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Date

   
   
   

  

LIBRARY

Michigan State
University

This is to certify that the

thesis entitled

SHORT DURATION EVAPOTRANSPIRATION ESTIMATED
BY CLASS A PAN AND METEOROLOGICAL PARAMETERS

presented by

GHASSEM ASRAR

has been accepted towards fulfillment
of the requirements for

Ph . D. degree in Soil Science

2; Majoérofessor

 

 

él/éié/a/

 

0-7639

 

(«Am i

V“ is «“lry

 

 

OVERDUE FINES:

25¢ per day per item

RETURNING LIBRARY MATERIALS:

Place in book return to remove
charge from circulation record

 

 

 

 

SHORT DURATION EVAPOTRANSPIRATION ESTIMATED BY
CLASS A PAN AND METEOROLOGICAL PARAMETERS

BY

Ghassem Asrar

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Crop and Soil Sciences

1981

G//é§7é

ABSTRACT

SHORT DURATION EVAPOTRANSPIRATION ESTIMATED BY
CLASS A PAN AND METEOROLOGICAL PARAMETERS

BY

Ghassem Asrar

It is generally recognized that climate is one of the
most important factors determining the amount of water loss
by evapotranspiration. Hence, meteorological budgeting
techniques have been used for estimating soil water losses.
However, monthly or weekly values of the climatic elements
frequently mask daily extremes during the course of a season
and thereby bias the final result. Any analysis designed
for greater accuracy of determining soil moisture losses must,
of necessity, be based on daily, hourly or even shorter
measurement periods.

The objectives of this study were to: (l) establish a
relationship for estimating potential evapotranspiration with
a U.S. Class A evaporation pan and correlate these data with
micrometeorological measurements taken over short time inter-
vals, and (2) improve and test an explicit aerodynamic evapor-
ation model based on the concept of turbulent diffusion.

A field study was conducted over a short grass covered
area with a fetch to height ratio of 30:1 at the Michigan

State University Soil Science Research Farm. Soil properties

Ghassem Asrar

measured in this study were: (1) gravimetric moisture content,
(2) soil moisture potential by tensiometers, (3) bulk density,
(4) soil moisture—matric potential by pressure plate, and

(5) profiles of soil temperature.

A U.S. Class A pan was used in conjunction with a moni—
toring system based on a stress-strain concept to measure
water losses from the pan over short periods.

Profiles of air temperature, wind-speed and absolute
humidity were obtained by measuring and recording the values
of these parameters every two minutes at five different eleva-
tions. These data were later smoothed, combined and averaged
for ten—minute periods.

Gravimetrically determined soil moisture and soil moisture
potentials, measured by tensiometer, indicated that the evapo-
transpiration under the irrigated treatments of this study was
at its potential rate during the entire season. The rate of
evapotranspiration under such conditions is controlled primarily
by the weather conditions. However, under non-irrigated treat—
ments and in general, in the absence of adequate soil moisture,
the evaporation rate is controlled either by soil and/or weather.

Cummulative pan evaporation measured over periods of a
day indicated linear, but different, increases with time for
all the periods of this study. Simple correlation coefficients
between the cummulative pan evaporation, pan temperature, air
temperature and wind-speed were positive and highly signifi-
cant at the one percent level of probability. A highly
significant but negative correlation coefficient was obtained

between cummulative pan evaporation and atmospheric humidity.

Ghassem Asrar

Air temperature profiles indicated, at some time, the
presence of an unstable atmospheric condition. This usually
occurred late at night or very early in the morning but
changed to a more stable condition due to an increase in air
temperature during the daylight hours.

Profiles of wind-speed showed the formation of turbulent
boundary layers above the ground surface and an increase in
their thickness with time during the day. A graphical pro—
cedure was used to obtain the aerodynamic parameters related
to these profiles.

Profiles of absolute humidity usually indicated a gradual
decrease in humidity with elevation above the ground. This
relationship was reversed for late evening and early morning
hOurs.

Detailed analyses of temperature, wind—speed and humidity
profiles indicated that the classical equations of heat, momen-
tum and water vapor transport should be modified to better
represent these phenomena under a wide range of atmospheric
conditions.

The profiles of air temperature, wind—speed and absolute
humidity were used to study the effectiveness of a defined
stability parameter, S, and the functions, f(S), in adjusting
for the influence of atmospheric stability upon the transport
of water vapor. The results indicated that the model proposed
in this study, proved to be more accurate than the original
equation of Thornthwaite-Holzman in approximating evapotranspir-
ation fromailysimeter and evaporation from a Class A pan over

short periods.

To Peace and Brotherhood

ii

ACKNOWLEDGEMENTS

The author wishes to thank Dr. Raymond J. Kunze under
whose guidance and encouragement this project was developed
and carried out. I would like to express my sincere apprecia-
tion to Dr. Dale E. Linvill (Agricultural Engineering),

Dr. Reinier.J.B. Bouwmeester (Civil Engineering) and
Dr. Maurice L. Vitosh (Crop and Soil Sciences), members of
my Guidance Committee.

Thanks to Dr. Gary L. Cloud and Mr. David Kanistanaux
(Metallurgy, Mechanics, and Materials Science), for their
advice and use of their facilities in automating the Class A
pan.

A special thanks is extended to Messer's Gary F. Connor
(Agricultural Engineering) and Dallas A. Hyde (Crop and Soil
Sciences) for their assistance in preparing and installing
the weather station.

A final thanks to Messer's Anders G. Johanson, Mark R.
Riordan and Richard Wiggins (Computer Laboratory) for their

help in data manipulation and programminggflmses of this study.

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . .
LIST OF FIGURES . . . . . . . . . . . . . . . . . .
LIST OF APPENDICES . . . . . . . . . . . . . . . . .
LIST OF SYMBOLS . . . . . . . . . . . . . . . . . .
INTRODUCTION . . . . . . . . . . . . . . . . . . . .
LITERATURE REVIEW . . . . . . . . . . . . . . . . .
THEORETICAL MODEL DEVELOPMENT . . . . . . . . .
.EXTENSION OF THEORETICAL MODEL DEVELOPMENT . . . .
MATERIALS AND METHODS . . . . . . . . . . . .

Soil Measurements . . . . . . . . . . . . . .

Evaporation Measurements from Class A pan . . .

Micrometeorological Measurements . . . . . .

Collecting and Analysis of Data . . . . . . . .
RESULTS AND DISCUSSION . . . . . . . . . . . . . . .

I. Evapotranspiration from Soil . . . . . . .

II. Evapotranspiration from Class A pan .

III. Evaporation Estimated by Aerodynamic Models
CONCLUSIONS . . . . . . . . . . . . . . . . . . . .
APPENDICES . . . . . . . . . . . . . . . . . . . . .

LIST OF REFERENCES . . . . . . . . . . . . . . . . .

Page
iv
vi

viii

12
21
24
26
29
36
40
43
43
49
65
86
88

126

Table

10

LIST OF TABLES

Page

Soil moisture content influenced by irrigation,
rainfall and type of crop during the experi-

mental study . . . . . . . . . . . . . . 45
Bulk density and moisture holding capacity of

Metea loamy sand at different potential levels

and sampling depths . . . . . . . . . . . . . . 47
Regression equations representing cumulative

pan evaporation over short periods . . . . . . . 50

Simple correlation coefficients between

cumulation pan evaporation, pan temperature and
weather parameters for short duration

measurements . . . . . . . . . . . . . . . . . . 55

Pan coefficient (Kp) for Class A pan for
different ground covers, relative humidity and
wind speed . . . . . . . . . . . . . . . . . . . 58

Reference evapotranspiration (ETO) computed
from cumulative pan evaporation (Epan) and
pan coefficient (Kp) . . . . . . . . . . . . . 59

Cumulative actual evapotranspiration (ET) for

corn, soybeans and turfgrass computed from
reference evapotranspiration (ETO) and crop
coefficient (Kc) . . . . . . . . . . . . . . . 64

Displacement height, roughness parameter,
frictional velocity and shear stress determined
from wind speed profiles . . . . . . . . . . . . 78

Evaporation rates measured with an automated

Class A pan and computed according to the
Thornthwaite-Holzman and a modified version of

this equation from atmospheric profile data

over short periods . . . . . . . . . . . . 81

Evapotranspiration rates measured with lysimeter
(after Morgan et. a1.) and computed according

to the Thornthwaite—Holzman and modified
Thornthwaite—Holzman equations from

atmospheric profile data . . . . . . . . . . . . 84

iv

LIST

Table

B-1

B-2

OF TABLES (cont'd.)

Smoothed weather data averaged over
minute periods, July 24, 1980 . .

Smoothed weather data averaged over
minute periods, July 25, 1980 . . .

Smoothed weather data averaged over
minute periods, July 30, 1980 . . .

Smoothed weather data averaged over
minute periods, August l, 1980. .

Smoothed weather data averaged over
minute periods, August 4, 1980. . .

Smoothed weather data averaged over
minute periods, August 7, 1980. .

Smoothed weather data averaged over
minute periods, August 8, 1980. . .

Page

101

103

105

107

109

113

115

Figure

1

10

11

12

13

14

LIST OF FIGURES

Schematic diagram of the experimental site
on the Michigan State University Soil Science
Farm . . . . . . . . . . . . . . . . . . . .

Soil moisture content-matric potential
relationship for Metea loamy sand . . . . . .

Position of strain gages (a) on an active-arm
and (b) their full—bridge arrangement . . . .

Calibration curve for pan assembly . . . . . .

Tachometer 555—circuit for conditioning
anemometer signals . . . . . . . . . . . . . .

Cross sectional (a) and close up (b) views of
a psychrometer unit . . . . . . . . . . . .

Schematic view of all sensors and data
acquisition system . . . . . . . . . . . . . .

Rainfall distribution and soil moisture status
during the growing season as indicated by
tensiometers placed in irrigated corn and
soybean plots. . . . . . . . . . . . . .

Air, soil and Class A pan temperature averaged
hourly, July 25, 1980 . . . . . . . . . . . .

Air, soil and Class A pan temperature averaged
hourly, August 4,1980 . . . . . . . . . .

Air, soil and Class A pan temperature averaged
hourly, August 7, 1980 . . . . . . . . . . . .

Crop coefficient as related to percent of
growing season for corn in Michigan . . . . .

Crop coefficient as related to percent of
growing season for soybeans in Michigan .

Crop coefficient as related to percent of
growing season for turfgrass in Michigan . . .

vi

Page

25

28

33

35

38

39

41

44

52

53

54

61

62

63

LIST OF FIGURES (cont'd.)

15

16

17

18

19

20

21

22

23

24

Air temperature profiles at different hours,
above a short turfgrass cover, July 25, 1980 .

Air temperature profiles at different hours,
above a short turfgrass cover,
August 4, 1980 . . . . . . . . . . . . . . . .

Air temperature profiles at different hours,
above a short turfgrass cover, August 7, 1980

Wind speed profiles at different hours, above
a short turfgrass cover, July 25, 1980 . . . .

Wind speed profiles at different hours, above
a short turfgrass cover, August 4, 1980

Wind speed profiles at different hours, above
a short turfgrass cover, August 7, 1980 . . .

Humidity profiles at different hours, above a
short turfgrass cover, July 25, 1980 . . . . .

Humidity profiles at different hours, above a
short turfgrass cover, August 4, 1980 . . . .

Humidity profiles at different hours, above a
short turfgrass cover, August 7, 1980 . . . .

Functional relationship of stability para—
meter (S) and Richardson number (Ri) under
different atmospheric conditions . . . . . .

Page

66

67

68

70

71

72

74

75

80

LIST OF APPENDICES

Appendix Page
A. FORTRAN IV Program for Data Processing and

Data Conversion . . . . . . . . . . . 87
B. Smoothed and Averaged Field Data . . . . . . . . 98

C. Integration of Equation [29]. . . . . . . . . . . 117
D. Illustrative Examples for Computing

Evaporation Rates from Equations [32]
and [35] . . . . . . . . . . . . . . . . . . . . 121

viii

Symbols

AEB
AL
Aq
AR
AT
AU
Az
aT/az

aU/BZ

Eaero

EB
Ecum

E1

LIST OF SYMBOLS

Meaning
z(aT/aZ)
z(aU/aZ)
constant of proportionality
centibar
displacement height
diameter
change in bridge output
change in length
change in water vapor concentration
change in bridge resistance
change in temperature
change in wind speed
change in elevation
temperature gradient
wind speed gradient
thickness
flux of water vapor
evaporation computed from aerodynamic models
bridge output in milivolts
cumulative pan evaporation

modulus of elasticity

 

Symbols
ETO

ET

Epan

GF

Kc
Kh
Km
KP
KX

Ky
Kz

Meaning
reference evapotranspiration
potential evapotranspiration
pan evaporation
strain
acceleration of gravity
gage factor
VonKarmen constant
crop coefficient
heat transfer coefficient
mass transfer coefficient
pan coefficient
water vapor transfer coefficient
diffusion coefficient in x—direction
diffusion coefficient in y-direction
diffusion coefficient in z-direction
mixing length
length
natural logarithm
power coefficient
applied load
water vapor concentration
simple coefficient of correlation
coefficient of determination
bridge resistance
Richardson number

average Richardson number

xi

Meaning
density of air
density of water
stability parameter
strain per unit load
summation of several terms
time
absolute temperature
air temperature
pan temperature
shear stress
gravimetric soil moisture content
velocity component in x—direction
wind speed
frictional velocity
velocity component in y-direction
voltage
velocity component in z—direction
horizontal direction
transverse direction
vertical direction
elevation above the ground surface

roughness coefficient

INTRODUCTION

Maintaining soil moisture conditions near optimum levels
for a given crop requires reliable estimates of the constantly
changing water demands. Frequent soil moisture measurements
are required if the status of soil moisture conditions are
to be maintained near such levels. Water stored in the soil
and additions of irrigation water can be managed efficiently
only if the expected evapotranspiration and other water losses
are known.

There is a continuing need for improving the methodology
of measuring soil moisture losses. The soil moisture losses
can be obtained by direct measurement or computation of the
water vapor flux to the atmosphere. Generally, measurement
of evapotranspiration rates are obtained as follows: (1) the
direct measurement of water losses from soil and vegetated
surfaces by obtaining differences in soil water content for a
given time period, (2) the transformation of water loss
measurements made for non-vegetated surfaces (i.e., evaporation
pans and tanks), and (3) empirical formulae based on climatic
data. Often because of difficulties in obtaining accurate
direct measurements of soil moisture losses under field
condition, the second and third approaches are preferred above

the first.

2

It is generally recognized that climate is one of the
most important factors determining the amount of water loss
by evapotranspiration, particularly when crops are grown
under optimum growth conditions. Hence, meteorological
budgeting techniques have been used, with some degree of
success, for estimating soil water losses. However, monthly
values of the important climatic elements frequently mask
daily extremes during the course of a season and thereby bias
the final result. Any analysis designed for greater accuracy
of determining soil water losses should be based on daily,
hourly, or even shorter, periodical weather observations.

The objectives of this study were to establish a rela-
tionship for estimating potential evapotranspiration from a
U.S. Class A evaporation pan and to correlate these data with
micro-meteorological data on a short-term basis. A final
objective was to modify and test an explicit aerodynamic

evaporation model based on the concept of turbulent diffusion.

'57

LITERATURE REVIEW

Many aspects of water resource planning are not as
critical in humid areas as in the more arid regions. However,
pressures on the currently adequate water resources of humid
areas are increasing. With greater competition for these
resources, there will be greater demand for increasing the
efficiency of their use, particularly as use is related to
water loss. At least 90 percent of water used for irrigation
in the State of Michigan is lost to the atmosphere through
evapotranspiration while consumptive losses for most other
water uses is less than 10 percent (1,57). Evapotranspiration
rates are minimal in areas under water conservation practices
and maximal in areas of wastewater disposal (81). The rates
of evapotranspiration and the factors affecting them have been
the subject of much work and research. Present methods of
measuring or estimating evapotranspiration are in part extensions
or modifications of methods for measuring evaporation since
the two are similar physical processes.

The soil is the source of water for transpiring plants.
Hence, soil moisture measurements are still an important supple-
ment to evapotranspiration studies. Any soil parameter such
as texture, structure, or pore space which affects the conduc—

tivity, hydraulic gradient, vapor pressure, or vapor diffusion

near the soil surface will indirectly affect the rate of
evaporation from the soil surface (69).

The water potential and hydraulic conductivity of the
soil influence the rate at which a plant transpires (87).

If the soil potential is high, the soil can supply water to
the plant roots nearly at the same rate as it is transpired
by the plant. Thus, in a moist soil, the transpiration is
at potential rate and is primarily determined by weather
conditions (73).

The classic definition of potential evapotranspiration
is "evaporation from an extended surface of a short green
crop, actively growing, completely shading the ground, of
uniform height and not short of water." Provided that all
restrictive conditions are fulfilled, the definition suggests
that potential evapotranspiration represents the maximum
possible rate of water loss from a vegetative-covered surface
(94,97).

VanBavel (93) redefines potential evapotranspiration for
any vegetation in terms of appropriate meteorogical variables
and aerodynamic properties of the cover suggesting that "when
the surface is wet and imposes no restriction upon the flow of
water vapor, the potential value of evapotranspiration is
reached." For soil moisture contents equivalent to or greater
than the field capacity, the evaporation is considered as I
. potential evapotranspiration (16,26). As the soil dries out,
the hydraulic conductivity decreases and eventually the soil
cannot supply sufficient water to the plant. Consequently,

the actual transpiration falls below the potential one (69).

Therefore, when the soil is unable to supply sufficient water
to maintain potential evapotranspiration rate under a given
set of atmospheric conditions, the rate of evapotranspiration
is controlled by soil properties (55,77).

The ratio between potential evapotranspiration and actual
evapotranspiration for an area is related to the rate of
moisture supply to the soil surface (81). Soil moisture
measurements are generally adequate for long—time evapotrans-
piration averages, but unfortunately, technical difficulties
prevent the use of soil moisture depletion measurements for
short-time evapotranspiration studies (28,87).

Measured values of evapotranspiration obtained by monitor-
ing soil moisture over a period of years also show considerable
variation in standard error of determination (86). This
investigation shows an average year to year variation of
111% of the average mean evapotranspiration from the same
crop at the same location. Hence, the error of 111% for
predicting future evapotranspiration from soil sampling appears
to be about the same as the error to be expected from estimates
obtained based on other empirical methods.

Tensiometers have proven to be very suitable for monitoring
the soil moisture in coarse textured soils (21). This is true
primarily because of the larger amount of available soils
moisture that is held by the soil in the measurable tension
range of these instruments.

There are two principal factors associated with the

influence of cover crops on evapotranspiration (87). The

first is related to light reflection. Reflection of light

from a bare soil especially when wet, is usually lower than

that from a dense crop canopy. Based on the reflection alone,
evapotranspiration would normally be expected to increase as

the percent of cover decreased. The second factor is associ-
ated with the relative evaporation rates from a bare soil and

a transpiring crop. Evaporation from moist bare soils decreases
rapidly one or two days after irrigation or rainfall; however,
soil water storage usually is sufficient to maintain trans-
piration from the soil for a considerable period of time (26,55).
Consequently, evapotranspiration increases as the percent cover
increases relative to evaporation from a bare soil.

Many empirical formulas relating climatological measure—
ments and evapotranspiration have been developed. These
formulae were based on the empirical relations obtained between
the observed evaporation and climatic data for a specific crOp
and region. Therefore, in order to be able to use them in
another region, they must be tested and adjusted to the condi-
tions of the new area. Empirical methods have the greatest
usefulness when correlated with potential evapotranspiration
(39,85). Empirical methods can be grouped into four classes:
(1) those depending primarily on the relation of evapotranspir-
ation to radiation, (2) temperature methods, (3) humidity
methods, and (4) evaporimeters.

