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This is to certify that the
dissertation entitled
Evaluation of Ordinary Cokriging and Artificial
Neural Networks for Optimizing Rainfall Estimate
Using Stage HI NEXRAD Precipitation Surfaces
and Rain Gage Measurements

presented by

Chia-Yii Yu

has been accepted towards fulfillment
of the requirements for

Ph. D. degree in Biosystems Engineering

 

4447 Aux/Q

Ma jtfi' professor

Date l/MO3

MS U is an Affirmative Action/Equal Opportunity Institution 0- 12771

 

_UBRARY
Michigan State
University

 

 

 

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EVALUATION OF ORDINARY COKRIGING AND ARTIFICIAL NEURAL
NETWORKS FOR OPTIMIZING RAINFALL ESTIMATE USING STAGE III
NEXRAD PRECIPITATION SURFACES AND RAIN GAGE
MEASUREMENTS
By

Chia-Yii Yu

A DISSERTATION

Submitted to
Michigan State University
in partial fiilfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

2003

Cepyright by
CHIA-YII YU
2003

ABSTRACT
EVALUATION OF ORDINARY COKRIGING AND ARTIFICIAL NEURAL
NETWORKS FOR IMPROVING STAGE III N EXRAD PRECIPITATION
SURFACES USING RAIN GAGE MEASUREMENTS
By
Chia-Yii Yu

The deployment of the National Weather Service Weather Surveillance Radar-
19S8 Doppler (W SR—88D) has provided an improved tool for monitoring real-time areal
mean. precipitation spatial distribution (4-km resolution) for hydrometeorological
‘modeling. Unfortunately, a number of factors introduce discrepancies between radar
precipitation estimates and actual precipitation at the Earth‘s surface. In this project, a
pilot snidy was performed by making two types of statistical analyses to describe the
correlation between SEMCOG rain gage values and stage III NEXRAD: (1) the
agreement of occurrence of precipitation between the two sources and the magnitude of
error in precipitation when there is disagreement of occurrence, and (2) the error in
magnitude between rain gage measurement and NEXRAD estimate when they both
register a precipitation amount. These analyses provided a basis of justification for using
models to improve the correlation between the two sources of precipitation measurements.
Twenty-two. daily precipitation events (partial and full rainfall coverage) during the
months of May through September in 1999 and 2000 were selected to estimate the
precipitation using Stage III NEXRAD data and SEMCOG rain gage measurements.
Artificial neural network and ordinary cokriging models were evaluated by the
performances of improved precipitation estimates. The best performing model, the ANN

model, significantly improved the accuracy of the radar-derived precipitation surfaces

(Average correlation coefficient was improved from 0.61 to 0.76).

The ANN model was applied to improve the precipitation estimate of the entire
state of Michigan. The 16-km NEXRAD grid size was used for improving the Stage III
NEXRAD data for the entire state of Michigan. Six daily precipitation events (partial and
firll rainfall coverage) were selected to optimally estimate the precipitation by combining
Stage III NEXRAD data with forty-two National Weather Service Fisher & Porter rain
gages distributed around the Michigan. The results showed that the Stage III NEXRAD
precipitation surfaces were fairly improved (Average correlation coefficient was

improved from 0.72 to 0.87). .

ACKNOWLEDGEMENTS

I like to express my sincere gratitude to my major professor, Dr. William J.
Northcott for his never-ending support and guidance of this study.

My sincere thanks to my committee members, Dr. J. Andresen, Dr. J. Bartholic,
Dr. F. Numberger, and B. Pijanowski for their insight, guidance, and support in this study.

I would like thank the faculty and staff of the Department of Agricultural
Engineering for providing a challenging learning environment. Special thanks to
Departmental Chairman, Dr. Ajit K. Srivastava, for his support and encouragement.

Finally, a very special thank you to my parents, parents-in-law, and wife Tsui-

Ting Yang, for their never-ending love, support, encouragement, and guidance.

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

LIST OF TABLES

LIST OF FIGURES
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 LITERATURE REVIEW 4
2.1. Rain Gage Measurement and Spatial Estimation 4
2.2. NEXRAD Measurement and Rainfall Estimation 5
g 2.3. NEXRAD System and Data 10
2.3.1. NEXRAD System 10
2.3.2. Z-R Relationship and Accuracy of Rainfall Estimations 1 1
2.3.3. NEXRAD Products 11
2.4. Ordinary Cokriging (0C) 14

 

2.4.1. Random Function Model and Second-Order Stationarity ------14

2.4.2. Semivariogram Cloud, Semivariogram, and Cross

 

Semivariogram 15

2.4.3. Model Fitting of Semivariogram Using Weighted-Least-Squares

 

 

 

 

 

Method 18

2.5. Artificial Neural Networks (ANNs) 20
CHAPTER 3 STUDY AREA 24
3.1. SEMCOG Rain Gage Network 24

3.2. National Weather Service Rain Gage Network in Michigan 27
CHAPTER 4 METHODOLOGIES 29

 

Pilot Study: Statistical Analysis and Model Development in the SEMCOG Rain

vi

Gage Network 29

 

 

 

4.1. Precipitation Data Sources and Their Measurement Devices —- 29
4.2. Software 30
4.2.1. ArcView GIS Software and Its Extension Programs —-----30
4.2.2. MATLAB Software with Neural Network Toolbox -—-----32
4.3. Methods 33

 

4.3.1. Data Managements for SEMCOG Rain Gage Measurements

and NEXRAD Stage III Rainfall Estimates 33

 

4.3.2. Statistical Analysis of SEMCOG Rain Gage Measurements and

 

 

 

NEXRAD Stage III Rainfall Estimates 35

4.3.3. Model Justification 37
Ordinary Cokriging (OC) Model 38
Artificial Neural Network (ANN) Model 38

 

Selection and Classification of Examined SEMCOG

Precipitation Events 39

 

Assignments of Model Processing Data Sets and Model

 

Efficiency Criteria 39
Adjusting NEXRAD Precipitation Surface Using Ordinary

Cokriging and ANNs 44

 

Adjusting NEXRAD Precipitation Sud'ace

 

Using Ordinary Cokriging 44

Process Procedures of Ordinary Cokriging 46

 

Adjusting NEXRAD Precipitation Surface Using AMVs47

vii

 

 

 

 

 

 

 

 

Process Procedures of ANN Model 56

Application of the Modeling Methods in Michigan
4.4. Precipitation Data Sources and Their Measurement Devices 60
4.5. Methods 60

CHAPTER 5 RESULTS AND DISCUSSION

Pilot Study: Modeling SEMCOG, Michigan 63
i 5.1 Results of Statistical Analyses for Pilot Study 63
I 5.2. Results of Pilot Study: Modeling SEMCOG, Michigan 68
5.2.1. Results of Precipitation Event 05/06/1999 69
InitiaILSynthetic Statistical Analysis 69
Results of OC Model D 78
Results of ANN Model 85

 

Performance Evaluations of Both OC and ANN Models ---87

 

 

 

5.2.2. Results of Precipitation Event 08/06/2000 89
Initial Synthetic Statistical Analysis 89
Results of OC Model 91
Results of ANN Model 97

 

Performance Evaluations of Both OC and ANN Model -—- 98

 

5.3. Discussion of Modeling SEMCOG, Michigan

Results of Modeling State of Michigan

 

 

5.4. Results of Selecting the NEXRAD Grid Size

5.5. Results and Discussion of Precipitation Event 07/01/1999

 

 

5.5.1. Initial Synthetic Statistical Analysis

viii

101

105

105

106

106

 

5.5.2. Results of After Processing ANN Model 11 l

 

 

CHAPTER 6 SUMMARY AND CONCLUSIONS 1 17
CHAPTER 7 RECOMMENDATIONS AND FUTURE STUDY 118
REFERENCES 119

 

 

APPENDICES 123

ix

LIST OF TABLES

Table 4.1 Possible Combinations of Precipitation Occurrences between SEMCOG Rain

 

Gages and NEXRAD Radar Estimates 37
Table 5.1 Hourly Precipitation Distribution Conditions from May through September -63
Table 5.2 Hourly error between NEXRAD and Gage Values in Condition 1 ---------64
Table 5.3 Hourly Errors between NEXRAD and Gage Values in Conditions 2 and 3 --66

Table 5.4 Results of the Examined SEMCOG Slight Precipitation Events (Full Coverage)

 

 

 

 

70

Table 5.5 Results of the Examined SEMCOG Slight Precipitation Events (Partial
. Coverage) 72
Table 5.6 Results of the Examined SEMCOG Medium Precipitation Events --73
Table 5.7 Results of the Examined SEMCOG Heavy Precipitation Events 75

Table 5.8 Results of the Examined Michigan Precipitation Events 107

 

LIST OF FIGURES

 

 

Figure 2.1 NEXRAD radar sites distributed in the United States 6
Figure 2.2 Typical Structure of A Multi-Layer Feedforward Neural Network - ------ 22
Figure 3.1 SEMCOG Rain Gage Network 25
Figure 3.2 SEMCOG Rain Gage Network and the Covering NEXRAD Stations --—---26

Ifigure 3.3 Michigan National Weather Service Rain gage Network and Covering 9

 

NEXRAD Radar Stations 28

Figure 4.1 NEXRAD Stage III Data of Midwestern Area (Projected by Michigan Georef

 

System) 3 1
Figure 4.2 SEMCOG NEXRAD Grid Centroids of Calibration and Validation Used

in ANN Model 42

 

Figure 4.3 Feedforward Neural Network with Inputs (Coordinate X and Y) and Output

(R'OL Y» 59
Figure 5.1 Monthly mean bias between hourly NEXRAD and rain gage network in 1999

 

55

 

Figure 5.2 Monthly mean bias between hourly NEXRAD and rain gage network in 2000

55

 

Figure 5.3 Frequency distribution of condition 2 bias averaged across SEMCOG gages

for 1999 67

 

Figure 5.4 Frequency distribution of condition 2 bias averaged across SEMCOG gages

for 2000 57

 

Figure 5.5 A Bivariate Scatter Diagram for Both Raw Stage III NEXRAD Data and

SEMCOG Rain Gage Measurements (Daily precipitation event occurred on

xi

 

05/06/1999). Light Precipitation Event 77
Figure 5.6 Daily Raw Stage III NEXRAD Precipitation Surface (Daily precipitation

event occurred on 05/06/1999). Light Precipitation Event 79

 

Figure 5.7 Isotropic Variogram of Stage HI NEXRAD Data (Daily precipitation event

occurred on 05/06/1999). Light Precipitation Event 81

 

Figure 5.8 Isotropic Variogram of SEMCOG Rain Gage Measurements (Daily
precipitation event occurred on 05/06/1999). Light Precipitation Event ------ 82

Figure 5.9 Isotropic Cross Variogram of SEMCOG rain gage measurements (Daily
precipitation event occurred on 05/06/1999). Light Precipitation Event ------ 83

Figure 5.10 Ordinary Cokriging-Adjusted Stage III NEXRAD Precipitation Surface

(Daily precipitation event occurred on 05/06/1999). Light Precipitation

 

Event 84
Figure 5.11 ANN-Adjusted Stage III NEXRAD Precipitation Surface. (Daily
precipitation event occurred on 05/06/1999). Light Precipitation Event ----- 86
Figure 5.12 Performance of OC- and ANN-Adjusted Stage 1]] NEXRAD Data (Daily
precipitation event occurred on 05/06/1999). Light Precipitation Event ----- 88
Figure 5.13 A Bivariate Scatter Diagram for Both Raw Stage III NEXRAD Data and
SEMCOG Rain Gage Measurements (Daily precipitation event occurred on

08/06/2000).Heavy Precipitation Event 90

 

Figure 5.14 Daily Raw Stage III NEXRAD Precipitation Surface (Daily precipitation

event occurred on 08/06/2000).Heavy Precipitation Event 92

 

Figure 5.15 Isotropic Variogram of Stage III NEXRAD Data (Daily precipitation event

 

occurred on 08/06/2000). Heavy Precipitation Event 94

xii

Figure 5.16 Isotropic Variogram of SEMCOG Rain Gage Measurements (Daily
precipitation event occurred on 08/06/2000). Heavy Precipitation Event----95

Figure 5.17 Isotropic Cross Variogram of SEMCOG rain gage measurements (Daily
precipitation event occurred on 08/06/2000).Heavy Precipitation Event ----96

Figure 5.18 Ordinary Cokriging-Adjusted Stage III NEXRAD Precipitation Surface.
(Daily precipitation event occurred on 08/06/2000). Heavy Precipitation

Event 99

 

Figure 5.19 ANN-Adjusted Stage III NEXRAD Precipitation Surface. (Daily
precipitation event occurred on 08/06/2000). Heavy Precipitation Event-- 100

Figure 5.20 Performance of OC- and ANN -Adjusted Stage III NEXRAD Data (Daily
precipitation event occurred on 08/06/2000).Heavy Precipitation Event -— 102

Figure 5.21 A Bivariate Scatter Diagram for Both Raw Stage III NEXRAD Data and

Michigan NWS Rain Gage Measurements (Daily precipitation event

 

occurred on 07/01/1999). Heavy Precipitation Event 109

Figure 5.22 Daily Raw Stage III NEXRAD Precipitation Surface (Daily precipitation

 

event occurred on 07/01/1999). Heavy Precipitation Event 110
Figure 5.23 Daily Rescaled 16-km Stage III NEXRAD Precipitation Surface (Daily

precipitation event occurred on 07/01/1999). Heavy Precipitation Event-- 112
Figure 5.24 Daily ANN -Adjusted 16-km Stage III NEXRAD Precipitation Surface

(Daily precipitation event occurred on 07/01/ 1999). Heavy Precipitation

Event 1 14

 

Figure 5.25 Transformed Daily 4-km Stage III NEXRAD Precipitation Surface from

ANN-Adjusted 16-km Stage III NEXRAD Precipitation Surface (Daily

xiii

precipitation event occurred on 07/01/1999). Heavy Precipitation Even -- 115
Figure 5.26 Performance of ANN -Adjusted Stage HI NEXRAD Data. (Daily

precipitation event occurred on 07/01/1999). Heavy Precipitation Event-- 116

xiv

Chapter 1 INTRODUCTION

Being able to accurately estimate the distribution of rainfall over a region is an
important aspect of water resources management. Accurate estimation of rainfall over
large areas allows for prudent management decisions in numerous areas such as
agricultural production and irrigation timing, flood forecasting, hydrologic and water
quality modeling, and groundwater recharge. Historically, accurate spatial rainfall
estimation attempts have used dense networks of rain gages, incorporating spatial
interpolation using such methods as Theissen Polygons and Inverse Distance Weighting
(IDW) to estimate rainfall amounts between point gage locations (ASCE, 1996).
Currently, the National Weather Service (NW S) operates over 8,000 daily non-recording
rain gages, but with spatial distances between gages of greater than lOOkm, it is possible
that these networks do not capture the spatial variability of rainfall events (Groisman and
Legates, 1994). More recently, Next Generation Radar (NEXRAD), a weather radar
system with nationwide coverage, has become a promising new tool for high spatial and
temporal resohltion estimation of rainfall.

Weather radar works on the premise that reflected emitted radar energy that is
reflected by precipitation can be converted to precipitation rate by means of an empirical
relationship (NCAA, 1991). The NEXRAD system consists of 161 individual radar
stations within the United States and provides overlapping coverage of radar reflectivity. 4
Since its deployment in 1995, NEXRAD has become a useful tool for tracking severe
weather patterns in real time. Raw Stage I NEXRAD data allows 5-6 minute sweeps of an
area with a radius of 230 km and can provide very high-resolution (~1km) estimates of

rainfall intensity.th its Stage III data, NEXRAD ofl‘ers hourly estimation of rainfall

over large areas with a 4 km resolution. While the NEXRAD system provides real-time,
high-resolution relative rainfall intensity; the system is not without its faults. It has been
shown that, in general, NEXRAD underestimates rainfall amounts when compared to
ground gage data. There are several explanations for these underestimations and
discrepancies that include rainfall missed between radar sweeps, systematic and random
errors, and inaccuracy in the empirical methods to convert fiom radar reflectivity to
rainfall. These errors and discrepancies can lead to as much as 100% differences between
radar rainfall estimation and ground gage values (Matsoukas et al., 1999).

Because there is promise in developing NEXRAD as a tool for real-time spatial
rainfall estimate, there have been several research attempts to develop a method for
“correcting” the NEXRAD products to provide a more accurate rainfall surface. Much of
this research has focused on adjusting the NEXRAD rainfall surface in smaller, local
areas based on actual values from ground-based rain gage networks (Eddy, 1979;
Brandes, 1975). A number of techniques have been used to adjust the NEXRAD surface.
These techniques have incorporated simple methods such as linear adjustment based on
Thiessen Polygons (Johnson et al., 1999), to more complex methods such as geostatistical
methods that incorporate kriging (Seo et al., 1990a and 1990b; Seo et al., 1996) and
ordinary cokriging (Seo et al., 1990a and 1990b; Krajewski, 1987), and more recently,
artificial neural networks (ANN s) (Matsoukas et al., 1999). These have provided with
varying degrees of success. This method holds promise for becoming a powerful tool in a
wide range of hydrologic applications, especially in the area of quantifying regional
water balances. The overall goal of this study is to improve the accuracy of NEXRAD

rainfall Stu-faces across the state of Michigan using ground gages and computer modeling

techniques. Specifically, the objectives are to:

1. Perform a statistical analysis on hourly Stage III NEXRAD data and hourly rain
gage data from rain gages in the Southeast Michigan Council of Government
(SEMCOG) rain gage network.

2. Perform a pilot study using ordinary cokriging (OC) and artificial neural network
(ANN) models to calibrate and validate daily NEXRAD Stage HI rainfall surface
in the SEMCOG rain gage network.

3. Apply an ANN-based model to adjust Stage HI NEXRAD data across the State of

Michigan using National Weather Service gages and evaluate its performance.

Chapter 2 LITERATURE REVIEW
2.1. Rain Gage Measurement and Spatial Estimation

Rain gage measurement dates back at least to the 4'” century BC, when a
network of rain gages was established in India (Biswas, 1967). Rain gages were used in
Palestine in the 1‘ century BC, in China in the 13m century AD., and in Korea in the
15th century AD. (Biswas, 1970). The Chinese and Korean gages were cylindrical or
barrel-shaped and had approximately the same characteristics and accuracy of many of
the rain gages in widespread use today. Rain gages were first used in Europe in the 17“1
century. The 18" century was marked by the development and use of numerous designs
of gages around the world. The measurement of the “exact quantity” of rainfall that falls
upon a hOrizontal surface has been the subject of a large number of investigations in the
past two hundred years. For years, rain gages have become more and more
technologically advanced and are currently characterized by automated features and high
temporal resolution (ASCE, 1996). However, gages producing real-time ground point
measurements are not sufficiently dense to represent a larger area.

The United States meteorological network consists of about 8,000 daily rainfall
non-recording stations (Groisman and Legates, 1994). Distances between rain gage
stations often exceed lOOkm providing inadequate spatial rainfall sampling, i.e. the
variance of the sample long-term mean area rainfall and mean area rainfall of a storm
event becomes large (Rodriguez-Iturbe and Mejia, 1974). Therefore, the variance, a
filnction of correlation in time, space, length of operation of the network and the
geometry of the gauging array, is an important index for the framework design of the rain

gage network. In addition, rain gage measurement errors produced by wind/turbulent

losses, gage wetting, splash into and out of the gage, condensation, evaporation, and
measurement correction compound the estimation problem (ASCE, I996; Groisman and
Legates, 1994). However, compared to the errors of the radar-derived rainfall surface, the
errors of the rain gage measurement are small and thus rain gage measurements can be
regarded as the true rainfall values.

Because of the drawbacks of point measurements in rain gage networks, many
methods have been used to interpolate or extrapolate point rainfall values. These methods
include the use of Thiessen polygons (Croley and Hartmann, 1985; Shih and Hamrick,
1975; Diskin, 1969), isohyetal (France, 1985; Hamlin, 1983; Linsley et al., 1949), linear
and multi regression (Salas, 1993), polynomial interpolation (Tabios and Salas, 1985;
Chidley and Keys, 1975; Unwin, 1969), objective analysis, and kriging methods (Seo et
al., 1990, Yates and Warrick, 1986a and 1986b; Yates, 1986; Dingrnan et al., 1988;
Tabios and Salas, 1985; Creutin and Obled, 1982; Chua and Bras, 1982; Montmollin et
al., 1980). More recently, volumetric estimation of rainfall using radar technology has
shown promise for real-time estimation of rainfall with high spatial resolution.

2.2. NEXRAD Measurement and Rainfall Estimation

Weather radar has been used for measuring rainfall values since the 1950’s. In the
19805, the US. National Weather Service (NWS) began installing the Weather
Surveillance Radar-1988 Doppler (W SR-88D), Next Generation Weather Radar
(NEXRAD) and finished the deployment of the NEXRAD stations in 1995. 161
NEXRAD stations are distributed throughout the US. and selected overseas locations to
form a meteorological network for rainfall measurements (Figure 2.1). The NEXRAD

network is a joint effort of the US. Departments of Commerce (DOC), Defense (DOD),

 

Figure 2.1. NEXRAD radar sites distributed in the United States.

and Transportation (DOT). The controlling agencies are the National Weather Service
(NWS), Air Weather Service (AWS) and Federal Aviation Administration (FAA),
respectively (The NEXRAD Joint System Program Ofiice, 1986a).

The primary advantage of radar as a rainfall measurement system is that it can
estimate rainfall at high spatial (in NEXRAD volumetric-averaged measurement up to
230 km from the radar site) and temporal (real-time) resolution (ASCE, 1996). The
rainfall locations, boundaries, and intensities shown as the radar echoes, and their
changes with time, may be accurately determined either visually or digitally.
Unfortunately, a number of errors, such as systematic and random errors of the radar and
Z-R relationship conversion error, may introduce over 100% discrepancies between
NEXRAD rainfall estimate and actual rainfall at the Earth's surface (Matsoukas et al.,
1999; Smith et al., 1996). Although the NEXRAD network provides detailed rainfall
information that is readily available to the user, these data are not being used to the filllest
extent. Confusion and misunderstanding about the ability of the NEXRAD to measure
rainfall and about the factors that contribute to errors lead to this underutilization of the
data.

Since 1970’s, there has been an increasing amount of research relating to the topic
of radar and rain gage data validations and cOmparisons. The methods used in these
studies include: objective analysis (Eddy, 1979; Brandes, 1975), kriging (Krajewski, i
1987; Seo et al., 1990a and 1990b; Seo, 1998a and 1998b; Matsoukas et al., 1999), and
artificial neural networks (ANNs), (Matsoukas et al., 1999).

Eddy (1979) used an objective analysis model to make maximum likelihood

estimates of convective storm-total rainfalls in Montana by using the High Plains

Cooperative Program (HIPLEX) radar reflectivity data combined with the optimal
deployment of the rain gage network Brandes (1975) used an objective analysis scheme
to calibrate the radar rainfall surface based on rain gage observations by determining
multiplicative calibration factors at each rain gage site. Rainfall estimates are improved
when rain gage observations are used to calibrate quantitative radar, as well as, to
estimate rainfall in areas without radar data. Estimated areal rainfall depth errors for nine
rainfalls over a 3,000 1cm2 watershed averaged 13% and 14% (1.5 and 1.8mm) when the
radar was calibrated by rain gage networks having densities of one gage per 900 and
1,600 krnz, respectively Areal precipitation estimates derived from rainfalls observed at
the gages alone produced errors of 21% and 24% (2.5 and 3.0mm). Adjusting the radar
data by a single calibration factor resulted in an error reduction of 18%. Radar data added
to gage observations also increased the variance in point rainfall estimates above that
from gages alone, from 53% to 77% and 46% to 72% for the above gage densities.
However, the objective analysis methods failed to account for the spatial autocorrelation
between rain gages and radar directly.

Krajewski (1987) developed an ordinary cokriging procedure to optimally
combine 245 daily rain gage observations with radar data. The covariance matrices
required to perform ordinary cokriging are computed from single realization data, using
the ergodicity assumption. Because the ground truth and the errors of the radar data are
unknown, parameterization of the covariance between radar and the true rainfall is
required. This procedure removes the bias in radar very well. Seo et al. (1990a and 1990b)
evaluated the performances of ordinary, universal, and disjunctive cokriging by

combining rain gage measurements and radar rainfall data. Two simulation experiments

were used to evaluate these three models. The first experiment assumed that high quality
radar rainfall surfaces to be ground truth rainfall fields and the second experiment used a
stochastic, space-time rainfall model to generate the assumed ground truth rainfall
surfaces of various characteristics.

Matsoukas et al. (1999) developed an ANN approach that combined radar-
measured a rainfall surface with rain gage measurements and evaluated the performance
of the ANN method by validation and comparison to ordinary cokriging method. Four
hourly storm events (two events from the summer and two events from the winter seasons)
from Tulsa, Oklahoma were examined. Forty-three rain gage measurements and 4km
resolution radar data were used. Three types of sample-splitting (80%-20%, 50%-50%,
and 20%-80%) were used for training the neural network model and to determine the
semivariograms in ordinary cokriging model, and validations of both models. The
comparison of rainfall estimation using ordinary cokriging and ANN models suggests
that the performance of the ANN model provides better rainfall estimations than that of
the ordinary cokriging model for Oklahoma.

Because of the great variability in the intensity and structure of rainfall events,
more radar-gage validations and comparisons should be made in order to cover a larger
number of storms for different geographical locations. It is important to have an
understanding of the physical factors impacting the NEXRAD rainfall estimate accuracy
to make the best possible estimate of surface rainfall from the NEXRAD and rain gage

data available for a particular event.

2.3. NEXRAD System and Data
2.3.1. NEXRAD System

The NEXRAD system consists of three functional components: Radar Data
Acquisition (RDA), the Radar Product Generator (RPG), and the Principal User
Processor (PUP) (Federal Coordinator for Meteorological Services and Supporting
Research, 1990; The NEXRAD Joint System Program Office, 1984). To adequately
sample the rainfall the RDA uses four types of Volume Coverage Patterns (VCPs): VCP
11, VCP 21, VCP 31, and VCP 32 (The NEXRAD Joint System Program Office, 1990;
The NEXRAD Joint System Program Office, 1985; The NEXRAD Joint System Program
Office, 1984). The VCP is the series of 360-degree sweeps of the antenna at selected
elevation angles completed in a specified period of time with various microwave
wavelengths. The RDA emits a beam of energy, a microwave signal, at an object and
measures the reflected energy. When the energy strikes an object, the energy is scattered
in all directions. A small fraction of that scattered energy is directed back toward the
NEXRAD. This reflected energy is received by the RDA during its signal-receiving
period and contains: reflectivity of the returned pulse, radial velocity, and spectrum width
of the reflected signal.

The function of the RPG is to use computer algorithms to convert the reflectivity
of the returned pulse fi'om the RDA into various meteorological and hydrological data.
The computer algorithms of the RPG convert the reflectivity, (Z, unit: dBZ), into rainfall
rate, (R, unit: mm/hr) by a Z-R relationship formula, Z = aR", where a and b are
coefficients. The NEXRAD products are stored on a Write Once Read Many (WORM)

optical disk that is sent to the National Climatic Data Center for archive and

10

dissemination. The main function of the PUP is to display the NEXRAD products, such
as reflectivity, mean radial velocity, echo-top height, and precipitation accumulation
amounts, generated at the RPG by the advanced microcomputers and peripheral systems.
2.3.2. Z-R Relationship and Accuracy of Rainfall Estimations

The Z-R relationship linking rainfall rate to radar reflectivity is complex,
nonlinear, and inexact. Rainfall rates are proportional to the volume of the raindrops, but
also to raindrop surface area. Therefore, a raindrop size distribution must be converted
fi’om reflectivity to rainfall rate, is. the reflectivity is a filnction of the numbers and sizes
of the raindrops, snow, ice, and hail; reflectivity is converted into a rainfall rate by the Z-
R relationship using the formula: Z = aR", where a and b are coefficients.

A significant problem is that the Z-R relationship values vary as a function of
storm types because of the differences in raindrop size distributions (Joss and Lee, 1995).
For convective type storms, Z = 300R” works very well for deep convective storms but
severely underestimates other types of storms. Z = 250Rl‘2 is used for hurricanes, tropical
storms, and small scale deep-saturated storms. z = 200R“ is used for the stratiform type
of storms; for winter stratiform type of storm at sites east, Z = 130R”, and sites west, Z =
75R2'0 of the continental divide. In addition, there are additional factors complicating the
Z-R relationship including: beam attenuation, range effects, temperature and vapor
gradients, hail and vertical air motions, accretion and evaporation (Wilson and Brandes,
1979; Lhermitte and Gilet, 1975).
2.3.3. NEXRAD Products

The NWS has developed a set of post processing algorithms for NEXRAD

rainfall estimates that are referred to as Stage I, II, and III rainfall estimates. The Stage I

ll

rainfall estimate transforms the raw reflectivity data from the RDA into the rainfall rate
by a reflectivity and rainfall rate relationship, i.e. a Z-R relationship. The Stage II rainfall
estimate is processed by utilizing “ground truth” rain gage measurement to remove a
mean field bias in the radar rainfall estimates. Since 1992, the NWS River Forecast
Centers (RFCs) have been using a prototype Stage II algorithm to combine NEXRAD
hourly Stage I rainfall estimates with the adjustment of the local rain gage observations.
The main purpose of using Stage II products is to provide an optimal estimate of the
rainfall that has fallen during a given clock hour using a combination of radar and hourly
rain gage observations. The procedure is carried out on the I-IRAP grid which is a polar
stereographic map projection with approximately 4-km resolution.

The Stage III algorithm currently used at the RFCs takes the Stage II multi-sensor
rainfall estimates from multiple NEXRAD stations and mosaics them together to provide
hourly rainfall estimates covering the entire RFC area of responsibility. The Stage III
rainfall estimate is created specifically for the NWS RFCs which need rainfall estimates
over a much larger area than covered by an individual radar station. Therefore, the Stage
III algorithm mosaics together Stage II rainfall estimates from multiple NEXRAD onto a
subset of the NWS Hydrologic Rainfall Analysis Project (HRAP) grid covering the RFC
area of responsibility. In areas where data from two or more NEXRAD sites overlap, the
mean or maximum value is used. I

The NEXRAD WSR-88D rainfall algorithm generates a one—hour rainfall product
that has been remapped from a local, radar-centered, polar grid into the national, quasi-
rectangular HRAP grid of nominal grid size of 4 km x 4 km. The polar-to-HRAP .

coordinate transformation is performed within the NEXRAD WSR-88D algorithm. The

12

latitude-longitude grid cell locations based on the NEXRAD polar-to-HRAP
transformation equations is compared with the corresponding locations determined by the
equations used in the River Forecast System and Stage III Precipitation Processing
operational software applications that use these HRAP rainfall products for follow-on
hydrologic processing within the NWS. An error assessment is performed. These
locations are also compared with those computed within the GENHRAP program. This
information will serve as guidance for NWS users as well as users from other commercial
or governmental organizations who wish to use high resolution NEXRAD WSR-8 8D
HRAP rainfall estimates within GIS-based distributed hydrologic models or other
applications.

