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VOL. 8, NO. $
WATER RESOURCES RESEARCH
OCTOBER 1972
Model [or Predicting Evaporation [roma Row Crop
with Incomplete Cover
JOE T. RITCHIE
USDA Soil and Water Conservation Research Division, Blacklmzd Conservation
Research Center, Temple, Texas 76501
Abstract. A model is presented for calculating the daily evaporation rate from a crop sur•
face. It applies to a row crop canopy situation in which the soil water supply to the• plant
roots is not limited and the crop has not come into an advanced stage of maturation or
senescence. The crop evaporation rate is calculated by adding the soil surface and plant
surface components (each of these requiring daily numbers for the leaf area index), the
potential evaporation, the rainfall, and the net radiation above the canopy. The evaporation
from the soil surface E8 is calculated in two stages: (1) the constant rate stage in which E,
is limited only by the supply of energy to the surface and (2) the falling rate stage in which
water movement to the evaporating sites near the surface is controlled by the hydraulic
properties of the soil. The evaporation from the plant surfaces Ep is predicted by using an
empirical relation based on local data, which shows how Ep is related to Eo through the leaf
area index. The model was used to obtain the total evaporation rate E ---- E8 q- Ep of a de-
veloping grain sorghum (Sorghum bicolor L.) canopy in central Texas. The results agreed
well with values for E measured directly with a weighing lysimeter.
The rate of the transfer of water from soil,
through plants, to the atmosphere in a devel-
oping row crop with a uniform but incomplete
canopy may be limited by soil, plant, and
atmospheric factors. When annual row crop
plants are in an early growth stage with little
vegetative cover, the evaporation rate from the
entire field surface is dominated by the soil
evaporation rate. Evaporation from practically
bare wet soil surfaces is primarily influenced by
the energy available for evaporation. As surface
drying proceeds, evaporation becomes more de-
pendent on the hydraullc properties of the soil
near the surface. As the plant cover increases,
the evaporation rate becomes more dependent
on the leaf area [Penman et al., 1967] and the
potential evaporation so long as the soil water
available to the plant roots is not limited. In
some species an advanced stage of maturity or
seneseence will also limit evaporation.
Several models used to predict evaporation
from plant and soil surfaces (exclusive of those
that require details of canopy resistance values)
include a plant factor for calculating the actual
evaporation from the potential evaporation.
Such plant factors vary with plant species and
stage of development [Penman, 1956; Criddle,
1958; Blaney, 1959; Jensen and Haise, 1963].
Recently, Jensen et al. [1969] developed an
improved plant factor used in predicting evap-
oration that can be adjusted to reflect changes
in surface wetness caused by irrigation or rain-
fall.
This paper presents a new and practical ap-
proach for calculating daily evaporation rates
from row crop canopies. Evaporation from soil
surfaces and evaporation from plant surfaces
are considered separately. Most of the equations
used are semiempirical relations derived from
field measurements of evaporation using repre-
sentatively exposed weighing lysimeters. The
model applies only to a developing canopy that
is 'freely evaporating,' i.e., in which the water
uptake by plant roots is not greatly affected by
a lack of available soil water.
MODEL
A flow diagram of the entire model is given in
Figure 1. Explanations of the symbols used are
given in the notation section. The daily inputs
required are shown at the beginning of the flow
diagram. Potential evaporation Eo is calculated
first as a subroutine. A combination equation
[Penman, 1963] is used to define the approxi-
1204
Evaporation 1205
mate Eo as follows:
Eo = [•Rno •0.262
.(1
a,
U,
eo,
Ca,
1) -1 (1)
slope of the saturation vapor pressure curve
at mean air temperature;
constant of the wet and dry bulb psychrom-
eter equation;
wind speed at a height of 2 m;
saturation vapor pressure at mean air
temperature, millibars;
mean vapor pressure of the atmosphere
calculated from Tw and T• as measured
during a day, millibars.
The empirical wind function in (1) contains 'an
allowance for the extra roughness of a crop as
co•pared with open water' [Penman, 1963].
The soil heat is neglected in evaluating Eo with
(1), and Rno is estimated by using an empirical
equation developed locally [Ritchie, 1971] be-
tween Rno and the net solar radiation (incomin, g
minus reflected radiation). Albedo values ß used
for converting daily solar radiation Rs to net
solar radiation are calculated for a developing
canopy on the basis of the leaf area index
from an empirical equation developed from
local data,
e = ½• -4- 0.25(0.23 -- (}s)nai (2)
O<Lai•__4
where ß• is the average albedo for bare soil and
ß for a full canopy is 0.23. Other methods for
estimating Rno from Rs are discussed in Penman
[1963] and Jensen et al. [1969].