One of the earlier writers on the subject of evapotrans-
piration was Dalton (14), who showed that the rate of evapora-
tion was proportional to the difference between the water

vapor pressure at the evaporating surface and in the

 

atmosphere. This principal, based on the vapor transfer
concept, has been used in all of the evaporation and evapo-
transpiration methods developed since that time.

In 1942, Blaney and Morin (4) published an empirical
formula for estimating monthly pan evaporation or evapotrans-
piration as a function of monthly mean temperatures, monthly
percent of annual daytime hours, and monthly mean relative
humidity. This formula was later modified by Criddle (13),
by omitting the humidity factor and introducing a new constant
of proportionality into the equation. This new formula also
gave an estimate of the monthly mean evapotranspiration rate.
However, Blaney (3) has suggested that this formula can also
be used for estimating pan evaporation with the use of appro—
priate coefficients.

In 1956, Hargreaves (37) proposed an empirical method
of estimating pan evaporation from a study of temperature,
humidity and monthly daytime relations. This model was later
tested by a number of his graduate students (38,63) and was
considered to be fairly good for normal wind velocities under
a wide range of climatic conditions. In 1968, an empirical
method of estimating pan evaporation from climatic data was
proposed by Christiansen (10). Later Christiansen and
Hargreaves (11) developed a series of formulas for converting
pan evaporation directly to potential evapotranspiration and
calculating potential evapotranspiration from climatic data.

The basic deficiencies of any empirical approach are
generally estimates of evapotranspiration over very short

time periods (8).

Evaporimeters measure the drying ability of the air.
Evaporation from a pan or free water surface is a physical
process that depends on the availability of energy to
evaporate the water. The rate of evaporation is, therefore,
largely dependent on climatic parameters such as solar radia-
tion, air temperature, wind velocity and relative humidity
(11,44). Meteorological factors have similar influences on
evaporation from free water, soil surfaces and transpiration
from plant surfaces (31). The major differences between
these forms of water loss are; (l) changing characteristics
of the plant surfaces during growing season, (2) availability
of water for evaporation, and (3) differences in energy absorp-
tion characteristics. Thus, it appears that evaporimeters
could only provide an integrated measurement of complex
meteorological factors affecting evapotranspiration.

Among the pans and tanks tested, the U.S. Weather Bureau
Class A pan provides the best correlation with, and the most
practical and economical method of estimating potential
evapotranspiration (5,71,78). Class A pan evaporation data
provide a useful general reference over a wide range of
climatic circumstances (29). With measurements from a care-
fully sited Class A evaporation pan in a locality, it is
possible to calculate the cumulative evapotranspiration in a
simple way (41). The pan coefficient, Kp, is given by the
ratio ETp/Epan, where ETp is potential evapotranspiration and
Epan is pan evaporation. The coefficient is used in practices

as an "adjusting factor" for pan losses to give an estimate

of potential evapotranspiration (18,31). This ratio was
found to change during the course of the growing season,
primarily during the following two periods: (1) from
planting until 5 to 6 weeks of age, during which evapotrans-
piration is controlled by moisture content of the upper soil
layers, and (2) from the beginning of flowering, evapotrans—
piration increases rapidly as the plant cover the ground,
reaches a maximum at peak flowering, and then decreases until
harvest (8,34). The coefficient Kp also depends on the type,
size and environment of the pan (100). The use of a single
ratio to estimate water requirements using Class A pan data
will introduce only small errors. These generally are lower
than or comparable to the uncertainties in water requirement
values obtained from intensive soil moisture measurements

in gravimetric methods (32). Measurements of Class A pan
evaporation losses from different parts of the United States
suggest a standard deviation of 10% for annual evaporative
losses within regional zones (79).

One of the shortcomings of using pans for estimating
evapotranspiration is the formation of surface films compressed
sufficiently to reduce the evaporation rate. The rather large
reduction of evaporation, up to 20%, by naturally occurring
surface films indicates that their frequency of occurrence
and areal extent may need to be estimated and, if possible,
taken into account when evaluating the evaporation from a pan
in which the surface is assumed to be contaminated (15).

However, the major problem in using the Class A pan is that,

10

the time period for which reasonable estimates can be made
is relatively long, particularly in humid regions where
climate is variable (85). In spite of the limitations,
Class A evaporation pans do provide fairly satisfactory
indices of evapotranspiration especially where installation
and operating standards are complied with (11).

Physics of evaporation is complexed by energy exchanges
and transformations, some being controlled by aerodynamic
factors. Both energy exchanges and aerodynamic transfers
are essentially meteorological; thus, the maximum rate of
evaporation is determined primarily by climatological factors
(48,77). Micrometeoroloqical methods provide a measurement
of the flux density of water vapor in the boundary layer of
the atmosphere. Though these methods have limitations as to
where and how they can be used as well as instrumental diffi-
culties, they have important advantages. When applicable,
micrometeoroloqical methods can measure the potential evapo-
transpiration over very short periods (66). Evapotranspiration
correlates best with meteorological elements when the crop is
transpiring at the potential rate. This rate will not be
reached until the crop has attained full ground cover and is
adequately supplied with water (39). Micrometeorological
methods in greatest use are the energy balance method,
aerodynamic method and a combination of the two. In the
energy balance method the principle of conservation of energy
to the surface of the ground gives some basic equation that

can help us to understand evapotranspiration (74). All energy

ll

arriving at the soil and plant surfaces must be accounted for
in this approach (64). Jensen and Haise (43) developed a
formula for estimating evapotranspiration using solar radia-
tion and climatic data. This model has given fairly good
results where the radiation and heat flux data are available.
The upward flux of water vapor in the surface layer of the
atmosphere is the resultant of turbulent diffusion carried
along a mean gradient of water vapor concentration (23,81).
Therefore, evaporation and hence evapotranspiration can be
estimated based on the vapor flow rate from the evaporating
surface. This may be done by the use of aerodynamic methods,
either implicitly as a bulk aerodynamic method or explicitly
as a profile method. The profile method will be presented

in more detail in the following section. In the combination
method, one energy balance equation and one aerodynamic
equation are combined to produce an equation that can be used
to estimate potential evapotranspiration. In 1948, Penman
(65) was the first to develop a formula based on this concept.
Although his formula is considered to give the best results,
it is seldom used because of its complexity and the availa-

bility of several parameters required in the model.

THEORETICAL MODEL DEVELOPMENT

Recent advances in understanding of boundary layer
phenomena have provided potential means of monitoring evapo-
transpiration by measuring water vapor transfer into the
atmosphere. In the case of air flow over land surface, the
lower atmosphere may be divided into two layers (27). First,
is the laminar layer at the surface. The thickness of this
layer is of the order of several millimeters; and temperature,
humidity and wind velocity vary almost linearly with height.
Transfer of heat, water vapor and momentum through this layer
are essentially molecular processes. Second, is the turbulent
boundary layer with varying thickness depending on the level
of turbulence. In this layer wind velocity, water vapor and
temperature vary, approximately, linearly with logarithm of
height. Transfer of heat, vapor and momentum through this
layer are turbulent processes (74). The capacity for water
movement in the processes of turbulent transfer are more than
100 times greater than the molecular transfer processes (81).
The process of evaporation and diffusion of water vapor into
the earth's turbulent air stream, above or downwind from free
liquid or saturated solid surfaces is practically one of

gaseous diffusion and can be represented by

93=—§—(Kxiq)+%[xy%g)+i[x 3A.) . . . . [1]

3x 82 Z 32

12

13

where q is the water vapor concentration, K's are effective
coefficients of diffusion, t the time and dq/dt denotes the
change in vapor concentration with time. If u, v and w are
the components of the velocity and q is assumed to be a
function of x, y, z and t, the total differential can be

represented by

$149.21 .33 ‘23 is
dt 3t+u8x+vay+waz ......[2]

However, according to Sutton (82), evaporation from a saturated
soil or reservoir which is part of a very large homogenous area

depends only on height and time. Equation [1] then reduces to

3_<1=_3_ 3.51
8t 32 [K2 82) . . . . . . . . . . . . . [3]

Integrating Equation [3] from 0 to Z gives

211 =11. .M
g at dz pa Kz Bz . . . . . . . . . . [4]

where E/pa is the integration constant proportional to water
vapor flux (E) divided by density of air (pa) at the surface
(6). The quantity of aq/at is always limited under actual
conditions. Thus for sufficiently small Z, such as the one
considered in micrometeorogogical studies, the first (integral)
term in Equation [4] is negligibly small when compared with

the remaining two terms in the equation. Therefore, it reduces

to

a
E=-paKz-5-g-..............[5]

The negative sign represents the downgradient flux of water
vapor. Other researchers have used a different approach to

derive the equation of vertical flux of water vapor based on

14

the Reynold's formulation of turbulent stress. The final
results are the same as Equation [5]. If eddies of trans—
ferred substances can be measured in their upward movement,
an analysis of the resulting air layer can be considered.
Within the limits of this layer the evaporation is exclusively
determined by the value of turbulent exchange coefficient,
and the vertical gradient of transferred substances (6).
Therefore, the rate of evaporation could be obtained from
data on the humidity profile in the surface air layer, pro-
vided that the value of turbulent exchange coefficient for
water vapor is known. But, since the laws governing the
turbulent motion are extremely complicated, there is no
accurate, theoretical method for determining the turbulent
exchange coefficient in the atmosphere. Hence, many investi-
gators have made extensive use of approximations obtained by
processing various empirical data in a variety of ways in
attempts to model these meteorological phenomena. The substan—
tial variability of the transfer coefficients with landscape
and atmospheric conditions permits the use of such modeling
attempts (70).

The increase in wind speed with height over an extended

uniform surface can be represented by

_ U* Z—d
U — T? 1n 20 . . . . . . . . . . [6]

when the atmosphere is near a state of neutral stability (66).
In Equation [6], U is the wind velocity at height Z above ground
and Z0 is the roughness coefficient. The displacement height,

d, represents the effective raising of the boundary due to

15

roughness, k is VonKarman constant (k=0.4l), and U* is the
friction velocity which represents the characteristic velocity
in a turbulent boundary layer. The magnitude of U* is

determined by

2. .. . .. . .. . .. . .[7]

where r is the shear stress, the flux of horizontal momentum
transferred vertically and absorbed by the ground and assumed
to be constant in the lower layer of atmosphere. paiS the
density of air. Based on the assumption of constancy of
shear stress with height, we can define

(3:):ng—‘zi............[81

where Knlis the transport coefficient for the momentum and
frequently known as eddy diffusivity. Combining Equations [6],
[7] and [8] yields
Km=kU*(Z—d) ............[9]

The effect of aerodynamic roughness on turbulent transfer of
moisture and energy from vegetative surfaces is an important
factor in evapotranspiration. In general, evapotranspiration
increases with vegetation height due to increased roughness
and zero-plane displacement (d) at a given windspeed, which
in turn increases the coefficient of turbulent exchange (74,84).
Reducing the turbulent transfer offers some potential for
increasing water use efficiency because it is the linking
mechanism between crop surface and bulk atmosphere (36).

When thermal stratification prevails, the logarithmic

wind profile, Equation [6], no longer holds (83). In this

16

case, buoyancy due to temperature gradient in the atmosphere
boundary layer also plays a major role in the transport and
mixing of the air and entities contained therein (74).
Therefore, since turbulence can either be generated thermally
or mechanically, both temperature and wind speed play an
important role in stability of air (59).

Generally, the temperature induced eddies are more
efficient in transport and mixing, than mechanical eddies (61).
A convenient stability parameter for use in this area is the
Richardson number, Ri. It approximates the ratio between the
forces producing thermal and mechanical turbulences. In

gradient form it appears as

(All
Ri=3—-3—z——...........[101

T (53—312

where g is the acceleration due to gravity, T—temperature,
aT/BZ—temperature gradient and aU/aZ-wind velocity gradient.
Under neutral or adiabatic atmospheric conditions (Ri=0), the
transfer mechanisms for heat and water vapor are identical for
freely evaporating surfaces (23,24). Therefore, the eddy
diffusivities for momentum, heat and water vapor are identical
(Km=Kh=Kw) and all could be obtained from Equation [9]. Under
most conditions, however, adiabatic or near neutral conditions
are seldom realized, and predictions of all three fluxes be-
come complex. In an unstable atmospheric condition (i.e.,
lapse, aT/BZ negative), the profile of wind, humidity and
temperature remain similar and ratio of Kh/Km, Kw/Km, hence

Kh/Kw remain constant (unity) for R1 ranging from 0.0 to -0.1 (99).

However, for very unstable conditions, R1 is quite dependent

 

17

on the wind profile, i.e., Ri is less than —0.las the wind
gradient diminishes, and the ratio Kh/Kw will depart smoothly
from unity and becomes greater than one (12,49).

In stable atmospheric conditions (i.e., inversion, aT/az
positive), the eddy diffusion of momentum, heat and water vapor
is also constant up to Ri of +0.1 (47). But, at Richardson
numbers greater than +0.1,Kh/Kw will be less than unity (58,
98). The influence of atmospheric conditions represented

by Richardson numbers are shown schematically below.

 

 

 

 

 

 

very A very
unstable unstable neutral stable stable
12 is negative A: = 0 93 is positive
2 z z
Kh Kh K
—>10 ——-=1.0 _h
Km Km Km< 10
K Kh K
—h>1.0 “=1” i<10
Kw Kw KW
¢_———__———— -0.1 0.0 +0.1 ———————————-+

Ri

18

Under conditions of veryistrong stability, it has been

 

suggested that turbulence changes character to gravity

waves (49). At very strong stabilities a value of (Riimax

is reached where turbulent motion ceases entirely. Turbulence
is then replaced by laminar flow governed by molecular rather
than turbulent diffusion (59). Evaporation under stable
condition decreases rapidly with increasing Ri. This decrease
is constant throughout turbulence decay and indicates that

R1 is no longer a useful stability criterion in profile
equations (12). It appears that the largest departure of
Kh/Kw from unity will occur when either temperature or
humidity is passive additive or the temperature gradient is

of opposite sign to the humidity gradient (95). since the
logarithmic law does not fit the wind profile under non—neutral
conditions, various proposals have been made to modify it.

In 1935, Rossby and Montgomery (75) tried to implement
Prantdl's views on the semi—empirical theory of a boundary
layer problem and develop a relation for the coefficient of
turbulent mixing under adiabatic conditions. They assumed
that under adiabatic temperature distribution the mixing
length in the lower layer of the atmosphere varied linearly
with height, reaching a value proportional to the roughness
of underlying surface at 2:0

1 = k (Z + 20) . . . . . . . . . . . . . . [11]
where l is the mixing length, Z0 is the roughness coefficient
and k is the non-dimensional VonKarman constant (k=0.4l). In

the mixing length theory, it has been assumed that a discrete

19

mass of fluid with a given property leaves a level and
retains this property for some characteristic vertical
distance before mixing and becomes once again indistinguish-
able from its mean surrounding. Rossby and Montgomery assumed
that the influence of stability on exchange is determined at
a given elevation by the Richardson number and is not depen-
dent on the Ri numbers corresponding to other elevations (75).
Based on this assumption, and for stable atmospheric conditions
they derived the general equation

Km = kU*Z (1+BRi)'% . . . . . . . . [12]
where Km is a function of Ri and B=9. The equivalent form of
this expression proposed by Holzman (40) for unstable cases
is

Km = kU*Z (1—BRi)+% - - - - - - . - [13]
Measurements by Panofsky, Blackadar and McVehil (60) and
observations of temperature fluctuations by Priestly (70)
lead the way to deriving a modified equation which covered a
broader range of stability. Such an equation was first sug-
gested by Ellison (27) and is introduced in the literature
under the name KEYPS (47). The KEYPS relationship for a
stable atmospheric condition is

Km = kU*Z (1+BRi)-% . . . . . . . . [14]
The equivalent KEYPS equation for an unstable condition is

Km = kU*Z (1—BRi)+% . . . . . . . . [15]
where B takes the same value for both stable and unstable

conditions at a given location.

20

Morgan et. al. (52) suggest that, for a wide range of

stability, the general form of the equation should be
Km= kUkZ (1+BlRil)in. . . . . . . . [16]

which offers the best mathematical representation of Km(Ri)
relationship. However, for their data obtained at the
University of California at Davis, the authors suggest that
the exponent n apparently needs to be 33% higher than the
(a) power proposed by Ellison as used in KEYPS profile.
On the other hand, the exponent of (%) suggested by Holzman
(40) was too high for their data. The Davis data indicate
one could use a B value significantly smaller than 9.0,
originally proposed by Holzman, to extend the usefulness of
the expression over a range of R1 from —l.0 to +1.0. However,
this is at the expense of errors in Km of up to 10% to 15%

in the zones of Ri around -0.1 to +0.1 (52).

EXTENSION OF THEORETICAL MODEL DEVELOPMENT

A modified version of Equation [5] under thermal

stratification gives
8
E =-paKm-5% o o o o o O o o o o c o [17]

After rearranging the terms, Equation [17] can be presented

as

 

.M=_ E ............um

Substituting for Km from Equation [16] into Equation [18]

 

gives

.29 = _ E -

az pakU*Z(l+B|Ril)in [19]
From Equations [7] and [8] we have

21-21

32 — KIn [20]

Under non-neutral conditions, we can rewrite Equation [20] as

Q)

 

u_ U)!
72" k2(1+B|Ri])in . . . . . . . . . [21]

Then substituting for U* in Equation [19], its equivalence

from Equation [21], we get

 

 

is = _ E ' 1 22
az pak222(1+B|Ri|)i2n §g_ [ 1
32

21

22

or by introducing the definition of Ri as given in

Equation [10] we obtain

 

231 = _ i 2 E . 1 . . [23]
az oak Z [HI—Bi . (3%) [1’52“ 3‘;
T "TE—2 1
(37

Equation [23] is very difficult to integrate in its present
form. Therefore, in order to change this equation into a
more suitable form, we assume, as Holzman (40) suggested,
the logarithmic distribution of properties near the ground.

Making this assumption we obtain

21 = s . . . . . . . . . . . . . . . . . [24]
82 Z

and
12.: h [25]
82 Z

Substituting these relations into Equation [23] gives

 

is = _ l . E . . . [26]
82 paRZZb g
[1.423 i ”in
(2)2
Z
or
is = _ __l __1.E __ _. . . . . . .
82 pakgg ' Z(1+LSE])i2n [27]
where
= Bea . . . . . . . . - . . . . . . . [28]
5 sz

The variable S from hereon is referred to as a stability
parameter. Selecting a for n according to KEYPS, Equation [2]]

becomes

93:11} ._1.Ah- ...... mm
32 pdkzg Z(1+[SZI)1%

23

Integrating Equations [24] and [25] and expressing the changes
of temperature and wind-speed in finite difference notation,

we obtain

=_T2:_:.1_=__A_g._ ........[30]
IHLTZ‘i—J ltd—2%]
and
b-112ih_= AU.........[31]

 

’ z z
1n (2%) 1n (if)

Integrating Equation [29], see Appendex C for detail of the

procedure, substituting for b and solving for E we have

 

p kZAqAU
E=_a_z_.f(3)........[32]
lntfifl
where
f(S)= l ..[33]

[1+szfigi. 71+szl+1|

1n]
/1+szz+1 71+szl-1
for unstable atmospheric conditions (Ri and/or 8 negative,

n positive), and

f(S) = 1 . . [34]

[2[/1+322 - /1+szl] + 1n|L1i§§%Fl-- ‘1TEE_+1|]
71+szl+1 /i¥szl—1

for stable atmospheric conditions (Ri and/or S positive,
n negative). When neutral or near adiabatic conditions prevail
in the atmosphere, the function f(S) becomes unity and

Equation [32] becomes
DaszqAU
= T [35]
[11421)]
which is the original expression suggested by Thornthwaite

and Holzman (88).

