turbine might

be expected to be producing its rated (maximum) power. Calculations are

based on a 50 m turbine hub height with a rated power range at 50 m of 12

to 25 m s". ...................................................................................................................... 1 10

xiii

Figure 3.27 Power output in kilowatts over the period of record from a
Vestas 850 kW wind turbine ........................................................................................... l 11

Figure 3.28 Standard deviation of wind speeds by season (1 1/2002 -

6/2004). While the highest wind speeds occur in the winter, so does the

greatest variability in wind speeds. As expected, summer, with the lowest

mean speeds also has the smallest variation. .................................................................. 1 14

Figure 3.29 Prevailing winds during each season (1 1/2002 - 6/2004) at the

stations in the study area. The dominant direction in all seasons except

Spring is southwesterly. Spring is characterized by predominantly

northerly and northwesterly winds. Station wind arrows are scaled by

seasonal mean wind speed. ............................................................................................. 116

Figure 3.30 Seasonal wind roses at Beaver Island, MI (KSJ X) for the
period of record. This station is consistent with the regional prevailing
ﬂow regime. .................................................................................................................... 1 19

Figure 3.31 Seasonal wind roses at Traverse City, M1 for the period of
record. In its bay location, lake breeze circulation and localized ﬂow
predominates, especially in Spring and Summer ............................................................ 121

Figure 3.32 FFT seasonal power spectra at Holland, M1 for the period of

record. Upper ﬁgures indicate the power of the signal at any given

frequency. Lower ﬁgures translate the power into a percentage of

explained variance of each signal relative to its periodicity ........................................... 122

Figure 3.33 Spatial coverage of the 3 domains of FSMM5. The coarsest

resolution (36 km) covers the contiguous United States, some of Canada

and Mexico. The intermediate (12 km) covers the east-central portion of

North America. The ﬁnest resolution (4 km) includes most of the Great

Lakes region .................................................................................................................... 127

Figure 3.34 Spatial coverage of the 4-km (West) domain of FSMM5 over

the study region (41° - 50° N by 76° - 97° W). This is the ﬁnest resolution

domain run by the model and covers much of the Great Lakes. Each dot

represents a domain grid cell corner point ...................................................................... 127

Figure 3.35 Spatial coverage of the 12-km FSMM5 domain over the study
area (41° - 50° N by 76° - 97° W). Each dot represents a domain grid cell
corner point. .................................................................................................................... 128

Figure 3.36 Spatial coverage of the FSMM5 36-km domain over the study
area (41° - 50° N by 76° - 97° W). Each dot represents a domain grid cell
corner point. .................................................................................................................... 128

xiv

Figure 3.37 Mean daily (thin line) and mean monthly (thick line) lO-m

wind speeds at Toronto, ON (CYYZ) from the 12-km run of F SMM5 and

using an inverse distance weighting of estimates from the nearest 4 grid

cross points. .................................................................................................................... 132

Figure 3.38 Examination of model estimates of wind speed versus

observed wind speeds at Grand Rapids, MI (KGRR) from the 4 km

domain over the period of record. There is little degradation of estimation

with departure from initialization time. Similar results were obtained at all

stations and grid resolutions. RMSE is root mean squared error (m s"),

with RMSEs and RMSEu being the systematic and unsystematic

components. MAE is mean absolute error (m s"), while r is the

correlation coefﬁcient and d2 is Willmott’s (1982) index of agreement ........................ 135

Figure 3.39 An idealized example of a semivariogram. The solid

horizontal line represents the variance of the data interest, while the

dashed line is the semivariance (7..) at any given distance interval (h). The

nugget represents the minimum achievable semivariance due to localized

effects .............................................................................................................................. 142

Figure 3.40 Idealized relationships between two variables and their

corresponding Pearson’s correlation coefﬁcients. Of the top row, each of

which exhibits a perfect or near-perfect correlation between the two

variables, only the ﬁrst (a) would represent a truly error-free model,

whereas (b) and (c) exhibit systematic error not taken into account. On the

bottom row are three idealized examples of variables that show little or no

correlation. However, like (b) and (c), (d) is a function of systematic bias.

Figure (e) shows the inﬂuence of two extreme outliers. Only (0

represents a randomly generated data set where no correlation is expected. ................. 158

Figure 4.1 One week moving averages of the ASOS observed (top) and

FSMM5 forecast (middle) wind speeds at Fulton, NY (KFZY) for the

period of record. The bottom ﬁgure is a 1-week moving average applied

to the hourly differences (O—P) between observed and predicted wind

speeds. The moving average was used to more clearly illustrate the degree

of variability that exists. All stations exhibit similar variability. .................................. 171

Figure 4.2 Comparison of the FSMM5 estimated Weibull pdf (left, line)
and cdf (right, line) at Holland, MI (KBIV) and the observed wind speed
distribution (leﬁ, bars; right, crosses) for each of the three domains, (a) 4
km, (b) 12 km and (c) 36 km over the period of record. ................................................ 177

Figure 4.3 Wind speed distribution frequency differences (FSMM5 -

ASOS) at Holland, MI (KBIV) for the (a) 4 km, (b) 12 km and (c) 36 km
domain over the period of record .................................................................................... 177

XV

Figure 4.4 Wind roses at Holland, MI (KBIV) from the 12 km F SMMS
domain showing the observed wind direction distribution (left) and the
FSMM5 estimated direction distribution (right) from 11/02 - 6/04. .............................. 179

Figure 4.5 Frequency differences between F SMMS and ASOS observed
wind directions at Holland, MI (KBIV) for the (a) 4 km, (b) 12 km and (c)
36 km domains for the period of record. ........................................................................ 179

Figure 4.6 FSMM5-estimated mean wind speeds over the study region

over the three model domains using an inverse distance weighting

technique on the nearest 4 grid points to a station ﬁom 1 1/02 to 6/04. The

negative mean speeds in (b) are a function of the spatial interpolation

scheme extrapolating beyond the observation network and should be

ignored. ........................................................................................................................... 180

Figure 4.7 Mean Absolute Error of wind speed histogram frequencies

between FSMM5 and observed data over the study area on the three model

domains from 11/02 to 6/04. All estimates were interpolated to stations

using an inverse distance weighting technique on the nearest 4 grid points.

Negative MAE values are the result of the biharrnonic spline procedure

extrapolating beyond the range of the stations and should be ignored. .......................... 182

Figure 4.8 Index of agreement (d2) for FSMM5 estimates of the wind

resource over the (a) 4 km, (b) 12 km and (c) 36 km domains from 11/02

to 6/04. Values outside the range 0 - 1 are extrapolation artifacts and

should be ignored. ........................................................................................................... 185

Figure 4.9 Systematic component of the Root Mean Squared Error

(RMSEs) over the study region from the (a) 4 km, (b) 12 km and (c) 36 km

FSMM5 domains from 11/02 to6/04. Negative values are an extrapolation

artifact and should be ignored ......................................................................................... 186

Figure 4.10 Fitted trend surfaces of FSMM5-Observed histogram

residuals over the study area from the (a-b) 4 km, (c-d) 12 km and (e-f) 36

km domains from 11/02 to 6/04. In the right hand ﬁgures, the X-axis is

Longitude, the Y-axis is Latitude, and the Z-axis are the trend surface

residuals corresponding to the left-hand ﬁgures ............................................................. 188

Figure 4.11 First-order trend surface of residuals (mean FSMM5 - mean

Obs) over the study area ﬁom the 36 km domain, 1 nearest neighbor
FSMM5 variant from 11/02 to 6/04 ................................................................................ 196

xvi

Figure 4.12 Fit of model estimated Weibull distribution (line) to observed

wind speed data frequencies (left, bars; right, crosses) at Chapleau Airport,

ON (CYLD) for the period 11/02 to 6/04. Left plots are the probability

density function, and right plots are the cumulative density function. The

models are: the 36 km domain, 1 nearest neighbor F SMMS (a,b), the joint

probabilistic model (c,d), and the measure-correlate—predict model (e,f). ..................... 204

Figure 4.13 Wind speed frequency histogram differences (Estimated -

Observed) for three wind models [(a) 36km/1 nearest neighbor F SMMS,

(b) joint probabilistic, and (c) measure-correlate-predict] at Chapleau

Airport, Ontario (CYLD) for the period 11/02 to 6/04 ................................................... 205

Figure 4.14 Terrain Complexity Index (TCI) obtained for the study area
by calculating the standard deviation of elevation of the 16 grid points (12-
km MM5 domain) surrounding each station location ..................................................... 207

Figure 4.15 Surface elevation of the area encompassing the study region,
from the 12-km domain of F SMMS. .............................................................................. 208

Appendix D. ASOS 10-m Wind Observations .............................................................. 231

xvii

FSMM5
GMT

kW
kWh

m s‘
METAR
MM5
MSE

NOAA
NWS

QC
RMSE

uorU
UTC
vorV

WECS

KEY TO SYMBOLS OR ABBREVIATIONS

degrees (unit of compass direction)

Air density (kilograms per cubic meter)
Anderson-Darling test statistic

Anderson-Darling test statistic for small samples
Automated Surface Observing System

Automated Weather Observing System

Weibull distribution scale parameter (in m 5“)

Index of Agreement (based on MSE)

Index of Agreement (based on RMSE)

Residual of estimated values or inverse of natural logarithm
East

US. Federal Aviation Administration

US. Forest Service operational MM5 model
Greenwich Mean Time (see also UTC or Z)

Weibull distribution shape parameter

knot (nautical mile per hour)

Kilowatts (1000 watts)

Kilowatt hours

meters

meters per second

Routine meteorological report

Mesoscale Model Version 5 (Pennsylvania State University)
mean squared error

Megawatts (1000 kW)

frequency count

North

US. National Oceanic and Atmospheric Administration
US. National Weather Service

probability level

Wind Power (usually in w m2)

Quality Control

root mean squared error

standard deviation

South

Student’s T-test statistic

horizontal wind speed

Universal Time Coordinated (see also GMT or Z)
horizontal wind speed (used for wind vectors to differentiate from u)
West

Wind Energy Conversion System (e.g., wind turbine or wind farm)
height (in m) above the ground

Zulu time (see also GMT or UTC)

xviii

Chapter 1. Introduction

The power contained in moving air has been harnessed for work by human beings
for thousands of years. The use of wind power has included sailing ships, grinding grain,
pumping water, and most recently the generation of electricity. A key component of the
efﬁcient use of wind power is some prior knowledge of the magnitude and consistency of
the resource. Optimal locations for exploiting the wind resource have long been
identiﬁed as those having relatively consistent, moderately high wind speeds. Prior to the
introduction of meteorological instruments or observations, the identiﬁcation of such
locations, both on land and over water was generally made through personal experience
and knowledge handed down between generations. Such thought and planning is clearly
evident in the presence of antique wind mills in many of these locations, the continued
use of older sailing routes by modern vessels, as well as in the place names of many of
locations to reﬂect the windy conditions (e. g., Vindeby, Denmark; Punta Viento, Puerto
Rico; Venta de Olivos, Spain; Windy Point, Canada; Buenos Aires, Argentina).

However, prior to the development and installation of modern wind energy conversion
systems (WECS), or wind turbines for the generation of electricity, there was little need
to quantify the wind resource. The wind was simply utilized when it blew, and locations
without sufficient wind resources were usually abandoned in favor of winder locations.
Although primitive anemometers have been in existence since at least 1000 AD (Pr'itz,
1988), and wind vanes from several millennia earlier (Neumann and Parpola, 1983) the
relatively low power required by wind mills and sailing vessels was generally satisﬁed by

siting in consistently windy locations (e. g., hillocks, ridges, coastal bluffs) and supported

by the use of alternative energy sources when the wind was unavailable (e. g. , animal or
water driven mills, cars on sailing vessels). Put simply, either it was suitably windy, or it

was not. Any resulting assessment was therefore qualitative rather than quantitative.

The concept of generating electricity by connecting a windmill rotor to a turbine
is a relatively recent one in the history of wind power. Arguably the ﬁrst successful wind
turbine was the Brush post mill turbine in Cleveland, Ohio in 1888 (Dodge, 2002, DWIA,
2003). However, the Brush turbine and subsequent attempts at electricity generation
from the wind met with limited success, until the 19203 when the more aerodynamic
design of aircraft propellers and more efﬁcient turbines became available. In the 19203,
many hundreds of small Jacobs Wind-machines were used at rural farms throughout the
US and Canada (Dodge, 2002). Although these turbines were abandoned after the US
govemment’s rural electrical cooperative program brought grid electricity to rural areas
in the early 1930s, the intermittent operation of these turbines as a result of variable
winds clearly highlighted the need for a better understanding and quantiﬁcation of the

wind resource if wind energy was to become a viable source of grid-based electricity.

The Danes were the ﬁrst to experiment with the commercial production of wind
electricity, taking advantage of the naturally moderate and steady winds over the Danish
peninsula (DWIA, 2003). However, low fossil fuel prices rendered the numerous Danish
wind turbines economically obsolete soon after World War I. The United States took
advantage of a suitably windy location, Grandpa's Knob in Rutland, Vermont to establish

a grid-connected 1.25 Megawatt (MW) turbine during fuel shortages of WW II in 1941.

Experience with this turbine further highlighted the need for a scientiﬁc approach to wind
turbine siting when in 1945, after only a few hundred generation hours, high winds broke
oﬁc a blade, ending its operational life (Dodge, 2002). Unfortunately, interest in wind as
an energy source waned with the ample and inexpensive generation of fossil and nuclear
energy in the 19503 and 19603. Thus there was also little interest at the time from the

scientiﬁc community in better understanding the wind as a resource.

Unlike a conventional windmill that simply transforms wind power directly into
an end use (grinding or pumping), the quantity of electricity generated by a wind turbine
is not only dependent on the design of the turbine, but is also highly dependent on the
magnitude of the wind speed. Following Rohatgi and Nelson (1994), the power density
(P) of the wind is a function of the air density (p), the cube of the wind speed (V) and the

swept area (A) which can be written functionally as:

P=1/2pV3A 1.1

Although a wind turbine may sweep a large area, a further consideration is that a
turbine can physically extract only a fraction of the overall wind power ﬂowing through
the turbine’s swept area before the loss of kinetic energy to the turbine becomes too great
to maintain inﬂow speeds. This limitation is roughly 59% of the power potential
calculated by Equation 1.1 and is known as Betz law (Betz, 1926, Rohatgi and Nelson,

1994, Hansen, 2000). Additionally, due to the loss of energy to the internal mechanisms

of the turbine itself (e.g., gears), modern turbines are capable of extracting around 30% of

the overall power contained in the wind. This proportion is the turbine’s efﬁciency.

Due to the turbine efﬁciency and engineering factors such as blade aerodynamics,
wind turbines have an operating envelope such that peak power production is only
possible in a range of relatively strong wind speeds (e.g., 15-25 m 3"), called the rated
speeds. Below about 3 m 3", there is insufﬁcient wind power to turn the turbines. Above
that speed, often called the startup speed, the turbine will generate exponentially more
power as wind speeds increase, until peak production is obtained at the rated wind
speeds. Beyond the envelope of rated wind speeds, the turbine blades are feathered and
the turbine is shut down to prevent potential damage from over speeding. Figure 1.1
represents a turbine power curve from the Bonus 2 Megawatt (MW) wind turbine (data
source: http://www.bonus.dk) and illustrates the relationship between wind speeds and
turbine power production. The Bonus turbine produces no power below 4 m s'1 or above
25 m s", and rated (2 MW) power only when winds are between 16 and 25 m 3". While
the power curve of Figure 1.1 describes the Bonus 2 MW turbine in terms of
aforementioned critical wind speeds, most wind turbines exhibit a similar proﬁle. Thus,
while a wind turbine is similar to a conventional windmill in that it will produce power
under almost any wind, its optimal efﬁciency is limited to a rather small range of
moderately high wind speeds. To properly site a turbine, a location is sought where wind

speeds fall within the operational range with relatively high frequency.

Furthermore, it is undesirable to have a turbine in a location where winds
experience rapid and/or frequent changes in speed or direction. Such wind variability
results in excessive stress being placed on the turbine orientation gears and on the blade
angle gears. As a wind turbine may cost well over one million US dollars to install and
have a lifespan of 20-30 years (AWEA, 2002), it is advantageous for a turbine operator to
not only identify a location where winds are frequently within the peak operating range of
the turbine in order to maximize the potential power output from the turbine, but also
where ﬂuctuations in wind speed and direction are relatively low to minimize overall

wear and tear on the turbine.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 1.1 An idealized wind turbine power curve, derived from the Bonus 2 MW wind turbine (data
sources: http://www.middlegrunden.dk and http:/lwww.bonus.dk).

Although the energy crisis of the 19703 renewed interest in wind energy, a
shortcoming to early WECS development was the relative inefﬁciency and low power
output of early wind turbines. In general, turbines were limited to under 1 MW of rated
power output (i.e., output at rated wind speeds) so a great number of turbines were
required to generate commercially viable quantities of energy (e. g., the massive array at
Tehachapi Pass, CA). Additionally, turbines of the 19703-19903 had relatively high
startup and rated speeds. These limitations necessitated the identiﬁcation of locations
that met the stringent resource criteria of contemporary turbines. As a result there was a
great deal of scientiﬁc interest in accurately estimating the wind resource and a number
of notable works, such as the United States Wind Atlas (Elliott et al., 1987) were
published (see Figure 1.2). Unfortunately much of the wind resource research at the time
was based on a sparse, irregular and often inhomogeneous network of anemometers (e. g.,
Elliott et al., 1987, Goodin et al., 1979). As a result, many regions deemed as having
insufﬁcient winds to generate consistent power from WECS were dismissed from
consideration. Similarly, subsequent research on estimating wind resources in such

locations was largely overlooked with but a few exceptions (e.g., Wendland, 1982).

Recent advances and improvements in wind energy conversion systems (WECS)
technology have led to wind power becoming a viable commercial form of electricity
production in many parts of the world. Turbine efﬁciency, blade aerodynamics and tall
tower engineering have all advanced to where it is now possible to produce electricity
from a wind turbine at a cost of less than 5 cents per kilowatt hour (kWh) in optimal

geographic locations. Such a cost is similar, if not less than the costs associated with

producing that power from fossil fuels or radioactive materials, and without many of the
environmental issues associated with the latter generation methods (IEA, 2001 , Thor and
Weis-Taylor, 2002). These technological advances have, in many places, been matched
by a favorable administrative climate that has enacted tax credits, removed zoning
restrictions and offered grants or low-interest development loans in an effort to actively
develop the wind energy potential in those regions (e. g., Germany, Denmark, United

States, Spain, India; AWEA, 2004a).

UNITED STATES ANNUAL AVERAGE WIND POWER

 

Figure 1.2 Wind power potential for the United States, from the Wind Energy Atlas of the United States
(Elliott er a]. , 1987). Darker shaded regions have greater potential than lighter regions. See Elliott er al.
(1987) for a quantitative description of each wind power category.

As a result of new technologies, governmental support, and a recognized need for
localized energy production (as evidenced by the California energy crisis of 2000), over
8,000 MW of wind power generation capacity was installed worldwide in 2003 (with
1,687 MW installed in the United States and 5,467 MW in Europe). This brings the total
worldwide wind power conversion capacity to over 40,300 MW as of early 2004, up from
24,000 MW in 2001 (AWEA, 2002, 2004b). This developmental trend shows no signs of
slowing and includes newly industrialized and developing countries which seek to meet
increasing electricity demands and build energy independence. It is estimated that an
installed wind energy capacity of over 200,000 MW will be in operation by the end of the
decade (EWEA and Greenpeace, 2002). Several German States obtain more than 10% of
their electricity from wind and Denmark produces over 20% of its electricity from wind
(AWEA, 2004a). If current development trends continue, many wind farms will, by
necessity be developed in locations for which wind data are sparse and where past studies

had deemed the wind resource to be insufﬁcient.

In general, the historical collection of wind speed and direction data has
historically, like most meteorological data collection, been limited to discrete locations
comprising a sparse and irregular network of observation stations, and generally limited
to more populated areas. However, the most favorable locations for wind energy
conversion systems are those regions with strong (e. g., mean wind speeds (u) exceeding
around 7 m s") but steady winds. Due to either relatively harsh environmental conditions
or physical limitations on human habitation, these areas generally tend to have low

populations or may be devoid of people altogether (e. g. , offshore) and thus usually

contain few meteorological observation stations (e.g., Willmott et al., 1991, Robeson,
1993, Klink, 1999). It is therefore necessary to somehow estimate the wind resource

over regions where little or no observational data exist.

Although a great deal of early research on wind resources has been devoted to the
estimation of speeds at locations lacking adequate observations, such estimates have
invariably been hindered by the underlying characteristics of the wind ﬁeld (e. g., serial
correlation, non-stationarity, anisotropy). The successes and limitations of earlier works
will be discussed in more detail in the following chapter. Despite limitations to the
success of estimating the wind resource at poorly instrumented locations, certain regions

have been identiﬁed that clearly have wind resources amenable to WECS development.

Offshore (i.e., over open water) and coastal winds in particular have long been
acknowledged as being generally stronger and exhibiting greater persistence than nearby
inland winds due to large fetches of low surface roughness over the water bodies (e. g.,
Eichenlaub, 1979, Pryor and Barthelmie, 2001, Palutikof et al., 2002). Additionally,
offshore locations may not be as limited by many of the societal objections and zoning
issues often associated with land-based WECS development (Still, 2001). Thus it is not
surprising that within the wind energy sector an increasing number of WECS
development initiatives are focused offshore and along coastal bluffs. Indeed, several
along-shore and offshore (hereafter referred to as the shore zone) wind farms are already
Operating in the UK, Denmark and Germany. Additional shore zone projects are under

consideration for the United States, Brazil, and Ireland (AWEA, 2004a). Because of the

importance of the shore zone wind resource to developing wind energy capacity, there is
a critical need for its accurate estimation of potential wind resource (Troen and Petersen,

1989)

Unfortunately, unless a sufﬁcient series of wind data exists for a considered
location, the identiﬁcation of an optimal WECS development site can be difﬁcult. Most
wind farm locations are initially selected a priori, from regionalized isotach (wind speed)
and isogon (wind direction) maps in wind atlases (e. g., Elliott et al., 1987, Troen and
Petersen, 1989). Once selected, a developer is advised to erect an anemometer and
collect wind data for a year or more, subsequently employing empirical interpolation

techniques to decide whether the site is optimal or not.

The empirical techniques that are used in estimating the wind resource of a
location have been shown by numerous researchers to work reasonably well for
estimating wind at a candidate location if that location is within a relatively short distance
of the nearest meteorological station and the intervening terrain is relatively
homogeneous (e. g., Justus er al., 1976, Goodin et al., 1979, Haslett and Raftery, 1989).
Because such techniques are empirical, their potential accuracy is limited both spatially
and temporally. Temporally, the accuracy of wind resource estimation tends to be
limited to the data which are available. No information is available for trends, cycles or
anomalies beyond the period of record. Additionally, such methods are limited by the
degree of spatial coherence present in the wind ﬁeld and the distance from the location of

interest and the surrounding meteorological stations. In this context, such methods

10

cannot address any of the smaller scale inﬂuences on wind that may occur between the
candidate location and the meteorological series, instead aggregating the inﬂuences of
such local-scale contributions into a set of static coefﬁcients and shunting any departures
from those terms into the error of the model. Although such issues can be investigated
through an assessment of spatial coherence, only a few works have addressed these issues

outside of complex terrain (Robeson and Shein, 1997, Klink, 1999).

As the lack of an adequate observational network has been repeatedly recognized
as a limitation to reliable and accurate wind resource estimation over large regions, the
use of dynamical atmospheric relationships to produce plausible wind estimates at
uninstrumented locations has been investigated. Over the past few decades, there has
been a growing interest in the use of numerical weather models for forecasting the wind
resource over a region, with a number of such models subjected to testing and validation
over different areas (e.g., Sherman, 1978, McQueen et al., 1995, Frank et al. 2001).
However, again, the performance of these models with respect to wind over non-complex
terrain has been largely overlooked and little work has investigated the ability of such

models to adequately reproduce the statistics of the long-term wind resource.

1.1 Statement of Purpose

A review of the literature, which follows in the next chapter, reveals that short-

terrn forecasting is the primary reason for interest in using RCMs in the context of wind

11

energy. In such context, RCMs have been extensively investigated for producing a wind
forecast out to about 48 hours at speciﬁc locations, and individual wind speed estimates
are validated for accuracy. Although a cursory examination of observed versus model
estimated hourly wind speeds is conducted herein, it is not the purpose of this research to
perform such an evaluation. Rather, an RCM can also be used to generate a longer-terrn
distribution of wind speeds for a location or over a region of hundreds of square
kilometers. While individual estimates may differ substantially from their respective
observations, the overall distribution, if accurate, would permit high conﬁdence a
posteriori selections of optimal WECS locations within the region at locations where

few, if any, observations exist.

Unfortunately, this use of the RCM in wind energy has been largely overlooked
on this point. In fact, the literature appears to be uncharacteristically silent on the use of
an RCM as a method for generating spatially coherent and accurate estimates of the long-
term wind resource over a region. This research seeks to remedy that deﬁciency in the
science by taking the ﬁrst step and validating the performance of an RCM for estimating
the climatology of wind speeds over a region. Therefore, it is the goal of this research to
investigate the utility of a regional-scale numerical climate model (or RCM) as a means
to accurately estimate the wind resource over the Great Lakes region of North America

(Figure 1.3), an area that is currently of interest for WECS development.

12

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Figure 1.3 The study area; the Great Lakes region of North America.

Within the scope of this research, the foci are fourfold. The primary goal of this
research is to determine whether a regional numerical climate model can adequately
estimate the wind climatology over a region. Before a numerical climate model can be
expected to be capable of plausibly estimating the long-term climatology of the wind
ﬁeld over a region, it must be shown that the model can adequately reproduce the
statistics of the regional wind ﬁeld as derived from observational data. To that end, the
ﬁrst focus of this research is to validate the estimative ability of the near-surface wind
output from a widely used RCM, the Pennsylvania State University / National Center for

Atmospheric Research (PSU/N CAR) Mesoscale Model, more commonly known as MM5

l3

(Haagenson et al., 1994). This validation will serve as the framework under which the

subsequent analysis of this research will be conducted.

Second, execution of regional-scale numerical climate models tends to be
computationally intensive. One of the most critical factors governing computational
intensity, as well as estimation accuracy is the resolution, both spatial and temporal of the
model simulation. To optimize the performance of an RCM, a balance must be achieved
between computational intensity and estimation bias. The use of ﬁner spatial or temporal
resolution must be justiﬁed by appropriate levels of error reduction. If error cannot be
signiﬁcantly reduced by increasing resolution, the increase in computational intensity
may not be justiﬁed. However, decreasing resolution to reduce computational intensity
may mask many local-scale effects (e. g., boundary layer, land cover) and increase error
to unacceptable levels. To address this issue, this research will seek to establish the
optimal spatial and temporal resolution for wind resource estimates over the Great Lakes.
Such Optimization will allow the RCM to be run most efﬁciently in terms of CPU

utilization and bias minimization.

Third, because dynamically-driven RCMs such as MM5 tend to be
computationally intensive at any meaningful resolution, and require both meteorological
and computer expertise to install, run and properly interpret output, there must be a
compelling advantage to their use over established stochastic and probabilistic methods

of wind resource estimation. To that end, this research will assess the performance of

14

wind resource estimates of the MM5 RCM against the performance of traditional

estimation methods commonly employed in the wind energy industry.

Finally, the output of the MM5 RCM will be analyzed to determine whether
stochastic corrections can be applied to reduce any systematic bias in the estimates
produced. Several researchers have raised the question of spatio-temporal accuracy in
RCM forecasts of meteorological variables (Colle et al., 1999, Tustison et al., 2001,
Mass et al. 2002). While a model may produce accurate estimates of a variable, those
estimates may be systematically shifted in space-time such that it appears the model has
low skill. This research will seek to identify what, if any systematic bias is occurring in

the RCM output and attempt to explain the cause of that bias.

Given that the overall goal of this research is to reduce the uncertainty
surrounding RCM estimates of a regional wind climatology, it is expected that this
research will facilitate the integration of regional-scale dynamical models of the
atmosphere into wind farm siting approaches and allow developers to select sites with
greater conﬁdence in the wind climatology than had previously been available ﬁom a
priori approaches. Such research is especially relevant to regions where wind
observation networks may be too sparse to achieve a meaningful wind energy

climatology.

15

Chapter 2. Literature Review

As was discussed in the previous chapter, the accurate estimation of the wind
resource of a location is of critical importance to the success of any WECS installed
there. The capital costs of installing a wind turbine or wind farm are currently estimated
to be about $1000 US per kilowatt of energy capacity (IEA, 2001). Thus, simple
economics dictate that if the wind resource at a location is deemed insufﬁcient for the
proﬁtable production of electricity, the site ought not be considered for WECS
development. In addition to the consideration of the overall wind resource at a location,
it has become increasingly necessary to more precisely specify the resource in terms of its
distribution. This is largely due to the fact that turbine manufacturers such as Vestas or
GE now offer a series of wind turbines, each speciﬁcally designed for different wind
climatologies such as lighter or more variable wind speeds (Filtenborg, 2004). Also, as
the number of WECS installations increase worldwide, there is growing interest in
exploiting wind resources in more remote locations; locations that may not have adequate

wind measurements.

To those ends, most research directed toward wind energy climatology has
focused on accurately estimating the statistical properties of the wind at a location or over
a region, providing robust estimations of the distribution of those winds, and the
estimation of wind regimes in locations for which there exist few or no data. Within the
context of this research, a discussion follows of the advances and limitations offered by

prior work in this area.

16

2.1 Wind Resource Identification and Analysis

The goal of wind resource estimation in the context of wind energy conversion is
to reproduce the statistical properties of the long-term wind ﬁeld at a “candidate”
location, or over a geographical area such that errors between the observed wind
climatology and that which is estimated are minimized. Thus, nearly all wind energy
climatological analysis is concerned with either statistical evaluation or modeling the
resource, or most ﬁ'equently, both. Unfortunately, while the use of wind as a source of
power is not a recent idea, it was not really until the energy crisis of the 19703 that it
became the focus of substantial scientiﬁc investigation. As such, little research on wind

climatology is known prior to that time period.

A number of early works (e. g., Putnam, 1948, Dinkelacker, 1949, Golding, 1955;
Hewson, 1975, Justus et al., 1976, Hennessey, 1977, Widget, 1977) sought to examine
the statistical properties of winds at locations where there existed relatively long (10-30
years) records of wind observations. Much of this work assumed that the locations at
which one might wish to consider a wind turbine installation were rural or remote
locations at which the wind record was sparse at best. Thus, from the beginning most
research has sought to evaluate and summarize the wind regime at locations where the
wind data must be estimated prior to undertaking a summary analysis. Whether a
researcher is concerned with evaluating the wind at a speciﬁc location or over a wide

area, both methodologies involve interpolative modeling.

17

Even the earliest approaches (e.g., as discussed in Putnam, 1948), recognized that
the properties of wind within the boundary-layer were such that the wind at a location
could not simply be assumed equivalent to the wind measured at a nearby anemometer.
The primary reason is the effect of localized variations in surface conditions and
atmospheric modiﬁcations operating on spatial scales less than the distance between the
two points, such as thermal and mechanical turbulence. A thorough discussion of the
inﬂuence of many of these small-scale effects can be found in such boundary-layer

references (e.g., Oke, 1988; Geiger et al., 1995; Stull, 1999; Arya, 2001).

However, it is also well known that the winds at all levels are driven by the
overlying pressure gradient that exists at much larger (synoptic and even global) scales
(Panofsky, 1958; Wallace and Hobbs, 1977). Thus, while not equivalent, the winds at
one location will tend to be somewhat related in space and time to winds at a nearby
location. It is this assumption that has driven most empirical estimation techniques

developed for wind resource estimation.

2.1.1 Properties of the wind ﬁeld

In order to instigate a model of winds at a location or over a region, it ﬁrst is

necessary to understand the properties and behavior of the wind resource as it pertains to

wind energy conversion. On this point there exist a number of useful references.

18

2.1.1.1 Statistical measures

The properties of the wind ﬁeld over a location or region have been known for
some time. Putnam (1948), Dinkelacker (1949), and Golding (1955) each address many
of the aspects of the wind ﬁeld that are important to wind energy conversion. Among the
most important in their estimation were the mean and standard deviation of the wind
speed. Although the direction of the wind is important from a climatological standpoint,
it is generally less critical for wind turbine operation in that even the earliest turbines
were mounted on a pivoting gear that allowed for their continual orientation into the wind
(Putnam, 1948). Thus, initially the variability of the wind direction was solely important
as a measure of stress on the pivot gear. Greater directional variability meant the turbine
would be shifting direction more frequently to capture the wind. More recently, with the
implementation of complex models for wind speed estimation, knowledge of the wind

direction has become critical (e. g., Walmsley et al., 2001).

Although a number of notable works, primarily wind energy atlases (e. g., Elliott
et al., 1987 and Troen and Petersen, 1989) have focused on estimating and presenting the
mean and standard deviations of wind speed and power over large regions, they have not
been limited to those variables. The mean and standard deviation of wind velocity are
now recognized as rather basic reference statistics of somewhat low utility to wind
energy conversion (Justus et al., 1976). Instead, the extractable wind power is largely a

function of not only the wind speed, but also the distributions of those speeds. Rohatgi

19

and Neslon (1994) present an excellent overview on the characteristic relationships

between the wind resource and wind power.

In order to derive total potential power of the wind, it is only necessary to have
information on the wind speed and the air density. From Equation 1.1, if area A is set to
1 square meter, the power contained in a square meter of wind will be equivalent to half
the quantity of the air density times the cube of the wind speed, with resulting units in
Watts. Because of its exponential relationship with wind speed, this formulation more
heavily weights strong winds. This relationship is well described in Shein (1995).
Unfortunately, this power also is of limited utility, for wind turbines are incapable of
utilizing the entire spectrum of wind speeds with maximum efficiency. Appropriate
estimation of wind power requires the calculation of extractable power, not only as a
function of wind speed, but also as a function of the extraction performance of the turbine
itself. This latter factor relies heavily on the capacity of the turbine and its performance

through the various portions of the wind speed distribution.

2.1.1.2 Wind speed distributions

Justus et al. (1976) properly addressed this issue by examining the distribution of
wind speeds relative to an idealized turbine Operation curve (such as is presented in
Figure 1.1). In such a curve, a turbine does not operate when wind speeds are below its
so-called cut-in threshold (normally about 3 or 4 m s"). Above that threshold, the turbine

will produce only an exponentially incremental proportion of its maximum power until

20

wind speeds reach the turbine’s rated speed (normally around 12 m 3"). Between this
speed and an upper threshold, the turbine will produce its rated power. But when wind
speeds exceed the upper rated threshold (often called the cut-out speed; about 25 m s"),
the turbine will cease operation to prevent wind related mechanical damage. Thus, any
wind speeds below the cut-in or above the cut—out speeds are lost to power production,
and thus the actual convertible wind power at those speeds can be set to zero. As an
example, a calculation of potential power over the rated speed range (12-25 m 3") yields
1,037 W In2 to 9,375 W m'z. Assuming a turbine with 1 megawatt (MW) of rated power
sweeping an area of 5,027 m2 (40 m rotor radius), the potential power of the wind
through the turbine blades ranges from 5.22 MW to 47.13 MW. Even after factoring in
the Betz limit (as discussed in the previous chapter) of 59% extractability, the potential
wind power is 3.08 to 27.8 MW. The turbine, limited to 1 MW output at all rated speeds
converts only from 4% to 32% of the available wind power. The rest of the power is
simply not extractable by the turbine. The same relationship holds true for the range of
speeds between the cut-in and rated speed. Thus is it perhaps more appropriate to
describe the power contained in the wind as a ﬁrnction of the actual power produced by a
turbine, or, in the absence of that, to examine the distribution of the wind speeds relative

to an idealized power curve, as described by Justus et al. (1976).

As a result of the importance of variable power output relative to wind speed, the
investigation of wind speed distributions has rightly occupied a substantial portion of
wind power climatology research. Even prior to the surge of interest in wind energy

applications in the 19703, a number of early works addressed wind speed frequency

21

distributions. Dinkelacker (1949), for example determined a Plank distribution to be
appropriate for wind speeds in Germany. Crutcher and Baer (1962) enjoyed some
success ﬁtting a bivariate normal distribution instead. However, Smith (1971) and later
Hennessey (1977) correctly noted that the bivariate normal distribution involves
mathematical complexities that limit its utility for wind energy applications. It should
also be noted that under certain circumstances, the bivariate normal distribution can be
simpliﬁed to a Rayleigh distribution (Hennessey, 197 7). In 1948, Putnam had suggested
that wind speed distributions could be approximated with a Pearson Type III distribution,
more commonly known as a Gamma distribution. Sherlock (1951) corroborated the
utility of this distribution. Although it took approximately two decades, in the mid-1970s
a number of researchers converged upon a special two—parameter case of the Gamma
distribution known as the Weibull distribution (Weibull, 1951) that had been used

extensively in engineering failure analyses.

Because of its two (and occasionally three) parameters, the Weibull distribution
quite often provided more accurate ﬁts to empirical data. The aforementioned Rayleigh
distribution is actually a special case of the Weibull distribution. It appears that the
earliest known application of the Weibull distribution to near surface wind speed was
Davenport (1963), who used the distribution to discuss wind loadings on buildings.
Among the ﬁrst studies to investigate the use of the Weibull distribution for wind speeds
in the context of wind energy research was Justus et al. (1976) who compared the
Weibull distribution to a lognorrnal distribution (as had been employed with success by

Luna and Church, 1974) and found it to be superior.

22

Since 1976, the Weibull distribution has gained wide acceptance among wind
energy researchers (e.g., Justus et al., 1976, Hennessey, 1977, Corotis et al., 1978, Brown
et al., 1981, Conradsen et al., 1984, Poje and Cividini, 1988; Wieringa, 1989; Beyer and
Nottebaum, 1995). Even though a particular wind speed distribution cannot
automatically be assumed to follow a Weibull distribution, the Weibull probability
density function (elaborated upon in Chapter 3) is versatile enough to accommodate a
great many of the unimodal, zero-bounded distributions of wind speed that could
conceivably be found in nature. To that end, even a distribution that approaches
normality (save for the zero bound) can be adequately approximated by a Weibull

distribution by setting the shape parameter equal to 3.7.

2.1.1.3 Data collection

In addition to providing a description of the wind resource in terms of summary
statistics and probability distribution functions, there are the added issues of the
collection and behavior of the resource itself. If the data are of low quality or not
representative of the true winds at a location, any resulting analysis will be suspect.
Because this issue is quite involved, and has been addressed in other notable works (e. g. ,

Peterson et al., 1998a) it will only be cursorily summarized here.

In terms of wind data, there are three areas in which measurement error can be

introduced. The ﬁrst is from the instrument itself. Although a number of instruments are

23

available to a wind researcher, including pressure plates, pitot tubes, and more recently,
propeller vanes and thermal and ultrasonic anemometers, the three-cup anemometer has
emerged as the most widely used anemometer for wind speed information (Fritschen and
Gay, 1979, Wyngaard, 1981, Beljaars, 1987, Kristensen, 1999). The three-cup
anemometer has been widely utilized since its invention in 1846 and is prized for its
robustness and reliability (Kristensen, 1999). While two notable shortcomings of the cup
anemometer are its threshold speed (the speed below which the momentum of the wind is
insufﬁcient to initiate rotation) and a tendency for the anemometer to over-speed in
higher wind speeds (Kaganov and Yaglom, 1976, Wyngaard, 1981, Kristensen, 1999,
2002), it is the nature of the observation (wind power production) that largely negates
these shortcomings in the data collection (Palutikof et al., 1984). Thus, if the
anemometer being utilized is properly maintained and calibrated, instrumental error in
wind resource research using data collected by such instruments can generally be

considered inconsequential.

A second issue related to wind data collection is the representativeness and
homogeneity of the data. Although a great deal of research has been done in the area of
wind resource analysis, very little has examined how representative a wind observation is
of the true wind regime over the immediate vicinity. With speciﬁc mention to wind,
Wieringa (1980) examined the regional representativeness of winds measured by
anemometers at airports and found that, with the exception of locations where the wind
ﬁeld was modiﬁed by local terrain or other obstacles, measurements were indeed

representative of the immediate vicinity. However, Shein (1995) noted that at several

24

airport locations in the Midwest United States, anemometers were placed in locations
where the wind ﬁeld would be at least partially biased by obstacles. It is assumed, based
on the criteria set forth for the new generation of automated surface observing systems by
the US Federal government (OF CM, 1994) and later reﬁned by the Federal Aviation
Administration (FAA, 1999) and the National Oceanic and Atmospheric Administration

(NOAA, 2000) that such unrepresentative siting has been since rectiﬁed.