The NEXRAD WSR-88D HRAP rainfall product contains mean ' areal rainfall
over the HRAP grid box where a grid box is defined as the area enclosed by four
contiguous HRAP grid points (I, .D where I, J are integers. Thus the HRAP rainfall
estimates are actually centered at HRAP grid points (I + 0.5, J + 0.5).. All rainfall
estimates on the polar grid whose cell centers lie within the boundary of an HRAP grid
box are averaged to become the rainfall estimates for that HRAP box regardless of how
much of the polar grid box may lay outside of the given HRAP grid box. This is a simple
and efficient method of remapping the polar data into the quasi-rectangular HRAP grid
within the operational rainfall algorithm.

NEXRAD reflectivity data spatial resolution at each radar site is initially 1 degree
by l-lcm with time steps of five, six, or ten minutes depending upon weather conditions
and the applied VCP type. When rain is detected within an individual radar coverage area,

radar scan intervals are five or six minutes. To compute rainfall estimates, the NWS re-

13

maps the original 1 degree by l-km polar coordinate data through a series of intermediate
resolutions to the HRAP grid, with an approximate resolution of 4-km in hourly time
steps. This resolution is intended to meet the needs of the NWS river forecast mission,
which primarily services large river systems where hourly 4-km resolution is appropriate.
2.4. Ordinary Cokriging

Kriging provides the best linear unbiased estimator (BLUE) of characteristic
studies about unknown variates. Ordinary cokriging is an interpolation technique that
allows one to use a more intensely sampled covariate in the estimation of values for a
related variate. If the primary variate is difficult or expensive to measure and it is
correlated with a more available covariate, ordinary cokriging can greatly improve
interpolation estimates. (Matsoukas et al., 1999; Seo et al., 1990a and 1990b; Krajewski,
1987). Ordinary cokriging characterizes simultaneous regionalized K
variables {zk (x), k = l to K } by a set of K spatial inter-correlated random
filnction {Z k (x), k =1 to K} (Deutsch and Journel, 1998; Goovaerts, 1997; Isaaks
and Srivastava, 1989; Journal and Huijbregts, 1979). Ordinary cokriging assumes second-
order stationarity of these random filnctions: (1) for each random filnction Zk(x), the
mathematical expectation is: E {Z k (x)} = Mk = constant, Vx, (2) for each pair of
random function Zk(x) and Zk'(x), the cross covariance is:
E{Zkv(x+h)-Zk (x)}—mkl mm = Ckvk (h), Vx, and (3) for the cross variogram:
E{[Zk'(x+h)-Zk'(x)][Zk(x+h)-Zk(x)]} = Zrk'k(h), Vx.
2.4.1. Random Function Model and Second-Order Stationarity

The concept of the random function model is very important to ordinary cokriging.

The random function model joins together two different aspects: regionalization and

14

randomness (Wackemagel, 1998). The regionalization aspect is that the spatial data
values stem from a physical environment (time; and 1, 2, and 3D space) and are in some
way dependent on their location in the region. The randomness aspect is that the
regionalized sample values are continuous over an entire surface but they cannot be
modeled with a simple deterministic function because of the spatial variations. Therefore,
the ‘ probabilistic approach is used to regard these data values as outcomes of the random
mechanism.

' Stationarity is a property of the random function model meaning that
characteristics of a random function stay the same when shifting a given set of n points,
{1:}, x2, x,.}, from one part of the region to another (Deutsch and Joumel, 1998;
Wackemagel, 1998). Stationarity expresses the property of a random function that certain
joint distributions or that certain moments of the random filnction are translation invariant.
Therefore, second-order stationary assumes the stationarity of the first two moments of
the variable considering only pairs of points {x1, x;} in the domain and tries to
characterize only the first two moments, not a full distribution.

2.4.2. Semivariogram Cloud, Semivariogram, and Cross Semivariogram

Pairs of sample values are evaluated by computing the squared difference
between the values (Deutsch and JOurnel, 1998; Wackemagel, 1998). The resulting
dissimilarities are plotted against the separation of sample pairs in geographical space and

form the semivariogram cloud:

fl!» = gum.)— 2(xa 442)]2 2.1

15

where 7°(h) is the dissimilarity depending on the spacing and on the orientation of the
point pair described by the absolute values of the spatial separation vector, h.

The semivariogram cloud is classified according to separation in space and the
average dissimilarities in each class form the sequence of values of the experimental
semivariogram. The plot of the semivariogram cloud depicts the individual point-pair
contributions to the final semivariogram. When comparing with the simple
semivariogram it allows a subjective impression of whether the apparent pattern of spatial
variation is related to systematic trends in the data (spatial dependence) or to unusual
points (spatial outliers) (Bailey and Gatrell, 1995).

The empirical semivariogram depicts the semivariance among sets of pairs of
points, summarized by increasing distances wong points (Deutsch and Joumel, 1998;
Wackemagel, 1998). The directional empirical semivariogram constructs individual
semivariograms arranged by estimate of anisotropy and isotropy. Anisotropy is processed
when spatial dependence is a function of distance and direction; and isotropy is processed
when spatial dependence is a function of distance only (direction does not matter) (Bailey
and Gatrell, 1995). Two experimental measures of spatial variability or continuity are
used for semivariogram model fitting in ordinary cokriging. One is the semivariogram
and the other one is cross semivariogram.

The semivariogram is a measure of dissimilarity. The semivariogram is a plot of
semivariance against spatial separation vector, h. It can be used to find the rate at which a
regionalized variable changes along a specific direction. It is defined as half of the

average squared difl‘erence between two attribute values approximately by vector h:

16

N (h)

701) = 27105 1:31 [z(x,- ) — z(x,- + h)]2 2.2

where N0!) is the number of pairs, 2a..) is the value at the start of the pair 1', z(x,- + h) is
the corresponding end value, and h is the separation vector specified with some direction
and distance (lag) tolerance (Deutsch and Joumel, 1998).

The cross semivariogram measures cross variability for the possibility of mutual
correlation estimation of several interconnected data. It is defined as half of the average

product of h-increments relative to two different attributes:

N01)
Z[W(xi)-W(xi +h)]ly(xi)-y(xi +h)] 2-3

i=1

72y(h)=m

where Wm) is the value of attribute w at start of the pair 1' and w(x, + h) is corresponding
end value; the locations of the two values w(x,-) and w(x,- + h) are separated by vector h
with specified directions and distance tolerance. [y(x,- ) - y(x,- + h)]is the corresponding
h-increment of the other attribute y (Deutsch and Joumel, 1998; Wackemagel, 1998;
Goovaerts, 1997).

The constructions of the semivariogram and cross semivariogram become more
complex when more reality is introduced. For example, in the simplest model the
regionalized variable is assumed to be stationary. A stationary variable has the same
mean everywhere although not all locations within a region have the same value.

However, many regionalized variables are not stationary and exhibit drift such that the

17

mean varies with location. Another problem is that the semivariogram and cross
semivariogram assume that data points are evenly spaced. Ifthis is not the case, then the
semivariogram must be modeled.
2.4.3. Model Fitting of Semivan'ogram Using Weighted-Least-Squares Method

The objective of semivariogram model fitting is to identify a semivariance value
for the behavior of the attribute at different distances (lags) (Bailey and Gatrell, 1995). In
this study, five co-regionalized models (nugget effect, exponential, Gaussian, spherical,
and linear models) are used to fit the semivariogram or cross semivariogram. The best-
fitting model, representing the spatial dependence of the phenomenon, would be used as
input for the ordinary cokriging model. These five co-regionalized models are shown as

follows:

0, If h = O
1, otherwise

1. Nugget effect model: 7(h) = { 2.4

2. Exponential model defined by an effective range a and positive variance

contribution or sill value c. 7(h) = c - Erma) = c - [I — expo-1’39] 2.5
a a

3. Gaussian model defined by an effective range a and positive variance contribution

 

02

2
or sill value c. 7(h) = c - [1 - exp(— (3h) )] 2.6

18

4. Spherical model defined by an actual range a and positive variance contribution or

h h 3 .
-1.5——O.5— Oshs
sill value c. 7(h) = c - Sph(fl) = c l: a (a) ] If a 2.7
a c, if h 2 a
5. Linear model defined by w the slope at the origin. y(h) : w - h 2.8

The nugget effect model is an apparent discontinuity at the origin of the
semivariogram model, i.e., a nugget constant can be interpreted as a transition structure
reaching its sill value at a very small range compared with the available distances of
observation (Goovaerts, 1997; Bailey and Gatrell, 1995; Joumel, 1978). The sill is the
maximum level of semivariance reached by a transitive semivariogram. The range is the
distance at which the maximum semivariance is attained by a transitive semivariogram.

Exponential, Gaussian, and spherical models can be classified as models with a
sill and range (Joumel, 1978). Exponential and spherical models present a linear behavior
at the origin; Gaussian model present a parabolic behavior at the origin. Linear model can
be classified as a model without a sill. For the nugget effect model, the sill is reached as
soon as h > O. The spherical model reaches its sill at distance a (actual range) (Goovaerts,
1997). The exponential and Gaussian models reach their sill asymptotically. A practical
range a is defined as the distance at which the model value is at 95% of the sill.

The weighted-least-squares method is used to iteratively fit a linear co-
regionalization model to obtain the best set of range and sill numbers for the ordinary
cokriging model (Goovaerts, 1997). It starts to modify one arbitrary co-regionalized

matrix at a time iteratively so as to minimize the criterion under the constraint of positive

19

semi-definiteness of that matrix. The criterion is

 

’6 Nva h
WSS= Z 2 2w w(hk )- [71“ “07:1.(hknz, where w(hk) is the weight of the k-th lag
k=1i=1j=l J

and is chosen by: (l) proportional to the number N(hk) of pairs used in the estimate and (2)

N(hk)

2 to gain more weight for the first lag.
m,- (ht )1

proportional to the quantity

- In this study, the ordinary cokriging model (Marcotte, 1991) is integrated with the
weighted-least—squares method (Goovaerts, 1997) to calibrate NEXRAD rainfall surface
based on rain-gage network measurements.

2.5. Artificial Neural Networks (ANNs)

ANN s are computer-based systems that are designed to emulate some of the
learning and pattern recognition abilities of the human brain. The human brain is made up
of billions of cells called neurons (Haykin, 1999; Bose and Liang, 1996). A general
biological neuron is composed of four components: (1) a dendrite for receiving a signal,
(2) a cell body or nucleus for synthesizing signals using nonlinear threshold effect, (3) an
axon for transmitting signals, and (4) a synapse for transmitting weighted signals to other
neurons. These neurons are all linked to each other and establish an intelligent system
network (parallel complex network or information processor). This biological neural
network performs various human brain abilities such as learning, analysis, prediction, or
recognition.

ANN s are known as a “data-driven” modeling approach (Chakraborty et al.,
1992). ANN s are well suited to solve complex problems where the relationships between

the variables to be modeled are not well understood (Maren et al., 1990). ANN 3 use

20

parallel processing to learn an approximation to the underlying rules governing the
relationship between inputs and output variables. However, the internal structure or
topology of the best possible ANN model is generally unknown and must be developed
by a trial and error process (see Figure 2.2).

ANNs can be applied in a broad range of fields, including image processing,
signal processing, medical studies, financial predictions, power systems, and pattern
recognition among others. Because ANN models have the ability to recursively learn
from the data, they are particularly useful for applications involving complicated,
nonlinear processes that are not easily modeled by traditional means. These successes
have also inspired applications to water resources and environmental systems.

Shamseldin et al., (1997) merged the estimated output from various rainfall-runoff
models to produce an overall combined estimated output to be used as an alternative to
that obtained fiom a single individual rainfall-runoff model. The estimated discharges of
five rainfall-runoff models for eleven catchments were used to test the performance of the
three combination methods: the simple average, the weighted averaged, and the neural
network methods. The results confirmed that the combined model outputs of various
models performed the best discharge estimates.

Bruton et al., (2000) used a three-layer, back-propagation neural network to
predict daily pan evaporation for missing data or remote areas based on easily measurable
weather variables. In this study, they trained the model using 11 weather variables from
three sites in Georgia collected fi'om 1992 ~ 1996. They performed several modeling
scenarios with different combinations of weather variables as inputs into the network.

They found that the model performed best (R2 = 0.717) with all available weather data.

21

Input Array

 

 

Output Array

Figure 2.2. Typical Structure of A Multi-Layer Feedforward Neural Network.

22

Yang et al., (1996) utilized an artificial narral network to aid in land drainage
engineering. They used 26 years of DRAINMOD—simulated mid-span water table depths
to train a one-layer ANN. After training, they found that the ANN could simulate water
table depths faster and with less input data than DRAINMOD.

Maier and Dandy (1996) trained a neural network with four years of river levels,
flow rates, and salinity for the River Murray in South Australia. They used the model to
provide a 14-day forecast of river salinity. Their model provided an average annual

percent error in river salinity of 6.5%.

23

Chapter 3 STUDY AREA
3.1. SEMCOG Rain Gage Network

The SEMCOG (South Eastern Michigan Council of Governments) rain gage
network is located in southeast Michigan. The SEMCOG area contains 7 counties:
Livingston, Macomb, Monroe, Oakland, St. Clair, Washtenaw and Wayne Counties. The
rain gage network is restricted to just 5 counties. A 108 universal weighing rain gage
network used for this study is only distributed across 5 counties of the SEMCOG area,
which are Livingston, Macomb, Oakland, Washtenaw, and Wayne Counties, covering an
area of about 1,514 km2 (see Figures 3.1 and 3.2). Only 66 ~ 68 rain gages are active
during the study time periods, from the months of May to September from the year 1999
to 2000.

The distribution of the rain gage network was set up to reflect the population
density within the five-county area. The highest density of the rain gages is in the city of
Detroit, while for the least dense, the maximum spacing between the rain gages is 40km.
Therefore, the rainfall patterns in the SEMCOG rain gage network are over a primarily
urban setting.

The area of the SEMCOG rain gage network is covered by the overlap of four
NEXRAD sites, located at Detroit-Pontiac and Grand Rapids, MI, North Webster, IN,
and Cleveland, Ohio. The maximum scan range of each NEXRAD is 230km. The
NEXRAD Stage III data are developed from the mean or maximum values of these four
NEXRAD stations. Because of the spatial and temporal overlap of the rainfall
measurements by the rain gage and NEXRAD networks, merging these two types of

measurements (i.e. the high spatial resolution of NEXRAD with the measurement

24

[:3 SEMCOG
|' SEMCOG Rd» Gage Invert

 

 

N

30 0 30 60 Kllomstsra
H S

 

Figure 3.1. SEMCOG Rain Gage Network.

25

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0Q
Green gay. I
Nilwau .WI
0 rs
CHM , L /\\ I
’90 North Webster. IN
100

 

 

 

 

Kilometers

 

e SEMCOG Ralngago Network

t NEXRAD sum
emcee Am
Ilchlgan sure

W

Cleveland. 0

Figure 3.2. SEMCOG Rain Gage Network and the Covering NEXRAD

Stations

26

accuracy of the rain gages) will give estimates that are superior to estimates obtainable
from each individual device alone.
3.2. National Weather Service Rain Gage Network in Michigan

The total area of Michigan is about 170,312 kmz. The land area is about 147,134
km2 and the water area is about 103,602 kmz. The mean elevation of Michigan is
174.32m above sea level. The major lakes of Michigan are Lake Michigan, Lake Superior,
Lake Huron, Lake Erie, and Lake St. Clair. The period of the study was the months of
May through September for the years 1999 to 2001.

In this study, rainfall measurements 42 National Weather Service observing sites
distributed across the entire state of Michigan were used to calibrate and validate the
NEXRAD Stage at rainfall surface. Twelve of these sites are distributed across the
Upper Peninsula and 30 are distributed across the Lower Peninsula (see Figure 3.3).
Michigan is overlapped by the sweep ranges of the following ten NEXRAD radars, which
are Marquette, Gaylord, Detroit-Pontiac, and Grand Rapids, MI; North Webster, IN;
Cleveland, Ohio; Chicago, Illinois; Duluth, Minnesota; and Milwaukee and Green Bay,
Wisconsin (see Figure 3.3). The NEXRAD Stage III data for Michigan is produced by

mean or maximum values of these ten NEXRAD rainfall surfaces.

27

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Duluth, MN
81 u 9. MI
1 .c‘
er
I
/
Milwaul; ,Wl Gra a
, [in 17 ]

Chlcag 'IL ’A J Clevela d

redrawn-term f '

f
t
f
i
300 0 300 600 Kllometers
N
t NEXRAD Sltes W E
[:3 Mchlgan State Boundary
S
Figure 3.3. Michigan National Weather Service Rain gage Network and Covering 9
NEXRAD Radar Stations.

28

Chapter 4 METHODOLOGIES
PILOT STUDY: STATISTICAL ANALYSIS AND MODEL DEVELOPMENT IN
THE SEMCOG RAIN GAGE NETWORK

The SEMCOG rain gage network is one of the few, large, high-density rain gage
networks in the US. The purpose of the pilot study was to take advantage of the data
from this network and to: (1) perform a statistical analysis between Stage III NEXRAD
data and the ground gages to determine the frequency and type of disagreement, and the
magnitude of error between radar and ground gages, and (2) use the SEMCOG network
as a testing ground for developing and testing ordinary cokriging and artificial neural
network models for improving spatial rainfall estimation.

4.1. Precipitation Data Sources

The hourly and daily rain gage data of the SEMCOG network used for this study
were obtained from the SEMCOG web site:
http://35.9.73.71/SemngSEWsemtable.htng. The SEMCOG rain gage network consists
of 108 universal weighing rain gages recording real-time rainfall information. The
universal weighing rain gages in the network consist of a shelter, firnnel, collection
bucket, weighing device and recording chart. Precipitation falls into the universal gage
receiver, where it is filnneled into a collector mounted on a weighing mechanism. The
weight of the precipitation compresses a spring, which is connected to a pen (ink) arm.
Ink from the pen leaves a trace on a paper chart, wrapped around a clock-driven cylinder.
The cylinder rotates continuously, making one revolution every 24 hours. Ink tracings on
the chart provide historical precipitation rates and amounts. Charts are graduated to the
nearest 1.270 mm and read to the nearest 0.254 mm by interpolation. Maximum capacity

is 304.800 mm. Charts are changed once a week or within 24 hours after a precipitation

29

event. The time periods of the data used for this study were fiom the months of May
through September fiom 1999 to 2000. During the study time periods, only about 66 to
68 universal weighing rain gages were active.

The hourly NEXRAD Stage 111 data of the Midwest was obtained from the
Hydrology Laboratory in the Office of Hydrology Development at the National Weather
Service. These data are stored in binary data format called XMRG and are mosaiced
Stage II rainfall estimates from the NEXRAD radar sites located in the Midwest. The
NEXRAD data are projected onto a subset of the national HRAP grid, the coordinate
system that defines the locations of XMRG data values (see Figure 4.1).

4.2. Software

Since this study involves detailed spatial analysis of rainfall distribution, ArcView
GIS 3.3 software with extensions made by Environmental System Research Institute
(ESRI) Inc. and MATLAB 6.1 for Windows NT with toolbox made by The MathWorks
Inc. were used in this study to aid in processing NEXRAD and rain gage data.

4.2.1. ArcView GIS Software and Its Extension Programs

ArcView GIS 3.3 has the ability to: ( 1) display spatial data, (2) query data, (3) create data,
and (4) use other type of data, e.g. CAD data. ArcView GIS 3.3 displays data by creating
a map in a variety of spatial data formats; e. g. the ARC/INFO spatial data formats. It can
display tabular data about ground covers, land formations, and water quality to a map. I
The software is able to represent data on a map by symbolizing and charting the data, by
labeling the map with text and graphics, and by choosing map projections. ArcView GIS
3.3 can also design and print various map layouts (ESRI, 2002).

ArcView GIS 3.3 can create new data by: (1) developing additional spatial data,

30

 

1000 0 1000 2000 Kllomotors

 

0 NEXRAD 81!”
USA
ESTWOOOOHOOIIIII)
0

£633“ N

[31226 -1szs
-1sao-2rs1

- 2132-3“: \V E
- sue-czar

- sass-1612

-7s1:1-12544

[:jNoData S

Figure 4.1. NEXRAD Stage III Data of Midwestern Area (Projected by
Michigan Georef System).

31

(2) editing existing spatial data, and (3) digitizing a map. The software creates new
spatial data either by developing a new point theme, line theme, or polygon theme, or by
using a digitizing tablet to digitize a map into a point feature, a line feature, and a
polygon feature. Editing spatial data can be done within certain existing themes.

ArcView GIS 3.3 data is compatible with several other data types, e. g. image-type
data, Computer-Aided Design (CAD) data, Spatial Database Engine (SDE) data (ESRI,
1996). Image-type data includes scanned-map data, the aerial-photograph data, and
satellite-imagery data. CAD data are a set of non-GIS graphical data for engineering or
architecture design, and can be employed as if it is GIS data in ArcView GIS 3.3. With
the spatial Database Themes extension of ArcView GIS 3.3, SDE data can be added to
the database of a map in order to explore, query, and analyze the map data in ArcView
(ESRI, 1996).

In this study, additional extension programs were used with basic ArcView GIS
3.3: (1) MI DNR Projection Extension, (2) ArcView Spatial Analyst, and (3) Grid
Analyst.

4.2.2. MATLAB Software with Neural Network Toolbox

MATLAB is a high-performance language for technical computing. It is typically
used in: (1) mathematics and computation, (2) algorithm development, (3) modeling,
simulation, and prototyping, (4) data analysis, exploration, and visualization, (5)
scientific and engineering graphics, and (6) application development, including graphical
user interface building. MATLAB is an interactive system whose basic data element is an
array that does not require dimensioning. This can solve the technical computing

problems, especially those with matrix and vector formulations. In addition, MATLAB

32

features a family of application-specific solutions called toolboxes that extend the
MATLAB environment to solve particular classes of problems.

In this study, MATLAB 6.1 for Windows NT software with Neural Network
Toolbox was used to load and process the ordinary cokriging (Marcotte, 1991) and ANN
models. For processing the ordinary cokriging model, only MATLAB 6.1 for Windows
NT software was used. For processing the ANN model, MATLAB 6.1 for Windows NT
software with Neural Network Toolbox was used. The Neural Network Toolbox contains
the feed-forward neural network with the Levenberg-Marquardt (LM) algorithm (Demuth
and Beale, 2001), which is the main algorithm used to process the ANN model in this
study. The relative principles and details of ordinary cokriging and ANN approaches are
described in Section 2.4 and 2.5, respectively.

4.3. Methods
4.3.1. Data Management for SEMCOG Rain Gage Measurements and NEXRAD
Stage III Rainfall Estimates

ArcView with MI DNR Projection Extension, Spatial Analyst, and Grid Analyst
extension programs were used to manage both the SEMCOG hourly and daily rain gage
data and hourly NEXRAD Stage 111 data from the months of May to September fi'om
1999 to 2000. In this study, ArcView GIS software was used to:

(1) Develop GIS precipitation maps with the same time zone (East Standard Time),
time scale (Daily rainfall), and georeferenced system (Michigan Georef system)
by merging SEMCOG hourly and daily rain gage measurements and hourly

NEXRAD Stage III precipitation surface together.

33

(2) Extract corresponding NEXRAD and rain gage data for making two types of
statistical analyses.

(3) Develop a MATLAB-based large matrix inputs for the OC and ANN models.

(4) Display the results after processing both the OC and ANN models.

Using ArcView, the data from both sources (rain gage and NEXRAD Stage III
values) were adjusted so that they were in the same time zone, time scale, spatial
projection, and coordinate system (Michigan Georef). I

. Initially, the SEMCOG rain gage (hourly and daily) and hourly NEXRAD Stage
, II] data were recorded in different time zones and time scales. The SEMCOG hourly rain
gage data were recorded in EST, while the NEXRAD Stage III data were recorded in
Greenwich Mean Time (GMT), a difl‘erence of five hours. To bring both data sets into the
same time frame, the hourly NEXRAD data were shifted back five hours. The shifted
hourly data were then summed to daily totals This was accomplished by using Map
Calculator in ArcView by summing up 24 initial hourly NEXMD data from the 6"I hour
of the first day to the 5"I hour of the second day to get the corresponding daily NEXRAD
Stage [II data in EST (fiom the 1‘t hour to the 24"I hour). 3

Both the SEMCOG rain gage measurements and NEXRAD Stage 111 data were
projected in different georeferenced Systems. The SEMCOG rain gage measurements
were projected in the Geographic Lat/Lon system and the NEXRAD grid themes were
projected in the Michigan Georef system. Since both data must be georeferenced in the
same projection in order to be compared against each other, the SEMCOG rain gage text
files were converted into ArcView shape files by using the Add Event Theme and the

Convert to Shapefile functions in ArcView. Then, the MI DNR Projection Extension was

34

used to re-project the Geographic Lat/Lon projected rain gage measurements into the

Michigan Georef Projection. These techniques allowed for both data sets to be compared

both spatially and temporally.

4.3.2. Statistical Analysis of SEMCOG Rain Gage Measurements and NEXRAD
Stage III Rainfall Estimates

It has been previously noted that NEXRAD radar usually underestimates the
convective precipitation events and overestimates stratiform precipitation events
(Groisman and Legates, 1994). Many possible approaches can be taken when comparing
point rain gage data to NEXRAD Stage III estimates. In this study, two types of statistical
analyses were performed to describe the correlation between SEMCOG rain gage values
and stage III NEXRAD. The first statistical. analysis focuses on the agreement of
occurrence of precipitation between the two sources and the magnitude of the differences
in precipitation when there is disagreement of occurrence. The second statistical analysis
Simply examines the differences in magnitude between rain gage measurement and
NEXRAD estimate when they both register a rainfall amount. These analyses were
performed to determine the differences between rain gage measurements and the
NEXRAD estimates and to provide a basis of justification for using models to improve
the correlation between the two sources of rainfall measurement.

There are several possible situations during a rainfall event that can cause
disagreement between rain gage and NEXRAD. These include situations such as rainfall
being registered by NEXRAD, but evaporating before it reaches the rain gage, and
rainfall that is measured by the rain gage, but not measured by NEXRAD due to radar

beam attenuation caused by heavy precipitation. The disagreement between these two

35

sources is compounded by the fact that the rain gage measurement represents a point
measurement, while the Stage III NEXRAD is an estimate made over a 4 km by 4 km
area, i.e. within-cell rainfall variability.

To determine the correlation of rainfall occurrence between SEMCOG rain gages
and NEXRAD radar estimates, hourly rainfall values for each rain gage in the network
and corresponding NEXRAD estimate were extracted and separated into one of four

possible classes or conditions. Each condition is described below:

Condition 1 — Both the rain gage and NEXRAD registered a precipitation event.
Condition 2 — The rain gage registered a precipitation event, but the NEXRAD did not.
Condition 3 — The rain gage did not register a precipitation event, but the NEXRAD did.

Condition 4 — Neither the rain gage nor did NEXRAD register a precipitation event.

These conditions are summarized in Table 4.1. It should be noted that throughout
1999 and 2000, there were several periods of time when either a certain rain gage in the
network was not operational or NEXRAD was not available. The data used in this
analysis includes all available hourly data for the more or less 10—month period, roughly
500,000 rain gage-hours.

A further analysis of these data focuses in more detail on the magnitude of 5
difference between the SEMCOG rain gages and their corresponding NEXRAD estimate.
These initial statistics consists of a set of synthetic statistical matrices used to describe the
difl'erences of each examined precipitation event between the SEMCOG daily rainfall

and daily NEXRAD Stage III data. These synthetic statistical matrices consist of the

36

Table 4.1. Possible Combinations of Precipitation Occurrences between SEMCOG Rain
Gages and NEXRAD Radar Estimates

 

Precipitation SEMCOG NEXRAD
Conditions m Gage Stage III
Network
1 Yes" Yes
2 Yes No“
3 No Yes
4 No No

 

*Yes means that the device registers precipitation information.
”No means that the device does not register precipitation information.

mean,- the mean bias (W), and the absolute mean bias (AW).

To make these two types of statistical analyses, the hourly NEXRAD Stage III
grid values where the rain gages were present were extracted and compared with the
SEMCOG hourly rain gage values. The hourly NEXRAD Stage III grid values were
extracted by using a filnction of the Grid Analyst extension named Extract X, Y, and Z
Values for Point Theme fi'om Grid Theme. The descriptive table containing the extracted
hourly NEXRAD Stage III grid values was joined with the descriptive table of the
SEMCOG hourly rain gage measurements by using the Join function of the ArcView GIS
software, respectively.

4.3.3. Model Justification

In this study, ordinary cokriging and artificial neural network models were
selected for adjusting the daily NEXRAD Stage III rainfall surfaces using the ground
gage measurements. The approaches for these two models are very different fi'om each
other, but both have the potential to improve the NEXRAD estimate by incorporating

ground rain gages.

37

Ordinary Cokriging (OC) Model

Ordinary cokriging (OC) was originally developed as geostatistical tool for the
mining industry. The method can obtain the spatial correlation between two or more
variables. In this study, the ordinary cokriging method was applied to Spatially estimate
rainfall by combining rain gage measurements and radar rainfall data. It uses the rain
gage measurements and the NEXRAD-derived rainfall surface, to obtain the Spatial
correlation between the rain gage measurements and NEXRAD-derived rainfall. It
minimizes the estimation variance, considering the statistical properties of radar rainfall
data, the measurements of the rain gage network, and the dependence of each of
measurements on the other (Matsoukas, 1999; Seo et al. 1990a and 1990b). It assumes
second-order stationarity and ergodicity, and models the spatial dependence of each
measurement of device on itself and on each other in terms of the estimations of
semivariogram and cross semivariogram. However, the estimations of semivariogram and
cross semivariogram are usually not well behaved for rain gage measurements. For the
past two decades the ordinary cokriging approach has been used for the studies of the
radar rainfall estimation and shown good results.
Artificial Neural Network (ANN) Model

Artificial neural networks are computer-based systems that are designed to
emulate some of the learning and pattern recognition abilities of the human brain. The
approach of the ANN is known as a “data-driven” modeling approach (Chakraborty et al.,
1992). ANNs are well suited to solve complex problems where the relationships between
the variables to be modeled are not well understood (Maren et al., 1990). ANNs use

parallel processing to learn an approximation to the underlying rules governing the

38

relationship between input and output variables. However, the internal structure or
topology of the ANN model is generally unknown and must be developed by a trial and
error process. For the past decade ANNs have been gradually applied to problems in
hydrometeorology and have Shown promising results.
Selection and Classification of Examined SEMCOG Precipitation Events

In this study, twenty-two daily precipitation events from the SEMCOG network
were selected for examining the performances of both the OC and ANN models. The
events were divided into two types: full and partial Spatial coverage. In the first type of
the precipitation event, the SEMCOG network was fully covered by the precipitation.
Sixteen of twenty-two events were full coverage events, in which each rain gage
registered precipitation. The remaining six events were partial coverage events, where a
portion of the rain gage network recorded no rain. The twenty-two daily precipitation
events were firrther classified into three levels of daily mean rain gage values using the
natural break method. The three types of precipitation events were light, moderate, and
heavy precipitation events. The ranges of each level of daily precipitation events are:
light (< 8.18 mm), moderate (8.18 - 18.84 mm), and heavy (> 18.84 mm).
Assignments of Model Processing Data Sets and Model Efficiency Criteria

Calibration and validation encompass accuracy, robustness, consistency, fault
tolerance, and sensitivity. Standard statistical and pattern recognition techniques were
used to investigate the efficiency of OC and ANNs methods.