'vv

MATERIALS AND METHODS

This study was conducted at the Michigan State University
Soil Science Research Farm. The farm is located on the
corner of South Hagadorn Road and Mt. Hope Highway, two
miles southeast of the center of the campus. A small
weather station was established on grass plots in the mid-
section of the northern portion of the farm, Figure l. The
fetch to height ratio for the eight—meter level of measure-
ment was approximately 30:1 in the west to southwest
direction.

The soil type for this study, according to Ingham County
Soil Survey Report (92) and on site inspection by Dr. D. Mokma,
soil survey and classification specialist in the Department
of Crop and Soil Sciences, was Metea loamy sand, hereafter
referred to as MtB. Typically, the surface layer of MtB
series is a dark, loamy sand, 10 cm thick and a B—horizon
about 85 cm thick. The upper part of the B horizon is
yellowish brown to dark brown and very friable, loamy sand.
The lower part is yellowish brown, loose sand. Permeability
is very rapid in the upper part of MtB soil and moderate in
the lower part. The available water holding capacity of

this series is described as moderate.

24

IIIr

25

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.Enmm mocofiom HHom sz osu co muflm Hmucosfluwaxo wnu mo Emuwmww owumsocom .H ouswflm
(V \V
zmoo
zmoo
mmHQEMm Hfiom MV
U I
ucmfimflsqm 89mm
spam
mm<mw
mmouu
boom
4 memEmm aflom
I I

H mm<m0 mméo mamfimw HHom

o

9 cos m m o mMOm

mm<mo P .u om M cum 3 mz<m
I s
memEmw HHom
I
z<mmw0m z<mmw0m zmou
LT é‘

 

 

 

26

Michigan State University is located at East Lansing
in the northwest corner of Ingham County and within the
south central climatic division of Michigan. East Lansing's
inland location substantially reduces the climatic influence
of the Great Lakes. The prevailing local wind is generally
from the southwest averaging about 5 m/s. The average mid-day
relative humidity varies from 51% in May to 78% in December.
Precipitation is well distributed throughout the year; the
growing season, May-October, receives an average of 45 cm or
61% of the average annual total. Summer precipitation is
mainly in the form of afternoon showers and thundershowers.
Potential evapotranspiration, based on Class A pan observa-
tions, exceeds the average precipitation by 90% during the

growing season (90).

Soil Measurements

 

Soil properties measured in this study were as follows:
profiles of gravimetric moisture content, soil moisture-matric
potential values, bulk density and the soil temperature pro—
file. Soil samples of known volume were taken early in the
morning and late in the afternoon during days with no rainfall
from 5, 10, 20, 40, and 80 cm depths at three different loca—
tions, using a Veihmeyer tube—type sampler. The sampling sites
were: (1) a "High Yield Corn Study" — treatment 5 (Zea maize,
var. M5922) with 75—cm row spacing and population of 84,000
plants per hectare, (2) a non—irrigated section of an
"Irrigation Management Study for Soybeans" - treatment 1

(Glycine max, var. Gnome with 45-cm row spacing and population

 

 

 

27

of 150,000 plants per hectare, and (3) the same as site 2,
except the plots were irrigated at a matric potential of
less than 50 centibars during the entire growing season.
Additional soil moisture data for non—irrigated corn (Zea
maize var. P—3780), 75—cm—row spacing and population of
60,000 plants per hectare were obtained through an exchange
of information with Mr. V. Braults of Department of
Agricultural Engineering.

Tensiometers were also used to monitor the soil moisture
status and irrigation requirements of the soybean and corn
crops. In the corn plots, ll tensiometers were installed at
depths of 25 cm, between the rows and at 25— and 40—cm depth
in the planted row. In the soybean plots a total of 9 tensio—
meters were used at depths of 25 cm and 40 cm in and between
the planted rows.

Tensiometer data were obtained from all plots in one- or
two—day periods based on the weather conditions. During the
cool, humid and less windy days, the data were obtained once
every two days in the afternoon. In the hot, less humid and
windy periods, tensiometers were read at the end of each day.
Five composite, disturbed soil samples were taken from each
level of all three sites and were analyzed in the laboratory
for soil moisture retention according to Richards (72), see
Figure 2.

Profiles of soil temperature were obtained at the
experimental site by placing 22—gage copper-constantan
thermocouples at 5, 10, 20, 40 and 80 cm below the soil

surface. The soil temperature probe was constructed from a

 

Metric Potential (centibar)

28

   

 

 

  

 

 

 

 

@m(8/g)
I 7.5 |5.0 22.5 30.0 37.5
' 5:419
H
.S‘=/.56‘
-l O .—
H
$30.58
-IOO "
H
5=0./3
5: s/an dara’ deviation
530.23
-|OOO H

Figure 2. Soil moisture content-matric potential relationship for Metea
loamy sand. Each point is the mean of 25 measurements -
five measurements being taken at 5, 10, 20, 4D and 80 cm depths.

[5.

29

wooden stake, 6x3 cm and 150 cm long. Two small grooves

were cut 5 mm deep, 4 mm wide and about 1 cm apart from.
.each other in the oblong section of the stake. Thermocouple
wires were placed inside the grooves. The assigned
thermocouples were marked on the stake and fastened by
masking tape. The soldered junction of thermocouples were
insulated by an electrical insulating varnish to prevent

any electrical conductance. Then the junctions were turned
180° such that they were lying flat on the taped section of
the stake. Installation was completed by driving the stake
into the ground. This approach had some inherent advantages
over older excavation methods: (1) it eliminated the
possibility of any loose contact between the soil and thermo-
couple, (2) reduced the labor and error of excavating and
disturbing the soil and (3) consumed less time for installa-
tion. The signals, generated by the five thermocouples, were
transmitted through a reference junction board and channel

expander to the data acquisition system.

Evaporation Measurements from Class A Pan

 

A U.S. Class A evaporation pan was automated and used
for monitoring evaporative losses continuously. The U.S.
Class A pan, 121 cm in diameter, 25 cm deep and normally
constructed of galvanized iron, was mounted on an open frame
such that the pan base was 15 cm above the ground. The
water level in the pan was monitored at 5 cm below the rim.

In addition to measuring water losses electronically,

30

measurements of the water level were made daily by a fixed
gage (41). Although one-day interval, Class A pan evaporation
measurements have given reasonable estimates of potential
evapotranspiration especially under humid conditions, its
major limitation is the inaccuracy for which reasonable
estimates of evaporation can be made for shorter time periods
(62,85). One objective of this study was to design a
monitoring assembly that when combined with a Class A pan
experiment, would give an accurate, continuous assessment

of water losses over short time periods.

A number of available systems which could be utilized
for this purpose were assessed. All were complicated and
costly (9,68). Some equipment which was applicable to
our needs was insensitive and unstable over the load range
of a Class A pan (7,30). After much deliberation and
searching, a unique combination of the Wheatstone bridge
circuit in conjunction with an elastic stress system was
selected for monitoring the water losses. Considerable
effort was put forth in selecting a set of strain gages
(stress transducer sensors) and an appropriate Wheatstone
bridge that would maximize the desired output. A change in
electrical resistance of the wire gages as a result of a
change in strain is the basic principle upon which this
system works (67).

The selection of wire resistance-strain gages and strain
transducer materials depends on the load, precision and

accuracy required (101). Proper transmission of strain to

31

the gage requires the gage wire to be as thin as possible.
However, wire thinness causes a higher gage resistance and
thus a higher voltage output at a given gage current which,
in turn, is limited by the amount of heat generated in the
gage. A higher resistance gage can, of course, also be
obtained with longer wires (53). The transducer materials
should have a small length to radius ratio to ensure freedom
from buckling (67). The precision with which strains can
be measured also depends on hysteresis, creep and fatigue
properties of transducer materials and the environment of
the gage, especially temperature and humidity (54).

A basic device which can be used to measure all classes
of strain is the Wheatstone bridge. Its function is to
determine resistance with the required degree of precision.
The amount by which resistance changes in relation to change
in strain is an index of what is known as strain sensitivity
of wire or "strain gage factor" (51). For a uniform straight

wire this may be expressed as

_ AR/R
GF — ——AL/L . [1]
where GF = strain gage factor

R = resistance

AR = change in resistance

L length
AL = change in length
The higher the gage factor, the more sensitive is the gage

and the greater is its electrical output for indication and

recording purposes (53).

32

To automate the Class A evaporation pan, sixteen general
purpose, self-temperature compensated, constantan strain
gages, type CEA -l3-250UW-120, were mounted on four metal
cylinders (arms), these being the strain transducer materials.
The arms were made of aluminum pipe, each 30 cm long, 15 cm
in diameter and 5 mm thick. The low modulus of elasticity
of aluminum (i.e. E1=55-70x109 N/mz), increased the output
voltage of the gages by increasing the strain per unit load
(17). Figure 3-a shows the arrangement of gages on one arm.
More information on surface preparation and application of
strain gages is presented in "Micro-Measurement Catalog and
Technical Data" published by Vishay Intertechnology, Inc. (51).

An important feature of this system was the spatial
arrangement of the strain gages which were inherently temper-
ature compensated. For a tension load applied on each arm,
gages l and 3 were in compression and gages 2 and 4 were in
tension. With the bridge arrangement shown in Figure 3—b,
these effects were additive resulting in a larger output.

To increase the sensitivity of the system and also protect the
gages against the outdoor environment, all gages were covered
with a special combination of three different coating
materials, M-COATS B, D and G, obtained from "Micro-Measurement
Inc." These were applied as follows: After installation of
the gages on the supporting arms, M-COAT B was applied and
cured for 24 hours, followed by a coating with M—COAT D.
Another 24 hours later M-COAT G was applied and cured for a

period of 48 hours. The combination of these three coating

33

 

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34

materials gave a good, short and long term stability to the

gages and also protected them against the outdoor environment.
In order to level the arms under the pan and prevent

any heat conduction between the arms and the pan, the arms

were placed between two pieces of plywood, 120x120 cm and

1.25 cm thick. This enabled the system to meet the Weather

Bureau requirement that the pan base be at least 10 cm above

the ground. A Sanborn dual—channel, carrier amplifier recorder,

Model 321, was used to record the output voltage generated

by the strain gages. A full—bridge arrangement of strain

gages with the recorder is shown in Figure 3—b. The relation—

ship between the bridge output (EB), bridge supply voltage (V),

strain (5), gage factor (CF), and percent resistance change

in the gages for a four active arm bridge is

=.y gAR] ZARZ gARs EAR]
AEB 4 ( 2R1 + 2R2 + 2R3 + 2R” ) . . . [36]
or
AEB =-% [sO.GF).P . . . . . . . . . . . . [37]

Equation [3] can be rearranged and expressed as

AEB = e-GF
V-P 4 . . . . . . .

[38]
where s = So=strain per kilogram load on the arm

P = load applied, kilogram
The output of the system was in milivolts (mv) bridge output/
volts bridge supply/kilogram axial load applied. A calibra—
tion curve (see Figure 4) was obtained for the system by adding

and subtracting small aliquots of water (0.375 cm water/area of

pan). Both the eye-fitted line and coefficient of determination

35

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36

(r2=0.99) are indicative of linear response of the system
to changes in water levels over a wide range.

The sensitivity of this system was estimated as

 

A(cm of water)
A (EB)

 

Sensitivity = [39]

where

 

A(cm of water)= average quantity of water added
to or subtracted from the pan, cm

A( B)

average change in bridge output

for a given quantity of water

added to or subtracted from the

pan, mv.

Based on this relationship and data obtained from the cali-
bration procedure, sensitivity of the system in predicting
water loss was 0.034 mm water/0.1 mv bridge output. Since

0.1 mv was the smallest voltage change detectable, then 0.034nm1

water was the smallest water loss that could be accounted for.

Based on total weight, 1 g in 6000 g was detectable.

Micrometeorological Measurements

 

Two atmospheric profile measurement masts were constructed
from lO-m long, 7.5-cm diameter, aluminum, irrigation pipe,
mounted on a tilt-up base staked to the ground. Arms for
mounting instruments were constructed of 1.25-cm diameter,
galvanized steel pipe and mounted on the masts with saddle-T
risers.

Wind profiles were measured over two-minute intervals
with 3-cup anemometers, Climet Model 011-1, mounted at 50, 100,
200, 400 and 800-cm levels on the first mast and 200- and 400—cm

levels on the second mast. The digital signal from these

37

seven light-chopper-type anemometers were transmitted via
wire to a Tachometer 555 circuit to fix the width and height
of pulses, Figure 5. The conditioned pulses were then trans-
mitted through a channel expander to specially modified
channels of the data acquisition system.

Wind directions were measured over two-minute intervals
with a Climet Anemovane. The calibration for this system was
established by adjusting the pointer between zero and 1180 mv
output, corresponding to north and south, respectively. The
range between these limits was divided into 8 equal quadrants
for wind direction analyses. The output of this unit was also
transmitted via the channel expander to the data acquisition
system.

Temperature and humidity profiles were measured over two-
minute periods at the 50—, 100—, 200-, 400—, and 800—cm levels
on the first mast and at 100-, 200—, and 400—cm levels on the
second mast, using aspirated, adjustable water level, radiation
shielded psychrometers. The psychrometers were constructed
out of dual bakelite tubes for radiation shielding (32), a
squirrel cage fan for aspiration (300 cm sec'l), plexiglas
water reservoir and 22-27 gage copper—constantan thermocouple
wires as dry and wet bulb sensing elements (56). Figures 6—a
and 6—b show a schematic and a close-up View of one of these
units. The thermocouples were calibrated in the laboratory by
testing them in the ice and hot water baths at 0°c and 100°C,
respectively. The milivolt analog signals from the psychrometers

were transmitted via thermocouple wires to a 24-point reference

 

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psychrometer unit.

4O

junction board and channel expander to the data acquisition

system.

Collecting and Analysis of Data

 

The data acquisition system for this study was an
Esterline-Angus Recorder Model D-2020 combined with a Channel
Expander and a FACIT paper tape recorder Model 4070. The
combination of the expander and recorder provided up to 100
channels for recording. Only 54 of these channels were
utilized in this study. All signals processed by the recorder
were transmitted to the paper-tape unit and were recorded on
the standardized, 8-channel, paper tape according to the
American Standard Code for Information Interchange (ASCII),
1968 version, Figure 7.

The data on paper tapes were read using the University
of Michigan computer facilities (MTS). The MERIT computer
network was used to transfer the data from the University of
Michigan computer to the Michigan State University computer
system (CDC). A FORTRAN IV computer program was written to
convert the milivolt analog signals to digital engineering
units, Appendix A. Also, a FORTRAN Psydhrometric Model written
by Mr. Lloyd Lerew of the Department of Agricultural Engineering
(46) was used to compute the atmospheric humidity based on the
wet and dry-bulb temperatures.

A binomial scheme recommended by Bevington (2) involving
three sequential measurements was used to smooth the data.

Then five smoothed data points, each covering a period of

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42

two minutes, were combined and averaged to obtain a single

reading for a period of ten minutes.

RESULTS AND DISCUSS ION
I. Evapotranspiration from Soil

Soil moisture status was monitored daily at four different
locations in the vicinity of the weather station both gravi-
metrically and by tensiometers during the course of the
study, see Figure l. The gravimetric moisture determinations
for the period of this study are presented in Table 1. The
results show changes in soil moisture content with time. The
magnitude of changes are greater in non-irrigated areas than
in the irrigated areas. This general pattern holds for the
entire period of study. Hence, it was not possible to obtain
a meaningful water loss relationship over short time periods
in a given treatment. This difficulty was due to frequent
changes in soil moisture content due to intermittent rainfall
which was received during the course of this study.

The rainfall distribution and changes in soil moisture
potential, measured by tensiometers, for irrigated corn and
soybean treatments are presented in Figure 8. According to
these data, the lowest soil moisture potentials for corn and
soybeans were -44 and -39 centibars, respectively. These
values were obtained in September 8, 1980 late in the growing

season. Another record low potential was -38 centibars

43

44

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45

 

 

 

 

 

 

 

 

 

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mono mo mean can Haemcwmu .coeummflnhfi he coocosamcfl “coucoo ousumeoe HHOw .H canoe

46

recorded for soybeans earlier in the growing season, July 25,
1980. In spite of these record lows, tensiometer data do not
show potentials lower than -50 centibars at any time during
the growing season. This limit is considered to be safe for
the crOps growing in medium textured soils used in this study
(21). Hence, during the course of this study the soil
moisture level did not impose any restriction on the rate of
evapotranspiration from the irrigated treatments.

This supposition was supported by measuring the water
holding capacity of the Metea loamy sand at different tension
levels in the laboratory, Table 2. From the data in Table l
and Figure 8, one can conclude that the soil moisture contents
in the irrigated corn and soybean treatments were greater than
the equivalent moisture content held in the soil at -33 centi—
bars. Therefore, evapotranspiration from these treatments
was at its potential rate during the entire season (16,97).

The rate of evapotranspiration under this condition is
determined primarily by the available energy and indicated by
weather parameters (73). However, this was not the case in
non-irrigated treatments. Generally, in these treatments soil
moisture contents varied between the equivalent moisture
potentials held at —33 to -750 centibars, respectively, see
Figure 2. On one occasion (July 24) the soil moisture content
in a soybean area fell below the equivalent moisture content
held at ~1500 centibars, normally considered as the end-point
for moisture availability to plants. Therefore, under

the non-irrigated treatments, evapotranspiration was

47

 

 

 

 

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uconommwc um comm memoa nouns mo mueommmo mcfioaoc onsumwoa cam mafimcoc xasm .m mange

48

controlled by the soil, and weather parameters were only

of secondary importance (55,69).

II. Evapotranspiration from Class A Pan

A specially modified U.S. Weather Bureau, Class A,
Evaporation Pan was used to monitor quantities of water loss
from the pan over short time periods. Two-minute intervals
were selected for measuring the amount of water lost from
the pan. However, during smoothing and processing, the data
were combined and averaged over periods of ten minutes. The
final results are presented, as mm of water loss from the
pan in ten-minute intervals, in column 21 of Tables B—l thru
B-7 in Appendix B. These data can also be presented as
linear regression equations for each date of measurement,
Table 3. The good fit of these regression equations is
indicated by the coefficients of determination, r2. The
changes in slopes and intercepts of these equations represent
the variation in cumulative pan evaporation under different
weather conditions on different dates. Generally, if cumula—
tive evaporation started slowly early in the morning and
increased gradually during the day, the regression equations
had a small slope coefficient and a negative intercept (see
regression equations for July 25 and 30). On the other hand,
if cumulative evaporation increased uniformly with time, these
equations had a larger slope coefficient and a positive

intercept (see regression equation for July 24). Similar

50

Table 3. Regression equations representing cumulative Pan
evaporation over short periods at different dates.

 

 

 

 

 

 

Number of

Datg Measurements Regression Equation r2
July 24 21 Y=0.0760+0.0196X@ 0.9964
July 25 59 Y=-0.0252+0.0125X 0.9876
July 30 26 Y=-0.1567+0.0110X 0.9888
August 1 30 Y=-0.2161+0.0114X 0.9976
August 4 50 Y=0.0835+0.0097X 0.9978
August 7 25 Y=-0.27l6+0.0098X 0.9936
August 8 15 Y=-0.2667+0.0110X 0.9826
All Dates,

cumulatively 226 Y=3.3310+0.0100X 0.9962
All Dates,

separately 226 Y=0.l760+0.0101X 0.9016
@
X = time, min.

K:
II

cumulative Pan evaporation, mm

51

expressions have been established and reported for seasonal
cumulative pan evaporation based on daily or weekly observa-
tions (8,62). But, due to limited number of measurements
and the variation of weather, the quality of such regression
equations indicated by r2 is not as good as the ones obtained
on the short time basis for daily observations in this study.
This is also indicated by a decrease in the magnitude of r2
when cumulative pan evaporation from all dates in this study
were used to obtain a regression fit, Table 3. In order to
be able to use such equations more reliably in a given region,
similar experiments should be conducted for more than one
growing season to include all possible variations due to
changes in weather (10,11,25,41).