Furthermore, if one examines the station histories of many of the anemometers
used in wind resource studies to date, one will often ﬁnd a history ﬁlled with
discontinuities associated with station relocations and anemometer height adjustments
(Shein, 1995, NCDC, 1994a and b). Thus it is often necessary to adjust the observed data
from one height to another in order to standardize it (Peterson et al., 1998a, Robeson and
Shein, 1997, Klink, 1999). If information on roughness length is available, the log-wind
proﬁle can be used to adjust the wind speeds from one height to another (Tennekes,
1973). Where this information is unavailable, the wind speed power law is utilized
(Touma, 1977, Petersen and Hennessey, 1978). Invariably, either adjustment will
introduce some bias into the observations as both provide estimates of wind speed at the
adjusted height. Again, OF CM (1994) prescribes a set of anemometer siting standards
that set the height at the World Meteorological Organization standard of 10 m (although

procedures for station relocation are not discussed).

Much of the bias in empirical methods of low-level wind vector estimation can be

attributed to a failure to appropriately account for the boundary-layer dynamics (e. g.,

25

stability, turbulence, thermal structure, roughness) that modify the wind vector from one
location to the next and from time t to H]. Furthermore, each of these boundary-layer
conditions acts on the wind at different temporal and spatial scales, resulting in a wind
vector response at certain scales more so than others. Thus, the scale at which the data is

collected, both spatially and temporally is important.

In general, the collection of data on wind speed and direction has, like most
meteorological data collection, been limited to heavily populated areas. However, the
most favorable locations for wind energy conversion systems are those regions with
strong but steady winds. These areas generally tend to have low populations or may be
devoid of people altogether (i. e., offshore) and thus contain sparse and irregular networks
of meteorological observation stations (e. g., Willmott et al., 1991; Robeson, 1993; Klink,
1999). As such, the spatial scale of observations of wind may be on the order of 100 km.
Any variations in surface roughness, albedo, obstacle height or density, or terrain at
scales below that of the network density will generate smaller scale inﬂuences on the

regional wind ﬁeld that would be invisible to the observation network (Tetzlaff, 1984).

The same consideration is important for the temporal resolution of the network.
Van der Hoven (1957) describes a number of signiﬁcant signals within the wind speed
spectrum. If the sampling interval is too small, the signal will be dominated by the noise
of localized inﬂuences such as thermal and mechanical turbulence and be useless to wind
power estimation. If the sampling interval is too large, a number of regional or synoptic

signals of critical interest to a wind resource modeler (e.g. , the diurnal cycle or a sea

26

breeze circulation) would not be resolved by the data. Most wind energy research has
settled on the use of hourly wind observations as a good tradeoff between the reduction
of localized “noise” and the capture of the majority of regional signals. However, it is
unclear whether this hourly temporal resolution is selected by choice or simply because a

majority of wind observing stations collect observations at this resolution.

2.1.1.4 Serial correlation and stationarity

As interest in modeling wind speeds and wind speed distributions has grown,
other statistical properties of the wind have gained importance. These properties, such as
serial correlation and stationarity, are most important in stochastic model construction,

but also are critical in the statistical evaluation of model performance.

As a result of wind being a continuous ﬁeld, serial correlation in wind speeds
exists in both space and time. To that end, a wind speed observation at a speciﬁc place or
time cannot be truly considered independent of the wind speed that was observed at a
preceding time or an adjacent place. Serial correlation in space is the measure of
covariance between simultaneous observations from adjacent locations, often as a
function of the distance between them (Davis, 1986). Temporally, serial correlation, also
called autocorrelation, is the measure of covariance between sequential observations at

the same location, and is a function of the time between observations (Wilks, 1995).
Terrain complexity plays a large deterministic role in the degree of serial correlation,

both spatial and temporal. Spatially, as local terrain and obstacle inﬂuences tend to

27

modify near-surface ﬂow rather rapidly (depending on surface complexity), the modiﬁed
ﬂow will appear to be less related to the ﬂow measured at an adjacent station as the
distance between the stations increases (Steinitz et al., 1971, Wylie et al., 1985). At
distances more than a few kilometers, most of the synoptic and diurnal thermal signal that
is manifested as serial correlation appears to be lost in localized noise (Wylie et al. , 1985,
Robeson and Shein, 1997, Toriumi et al., 2000). Thus, for most wind resource studies,
where stations typically are tens if not hundreds of kilometers apart, spatial serial
correlation is generally minor and usually ignored. In addition, Robeson and Shein
(1997) also have demonstrated that temporal sampling intervals also play a critical role in

determining spatial coherence (i. e., distance decay of serial correlation).

Temporal autocorrelation of winds also has been explored in the literature (e.g.,
Wylie et al., 1985, Brett and Tuller, 1991) and found to be rather substantial at short lags.
Like with space, serial correlation in time is largely a function of the distance (in this case
the temporal distance between observations) and the relative inﬂuence of the local
terrain. A number of works have examined the behavior of wind speed at various
sampling intervals and have found that shorter sampling intervals tend to capture a
greater amount of the temporal autocorrelation, up to a point (Beljaars, 1987). Beljaars
(1987) conﬁrmed Fiedler and Panofsky’s (1970) assertion that a sampling interval of 10
minutes represents the boundary of the spectral gap dividing the synoptic signal and local
turbulence. At higher frequency sampling intervals, temporal autocorrelation drops as
local turbulent inﬂuences dominate. Furthermore, Shein (1995) noted that both spatial

and temporal autocorrelation became incoherent at aggregation intervals greater than

28

daily. Thus, it appears that the greatest temporal autocorrelation appears in wind
observations where the sampling or averaging interval is between 10 minutes and 1 day.
Additionally, Brett and Tuller (1991) and Shein (1995) have demonstrated that temporal
autocorrelation at the hourly level is often quite high (e.g., around 0.9) at a lag of one
hour, but decreases rapidly with subsequent time intervals. Brett and Tuller (1991) also
indicated that lag 1 temporal autocorrelation also decreases noticeably as the surrounding
terrain becomes less homogeneous, indicating a decrease of synoptic inﬂuence.
Unfortunately, most wind studies utilize either hourly or three-hourly observations and
lag 1 temporal autocorrelation values remain high, even in relatively complex terrain.
However, work in autocorrelation modeling and statistical testing (e. g., Bayley and
Hammersley, 1946, Box and Jenkins, 1976, Wilks, 1995) has provided methods for
computing “effective” sample sizes that compensate for the dependence induced by serial
correlation in a data series. Wilks (1995) also describes a variance inﬂation factor that
can be used to estimate the time interval between “effectively independent samples.”
Often the autocorrelation in the wind speed itself is used as a modeling tool as with
Markov chains (e. g., Dukes and Palutikof, 1995) or with autoregressive models (e. g.,

Brown et al., 1984).

Non-stationarity is another issue in wind speed modeling. It refers to a mean
value that is changing as part of a trend, linear or otherwise, over a given period of time
or a given area of space (Cressie, 1993). Non-stationarity often is referred to as drift or
anisotropy. The difﬁculty with non-stationarity is that most statistical procedures for

evaluating a series of data in either space or time are invalidated by non-stationary data.

29

Put simply, most statistical procedures rely on an unchanging mean (Box and Jenkins,
1976, Davis, 1986). A trend in the mean of the data over space or time represents a
systematic behavior and a level of dependence to an external factor. Thus, any change in
the mean over space or time must either be accounted for, as in a model, or removed prior
to statistical evaluation to ensure stationarity. For example, in the kriging work of Haslett
and Raftery (1989) or the time-series modeling of Brown et al. ( 1984), the spatial and
temporal drift in wind speeds was determined to be signiﬁcant and had to be accounted
for as part of the resulting models to ensure that the residuals would be independent and

randomly distributed.

2.1.1.5 Resource variability

Lastly, while the standard deviation of the winds about a mean value, and the
wind speed frequency distribution hint at the degree of variability inherent to the data,
these measures do not reveal longer-terrn behavior in the resource. In fact, the idea of a
single statistic such as standard deviation, or a single distribution encompassing all
available data implies an assumption that the data are indeed stationary and unchanging
in time. A number of works have clearly demonstrated that this is not the case (e. g. ,

Haslett and Raftery, 1989, Palutikof er al., 1986, 1987, 1993, Shein, 1995, Klink, 1999).
Palutikof et al. (1987) for example, showed that mean wind speeds at a single

station in the UK varied between 5.2 and 7.3 m s'1 over a period of 56 years. Klink

(1999) corroborated work by Shein (1995) that the variability of wind speeds about the

30

annual mean also could not be considered constant. All of the aforementioned works also
demonstrated that the interannual variability in winds at a location are not necessarily
consistent over the surrounding region. Klink (1999) noticed that interannual variations
in mean and variability had a strong seasonal component, implying that seasonal changes
in surface roughness, and thus local changes may exert a large inﬂuence. Palutikof et al.
(1986, 1993) alternatively suggested that a portion of the non-stationarity in wind records
is likely due to external forcings such as larger-scale climatic change. Spatially, Carlin
and Haslett (1982) looking at wind speed distributions concluded that the variability from
station to station was such that a Weibull distribution ﬁt to one station was not

necessarily transferable to other locations.

However, despite the aforementioned evidence of long-term variations in wind
speed, other researchers claim the degree of variability is statistically insigniﬁcant for
resource analysis. Golding (1955) for example, referencing the same observation station
as Palutikof et al., (1987) — Southport (UK) -— indicated that annual means of 37 of the
years of record were within 10% of the long-term mean. Justus et al. (1979) and Corotis
et al. (1977) further corroborate (to a 0.1 conﬁdence level) that annual mean wind speeds
at a location fall within 10% to 18% of the long-term mean. However, neither of these

researchers investigated the presence of trends or long-term cycles in their data, thus
ignoring the possibility that the reported deviations might not be constant in time. For
example, both Shein (1995) and Lun and Lam (2000) demonstrate that certain trends in

Weibull parameters exist over long periods of data.

31

Clearly, no model or statistical evaluation of the wind resource at a location or
over a region can ignore any systematic behavior such as longer-term or spatial
variability in the data and be capable of achieving robust or unbiased results.
Additionally, the presence of longer-term or spatial variability raises the question of how
much data and how dense a network is necessary to accurately address the wind resource.
Concerning temporal series lengths, Justus et al. (1979), based on their aforementioned
results concluded that longer periods of record do not signiﬁcantly increase estimation
accuracy, and thus are unwarranted. However, despite this assessment, there remains
some debate in the literature surrounding how much data is needed to assess the long-
terrn wind resource at a location. Estimates range from as low as less than 1 year
(Barros and Estevan, 1983) up to 20 years (Petersen et al., 1998a). General consensus in
the literature is that 1 year is a minimum amount, with 3 to 10 years being the standard,
and if examining longer-term variability (e. g., Palutikof et al., 1987) several decades are

mandated.

Commonly, models have been used to stochastically generate longer, synthetic
series of data at locations where the researcher feels the observational record is too short
(e.g., Justus et al., 1979, Haslett and Raftery, 1989, Derrick, 1992, Hannah etal., 1992,
Dukes and Palutikof, 1995, Garcia-Rojo, 2004). In general, it is these models that form
the basis of most wind energy resource estimation and thus are discussed in the next
section on wind resource modeling. However, one of the primary shortcomings of these
models is that they attempt to correlate data between stations that may be some distance

from one another.

32

Spatially, sparse anemometer networks have always presented a problem.
Although there may well exist a systematic relationship between two stations, it is likely
to be of low signal strength and obscured by irresolvable local noise generated at the sub-
network scale (i. e., at distances less than the distance between stations). The spatial decay
of this spatial serial correlation, which ultimately forms the basis for most stochastic
resource models, decays rapidly with distance, even over relatively homogeneous terrain
(Robeson and Shein, 1997). While the local inﬂuence on a wind speed record at two
adjacent locations might be empirically deduced, it becomes a much more complex issue
when the model attempts to interpolate at too many locations or continuously over a
larger region (e. g., Nielsen, 1999). To that end, some researchers have sought out more
spatially continuous alternative wind data such as those derived from satellite sampling
(Pryor et al., 2004) or gridded geostrophic wind ﬁelds (Palutikof et al., 2002), relegating
anemometer-based observations to model validation. Dynamically-driven, numerical
climate models represent an alternate approach (e.g., Pielke, 1985, Draxler, 1990, Ayotte
et al., 2001, de Rooy and Kok, 2004). Currently however, the majority of research using
numerical models is focused on forecasting wind velocities rather than estimating wind
characteristics over extended periods of time (e. g., Perez et al., 2003). This research

seeks to rectify that deﬁciency.

33

2.2 Statistical Wind Field Modeling

The preceding section discussed the basis for evaluating the wind regime over a
location or an area. These aforementioned considerations subsequently lay the
groundwork for most modeling efforts that have been developed to describe wind
resources. Methods for estimating the wind resource can be divided into three categories
or types, which are not mutually exclusive: stochastic models, probabilistic models, and
dynamical models. Strictly speaking, probabilistic models are also stochastic in that they
are based on empirically-estimated parameters, and many models that are described as
‘stochastic’ function only with the proper speciﬁcation of an underlying frequency
distribution. Thus, although they are separated for clarity in the subsequent sections,
most models share some underlying theoretical background and are not exclusive to those

categories.

2.2.1 Stochastic models

Much early work on wind resource estimation involved the development and use
of stochastic models. Early attempts to estimate the wind at a candidate location were
largely parametric and usually limited to the identiﬁcation of a long-term mean wind
Speed (e.g., Hewson, 1975, Baker etal., 1979, Justus et al., 1979). Because the
variability of the wind was largely ignored, it is not surprising that these early models met

with only limited success and utility.

34

Among the earliest stochastic methods were so-called method-of-ratios, or
climatological reduction approaches (Putnam, 1948, Conrad and Pollack, 1962). This
approach estimates the long-term mean wind speed at the candidate site from the linear
relationship between short-term records at the candidate site paired to observations at
nearby anemometers having longer observational records. Climatological reduction is
the forerunner of the more recent Measure-Correlate-Predict model that will be discussed
later. The reduction approach was further advanced by Feller (1966), who incorporated
the idea that spatial cross-correlation could be used to identify and give preference to
those neighboring stations that shared the greatest similarity with the short record at the
candidate site. A major shortcoming of the reduction method is that it relies heavily on
the quasi-stationarity of observational anomalies at both the candidate location and the
anemometer location (Justus et al., 1979). As was previously mentioned, in most cases
the behavior of wind speed is heavily inﬂuenced by autocorrelation, non-stationarity and
cyclical inﬂuences (e. g., diurnal and seasonal signals), the behavior of which may be
non-linear and vary substantially from one location to another, even over small distances

(Justus et al., 1979).

Stochastic models of wind resource estimation have more frequently trended
toward regressive type models that take advantage of the known dependence of either the
observations to previous observations in time (autoregressive models), the relationship
between observations at one location and another (correlation models), or a combination
of the two. Autoregressive models were originally developed to forecast the behavior of

economic indicators (Box and Jenkins, 1976), but their versatility toward any variable

35

that demonstrated a temporal dependence tendency, such as wind, was quickly

discovered (Katz and Skaggs, 1981).

Among the ﬁrst researchers to examine the use of autoregressive (AR) models for
wind speed estimation were Goh and Nathan (1979), but they met with limited success
due in part to their assumption of a stationary Gaussian wind speed distribution. Chou
and Corotis (1981) rectiﬁed this issue by employing a non-stationary Weibull function as
the underlying distribution. However, a difﬁculty with early AR models, such as that
developed by Eidsvik (1981) was the lack of explicit inclusion of a diurnal cycle. As
such, early AR models were clearly not parsimonious at orders of 24 hours and greater
(Eidsvik, 1981). Following early attempts, McWilliams and Sprevak (1982) and Brown
et al. (1984) presented AR model approaches that took both a non-Gaussian distribution
and diurnal cycle into account and constructed second order autoregressive models that
used the autocorrelation function and diurnal signal to transform the data into a stationary
Gaussian distribution that could be more accurately estimated. Haslett and Raftery
(1989) developed an autoregressive-moving average model to estimate long-term wind
power potential at several locations in Ireland, with good success. Similar regression
model approaches have been undertaken by Goh and Eu (1986), Hannah et al. (1992),
Sfetsos (2000), Walmsley et al. (2001), and Milligan et al. (2003). Finzi er al. (1984)
elaborated upon the AR model by including the 500 mb geopotential height (as a measure
of geostrophic ﬂow) and found success in forecasting winds over the Po Valley.

Additionally, Haslett and Raftery (1989) extended their autoregressive modeling into the

36

spatial domain, developing a Krige model to estimate long-term resources over the entire

country of Ireland.

Unlike autoregressive models, correlation-based models do not model nor imply
dependence of a wind speed record upon itself. Rather, these models attempt to
statistically assess the systematic covariance between two separate wind speed series. In
doing so, such models seek to develop a relationship that describes and exploits the
similarities of the two series in order to synthetically extend the length of one to the limits
of the other (Sansom and Tait, 2004). As such, correlation models have found a great
deal of favor and use in wind resource estimation, primarily due to the sparse networks of

anemometer stations normally available to researchers (e. g. , Barres and Estevan, 1983).

Correlation models take several forms and can be both stochastic as well as
probabilistic. Although spatial correlation is discussed in Putnam (1948) and Golding
(1955), it is not until Walmsley and Bagg (1978) that a spatial correlation model for wind
appears in the literature. Walmsley and Bagg used a correlation matrix from a short
record of data and multiplied it by longer series data to develop synthetic data series at
the locations in their study. Gunst (1995) described several methods for spatially
correlating multiple meteorological variables, including optimal spatial-averaging. Gunst
pointed out that the discounting of non-stationarity and autocorrelation limited the utility

of most spatial correlation methods.

37

In 1992, Derrick developed what he called a Measure-Correlate-Predict (MCP)
model. Since then, this type of model has become a standard tool in wind resource
analysis. Derrick (1992) separated by direction, paired observations of wind at two
stations. For each direction, a linear regression equation was ﬁt to the data, using the
data from the long-record station as the predictor, and the data from the shorter-record
station as the predictand. From these equations, a long-term synthetic series could then
be generated at the short-record location given the speed and direction at the long-record
station. There are a number of limitations to the implementation of such a scheme,
including the distance between the stations involved, the potential non-linearity of the
relationship, and the potential for the relationship to vary in time. Additionally, Van
Lieshout et al. (2004) note that the MCP did not perform well in complex terrain.
However, since its formal introduction, most spatial correlation techniques have utilized
some variation of an MCP approach (e. g., Gerdes and Strack, 1999, Salmon and
Walmsley, 1999, Toriumi et al., 2000). Related alternatives to MCP are a similar joint-
probabilistic approach or a categorical probabilistic adjustment which are discussed in a

later section.

An area of recent increased interest is in the use of artiﬁcial neural networks
(ANN) for the spatial correlation of wind Speeds. A number of researchers have
experienced moderate success in their development and application of ANNs to near-
surface wind speeds (e.g., Kariniotakis et al., 1996, Alexiadis et al., 1998, 1999, Pinson
et al., 2003, Kretzschmar et al., 2004). However, while this approach may provide

accurate results, it is used primarily in wind energy forecasting rather than the estimation

38

of a wind resource climatology and thus is of limited relevance to this research.
Additionally, subsequent replication of this method can often be confounded when the
physical underpinning of the so-called hidden layers of the ANN model are not clearly

described.

Often a researcher requires an estimation of the properties of the long-term wind
resource over a region rather than at a speciﬁc location. As such, a logical extension of
spatial correlation methods is to apply the methods to either a series of regular (grid)
locations over a region in order to develop a continuous surface (e. g., Haslett and Raftery,
1989), or to utilize the information at existing locations to specify a regional value that
abuts other regional values to form a continuous surface (e. g. , Goodin et al., 1979 or

Nielsen, 1999).

However, rather than estimating synthetic series at hundreds or thousands of grid
points over a region, most all spatial ﬁtting techniques used in wind resource estimation
focus on the more economical ﬁtting of the statistical parameters of the wind record, such
as the mean or variance. There exist a number of methods for providing this spatial
interpolation. Techniques include inverse-distance weighting (Sherman, 197 8, Goodin et
al., 1979, Palomino and Martin, 1995), kriging (Haslett and Raftery, 1989), and optimal
spatial interpolation (Julian and Thiebaux, 1975; Thiebaux, 1975). However, many of

these models are hampered by relatively sparse anemometer networks (Goodin et al.,

1979). If interpolation must take place over large areas and long distances, local inter-

39

station effects on wind speed (and associated errors), although important, will be not be

resolved.

Interest in including terrain effects in spatial interpolation models of wind speed
has led to a number of advances in improving spatial estimations. Developments in this
area include an elevation difference variable incorporated into an inverse-distance
weighting scheme (Palomino and Martin, 1995). Taylor and Lee (1984) present a
comprehensive work regarding the theory and applications of ﬂow over low hills. Flow
over more complex terrain, however, is not as well understood, although signiﬁcant
advances have been made (e. g., Gunn and Furmage, 1976; Sherman, 1978; Weber, 1990,

Ayotte et al. 2001).

2.2.2 Probabilistic models

Because of the importance of the distribution of wind speeds to wind power
production, it is not surprising that a majority of wind speed models have been of the
probabilistic type. The appeal of probabilistic models is largely a result of their ability to
reduce a broad spectrum of wind speeds to just a few parameters that, in turn can be
utilized to estimate wind power at a location. In their simplest form, these are models
that seek to ﬁt a theoretical probability distribution to observed data at a location. The

transformation from an empirical to a theoretical distribution more readily facilitates a

statistical analysis of the distribution. More complex approaches attempt to develop

40

correlations in distributions between stations in order to produce a regional wind

distribution estimation (e. g., Justus et al., 1976, Haslett and Raftery, 1989).

Among the simplest probabilistic techniques used in wind resource analysis are
so-called Monte Carlo simulations such as Markov chains (e. g., Sahin and Sen, 2001).
These methods utilize either the empirical probability density function of the observed
data or the transitional probability of one observation to the next to generate a synthetic
series with the same underlying distribution as the original data and the same transitional
probabilities between events. Such methods have been used with success by many
researchers. Kaminsky et al. (1991) for example, used a “one-step” Markov chain to
simulate high frequency wind speeds. Unfortunately, such models appear to
underestimate the probability of low frequency events (Dukes and Palutikof, 1995).
Dukes and Palutikof(1995) used a similar approach to generate an hourly-averaged wind
speed series as well as 3-second gust information. Others who have utilized Markov
chain approaches include Sahin and Sen (2001) and Nfaoui et al. (2004), but it appears
from the literature that such approaches are less preferable than modeling empirically-ﬁt

theoretical probability distribution functions to observed series.

As has been mentioned earlier in the chapter, there has been a wealth of research
devoted to accurately specifying the generalized distribution of wind speeds. A number
of potential distributions have been investigated, including the Gaussian (or so-called

normal) distribution (Justus et al., 1979, McWilliams and Sprevak, 1982), the inverse

41

Gaussian distribution (Bardsley, 1980), a truncated normal distribution (Al-Alawy and
Mohammed, 1985), and a log-normal distribution (Luna and Church, 1974).

However, as has been discussed, the simplicity and versatility of the Weibull variant of
the Gamma distribution eventually was identiﬁed as the most versatile option for
continued model development (Corotis et al., 1978) and has been repeatedly proven to
provide an acceptable ﬁt to a wide variety of wind speed distributions (e. g., Justus et al.,
1976, 1978, Corotis et al., 1978, Hennessey, 1977, Brown et al., 1981, Carlin and
Haslett, 1982, Conradsen et al., 1984, Rainbird et al., 1996, Torres et al., 1999, Quine,
2000, Celik, 2003). As a result, it has received widespread use in estimating the wind

resources of a variety of locations.

If long records of wind speed data are available at a location (or locations), the
ﬁtting of a theoretical probability distribution, like a spatial correlation method, becomes
unnecessary for describing the wind resource. An empirical distribution of the data
record will suffice and summary statistics may be produced. The utility of ﬁtting a
Weibull probability density function to the data occurs when the data at a location are not
of sufﬁcient length, or perhaps non-existent. In these cases, a Weibull probability model
may be estimated from available data at a location or interpolated from the data of a
nearby location. These techniques generally follow the spatial correlation and

interpolation methods described previously.

Using Weibull probability models, researchers have estimated the wind resource

at locations worldwide. For example, Merzouk (2000) used the Weibull distribution to

42

estimate the wind power potential at 64 locations in Algeria and surrounding countries.
Poje and Cividini (1988) performed a similar Weibull analysis of locations in Croatia.
Perhaps the greatest use of the Weibull function in wind resource analysis work is with
respect to the numerous wind resource atlases that have been produced over the past three
decades (e.g., Elliott et al., 1987, Troen and Petersen, 1989). Weibull modeling has been

used extensively in the case of the European Wind Atlas (Troen and Petersen, 1989).

In the European Wind Atlas, a noteworthy Weibull model was utilized. The
model is known as the Wind Atlas Analysis and Application Program, or WASP
(Petersen et al., 1984, Mortensen et al., 1993). WASP is primarily a probabilistic model
because its basis is a Weibull distribution. However, the versatility of WASP lies in the
numerical way in which it migrates a distribution calculated at one location to estimate
the wind resource at another location from which no data are available. WASP
accomplishes this by ﬁrst separating wind speed data from established anemometer
locations into 12 directional bins. These distributions are then upscaled to be regionally
representative (in an area of approximately 100 km radius surrounding the station) by
applying numerical transfer functions that are designed to remove the station observation
bias introduced by local surface roughness, sheltering obstacles and local orography
(Troen and Petersen, 1989). The adjusted observational series is then used to estimate a
regionally representative Weibull distribution. Transference to another location within
that 100 km radius is then accomplished by reversing the model and adding in local

characteristics for the new location. Troen and Petersen (1989) note that the greatest

43

6011‘.

her

0‘)
’H

3r

conﬁdence in WASP results is obtained in regions of relatively low complexity and high

homogeneity.

2.3 Dynamical Models

The alternative to the aforementioned stochastic, probabilistic and empirical
approaches to wind resource estimation is the use of a numerical model to estimate and
forecast wind vectors. Due primarily to computing limitations, early work in this area
focused on the use of primitive equation general circulation models of the atmosphere to
provide low-resolution (e. g., greater than 2° Latitude by Longitude) estimates of the wind
resource at relatively coarse time intervals such as 12- or 24-hours. When the objective
was to simulate higher resolution (both spatially and temporally) wind ﬁelds, generally
for forecasting, more compact mesoscale atmospheric models were employed, and their
potential usefulness in wind research has been explored (e. g., Pielke, 1974; Sherman,
1978; Diab and Garstang, 1984; Rohatgi and Nelson, 1994; Frank et al., 2001) though

seldom in the context of wind climatology.

Regional climate models were deveIOped in response to the climate modeling
community needs for physically-based dynamical models of the atmosphere that were
capable of running on a much ﬁner resolution grid than general circulation models
(Williamson et al., 1995; Henderson-Sellers and McGufﬁe, 1997). These regional

climate models, or RCMS, are often nested in the grids of coarser scale general

44

circulation models (GCM) and cover a region that may span only a few thousand square
kilometers. As a result, the output from RCMS provides estimates of meteorological
variables that potentially are able to resolve some of the small-scale variability inherent
in mesoscale meteorological processes and landscapes (e. g., the inﬂuence of

heterogeneous land cover) that are not available directly from GCM output.

A number of regional climate models have been developed over the past two
decades. Most notable are the Regional Atmospheric Modeling System (RAMS) model
deveIOped by the National Centers for Atmospheric Research (N CAR) (Pielke et al. ,
1992), and the 5th Generation Mesoscale Model (MM5), developed by the Pennsylvania
State University and NCAR (Haagenson etal., 1994). These models operate by ingesting
either observed or modeled data as initialization input and then approximating the mass,
energy, and momentum transfer of the atmosphere (on a regular grid) using the so-called
primitive equations (Pielke et al., 1992). The grid is three-dimensional and consists of
several layers arrayed logarithmically in distance from the surface. Such a grid structure
is designed to provide a detailed analysis of the mixed layer near the surface. The
application of the primitive equations produces iterative estimates of meteorological
variables at each grid point (time steps are often around 15-30 seconds). Temporal
averaging is used to generate hourly values for these estimates at each of the layers in the
grid. The output of the RCM is a synthetic time series of the variable of interest at each
grid point of interest. To that end, an RCM is capable of producing estimates of the wind
resource over a region at a relatively high resolution. In fact, it is likely that the density

of grid points in an RCM far exceeds the density of the instrumental network in the area.

45

.mrr-

of

011

However, despite much success in the use of RCMS for the analysis and prediction of
other meteorological variables (i. e., temperature, precipitation, cloud cover, pressure),
only recently has extensive work been focused on the ability of an RCM to accurately

estimate wind speeds over a region.

The most concentrated application of numerical weather prediction (NWP)
models to wind energy research has been in the area of wind speed prediction. Although
a great deal of work has been done to forecast wind speeds using stochastic methods
(e.g., Nielsen, 1998; Alexiadis et al., 1999; Nielsen, 1999; Landberg, 1998, 2001;
Sfestos, 2000, 2002), these studies have met with limited success largely due to their
empirical nature. Early work using NWP in wind forecasting was performed by Diab and
Garstang (1984) who predicted coastal wind speeds with the University of Virginia
Mesoscale Model. Draxler (1990) coupled a boundary-layer model to the output from the
US. NOAA Nested Grid Model (NGM) with limited predictive success. Whiteman and
Doran (1993) nested a hydrostatic mesoscale numerical model in a GCM to better predict
valley winds. Petersen et al. (1998b) outlined the use of NWP models to estimate winds
at speciﬁc wind farm locations in Denmark, the UK and Greece by dynamically
downscaling GCM output to the surface via the High Resolution Limited Area Model
(HIRLAM) run by the Danish Meteorological Institute and then accounting for local

topography with WASP.

However, despite the interest in mesoscale numerical models for forecasting

winds over a region, few investigations have explored the use of RCMS for wind resource

46

evaluation. An early investigation into RCM wind climatology estimation was Pielke et
al. (1983), who used a mesoscale numerical model to evaluate pollutant transport over
the Chesapeake Bay region. At that time, they felt the method held promise but would
require improved model speciﬁcations of boundary layer processes. Frank and Landberg
(1997) used the Karlsruhe Atmospheric Mesoscale Model (KAMM) to provide input to
WASP and estimate the wind resource over Ireland. Frank et a1. (2001) covered a larger
portion of Europe using the same method. Both Frank and Landberg (1997) and Frank et
al. (2001) met with moderate success, but agreed that further reﬁnement was necessary to
achieve desired levels of accuracy. Unfortunately, none of these investigations evaluated
the RCM wind speed distribution estimates directly in the context of the overall wind
climatology of the region. It is this point that this research seeks to address by answering
the question of whether or not an RCM is directly capable of reproducing the wind
climatology over a region with sufﬁcient accuracy such that the climatological statistics
produced from the model output can be used effectively by wind farm developers for site

selection.

Whereas stochastic and probabilistic models are generally limited in scale to that
which can be resolved by the observation network, dynamic models allow spatial and
temporal resolution to be identiﬁed by the modeler. Thus, scale represents a signiﬁcant
challenge to models attempting to characterize wind vectors for wind energy conversion
systems. Critical temporal scales range from decadal periods with climatological
information to hourly forecasts. In a spatial sense, wind farm developers often use coarse

resolution wind data to identify regions of interest, but then are keen to have a high

47

resolution regional wind map from which to identify prime WECS locations within that
region. On the forecast side, point forecasts are desirable for single turbines and wind
farms may desire a spatial resolution of less than 10 km. However, several contradictory
studies raise questions as to whether or not an increase in spatial resolution will result in a
corresponding increase in forecast accuracy (e. g., McQueen et al., 1995, Buckley and
Leslie, 2000, Mass et al., 2002). The identiﬁcation of optimal spatial resolutions for
RCMS in the context of wind estimation is something that has to date been largely
ignored, even in investigations utilizing RCMS for forecasting wind speeds. The question

of what spatial resolutions are optimal is one that is addressed by this research.

2.4 Model Comparison and Validation

Although thousands of models have been developed for climatological analysis
and of those hundreds address the wind resource, only a handful of procedures exist that
provide robust and reliable evaluations of a model’s performance. While some of these
procedures can be quite complex, in most cases only simple measures are truly necessary

to determine the utility of any given model.

Fox (1981) identiﬁes three groups of data that ought to be compiled to facilitate
model evaluation in air quality modeling. Of those, two are applicable to a broad
spectrum of models and permit subsequent evaluative measures. These two groups are

paired observed and estimated observations for a particular location at a particular time,

48

in

and the empirical frequency distributions of both the observed and estimated data.
Willmott (1981, 1982, 1984) and Willmott et al., (1985) present a suite of statistical
measures by which a robust and conﬁdent appraisal of the performance of a model may
be conducted. The measures are the means and standard deviations of the observed and
estimated data, the Pearson product moment correlation coefﬁcient (r), the intercept (b0)
and slope (b,) of a linear regression of the estimated data on the observed, the mean
absolute error (MAE), the root mean squared error (RMSE), the systematic (RMSEs) and
unsystematic (RMSEu) components of the root mean squared error, and an index of
agreement (d2) developed by Willmott (1982). While this set of evaluative statistics is by
no means exhaustive, the majority of comprehensive model evaluations in the literature

include all or at least some of these measures.

In addition, Wilks (1995) and Murphy (1988) discuss the use of skill scores for
the evaluation of forecasting models. Skill scores are used extensively in the evaluation
of model forecasts of many and diverse meteorological variables. However, as Murphy
(1988) correctly notes, many of these so-called skill scores are based upon the mean
square error and, when decomposed reveal the correlation coefﬁcient and measures of the
systematic and unsystematic bias in the estimates. Thus, while skill scores can be a
useful measure for forecast model evaluation, they are in essence redundant to the more
readily interpretable statistics presented by Willmott (1981), which can therefore be
considered sufﬁcient for the evaluation of any model concerned with producing estimates

of a wind resource climatology as opposed to individual forecast wind speeds.

49

Chapter 3. Study Area, Data and Methods

3.1 Study Area

The Great Lakes region of North America has seen moderate wind energy
development over the past several decades. Commercial wind turbines are operating in
all of the states and provinces surrounding the lakes, and the lakes themselves are
estimated to have a substantial wind resource (Elliott et al., 1987). As noted in the
previous chapter, wind resource potential over much of the land surface portions of the
region was originally categorized as low by the United States Wind Atlas, but a number
of factors including reanalysis of the wind resource, recognition of localized wind speed
enhancements, and advances in turbine technology and siting practices have recently
combined to make wind energy conversion in the Great Lakes region an economically
viable possibility (Schwartz and Elliott, 2002). In particular, the relatively low surface
roughness over the water areas of the region contributes to the generation of stronger

winds along coastal and near-coastal areas of the region than had been estimated earlier.

However, despite the promising nature for wind energy deveIOpment in the
region, a major hurdle remains the relative sparseness of wind observing stations. The
low number and irregular placement of existing station series limits the quality of any
interpolated estimates of the wind at uninstrumented locations. Established
meteorological observation stations in the region with recorded wind speeds and direction
are, on average, over 100 km apart. Robeson and Shein (1997) showed that in the

Central United States, the decay of nearest-neighbor wind correlations becomes

50

Elf

clrr

su'r

311

it

exceedingly high over relatively short distances. A dynamically-based regional
circulation model-based simulation of winds over the region may therefore provide a

substantial improvement in the accuracy of wind speed estimates.

To that end, the Great Lakes region has been chosen as the study area of this
research (Figure 3.1). The region of interest extends from 76° W to 97° W Longitude
and from 41° N to 50° N Latitude. Within this area lie the majority of the open waters of
the Great Lakes and the adjacent coastal areas that are of potential interest to wind farm
developers. For reference, all maps in this study are displayed using an Albers Equal-
Area Conic projection that was produced using a suite of mapping algorithms,
collectively called M_map, developed for Matlab by Dr. Rich Pawlowicz at the
University of British Columbia (Pawlowicz, 2004). Matlab itself is a commercially
available numerical analysis, simulation and graphical representation software
(MathWorks, 2005). Matlab version 5.11 is used exclusively in this research due to its
versatility in permitting a user to create unique code, the ability to efﬁciently handle very
large data sets by virtue of matrix-based processing algorithms, and its generally
excellent graphical display properties. All processing, analysis and display routines were
subsequently written by the researcher in Matlab with the exception of M_map. The
Albers Equal-Area Conic projection was chosen because, of the projections offered by

M_map, a conic projection is best suited for a region the extent of the study area,

Providing a minimum of geographic distortion.

51

 

50°N

 

46°N

44°N

42°N

 

 

Figure 3.1 A map of the study area, which includes the majority of the Great Lakes region of North
America. The dots represent the ASOS/AWOS stations used in this study.

3.2 Observational Data Types and Sources

Accurate observational records of meteorological conditions are a critical
component of assessing the performance, accuracy, sensitivity and validity of any
meteorological model. The assessment of the MM5 model in this research is no
exception. Observational data for this research were obtained from the network of
automated surface observing systems (ASOS) and automated weather observing systems

(AWOS) installed at a number of airports throughout the study region.

The ASOS/AWOS network provides the most abundant available source of

meteorological data within the study region. Because the areas of primary interest are the

52

coastal regions surrounding the Great Lakes, many of the ASOS stations selected for
inclusion lie in close proximity to one or more of the lakes themselves. The remaining
stations (primarily in the interior of Michigan’s Lower Peninsula) were included to retain
a spatial coherence across the region. This criterion resulted in the identiﬁcation of 115
ASOS and AWOS stations that would be used to provide the majority of observational
wind data to this study. Of the 115, two were subsequently omitted due to data issues (as
described further on). The listing of these stations along with the station type

(ASOS/AWOS) is given in Appendix A and is displayed graphically in Figure 3.2.

 

 

50°N m,“ AWL.
““"‘T¥*T MI
112
71 . ' PO
,0 p 102
28 ‘7 ON
89 .
35 ,111
46°N 27 ' so 53 104
92 34 22 43 1‘21
46 ' 8 52 14 106 103
' 1229
. 98 , 7 24 3
0 WI 90 61 26 _51
44 N 94 42 11 32 : "
'54 81
97 40 1o 5 105 "3
100 . 48 56- 114 ‘ 1. . 77
49 MI 2 57 107 ’ 78 79 80
95 39 23 555 , 108 .75
93 96 3‘ 2513 33 53 9.110 - 109 NY
N [A p 37 4436 4 21115
63‘ 9 6016 30 47' .
' . . 1 , .
[L .65 67 66 8 38 838482 PA
“KR IN 86 i 85 I
o “\4_%______ _ l __/_,ou.,J/-/ °w
92 w o o °w 76
88 W 84 W 80

Figure 3.2 ASOS/AWOS stations used in this research. Each number corresponds to the list of stations in
Appendix A. Stations may also be referenced by their geographic coordinates, also in Appendix A.

53

The ASOS/AWOS network is an international network of airport-based stations
designed to provide regular, automated, instantaneous meteorological observations in
support of aviation activities (FAA, 1999). In the United States, the Federal Aviation
Administration (FAA), in conjunction with the National Weather Service (N WS), and the
Department of Defense (DOD) sponsor the ASOS/AWOS network. In Canada, the
network is operated by the Meteorological Services (MSC) division of Environment
Canada. In the United States, all ASOS and numerous AWOS stations are installed and
maintained by the Federal government. In addition, a number of the AWOS systems
have also been installed and maintained by non-federal entities such as airport authorities,
state, local or private organizations. Normally, non-federal AWOS systems that are
linked to the NWS reporting network have been installed with the assistance of the
FAA’s Airport Improvement Program (AIP), and as such are subject to federal

meteorological observation standards as well (FAA, 1999).

Of the 113 ASOS/AWOS stations used in this study, 43 were identiﬁed as being
maintained by the FAA, 22 by the NWS, 33 by non-federal entities, 2 by the US
Department of Defense, 1 by a private Canadian entity, and 12 by MSC. Appendix A
contains a breakdown of station responsibility as well as references for several sources

from which the aforementioned information was obtained.