Since rain gage values are the best estimate of precipitation at a point, they are
assumed to be “ground truth.” Rain gage and NEXRAD data from each event were

separated into two datasets, one set for calibration and the 'other for validation. Figure 4.2

39

depicts the locations of the NEXRAD data that were used for calibration and validation in
the ANN model. The assignments of the calibration or validation data sets of the rain
gage measurements were the same as where their located NEXRAD grid were allocated
to the calibration or validation data sets. The same calibration and validation data sets of
the rain gages used in the ANN model were used in the OC model for cross validation
and validation, respectively. Because of this calibration / validation process, it is possible
that the split of rain gages for calibration / validation may not have been equal.

During the calibration and validation phases of the numerical processes, the
model output at a grid point with a rain gage was compared to the value recorded by the
rain gage values. Goodness-of-fit metrics that will be estimated are the correlation
coeflicient (CC), the R2, the mean bias (MB), the absolute mean bias (AMB), the
normalized mean bias (NBIAS), the normalized root-mean-square error (NRMSE),
Arithmetical Averaging method (mean), and the Thiessen Polygon method (F ).

The holdout method was used for calibration and validation using the N extracted
radar values with their N rain gage measurements. The N rain gage measurements are
Split into two data sets: Nd, which were used to develop the training algorithm, and Nv,
which are used in validation. The I-th rain gage, which belongs in the calibration or
validation subsets 16 {1,2,..., N }, has spatial coordinates x(l), yfl) and in reality, records
rainfall Rg(x(l),yfl)), and the brevity of Rg(x(l),y(l)) is denoted as Rgl. Rgl in this location
is assumed the absolute truth rainfall value, while our calibration and validation outputs
are R ’I. Then, the definitions of the comparison metrics are:

N, N d , N v ,

2 (RI _ Rgl)

= [=1 41
(NaNdsNV) ' .

40

N,Nd,Nv ,

 

 

 

 

 

2“. (RI-Rgl)
AMB=Absolute( ’ =1 )
(N.Nd.Nv)
N,Nd,Nv ,
121 (RI‘RgI)
NBIAS= N.Nd.Nv
2R1
1:1 g
N,Nd,Nv 1 2
[Z (RI-Kg!)
ARM _ =1
SE N,Nd,Nv _
2: (Rgz-Rgz)
1:1
N,Nd,Nv
{(Rgl)
Arithmetical Averaging method: mean = ’=1
NsNdsNV

N
23' 'Ai
Thiessen Polygon method: I7 = 53%——
2 At
i=1

41

4.2

4.3

4.4

4.5

4.6

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(909.9.006)

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and Validation Used' In ANN Model

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in ANN Model.

42

CC measures how well the adjusted radar values correlate with the rain gage

values. Either raw radar values or adjusted radar values and rain gage values have the

best correlation coeflicient when CC = 1.0. R2 measures how well the adjusted radar
values match the rain gage values. NBIAS indicates the degree of bias between either raw
radar values or adjusted radar values and the ground truth values (gage values). When
NBIAS = 0, either raw radar values or adjusted radar values and gage values are identical.
NRMSE indicates the closeness of either raw radar values or adjusted radar values to the
gage values and is used to measure the error between either raw radar values or adjusted
radar values and gage values. A perfect NRMSE means either all raw radar values or all
adjusted radar values are identical to the gage values exists only if NRMSE = 0.

The arithmetical averaging method is performed by dividing the summed
accumulation of each rain gage measurement by the number of the rain gages
(N, Nd,Nv ). This method is good for the region with the plain topography and small
precipitation variance.

The Thiessen polygon method is a technique for approximating the distribution
area around precipitation gages for the purpose of distributing average precipitation
depths over an area. A Thiessen polygon network is constructed using perpendicular
bisectors to lines between gages and carefully removing overlapping bisectors until an
even spatial distribution is obtained. The area of polygon (A;) is multiplied by the

representative depth of rain gage (Pi) and summed over the total area of interest. This

sum is divided by the total area to obtain the average depth (15 ).

43

Adjusting NEXRAD Precipitation Surface Using Ordinary Cokriging and ANN s
Adjusting NEXRAD Precipitation Sufi'ace Using Ordinary Cokriging
A linear ordinary cokriging estimator combining radar—derived rainfall with rain

gage measurement has the following form (Seo et al., 1990; Krajewski, 1987; Joumel,

1978):
”g ”g

zg(U0)= 2 Ag,- -Zg(U,-)+ 21,]- -Z,(Uj) 4.7
i=1 i=1

where

Z g (U 1') Spatial averaged gage rainfall centered at (1,;
Ag,- , 2,]. : Weighting coefficients to be determined;

Ng: Number of Spatially averaged gage rainfall data;

Z r (U j ): Radar rainfall at the bin centered at U,-;

N,: Number of radar rainfall data surrounding U0;

Z g (U 0 ): Estimated gage rainfall averaged over A and centered at an arbitrary location

U0.
When the mean and the covariance of the rainfall measurement fields are perfectly
known, the weighting coefficients that give the unbiased, minimum-error-variance

estimate are found by minimizing

2
ragga/Jpn {zg(u,)_zg(uo)} 4s

44

where a g (U 0) is the estimation error at the location U0,

The solution for this problem can be obtained by the simple application of the

Gauss-Markoff theorem (Liebelt, 1967) and is given by:

-1
Z.g(Uo)-mg+(Qongr)o[Qrg er] [Zr- Mr] 4.9
Q Q ‘1
V‘”[‘g(Uo)]=°'§‘(QOQor-)'[Qf: Qij (ngQro) 4-10
where

Qog : (1 x Ng) covariance vector of the unknown gage rainfall and the sampled gage
rainfall data;

Qor : (I x Nr) cross-covariance vector of the unknown gage rainfall and the sampled
radar rainfall data;

Qgg: (Ng x Ng) covariance matrix of the sampled gage rainfall data;

Qrg: (Nr x Ng) cross-covariance matrix of the sampled radar rainfall data and the
sampled gage rain fall data;

er: (Nr x Nr) covariance matrix of the sampled radar rainfall data;

mg: mean of the gage rainfall;

cg: variance of the gage rainfall;

m,: mean of the radar rainfall;

Mg: (Ng x I) gage rainfall mean vector equal to (me... myT;

45

Mr: (Nr x 1) radar rainfall mean vector equal to (m,... m,)T.
When the gage rainfall field and the radar rainfall field are jointly second-order
homogenous, and both the mean of the gage rainfall field and the mean of the radar

rainfall field are unknown but constant, and the minimization of
2
/\
Varle g (U0 )1: {Zg(Uo)— Z g (U0 )} is made subject to the following constraints to

force unbiasedness:

N8 Nr

23y“: 24.1%. _ 4.11
i=1 j=1

the role of the above constraints becomes:

A N8 Nr N8 Nr
Zg(Uo) = ngia[zg(U,-)]+ Za,,~s[z,(UJ-)]=mg - 2,18,- +m, 271,]- =mg
i=1 j=l - i=1 j=l

4.12

where mg is unknown but mean of the gage rainfall field is constant and m, is the
unknown but mean of the radar rainfall field is constant.
Process Procedures of Ordinary Cokriging

The process procedures of the OC model based on the equations are described as

follows:

46

1. Produce a semivariogram and cross semivariogram to find the spatial surface
trend of each rainfall measurement on itself and on each other.

2. Find the parameters (sill and range) from the best-fit model of semivariogram or
cross semivariogram by using Nugget Effect, Exponential, Gaussian, Spherical,
and Linear models. The weighted-least-square method is used to automatically
model semivariograms and cross semivariogram instead of using manual
operation.

3. Use the parameters (sill and range) obtained from the best-fit model to the OC
model for cross validation and validation.

After finding the well-behaved semivariogram, five models and the weighted-
least-square method were used to model the semivariogram and cross semivariogram in
order to rapidly find the sill and range values. After finding the best set of sill and range
values, these two values were used to process cross validation and validation in the OC
model. I
Adiusting NEXRAD Precipitation Surface Using ANNs

This study used a multi-layer feed-forward neural network with a Levenberg-
Marquardt (LM) training algorithm and one single output to calibrate and validate
NEXRAD rainfall surface based on rain gage measurements (Haykin, 1999; Demuth and
Beale, 1997; Hagan et al., 1996). This model is a network composed of a number of i
interconnected artificial neurons (the hierarchy of the information processing units)
organized in a series of two or more mutually exclusive sets of neurons or layers. Each

neuron has an input/output (I/O) characteristic and implements a local computation or

47

function. The output of any artificial neural unit is determined by its I/O characteristic, its
interconnection to other units, and external inputs (W echsler, 1992).

The input layer serves as a holding site for the inputs applied to network. The
output layer is the point at which the overall mapping of the network input is available.
Zero or more layers of hidden units lie between these two layers as internal layers where
additional re-mapping or computing takes place. Connection weights link each unit of
neuron in one layer only to those in the next higher layer. There is an implied
directionality in these connections, in that the output of a unit, scaled by the value of a
connection weight, is fed forward to provide a portion of the activation for the units in the
next higher layer.

Initially, the input data was multiplied by a randomly generated initial connection
weight for each neuron connection path. The total sum of these weighted inputs plus a

constant term yields the actual net input Ya“, that is:

N
rm, = ZYiwi +wo, 4.13
i=1

where N is the total number of neurons in the preceding layer, Y.- is the neuron input
received fi'om the ith neuron in the preceding layer, w,- is the connection weight assigned
to the path linking the neuron to that i'" neuron and w(, is the neuron threshold value
(Blum, 1992). The neuron threshold value provides the means of adding a constant value

to the summation term, which can be used to scale this term into a useful range of values.

48

Next, the neuron input Yne, is transformed to the neuron output Y a.“ by passing
through the hidden layer(s). The non-linear hyperbolic tangent transformation function
was used to represent each hidden layer, that is

N N
Yout =f(Ynel)=f(iEi’iWi+W0)=tanh(i§1YiWi +WO) 4-14

The topology of the multi-layer neural network belongs to the class of data driven
approaches, and hence requires the specific factor (i.e. the number of hidden layers and
the neuron number in a hidden layer) for keeping the network structure being minimum
and obtaining maximum efficiency (F ausett, 1994). The determination of the appropriate
number of hidden layers and the neural number (number of nodes) in a hidden layer are
important for the success of the neural network, since it greatly enhances the performance
of the neural network, i.e. the network efficiency is sensitive to these two types of
numbers. If the neural network has too few hidden layers or too few neural numbers in
the hidden layer i.e. the network is too parsimonious in its use of parameters (wo and w,),
then the performance of the neural network may deteriorate below that of the appropriate
number. Reversely, too many hidden layers or too many neural numbers in a hidden layer
will increase the number of the parameters and cause it to over-fit the calibration (training)
data set. The strategy used for selecting the appropriate number of hidden layers was
done by a trial and error procedure to select the least number of hidden layers and the
least neural numbers in a hidden layer for the best performance of the ANN model.

The Levenberg-Marquardt (LM) algorithm was applied to a multiplayer feed
forward network for this study. The detailed presentations of LM algorithm can be found
in Demuth and Beale, (2001); Hagan et al., (1996); and Marquardt, (1963) for the

applications and the original description. In this section, the equations (Equation 4.15 —

49

4.29) of the back-propagation algorithm are briefly present (Haykin, 1999; Bose and
Liang, 1996) for the purpose of introducing notation and concepts which are needed to
describe the LM algorithm (equation 4.30 - 4.40).

The net input to unit i in layer k+1 is:

Sk

nk+1(r) = Zwk+1(i, flak 0).. ok+1(r) 4.15
1:1

The output ofunit i will be: aK+1 (i) = fk+1(nk+1(i)) 4.16

For an M layer network the system equations in matrix form are given by
a0 : P 4.17
gk+1 zlk+l(wk+lgk +ék+1), k = 0,1,..,,M_1 4.18

The task of the network is to learn associations between a specified set of input-output

pairs {@111}(£2’EZ)""(BQ’ZQ)}

The performance index for the network is

(Eq ‘93!) (is "9914):; £951? 4'19

where oM is the output of the network when the qth

—q input, E q 15 present and

g q = r q — g2! is the error for the qth input. For the standard back-propagation
algorithm we use an approximate steepest decent rule. The performance index is

approximated by
E; E 4.20

where the total sum of squares is replaced by the squared errors for a single input/output

pair. The approximate steepest (gradient) descent algorithm is then

 

/\
M" (i, j) = —a —‘%V—— 4.21
6w (1.1)
A
Abk (i) ___ -—a akV 4.22
an (i)
/\
6V

4.23

 

where a is the learning rate. Define 5" (i) = k
6" (i)

as the sensitivity of the performance index to changes in the net input of unit i in layer k.

Using 4.15, 4.20 and 4.23:

51

 

a? _ a9 (#0) -d"(i)-a"+l(i)

 

 

 

 

 

_ _ 4.24
aw"(i,j) an"(i)6w"(i,j)
/\ /\ k '
6):! = 5: ankh): 61.0,) 4.25
an (i) an (0% (i)
The sensitivity satisfies the following recurrence relation:
Ok 1'
where
- k _
f (hit (1)) o o
k k
0 O
F (3"): o f (#0)) . o 4.27
0k k
0 0 f (n (s10)
k
e k
df
d =—
an f (I!) ah 4.28

52

This recurrence relation is initialized at the finial layer:

.M

QM =—F [nMJQq —aq) 4.29

The overall learning algorithm proceeds as follows:
1. Propagate the input forward using 4.17 and 4.18.
2. _ Propagate the sensitivities back using 4.29 and 4.26.
3. Update the weights and offsets using 4.21, 4.22, 4.24, and 4.25.
While back propagation is a steepest descent algorithm, the LM algorithm is as

approximation to Newton’s method. Suppose that a firnction V05) has to be minimized

with respect to the parameter vector; , and then Newton’s method would be:

A; = {r72 ~V(§)]-1VV(25) K 4.30

where V2V(_{) is the Hessian matrix and VV(J_c) is the gradient. Ifwe assume that V05)is

N
a sum of squares function V(§) = Eel-2 (15) 4.31
i=1

then it can be Shown that VV(_J§) = JT(§)§_(15) 4.32

53

VZVQE)= JTQ)-J(r_t)+s(r_r) 4.33

where Jacobian matrix:

 

 

 

ré‘fl M 59—105)—
6x 6x ax
66213‘) 88266) aez'fx)
JOE): 6:51 arz . 5’5" 4.34
amt/(x) ' fies/(x)
_ 6"1 6"n _
N
and S(gc_) = Zei(x)oV2ei(x) 4.35

i=1
For the Gauss-Newton method:

19(5):: 0
—>(16) is updated: A§=[JT(1_c)oJ(J_c)]—1JT(§)-g(x) 4.3a

The LM modification to the Gauss-Newton method is:

Ar=[JT(r)-J(r)+#-I]—1JT(r)-2(r) 4.37

The parameter p is multiplied by some factor (,6) whenever a step would result

in an increased V (35) When a step reduces V (15), ,u is divided by ,6. When ,u is large the

54

algorithm becomes steepest descent (with step 1/ ,u ). When [1 is small, the algorithm
becomes Gauss-Newton.

The computation of the Jacobian matrix is very important to the LM algorithm.
For the neural network mapping problem, the terms in the J acobian matrix can be
computed by a simple modification to the back-propagation algorithm. The performance
index for the mapping problem is given by (4.19). This is equivalent in form to (4.31),

where

g = [w1(1,1)w1(1,2)...w1(51, R)b1(1)...b1(Sl)w2(l,l)...bM (SM)]T, and N = Q x SM.

SM 2
.. 62 eq(m)

Standard back-propagation calculates terms like [W = m =1 4.38

aw" (1:1) aw" (i. j)
The term needs to be calculated for the element of the J acobian matrix that is needed for

aeq (m)

k . 4.39
aw (in

the LM algorithm:

These terms can be calculated using the standard back-propagation algorithm with one

modification at the final layer AM 2 —FM (QM . 4.40

55

The LM algorithm modifies the back-propagation algorithm and proceeds as

follows:

1.

Present all inputs to the network and compute the corresponding network outputs

(using 4.17 and 4.18), and errors ((gq = r q — £34 ) . Compute the sum of squares

of errors overall inputs (Ng)).

Compute the Jacobian matrix (using 4.40, 4.26, 4.24, 4.25, and 4.34).

Solve 4.37 to obtain A; .

Re-compute the sum of squares of errors using 5 + Art. Ifthis new sum of squares
is smaller than that computed in step 1, then reduce p by ,6 , let; = _x + Ag, and go
back to step 1. Ifthe sum of squares is.not reduced, then increasepbyfl and go

back to step 3.
The algorithm is assumed to have converged when the norm of the gradient (4.32)
is less than some predetermined value, or when the sum of squares has been

reduced to some error goal.

Process Procedures of ANN Model

The ANN model used a feed-forward neural network with the Levenberg-

Marquardt algorithm to calibrate and validate the NEXRAD Stage 111 data. The activation

filnction or transformation function used for the ANN model was a hyperbolic tangent

function. This network was selected because it has been Shown to be a good choice for

solving nonlinear relationships (Haykin, 1999; Demuth and Beal, 2000). Also, the

Levenberg-Marquardt algorithm is a global search algorithm that decreases the mean

square error between the actual output and estimated output much more rapidly with time.

56

Input data into the neural network were rescaled and the equation is shown as

 

follows:
Ri

RRemled = 0.1+ 0.65 x (R ) 4.41
max

where the RRe scaled , bounded between 0.1 and 0.75, is the rescaled coordinate

components (X, Y), raw NEXRAD grid values or compound training or testing data sets
that rain gage and NEXRAD data are lumped together, where the Ri is the initial
coordinate components (X Y), raw NEXRAD grid values or compound training or
testing data sets that rain gage and NEXRAD data are lumped together, where the Rmax
is the maximum value of the coordinate components (X, Y), raw NEXRAD grid values or
compound training or testing data sets that rain gage and NEXRAD data are lumped
together.

The available NEXRAD Stage II] data were daily rainfall in a 27 x 32 grid. This
data set is transformed into 27 x 32 = 864 triplets of inputs. The X and Y coordinates of
each pixel form two of the three inputs; the third input is the radar-measured rainfall
Rr(x, y) (see Figure 4.3). The same transformation is performed on the SEMCOG rain
gage data with the only difference that the third input is the gage-measured rainfall
Rg(x,y). The data sets of NEXRAD Stage III and rain gage triplets constitute the
compound data set that is available for training and testing the feed-forward neural
network. The X and Y coordinates serve as inputs to the network, Rr(x, y) or Rg(x, y) is the

desired output, and Rr ’(x, y) or Rg ’(x, y) is the estimated radar precipitation (the actual

57

output of the single neuron in the output layer). Each of these triplets represents a rainfall
pattern.

The neural network was trained in two phases: primary and secondary. During the
primary training phase, the desired output was the radar-derived rainfall surface only. The
process was repeated until the network learned a functional representation of the radar-
derived rainfall surface, which was close to the original radar image. The second training
phase used the same network without reinitializing its connection weights. The new
patterns that the network was asked to learn consist of the gage measurements and the
remaining new patterns were selected points in the radar image, with different
coordinates from the rain gages. The inputs to the network will still be the coordinates X
and Y. The radar- or rain gage-measured values of rainfall will be the desired output.

The optimal topologies (hidden layer number and neuron number in a hidden
layer) of the feed-forward neural network were determined by the trial-and-error method.
This was to test what type of the topology of the ANN model performs the best by
varying with from one hidden layer to three hidden layers and various neuron numbers in
each of hidden layer. The best set of the connection weight trained by the calibration of
the ANN model was used to validate the validation data set. The performances of both
the OC and ANN models were examined by the model efficiency criteria. The best
performance of the model was used to adjust the NEXRAD Stage III data for the entire

state of Michigan.

58

Input Layer

Coordinate
Component X

 

093.2"! lawyer
' G) ’r— R’ (X. Y)

Coordinate —
Component Y

 

Input Array \ Hidden Layer Output Array

Figure 4.3. Feedforward Neural Network with Inputs (Coordinate X and Y) and
Output (R (X, Y».

59

APPLICATION OF THE MODELING METHODS IN MICHIGAN

The main purpose of modeling Michigan is to apply the ANN-based model to
adjust Stage III NEXRAD data across the State of Michigan using National Weather
Service gages and evaluate its performance. In this study, the ANN model is used for
modeling the entire state of Michigan. Also, the performances of three types of
NEXRAD grid sizes are evaluated by the improved performance of the Michigan daily
Stage III NEXRAD data.
4.4. Precipitation Data Sources

Hourly rain gage observation data from Michigan used in this study were obtained
from the Michigan Climatological Resources Program. Forty-two Fisher & Porter rain
gages were used to record real-time rainfall information. The Fisher & POrter rain gage
consisted of a collection bucket, a weighing device, an indicator dial and a paper tape for
recording. Precipitation amounts were recorded at 2.54 mm increments. The maximum
capacity was 495.3 mm. A machine punched holes in a paper tape on a moving scroll
every 15 minutes. Around the first of the month the paper tapes were sent to Asheville,
North Carolina where they were read and published. The time periods of the data used for
this study were fiom the months of May to September fiom 1999 to 2000. The same
hourly Stage III NEXRAD'data of Midwestern area used in the pilot study is used for this
study.
4.5. Methods

The methods of GIS data management used for modeling the state of Michigan

are the same methods as described in Section 4.3. 1. The only different one is to rescale

6O

the 4-km NEXRAD data into 16-km resolutions and transform back to the 4-km
resolution NEXRAD grids.

In this study, six daily precipitation events occurring in Michigan were selected
for examining the performances of ANN model. These 6 precipitation events are divided
into two types of the precipitation events: fill] and partial coverage. The first type of the
precipitation event was that the Michigan NWS rain gage network was fully covered by
the precipitation. Three of six events were full coverage events, in which each rain gage
registered precipitation. The remaining three events were partial coverage events, where a
portion of the rain gage network registers no rain. These six daily precipitation events
were further classified into three levels of precipitation events by their daily mean rain
gage values by natural break method. These three types of precipitation events were light,
moderate, and heavy precipitation events. The ranges of each level of daily precipitation
events are: light (< 6.73 mm), moderate (6.73 — 9.71 mm), and heavy (> 9.71 mm). These
three ranges are different fi'om the traditional one. The range of the heavy precipitation
events are equivalent to that of the moderate precipitation events of the traditional

classification method.

61

Chapter 5 RESULTS AND DISCUSSION
PILOT STUDY: MODELING SEMCOG, MICHIGAN

5.1 Results of Statistical Analyses for Pilot Study

In the pilot study, hourly precipitations were analyzed to determine the agreement
of occurrence of precipitation between the two rainfall sources and the magnitude of the
difference between the rain gage measurements and the NEXRAD estimate. This analysis
was performed as a preliminary study to justify the use of further post processing of the
NEXRAD surface with ground gages using artificial neural networks and ordinary
cokriging. In the first portion of the analysis, hourly gage rainfall values and NEXRAD
estimates within the SEMCOG network were compared against each other to determine if
there was agreement on the occurrence of rainfall. The comparisons were grouped into
one of four possible conditions (See Table 4.1). For each year in the study, the gage-
hours in each condition were summed over the year. Over the 10 month time period there

were approximately 500,000 gage-hours. These data are shown in Table 5.1.

Table 5.1 Hourly Precipitation Distribution Conditions from May through September.

 

 

 

1999 2000
Condition Occurrence Percent of Total Occurrence Percent of Total
10336 - hr) (%) (Gage - hr) (%)
1 4092 1.69 7895 3.17
2 11326 4.67 . 13442 5.40
3 5091 2.10 6368 2.56
4 221867 91.54 221247 88.87

 

It is obvious fiom Table 5.1 that for the vast majority of the time fi'om May
through September, neither the rain gages nor NEXRAD recorded rainfall events.
Somewhat disturbing though, the occurrence of condition 2 is twice as fi'equent as
condition 1. This means that during a given rainfall event, NEXRAD is twice as likely to

not register a true rainfall occurrence. Similarly, condition 3 occurs roughly with the

62

same frequency as condition 1. This suggests that false positives are recorded by
NEXRAD with roughly equal frequency as it records “true” rainfall. Further analysis was
performed to examine the magnitude and significance of these errors in conditions 1 — 3.

Errors between NEXRAD and gages occurring in condition 1 are Shown in Table 5.2.

Table 5.2 Differences between Hourly NEXRAD and Gage Values in Condition 1.

 

 

1999 2000
Mean Bias (mm) -0. 12 0.32
Absolute Mean Bias (mm) 3.11 3.29
Mean, rainfall across gages (mm) 2.68 3.05

 

It can be seen from Table 5.2 that in 1999, NEXRAD on average underestimates
hourly rainfall by 0.12 mm, which is in agreement with most previous studies. However,
in 2000, NEXRAD overestimated hourly rainfall by 0.32 mm. The absohrte magnitude of
error between gages and NEXRAD is quite high, greater than 3 mm per hour in both
years, which is greater than the mean hourly rainfall recorded at the gages. Additionally,
the error between gages and NEXRAD during these time periods was quite variable.
Figures 5.1 and 5.2 display the monthly mean bias between NEXRAD and gages for
1999 and 2000, respectively. It can be seen that across the time period NEXRAD both
overestimates and underestimates monthly rainfall. These inconsistencies are most likely
due to the distribution of storm types throughout the Study period since NEXRAD
generally underestimates convective storms and overestimates stratified storms. So for
any given time period, the agreement between NEXRAD and gages will probably be
depended on the distribution of storm types across the rain gage network. This adds quite

a bit of uncertainty in using raw Stage III NEXRAD for rainfall estimation.

63

 

 

 

 

1.5 1
E 1— -
3
m 0.5 a _
2 0
>5 —
e
8 -05 ~ '-
2

-
'1 l 1 T I I
May June July August September
Month

 

 

 

Figure 5.1 Monthly mean bias between hourly NEXRAD and rain gage network in 1999.

 

 

 

 

1.5 -
a r- -
2.3“ .—
55 0.5 - .—
2 0 4—.
5
8 -0.5 - .—
E
'1 I T I l I
May June July August September
Month

 

 

 

Figure 5.2 Monthly mean bias between hourly NEXRAD and rain gage network in 2000.

Table 5.3 displays the absolute mean bias between hourly gages readings and
NEXRAD for conditions 2 and 3. The bias associated with condition 2 was similar
between 1999 and 2000. Examining the bias in condition 2 provides some insightful
information. It gives a threshold hourly rainfall rate at which NEXRAD is not able to
register a true precipitation event. With the SEMCOG data, this corresponds to an hourly
rainfall rate of roughly 1.25 mm/hr. This shows that while condition 2 occurs much more
fi'equently than conditions 1, the rainfall rates involved are quite small. This suggests that
condition 2 is occurring in lighter intensity rain events or is occurring during periods of
light rainfall during more intense storm events. Figures 5.3 and 5.4 display the histogram
of the distribution of average condition 2 error at each gage in the network for 1999 and
2000, respectively. It can be seen from these two figures that the error associated with

condition 2 appears to be fairly well behaved, but Slightly skewed.

Table 5.3 Hourly Errors between NEXRAD and Gage Values in Conditions 2 and 3.

 

 

 

 

 

 

1999 2000
Condition 2 - gage value
Absolute Mean Bias (mm) 1'22 1-23
Condition 3 — NEXRAD value 2 37 3 21
Absolute Mean Bias (mm) ' -

 

65

 

 

 

Frequency
+ Cumulative %

 

 

   

    

J 100%
—80% a:
5‘
8
—60% g.
[14
40% ,3
g
:3
-20% E,
U
—o%

 

0 0.26 0.53 0.79 1.06 1.32 1.58 1.85 More

Bias (mm)

 

Figure 5.3 Frequency distribution of condition 2 bias averaged across SEMCOG gages

 

 

 
    

 

for 1999.

30 100%
A25 4 -Frequency P 80% §
3 + Cumulative % 5‘
s20 — s
59 ~ 60% :3
a 15 — 5
t: B4
3 — 40% g
E 1° ‘ i

5 _{ ' 200A) g
O
O J l I ‘ 00A)

 

   

 

 

 

0 0.23 0.45 0.68 0.90 1.13 1.35 1.58 More

Bias (mm)

 

Figure 5.4 Frequency distribution of condition 2 bias averaged across SEMCOG gages

for 2000.

66

 

 

When condition 3 occurs, hourly NEXRAD delivers a “false positive” for the
occurrence of rainfall. From Table 5. 1, condition 3 occurs roughly as frequent as
condition 1. The magnitude of this error was quite high, 2.37 mm/hr in 1999 and 3.21
mm/hr in 2000. This condition describes NEXRAD by overestimation rainfall in a given
area.

The overall conclusions that can be drawn fi'om this analysis is that not only is
there error between rainfall values between NEXRAD and rain gages, there is fiequent
disagreement between the two sources on whether or not it is even raining in any given
hour. There are many physical explanations that have been presented in the literature
review on why there is disagreement on rainfall occurrence. It has been Shown in this
study that NEXRAD frequently fails to register a true rainfall occurrence (condition 2),
but the intensity/volume of rainfall involved in this is small (~ 1.25 mm/hr). In a spatial
water balance application using NEXRAD, this most likely would not greatly affect the
outcome. Conversely, when NEXRAD registers a “false positive” for rainfall occurrence
(condition 3), the magnitude of error is quite high, more than twice as high as condition 2.
In the same spatial water balance application, this error would probably affect the
outcome by overestimating rainfall amounts. The results of this analysis suggest that it
would be advantageous relay to improve the NEXRAD Stage HI data using models (i.e.
artificial neural networks and ordinary cokriging) to reduce the occurrence and
magnitude of errors associated with conditions 1, 2, and 3.

5.2. Results of Pilot Study: Modeling SEMCOG, Michigan
The Stage III NEXRAD precipitation estimates provided excellent storm-scale

information about the spatial and temporal evolution of precipitation systems; often much

67

better than rain gage networks. Also, Stage III NEXRAD precipitation estimates provided
very valuable input as part of a comprehensive, multi-sensor precipitation system.
However, many research have shown that hourly, daily, and monthly mean areal
precipitation values derived from Stage III NEXRAD were generally biased low
compared with gage—derived estimates, especially for convective precipitation events.
Therefore, the goal of this study was to optimally combine these two types of
measurements giving estimates that were superior to estimates obtainable from each
individual device alone.

In this study, the rain gage measurements from the SEMCOG rain gage network
were regarded as ground truth measurements used to improve the daily NEXRAD Stage
III precipitation fields. Twenty-two SEMCOG daily precipitation events were used to
evaluate both the OC and the ANN models by calibrating and validating the daily Stage
III NEXRAD data.

Tables 5 .4 - 5.7 show the results of modeling the twenty-two SEMCOG
precipitation events by evaluating the performances of both the OC and the ANN models.
These tables also compared with the initial synthetic statistical matrices to learn whether
both models improved the initial synthetic statistical matrices of the raw Stage III
' NEXRAD data. Two daily precipitation events are demonstrated in details in Sections
5.2.1 and 5.2.2.