Table 4 represents the simple correlation coefficients
(r), between pan evaporation rates, pan temperature, air
temperature, relative humidity and wind speed on different
dates. All correlation coefficients, with exception of the
one between cumulative pan evaporation and relative humidity
on August 7, were highly significant at the one percent level
of probability. However, the strongest correlation was obtained
between pan evaporation rates and pan temperature. The
correlation coefficients obtained between pan evaporation and
air temperature, measured at 50 cm above the ground surface,
were generally smaller than the ones given for pan temperature.
Hence, water temperature is more representative of water loss
from the pan than air temperature at a given period, Figures

9, 10 and 11. These figures were prepared by choosing the

52

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53

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com .cowumuomm>o com o>HumasEDU coozuon mecmAOHmmooo cospmaonsoo oaeeflm .v dance

56

starting points of the curves at different hours of different
days. They all show pan temperature increases more than air
and soil temperature over the same period. This is related

to the limited and discontinuous mass of water in the pan

and the low reflection of solar radiation from the water
surface (18). This increase in water temperature contributes
to a greater loss of water from the pan and thereby causes an
overestimation in pan evaporation as compared to potential
evaporation from soil (41,100).

A comparison between profiles of air and soil temperature
indicated that generally air temperature was lower than soil
temperature during the course of this study, see Tables B-l
through B-7. This was caused by the replacement of normal,
warm summer air as indicated by U.S. Weather Service data
for the months of July and August, by a cool air front. For
example, the cooler air temperature on July 24 was caused by
lower than normal air temperature for that time of year. The
data indicated an average July temperature of 21.10°C and the
average temperature for July 24, 1980 was 18.06°C. The
presence of a turfgrass cover acted as an insulating layer,
which helped in maintaining the higher soil temperature (74,87).

The only non-significant correlation coefficient found
between pan evaporation rate and relative humidity, measured
at 50 cm above the ground surface, was for the data of
August 7, 1980. These data were obtained during the night
and early hours of the morning. Small quantities of water
loss and mild changes in atmospheric humidity during these

hours probably contributed to the weak correlation. The

57

rest of the coefficients indicate a very strong negative
correlation between pan evaporation rates and relative
humidity.

The coefficients between pan evaporation and wind-
speed are also highly significant. However, the magnitude
of these coefficients are smaller compared to the other
positive relationships in the table. This is probably due to
rapid changes in wind-speed during the day. If these changes
had not been considered and accounted for, probably signifi—
cant correlations would not have been obtained between pan
evaporation and wind—speed (29). Such cases have been reported
in the literature (39,42). In all of these reports, researchers
were not able to establish any significant relationship
between pan evaporation and wind—speed. This study indicates
that the absence of such a relationship was caused by the
use of a single daily averaged value for the wind—speed.
Obviously, this cannot be the representative of the influence
of wind-Speed on pan evaporation over long periods.

In the process of relating pan evaporation (Epan) to
reference evapotranspiration (ETO), the climate and environ-
ment of the pan should be considered. Such considerations
are usually made by introducing a pan coefficient (Kp). This
coefficient is defined as the ratio of potential evapotrans—
piration (ETp) to pan evaporation (Epan). Unfortunately, it
was not possible to establish a reliable pan coefficient for
this study because of the uncertainties in the soil moisture

data. However, values of this coefficient were obtained

58

 

 

 

 

 

 

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59

 

 

 

 

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III"

60

based on the wind—speed and relative humidity data and the
recommended relations suggested by Doorenbos and Pruitt (81).
These relations with minor modification in the unit of wind
speed are given in Table 5. The measured pan losses and
selected pan coefficients were multiplied to give computed
reference evapotranspiration for different dates as shown in
Table 6.

To obtain actual crop evapotranspiration, reference
evapotranspiration values must be multiplied by a crop
coefficient, KC. This coefficient is dependent on the type
of the crop and the stages of growth (19). Stages of growth
is a primary variable that must be considered in computation
of actual evapotranspiration. It is obvious that plants in
rapid growth stages use water at a greater rate than early
seedling stage. The relationship between crop coefficient
and percent of growing season for three main crops under
consideration in this study, namely corn, soybeans and turf—
grass, are given in Figures 12, 13 and 14, respectively.
These crop coefficients are presently recommended for the
State of Michigan (96). The appropriate KC values selected
from Figures 11, 12 and 13 for the periods of interest give
actual evapotranspiration when multiplied by the reference
evapotranspiration. These are shown in Table 7. Generally,
the variations in actual evapotranspiration throughout the
growing season is greater for annual crops such as corn and

soybeans than for perennial crops such as turfgrass (89,91).

61

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62

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63

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64

 

 

 

 

 

 

 

 

 

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III. Evaporation Estimated by Aerodynamic Models

The data reported herein were collected during the months
of July and August, 1980. Data collection was conducted for
seven days and was limited to days and times when the sky was
clear and cloudless and wind movement was mostly out of the
south to southwest. Because of the large volume of the data
collected, only three days of data were selected for presen-
tation in this section. Originally, measurements were taken
and recorded every two minutes, but during smoothing and
processing they were combined and averaged to represent ten
minute periods (see Tables B-l to B-7 in Appendix B).

The air temperature profiles, representative of three-
hour intervals on July 25, August 4 and 7, are presented in
Figures 15, 16 and 17, respectively. These figures show the
variation of each profile with elevation from the ground
surface and also the change in slope of the profiles with
time for a given date. Generally, all three figures indicate
at one time or another the presence of an unstable atmospheric
condition (aT/az negative) particularly late at night and
very early in the morning. This changes gradually to a more
stable condition (aT/az positive) with an increase in air
temperature. The absence of stable temperature profiles
(i.e. inversion), in Figure 17 for 2400 and 200 hr, was due

to high soil temperatures. This resulted in a reversal of

65

Elevation (Cm)

800

700

600

500

400

300

200

IOO

50

66

 

 

 

 

 

 

 

  
  
        
 

3 1‘7\
_ AT
0 3"-_
("152
l
e § e
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_ 0) \ \
‘0
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‘t

 

(DO @@

l l l l l

 

[9 20 2| 22 23

Temperature (°C)

Figure 15. Air temperature profiles at different hours above a short
turfgrass cover, July 25, 1980. Richardson numbers and 573
are the average values for the entire profile.

 

Elevation (Cm)

67

 

 

 

 

 

 

 

 

 

 

 

800 ~ , ~
[ l l] —
_ AT
0::Q :22
.e ;§ .e J: 23 '13?
700- ‘> 9* e ‘e
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400~ .
300+
200- ° °
l00-
50-— o
(D O O @O
L l L l l
:9 20 2| 22 23

Temperature (°C)

Figure 16. Air temperature profiles at different hours above a short__
turfgrass cover, August 4, 1980. Richardson numbers and a's
are the average values for the entire profile.

Elevation (Cm)

68

 

800 %‘ 7 1.7 1‘
L 1 ZS— [
212—":-
QnEEL
2!
700 -
1 . 8
K
600 - g g g g
N ‘1» S \
N N v
\ \ V‘
“a 8. ‘2. S
500 T T T g [3:
'8 I2 " h
k“ . R”
5 5 2'
400 - It“ [3% ° [31°
300 -
200 t
100 -
50+-
(0 <3 C)

 

        

 

    

 

 

 

 

 

:9 20 2| 22 23

Temperature (°C)

Figure 17. Air temperature profiles at different hours above a short_
turfgrass cover, August 7, 1980. Richardson numbers and a's
are the average values for the entire profile.

69

the heat gradient causing heat to flow from the soil to the
air layer above it, see Figure 11. This phenomenon was
further intensified by exceptionally high wind speeds recorded
during these specific hours, see Figure 20.

The changes in temperature gradient provide a thermal
stratification in the atmosphere. The buoyancy caused by
this gradient induces thermal turbulence and plays an impor-
tant role in the mixing and transport of water vapor (58,59,
74). To include this phenomena in our theoretical develop-
ment, we introduced the variable 5 in the definition of
stability parameter, S (see Equations [24] and [28]). The
sign and magnitude of 3 determine the role of the temperature
’gradient on the atmospheric stability and the extent of its
departure from neutrality. The computed values of 5 and
Richardson number for temperature profiles are presented in
Figures 15, 16 and 17. A comparison between these two para-
meters helps to understand the role of each in predicting
the condition of the atmosphere. The parameter 5 illustrates
the influence of changes in air temperature on atmospheric
stability. Richardson number is indicative of the combined
influence of air temperature and wind speed on the stability
of atmosphere.

The profiles of wind speed for July 25, August 4 and 7
are presented in Figures l8, l9 and 20, respectively. These
figures show the formation of mechanically induced turbulent
boundary layers (profiles) above the ground surface and also

their changes with time for a given date. All three figures

Elevation (Cm)

70

 

800
700 -
g
600 - a
C)
o;
8
500 - Q.
I
Le
b:
02
400 - no
1%
300-
200 ~ 0
100 -
50 -
(D O O O

 

 

 

 

 

 

 

 

Figure 18.

[00 200 300 400 500

Wind Speed (Cm sec‘l)

Wind speed profiles at different hours above a short ._
turfgrass cover, July 25, 1980. Richardson numbers and b's
are the average values for the entire profile.

Elevation (Cm)

71

 

 

 

 

 

      
       

     
       

 

 

 

 

 

   

 

 

 

800 r ‘T
f T 3 AU
Win};
2|
700 —
600 -
e e e e
500 - 0 Q Q 0
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5:? '8 ”I"?
IQ IQ IQ
200 -
IOO -
50 -
(5)0) @@ O
1 1 L 1 l
ICC 200 300 400 500

Wind Speed (Cm sec'l)

Figure 19. Wind speed profiles at different hours above a short __
turfgrass cover, August 4, 1980. Richardson numbers and b's
are the average values for the entire profile.

Elevation (Cm)

72

 

 

 

 

 

 

 

 

 

800 ST T e
_ Au
b:
OnZE
2:
700-
600- 3 g i
8 8 8
N N \
~e ' 3} ‘~
500- s. n '2
l l .3
lb: Iii [‘65
400- '34 8
a; «‘1
Is Ii's
300-
200~
lOOt
50
O 0
[00 200 300 400 500

Wind Speed (Cm sec—1)

Figure 20. Wind speed profiles at different hours above a short
turfgrass cover, August 7, 1980. Richardson numbers and

‘B'S are the average values for the entire profile.

73

indicate that the thickness of the boundary layers gradually
increases, starting early in the morning until mid-day and
then decreasing in the latter hours of the day. To include
these changes in our theoretical developments, we introduced
a variable, 3, into the definition of stability parameter S
(see Equations [25] and [28]). The parameter S does not
have any influence on the sign of S. This is due to positive
wind speed gradient above the ground surface at all times
and also the squaring of b in Equation [28]. However, 5
strongly affects the magnitude of S. The computed E values
and Richardson numbers are shown in Figures 18, 19 and 20.
As indicated by Equation [31], the parameter B only illustrates
the influence of mechanical forces of wind on the formation of
a turbulent boundary layer and its stability under certain
atmospheric condition. But, Richardson number represents the
combined influence of mechanical forces of wind speed plus
the buoyancy effects due to thermal gradient on atmospheric
conditions. However, the changes in both of these parameters
also represents the variation of the turbulent boundary layer
(wind speed profiles). Under extremes of atmospheric condi-
tions (i.e. very stable and/or very unstable), the logarithmic
law applied to wind speed profiles needs to be modified to
include the effects of air temperature (47,99).

A graphical procedure was used to obtain aerodynamic
parameters such as displacement height(d), roughness coeffi-
cient(Zo), frictional velocity(U*) and shear stress(r) from

the wind speed profiles (61,74). The results are given in

Elevation (Cm)

800

700

600

500

400

300

200

[00

50

74

 

 

 

 

 

 

3 e «3 e
<5 0 0
8 0 0 g
o, 3 1° \
.. 1) ‘i [L [L
Q N
“i s. 8 R.
8. s e‘ e‘
.' +» | I
.\ .ll _lg fl
- In; In} Iq‘z in}
b o
— o

 

 

 

(D C?) @O

 

l I l

 

 

l I
6.0 7.0 8.0 9.0 l 0.0
Absolute Humidity (g cm‘3 x 106)
Figure 21. Absolute humidity profiles at different hours above a short

turfgrass cover, July 25, 1980. Richardson numbers are the
average values for the entire profile.

Elevation (Cm)

75

 

 

 

 

 

 

 

 

800 , F 4} -r 1
700—
600-
s s i i 5:
C3 C)
a s a e. a.
Cu(’ - \\ \~
40()_. :; > a; St” :::)§§>
6 Q Q Q‘ Q
* ‘1. t d d
l'Q "‘ Io: lb: I"
300-
200- <
IOO - o
50>
G) (5 ® (3 @
6.0 70 80 90 l0.0

Absolute Humidity (g cm'3 i 106)

Figure 22. Absolute humidity profiles at different hours above a short
turfgrass cover, August 4, 1980. Richardson numbers are the
average values for the entire profile.

 

Elevation (Cm)

800

700

600

500

400

300

200

l00

50

76

 

 

 

 

 

*5E3/ /800br

 

 

 

E

 

® ® (D

L

 

6

Figure 23.

l l 1
.0 Z0 00 90 |00

Absolute Humidity (g cm—3 x 106)

Absolute humidity profiles at different hours above a short
turfgrass cover, August 7, 1980. Richardson numbers are
the average values for the entire profile.

 

77

Table 8. According to these data, the magnitude of aero-
dynamic roughness coefficients and displacement height
values were not large enough to significantly influence Km,
the coefficient of turbulent exchange, see Equations [6] and
[9]. From Equation [17] the corresponding influence of Km
on E, the rate of water vapor transport, is readily apparent.
The data obtained for these parameters fall within the
range of values previously reported for short, green grass
crops (76,80,81).

Profiles of absolute humidity for July 25, August 4 and
7 are presented in Figures 21, 22 and 23, respectively. The
profiles in all three figures show a gradual decrease in
humidity with elevation from the ground surface in a given
day. However, this relation is reversed for late evening
and early morning hours. For profiles with Richardson
numbers of less than -0.1 (very unstable atmosphere), the
ratio of heat to water vapor diffusivity coefficients (Kh/Kw)
will depart smoothly from unity and become greater than one
(12,49). This ratio also departs from unity for the
Richardson numbers greater than +0.1 (very stable atmosphere)
and becomes less than one (98). The Richardson numbers at
2100 and 2400 hours on August 7 reach their absolute maximum
and minimum values, respectively. In these cases the turbu-
lence has vanished and the main mechanism for water vapor
transport is probably molecular diffusion (59). This is
supported by the fact that no air motion was detected at

these hours (see Figure 20).

78

 

 

 

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wwwupw MawSm paw moflooaw> HMcOHpoHHw .proEmumm mwocnmsou .ynmflmn ucwfimomHmmHQ .m magma

79

Previous discussion of temperature, wind speed and
humidity profiles support the idea that equations of heat,
momentum and water vapor transport should be modified such
that they are representative of these phenomena under a
wide range of atmospheric conditions (12,23,40,50). This
suggestion prompted the derivation of a new equation describing
the transport of water vapor in this study. The equation
is an extension of an evaporation equation of Thornthwaite
and Holzman (88). Their equation was modified for all
conditions of atmospheric stability by introducing the
stability parameter S, Equation [28]. This introduces a
correction factor to the original equation of Thornthwaite-
Holzman for the cases of unstable and stable atmospheric
conditions as given in Equations [33] and [34]. Temperature,
wind speed and humidity data of Appendix B were used to
investigate the feasibility of S as a function of Richardson
number. The results are shown in Figure 24. The linear,
functional relationship between these two parameters show
that S like the Richardson number can account for all the
possible changes in temperature and wind speed profiles under
a wide range of atmospheric conditions. It was not possible
to use and manipulate the Richardson number in its defined
form, Equation [10], as a stability criterion in the proposed
analytical development. This difficulty was resolved by
the use of the stability parameter S.

Table 9 shows a comparison between the evaporation rates

measured by the automated Class A pan, the computed rates

Stability Parameter (S)

80

 

  
 

 

 

 

|.O _ l
3 l
I I
: : VERY
— STABLE
I
r |
OJ : L ———————
00' _ STABLE
0001: NEUTRAL 1
-0001 [
*- O
"00' : UNSTABLE
E 0
—OJ 3 r _______
l
- I
— I VERY
— { UNSTABLE
3 l
_lo I llllllll 1 llllllll l llllllll 1 1111111: 1 Illllll
' 0000: 000I 00I 010 ID

Richardson Number IRiI

Figure 24. Functional relationship of stability parameter S, and
Richardson number Ri, under different atmospheric conditions.

81

 

 

 

 

 

 

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82

obtained from the original equation of Thornthwaite-Holzman,
Equation [35], hereon referred to as TH, and the modified
version, Equation [31], hereon referred to as MTH. The
computed evaporation rates from both the TH and MTH equations
are smaller than the measured pan evaporation rates.

However, in general the MTH equation estimates pan losses
better than the TH equation, see Table 9. The MTH equation
approximates pan evaporation best under unstable atmospheric
conditions when S and Richardson number are negative. Under
these conditions the accuracy of approximation increases as
the magnitude of S or Ri increases. The computed evaporation
rate for July 25 is representative of this case. Detailed
analysis of the profile data indicate that unstable atmos-
pheric conditions prevailed most of the time during this

date (see Ri values in Table B—2).

Under stable conditions, the MTH equation approximates
pan evaporation best when S and Richardson number are positive
in sign and small in magnitude; however, the degree of
improvement in approximating pan evaporation under these
conditions is not as good as under unstable atmospheric condi-
tions. This may be observed by referring to computed evapora—
tion rates for July 24 and 30, in Table 9. Detailed analysis
of the profile data indicate that stable atmospheric conditions
prevailed most of the time on these dates (see Ri values in
Tables B-1 and B—3). Sample calculations for both stable and
unstable atmospheric conditions are presented in Appendix D.

When a combination of both stable and unstable atmospheric

conditions prevailed, the degree of improvement in

83

approximating pan evaporation based on MTH equation was about
7 to 12 percent better than the original TH equation. The
data for August 1 and 4 indicate that both stable and unstable
conditions prevailed on these dates (see Ri values in
Tables B—4 and B-5). This improvement in calculating the
pan evaporation from meteorological profile data is a
definite advantage for the equation proposed in this study.
To illustrate the accuracy of the proposed model in
estimating evapotranspiration rates, there was a need for
measuring soil water losses over short periods. Generally,
weighing lysimeters are used for this purpose. Since such
a device was not available in the vicinity of the experimen-
tal site, the data of Morgan et. a1. (52) were selected and
used for analysis. Six days of data were selected randomly.
These data included evapotranspiration rates measured by a
6.1-meter lysimeter, air temperature, wind speed and absolute
humidity profiles recorded over 30 minute periods in 1966
at the University of California, Davis. Table 10 presents
the evapotranspiration rates recorded by the lysimeter and
rates computed according to the TH and MTH equations. The
meteorological profile data selected for this analyses were
obtained between 700 and 1900 hr at the 25 and 50 cm levels
above a short grass cover.
Generally, both TH and MTH underestimated the evapo-
transpiration losses from the lysimeter when unstable
atmospheric conditions prevailed. The error of estimate by

MTH was about 4 to 17 percent smaller than TH for days with

84

 

 

 

 

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can A.Hm .uw cmmuoz Hopwmv Hopwfifimma cues pmHSmMmE moumu coflumuflmmnmuuomm>m .oa mange

85

unstable atmospheric conditions. The one exception,
September 29 was for stable atmospheric conditions. For
the profile data of September 29 both TH and MTH equations
overestimated evapotranspiration losses recorded by the
lysimeter.