All regular and Special ASOS and AWOS reports from the United States are

transmitted to the NWS Systems Monitoring and Coordination Center (SRRS) where

they are then disseminated to non-aviation interests and an archive tape is sent to the

54

National Climatic Data Center (N CDC). In addition, data from elsewhere in the world
(including Canada) are retrieved and processed for dissemination by the National

Weather Service.

3.2.1 ASOS/AWOS wind sensors and siting

As wind information is commonly acknowledged to be a critical meteorological
component of near surface aviation activities, accurate and timely reporting of wind
vector information is key to ASOS and AWOS system operations (hereafter referred to
collectively as ASOS). Although a number of conﬁgurations for AWOS systems exist
(of which ASOS is the most advanced), all observe wind speed and direction at a 10 m
height with identical performance standards (NOAA, 2001), which are set forth in the
Federal Meteorological Handbook (OFCM, 1995). Furthermore, Federal and non-
Federal AWOS systems installed in the United States, as well as those installed in
Canada have been provided by one of three vendors certiﬁed by the FAA and Transport
Canada. These vendors are SMI, Inc., Qualmetrics and Vaisala/Artais. Both SMI and
Qualmetrics are subsidiaries of All Weather, Inc. All AWOS sensors manufactured by
these vendors have been certiﬁed to meet or exceed the standards of the FAA, Transport
Canada, International Civil Aviation Organization, and the World Meteorological
Organization (All Weather, 2004). In fact, according to All Weather (2004) the wind
sensor resolution (<1 kt, < 1°), accuracy (i 0.5 kt, :1: 2°), and threshold (0.5 kt) for non-
federal and Canadian AWOS systems are considered to be superior to the stated

performance standards of the US Federal ASOS arrays (discussed next; NOAA, 2000)

55

and to the resolution of the observations that are disseminated (1 kt and 10°). Although
other AWOS systems may be operational in the study area, observations from uncertiﬁed
systems are not available ﬁom the NWS and are not considered in this study. Based on
the published ASOS/AWOS instrument and network operational speciﬁcations, the
researcher judged wind observations to be of sufﬁcient accuracy and quality for use in the

study.

The ASOS wind sensor array (see Figure 3.3) consists of a cross-ann support that
holds a separate anemometer transducer and wind vane transducer (the Bellfort 2000
sensor array). A wind sensor electronics enclosure is housed separately. Wind speed is
measured by a 3-cup anemometer that measures rotation with a photo-interrupt
transducer. Wind direction is measured by a wind vane attached to a precision
potentiometer (N OAA, 1998). The speciﬁed accuracy of the wind vane is :l:5° when
wind speeds exceed 5 knots. Anemometer speciﬁed accuracy is given as i2 knots or 5%
of the wind speed whichever is greater. The resolutions are 10 and 1 knot respectively.
These tolerances fall within US. federal guidelines for meteorological observation

instrumentation (OFCM, 1995).

56

Wind Direction _j“;-ﬂl

Sensor A3 F,_;,_,5 ‘1- Wind Speed
Iii Sensor A2
- Fl -Aircraft
Crossarm l Obstruction
Support *f Lights
l
l:
1%
p
it
Top j?
Horizontalx r11
Retaining l"~l;ElU Wind Sensor
Beam l: fLs-””E Electronics
(2 Places) 1 ; if Enclosure A1
Bottom._m_w_ ll_.il
Horizontal giiriix+,_up_
Retaining- J farm... - "fritnﬂlntmz-tiz
Beam
(2 Places)

Figure 3.3 An ASOS wind sensor array (from NOAA, 2000).

The establishment of ASOS stations is prescribed in the Federal Standards for
Siting Meteorological Sensors at Airports (OFCM, 1994). Typically, stations are located
near the touchdown zone of the primary instrument runway or, if conditions preclude this
siting, the station may be located at center ﬁeld (NOAA, 1998). In either case, the station
is sited in an area of ample, low roughness fetch. At a typical medium size airport (e.g.,
one capable of supporting commercial air trafﬁc), such a station would generally be at

least a kilometer from the nearest major obstructions (e. g, a terminal or hangar buildings)

57

if wind observations are to be considered to be representative of the surrounding 1-2 km
as outlined in OF CM (1994). Additionally, federal standards direct wind measurements
to be taken at a height of 10 meters above ground level (10 m AGL). However, for
reasons that could not be established by the researcher, winds are typically measured at
either 27 or 33 feet (8.23 m or 10.06 m). Given the relatively low surface roughness, and,
that the incongruity in speeds due to the height difference was assumed not to exceed the
2 knot error tolerance of the instrument, observations from these differing heights were

included in the study without adjustment.

Unfortunately, in many mid-latitude locations, occasional ice accretion may
artiﬁcially slow or even stop an anemometer, leading to underreporting of wind speeds.
While equivalent AWOS wind sensor arrays offered optional heat, the aforementioned
ASOS wind sensor arrays were unheated and as a result suffered operational degradation
when experiencing ice buildup during super-cooled droplet precipitation events (N 0AA,
2003). In response, the NWS undertook efforts to replace the wind sensor array with one
that would remain relatively ice free. In 2002 the Vaisala 425NWS Ice Free Wind Sensor
(IFW), a 2-dimentional ultrasonic anemometer, was adopted. ASOS anemometers were
scheduled to be changed over to the IFW sensors at all 313 NWS systems by 01 October,
2002, and all of the 569 FAA-operated ASOS systems during the period 2003-2005.
However, as of 15 May, 2003 (the latest date for which information was available), of the
ASOS stations used in this study, only Hancock, M1 (on 26 November, 2002) had been
changed (NOAA, 2003). Although continuity testing from the old to the new

anemometers was undertaken by the NWS, the tests have not yet been completed and

58

results are not available. However, as the majority of the series from Hancock was
observed with the IF W anemometer, series discontinuities due to instrumentation
changeover were eliminated by truncating the start of the series to 26 November, 2002.

The IFW sensor also complies with the observing standards of OF CM (N 0AA, 2003 ).

3.2.2 ASOS/AWOS wind observation and reporting

In order to obtain what the FAA and the NWS consider to be a representative
wind observation for the surrounding area of interest (identiﬁed as a radius 1-2 miles
around the station; NOAA, 1998), several post-measurement processing algorithms are
employed operationally in the networks. The ASOS software is programmed to collect
observations from the sensor every second (1 Hz). Every 5 seconds, the previous 5 1-
second observations are averaged and stored. For wind direction, every minute, a 2-
minute moving average of 5-second average wind directions is calculated and reported.
These l-minute averages are rounded to the nearest 10 degree increment. It is this
measurement that becomes the wind direction observation at the time the METAR or
SPECI report is issued. The wind speed determination is similar. Wind speeds are a 2-
minute moving average, updated every 5 seconds, and reported once every minute.
Although wind gusts, peak winds, variable wind directions, wind shifts and even squalls
are reported by ASOS, their only role in this research is as a modiﬁer in extracting the
wind speed and direction observations. This will be discussed further in a subsequent

section on quality control (QC)-

59

Although the network provides high quality meteorological observations over a
geographically dispersed array of stations, research activities are not considered to be a
primary data use or application. For this reason, sources for obtaining archived data are
limited in number. The NCDC receives a daily archive tape from the NWS SRRS, but
due to cost recovery efforts by NCDC, the cost of obtaining such a volume of data would
have been prohibitively expensive. Therefore, as soon as the station site series needed for
the study was identiﬁed in early January, 2003, an alternate source was sought from
which to retrieve the data. The most expedient source was determined to be the Internet

site of US Weather, Inc. (http://www.uswx.com).

Access to all ASOS observational reports (hereafter referred to as METARS) was
provided without charge by US Weather, Inc. via their Internet site. However, the data
displayed by the US Weather, Inc. site was limited to the most recent 1440 observations.
Due to this limitation, the earliest date for which data exist at any of the study stations is
late October, 2002. As data from most of the stations were available as of 01 November,
2002, this date was chosen as the starting date of this research. The ending date was set
to be 30 June, 2004, which was chosen to allow appropriate time for data analysis and the

dissemination of the results.

Although the METAR reports are available ﬁom US Weather, Inc. in both raw
(i.e., encoded) and decoded formats, the researcher chose to archive and extract the
necessary information from the raw reports rather than relying on the decoded data. The

reason for this choice was to maintain better control over the decoding and processing

60

algorithms rather than relying on the quality of the undisclosed decoding algorithms used

by US Weather, Inc.

Current meteorological observations are available instantaneously to pilots via
VHF radio frequencies; however, standard METARS are only issued to non-ﬂying
interests on either an hourly or special issue basis. Standard observations are identiﬁed
by the term METAR preceding the report. If meteorological conditions change beyond
the limits of thresholds prescribed in the ASOS software, or if an operational observer
feels conditions warrant mention, a special report is issued. Such irregular reports are
preceded by the ‘SPECI’ report identiﬁer (FAA, 1999). AS such, there is no consistent
number of reports for a speciﬁc period of time. However, the majority of ASOS stations
in the research network appeared to report with a frequency such that 1440 observations
comprised at least a two week period. Thus, for each ASOS station used in this study, the
appropriate US Weather URL was accessed every two weeks (see Appendix A for a
complete list of URLs). The resulting Web page displayed the 1440 raw METARs issued
prior to the web page access. The entire Web page was saved as an ASCII text ﬁle.
After all ASOS station reports were saved, all extraneous information (e.g., graphics,

HTML, advertisements) was removed, leaving only the observation reports.

61

3.3 Observational Data Quality Control

After retrieving the raw METAR reports, it was necessary to extract the
time stamp and wind vector information from each report. Each METAR or SPECI
report includes a number of schedule-driven elements (i.e., observations for continuous
variables) and, depending on conditions event-driven variables (e. g., precipitation,
lightning). The overall format of a METAR report is outlined in numerous publications
(e.g., NOAA, 1998, FAA, 1999), therefore only report information relevant to this

research will be subsequently discussed.

Each report follows a predetermined format that begins on the left with the type of
report (METAR or SPECI), the station identiﬁer, the time stamp (Day, Hour and Minute)
in Universal Time Coordinated (UTC, also known as Zulu (Z) time), a modiﬁer if
applicable (e.g., corrected or automated reports), wind, visibility, weather phenomena,
sky coverage, temperature and dew point, pressure, and remarks if applicable. Thus, a

typical report may resemble:
METAR KLAN 031152Z AUTO 30013KT SSM —RA OVC025 20/19 A2990 RMK A02

The preceding report is a routine (METAR) report for Lansing, MI (KLAN) issued on the
3rd day of the month at 11:52 Z, or UTC, and it was issued without an observer logged
onto the system (AUTO). Winds were from 300° at 13 knots (30013KT), 5 statute miles

visibility (SSM) in light rain (-RA) with an overcast ceiling at 2500 feet (OVC025), a

62

temperature of 20° C and a dew point of 19° C (20/19) and a sea level pressure of 29.90”
Hg (A2990). The remarks (RMK) indicate that the station is an automated station with a
precipitation discriminator (A02). To highlight the format of the METAR data ﬁles
received from US. Weather, Inc. every two weeks, a sample of the raw data is provided

in Appendix B.

A problem with a standardized extraction procedure arises however, because
ASOS and AWOS networks are designed so that missing meteorological elements are
neither estimated nor listed as missing in the recorded observation. If less than 75% of
the observations that comprise the value of an element at a given reporting time are
missing, that element is simply omitted from the observation. All subsequent elements in
the observation are shifted to the left to eliminate the space left by the missing element.
As the report type element (METAR vs. SPECI) and station identiﬁer element are always
present and always of the same length (RRRRR SSSS), extraction of the time stamp is
straightforward (simply the 12th to 1711. characters in the report, followed by the letter “Z”
to denote Zulu time or UTC). The event-driven inclusion of a report modiﬁer and of
several possible wind modiﬁers, however, makes it more difﬁcult to extract the wind

element as will be discussed shortly.

In order to identify the appropriate month and year of the report, the date of the
last entry in the record ﬁle was compared against the date on which the ﬁle was saved. If
they were not the same, it was assumed that the station had not been reporting for an

undetermined period of time prior to the date of ﬁle saving. This station ﬁle was then

63

ﬂagged and manually checked to identify the month and year of the last valid report. In
two instances it was determined that the ASOS station had ceased reporting during the
study period. The ﬁrst site was Meigs Field in Chicago, IL USA (KCGX). On 04 April,
2003 the ASOS station ceased operation when the airport was closed without warning by
the Mayor of Chicago. The other station was Caribou Island, Ontario (CWCI), which
ceased reporting on 28 May, 2003. The researcher was not able to determine an
explanation for the failure of this station. For these two stations, the observational series
were substantially shorter than the other series (642 and 3957 observations respectively),
so they were omitted from the study. For stations other than KCGX and CWCI,
observational reports were largely available throughout the study period of 01 November,

2002 to 30 June, 2004.

Once the observation time stamps in each downloaded ﬁle were veriﬁed for
continuity the time stamp, wind speed and direction of each observation was extracted.
The time stamp was simply the 12th through 17th characters in the report. These data
were parsed into day, hour and minute (Z, or UTC time). After all extraction was
completed, the month and year of the report were added to the time stamp. The

extraction of wind speed and direction presented more of a challenge.

Before the winds could be extracted, it was necessary to determine if a report
modiﬁer element was included. There are two basic types of modiﬁer that may be added
to a METAR report. The ﬁrst is AUTO to signify that the report was generated without

an observer being logged onto the system. The second is COR to alert that the report is a

64

correction to a previously issued report. A number may be added to the COR element

(e. g., COR] , COR2) to signify the sequence of corrections issued to the original report.
If a COR ﬂag was encountered, it was necessary to determine if the subsequent wind
element had been changed. If the wind element in the corrected report differed from that
in the original report, the original value was discarded in favor of the corrected value. In
all cases, the presence and length of the modiﬁer element determined the report position

of the wind element for extraction.

In METAR observation reports there are several variations in the way winds are
reported. Winds are reported based on continuous observation in the 5 minutes preceding
the report issuance. This 5-minute observation is described in the previous section and in
NOAA (1998) and FAA (1999). When winds are relatively steady during the 5 minutes
prior to the observation, they are simply reported in the format DDDSSKT, where DDD
represents the compass direction in tens of degrees from true North, SS represents the
wind speed and KT indicates the measurement units of the wind speed. Because
METAR observations are collected and disseminated worldwide and do not need to
adhere to a standard reporting unit for wind speed, the addition of the unit identiﬁer is
necessary. In the US and Canada, nautical miles per hour, or knots is the chosen unit of

wind speed (1 knot = 0.5148 m 3").

If winds during the 5 minutes prior to the observation exhibit a strong ﬂuctuation

in speed, the wind observation will reﬂect that by adding a gust observation between the

5-minute average wind speed and the unit identiﬁer (e. g, DDDSSGssKT). The addition

65

of “G” indicates a gust measurement, followed by a two-digit gust Speed value (ss). This

gust observation is the highest wind speed observed during that S-minute period.

Additionally, should the wind direction vary by more than 60 degrees during the 5
minutes preceding the observation, the wind direction will be identiﬁed as variable. If
wind speeds are less than 6 knots, the wind direction is replaced by the code VRB (and
thus no directional wind information is available). If the wind speed exceeds 6 knots and
the wind is variable by the aforementioned deﬁnition, an average wind direction is given
in the wind observation, and the entire wind observation is followed by a variability
observation that reports the extremes of the wind direction separated by the letter V (e. g. ,

18OV310).

Although there may be additional information regarding the wind in the remarks
section of the METAR observation, such remarks are generally limited to either the time
of peak wind occurrence should the wind report exceed 25 knots sustained or the time of
a Signiﬁcant wind shift (NOAA, 1998, FAA, 1999). For the purposes of this research,
only the 5-minute average wind speed and direction were extracted. Gust values were
ignored. Where winds were of variable direction and less than 6 knots, the extracted
wind direction value was ﬂagged as missing. For variable direction winds exceeding 6
knots, the average wind direction was extracted from the two wind directions given by
the variability report. Additionally, no wind information was extracted from the remarks

section of the reports (1'. e. , peak winds).

66

One additional problem that arose during the extraction of time stamps and wind
data from the METAR reports was the occasional occurrence of keystroke errors. While
rare, computer data transfers and operator errors can and do lead to the deletion, addition,
or reformatting of data bits. On occasion, characters were added or omitted on the report
modiﬁer element (e.g., AUTO became AUT, UTO, or AUTOO), in the time stamp (the Z
was occasionally omitted), and even in the wind element (KT became K, G became K,
VRB became VR or RB, etc.). For this reason, careful attention was paid to the error
checking algorithms in the extraction program such that any potential keystroke errors
could be detected, recorded, and ﬂagged for later manual examination. Ultimately, of all
observations at all the station sites considered in the study, only 28 so-called keystroke

errors were encountered.

The result of the extraction process was a series of records with time steps and
corresponding wind direction and speed observations. In many instances, the original
reports had been duplicated anywhere from two to ﬁve times in the record ﬁles. While it
would have been straightforward to simply eliminate all duplicate report entries from the
series, a number of observations were out of order, and thus it was necessary to identify
which of the duplicate entries, if any, were in the right location in the series. This
involved iteratively processing each of the observation series ﬁles to place the
observations in their correct temporal order, then eliminating any duplicate entries from
the series. Each ﬁle subsequently contained a series of sequential wind observations with
no duplicate entries. All series ﬁles corresponding to a particular ASOS/AWOS station

were then appended to each other, removing any overlapping reports so that one ﬁle

67

containing all available observations available between 01 November, 2002 and 30 June,

2004 was created for each station.

Lastly, in terms of quality control, all wind observations of zero knots were
ﬂagged. This determination was made because whenever observed 5-minute average
wind speeds were below 2 knots, the wind was reported by ASOS/AWOS as calm, and
the recorded observation given a speed value of 0 and a direction value of 0 degrees
(NOAA, 1998). While the direction is not confused with northerly winds (northerly
winds are recorded as 360°), the ﬂag permits a zero wind speed report to be separated
when comparisons are made with model estimates of winds (which do not have a 2 knot
threshold) at those times. Wind directions described as variable were treated as missing
data and not included in the analysis.

Despite the ASOS operating agencies’ collection of quality, standardized wind
data, it must be remembered that these data are intended for instantaneous aviation
operations rather than for research purposes. Therefore, prior to their use, the data had to
be transformed into a series that was more compatible with the goals of this research.
This post-processing involved two steps. First, the observations, which are reported at
various times within an hour, had to be adjusted to generate a series with data either as an
hourly average, or interpolated to the top of the hour of record. This step was necessary
to create series that could be compared to subsequent model output. Secondly, as the
observational series comprise a short period of record relative to the average expected
lifespan of a wind turbine, some assessment of the longer-term representativeness of the

observational data had to be made. While assessing the representativeness of the

68

observational data is a necessary step in this research, it is outside the realm of the
analysis of evaluating model performance. Rather it is an integral part of the
observational data collection and use. Therefore, these steps are discussed in the

following sections rather than in Chapter 4.

3.3.1 Data homogenization and aggregation

Once the ASOS data had been extracted and quality controlled, it was necessary
to generate series that would pair with wind estimates generated by the MM5 model. The
MM5 used in this research generates estimates of instantaneous wind speed and direction
on an hourly basis at the top of the hour. Therefore, an attempt was made to adjust the
observational data to match the time steps of the MM5 data. In most instances, the ASOS
stations issued hourly automated reports. However, these varied from station to station in
terms of the time of the hour in which they were issued. Unfortunately, several of the
stations did not regularly issue reports within 10 minutes of the top of the hour. As a
result, the number of total observations in some of these top-of-the-hour adjusted series

was much less than the potential total.

In addition to the routine reports, when an operator was logged on to the ASOS
system, additional observation reports were sometimes issued at 15 or 20 minute
intervals. Therefore, in many cases, several observations were available for a given hour.

Lastly, special (SPECI) reports are issued whenever conditions warrant. During rapidly

69

changing weather conditions, SPECI reports may outnumber routine reports and several

may be present during a given hour.

Thus in order to pair observed wind data with modeled estimates, and to ensure
that each station would have a representative series that was not unduly truncated, two
hourly-resolution time series for each station were created and compared. First, the time
stamp of each report was analyzed and if found to be within 10 minutes of the top of a
given hour, was used as the wind observation for that hour. In cases where two or more
observations occurred within 10 minutes of the top of the hour, the observation closest to
the top of the hour was used, and where two observations were equally close to the top of
the hour (e. g., 0:55 and 0:05), the average speed and direction of the two was taken. If
there was no observation within 10 minutes of the top of a particular hour, that hour was
assigned a missing value. In this way, an hourly series of more-or-less instantaneous
wind observations was created, referenced to the top of each hour. Due to generally
strong temporal autocorrelation in hourly wind speeds (Brett and Tuller, 1991, Robeson
and Shein, 1997), it is not anticipated that the hourly mean values would differ
substantially from an instantaneous wind speed or direction value within that hour, except
for the occasional instance where a weather event (e. g., frontal passage or thunderstorm)
occurs near the top of the hour. Thus, the second hourly time series was generated by
averaging all observations between 30 minutes prior to and 29 minutes after the top of an
hour. In cases where all observations for the hour in question were missing, the average
for the hour also was set to missing. This processing resulted in an hourly resolution time

series of averaged hourly values.

70

The resulting observational time series for each station have a total
potential size of 14,617 hours (00:00Z 01 November, 2002 — 23:00Z 30 June, 2004).
However, when missing values were not counted the series length at each station varied.

The number and percentages of valid hourly values are presented in Table 3.1.

 

 

 

 

 

 

Non-missimbservations [n(%)]
Mean Median Std. Dev. Max Min
Top of hour 11,861 12,312 1,832 14,154 642
(81%) (84%) (13%) (97%) (4%)
Hourly Average 12,041 12,298 1,657 13,843 2,298
(82%) (84%) (11%) (95%) (16%)

 

 

 

 

 

Table 3.1 Statistics of the counts (and percentages) of non-missing values (out of 14,617 possible
observations) from series constructed with top-of-the-hour observations and with hourly averaged values.

From Table 3.1 it is evident that the differences between the instantaneous and
averaged series are rather small. The biggest difference was associated with sample
reductions from each of several stations that did not consistently report observations
within 10 minutes of the top of the hour. This is evident in the less peaked distribution of
non-missing observations by station in Figure 3.4. If indeed the hourly-average series
would present a larger and more consistent regional data pool, it is preferable to utilize
these data over the less homogeneous instantaneous series. However, in order to rely
solely upon the hourly-average series, it is ﬁrst necessary to establish that these data are

not signiﬁcantly different from the instantaneous data.

71

 

Top of the hour Hourly Average

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

70 f O‘— 70 1 r
,7
60 L J 60 r
50 ” 50 r
40f —.—l a 40
1: ‘ 1::
._. a 7
30 - - soy 4
20 '4 20p ‘
10 - 10 ~ i
0 _I:] E I I J l 0 I I It I: m—J’
0 5000 10000 15000 0 5000 10000 15000

Non-missing obs Non-missing obs

Figure 3.4 Histograms of the number of non-missing observations at the stations in the study region. Top-
of-the-hour observations were those taken within 10 minutes of the top of the hour, while hourly averaged
observations included an average of all observations from within 30 minutes of the top of the hour.

To establish the similarity of the two data sets, the two series from each station
were subjected to a Student’s paired two-tailed T-test for difference of means (Rogerson,
2001). In order to ensure that the assumption of independent, randomly distributed data
was not violated by the properties of the wind speed distributions, 1000 random, pair-
wise observations were selected to be used in the T-test. In all 113 instances, the
calculated T score remained below the critical value at an alpha level of 0.05, indicating
that the differences in the means of the instantaneous and averaged series were not
statistically signiﬁcant. Overall, a comparison between the two series is best done

graphically. Figure 3.5 illustrates, over all stations, the similarity in mean values.

72

Mean wind speeds - all stations
8 1 ﬁt If f 1 ﬁ ﬁ—

7 _ r = 0.9996 //

 

M
,
+\

_L_

Hourly Average (m s")
b

9.)
ﬂ
4

 

 

0 _l l l 1 L 1*

0 1 2 3 4 5 6 7 8
Top of the Hour (m 3‘)

y-

 

Figure 3.5 A comparison of observed mean wind speeds when using only the observation closest to the top
of the hour (x) or the average of all observations for that hour (y).

Over the 113 stations, the average correlation between the instantaneous and
averaged series was 0.96 with a standard deviation of just 0.04 and a minimum
correlation of 0.8. To that end, it was decided that in the interest of maximizing

observations and data homogeneity in this analysis, only the hourly average series would

be carried forward.

73

3.3.2 Representativeness of ASOS data

An important issue regarding the observational ASOS data series is whether or
not the data are representative of the long-term wind resource over the region. A number
of previous works (e. g., Corotis, 1977; Justus et al. 1979; Barros and Estevan, 1983;
Barthelmie and Pryor, 2003) have concluded that characteristics of an annual wind series
do not differ substantially from the long-term statistics at a given location, especially in
the US. Midwest. However, it is generally acknowledged that at least a year of data, and
preferably more than two or three years, is most desirable when evaluating the long-term
wind resource of a location or region (Hannah et al., 1996). To that end, the
observational data used in this study were subjected to an analysis of representativeness
in order to determine how well they could be expected to reﬂect the long-term wind

resource over the study area.

In order to establish representativeness, 20 of the study stations were identiﬁed
for which quality controlled, long-term data and metadata records were available. These
stations are listed in Table 3.2. ASOS stations represent a relatively low cost investment
in installation and maintenance and have been installed at a number of locations that
previously were not included in the National Weather Service’s pre-ASOS station
network. Only 20 of the stations used in this research existed under the pre-ASOS station

network (Table 3.2).

74

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stations having long-term data
ASOS SAMSON
ID Name LaﬂN) Lon (W) EleﬂmL u s u 3

AN] Sault Ste Marie, MI 46° 28’ 84° 22’ 218 3.48 2.11 3.93 2.17
APN ﬂena, MI 45° 04’ 83° 34’ 210 3.42 2.20 3.77 2.09
BUF Buffalo, NY 42° 56’ 78° 44’ 211 4.53 2.59 5.01 2.63
CLE Cleveland, OH 41° 25’ 81° 51’ 233 4.38 2.44 4.58 2.30
CMX Hancock, MI 47° 10’ 88° 29’ 326 4.48 2.82 4.08 2.10
DET Detroit, MI 42° 24’ 83° 01’ 190 3.80 2.17 4.64 2.42
DLH Duluth, MN 46° 51’ 92° 12’ 435 4.61 2.44 4.71 2.30
ERI Erie, PA 42° 05’ 80° 11’ 222 4.35 2.48 5.20 2.53
FNT Flint, MI 42° 58’ 83° 45’ 233 4.08 2.36 4.40 2.31
GRB Green Bag, W1 44° 29’ 88° 08’ 208 4.06 2.39 4.32 2.32
GRR Grand lgpids, MI 42° 53’ 85° 31’ 237 4.48 2.52 4.37 2.32
INL International Falls, MN 48° 34’ 93° 24’ 360 3.59 2.15 3.88 2.18
LAN LanﬂMl 42° 47’ 84° 35’ 264 4.13 2.49 4.46 2.54
MKE Milwaukee, WI 42° 47’ 87° 54’ 206 4.57 2.47 4.99 2.43
MKG Muskegg MI 43° 10’ 86° 14’ 191 4.45 2.62 4.82 2.53
ROC Rochester, NY 43° 07’ 77° 41’ 178 4.21 2.61 4.43 2.46
SBN South Bend, IN 41° 42’ 86° 19’ 237 4.23 2.49 4.49 2.39
SYR Sﬂcuse, NY 43° 07’ 76° 06’ 127 3.78 2.52 4.18 2.49
TOL Toledo, OH 41° 35’ 83° 48’ 210 3.92 2.66 4.20 2.23
TVC Traverse City, MI 44° 44’ 85° 34’ 190 3.14 2.26 3.95 2.34

 

Table 3.2 20 NWS weather stations that existed in the study area prior to the ASOS transition during the
mid-19903. Each station corresponds to an ASOS station used in this study and is used to compare the
study period data to the long-term (1961-1990) wind climate at the station. Mean wind speeds (u) and
standard deviations (s) are based on wind speeds (including zeros) given in m s".

 

 

 

In addressing whether pre- and post-ASOS installation data from these stations
would indeed be comparable, stations were examined to determine whether they existed
in the same physical location before and alter the ASOS installation. Initially it appeared
that 19 of the 20 stations had been relocated (although all were on airport grounds and
remain so), however, NCDC (2002) indicated that the stations had not actually been
relocated, but rather that a more precise GPS method of positioning had been used to
determine the position of the station. Pre-GPS geographical positioning had been
obtained by traditional survey methods and the resulting position often was rounded or

truncated. The re-measurement of position resulted in a more precise assessment of

75

geographic position and elevation that accounts for the differences between pre- and post-

ASOS installation position measurements for the 20 stations under investigation.

At the 20 stations listed in Table 3.2, hourly wind data were available to the
researcher for the period 1961-1990 as part of the National Renewable Energy
Laboratory (N REL) Solar and Meteorological Surface Observation Network 1961-1990
(hereafter called SAMSON) data set (NREL, 1993). As noted by Shein (1995),
SAMSON data have not been standardized or homogenized for the height of observation.
Therefore, it was ﬁrst necessary to adjust all of the wind speeds to a IO-meter height so as
to permit comparison with the ASOS data series. This adjustment was accomplished
using methods outlined in Shein (1995) and Robeson and Shein (1997). With the
exception of Traverse City (KTVC) and Houghton (KCMX), anemometer heights were
identiﬁed from station histories (N CDC, 1994a and b) and the speeds observed at those

heights adjusted to 10 meters by applying the wind speed power law:

fl
U=Ur — (3.1)

where U is the wind speed at level 2, U, is the wind speed at reference level 2,, and a is an
exponent, which was assumed to be 1/7. Counihan (1975) and others (e.g., Touma, 1977,
Petersen and Hennessey, 1978) have concluded that although empirically derived for
neutral stability conditions, an exponent value of 1/7 provides reasonably accurate

estimates for the proﬁle of wind speeds up to several hundred meters within the boundary

76

layer. Because their anemometer heights could not be identiﬁed, KTVC and KCMX data

were left unadjusted.

Once the SAMSON data were adjusted to a standard IO-meter height,
characteristic statistics (i. e., mean, standard deviation, probability distribution) were
calculated for both the SAMSON and ASOS data (Table 3.2). The aforementioned
statistics were calculated for the overall series as well as for each year and by aggregate
season (e. g., all winter observations). These statistics were subsequently evaluated

graphically and statistically for goodness-of-ﬁt and correspondence.

A Student’s T-test for difference of means was conducted to determine whether or
not the two samples (SAMSON and ASOS) came from the same population (Rogerson,
2001). To ensure independence of the sample observations, 1000 observations were
randomly selected (without replacement) from each series. At a signiﬁcance level of
0.05 (2-tailed) that there was no difference in the means of the two data sets, the null
hypothesis was rejected at all 20 stations. Seasonally, the same analysis was conducted
and again, for all of the 20 stations, there was no statistically signiﬁcant difference in
their means and it was therefore concluded that regionally, the winds observed between
November, 2002 and June, 2004 likely came from the same population that produced the

winds observed between 1961 and 1990.

Wind speed ﬁ'equency distributions have long been used in providing a measure

of wind power potential for a location, and in particular, the Weibull distribution has been

77

found to provide an excellent ﬁt to wind speed data in the middle latitudes (e. g., Justus et
al., 1976, Corotis et al., 1977, Hennessy, 1977, Conradsen et al., 1984, Troen and
Petersen, 1989). As the empirical distribution of wind speeds at the stations used in this
study most widely appear to graphically approximate the shape of a Weibull distribution

(Figure 3.6), its selection as a theoretical distribution for the data was not unreasonable.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2500 . , ﬂ .
7"‘l
2000— .4 - i
1500+ 4 .
1: --——«
1000» —— .
seal .
0 l 25
o 5 1o 15 20

Wind speed (m s")

Figure 3.6 A wind speed distribution (with calms removed) from KP59 (Copper Harbor, MI). While the
distribution may vary ﬁ'om one station to another, all stations in the study exhibit a srmrlar distribution
shape, Supporting the use of a Weibull distribution for wind speed description.

Therefore, the Weibull probability distribution function was estimated for the
same subset of stations as before and compared graphically and statistically for goodness

of ﬁt. Analysis of Weibull distributions took two forms. First, it was necessary to

78

determine whether the selection of a Weibull distribution was an appropriate ﬁt to the
data from which it was estimated. Second, the interchangeability between SAMSON
derived and ASOS derived distributions had to be assessed (i. e., could the ASOS data be
drawn from a distribution empirically derived from the SAMSON data) as statistical

testing has suggested.

A Weibull distribution is a variation of the classic gamma distribution. It has two
parameters describing shape and scale. A third parameter, location, may also be included
to shiﬁ the distribution along the abscissa. However, as winds are a zero limited variable,
the location parameter can be set to zero and its inclusion becomes irrelevant to the
distribution. The Weibull probability density function (from Weibull, 1951) takes the

form:

f(U) = 5(9. Jk—le_[%lk (3.2)

where k is the shape parameter, and c is the scale parameter (in units of the variable U).

The Weibull cumulative distribution function is

F(U)=1— [Er (3.3)

79

The parameters of the Weibull distribution (k and c) can be estimated in one of
two ways. The ﬁrst is via maximum likelihood estimation (MLE), and the second is by
ordinary least squares (OLS) regression. There does not appear to be a preference in the
literature for one method over the other, and previous work (Justus et al., 1976) has
shown that parameters estimated by the OLS technique do not differ greatly from those
estimated by MLE. To be certain, Weibull parameters were estimated using both MLE
and OLS techniques at 20 stations within the study area. Overall, the OLS technique
provided slightly more conservative parameter estimates. Also, the greatest difference in
k was 0.8 and for c, just 0.3 m s". As the OLS technique is much less computationally
intensive, it was chosen here for the remainder of the stations. In the OLS method (see
Justus et al., 1976, Rohatgi and Nelson, 1994, Romeu, 2003a), Equation 3.3 can be

rearranged by taking the double natural log of both sides as such

mbhm—Fﬂﬂﬂzkhﬂﬂ—klﬂd (an

Functionally, Equation 3.4 now takes the form of the standard linear regression equation:

y=b0+qx (13

where, for the variable ln( U), k is equal to the slope of the line (b,), and the intercept (b0)

occurs at —k ln(c).

80

Based on the OLS estimation procedure, a theoretical Weibull distribution was ﬁt
to each set of the data from the 20 evaluation stations. The shape parameters ranged from
1.67 to 3.29, with a mean of2. 12 and a standard deviation of 0.41. The scale parameter
ranged from 4.04 m s" to 5.86 m s", with a mean of 4.96 m s'l and a standard deviation
of 0.45 m 3". To establish the goodness of ﬁt, each data set was binned and plotted
against both the probability and cumulative Weibull density functions (Figures 3.7 and

3.8). This graphical procedure has been well established (e. g., Nelson, 1982, Rohatgi and

Nelson, 1994, Romeu, 2003a).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Weibtl PDF WeibdlCDF
0.12 ﬂ . 1 10° . .
r
r
r
0.1 ~ Fl, — ‘
' LL L
ll) - r
l a
a a
§ 006 - §10‘ -
g ‘1 l
Q F E' l
a + «
o
T
0.04 r - 4
0.02r 1 — L
0 ,,, -— 10'20 1 4_L..r4441 4 .i..
0 5 10 15 20 1o 10 102
Wind Speed (ms’l) wm Speed (ms'l)

Figure 3.7 Wind speed frequency distribution (r) and cumulative frequency distribution (1) at Rochester,
NY (KROC) for ASOS data. Theoretical Weibull distributions are shown as solid lines.

81

Weibul PDF Weibul CDF
0.12 1 a T 10 . ﬂ a. .

 

 

 

0.1 r

M
_i

m, x .

Probability
p
8
if
Cum. Probability

0.04 - K

0.02 f

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 i 10‘ . .ri...ri _n ....444
0 5 10 15 20 10° 10'

MM Speed (ms'l) Wind Speed (ms'1)

 

Figure 3.8 Wind speed frequency distribution (r) and cumulative frequency distribution (1) at Traverse
City, MI (KTVC) for ASOS data. Theoretical Weibull distributions are shown as solid lines.

As expected, given empirically derived shape and scale parameters, the two-
pararneter Weibull distribution provided a good ﬁt to the majority of wind data from all
series. Figure 3.7 is the distribution of wind speeds at Rochester, NY, and represents
what appears, graphically, to be the worst Weibull ﬁt of any of the 20 stations.
Conversely, Figure 3.8 is the wind speed distribution at Traverse City, MI, arguably the
best Weibull ﬁt of the 20 stations. It should be noted that most of the 20 stations more
closely resembled the Traverse City ﬁt than the Rochester ﬁt. Even so, the Rochester ﬁt

does not appear to be inappropriate to the data.

82

While the ASOS data have already been determined to be representative of the
long-term wind regime over the study area and the Weibull distribution was found to be a
good visual ﬁt for the ASOS data, it was still necessary to determine statistically whether
Weibull is an appropriate choice of distribution, and if so, could the ASOS data be drawn
from the Weibull distributions of the long-term SAMSON data as might be assumed
given the results of the T-test. To that end, the Weibull distribution that had been
empirically ﬁt to the SAMSON series was applied to the ASOS data. One tendency in
ASOS wind data noted by an earlier study is a general reduction of ASOS-observed wind
speed data relative to pre-ASOS observations (Powell, 1993). The ASOS data used in
this study were found to follow the same pattern (see Table 3.2), in most cases, with the
distribution of ASOS wind speeds, while similar to SAMSON counterparts, shifted to a
lower mean wind speed (see Figure 3.9). Again, a graphical approach for the goodness-
of-ﬁt was used to determine whether ASOS data could come from a distribution
empirically speciﬁed by the long-term SAMSON data. While graphics showed some
degradation in ﬁt (Figure 3.9), overall, it appeared that the ASOS data could be derived
from the SAMSON Weibull distributions, especially if the systematic shift of the wind

speed distribution were accounted for as instrument discrepancy.

The ﬁnal step in determining the appropriateness of a Weibull distribution. to the
ASOS data was to statistically test the goodness-of-ﬁt. Although several methods for
testing the goodness-of-ﬁt of a distribution to data exist, the Anderson-Darling test

(Anderson and Darling, 1954) was selected as the most appropriate.

83

Weibul PDF KUGRR ASOS data and SAMSON Weibull PDF
0.1 ﬁ T . 10 f

 

 

1*va

 

 

 

 

Cum. Probability
8..

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ﬂ _ 10'2 r r rLLriii r i A ..
0 5 10 15 20 10° 10‘ 102

Wind Speed (ms'l) Wind Speed (015”)

 

Figure 3.9 Weibull pdf (r) and cdf (1) (solid lines) at Grand Rapids, MI (KGRR) derived from 30-year

hourly data (1961-1990) applied against the ASOS observed (1 1/2002 - 6/2004) wind speed distribution
[bars (1) and + (r)]-

A number of so-called distribution free goodness-of-ﬁt tests exist to evaluate how
well a chosen probability distribution ﬁts to a sample of data. The most common of these
tests are the Chi-square and Kolmogorov-Smimov tests. Such tests are referred to as
distribution free, or empirical distribution functions (EDFs) in the sense that their critical
values do not depend upon the speciﬁc theoretical distribution function being tested and
the parameters of the distribution may be empirically derived from the data itself

(Bimbaum, 1953). The X2 test is among the most commonly used tests in that it is

84

relatively easy to calculate (Davis, 1986, Snedecor and Cochran, 1989). However, the X2
test is of low statistical power and requires relatively large bin counts to ensure the
robustness of results (Snedecor and Cochran, 1989). A slightly more powerful test is the
Kolomogorov-Smirnov, or K—S test (Davis, 1986). One major advantage of the K-S test
over the X2 test is that it is considered an exact test as it does not require the data to first
be binned as with the X2 test, thus increasing its power (Davis, 1986). However, the K-S
test has several important limitations. First, it tends to be less sensitive to data in the tails
than near the center of the distribution. Secondly, and perhaps most importantly, the
distribution being tested must be fully speciﬁed. In other words, the distribution cannot
be evaluated against the data from which the distribution parameters were empirically
estimated. In such cases, the critical region is no longer valid and must be estimated by
repeated simulation (F illibin and Heckert, 2003). Furthermore, both the X2 and K-S tests
suffer from the limitation of requiring continuous, rather than discrete distributions

(Fillibin and Heckert, 2003).