5.2.1. Results of the Precipitation Event (15/06/1999
Initial Synthetic Statistical Analysis
This precipitation event was grouped as a light precipitation event. It only covered

half of the SEMCOG area. In Table 5.5, 62 SEMCOG rain gage measurements and

68

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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74

corresponding NEXRAD grid values were compared by statistical analysis. The results
indicated poor correlation between rain gage and radar measurements. Table 5.5 also
showed the difference between the average of rain gage values and the average of Stage
III NEXRAD values produced by arithmetical averaging method. This showed the
precipitation patterns measured by both devices were poorly correlated, but the areal
average precipitation distributions measured by both devices were very different.

The small positive MB and NBIAS showed that the radar-derived precipitation
values slightly overestimated the precipitation values. Both AMB and NRMSE values
were greater than 1.0 suggesting that the measurement error of NEXRAD radar was large.

Table 5.5 and Figure 5.5 depict the initial synthetic statistics of this examined
precipitation event. Normally, the dependence between raw NEXRAD data and rain gage
data showed up in a bivariate scatter diagram as a tendency to form an elliptical cloud
along a diagonal. The cloud had a major axis along the line at 45 degree to the positive
transverse axes in the case of positive correlation (CC = 1), and a major axis along the
perpendicular line at 135 degree to the positive transverse axis in the case of negative
correlation (CC = -1). According to the results of Section 5.1, the number and percentage
of the Condition 2 by hourly, daily, monthly, and yearly were very high. Thus, most of
the slopes of the trend line equations in these twenty-two bivariate diagrams were much
less than one, especially the light precipitation events.

In Figure 5.5, the trend line equation showed a low slope value (0.49) and the
bivariate scatter diagram depicted an elliptical shape with a wide minor axis. This showed
that both measurements present many disagreements but are still slightly correlated with

each other.

75

 

 

RawNEXRADStageIIIDatavs. SWCOGRairmgehdeasueumIs
(Dainrec'piatbnEm Occmed onOS/06/1999)

 

co
I

O

N)
J

y = O.4885x+ 1.1585

R2 = 0.3828
cc = 0.6187

M 0‘
J
O

RawNEXRAD Stagem Values (rm:
&

 

 

 

10 12

 

 

 

Figure 5.5 A Bivariate Scatter Diagram for Both Raw Stage III NEXRAD Data and
SEMCOG Rain Gage Measurements (Daily precipitation event occurred
on 05/06/1999). Light Precipitation Event.

76

Figure 5.6 depicted the daily raw NEXRAD Stage III precipitation surface.
Approximately one half of the SEMCOG network was covered by the precipitation.
Twenty-eight rain gages (yellow stars) were used for calibration (or cross validation), and
thirty-four rain gages (white stars) were used for validation. The data used for calibration
had higher cc and R2 values than the data used for validation. The negative MB and
NBIAS values in the calibration showed that the NEXRAD radar underestimated the
precipitation. The positive MB and NBIAS values in the validation showed that the
NEXRAD radar overestimated the precipitation. The AMB and NRMSE values of the
validation were higher than those of the calibration showed that the radar estimation error
in the validation was higher than that in the calibration.

No two or more rain gage points occupied a NEXRAD yid cell. Therefore, the
percentage of the density distribution of the SEMCOG rain gages in the SEMCOG area
with 27 by 32 4-lrm yids were calculated by the 62 gage-occupied yids divided by 864
NEXRAD yids and multiplied by 100%, which was 7.2%.

Results of 0C Model

The OC approach provided an estimate of the precipitation surface assuming
second-order stationarity to minimize the uncertainty associated with semivarioyam
estimation. It considered the statistical properties of the rain gages, the radar, and the
dependence of each of the devices on each other, and eliminates the error due to point
sampling of rainfall by rain gages.

The first step of processing for the 0C model is to produce the semivarioyams
for NEXRAD radar and rain gage variates, and cross semivarioyarn for both variates.

The two semivarioyams and cross sernivarioyam are shown in Figure 5.7, 5.8, and 5.9,

77

Raw NEXRAD Stage III Precipitation Surface
(Daily Precipitation Event Occurred on (15/06/1999)

1': 8050099 Rang-9n
f NW8 Test Rangoon

-1

“‘

hue.’??
I

“‘

de

 

20 O 20 40 60 80 I‘Glomaton

t'll

Figure 5.6 Daily Raw Stage III NEXRAD Precipitation Surface (Daily
precipitation event occurred on 05/06/1999). Light Precipitation Event.
*The SEMCOG area was partially covered by the precipitation event.
"The yellow and white stars were used for the calibration and
validation rain gages, respectively. They were used in the processes of
the 0C and ANN models.
*“Four purple rain gages were the NWS test rain gages used to
evaluate the performance of the 0C and ANN models. These four
NWS rain gages were not involved in the processes of both 0C and
ANN models.

78

3 SO

1 90

Sernrvarrance

0 95

 

Isotropic Variogram of NEXRAD Stage III Data (05 06/1999)

 

 

0.00

0 18000 36000 54000 72000

Separation Distance (111)

Spherical model (Co = (l 7‘7; Co + C = 3 829. Ao = 9540f 1.00; r2 = (i) 800‘

RSS=120>

Figure 5.7 Isotropic Variogram of Stage III NEXRAD Data (Daily precipitation

event occurred on 05/06/1999). Light Precipitation Event.

*The best-fit model was spherical model.

"Nugget variance: Co = 0.777; structural variance: C; sill = C0 + C =

3.829; range: A0 = 95400.
*"Active lag distance: 72,000 m and lag interval: 8,500 m.
""R2 or Reyession Coefficient was to indicate how well the model fits
the variogram data. R2 = 0.800.

***** RSS or Residual Sums of Squares was used to indicate how well
the model fits the variogram data; the lower the reduced sums of
squares, the better the model fits. RSS = 1.20.

79

Isotropic Variogram ofRaurgage Measurements (05 06» 1999)

54"

410

Sernrvarriulce

 

137

 

 

0 0t“; 5 -
0 00 18000 00 36000 00 54000 00 73000 00

Separation Distance (in)

Spherrcztl model (Co = 1 660. Co + C = 7329, A0 = 158300 00. L? = 0 822.

RSS: 1.6")

Figure 5.8 Isotropic Varioyam of SEMCOG Rain Gage Measurements (Daily
precipitation event occurred on 05/06/1999). Light Precipitation Event.
*The best—fit model was spherical model.

"Nugget variance: Co = 1.660; structural variance: C; sill = C0 + C =

7.329; range: A0 = 158,300.
*"Active lag distance: 72,000 m and lag interval: 8,400 m.
****R2 or Reyession Coefficient was to indicate how well the model fits
the varioyam data. R2 = 0.822.

***** RSS or Residual Sums of Squares was used to indicate how well
the model fits the variogram data; the lower the reduced sums of
squares, the better the model fits. RSS = 1.67.

80

4‘3")

3.17

Cross Serurvarrance

l 06

Isotropic Cross Var rogrmn (05.061999)

 

 

 

0 00

O l 8000 36000 54000 ”2000

Sep'cu‘atron Distance

Spherical model (Co = 0.450. Co + C = 4.909. A0 = 129100 00. r2 = O. 7’65.

RSS = 2.53)

Figure 5.9 Isotropic Cross Varioyam of SEMCOG rain gage measurements (Daily

precipitation event occurred on 05/06/1999). Light Precipitation Event.

*The best-fit model was spherical model.

“Nugget variance: Co = 0.450; structural variance: C; sill = C0 + C =

4.909; range: A0 = 129,100.
"*Active lag distance: 72,000 m and lag interval: 9,000 m.
****R2 or Reyession Coefficient was to indicate how well the model fits
the variogram data. R2 = 0.765.

***** RSS or Residual Sums of Squares was used to indicate how well
the model fits the variogram data; the lower the reduced sums of
squares, the better the model fits. RSS = 2.52.

81

respectively.

The second step was to model the two semivariograms and cross semivarioyam
to find the best set of parameters (sill and range) for the 0C model. In this case, the
spherical model was the best-fit model for these semivarioyams and cross
semivarioyam. The last step was to use the best set of parameters (sill and range) to
process the 0C model to derive the OC-adjusted NEXRAD precipitation surfaces. Table
5.4 shows the results by the synthetic statistic matrices. t

Range is a scalar that controls the deyee of correlation between data points,
usually represented as a distance. A large range value shows that more spatial continuous
behavior and the variable are well correlated in space, and thus predictions resulted in
fairly smooth maps of the variable of interest. Because the range values of these
semivarioyams and cross semivarioyam are very large, the cross validation were well
correlated in space. The Sill value was the maximum value of semivarioyam or cross
varioyam. Sill value of the semivariance as the lag(h) goes to infinity and it was equal to
the total variance of the data set. The larger the sill value is, the larger the prediction
variance. Because the sill values of these semivarioyams and cross semivariogram were
small, the prediction variance becomes small. This will rarely affect the prediction result.

Table 5.5 shows the results afier processing the 0C model. Overall, the results of
the cross validation were also worse than those of the initial condition. The results of the
validation were slightly improved. The results of combining both cross validation and
validation data were worse than those of the initial condition. Figure 5.10 depicts the OC-
adjusted Stage III NEXRAD precipitation surface. Comparing with Figure 5.6, the OC-

adjusted precipitation patterns deyaded the valuable NEXRAD precipitation patterns.

82

Ordinary Cokriging-Adjusted NEXRAD Stage III Precipitation Surface
(Daily Precipitation Event Occurred on 05I0611999)

| SEMCOG
SO50699_OC_mm

 

w * E
30 0 30 60 Kilometers

Figure 5.10 Ordinary Cokriging-Adjusted Stage III NEXRAD Precipitation Surface.
(Daily precipitation event occurred on 05/06/1999). Light Precipitation
Event.

83

Although OC offered a minimum variance estimate and was the best linear estimator, the
senrivarioyams and cross semivarioyam were not well behaved for both measurements,
even though the model fit both semivarioyam and cross semivarioyam very well.
Results of ANN Model

The ANN model provided a transformation from the spatial learning of the
NEXRAD precipitation surfaces into the accurate reproduction of the rain gage values.
The optimal topology of the neural network was determined by a trial-and-error method.
This was to test what type of topology of the ANN model performs the best by varying
with from one hidden layer to more hidden layers and various neuron numbers in each
hidden layer. The best set of the connection weights trained by the calibration of the
ANN model was used to validate the validation data set. The neural netWork topology
was 2—75—1 denoting (from the most left to the most right) the neuron numbers in the
input layer, the first hidden layer, and the output layer, respectively. In this study, the
topology of the ANN model with one hidden layer performed the best. The best set of
connection weight was iteratively trained by 25 epochs per time. Over 750 times of 25
epochs were used to find the best set of connection weight. The total time spent on
training and testing was about 5 hours.

Table 5.5 shows the results after processing the ANN model. Overall, the results
of the calibration and validation were better than those of the initial condition. The results
of combining both calibration and validation data were better than those of the initial
calibration. Figure 5.11 depicts the ANN-adjusted Stage III NEXRAD precipitation
surface. Comparing with Figure 5.6, the ANN-adjusted NEXRAD precipitation patterns

improved the valuable NEXRAD precipitation patterns very well.

84

ANN-Adjusted NEXRAD Stage III Precipitation Surface
(Daily Precipitation Event Occurred on 05I06I1999)

SEMCOG
$050699_ANN_mm
- 1 - 2

- 3

 

30 0 30 so Nlomotorc

 

Figure 5.11 ANN-Adjusted Stage III NEXRAD Precipitation Surface. (Daily
precipitation event occurred on 05/06/1999). Light Precipitation Event.

85

Performance Evaluations of Both OC and ANN Models

Two types of performance evaluations were performed by: (1) comparing the
initial synthetic statistical matrices with the synthetic statistical matrices of both models,
and (2) comparing the synthetic statistical matrices of both models

Table 5.5 shows that after processing the OC model, the cross validated synthetic
statistical matrices did not improve the initial synthetic statistical matrices, and the
validated values only slightly improved the initial synthetic statistical matrices. Both
cross validated and validated values were combined together and regarded these values as
the improved NEXRAD values. The adjusted NEXRAD synthetic statistical matrices
were compared with the initial synthetic statistical matrices. Table 5.5 shows that the

Table 5.4 shows that after processing the ANN model both calibrated and
validated synthetic statistical matrices improved the initial synthetic statistical matrices.
Both calibrated and validated values were combined together and regarded these values
as the improved NEXRAD values. The combined synthetic statistical matrices were
compared with the initial synthetic statistical matrices. Table 5.5 shows that the
calibration performance of NEXRAD precipitation surface by the ANN model improved
the initial synthetic statistical matrices.

Table 5.5 shows that the synthetic statistical matrices of calibrated, validated, and
combined ANN-adjusted NEXRAD precipitation were better than those of cross
validated, validated, and combined OC-adjusted NEXRAD precipitation.

Figure 5.12 depicts the performances of OC- and ANN-adjusted Stage III
NEXRAD data. The ANN-adjusted NEXRAD precipitation presented the best correlation

with the rain gage values, because the slope of the trend line equation was very high

86

 

Various NEXRAD Stage III Values (rnr

 

PerfirrrmmesofOC- anlANNAdjustedNEXRADStageHIData
(Daiy Prcc'piat'nn Evert Occtned on 05l06/l 999)

 

ANN Adjusted
y = 0.8581x+ 0.5195
R2 = 0.584
CC = 0.764

0C Adjusted i

y = 0.4414.\'+ 0.8698 f
R2 = 0.358 ;

CC. = 0.598 |

i

i

 

i o RaWNEXRAD

/ ’ 1 - OCAdjtsted
, ’ a ANNAdeBled
— —L'near(RawNEXRAD)
-- - -L'nenr(oc Adjusted)
’ —Liw(ANNAdeBN)

 

 

 

Raw NEXRAD

y = 0.4885x+ 1.1585
R2 = 0.383
cc = 0.619

 

 

 

 

0 2 4 6 8 10 12
Ra'nyge Vahes (run)

 

Figure 5.12 Performance of OC- and ANN-Adjusted Stage III NEXRAD Data
(Daily precipitation event occurred on 05/06/1999). Light Precipitation
Event.

87

 

(0.86), i.e. the difference between rain gage values and ANN-adjusted precipitation
values were small. The OC-adjusted NEXRAD precipitation presented the worst
correlation with the rain gage values, because the slope of the trend line equation was
very low (0.4414), i.e. the difference between rain gage values and OC-adjusted
precipitation values were large.

5.2.2. Results of Precipitation Event 08/06/2000

Initial Synthetic Statistical Analysis

This precipitation event was youped as a heavy precipitation event. The
SEMCOG area was fillly covered by the precipitation. In Table 5.7, 61 SEMCOG rain
gages measurements and NEXRAD yid values where these 61 rain gages were present
were used to compare with these 61 SEMCOG rain gages measurements for the statistical
analysis. The results of the combination presented that both correlation coefficient and R2
values showed poor correlation between rain gage and radar measurements. Table 5.7
also showed difference between the average of rain gage values and the average of Stage
III NEXRAD values produced by arithmetical averaging method. These show the
precipitation patterns measured by both devices were poorly correlated, and the areal
average precipitation distributions measured by both devices were different.

The negative MB and NBIAS showed that the radar-derived precipitation values
underestimated the precipitation values. Both AMB and NRMSE values were high
meaning that the measurement error of NEXRAD radar was large.

Table 5.7 and Figure 5.13 shows and depicts the initial synthetic statistics of this
examined precipitation event, respectively. In Figure 5.13, the trend line equation shows

a slope value (0.71) and the bivariate scatter diayarn depicted a wide scattered

88‘

 

 

RawNEXRADStay III Datavs. SEMCOGRaipy Mam
(Precipiat'nn EventOcairred on08/06/2000)

 

30

N
M

y = 07132:: + 1.5703 ° ‘
1?.2 = 0.5445

N
O
1

Raw NEXRAD Stage III Values (run
3

 

   

 

 

10 4
o O 0 ° ‘
5 .1
O
0 T I I I I T
0 5 10 15 20 25 30
WWII“ (um)

40

 

Figure 5.13 A Bivariate Scatter Diayam for Both Raw Stage III NEXRAD Data and
SEMCOG Rain Gage Measurements (Daily precipitation event occurred

on 08/06/2000).Heavy Precipitation Event.

89

 

distribution. This shows that both measurements presented disayeements but nicely
correlated each other. These were also approved by the results of the above initial
synthetic statistics.

Figure 5.14 depicts the daily raw Stage III NEXRAD precipitation surface. The
SEMCOG area was fully covered by the precipitation. Thirty-three rain gages (yellow
stars) were used for calibration (or cross validation), and twenty-eight rain gages (white
stars) were used for validation. The data used for both calibration and validation had
good _CC and R2 values. The negative MB and NBIAS values in both calibration and
validation show that the NEXRAD radar underestimated the precipitation. The AMB and
NRMSE values of both calibration and validation show that the radar estimation errors
were large.

No two or more rain gage points occupied a NEXRAD yid cell. Therefore, the
percentage of the density distribution of the SEMCOG rain gages in the SEMCOG area
with 27 by 32 4-km yids were calculated by the 61 gage-occupied yids divided by 864
NEXRAD yids and multiplied by 100%, which was 7.1%.

Results of OC Model

The OC approach estimates the precipitation surface assuming second-order
stationarity to minimize the uncertainty associated with semivarioyam estimation. The
OC approach considers the statistical properties of the rain gages, the radar, and the
dependence of each of the devices on each other, and eliminates the error due to point
sampling of rainfall by rain gages.

The first step of precessing OC model was to produce the semivarioyams for

NEXRAD radar and rain gage variates, and cross semivarioyam for both variates. The

90

Raw NEXRAD Stage III Precipitation Surface
(Daily Precipitation Event Occurred on 08/06/2000)

7‘: 8080600 Ralngagea

f NW8 Test Ralngagea
:1 SEMCOG
$080600_Rew_mm

 

20 0 20 40 60 90 Niometera

Figure 5.14 Daily Raw Stage III NEXRAD Precipitation Surface (Daily
precipitation event occurred on 08/06/2000).Heavy Precipitation Event.

*The SEMCOG area was fully covered by the precipitation event.

"The yellow and white stars were used for the calibration and
validation rain gages, respectively. They were used in the processes of
the OC and ANN models.

"*Four purple rain gages were the NWS test rain gages using to

evaluate the performance of the OC and ANN models. These four
NWS rain gages were not involved in the processes of both OC and
ANN models.

91

two semivarioyams and cross semivarioyam were shown in Figures 5.15, 5.16, and 5.17,
respectively.

The second step was to model the two semivarioyams and cross semivarioyam
to find the best set of parameters (sill and range) for the OC model. In this case, spherical
model was the best-fit model for the semivarioyam of the Stage III NEXRAD data. The
linear model was the best-fit model for the semivarioyam of rain gage measurements and
cross semivarioyam. The last step was to use the best set of parameters (sill and range)
to process the OC model to derive the OC-adjusted NEXRAD precipitation surfaces.
Table 5.7 shows the results by the synthetic statistic matrices.

Range was a scalar that controls the deyee of correlation between data points,
usually represented as a distance. A large range value showed that more spatial
continuous behavior and the variable were well correlated in space, and thus predictions
resulted in fairly smooth maps of the variable of interest. Because the range values of
these semivarioyams and cross semivarioyam were very large, the cross validation were
well correlated in space. The sill value was the maximum value of semivarioyam or
cross varioyam. Sill value of the semivariance as the lagflz) goes to infinity and it is
equal to the total variance of the data set. The larger the sill value, the larger the
prediction variance. Because the sill values of these semivarioyams and cross
semivarioyam were large, the prediction variance becomes large. This will affect the
precipitation results.

Table 5.7 shows the results after processing the OC model. Overall, the results of
both cross validation and validation did not improve those of the initial condition. The

results of combining both cross validation and validation data did not improve the initial

92

Isotropic Variogram ofNEXRAD Stage III Data (08 06 2000)

 

 

 

59 2 0
O
0 U

44 4
3:): D
E
5
g. :9 6
55 . . . a .0...

l4 8 a

D
D
O (i -
0 2427: 48544 "-281“ 9‘089

Separatlon Distance ( m)

? sphet-tcal model (Co = 0100. Co + c = 49 650. Ao = 8260000. r: = 085'.
' RSS = 630 1

Figure 5.15 Isotropic Varioyam of Stage III NEXRAD Data (Daily precipitation

event occurred on 08/06/2000). Heavy Precipitation Event.

*The best-fit model was spherical model.

"Nugget variance: Co = 0.100; structural variance: C; sill = C0 + C =

49.650; range: A0 = 82,600.00.
"*Active lag distance: 97,088.70 m and lag interval: 9,708.87 m.
****R2 or Regression Coefficient was to indicate how well the model fits
the variogram data. R2 = 0.857.

***** RSS or Residual Sums of Squares was used to indicate how well
the model fits the variogram data; the lower the reduced sums of
squares, the better the model fits. RSS = 620.

93

50.6”

Semival‘lance

 

Isotropic Variogram ofRarngage Measurements (08 062000)

 

1 6f. 100 32000 48000 64000

Separation Distance (in)

Linear model (Co = 0100. C0 + C‘ = 67,980, .-\0 = 64400.00. 13 = 0.9"2'.

RSS = 244.)

1

Figure 5.16. Isotropic Variogram of SEMCOG Rain Gage Measurements (Daily

precipitation event occurred on 08/06/2000). Heavy Precipitation Event.

*The best-fit model was linear model.

"Nugget variance: Co = 0.100; structural variance: C; sill = C0 + C =

67.980; range: A0 = 64,400.00.
"*Active lag distance: 64,000 m and lag interval: 9,708.87 m.
""R2 or Regression Coefficient was to indicate how well the model fits
the variogram data. R2 = 0.972.

***** RSS or Residual Sums of Squares was used to indicate how well
the model fits the variogram data; the lower the reduced sums of
squares, the better the model fits. RSS = 244.

94

 

Isotropic Cross Yal‘ioyalli ( 08:? itir'2(10( 1 )

 

 

31.4 ‘3 /,/
o
://
o 25 3 /’
o
'53 /'
5 151 x/
U} ‘ / 0
5:; /// U
" ,/
7 O ///
/
/ D 0
V//
-l.l n
0 I 2000 24000 36000 481110

Separation Distance tin)

Linear model (Co = 0.100. Co + C = 40.310. Ao = 64350 00‘. r2 = 0940',
RSS = 319.)

Figure 5.17 Isotropic Cross Varioyam of SEMCOG rain gage measurements (Daily
precipitation event occurred on 08/06/2000).Heavy Precipitation Event.
*The best-fit model was linear model.
"Nugget variance: Co = 0.100; structural variance: C; sill = C0 + C =
40.310; range: A0 = 64,250.
"*Active lag distance: 48,000 m and lag interval: 5,000 m.
****R2 or Reyession Coefficient was to indicate how well the model fits
the variogram data. R2 = 0.940.
***** RSS or Residual Sums of Squares was used to indicate how well
the model fits the variogram data; the lower the reduced sums of
squares, the better the model fits. RSS = 219.

95

condition. Figure 5.18 depicts the OC-adjusted Stage III NEXRAD precipitation surface.
Comparing with Figure 5.14, the OC-adjusted precipitation patterns slightly deyaded the
valuable NEXRAD precipitation patterns.

Results of ANN Model

The ANN model provided a transformation from the spatial learning of the
NEXRAD precipitation surfaces into the accurate reproduction of the rain gage values.
The optimal topology of the neural network was determined by a trial-and error method.
This was to test what type of the topology of the ANN model performs the best by
_ varying with from one hidden .layer to more hidden layers and various neuron numbers in
each of hidden layer. The best set of the connection weight trained by the calibration of
the ANN model was used to validate the validation data set. The neural network topology
was 2-200-1 meaning (fiom the most left to the most right) the neuron numbers in the
input layer, the first hidden layer, and the output layer, respectively. In this study, the
topology of the ANN model with one hidden layer performed the best. The best set of
connection weight was iteratively trained by 10 epochs per time. Over 650 times of 10
epochs were used find the best set of connection weight. The total time spent on training
and testing was about 5.4 hours.

Table 5.7 showed the results after processing the ANN model. Overall, the results
of both calibration and validation were better than those of the initial condition. The
results of combining both calibration and validation data were better than those of the
initial condition. Figure 5. 19 depicted the ANN-adjusted Stage III NEXRAD
precipitation surface. Comparing with Figure 5.14, the ANN-adjusted NEXRAD

precipitation patterns improved the valuable NEXRAD precipitation patterns.

96

Ordinary Cokriging-Adjusted NEXRAD Stage ill Precipitation Surface
(Daily Precipitation Event Occurred on 08I06l2000)

D SEMCOG
sososoo_oc_mm
- 5 '6
- 7 -9
_10 .11
:j 12 -13
14 -16
["__']17 .19
E! 20 -21
[.1 22 -23
Vii-J 24 . 26

30 0 30 60 Kilometers W * I!

Figure 5.18 Ordinary Cokriging-Adjusted Stage III NEXRAD Precipitation Surface.
(Daily precipitation event occurred on 08/06/2000). Heavy
Precipitation Event.

    

 

97

ANN-Adjusted NEXRAD Stage III Precipitation Surface
(Daily Precipitation Event Occurred on 08I06I2000)

[:SEMCOG
$080600_ANN_mm
1-7
8-11
- 12-15
[316-18
19-21
[I 22-25
E???" 26-29
- 30-37
1:0
ENoData

w * a
30 0 30 60 Ntornetara

S

  
  
   
   
  
 

Figure 5.19 ANN-Adjusted Stage III NEXRAD Precipitation Surface. (Daily
precipitation event occurred on 08/06/2000). Heavy Precipitation Event.

98

Performance Evaluations of Both 0C and ANN Models

Two types of performance evaluations were performed by: (1) comparing the
initial synthetic statistical matrices with the synthetic statistical matrices of both models,
and (2) comparing the synthetic statistical matrices of both models.

Table 5.7 shows that after processing the OC model both cross validated and
validated synthetic statistical matrices did not improve the initial synthetic statistical
matrices. Both cross validated and validated values were combined together and regarded
these values as the improved NEXRAD values. The OC-adjusted NEXRAD synthetic
statistical matrices were compared with the initial synthetic statistical matrices. Table 5.7
shows that the calibration performances of NEXRAD precipitation surface by the OC
model did not improve the initial synthetic statistical matrices.

Table 5.7 shows that after processing the ANN model both calibrated and
validated synthetic statistical matrices improved the initial synthetic statistical matrices.
Both calibrated and validated values were combined together and regarded these values
as the improved NEXRAD values. The combined synthetic statistical matrices were
compared with the initial synthetic statistical matrices. Table 5.7 shows that the
calibration performance of NEXRAD precipitation surface by the ANN model improved
the initial synthetic statistical matrices.

Table 5.7 shows that the synthetic statistical matrices of calibrated, validated, and
combined ANN-adjusted NEXRAD precipitation were better than those of cross
validated, validated, and combined OC-adjusted NEXRAD precipitation.

Figure 5.20 depicts the performances of OC- and ANN-adjusted Stage III

NEXRAD Data. The ANN -adjusted NEXRAD precipitation improved the correlation

99

 

Raw NEXRAD Stage III Values (mn

 

Perirrrmmes of OC- and ANN Adjusted NEfRAD Stay III Data
(Daiy Precipiation Ever! Occurred on 08/06/2000)

 

 

 

 

 

 

 

 

 

 

4o -*
a ANN Atliiihlt‘d
35 - 0C Adjusted y 0 walk - 2 052‘)
y = 0,6122x + 4.0147 R3 0 on
30 - R2 50.526 a A ‘ A (‘c 0707,
cc = 0.72' A
3 A ‘ A p e RawNEXRAD
25 - ’ ‘ ~
/ a OCAdlebd
20 z . a ANNAdjustcd
_ _Im‘ r(RawNEXRAD)
15 _ _ . .IM- me Adjused)
—Linear(ANN Adjtmd)
10 - Raw NEXRAD
y= 0.71325; + 1.5703
5 - R2 = 0545
CC = 0.738
0 A
s 10 15 20 25 30 35 40

Rakes: Values (m)

 

 

Figure 5.20 Performance of OC— and ANN-Adjusted Stage III NEXRAD Data
(Daily precipitation event occurred on 08/06/2000).Heavy Precipitation
Event.

with the rain gage values, and the slope of the trend line equation of the ANN model was
the best (0.99), i.e. the difference between rain gage values and ANN-adjusted
precipitation values were much improved. The OC-adjusted NEXRAD precipitation
presented the worst correlation with the rain gage values, and the slope of the trend line
equation was not the best (0.61), i.e. the difference between rain gage values and OC-
adjusted precipitation values were not improved.
5.3. Discussion of Modeling SEMCOG, Michigan

FNN with LM algorithm considered the problem of exact interpolation in
hydrological applications given a set of N input vectors x1, x2, rm and the
corresponding desired outputs ortargetsyr, y), yN. F(x.) = y,, i= 1, 2, 3, N. x is a p-

dimensional input vector. The exact interpolation of the generalized FNN was

N N

F (x) = f (2 Yiwi + W0) = tanh( ZYiwi) , where the activation function was hyperbolic
i=1 i=0

tangent function.

The goal of interpolation by Feedforward neural networks was to minimize an
T

Q Q
errorfunctionas E(F)=l Z ({q #11:!) (Eq -gy)=-]— Zgggq.
2q=l . 2q—l

OC model was one of the popular statistical models used for interpolating spatial '
data in hydrological applications such as rainfall estimate based on rain gage
measurements and radar estimates using ordinary cokriging model. Given a set of n

spatial locations x,, 1:), x" where a property, v, is measured as v], V), v,.. CC

101

assumed that the value of v at some other spatial location x was given by a linear

combination of measured values as v = Z w,v,. .

i=1
The weights 11),, i = 1, 2, n depended on the spatial location x, and are
determined from the matrix equation [C] [w] = [C0], where [C] is a matrix containing
covariance among v values at measured locations, [Co] is a vector of covariance of the v
values between measured locations and the interpolation point, and [w] denotes the
weight vector (Journel and Huijbregts, 197 8; Isaaks and Srivastava, 1989).
i The similarities and differences between interpolations using FNN and 0C were
as follows.

1. OC visualized the interpolation as a realization of a random field. In addition, it
imposed second-order stationary requirements to estimate the statistics of the
random field from a single realization. Neural networks had their origin in
reyession-based methods and were based on interpolation theory.

N
g
2. OC produced unbiased estimates so that any spatial location 2 2g,- =1 and
i=1

Nr
2,1,1- 2 0 (See equation 13 in Section 3.4.4). This led to exact interpolation

j =1

when x coincides with a measurement location, just as in the case of FNN with
LM algorithm. OC was based on the idea of producing a best linear unbiased
estimate (BLUE). It was the best in the sense of minimizing the variance of

estimation error. The goal of interpolation by FNN with LM algorithm was to

102

minimize an error firnction

1 Q T 1 Q
aSE(F):§q§1(€q"—'y) ({q‘gyJZEElgng'

. A major operational difference existed between OC and FNN with LM algorithm.