The next calculation required for predicting
soil evaporation when the surface is freely evap-
orating is the potential evaporation below the
canopy Eso. When plants provide shade for part
of the soil surface, Es is not expected to be the
same as it is for a bare soil. Wind speed, Rno,
and the vapor pressure deficit are all lowered in
approximate proportion to the canopy density.
If the term in (1) containing the vapor pres-
sure deficit and the wind function is assumed
to be negligibly small, Eso is calculated as fol-
lows:
where Rns is the average net radiation at the
soil surface. The fraction of R•o at the soil sur-
face has been measured by several workers for
several annual plants with various La,; their
results are summarized graphically in Figure 2.
The solid curve in Figure 2 is a plot of
R•8 = R•o exp--0.398Lai (4)
Combining (3) and (4) yields the equation
Rso = [A/(A -4-q•)]R•o exp--0.398Lai (5)
Equation 5 is admittedly lacking when the
canopy is small at the beginning of a season
because of the neglect of the wind and vapor
pressure deficit term; however, conditions fav-
oring free evaporation from the soil surface do
not exist for very long periods when the cover is
sparse. During periods when the surface is dry,
(5) is not used.
After the necessary evaporation potentials Eo
and Eso have been evaluated, the soil evapora-
tion Es and the plant evaporation Ep are cal-
culated separately as is shown in the flow
diagram (Figure 1). The parameters Es and Ep
are calculated, respectively, from the equations
in the upper and lower parts of the flow dia-
gram. Some equations shown in the diagram are
written in computer programing logic; e.g., the
equation •]Es• = •]Es• -- P is interpreted to
mean that a new value of •]Es• is equal to the
previously calculated value of Y. Es• minus P.
EVAPORATION FROM SOIL
Most Es takes place in two stages: the con-
stant and the falling rate stages [Philip, 1957].
In the constant rate stage (stage 1), the soil
is sufficiently wet for the water to be trans-
ported to the surface at a rate at least equal
.to the evaporation potential. In the falling rate
stage (stage 2), the surface soil water content
bas decreased below a threshold value, so that
Es depends on the flux of water through the
upper layer of soil to the evaporating site near
the surface. This two-stage evaporation process
can be demonstrated with data obtained locally
for Houston black clay and with data obtained
from several other soils by other investigators
(Figure 3). The parameter Es was measured
under field conditions during a single drying
cycle lasting about 14 days [van Bavel and
Reginato, 1965; Black et al., 1969] (W. O.
Pruitt, personal communication, 1971). These
workers used precise, well-exposed, drainable
weighing lysimeters to measure Es. In each case
the soil water content was at least to field
n•
yes
Es-f(t)
[q. [8]
<•, •"' [?]
tREAD Th ,Ti ,Tw, ! Td' U•Rs•Løi' l
c•,cu,• •o, •.. [•]
CALCULATE E•o • Eq. [5]
yes
Es- Eso-.4([Esi -U)
.6( :[Es: -U)
f (:[Es2)
yes
Eq:
Y"" E:P-i•-œ, , Ep-•
s I
I .
Fig. 1. Flow diagram of the evaporat,ion model.
-•Es• ' •Esl +Eso [ ,
Es'Esø I
P'P-•Es• • •Es• '0'• yes
•EEs• - U-P
Evaporation
capacity at the beginning of the drying cycle.
The evaporative demand appeared to be typical
of warm season values for the region where the
measurements were made. These data demon-
strate that the initial fast rate of drying is
followed by a decreasing rate.
The parameter E8 is predicted in stage I or
stage 2. The program branches at A in the flow
diagram to the right for stage I evaporation and
to the left for stage 2 evaporation. For the best
accuracy, the co•nputations should be started on
a day after rainfall or irrigation when the sur-
face 50 cm of soil is wet to field capacity so
that •]Es• can be given an initial value of 0.
Stage 1. During stage i drying, the supply
of energy reaching the soil surface limits E•.
1207
g 2o
• Houiton Black Cla
•) 16
• •2 ß '
I I I I• I ß
0 2 4 6 i0 12 14
DAYS AFTER RA,NFALL
Fig. 3. The cumulative evaporation after rain-
fall or irrigation for four soil types. The curves for
Adela•to clay loam are from van Bavel and
Reginato [1965], those for Yolo loam are from
W. O. Pruitt (personal communication, 1971), and
those for Plainfield sand are from Black et al.