The Anderson-Darling test is a special case of the Kolmogorov-Smirnov test that
is more sensitive in the tails of the distribution (Stephens, 1974, Romeu, 2003b). In
addition, the distribution in question does not need to be fully speciﬁed. That is, the
parameters of the distribution can be estimated from the data being evaluated without
invalidating the critical region of the test (Anderson and Darling, 1954, Fillibin and
Heckert, 2003). Strictly speaking, however, the Anderson-Darling test, while an EDF, is
not distribution free. Its critical values are dependent upon the distribution being

evaluated (Lewis, 1961, Stephens, 1976). While the speciﬁcation of a distribution makes

85

the Anderson-Darling (A2) test more powerful and sensitive than the K-S test, it also
means critical values must be calculated for the speciﬁc distribution. Fortunately,
because the Weibull distribution is used extensively in engineering, failure and lifetime

studies, critical values of A2 have already been speciﬁed (Stephens, 1974, 1976).

The disadvantage of a more powerful statistical test tends to manifest itself in the
complexity of its calculation. The Anderson-Darling test is no exception, and is more
complex than either the X2 or K—S tests. For asymptotic distributions the test statistic, A2

is given by Anderson and Darling (1954) as

n
A2 = —n—lz(2i— l)[an,~ + ln(l —U,,__,-+1)] (3.6)

i=1

where n observations of x are ordered and U,- is the function Fm). Substituting the
Weibull distribution for the standard normal distribution, the A2 equation becomes

(corrected from Romeu, 2003b)

A2 _—. _n — %[Z(2i — 1){1n(i - exp{— 2,. })— z,,_,-+l ] (3.7)

i=1

where

X' k

86

and where k and c are the empirical estimates of the Weibull shape and scale parameters

respectively. For small samples, the test statistic is modiﬁed by Equation 3.9.

A” =[1+005'2}42 (3.9)
n . .

However, there are no set guidelines as to what constitutes a small sample and critical

 

values are calculated such that they must be compared with this modiﬁed test statistic
(Stephens, 1974, 1976). Because small sample size tends to lead to a more conservative
critical value, this only strengthens the results of the test. Therefore, all test statistics
were calculated for small samples (and subsequently both the notation A2 and All refer to

the small sample statistics interchangeably in this research).

The null hypothesis of the Anderson-Darling test used in this study states that the
data were drawn from the speciﬁed Weibull distribution. The alternative hypothesis
therefore is that they were not. Rather than continually refer to calculated tables to assess
the test outcomes, the observed signiﬁcance level (OSL) of the modiﬁed test statistic

(A?) was calculated empirically using

p =1/{g+expl—0.1+1.24inlA2*)+4.4s(A2*)J} (3.10)

87

as described by Romeu (2003b). The observed signiﬁcance level is the probability (p) of
the null hypothesis being true. Unless the OSL is smaller than the critical probability
level (i. e., alpha level), the null hypothesis may not safely be rejected without an undue

risk of committing a Type I statistical error.

Like any statistical hypothesis test, certain assumptions must be met. For the
outcome of the Anderson-Darling test to be considered statistically valid, the data being
evaluated must be independent and come from a Weibull distribution (Romeu, 2003 a).
In order to meet the assumption of independence, 100 wind speed observations were
randomly selected without replacement from the ASOS data for each station. Anderson-
Darling has been used with n as small as 6 with robust results (Romeu, 2003a) and thus
an n of 100 is assumed to be sufﬁciently large. This procedure was repeated 100 times
for each station. Because the Weibull distribution is mathematically unable to
accommodate calm (0 m s") values, only wind speeds above the 2 knot threshold were
included in the random selection. However, the exclusion of these calm wind speeds
does not necessarily invalidate the assumption of independence of the selected wind
Speed observations because the randomization ensures that each sampled speed is
unrelated in time to every other sampled speed in the subset. The A2 test was applied to
each of the 100 random series for a given station using the empirically derived Weibull

shape and scale parameters from the 30-year SAMSON record of wind speed at the same

stations, and the results are presented in Table 3.3.

88

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Weibull and A2 statistics at selected stations
ASOS SAMSON
ID Name k c A" k c

ANJ Sault Ste Marie, MI 2.01 4.03 2.6142 2.15 5.5

APN Alpena, MI 2.31 4.18 2.1210 1.85 4.29
BUF Buffalo, NY 1.98 5.16 1.9197 2.46 7.00
CLE Cleveland, OH 2.16 5.14 1.7692 2.56 6.53
CMX Hancock, MI 1.77 5.30 2.1641 1.92 6.53
DET Detroit, MI 2.07 4.46 2.3177 1.73 6.66
DLH Duluth, MN 2.03 5.34 2.1491 2.70 6.69
ERI Erie, PA 2.10 5.01 1.7748 2.32 7.93
FNT Flint, MI 1.97 4.82 2.2716 1.83 6.38
GRB Green Bay, WI 3.23 5.86 2.1550 2.46 6.23
GRR Grand Rapids, MI 2.06 5.11 1.6503 2.23 5.91
INL Intemational Falls, MN 3.29 5.53 2.0812 2.59 5.99
LAN LanSM 2.06 4.99 1.9886 2.40 6.52
MKE Milwaukee, WI 2.04 5.32 2.1747 2.25 6.39
MKG Muskegon, MI 2.00 5.28 1.8537 2.59 6.36
ROC Rochester, NY 1.80 4.96 2.4818 2.07 5.83
SBN South Bend, IN 2.12 4.93 1.8412 2.43 7.02
SYR Syracuse, NY 1.67 4.56 3.2709 2.13 5.83
TOL Toledo, OH 1.80 4.89 2.4188 2.37 5.76
TVC Traverse City, MI 1.85 4.04 3.3116 2.58 6.25

 

 

 

 

Table 3.3 Wind data distribution and goodness-of-ﬁt statistics for 20 ASOS stations in the study area with
long-term (1961-1990) wind records. Weibull shape (k) and scale (c) parameters are given for short
(ASOS) and long-term (SAMSON) speeds. Average Anderson—Darling (A2 ) test statistics based on 100
trials of 100 observations are given for the ASOS data.

At a signiﬁcance level of p = 0.01 , the results were mixed and in general
inconclusive. The null hypothesis (that the ASOS data came from the SAMSON-derived
Weibull distribution) was accepted about half the time when averaged across all 20
stations. While the most of the stations were able to accept the null in more than 50% of
the trials, a few stations were unable to accept the null more than a few times. The
overall average was reduced by the results from Traverse City, MI (KTVC) at which the

null was rejected in all cases. Overall, however, for all stations the distribution of test

89

statistics was negatively skewed toward more conservative values (Figure 3.10), and it

appears that the average test statistics were by-and-large skewed by a few large outliers.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30 l ﬁT— T— 'V f l l 7— T l
I
'
25 L. . .. . . ' ' _ . Mean = 1.8537ms'1 Std = 0.79927
20 L -
E
3'15 b 1
0
m , .
10 L ' ‘I 7 l . —1
5 a r
0 . u , l l 7
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
A2 test statistic

Figure 3.10 The distribution of Anderson-Darling (A2) test values from 100 random samples of 100 ASOS
wind speed observations at Muskegon, MI (MKG). The critical value (dashed) of 1.943 is shown, as is the
mean test statistic (solid) and 95% conﬁdence intervals (dotted). This station accepted the population
Weibull distribution 66/ 100 times.

This behavior corresponds with the results of Shein (1995) who demonstrated that
signiﬁcant variation in empirically-derived Weibull parameters may occur from one year
to the next, but that even though one year’s distribution may vary from another, both are
drawn from the same long-term population, both ﬁt a Weibull distribution, and both are
representative of the long-term wind speeds at a station. Therefore, the results of this

representativeness analysis suggests that while the statistical summary of trial samples

90

(ASOS) may not have agreed with the long-term Weibull parameters (SAMSON), the
preponderance of null-acceptance trials coupled with the graphical and statistical
similarity between the two data distributions were enough for the researcher to conclude
that the ASOS data are, in general drawn from a population that is distributed according
to a Weibull function, and that it appears the ASOS data are, in general representative of

the long-term wind speed climatology of the region.

Once the general goodness-of-ﬁt of the Weibull distribution for data within the
region and conﬁdence that the data were not materially different from the long-term wind
regime had been established, OLS was used to estimate the Weibull parameters for the
ASOS data at the remainder of the 113 stations. The shape parameters ranged from 0.96
to 4.89, with a mean of 1.76 and a standard deviation of 0.41. The scale parameter
ranged from 2.19 in s'1 to 7.48 m s", with a mean of 4.10 m s‘1 and a standard deviation
of 0.98 m s". This relatively low variation with respect to the parameter means suggests
that wind speed distributions across the region do appear to exhibit some spatial

coherence. Station values of shape and scale are presented in Appendix C.

3.4 Spatial and Temporal Behavior of Observational Data

3.4.1 Non-seasonal assessment

Prior to evaluating the estimative ability of a model, it is necessary to develop an

understanding of the properties and behavior of the variable to be modeled. The Wind

91

Energy Atlas of the United States (Elliott et al., 1987) indicated that, with the exception
of the over-water and coastal zones, the Great Lakes region has a relatively low wind
power potential, based in large part on the relatively low observed mean wind speeds
over land in the area (Figure 3.11). Despite the increase in the number of stations in the
study area in recent years relative to when the Atlas was compiled, wind statistics from

the study period suggest that the results of the Atlas were not in great error.

UNITED STATES ANNUAL AVERAGE WIND POWER

 

Figure 3.11 Average wind power map (at SO-m) of the contiguous United States from Elliott er al., (1987).
Darker areas represent greater wind energy potential. Values (as found in Elliott etal., 1987) are based
“P011 Wind speed observations ﬁom lower heights, and many of the over-water estimates are of low
conﬁdence due to limited data availability. A substantial portion of the over-land parts of the study area are
listed as category 2, or very low wind speed potential.

 

 

 

 

Figure 3.12 Annual mean wind speeds (in m s") for the period of record across the study region. Negative
values are invalid byproducts of interpolation and should be ignored.

Over the Great Lakes region the mean wind speeds from the period of record
range from 2.06 to 7.10 m s'1 with a mean regional speed of 3.77 m s". The strongest
speeds appear to be concentrated near Long Point, ON with the weakest in SE Michigan
(Figure 3.12). There appears to be a fair amount of variability about the means at a
number of stations. Stationwise standard deviations range ﬁom 1.60 m s‘l to as much as
3.77 m s", with a mean standard deviation of 2.38 m s". Regionally, however, variability
is much less. The standard deviation of station means over the region was just 0.75 m 5",
indicating that there appears to be some degree of homogeneity in the regional wind ﬁeld,

and that much of the variability is the result of local scale inﬂuences. Means and

93

standard deviations of all stations are presented in Appendix C. However, it should be
noted that the values in Appendix C are calculated only from non-zero wind speeds.
While this results in slightly higher values, the omission of calm winds is because several
stations suspend observations during the night when the airport is closed. Thus the
means for these stations would be lower than those at 24-hour stations that are more

greatly inﬂuenced by nighttime calms, which are common over the study region.

A biharmonic spline interpolation algorithm, developed by Sandwell (1987),
originally for interpolating GOES data was used to generate the contour maps of each
variable over the region. Figures 3.12 and 3.13 both employ this method, as do all
subsequent contour maps. The choice of this interpolation method was based on a
comparison of several available alternative methods such as standard linear interpolation,
cubic interpolation, and nearest neighbor interpolation. Standard linear, cubic, and
nearest neighbor interpolation methods are all based upon Delaunay triangulation. The
linear method contains discontinuities at its ﬁrst derivative, and the nearest neighbor at its
zeroth derivative. The cubic, while producing a smooth surface, was not equipped to

perform extrapolation over the region.

In addition to the mean wind speeds over the region, the prevailing winds also
were examined (Figure 3.14). When averaged over the study period, a general
southwesterly prevailing wind direction was found at most stations. Such behavior is
expected as the overlying synoptic scale ﬂow at these latitudes is largely westerly, often

with a southerly component when a trough resides over the Great Plains region

94

(Eichenlaub et al., 1990). It is interesting to note that several stations do not conform to
this pattern, instead demonstrating southeasterly prevailing winds. It is likely that these
stations are more greatly inﬂuenced by high levels of localized ﬂow modiﬁcation, due

either to mechanical (terrain) or thermal (sea breeze) factors or a combination of both.

 

 

 

 

Figure 3.13 Stande deviations (m 3") about mean annual wind speeds over the study region for the
period of record.

From the wind roses produced for each station, overall annual prevailing wind
directions were identiﬁed at each station. The majority of stations exhibited prevailing
winds from westerly directions. However, although a prevailing direction could be

established for each station, most stations exhibited a multimodal wind rose and the

95

prevailing direction was not clearly dominant when non-seasonal (all data) were used

(Figure 3.15; Appendix D).

 

 

 

 

 

 

w W .
All seasars: Prevailing wind direction

Figure 3.14 Prevailing wind directions (arrows are scaled by mean speed) at the stations used in this study.
Prevailing winds are derived from all available data from all seasons in the period of record.

Furthermore, most stations exhibited a great deal of diversity in their wind rose
distributions, both seasonal and overall. This suggests that the region is inﬂuenced by
different ﬂow regimes at different times of year, each contributing to the overall behavior
of the wind ﬁeld at each station. It also suggests that localized inﬂuences may play a

larger than expected role in determining the behavior of the wind ﬁeld at a given station

96

site, which may complicate the wind ﬁeld estimation of a non-local scale physically-

based model.

 

Figure 3.15 Annual wind roses at four stations across the study area [(a) Chapleau, ON, (b) Bellaire, MI,
(c) Sault Ste. Marie, MI, and (d) Buffalo, NY]. Wind regimes over the study region are very diverse over
the period of record (see Appendix D)-

97

Temporal Autocorrelation at CYYZ

 

0.8 ~

0.7 e

h0.5-

0.3

l

0.2 r

 

 

0.1 ’ 1 ‘ 1 ‘
0 5 1 0 15 20 25 30
Lag (hours)

 

Figure 3.16 Temporal autocorrelation of non-seasonal wind speeds at Toronto, ON (CYYZ) over the
period of record. This autocorrelation behavior is typical of wind speeds across the Great Lakes.

It is commonly accepted that wind speeds tend to exhibit a strong degree of
temporal autocorrelation. An autocorrelation function was applied to the data in this
study at each station and the results for the ﬁrst 26 hour lags are plotted in Figure 3.16.
Distinct autocorrelation was found at all locations, necessitating steps to minimize this
behavior when statistically assessing the data. At a lag of one hour, autocorrelations
ranged from 0.93 to 0.78, with a regional mean of 0.88 and a standard deviation of 0.03.
The majority of strong lag-1 autocorrelations appear to come from stations that extend

into the water regions of the Great Lakes (Figure 3.17). This suggests that the relatively

98

low roughness of the lakes limits localized inﬂuences on the wind regime and may
facilitate the success of autoregressive type models for wind speed forecasting over the
water. However, given a correlation of 0.36 between the standard deviation of wind
speeds and the autocorrelation coefﬁcient, it does not appear that an increase in station

speed variability necessarily results in decreased autocorrelation.

In addition to the temporal autocorrelation of the hourly wind speed observations,
it is also noteworthy to describe additional patterns that may be present in the data.
These include the possibility of both diurnal and seasonal (annual) patterns. Neither
signal is inappropriate for the region. Near surface wind speeds tend to reach their zenith
during the afternoon hours, when maximum local insolation has generated the strongest
thermal gradients and turbulence over an area. Nighttime generally brings the slowest
speeds as thermal activity is minimized and the boundary layer may decouple from the
free atmosphere. This behavior also is manifested in an annual signal, but in reverse.
Strongest winds over the Great Lakes tend to be exhibited in winter, at the time of the
greatest hemispherical pressure gradients, and weakest in summer, when the polar front

migrates well north of the region (Eichenlaub, 1979, Eichenlaub et al., 1990).

99

 

 

 

Figure 3.17 First order (lag l) autocorrelation coefficients over the study area for the period of record.
Although all stations are strongly autocorrelated, the highest autocorrelations appear to occur at stations
most isolated from major land regions.

The seasonal signal is demonstrably recognizable in a time series of wind speeds
at any station within the study area (Figure 3.18) and can also be visualized in a
comparison between summer and winter wind speeds as will be discussed in the next sub-
section. Several stations were found that did not exhibit a pronounced annual cycle.
These stations tend to be relatively exposed (e.g., Erie, PA) or in complex terrain (e.g.,

Ironwood, MI) and as such may have a seasonal signal that is damped by local effects.

100

KBEH Time Series (2411 MA)

 

 

 

12 ﬁ— ﬁ l—— ‘1 T , r T r
10~ —
8- s
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A 3: . L '
'- 3;- I j- : - .
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3 s r; z: 1;, 2: , :3: 1 31.15%: i. s
l .3: z“ t‘ I? ': :‘; 1:11: "if? * '~51’:'17323 3” 1
3;: ;7 , .37 I1 :3} :73}?- ,§: ‘ :‘1‘3133'5 :‘ ,E
4.. ﬂ -; - - - W :~ ~ v TV -A' A L' .t-‘k ..
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2— ~ ' Wit 7'25 f 39;; “
y 7.; n l 1::
1' 4'
1’1: 5

 

 

 

0 I l I l l l 1 1
2002.8 2003 2003.2 2003.4 2003.6 2003.8 2004 2004.2 2004.4 2004.6
Time (year)

Figure 3.18 A 24-hour moving average time series of wind speeds at Benton Harbor, MI (KBEH) over the
period of record. Lowest wind speeds are found during the summer months, while strongest winds are
experienced in winter. All seasons appear to exhibit substantial variability about the station mean.

The diurnal cycle of wind speeds tends to be more difﬁcult to visualize than the
longer annual cycle. However, by decomposing the time series of hourly wind speed
observations into its component cycles, the dominance of a diurnal cycle quickly
manifests itself at most stations in the study region. The transition of data from the time
domain to the frequency domain was accomplished by employing a Fast Fourier
Transformation on the data at each station. The results of the transformation highlight
the relative importance of the diurnal signal (and thus the effects of local inﬂuences) to

the behavior of the wind ﬁeld at a given location (Figures 3.19 and 3.20). Somewhat

101

surprising was the relative strength of the diurnal cycle, which was found to be fairly
constant across the region, indicating that lake breeze circulations along the coasts may

not have as much of an inﬂuence on diurnal wind speeds as had been previously thought.

Power spectrum KLDM
1 l I F I I F I I I

 

9
(D
l

l

 

 

l;

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frequency (cycles/hr)

 

O) O)
T
u—i
l

#
I

N
l

Explained Variance (%)
U
l

d
T

 

l A ‘
.n. r- A .~ _ - ,
f y ‘1 f I «‘ / ‘. \v" - ,J’ ‘ ‘x

1 I A . A. j‘ A
u. .iJ I. in a“ LAM JLQJ tnhdﬂ [$1114 .4; 'IJJ‘VVJ LY'JI‘a—N ' 1. "'J 112 .2; 1
2 3 4 5 6 7

Periodogram (days/cycle)

 

 

 

O
o
,_._
i
_L

Figure 3.19 Power spectrum of wind speed at Ludington, MI (a coastal location) from 11/02 to 6/04. The
diurnal cycle near 0.04 cycles/hr is dominant, accounting for 5% of the explained variance in the data.

102

Power spectrum KLAN

1 I I ' I I l I I I

 

 

 

 

 

 

 

 

 

0.8 - _
8 0.6 ~ —
3
‘1 0.4 — —

0.2 - _

o 1.. us 4.. 2‘. L - ._2 l L J 1 1 AL l
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frequency (cycles/hr)
8 I I I I I l
5,?

o 6 7 q

0

C

a

'5

> 4 - -
B
.5
£2 - _
131
0 gt ______ La JLJM u a HLLMJ’XLrLAmJ'W‘SHAAX -L .-"‘i’J‘/\.~_/k- "fur "jxx ‘L/Ax‘x‘ﬁ‘blr ~'\v~-"\_—"" "R's."
0 1 2 3 4 5 6 7
Periodogram (days/cycle)

Figure 3.20 Power spectrum of wind speed at Lansing, MI (an inland location) from 11/02 to 6/04. The
diurnal cycle near 0.04 cycles/hr is dominant, accounting for 7% of the explained variance in the data.

The annual distribution of wind speeds at the stations in the study area has already.
been discussed earlier in this chapter. However, while the frequency distributions of
wind speeds over the study region appear to be well approximated by a two-parameter
Weibull distribution, there was some variability in the parameters of the distribution over
the region. The shape parameter (k) appears to be the least spatially variable (Figure
3.21). This is the parameter that controls the peakedness of the distribution (Figure 3.22).
The larger the value of the shape parameter, the lower the variability about the mean, or

stated another way, the greater the probability of experiencing a wind speed observation

103

near the mean speed. From the data in Figure 3.21, it appears that the least variable
winds (largest shape values) occur systematically toward the southern areas, centered
about the tip of Lake Michigan. A lack of spatial variability in the Weibull shape
parameter indicates that the variability of wind speeds about their mean does not vary

appreciably over the region.

 

 

 

 

Figure 3.21 Annual Weibull PDF shape parameters over the study area for the period of record. Highest
values indicate highest probabilities of winds near the mean wrnd speed.

014"

-1
0.12_ chcld constantatsms

0.1" <—k=6

0.08 —

probability

0.04 -

3'
ll
—L

0.02 L

 

 

0 l l l t
o 5 10 15 20 25 30
Wind Speed (m s")

Figure 3.22 The inﬂuence on a Weibull PDF when the shape parameter is varied. A shape value of 1 is an
exponential distribution, 2 is a Raleigh distribution, and 3.7 approximates a normal distribution. Below a
shape value of 3.7, the distribution is right skewed, and above it left skewed.

Annually, the Weibull scale parameter (c) appears to be much less systematic in
its behavior (Figure 3.23). However, one must remember, that the scale parameter is
largely a measure of the ﬁrst and second moments of the distribution (mean and standard
deviation). The scale parameter value represents approximately the 63rd percentile of the
distribution. Thus, as scale increases, the distribution is necessarily stretched toward the
right tail because the distribution is bounded by zero on the left. Conversely, as scale
decreases, the distribution is squeezed toward zero (Figure 3.24). Over the region, the

highest scale parameters tend to occur in locations with high mean wind speeds. This is

105

logical as a higher mean moves the distribution away from the lower zero bounds, thus

stretching the distribution toward the right tail.

 

 

 

 

Figure 3.23 Non-seasonal (all data) Weibull PDF scale (0) parameters over the study area. lt is clear that
as with the shape, the distribution parameters cannot be considered regionally constant.

An alternative way in which to visualize and compare the distribution of wind
speeds over the region is through schematic plots. Because schematic plots utilize more
robust and resistant statistical measures (e. g., median and IQR), such plots are arguably
more robust than graphics that employ moment-based (e. g., mean and standard deviation)
measures (Wilks, 1995; Tukey, 1977). Additionally, more information can oﬁen be

captured and presented in a schematic plot than in a standard frequency distribution

106

histogram. For example, not only is the median presented, but additionally, it
demonstrates the degree of spread of data about that median value; whether or not the
data are symmetrically distributed and if high or low values are legitimately part of the

main body of the distribution or whether they are outliers.

 

0.12 ﬂ r 1— n— ﬂ

0.1 T k held constant at 2 i

‘—‘ c=4ms'l

0.08 P _

Probability
1°
8
I
(i
n
00
3
I’ll

0.04 t- /
0.02 \ ‘

 

 

 

0 5 10 15 20 25 30
Wind Speed (ms'l)

Figure 3.24 Variations in the Weibull scale parameter result in a stretching or squeezing of the distribution
and reﬂect the behavior of the mean and standard deviation of the wind speed distribution.

Schematic plots of the wind speed series at each station were constructed as a
notched box and whiskers plot, whereby the lower and upper bounds of the box are the

lower and upper quartile respectively. The median bisects the box, and the notch

107

represents a robust estimate of the uncertainty about the median value for comparison
with other plots. The so-called whiskers that extend from the box ends represent the
outer fences of the data, or 1.5 times the interquartile range (IQR). The whiskers help to
illuminate the extent of the more unusual data within the distribution. Lastly, outliers, or
those values that exist beyond the outer fences are illustrated independently as points on
the plot. Overall, the schematic plots allow a great deal of information regarding the
distribution to be presented and graphically compared to other distributions. Three
example schematic plots are presented in Figure 3.25. Schematic plots for all stations can

be found in Appendix D.

Surprisingly, when the outliers are clearly identiﬁed and excluded, it appears that
there is not a great deal of variation between stations. This clearly illustrates the
dependence of the mean wind speed on extreme outlier values. In general, most plots
show a median value of between 4 and 5 m s'l and an IQR of only about 2-3 m s",with
much of the higher winds constrained to the upper outer fence region and but a few
extreme outliers. Unfortunately, it appears that, based upon these distributions, very few
of the stations would have wind speeds sufﬁcient to economically support wind energy
conversion as the entire IQR resides below the peak power thresholds (the lower bounds
of rated power output) of most turbines (about 9 m s" when adjusted to lO-m height). As
expected, however, it was the distributions at stations extending into the lakes or along
the windward shores in which the peak power threshold occurred within the upper

whisker region of the plot.

108

KGYY wind speed distribution.

T T j l I T l ]

 

 

 

 

 

 

 

 

— it er —————————— 4 ————————— + are a 1r 4. it» «
_L l 1_ A _L l _L
0 2 4 6 8 10 12
-1
Wind speed (m s ) (a)
KIAG wind speed distribution.
1 I I I 1 ﬁ ﬁ 1— I— I

 

P ———————— i ————————————————— +oomm+4n4 were” 411 «

l l l 1 1 1 1 l l I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 2 4 6 6 10 12 14 16 18
-1
mm speed (m s ) (b)
KMKG wind speed distribution.
1 ﬂ I I
[- __________ i --------------------- +4 114 we” 11+ 4 ~
1 I l J i
0 5 10 15
.1
Wind speed (m s ) (c)

Figure 3.25 Schematic plots of non-seasonal wind speed distributions at 3 stations [(a) Gary, IN, (b)
Niagara Falls, NY, and (c) Muskegon, M1] for the period of record. Most of the variability appears to be
not in the main body (IQR) of the distribution, but rather in the presence of high wind speed outliers. This
information likely skews both the mean and standard deviation of the distributions toward higher values.
See Appendix D for plots for all stations.

109

To further examine the wind power potential of the region, a power analysis was
undertaken. This involved examining two factors. First was the amount of time a turbine
would experience winds in the range at which it would produce its maximum (or rated)
power. This amount of time is called TARP, or time at rated power (Shein, 1995) and,
for this study area is largely dependent on the winds in the upper whisker region of the
aforementioned schematic plots. The rated power calculations were based upon an
idealized turbine with a rated wind speed range of 12 to 25 m s'1 at a hub height of 50
meters. The results of this analysis are presented in Figure 3.26. It appears that, as
expected, the overall percentage of time that the wind speeds fall within the rated power

portion of the turbine power curve is relatively low; under 20% for the entire region.

 

 

 

All seascm: Tire a: rated power CA)

Figure 3.26 Percent time at rated power (TARP) over the study area for the period of record. This is a ratio
of the total time a wind turbine might be expected to be producing its rated (maximum) power.
Calculations are based on a 50 m turbine hub height with a rated power range at 50 m of 12 to 25 m s".

110

As expected, the greatest TARP percentages were over Lakes Superior and Eric,
as well as Georgian Bay. However, TARP does not include those wind speeds at which
the turbine would be producing power at less than its rated capacity. Thus, an estimation
of total actual power potential was called for. This power estimate was obtained by
adjusting the wind speeds to 50 meters using the wind speed power law (Equation 3.1)
with the 1/7lh exponent, and using the actual power curve of a moderate sized wind
turbine that might reasonably be installed in the study region. The turbine used was a
Vestas 850 kW with a 50—m hub height. By translating 50—m wind speed estimates into
estimated turbine power output, a realistic measure of wind power potential over the

region could be obtained (Figure 3.27).

 

 

 

 

 

 

 

 

Airmzmbmpowerowpmasomkm x106

Figure 3.27 Power output in kilowatts over the period of record from a Vestas 850 kW wind turbine.

lll

From Figure 3.27 it is rather clear that coastal regions that can be expected to
have a substantial over water fetch appear also to be the most productive in terms of
power output from a turbine placed at those locations. In particular, Long Point and
Georgian Bay in Ontario as well as the Lake Michigan shoreline and Keweenaw
Peninsula in Michigan would be most appropriate for WECS development. This spatial

pattern of Figure 3.27 appears to share some similarity over the region with the US. wind

power map in Figure 3.1 1 (Elliott et al., 1987).

3.4.2 Seasonal assessment

An examination of the wind ﬁeld over a region such as the Great Lakes would not
be complete without an assessment of the seasonal variations in that ﬁeld. As has been
noted in the previous sub-section, the regional winds reach a maximum velocity in the
winter and a minimum in the summer. In addition, the overlying synoptic ﬂow patterns
are markedly different during the various seasons (Whittaker and Horn, 1981, Harman,
1987). In the winter, the polar front generally shifts south of the region, and so, with
frequent troughing over the area, a northwesterly wind might be expected (Eichenlaub,
1979, Eichenlaub et al., 1990). With the migation of the polar front to the northern
reaches of the study area, summertime is expected to bring a shift to a more
southwesterly ﬂow over the region, and, with a decreased pressure gradient over the
region, a weakened velocity structure. While strong summer winds do occur, they tend to

be inconsistent, occurring in coincidence with frontal passage and convective activity

112

rather than a strong upper-level ﬂow as is present in the winter. Overall, the year was
divided up into four parts of three months apiece to represent each of the seasons. Winter
was comprised of December, January and February. Spring was March, April and May.

Summer was June, July and August. Fall was September, October and November.

As the variation in mean wind speeds has been discussed in the previous sub-
section it is not necessary to repeat it here. However, an examination of differences in
seasonal variability is in order. Although it was thought that perhaps the transitional
seasons of Spring and F all would experience the greatest variability of wind speeds about
the mean, this was not found to be the case (Figure 3.28). Rather, winter, with its highest
mean speeds also had the highest standard deviations. Summer, in contrast, with its low

speeds tended to also have the lowest variation in speeds.

In addition to differences in variability of wind speed, it is also expected that there
exists a variation in prevailing wind direction from one season to the next. The
prevailing winds therefore were plotted over the region and examined by season. Figure

3.29 shows the transition from a summer regime to a winter one in terms of shifts in the

prevailing winds.

113

(a) Spring

 

 

 

 

(b) Summer

 

 

  

7

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 22 24

Figure 3.28 Standard deviation (in in s") of wind speeds by season (1 1/2002 - 6/2004). While the highest
Wind speeds occur in the winter, so does the greatest variability in wind speeds. As expected, summer,
with the lowest mean speeds also has the smallest variation.

114

(0) Fall

 

 

 

 

((1) Winter

 

 

 

Figure 3.28 Continued.

115

(a) Spring

 

 

 

(b) Summer

 

 

 

Figure 3.29 Prevailing winds during each season (1 1/2002 - 6/2004) at the stations in the study area. The
dominant direction in all seasons except Spring is southwesterly. Spring is characterized by predominantly
northerly and northwesterly winds. Station wind arrows are scaled by seasonal mean wind speed.

116

 

(c) Fall

 

 

 

 

((1) Winter

 

 

 

Figure 3.29 Continued.

117

Interestingly, the expected northwesterly ﬂow of a wintertime mid-latitude wind
ﬁeld did not materialize. Instead, this northerly ﬂow was restricted to the Spring months.
It is possible that a deviation from the regular winter synoptic patterns over the region
during the period of record led to this inconsistency. In addition, winter was the most
consistently southwesterly. In the Fall and Summer, a number of stations had prevailing
wind directions that did not adhere to the general regime of the region, likely the result of
a dominant local ﬂow pattern. Indeed, it is during these months that insolation is
maximized, and as a result the thermal lake breeze is strongest. This is evident in that the
stations having deviant prevailing winds all appear to be located in close proximity to a
coast, and the direction is largely perpendicular to the coastline. Winter shows the least

amount of variability from the prevailing southwesterly ﬂow.

Based on this seasonal variation, seasonal wind roses at the stations were
examined. The seasonal wind roses highlighted two important characteristics of the
regional wind ﬁeld. First, it was conﬁrmed that the majority of stations exhibited
seasonal wind roses that were consistent with the regional pattern (Figure 3.30).
However, the seasonal wind roses also demonstrated that in most cases there was a great
deal of variability in wind directions, and that the prevailing wind direction was not
dominant. In general, it appeared that Fall, closely followed by Winter exhibited the
greatest variability in wind direction. With a few exceptions, Summer was the least
variable in terms of wind direction. In addition, Summer wind roses at many of the
coastal stations exhibited a fair degree of bimodality, suggesting at least some local

thermal inﬂuences.

118

  

 

 

’_... " -

210“\\_1_/-./”150
180

(b) Summer

 

 

 

 

Figure 3.30 Seasonal wind roses at Beaver Island, MI (KSJX) for the period of record. This station is
consistent with the regional prevailing ﬂow regime.

Secondly, at station sites where it could be assumed that local terrain or local
thermal flow regimes might substantially affect the wind ﬁeld, a corresponding signal
was found in the wind roses (Figure 3.31). As mentioned earlier, a thermally induced
lake breeze circulation appeared to be commonly manifested in Summer wind roses as a

bimodal distribution of low variability. In other instances, such as the sheltered bay

119

surrounding Traverse City, M1, the wind ﬂow appears to be dominated by thermal
circulation guided by the orientation of the bay during the Spring and Summer, and

dominated more by the overlying westerlies the remainder of the year.

To better address some of the inﬂuences on the local station winds at different
times of year, it is perhaps advantageous to examine the dominant signals in each of the
seasonal wind speed series (Figure 3.32). In particular, three signals are of interest. The
ﬁrst is the diurnal signal, which may indicate a dominant thermally induced pattern of
winds (diurnal heating/cooling). At coastal locations in the Summer, a half-day signal
might also appear, the result of a lake breeze circulation. Lastly, cycles with periods of 3
to 7 days are of interest. This is approximately the frequency with which mid-latitude

synoptic systems pass over the region (Eichenlaub, 1979, Harman, 1987).

The behavior of the data in the frequency domain is exactly as expected for the
region. There is a diurnal cycle present at all stations. The diurnal signal also varies by
season. The diurnal signal has its most power in the Summer. For example, at Holland,
MI (Figure 3.32), the power of the daily cycle is nearly three times stronger than in either

the Spring or Fall. The daily cycle is at its lowest power during the Winter months.

Secondly, at stations near a coastline, such as Holland, MI, there is a distinctive
half-day cycle that is present in all seasons, but is weakest in the Winter (Figure 3.32).
The half-day cycle is of more-or-less equal power in the Summer and Fall, and only

slightly weaker in the Spring. It is likely that the half-day cycle during winter is more the

120

result of aliasing from the diurnal cycle than an actual thermally induced lake breeze
circulation. The cycle’s presence at predominantly coastal locations during months of
heightened insolation appears to conﬁrm the presence of a lake breeze circulation, as

aliasing is unlikely to account for the entire signal to that magnitude.

 

(d) Winter

(c) Fall

Figure 3.31 Seasonal wind roses at Traverse City. M1 for the period of record. In its bay location, lake
breeze circulation and localized flow predominates, especrally in Spring and Summer.

121

 

(a) Spring

 

 

 

 

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frequency (cycles/hr)

 

1
i
1

on
r
1

Explained Variance (%)
N

 

 

 

 

 

 

 

 

 

1 l. A _
0 1 2 3 4 5 6 7
Periodogram (days/cycle)
(b) Summer
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0.8 L ~
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o
0. O4 - .1
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0 ‘AI IMA..A.AA.JA. -AAL... .1..-AA_L 42-..“: ‘L‘ ‘An A.-.-._4L__ Ar
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frequency (cycles/hr)
15 I r T l I T
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8
.§ 10 l—
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0.
L11 /\ /\ ,
0 L 1 .1 rpm .19 M A. M mmdkg/Bx _./"’l/ \l' x __.//

 

 

 

0 1 2 3 4 5 6 7
Periodogram (days/cycle)

Figure 3.32 F FT seasonal power spectra at Holland, M1 for the period of record. Upper ﬁgures indicate the
power of the signal at any given frequency. Lower ﬁgures translate the power into a percentage of
explained variance of each signal relative to its periodicity.

122

(c) Fall

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 “—7”— I T tT—Afﬁ Iﬁ ﬂ'rm
0.8 L i
g 0.6 — J
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0 “.111“ -4; A)... ‘1 1.4 A -- n .24.. .4-..‘ “A- --.r_L..._ _._ r
O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Frequency (cycleslhr)
6 I I ﬂ I I ﬂ
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.5 ‘ *‘ 1
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0 1 2 3 4 5 6 7
Periodogram (days/cycle)
(d) Winter
1 ﬁ ﬁ I I I I I I ﬂ
0.8 ~ ~
.. 0.6 — ~
0. 0.4 F ~
0.2 -
0 ‘L‘l - A —A I AAA— A . ALL A LA A __..l A -—|— A A; A;
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Frequency (cycles/hr)
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8
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a I
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Periodogram (days/cycle)

Figure 3.32 Continued.

123

Lastly, as expected, all stations exhibited relatively strong signals between 2 and 7
days per cycle, but not equally in all seasons (Figure 3.32). This so-called synoptic signal
is most likely the result of mid-latitude syn0ptic systems traversing the region. As
expected, these signals were strongest in the Winter and weakest in the Summer. More

moderate synoptic signal strength was encountered in the Spring and Fall.

In summary, the wind ﬁeld in the region is characterized by two dominating
inﬂuences. There is a distinct inﬂuence by the overlying synoptic circulation of the mid-
latitudes. This is manifested in the predominance of a regionalized prevailing wind
direction and the fundamental similarity in mean wind speeds across the region. It is
likely that a regional scale, numerically driven climate model may capture this inﬂuence
with a high degree of conﬁdence. The other inﬂuence however, is a local component that
is the result of both differential heating from variations in land cover, and of terrain that
may channel the ﬂow. As this is a study primarily of coastal regions of the Great Lakes,
much of both inﬂuences is due to the land — water transition. From a thermal perspective,
the differences in speciﬁc heat between the lakes and the land adjoining them is quite
strong, but also can be variable depending on the land cover along the coast. From a
mechanical perspective, the land —- water transition zone often represents one of the most
acute changes in surface roughness in a region. It is likely that even the most well
speciﬁed dynamical models may have difﬁculty fully parameterizing these localized

effects, and it is likely that here is where much of the model error will occur.

124

3.5 FSMM5 Model and Wind Estimates

The major objective of this study is to evaluate the performance of the regional-
scale numerical climate model known as MM5 for use in identifying areas with wind
energy potential, and to identify techniques that may improve the performance of the
model. In order to accomplish this goal, MM5 estimates of the near-surface wind ﬁeld
were obtained over the region at a number of spatial resolutions. Because the
implementation and oversight of MM5 requires a substantial investment in both computer
and operator time, the performance of MM5 was also compared to estimates of the wind
ﬁeld derived from several other popular stochastic model approaches, such as Measure-
Correlate-Predict (Derrick, 1992). Each of the comparison models represents a technique
that has been used in wind energy research and is less complex than MM5. This chapter
discusses MM5 and the comparison models and outlines the methods for model

evaluation and comparison.