In OC, as the location x where an estimate was desired changes, the weight vector
w,- in v = Zwiv, changes and had to be obtained from an inversion of the matrix
i=1

[C] in [C][w] = [C0]. The linear unbiased (LU) decomposition of [C] (in lieu of
the inverse) for computing the inverse needed to be performed only once. In case
of FNN with LM algorithm, the weight vector changed with location x.

. Both kriging and FNN with LM algorithm were based on data exhibiting some
spatial continuity. In geostatistical applications, the semivarioyam or cross
semivarioyam function was a measure of the continuity that the quantity v
possesses. The varioyam is therefore crucial for CC. When using FNN with LM

algorithm, smoothness was imparted to the transformation through

1Q T 1Q T
E(F)=§Z(£q“—’Iri4) ({q’gyJZEEEq‘iq'

0:1

103

 

RESULTS OF MODELING STATE OF MICHIGAN
5.4. Results of Selecting the NEXRAD Grid Size

Six daily precipitation events were selected to examine the performance of the
ANN model. Two factors afl'ected the precipitation adjustment: density of rain gage
network and spatial variety of a precipitation event. The yid size presented the general
spatial information by distance. The density of the Michigan NWS rain gage network to
the Michigan 16-km NEXRAD yid was about 3.0% and to the Michigan 32-km
NEXRAD yid was about 13.8%. The density of the rain gage network used for 32-km
’ NEXRAD yid size was much. higher than that used for 16-km NEXRAD yid size.

The spatial variability of the precipitation usually was very high. This caused by
many factors such as topographical feature, wind directions and speeds, spatial
distribution of precipitation intensity of a precipitation event, and temporal factor. \

Table 5.8 shows the results of modeling the six Michigan precipitation
events by evaluating the adjusted NEXRAD performances using the ANN models. Table
5.8 also compares with the initial synthetic statistical matrices to learn whether the ANN
model improves the initial synthetic statistical matrices of the raw Stage III NEXRAD
data.

5.5. Results and Discussion of Precipitation Event 07/01/1999
5.5.1. Initial Synthetic Statistical Analysis

This precipitation event was youped into the type of the heavy precipitation event.
It firlly covered Michigan. In Table 5.8, 28 Michigan NWS rain gages measurements and
NEXRAD yid values where these 28 rain gages were present were used to compare with

these 28 SEMCOG rain gage measurements for the statistical analysis. The results of the

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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853 5. 50am” 85w «5 ma .5 Emma 58 Baum net-536.5
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105

combination presented that both correlation coeflicient and R2 values show good
correlation between rain gage and radar measurements. Table 5.8 also shows the large
difference between the average of rain gage values and the average of Stage III
NEXRAD values produced by arithmetical averaging method were also very different.
This shows the precipitation patterns measured by both devices were nicely correlated,
but the areal average precipitation distributions measured by both devices were different.

The negative MB and NBIAS shows that the radar-derived precipitation value
underestimates the precipitation values. Both AMB and NRMSE values are large which
means that the measurement error of NEXRAD radar is large.

' Table 5.8 and Figure 5.21 shows and depicts the initial synthetic statistics of this
examined precipitation event, respectively. Normally, the dependence between raw
NEXRAD data and rain gage data shows up in a bivariate scatter diagram as a tendency
to form an elliptical cloud along a diagonal. The cloud had a major axis along the line at
45 degree to the positive transverse axes in the case of positive correlation (CC = l), and
a major axis along the perpendicular line at 135 degree to the positive transverse axis in
the case of negative correlation (CC = -l).

In Figure 5.21, the trend line equation shows a slope value (0.5644) and the
bivariate scatter diagram depicted an elliptical shape with a wide minor axis. This shows
that both measurements present disagreements but correlated with each other. These were
also approved by the results of the above initial synthetic statistics.

Figure 5.22 depicts the daily raw Stage III NEXRAD precipitation surface. The
Michigan was firlly covered by the precipitation. Fourteen rain gages (yellow stars) were

used for calibration (or cross validation), and fourteen rain gages (white stars) were used

106

 

 

Raw NEXRADStag III Data vs. M’nhigmNWS 11311835 Measmermrls
(Daiy PrecbiatbnEverl Occurred on 07:0 1/1999)

J

888

y = 0.5644 -0.1207

R2 = 0.5631
CC = 0.7504

4L

    
  
 

N
O
1

 

Raw NEXRAD Stage III Values (mn
Lat)
c

 

 

10 ‘
. O
0 l I : *L T r r T 1
0 10 20 30 40 50 60
Mbm NWS Ram; Vahes (inn)

 

Figure 5.21 A Bivariate Scatter Diagram for Both Raw Stage III NEXRAD Data and
Michigan NWS Rain Gage Measurements (Daily precipitation event
occurred on 07/01/1999). Heavy Precipitation Event.

107

Michigan Raw NEXRAD Stage III Precipitation Surface
(Daily Precipitation Event Occurred on 07I01I1999)

 

60 0 60 120 180 240 300 360Kllomotor8
E

* Ml070199_Gages
[:j Mlchlgan
O70199_4km_Raw_mm

1 -7

Figure 5.22 Daily Raw Stage III NEXRAD Precipitation Surface (Daily
precipitation event occurred on 07/01/1999). Heavy Precipitation Event.
*The Michigan was firlly covered by the precipitation event.
"The yellow and white stars were used for the calibration and
validation rain gages, respectively.

108

for validation. The data used for calibration had good cc and R2 values, but the data used
for validation had poor CC and R2 values. The negative MB and NBIAS values in the
calibration and validation showed that the NEXRAD radar underestimates the
precipitation. The AMB and NRMSE values of both calibration and validation were very
high. This shows that the radar estimation error is very high.

5.5.2. Results of After Processing ANN Model

Figure 5.23 depicts rescaled l6-km Stage III NEXRAD precipitation surface. The
precipitation patterns of the rescaled 16-km Stage III NEXRAD precipitation surface are
similar with those of the raw 4-km Stage III NEXRAD precipitation surface. Comparing
Figure 5.23 with Figure 5.22, the precipitation values of the rescaled one was lower than
the raw one, because the rescaled one took the average value from the '16 4-km grid
values of a 16-km grid as the precipitation value of that 16-km grid. If the precipitation
values of the ANN-adjusted 16—km NEXRAD grids were close to the rescaled 16-km
NEXRAD grid values, then the ratio would get the ANN-adjusted l6-km NEXRAD grids
back to the suitable precipitation patterns. Therefore, the ratios were the most important
values derived by the ANN-adjusted NEXRAD 16-km grid values divided by the
rescaled 16-km NEXRAD grid values.

The ANN model provided a transformation from the spatial learning of the
NEXRAD precipitation surfaces into the accurate reproduction of the rain gage values.
The optimal topology of the neural network was determined by a trial-and-error method.
This was to test what type of the topology of the ANN model performs the best by
varying with from one hidden layer to more hidden layers and various neuron numbers in

each of hidden layer. The best set of the connection weight trained by the calibration of

109

Rescaled Michigan 16-km NEXRAD Stage III Precipitation Surface
(Daily Precipitation Event Occurred on 07/O1l1999)

 

60 0 60 120 180 240 300 Kilometers
E

[:J Mlchlgan
070999_10ltm_Mean_nln
- 1 - s N
6 - 9
10 - 13
E] 14 - 17
13 - 21 W E
22 - 25
B 20 - 29
37. 3. - 35 S

-0
Emma

Figure 5.23 Daily Rescaled 16-km Stage III NEXRAD Precipitation Surface (Daily
precipitation event occurred on 07/01/1999). Heavy Precipitation Event.

110

the ANN model was used to validate the validation data set. The neural network topology
was 2-175-1 meaning (fi'om the most left to the most right) the neuron numbers in the
input layer, the first hidden layer, and the output layer, respectively. In this study, the
topology of the ANN model with one hidden layer performed the best. The best set of
connection weight was iteratively trained by 25 epochs per time. Over 550 times of 25
epochs were used to find the best set of connection weight. The total time spent on
training and testing was about 5.9 hours.

Table 5.8 shows the results after processing the ANN model. Overall, the results
of both calibration and validation were better than those of the initial condition. The
results of combining both calibration and validation data were better than those of the
initial condition. Figure 5.24 depicts the ANN-adjusted Stage III NEXRAD precipitation
surface. Comparing Figure 5.24 with Figure 5.23, the ANN-adjusted NEXRAD
precipitation patterns improves the valuable NEXRAD precipitation patterns. The
drawback is the spatial discontinuity of precipitation patterns. Figure 5.25 depicts the
transformed daily 4-km Stage III NEXRAD precipitation surface from ANN-adjusted 16-
km Stage III NEXRAD precipitation surface. The same drawback, which is the spatial
discontinuity of precipitation patterns depicted in the precipitation surface.

Figure 5.26 depicts the performances of the transformed 4-km Stage III NEXRAD
data. It presents the better correlation with the rain gage values and the slope of the trend
line equation is improved (0.69), i.e. the difference between rain gage values and ANN -

adjusted precipitation values are smaller.

111

 

ANN-Adjusted Michigan 16-km NEXRAD Stage III Precipitation Surface
(Daily Precipitation Event Occurred on 07I01l1999)

 

60 O 60 120 180 240 300 Kilometers
E

[:1 Michigan
070999_16km_ANN_mm

 

Figure 5.24 Daily ANN-Adjusted l6-km Stage III NEXRAD Precipitation Surface
(Daily precipitation event occurred on 07/01/1999). Heavy Precipitation
Event.

112

Transformed Mlchlgan 4-km NEXRAD Stage III Precipitation Surface
from ANN-Adjusted 16-km NEXRAD Stage ill Precipitation Surface
(Daily Precipitation Event Occurred In 07l01/1999)

 

60 0 60 120 180 240 300 360 Kilometers
E

Michigan
o7o199_4km_ANN_mrn
1 - 7
- 8 - 12
- 13 - 17 N
_ 18 - 22
[.71 23 - 27
28 - 33
34 - 40 W E
as 41 - 52
1.; o

muons-ta s

  

 

Figure 5.25 Transformed Daily 4-km Stage III NEXRAD Precipitation Surface fi'om
ANN-Adjusted l6-km Stage III NEXRAD Precipitation Surface (Daily
precipitation event occurred on 07/01/1999). Heavy Precipitation Event.

113

 

 

Perbmnnce of ANN -Tramibrned NEXRAD Stag III Data
(Daiy Prec'p'tat’nn Evert Oocmed on 07/01/1999)

 

 

 

   

 

60 -

g 50 q ’ 4-kmANN-Tmmfomlcd NEXRAD

% 4-km Raw NEXRAD y = 0.6907x - 00217

> 40 ‘ y — 0.52644.\+ 0.1207 I R: = 07938

E R = 05631 , . ’- CC = 0.8909

g, 30 , CC = 0.7504 " ' , x

U)

a

a e RawNEXRAD

8 - ANN-Tramlbmed

> 60 —L'n:ar(RawNEXRAD)
Michigan NWS Ran’ pg Vales (nm) — - -L'mar(ANN-Tramfiimed

NEXRAD)

 

 

 

Figure 5.26 Performance of ANN-Adjusted Stage III NEXRAD Data. (Daily
precipitation event occurred on 07/01/1999). Heavy Precipitation Event.

114

Chapter 6 SUMMARY and CONCLUSIONS
Statistical Analysis

In the statistical analysis, the results represent the significant discrepancies
between rain gage and Stage III NEXRAD data by hourly and by daily. The frequency of
the difference of the most of heavy precipitation events is smaller than those of the
moderate and the light precipitation events; the magnitude of the difi‘erence of the most of
heavy precipitation events is greater than those of the moderate and the light precipitation
events. Because the radar-derived rainfall provides valuable rainfall estimates in high
‘ spatial and temporal resolutions, it is necessary to reduce the magnitude of the
considerable difference between rain gage and Stage III NEXRAD data by optimally
combining both measurements to derive the more accurate rainfall surfaces.

Modeling SEMCOG Area and Entire State of Michigan

In this study, two methods, ordinary cokriging and ANN s, utilizing information
fi'om two sources of rainfall measurements are presented. A feed—forward neural network
with Levenberg-Marquardt algorithm trained in two phases, primarily with daily radar
precipitation data and, secondly, with rain gage data is applied to improve the radar-
derived rainfall surfaces for the SEMCOG area and the entire state of Michigan. The
results show a network that is able to'reproduce the rainfall structure by the high spatial
resolution of the radar and at the same time adjust it accordingly, so that it agrees with the
more accurate ground rain gages. In the current implantation the neural network is trained
and tested by the precipitation patterns and the spatial coordinates x and y. This approach
generally provides much better results than the ordinary cokriging in terms of the model

criteria. It is very important that the ANN model provides a robust spatial interpolation of

115

 

the rainfall field in high spatial resolution without rain gages, uses the fewer rain gage
measurements to improve the accuracy of the rainfall estimates, and is able to well

improve the accuracy of both full and partial spatial coverage.

 

116

Chapter 7 RECOMMENDATIONS FOR FUTURE STUDY
Listed below are some recommendations for fixture study:
. Incorporate into an operational model to improve daily rainfall data.
. Experiment with hourly rainfall data.
. Statistical analysis for connection weights and biases of the ANN model using

pattern classification technology to find the global connection weights and biases. I

 

117

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Anonymous. 1985. Next Generation Weather Radar Algorithm Report. No. R400-AR301.
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Anonymous. 1986a. Next Generation Weather Radar Product Description Document. No.
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Anonymous. 1986b. NEXRAD Technical Requirements. No. R400-SP301. The __
NEXRAD Joint System Program Office. }.

Anonymous. 1990. Federal Meteorological Handbook No. 11: Doppler Radar
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Anonymous. 1996. Hydrology Handbook 2'“1 Edition. ASCE. New York, NY.

Bailey, T. C., Gatrell, A C. 1995. Interactive Spatial Data Analysis. Longman Scientific
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Biswas, AK. 1967. Development of Rain gages. Journal of the Irrigation and Drainage
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Biswas, AK. 1970. History of Hydrology. American Elsevier Pub. Co., New York, NY.

Blurn, A 1992. Neural Networks in CH: An Object-Oriented Framework for Building
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Bose, N.K. and Liang, P. 1996. Neural Network Fundamentals with Graphs, Algorithms,
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121

APPENDICES

122

 

Appendix A
Various SEMCOG Precipitation Data
(Precipitation Event 05/06/1999)

sue-m X Y NEXRAD-n Gep_- ANN_- 0C_-
A3 661857.143789 192530.880673 1.800 2.540 2.386 3 132
L3 668048272705 241521550493 3.440 4.826 3.364 4.432
L 7 681514.971760 222057.746602 4.840 3.810 4.466 2.357
L10 658405618120 224659 693526 3.920 5.334 4.457 3.519
M 2 756937 867805 232774 056329 4.520 4.572 4 097 2.791
M 4 762562920492 230609680239 2.170 0 254 2 797 3.760
M8 746972860607 254820071250 1.820 3.556 2.209 2.354
M9 742960.436068 231431293091 1.620 0.762 1.031 1.782
M10 749986779148 230140.273915 2.940 2 794 3.547 3.102
M12 765224.025423 256122102610 1.540 5.842 3.364 2.615
M13 750684183706 240383890687 2.610 3.302 3.526 2.934
M14 765682093654 241381302807 3.070 2.794 1.937 2341
M16 755400.233316 223825771085 3.120 5.334 3.810 1.912
M17 744337.430006 224781756367 2.130 2.286 2.509 1.696
M19 755951048949 217610.399169 0.440 2.794 2.820 3.681
03 735369246078 230672.594422 0.230 0.254 0.420 0.925
04 734168924612 255016.775493 2.670 2.794 2.408 2.084
0 5 713090146295 246701551082 2.750 1.270 3.898 2.309
09 726130235853 247275671191 2.240 2.032 2.678 2.178
018 731346.624696 216708.011455 0.180 0.000 0.000 0.326
024 715654088076 215086283082 0000 0.508 0,499 0.617
025 731861.017503 225830.555575 0,170 1.270 0.813 0.319
W14 753133344245 209696295155 1.010 0.000 1.440 2.836
W18 745604.881900 214856586919 1.530 1.524 2.731 1.504
W20 735298.537945 199341 .859541 0.000 0.000 0.009 0.243
W23 724714028432 197970368012 0.000 0.000 0.314 0.000
W33 755386272117 215582872187 3.910 4.064 3 405 0.605
W48 709614.370019 201814621439 0.180 1.524 1.387 0.588
A1 678039980433 195924936908 10.600 2.540 3.521 2.074
A 2 663120262649 212553.141409 2.690 1.270 3.519 3.460
A 5 695810135030 191348250416 0.000 1.524 0.036 1.028
L1 656935798800 236936068948 3.380 4.572 5.860 3.684
L2 655307.791” 245383.380983 8.150 3.302 8.901 3561
L 5 655433651803 217957872282 9.390 5.588 8.333 3.580
L6 68(319554474 212103804745 3.420 3.048 5658 3.568
L8 683827288566 245447601664 5.360 4.572 5.732 3.631
L9 685117095706 233972632310 5.070 7.366 5.655 3.941
L11 671537 470375 229482547174 2.590 2.286 3.588 4.173
M1 754440159488 258799157739 1.110 3.302 2.078 1.814
M3 753510.085060 218106602475 3.910 4.826 4.387 1.914
M 5 756874108802 227770.456845 2.390 3.556 4.450 3.373
M7 739614099028 250112.456291 2.360 3.810 3.532 2.141
M18 745887802536 226750940884 3 430 2.286 2.243 2.297
02 730402927052 221676374291 0.170 0.254 0.772 0.172
O 7 717831717332 237839089634 6.970 2.540 4.415 1.701
08 725348147988 235798.729758 2.970 4.064 3.762 1.061
010 694269889040 228610917000 0.300 0.000 0.197 3.247
013 705431001880 220697610715 0.460 1.016 0689 1.509
019 722772817043 220375.078922 2.310 0.000 0 737 0.123
022 736583.803510 221238.380171 0.400 1.016 0 702 0.724
028 694588732145 213376137195 0.660 2.286 0.054 2.423
W2 708078587107 194300.186312 0.000 2.032 1.489 0.319
W16 734607714135 203484977237 0.000 0.508 0.081 0.111
W22 727994066738 195084409450 0.000 0.000 0.048 0.000
W25 732161.441554 213556429868 0.120 0.000 0.000 0.229
W27 726187905777 204715689118 0.000 1.016 0.180 0012
W29 742838247435 203183487706 3.530 3.556 1.549 0.426
W35 732221251123 179084322024 0.070 0.254 0008 0.116
W42 754665813608 213426186194 4.120 2.36 3.538 2.863
W43 733804150235 197470094732 0110 0.254 0000 0.000
W45 736867359922 197018.994551 1 690 0.508 0.724 0.059
W46 734124847745 185969011278 0000 0.000 0.860 0.091

123

Appendix B
Various SEMCOG Precipitation Data
(Precipitation Event 05/17/1999)

MID X Y NEXRAD-I Gaga- ANN 0C

A3 661857143789 192530880673 32 490 11.430 12.665 21.444
L3 668048.272705 241521.550493 12.590 6.096 9.997 13071
L 7 681514971760 222057.746602 18.480 9.144 12.902 31.597
L10 658405618120 224659.693526 9.850 5.588 6.403 17.038
M2 756937.867805 232774056329 22.730 8.128 11.254 29.709
M4 762562.920492 230609680239 22.500 8.382 14.586 25.104
M8 746972.860607 254820.071250 33.120 16.764 17.587 33 930
M 9 742960436068 231431293091 44.400 18.034 31.760 39.076
M10 749986.779148 230140273915 36.490 11.176 16.579 31 911
M12 765224.025423 256122.102610 34.180 13.970 21.034 30.082
M13 750684.183706 240383.890687 38.050 17.272 30.947 34.445
M14 765682093654 241381302807 29160 8.636 4.352 27.814
M16 755400233316 223825.771m5 28.380 7.112 12.595 29.770
M17 744337430006 224781.756367 28.220 12.700 24.746 36.313
M19 755951048949 217610399169 34.080 6.350 9.729 23.418
03 735369246078 230672.594422 46.810 22.606 34.658 40.567
0 4 734168924612 255016775493 29.610 16.256 20.632 38.967
05 713090146295 246701.551082 34.140 14.224 17.525 38250
09 726130235853 247275671191 42.700 13.970 24.687 35.577
018 731346.624696 2167(8011455 26.650 11.430 22.830 36.434
024 715654.088076 215086283082 60.630 33782 42.147 39.279
025 731861017503 225830555575 37.390 21.590 29.390 40.055
W14 753133344245 209696.295155 36.300 5130 10.502 22.997
W18 7456048819“) 214856586919 26.580 16.256 24.487 28 632
W20 735298537945 199341 .859541 28.800 18.542 25 921 26.979
W23 724714028432 197970368012 27.430 15.240 26.895 40.024
W33 755386272117 215582872187 22 310 7.620 9.401 34.239
W48 709614.370019 201814621439 56.460 16.002 27.134 41.049
A1 678039.980433 195924.936908 46.150 26.162 48.680 34.979
A2 663120.262649 212553.141409 19.380 10.668 14.168 18.991
A 5 695810135030 191348250416 43.540 23.368 36.549 44.101
Ll 656935798800 236936068948 12.070 11 684 26.236 10.028
L2 655307.791m8 245383380983 23.530 13.462 20.541 10.486
L 5 655433.651803 217957.872282 13.250 2.540 11.323 13.967
L6 68(819554474 212103804745 39.340 12.700 37.506 27.161
L8 683827288566 245447601664 17720 7.366 19.276 19967
L 9 685117095706 233972.632310 16.570 5.588 19.535 21.784
L11 671537470375 229482547174 7.250 10.160 12.859 13.807
M1 754440.159488 258799.157739 36.030 19.304 32.375 33.083
M3 753510.085060 218106.602475 22.310 6.350 14.085 29.437
M 5 756874.108802 227770456845 20.660 5.334 13.172 26.105
M 7 739614099028 250112456291 40.080 16.764 28.749 35.573
M18 745887802536 226750940884 41.740 11.176 26.656 32.720
02 730402927052 221676374291 37.390 19.812 33.877 34.085
0 7 717831.717332 237839089634 52.560 15.494 30.361 42155
08 725348147988 235798729758 56.700 37.084 54.723 44.840
010 694269.889040 228610917000 30.090 7.620 21.161 32.253
013 705431001880 220697610715 59.720 34.290 58.775 48.973
019 722772817043 220375078922 69.270 46.736 63.864 44.604
022 736583803510 221238.380171 41.000 10.414 30.520 29.892
028 694588732145 213376137195 59.930 20.828 62.919 40813
W2 708078587107 194300186312 35.820 24.892 25.045 47.673
W16 734607.714135 203484977237 28.800 15.240 31.929 28.235
W22 727994066738 195084409450 34.590 16.256 25.694 28.115
W25 732161 .441554 213556429868 30.040 16.256 24.150 27.393
W27 726187905777 204715689118 27.430 12.192 21.909 32.503
W29 742838.247435 203183487706 25.010 9.144 28.712 29.628
W42 754665813613 213426186194 24.570 6.350 5.330 27.132
W43 733804150235 197470094732 36.690 8.128 25.179 28.424
W44 733662817575 179256.261133 16.470 12.954 18.657 31.920
W45 736867359922 197018.994551 24.020 13.462 25 032 28.899
W46 734124847745 185969011278 15 500 9.144 25.544 30 347

124

 

In? Int-“WV KPH!-
i

Appendix C
Various SEMCOG Precipitation Data
(Precipitation Event 05/23/1999)

Mull) X Y NEXRAD- Gn'_- ANN 0C

A3 661857.143789 192530.880673 6.110 9.144 6.805 4 639
L3 668048.272705 241521.550493 3.440 3.810 3.464 2.866
L 7 681514971760 222057.746602 2.410 8.636 4.948 4.107
L10 658405.618120 224659.693526 4.690 6.604 5.588 4 078
M2 756937867805 232774.056329 4.130 8.890 4.507 3.458
M4 762562.920492 230609.680239 4.050 2.794 1.431 3975
M8 746972.860607 254820.071250 1.260 7.874 3.322 1.361
M9 742960.436068 231431.293091 2.320 10.668 6.547 2.394
M10 749986.779148 230140.273915 3.310 11.684 7.372 2.800
M12 765224025423 256122102610 3.080 9.906 6.107 2.803
M13 750684.183706 240383.890687 2.280 8.636 5.459 2.993
M14 765682.093654 241381302807 4.180 10414 7.872 3.688
M16 755400233316 223825.771085 2.590 3.048 0.469 3.487
M17 744337.430006 224781.756367 2.410 8.128 3.757 2.562
M19 755951048949 217610.399169 3.220 4.826 4.949 2.719
03 735369 246078 230672.594422 1.900 11.938 6.473 2.364
O 4 734168924612 255016.775493 0.090 4.318 6.174 2.773
O 5 713090.146295 246701.551m2 0.780 5.588 3.998 3.764
09 726130235853 247275.671191 4.620 6.096 5.269 0.632
018 731346.624696 2167(B.011455 3.260 13.462 6.568 2.912
024 715654.(88076 215086.283082 3.790 9.906 6.927 3.484
025 731861017503 225830555575 2.210 7.874 5.507 2.454
W14 753133.344245 209696.295155 3.350 5.080 3 842 3 032
W18 745604.881900 214856.586919 2.930 5.588 0.000 2.939
W20 735298.537945 199341.859541 3.860 4.572 1.212 3.825
W23 724714028432 197970.368012 4.130 6.096 3.294 4.206
W33 755386272117 215582.872187 2.730 0.254 0.000 3.242
W48 709614.370019 201814.621439 4.840 12.700 7.742 4153
A1 678039.980433 195924.936” 5.950 6.350 7.323 5.118
A 2 663120.262649 212553.141409 2.410 7.874 2 232 4.768
A 5 695810.135030 191348.250416 5.230 12.700 4.539 5.081
L1 656935.798800 236936068948 3.180 6.350 2.772 4.125
L 2 655307791138 245383.380983 2.410 5.588 3.643 3826
L 5 655433651803 217957872282 3 510 18.034 5 323 4.983
L6 68(319554474 212103.804745 3.340 5.842 2.183 3625
L8 683827288566 245447.601664 3.570 5.842 5.515 2.128
L 9 685117.095706 233972.632310 2.650 6.096 4.920 2.273
L11 671537.470375 229482547174 5.160 5.842 3.267 3.315
MI 754440.159488 258799.157739 1 220 7.874 0.331 1.875
M 3 753510.085060 218106.602475 2.730 4.064 0.785 2.885
M 5 756874.108802 227770.456845 2.140 1.270 5.293 3.412
M7 739614.099028 250112.456291 1.920 7.366 0.735 1.282
M18 745887802536 226750940884 4.280 11.684 10.511 2.590
02 730402.927052 221676374291 2.210 9.652 5.735 2.750
O 7 717831 .717332 237839.(B9634 4 480 12.192 5.656 2.481
08 725348.147988 235798729758 2.850 9.652 11.378 2.894
010 694269889040 228610917000 2.030 8 382 2.672 2.324
013 705431.001880 220697610715 1.270 8.128 2.851 3.176
019 722772817043 220375.078922 3.390 9.906 7.300 3.120
022 736583 803510 221238380171 3.670 6.604 7.405 2.595
028 694588 732145 213376.137195 2.970 11.684 4.264 3.465
W2 7&078587107 194300.186312 4.500 13.716 10.053 4.978
W16 734607714135 203484.977237 3 860 6.858 1.080 3.724
W22 727994.066738 195m4.409450 3.480 3.810 4.555 4.128
W25 732161.441554 213556429868 4.350 11.938 3.638 3.370
W27 726187.905777 204715.689118 4.130 10.668 0.000 3.915
W29 742838247435 203183487706 3.320 6.604 1.462 3.583
W35 732221251123 179(34322024 4.400 5.842 5.177 4.339
W42 754665.813“ 213426.186194 2.560 5.334 2.289 2.950
W43 733804150235 197470.094732 3 010 3.302 2.002 3 942
W45 736867359922 197018994551 3.880 9.398 2.034 3.895
W46 734124847745 185969011278 4.520 6.096 5.014 4.199

125

Appendix D
Various SEMCOG Precipitation Data
(Precipitation Event 05/24/1999)

81.11.. I!) x v sax-1:11) Gag-J.- ANN oc

A3 551857.143789 192530.880673 0.000 1.778 0.275 0.227
1.. 3 668048272705 241521 .550493 0.“ 1.524 0.367 0.000
L 7 681514971760 222057746602 0“» 1.524 0.331 0.046
L10 658405618120 224559.593525 0.000 1.524 0.472 0.000
M 2 756937.867805 232774.055329 0.000 3.302 1.842 0.000
M 4 752552.920492 230509580239 0.000 4.054 2.232 0 207
M 8 746972860607 254820071250 0W 1.27 0.291 0.100
M 9 742960436068 231431.293091 0“” 1.016 0696 0000
M10 749986779148 230140.273915 0.000 2.54 1.357 0000
M12 755224025423 255122.102510 0.380 5.842 3.458 0 151
M13 750684183706 240383890587 0.000 0.752 0.235 0 025
M7 4 765682093654 241381302807 0.240 3.556 2.037 0.172
M16 755400233316 223825771085 0 (XX) 3.302 1.269 0395
M17 744337430005 224781 .755357 0.000 3.048 0.995 0 000
M19 755951048949 217610399169 0.950 1.524 1.207 0.168
0 3 735369.246078 230572594422 0.000 1.27 0.357 0 000
04 734158.924512 255015775493 0.000 0.752 0.217 0.000
0 5 713090146295 246701 .551082 0“” 1.524 0.444 0 000
09 726130.235853 247275571191 0.000 0.752 0.217 0.000
018 731345.524595 216708011455 0.100 4.054 1.149 0.121
024 715654.W8076 215086283082 0.090 2.032 0.476 0.154
025 731851017503 225830555575 0000 1.015 0.557 0.000
W 8 732252958427 1979423112800 0890 1.27 0.535 0.521
W14 753133344245 209696295155 1.410 1.778 0.834 0.273
W18 745604881900 214856.586919 0.000 3.048 0.958 0590
W23 724714028432 197970368012 0 500 4.572 1.542 0.684
1133 755386272117 215582872187 0.2 0 1.325 1 025
W48 709614370019 201814.621439 0.350 1.778 0.695 0 252
A 1 678039980433 195924935908 0.000 1.015 0.015 0.109
A 2 553120. 252549 212553141409 0.070 2.032 .0079 0 001
A 5 595810.135030 191348250416 0 000 0.752 0.212 0.320
L 1 555935798800 236936068948 0.000 1.524 0084 0.000
1. 2 555307791088 245383380983 0 000 1.015 0.000 0 000
L 5 655433651803 217957872282 0.“ 1.27 0.323 0.“
1. 5 580819554474 212103.804745 0 000 2,032 0.000 0048
L 8 583827.288555 245447.501554 0.070 1.015 0.000 0.000
1. 9 585117.095705 233972532310 0.000 1.27 0.000 0.000
1.11 671537470375 229482547174 0.000 1.016 0.000 0.000
M1 754440159488 258799.157739 0 W 1.27 0 000 0.157
M 5 756874.1(BSO2 227770456845 0“” 2.794 1.148 0 000
M 7 739614099028 250112.455291 0.000 0.752 0.138 0.000
M15 755444220459 218949865155 0.240 7.285 0834 0.591
M18 745887802536 22675094384 0.080 1.778 0.679 0.000
O 2 730402927052 221 676. 374291 0.000 0.254 0.310 0 028
o 7 717831.717332 237839089534 0.000 1.778 0.010 0008
o 8 725348147988 235798729758 0.000 0.752 0.000 0.002
010 694269889040 228610917” 0 000 2. 54 0.045 0 011
013 705431 .001880 220597.510715 0.000 3.302 0.000 0.058
019 722772817043 220375078922 0.000 2 794 0 169 0 051
022 736583803510 221238380171 0 000 1.778 0.375 0.009
028 694588 732145 213376.137195 0 000 0.254 0 000 0 102
W2 708078587107 194300185312 0350 3.81 0.471 042

