Directory UMM :Data Elmu:jurnal:A:Agricultural Water Management:Vol43.Issue1.Feb2000:
Agricultural Water Management 43 (2000) 1±14
Estimation of maize evapotranspiration under
water deficits in a semiarid region
Kang Shaozhonga,b,*, Cai Huanjiea, Zhang Jianhuac
a
Institute of Agricultural Soil and Water Engineering, Northwest Agricultural University,
Yangling, Shaanxi, PR China
b
Institute of Soil and Water Conservation, Chinese Academy of Sciences
and Ministry of Water Resources, Yangling, Shaanxi, PR China
c
Department of Biology, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Accepted 18 June 1999
Abstract
A field study was conducted to investigate the response of leaf water potentials ( l) and stomatal
conductance (Cs) of maize crop to soil water availability, and to test and compare the soil water
adjustment coefficient (Ks) functions for estimation of actual evapotranspiration (ET) under water
deficits. The results showed that correlation coefficients of Ks to Cs and l peaked at 09:30 hours,
and then decreased, indicating that l and Cs at 09:30 hours were better predictors of plant water
status. The correlations of Ks to relative leaf water potential ( l/ lm) and relative leaf stomatal
conductance (Cs/Csm) were better than that of Ks to l and Cs directly. Kswas also significantly
related to soil water availability (Aw). Correlation with Ks was reduced in the following order: Cs/
Csm > Aw > l/ lm. The procedure was used that reference crop evapotranspiration (ET0) was
estimated by the modified Penman formula and with a crop coefficient (Kc) and different Ks
functions. The results showed that it was the best estimation with Ks function based on the relative
stomatal conductance, and at least in the case of maize that the soil water adjustment coefficient Ks
based on relative stomatal conductance Cs/Csm provided a means of predicting required adjustments
in ET estimation for different soil water status. # 2000 Elsevier Science B.V. All rights reserved.
Keywords: Evapotranspiration estimation; Water deficits; Stomatal conductance; Soil water adjustment
coefficient; Maize (Zea mays)
*
Corresponding author. Tel.: 86-910-7092942; fax: 86-910-7012559.
E-mail address: kangshaozhong@163.net (K. Shaozhong)
0378-3774/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 3 7 7 4 ( 9 9 ) 0 0 0 6 3 - 3
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
1. Introduction
Evapotranspiration is a very important parameter in irrigation management and is
usually estimated by a reference crop evapotranspiration (ET0), and crop coefficient
(Kc) as well as soil moisture adjustment coefficient (Ks) (Doorenbos and Pruitt, 1977;
Kang, 1986, 1992; Kerr et al., 1993). Reference crop evapotranspiration can be
estimated by many methods (Jensen, 1974; Hill et al., 1985; Kang et al., 1994), but
the most popular one is the Penman equation and the modified Penman formula
(Doorenbos and Pruitt, 1977). Crop coefficient changes with growing stages and can
be determined by dividing measured potential evapotranspiration with a reference crop
evapotranspiration. Soil moisture adjustment coefficient changes with soil water
availability and usually can be calculated by an empirical formula based on soil
moisture contents and matric potential or relative soil available water contents (Jensen
et al., 1970, 1971; Boonyathorobol and Walker, 1979; Wright, 1982; Kang, 1986).
Much work has been done to develop methods for estimating ET0 and Kc. The application of the popular method has been successful to many crops and locations. Also
several different versions of Ks were studied, and straight line, cosine, and logarithmic
functions, with and without threshold soil water depletion values, were used to provided
adjustments representing Ks versus soil water depletion curves with various slopes and
shapes (Kerr et al., 1993).
However, the soil moisture adjustment coefficient is mainly estimated by a relationship
to the average soil moisture contents or matric potential in a soil layer. Since water uptake
by roots is not the same in different soil layers, the treatment of the soil profile as a single
layer is inaccurate. Moreover, measurements of soil water status have been widely used
for calculating evapotranspiration. However, determination of soil water availability
requires numerous discrete spatial measurements and an integration of such measurements. The number of required measurements is particularly large under interval furrow
irrigation, wide-spaced furrow irrigation and drip irrigation, where two- or threedimensional gradients of water content exist. Furthermore, measurements across the
furrow or around many emitters are needed to average soil water contents in fields
because of spatial variability of soil hydraulic parameters.