[1969].
Rfis
Rno
1.00
.90
.80
.70
.60
.50
.40
.3O
.25
.20
.15 -
.10
0
o
o
\o
- .398
Rns:Rno e Lai
x
.
I I I
1 2 3 4 5
Fig. 2. The relation between the fractional net
radiation at the soil surface R•fR•o and the leaf
area index for several crops. Circles represent
grain sorghum and cotton [Ritchie and Burnett,
1971], dots represent corn [Denmead et al., 1962;
Allen' et al., 1964], crosses represent soybeans
[Singh et al., 1968], triangles represent corn
[Allen et al., 1964], and squares represent snap
beans [Black et al., 1970].
The amount of drying required before the soil
water transport restricts E• has been shown to
be dependent on the soil depth, the hydraulic
properties of the soil, and the evaporative con-
ditions [Garner and Hillel, 1962]. The hy-
draulic properties of the soil appear to cause
the main differences in the amount of drying
before stage I evaporation ends for the soils
shown in Figure 3. In the Adelanto soil, the
evaporation rate began to decline below the
approximate Eo of 8 mm/day when the cumula-
tive evaporation reached about 12 mm. In the
Houston soil, the evaporation rate began to
drop below the approximate Eo of 5 mm/day
when the cumulative evaporation was only
about 6 mm. Unsaturated hydraulic conductiv-
ities at -0.1 bar soil water potential for these
two soils are reported to be about 0.19 and
0.06 cm/day (Table 1). Table I gives the
cumulative evaporation amount for stage I dry-
ing U as estimated for the four soils shown in
Figure 2 and the hydraulic conductivities at
-0.1 bar for each of the soils as given in the
references listed in Table 1. During stage 1
drying, E• was calculated by using (5). The
1208 JOE T. RITCHIE
TABLE 1. Hydraulic Conductivity K at -0.1 Bar Soil Matric Potential, Upper Limit of Stage 1 Cumu-
lative Evaporation U, and Calculated Coefficient a for (6) for Four Soil Types
, U, •g,
Soil cm day -• mm mm day -•' Reference
Adelanto clay loam 0.15 12 5.08 van Bayel et al. [1968]
Yolo loam 0.10 9 4.04 LaRue et al. [1968]
Houston black clay 0.06 6 3.50 Ritchie et al. [1972]
Plainfield sand 0.05 6 3.34 Black et al. [1969]
TABLE 2. Summary of Daily Tests of the Model to Estimate Evaporation from Grain Sorghum for a
37-day Period
1969 L,•i P Eo E, E•, E Em E- Em
April 27
April 28
April 29
April 30
May 1
May 2
May 3
May 4
May 5
May 6
May 7
May 8
May 9
May 10
May 11
May 12
May 13
May 14
May 15
May 16
May 17
May 18
May 19
May 20
May 21
May 22
May 23
May 24
May 25
May 26
May 27
May 28
May 29
May 30
May 31
June 1
June 2
0 03
0 o4
0 o5
0 06
0 07
0 o8
0 09
0 10
0 11
0 12
0 13
0 15
0 18
0 22
0 27
0 32
0 38
0 45
0 53
0 62
0 72
0 83
0 93
I 04
I 15
I 26
I 37
I 48
I 58
I 69
I 80
I 91
2 02
2 13
2 23
2 34
2 45
22.4
0
0
0
0
0
0.8
5.1
15.0
0
1.3
3.8
0
0
0
0
0
0
0.5
11.4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
70
56
37
44
44
27
22
53
22
20
29
70
64
64
37
43
48
40
22
3.4
46
6O
64
64
52
67
6.5
6.4
59
63
66
47
64
67
47
67
30
42
18
12
10
09
16
20
42
17
13
24
34
17
1 1
09
0.8
0.7
1.2
1.5
27
17
12
10
O9
O8
O7
O7
O6
O6
O6
O5
O5
O5
O5
O5
0.4
0
0
0
0
0
0
0
0
01
01
01
O2
06
O8
1.0
O7
10
12
12
O7
O7
2O
28
32
35
3O
41
42
43
41
46
5O
37
52
6O
4O
5.9
30
42
18
12
10
09
16
2O
43
18
I 4
26
4O
25
21
16
18
19
24
22
34
37
4O
42
44
38
48
49
49
47
52
55
42
57
65
45
63
37
46
16
11
10
11
10
11
38
1.4
14
24
37
24
24
11
16
21
19
09
29
34
41
44
46
39
53
51
47
48
52
58
41
61
57
41
61
-0.7
-0.4
0.2
0.1
0
-O.2
0.6
0.9
0.5
0.4
0
0.2
0.3
0.1
-0.3
0.5
0.2
-0.2
O5
13
O5
O3
-0 1
-02
-O.2
-0.1
-0.5
-O.2
0.2
-0.1
0
-0.3
0.1
-0.4
0.8
0.4
0.2
Values of Lai and P are given for each computation date during the 1969 grain sorghum growing season.