W16 734607714135 203484977237 0.890 3.048 0.350 0.675
W19 743359.844905 202028.959810 0.000 2.285 0.184 0.971
W22 727994.066738 195084.409450 0.440 3.555 0.867 0.733
W25 732161.441554 213556429868 0.570 3.556 0.615 0.194
“'27 726187.W5777 204715689118 0.500 3.556 0 694 0.419
W42 754665813608 213425.185194 0.500 2.285 0.823 0.535
W43 733804.150235 197470.094732 0.310 2.54 0.414 0.917
W44 733662817575 179255251133 0.350 2.032 0.085 1 .052
W45 735857.359922 197018.994551 0 270 2.794 0.188 0 972
W45 734124 847745 185959.01 1278 0.350 2.286 0.27 1.029

126

 

 

Appendix E
Various SEMCOG Precipitation Data
(Precipitation Event 06/09/1999)

Station ID X Y NEXRAD .- Gnggu ANN 0C
A 3 661851143789 192530880673 14.840 13.2080 17.024 0.408
A 4 697211999775 189629477045 0.940 0.2540 0 000 4.355
L 3 668048272705 241521550493 6550 10.6680 10.025 0.227
1. 7 681514971760 222057746602 0 940 0.5080 0000 3 562
1.10 658405618120 224659693526 0.810 2.5400 5.436 8.438
M 2 756937367805 232774056329 0.000 0.5080 0.931 0.175
M 4 762562920492 230609680239 0.000 0.2540 0 000 0097
M8 746972860607 254820071250 3.510 0.7620 2.824 1418
M9 742960436068 231431293091 2.450 0.7620 2.111 1.498
M10 749986779148 230140273915 0.250 0.0000 0.000 0721
M12 765224025423 256122102610 0.860 0.7620 0.000 1.565
M13 750684183706 240381890687 0.940 0.0000 1.254 1.621
M14 765682093654 241381302807 0.140 0.0000 0.124 0353
M16 755400233316 2223825771085 0200 0.0000 0.036 0.000
M17 744337.4300M 224781.756367 0.080 0.2540 1.657 1.140
M19 755951048949 217610399169 0.000 0.0000 0.706 0022
O 3 735369246078 230672594422 3.480 0.2540 2.515 1.560
O 4 734168924612 255016775493 1.700 0.0000 0 882 2.564
05 713090146295 246701551132 1.360 0.0000 0000 2.003
0 9 726130235853 247275671191 1.470 0.7620 0.000 1.924
018 731346 624696 216708011455 0.410 0.5080 0.000 0.233
024 715654088076 215086 283082 0090 0.2540 0.000 0.493
025 731861017503 225830555575 0 880 00000 0.324 2.092
W8 732252968427 197942382800 0.000 0.7620 1.659 0.000
W14 753131344245 209696295155 0.000 0.0000 0000 0.000
W18 745604881900 214856586919 0.000 0.0000 0.000 0.000
W23 724714028432 197970368012 0 000 1.0160 0.000 0.041
W33 755386272117 2155821172187 0000 0.0000 0.754 0.000
W48 709614370019 201814621439 0.200 0.5080 0.031 0.105
A1 678039980433 195924.936” 2.800 1.270 0 469 6.949
A 2 663120262649 212551141409 0.000 0.000 2.325 5.114
A5 695810135030 191348250416 1.240 0.254 0.000 1.348
L1 656935798800 236936068948 13.700 24.892 30.611 4.179
2 655307791088 245381380983 9. 280 1.524 4.626 5.441
L S 655433651803 217957872282 12 000 3.302 4 220 3.774
L6 680819554474 212101804745 0.260 1.016 0.000 2.709
I. 8 683827288566 245447601664 3.230 1.270 2.292 3 783
1. 9 685117095706 233972632310 2.610 1.524 0.000 2.275
1.11 671537470375 229482647174 0.000 0.762 0.824 2.752
M 1 754440159488 258799157739 4.150 1.270 2.022 2.323
M 5 756874 1(8802 227770456845 0 350 0.000 O 000 0 047
M 7 739614099028 250112456291 1.040 0.762 1.860 2.469
M15 755444220459 218949865155 0.000 0.000 0.454 O 028
M18 745887 802536 226750940884 1.300 0.000 0011 0.471
0 7 717831.717332 237839089634 2.180 0 000 2.470 1.360
08 725348147988 235798729758 2.790 0.000 3.078 1.828
010 694269889040 228610917000 1.500 1.016 2 827 1.151
013 705431001880 220697610715 1.840 0.508 2.485 0.533
019 722772817043 220375078922 1 150 0000 1.849 0.485
022 736581803510 221238380171 0.660 0.000 0.847 0.631
028 694580732145 2131376137195 0450 0.000 0.861 0.991
W2 708078587107 1943m186312 0.140 0762 0000 0.341
W16 734601714135 203484977237 0.000 0.762 0.000 0.016
W22 727994066738 195134409450 0.000 0000 0.535 0.007
W25 732161.441554 2135564291168 0000 0.000 0.294 0.248
W27 726187905777 204715689118 0.000 0.508 0.000 0017
W29 742838247435 203181487706 0.440 0508 0,000 0 000
W42 754665313608 213426186194 0.000 0.254 0.003 0.000
W43 733804150235 197470094732 0000 0000 0.874 0.000
W44 733662817575 179256261133 0.000 0.254 0.318 0041
W45 736867359922 197018994551 0.400 0.508 0.391 0.000
W46 734124847745 185969011278 0 000 0.762 0.087 0.005

127

 

 

Appendix F
Various SEMCOG Precipitation Data
(Precipitation Event 07/01/1999)

Shih-ID X Y NEXRAD- Gag-_I- ANN 0C
A3 661857.143789 192530.880673 19.680 34.036 22.386 13.264
1. 3 668048.272705 241521.550493 17.600 30.48 24.040 17.475
L 7 681514.971760 222057.746602 18.030 32.766 22.796 16.056
L10 658405.618120 224659.693526 16.630 31.496 23.956 18.902
M2 756937867805 232774.056329 20,540 19.05 18.344 19.557
M4 762562.920492 230609.680239 27.420 11.176 12.346 18.274
M8 746972.860607 254820.071250 25.640 45.466 30.243 13.559
M9 742960436068 231431.293091 15.410 20.32 17 045 12.844
M10 749986779148 230140.273915 12 920 20 828 20 907 13.999
M12 765224025423 256122.102610 9.700 20.066 15.684 24.451
M13 750684.183706 240383.890687 13.160 16002 17.894 20.252
M14 765682093654 241381 302807 22.870 28.956 28.524 19.346
M16 755400.233316 223825.771085 10.530 11.684 8.839 12.340
M17 744337.430006 224781756367 10370 14986 12130 11209
M19 755951 .048949 217610.399169 5.260 6.35 5.531 7.500
O 3 735369.246078 230672594422 14.400 23.368 20 970 16.602
04 734168.924612 255016.775493 16.530 39.116 31.537 25.790
0 5 713090146295 246701551082 16.760 39.37 28.026 23.884
09 726130.235853 247275671191 27.340 45.72 30.106 16.150
018 731346.624696 216708011455 14220 21.59 15.281 11.509
024 715654188076 21936283082 13.220 23.114 18.839 13.296
025 731861 .017503 225830.555575 15.820 20.066 17.946 14.740
W8 732252968427 197942.382800 6.990 9.144 6.587 5.592
W14 753133.344245 209696.295155 3.980 5.588 6.233 4.688
W15 750221.159860 206719251289 3.840 5.588 4.273 4.471
W18 745604881900 214856586919 6.150 11.684 8.437 6.884
W23 724714.028432 197970.368012 5 890 12 954 10.619 8.198
W33 755386.272117 215582 872187 5.950 7.874 6.468 4.957
W48 709614.370019 201814.621439 9.610 16.764 8.701 10.785
A1 678039.980433 195924936908 28.330 45.466 25.133 16.477
A2 663120262649 212553.141409 18070 30.988 19.053 17.853
A 5 695810.135030 191348.250416 8.760 21.59 8.165 12.222
L1 656935798800 236936.068948 14.240 41.656 15.932 17.283
2 655307791138 245383380983 15.690 44.45 44.022 17.539
L 5 655433651803 217957.872282 16.280 34.29 23.207 17.439
L6 68(319554474 212103804745 17.320 31.242 14.069 17.014
L8 683827.288566 245447.601664 17.890 36.576 19.463 17.507
1.9 685117095706 233972632310 17.610 41.656 18.859 17.477
1.11 671532470375 229482547174 18.950 35.306 18.605 17 570
M1 754440159488 258799.157739 25.330 33.274 31.027 18.362
M 5 756874.1(3802 227770.456845 19.610 11.176 19.432 16.835
M 7 739614.099028 250112.456291 28.830 46.228 28.897 20.308
M15 755444.220459 218949.865155 5.950 9.906 9.121 6.385
02 730402927052 221676.374291 15.820 19.812 17.258 15 183
07 717831.717332 237839.089634 18050 46.99 20.415 19.096
08 725348.147988 235798.729758 22.120 41.148 27.426 19.631
010 694269889040 228610917000 16230 39.37 20.034 16793
013 705431001880 220697.610715 13.350 37.084 18.141 15.147
019 722772817043 220375078922 13.640 21.336 16.217 15.045
022 736583.803510 221238.380171 15.520 25.908 20001 12.814
026 702230.908441 220046898222 15.190 36.068 15.578 15.229
028 694588732145 213376.137195 17.090 31.75 16.899 15.030
W2 708078.587107 194300186312 8.030 16.51 10.622 9.224
W16 734607.714135 203484.977237 6 990 9.398 7.474 7.685
W19 743359844905 202028959810 4.800 3.302 3.774 5 241
W25 732161 .441554 213556429868 9.630 21082 13.919 12.203
W27 726187.905777 204715689118 5.890 14.732 8.476 8.896
W35 732221.251123 179084322024 4.540 6.858 -0.396 4.466
W42 754665.813“ 213426186194 4 360 5 588 6 541 5.242
W43 733804.150235 197470 094732 4.430 6.35 2.788 6.643
W45 736867.359922 197018 994551 4.610 10.668 0.792 6.036
W47 731495224830 195941679285 5.730 9.144 4.430 6.382

128

Appendix G
Various SEMCOG Precipitation Data
(Precipitation Event 07/23/1999)

swam x Y 18mm.- ,3. ANN .— oc .-

713 661857.143789 192530 880673 6.620 -7.620 7.503 13.970
1.3 668048.272705 241521.550493 20670 23.876 21.366 10.260
1.7 681514.971760 222057.746602 9.900 3.810 2.3616 18.820
1.10 658405618120 224659693526 8.540 6.858 9.2393 12 940
M 2 756937867805 232774.056329 26.870 20.320 22.156 23 470
M 4 762562920492 230609.680239 29.960 25.908 23.844 24600
M 8 746972.860607 254820.071250 10.530 7.112 6.9955 8010
M9 742960.436068 231431.293091 17.990 13.970 13.632 18.410
M10 749986.779148 230140.273915 18.600 12.446 14.884 22.950
M12 765224.025423 256122102610 8.470 5.588 6.2693 13 240
M13 750684.183706 240383.890687 13.730 14.224 15.596 17.660
M14 765682.093654 241381.302807 17.840 4.064 5.3483 20.070
M16 755400 233316 223825.771085 26 930 21.082 24.373 22 350
M17 744337 430006 224781756367 23 340 20.320 22.667 18.230
03 735369246078 230672.594422 17.380 13.970 20.95 18.850
04 734168924612 255016775493 7.180 8.382 6.8421 17.540
0 5 713090.146295 246701.551082 24.710 23.114 26.476 21.100
09 726130.235853 247275.671191 24.470 14.224 17.085 15.310
018 731346624696 216708011455 21.960 31.242 29 442 20.970
024 715654.088076 215086.283082 23.750 28.194 23.209 25080
025 731861.017503 225830.555575 18.770 16.256 21.677 19.740
W8 732252.968427 197942.382800 29.380 23.876 21.131 26.770
W14 753133.344245 209696295155 20.240 10.414 7.3259 17.860
W15 750221.159860 206719251289 21.420 3.556 69491 20550
W18 745604.881900 214856.586919 15.350 19.050 17.912 22.480
W23 724714.028432 197970.368012 29.530 28.956 29.272 29.590
W31 756733.582014 214398.150256 13.030 16.002 15.468 19320
W33 755386272117 215582.872187 18.080 18.796 20.52 15.310
W48 709614.370019 201814.621439 30940 50038 41.267 23.460
A1 678039980433 195924.936908 16.520 7.366 1.613 12.690
112 663120262649 212553.141409 9.020 4.318 6.672 7.660
A 5 695810135030 191348250416 39.670 43.688 45.048 22.230
L1 656935798800 236936068948 16.760 27.178 29.589 14.400
L2 655307.791088 245383380983 22.240 26.67 24395 16440
1. 5 655433.651803 217957.872282 13.980 4.064 14.886 7.570
L6 680819.554474 212103.804745 14.380 7.112 12.212 11.630
L8 683827.288566 245447.601664 24.990 27 686 26.892 19.830
L 9 685117.095706 233972.632310 17.340 7.112 26331 16.690
1.11 671537.470375 229482.547174 5.670 2.794 4.191 13 200
M1 754440159488 258799.157739 9.860 10.16 24.493 8 920
M 5 756874.108802 227770.456845 29.670 14.224 23.159 27 260
M 7 739614.099028 250112.456291 13 300 6.096 3.301 10.910
M15 755444220459 218949865155 18.080 23.876 30819 21210
02 730402.927052 221676.374291 18.770 28.702 18.122 20.410
07 717831.717332 237839089634 21.260 19.558 27.946 23 730
O8 725348.147988 235798.729758 21.040 15.748 23.079 21.880
010 694269889040 228610917000 11.060 6.858 3.751 18.100
013 705431.001880 220697.610715 14.750 19.558 12.920 21.740
019 722772.817043 220375078922 27.030 30.988 31.685 22.030
022 736583.803510 221238.380171 23.060 21.844 23.876 20.190
026 702230.908441 220046898222 12.070 17.272 15.236 21.190
028 694588732145 213376.137195 18060 11.176 20.481 18.530
W2 708078.587107 194300.186312 41.630 49.784 45.969 28.800
W16 734607.714135 203484977237 29380 41.91 39.841 25.890
W19 743359844905 202028959810 28680 21.336 30.581 23.770
W25 732161.441554 213556429868 24.190 31.242 30.147 22.510
W27 726187905777 204715689118 29530 52.07 32.815 27.100
W42 754665.813608 213426.186194 12.850 12.192 20.453 16.570
W43 733804150235 197470.094732 22.200 16.764 19.646 28.800
W44 733662.817575 179256.261133 23.620 28.448 19.011 29.670
W45 736867359922 197018.994551 25.420 21.59 30830 27,660
W47 731495.224830 195941 .679285 20 240 15.494 24.465 29.590

129

026

X Y
661857.143789 192530.880673
668048272705 241521.550493
681514.971760 222057.746602
658405.618] 2O 224659.693526
756937867805 232774.056329
762562.920492 230609.680239
746972860607 254820.071250
742960.436068 231431.293091
749986.779] 48 230140.273915
765224.025423 256122.102610
750684. 183706 240383.890687
765682.093654 241381.302807
755400.233316 223825771085
744337.430006 224781 .756367
755951 .048949 217610.399169
735369.246078 230672. 594422
734168924612 255016775493
713090.146295 246701 .551082
726130235853 247275.671 19]
731346624696 216708.011455
715654138076 215086283082
731861017503 225830555575
753133.344245 209696.295] 55
750221.159860 206719.251289
745604.881900 214856.586919
735298537945 19934] .859541
724714.028432 197970.368012
755386.272] 17 215582.872187
709614.370019 201814.621439
678039980433 195924936908
663120.262649 212553.141409
695810.] 35030 191348250416
656935.798800 236936068948
655307. 791 088 245383380983
655433651803 217957.872282
680819.554474 212103.804745
683827.288566 245447.601664
685117.095706 233972632310
671537.470375 229482547174
754440.] 59488 258799.] 57739
753510.085060 218106602475
756874108802 227770456845
739614 099028 250112.456291
730402.927052 221676374291
717831.717332 237839m9634
725348147988 235798.729758
694269889040 228610.917000
705431.001880 220697 .61 071 5
722772.817043 220375078922
736583803510 221238.380] 71

702230.908441
694588.732145
708078.587] 07
734607714135
732161.441554
726187.905777
742838.247435
754663813608
733804.150235
733662.817575
736867.359922
731495.224830

220046.898222
213376.137195
194300186312
203484977237
213556429868
204715.689] 18
203183.487706
213426186194
197470094732
179256.261133
197018.994551
195941679285

9.910
3.260
8.850
18.500

3.930
10.540
3.720
2.550
8.090
10.450
3.750
7.800
7 660
20.150
8.620
7.790
10.330
12.060

6.720
4.320
12.020
14.910
11.260
11.450
8.850
18.300
7.290
3.830
9.350
3.610
1.970
0.620
8 980
8.870
3.640

14.510
. 13.410
18.300
6.120
5.160
4.320
19.220
26.260
5.520
8.430
6.980
4.120
6.150
6.370
4.680
11.450
9.260
8.850
14.770
19.500
14.930
14.820
17.690
14.730

Appendix H
Various SEMCOG Precipitation Data
(Precipitation Event 07/31/1999)

7.62
1.016
16.764
20. 574
1.016
4.318
1.016
3.048
1.778
0.508
9.398
8.636
8.382
2.032
13.716
3.81
1.016
9.906
5.334
7.112
4.572

3.302
2.032
11.938
5.588
2.032
16.002
1 016
2.540
15.494
5.080
0.508
8 636
1.016
10.922
2.794
13.208
10. 160
0.762
3.810
4.572
13.970
4.826
20.320
14.224
2.286
4.826
1.524
15.748
15.748
6.858
2.794
2.286
7.620
1.524
9.144
9.398
3.556
13.462
7.874
9.398

7.850
0.000
13.025
17.318
1.019
5.174
0.000
6.161
0.000
0.903
9.468
5.842
6.301
6.209
15.702
6.082

2.274
5.394
8.172
6.963
3.213
4.644
2.538
10.907
8.563
3.897
14.690
2.006
3.204
7 489
5.010
0.372
7.538
1.736
6.409
15.639
8.587
10478
0.551
5.088
3.594
9.574
6.1 14
16.190
21.684
6.533
6.114
6.535
6.834
6.834
6.782
0.167
9.382
7.762
8.225
13.073
14.507
7.794
17.1 16
9.472
6.554

130

NEXRAD.- Gnggu ANN-n 0C.-

15.541
15.024
9.416
6.206
4.470
5.699
8.683
6.961
5.553
7.036
4.448
6. 541
9.239
5.828
16.809
5.062
11.597
9.590
8.676
7.140

8.037
16.993
1 1.946
11.466
11.024

9.677
17.406

7.972

9.624
14.183

8.608
10.874

8.373
16.806

9.760

5.640

6.921

9.551

9.476
14.119

5.109

9.443

5.576

9.447

8.814

7.652
6.312
6.947
7.426

8.128
10.661

8.058

8.584
12.921
17.080
11.188
12.217
11.971
10.721

 

 

 

Appendix I
Various SEMCOG Precipitation Data
(Precipitation Event 07/09/1999)

Static-ID X Y NEXRAD- Gaga.- ANN_- 0C_-

A3 661857.143789 192530.880673 23.160 13.716 16.43 15.870
1.3 668048272705 241521550493 14.930 9.906 12.14 19.600
L 7 681514971760 222057746602 19.430 9.398 13.73 17.860
L10 658405.618120 224659.693526 18.450 15.494 16.55 18.550
M2 756937867805 232774.056329 9.170 4.064 4.20 9.010
M4 762562.920492 230609680239 8.410 5.334 5.52 8.900
M8 746972860607 254820.071250 8.170 6.096 6.65 9.390
M9 742960.436068 231431.293091 13.650 6858 9.30 11.260
M10 749986779148 230140273915 9.750 6.35 7.70 9.980
M12 765224025423 256122102610 5 630 1.778 2.67 9.470
M13 750684.183706 240383890687 9.810 6.604 6 58 10.630
M14 765682.093654 241381.302807 11.110 6.604 6.21 7.360
M16 7554m233316 223825.771085 7.150 7.112 6.5] 8.250
M17 744337430006 224781756367 9.910 6.096 7.63 11.400
M19 755951.048949 217610399169 7 700 7.366 7.70 7.910
03 735369.246078 230672.594422 13.750 7.112 11.10 14.870
04 734168924612 255016.775493 11.610 7.62 8.15 14.360
05 713090.146295 246701551082 22.790 11.938 18.27 18.530
09 726130235853 247275.671191 19.200 10.414 13.95 16.430
018 731346.624696 216708011455 15.500 10.922 12.60 13.340
024 715654088076 215086.283082 16.110 11.43 14.07 15.230
025 731861.017503 225830555575 15.070 9.906 1263 14.770
W8 732252968427 197942382800 10.070 9.398 10.60 9970
W14 753133344245 209696.295155 8.280 6.35 6.55 7.980
W15 750221159860 206719251289 7.950 3.81 5.08 8.700
W18 7456048819“) 214856586919 9.600 9.144 9.32 9.740
W23 724714028432 197970.368012 10.180 7.874 9.30 11.060
W33 755386272117 215582872187 8.220 8.89 7.86 7.850
W48 709614.37(X)19 201814621439 11.540 9.652 10.92 14.510
A1 678039.980433 195924936913 18.310 10.414 14.128 19.480
A2 663120.262649 212553.141409 10.350 9.652 13.985 20.220
A5 695810.135030 191348.250416 13.920 10.16 15.233 15.000
1. 1 656935798800 236936.068948 15.950 12.954 14.118 16.640
L2 655307791088 245383380983 15.200 11.176 17.439 16.120
L 5 655433651803 217957872282 13.670 10.16 18.412 19.600
L6 680819554474 212103804745 14.710 6.096 17.779 19.150
1. 8 683827 288566 245447601664 19.270 12.192 21.125 17.860
L9 685117.095706 233972.632310 17.310 12.192 19.271 18.630
L11 671537.470375 229482.547174 19.760 12.7 21.9% 17.770
M1 754440159488 258799.157739 5.090 5.842 5.323 7.080
M 3 753510.085060 218106.602475 8 220 8.636 6.292 7.970
M 5 756874.108802 227770.456845 7.220 3.302 4.187 8.010
M7 739614099028 250112456291 10.520 8.128 8.646 11.200
02 730402 927052 221676.374291 15.070 10.16 16.717 15.460
07 717831.717332 237839.089634 20.500 8.89 26493 20.420
08 725348147988 235798729758 19.430 8.128 24.480 18.000
010 694269889040 228610917000 20.530 11.684 20.992 19.220
013 705431001880 220697610715 18.830 10.16 21.538 17.950
019 722772.817043 220375078922 20.790 10.414 22.844 16.560
022 736583803510 221238.380171 13.270 8.89 11 839 13.400
026 702230.908441 220046898222 20.130 11.938 22.077 17.870
028 694588732145 213376137195 18.640 7.874 18.432 17.380
W2 713078587107 1943111186312 12.250 9.652 13.526 11.770
W16 734607.714135 203484.977237 10.070 7.62 11.683 10.910
W25 732161.441554 213556429868 13.360 10.668 11 012 14.210
W27 726187.905777 204715689118 10180 7.874 11.381 12.190
W29 742838.247435 203183487706 8.780 6.858 8.736 9.280
W35 732221251123 179134322024 8.890 11.43 11.672 8.400
W42 7546658136“ 213426186194 9.770 7.366 8.833 8.240
W43 733804.150235 197470.094732 11.140 7.366 11.382 9.860
W45 736867359922 197018994551 10.970 9.906 10.338 9.490
W47 731495224830 195941679285 10690 8.382 11.272 9.770

131

Appendix J
Various SEMCOG Precipitation Data
(Precipitation Event 08/13/1999)

Shih-ID X Y NEXRAD - GI'O_- ANN I. 0C .-

A 3 661857.143789 192530.880673 10010 1.778 3.721 9.164
A4 695810.135030 191348.250416 7.580 4.318 4.235 6.212
I. 7 681514.971760 222057746602 17.490 27 94 20.146 12.252
L10 658405618120 224659.693526 11.210 8.636 8 874 14.724
M 2 756937.867805 232774056329 14.670 13.716 15.786 14.126
M 4 762562.920492 23(509680239 11.020 13.2% 10.292 12.804
M 8 746972.860607 254820071250 9.300 18.796 11.475 8.103
M 9 742960.436068 231431 .293091 25.730 30.734 21.956 20.064
M10 749%6779148 230140.273915 20 210 25.654 19.884 19.102
M12 765224.025423 256122.102610 5.670 17.78 15.516 7.425
M13 750684.183706 240383.89M87 13.760 17.526 16.341 16.221
M14 765682.093654 241381302807 8.890 20.32 17.298 8.991
M16 7554m233316 223825.771m5 15.650 26.924 19.167 17.234
M17 744337.430006 224781.756367 19.160 18.288 18.856 20.975
0 3 735369246078 230672.594422 21.470 34.544 26.333 20.342
0 4 734168924612 255016.775493 6.970 19.05 12 634 13.789
0 5 713090.146295 246701.551082 15.480 20.32 16.895 17.183
0 9 726130.235853 247275.671191 17.530 24.13 17.264 13.150
018 731346.624696 216713011455 18.710 26.924 21.975 15.161
024 715654138076 215086 283082 18.790 38.608 22.950 11.948
025 731861.017503 225830.555575 17.140 18.796 20.156 20.534
W 8 732252968427 197942.382800 8.310 7.62 6.706 6.251
W14 753133.344245 209696.295155 7.110 4.572 6.573 14.219
“’18 745604881900 214856586919 13.500 17.78 16.497 14.562
W23 724714.028432 197970368012 5.170 7.112 7.502 8.265
W31 756733582014 214398150256 15.510 10.922 18.677 15.897
W33 755386272117 215582872187 18.480 17.78 16.297 15.002
W48 709614.370019 201814.621439 5.070 5.334 5.488 10.879
A 1 678039980433 195924936908 2.970 8.128 3.91 1 10 292
A 2 663120.262649 212553.141409 4.880 4.064 5.236 11.921
A 5 695810.135030 191348.250416 4.770 6.096 0.949 7.580
I. 1 656935798800 236936068948 9.850 7.874 13.062 12.035
1. 2 655307.791 (38 245383380983 13.900 10.16 11.895 12.044
L 5 655433.651803 217957872282 11.420 3 048 10. 297 11.076
L 6 680819554474 212103.804745 23.120 17.018 21.224 14.212
L 8 683827288566 245447.601664 14.300 22.098 15.502 15.025
1.9 685117095706 233972.632310 17.750 23.114 18.086 16.506
L11 671537.470375 229482547174 13.980 5.334 14.329 14.689
M 1 754440159488 258799157739 9.130 19.812 4.711 7.050
M 5 756874108802 227770.456845 16.170 16.002 16.586 15.103
M 7 739614.0990fl 2501 12.456291 15.350 23.368 10 649 11.334
M15 755444.220459 218949865155 18.480 17.018 20.824 17.228
0 2 730402.927052 221676.374291 17.140 15.748 20 093 18.093
0 7 717831.717332 237839089634 25.890 32.512 22.324 18.073
0 8 725348.147988 235798729758 24.680 24.13 27.400 18.742
010 694269889040 228610.917” 21.990 26.162 20.672 17.073
011 705431 .001880 220697610715 25.490 16. 51 16.336 16.937
013 705431.“)1880 220697.610715 14.660 27.686 16.277 16.937
019 722772817043 220375078922 15.450 23.876 15.747 18 505
026 702230908441 22m46.898222 16.650 32.004 19.309 16.434
028 694588732145 213376.137195 23.950 36.322 21.041 13.963
W 2 708078.587107 [943%.186312 5.370 8.128 7.179 4.727
W16 734607714135 203484977237 8.310 10.668 4.794 10.349
W22 735298537945 199341859541 4.290 7.366 7 837 8.638
W25 732161.441554 213556429868 11.160 23.368 18.214 16.541
W27 726187.“)5777 204715689118 5.170 7.874 6.345 10.409
W29 742838247435 203183.487706 10.230 10.414 7.316 8.642
W42 7546658136“ 213426186194 12.520 9.906 11.189 14.234
W43 733804.150235 197470094732 5.960 4.826 7 836 8.053
W44 733804.150235 197470094732 2.550 2.286 2 000 8 053
W45 736867.359922 197018.994551 5.450 10.922 10.309 7.613

132

Appendix K
Various SEMCOG Precipitation Data
(Precipitation Event 09/24/1999)