3.5.1 Model implementation and domains

Simulated wind data for the study were obtained from version 3.4 of the non-
hydrostatic 5th Generation Mesoscale Model (MM5), developed at the Pennsylvania State
University and NCAR (Haagenson er al., 1994). This version of MM5 (hereafter
FSMM5) has been implemented for operational and research use by the US. Forest
Service North Central Research Station in East Lansing, MI (USDA, 2002). FSMM5 has

been run operationally since the summer of 2002 and produces 48-hour hourly forecasts

125

of several meteorological indices of importance to forest ﬁre risk and mitigation
(Chamey et al., 2003, Heilman et al., 2003). F SMMS is run at 36 vertical sigma layers
(non-spectral) on a 36-km grid that covers much of eastern North America and a 12 km
domain that extends from 31.9° N, 101.9o W (lower left) to 51..9° N, 63.7° W (upper
right). Within the 12-km domain a 4-km grid is nested to provide greater spatial
resolution (Figure 3.33). The distribution of grid points over the study area is presented
in Figures 3.34 to 3.36. The domain layers are variably distributed according to pressure,
with the lowest at around 2 meters (surface) and the t0p layer at approximately 12 km
(100 mb). Within the vertical domain, near surface layers are more closely spaced
(corresponding to vertical pressure gradients), gradually increasing from about a 10 meter
spacing between the bottom layers to about 1500 meters of spacing between the upper-

most layers (In er al., 2004).

Each of the domains is speciﬁed using a Lambert Conformal projection with true
latitudes at 40 and 60 degrees (Charney, 2004 personal comm). The study area (Figure
3.1) is fully enclosed by the 36 and 12 km domains (Figures 3.33, 3.35 and 3.36), and
partially by the 4 km domain (106 of the 113 ASOS stations are situated therein — the
stations outside the domain are omitted from analysis at this resolution) as shown in
Figure 3.34. Based on these grid domains, FSMM5 is capable of producing estimates of

the wind resource over a region at a relatively high resolution.

126

’ 140' 130' 1' 110° 100' - ~ . . . . .

 

 

 

 

 

 

 

 

 

é
a
50.. 50
.40.
‘0“ .40.
.50.
:10" .30.
2°“ .20.
‘ 500 0 500 1000 1500 2000 Kilometers
E

 

 

120' 110' 100' 90' 80' 70'

Figure 3.33 Spatial coverage of the 3 domains of FSMM5. The coarsest resolution (36 km) covers the
contiguous United States, some of Canada and Mexico. The intermediate (12 km) covers the east-central
portion of North America. The ﬁnest resolution (4 km) includes most of the Great Lakes region.

 

 

 

 

97. 9?. 87' 82' 71. no 5].
0
51 V
a
I ,,.
46" .72.
m 11'
41"; K (K
h 0 100 200 300 400 500 600 700 800 K110112165
fr

 

 

an 92' a'r 52-
Figure 3.34 Spatial coverage of the 4-km (West) domain of FSMM5 over the study region (41° - 50° N by

76° ' 97° W). This is the ﬁnest resolution domain run by the model and covers much of the Great Lakes.
Each dot represents a domain grid cell comer point.

127

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V V

97' 92° 8? 82' 77'

Figure 3.35 Spatial coverage of the 12-km F SMM5 domain over the study area (410 - 50° N by 76° - 97°
W). Each dot represents a domain grid cell corner point.

 

Figure 3.36 Spatial coverage of the FSMM5 36-km domain over the study area (41° - 50° N by 76° - 97°
W). Each dot represents a domain grid cell corner point.

128

Within FSMM5, a 5-minute (5-9 km grid) digital elevation model (DEM)
obtained from the US. Geological Survey (USGS) characterizes the land surface of a
region. The FSMM5 model runs used in this study were initialized using 40-km
resolution Eta (now known as NAM; North American Meso) model initialization analysis
from the National Centers for Environmental Prediction (N CEP). F SMMS employs the
following atmospheric physics parameterizations: the Kane-Fritsch cumulus scheme for
simulating convection (Kain and Fritsch, 1990), Dudhia’s (1989) cloud radiation model,
the Mellor—Yamada turbulent kinetic energy model for the boundary layer (Mellor and
Yamada, 1974, 1982, Gerrity, 1994) and Reisner ct al’s (1998) mixed phase cloud
microphysics model. These pararneterizations and schemes have been used with success

in a wide variety of MM5 implementations (Dudhia, 2004).

F SMMS is run operationally on a Linux based Beowulf cluster (Adams and V08,
2002) comprised of 16 individual processor nodes and is capable of producing a 48-hour
12 km simulation in 1 hour and a nested 24-hour 4 km simulation in 4 hours (Charney,
2002 personal comm). Computational schematics of FSMM5 are discussed in detail by

Heilman et al. (2003).

3.5.2 Model output

FSMM5 estimates the u and v components of wind at each vertical level for each
grid point location. Unlike precipitation and temperature, which are calculated by MM5

at dot points (grid cell center points), wind components are estimated directly at grid

129

cross points (the grid cell corners). The four estimation levels that were available for this
study were the surface (2 meters), 30 meters, 50 meters and 80 meters and are the mean
height of the level. As MM5 performs its calculations on spectral levels an interpolation
to physical altitudes was subsequently necessary. The aforementioned wind speed
altitudes were conﬁrmed by Forest Service personnel (Bian, 2004 personal comm.) at the
time of data transfer. Wind speeds were estimated by MM5 as u (zonal) and v
(meridional) wind vectors in meters per second (m s") at each grid point (and are not grid
cell averages) within the aforementioned domains. Although the computational time step
for the 36, 12 and 4—km spatial resolution domains is 90, 30, and 20 seconds respectively,
the output wind vectors were estimated as instantaneous values for a given time, rather
than an aggregate over the entire preceding time step (Charney, 2004 personal comm).
Thus, a wind vector estimate for 0000 UTC, for example, was the instantaneous estimate
at that time, rather than an average of prior time-step estimates. Such model behavior
must be noted when any comparison with observed values is attempted as most observed

values are temporally-averaged over some speciﬁed period.

The wind vector output available for this study included hourly estimates of the
wind vectors at each grid cross point of each domain for either a 48-hour lead (36 and 12
km), or 24-hour lead (4 km). The FSMM5 model is run twice each day at 0000 and 1200
Z, but only the 0000 Z analyses output was available for this research. Furthermore,
output from several model runs were not available to the researcher, resulting in
approximately one to three missing days of estimates per month. In particular, 10 days of

model output was missing from the month of December, 2002. In order to maintain a

130

continuous series that matched the ASOS data, these days’ estimates were indicated with
missing number ﬂags (N aN in the data coding). Ultimately, each model run provided
62,245 grid point estimates in the 4-km West domain, 34,118 estimates in the 12-km
domain, and 13,500 in the 36-km domain for each hour time step. Overall, for the study,
and including all missing or unavailable output, a total of 14,617 hourly estimates were

available at each grid point in each domain during the period of record.

3.5.3 FSMM5 wind estimates

Wind estimates generated from the F SMMS model had to be extracted from the
domain grids in order to create meaningful and coherent time series of estimates for each
station. To generate paired comparison data sets for model evaluation where one data set
is gridded and the other is an irregularly spaced network of points, two approaches are
available. Either the data from the irregular network must be interpolated to nearby grid
points, or the gridded data must be interpolated to the network locations. This research
selected the latter method as the networked data was the observational data. In model
evaluation, it must necessarily be assumed that the observational data being used for the
evaluation are free from error (Willmott, 1981). lnterpolating estimates to observation
locations preserves this status, whereas interpolating the observational data from their
collection locations would unnecessarily introduce bias into the observed data, and the
resulting model evaluation would have been comparing model estimates to observational

estimates, where the bias could not be assumed to reside in the model estimates.

131

 

 

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—1

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O
i

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2 , . 7 7 [1|] 1, l I f 1’ 1:? .1, 1 ' _
(g6 , , 1 I '1‘ L'ii i , g. 1, i I I1 L ‘1": 11'1“ 9 1H 1““. E. 1
2' . 1 ”111111111 ['1' ”1"1'1,'~H11 ' I l' WW 1 l: _
21— : ‘ r I ) —
2802.8 ﬂ 2003.2 2003.4 2003: ( 20008 2004 2004—2 2004.4 2004.6
ime year

Figure 3.37 Mean daily (thin line) and mean monthly (thick line) lO-m wind speeds at Tomato, ON
(CYYZ) from the lZ-km run of F SMMS and using an inverse distance weighting of estimates from the

nearest 4 grid cross points.

As a critical issue surrounding the performance of a numerical model is the
possibility that systematic spatial bias may exist, a number of different interpolation
methods were used to generate the series used for model evaluation in order to evaluate
the potential spatial systematic component of model estimative error. First, a series was
created that simply assigned the wind estimates from the grid point nearest a station
location to that station’s ﬁle. Given the rapid distance decay of correlations (Robeson
and Shein, 1997), this series represents only a “ﬁrst guess” estimate of the wind around
the station location. The second and third series were derived by taking the 4 grid points
nearest a station location and assigning an unweighted average of the wind vector to the
second series, and for the third series calculating an inverse-distance weighted average
(Figure 3.37). In recognition of the possibility of potential systematic spatial bias (as
discussed in the preceding chapter), unweighted average series were also generated from

the 16 and 36 grid points nearest to a given station. If a systematic spatial bias exists, it is

132

likely that the coarser 16 and 36 point average series will show signiﬁcantly less of this
bias than the 1 or 4 point series. The degree of difference in performance is also an

indicator of the magnitude of this spatial bias.

Once the aforementioned estimate series were generated for each station, it was
necessary to estimate the winds at the standard observational height of 10 meters for
comparison with the observed series. This was accomplished by ﬁtting an exponential
curve to the 2-, 30-, 50-, and 80-meter estimates in order to generate an exponent that can
be used in the wind speed power law (Equation 3.1). Whereas the SAMSON data used in
the previous chapter provided wind speed information at only one height and an exponent
of II? was assumed (Touma, 1977, Petersen and Hennessey, 1978, Counihan, 1975),
FSMM5 data were given at 4 levels. Thus the wind speed power law (Equation 3.1) was
simply reversed and used to explicitly derive an exponent that ﬁts each hour’s data.

Thus, from the hourly data at the four FSMM5 levels, the empirically derived exponent

facilitated the interpolation of wind estimates at 10 meters for each station location.

Although Holton (1979) felt that Ekman spiraling was not great in the lowest few
meters of the atmosphere and Klink (1999) chose to ignore it in directional height
corrections, there was a noticeable shiﬂ in wind direction from one FSMM5 level to the
next based on 100 random samples of the 4-1evel wind estimates. Thus, as it was not
computationally intensive, wind direction at 10 meters was estimated in this study with a
process utilizing the concept of Ekman spiraling. Resulting lO-meter wind direction was

non-linearly interpolated from 2 meters using the same exponential proﬁle function

133

earlier derived for the wind speed to produce altitude weights that were subsequently
applied to the 2-meter wind directional shifts. This adjustment simply created a
directional shiﬁ in proportion to the level at which the estimates could be compared with

the observations.

One critical issue of note in this analysis is that the data from the F SMMS model
are forecasts of wind speed and direction, which are based upon a set of initial
meteorological conditions. The model is run twice each day, and for the 12 and 36-km
grid domains, forecasts are generated hourly at lead times up to 48 hours (24 hours for
the 4-km domain) beyond the model initialization time. Thus, although the physical basis
of the equations do not change from one forecast time to a subsequent time, the laws of
entropy dictate that the model error and potential bias in the forecasts will increase with
greater lead times. To that end, model estimates at each hourly time step (e. g., all 002
data, 01 Z data) were interpolated to the location of each station and examined. No
appreciable increase in estimation bias for longer lead times versus short lead times was
found at any of the station locations (Figure 3.38). As a result, all model estimates were
weighted equally in the subsequent analysis of model performance, regardless of their

lead time.

134

 

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Figure 3.38 Examination of model estimates of wind speed versus observed wind speeds at Grand Rapids,
MI (KGRR) from the 4 km domain over the period of record. There is little degradation of estimation with
departure from initialization time. Similar results were obtained at all stations and grid resolutions. RMSE
is root mean squared error (m s"), with RMSEs and RMSEu being the systematic and unsystematic
components. MAE is mean absolute error (m 3"), while r is the correlation coefficient and d2 is Willmott’s

(1982) index of agreement.

3.6 Statistical Model Identiﬁcation and Construction

One of the objectives of this research is to determine whether or not a

numerically-driven regional climate model might out-perform traditional stochastic and

probabilistic methods for wind resource estimation. To that end it is necessary to

135

construct and test established wind estimation techniques and compare their performance
to the estimates derived by the MM5 model. The majority of wind resource estimation
techniques are statistical in nature and take advantage of the common geographic
assumption that objects in close proximity are more related to one another than are distant
objects (i.e., Tobler’s First Law of Geography; Tobler, 1970). Thus, all statistical

models for wind resource estimation at a location rely upon establishing a statistical

relationship with nearby locations having long wind records.

Because of the aforementioned fundamental similarity of statistical wind resource
estimation techniques, three representative statistical estimation methods were selected
for evaluation. These include two stochastic models and one probabilistic model. Of the
two stochastic models, while both are nearest neighbor-type functions, the ﬁrst involves
point source relationships whereas the second takes advantage of regionalized geographic
behavior. The ﬁrst of the stochastic models is a Measure-Correlate-Predict function as
described in Chapter 2. The second is a Krige model similar to that described by Haslett
and Raftery (1989). Lastly, the third model is a probabilistic model based on the joint

probability of winds at two locations.

3.6.1 Measure-Correlate-Predict

One of the most straightforward stochastic approaches to wind resource

estimation is the use of nearest neighbor interpolation. As discussed in the previous

chapter, this method involves the spatial interpolation to a location from one or a set of

136

neighboring locations for which data exist. Nearest neighbor interpolation can range
from simple (unweighted, linear, low sample size) to highly complex (distance and

roughness weighted, non-linear, high sample size).

The Measure—Correlate-Predict (MCP) model is a variation on nearest neighbor
interpolation that has been used extensively in wind energy resource estimation (Derrick,
1992, Barthelmie et al., 1999). The goal of the MCP scheme is to effectively estimate the
long-term wind speed record at a location by linearly correlating a short record at that
location with a long-term series from a nearby reference location. It is assumed that the
reference anemometer record is representative of winds at both sites as a ﬁrnction of the

overlying non-local wind ﬁeld.

The MCP model is derived by ﬁrst extracting from the reference record a series of
wind speed and direction observations corresponding to the short record at the location of
interest (hereafter called the short location). These paired observations are subsequently
binned according to the wind direction at the reference location. The number of
directional bins is entirely arbitrary, though a set of 12 or 16 bins is commonly employed

(Derrick, 1992).

Once the short, paired records have been binned according to direction, a simple

linear equation of the form:

Us] =b0 +blUref (3.11)

137

is applied to the paired wind speed data for each of the directional bins. In Equation 3.11,
Umfis the wind speed at the reference location, Us; is the corresponding wind speed
observation at the short location, b, is the slope of the equation and by is the intercept.
While this method is identical to that of ﬁtting an ordinary least squares regression to the
reference speed data, the MCP makes no assumptions regarding causality and is therefore

not considered a regression from a statistical standpoint.

A synthetic long-term series at the short location is subsequently generated in two
steps. First, the entire long-term series from the reference location is binned by direction.
Second, the directionally-based linear relationships between the reference speeds and
short location speeds (deﬁned by Equation 3.11) are applied to each directional bin of the
long-term series wind speed data to estimate the long-term wind speed record at the short

location.

While it may seem that the linear relationships assumed by MCP may not be
appropriate, Derrick (1992) and others have shown that for most non-complex terrain,
such an assumption is not unreasonable. Furthermore, if it becomes clear that a linear
relationship is not appropriate for a particular bin (e. g, local inﬂuences may exhibit an
exponential inﬂuence on increasing wind speeds), the MCP is highly modiﬁable by
simply ﬁtting an appropriate non-linear function to that particular directional bin, or by

ﬁrrther categorizing the bin by wind speed.

138

As this research is designed to explore the relative success of wind resource
estimation techniques over a large region, the decision was made to apply the same MCP
technique, as described above, to all stations in the study area. While the MCP method
has a number of challenges, as discussed in the previous chapter, for the purposes of this
model and this research over this study area, the relationships between nearest neighbor
wind speeds are assumed to be linear, regardless of local surface differences.
Furthermore, the problems of representativeness due to seasonality, runs autocorrelation
and anisotropy in the short location record were overcome by randomly selecting 1500
(approximately two months) pairwise observations from each station and its nearest
neighbor. The random selection process resulted in a theoretically de-seasonalized and
stationary distribution. The random short record from each station and its nearest
neighbor was used to create estimations of the long-term record at the station of interest.
The climatology and biases of the synthetic series were then assessed relative to the
complete observational series at the station of interest and to the results of the other

models. The results are presented in the next chapter.

3.6.2 Krige model

One of the primary limitations of the simple nearest neighbor interpolation model
is that the relationship between the wind speeds at the two locations may vary quite
strongly with wind direction. That is, the relationship exhibited when the wind vector is
parallel with the station-to-station azimuth may be entirely different than when it is

perpendicular. In fact, from certain directions, it is entirely possible that the wind speeds,

139

even at stations in close proximity with one another, may exhibit no coherent relationship
at all. Thus another method must be sought; one that accounts for the winds over the

entire region surrounding the location of interest.

While the concept of a regionalized variable is not new, with a few notable
exceptions discussed in the previous chapter, it has not enjoyed wide use in wind
resource estimation with the exception of Haslett and Raftery (1989). However, near
surface wind is a spatially continuous variable that is driven by a coherent overlying
circulation structure and is normally highly correlated over short distances. As such,
wind exhibits a behavior that exists between truly random and entirely deterministic.
Therefore, the near surface wind can quite legitimately be considered a regionalized
variable and lends itself quite well to a spatially driven interpolation scheme (Davis,
1986). The researcher has chosen a universal kriging function as an appropriate wind

resource estimation model.

Kriging is a method by which the value of a regionalized variable can be
estimated at any location within a speciﬁed region based on values observed at discrete
locations within the region. While a simple linear interpolation using all observations
within the region regardless of relevance could produce estimates of a regionalized
variable, such a methodology would be highly inefﬁcient and would not easily yield
measures of statistical certainty. Because of the method by which a kriged surface is
obtained, one can be assured that measures of uncertainty are inherent to the model and

that only an optimal set of nearest neighbor stations is used in the construction of the

140

model. The optimal set of neighbors, and their corresponding bias-minimizing weights is
derived from a semivariogram. A much more detailed description of kriging can be

found in Davis (1986).

It has already been established that near-surface wind suffers varying degrees of
anisotropy. Therefore, it is necessary to employ a universal, rather than punctual kriging.
Universal kriging not only assumes driﬁ in the observations, but calculates and removes

it as well. The drift is then returned to the estimates once derived.

For this research, the universal krige model was speciﬁed as follows. The ﬁrst
step in the analysis was to obtain sernivariances for each station. Semivariance is a
measure of spatial dependence between observations separated by a distance (h). It is
computationally identical to ﬁnding the sum of squared differences between observations

at two points separated by distance h. The semivariance is given by the equation,

71. = 201—01,0212" (3.12)

where 0,- is the observation at location i, 0w. is the observation at a point h distance
away, and n is the number of points (from Davis, 1986). Using the semivariance for a
location, a distance can be established beyond which further increasing the distance has
little effect on increasing the semivariance value. Graphically this analysis is called a

semivariogram, an example of which is presented in Figure 3.39.

141

 

 

_~—_———_————

nugget r

 

 

 

Figure 3.39 An idealized example of a semivariogram. The solid horizontal line represents the variance of

the data interest, while the dashed line is the semivariance ('11,) at any given distance interval (h). The
nugget represents the minimum achievable semivariance due to localized effects.

Two portions of the semivariogram were of interest in the krige analysis. The
ﬁrst is the portion of the semivariogram known as the sill. This is the region where
increasing distance from the location of interest no longer has much of an effect on the
value of the semivariance, and theoretically has leveled off at the autocovariance (the
variance of the original data). Stations existing beyond the distance marking the
beginning of the sill are extraneous to the analysis and can be safely omitted (Davis,

1986).

As with the MC P model, in order to reduce the effects of non-stationarity and
seasonality, a set of 1500 random times were selected and extracted from each station as
a subset. This pairwise subset was used to generate the semivariances and ultimately the
krige model. Once the semivariance was calculated for each station relative to all its

neighbors. the semivariogram was analyzed to ﬁnd the approximate distance to its sill.

1A”)

This was accomplished computationally by ﬁtting a second-order polynomial to the
semivariances and establishing when the value of the semivariance ﬁrst came within 95%
of the autocovariance. This distance was then deemed to be the furthest distance from the
station that an observation from a neighbor station could be correlated. Thus, only
neighbor stations falling within the estimated relevant distance were used in subsequent
calculations. Once the sill distance for each station was established, the sill distances
were used to determine how many nearest neighbor stations should be used in the krige
model. To ensure uniformity over the region, this number was then averaged over all
stations. This analysis determined that on average 5 nearest neighbors were sufﬁcient to
account for most of the variance in the station. Thus, the ﬁve nearest neighbor stations

were used to construct the krige model.

The other region of interest in the krige analysis is the so-called nugget.
Theoretically, the semivariance at a distance of zero should equal zero. However, in real-
world instances where there exist localized inﬂuences operating beneath the resolution of
the data points, local noise may be introduced into the semivariance and, according to
Davis (1986) the semivariogram will almost instantaneously track from zero to the
nugget point over a distance shorter than the sampling interval. For wind speed, the
nugget is an important piece of information. It provides revealing evidence of the
magnitude of localized inﬂuences (e. g., terrain roughness, obstructions and obstacles to
the ﬂow). As the nugget increases, the ability of any regionalized model to accurately

estimate the wind at that location will decrease proportionally.

143

Once the representative number of nearest neighbors had been established, the
problem became one of a more straightforward weighted spatial average. The universal
krige model was applied to determine the optimal weights for each station used in the
subsequent interpolation. By optimal, it is meant that kriging produces a set of weights
for each station that will result in a minimization of the estimation error, or error

variance,

5% = (3.13)

where Yp is the estimate and Y1, is the actual observation. The determination of the
optimal weights for the 5 nearest neighbors was accomplished by solving a set of eight
simultaneous equations (3.14). The ﬁrst 5 equations are used to determine the actual
weights, while the 6th equation determines the coefficient for the constraint 01.) of weight

unity (e. g., a Lagrange multiplier), and the last two equations solve the coefﬁcients of the

drift of the surface.

”117(hll)+W2}’(h12)+W37(hl3)+W47(hl4)+W57(h15)+1+alel+a2X21 = 7(hlp)
"/170112)+W27(h22)+W3y(h23)+W47(h24)+W57(h25)+’1+a1X12 +a2)(22 = 7(th)
"/170113)+W2y(h23)+”/37(h33)+W4y(h34)+W5y(h35)+l+alX13 +a2X23 : 7(h3p)
VVIKhM)+W27(h24)+W3Y(h34)+W47(h44)+W57(h45)+l+a1X14 +a2X24 = Kill”)
MKhl$)+W27(h25)+W37(h35)+W4y(h45)+W57(h55)+l+a1X15 +a2X25 = Ah )

W1 +W2 +W3 +W, +W5 +0+O+0=1
W1X11 +W2X,2 +W,X,,+W4X,,+W5X15+0+O+0=X1p
W1X21+W2X22 +W3X23 +W4X24 +W5X25 +0+O+O=X2p

144

In the set of equations (3.14), Wig) is the semivariance for the distance between two
control points, i and j. X11 is simply the East-West coordinate for the control point, 1',
while X 2,- is the North-South coordinate. Both coordinates were given in degrees
(Longitude or Latitude respectively). The coefﬁcients, on and (12 are the coefﬁcients of

the linear drift equation,

Dp =a1X11+a2X21 (3.15)

where Dp is the linear drift at point p. To ﬁnd the drift and the weights, the simultaneous
equations were solved using matrix algebra, whereby the components of the equations

were rearranged according to the matrix equation 3.16.

it’lhri) 70112) 70113) 70114) 70115) 1 X11 eri ”W17 "rihrplI
70112) 70122) 70123) 70124) 70125) 1 X12 X22 W2 Tlth)
70713) 70123) 70133) 70134) 70135) 1 X13 X23 W3 h3p)
70114) 70124) 70134) 70144) 70145) 1 X14 X24 . W4 : h4p) (3.16)
70115) 70125) 70135) 70145) 7(h55) 1 X15 X25 W5 hSP)
l l l l l 0 0 0 It 1
X11 X12 X13 X14 X15 0 0 0 a, X11,
-er X22 X23 X24 X25 0 0- 10‘21 -XZP-

 

 

 

 

 

 

Multiplying by the inverse of the semivariance matrix thus solves the weights matrix.
Once the weights and drift for each station were determined, they were applied to the

observational series of each of the 5 nearest neighbor control points to generate a

145

 

synthetic series of wind speeds at the station of interest. Climatological differences

between the observed and estimated series are presented in the next chapter.

3.6.3 Joint probabilistic model

As has been discussed in Chapter 2, probability density functions have long been
used to describe the wind resource at a location. While wind speeds may vary a great
deal over short distances, spatial variations in the overall distributions of wind speeds are
much lower because while the magnitude of the wind speed itself may be governed by
boundary layer characteristics (e. g., roughness, zero-plane displacement, eddy
diffusivity), the relative, overall distribution of speeds are governed more by the
overlying synoptic ﬂow. Thus, if the boundary layer modiﬁcation of surface winds can
be known (i.e., surface roughness), the overlying probability distribution of the wind
resource can be adjusted to properly estimate the wind speed distribution at an
uninstrumented location. This method has been used with great success by the
developers of WASP, and the resulting Danish and European Wind Atlases (Troen and

Petersen, 1989).

In addition, as with the linear interpolation model and the MCP model, the
probabilistic model seeks to estimate the resource at one location using information
derived from its nearest neighboring station. Such modeling may, at its most simplistic
be accomplished by assuming the wind at the location of interest possesses a probability

density function identical to the wind at its nearest instrumented location. In regions

146

where the terrain is relatively homogeneous and not overly complex, and obstacles to the

near-surface ﬂow are few and far between, such a model may indeed produce plausible

However, where terrain is more heterogeneous or frequent obstacles disorganize
or impede the near-surface ﬂow, a more complex variation on the probabilistic model is
suggested. Such a model would be better served if the distribution assumed to exist at the
location of interest was one that was regionally representative. To obtain a more
regionalized distribution function, it would be necessary to construct a synthetic long-
term series derived from all neighboring stations within a given distance of the location
of interest. The distribution of this synthetic series could then be applied to the location
of interest with greater conﬁdence. With the exception of WASP, the researcher knows
of no studies that have explored regionalized probability density functions in any detail

with respect to near-surface winds.

Garcia-Rojo (2004) suggests an alternative to the aforementioned probability
models. The alternative is a joint-probability model that, like MCP, makes use of a short
wind record at the location of interest paired with a longer series at a nearby reference
station. In addition, like the MCP approach, and unlike more simplistic probability
models, Garcia-Rojo’s (2004) joint-probabilistic approach makes use of the directional
information to reﬁne in greater detail the estimates obtained from the model. In the case
of the joint probability approach, it is the probability of joint occurrence of wind speeds
at the reference site and the site of interest that is assessed, rather than the linear

correlation between speeds within the two series (Garcia-Rojo, 2004). It is this joint-

147

probabilistic model, named J PWIN D by Garcia-Rojo, that will be used in this research to

assess the performance of a probabilistic wind model relative to MM5.

The joint probability mass function, or the probability that two sets of
meteorological events, in this case wind direction and speed at each location, occur

simultaneously is deﬁned by Garcia-Rojo (2004) as:
0 S fldref r Uref ; dsite r Usite)$1 (3°17)

Where dmf and Uref refer to the direction and speed at the reference location, and d511e and

U511. are for the site of interest. The function sums over all of the probability space as:

X 2 fldref’ Uref; dsiter Usite ) = 1 (3.18)
{‘1 ref svref lid site aVsite}

Thus, the probability of measuring an event (d311,, Um) at the location of interest
independently of what is measured at the reference location can be determined from the

marginal probability mass of events (Garcia-Rojo, 2004):

P(dsite ’ vsite ) = 2 f(dref ’ Uref idsite ’ Usite) (3-19)
{dref rVref

Similarly, once the marginal probabilities have been determined from the short, paired

records for each event (d511,, U511.) at the site of interest, it is then possible to use these

148

probabilities to derive their probability of occurrence given an independent event

occurring at the reference location.

As with the other models, 2000 wind speed and direction observation times were
randomly selected for each station / nearest neighbor pair. Wind speed and direction data
corresponding to those observation times were extracted from both the station and its
nearest neighbor to create a deconvoluted “short” time series of paired observations of
approximately two months in length. These short series were used to obtain the joint
probability function for the station. The function was subsequently applied to the full
record from the nearest neighbor station to generate a synthetic full series for the station
of interest. The results of this analysis are presented in the next chapter and compared

with the results from the other models.

3.7 Model Evaluation

Model evaluation is critical to the acceptance of any model and any comparison
between models. Many of the important issues related to model evaluation are succinctly
advanced by Beck et al. (1993) and as such will be only brieﬂy outlined forthwith. The
evaluation of each of the aforementioned models is accomplished using several standard
evaluative procedures. With respect to this research, the evaluation of model

performance falls into two categories, probabilistic and deterministic.

149

3.7.1 Probabilistic evaluative statistics

Probabilistic performance measures seek to evaluate the legitimacy of the
statistical properties of the distribution of estimated data against those of corresponding
observed data. Unlike deterministic methods, probabilistic methods are stochastic in
nature in that they are not concerned with the exact replication of the variable being
modeled, but rather the replication of the distribution of the data, or the internal behavior
of the system (Beck etal., 1993). As this research is primarily concerned with the ability
of F SMMS to provide accurate estimates of the regional wind climatology, rather than the
hour-to-hour accuracy of actual forecast values, probabilistic performance measures are

given the most weight of the evaluative techniques employed herein.

There are a number of techniques available to the researcher seeking to evaluate
the probabilistic performance of a model. Among the most widely used are comparisons
of means and of variances. These two statistics represent the ﬁrst and second moments

(respectively) of the distribution of the data in question and therefore, provide perhaps the

most powerﬁrl assessment of the similarity of two distributions of data.

(7 = n‘12U1 (3.20)

32 = n’12(U1—l7)2 (3.21)

150

 

where U is the sample mean and s2 is the sample variance. In both Equation 3.20 and
3.21, Roman letters, rather than Greek, are used to symbolize that these statistics are
derived from a sample, rather than from the unknown population. Unfortunately, because
it has been squared, the variance does not have units of the original data. Thus it is more
common to report the square root of the variance, or standard deviation, as the measure of

spread of the data about the mean value.

Comparison of means is often conducted by using the Student’s T test. This
method is adequately described in a number of reference works (e.g., Davis, 1986, Wilks,
1995, Rogerson, 2001) and thus only a synopsis is presented here. Student’s T-test is a
procedure by which the distributional statistics of a sample may be compared against a
hypothetical population, or more importantly for this research, the statistics of two
samples can be compared to determine whether they are derived from the same
population. The T distribution is a statistical modiﬁcation of the Gaussian Z distribution,
and the T-test has been made more conservative than the Z-test to account for a lack of
knowledge about the parameters of the population in question. In order to examine the
null hypothesis that the means of the populations, from which both the observed and

estimated data sets were drawn, are identical. The two-sample T statistic is calculated as,

(7 —U
t=-—E——0- (3.22)

151

where U5 is the mean of the estimated sample, U0 is the mean of the observed sample,
and s, is the standard error of the mean (after Davis, 1986). Because two samples are

used, 3,. must necessarily be a function of both samples.
Se = Sp (n;1 + n_l) (3.23)

In Equation 3.23, 5,, is the pooled standard deviation as determined by,

0.5
n —lsz+n -—l 2
Sp: (E )E (O )50 (3.24)
nE+n0—2

 

When the t-statistic has been calculated from Equation 3.22, it is compared against a
critical value that has been obtained based on the number of degrees of freedom of the
test and the proportional level of rejection of the null hypothesis to determine whether the

populations from which the two samples were drawn do indeed have the same mean.

Additionally, the parameters of empirical distribution functions derived from both
the observational and the model-produced synthetic series may be evaluated for
differences by using simple comparisons and more complex statistical methods such as
the Chi-Square, Kolmogorov-Smirnov or Anderson-Darling test statistics outlined
previously (Anderson and Darling, 1954). These methods illuminate the so-called
goodness-of-ﬁt of a set of data to a distribution function deﬁned by the data from which

the candidate series is suspected to have come. In doing so, they also provide valuable

152

 

 

information about the similarity of variance between the two sample distributions. In the
case of this research, it is assumed that the observational data were drawn from a
population comprising all possible wind speeds and directions at a given location. Thus,
theoretically, the statistics of these sample observations represent the overall statistical
parameters of the population from which the data were sampled. Furthermore, it is
hypothesized the estimated data have been drawn from the same population. If this is
indeed the case, then the aforementioned goodness-of-ﬁt methods will reﬂect that both
the observed and estimated data are not derived from different populations, and therefore,
the estimated data can be deemed a surrogate for the observed. Additionally, the degree
of ﬁt, in the form of the magnitude of the test statistic can be used as a simple way to

determine which of the models provides the best general ﬁt to the data.

Graphical methods and the Anderson-Darling goodness—of-ﬁt tests were described
in great detail earlier in the chapter and so are not discussed here. However, the
Kolmogorov-Smirnov and Chi-squared tests were only cursorily mentioned and so
deserve elaboration. While these latter methods are statistically less powerful than the
Anderson-Darling test, they nevertheless contribute a meaningful support for the

conﬁrmation or denial of ﬁt of a particular sample of data to an expected distribution.

The Chi-squared test is the least powerful of the goodness-of—ﬁt statistical tests. It

simply divides a sample into discrete probability bins, and compares the observed

frequencies of occurrence to those that would be expected if the sample data were drawn

153

 

from a given distribution. The null hypothesis is that the sample data does indeed come

from the population distribution. The test statistic (X2) is calculated as,

X2 = iloj "Ejiz

(3.25)

Where Q,- is the observed frequency and E,- is the expected frequency for the value range
bin j out of 2 possible bins (from Davis, 1986). The calculated X2 statistic is compared
against a critical value, again based on the degrees of freedom of the test and a pre-

determined critical probability level for the rejection of the null hypothesis.

The Kolmogorov-Smimov, or K-S test is an alternative, non-parametric
goodness-of-ﬁt method to the Chi-square test. The K-S test statistic is exceedingly
straightforward. It is simply the maximum difference between the cumulative probability
levels of the observed frequency distribution and the expected frequency distribution.
The difference is the test statistic and is compared against a critical level in the same
manner as other hypothesis tests. The null hypothesis is that the discrete distribution of
the data is equal to the distribution to which it is being compared. Normally, the K-S test,
like the Chi—squared test or other goodness-of-ﬁt methods is used to evaluate the
hypothesis that a particular sample distribution is derived from a theoretical parent
distribution function where the parameters are either known (parametric) or not (non-
parametric). That is, these tests evaluate whether or not a sample “ﬁts” a particular

distribution, as was accomplished in the prior chapter. However, in the comparison of

154

models, the observed data is, in effect, the population whose distribution forms the basis

for the goodness-of-ﬁt.

To adequately address the probabilistic evaluation of FSMM5 and compare it to
the other models, this research has calculated, reported and interpreted the mean, standard
deviation, and empirical distribution statistics for each of the model estimated data sets as
well as for the observed data (as described in the previous chapter). The veracity of both
the estimative probabilistic statistics and the empirical distribution parameters was
determined through the use of a bootstrap resarnpling procedure as outlined by Efron and
Gong (1983). In this case, 10,000 bootstrapped series of 1000 estimated values each
were sampled with replacement from the entire model-estimated series. From these

samples, conﬁdence limits were generated for estimated data statistics.

3.7.2 Deterministic evaluative statistics

Deterministic evaluation methods seek to evaluate the performance of the model
in terms of its ability to replicate reality (i.e., the observed data). Such measures are more
appropriately termed model validation methods as they seek to determine the validity of
the model estimates themselves by examining the properties of the residual differences
between the estimated and observed data (Beck et al., 1993). Methods for the validation
of models are normally used to determine how well a model has been able to replicate the
variables it is estimating, and a model is generally not considered validated unless all

systematic behavior in the residuals had been eliminated and/or accounted for within the

155

model proper (i.e., residuals are independent and normally distributed with a mean of
zero). While the goal of this research is not to assess the forecasting abilities of MM5 or
any of the other models evaluated, a thorough analysis of the residual bias of all models
was conducted. The rationale for performing a deterministic evaluation is that a model’s
ability to accurately approximate actual values and minimize the systematic bias in its
residual values are measures of how comprehensively the model has been speciﬁed, and
how reliable is its output for generating an overall climatology. While it cannot
necessarily be assumed that a model that performs well is correctly speciﬁed (small, non-
systematic residuals could be obtained by random chance), an appropriate model
construction is most likely. Such behavior is preferential to a model that performs poorly
(large, or systematic residuals) and likely has been, in some way, incorrectly speciﬁed.
As a variable’s climatology is a function of the individual observations (or estimates of
those observations), a model that produces small, randomly-distributed residuals can be

expected to also produce a plausible climatology of the variable being investigated.

Each model’s residuals were used to determine the validity of the speciﬁc model,
and are further compared with the residuals behavior of the other models. The measures
that are used in this analysis include MAE, RMSE, Pearson’s r, and the index of
agreement ((1). These measures are detailed in Willmott and Wicks (1980), Willmott

(1982), Willmott et al., (1985), and Wilks (1995) but also are outlined below.

By far the most widely used measure of the performance of a model is Pearson’s

product moment correlation coefﬁcient (r).

156

2021’
0P— ————-—

11—1——11

 

where 0 and P are two series of data of length n. Pearson’s r is thus a measure of the
degree of covariance of the two variables, or how linearly related their behavior appears
to be. From equation 3.26 it is clear that if the series 0 and P vary identically, r will
equal 1.0, or -1 .0 if they vary perfectly inversely. If there is no similarity between the
variances of the two series, the correlation coefﬁcient will equal zero. Theoretically, if a
model is perfectly speciﬁed (i. e., observations are perfectly reproduced), the model-
estimated series would be identical to the observational series, and the correlation would
equal 1.0. Practically, however, all models contain some estimation error, supposedly
reducing the value of r. Unfortunately, because Equation 3.26 does not take into account
the magnitude of the differences between the observed and estimated values, it ultimately
fails to capture much of the model’s true ability to reproduce reality, nor does it provide
any measure of how much of the model’s error is systematic, and is thus correctable.
Figure 3.40 highlights some of the drawbacks of relying solely on Pearson’s correlation
coefﬁcient for model evaluation. An alternative, the index of agreement, is presented
further on. Despite the limitations of Pearson’s r, it remains a widely recognized measure

of the correspondence between to variables, and as such will be reported in this research.

157

sh

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 f 10 ' L 10’? at— r
(a) (b) i (C) *
8' 4 8- *6 . 8*
air air-
6 6 “It 6 91E
*- *-
4 4 are 4 are
it it
2 2- er 2 are
[=10 ak- f=0.94 r=-1.0
0 0 g 0 4
0 5 10 0 5 10 0 5 10
10 ﬁ— 10 %’ﬁ 10 *6 is
8’ (d) 1 8’ (9) . 8‘ (f) ‘llé *- .
5* alt
6 ‘31? iii- 6 6 91"
9F 3i? 3* alt- as
41 9* 91% i 4 4
9K- 3K
21 2- 2 .
r=0.1 r:0,02 e r=-0.2
0 5 10 0 5 10 0 5 10

Figure 3.40 Idealized relationships between two variables and their corresponding Pearson’s correlation
coefﬁcients. Of the top row, each of which exhibits a perfect or near-perfect correlation between the two
variables, only the ﬁrst (a) would represent a truly error-free model, whereas (b) and (c) exhibit systematic
error not taken into account. On the bottom row are three idealized examples of variables that show little
or no correlation. However, like (b) and (c), (d) is a function of systematic bias. Figure (e) shows the
inﬂuence of two extreme outliers. Only (0 represents a randomly generated data set where no correlation

is expected.

Because of the limited ability of Pearson’s r to adequately assess the performance
of a particular model, it is more telling perhaps to assess the magnitude and behavior of

the actual differences, or residuals, between observed values and those estimated by the

model.

158

 

 

0i = H +811 (3'27)

In Equation 3.27, the observation 0 of a variable at a point i in either space or time (or
both) can be replicated precisely from the model estimate P of that variable for the same
point and a resultant error e, also known as model bias, or the residual of the model.
From this point forward, the model estimated variable is deﬁned as P (for predicted; even
though it is not truly a prediction), because the use of E might needlessly confuse the
estimated variable with the error term e. Because it must be assumed that no error exists
in the observed variable (otherwise it would have been corrected prior to analysis), it
follows that the error e is solely a product of the model (Willmott et al., 1985). It is the
series of model-introduced bias terms that is ultimately evaluated in an effort to discover

the utility of the model.