The values for P, Eo, Ea, E,,, E, E,,,, and E - E• are in millimeters per day.
Evaporation
equation given in the flow diagram (Figure 1)
at B is used to predict E8 on the day when the
cumulative evaporation is in transition between
stage I drying and stage 2 drying. On this day,
E8 = E,o until •]E,• = U; for the rest of the
day, E, = 0.6E, o.
Stage 2. During stage 2 drying, E8 from
below a canopy is assumed to be identical to
evaporation from a bare soil surface because
E, in this falling rate stage is more dependent
on the hydraulic properties of soil and less
dependent on the available energy. Black et al.
[1969] have shown by the solution o.f the flow
equation that cumulative evaporation in the
stage 2 drying of an initially wet, deep soil can
be expressed by the equation
= (6)
where a is dependent on the hydraulic prop-
erties of the soil. Values for • can b'e deter-
mined experimentally from cumulative evapo-
ration data for a single drying cycle. The E•
data for the four softs given in Figure 3 are
plotted in Figure 4 as a function of t •/•. The
U values given in Table 1 were subtracted
from the cumulative evaporation curves of Fig-
ure 3 to obtain the •E• values given in Figure
4. Time 0 for each curve in Figure 4 corre-
sponded to the time when the cumulative evap-
oration in Figure 3 reached the appropriate U
value. Calculated values of • for each soil are
1209
given in Table 1. In comparing soils, the mag-
nitude of the a values is approximately pro-
portional to the magnitude of the measured
values of the hydraulic conductivity of the soil
at --0.1 bar soil matric potential. This result
indicates that approximate values of a can
be obtained for deep soils from hydraulic con-
ductivity data without making direct measure-
ments of the cumulative evaporation during a
drying cycle.
Values of •E• for the days when drying
continues beyond U in stage 1 drying are ob-
tained as is shown in the flow diagram at B.
Rearranging (6) to obtain time as a function
of •E8 gives the following expression for the
beginning time to use in calculating •]E• with
(6)
t = (•". E,,./a)" (7)
For each subsequent day, the daily evaporation
rate is obtained from (6) by updating time,
calculating the new •E•.•, and subtracting the
previous day's •]E• value as given in the equa-
tion
t •/• ot(t 1) •/•
= - - (s)
At any point in stage 2 evaporation when
P > •]E•, the evaporation prediction branches
back into stage 1 as is shown at C in the flow
diagram.
Twice during stage 2 drying E8 as calculated
Fig. 4.
24 I I I I I I I I [
20 i /
• Adelanto ß •a½
,., e Yolo
= / .ou,,o /
4
0 • • I I I I I I I /
0 0.5 1.0 1.5 2.0 2.5 •.0 •.5 4.0 4.5
TIME •/• (days) •/•
•[age 2 cumulative •ofi ewpora[io• •E,• as te]a. ted [o [he squ•re •oo• of time for
four •fis.
1210 JOE T. RITCHIE
by (8) does not apply. The first time is when
P < •]Es.• as is shown in the flow diagram at D.
The water content of the soil near the
surface increases in proportion to P. The evap-
oration rate in this special case E, is first
approximated as equal to 0.8P. This relation
was obtained locally from bare soil lysimeter
evaporation measurements after small rains
(1-6 mm) that came when the surface soil was
relatively dry. There are two possibilities for
modifying the first approximation of Es•. If
Es• as calculated is less than or equal to Es
calculated from (8), Es• is equated to the pre-
dicted Es q- P, when P values are unusually
small. However, if P is rather large, so that
Es• > Eso, then E, is limited to Eso.
The second time in stage 2 drying when (8)
does not apply occurs when the predicted
Es > E so. Then Es is limited to E so as is shown
in the flow diagram at F.