The results of estimating evapotranspiration from a
lysimeter and evaporation from a Class A pan using the MTH
equation illustrate the degree of effectiveness of the S
parameter and its related functions f(S) in adjusting for
the influence of the changing atmospheric conditions in trans—
port of water vapor. Based on these results it was found
that the proposed MTH equation performed better in estimating
water losses from a lysimeter than a Class A pan. This was
probably due to less variation in meteorological conditions
at Davis as compared to the conditions found in Michigan.
However, in both cases the MTH equation performed the best

under unstable atmospheric conditions.

CONCLUSIONS

The following conclusions have been drawn from this

investigation:

(1)

(2)

(3)

(4)

(5)

Under optimum soil moisture conditions evapo—
transpiration reaches its potential rate. As
such, it is controlled primarily by weather
parameters.

Cumulative pan evaporation measured over short
periods increased linearly with time during each
measurement period but changed significantly from
one day to the next during the period of study.
Cumulative pan evaporation measured over short
periods correlates best with pan temperature
followed by air temperature and wind speed.

Simple correlation coefficient between cumulative
pan evaporation and atmospheric humidity indicated
a very significant negative correlation between
these two parameters.

Detailed analysis of air temperature, wind speed
and absolute humidity profiles obtained over short
periods, indicated a need for the modification of
heat, momentum and water vapor transfer equations
to better represent these processes under a wide

range of atmospheric conditions.

86

(6)

(7)

(8)

87

A proposed stability parameter S proved to be
more effective than Richardson number in taking
into account all possible changes in atmospheric
conditions, but unlike Richardson number S is
very easy to use in the analytical development of
the proposed evaporation model.

The modified version of the Thornthwaite-Holzman
equation proposed in this study proved to be more
effective than the original form in estimating
evapotranspiration rates from a lysimeter and
evaporation rates from a Class A pan over short
periods.

The proposed model developed in this study will
work for all conditions of atmospheric stability,
but it approximates evapotranspiration from
lysimeter and pan evaporation best under unstable

atmospheric conditions.

APPENDICES

APPENDIX A

FORTRAN IV PROGRAM FOR DATA PROCESSING AND DATA CONVERSION)

88

The following FORTRAN IV program was used to read the
analog, digitized data from paper tapes and convert it to
digital forms with appropriate engineering units by means
of specified calibration curves and/or functional relation-
ships. The program consisted of the main program GAWTHR;
subroutines PAUXCYBER, GETDAT and SMOOTH; and function FNR.

The main program in addition to converting the analog
data into useful digital numbers also computed certain
parameters such as water vapor flux, Richardson numbers and
stability functions based on the atmospheric profile data.

Subroutine PAUXCYBER was written by Mr. Lloyd Lerew
of the Department of Agricultural Engineering at Michigan
State University (46). This subroutine was called in the
main program to compute the moisture concentration in the
air from dry and wet-bulb temperatures.

Subroutine GETDAT read the converted digitized data
into common blocks. This subroutine also checked for bad
or missing data points during processing.

Subroutine SMOOTH used a binomial distribution procedure
(2), to smooth the data over 2 data points. The magnitude
of n could vary between 3 to 9.

Function FNR converted the wet and dry bulb air tempera-
tures from degrees Centigrade to degrees Fahrenheit for use

in subroutine PAUXCYBER.

nnnnn

nnnnnnn

O

f}

C

89

PROGRAM GAUTHR(OUTPUT.TAPE2=I182vRLPORT.TAPEb=REPORT|TAPEIu
OREPDT20TAPE7:RCPRT2)

ANDERS G JOHANSON AUGUST 1980

FOR C1050 GHASEM ASRAR

TO REA” ANALOG DIGITIZCO TAPE 0UTPUT(INPUT TO THIS PROGRAM)

AUG PROUUCF CUSTOM REPORT AND POSSIBLY CONVERTED DATA FILE OUTPUT

counon IPKESS/ PATH
COMMON /°RESET/ xMD.STAR
COMMJN /TntoATA/ JDATttz).JTTMET2T.CHNL(100T.IEOF
COMMON /R£SULTS/NUIND.TEMP(ID).HUH(5).UINDV(5)oEVAPF.SOILT(5)9PANT
DIMFNSInN IHTNDV(5)91TEMP(10)
o .HGTTST.Rw(a).EAEROtA).PSOILTt5)
(DIMENSION PTEMP(10)9PUINDV(5)
DIMENSION IEPRX(6)
RtAL KAT
DATA IERRX/Uv'O.‘000c‘0o~0/
DATA ITEMP /5.A.7.a.q.12.13.14.25.2e/. NTEMP/lO/
DATA lewov /Too.1.2.3.20/. waxwov /5/
DATA IEOF /0/.UINDV/5t099.9/oSOILT/St99.99/.PSOILT/5t99.99l
DATA MLIHCS /90/.HUM/5fi999.0/.TEMP/l0‘999oql
DATA HGT /50..1oo..2no..Acc..qoo./
DATA XMn/9.9999/. STAR/8.8888/oIS“OOTH/IH /
DATA PATAnv/Sau99.9/.PTEMP/10.999.9/.PANT/99.99/
DATA PPANT/99.77/.EVAPF/999.9/.PEVAPF/999.9l
JDATE(1) : MOMTH. (2) : DAY
JTIHE (1) = Houa. (2) : MINUTE
CHNL (I) CONTAINS VALUE Fua CHANNEL 1. 1:1.q9 1:0 As 100
IEOF : 1 HHLW END-FILE READ TTL THE» aer

INITIALIZE

CALL SYSTEMC(739IERRX)

NVALS 2 NUMBER OF POIUNTS TO USE IN SHOOTHING
NVALSZ 9
"PM"4 = 14.696

MUST [GNORE Oiitttltttttt
HHAT : 1.0

fi-O- FOR SPECIAL IOHIN AVG DATA FILE

lFoF = 1
N'I'ALS =4
ISMODTH = 2HNO
GO TO 890

100 CALI GETDAT

C

IF (IEOF.EO.1) 00 T0 900
PROCESS WIND VELOCITY
D? 250 ' = IuNUINDV
J = IUINUV (I)
IF (CHNL(J).LT.O) GO TO 230
IF (CHNL(J).GT.50) GO TO 220
VALUE 3 (CHNL(J) - (0.01 a CHNL(J) - 2.27)) t 19.51 ~ 42.26

60 T0 240
) 50
220 VALUE = PHINUV (I)
GO TO 240

C < 0

230 VALUE 2 0

2A0 UINDV (I) = VALUE
250 CONTINUE

C

EVAPORATION

90

C CHANNEL 11
E

VAPO = ABS((CHNL(11) - (0.01 ' CHNL(11) - 2.27))) i 0.35 - 0.08
PF 2 PEVAPF - EVAPO

C UIND DIRECTION CHANNELL 10

CHNLTTo) = CHVLtio) . 100.
IVALUE = 2HN .

IF (CHNL(10).LT.22.5 .ANo. CHNL(10).GT.-22.5) GO To 300

TVALUE = 2HNU |

IF (CHNL(10).LT.67.5 .AND. CHNL(10).GE.622.5) GO To 300

IVALUE = 2HV

IF (CHMLAID).LT.102.5 .AND. CHNL(10).GE.+67.5) so To 300

TVALUE = 2Hsu

IF (CHVL(10).LT.157.5 .AND. CHNLTTO).5E.+102.5) so To 300

IVALUE : ens

IF (CHVL(10).GE.157.5 .OR. CHNL(IO).LT.-157.S) Go To 300

[VALUE = 2HNE

IF (CHML(10).LE.-22.5 .AND. CHNL(10).GT.-67.5) GO To 300

IVALUE : ZHE

IF (CHHL(IO).LE.-67.S .AND. CHNL(10).GT.-102.S) so To 500

IVALUE : 2HSE .
uwxu. : IVALUE ‘

300
C TEMPERATURE

330
340

00 350 I = lvNTEMP

J = ITFWP(I)

IF (CHUL(J).LT.0) GO TO 350

IF (CHML(J).EO.STAR) GO TO 350

IF (A83(CHNL(J)).GE.2.99) GO TO 330

VALUE = -0.0951 0 26.0544 * CHNL(J) - 0.6801 I (CHNL(J)OCHNL(J))
GO TO 340

VALuE = ”TEMP(I)

TF"P(I) = VALUE

CONTINUE

550
C HUMIDITY

450

N = NTEHP / 2

DD #50 I = ION

J I 2 ' I - 1

: FNR(TEMP(J))

HR = FNR(TEHP(J§I))

PV 2 PVOBUB(DHVUB)

HUH(I) = (HAPV(PV) I 0.001157) ‘ 1000000.
IF(LEGVAR(HUH(I))oNE.0)HUH(I) = 0.0
CONTINUE

C SOIL TEMP - CHANNELS 45 - 49

480
A90
500

00 500 I=Iu5

J=I . 44

IF(CHNL(J).LT.0)GO TO 480

IF(CHNL(J).E0.STAR)GO TO 480

IF(AHS(CHLL(J))oGE.2.09)GO T0 480

VALUE = -0.0951 9 26.0544 i CHNL(J) - 0.6801 ' (CHNL(J)'CHNL(J))
GO TO 430

VALUE 2 H301LT(I)

SOILT(I) = VALUE

CONTINUE

C PAN TEA? CHANNEL 52

x1“

IF(CHNL(52).LI.0)GO T0 510
IF(CHML'63).EQ.§TAR)CO TO 510
IF(\YS(CATL152)).GC.?.99)GO TO 510

VfiLHE t -U.““H1 * 26.U*44 t CHNL(52) - 0.00CI t
o(CITL( ')---w.L(fi_))

5) YT W'd

V In" -' ..T

91

520 PANT = VALUE

C ABOVE READS RAH DATA

P0

5 CONTINUE

ENTER HERE UHEN READING8 PROCESSING SMOOTHED DATA
AS FOLLOWING PERFORMS ALL CALCULATIONS AND PRINTS RESULTS

FIOOF)OU10

RICHARDSON NUHBER
KI = 1

DO 550 I = 1.4
C 546 DELOH FOR ABS TENP
X1 : 1980. I ((TEHP(KI)*TEHP(KI02)) 6 596.)
DELI = TEMP(KI‘2) - TEMP(KI)
DELU 2 (UINDV(IOI) - HINDV(I))
DELI = HGTIIOI) - HGT(I)
RN(I) = (XI'DELT/DELZ) / ((DELU-DELU)/(DELZ*DELZ))
KI = KI * 2
550 CONTINUE

 

C EAERO
KI = 1
DO 590 121.4

KI — K1 0 2

DELI = TEHP(KI+2) - TEMP(KI)

DELU 7 (HINDV(IOI) - UINDV(I))

AYE = DELI / ALOG(HGT(IOI)/HGT(I))
BEE = DELU / ALOG(HGT(I‘I)/HGT(I))
TAVG = (TEMP(KI) 9 TEHP(K1*2)) / 2.0
IF (ASS(JEE).LT.0.00001) GO TO 560
ESS = (18.0-881.0-AVE) / (BEE-DEE-TAVG)
IF (ESS.EO.C) GO TO 580

IF (ESS.GT.0) GO TO 535

SUHI ' SORT(1.0-(ESS I HGT(IOI)))-1.0

SU12 = SORI(I.0-(ESS * HGT(I¢1)))+1.0
SUNS = SORT(1.0-(ESS 0 HGT(I)))-1.0
SUM4 = SORT(1.0-(ESS I HGT(1)))01.0
GO TO 550

555 CONTINUE
SUMI S0RT(1.00(ESS HGT(I¢1)))-1.0

: .
SUEZ = SGHT(1.0*(ESS * HGT(I'1)))91.0
SUNS = SORT(I.0*(ESS ' HGT(I)))-l.0
SUN“ 2 SORT(1.00(ESS t HGT(I)))01.0
559 CONTINUE
COEFF = ALOG(ABS((SUH1/SUM2) ' (SUMB/SUM4)))
IF (ESS.GT.0) COEFF = _
O 2.0 ' ALOG(ABS((SUH101.0)/(SUM5*1.0))) 9 COEFF
COEFF = 1.0 / COEFF
GO TO 570
560 COEFE = 1.0
570 DELO = HUH(I) - HUM(191)
C ADJUST FOR HUM-1000000

C OELO = DELQ / 1000000.
RHD = 0.0012
KAY = 0.41

EAERO(IZ=((RHO * (KAY-'2.0) * OELO I DELU)/ALOG(HGT(101)/HGT(I)))
* ' COEFF
GO TO 590
580 EAE°0(I) = 0.99999
C SET TO PHONY VALUE IF RN‘I) ILLEGAL
590 CONTINUE

92

IF(ISMO0TH .NE. 1H )60 TO 605

C
C SET TO PREVIOUS VALUES
C
PEVAPF = EVAPO
DO 600 I = loNTEHP
600 PTEMP(I) = TEHPCI)
DO 601 I = IQNUINDV

601 PUINDV(I) = UINDV(I)
PPANT=PANT
DO 602 1:195
PSOILT(I) = SOILT(I)

602 CONTINUE

C URITE OUT CONVERTED DATA

c _
UPITE(2.2) JDATEoJTIHEoNUINDoTEHPoHUHoUINOVoEVAPFQSOILTQPANT
2 FORMAT(012.A2.10F5.105F10.305F6.19F6.2.5F6.2.F6.3)
c .
C OUTPUT

605 1F(JDATE(2).NE.LDATE)NLINES=90
LDATE=JDATE(2)

C
IF (NLINES.LT.50) GO TO 650
NLINES = 0
URITE(6.20)ISHO0TH
20 F0RMAT(1H19A10)
URITE(6.8)
8 F0RWATt1X.”TI“E"912X9'TEHPERATURE”.32X9'ABSOLUTE HUMIDITY'033X9

*"UIND SPEED")
URIIE((1'9)
9 FORMAT(18X."DEGREES C'930x.'GRAHS PER CUBIC CMt10-i6'929X.
+"C1 PER SEC")
URITE(8.10)JDATE '
10 FORMAT(1X.12.1H/.I2.4X.'50 100 200 400 800'.10X.
0'50 100 200 400 800'96Xo
‘”50 100 200 400 800')
URITE(I..11)
11 FORMAT(1H .132("-“))
URITE(6.10)
19 F!)R‘1AT(1H I
URITE(7.20)ISHOOTH
URITE(7.13) _ .
13 FORMAT¢6X9"RICHAROSON NUMBER'.9X.'EVAPORATION".12X.”EAERO filOti6'
0918!. “SOIL TEMPERATURE".18X9'PAN'95X.'HIND')
URITE(7.14)
14 FORMAT(9X."FOR INTERVALS'.33X.'FOR INTERVALS”.21X."DEGREES C".
9 21X."TFMP".4X.“DIR")
URITE(7.15)

15 FORWAT(‘K."50-100 100-200 200-400 400-800"013X9
*"50‘100 100-200 200-400 400-800“05X0
O."5 10 20 40 80“.CX"DEG C")
URIIE(7916)
l6 FORMAT(1H 9132(”-"))
URITE(7.18)
18 FORMATIIH )

C OOOBELOU T0 ELIMINATE BAD DATA AT START OF A PARTICULAR TAPE
C "* DATE % TIME MUST CHANGE FOR EACH TAPE PROCESSED
650 IF (JOATE(1).EO.7 .AND. JDATE(2).EO.2A .AND. JTIHE(1).EG.16
0 .AND. JTIME(2).LT.11) GO TO 655
NLINES 2 NLINES 0 1
URITF(h.H) JTIME.(TEMP(I).I=1.9.2).HHV.UINDV

93

6 FDRHAI(1XQIZQIH:012.292XQSIF50292X)91X95(F10.391X)91X.
05(F5.192X))
URITEI7917)(RN(I)912104)QEVAPFOEAEROQSOILTQPANTvNUIND
17 FORMATC1X94F8o30F8o203X94F89505F3.2g2X9F6.2g
o 3X9A2)
655 CONTINUE
IF (IEOF.E0.0) GO TO 100
C IoE. IF RAH DATA GO BACK AND READ NEXT RAH OBS
C ELSE SMOOTH NEXT DATA ELEMENT FIRST
890 CALL SMOOTH(NVALS)
IF (IEOF.EQ.2) GO TO 990

GO TO 525
C THEN GO TO CALC & PRINT ROUTINES
C
C HERE WHEN RAH DATA AT EOF
C

900 URITE(6.7)
URITE(T.T)
7 FORMAT(1H1)
ENCODE (10.901.ISMO0TH) NVALS
901 FORMAT(8HSMO0THED.12)
NLTNES = 90
C RESET FOR PAGE HEADINGS TO START SHOOTHING
REUINO 2
REUIND 6
REUIND 7
GO TO 890
990 CONTINUE
IF (NVALS.GT.3) GO TO 995

RFUIND C
NVALS = 5
GO TO 900

995 CDHTI”VJE
HPITFIGQ7)
UHITE(707)
END
SUHROUTINE GETDAT

C READS DIGITIZED DATA TAPE INTO COMMON BLOCK
COUPON /°RESET/ XHD.STAR
COMMON /THEDATA/ JOATE(2)9JTIHE(2)oCHNL(100)oIEOF
DIMENSION INI4)QIN2(5)QITIHEIZIQIDATEIZI
DATA IFIRST/O/ ‘ .
DATA TCT/O/oKCT/O/ '
DO 10 1': 10100

10 CHNL(I) = XMD
JUATE (I) = -1
KCT : KCT 0 1
C IF (KCT.GT.100) GO TO 900

IF (IFIRSToEQol) GO TO 100.
IF (IFIRST.EO.2) GO TO 900
IFIRST L 1
C ONLY FIRST TIME CALLED
C ELSE SKIP READ AS DATA ALREADY IN
50 READ(101) IN
1 FORMATISRIOAB)
IF (EOF!1)) 7909100
100 ICT 2 ICT + 1
C IF (ICT.CT.1000) GO TO 900
IF (INII).EO.IRC) GO TO 200
C IGNORE DATA LINES WITH SPACE AT BEGINNING

94

C CHK TO MAKE SURE UE HAVE HR RECORD
K = IN(4).AND.77770000008
C ASSUMES 1 DIGIT MONTH
K : SHIFTIKv-IB)
IF (KoEQo2RHR) GO TO 55
PRINT SIOKCTQICTIIN

51 FORHAT(' BAD RECORO'oZISo' REC-'vSRloAa)
GO TO so . .

55 CONTINUE

c

c

C MUST BE TIME MDDHH:MMHR
C SET FOR 1 DIGIT MONTH ONLY
IDATE (I) = IN(1) - 338
IOATE (2) = (IN(2)-338)*10 9 (IN(3)-338)
DECODE(591059IN(4)) IN2
105 FORMAT(5PI)
' ITIME (I) = ((IN2(1)-53B)*10) 0 (IN2(2)-338)
ITIME (2) = ((TN2(4)-338)t10) 0 (IN2(5)-338)
C ITIME(2) NE JTIME(2) CAUSES ALL 3 OBS FOR SAME TIME PER
C TO BE ACCEPTED AS ONE 083
IFTJDATE(1).MEo-loAND.ITIME(2).NE.JTIME(2))RETURN

JTIME(1) 2 ITIMETI)
JTIMEI2) = ITIMETZ)
dOATEIl) = IDATE(1)
JDATEIZ) = IDATETQ)
GO TO 50

200 IF (JDATE(1).EQ.-1) GO TO 780

C CHANNEL DATA. CONVERT
ICHNL = (IN(2)-358)*10 9 (IN(3)-338)
IF (ICHNL.EQ.0) ICHNL = 100 V
IF (ICHNl.LT.l .OR. ICHNL.GT.100) GO TO 770
K : SHIFT¢IN(4)¢6).AND.77B '
IF (K.EO.1Rt) GO TO 290
IF (K.EO.lR-) GO TO 260

C POSITIVE VALUE
DECCOE(59245.IN(4)) VALUE

245 FORMATIF5.0)
GO TO 500

C NEGATIVE VALUE

260 DECODE(6.26191N<4)) VALUE

261 FORHAT(F6.0)
GO TO 500

290 VALUE = STAR

500 CHNL(ICHNL) = VALUE
GO TO 50

C

770 PRINT 771'KCTgICTvIN

771 FORMAT¢9160”0 ILLEGAL CHANNEL-'OSRIQAIO)
GO TO 50

780 PRINT THIQKCTQICTQIN

781 FORHATI216o"s N0 DATE YET-”c3RloAlO)
GO TO 50

790 IFIRST : 2

C EOF HAS OCCURRED. SET IFIRST INDICATOR

C THEN CHECK IF ANY DATA PRESENT
IF (IDATEII).EQ.-l) GO TO 900

C YES . SEND DATA BEFORE EOF INDICATON
RE TURN

C

900 1L0? ; 1

 

95

RETURN
END
FUNCTION FNR(T)

C CONVERT FROM CEL TO FAREN REL

EN = 108 . T 0 320

FNR 2 FN . 459.67

RETURN .