Because the model bias exists for each observation/estimate pair, the residuals
themselves form a series of values that can be evaluated statistically. Of the statistics that
summarize the behavior of the residuals, the means of the residual series are most
commonly used in the Geo and Atmospheric sciences (Fox, 1981; Willmott, 1982). In
particular, the mean absolute error (MAE) and to a lesser extent the mean squared error
(MSE) and root of the mean squared error (RMSE) are widely used to evaluate the

performance of a model against a set of observations.

MAE = n‘lzm - 01| (3.28)

159

MSE = n‘lz (P,- — 0,. )2 (3.29)

RMSE = M5505 (3.30)

Such measures as MAE, MSE and RMSE provide a clear assessment of the overall
performance of a model in that they provide a ﬁrst moment statistic for the differences
between the observed and estimated variables. Of the three measures, MAE and RMSE
are most used because they report the error in units of the variable. Furthermore, these
measures are more greatly mathematically tractable than is the simple mean error. In
fact, the reporting of the mean of the observed values and the mean of the estimated
values is generally preferred to the simple mean error because the former are more easily
understood, and they provide greater versatility in computing additional statistical

measures than does the mean error (Willmott, 1982).

What is more, the MSE (and therefore also the RMSE) has certain properties that
allow it to be mathematically parsed into measures of the degree of systematic
(correctable) and unsystematic (random) error contained within the overall residual
values. The systematic (MSE,) and unsystematic (MSEu) components of the bias of a

model are given as,

MSE, = 124203,- —0,-)2 (3.31)

160

MSE“ = 124203. — 16,-)2 (3.32)

In Equations 3.31 and 3.32, P represents an estimated series derived from the least-

squares regression of the model-predicted variable on the observed variable. The RMSE
versions simply take the square root of equations 3.31 and 3.32, and are preferred as they
retain the units of the original variable. However, in their MSE form, Equations 3.31 and

3.32 are conservative.

MSE = MSES + MSE“ (3.33)

The relationship expressed in Equation 3.33 means that the relative proportions of
systematic and unsystematic bias may also be calculated by dividing MSE, or MSE, by
the MSE. Measures of systematic and unsystematic bias are quite important as measures
of the veracity of the model. As a model’s performance is improved, the systematic
component of its bias must tend toward zero, while the unsystematic, or random
component (RMSEu) is minimized toward the value of the overall RMSE (Willmott,

1982)

In addition to the mean values of the residuals, Willmott (1981) recommends the
calculation, reporting, and interpretation of a set of “summary measures” that will aid in

standardizing the comparison of performance between models. These measures include

the mean of the observed variable (0), the mean of the predicted (P ), the standard

161

deviations of both series (so and Sp), and the s10pe and intercept parameters (m and b)
from an ordinary-least squares ﬁt of the observed to the predicted variable (Willmott,
1981). The researcher is in agreement with Willmott (1982), who feels that such
measures are readily recognized and understood by the scientiﬁc community, and that
these measures form the basis for many higher-level statistical measures such as skill
scores. As such, these measures are reported along with MAE and RMSE in the next

chapter for each model.

Given the aforementioned limitations surrounding the meaning and interpretation
of Pearson’s product moment correlation coefﬁcient (r), a more statistically meaningful
and descriptive expression is desirable. One such alternative is the so-called Index of

Agreement proposed by Willmott and Wicks (1980).

203' “002

d=1— ,Osdsl (3.34)

Zia-1+ 0: )2

 

 

 

From Equation 3.34, the Index of Agreement (d) is a function of the MSE and of two
difference series P’ and 0’, where P,'= P, — 5 and 01' = 0,. - 5 . Unlike Pearson’s r,
Willmott and Wicks’ Index of Agreement (d) is not a measure of association. It does not
attempt to explain the degree to which the observed and estimated variables co-vary.
Instead, d is “a measure of the degree to which a model’s predictions are error free”

(Willmott and Wicks, 1980). As it is bounded between 0 and 1, a perfect, error free

model would obtain a value of 1, whereas a purely random model would be expected to

162

have d = 0. Furthermore, because it is bounded, d can be used as a relative measure,
comparing the performance of one model against another. As such, it is a powerful
assessment tool and is reported in the suite of evaluative statistics for each model.
Because this research reports the index of agreement based on the RMSE rather than

MSE, it is noted as d; rather than d to avoid confusion.

Thus, in the next chapter, the results from each model are reported as a suite of
statistical measures as outlined in this section. The use of a standard set of statistics not
only permits a thorough evaluation of the performance of an individual model, but
additionally sets a standard measure that permits the performance of one model to be

compared against the performance of other, perhaps disparate models.

3.7.3 Spatial analysis of model evaluation

Evaluation of model performance in this study was complicated by the spatial
character of the analysis, with comparative statistics derived at over 100 individual
stations sites. In fact, the primary goal of this analysis is to illuminate the relative ability
of FSMM5 to estimate wind climatology across the region. One of the primary beneﬁts
of utilizing a numerically-based regional climate model is its perceived ability to generate
representative values of meteorological variables in locations where few data
observations exist, such as in complex terrain or in coastal zones. As such, it is highly

desirable to identify not only differences between observed and estimated wind values at

163

individual stations, but also evaluate these differences with respect to their position

within the study region.

3.7.3.1 Trend surface analysis

Geographic analysis provides several methods by which the spatial behavior of
the model residuals may be assessed. Two of these methods were employed in this study,
trend surface analysis and isopach analysis. Trend surface analysis is widely used in the
Earth sciences as a means of apportioning the spatial behavior of a variable into a
regional component of variability and a local component at any given location in space.
In this respect it is similar to the division of the bias of a temporal series into its
conservative systematic and unsystematic components. In trend surface analysis, a
surface is empirically ﬁt to the data occurring over a region. Numerical description of
the ﬁtted surface can range from a simple ﬁrst-degree linear plane to an n-degree non-
linear surface, with the choice of equation complexity dictated by deference to
parsimony, the spatial scale of the data, and its spatial behavior. Due to their simplicity
of calculation, low degree (e. g., 2nd or 3rd order) polynomials are commonly chosen for
this type of analysis. These levels of complexity offer a balanced alternative to purely
stationary planar surfaces and hi gher-order non-linear equations, neither of which easily

lend themselves to meaningful interpolation.

Davis (1986) offers an excellent description of the construction and interpretation

of trend surfaces for geographical analysis applications and a discussion on the selection

164

of parsimonious trend surface equations. As near surface winds are spatially continuous
and partially governed by a relatively coherent overlying geostrophic ﬂow, a second-
order polynomial trend surface was deemed to be most appropriate for the analyses used
in this study, and was subsequently applied to both observed and model estimates. The

equation took the form,

O=b0+b1X+b2Y+b3X2 +b4Y2+b5XY (3.35)

where the regional estimate of the observation 0 is a ﬁrnction of the geographic
coordinates, X and Y (Longitude and Latitude respectively), their squares and their cross

product (Davis, 1986).

Surfaces calculated with this equation provide an estimation of the regional
component of the spatially distributed variable. The difference between the value of the
surface at a location and the measured (or estimated) value of the variable at that same
point can therefore be interpreted as a measure of the proportion of the variable’s value
that is not explained by a regional behavior. Instead, this spatial residual value is
assumed to reﬂect the degree of localized inﬂuences that have shifted the value away

from the regionally inﬂuenced surface (Chorley and Haggett, I965).
The analysis of trend surfaces for both the observed and model estimated values
lends insight to the degree the model reproduces the regional wind ﬁeld, in that it can act

as a low pass ﬁlter. That is, when only the trend surfaces are compared, the high

165

frequency, or localized behavior has been removed, leaving an estimate of the regional
wind ﬁeld relative to the observed regional wind ﬁeld, which has been calculated in the
same manner. Furthermore, if the differences between the two trend surfaces (i.e.
observed and model estimated) are mapped, a spatial behavior of the accuracy of the
model can be obtained. On the other hand, the localized wind, as represented by the
difference of the trend surface and the actual data or estimates (acting as a high pass
ﬁlter), can be assessed spatially and used to evaluate a model’s ability to account for local

inﬂuences in generating estimates.

3.7.3.2 Isopach analysis

The second geographical method for the spatial analysis of data that has been
employed in this research is known as isopach analysis (Davis, 1986). An isopach is
simply a contour map of differences of a variable over space. The variable being mapped
can be anything, and as such, isopach analysis is ideally suited for the evaluation of
spatially-based model output. As was discussed in the previous paragraph, maps of the
differences in trend surfaces are actually a form of isopach analysis. Many of the model
evaluative statistics that were produced for the observed data and each series of model
estimates were subsequently subjected to isopach analysis to highlight the magnitudes
and spatial distribution of observed-estimated differences across the study region. In
particular, isopach maps often are able to graphically illustrate geographic patterns in
spatial bias. A variety of isopach maps therefore are presented in the next chapter and

used to assist in identifying the spatial variability of overall model performance.

166

Chapter 4. Results

The ability of a numerical climate model (F SMMS) to accurately estimate the
wind resource of the Great Lakes region was the primary goal of this study. To that end,
potential near surface winds over the study area were estimated by the FSMM5 model
and evaluated for accuracy. Due to the complexity of numerical models relative to
established statistical techniques, it was necessary to compare the relative performance of
each type of model. This was accomplished by constructing and applying three statistical
models (two stochastic and one probabilistic) to estimate the wind resource at the same
geographical locations as FSMM5-derived output estimates. A comparison of relative
model accuracy is subsequently presented. The ﬁnal objective of this study was to
evaluate the bias of the FSMM5 model estimates and determine the degree of systematic
error that could potentially be removed from the model estimates in order to increase

accuracy.

4.] FSMM5 Model Performance

The statistics used to evaluate model performance were chosen to quantify
differences and similarities between model-estimated and observed wind ﬁelds. The
mean and standard deviation of both observational data and model estimates (hereafter
noted as 0, so, e and Se respectively) describe the basic similarity of both distributions.
The Pearson product moment correlation coefﬁcient (r) describes the degree of

covariation between the observed and estimated data. The mean absolute error (MAE)

167

and root mean squared error (RMSE) are measures of the magnitude of the overall bias
contained in the estimates, and RMSEs and RMSEu are the systematic and unsystematic
components of the root mean squared error. Tire percentage of the total bias that was
systematic (hereafter SB%) was included to help lend clarity to the interpretation of the
results. Lastly, Willmott’s Index of Agreement (d2, based on RMSE) is presented as a
measure of the non-biased proportion of the estimate. While often useful where the
systematic bias of the model estimation error results in a consistency of under or over
estimation, the mean error (ME) was unfortunately of limited use in this analysis because
the variability of the unsystematic bias resulted in both under and over estimates,

generating mean series errors near zero over much of the study area.

Additionally, two sets of evaluative statistics are presented. The ﬁrst isan
evaluation of model-derived estimates at individual time steps, hereafter referred to as
forecast accuracy. The second is the evaluation of the estimates of the distributional
parameters of the wind resource, referred to as resource accuracy. While the evaluation
of forecast accuracy is important, it is not as critical to wind resource estimation as is the
resource accuracy. A model can, for example, exhibit low forecasting skill in that it
never precisely estimates the observed wind speed at a given time or place, but that same
model may be of exceedingly high skill in estimating a distribution of wind speeds that
closely approximate the observed distribution at a given location. In this study, relatively
greater emphasis was therefore placed on evaluating resource accuracy to determining the

level of model skill.

168

Overall, the performance of F SMMS in describing wind ﬁelds over the Great
Lakes was variable, and in many cases, poor. Evaluative statistics of forecast accuracy
from all implementations of the model are given in Table 4.1. Evaluative statistics of the
resource accuracy of the same model implementations are given in Table 4.2. As was
discussed in the previous chapter, wind estimates obtained from FSMM5 were
disseminated into 15 model variations. Wind estimates from each of the three domain
resolution (36-km, 12-km, and 4-km) runs were interpolated from the domain grids to the

station sites using unweighted l, 4, l6, and 36 km nearest neighbor schemes and a 4 point

inverse distance weighted procedure.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FSMMS Performance evaluation (forecast accuracy)

Xmi. i sit xmax
o (m s") 2. 05 3. 76 0. 70 7. 05
e(m s?) 3.05 5.26 1.51 8.12
s, (m s") 1.63 2.41 0.30 3.88
s. (m s") 1.52 2.49 0.69 4. 09
r 0.00 (.011) 0.17 0.20 0.72
MAE (m s") 1.57 2.99 0.96 5.19
RMSE g?) 2.01 3. 72 1.12 6.24
RMSEs (m s“) 1.10 2.84 0. 98 5.07
RMSEu (m s") 1.46 2.38 0.64 3. 79
53% (%) 20.95 57.84 8.91 71.38
4, 0.27 0.44 0.1 1 0. 79

 

Table 4.1 Evaluative statistics of FSMM5 model performance obtained from wind estimates of 15
variations (X1) of the model over the period of record . The 011 value for minimum r is the lowest
negative correlation obtained (0 .00 was the lowest absolute correlation obtained).

169

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F SMMS Performance evaluation (resource accuracy)
32in f 5x XML

0 (m s") 2. 05 3. 76 0.70 7.05

e (m g) 3.05 5.26 1.51 8.12
Mm s5 1.63 2.41 0.30 3.88
s, (m s} 1.52 2.49 0.69 4.09
k, 1.21 1.94 0.38 4.81

k, 1.07 1.98 0.38 2. 70

c, 2. 70 4.53 0.89 7.52

c, 2. 61 5.55 1.61 9.08

r 0.01 0.78 0.21 0.97
MAE (n) 54.44 (0.48) 228.46 (2.02) 118.19 Q 06) 535.85 (5.2 7)
RMSE (g) 96.80 (0.81 401.60 (3.55) 159.81 @4) 843. 71 (7. £1)
RMSEggn) 0.13 (0.00) 183.57 M4) 175. 75 (1.57) 661.10 Q80)
RMSEu (11) 87.55 (0.73) 335.19 (2.96) 99. 4,610. 89) 588.24 (6. 41)
SB% (°/_..) 0.00 21.32 22.15 79.30
11, 0.34 0.86 0.14 0. 98

 

Table 4.2 Evaluative statistics of FSMM5 model performance obtained from wind estimates of 15
variations (X,) of the model over the period of record. The mean error statistics are given in bin counts and

the numbers in parentheses in the mean error rows are the percentage of total n. k and c are Weibull shape
and scale parameters respectively.

It is clear from Table 4.1 and from Figure 4.1 that FSMM5 is of somewhat limited

utility as a model for forecasting hourly wind resources for wind energy production at a
given location, Minimum bias is on the order of just over 1 m 8". While this level of
accuracy may be acceptable for other applications, given the sensitivity of turbine power
output to wind speed (see Figure 1.1), even a l m s'1 deviation from actual values could
mean an exponentially larger error in power output, which would in turn become even
larger when multiplied by a number of turbines in a wind farm reliant upon that wind
speed. Unfortunately, errors in the 1 m 5'1 range are limited to just the best of the model

variants, and even then only at certain locations within the study area. On average over

170

the study area and across all FSMMS variants, MAE and RMSE were on the order of 3 to

4 m s", which is unacceptable accuracy within the realm of wind power forecasting.

Obs vs. MM5 at KFZY : 1w ma

 

 

10 W— 1 ﬂ T— _l T ﬂ r—
A
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I
40
§ 5— -
vi
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o

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0 l J 1
2002.8 2003 2003.2 2003.4 2003.6 2003.8 2004 2004.2 2004.4 2004.6

 

 

 

 

10 l l ﬁ T l l T l
/
g 5 L _
E
o.
o L l I 1 L 4 A ;
2002.8 2003 2003.2 2003.4 2003.6 2003.8 2004 2004.2 2004.4 2004.6

 

l I l l l I l l :1

ON
j

—u

0‘

 

I
«h

 

O—P Anomaly (m s")
r'o
I

I l l l l l 1 l 1
2002.8 2003 2003.2 2003.4 2003.6 2003.8 2004 2004.2 2004.4 2004.6
Year

 

Figure 4.1 One week moving averages of the ASOS observed (top) and FSMM5 forecast (middle) wind
speeds at Fulton, NY (KFZY) for the period of record. The bottom ﬁgure is a l-week moving average
applied to the hourly differences (O—P) between observed and predicted wind speeds. The moving average
was used to more clearly illustrate the degree of variability that exists. All stations exhibit similar

variability.

Furthermore, an assessment of correlation indicates a very low degree of
covariance between model-estimated and observed wind speed values over the study

area. The best correlation obtained was 0.72, with a mean correlation of just 0.2 and

171

several occurrences of nearly perfect non-correlation (0.00). These low correlations and
relatively large errors (with respect to the mean speeds) are corroborated by the low index
of agreement (d2) scores. A mean 412 of 0.44 indicates that, on average only about 44% of

the model estimate is error free.

Fortunately, it appears that a great deal of the bias residing in the FSMM5
estimates is systematic in nature. Based on the calculation of the systematic component
of the RMSE, anywhere from 21% to 72% of the bias in the model estimates can
potentially be accounted for within the model. However, that is beyond the scope of this

research.

Rather, the focus of this study is in the ability of the model to accurately estimate
the overall (not time dependent) distribution of the wind resource over the study region.
In this respect, F SMMS performs notably better (see Table 4.2). To perform this
assessment, observed and estimated wind speed values were sorted into 1 m s‘1 histogram
bins. The bin counts of the observed and estimated wind speed distributions were then
assessed for differences. While mean absolute and root mean squared errors still appear
to be rather large (they are presented in terms of bin frequencies), they actually represent
a very small proportion of the number of observations from which the histograms were
obtained (on average 11,396 values). Thus, in fact the MAE and RMSE are relatively low

(on average just 2 and 3.5% of total sample size respectively).

172

Additionally, the mean correlation (r) jumps from 0.17 for the forecast estimation
to 0.78 for the resource estimation (with similar standard deviation). Despite this
improvement, very low resource estimate correlations were observed at some stations and
model variants, ,while exceptional correlations were observed at others. The overall
good agreement is further reinforced by the noticeably increased index of agreement,

with a mean of 0.86 (or 86°/o error-free estimate).

While the means of the observed and model estimated distributions do not appear
to readily agree, there is still remarkable similarity of the shape (k) and scale (c)
parameters of the Weibull density functions that had been empirically ﬁt to the observed
and estimated data. Furthermore, it appears that while some stations or model variants
exhibit a great degree of systematic bias (a maximum of 79% was encountered), the mean
systematic bias was just 21%, indicating that most of the variability between the observed

and model estimated wind speed distributions was not associated with the model.

While an evaluation of the overall performance of FSMM5 reveals a substantial
amount of systematic bias and a relatively large variability in the error, it does not
address the causes of that bias. To more appropriately evaluate the performance of the
FSMM5 variants, a more detailed analysis of model performance is warranted. First, the
relative performance of the three model domain resolutions (i. e., 4 km, 12 km and 36 km)
is compared, followed by the inﬂuence of spatial aggregation on model performance.
This evaluation will largely determine which of the model variants exhibits the lowest

resource estimation error.

173

4.1.1 Performance based on grid resolution

For each FSMM5 domain, 5 variants were considered (based on aggregation
resolution as discussed in Chapter 3). The statistics presented in this subsection for each
domain were derived from a grouped analysis of those 5 variants. Table 4.3 describes the
relative performance of the model variants within each grid domain. The evaluation
statistics are based upon the observed versus estimated resource distributions and not on

the individual time-step model estimates (i.e., forecasting evaluation).

From Table 4.3 several patterns are evident. In particular, mean differences
between the observed and estimated mean wind speeds tend to decrease with decreasing
spatial resolution. Furthermore, the mean standard deviation of estimated speeds also
decreased appreciably. Despite the general agreement between ﬁrst and second moments
of the distributions, given the large 11, they were all found to be signiﬁcantly different (t2,
0,99 - note: statistical tests are identiﬁed with the number of tails and signiﬁcance level as
a subscript). However, the mean of the 36 km domain distribution is signiﬁcantly lower
than that of the 12 km domain “19.90) This improvement in estimative accuracy is borne
out in the parameters of the theoretical Weibull pdf. While the parameters of all domains
appear to be in good agreement, it is only with the 36 km domain that neither mean
estimated shape nor mean estimated scale are signiﬁcantly different from those ﬁt with

the observed data 02,099).

174

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FSMM5 Evaluation Statistics by Domain
4 km 12 km 36 km
1? s, 2? s, 7c s,
o (m s? 3. 76 0. 70 3. 77 0. 70 3. 76 0. 70
e (in?) 5.80 0.95 5. 93 1.88 4. 04 0.37
s,(m s") 2.41 0.30 2.41 0.30 2.40 0.30
s, (m s5 2. 76 0.54 2. 77 0.80 1.94 0.28
k, 1.94 0.38 1.94 0.38 1.94 0.38
k, 1.90 0.29 1.93 0.31 2.12 0.47
c, 4. 53 0. 89 4.54 0.89 4.53 0. 89
c, 6.03 1.04 6.20 2.09 4.41 0.59
r 0. 76 0.17 0. 69 0.27 0.89 0.07
MAE (n) 252.02 102.96 262.92 152.90 170.44 53.49
2.23 % 0.91 % 2.34 % 1.36 % 1.50 % 0.49 %
RMSE M 419.33 147.31 436.77 193.76 348.71 114.48
3. 71 % 1.32 % 3.89 % 1.74 % 3.06 % 1.04 %
228.79 155.94 239.34 220.97 82.58 65.17
RMSE‘ (‘9 2.03 % 1.40 % 2.15 % 1.97 % 0.73 % 0.62 %
RMSE” (n) 336.65 86.92 334.92 100.36 334.01 109.90
2.97% 0.76% 2.98% 0.90% 2.93 % 0.98%
SB% (%) 29.22 19. 91 27.18 27.02 7. 74 8.59
d; 0.85 0.12 0.80 0.19 0. 93 0. 04

 

Table 4.3 Evaluative statistics of F SMMS model performance obtained from the 5 variants (X,) of the
model within each of the 3 model domains over the period of record. The mean error statistics are given in
bin counts and are followed by the percentage of total 11. k and c are Weibull shape and scale parameters

respectively.

The measures of agreement also demonstrate improvement of skill with

decreasing domain resolution. The 36 km domain again was associated with the lowest

overall bias, which is signiﬁcantly lower than both the 12 and 4 km domain (twigs).

However, interestingly the 12 km domain exhibits higher model bias than the 4 km

domain. Additionally, while there is no statistically signiﬁcant difference in

unsystematic bias between model domains, there is a signiﬁcant improvement in

systematic bias with the 36 km domain over both other domains (tings). Furthermore, the

175

 

systematic error becomes a much smaller proportion of the overall error as coarser
domains are selected, as evidenced by the drop in systematic bias percentage (SB%) from
around 30% at 4 km to just 8% at 36 km. Thus, not only do modeled resource estimates
appear to improve signiﬁcantly at coarser resolutions, but their systematic component

also decreases, indicating that perhaps there is spatial bias inherent in the domain itself.

The behavior of the model over the three domain resolutions can be better
illustrated by graphical methods. Two graphical analyses in particular demonstrate the
behavior of the F SMMS model bias. The ﬁrst, Figure 4.2, is a representative plot of the
goodness of ﬁt between the observed data and the Weibull pdf obtained from the FSMM5
estimates that were interpolated ﬁ'om each domain to the locations of the ASOS stations
using the nearest 4 grid points and an inverse distance weighting technique (the same

technique is applied to all comparisons in this subsection).

From this ﬁgure (especially from the cdf) it is clear that the 36 km domain did the
best job estimating the wind speed distribution. The primary reason for the
overestimation of speeds near the mean is because FSMM5 had not estimated enough
high wind speeds to shift the scale parameter to the right and “stretch” the distribution.
Although Figure 4.2 represents just one station, similar behavior exists at most stations in
the study area. Alternatively, model bias may be viewed with respect to the distribution

of wind speeds by graphically assessing the variability of bin frequencies (Figure 4.3).

176

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a)
0 5 10 15 20
0
0.2 ﬂ 1 :
+++ l g
E0 15- +++ g
'3 + <
«I 01 L (b) 0.5 + 0
e .3“ 3.!
50.05 ++ gr
0 -— 0 2 g
o 5 1o 15 20 o 5 1o 15 20 ,5
0.2 2 ﬂ 4 1 ?
0.15l i
0.1 . l (C) 0.5
0.05
0 ,,,,, a 0 n . . +
0 5 10 15 20 0 5 10 15 20
Wind speed (m s")

Figure 4.2 Comparison of the FSMM5 estimated Weibull pdf (left, line) and cdf (right, line) at Holland,
MI (KBIV) and the observed wind speed distribution (left, bars; right, crosses) for each of the three
domains, (a) 4 km, (b) 12 km and (c) 36 km using the 4 weighted nearest neighbors, over the period of

record.

 

 

 

 

 

 

 

 

 

 

 

   

E . - .
V 500 500 t
g. (c)
C
3
8. 0 0
u':
3 -500 -500
Q
"2’
E 4000 -1000 ‘ ‘ ‘
0 10 20 20
Wind speed (m s")

Figure 4.3 Wind speed distribution frequency differences (FSMM5 - ASOS) at Holland, MI (KBIV) for
the (a) 4 km, (b) 12 km and (c) 36 km domain using 4 weighted nearest neighbors, over the period of
record.

177

Figure 4.3 illustrates several issues regarding the estimation of wind speed
distributions by F SMMS. First and foremost, the model greatly under represents the
frequency of calm periods (i.e., < 1 m s"), This under-representation is systematically
present over all domains and decreases only slightly over the 36 km domain. The second
issue appears to be a systematic under and over estimation of wind at certain speeds. At
the coarsest resolution, low wind speeds appear to be over-estimated while higher speeds
are under-reported. Over the 4 and 12 km domains, this relationship appears to be
reversed, where the frequency of low wind speeds is systematically under-estimated
while the frequency of stronger winds is over-estimated. As with the overall distributions

highlighted in Figure 4.2, this systematic behavior is present throughout the study region.

The systematic bias observed in Figure 4.3 is also present when wind directions
are examined. Figure 4.4 presents the observed and estimated wind roses at Holland, MI,
while Figure 4.5 shows the differences in directional frequency observed at that same
station. As with previous ﬁgures, statistics from the Holland, MI (KBIV) location are
displayed because the behavior of model estimated winds relative to ASOS observed
winds are representative of the results across the study area. As displayed in Figure 4.4,
there is a fair amount of dissimilarity between observed and model estimated wind
direction distributions. Once again, much of this dissimilarity appears to be systematic
(Figure 4.5). In general, winds from the northeast appear to be consistently over-
estimated whereas the frequency of winds out of the southwest (the prevailing direction)

is most often under-estimated.

178

 

Obs. at KBIV MM5 at KBIV

Figure 4.4 Wind roses at Holland, MI (KBIV) from the 12 km FSMM5 domain showing the observed wind
direction distribution (left) and the FSMM5 estimated direction distribution (right) from 11/02 - 6/04.

 

 

 

 

 

   

 

MM5-Obs frequency (n)

 

 

   

0 90180270360 0 90180270 360

Wind direction (deg)

Figure 4.5 Frequency differences between F SMMS and ASOS observed wind directions at Holland, MI
(KBIV) for the (a) 4 km, (b) 12 km and (c) 36 km domains for the period of record.

Given the apparent systematic bias inherent in the wind regimes estimated by
FSMM5 over the study region, an examination of the spatial variability of the resource
estimates is in order. For example, the spatial variability of the model estimates of mean
wind speed over the three domains is demonstrated in Figure 4.6. It is clear from Figure

4.6 that substantial differences exist in the model’s calculation of wind speeds at the

different domain resolutions.

179

 

 

 

 

 

Figure 4.6 FSMM5-estimated mean wind speeds (in m s") over the study region over the three model
domains using an inverse distance weighting technique on the nearest 4 grid points to a station from 1 1/02
to 6/04. The negative mean speeds in (b) are a function of the spatial interpolation scheme extrapolating
beyond the observation network and should be ignored.

180

(c) 36 km

 

 

 

Figure 4.6 Continued.

As expected, the 4 km domain estimates appear to produce the most spatial
variation in mean wind speeds over the region. Much of this variability is likely due to
the boundary layer conditions of the model operating on such a ﬁne resolution.
Coherence of mean speeds increases at the 12 km domain, however there appears to be a
systematic over estimation of mean speeds over the Lake Huron and Lake Erie regions.
The 36 km domain (Figure 4.6c) exhibits the most coherent behavior as well as the most

agreement with the observations (Figure 4.7c).

181

(a)4km

 

 

 

 

(b) 12km

 

 

 

Figure 4.7 Mean Absolute Error (in bin counts: 11) of wind speed histogram frequencies between FSMM5
and observed data over the study area on the three model domains from 1 1/02 to 6/04. All estimates were
interpolated to stations using an inverse distance weighting technique on the nearest 4 grid points.
Negative MAE values are the result of the biharmonic spline procedure extrapolating beyond the range of
the stations and should be ignored.

182

(c) 36 km

 

 

 

 

Figure 4.7 Continued.

Model bias in the three domains is demonstrated spatially in Figure 4.7. In
general, it appears that the highest mean absolute errors occur in the 12 km domain in the
same areas over which the mean speeds were most systematically over-estimated (1'. e.,
Lake Huron and Lake Erie regions). There appears to be little difference in the
magnitude of the errors between the 4 and 36 km MAE, but in general, the 36 km domain

appears to exhibit more spatial coherence in bais (i.e., more spatially systematic).

The spatial component of the degree of bias in the model estimates of the wind
resource can perhaps be best described by variations in the index of agreement (d2) over
the region. This is presented for each model domain in Figure 4.8. As expected, F SMMS

exhibits its most spatially coherent model bias at the coarsest (36 km) domain. The 12

183

km and 4 km domains both exhibited consistently lower indexes of agreement over the
study area and are dichotomous in their behavior. The 12 km domain is very spatially

systematic in the distribution of index values, whereas the 4 km domain is not.

Lastly, the spatial behavior of the systematic error of the model estimated wind
resource can be visualized both by plotting the systematic error component of RMSE over
the region as well as by examining the trend surfaces of the residuals of the mean wind
speed. The systematic RMSE is presented in Figure 4.9, and the trend surface analysis in

Figure 4.10.

The spatial patterns of systematic bias over all domains closely mirror the
behavior of the overall bias presented in the preceding ﬁgures. The 36 km domain
exhibits the most spatial consistency in systematic bias whereas the 4 km domain is the
most spatially inconsistent. Again, the greatest systematic bias over the 12 km domain

was coincident with locations where the model substantially over-estimated the mean

speeds.

184

(a)4km

 

 

 

 

 

(b) 12km

 

 

§".';"4 l 1 ' l J 1 t
-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Figure 4.8 Index of agreement (11;) for FSMM5 estimates of the wind resource over the (a) 4 km, (b) 12 km
and (c) 36 km domains from 1 1/02 to 6/04. Values outside the range 0 - l are extrapolation artifacts and
should be ignored.

185

(c) 36 km

 

 

 

 

Figure 4.8 Continued.

(a)4km

 

92“” 88°w s4°w so°w

 

 

 

4300 400 -ZI) 0 2X) 4CD GI) an 1000

Figure 4.9 Systematic component of the Root Mean Squared Error (RMSEs) over the study region from the
(a) 4 km, (b) 12 km and (c) 36 km FSMM5 domains from 11/02 to6/04. Negative values are an
extrapolation artifact and should be ignored.

186

(b) 12 km

 

 

 

(c) 36 km

 

 

 

Figure 4.9 Continued.

187

(a) 4 km contour

 

 

 

 

(b) 4 km surface

(m 8")

N
UI to
1 1

0
01%

N
I

 

 

Trend Sfc. Residuals
. T‘
0|

  

   
 
  
  

8

    

48
4

[’0qu 44 42

Figure 4.10 Fitted trend surfaces of FSMM5-Observed histogram residuals (m s") over the study area from
the (a-b) 4 km, (c-d) 12 km and (e-f) 36 km domains from 11/02 to 6/04. The lower ﬁgures are 3-
dimensional representations of the ﬁrst-order trend surfaces that are contoured 1n the upper ﬁgures.

I 85 (wt
90 Longnude

188

(c) 12 km contour

 

 

 

(d) 12 km surface

.g .6.
\

. V
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4 . .
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Figure 4.10 Continued.

189

(e
) 36 km cOntour

 

 

 

(t)
36 km surface

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190

The use of trend surface analysis was discussed in the preceding chapter as a
means of extracting information regarding the behavior of a variable in space. Trend
surfaces are simply multiple regression equations that utilize Longitude and Longitude as
the regressor variables. Initially a second order trend surface was ﬁt to the data, however,
it was subsequently determined that in all instances, the additional regression coefﬁcients
were not signiﬁcantly different from zero and were thus extraneous. A more
parsimonious ﬁrst order linear trend surface was therefore ﬁt to the data and the results

are presented in Figure 4.10.

The presence of a strong trend, both latitudinally and longitudinally reveals the
relative link between geographical location and model bias. Figure 4.10 demonstrates
that the coarsest resolution domain (36 km) appears to exhibit a distinctly latitudinal
trend, but only slightly dependent on longitude. The 12 km domain has less of a
latitudinal trend, but more pronounced dependence on longitude. The 4 km domain
pattern is completely the reverse of the 12 km domain, with increasing residual values
from northeast to southwest across the region. When these trends are compared with the
overall model systematic error over each domain, the 36 km domain appears to be the
most promising for wind resource estimation. In addition to being associated with the
overall lowest model bias, much of that systematic bias might be spatial in nature and

was accounted for by Latitude.

19]

4.1.2 Performance based on spatial aggregation resolution

The FSMM5 was also evaluated to determine which of the 5 interpolation
schemes yielded the best wind estimates at the site locations. In review, wind estimates
were calculated at each station locations within the study network using interpolated grid
point estimates from each model domain with ﬁve different interpolation schemes. In the
ﬁrst method the location of interest simply assumed the value from the nearest model
grid point. The second estimated each location value as an unweighted average of the
nearest 4 grid points. The third used a linear inverse distance weighting scheme on those
same 4 points. The fourth and ﬁfth methods produced an unweighted average of the
nearest 16 and 36 grid points respectively. The increasing number of nearest neighbor
grid points was considered in order to investigate the inﬂuence of spatial aggregation, and
perhaps uncover the degree of spatial bias inherent in the different model domains. Some
of the results of the third interpolation method were presented in the preceding chapter.
All ﬁve are assessed here and are limited to the 36 km domain which was found to be

superior to the other domain resolutions.

An analysis of the model evaluation statistics is presented in Table 4.4. Based
upon these statistics, there does appear to be a trend in the behavior of the various
interpolation schemes. It was initially suspected that the estimates calculated with the
greatest number of grids (and from the greatest areas) would provide the best results in
that they would be largely devoid of any localized inﬂuences. This was not the case,

however, as the larger sample estimates were found to be associated with the poorest

192

performance. This may imply that the localized component of the wind resource at a
location is a substantial portion of the overall wind regime. Larger aggregation intervals

would tend to mask that inﬂuence.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model evaluative statistics for 5 interpolation schemes on the 36 km domain
Nearest
‘ neighbors I 4 4 (IDW) 16 36
1? s, 1? s, 1? Si 2? 8. if s,

o (m s“) 3. 76 0.70 3. 76 0.70 3. 76 0. 70 3. 76 0.70 3. 76 0.70

e p11 s") 4. 03 0.46 4.02 0.39 4. 03 0.43 4. 04 0.29 4.07 0.26

s, (m s5 2. 40 0.30 2. 40 0.30 2. 40 0. 30 2. 40 0. 30 2. 40 0. 30

s,(m Q) 2.11 0.30 1.99 0.25 2.04 0.27 1.84 0.19 1. 73 0.16

IgL 1.94 0. 38 1.94 0. 38 1.94 0. 38 1.94 0. 38 1.94 0. 38

_k, 2.14 0.17 1.94 0.14 1.52 0.25 2.27 0.30 2. 76 0.26

CL 4. 53 0. 90 4. 53 0. 90 4. 53 0. 90 4. 53 0. 90 4. 53 0.90

_c, 4.62 0.51 4.26 0.47 3.81 0.61 4.52 0.41 4.85 0.31

r 0. 91 0.07 0.89 0. 08 0. 90 0.07 0.88 0.07 0.87 0.08

MAE (M 151.17 52. 72 164. 61 53. 70 157.72 52.56 182.39 48.10 196.31 47. 74

1.33% 0.50% 1.45% 0.50% 1.39% 0.50% 1. 60% 0.44% 1.72% 0. 43

RMSE (n) 296.43 106.11 335.75 110.17 314.51 107.68 380.14 103.35 416. 72 102.75

2.61% 1.00% 2.95% 1.03% 2. 77% 1.03% 3.33% 0. 94% 3.64% 0.88%

RMSEs m 71.17 67.49 73. 79 65. 70 71.85 67.30 89.03 57.44 107.03 60.99

0.64% 0. 66% 0.66% 0.64% 0.65% 0.66% 0.79% 0.54% 0.94% 0.53%

RMSE“ (M 282.64 98.25 322.80 104.53 301.18 100.67 365.47 102.07 397.97 103.38

2.48% 0. 90% 2.83% 0. 94% 2.65% 0.61% 4.52% 0.41% 4.85% 0.31%

58% (%) 8.28 10.01 7.31 8.67 7. 77 9.35 7.85 7. 72 9.17 8.02

d, 0.95 0. 04 0.94 0. 04 0.94 0. 04 0. 93 0. 04 0.92 0. 04

 

 

Table 4.4 Evaluative statistics of 5 spatial aggregation schemes applied to the FSMM5 36 km domain wind
speed estimates over the period of record. Percentage values in the error statistic cells are the error (bin
frequency) as a percentage of the overall number of estimates. Bold values are statistically signiﬁcant
improvements over the next higher model (tLogg).

Initially, even though there appears to be a trend toward better model performance
with smaller spatial aggregation intervals, the differences between aggregation schemes
do not appear to be substantial. Statistical testing conﬁrmed this observation. A one-
tailed t-test with an alpha level of 0.01 was applied to the data to evaluate the statistical

signiﬁcance of the relationships in the data. Except where indicated, all statistical tests in

193

this section are one-tailed t-tests with an alpha of 0.01. With respect to the observed and

estimated means, signiﬁcant differences were found for all model variants.

Another set of variables examined for statistically signiﬁcant differences were the
parameters of the observed and estimated Weibull density functions. With a T-test, no
signiﬁcant differences were found between the observed and estimated shape (k) or scale
(c), with the exception of the scale parameter in the 36 nearest neighbor variant which
was signiﬁcantly different at the critical level of 99%. Furthermore, there appears to be a
strong correlation between observed and estimated wind speed histograms, as evidenced
by the high, and statistically signiﬁcant r values (tLogg). However, with the correlation
- coefﬁcients, differences in the model variants begin to appear. Although the differences
between variants are not statistically signiﬁcant, the highest correlation is exhibited by

the lowest-order aggregation scheme (one nearest neighbor).

It was therefore necessary to evaluate the behavior of the estimation bias. With
the exception of the 4 nearest neighbors variant, the models all tended to exhibit
decreasing error as the level of spatial aggregation was reduced. Most of the
improvements in MAE or RMSE were not, however statistically signiﬁcant, with the
exception of those indicated in bold in Table 4.4. Notably, the most improved model
variant was the 4-neighbor inverse distance weighting (IDW) scheme, with statistically
signiﬁcant improvements in all but systematic error. In fact, no aggregation model

signiﬁcantly improved the systematic bias of the 36 km domain.

194

Given the lack of distinctiveness between the 5 aggregation variants over the 36
km domain, it was apparent that while any of these approaches would provide a
reasonable estimate of the wind resource at a location over the region, the one nearest
neighbor variant is the most parsimonious from a Spatial standpoint and as such, there is

no reason to prefer the more complex aggregation approaches.

At 8.28% of overall model error (with a standard deviation of about 10%), the
mean systematic resource bias of the 36 km, 1 nearest neighbor model variant is
relatively low. Furthermore, the reduction of this bias would result in an improvement in
the model estimation of the resource. However, given the low proportion of bias that is
systematic, it is unlikely that any adjustment would be regionally signiﬁcant. Still, if the
ﬁrst order trend surface of the residuals is examined, there does appear to be a strong
latitudinal component that might permit a systematic improvement in model accuracy

(Figure 4.1 1).