A final step in calculating stage 2 evapora-
tion is shown at G in the flow diagram. An up-
dated value for •]Es2 is calculated, and the
time is adjusted if Es was determined where
(8) did not apply.
Ritchie andsBurnett [1971] have shown that,
when water movement to the plant roots is not
limited, the evaporation rate from developing
cotton and grain sorghum (Sorghum bicolor L.)
canopies E,in central Texas is related to Eo
and La, by
E,, = Eo(--0.21 + 0.70L,•i '/•) (9)
0.1 _< La,: <_ 2.7
1.0 r
.6
,Eo .4
i i . ! i
Ep/Eø : -'21' '70 Lo' l/'•
i
ß 4 .8 1.2 1.6 2.0 2.4
2.8
LEAF AREA INDEX
Fig. 5. The plant evaporation E• relative to the
potential evaporation Eo as influenced by La•
when the soil water is not limited [Ritchie and
Burnett, 1971].
In developing (9), Ritchie and Burnett used R,o
rather than a combination equation as an esti-
mate of Eo. This discrepancy is of little conse-
quence, however, since the normal temperature,
vapor pressure, and wind speed conditions exist-
ing (luring the growing season when the data
used in developing (9) were taken [Ritchie,
1971] combine in (1) to be approximately
equal to R,o. A plot of (9) expressing Ep as a
fraction of Eo versus L•, is given in Figure 5.
The nonlinearity of the relation between E, and the leaf area is the result of at least two
interacting factors' (1) less competition for
radiation per unit of leaf area during the initial
stages of plant growth and (2) the repartition-
ing of a large fraction of the net radiation at
the dry soil surface between plant rows to
sensible heat flux causing increased canopy
temperatures and consequently increased E,
This last influence may be considered as a
localized 'clothesline effect' in which the hot
air originating between plant rows becomes a
significant source of energy contributing to E•.
The upper limit of 2.7 for L•, in (9) was
reported by Ritchie and Burnett [1971] to be
an apparent threshold L•, representing the min-
imum L•, necessary to constitute an apparent
'full cover' canopy. For row crop canopies with
an La• greater than 2.7, E• becomes almost en-
tirely dependent on Eo until the soil water avail-
able to plant roots becomes limited. When
La• values are _<0.1, Ep is small compared
with Es and is considered negligible; therefore
E--Es.
Since (9) is empirical, its ability to be used
with other climates and crops remains in doubt.
There are indications, however, that it is approx-
imately correct from data of Monteith et al.
[1965] for barley in England and of Brun
et al. [1972] for soybeans and sorghum in
Kansas.
TEST OF MODEL
The model was tested during a part of the
1969 grain sorghum growing season when the
plant canopy was incomplete. Evaporation was
measured with a weighing lysimeter [Ritchie
and Burnett, 1968]. The test was conducted at
Temple, Texas (97ø21%V, 31ø03'N). The soil
at the experimental site is classified as Houston
black clay, a fine montmorillonitic clay in the
thermic family of Udic Pellusterts. Plants were
Evaporatio•
grown in 0.46-m rows with a population of
approximately 197,000 plants per hectare. The
date of plant emergence was April 10. The test-
ing period was April 27 to June 2. Periodically
through the season La, values were measured
with daily values being interpolated from
smoothed curves drawn through the data. Peri-
odic measurements of the leaf relative water
content and stomatal resistance indicated that
the soil water supply to plant roots was not
limited during the test period.
The model was used to compute daily Es, Ep,
and total E. The daily values of P, La,, and
used in the model are given in Table 2 with the
computed values of Es, Ep, and E. The daily
evaporation measurements E•, made with the
lysimeter and the deviation of E from E•, are
also given in Table 2.
The deviations of the calculated E from
in Table 2 show that the absolute error on most
days was less than 1 mmfday. The 1.3 mm
deviation from measured E on May 16 points
out a problem associated with the use of daily
precipitation in the model when Es is calcu-
lated in stage 2. It was assumed that the rain-
fall was received at the beginning of the day,
and therefore Es was calculated as if the surface
was freely evaporating for the entire day. How-
ever, the 22.4-mm precipitation received on May
16 did not begin to fall until about noon. Since
the soil was relatively dry before the. rainfall
was received, Es would be expected to be lower
than the value predicted by the model.
The total evaporation calculated for the test
period was 125.0 mm, which, compared with
measured water loss of 120.6 mm, is an excellent
agreement. The soil evaporation amounted to
41% of the total evaporation during the test
period. Before May 20 when L•, was less than
1.0, Es accounted for 7•5% of the total water
loss. For the rest of the test period, Es amounted
to only 13% of the total evaporation.