Shit-1D X Y NEXRAD- Gap_- ANN I. 0C_-

A3 661857143789 192530880673 0.910 2.794 0.886 1.509
A4 695810135030 191348.250416 1.360 3.556 1.718 0.981
L7 681514.971760 222057746602 3.490 5.588 3.547 1.301
1.10 658405618120 224659693526 1.200 4.318 2.680 2.849
M2 756937867805 232774.056329 1.460 2.54 2.964 1.718
M4 762562 920492 230609.680239 2.080 6.096 4.305 2403
M8 746972.860607 254820071250 1.340 2.286 2.448 1.938
M9 742960436068 231431293091 0.610 3.048 1.680 1.262
M10 749986779148 230140.273915 0.880 3.302 2.144 1.600
M12 765224.025423 256122.102610 1.760 3.302 2.149 2.482
M13 750684.183706 240383.890687 0.930 5.08 2.645 1.186
M14 765682.093654 241381302807 3.070 5.08 4.082 1.705
M16 755400233316 223825771135 2.860 2.794 3.032 1902
M17 744337.430006 224781.756367 2.410 2.54 1.983 1.191
03 735369246078 230672594422 0.970 1.524 1.837 0.864
04 734168.924612 255016775493 2.730 6.096 3.718 2.332
O 5 713090146295 246701551082 3.480 6.858 4.110 2.935
09 726130235853 247275671191 3.170 5.842 3.382 2 521
018 731346624696 216708011455 0.720 1.778 1.353 1.132
024 715654.“8076 215“6.283“2 0.180 2.032 0.519 0.960
025 731861017508 225830555575 0.480 1.27 0.604 1.018
W8 732252.968427 197942382800 2.100 3.302 1.903 1.706
W14 753133344245 209696.295155 2.470 3.81 3.622 2.346
W18 745604881900 214856.586919 2.280 4.064 2.736 2.251
W23 724714028432 197970.368012 1.470 1.778 1.502 1.493
W31 756733582014 214398.150256 2.320 4.318 3.371 2.371
W33 755386.272117 215582872187 2.270 4.064 3.695 2.424
W48 709614.370019 201814.621439 0.360 2.794 0.990 1.038
A1 678039.980433 195924.9369“ 0.760 2.286 1.163 1.463
A2 663120.262649 212553141409 1.550 3.81 2.878 1.521
A5 695810135030 191348.250416 1.250 3.302 2.401 1.360
1.1 656935798800 236936068948 1.550 9.398 5.025 1.795
1.2 655307.791“8 245383380983 2.630 4.064 1.524 2.025
L 5 655433.651803 217957872282 1.070 2.54 4.286 1.176
L6 680819.554474 212103.804745 1.780 3.048 3.159 2.419
1.8 683827288566 245447.601664 1.830 5.588 3.104 3.116
L9 685117.095706 233972632310 1.740 5.842 2.653 3.144
L11 671537470375 229482547174 1.080 3.556 2.220 2.585
M1 754440.159488 258799.157739 1.040 4.826 2.087 1.587
M5 756874108802 227770.456845 2.870 5.334 4.599 2.116
M 7 739614099028 250112.456291 2.300 8.128 5.197 1.849
M15 755444.220459 218949.865155 2.270 5.588 5.197 2.542
02 730402927052 221676374291 0.480 1.524 1.303 0.569
O 7 717831.717332 237839089634 3.160 8.636 3.493 2.391
08 725348.147988 235798729758 3.“0 6.604 4.827 1.747
010 694269889040 228610.917000 4.260 6.858 5.071 2.752
013 705431001880 220697.610715 1.500 4.572 3.945 1.350
019 722772.817043 220375078922 0.850 2.032 1.533 0.497
028 694588732145 213376137195 1.520 3.302 2.713 1.893
W2 708078587107 1943411186312 1.420 4.064 1.536 0.861
W16 734607714135 203484.977237 2.100 3.556 3.171 1.878
W47 736867359922 197018994551 1.610 2.286 2.113 2.210
W25 732161.441554 213556.42” 1.520 2.54 1.609 1.051
W27 726187905777 204715.689118 1.470 3.81 1.540 1.207
W29 742838.247435 203183.487706 3.230 3.556 3.060 2.248
W42 754665.8136“ 213426186194 2.500 3.302 5.727 2.339
W43 733804150235 197470.094732 1.880 1.27 2.693 2.146
W44 733804.150235 197470.094732 2.420 3.556 2.275 2.146

133

Appendix L
Various SEMCOG Precipitation Data
(Precipitation Event 05/16/2000)

Shun-ID X Y NEXRAD- ch_- ANN .- OC .-

A 3 661857143789 192530.880673 0.780 5.334 1.523 1.950
L 3 668047850000 241521480000 2 500 10.922 1.733 2.804
L 7 681514971760 222057.746602 0.000 7.62 1.037 2.898
1.10 658405618120 224659.693526 2.500 8 636 4.554 1.167
M 4 762562920492 230609.680239 0.000 7.112 2.301 0 000
M8 746972.860607 254820.071250 0.000 7.62 0.187 0.000
M9 742960436068 231431.293091 0.000 6.858 0.000 0078
M10 749986.779148 230140273915 0.000 7.366 1.898 0.000
M12 765224025423 256122102610 0.340 4.064 0.180 0.000
M14 765682093654 241381.302807 0.000 4.572 0870 0.046
M16 755400233316 223825 771085 0.000 7.874 3.037 0000
M17 744337.430006 224781.756367 0.000 7.874 0.000 0.000
M19 755950630000 217610330000 0.000 3.556 0.000 0.000
03 735369.246078 230672594422 0.000 7.62 0.946 0.714
O 4 734168.924612 255016.775493 0.000 8.89 1.563 4.179
O 5 713090146295 246701.551m2 7.750 11.684 8.047 4.773
09 726130235853 247275671191 7.280 11.938 5.265 2.855
018 731346624696 216708.011455 0000 3.302 0.000 0.168
024 715654088076 215086283082 0.000 9.398 0.000 2.336
025 731861 .017503 225830555575 0.000 6.858 2.829 0.233
W14 753133.344245 209696295155 0.000 3.302 0.000 0.000
W15 750220740000 206719.180000 0.000 3.048 0.000 0.388
W18 745604881900 214856.586919 0.000 5.08 0.000 0.107
W20 735298110000 199347790000 2.270 2.794 0.000 1.243
W23 724714028432 197970.368012 2.270 3.302 1.805 2.333
W33 755386272117 215582872187 0.000 5.842 1.536 0.000
W48 709614.370019 201814.621439 3.480 5.334 3808 0.831
A1 678039.980433 195924.936908 5.070 3.81 4.843 1.117
A2 663120262649 212553.141409 0380 6.604 3.836 1.328
A 5 695810135030 191348.250416 4.670 6.096 5.405 2.255
1.1 656935.798800 236936068948 2.500 9.652 6.179 2.606
L2 655307.791088 245383380983 4.190 11.176 7.101 2.846
L 5 655433.651803 217957.872282 3.280 8.89 6.580 2.034
L6 680819.554474 212103804745 0.500 7.366 1.857 0.600
L8 683827288566 245447601664 0.000 10.922 5.841 3.416
L9 685117.095706 233972.632310 0.000 12.954 5.893 2.117
L11 671537470375 229482.547174 2.500 8.128 5.103 1.570
M1 754440.159488 258799.157739 0.000 9.398 3.135 0.124
M5 756874108802 227770456845 0.000 5.842 3.033 0000
M7 739614099028 250112.456291 0.000 9.906 1.793 0.563
M15 755444220459 218949.865155 0.000 4.572 2.546 0.000
M18 745887380000 226750.870000 0.000 6.096 2.162 0.000
02 730402.927052 221676.374291 0.000 7.62 4.592 0.000
O 7 717831.717332 237839089634 7.750 9.398 9.687 5.311
08 725348147988 235798729758 7.470 10.668 7.516 3.653
010 694269.889040 228610917000 0.000 8.128 5.024 2.184
013 705431001880 220697.610715 7.320 8.382 7.639 1.737
016 693745.730000 252604490000 0.000 11.684 9.797 4.810
019 722772817043 220375078922 7.280 7.62 5.593 0.434
020 736063.850000 218411.640000 0.000 4.826 2.117 0046
026 702230480000 220046830000 7.300 7.874 5.105 1.728
028 694588.732145 213376.137195 0.000 6.35 2.918 1.292
W2 708078.587107 194300186312 3.750 4.826 4.635 3.091
W16 734607.714135 203484977237 2.270 3.81 1.647 1.620
W19 743359.420000 202028890000 0.000 3.302 0.461 1 079
W25 732161.441554 213556429868 00(1) 3.302 0433 0.321
W27 726187905777 204715.689118 2.270 5.08 2.376 1.546
W42 754665.813“ 213426186194 0.000 4.318 2.239 0.000
W43 733803730000 197470030000 2.270 0.762 0.438 2.325
W44 733662.390000 179256190010 1.530 3.302 2.483 2.325
W45 736866940000 197018.930000 2.270 3302 0.341 2.185
W47 731494800000 195941 .610000 2.270 3.048 1.180 2.390

134

Appendix M
Various SEMCOG Precipitation Data
(Precipitation Event 05/18/2000)

Shih-ID X Y NEXRAD- Gm_-I ANN .- OC .-
A3 661857143789 192530.880673 48.600 39.370 41.675 27.861
L3 668047.850000 241521.480000 38 840 32004 33.085 26 648
L 7 681514971760 222057.746602 22.800 33.274 28.889 33 505
L10 658405 618120 224659.693526 28.420 37.084 36.614 38.974
M4 762562.920492 230609.680239 25.210 22.606 21.610 23.264
M8 746972.860607 254820.071250 45.300 51.816 44.240 37.296
M9 742960436068 231431.293091 25.040 24.130 22.525 25.192
M10 749986.779148 230140273915 28 870 29972 25.811 25.355
M12 765224025423 256122.102610 40.220 38.100 39.345 33.624
M14 765682093654 241381.302807 22.810 19.812 22.727 32.676
M16 755400.233316 223825771085 23.200 25.400 24 340 22.352
M17 744337430006 224781.756367 22.120 21.844 21.430 22.371
M19 755950630000 217610.330000 17.740 26670 24011 20.077
03 735369246078 230672.594422 19.690 26 162 24.097 23.388
04 734168924612 255016.775493 38.190 39.116 38.754 35.675
0 5 713090.146295 246701551082 29.820 32.766 34.356 26.581
09 726130235853 247275.671191 25.360 38 608 37.093 31.701
018 731346.624696 2167(3011455 18.130 26.670 21.034 21 079
024 715654088076 215086283082 20.690 40.132 32.437 26 166
025 731861.017503 225830555575 21.240 29.210 29.047 19.101
W14 753133.344245 209696.295155 17.260 25.400 24.356 17.811
W15 750220740000 206719.180000 17.260 22.352 22.658 18.533
W18 745604881900 214856586919 17.690 26.162 23.723 19.223
W20 735298110000 199341.790000 26.550 26.416 28.333 22.864
W23 724714028432 197970368012 28.220 29.464 25.101 27.885
W33 755386.272117 215582872187 19.200 29.210 24.938 17.518
W48 709614370019 201814.621439 32.610 30.480 29891 26.946
A1 678039980433 195924.936908 44.770 33.528 54.167 39.065
2 663120262649 212553141409 42.850 43.434 43.273 33490
A 5 695810135030 191348.250416 39.140 33.782 38.901 36455
L 1 656935798800 236936068948 30.000 41.656 36.081 34.898
L2 655307791088 245383.380983 41.740 47.498 47.224 37 902
L 5 655433651803 217957872282 39.530 42.418 44.440 32.471
L 6 680819554474 212103804745 32 7 31.496 28 264 28.688
L8 683827288566 245447.601664 39.570 39.37 43.660 33.220
L9 685117.095706 233972.632310 37.790 39.878 40.287 27.913
L11 671537.470375 229482547174 24.400 31.496 26.990 29.514
M1 754440159488 258799157739 40.790 39.624 45.893 43.843
M 5 756874108802 227770456845 22 650 25.908 34.790 25 344
M 7 739614.0990fl 250112.456291 38.950 43434 44916 37.196
M15 755444220459 218949865155 19.200 29.464 26.431 18 908
M18 745887.380000 226750870000 28.550 24.384 22.063 24.088
02 730402.927052 221676.374291 21.240 29.464 25.486 19.724
0 7 717831.717332 237839.089634 24 140 28.448 24.542 24 414
08 725348147988 235798.729758 21.270 26.67 19.553 22.754
010 694269889040 228610917000 19.060 33.782 23.876 25.196
013 705431.001880 220697610715 23.090 32.512 23.694 23.582
016 693745.730000 252604.490000 43.390 43.688 56.795 34.173
019 722772817043 220375.078922 23.390 27.686 25 996 20274
020 736063850000 218411.640000 21.690 28.956 24.620 18.949
026 702230480000 220046830000 23.000 35.56 27.896 24.318
028 694588.732145 213376.137195 30280 29972 25.76] 27.136
W 2 708078.587107 194300.186312 35.260 35.814 33.504 34.183
W16 734607.714135 203484.977237 26.550 32.512 22.491 24087
W19 743359420000 202028.890000 21.860 28.194 20.910 21.412
W25 732161.441554 213556429868 17.670 24.384 21.995 19.270
W27 726187.905777 204715.689118 28.220 27.178 27.318 24.875
W42 754665813608 213426.186194 16.520 23.876 20 370 18.406
W43 733803730000 197470030000 28.860 25.908 26.946 27 010
W44 733662390000 179256.190000 31.790 32.766 27.104 27.010
W45 736866940000 197018930000 33.560 32.258 24.630 26.161
W47 731494800000 195941 .610000 33 690 29.972 33 253 27.591

135

Appendix N
Various SEMCOG Precipitation Data
(Precipitation Event 05/28/2000)

Shih-ID X Y NEXRAD- Gap_— ANN .- OC .-

A3 661857.143789 192530880673 23 840 33.020 27.618 17.773
L3 66804785(XX)0 241521.48m 20.440 18.034 18.067 13.186
L7 681514.971760 222057.746602 15.290 20.828 19.050 15.408
L10 658405.618120 224659.693526 16.390 16.764 15 237 21.479
M4 762562.920492 230609.680239 1.520 4318 2.949 2.022
M8 746972860607 254820071250 1.850 3.048 2.287 2.944
M9 742960.436068 231431.293091 1.990 6.858 6.078 1.570
M10 749986779148 230140.273915 0.850 5.334 2.596 1.879
M12 765224025423 256122.102610 0.600 3.302 0.000 2.121
M14 765682.093654 241381.302807 2.340 3.048 2.186 0.934
M16 7554411233316 223825.771085 2.330 7.112 3.263 1.268
M17 744337430006 224781.756367 1.930 8.636 5.333 1.996
M19 755950630000 217610.330000 1.720 7.620 5.993 1.822
03 735369246078 230672.594422 2.200 10.668 6.595 3.132
04 734168.924612 255016775493 4.940 8.636 5.427 4.132
O 5 713090146295 246701.551082 4.900 5.842 4.687 8.087
09 726130.235853 247275.671191 6.260 3.556 5.393 4.470
018 731346624696 216708011455 3.400 16.002 5 508 5.433
024 715654.088076 215(36 283082 3.730 14.732 8.371 9.684
025 731861.017503 225830555575 3.400 11.938 6.118 2.467
W14 753133.344245 209696.295155 4.750 14.478 9.491 4.914
W15 7502207400“) 2067191800“) 7.050 13.208 9.555 6.510
W18 745604.881900 214856.586919 3.960 13.462 7.876 4.231
W20 735298.110w0 199341790100 14.450 10.414 12.403 10.950
W23 724714.028432 197970.368012 14.450 11.684 13.553 13.717
W33 755386272117 215582872187 1 710 11.176 6.756 2.432
W48 709614.370019 201814621439 14.920 13.462 14.891 11.847
A1 678039980433 1959249369“ 26.460 0.508 30.378 20.371
A2 663120262649 212553.141409 13.000 14.22 17.050 18.713
A 5 695810.135030 191348.250416 16130 12.7 15 353 18.764
L1 656935798811) 236936068948 15.350 17.526 12.885 18.854
L2 655307.791088 245383380983 9.710 19.812 11.350 19.355
L5 655433.651803 217957872282 20.060 17.78 14.890 18.115
L 6 680819554474 212103804745 19990 18 034 17.835 16.707
L8 683827288566 245447601664 12.610 13.97 14.796 14.523
L9 685117.095706 233972.632310 20.770 18.796 17.061 14.049
L11 671537.470375 229482547174 17.520 23 622 22.454 17.241
M1 754440159488 258799.157739 0.760 3.048 0.584 1.393
M 5 756874.1(3802 227770456845 0.380 4.826 2.372 1.702
M 7 739614099028 250112456291 4.750 5.588 3.990 3.513
M15 755444220459 218949.865155 1.710 8.382 3.087 1.832
M18 745887.38mw 2267508700“) 2160 7.874 4.416 1.655
02 730402.927052 221676374291 3 400 13.208 2.489 3.249
O 7 717831.717332 237839089634 7.280 9.398 4.325 4.772
08 725348147988 235798729758 4.980 11.684 5.712 4.160
010 694269889040 228610.917” 13.440 14.732 13 807 11.065
013 705431.“)1880 220697.610715 6.020 12.954 4.988 7.625
016 693745.730000 252604.490000 10.850 10.16 23.905 11 267
019 722772.817043 220375.078922 2.800 13.716 2.458 3.458
020 7360638500“) 2184116400“) 3.740 11.938 6.517 3.592
026 702230.480000 2200468300“) 7.740 13.462 9.088 9.083
028 694588732145 213376137195 11 820 13.97 11.152 13.224
W2 708078.587107 194300186312 15.240 15.24 14 739 17.088
“’16 734607714135 203484977237 14.450 13.462 7.393 11.686
W29 742837.820000 203183.420000 5.890 15.748 3.740 10.148
W25 732161.441554 213556429868 3.330 15.24 5.151 5.175
W27 726187.905777 204715.689118 14.450 13.97 14 152 10.832
W42 7546638136“ 213426186194 3.200 8.89 6.585 2.775
W43 733804150235 197470094732 14420 9.906 12.738 14.754
W35 7322208300“) 1790842500“) 17.220 16.256 16 677 16.307
W45 736866.940000 1970189300“) 14.450 11.938 11.900 14.389
W47 7314948000“) 195941.610000 14.450 12.446 13.069 15.028

136

Appendix 0
Various SEMCOG Precipitation Data
(Precipitation Event 05/31/2000)

MI ID X Y NEXRAD I. “_I- ANN_- 0C_-

A 3 661857143789 192530.880673 1.680 0.508 3.722 18 507
L 3 66804785m 241521 .480000 0.420 0.508 0.000 13062
L 7 681514971760 222057.746602 15.920 5.334 9.469 5.436
L10 658405618120 224659693526 14.690 12.954 11.141 4.197
M 4 762562920492 230609680239 0.500 0 0.000 0.020
M 8 746972.860607 254820.071250 0 000 0 0.583 0 000
M9 742960.436068 231431.293091 0.000 O 0.000 1.090
M10 749986779148 230140273915 0.000 0.254 0.000 1.036
M12 765224025423 256122.102610 0.000 0.508 0 000 0.000
M14 765682.093654 241381302807 0.000 0 508 0.000 0027
M16 755400233316 223825771085 0.800 0.508 0.743 1 392
M17 744337.430006 224781 .756367 5.040 0 0.291 2.154
M19 755950630000 217610330000 1.840 1.524 1.219 2.191
O 3 735369.246078 230672594422 0.000 0.254 0.196 1.137
O 4 734168.924612 255016.775493 0.000 0 0.000 0.327
O 5 713090.146295 246701551082 1.190 0.762 0.000 1.509
0 9 726130.235853 247275.671191 1.040 0.762 0.170 0.173
018 731346624696 216708011455 8.110 3.048 5.191 5.971
024 715654088076 215(36283082 3.340 2.032 4.476 9.385
025 731861 .017503 225830555575 1.910 O 0.868 2.977
W14 753133.344245 209696.295155 6.590 1.524 3.612 5.687
W15 7502207400“) 206719180000 7.440 4.064 5.081 7.829
W18 745604881900 214856586919 7.200 5 (B 5360 6 261
W20 735298.11m00 199341790000 10.920 10.668 11.049 15.637
W23 724714.028432 197970368012 20310 8.89 13.441 10.725
W33 755386 272117 215582872187 2.590 2.54 2.798 3.141
W48 709614370019 201814.621439 10.680 3.048 10.649 12.443
A1 678039980433 195924936908 14.220 6.35 19.704 8.233
A 2 663120.262649 212553.141409 5.580 6.604 10.024 11.472
A 5 695810135030 191348250416 20.950 16.764 25.376 10.931
L 1 656935.798800 236936068948 0.000 0.254 0.000 6.734
L 2 655307791088 245383380983 0.000 1.27 0.614 3.327
L 5 655433651803 217957.872282 13.350 9.398 13.994 12.298
L 6 680819554474 212103804745 12340 1.27 17 866 13 069
L 8 683827288566 245447.601664 0.000 0.254 0.000 2946
L 9 685117.095706 233972.632310 0.520 0.254 0.268 8102
Lil 671537470375 229482.547174 4.860 0.762 1.470 10369
M 1 754440159488 258799.157739 0.000 0.508 0.000 0.000
M 5 756874.1(3802 227770.456845 0.610 0.254 0.221 0.316
M 7 739614.099028 250112.456291 0.000 0.508 0.000 0.000
M 3 753509660000 218106530000 2.590 3.556 0.620 2.687
M18 745887.380000 226750870“ 0 000 O 0.000 2.967
O 2 730402.927052 221676 374291 1.910 0 1 819 4.577
O 7 717831.717332 237839.089634 0.000 1.27 5.342 1.339
O 8 725348147988 235798729758 1.150 1.778 2.444 0.751
010 694269.889040 228610917000 8.250 0 2.920 8.269
013 7054311111880 220697.610715 1.830 4.572 2.462 5.978
016 6937457300“) 25260449001!) 0.000 0.254 00(1) 0.998
019 722772817043 220375078922 1.320 0 0.000 4.046
020 736%385001!) 218411.640000 0.590 2.032 1.266 6.873
026 702230480100 220046830000 2.930 4.318 3.581 7.135
028 694588732145 213376137195 5.900 4.826 12.236 10.499
W2 708078587107 1943111186312 16.950 4.318 13.062 12800
W16 734607714135 203484.977237 10.920 5.588 12.209 11 197
W29 742837320000 203183.420000 15.640 5.334 12.612 9.392
W25 732161.441554 213556429868 9000 3.302 9.532 9 102
W27 726187.905777 204715689118 20310 5.08 14.937 13.855
W42 7546658136“ 213426186194 5.950 1.27 3.857 41%
W43 733804150235 197470094732 17.350 8.382 13.507 12.922
W35 732220330000 179034250000 11.530 4.572 8.791 15.763
W45 73686694000) 197018.930000 13 570 1016 13.145 11.644
W47 731494.800W 195941610!!!) 15 510 7.62 15.546 15.169

137

Appendix P
Various SEMCOG Precipitation Data
(Precipitation Event 07/28/2000)

Static-ID X Y NEXRAD- Ga'_— ANN .— OC _

A3 661857.143789 192530880673 74.040 45.720 52.422 64.179
L3 668047850000 241521480000 103.720 55.880 71.512 88.484
L 7 681514971760 222057746602 134.800 56.896 86.268 65.930
L10 658405618120 224659 693526 70.310 37.134 46.501 109.255
M2 756937449154 232773.992790 133.970 39.116 44.957 77.421
M4 762562920492 230609 680239 88.820 27.686 38 802 99.972
M8 746972860607 254820071250 74.340 22.860 38.145 55.000
M9 742960.436068 231431.293091 51 470 19.304 41.638 59.743
M10 749986779148 230140.273915 60.950 13.970 36.763 80.872
M14 765682.093654 241381 302807 62.300 23.876 32.041 102.127
M16 755400233316 223825771085 73.130 67.564 80.997 58.781
M17 744337430006 224781756367 35.310 13.208 31.777 47.935
M19 755950 630000 217610330000 29.790 21.590 15.484 62.191
03 735369246078 230672594422 70.040 45.212 54.022 51.320
0 4 734168.924612 255016.775493 38.470 17.526 23 242 67.790
0 5 713090146295 246701551132 50.110 36.068 50.005 71.591
09 726130.235853 247275.671191 62.440 32.766 39.139 49.098
024 715654138076 215086.283m2 45.610 35.052 39.811 36.322
025 731861017503 225830555575 51.140 52.578 43.006 56.357
W20 735298119300 199341796003 41.590 75.692 70.994 18.437
W14 753133344245 209696295155 15.840 15.240 13 100 43.728
W15 7502207400“) 20671918m 35.330 17.018 20.574 19.278
W18 745604881900 214856.586919 33.200 16.510 30.432 35.262
W23 724714028432 197970368012 14150 3.810 10435 32.647
W33 755386272117 215582.872187 59.280 19.304 22.256 25.791
W48 709614370019 201814621439 11.340 11.684 9.925 43.363
A1 678039980433 195924.936” 57.160 30.480 81.760 71.542
A2 663120.262649 212553141409 71.880 8.128 90.572 84.560
A5 695810135030 191348250416 31.860 12.446 20.102 40.366
L1 656935.798800 236936.068948 98.370 39.878 56.464 85.651
L2 655307791m8 245383.380983 66.540 29.464 58.139 88.476
L 5 655433.651803 217957.872282 104.000 67.056 84.064 73.630
1.6 680819554474 212103804745 123.670 64.262 135.333 102.653
L8 683827288566 245447601664 120.150 56.134 128.582 97.336
L9 685117.095706 233972632310 118.640 56.134 110850 109981
L11 671537.470375 229482547174 90.290 53.340 118.818 108.168
M1 754440159488 258799157739 83.380 48.260 73.325 69.612
M5 756874.1(3802 227770456845 92.390 72.390 48.492 93.855
M7 739614099028 250112456291 48640 35.814 33.924 60.294
M3 753509666411 218106538937 59.280 32.258 90.793 42.035
M18 745887380000 226750870000 44.360 11.176 43.894 43.249
02 730402927052 221676.374291 51.140 12.954 41.424 46.401
07 717831.717332 237839089634 55.930 25.654 42.101 58.634
0 8 725348147988 235798 729758 502 35 814 53 682 61.145
010 694269889040 2286109170“) 75.160 34.544 67.083 96.552
013 7054311111880 220697.610715 86.3“) 57.658 83.062 64.621
016 693745.731XX10 252604.49m 130.970 58.166 106.338 80.287
019 722772817043 220375078922 36.550 12.954 34 559 47.406
020 736063850000 2184116400“) 27.730 22.606 17.480 38.314
028 694588732145 213376.137195 95.560 72.390 143.297 78.729
W2 708078587107 1943m.186312 10.090 8.382 10.281 17.167
W16 734607714135 203484977237 41.590 49.022 54.561 37.570
W22 727993648094 195W.345910 44.520 14.986 36 953 24 892
W25 732161.441554 213556429868 68.850 14.478 22 411 37.457
W27 726187.905777 204715.689118 14.150 4.064 7.010 28.490
W19 743359.426259 202028896272 81.740 82.042 104.934 36671
W42 754665813613 213426186194 42.650 11.430 0.000 43.193
W43 733804150235 197470094732 87.950 27.432 71.131 40.479
“'35 732220832480 179184258487 34.770 11.430 23 411 22.756
W45 736866941111) 197018.93m 108 300 49.022 93 903 38 886

138

Appendix Q
Various SEMCOG Precipitation Data
(Precipitation Event 07/31/2000)

Static-ID X Y NEXRAD— Gap_- ANN .- OC .-
A3 661857.143789 192530880673 0 0.508 1.126 3.269
L3 668047.850000 241521.480000 0 0 0.000 0.988
L7 681514.971760 222057.746602 3.980 3.048 2.001 0.830
L10 658405618120 224659693526 0000 0.508 0.928 0.600
M2 756937.449154 232773992790 10.350 2.54 5.567 17.183
M4 762562.920492 230609.680239 2.170 1.778 2.520 10.411
M8 746972.860607 254820071250 1.360 2.286 3.560 2.483
M9 742960436068 231431.293091 1.190 0 5 753 15.234
1.110 749986.779148 230140273915 43.340 0.508 8.119 5.519
M14 765682.093654 241381.302807 0.920 1.016 0.000 4363
M16 755400.233316 223825.771085 11.730 12.446 13.148 20.879
M17 744337.430006 224781.756367 0.000 1.778 2.316 10.947
W31 756733.163365 214398086719 36660 31.75 29.843 20.905
03 735369246078 230672594422 0.790 0.254 0.000 0.000
04 734168.924612 255016.775493 0.000 0.508 0.000 0.361
O 5 713090.146295 246701.551082 0.000 0.508 1.564 0.000
09 726130.235853 247275.671191 0.000 0 0.591 0.156
024 715654088076 215086283082 1.480 4.318 2.385 0.572
025 731861 .017503 225830555575 0000 0 0.000 0000
W8 732252549782 197942.319261 0.660 0 0.709 3.172
W14 753133344245 209696.295155 26.070 6.604 10.341 21.253
W15 750220740000 206719.180000 14.950 8.128 7.070 18.986
W18 745604881900 214856.586919 0.000 0.254 2.516 8.519
W23 724714m432 197970.368012 0.840 0.508 0.000 1.691
W33 755386272117 215582872187 19.900 33.528 23.516 30.258
W48 709614.370019 201814.621439 5.120 30.48 16.099 1.426
A1 678039.980433 195924936913 7.390 4.318 10.445 2.361
A2 663120.262649 212553141409 0.000 0 0.000 0.964
A 5 695810.135030 191348250416 0.490 1.016 0.000 4.145
L1 656935.798800 236936068948 0.000 0 0.000 0.000
L2 655307.791088 245383.380983 0.000 0 0.662 0.000
L 5 655433.651803 217957.872282 0.920 0 0.000 0.067
L6 680819554474 212103.804745 10.670 2.032 3.275 3.359
L8 683827288566 245447.601664 1.160 1.524 1.845 0.845
L9 685117.095706 233972.632310 1.750 5.08 0.000 2.173
L11 671537.470375 229482.547174 0.000 0.508 0.705 1.558
M1 754440.159488 258799.157739 0.750 0.762 0.000 0.740
M5 756874108802 227770.456845 3.390 6.35 4.339 14.244
M7 739614.099028 250112.456291 0.930 0.254 1.091 1.991
M15 755443.801809 218949.801618 19.900 31.75 16.963 16.532
M18 745887380000 226750.870000 3.510 0 12.523 10.815
02 730402.927052 221676.374291 0.000 0.254 0.000 0.000
O 7 717831.717332 237839089634 0.000 1.524 0.000 0.285
08 725348.147988 235798.729758 0.000 0.508 1.778 0.293
010 694269.889040 228610917000 0.310 0.254 0.468 2.635
013 705431.001880 220697.610715 0.000 O 0.000 2.110
016 693745.730000 252604490000 1.050 0 1.140 0.000
019 722772.817043 220375078922 0.000 0 1.956 0.000
22 736583.384861 221238316631 0.000 0.508 0.000 0.000
028 694588.732145 213376.137195 7.010 7.366 4.288 3.736
W2 708078587107 194300.186312 8.950 8.128 17.896 4.641
W16 734607.714135 203484.977237 0.660 0 0.407 0.511
W22 727993648094 195084345910 1.010 0 0.857 1.645
W25 732161.441554 213556429868 0.250 0 1.227 0.000
W27 726187.905777 204715689118 0.840 0 0.000 0.000
W19 743359426259 202028.896272 6.530 0 3.526 7.133
W42 754665813608 213426186194 23.980 21.59 25.061 26.673
W43 733804150235 197470.094732 0.730 0.254 0.406 1.675
W44 733662398932 179256.197595 0.800 1.778 0.145 87
W45 736866.940000 197018.930000 0.640 0 0.379 3720

139

Appendix R
Various SEMCOG Precipitation Data
(Precipitation Event 08/06/2000)