END .

SUBROUTINE SMOOTH(NVALS)

COMMON /THEDATA/JDATE(2)QJTIME(2)9CHNL(100)QIEOF

COMMON lRESULTS/NUINDoTEMPIIO)oHUMI5)oHINDV(5)QEVAPFQSOILTCSJQPANT

C REAL FLG ONLI TO FAKE COMPILER INTO NOT CONVERTING FROM REAL'INTEG

0000

101
102
104

C ADD

0
Q

'nrunIWruw

HflnnUI‘J

003

004

END

OOOOUQOOOH

REAL JDATEvJTIMEoNUIND
DIMENSION SMDAT(7132)
DATA IFIRST/O/olSET/S/

FIRST TIME ONLY TO SET.BEGINNING ARRAY CONFIGURATION
TO BEGIN, READ THE FIRST RECORD OF DATA '

IF (NVALsoNE.10) GO TO 104

READT2o100) JDATEoJTIMEoNUINDoTEMPoHUMoUINOV9EVAPFQSOILTgPANT
IF (EOF(2)) 101.102

IEOF = 2

RETURN

CONTINUE

IFTIFIRST .NE. 0160 TO 4

IFIRST = 1

1 TO ISET AS THIS VALUE‘GETS SHIFTED DOUN
ISET = ISET 9 1
READ(2¢100)(SMDAT(lod)od=1032)
FORMAT(4I29A2¢10F5.195F10.395F6o1gF6.496F6.1)

DUPLICATE THE FIRST OBSERVATION IN THE CORRECT NUMBER OF
LINES OF THE ARRAY *1 SO AS TO ALLOU THE MAIN LOOP TO
SHIFT AND READ ON THE FIRST PASS

DO 3 I=2.ISET

DO 2 J=1032

SHOATIIoJ) = SMDAT(1!J)
CONTINUE

CONTINUE

FILL THE REMAINING nous or THE ARRAY WITH THE NEXT

K = NVALS - ISET

IF (K.LE.0) GO TO 1004

ISET = ISET + 1

READ (29100) (SHORT‘ISETOJ)OJ:1932)
GO TO 1003 ‘

ISETs= (NVALSOII / 2

INITIALIZATION. BEGIN REGULAR PROCESSING

CONTINUE

MAIN LOOP BEGINS HERE
FIRST SHIFT 2v 4' OR 6 ROHS OF THE ARRAY
TO MAKE ROOM FOR A NEH OBSERVATION

NLIHES : NVALS - 1
00 h IIIHJLINES

 

OOOOOU‘U‘

GOOD non

N

“(“200

11
C

~C
C

a

OOOOOOHOOOOOOnfit-‘n

0000

7

96

DO 5 J=1o32

K=Iol

SHOATIIoJ) = SMDATIKgJ)
CONTINUE

CONTINUE

NOU READ IN THE NEXT OBSERVATION POINT
INTO THE CORRECT ROU OF THE ARRAY USING NVALS
CHECK FOR END OF FILE‘AT THIS POINT

REAOCZQIOO)(SMDATTNVALSQJ)9J=1932I
IF(EOF(2) .NE. 0160 TO 25

THIS NEXT PART SMOOTHS THE DATA

IF(NVALS .EO. 5)GO TO 10
IF(NVALS oEO. 7)GO TO 14

THIS IS FOR NVALS = 3

DO 7 J26032

SHDATIIQJ) = (0.25'SMDATCloJ))§(0.5*SMDAT(2QJ))0
* (0.25'SMDAT(30J))

CONTINUE

GO TO 17

NOU FOR NVALS = 5

CONTINUE

oo 11 J-s.32 f ,

SMDATIlod) = I0.0625asMoAI(I.JI1+Io.25csnoAII2.J)1o
+ I0.375‘SHDATIScJ))+(0.25tSMDAT(4od))+
. (U.O625*SHDAT(S¢J))

CONTINUE

GO TO 17
LAST FOR NVALS = 7

CONTINUE
DO 15 J36032
SHDATIIQJ’ 2 (”-"‘--"".-.‘)§
9 ( )0
0 . .
o
15 CONTINUE
16 CONTINUE

CONTINUE

NOU MOVE THE DATE AND TIME INTO THE

FIRST ROU OF THE ARRAY UITH THE SMOOTHED VALUES
THE FIRST ROH IS USED AS IT IS SHIFTEO OUT ON THE
NEXT PASS

DO 9 K2195
SHDAT(10K) = SMDAT(ISET9K)
CONTINUE

LAST. REPLACE THE SMOOTHED DATA IN THE
COMMON BLOCK ARRAYS AND RETURN TO THE RAIN

97

C ROUTINE
C
DO 18 I=1o2
d = I 0 2
JDATEII) = SHDAT<1¢II
JTIMEII) : SHDATIIgJ)
18 CONTINUE
NUIND = SMDATII'SI
EVAPF = SHDATIIoZE)
PANT = SMDATtchZI
DO 19 121.5

J = I 6 15
K = I o 20
L = I + 26

HUM(I) = SMDAT(19J)
HINDVTI) = SMDATTIQK)
SOILTII) = SMDAT‘IQL)

19 CONTINUE

DO 20 I=1¢10

J = I o 5

TFMPII) = SMOAT(1.J)
20 CONTINUE

RETURN
C

C LAST NVALS/P POINTS ARE LOST AND NOT SMOOTHEO
C IF THIS IS NOT DESIREOoMUST CHANGE

C

25 IEOF = 2
RETURN
END

PROGRAM CNVRTITAPEloTAPE22/18290UTPUT)

C AGJ 12/80 FOR 1050 GoA.

C TO CONVERT KEYED 10 HIN AVG DATA TO PROGRAM FORMAT
DIMENSION IN(4)QXN(27)
DATA ICT /0/

PEUINO I
PEUIND a
10 READ(IOI) INoXNoIUIND
l FORMAT!I191X9I291X0I201X0I2choS(FS.20FI-0)9F50294F6020F7o2/

.° FP¢QOJF7¢ROF50205F60POFBOQOIXIAQT
IFIEOFTIT) 99.20

20 ICT 2 ICT 0 I
DO 25 I 2 11915
25 XN(I) = XNII) I 3.0
IFIIN(I)¢NE.0) GO TO 50
INTII=IHON
INT?) = IOAY
30 URITE(292) INQIUIND'XN
2 FORMATI412.A2.10F5.1o5F10.3.5F6.1.F6.2.5F6.2.F6.3)

IOAY~= INIZ)
IMON = 1N(1)
GO TO 10
99 PRINT IDDQICT
100 FORRAT(" RECS CONVERTED = “'16)
END

APPENDIX B

SMOOTHED AND AVERAGED FIELD DATA

99

The raw data which were gathered over two-minute periods
during this field study were processed and smoothed by
computer into ten-minute mean values. The results are pre-
sented in Tables B-l to B-9 in the following pages. Each
table contains 32 columns which are printed on two separate
pages. The first column on the first page shows the sampling
time. The next five columns present the dry-bulb air tem-
peratures, expressed in degrees Centigrade and measured at
five different elevations above the ground surface. These
elevations are .5, l, 2, 4 and 8 m. Absolute humidities,
expressed in grams moisture per cubic centimeter of dry air
based on the measured dry and wet-bulb temperatures at five
elevations are presented in columns 6 to 10. Wind speeds
at five indicated elevations are given in columns 11 to 16.
Richardson numbers were computed for four different elevation
intervals based on measured dry air temperature and wind speeds.
Computed Richardson numbers are giVen in columns 17 to 20
starting on the second page of each table. The water loss
from the automated Class A pan is presented as millimeters
of water per ten minute period in column 21. Columns 22 to
25 of these tables show the computed water vapor flux based
on the modified version of Thornthwaite-Holzman equation for
four different elevation intervals. These fluxes have the

dimensions of gram per square centimeter per second. Soil

100

temperatures were measured in degrees Centigrade and are
presented in columns 26 to 30. Column 31 shows the water
temperature for the Class A pan in degrees Centigrade.
Recorded wind directions are presented in the last column

of each table.

 

Smoothed atmospheric and soil data averaged over ten-minute periods,

Table B-l.

1980.

July 24,

TI.“.E

800

400

50

800

800

400

50

101

ohoecwownn—‘umoruco—somNNcoo
0.0.0......OOOOOOCOOOOOOO
mih€mc~0¢~06~‘3N-‘t04C—flo‘OL‘NwOO
fir‘lU‘¢Z~foflflfi-OO "HIOU :3"?th JO‘
finN—Nn'fiNdNNNNNN—Num‘oan—o

om6wmc¢mn¢m~r~aw¢woozomnooc
OoooooocoopOOOOOo0000....
homo~a~mmr~mocw1NonOm~~¢o nwoo
Nmn-orumhmmsmomhu'xcrcacnum
NNN—‘NNN—GMNNNCJ—QNH—t—C—OHHN

Nonwnnnwanmnauommmmwwvhoo
.OOOOIOOOOOOOOOOO000000..
nonncbomtcr-Nsoch-tesmnoh—noo
dcoe-«o'no~~~~o~oa~r~nmr~n~~r~
NNAdNNNddNNNNHfl-‘ddfiv—Gfid

«wnnmaummowrc¢~0c>nmnwoo¢oo
00.000.000.00...000000.00
oomnd'nhmcm‘nhercrmmo-ono—ocuoo
«nw~r~nmn~cu~—-¢3:m¢enmwoam
NN—on—aNN-yaH-awnuunuannaa

@nmmuoasmnwwhnnwmwmmb«coo
....OOOOOOOOOOOOO00......
m:omaomomwwmwowaunmnfintrooo
nonoawnoocthNONA-‘Jnflmh
fidd—IHHNN-«H—tu—Iddfidfi—Idd

OOOONonnhNNNNNOODONFOVOVONN
unmxomhoo:m~mm—«00~rc~mmn¢nm¢\o
mnmhmoo-n'ncroONNHflhN-Dmnwwr‘o

00.00.00.000.000000000000
mommmmmmmmwwmhhhhhshhr-oom

hhnnhcoov~r~r~r~nonconnNOhooh
wm¢¢N¢o¢~¢ooncnmmdnenh¢nw
Onnmhnnhondnmnw€¢mh~O¢N0rzjh

.OOOOQOOOOOOOOOOOOOOOOOO.
oat»mmwamomwwchshsshhhhooo

Ohhnohhhocnnfirfi'flhnoooonlflho
er«onowns-Nmnooo'no-a-ofibrnmnnoo
«cover-~010Mbtnnmenmombhmnogm

00.000.000.000...0.9.000.
ONOG‘O‘QO‘U‘GDO‘O‘O‘U‘thhmhhfihhfiom

honfioosnooocohonnnooonhoo
wayammflwmmwm¢~nocmhmwow~
nvoma‘nnm~¢nnmmfl~oomran~moc~m

0.0.090...DOOOOOOOOOOOOO.
mwchu‘mo‘maocr~a~o~a~ccr~r~r~col~|~hr~r~r~o~o

onnNnhoonnhnh-Ohonnnhnnobh
QNHNAWN—«Jhmecho—«hoamomocn
nmmn—aummnmmar-awhaor-w-nrrc-o-xnv-aocr

....OOOOOOOOOOOOOOOOI0.0.
0‘0‘0‘0‘0‘0‘0‘O‘C‘O‘O‘O‘O‘hfih-DSNNHNNF—Q

OOODOOQOOOOOOOOOOOOOOOOOO
hhmmo~oma‘n—cmmrvomc.n~o®ommr~

000'000000000900000000000
HHHOQOADO-«Hddhhhr'z‘rJfrsrhhh
NNNNOJNNNNOJNNNraHHHfiHfir'dflH—a

oooooooooooooomornoonoooo
\DMOJC’C‘”QC‘JNOU‘OfDm‘?O-(‘Jv-‘(L‘N'Tfno-Aelfi

00.0.0.0...OOOOOOOOOOOOI.
flHHOO‘OOOOAOHONNht‘r-TLI‘NF-Nhfif‘
NOJNNo—IFJO;?JCJNNNC~1P‘~HHHHHr‘fififird

ooooooooooooooooonooooooo
mflnfirc-L'Du (Isn‘t? ~1nr~~ot~ml~¢c~mm
.....OOOOOOOOOOOI00.0....
HHHOC‘OODOODOONNNU'TNHFNmNN
NCJNCJr‘NNCJNNOde—tu—d—ar4fiH-dHHHI-lo-l

DOCOOOOOOOOCJCOODCGF‘OC)ODOO
O‘mCDNQ’U'NC'mNW‘DIPV)H\J—a:r \ru‘ GPerJN
00000000000000.0090...000
DCCOO‘OOU‘OOOOU‘FNNQ‘NNNNN\LI‘H
NNN\\Ju-ONNHNNC\JO.NHH'v-—anr<fl—‘me—d

ooooooooooooooooooooooooo
GnONNNOJN¢D®WNOODTOJW“N~O

......C....O.....00......
ODOU‘O‘GO‘O‘unwor‘rhshxr‘ruxrsrs.pph
NNNH—qmn—cmunm~.—.-<u.4.-4-u—a-<—4.—.—u-¢

OOOOOC‘OOCOODC‘OOCDC-OOu‘ LDCQC‘Q
Nflqurowr-,~‘.¢mo—qnn .‘-{‘f.‘r¢¢‘v"') 'TU‘nfifl
OI00.0-0..his.ooouuooionllcooulolo..concocoocoltuo
-.n-.O\o~r.r~r~l\~|~r~a‘q‘o..:‘vr'1 :‘PL‘C I‘T‘c‘ot‘o
HHHfiHHP‘Hfiflr‘fifififlHF‘rop<r‘—<rflh\lc.m

Table B-1 (cont'd.)

0.0
III.)
<UO
Q)-

80

‘Q0

5

EVAPORATION

0-400 GOO-800

UMBER
VALS
20

102

333113133333113333113331‘93
MWWVIWWWVIWW WMMWW'AWWWWWWW

cmmhmmmmwnhhoosw-oon—anmnm
nmmmmmooo~o0hmmmnohmmnocm

00000000000000...00......
ooooooo¢ooooo~0m3mmmmmmm¢
nnnnnnnwnnnnwmwmmNNNNNNNN

NNmFsho~0onwommaumowoONFN
hunnn~¢cl~cOM¢N¢Vzo'nmohtr-Q’Nn

000.000.00.000...00......
OODOOODOOOOOOfihNNNNQflwhmm
NNNNNNNNNNNNNHdHflflHo-IdHo-IHH

nmr~mmmmoomna~aomn~a~m~o~0r~na~o
QQO‘BFNNQOONmmDO‘O‘CDDOHov-INOJID

00.000000000000000...00.0
ooooooooHv-aoooa‘hhr‘rncowcocncncncn
NNNNNNNNNNNNNHP‘fiHdHHHdd-‘fld

Nnmonmmo¢r~r~¢m~0ocwmwoxonncra
¢¢¢v¢¢mmomchommmxmoaaammn

0.0.0.000000000000000000.
d—oddfl—IAH—IHOfi—aa‘wwmma‘c‘a‘O‘O‘U‘O‘
NNNNNNNNN‘VNNNHfiv-IHHHHHFINN".

hmhunmwnohmnmmwmwaa‘hcomo~o
~0~Inm~r~r~aommcnc~owcflomw—«HoN—cww

.....OOOOOOOOOO00.0.00...
NNNNNNNNNNNnNooooooooooon
NNNNNNNNNNNNNNOJNNNNNNNNNN

ohmwnmedmohmc’oNhN-domooa‘nco
wwwo‘oncmov—cmhmdwomfidoaohhHv-ut

...OOOIOOOOOOOOOOOOOOO...
aomcococcaoaocmoo‘och-mmnmm¢¢¢e¢n
NNNNNNNNNNNNNNNNNNNNNNNNN

HUNOIDNIDFC"~?O‘O\DO‘O"I~O“D(‘I¢DN¢!-Noo
n¢~¢¢~cc~at~oa~c~amr~a~~3¢~cmo~c~ooo
nvom<erN~oohhmmCC-rr—unho-«rrs—ooo
mnnamN—qnwhauaaflNOJ—aomaofloo
OOODOOOOOODODDOOOOOOOOOOO

00000.00...00000000000000

IIIIIIIIIIIIIIIIIIIIIIIDO

H0~NN~monmmmnmomssmmomaoa-woo
mnnxmmnnmcmcmndhmmmmmmmoo
CIOF‘kflno-‘NNOHMHOONOfiODC‘JP‘OOOO
ooooooooooooHoooooooooooo
6000000DDOQOODOQOODOODOQO
00.000.000.000...00000000
I I I I I of:

m¢¢-70~O‘N¢mr~r~momnoocur-tanoéroa
O‘0\D¢N€D¢Ln—df10‘<r¢OdOO‘O‘—\OOUW~O~DO
ooo~~o¢noomo~~onmoo¢®o~00
ooooocaoooooocrooooooooooo
ooooooooocoozsooooDooooooo
0000.00.00.00000.000.0000
I I l I I I I I I I I I I DO

maomnaoncnamonmommowosco—«oo
q’cn—Iscum-Noocah\cd'v-ch‘omv-‘d'fia‘mwoo
cot){underage—Imam:Amflonoooraooo
ooomooooooncnao-«cooooooooo
oooooooooofloonoooooooooon

........OOOODOOOOOOOOOOOO

I IIIIII III I IIOO

or.)oomoooomommooooomoomooo
NF:NF)HOJ~~NHNflWOJWOJHm—1NNrip-IN")
......OOOOOO...0000......

\Dbm-n-‘J‘O‘O‘U'I—AC‘\DNGD'I'JIDO)OO‘VOCDO¢O‘¢ZOC
H-Q'nfx‘nhoHmr.mOI\O‘.OIOOF1!~DU‘¢O)
C’OOflOOflv-HONOJwu-IHHOOOrOGWOO‘\O
10.40900000000000000o00
I '4 woo-4 N I0
I

dobcm¢¢n~oor~~r~m¢rmmamnnmo¢x
Nronc‘mm‘onrsmmmc:hxo~o¢m~3mmmh
IONCDOv-‘o-dmv—Iu‘.HO‘U‘OQ'flI‘CmNOWEHO
OOOOOOOOOOOOOOOOOOOOOOO

'4 I N .... dun

O)\DN'~C"NIOI~~O¢CDO‘O-hdcrofimo—ufixwoc
O‘Qr‘n’.‘r‘TU‘I’H‘JO‘.7xn'4v-«D:nc}:lnov*nf\j
hy’TC‘zC‘fJCC‘JCDu'CJVIO HIHI‘IOOHNNOCJF’W
oocoooooooooooooooooooo
OH I ¢ «7' 0 rd

N

nwnhOI¢¢0m¢¢om¢QOhOlnVwmvmm
QHOwIHaNTFu—Ci—F-(h"DfiOfiNHF‘fl
Defihmcfiofilu—‘ONOC‘IC‘(‘OOV‘I'DO
......OOOOOOOOOOCCOCOCO

fl 0 N

ds,

10

te per

Smoothed atmospheric and soil data averaged over ten-minu

Table B-2.