One limitation of some of the equations used
in the model is the apparent overprediction of E
on days when the canopy is in an advanced
stage of development and the soil surface is
wet. For example, consider a case in which the
average air temperature is 32øC, La, = 2.7,
R,•o = 5.0, Eo = 5.0, and Y..Es:,_ < U. Equa-
tion 5 predicts Eso = 1.2, and therefore Es =
1.2. Equation 9 predicts E• = 4.6, and thus
E = 5.8 or 0.8 > Eo. Even though in using
1211
the model one must set E -- Eo on any day
that the predicted E > Eo, there is a question
as to which component Es or E,, is in error. The
most likely source of error is the prediction of
Ep from (9). When (9) was developed in the
investigation of Ritchie aad Buraett [1971],
was limited most of the time by partially dry
surface soil. Consequently, the relation is likely
biased toward a more accurate prediction of Ep
when the soil surface is relatively dry. The
Rns is primarily repartitioned to Es when the
surface is wet and to sensible heat when the
surface is dry. Therefore, for a given
should be greater over a dry soil than over
a wet soil as a consequence of the ad-
ditional source of energy for Es. This result
emphasizes that E• is not completely indepen-
dent of Es.
Other sources of inaccuracy in the model are
the methods used to calculate Eo and Eso. The
use of daily averages for air temperature, vapor
pressure, and wind speed where, in principle,
instantaneous values are required decreases the
accuracy of Eo estimates. In spite of these and
other inaccuracies arising from some of the
empirical relations used, the method appears to
be a practical and useful procedure for obtain-
ing daily evaporation estimates for crops whose
cover is incomplete.
CONCLUSIONS
As the competition for water resources in-
creases, the need for more accurate prediction
of evapqration becomes evident, since evapora-
tion is a large component of the water balance.
This model, developed from several recent ex-
periments in which the evaporation rates of
annual row crops were accurately measured
under typical field conditions, offers possibil-
ities for the prediction of evaporation for a
wide variety of soil types and climatic condi-
tions. It takes into account the variation in
water use caused by different rainfall patterns
when a crop canopy is developing.
The inclusion of La, input restricts the
model's usefulness to cases in which L•, is
known or can be reasonably estimated. In the
future, one should be able to estimate L•,
reasonably with a separate model similar to
some presently being used to predict photo-
synthesis rates and thus eliminate La, as a
direct input.
1212 JOE T. RITCHIE
E,
ES0,
ESX,
Lai,
R•O ,
R•8 ,
RS,
t,
Td,
Th,
T•,
T•,
U,
NOTATION
total evaporation rate from soil and
plant surfaces, evapotranspiration, mil-
limeters per day;
evaporation rate measured with a
weighing lysimeter, millimeters per day;
potential evaporation rate above the
plant canopy, millimeters per day;
evaporation rate from plant leaves,
transpiration, millimeters per day;
evaporation rate from the soil surface,
millimeters per day;
potential evaporation rate below the
plant canopy at the soil surface, milli-
meters per day;
evaporation rate from the soil surface
during stage 2 evaporation on a day
when P • • E82, millimeters per day;
leaf area index, dimensionless;
rainfall or irrigation rate, millimeters per
day;
net radiation above the canopy (1
mm/day is equivalent to an energy flux
of 59 cal cm-'- day-•);
net radiation at the soil surface below
the canopy, millimeters per day;
solar radiation, millimeters per day;
time, days;
dry bulb temperature, øC;
maximum daily temperature, øC;
minimum daily temperature, øC;
wet bulb temperature, øC;
wind speed, kilometers per day;
upper limit of cumulative evaporation
from søil during stage 1 drying, milli-
meters;
cumulative evaporation from the soil
surface during stage 1, millimeters;
cumulative evaporation from the soil
surface during stage 2, millimeters.
Acknowledgments. I wish to express apprecia-
tion to Mr. Clarence W. Richardson, Agricultural
Engineer, USDA Soil and Water Conservation
Research Division, Agricultural Research Service,
Riesel, Texas, for assistance in programing and
testing this model. This paper is a contribution
from the USDA Soil and Water Conservation Re-
search Division, Agricultural Research Service and
the Texas Agricultural Experiment Station, Texas
A&M University.
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(Manuscript received November 12, 1971;
revised May 8, 1972.)