84:80.11) X Y NEXRAD- Giggl- ANN .- OC .-

A3 661857.143789 192530.880673 18.980 29.464 26.065 13.680
L 3 668047.85m 241521.48m 6.580 15.494 12.100 7.500
L 7 681514971760 222057.746602 11.290 20.828 16.903 14.362
1.10 658405618120 224659.693526 7.020 19.558 15.903 10.213
M2 756937449154 232773 992790 13.670 17.272 17.264 13.919
M4 762562.920492 230609.680239 12.290 18.288 17.487 13.909
M8 746972.860607 254820.071250 15.330 13.97 15.085 11.086
M9 742960.436068 231431.293091 18.710 21.336 20.882 17.820
M10 749986779148 230140273915 15.470 22.098 20.490 17.832
M12 765223.606768 256122.039071 12.080 12.446 12.818 11.367
M14 765682093654 241381302807 10.200 14.986 14.266 11.999
M16 7554m233316 223825771m5 20.320 18.542 18.505 15.910
M17 744337.43CXX16 224781.756367 20.470 22.352 20.940 19.937
M19 755950.630299 217610335632 17.050 21.082 21.552 19.276
0 3 735369246078 230672.594422 19.730 25.908 24.016 21.214
04 734168.924612 255016.775493 10.230 11.176 11.408 14.908
0 5 713090.146295 246701551082 14.870 17.018 14.702 13 959
O9 726130.235853 247275.671191 15.040 18.288 16.192 13.949
018 731346.206049 216707947915 22 25.9“ 25.400 23.287
024 715654088076 215(36283082 22.360 31.496 27.650 22.990
025 731861.017503 225830555575 24.100 23.368 23.782 20.731
W8 732252.549782 197942.319261 23.050 26.924 24.587 21.706
W14 753133344245 209696.295155 17.550 24.892 24.030 18.633
“’15 750220740000 206719.181Xm 18.370 24.384 24.235 18.764
W18 7456048819“) 214856586919 21.0“) 22.352 22.471 20.268
W23 724714028432 197970368012 22.700 24.892 24.287 24.149
W33 755386.272117 215582872187 19.090 18.796 18.274 17.255
W48 709614.370019 201814621439 26.790 34.544 30.143 21.241
A1 678039980433 195924936” 25 680 27.178 26.743 19.478
A2 663120262649 212553141409 9.400 21.59 7.277 11.856
A 5 695810135030 191348250416 24.160 30.226 30.706 23.497
L 1 6569357988“) 236936.068948 6.290 9.652 4.195 6157
L2 655307791” 245383380983 3.390 9.652 4.091 5.795
L 5 655433651803 217957872282 8.110 18.288 9.671 9.293
L6 68(319554474 212103.804745 13.770 18.034 11.950 14.955
L8 683827288566 245447601664 7.060 12.954 5.324 9.244
L 9 685117.095706 233972.632310 10.400 24.638 9.232 10.793
L11 671537.470375 229482.547174 7.440 19.558 7.428 8.378
M5 756874113802 227770456845 13.950 16.51 18.698 16489
M 7 739614.099028 250112.456291 15.840 16.764 12 872 13.538
M15 755443801809 218949801618 19.090 20.574 20.998 17.959
M18 745887.38m 2267508700“) 17.970 21.336 18.728 19.174
02 730402927052 221676374291 24.100 23.368 27.331 23.220
0 7 717831.717332 237839089634 18.300 8.89 14.411 17.566
08 725348147988 235798729758 16.110 19.05 16.924 18.931
010 694269.889040 228610917“ 15.050 22.352 14.995 14.456
013 705431.“)1880 220697 610715 17.160 17.018 19.405 19625
016 6937457300“) 252604.490000 6.290 13.716 0.783 10.579
019 722772817043 220375078922 21.420 22 23.635 22.355
022 736583384861 221238316631 23.240 24.892 25.989 22.340
028 694588.732145 213376.137195 18.090 25.146 20.037 18.680
W2 7(3078587107 1943m186312 25 450 30.48 37151 25400
W16 734607.714135 203484.977237 23.050 26.416 25.788 22.176
W19 743359.426259 202028896272 17.850 22.606 22.642 20.550
W25 732161 .441554 213556429868 23.040 28.448 28.120 22.086
W27 726187905777 204715689118 22.700 28.194 25.213 22.778
W35 732220832480 179084 258487 21.730 32.004 21.729 22 852
W42 754665813608 213426186194 17.420 19.05 20.556 18.582
W43 733804150235 197470094732 20.600 22.098 29.953 22.745
W45 7368669400“) 197018.93m 20.140 33.274 27.168 22.135
W47 731494806185 195941.615746 21.330 28.956 28.995 22.945

140

Appendix 8
Various SEMCOG Precipitation Data
(Precipitation Event 08/17/2000)

MI. I!) X Y NEXRAD .- Gag-_n ANN u 0C .-

A 3 661857.143789 192530.880673 7.210 14.732 7.263 8.406
L 3 668047.850000 241521.48m 5.970 10.668 6.858 7.608
L7 681514.971760 222057746602 8.110 11.430 7923 7 962
L10 658405618120 224659.693526 7.030 14.478 10252 6.562
M 2 756937.449154 232773.992790 10.050 11.430 12.323 9.161
M 4 762562920492 230609.680239 9.640 13.208 12 643 9.477
M 8 746972860607 254820.071250 7 820 11.176 6.582 8.313
M9 742960.436068 231431.293091 7.630 10.160 7.539 7.917
M10 749986.779148 230140.273915 8.140 11.938 8 706 8.282
M12 765223.606768 256122.039071 7.490 10.922 7.666 9082
M14 765682093654 241381302807 9.860 11.430 9.927 8.954
M16 755400233316 223825.771085 8.200 12.192 8.486 7.462
M17 744337.43m06 224781.756367 6.480 10 668 6.598 7.208
03 735369246078 230672594422 8.540 10.414 7.404 7.704
O 4 734168924612 255016.775493 8.270 8.636 6.411 8.072
O 5 713090.146295 246701.551082 9.030 12.700 9.670 8.073
0 9 726130.235853 24727 5.671 191 8.250 10.668 6.835 8.659
018 731346.206049 216707.947915 8.370 11.684 10.912 7.670
02 715654088076 21 5436283082 9.480 16.002 10.500 9.463
025 731861 .017503 225830555575 7.840 10.160 10.775 8.386
W 8 732252.549782 197942319261 8.540 8.890 9.851 8.507
W14 753133 344245 209696295155 4.750 7.366 5.766 6.135
W15 750220 740000 206719.18m 6.460 7.620 5.987 5.251
“’18 7456048819“) 214856.586919 5.660 8.890 5.325 6.354
W23 724714028432 197970.368012 9.370 10.414 10.477 9.192
W31 756733163365 214398186719 6.020 9.144 5.629 6.464
W33 755386272117 215582.872187 5.900 8.382 5.462 5.646
W48 709614.370019 201814.621439 10.560 11.430 10.853 9.253
A 1 678039980433 195924936943 10.060 12.192 1 1.348 8.304
A2 663120.262649 212553.141409 8.410 13.970 10.99 7.373
A 5 695810.135030 191348.250416 11.330 11.430 10.702 9.427
L 1 656935798800 236936.068948 6.770 16.256 11.605 6.329
L 2 655307.791” 245383.380983 6.740 12.446 9.3419 6.114
L 5 655433651803 217957.872282 7.420 14.224 10.688 7.047
L6 “(319554474 212103.804745 7.400 12.192 8.2915 8.355
L 8 683827288566 245447.601664 8.700 11.938 9.2444 7.275
L 9 685117.095706 233972.632310 6.260 16.002 11.486 7.767
L11 671537.470375 229482.547174 6.620 14.478 11.2 7.084
M 5 756874143802 227770456845 10.470 10.414 10.173 9.025
M 7 73961409903 250112.456291 7.140 9.652 6.8871 8.188
M3 753509.666411 21 8106. 538937 5.900 9.652 7.2586 6.141
M18 745887.38m 2267508700“) 7.800 10.414 8.6041 7.006
O 2 730402.927052 221676.374291 7 .840 11.938 9.3049 8.135
O 7 717831.717332 237839189634 7.940 9.652 9.0595 8.815
O 8 725348.147988 235798729758 7.860 9.906 8.7815 8.625
010 694269.889040 228610.917“ 8.540 12.954 10.029 8.579
013 7054311111880 220697.610715 11.5% 11.684 11.223 9.326
016 6937457300“) 252604.4m 7.980 8.890 8.5565 7.763
019 722772.817043 220375.078922 9.890 9.906 8.506 8.858
022 736583384861 221238.316631 61“) 10.414 9.3504 7.308
028 694588732145 213376137195 7.600 11.684 8.7439 9.222
W2 7&078587107 1943(X).186312 10.720 11.176 10.145 10.030
W16 734607.714135 203484.977237 8.540 10.668 9.1103 8.067
W47 731494.806185 195941615746 9.330 11.176 9.1818 8.662
W25 732161 .441554 213556429868 9.940 12.192 9.4018 8.174
W27 726187.“)5777 204715.689118 9.370 11.176 9.9609 9.017
W19 743359426259 202028.896272 7.220 7.874 6.3459 7.189
W42 754665813643 213426.186194 4.550 7.366 5.5561 5.445
W43 733804150235 197470094732 7.850 7 112 8.5817 8.379
W35 732220.832480 179084.258487 8.160 8.890 9.1281 8.719
W45 7368669400“) 197018.930000 7.610 10.414 8.1222 8.065

141

Appendix T
Various SEMCOG Precipitation Data
(Precipitation Event 09/11/2000)

Mull) X Y Wu. “_II ANN .- 0C .-
A 3 661857143789 192530880673 33.950 21.844 20.587 19254
L 3 668047818100 241521.480000 3680 1.524 1.412 8.290
L 7 681514971760 222057746602 15.220 13.462 13.649 17.761
L10 658405618120 224659693526 4.000 6.096 8.419 12.835
M2 756937.449154 232773992790 40.290 30.734 30.764 43.449
M 4 762562920492 230609.680239 34.110 23.876 26.925 43.404
M8 746972.860607 254820.071250 26.300 11.938 24 058 31.834
M9 742960436068 231431.293091 33.790 10.16 17.412 41.274
M10 749986779148 230140273915 53.230 21.336 36.096 41.067
M12 765223.606768 256122.039071 25.630 9.144 23.231 30.299
M14 765682.093654 241381.302807 34.790 26.924 34.984 30.776
3416 755400.233316 223825.771CB5 55.740 43.18 42.189 45.250
M17 744337.430006 224781.756367 34.280 25.4 33.306 39.080
M19 755950.630299 217610.335632 46.180 30.988 31.599 48.465
0 3 735369246078 230672.594422 36.180 24.638 30.831 24.965
04 734168.924612 255016.775493 32.290 27.432 23.341 35.981
0 5 713090.146295 246701.551m2 30.370 5.08 16.899 32.281
0 9 726130.235853 247275.671191 44.420 40.894 38.784 31.587
018 731346206049 216707.947915 11.760 6.096 9 548 25.837
024 715654138076 215086283132 26.790 13.716 20.500 26.193
025 731861017503 225830555575 16.030 17.018 16.443 26.490
W8 732252549782 197942.319261 41.390 91.44 75.493 47.495
W14 753133.344245 209696.295155 46.720 39.116 45.002 43.512
W15 750220.740000 206719180000 41.440 44.958 49 982 44.444
W18 7456048819“) 214856.586919 38.740 50.546 43.408 36.456
W23 724714028432 197970.368012 53.920 54.356 58.750 38.939
W33 755386.272117 215582872187 46.680 44.196 43.537 46.133
W48 709614.37m19 201814.621439 40.740 18.796 37.855 38.744
A1 678039980433 195924.936908 27.240 24.13 39.955 32.941
A 2 663120.262649 212553.141409 15.350 9.398 5.456 15.855
A 5 695810.135030 191348250416 77.980 44.196 94.181 41.047
L1 6569357988“) 236936068948 3.570 1.27 0.896 2.805
L 2 655307791” 245383.380983 2.740 3.81 8.034 2.988
L 5 655433651803 217957872282 9.520 10.16 6 054 9784
L6 68(319554474 212103.804745 14.100 7.366 18.038 21.836
L8 683827288566 245447601664 6.340 7.62 5.231 12.134
L 9 685117095706 233972.632310 4.330 3.302 10.602 13.746
L11 671537.470375 229482.547174 3.220 2.286 3.928 7.898
M 1 754439.740000 2587990!!!” 25.460 10.922 10.922 25.719
M 5 756874.108802 227770456845 41.390 32.258 31.951 48.131
M 7 739614.099028 250112.456291 35.960 14.732 27.828 33.082
M18 745887380000 226750.87“!!! 27.700 23.368 26.869 40.017
M3 753509.666411 218106.538937 46.680 57.658 47.284 47.142
2 730402.927052 221676.374291 16.030 12.192 21.386 13.947
0 7 717831.717332 237839139634 34.910 38.608 50.312 30.919
0 8 725348.147988 235798729758 30.700 20.574 46.791 32.530
010 694269889040 228610.917W 24.140 20.066 29.211 19.570
013 7054311111880 220697.610715 45.670 42.418 43.930 24.883
016 693745.730” 252604.4901XX) 3.610 2.54 4.623 17.977
019 722772.817043 220375.078922 27.140 11.176 20.274 18.778
022 736583.384861 221238.316631 19.700 8.128 19.790 21.168
026 702230.48W0 220046330000 41.340 32.004 46.360 24.871
028 694588.732145 213376.137195 39.540 18.034 37.641 26.255
W2 713078587107 194300186312 62030 55.118 47.247 44.691
W16 734607.714135 203484.977237 41.390 38.354 49.032 35.561
W22 727993648094 195134345910 77.760 84.582 84.049 49.804
W25 732161.441554 213556429868 19.140 8.128 10.536 18.740
W27 726187.905777 204715.689118 53.920 39.116 28.489 37.703
W29 742837828788 203183424168 52.970 43.18 61.474 38.445
W35 732220.832480 179084258487 68.160 48.514 77.127 51.435
W42 754665.813“ 213426186194 46.030 35.56 46.272 46.573
W43 733804.150235 197470094732 79.150 74.422 95.990 41.513
W45 736866940000 197018.930000 73.780 72.136 95.579 41.617

142

 

Appendix U
Various SEMCOG Precipitation Data
(Precipitation Event 09/12/2000)

Shih-ID X Y

NEXRAD-I ... ANN .- OC .-
A3 661857.143789 192530880673 0.890 1.778 0.989 3.296
L3 668047.850000 241521480000 2.230 0.762 1.492 1.865
1.7 681514.971760 222057.746602 3.560 2.794 2.455 5.072
L10 658405.618120 224659.693526 1.310 1.016 2.183 1.598
M2 756937.449154 232773.992790 4.950 5.08 4.608 5504
M4 762562.920492 230609.680239 6.220 6.35 5.768 5.354
M8 746972.860607 254820.071250 1.390 2.286 0.911 2.194
M9 742960.436068 231431.293091 6.900 4.318 4.031 3.839
M10 749986779148 230140.273915 5.080 5.842 5.053 5.12
M12 765223.606768 256122039071 1.890 2.032 0.969 3.730
1414 765682093654 241381302807 5.740 3.81 4.075 4.366
M16 755400.233316 223825771085 4.540 6.35 6.180 5.529
M17 744337.430006 224781.756367 3.600 3.556 3.664 5.282
M19 755950.630299 217610.335632 6.050 4.572 6.373 5.317
03 735369.246078 230672.594422 3.490 3.556 4.912 5.031
04 734168.924612 255016.775493 1.170 2.794 2.039 2.279
05 713090.146295 246701.551m2 3.480 2.032 2.974 4.222
09 726130235853 247275.671191 3.140 2.032 1.781 2.688
018 731346.206049 216707947915 3.400 0.762 3.680 6.651
024 715654.088076 215(36283m2 15.160 11.938 12.326 5.351
025 731861017503 225830555575 4.380 4.318 4.586 4.044
W8 732252.549782 197942.319261 6.690 8.128 7.365 4.782
W14 753133344245 209696.295155 5.880 5.842 6.064 6&1
W15 750220740000 206719.180000 6.300 5.842 7.611 5.748
W18 745604881900 214856.586919 4.830 4.826 5.426 4.481
W23 724714.028432 197970368012 4.870 2.54 1.679 7.563
W33 755386.272117 215582.872187 5.550 6.35 8.354 5.974
W48 709614.370019 201814.621439 8.460 2.794 3.362 9.025
A1 678039.980433 195924936908 7.100 2.54 9.737 3.305
A2 663120.262649 212553.141409 0.740 2.54 1.577 1.629
A5 695810.135030 191348.250416 7.540 2.032 5.497 5.565
L1 656935798800 236936068948 1.610 2.286 0.000 1.420
1.2 655307791138 245383.380983 1.320 1.27 0.645 1.337
1. 5 655433.651803 217957.872282 0.930 0.254 1.877 1.114
L6 680819554474 212103804745 10.450 5.842 7.632 4.008
L8 683827288566 245447.601664 2.910 3.556 2.793 3.181
1.9 685117095706 233972632310 1.570 2.54 2.846 4.046
L11 671537470375 229482547174 0.850 0.00 1.765 2.483
M1 754439.740000 258799090000 0.710 1.524 1.524 1.445
M 5 756874.1(3802 227770.456845 6.580 4.572 4.600 5.025
M7 739614099028 250112456291 4.290 3.556 2.074 2.190
M18 745887.380000 226750870000 6.890 3.302 7.014 4.527
M3 753509.666411 218106.538937 5.550 4.064 6.328 5.357
02 730402927052 221676.374291 4.380 4.572 3.497 4.575
07 717831.717332 237839139634 4.800 4.064 5.667 5.359
08 725348147988 235798729758 7.190 3.556 6.868 4.784
010 694269.889040 228610.917000 4.830 3.81 3.642 6.187
013 705431.001880 220697.610715 7.430 7.62 10.201 10.293
016 693745.730000 252604490000 1.160 2.794 0.000 2.954
019 722772817043 220375.078922 12.150 7.62 14.407 8.686
022 736583.384861 221238.316631 5.170 4.572 4.153 3.463
026 702230480000 220046830010 11.220 5.588 11.431 9.481
028 694588.732145 213376.137195 8.140 3.556 8.625 7.376
W2 713078587107 194300186312 7.880 3.302 1.670 6.736
W16 734607.714135 203484.977237 6.690 4.826 3.287 5.899
W22 727993648094 195084.345910 15.590 8.128 10.800 5.651
W25 732161.441554 213556429868 4.890 3.048 3.960 4.263
W27 726187905777 204715.689118 4.870 1.27 3.783 6.484
“H9 743359426259 202028896272 12.470 6.35 7.347 6.049
W35 732220832480 179084258487 1.800 2.032 1.698 6.094
W42 754665.813“ 213426186194 5.330 7.366 9.513 5.650
W43 733804150235 197470.094732 10.870 7.874 9.276 6.563
W45 736866940000 197018.930000 11.780 8.636 12.480 6.3%

143

Appendix V
Various SEMCOG Precipitation Data
(Precipitation Event 09/14/2000)

Sun-ID X Y NEXRAD— GQ_- ANN .- OC .-
A3 661857.143789 192530880673 10 730 15.24 13.990 10.068
L 3 668047.85m 241521 .48(X100 10.320 19.558 13.502 13.738
L 7 681514.971760 222057746602 9.400 17.78 12.027 11.049
L10 658405618120 224659 693526 13.260 18.034 14.443 10.217
M 2 756937449154 32773992790 8.420 10.668 9.228 7.817
M 4 762562920492 230609680239 76% 9.144 8.084 7.656
M8 746972.860607 254820071250 7.070 17.272 9307 8.574
M 9 742960.436068 231431 .293091 6.890 13.2% 11.867 7.726
8110 749986779148 230140273915 8.540 13.462 10.172 7.135
M12 765223.6m768 256122.039071 8.640 11.176 9 369 7488
M14 765682093654 241381.3(D807 7.920 13.716 12.865 8.259
M16 755400233316 223825771085 5.970 8.636 7 322 7.101
M17 744337.430” 224781756367 6.790 11.684 7.922 6.483
O 3 735369 246078 230672 594422 6960 16.256 10.1 12 7.312
04 734168.924612 255016775493 8.720 17.78 11.060 11.802
0 5 713090146295 246701.551m2 18.090 18 796 17.212 12.521
09 726130235853 247275.671191 14.830 17.018 11.889 11.819
018 731346.206049 216707947915 5.820 7.112 7.749 5.832
024 715654.088076 215086 283082 5.380 17.526 10.073 7.504
025 731861 .017503 225830.555575 6.190 14.478 9.681 6.838
W8 732252.549782 197942319261 5.350 7.112 5.160 5.596
W14 753133.344245 209696.295155 7.710 5.334 6.139 7.131
W15 750220.74(XX)0 206719.180m0 7.880 6.35 6.480 7.272
W18 7456048819“) 214856586919 6.410 9.144 6.888 6.590
W23 724714 028432 197970368012 4.860 7.62 5.653 5.618
W31 756733.163365 214398136719 6.440 6.096 7.986 5.975
W33 755386.272117 215582.872187 5.550 7112 5.883 6.439
W48 709614.370019 201814.621439 6.520 10.922 7.829 5.638
A1 678039980433 1959249369“ 10.460 12.192 12.640 9.246
A 2 663120262649 212553141409 14.6% 16.764 18.059 11.595
A 5 695810.135030 191348.250416 8.220 9.906 10.778 7.511
L1 6569357988“) 236936.%8948 10.650 23.622 12.779 12.024
L 2 655307.791088 245383380983 8.750 22.098 12(35 11.902
L 5 655433.651803 217957872282 11.780 15.748 15.041 12.744
L6 680819554474 212103804745 9.450 17.78 15.787 9.336
L 8 683827.288566 245447601664 9.450 20.066 10.759 12.285
L 9 685117.095706 233972.632310 10.680 23.622 13.466 11.048
L11 671537.470375 229482547174 13.210 17.526 15.151 10.873
M1 754439740000 258799.09(XX)0 8.950 19.05 19.050 7.881
M 5 756874113802 227770.456845 6.070 8.89 12.123 7.244
M 7 739614.099028 250112456291 7.670 19.558 14.735 8.311
M18 745887 38m 226750.87m 6.970 13.97 13.433 7.142
M3 753509.666411 218106538937 5.550 10.16 7.555 5.788
2 730402.927052 221676374291 6.190 16.002 10 679 6.008
O 7 717831.717332 237839.089634 16.4“) 21.844 24.460 13.645
0 8 725348147988 235798729758 14.450 17.018 17.656 11.025
010 694269889040 228610.917“ 8.740 20.32 16.768 10.674
013 705431.001880 220697.610715 14.670 16.764 18.590 8.614
016 693745.73w00 252604.49(XX)0 9.470 19.304 15.480 14.321
019 722772817043 220375078922 16.720 14.478 16.299 6.382
020 736M3852221 218411.644446 6.370 11.176 11.692 6.1%
026 7022304800“) 220046.830w0 14.500 16.764 16 973 8.699
028 694588732145 213376.137195 7.010 15.494 10.729 8.326
W2 7(3078 587107 1943m.186312 7.250 10.16 9.458 6.456
W16 734607.714135 203484.977237 5.350 9.652 7.936 5.745
W22 727993.648094 195(34345910 5.580 6.858 5.755 5.152
W25 732161.441554 213556429868 5.930 12.954 9.046 5.786
W27 726187.“)5777 204715689118 4.860 9.906 6.704 5.253
W29 742837828788 203183424168 8.690 6.604 8.161 6.741
W35 732220832480 179(34258487 3.430 2.794 4.214 5.954
W42 754665.813“ 213426186194 6.230 7.112 8.125 6.470
W43 733804150235 197470.094732 6 120 2.794 5.549 5.531
W45 736866.94m 197018930” 6920 8.382 7.350 5.884

144

Appendix W
Various Michigan Precipitation Data
(Precipitation Event 05/06/1999)

MN.W- Gap- ANN-

Kata: 20.320 15.000 16.162
88111.50 4.572 4.340 4.688
Newbcny 12.700 11.780 12.769
Ironthain 43.180 27.390 31.194
Bell-in 0.000 2 670 4 465
Alpcm 2.794 1.960 3.187
TnvCity 5.080 3.100 3.219
Gladw'm 10.160 16.600 8.999
Cm Ciy 2.540 2.120 2.702
m» 7.620 7.020 7.729
Val-t 0.000 4.700 3.510
Grind Rapib 2.286 2.160 0.803
Jackson 0.000 6.160 4.549
Ypsilni 0.000 0.000 1.831
Detroit Mot 0.254 0.250 0.000
South Bud 3.810 3.790 3.616
Coppa'Hn'ba' 11.100 20.320 7.091
WW 5.370 12.700 5.461
Gin: 3.510 15.240 9.515
Trout Lake 3.130 7.620 2.045
Glennie Aloom 4.420 7.620 3.644
Houdini: Labs 5.350 6.350 6.266
Megan 5.040 6.858 5.623
Km City 0.380 0.000 2.193
Grand Ham 3.620 5&0 6.488
Owen-o 6.180 5.080 5.311
Flint 5.320 5.334 4.609
Loin 3.550 3.556 4.132
Howell 2.590 2.540 4.205
Coldm 4.060 0.000 2.459
Toledo 0.000 1.270 0.114

145

Appendix X
Various Michigan Precipitation Data
(Precipitation Event 05/17/1999)

MN- NEXRAD_- qu— ANN-

Kentm 30.480 10.830 20.797
SSM-h 5.842 2.550 5.884
Newba-ry 10.160 4.290 5491
km Mani: 38.100 22.030 3.669
Bellaire 2.540 5480 4.701
Alp“ 3.810 3. 540 6.975
TrevCity 5.080 6.860 6.721
Gledw'n 17.780 23.310 20.431
Cue City 15.240 20.210 22.678
W 10.160 13.950 11.707
Vent 12.700 19.260 19.888
Grad Rapith 0.000 4.540 6.376
Jackson 7.620 15.380 21.009
Ypulum' 20.320 43.540 32.963
Detro'n Met 14.986 14.960 25.960
South Bend 5.080 5.070 4.459
Copper Huber 3.250 20.320 26.383
Wakefield 6.810 0.000 0.000
(hi-n 7.120 33.020 21.461
Tm Lake 5.390 10160 4.487
01mi- Aleona 4.860 7.620 9772
Hum Lake 21.770 18.542 16.395
Mukegon 4.380 3.556 3.768
Kan City 9.690 17.780 10.078
Grand Haven 4.510 10.160 3.649
Flint 6.590 6.604 11.013
11min; 9.380 9.398 8.513
Howell 7.250 10.160 16.702
Coldm 20.720 12.700 23.228
Toledo 39.390 27.686 25.538

146

Appendix Y
Various Michigan Precipitation Data
(Precipitation Event 05I28/1999)

SSMane 0.000 0 000 0.127
Newba'ry 0.000 o 000 o 000
Dan: Vin-p 0.000 o 000 o 000
Iron Mouta'n 7.000 0 000 0 942
Vanderbilt 0.000 0 000 0 000
Bella‘n 0.000 0 000 0 623
Alpcxa 0.390 0 000 O 322
Tnany 0.000 o 000 o 000
Glad'n 0.000 0 000 0 443
Can City 0.000 o 000 o 000
Van: 0.000 0 000 0 000
Quad Rapid- 23.090 23 114 23 390
Janina: 20.730 0 000 8 026
Ypatllm 16.130 12 700 16877
Demon Met 14.450 14 986 13 696
South End 17.500 18 288 18 985
Wakefield 1.540 2 540 0 550
Gum 0.000 0 000 0 000
Tm Lake 0.000 0 000 0 000
Gimme Alcoa 0.000 0 000 0 361
Wan Lab 0.000 o 000 0.302
Harbor Beach 0.000 0.000 0 297
Mmkegon 19.930 27.178 12.866
Gram! Haven 22.170 33.020 19.584
Lam 16.470 16.510 11.791
Howell 17.520 17.780 14469
Goldwater 15.240 38 100 21 .744
Toleh 42.190 34.798 29.259

147

 

Appendix Z
Various Michigan Precipitation Data
(Precipitation Event 07/01/1999)

own 4.280 30.480 11.089
Mia 1.020 12.446 7.151
'l'reu Lia 0.800 15.240 13.839
Beulah 5.940 33.020 1 1 .069
VIII-hilt 3.560 10.160 5.941
Giulia Alarm 2350 12.700 8.149
Oladw'u 16.000 10.160 16.276
H-ha'Daadi 17.660 43.180 38.899
Mlem 7.210 17.780 8.953
Howell 18.950 38.11» 32574
June. 22360 35.560 32.395
Ypihni 8.760 20.320 18.644
Salli Bod 53.310 53.136 35.027
Calm 26.91!) 40.640 25.189
Ceppc HM 2 850 0.000 0 058
Kauai 7.810 127(8) 2.003
w 2450 12100 8.980
Duet: Villqa 2 240 0.000 1.869
11mm 6.580 10.160 1.615
Bella'aa 1.820 10.160 4.221
Alpn 4.240 6.858 2.039
TnvC‘ay 12.360 10.160 5.056
W Lake 4.420 5.842 5.199
m 1.380 0.000 0.000
C. (3y 10.550 0.000 6.519
Kan C'ay 3.440 2.540 0.000
Crud Ham 6.020 10.160 7.887
mm 10.890 11.430 10.312

148

Appendix AA
Various Michigan Precipitation Data
(Precipitation Event 07/31/1999)

Stile-Nana NEXRAD 4k- Ga'a ANN_-

Mango 0.000 2.540 0.491
Kauon 0.000 0.000 0.941
SSMan'e 12.170 15.748 10.072
Newton-y 21.250 17.780 18.464
Detour Village 20.190 0 000 0 000
Iran Moutain 0.640 0.000 0 000
Bellaae 16.700 17.780 14 051
Alpena 4.620 0 508 4 416
'l'ravity 13.290 12.700 13 725
Case City 0.000 0 0(1) 1 404
Montague 0.000 0 000 0.923
Grand Rapids 0.000 0.000 0.341
Jacloai 8.370 10160 12 413
Ypadm 3.610 2 540 5 522
DetrottMet 12.180 12192 11896
South Bald 1.250 1 270 1 474
(Zappa-Huh“ 0.000 2.540 0.000
Wakefield 0.000 0.000 2.475
Tram Lake 54.760 53.340 45.692
Eecamha 4.760 0 000 0 000
Giana Aleom 0.790 0 000 0 568
Houdlton Lake 0.750 0 508 4 222
Harbor Beach 0.000 0 000 0 000
Milken 0.000 0 000 2 188
Km City 0.000 0 000 2 306
Ormd Ham 0.000 0.000 2 080
Flatt 0.000 0.000 0 000
Luna); 0.000 0 000 0 008
Allen 0.980 0.000 0.000
Howell 14.510 12.700 5.376
Coldwata' 3.940 0.000 11 .937
Toledo 0.000 0 000 3.299

149

Appendix AB
Various Michigan Precipitation Data
(Precipitation Event 09/14/2000)

Man Nua NEXRAD_- (Sgt- ANN_--

SSMmio 0.000 0.000 0.000
Newbeny 19.380 15.240 3.100
Detour Village 0.000 0.000 1.433
Vanderbilt 0.000 5.080 4.436
Bellaire 1.480 10.160 0.000
Alpena 3 070 2.540 1.766
TravCity 3.030 0.000 0.000
Gladwin 8.790 7.620 11.189
Grmd Rapids 14.940 17.780 6.443
Jackson 8.110 2.540 4.609
Ypsilanti 8.220 5.080 3.284
South Bend 4.300 27.940 9.765
Copper Harbor 0.000 0.000 0.000
Muskegon 11.610 22 860 16.717
Grand Haven 2.520 10.160 13.698
Allegan 8.040 12.700 10.895
Goldwater 2.950 7.1 12 9. 584
Toledo 5.220 27.940 25.712

150

 
  

    
 

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