1980.

July 25,

TIHE

800

400

50

800

50

800

900

50

7/25

103

nmmmmmwnommuvsac—«v¢th~omaomono~Nnmor~~Lua~a~r~r~~mv~m~r~ma~n~~ AFQC‘OIIDNNO
0000.00.00.00.000000000000030.loo-00.00.000.000... 00.0.0...
OLDC‘IO¢o-IC)CJC)C‘JI~o-¢U‘N-f'1na‘GOVT-"Hfi'rNFCJ‘S—G’L3.7r-‘v-nCJWOC‘VOQNJEtF-QZDNFQ'.m¢°Nfiddnm
mcmcemmofi—ur schmwhlomo-mom'roh-c ovumocnhen—owcsuoomc—ahm N¢nl~°f~hlfi~
numNmnfl~rv1¢¢ufimO¢ a comm10¢Nmnnnnon'nmnn-nnnnnnnmnnnmnnnv nnnnnwwww

c

~o~ococoamomero-ndvan-‘mcomaowmmmama-monohmhoouohnoc:co-n—«vsmh mncocoowou:
......OOOOOOOOOOOOOOO0.000000000900000...IOOQOOOOO 0.0.0.000
¢0w¢cnoflwmuawn¢cohmmnmna~nehmo¢nouno¢nw¢mr oowmeMflmw¢NO¢000
newnuonmm vzmu‘hocr domm-«mnflnnmonxd-r|nq~mn.-oq-Nor~n—owr “(Dasha-40mg: Naommcnwn
«uwwwnnnmnrv¢¢cwcvmcmcwmwnnnmntnmvtnnnwnnmwwwnnwnv mnn'ONNNNN

mumcwmhmmmmonmm0«Nnamnoo-ooowwhhh—aoa‘hhonemn-«o‘mn~~~a~ «ammo—«uncut
0000000000000000.000000.000000903oo00900000000000. 000000000
QNNQT If“ nouoo.ocooaMo—unmhnmnnNooo-nmc 7\\DQ'~N Ofl'ChNOO‘U‘fOflmNd-d nmwfimomho
”OOHU‘I‘DIDO\DDO‘—COQLDOOI\FO.7H¢QLfiV’IO‘O‘o’N?#xDIM-JINO‘~0¢Hmm~0vamP~HN «mwnowmoo
unwmdmnnnn¢n¢¢nnccvc-crc-u-u-‘an cnnncrnnnNNNn-ONNNNWNNP’It nNNnNNNo-cm

 

NWHOQO‘QFFG‘V’IOIOQHODNOQNNF’H’IQQOMOI’MDNOGJO‘mnI‘J—OU‘QO‘OU‘VDIDNWHQ ”O‘NNVOOWWC
..OOOOOOOOOOOOOOOOOOOOO0.00...OOOOOOOOOOOOOOOOOOOO 00.000090
J‘U‘NQNQL‘O'DDU‘G‘Nfi-‘U‘~‘PEY‘ITV‘V‘TT-fl—N‘JNOD'ONlT-OC"HONmCDxCHVIIDDU‘WTImN-flo NI’IL'HDG'U-‘CDO'O
NNmemOJT‘U‘I’)10".“)?VOI'JC‘M'JO‘MDNV‘I'OHDNMCOOU‘HC (PNQNGOJOI‘N-TNNMO’U‘U‘ a‘hmO‘moomO‘
«dd—OHNNP’IOH’N’)WHWHmFIWMMWMH—QNWOI VIVIN'OI’)NFINNNN-INCINNNCJCJNNIG NNNNNCJNHH

 

Lmncoo«nmna'sNaom—aomn—aaounonnaommwmo—Iomowumoq-Na-Nmaoacronn aomuhhmmnm
00.0.0.0...OOOIOOOIOOOOOOOOOOOO......QOOOOOOOOOOOO 000......
NNNownq—clsmh-«mnommw:rnNan-o-o—40hnwmoormmh-Nhao‘anmmm-rochsa,m-o~o~0~oo~oa~¢
DOQMfl333‘mOAN-«mor‘OI—do-IONDOC'FEJP‘Q'ICT'JU‘OCDQIDO‘O'XUJ‘OiVDU‘mnCJBN‘FWIOQWQU‘WnV
'4raw-IHHNNNN”WNWWnNnNWnVJnv-O'flflwfl NNNNNNNNNHNNNNNN-«NNNNIO:NNNNNo-av-u-IH

I

MNnOONOOflf‘OhnnOfihOhhnnhhfihrfinhhnonhlfloHOOOHNNQFOFOOOEOONI’IOIOOOO
nwoonoonN-«apnoa-‘oomrrNxomnnmnmn‘ommmmvu-noooocm-n—auuavsrsm‘o-cmmcncm0
Na'lntnxomboo-«oh~0n~nnn<rr~t~~o~>nm~or~mwo~a~r~rr~woauocuonmm::mmmm¢~oim~ommnooa\a\

00.0.0.0.........000.00.00.9000.000.00.09000000000‘0.0000...
«communes-hcocoaoaoaoaaaommaoooooaoaoaocowmuoaomoooccoaoo‘a‘aoa‘c‘mmaxa‘wmo‘mo‘a‘mimmmmmmo‘mm

...-1. .Ak. ... -

hhnohhhhoONFONONonoNnonohhnnoDoohhnthOOONhhothhMWGnhnfiooo
carcinomas-mood:<ra~~o<r~n~oo~o~o~na~¢u9¢~ombo~na~com~no.ro-‘mqacoh~r~nmanned—«woo
NWIDanmoo-«orsh-n—‘tc¢¢u:o;l~r~¢~o\c~0cc~0tnc>ocnc~mmfidmwuunnnn-toomONP-i cosmod'uuv-co
00.0000 .0 00000000009000... OOOQOIOOOOOOOOOOOOOOOO
woooomhgr:cocoaouocnaocncoaocsmccaornwooaoaoaocrm-‘wwmmomwoomowomo‘aowc‘ mo~o~o~o~a~o~c~a~

OOONONONNmNMNNOBWOWMNNnWOGmfiNNOHhhnOhnO“Dononfimnhhhfinnhnflfih

owmhoonommmwanooammwnm~~mn~nn~¢mhmfimonommoammomuovhmmapmowm

nommNOC~NHmm¢Nmsmmmwhm~~hmhmumcmoodwgnmuvmmmrhhfiommhchcduno

CIOOOOOIOOOCOOOO‘I.........00.00.00.00000000900...... 0....

moecwohh~mnmmmmmxwmmmmmmmmmmmmmmmmmmmmmammommawmommwoammmmm
H

coNCNNOQWHHnnhooomr~mmnr~r~or~mor~nonOWONohomooNnonnmon chhohnnnn

”\DI‘DdTDONHIJ‘U‘mIDOIOQ’P‘mO‘\DTJ’SEW-0133114000I)¢~)NOHOJO\DOL’OF)€DNI~OIDIO mommsowoArc'

nsomuorswadnawmmmmmfixcmccrxm~~®a~hhmmmooomnocmnmu‘hxor~mr~coow :mf‘thNN-d

0000.0 .00 0000.000. .0. 00...... 0.9....

so«nova~1:a~o:~.r~.r~.eccur:<30snarbcncnancouscousacct-100:1:ctr"cocrxa‘a:0:0:a~cr~cr~cr~a~o~mmawna~cr~u~tx~tr~oa~ O‘U‘O‘U‘U‘O‘ONU‘O
H

ooor~r~nocr~r~mr~nr~hnonmr~~0r~r~oof~r~nnmk~ohhanflfiknmfihonnhhfl anNONmON

OCDCNNIOO‘lNu‘ILn\DOHmlfl'firfi'J‘INrfiu-QO Kc#QNG‘Ihaunt-GHQ(‘J‘JOONDN'IMD‘DIFU‘G‘T‘HG'QO‘ \DIO\0¢$\OCDO‘<D

cemxoh—o«unwoomn-c-o‘of‘wodhmcn‘omhvfima Ham-Oq’omcrq-mQOOchxmtr—c‘ mommonnNo-d

00000000000000ooo.000000000§noon000.00.000.0000000 9.0000000

wxoxoxoxoohrsrsaommocoom-nmaoma‘comma:0cm:mmmwmc'mwmmmmommwwmmmmoa‘ O‘mO‘O‘U‘O‘O‘U‘O‘
H

ooooooocooooooocooooooocooooooooooooooooncoooooooo cocoooooo
oacmommhmocno‘o—arsm‘Loooomhcoucmono-v)q-uumnmm¢mmo~o~o¢om¢«tnncmn nvmnmmmwn
OOOOOOOOOOOOOOOOO00000000000000OOOOOOOOOOOOOOOOIO. 0.00.0000
U‘U‘O‘U‘O‘C‘O‘0‘C‘NNOJo—IOOO—dfi—IOOOOOOOOOODOODL'DODDHOO-«flda-Id—IHHo-od «pm-4.400000
NdduduwaHv-INNNNNNNNNNNNNNNNNNNNNC‘JC—NNCJNNNNNNNCJNNNNI‘INN NNNNNNNNN

OOOQOODODODOODCOOL’DOOOC)DODDODOOOODODOODOCODOOOOOOOO ooooooooo
Nmowemhmommq‘auomho*1:rmonnv~ocm¢~m~mn¢«monmmmmwnmommmhm mommmowmer
......OOOOOOOOIOOOO0.00.00.0000..OOOOOOOOOOOOOOOOO 0.0.0....
O‘O‘U‘UOO‘U madmmooooooooocoooocDonooooooo—aocaH-«H'HHHH—IH o-IHv-(HOHOOO
“'40-‘04I-Ido-QI-INNNOJNOJNNNNNNNNNNNCQNCJNNCJNNNNNC‘JNNNNNNNNNNNNN NNNNNNC‘JCJN

oooocooooonoooooooooooooooooooooooooooocoooocooooo ooooooooo
nmxommhqmcgr~¢~o m‘ccvsmsmrnms-rmrcfirrqxn .' ~7'.J~Du‘:ma‘n0‘vr~ttd30'mf0v40‘ ocrcaho—Iorun
0.0.0000...Dooooooootooooooooooo...OOIOOOOOIOOOOOO ......Qog
0‘0 0 U c 0 (r'rr'w—cm? JOOOfiOFJOC‘OOOODC‘013CJPOUOC3OOOflov-IHHH'QP4H'4—‘NPC (\quflfififioo
dHflr—«MHNHLVNCJNNNNNOJCJ NNNNNO NC-‘(NUK‘JNO CJNC; N6402NNCUNCJNNNNNNNN NNNNNNNNN

cooDoocoroonooOOQOOOQooooooooooOran0000000oooczoooooo'ooQoooooo
nub-crsrc OO:WOTU‘.GL’.T\SN~I¢Q~0~Gxotnlfl1‘c"I‘NTC‘OC‘QC‘:n-TOINC‘(DODO~NO fiOfiC’meNI'M‘I
......OIOOOOOIOOOOOO......OOOOOOOO0.000......O...’ 000099000
O‘CG‘LI‘O‘mU‘OO'dNNOOOOfJOC‘OC‘UOC’VOOOCJCCDOOOOOHO—‘H—‘CJHAOINNNNT‘JN NNNNHAHAH
thHrawfiHCJVNNNNNNNNNNO.(‘v<‘JCJr\N(‘JNWNA.(NC-.N(‘JNNNNNNNNNNNNNC‘INN NNNCJNNNNN

OOOODOOOOOOOOOOOODOOOOOOOODDOoOOOOOODOOOOOOOOOOOOO OOOQOOOOO
memo 17c Hfl¢rfi¢3tf~flm~jmr~~$ o¢nm®mm¢moor~aor-«urav-«Qq'sd’ oHrocJVN—owdw mum-«ccazmcn
...ICIOOOOOOOOOOOOOOO00.0.000000000000000000.9.... IOOOOOOOO
c‘ocamcCOOMNfiOC‘DCF—‘O’DCUOOODQCC—‘OL‘find—«FM.—P‘r‘r‘NHN".<\f;rJr4E‘J~ OJNOJCJHAv-Qv-Qfi
fiNNuHu-AIVNNCINOINOINNNNNNOJPINNNNCJC‘JCUNIVC‘JC‘J(NF.(‘JC‘JOIRCJI‘UC‘NVNCUI‘INPJNN NNNNNNNI‘JN

I

OOOOO(1C'QOOOOZ‘CDDCOOOGTDOCAC‘laffiomll€3C?(3CfioODQQOV‘CI'DODCOCWCO OC‘OOC:°COO
WONCIV) ru:c-—1PJIO¢J:(Wo—C'Fr¢lx‘ Cir—S fl¢|_‘C)-—<f‘;-).:I.'C_‘v-<(“¢F)¢J‘IC.‘-~f 'I:J'TI~CJ")~‘.”IIC’ ~0.I-')$'~."DHC»;V)
III...oonolonol‘oOOCOOOOOOIOOIOQIODDOIOQI~OIIOOOIoooogo-nggooinuu.Olgullouou’IciclfilouOIIO'tIOI'OOOC .....IUIIIOOCIOOD.
CDO‘G‘O O‘C"(7‘(noor”:odfiw—nmamfi'mmmm-O-n-r m‘fi'.~'.‘ r:: t sun-I-n‘n-nmrwm (NF-T" I‘NP-NNM'J‘G‘O‘)

er-dfifiHI-‘O-‘H”‘v-lO-‘vdfidddfiflflfiv4-fiflfir—oflrflo—a~'4~~p-qu-lpdo—Ip—v'1rdp-‘r‘flr‘ Hr<r4r¢HP4HHrC

Table B-2 (cont'd.)

0.0
2114.1
duo
(LI-

80

Q0

EVAPORATION

0-400 400-300

NUMBER
ERVAL
020

104

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1980.

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THE

800

400

so

800

800

430

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105

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......OOOCCOI.0......000..............
oaooooooooonmam0~nna :mmno mo-o-«moma‘nmhmn
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Table B-3 (cont'd.)

30

40

GOO-800

IQ------------------------------—‘-------—-—------------a------------O-------------------------------------------------.

EVAPORATION

106

33’)DjjjlfluuuquZZZJ‘lljflflj313333333331)
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(‘J

ds,

10

te per

-minu

Smoothed atmospheric and soil data averaged over ten

August 1,

Table B-4.

1980.

TIME

800

Q00

50

800

'50

800

400

50

RI

107

oNomNn-cnammomnnolnmnnm~ro~m c nn'ch-DNO
000000000000COOOOQOOOOOOOOI-IOOOO
mn—«u‘fimazm'fla‘m V‘w.c~c,r~-mnnr~ln~or~m r~- 1".th
V)\QN~'~N"‘\B“JNCTU fluid-QTY £N¢°nfifilxjr.7-- 'nrj- 7.006
In¢¢m¢nnn~rnnn¢cwwi:necnmncnnn-,nnnww

wa‘womsohnho‘na‘mmhommnrfi0c‘oc‘hmnflmfidw
.0000...00.000000000000000...I...
on-«zfineeomn—au'n DCOC‘¢\DI.DO¢-ODQ—c .' :I'Jauytc
H‘\flU‘U‘W‘DN'-'O\O|DNCO’CI~C.J‘(CWNH¢¢OI~Wu- ~o0~rr~N~D
Inn:crnnwnnnnmnnannmnnnwnvnnnI-annmwa

mQNmmthN—anNN(I'NNto—INNVIG'O‘OO 90%-01.06)st
00.00.00.000.00QOOOOOOOOOOOOOOOOO
InNcomhoammdmuosnnocnw-«c‘uqmon-r .TFJcsov-u-o
mmmnnmhumnnnonncomnwwnam¢9wcacao:
cmqwnmwmnnnnnmnmnwnnmmnnnmnmmnNH—I

r1Cf~fflwNflWO‘OIH’CIxOflxOU‘mmFU‘tO—d:xomord.fcr‘g‘panoq
0.0.0.000...00.100000000000000...
NNdmhfimofi~Du1HffiNdIF a~~n3~mnr-n~‘r fut- necn
Inn 006‘m~or~N~¢€rl~oG~mI~HN0~I~a0I~OIO .M‘ :01)de

.VON")GNNNNF’InNNnNNNWNNNNHNP‘INIC-H‘JFH‘INHF‘!‘

hoawncrq'nxonommHI-snd-oNHosO‘nmha'xo—apuoq-rs.‘
0000000000900000000000000..0000000
¢mMmTomomnhhofiamommuomflomhandflmmt
unn~50~o¢ma~comm-rmoow—«mruochep—a-J‘chm
nNNnN"'NCJNNNNNNC‘JNNv-INNu-{NNNNI‘J?;NHN¢-¢d

mnh-hNonNnoNHnNNQohonhoooononhfinhn
H‘no-DCJDHOP’JONV)": DHQOHWO‘moorlo-ODI' saauon
\Ommchl‘o‘axon—"40":Dam—amadmmauoct.u - Juan.»
OOIOOOOOOOOOOOOOOOOOIO00.0.0.0...
O‘IO‘wa‘U‘O‘U‘O‘O‘oooooooooooooooooomma‘mwa‘
fiHMHMdefldfiHfldH—Iwfl

nfimnomoONNOQOthOMNDnOnNhfifiNIflOOP‘Hfl
cm¢¢0n\ooI~N¢v~othomfiovmmomP-mq-n'rfimtn
hh-hCCUEOOdONN—H‘INNNNNNnnnm—oa-«Huwoazsoln
00.000.00.0000000IOOOOOOOOOOOOOOO
G‘O‘0‘0‘0‘00ooooonoocooooooooooouooU‘O‘O‘
fiHfiMMHNd—QM—Iddflflflfldud—Iflfid

nonohhh~r~r~hhr~finnnmnnhNONmn-cnohhnnfl
Irmotonmsnnmomvwmcc—a.«ruwnomxoenn‘n—noo'u‘oom
(robemauwma'q-na'runmwn:a'mmmnnwnnsomosso
.0.........O‘OOCO.....OOIOO......
(Pa-0‘omoooaooooooooooooooaoooouoomw
fiHHo-I—dr-IHMHHflHHflH-flcflflo—lr‘fidddflfi

OMmhnONOf—‘JP‘DHOONFHWOOfloonOnhhf‘r‘floh
U‘OmmmoN-«CONGfiCJHFm-I’NNOWONO WIODO‘DI’IOIO‘
ooooowmnmmmemnmaq-uumnxouao:rn-rnernnaors
00.00.00.0oooooooooooo-ooouuooogg
OQU‘QODOODDOOOOOOOOOOOOOGOOOOOOOO‘U‘
HH pic-IHHcdHu-I—uo-Ia-I«MflfiAHHd—aHfifiHHHflH—G

fihhmor-NOBNOVV‘oonhonhhoOCONn7~NflhOfl
n~ONa~°N~~Do~oln'nh-o<rm~mna~mm¢om~nr~~oc~r<~orn
NHHACJfl¢¢Lfi~CC®QQ~C¢~560~OI~I~I~~DID~OIDDID¢HOO
000000000...IOOOOIOOOOOOOOOOOQOOO
DCDCDC)C:>CH.DOCDOOc>c3c3c>oo<23DCDCJCDCDO(DomI'J'DCDIDC'JO~
uni—IMHFIH—u-I-«o-nH—dHfifirfiHn—I—Id-«a—Id—u—Ifludd