Based upon the results discussed in this section, it appears that the 36 km domain,
using a one nearest neighbor aggregation scheme provided the best model performance of
the 15 variants evaluated. It is therefore this variant that will be compared with the three

aforementioned statistical models for wind resource estimation.

195

(a) T

To
nd surface c
Ontour

3.1" 1%
2.1.13;

 

 

 

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196

4.2 Model Comparison

All three of the statistical models (two stochastic and one probabilistic) have been
either previously developed for or utilized with success in wind energy resource
estimation. It is for this reason that these models were chosen. One of the goals of this
research was to establish whether a highly complex numerical approach to wind resource

estimation represents a signiﬁcant improvement over established statistical methods.

4.2.1 Statistical model performance

As with the 15 FSMM5 variants in the previous section, the performance of the
three statistical models can be evaluated statistically. Statistics describing the relative
performance of the models are presented in Table 4.5. It is immediately clear from the
statistics that the Krige model does not appear to perform as well as the other two
statistical models. Even so, in an evaluation of difference of means between model
estimates and observed values, none of the models have a statistically signiﬁcant
difference from the observed mean (t2,o.99). Additionally, all have distribution

correlations that are signiﬁcant at the same level (p = 0.99).

In assessing the parameters of the Weibull density function ﬁt to the observed
data, again there were no statistically signiﬁcant differences between any of the
parameters with the exception of the shape (k) parameter of the Krige model. This

indicates that in general, at least two of the models are providing an excellent estimate of

197

the observed wind speed distribution. This is corroborated by the correlation ofthe

distributions. all of which are signiﬁcantly high. but thejoint probabilistic model appears

to correlate best with the observed data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Evaluative statistics for three statistical wind estimation models
Model JP MCP Krige

f 5? SL 5 5,,
o (m s") 3. 77 0.69 3. 77 0.69 3. 78 T 0.69
_e (m s'T 3. 79 0.67 3. 74 0.70 3. 71 1.02
S:(m?5 2.40 0.28 2.40 0.29 2.40 0.29
§e (m s") 2.12 0.24 2.02 0.29 2.63 1.19
3,, 1.94 0.39 1.94 0.38 1.94 0.37
kg 1.83 0.42 1.81 0. 62 1.56 0.44
9:, 4.54 0.88 4.54 0.88 4.52 0.88
ca 4.14 1.02 3.81 1.12 4.19 1.92
7 0.92 0. 07 0. 88 0.14 0. 76 0.18
MAE (M 130.14 43.99 114.15 44.80 116.89 81.94
1.17% 0.39% 1.03% 0.42% 1.25% 0.87%
313.18 133.45 270.99 131.02 247.34 161.38
RMSE ('0 2.80% 1.17% 2.42% 1.17% 2. 62% 1.72%
57.61 50.39 52.63 44.13 81.34 92.15
RMSE‘ (n) 0.52% 0.46% 0.48% 0.42% 0.88% 1.00%
305. 75 128. 71 263.45 128.42 226. 09 145.01
RMSE“ (n) 2. 73% 1.13% 2.35% 1.14% 2.39% 1.53%
88% (%) 4.41 5.15 5.81 6.64 12.37 15.11
42 0.94 0. 05 0. 95 0. 04 0. 93 0.11

 

Table 4.5 Evaluative statistics over the period of record for three statistical wind resource models, a joint
probabilistic model (JP), a measure-correlate-predict model (MCP), and a Krige model (Krige). Error
values are in bin count differences (n), and the percentages are relative to overall record length.

Although the Krige model ﬁtted values appear to have the worst agreement with

the observed data. it is helpful to consider the error statistics. Between the mean absolute

error and the root mean squared error there is minor disagreement between error

measures. In terms of absolute frequency. the MC P model has the lowest MAE. but the

Krige model appears to have a lower absolute RMSE. This is. however rectified by

198

 

examining the errors relative to the overall frequency count. When viewed as
percentages of total, the MCP model has the lowest MAE and RMSE. However, it should
be noted that at p = 0.99, a 2-tailed t-test failed to identify any statistically signiﬁcant
difference in the errors between the MCP model and either of the other models. In fact,
all three models have indexes of agreement over 0.90 indicating that the majority

proportion of their estimates are error free.

Thus, we must turn to the distribution of error among systematic and unsystematic
to determine whether one model outperforms the others. In all instances, the systematic
component of the RMSE was less than 1% of the length of record. Of the RMSEs values
however, the MCP model, with the lowest score was signiﬁcantly lower than the Krige
model 01.0.99)- There was no corresponding signiﬁcancc with the joint probabilistic
model. In fact, the joint probabilistic model actually has a lower percentage of systematic
bias relative to overall bias than does the MCP model. The bias in the Krige model on

the other hand is around 12%, nearly three times as high as the other models.

Overall, it appears that while the Krige model does perform reasonably well over
the region, its complexity relative to the other models would likely preclude its use.
Therefore, the model has been removed from ﬁrrther consideration and comparison with

the selected FSMM5 model variant.

199

4.2.2 Comparison of FSMMS to statistical models

The question that must now be asked is whether the best performing variant of the
FSMM5 model can perform better than established statistical wind energy resource
models. To assess this question, Table 4.6 and 4.7 are presented. Table 4.6 contains the
evaluative statistics for the resource estimation and Table 4.7 holds the statistics for the
forecast estimation from each of the models. The three models that are compared are the
joint probabilistic model, the measure—correlate-predict model and the 36 km FSMM5

with one nearest neighbor aggregation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Evaluative statistics for three wind resource estimation models
Model JP MCP FSMM5

r Sx r s,( r 3,,
o (ms’I) 3. 77 0.69 3.77 0. 69 3.76 0.70
e (m s'i 3. 79 0.67 3. 74 0. 70 4. 03 0.46
30 (m s") 2. 40 0.28 2. 40 0.29 2.40 0.30
Safm s") 2.12 0.24 2.02 0.29 2.11 0.30
. kn 1.94 0.39 1.94 0.38 1.94 0.38
k" 1.83 0.42 1.81 0.62 2.14 0.17
c: 4.54 0. 88 4.54 0.88 4. 53 0.90
cg 4.14 1.02 3.81 1.12 4.62 0.51
r 0.92 0.07 0.88 0.14 0.91 0.07
130.14 43.99 114.15 44.80 15117 52.72
MAE (n) 1.17% 0.39% 1.0 % 0.42% 1.33% 0.50%
313.18 133.45 270.99 131.02 296,43 106),
RMSE 0‘) 2.80% 1.1 7% 2.42% 1.17% 2.61% 1. 00%
57.61 50.39 52.63 44.13 71.17 67.49
RMSE‘ (n) 0.52% 0.46% 0.48% 0.42% 0.64% 0. 66%
305.75 128. 71 263.45 128. 42 282.64 98.25
RMSE“ (n) 2.73% 1.13% 2.35% 1.14% 2.48% 0. 90%
SB% (%) 4.41 5.15 5.81 6. 64 8.28 10.01
4, 0. 94 0. 05 0. 95 0. 04 0. 95 0. 04

 

Table 4.6 Evaluative statistics for the performance of three wind resource estimation models, joint

probabilistic (JP), measure-correlate-predict (MCP), and FSMMS running on a 36 km domain and utilizing
the one nearest neighbor scheme over the period 1 1/02 to 6/04. Error measures are given in bin count
differences and the percentages are relative to overall record length.

200

 

 

 

 

 

 

 

 

Evaluative statistics for three wind forecasting models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model JP MCP FSMM5

31' si f 8, f 3.
o m 1')!— 3. 77 0.69 3. 77 0.69 3. 76 0. 70
e (m s1 3. 79 0.67 3. 74 0. 70 4. 03 0.46
.8an s") 2. 40 0.28 2.40 0.29 2. 40 0.30
s, (m s'lL 2.12 0.24 2.02 0.29 2.11 0.30
r 0. 79 0. 08 0. 76 0.1 7 0.00 0. 05
MAE ar‘L 1.19 0.25 1.12 0.25 2. 62 0.26
WSﬂmﬂ 1.56 0.33 1.45 0.31 3.32 0. 35
RMSEs mi 0. 78 0.29 0. 79 0.32 2.55 0.31
RMSELLm E) 1.34 0.23 1.19 0.20 2.11 0.30
83% (m 24.36 9.13 29. 79 12.87 59.34 7.28
d, 0. 86 0.06 0. 88 0.06 0.37 0.03

 

Table 4.7 Evaluative statistics for the performance of three wind forecasting models, joint probabilistic
(JP), measure—correlate-predict (MCP), and F SMMS running on a 36 km domain and utilizing the one

nearest neighbor scheme for the period 11/02 to 6/04.

Although not a focus of this study, Table 4.7 demonstrates that as a wind power
forecasting model, it does not appear that on average the FSMM5 variant would be a
good choice. On all counts it appears to lack the performance of the statistical models.
From a statistical standpoint (b.0159), all of the FSMM5 model error statistics were
signiﬁcantly higher than those of either statistical model. However, from a wind resource
estimation standpoint, Table 4.6 demonstrates that perhaps the numerical F SMMS is not

as quite as erroneous, and performs on par with the other models.

In terms of mean wind speeds, the F SMMS estimates were signiﬁcantly different

from the observed value 62,099). However, neither the estimated Weibull shape nor scale

201

 

parameters were signiﬁcantly different from the observed parameters. In terms of the
shape (k) parameter, FSMM5 estimates the true values most closely more of the time
versus the other models. Although it appears, too, that the scale parameter was best
approximated by F SMMS, it was not consistent across the region and the statistical
models proved more reliable in this regard. Error statistics proved more difficult to
assess as the differences between the three models were not very great. The only
statistically signiﬁcant difference that existed was that the MAE for the F SMMS was
signiﬁcantly larger than either of the statistical models (t 1,0.99)- None of the instances
where the FSMM5 exhibited lower error than the statistical models was determined to be

a statistically signiﬁcant improvement.

One of the goals of this research was also to determine if the F SMMS model
would have a signiﬁcant advantage in estimative accuracy for remote locations where no
nearby long-term records exist. Thus, the ﬁve stations in the study that were most distant
from their nearest neighbors were selected for more speciﬁc model evaluation and
comparison. The analysis for Chapleau Airport, ON (CYLD), the most remote of the 5
(its nearest neighbor is Sault Ste. Marie, ON, approximately 180 km distant) is presented

in Table 4.8. The other 4 locations exhibited similar behavior and so are not discussed.

At Chapleau Airport (Table 4.8), both the joint probabilistic and F SMMS models
estimates of the mean speed were signiﬁcantly different from the observed value (@099).
Although the evaluative statistics indicated that the MCP model demonstrated the best

Weibull ﬁt, a graphical analysis revealed that the joint probabilistic model was the most

202

apprOpriate Weibull ﬁt to the data and that the F SMMS Weibull ﬁt was the poorest

(Figure 4.12). However, from Table 4.8 it is the MCP model that exhibits the lowest

correlation between the observed and estimated histograms. The histogram differences

are displayed in Figure 4.13.

 

Evaluative statistics for three wind resource estimation models.

7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chapleau Airport, Ontario (CYLD)
Model JP MCP FSMM5 T
0 (m S-I) 307 3.09 3.01
e (m s-T 3.18 3.14 4.50
L sCL (mﬁ 1.99 2. 00 1. 99
. s ‘(m ,4, 1.48 H5 2-36
kg 1.61 1.64 1.56
,k 2.19 2.09 2.28
en 3. 72 3.69 3.50
68 3. 76 3.29 4-90
r 0. 90 0.17 0. 88
142 150 147
MAE (n) [.8596 [909/5 [.8296
289 321 245
RMSE (n) 3.76% 4.06% 3.0 %
95 112 115
RMSEs (n) 1.23% 1.42% 1.43%
274 301 217
RMSEu (n) 3.56% 3.81% 2.70%
d; 0. 93 0.92 0. 93

 

 

 

 

 

Table 4.8 Evaluative statistics for model estimates of the wind resource at Chapleau Airport, Ontario

(C LYD). The models are joint probabilistic (JP), measure-correlate-predict (MCP), and the 36 km domain,

one nearest neighbor variant of F SMMS (FSMM5) for the period ”/02 to 6/04. Error values are given in

bin count differences and percentages are relative to the length of record.

Based upon the histogram differences, the inﬂuence of systematic error becomes

clear. While all three models exhibit some systematic bias, the FSMM5 model appears to

be the most systematic in its under-estimation of the occurrence of low wind speeds and

its over-estimation of the frequency of higher speeds (relative to the mean). Both

statistical models appear to over-estimate winds near the mean speed and under-estimate
all others (Figure 4.13). Furthermore, as hinted at by its low histogram correlation, the
MCP model greatly over-estimates winds near the mean observed speed at CYLD. This

is corroborated by the extreme peakedness of the Weibull distribution estimated from the

MCP model (Figure 4.12e).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

0.3 4 e
MM5
. (a)
20 30
I?
0.3 3 JP .3
N
.0
go... 9
0.
§ 3
h 0.1 .
o. 5
3
o - (c) E
o 20 30 5
0.3-
MCP
. (e) 0 , , , , (0
20 30 o 5 10 15 20 25
Wind Speed (ms‘)

Figure 4.12 Fit of model estimated Weibull distribution (line) to observed wind speed data frequencies
(leﬁ, bars; right, crosses) at Chapleau Airport, ON (CYLD) for the period 11/02 to 6/04. Left plots are the
probability density function, and right plots are the cumulative density function. The models are: the 36 km
domain, 1 nearest neighbor F SMMS (a,b), the joint probabilistic model (c,d), and the measure-correlate-

predict model (e,f).

204

2500 .
2000 -
1 500 -
1 000 ~

500 -

-500
-1 000

 

iii]

 

DEEMED:

 

 

0

10

Est-Obs frequency (h)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . 2500 . . .
MM5 a A
(l 5 2000» JP (b)
3
c 1500-
3
a. 1000-
2
u— 500’ ﬂfﬂ
m
______________- 9 o--» .3
Q ‘ “LP
E .500»
. -1000 1 ‘ 5 .
20 25 5 1o 15 20 25
2500 . .
2000p MCP (c)
1500-
F
1000-
500»
o. HUI-Jug
-500»
.1000 i i . i
0 5 10 15 20 25
Wind speed (m s")

Figure 4.13 Wind speed frequency histogram differences (Estimated - Observed) for three wind models
[(a) 36km/1 nearest neighbor F SMMS, (b) joint probabilistic, and (c) measure—correlate-predrct] at
Chapleau Airport, Ontario (CYLD) for the period 11/02 to 6/04.

This assessment of systematic bias is further supported by the percentage of

systematic bias reported in Table 4.8. At CYLD, the FSMM5 model bias was

approximately 22% systematic, compared to 11 and 12% for the joint probabilistic and

MCP models respectively. Thus, while all three models appear to perform with similar

accuracy, which in itself is remarkable, especially for the statistical models given the

205

great distance between CYLD and its neighbors, a correction of the bias in the F SMMS
model may in fact result in a substantial improvement of the model’s performance.
Additionally, given the lower unsystematic bias of F SMMS, it could be expected that an

adjusted model would outperform the two statistical models.

4.3 Accounting for spatial bias in F SMMS

A ﬁnal goal of this research was to establish whether or not any of the resource
estimation bias inherent to the F SMMS model could be reduced. Given the
aforementioned low levels of systematic bias, it is unlikely that a signiﬁcant
improvement could be made. However, with the small differences in model
performance, it is possible that a reduction in F SMMS’s systematic error could in fact
result in its outperforming the statistical models. To that end, the resource estimates of
the FSMM5 model (the estimated frequency distributions, Weibull shape and scale) were
subjected to a multiple regression that took into account two factors that would appear to
exert some inﬂuence on the model’s estimates. The ﬁrst is geographic location. Trend
surface analyses of the residuals of the model estimates indicated a distinct relationship
with both Longitude and Latitude. The second factor is terrain. Although F SMMS
contains a high resolution digital terrain model as part of its base information, it is
possible that the processes associated with various terrain types have not all been
properly speciﬁed. As such, certain types of terrain might be associated with higher

errors than others. To examine this possibility, a terrain complexity index ( T C1) was

206

created for each station location (Figure 4.14). This index was calculated as the standard
deviation of the elevations at the 16 grid nodes in the F SMMS 12 km domain nearest to a

station location (Figure 4.15).

 

 

 

 

Terrain Cambrity (m)

ndex (TCI) obtained for the study area by calculating the standard

. rrain C lexi I _ . _
Figure 4 14 Te omp ty d points (12-km MM5 domain) surrounding each station location.

deviation of elevation of the 16 gri

207

 

.k .9 .5

E

mumu0~=oa DOW GOP

nee.

 

 

 

6:3

 

       

 

38798” I
38.33 I
33.4.8». I
4.4.8-39 I
I
I
I

 

None . «.mmn
Nmmn - Qmmu
9me - 563
he” - n.3—
néi - —.3
<3 .. o

E cozmam

  

 

 

 

from the 12-krn domain of

Figure 4.15 Surface elevation of the area encompassing the study region

FSMM5.

208

Initial multiple linear regressions took the forms,

14:15O +b1k+b2¢+b321+b4TCI (4.1)

0:120 +b10+02¢+b3l+b4TC1 (4.2)

where k and c are the Weibull parameters estimated from the observed data, k and 0 are
the Weibull parameters estimated from the F SMMS model output, 0 is Latitude in
degrees, A is Longitude in degrees, and T CI is the aforementioned Terrain Complexity
Factor. Based upon the preliminary analysis of both equations, neither Longitude nor the
T CI variables were found to be signiﬁcant 02.0.9) and were removed from the equations.

The resulting multiple linear regression equations became,

k = 4.55— 0.1112— 0.0540 (4.3)

c=11.128+0.1855—0.169¢ (4,4)

As expected, given the rather low systematic bias inherent in the original F SMMS
estimates of the wind speed distributions, much of the error between observed and
estimated Weibull parameters was unsystematic and could not be resolved by the
regression adjustment. This is borne out by the rather low multiple correlation coefﬁcient
values (0.27 and 0.35 respectively), although an F test reveals both regressions to be
signiﬁcant at the 0.01 level. Thus, Equations 4.3 and 4.4 were applied to the F SMMS
Weibull parameter estimates in an attempt to reduce the error between them and the

observed parameters.

209

Indeed, the linear correction based upon Latitude generally improved the Weibull
estimates across the region. For the shape (k) parameter an average 0.23 ms'l MAE
improvement over the original estimates was obtained at over 70% of the stations.
Results were similar for the scale (c) parameter. An average MAE improvement of 0.46
m s'1 at 67% of the stations. In both shape and scale, this represented a statistically
signiﬁcant overall improvement in estimative accuracy from the original FSMM5
estimates as deﬁned by MAE (11,095). However, it still remained to be seen whether or not
the correction represented a signiﬁcant improvement in estimates relative to the other two

models.

Prior to the regression correction, there were no signiﬁcant differences (tugs)
between the MAE of the estimated shape parameters of any of the models. After the
regression correction was applied to the FSMM5 estimates, the MAE of the new FSMM5
estimates of k was signiﬁcantly lower than the MAE from the MCP estimates. 1
Furthermore, prior to the regression, the MAE associated with the scale estimates from
FSMM5 was signiﬁcantly higher than that of the joint probabilistic model (11,095) .
However, after the regression, there was no longer any statistically signiﬁcant difference
in the MAE associated with the scale estimates from any of the models (tugs) . Thus, it
appears that a simple multiple linear regression, as was conducted in this research is able
to substantially improve the estimative accuracy of the FSMM5 model over the Great

Lakes region in terms of wind resource estimation.

210

Chapter 5. Discussion

Since the advent of commercially viable wind energy conversion systems (1‘. e.,
wind turbines), there has been a great interest in the accurate point source or areal
estimation of wind resources. Early methods utilized climatological reduction
approaches, while later methods tended to be based on probability and correlation
methods. However, while many of these methods have been successfully applied under a
variety of atmospheric and geographical conditions, the degree of their success largely
remains dependent on the network of wind observation stations that may be employed.
Because many of the processes that govern the wind at a particular location are local or
quasi-local (e. g., a few meters to a few kilometers), most operational anemometer
networks are of a spatial resolution that is too coarse to resolve such sub-network
characteristics or behavior. As a result, a coarse instrumental network (e.g., on the order
of tens to hundreds of kilometers between stations) may only capture the regional
coherence and behavior of the wind ﬁeld unless local conditions between stations exhibit

a high level of correspondence.

Over the past several decades, there has therefore been growing interest in the use
of methods that are capable of addressing the localized component of near-surface
atmospheric motion. This need has led primarily toward the use of process-based
numerical models. Such models seek to account for local inﬂuences by incorporating the
known physical pr0perties of turbulence and momentum ﬂuxes within the boundary

layer. When applied at a ﬁne spatial scale, it is hoped that behavior at that scale can

211

subsequently be resolved and included in estimates of the near—surface wind ﬁeld. The
incorporation of numerically-based localized boundary layer conditions into wind
resource estimation models is not new. The WAsP system developed in Denmark has
done so for several decades with success (Petersen et al., 1988, Troen and Petersen,

1989)

One area of process-based modeling that has received increased attention is
regional-scale climate models. RCMs occupy a middle scale between boundary layer
models and coarser general circulation models. Such models operate on a scale and
resolution that make them ideally suited to estimating the wind resource over a given area
on the order of a few thousand kilometers at a resolution of use to wind farm developers
(e. g., < 10 km). However, until recently, because of their complexity and computational
needs, generating longer-term (e. g., > 1 or 2 years) series of estimates for wind resource
assessment has meant a large time commitment. As a result, RCMS have been used
primarily as a short-term (i. e., < 48-h) point forecasting tool, and substantial research has
been carried out regarding the ability of RCMs to estimate wind speeds at discrete
locations over a span of a few days (e. g., Nielsen, 1998, Alexiadis et al., 1999, Landberg,
2001, Sfestos, 2002). Unfortunately, using RCMS to estimate a region’s wind
climatology has been largely overlooked in favor of less complex stochastic approaches.

It is this gap in the science of wind ﬁeld estimation that this research has addressed.

As the resources needed to run RCMS become less expensive and the models are

more easily deployed, it has become apparent that such models may be able to provide

212

accurate estimation of the general wind resource over a region, especially those regions
that lack a dense network of observational locations. Such use has substantial
implications for the accurate selection of optimal locations for future wind farm
development. Unfortunately, until now the utilization of an RCM in this manner has
received limited attention despite its potential beneﬁt. Thus, it was not known how
accurately an RCM might reproduce the wind ﬁeld over a region of diverse geography.

That was the goal of this research.

5.1 Summary of Research

The primary objective in this study was an assessment of the performance of the
MM5 mesoscale numerical model over the Great Lakes region of North America,
implemented and run by the U.S. Forest Service North Central Research Station. In this
study, the gridded wind vector estimates from three model domain resolutions were
utilized (36 km, 12 km and 4 km). These gridded wind estimates were used to estimate
the wind speed and direction at the geographic coordinates of 113 automated wind
sensors throughout the region using ﬁve interpolation schemes. The ﬁrst utilized the grid
value nearest the station as the estimate. The second and third estimated the wind at the
location from the nearest four grid points using an unweighted and inverse distance
weighted average respectively. The fourth used an unweighted average of the nearest 16
grid point estimates, and the ﬁfth obtained the unweighted average of the surrounding 36

grid point estimates.

213

Based upon these 15 model variants (domain + interpolation scheme), estimates
of the distribution of wind speeds at each of the anemometer locations were generated
and compared to the distributions of the observed winds at these locations. It was
determined that the 36 km resolution model domain was most adroit at reproducing the
wind distributions at the stations in the study region. Furthermore, of the 5 grid-to-point
estimation techniques, the nearest neighboring grid point option proved to be the most

reliable estimator.

Additionally, while the F SMMS model did perform well in reproducing the
general wind resource over the region, it was important to compare its performance with
more established and widely used wind resource estimation models. Three models were
selected for comparative evaluation, two stochastic and one probabilistic. The stochastic
models were a traditional measure-correlate-predict model (Derrick, 1992) and a Krige
model (Haslett and Raftery, 1989, Davis, 1986). A joint probabilistic model (Garcia-

Rojo, 2004) rounded out the three as the probabilistic selection.

Both the measure-correlate-predict (MCP) and the joint probabilistic (JP) models
provided excellent results. From a forecasting standpoint it was determined that either of
these two statistical approaches easily outperformed the FSMM5 model. But, from a
resource estimation standpoint, all three models (FSMM5, MCP, and JP) performed
more-or-less equally well. In one aspect, however, the F SMM5 model held promise. A

substantially greater proportion of its model bias was found to be systematic, allowing for

214

a potential improvement of estimated wind resource over the region. To that end, a
multiple linear regression model was applied to the FSMM5 model estimates. Based on
earlier trend surface analysis, it was determined that geographic position could account
for some of the systematic bias. Initially it also was felt that the complexity of terrain
might be a systematic issue, however, that variable proved insigniﬁcant in the regressions
and was omitted. With the ﬁnal version of the multiple linear regression, estimates of the

Weibull distribution parameters were adjusted solely as a function of Latitude.

The regression correction improved a majority of the FSMM5 estimates over the
region to the point that in many instances, they exceeded the accuracy of those produced
by the statistical models. However, while the improvements in the F SMMS estimates
were in many cases quite substantial, and represented a statistically signiﬁcant
improvement over the original estimates, they were not signiﬁcantly better than the

estimates produced by either of the statistical models.

5.2 Conclusions and Discussion

Several conclusions were reached as the result of this research. The primary
conclusion is that while F SMMS was able to adequately reproduce wind speed frequency
distributions at most stations across the study region, it was not able to signiﬁcantly
outperform the more readily implemented statistical models, even at locations that were

remote from their nearest neighbors in the anemometer network. While its use might be

215

justiﬁed in regions where the observational data is considered to be of suspect quality or
the network of wind sensors is deemed too sparse, if a sufﬁcient network of quality
observations exists in a region, the use of a RCM at this point in time represents perhaps

an unnecessary addition of model complexity and resource utilization.

What this research suggests, however is that a numerical model approach to
regional wind resource estimation does hold some promise, particularly in areas where
few data exist and neighboring stations are distant (e.g., over water). Although most of
the bias encountered in the estimates of the wind distributions was unsystematic in
nature, there was sufﬁcient systematic bias to permit a simple linear model to improve
those estimates. It is likely that the improvement based solely on geographic position is
indicative of a spatial bias that is inherent to the model itself. One possibility is that as
the grid points become longitudinally condensed with increasing latitude, the
parameterizations that utilize the underlying terrain and land cover characteristics may
experience a degradation of spatial accuracy. This issue has a number of associated
aspects. One factor is the possible failure of the model to address the corresponding
decrease in grid area with increasing Latitude relative to its non-atmospheric components.
As a result, the terrain and land cover inputs may be systematically altered in space
relative to the grid and may no longer be fully appropriate to the grid cell being modeled.
Thus, momentum calculations within cells and transfers between grid cells may be
inappropriately speciﬁed. Secondly, it is possible that the terrain and land use model
projections differed slightly from that used to specify the model domain. If these data

sets were subject to a projection calculation other than that which was applied to the

216

model grid, the geographic coordinates (i.e., Latitude and Longitude) would not match
and substantial spatial bias, increasing with Latitude, would result. Both of the
aforementioned issues are inherent to the model development and implementation itself,
and thus were beyond the scope of this research. While it is possible that these issues
have already been addressed by the model’s developers, they would merit a closer

examination as part of subsequent research.

An additional possibility behind the poor performance of the model at many
locations is that there may be some misspeciﬁcation in the surface parameterizations of
the model. However, if this is the case, one would expect decreasing performance with
increasing surface complexity in terms of terrain and land cover. Thus, the most accurate
parameterizations should be expected over homogeneous terrain (e. g., open water or ﬂat
grassland). Unfortunately, it did not appear that model estimates at locations of greater
surface homogeneity consistently outperformed those at more heterogeneous sites. This
is borne out by the insigniﬁcance of terrain complexity as a factor in the model correction
algorithms. In order to more appropriately address this issue, future research might seek
to classify each of the anemometer sites according to surface characteristics beyond
simple terrain complexity and readdress this issue. Furthermore, as F SMMS utilizes
roughness look-up tables to determine surface roughness, a baseline assessment of model
performance might be conducted using only those estimates produced for grid points over
water where surface roughness is lowest according to the tables. These estimates could
be compared against observed buoy data. If the model performs similarly, it is not likely

that the surface parameterizations are to blame. However, substantial model

217

improvement might suggest that more complex terrain may be incorrectly parameterized
in the model. It is interesting to note that a recent independent analysis of F SMMS wind
forecasts over the Great Lakes region, though not focused on the evaluation of near
surface winds per se, achieved bias statistics that were of similar magnitude to those
calculated in this research and presented in Table 4.1 (Zhong et al., 2005). This leads this
researcher to believe that the bias is most likely a ﬁrnction of model misspeciﬁcation,

rather than of the observed data against which the model estimates were evaluated.

A tertiary conclusion concerns the spatial resolution and spatial aggregation of the
FSMM5 model. Over the Great Lakes, the coarsest model domain (36 km) consistently
produced the most accurate estimates of the wind resource. Interestingly, the 12 km
(intermediate) resolution domain consistently produced the worst estimates.

Additionally, the improved performance of the 4 km over the 12 km domain may actually
be an artifact of the nesting of the former in the later and therefore the distribution of the
spatial bias of the 12 km grid into smaller proportions on the 4 km grid. In the locations
where the higher resolution domains did outperform the coarser resolutions, the
differences were not statistically signiﬁcant. This issue may be related to many of the
same issues already mentioned regarding spatial or surface misspeciﬁcations. Thus,
based on these results, an increase in horizontal resolution of the FSMM5 model cannot
be justiﬁed in the modeling of near-surface wind distributions over the Great Lakes,
especially given the exponential increase in computing resources necessary to produce

estimates at the ﬁner resolution domains.

218

 

Furthermore, the increased accuracy with increasing aggregation parsimony was
of note. The use of a single nearest neighbor grid point proved a far more robust
estimator than using averages from the surrounding n > 1 grid points. This speaks to the
similarity of conditions over short distances throughout the region and that as more
distant grid cells are included in the averaging, that similarity is noticeably degraded. It is
therefore concluded that, at least over the Great Lakes region, the grid point nearest to a

location is the best estimator of the winds at that location.

A fourth conclusion is again related to the primary conclusion in that a substantial
portion of overall F SMMS estimate bias is systematic. Much of this bias was reduced
when a corrective measure was applied. Thus it is also concluded that the model
estimates can be improved by a suitable model output statistics scheme, and that such a
scheme is necessary for the most accurate estimation of the wind resource over a region.
This conclusion is supported by numerous previous works (e. g. , Frank and Landberg,
1997, Petersen et al., 1998b) that did not use RCM estimates of wind speed directly, but
rather employed them as initial input to some form of stochastic adjustment procedure
(e. g., WASP, MOS, downscaling) in order to produce satisfactory local-area wind

estimates.

Lastly, although it was not a stated purpose of this research, the performance of
either the measure-correlate—predict model or the joint probabilistic model was such that
this research recommends either of these approaches for future estimation of the wind

resources over the Great Lakes region. As has been demonstrated, the region has a

219

relatively dense network of automated wind sensors that are collecting data of acceptable
quality. Also, the wind ﬁeld appears to be such that robust correlations in wind speeds
and their probability distributions can be readily obtained. Thus, at least over this region,

the increased complexity of a numerical climate model is not warranted at this time.

5.3 Future Directions

This research, while extensive, has only begun to address some of the issues of
wind resource estimation accuracy regarding numerical models of the atmosphere. As of
this writing, F SMMS is being phased out in favor of the next generation Weather
Research and Forecasting (WRF) model (Michalakes et al., 2004). This new model
corrects a number of issues that were present in earlier models such as FSMM5 (a
discussion of which can be found in Michalakes et al., 2004). It is possible that WRF has
accounted for much of the systematic bias that existed in the FSMM5 wind ﬁelds and
may produce more accurate wind resource estimates (although it should be noted that
WRF uses the same boundary layer look-up tables as MM5). A potential direction of
future research is therefore to evaluate the wind resource estimates of WRF at various
resolutions relative to the estimates produced by FSMM5. If such research is performed
for the same locations using the same initial conditions to produce wind speed estimates
for the same period of time, the differences between FSMM5 and WRF can be compared.
Changes in boundary-layer ﬂow parameterizations can then be assessed for sensitivity

and robustness as a function of the differences between WRF and FSMMS estimates.

220

Additionally, while wind farm developers in the Great Lakes region are focused
on land-based wind farms, it is likely that offshore developments may be explored in the
future. Such developments are already operational in the offshore waters of Europe and
are being planned for New England coastal waters in the US. Given the relative lack of
wind observations over the Great Lakes themselves, a regional scale numerical model
may produce superior estimates of the wind resource over these water regions relative to
observation-based models such as MCP or JP. While this research has evaluated the
wind resources at wind sensor locations on several islands in the lakes, subsequent
research should evaluate the estimative ability of an RCM over open water through
comparisons with buoy data. In addition to validating the RCM over open water, such
research would be able to address variations in model error as a function of surface

parameterizations.

Lastly, the primary goal of using an RCM for wind resource estimation is to
produce a reliable estimate of the wind resource on a continuous ﬁne-scale surface over a
region such that suitable wind farm locations can be identiﬁed. Therefore, it remains to
be seen whether such a surface can successfully be developed and incorporated as an
automated decision-making criterion into a geographic information system (GIS). To
that end, additional research is necessary to better understand the possible inter-grid point
behavior of the wind ﬁeld at whatever domain resolution is chosen. It is then imperative
to develop a method of assessing model conﬁdence over the region such that the wind

resource estimate can be appropriately weighted in the decision making process.

221

In conclusion, this research has accomplished its stated goals in that it has
evaluated the performance of FSMM5 over the study region with respect to the model’s
ability to estimate the regional wind climatology at various spatial resolutions. It
identiﬁed that a coarser resolution domain was better able to estimate the wind resource
and concluded that important systematic bias was present at all spatial resolutions, but
that such bias could be accounted for. Finally, the research determined that in its present
implementation, the FSMM5 model did not present a signiﬁcant performance
improvement for estimates of the wind resource at ASOS locations across the Great
Lakes region compared with established statistical models. However, the FSMM5 model
did perform satisfactorily in some respects over the region and therefore may be useful in
the estimation of wind resources over more poorly instrumented portions of the Great
Lakes (e.g., offshore). As improvements are made in the parameterizations and
speciﬁcations of regional-scale numerical models (e.g., WRF), model resource
estimations are likely to improve, perhaps to the point of outperforming established
stochastic methods. Additionally, it is possible that the use of a sophisticated post-model
corrective procedure (e. g., WASP) could substantially improve the estimates ﬁom
FSMM5 or other RCMS over the region. Therefore, while the research cannot at present
recommend the use of an RCM as a stand-alone tool for wind resource estimation over
the Great Lakes region, that conclusion could easily change as newer RCMS are

evaluated.

222

Appendix A. Automated Reporting Stations Used

Please note, this appendix consists primarily of information in a tabular format, and is
therefore listed as “Appendix A” in the list of tables near the beginning of this document.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Station State/ . Latitude Lon 'tude A enc T e

ID* Prov Station Name M N) (d 9:? & g“ y 3:
1 KADG MI ADRIAN 41.867 84.083 FAA ASOS
2 KAMN MI ALMA 43.317 84.683 NF AWOS
3 KAPN MI ALPENA 45.067 83.567 NWS ASOS
4 RARE MI ANN ARBOR 42.217 83.733 FAA ASOS
5 KBAX MI BAD AXE 43.783 82.983 NF AWOS
6 KBTL MI BATTLE CREEK 42.317 85.233 FAA ASOS
7 KACB MI BELLAIRE 44.983 85.200 FAA AWOS
8 KSJX MI BEAVER ISLAND 45.700 85.567 NF AWOS
9 KBEH MI BENTON HARBOR 42.133 86.417 FAA ASOS
10 KRQL MI BIG RAPIDS 43.717 85.500 NF AWOS
1 l KCAD MI CADILLAC/WEXFORD 44.267 85.417 NF AWOS
12 KCVX MI CHARLEVOIX 45.300 85.267 NF AWOS
l3 KFPK MI CHARLOTTE 42 .567 84.817 NF AWOS
l4 KSLH MI CHEBOYGAN 45.650 84.517 NF AWOS
15 KCIU MI CHIPPEWA INT L 46.250 84.467 FAA AWOS
l6 KOEB MI COLDWATER 41.917 85.033 NF AWOS
17 KP59 MI COPPER HARBOR 47.467 87.883 NWS AWOS
l8 KDET MI DETROIT/CITY AIR 42.400 83.017 FAA ASOS
l9 KYIP MI DETROIT/WILLOW 42 .233 83.533 FAA ASOS
20 KDTW MI DETROIT/WAYNE 42.233 83.333 NWS ASOS
21 KONZ MI DETROIT/GROSSE ISLE 42.100 83.150 NF AWOS
22 KESC MI ESCANABA 45.750 87.017 FAA AWOS
23 KFNT M1 FLINT 42.967 83.750 NWS ASOS
24 KG LR MI GAYLORD 45.017 84.683 FAA ASOS
25 KGRR MI GRAND RAPIDS 42.883 85.517 NWS ASOS
26 KGOV MI GRAYLING AFB 44.683 84.733 DOD AWOS
27 KSAW MI GWINN/SAWYER AFB 46.350 87.400 FAA AWOS
28 KCMX MI HANCOCK 47.167 88.483 FAA ASOS
29 KMGN MI HARBOR SPRINGS 45.433 84.917 NF AWOS
30 KJYM MI HILLSDALE 41.917 84.583 NF AWOS
31 KBIV MI HOLLAND 42.750 86.100 FAA ASOS
32 KHTL MI HOUGHTON LAKE 44.350 84.667 NWS ASOS
33 KOZW MI HOWELL 42.617 83.967 NF AWOS
34 KIMT MI IRON MOUNTAIN 45.817 88.1 17 FAA ASOS
35 KIWD MI IRONWOOD 46.517 90. l 17 FAA AWOS
36 KJXN MI JACKSON/REYNOLDS 42.267 84.467 FAA ASOS
37 KAZO MI KALAMAZOO 42.233 85.550 FAA ASOS
38 KDUH MI LAMBERTVILLE 41 .733 83.650 NF AWOS
39 KLAN MI LANSING 42.783 84.583 NWS ASOS
40 KLDM MI LUDINGTON/MASON 43.967 86.400 NF AWOS
41 KMCD MI MACKINAC ISLAND 45.850 84.633 NF AWOS
42 KMBL MI MANISTEE 44.267 86.250 FAA AWOS
43 KISQ MI MANTSTIOLE 45.967 86.167 NF AWOS

 

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44 KRMY MI MARSHALL 42.233 84.950 NF AWOS
45 KTEW MI MASON 42.567 84.417 NF AWOS
46 KMNM MI MENOMINEE 45.117 87.617 FAA AWOS
47 KTTF MI MONROE 41.933 83.417 NF AWOS
48 KMOP MI MOUNT PLEASANT 43.617 84.733 NF AWOS
49 KMKG Ml MUSKEGON 43.167 86.233 NWS ASOS
50 KERY MI NEWBERRY 46.300 85.450 NF AWOS
51 KOSC Ml OSCODA/WURTSMITH 44.450 83 .400 NF AWOS
52 KPLN MI PELLSTON 45.567 84.800 FAA ASOS
53 KPTK MI PONTIAC 42.667 83.417 FAA ASOS
54 KP58 MI PORT HOPE 44.017 82.800 NWS AWOS
55 KPHN MI PORT HURON 42.917 82.517 NF AWOS
56 KMBS MI SAGINAW 43.533 84.083 FAA ASOS
57 KHYX MI SAGINAW/BROWNE 43.433 83.867 NF AWOS
58 KAN] MI SAULT STE MARIE 46.467 84.367 NWS ASOS
59 KMTC MI SELFRIDGE ANGB 42.617 82.817 DOD AWOS
60 KIRS MI STURGIS/KIRSCH 41.800 85.433 NF AWOS
61 KTVC MI TRAVERSE CITY 44.733 85.567 FAA ASOS
62 KCGX‘ IL CHICAGO/MEIGS 41.867 87.583 FAA ASOS
63 KPWK IL PALWAUKEE 42.1 17 87.900 FAA ASOS
64 KUGN IL WAUKEGAN 42.417 87.867 FAA ASOS
65 KGYY IN GARY REGIONAL 41.617 87.417 FAA AWOS
66 KGSH IN GOSHEN 41.533 85.783 FAA ASOS
67 KSBN IN SOUTH BEND 41.700 86.317 NWS ASOS
68 KDLH MN DULUTH 46.850 92.200 NWS ASOS
69 KEVM MN EVELETH MUNI 47.383 92.500 NF AWOS
70 KGNA MN GRAND MARAIS 47.750 90.350 NWS AWOS
71 KCKC MN GRAND MARAIS 47.833 90.367 NF AWOS
72 KINL MN INTERNTNL FALLS 48.567 93.400 NWS ASOS
73 KMZH MN MOOSE LAKE 46.417 92.800 NF AWOS
74 KTWM MN TWO HARBORS 47.033 91.750 NF AWOS
75 KBUF NY BUFFALO/CHEEKTOW 42.933 78.733 NWS ASOS
76 KDKK NY DUNKIRK 42.500 79.283 FAA ASOS
77 KFZY NY FULTON 43.350 76.383 FAA ASOS
78 KIAG NY NIAGARA FALLS 43.117 78.933 FAA ASOS
79 KROC NY ROCHESTER 43.1 17 77.683 NWS ASOS
80 KSYR NY SYRACUSE 43.1 17 76.100 NWS ASOS
81 KART NY WATERTOWN 43.983 76.033 FAA ASOS
82 KHZY OH ASHTAB ULA 41.783 80.700 FAA ASOS
83 KBKL OH CLEVELAND 41.533 81.667 FAA ASOS
84 KCLE OH CLEVELAND 41.417 81.850 NWS ASOS
85 KLPR OH LORAIN/ELYRIA 41.350 82.183 FAA ASOS
86 KTDZ OH TOLEDO 41 .567 83.483 FAA A808
87 KTOL OH TOLEDO 41.583 83.800 NWS ASOS
88 KER] PA ERIE 42.083 80.183 NWS ASOS
89 KASX WI ASHLAND 46.550 90.917 FAA ASOS
9O KGRB WI GREEN BAY 44.483 88.133 NWS ASOS
91 KDYT WI DULUTH SKY HARBOR 46.717 92.033 NF ASOS
92 KEGV WI EAGLE RIVER 45.917 89.267 NF AWOS
93 KENW W1 KENOSHA 42.600 87.933 FAA ASOS
94 KMTW WI MANITOWOC MUNI 44.117 87.667 FAA AWOS
95 KMKE WI MILWAUKEE 42.950 87.900 NWS ASOS
96 KRAC WI RACINE 42.767 87.817 FAA ASOS

 

 

 

 

 

 

 

 

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97 KSBM WI SHEBOYGAN 43.783 87.850 FAA ASOS
98 KSUE WI STURGEON BAY 44.850 87.417 FAA AWOS
99 KSUW WI SUPERIOR 46.400 92.050 NF AWOS
100 KETB WI WEST BEND 43.417 88.133 FAA AWOS
101 CWCI" ON CARIBOU ISLAND 47.317 85.817 MSC AWOS
102 CYLD ON CHAPLEAU ARPT 47.817 83.333 MSC CON
103 CWWX ON COVE ISLAND 45.317 81.717 MSC CON
104 CYEL ON ELLIOT LAKE 46.350 82.567 PVT PWS
105 CWGD ON GODERICH 43.767 81.7 1 7 MSC AWOS
106 CYZE ON GORE BAY AIRPORT 45.867 82.567 MSC AWOS
107 CYHM ON HAMILTON AIRPORT 43.167 79.933 MSC CON
108 CYXU ON LONDON AIRPORT 43.017 81.150 MSC AWOS
109 CWPS ON LONG POINT 42.567 80.033 MSC CON
110 CYZR ON SARNIA AIRPORT 43.000 82.317 MSC CON
111 CYAM ON SAULT STE MARIE 46.467 84.517 MSC CON
112 CYQT ON THUNDER BAY 48.367 89.317 MSC AWOS
1 l3 CYYZ ON TORONTO/PEARSON 43.667 79.617 MSC CON
114 CYKF ON WATERLOO WELL 43.467 80.367 MSC AWOS
115 CYQ ON WINDSOR AIRPORT 42.267 82.967 MSC CON

 

 

 

 

 

* The two grayed out stations (62 and 101) had insufﬁcient data and although processed, were not used in
this research.