00000000000OOOOOOOOOOOOQOOOOOOOOO
HOJNM¢\OMOL0®'JT¢IO¢NNWW¢WWHOFO$¢”Iv-‘NO‘VID

0000000090..oooooooOooooooooooooo
anflfiv):V'P’N’Mr)n-fi“1“)“IVIV7FONNNNHNN-4Ho4d—doo
NNNNOINNNNNNNNNNNNCJNC‘JNNNC‘JNCINCJI‘INNNN

ooooooooooaoonoooooooooooocoooooo
Haounmmm¢oenmnwannnmmenmaor0¢~mco

000.00.00.00000000000000000000IOO
nnmwonnnnm-nnmmnnmnmNmmN-am~-—~—n--—n—¢-~d
NNNNNNNNNNNOJNNNNNNNNNNNNNNNNNNNNN

oooooooooooooooooooOoooo300090000
oocommu'.~n ufinI‘IfirIOOCJH—amd‘w‘n "CI-fi~r~‘n’I-—h£h
0.0.0.0000...OOOOOOOOOOOCOOIOOOOQ
MN)0.V§¢JF\"PV3'IP§7‘""‘MflmflmI’ICICIOICIDH‘JCI'I(‘3f\.(‘JC.Iv-4d
O.NC\C.C~JCJ(‘JC\:NOJNOIC‘JNCJNNNNNCUOJNCUOJCJCJ".t‘ ”:NGN

canceraooooootaoooooocInoonc‘ooorsocco
COmCN~n¢n¢mooflocoooonflcwxhcrm¢¢rm

0.000.000...IIOOOOOOOOQOOOOIOOOOQ
(\INNOINH‘I-Onnmmnmnmmnmnnmwmwmmmmmum—«4
(\INWNCJNNNNNNNNNC-JOINNCJNNWNNNWNC.Nfi-NNN

00000000000OGOCC‘IGCOOOOCGO00069000
mhmx¢omnmmucccmrccmfloonrrabstwnoo

OOOOOIOOOOOOOOOIOOOOOOO0000.00...
NOJ'OWI‘IIOWU’ZF‘V‘I",I‘It‘qr’;N'S‘JC‘JCJCJFIV‘IWr-WCJCH‘ICIC‘:'If‘vf‘J—fio-d
NNNNNNNNNNniINC-4NCUOJNNCJCJNC‘JNNNC;CJ'J“ICIPJNN

OOODOGOCOOODC'C‘O'.3C‘C)C‘CCC'HOC)C"'-{“2306
DWCJV‘JfLJ O~~0.-?U'C‘HT."7 rLAOv-(‘xI‘7'fi‘13-fl .~,. C‘—-¢€N‘
.C'UII.‘-.OII'.ICOII..IIIIIII-O!IIIODIOOIIIOII'Olotnjinutoio'5'...
<rq-c-rorrznm'cmru" r\fl~n'r\.-\FNNNF~~" J: '. .- ‘- ‘13-‘7-
v-IrIa-apdo-d—d—lo-nv-Op-‘Hrlpa—npdp-ac-IHHHWNpqu—ad-‘rv.ao-v—-Na~d

 

Table B-4 (cont'd.)

p
G C

AN
EH

P
T
80

40

“DO-800

0O¢6
RVALS
0-400

HUD

EVAPORATION

108

33333333323333)133))JJJJ'I1333333)
UNI)

FNHNOV‘Ommefl—‘FU‘NO‘ONWWG#fl'OCCNCNQFCTV
N¢OQOHWWGNNCFOTmo‘ca‘mmhw¢fi0thNO-NWN

00000000....00.000900900090000...
OOOo—I—Iduo—A—IANHd—Hdmnfiua—QMQOOOOO‘O‘U‘
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnwwm

NU‘NQOFIDFO”mNWOnOHO‘wm3NOOU‘9‘OONQOOCO
oooouooooomooo—aOO‘OOnu—onnDOAIM'anc-IN

000.000.0000.00000000000000000000
H—‘Hr‘muundddm—I-«OI—fioAudfi—am—c—o—c—I—d—u—Qfidd
NNNNNNNNWNNNNNNNNNNNNNNNNNNNNNNNN

fiQ¢¢fl~D¢lfl°No¢lfln¢Nmfi$~DNoN~fIOIDOCD$Q¢IDO¢D
(Dmu‘mo‘a‘ooootOAHdNNdNn¢Q¢flfl¢9¢QN¢nm

000.000.0000.too-0000000000090...
ado-Id—IO-‘HNC‘JNNNNOINC-JNI‘JNNNNNCJNNNHNNNNNN
NNOJNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN

coconomomhnwomumc—nm¢nmmcmm~a~m~onon
O‘O‘noODHNWva-Ic'Nd'a'mOCdJInlnhqu‘Innd‘wVth
............00......OOOIIOOOOOOOO

- HHNOINC‘JNNNNNNNNNNOINNNNOJNPINOII‘INNNNNN

NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN

OQOO¢FNOON¢DNQFmsflfiQ¢¢mNQNNOU‘QWU‘NM
oomn~:—nmnr~¢~:mxmocohhmhhcmhhmwhm

0.000.000ooooooooooooooooooooouoo
NNNNNNNNNNNNNNNNI‘JNNNNNNNNNNNNNNNN
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN

NNNQCDV’IO‘Nv-fimtne#HONI’NOémNmIfl-«Hcmmhhw
~d~ownnmnaawoomnno—a—adu—shhrvmoxomcwn

0.0.0.9000...00.0.000000000000000
accommmaomaoaoaomco-cacmacaoaccmoaoacmhhhhhhrsfihh
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN

codes—Nanceumcmhcn—cmmmnmfiom:mnmvhhno
mo¢n0IcanI~m¢:Neoonnha‘mmcfic‘cma-cmnwmom
cmomwmdwnommo¢~oo~~m~omen¢m¢mvnmmr~accn
NO;NN—«NNNNNaNNNNdH-«N—GNN-ONNNNNNNNH"
OOOOOOOOOOOOOOOOOOOOGOQOOOOOOOOOO

000000000000000000000000000.0000.

QOT‘OING'OJNOP‘UWHHOOHWO‘CEN-«fim'fit‘zc:va-IINOQON
C‘fijfltrfNHN’r'N\Oq~TW~THHLONOJQOIVHPHI‘\DA\O¢I-’D0‘\no
IomoNo—odomcurl-Ovao-oNfidénwwmnnmawa-IWNNIONN
oomooooo—I—«oowouoooooooooooooocooo
oooooooooooooooooaooooooooooooooo
0.00.00.00.000000000IOQOOOOOOIOOO
II III I IIIIII IIIIIIIIIIIIIIII

v-uoou‘Ivmaorso\oammnmo‘mamcoo—.afim—«Nvoth
Q¢VIOI~VON¢INDH~7¢0flFNHOJw¢TN-DQ~T~DWF¢HO¢
OD—‘MU‘NIOON‘Ifi—dt‘O—oa—Lfiv‘:r—u-tOOCJOOOO—av-Iu—dv—INN
OOOOOODOOOOOOOOOOOOOOOOODODODODOO
OOODDOOOODOOOOOOOOOOOOOOOOOOQOOOO
000000000000000000000000000000...
IIIII IIIIIIIIIIIIIIIIIIIIIIIIII

Inhmo‘e#:mnnhnnmmmwon¢nI¢\s:v-mhnowdwolnh
cm—«mruho-ImoInccw'rr-hn~~~n~nwm~c~ood~~o~¢o~m
gN—Ioch—qoqooowaocaoo-«oogaooov-oHH—«fl—uO—«Do
OOQODOOOOOOOOOCOOQOOOOOODOOCOOOOO
oocooooooooooooooocoooooooooooooo

......IOOOOOQIOOODOOIOOOOOOIOOOOO

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

ooaooooomooomooooooooomooooooomom
OOHONF‘v‘NHHdr‘HI-dHdNfiF‘HHHflHNHdfiHHHc-‘N
oooooooooo'oQOooooooooo000900.000
OO O

WO‘NHO‘OO‘FOONQ'CDI‘JMO‘NOOIQEQO~¢¢GNHH¢NNQ
nc-utHACDmInxmrdNOIhu‘Ir‘IOemanIC‘UILCNroO‘OUEOIfim
MDH~OOOHCNMWNHOOOOCflm¢d“HOOWHNNcm
00090.000000.00000000000000.0000.

«4 o IIIIIIIIIIIIII

”mo‘lnc‘n3va-1xolnI'Dv-‘I'OVT‘IOFLOQ‘HNH'Q'O‘JDC‘C‘NGDO‘T'OO
m~~~v~¢monomnommm:afncmwomq-smmhflvoN
oorsoo~¢r~~~~o~ooooooocm~r1~1mr~mn¢mnn~

....OOOOOOOOOOOOOOOOOO0.0.000....

H Il—IIIIIIIIIIII
I

Nmmoommooomommmo¢o¢m~omxaumcoohma
OODWQNOQOONHHNfiDflWNMNflfiflCOfihmflflm¢
ooooCJ-«Nooor‘coco—40000000Gn—aov-«oonoo
OOOOOOOOOOOOOIOOOOOOOOO0.000.000.

N O IIIIIIIIIIIIII

#3anQv-‘f‘lmmv-IfiNGO‘mDI‘DC‘GIOW«?Q|DI~NO‘£DU"DN'I‘°
\r)a:F‘AJVTOID—‘H“UCJQflCJ~OC)C‘—Cnono‘r4HGFDV"OO"‘ON
Cancoooconncncoooor‘ccQC C‘OC‘CUL‘TTC'WOO
ooooOoooooooooooooooo00.000000...

II IIIIIIIIIIIIII

Smoothed atmospheric and soil data averaged over ten-minute periods,

Table B-5.

1980.

August 4,

500

400

800

50

800

400

TIME
/

 

109

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rmnoanwrr:mo1~c~~r~mo¢nmrrmnnnmvm-‘I-nr.-r~ur-nm :¢cr‘r.y~n~ rrat—cnuo

 

 

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‘Q‘-A§

Table B-5 (cont'd.)

300'

800

800

900

50

6]

mmeonooon~¢nv~on~no~rrcrook
00000000000000.0000...
lav-0660‘ U‘mmt‘onC‘0V701BwF)ON-4N
mnmwmoho-3I~¢NH¢~dInI-4Inn°~
nmnnmcuflwwwnnnNNNNNNNNN

\DOOHC-Oé'CDNO‘mN‘fv-(OP'flxOOOHM
00000000000000.5000...
Nncom¢om0¢~oommwr~m~r~n¢d~~
10°00‘Q'P'3‘1C1 ~f¢NC"JDv-H~O’ HOdC‘HDQ
”WNNNNgflNCJNWNNNHHN—QNNH—O

N9N¢NOQOMWVONO¢WOHOIDQI0HO

0000000000000000000000
htflomwgnnnmmmrr\omammoco
mmhhn-nnmwmmhhmmhmmw—oco
NNNNNNIONN—INNNumHo-qfimmutfi

Nonmmmqnhwonnhmvwocowuowh
0000000000....0000000.
mcmmmxcaqawncowoccno—o :nmofl
\D\DN¢U‘\D¢°U‘\DHN¢~O¢WI~¢I~I~NI’)
NNNNfiNNNdHNNNHHHHd—CHH"

nehwotnuomwwomonmnmwuw
0000000000000000000000
ahnmmonHnI-Iq-mammmn—nnom
#O‘O‘O'JWQOOIDLOC‘001NIOIONIDCDOH
NdHHflHNHfidHflN—Q—‘HHHH dd

Nehhchnnnflhnhhnhnonnhh
oooemxoncbfoaorxoxoo¢acoo~on~a~
ODO‘O‘U‘dODQUIWv-IO‘04fufiq'NNU‘t-Olnfl’
000.00.000.00000000000
oommmmwmo‘mammmmmmohpfih
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nhhnov~oor~r~oononhonnhc~t~
NWN¢NO®O~O<DO~DV19NNN¢COLOHI~
NHHHoomwm-zrnohmmnmfiosfimn
00000000000000 0000000
OOODOOU‘U‘U‘U‘U‘O‘QJCDCQCDQQNFFF
HHHHHH

nmonhhhhonofinoonnonnhn
cmhtnmammhcwoo~mmm¢~mo
QnNNdOC@NmnHm\O¢NHC:CCF~f.n
00000000000000 0 0
oooooooodmmmmmmmmmhhhb
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hhfihoshonnhnncoooohoon
coo‘mmhmoomoxonIomonNa‘ma-h
mmmnNOJ—Ioa‘xccmqu<rmr:ot:xe¢<\l
0 0 0 0 0 0 0 0 0 0 0 0
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r~m¢m¢nmr~~m~onor~m~oa~r~mna

00000000000000.0000000
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00000000000000.0000...
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OOOOOOOOOOOOOC‘QOOOOOOO
momwocufiqtfimnmomIOmH¢mwr-uo

0000000000000000000000
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NOJNNNNNNNNNNC‘JOIOJCVAOJNNNNN

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F'Qfltffi‘f'fifind'vfiv-dpafi‘I‘d'WN—dc‘hs‘rrfi

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NNNNNNNNNNNOJNNNOJNNCJNNN

DOO¢JOOOOOODOOOOOOOOOOO
mc‘b-commemmnmoohmnnwowom

0000000000000000000000
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000000000000000000000000090-0000.00-00.00...
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llO

 

(cont'd.)

Table B-5

0.13
22h;
Ill-10
Q0-

0 400-800

EVAPORATXON

200-400 ODD-800

NUMBER
VALS

 

111

33:33:33) 7013:1131 13133))111'13131111131‘2‘0111113131‘13
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Table B-5 (cont'd.)

30

0.0
223...)
(U0
a.»-

400-800

10"6
ERVALS
0-400

EVAPORAYION

SER
LS
200-#00 400-800

YUP.
RVA

 

3333111333333331131233
wmwmmwmmwmmm wmmmvnm

 

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TXHE

800

#00

50

800

800

I000

50

S/

113

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Table B-6 (cont'd.)

Q

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INTERVALS

RICHARDSON
FOR
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50-100

 

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1980.

August 8,

800

800

Q00

50

800

400

TIHE
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Table B-7 (cont'd.)

 

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APPENDIX C

INTEGRATION OF EQUATION [29]

118

The integration of Equation [29] was performed by the
following steps. First, consider the case of an unstable
atmospheric condition. The exponent n in Equation [29] is

positive and the equation becomes

341-

1 , 1
32"Emfi ffiqefifi‘ -'-’--”“

Separating variables gives

aq = --53%23 - 2T1:q%§%rfpg . . . . . . . [02] i
Writing the partial differentials as total differentials
and integrating between the corresponding limits of ql to
q2 and Z1 to 22 we have
2
qum z{ W ..[c31
The integration of the left—hand side is straightforward

and gives
Z2

dz C4]
z(1+|sz|)+3§ ' ' [

To integrate the right-hand side term we use formula 192.11

E
QI-qz = - aziza

of Dwight (22) and obtain

L
_ _ E (1+322)2—1 (1+sz])%—1
qZ'Q1 ‘ pakzb { 1“ I (1+szz)%+1 ["1“] (1+szl)z+1 } ' ° [05]

for a=l and (1+SZ)>0.
According to logarithmic properties, Equation [C5] can be

rearranged as

E I/1+szz—1 V1+Szl+1 I } [C6]
qz-Q1 = - 5—‘2‘ { n I ‘ ' ' ' ' ‘
ak b «I:§2;+1 /EI§E§L1

 

119

 

or
q _q = + E { n /1+szz:1_ /1+sz;+1 I} [07]
1 2 pakzb /I$§ZE+1 /Il§2f— 1
From Equation [31] we have
= H2_:_21 = AU . . . . . . . . . . . . . , [C8]

 

52 E2
1n(21) 1n(zl)

Substituting for b in Equation [C7] and solving for E gives

 

E = pak2( ‘ )(U ‘U ) . «r_’""‘l . . . [c9]
Z2 1+822-1 V1+szl+1
1n(Zl) {lni/l+SZ2+1 ' 1+SZI' I}

Rewriting Equation [C9] by expressing the changes in humidity
and wind speed in finite difference notation results in

2
= pak AgAU . f(S)

Z . . . . . [C10]
ln§%)
1
where
f(S) = 1 . . . . . . . . [011]

{1n|rli§22:1 . ili§§1ill}
/I+322+l /1+SZ1-1

Equation [C10] and [Gil] are Equations [32] and [33],
respectively.
Second, we consider the stable atmospheric conditions

when n is negative and Equation [29] becomes

§3_=__ l . E
32 WWWWW[CIZ]

or

§3 - E . Slii§§ili§ . . . . . . . . I . [c131

120

Separating the terms and writing the integrals as total

differentials we obtain

1i
E Z 1+SZ
£?2dq=_m [leLHl dz ........[c14]

The solution of the left-hand side integral is the same as the
previous case. To integrate the right—hand side term, we

use Formula 194.11 of Dwight (22) and obtain
E 9a $5 Z dz
- =——2— 21+sz —1+sz +7r2

The solution of the integral term on the right—hand side
is the same as the one obtained for the unstable case.
Rearranging Equation [C15], substituting for b and solving

for E, we obtain

2
E=E§€fl.f(s)..................[c16]
lug?)
1
where
f(S): 1 -s[Cl7]

 

{2[(/1+SZz)—(/1+SZ1)]+lnl_____']'+SZ7——]’ .____’1+SZ1+1|}
/1+szl+1 W4

and the function needed in Equations [32] and [34].

 

APPENDIX D
ILLUSTRATIVE EXAMPLES FOR COMPUTING EVAPORATION

RATES FROM EQUATIONS [32] and [35]

122

The following examples illustrate computational
procedures used in calculating evaporation rates from
TH and MTH equations under the same atmospheric conditions.
Both stable and unstable atmospheric conditions are con-
sidered.

First, we consider a case of stable atmospheric
conditions. For this case we use data obtained for the
50 and lOO-cm elevations at 1930 hr on July 24, 1980 (see
Table B-l). To evaluate the parameter S from Equation [28],

we must first compute a and B from Equations [30] and [31].

 

 

Thus,

AT Tz—Tl 290.6—290.5

_ = = = + .

a = hail) mil) 1:16—00) 0 14

21 21 50

—- = AU = UZ—Ul = 120.2—117.5 2

b lncgl) lncéZ) lncigg +3.90
21 21 50

Tavg. = T12+T2 = 290.6:290.5 = 290.55

Assuming a value of 18 for B, (52), 981 cm sec"2 for g and

compute S to find

8 = %§% _ (18)(981)(0.14) = +0.56

‘ (3.9)(3.9)(29o.55)
For this value of S and from Equation [34] we find f(S) to

be 0.225.

123

To evaluate the evaporation rate from Equation [35],
the TH equation, assume a value of 0.41 for k, 0.0012 g cm-3
for 0a and Table data for q, U and Z to get

E = pakZAgAU

[mg—>12
1

= pak2(q]-gz) (Uz-U1)
[huge]?-
1

(O.4l)(0.41)(0.12)(2.7)
[la—13370)?

= 1.13 x 10_'+ g CID—2 sec 1

 

= 1.13 x lO—L’ cm sec-1
Since all data are based on 10 minute intervals, we multiply
by 6000 (600 sec equal 10 min and 10 mm equal 1 cm) to obtain
0.068mm/10 min. Then the corresponding evaporation rate
from MTH was computed according to Equation [32] as

= ———9—pak2é‘ AU . f(S)
[ln(§f)]

_ (0.41)(0.41)(0.12)(2.70)
— 100 . (0.225)
1n (E)

= 0.177 X 10‘” g (:m—2 sec—1
: 0.177 x 10'” cm sec-1
= 0.0llmm/10 min
A similar procedure is used to compute the evaporation
rates from these equations under unstable atmospheric condi-
tions. For this case, we consider the data obtained for the

50 and lOO-cm elevations at 1650 hr on July 25, 1980 (see

124

Table B-2). The a, b and S parameters for this date are
-0.29, 29.58 and —0.02, respectively. Using the value
calculated for S and Equation [33], we find f(S) to be 0.448.
The next step is to compute evaporation rates from

Equations [32] and [35]. The computed rates according to

these equations are 0.002 and 0.005mm/10 min, respectively.

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