** Agency: The entity, governmental or otherwise, responsible for the maintenance and/or dissemination
of information gathered by the meteorological sensors deployed at the corresponding station.

FAA — Federal Aviation Administration (United States)

NWS — National Weather Service (United States)

DOD - Department of Defense (United States)

NF — Non-Federal entity; state, local or airport authority (United States)

MSC — Meteorological Services Canada (Canada)

PVT — Privately owned and operated (US and Canada)

*** Type: The type of sensor array deployed at the corresponding station.
ASOS — Automated Surface Observing System
AWOS — Automated Weather Observing System. A number of AWOS conﬁgurations exist,
however, the wind sensor array in each performs to the same standards. Therefore no
differentiation is made here (US and Canada).
CON - Contracted weather provider, station information unavailable (Canada).
PWS — Private Weather Station, station information unavailable (Canada).

Information on United States stations is derived from the following Internet resources:
Federal Aviation Administration ASOS Web page
(http://www.faa.gov/ASOS)

National Weather Service ASOS Operations and Monitoring Center
(http://www2.aomc.nws.noaa.govl)

Information on Canadian stations is derived from the following Internet Resources:

US National Weather Service Aviation Digital Data Service
(http://adds.aviationweather. gov)

225

National Climate Data and Information Archive — Meteorological Services
Canada - Environment Canada
(http://www.climate.weatherofﬁce.ec.gc.ca)

Observational data (METARs) were collected for each of the stations listed in the table
by accessing the appropriate URL at US Weather, Inc. The URL for any given station

can be obtained by placing the station identiﬁer (e.g., KAPN) at the end of the following
URL string:

http://www.uswx.conr/us/stn/?code=c&n=1440&stn=

The preceding URL will retrieve the latest 1440 observations for that station in encoded
format.

226

Appendix B. Raw METAR Report File

This appendix contains a sample of encoded METAR data via the US. Weather,
Inc. Internet site. Data are from Lansing, MI (KLAN) covering the period 00552 —
1355Z on 04 February, 2003. Wind data are marked in bold, and some remarks (RMK)
not relevant to this research have been truncated for space.

METAR KLAN 0400552 13007KT 28M -RA BR OVCOO3 03/03 A2925 RMK A02 SLP911 P0004

SPECI KLAN 0401192 VRBOSKT 3/4SM R28UP6000FT -RA BR OVC003 03103 A2924 RMK

METAR KLAN 0401552 02004KT 1/28M R28L/2600V3500FT RA FG OVC003 03/02 A2921

METAR KLAN 0402552 14005KT 1/28M R28UP6000FT -DZ FG OVC003 04104 A2918 RMK

SPECI KLAN 0403382 16009KT 18M R28L/P6000FT -RA BR BKN003 BKN075 OVC100 06/06

MET AR KLAN 0403552 1801 OKT 48M BR BKN003 OVCO70 07/07 A2910 RMK A02

SPECI KLAN 0404322 21012KT 108M BKN006 OVC010 08/07 A2910 RMK A02 CIG 004V008

METAR KLAN 0404552 2301 SKT 38M vRA BR OVCOO4 07107 A2911 RMK A02 RAB42 SLP864

SPECI KLAN 0405162 22020626KT 1 3148M -RA BR BKN006 OVC010 06/06 A2913 RMK A02
PK WND 2302710504 CIG 003V008 P0000

METAR KLAN 0405552 23021 GZ9KT 108M BKN010 OVC016 03102 A2913 RMK A02 PK WND
2503210538 RAE25 CIG 008V012 SLP871 P0000 60019 T00330017 10078 20028 55015

MET AR KLAN 0406552 24019624KT 10SM OVC010 02/00 A2914 RMK A02 PK WND
2403310643 CIG 007V012 SLP875 T00170000

SPECI KLAN 0407192 25024G3ZKT 73M -SN FEW008 BKN015 OVC022 011M01 A2915 RMK
A02 PK WND 2503310707 RABO657E1OSNB10 P0000

MET AR KLAN 0407552 24016624KT 108M UP BKN013 OVC020 011M01 A2917 RMK A02 PK
WND 2503310707 RABO657E10UPBZ1E24BSOSNB1OE21 SLP883 P0000 T00061011

SPECI KLAN 0408132 25024G3OKT 108M OVC015 01/M01 A2918 RMK A02 PK WND
2503010810 UPEOO P0000

METAR KLAN 0408552 25024632KT 1 OSM BKN017 OVCOZ7 001M02 A2919 RMK A02 PK
WND 2503210849 SLP893 P0000 60000 T00001022 53020

MET AR KLAN 0409552 28020626KT 108M BKN020 OVC027 M01/M04 A2924 RMK A02 PK
WND 2703310927 SLP910 T10061039

SPECI KLAN 0410182 27026G3ZKT 108M -SN SCT022 BKN030 OVCOGS M021M05 A2926
RMK A02 PK WND 2803211017 UPB10E17SN809E1OB17 P0000

SPECI KLAN 0410282 27024633KT 7SM ~SN BKN022 BKN030 OVCO47 M021M06 A2927 RMK
A02 PK WND 2603311024 P0000

METAR KLAN 0410552 2602OG2SKT 1 3148M -SN BR BKN017 OVC023 M021M04 A2928 RMK
A02 PK WND 2603311024 SLP924 P0000 T10221039

SPECI KLAN 0411352 26018KT 33M -SN BKN017 OVC041 M02/M05 A2931 RMK A02 PK
WND 2602711103 P0000

METAR KLAN 0411552 27017GZ3KT 53M -SN BR OVCO17 M021M04 A2932 RMK A02 PK
WND 2602711 103 SLP938 P0000 60000 70023 T10221044 10033 21028 51044

METAR KLAN 0412552 27018624KT 98M -SN BKN021 OVCOGO M021M05 A2938 RMK A02
PK WND 2802811226 SLP954 P0000 T10171050

METAR KLAN 0413552 27018627KT 68M -SN BLSN BKN020 OVCO33 M01IM04 A2942 RMK
A02 PK WND 2703011343 SNE1257B17 SLP968 P0000 T10111044

227

Appendix C. Selected Statistics from ASOS Stations

Please note, this appendix consists entirely of information in tabular format, and is
therefore listed as “Appendix C” in the list of tables near the beginning of this document.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. Non-calm Mean Std. Dev. c . 2

5‘23”“ ”if” ("1:") ("1:") 5* “2.8;" ”ﬁg" ”338“
l KADG 11168 4.14 2.03 1.84 3.81 1.319 0.052
2 KAMN 10499 3.75 2.09 1.57 3.24 1.577 0.054
3 KAPN 10736 4.03 1.81 2.03 3.91 1.141 0.071
4 KARB 10732 4.21 2.08 1.77 3.88 1.358 0.045
5 KBAX 10683 4.00 2.26 1.51 3.50 1.474 0.067
6 KBTL 12297 4.52 2.13 2.07 4.45 1.062 0.079
7 KACB 9097 2.88 1.53 1.43 2.38 1.962 0.038
8 KSJX 11407 4.08 2.07 1.75 3.86 1.215 0.082
9 KBEH 11036 4.57 2.21 1.58 4.20 1.467 0.051
10 KRQB 9625 3.47 1.95 1.42 3.02 1.480 0.061
11 KCAD 11132 3.83 2.04 1.74 3.45 1.479 0.065
12 KCVX 12005 4.12 2.33 1.63 3.91 1.059 0.100
13 KFPK 10777 3.56 1.95 1.47 3.10 1.583 0.058
14 KSLH 10857 3.64 2.13 1.41 3.21 1.330 0.072
15 KCIU 10108 4.18 2.28 1.57 3.90 1.215 0.074
16 KOEB 10678 3.76 2.14 1.44 3.34 1.410 0.064
17 KPS9 10973 5.49 2.87 2.00 5.96 0.840 0.123
18 KDET 11309 4.22 1.90 2.16 4.26 1.012 0.092
19 KYIP 11325 4.65 2.27 1.83 4.82 0.921 0.094
20 KDTW 12096 4.53 2.26 1.85 4.76 0.880 0.103
21 KONZ 1 1 183 3.78 2.00 1 .64 3.60 1.154 0.084
22 KESC 11351 4.00 2.01 1.70 3.74 1.270 0.081
23 KFNT 11941 4.48 2.09 1.97 4.54 0.913 0.103
24 KGLR 9629 4.29 2.00 1.80 4.23 1.122 0.079
25 KGRR 12844 4.79 2.31 2.35 5.49 0.858 0.124
26 KGOV 9991 3.43 1.81 1.62 3.12 1.355 0.077
27 KSAW 10987 4.28 2.27 1.65 4.03 1.169 0.086
28 KCMX 11430 4.87 2.59 1.76 4.96 0.907 0.101
29 KMGN 10692 3.26 1.97 1.57 2.89 1.416 0.069
30 KJYM 10761 3.57 1.96 1.49 3.15 1.514 0.053
31 KBIV 12098 4.67 2.43 1.67 4.62 1.006 0.080
32 KHTL 11365 4.13 1.91 1.61 3.48 2.113 0.023
33 KOZW 10938 3.42 1.89 1.55 3.19 1.158 0.092
34 KIMT 10036 3.93 1.91 1.80 3.60 1.375 0.050
35 KIWD 10316 4.09 2.13 1.66 3.75 1.295 0.072
36 KJXN 10608 4.24 1.99 1.80 4.01 1.278 0.056
37 KAZO 11731 4.28 2.02 2.01 4.12 1.164 0.062
38 KDUH 10093 3.27 1.87 1.52 2.99 1.149 0.090
39 KLAN 12239 4.66 2.16 2.19 4.97 0.825 0.124
40 KLDM 11401 3.94 2.20 1.55 3.71 1.109 0.093
41 KMCD 9730 2.89 1.69 0.96 2.19 2.234 0.007
42 KMBL 11483 3.89 2.19 1.54 3.60 1.143 0.088
43 KISQ 11192 3.90 1.95 1.61 3.49 1.517 0.054
44 KRMY 9938 3.41 2.05 1.45 3.15 1.142 0.081
45 KTEW 10703 3.45 1.93 1.55 2.88 1.801 0.047

 

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46 KMNM 10467 3.68 1.94 1.72 3.34 1.406 0.070
47 KTFF 10470 3.77 2.24 1.48 3.27 1.430 0.072
48 KMOP 10442 3.36 1.89 1.53 3.12 1.185 0.083
49 KMKG 12665 4.90 2.34 2.06 4.71 1.150 0.077
50 KERY 11335 3.68 1.96 1.54 3.24 1.485 0.061
51 KOSC 11074 4.07 2.28 1.53 3.84 1.071 0.095
52 KPLN 9832 4.52 2.24 1.64 4.26 1.215 0.064
53 KPTK 11503 4.41 2.07 1.96 4.71 0.872 0.107
54 KP58 9993 4.58 2.07 2.17 5.12 0.857 0.114
55 KPHN 10079 3.34 1.86 1.41 2.86 1.535 0.057
56 KMBS 12070 4.70 2.30 2.12 5.03 0.882 0.117
57 KHYX 11498 4.13 2.35 1.58 3.95 0.985 0.099
58 KAN] 11306 3.87 1.90 1.91 3.87 1.029 0.079
59 KMTC 9547 3.93 1 .98 1 .78 3.82 1 .092 0.078
60 KIRS 10820 3.79 2.11 1.54 3.36 1.477 0.060
61 KTVC 9194 4.09 1.88 1.95 4.23 0.897 0.106
62 KCGX" 2298 6.41 2.45 3.33 7.45 1.134 0.073
63 KPWK 10806 4.42 1.99 2.18 4.40 1.012 0.095
64 KUGN 11106 4.33 2.05 1.92 4.62 0.894 0.105
65 KGYY 7907 5.12 1.28 4.89 5.92 1.603 0.021
66 KGSH 11399 4.72 2.31 1.71 4.54 1.120 0.078
67 KSBN 11769 4.67 2.21 1.94 4.76 0.941 0.102
68 KDLH 12441 4.84 2.22 2.03 5.34 0.798 0.131
69 KEVM 10156 3.40 1.91 1.39 2.89 1.562 0.063
70 KGNA 8961 4.12 2.23 1.91 4.38 0.921 0.094
71 KCKC 11289 3.76 2.15 1.55 3.30 1.445 0.052
72 KINL 11507 4.06 1.85 2.05 3.85 1.273 0.058
73 KMZH 9920 3.20 1.73 1.47 2.68 1.831 0.051
74 KTWM 10693 3.24 1.99 1.30 2.85 1.261 0.065
75 KBUF 12252 4.79 2.43 1.89 5.11 0.805 0.121
76 KDKK 11171 4.75 2.39 1.77 4.80 0.943 0.103
77 KFZY 9793 4.05 2.13 1.68 3.98 1.026 0.079
78 KIAG 11452 4.97 2.60 1.89 4.97 0.945 0.101
79 KROC 11843 4.59 2.39 1.83 4.78 0.872 0.109
80 KSYR 11317 4.29 2.26 1.73 4.37 0.895 0.095
81 KART 10404 4.21 2.22 1.67 4.15 1.006 0.083
82 KHZY 10130 4.11 2.00 1.66 4.07 1.086 0.065
83 KBKL 1 1990 5.29 2.64 1 .87 5.67 0.853 0.117
84 KCLE 12012 4.76 2.17 2.00 4.90 0.953 0.097
85 KLPR 1 1067 4.58 2.31 1.87 4.45 1.071 0.083
86 KTDZ 11452 4.56 2.31 1.74 4.52 1.010 0.078
87 KTOL 11132 4.58 2.32 1.88 4.46 1.054 0.087
88 KER] 11823 4.74 2.22 2.02 4.94 0.872 0.105
89 KASX 10674 3.99 1.99 1.72 3.63 1.386 0.050
90 KGRB 11787 4.48 2.12 1.86 4.41 0.961 0.085
91 KDYT 10865 4.38 2.77 1 .43 3.91 1.220 0.089
92 KEGV 9643 3.27 1 .79 1 .45 2.76 1.637 0.059
93 KENW 12145 4.73 2.29 1.94 4.68 0.949 0.095
94 KMTW 10640 4.21 2.22 1.62 3.93 1.266 0.068
95 KMKE 12432 4.89 2.20 2.14 4.91 1.008 0.093
96 KRAC 12047 4.60 2.05 2.10 4.67 0.943 0.094
97 KSBM 11222 4.52 2.15 1.85 4.61 0.902 0.099
98 KSUE 11296 4.56 2.25 1.88 4.16 1.427 0.069

 

 

 

 

 

 

 

 

 

229

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

99 KSUW 10455 3.65 2.16 1.48 3.06 1.656 0.053
100 KETB 9439 3.89 2.10 1.58 3.31 1.809 0.052
101 CWCI* 3953 7.39 3.77 1.85 7.48 0.925 0.109
102 CYLD 7901 3.35 1.82 1.26 2.56 2.391 0.018
103 CWWX 12038 5.60 3.24 1.74 5.81 0.867 0.119
104 CYEL 5660 3.17 1.70 1.38 2.48 2.255 0.024
105 CWGD 12291 4.91 2.71 1.45 5.30 0.878 0.106
106 CYZE 1 1690 4.50 2.46 1.53 3.80 1.702 0.044
107 CYHM 12422 4.39 2.60 1.53 4.04 1.139 ‘ 0.078
108 CYXU 12411 4.22 2.35 1.61 4.37 0.839 0.128
109 CWPS 7627 7.16 3.85 2.00 7.37 0.932 0.104
1 10 CYZR 5974 5.04 2.65 1.75 4.73 1.241 0.080
111 CYAM 11253 3.82 2.02 1.53 3.44 1.314 0.057
112 CﬂT 12075 3.64 2.22 1.75 3.54 1.050 0.086
113 CYYZ 12627 4.72 2.76 1.79 4.95 0.863 0.123
114 CYKF 11329 4.25 2.61 1.28 3.33 1.840 0.038
115 CYQG 12700 4.72 2.51 1.85 5.11 0.790 0.133

 

 

 

 

 

 

 

* Although statistics are displayed here, the two grayed out stations (62 and 101) were deemed to have
insufﬁcient data and were not used in this research.

" Non-calm Observations (n) are the number of observations at a station that exhibited a speed above
zero. MeanO is the mean wind speed (in m s—l) for all non-zero wind speed observations. Std. Dev. 0 is
the standard deviation (in m s-l) nor all non-zero wind speed observations. These measures are reported
here instead of measures based upon all valid observations (including calms) because at a number of
stations, the airport is closed overnight and observations are suspended. Because nighttime represents a
period where calm winds are common over the study region, 24-hour locations would experience a greater
inﬂuence of calm winds in their average and standard deviation values. Therefore, to facilitate an equitable

comparison of means and standard deviations, only those observations above zero meters per second
(converted from knots) are utilized in these summary statistics.

”‘ Shape (k) and scale (0) parameters of the Weibull distribution were calculated for each station from all

non-zero valid observations for the period of record (1 1/2002 - 6/2004) using the Ordinary Least Squares
technique described by Rohatgi and Nelson (1994).

”” Median A2 is the median value of the Anderson-Darling test statistic for small samples. This value
was obtained from 1000 trials where samples of 100 wind speed values extracted from a station’s full series
with replacement were tested to see if they were obtained from the Weibull distribution speciﬁed by k and
c (reported in the previous two columns). The median was used instead of the average, because the
Anderson-Darling statistic has no upper bounds, and outlier values could exert undue inﬂuence. The
average Observed Signiﬁcance Level (Avg. OSL) is the average level of statistical signiﬁcance from the
1000 trials. Where the OSL is smaller than a critical signiﬁcance (or alpha) level (often 0.05) the null
hypothesis that the data came from that particular Weibull distribution can be safely rejected (with 100 x
(l-alpha) percent conﬁdence). Unlike the test statistic itself, the OSL is bounded between 0 and 1 and thus
is not likely to be unduly inﬂuenced by extreme outlier values. Therefore the average, rather than the
median is shown. Based upon these OSL averages, wind speeds at locations in the study region can
generally be well represented by a Weibull distribution. Of the 115 stations, only 10 rejected the Weibull
distribution at 95% conﬁdence, and only 1 rejected it at 99% conﬁdence.

230

 

 

 

 

 

 

 

 

Appendix D. ASOS lO—m Wind Observations

The distribution of ASOS observed lO-m wind speeds at each station are
displayed as a schematic (box and whiskers type) plot. As discussed in Chapter 3, the

lower and upper bounds of the box

are the lower and upper quartiles respectively. The

median bisects the box, and the notch represents a robust estimate of the uncertainly
about the median value for comparison with the other plots. The so-called whiskers
extending from the box are the outer fences of the data, or 1.5 the interquartile range.
Outliers are shown as points on the plot beyond the outer fences. ASOS observed 10-m
wind directions are displayed as wind rose frequency histograms over the period of

record indicated in Chapter 3.

Please note that the information in

this appendix is in graphical tabular format, and is

therefore listed as “Appendix D” in both the list of tables and list of ﬁgures near the

beginning of this document.

 

 

 

 

 

 

 

 

 

 

 

 

Station Schematic (box) plots of wind speed distribution
1
g L i -------------------------- ‘woww at H 4» 4 at as
0 5 1 0 1 5

Wind speed (m s“)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 2 4 6 8 10 12 14
WlHd speed (m s")
l l 1 I 1 1 ‘1—1
E 1— | ————————————————————————————————— 4+ Mk 4 at it
1 J 1 l l L 1
0 2 4 6 8 10 12
Wind speed (m s")

 

231

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T— 1— —T ﬂ
grl ——————————————————————————— +¢MH+4+ﬁ4+srer
L _J% l
0 5 10 15
Wind speed (m s1)
17 T f j— 1 T I ‘1— T I
1
ﬁ L ‘ ————— 1 ———————————————— measure are» tars at
g _l l l l g _L l l 1
0 2 - 4 6 8 10 12 14 16 18
mm speed (m s“)
l 1— ﬁ T
ff. 1‘ ———————————————————————————— +mmieeseeu
l l _l l
0 5 10 15
Wind speed (m s")
r I I I I T
m — ——————————————————————————— 1*44arw4444—
‘5
l l 1 l l l
0 2 4 6 8 10
Wind speed (m s")
I T 1 1 T I 1
L ————————————————————————————— emu-rm
a I
U)
M
l J g 4 l l 1
0 2 4 6 8 10 12
Wind speed (m s")

 

 

 

 

 

 

 

 

232

 

 

 

 

 

 

 

 

I —————————————————————————— loauoweﬁwar 4444—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:r:
E
1 l l l l 1 l l l
0 2 4 6 8 10 12 14 16
Wand speed (m 5'1)
I I I I
m ‘—— ————————————————————— M Hm meat 4 4 d
g
l l l l
0 5 10 15
Wind speed (m 5")
I I I I l I I
a l ----------------------------- 1km 4H!- 4
U
M
l l 4 l 1 l i
O 2 4 6 8 10 12
Wind speed (m 5'1)
I I I I I T I I I I
§ l ——————————————————————— Wear it *4 4 air ” 4 ~
0
>4
1 L 1 l l l 1 l l 1
0 2 4 6 8 10 12 14 16 18
Mnd speed (m s")
I I I I I T I
————————————————————————————— WW4W4- *4: —
g
l l l L I l 1
0 2 4 6 8 10 12
Wind speed (m s")

 

233

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I
...I
(I)
>4
1 1 1 1
0 5 10 15
Wind speed (m s")
I l I
____________________________ I..........,... mm... _
8
>4
1 1 1 1
0 5 10 15
Wind speed (m s")
I I I I I I I
m ——————————————————————————— ”minim ~
LL]
0
>4
1 1 l L 1 1 l 1
0 2 4 6 8 10 12 14
Wind speed (m s")
I I I I F I V I I I
————————————————————————————— 14444444444 -
Os
8
1 l 1 1 l l 1 1 1 1
0 2 4 6 8 10 12 14 16 18
Wind speed (m s")
I I I I
I
E— ’ ————————————————————————— itemsmmeariris 444 a
u.)
3 I
1 l 1 1
0 5 1O 15
Wind speed (m s")

 

234

 

 

 

 

 

 

 

—————————————— «.044444444W444 444

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e: ” """"" ’ ‘
>1
>4
1 l 1 l l 1 1 1
0 2 4 6 8 10 12 16
Wind speed (m s")
I I I I I I I I
I
E—’ ———————————————————————— +*****¥W*¥H¥ 44 —
1 I l l l 1 I 1 l
0 2 4 6 8 10 12 16 18
mm speed (m s")
I r I
N — ————————————————————————— “44444444444444.1144” 444 4 —
z
0
>4
1 1 l 1
0 5 10 15
Wind speed (m s")
I I I I I I I
- ———————————————————————————— w 44444444 4 4 4 ~
0
1’3
1 1 J l l 1 1
0 2 6 8 10 12 14
Wind speed (m s")
I I I I I I I I I I
E _ ‘ ———————————————————————— 4444444444 4444444 4 4 4 ~
1 1 1 l l J l 1 1 1
0 2 4 6 8 10 12 14 16 18
Wind speed (m s")

 

235

 

 

 

 

 

—————————————————— Emma-444444444 -

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

n4
._1
0
>4
1 l 1 l
0 5 10 15
mm speed (m 5'1)
I I I I I I I I
g —————————————————————————————— lon44444444444 4 44 —
0
>4
1 1 l l 1 l 1 l
0 2 6 8 10 12 14 16
Wind speed (m 5‘1)
I I I I I I
> ————————————————————————————— 44444444444444 4 44 —
O
0
>4
1 I 1 1 J l 1
0 2 6 8 10 12
Wind speed (m s")
I I I
———————————————————————— W 4 444 444 -
. I
<
V)
>4
1 1 l 1
0 5 10 15
Wind speed (m s")
I T I I I I I I I I
E l —————————————————————————— «1.3-M4m4 444 4 4 —
0
>4
1 L 1 l l 1 1 l 1 1
0 2 4 6 8 10 12 14 16 18
Wind speed (m s")

 

236

 

 

KMGN

 

 

 

 

 

 

—

l

l l

———————————————————— «FWWM 414 4 ~

 

N.—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 4 6 8 10 12
Wind speed (m s")
I I I I I I I I
S l ————————————————————————— W H '4 -‘
1 l 1 1 1 l 1 1
0 2 4 6 8 10 12 14
Wind speed (m s“)
I I I I I I I I
------------------------ “41644444 444 4 4 4 —
Z l
1 l l l 1 1 l l I
0 2 6 8 10 12 14 16 18
Wind speed (m s")
I I I I
1:] l ————————————————————————— 'u-me 4 444444 4 4 —
I 1 1 1
0 5 10 15
Wind speed (m s“)
I I I I I I
3 ————————————————————————— WW“ W 4 —
N
0
>4
1 1 1 l l 1
0 2 4 6 8 1O 12
Wind speed (m s")

 

237

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\Mnd speed (m s")

I— ——————————————————— mm4444444 4 —
l I l 1
0 5 10 15
Wmd speed (m s")
I I I I I I I
g — l ———————————————————————————— WWW4 4 4
Q
l l 1 1 I l l l
0 2 6 8 10 12 14
Wind speed (m s")
I I I I I I I I I I
g — I —————————————————————— lam 44444 44444 4 4 ~
1 1 l 1 l 1 l 1 1 l
0 2 4 6 8 10 12 14 16 18
MM speed (m s")
I I I I I I I I
— ———————————————————————————— 4444 444 4 4 4 4
<3» I ,1...
l l 1 l 1 L 1 l
0 2 4 6 8 10 12 14
Wind speed (m s")
I I I I I I I
g — l ———————————————————————— «144-444444444444444444 4 4 -
1 J l l l I 1
0 2 4 6 8 10 12

 

238

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l 1 1 l 1 1 I 1 1 l
0 2 4 6 8 10 12 14 16 18
Wind speed (m s")
I I I I I I I I I
I
2 ' —————————————————————— {W 44444 4 444 4 4 —
S
1 1 1 1 1 l 1 1 1 l
0 2 4 6 8 10 12 14 16 18
Wind speed (m s")
I I I I I I I
Q l- ————— P4 4 4 -
E
1 , l 1 l 1 1 l
0 5 10 15 20 25 30 35
Wind speed (m s")
I I f I I I I I I
.—I ' ———————————————————————— W 4 4444 4 4 4
1 1 I l l 1 1 1 l
0 2 4 6 8 10 12 14 16
Wind speed (m s“)
I I I I I I T I
——————————————————————————— 4444444444444 4 44 4 4 —
O
V)
52
l 1 1 1 l 1 l 1
0 2 4 6 8 10 12 14

 

Wind speed (m s")

 

239

 

 

KRMY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 4 6 8 1o 12 14
Wind speed (m s")
I I I I I I
3 ———————————————————————————— «l44w4444m4444 44 -
I.”
I—
M
I 1 1 1 l 1
0 4 6 8 10 12
mm speed (m s")
I I I
g l ———————————————————————— {Mi 4 4 4 ~
1 1 l 1
0 5 10 15
Wmd speed (m s")
I I T I I I I I
LL. l ——————————————————————— W4 44 44 4 4 4 —
54
1 1 1 l 1 1 1 l
0 2 6 8 10 12 14 16
Wmd speed (m s")
I I I
0.. l —————————————————————— «Ivmm 444 44 4 4 ~
3
1 l 1
3 5 10 15
mm speed (m s")

 

240

 

 

 

 

 

 

————————————————————— +444 444444

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O 44 -
E
1 1 1
0 1o 15
Wind speed (m 5'1)
I I I I I I I I
__________________________ H * —.
E I W
1 1 l 1 I 1 I 1
0 2 4 6 8 10 12 14
Wind speed (m 5'1)
I I I I I I I
U ———————————————————————— W444» 444 4 —
(I)
O
54
1 l 1 1 I 1 I
0 2 8 10 12 14 16
Wind speed (m 5")
I I I I I I I I
Z ______________________ +4mm44444444 4 4 ~
5
I 1 1 I 1 I 1 1
O 2 8 10 12 14 16 18
VWndspeed(ms’1)
I I I I I I I I
E. J ----------------- +m444444m44 4 444 4 —
1 1 1 1 I 1 I 1 I
0 2 8 10 12 14 16 18 20
mm speed (m s")

 

241

 

 

KP58

 

 

 

—____.___._..‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 2 6 8 10 12 14 16
Wind speed (m 5'1)
I I I
g |———— ——————————————————— 4444444444444» 444 4 4 —
1 I 1 1
0 5 10 15
Wind speed (m s")
I I I I I I I I I
m l ------------------------- {44444444444444444 4—
E
I I 1 I 1 1 I I 1
0 2 6 8 10 12 14 16 18
Wlnd speed (m s")
I I I I I I I
X l —————————————————————————— {WW 44 44 -
E
1 1 1 1 I 1 1 1
0 2 6 8 10 12 14 16
Wind speed (m s")
I I I I I I I
I ___________________________ «’MW*#** 4 -
E
1 1 1 1 I 1 L
0 2 4 6 8 10 12

Wmd speed (m s")

 

242

 

 

KMTC

 

 

—————————————— «.44444444444444444 4 4 —

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 5 10 15
Wmd speed (m s")
I I I I I I I I
m —————————————————————— W44 4 4 44 4 —
a:
52
I I 1 I 1 I I I
0 2 6 8 10 12 14 16
W1ndspeed(ms'1)
I I I I
U ———————————————————————— {444141-444 444 4 4 4 444 4 —
>4
1 1 I 1
0 5 10 15
VWnd speed (m s")
I I T
g ‘ ——————————————————————————— +4444444 4444444 —
1 I 1 1
0 5 10 15
Viﬁnd speed (m s")
I I I I I I I I T
————————————————————— .44444444444444 *~
2 I
O
:3
>4
1 1 I 1 I I 1 I I
O 2 6 8 10 12 14 16 18
Wind speed (m s")

 

243

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g: * * ——————————————————— J 4 4 4 4 4 4 —
0
>4
I I I I I I I
0 2 4 6 8 10 12
Wmd speed (m s")
I I I I I I I I
3: ——————————————————————————— 411444444 44444 4 4 444 —
2”:
>4
I I I I I l I I
0 2 6 8 10 12 14 16
\Mnd speed (m s")
I I I I I I I I
Z —————————————————————————— 4’4114—111-44144441444 4 444 4 4
m
U)
>4
I I I I I I I I
0 2 6 8 10 12 14 16
\Mnd speed (m 5'1)
I I I I I I I I I I
:1: '-—' —————————————————————— M414444444M4 4444 4 —
§
1 I I I I I I I I I
0 2 4 6 8 10 12 14 16 18
Wmd speed (m s")
I I I I I T I I
E l____ ————————————————— 44444444444444 4 4 4 ~
I I I I I I I I
0 2 6 8 10 12 14 16
Wlnd speed (m s")

 

 

 

 

 

 

 

 

 

244

 

 

 

 

 

 

 

 

 

_—._———..

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\Mnd speed (m s")

<
Z
0
>4
I I I I I I I I
0 2 6 8 10 12 14 16
Wind speed (m s")
l I I I I I I
U ——————————————————————— WWWM44 4 —
>4
0
>4
I I I I I I I I
0 2 6 8 10 12 14 16
Wind speed (m s")
I I I I I I I
Z l ————————————————————————————— [4:044 4444444 4 4 4 —
>4
J I I I I I I
0 2 4 6 8 10 12 14
mm speed (m s")
l I I I I I I
I ’-——- ——————————————————————— +4444“ 444 4 4 ~
5
I I I I I I I
0 2 4 6 8 10 12
Wmd speed (m s")
I I I I
E I —————————————————————— WWHHW —
I—
>4
I I I I
0 5 10 15

 

245

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

S ———————————————————————— Eve-444 44444 4 4 4 4 -
I I I I I I I I I I
0 2 6 8 10 12 14 16 18 20
Wind speed (m s'1)
I I I I I I I I I I
é , ———————————————————————— 4444 4mm 4 4 4 -
I I I I I I I I I I
0 2 6 8 10 12 14 16 18 20
mm speed (m s")
l I I I I I I I I
>‘ ——————————————————— WMMM4 4 4 4 -
E
I I I I I I I I l
0 2 6 8 10 12 14 16 18
Wind speed (m 9'1)
I I I I I I I I I
—————————————————————————— <P~OWH¥4W4 #4444444 4* —
O
<
52
I I I I L I I I I
o 2 6 8 1O 12 14 16 18
mm speed (m s")
I I I I l I I I I
l —————————————————————— HWWiki-irikdkikik *4} -
U
8
I I I I I l I I I I
0 2 6 8 10 12 14 16 18 20
Wind speed (m 5'1)

 

 

 

 

 

 

 

 

 

 

 

 

246

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E
>4
I I I I I I I I I
0 2 4 6 8 10 12 14 16
Wind speed (m s")
I I I I l I I I I
I— ( ———————————————————————— 4.44m. 4444 4 4 4 4 -
I I I I I I I I I
0 2 4 6 8 10 12 14 16
mm speed (m s")
I I I I I I I I I
>. I ————————————————————— me 444 44 4 4 4 4 4
I I I I I I I I I
0 2 6 8 10 12 14 16 18
Wind speed (m 5")
I I I I I
a ———————————————————————— W 4 4’ 4 4- 43444 4 4 4 4
I I I I I
0 5 10 15 20
Wind speed (m s")
I I I I I I I I I
I
__________________________ 4444.444 444 4 4 44 4 4 —
B
o I
>4
1 I I I I I I I I
0 2 4 6 8 10 12 14 16
Wind speed (m 5'1)

 

 

247

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

n4
5
I I I I I I I I
0 2 4 6 8 10 12 14 16
IMnd speed (m s")
l I I I I I I I
E ———————————————————————— +9444H444444 444 44 4 4 ~
>4
I I I I I I I I I
0 2 6 8 10 12 14 16 18
Wind speed (m s")
I I l I I I I I I
,_} —————————————————————————— W44 4 4 4 4 4 4 -
O
I—
>4
I I I I I I L I I
0 2 4 6 8 10 12 14 16
Wind speed (m s")
I I I I I I I I I
————————————————————————————— 4 4444 444444 4 4 4 -
E
I I I I I I I I I
0 2 4 6 8 10 12 14 16
Wind speed (m s")
I I I I I I I I I
’ ———————————————————————— W44444a44 444 4 —
g
I I I I I I I I I
0 2 4 6 8 10 12 14 16
\MI'Id speed (m 5'1)

 

 

248

 

 

 

 

 

 

 

 

 

—————————————————— «imam 444 444 444 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0
>4
I I I I
0 5 10 15
Wind speed (m s")
I I I I I I I I
g: . ———————————————————————— «W 444 4 4444 4
I I I I I I I I I
0 2 6 8 10 12 14 16 18
Wind speed (m s")
I T I I I
> l—--« —————————————————————————— «*4444444444444 4 —
“a”
I I I I I I
0 2 4 6 8 10
IMnd speed (m s")
I I I I I I I I I
E ! —————————————————————————— +4444 4» 4 *- 4- 4- 4 4b 4* 4- —
I I I I I I I I I
0 2 4 6 8 10 12 14 16
Wind speed (m s")
I I l I
E l ———————————————————————————— W4 444 4 -
I I I I
0 5 10 15
Wind speed (m s")

 

249

 

 

 

 

 

KMKE

 

 

———————————————— 4414444444444 444

 

 

 

I I I I I I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 2 4 6 8 10 12 14 16
Wind speed (m s")
I I I I I I I I
0 ~ ' ——————————————————————————————— 444444444444 4 444 —
I I I I I I I I
0 2 4 6 8 10 12 14
Wind speed (m s")
I I I I I I I I I
2 — ————————————————————— Jr.” 444-44 4 4 4 4 4 —
m
(I)
>4
I I I I I I I I I
0 2 4 8 10 12 14 16 18
Wind speed (m s")
I I I
4 ————————————————————————————— 44444444444444 4 4 4
§
>4
1 I I
0 10 15
Wind speed (m s")
I I I I I I I
— I ——————————————————————————— 4444444444444444444444 —
5%
>4
I I I I I I I
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