Transpiration accounts about 60±70% of evapotranspiration (Kang et al., 1994), and is
related to leaf stomatal conductance and water potential. Leaf water potential is a better
indicator than soil moisture content or matric potential because plant water status is an
function of soil water availability, hydraulic resistance along the water flow, plant water
capacitance, and meteorological conditions that determine atmospheric evaporative
demand. Rapid changes in climatic conditions may cause abrupt changes in plant water
status. The required threshold level of available soil water for crop under variable
climatic conditions may change because of the nonsteady water flow in the soil±plantatmosphere continuum. The difficulties encountered in determining soil water availability
make it desirable to use plant water status as an additional tool for soil water adjustment
estimation. Predawn and midday leaf water potential, leaf stomatal conductance have
been found to be in correlation with soil water content and closely represent soil water
availability. In this study we have selected these parameters for estimation of soil water
adjustment coefficient.
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
The objectives of the present investigation therefore are to study the relations of leaf
water potentials and stomatal conductance to soil water availability in a maize field and to
test and compare the soil water adjustment coefficient functions for estimating actual ET
in conditions of variable soil moistures.
2. Materials and methods
2.1. Experimental site
The experiment was conducted in 20 lysimeters during 1988±1996 at the Irrigation
Experiment Station, Northwest Agricultural University, Yangling, Shaanxi, China, on a
loess loam soil. The soil field capacity was about 23.5%, and the bulk density was about
1.35 g/cm3. The experimental site was located at 348200 N, 1088240 E, in a semiarid zone,
521 m above sea level. Average annual rainfall is about 630 mm, and groundwater table
lower than 50 m beneath soil surface. The size of lysimeters is 3 m long, 2 m wide and
2 m deep. Mobile rainproof shelter above the lysimeters was installed to control soil
water status. Planting and all the other field managements in all lysimeters were the same.
2.2. Experimental treatments
Maize plants were planted, at density of 40 cm 20 cm apart. Four soil water
treatments were designed with five replicates using a randomized block design. Each
replicate consisted of 36 plants. Each treatment was controlled by a pre-designed lower
limit of soil water contents. When soil moisture contents in lysimeters dropped to the
lower limits, the lysimeters were irrigated to 90% of their field capacity. Total water
use was calculated on the measured soil layer, 45 cm deep in vegetative period and
60 cm in reproductive period. The lower limit of water content for each treatment is
shown in Table 1.
2.3. Measurements and statistical analysis
Soil water content was measured with Time-Domain-Reflectometry (TDR, Trase
system, Soil Moisture Equipment). Seven waveguides were installed in the center at each
Table 1
The lower limit of soil moisture contents in different treatmentsa
Treatments
Well watered
Mild water deficit
Inter-medium deficit
Severe water deficit
a
Growth stages
Seedling
Jointing
Grain-filling
Maturing
65
50±50
45±50
40±45
70
55±60
50±55
40±45
70
55±60
50±55
40±45
65
50±55
45±50
35±40
Soil moisture contents is the percent of field capacity (23.5% of dry soil weights) in the soil layer irrigated.
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
20 cm depth in the soil profile in different lysimeters, and measurements were taken once
every 5 days at 8:00 a.m. Three readings were obtained for a waveguide each time.
Readings at each lysimeter were averaged. The measured actual evapotranspiration in
each lysimeter was calculated by the water balance equation based on soil moisture
content measurements. Evapotranspiration changes over the growing season and the nine
years study as well as the variability of values are in Figs. 1 and 2.
Meteorological data were measured in a standard weather station located in the
experiment station. Parameters measured included air temperature, air humidity, wind
speed at 2 m above ground, rainfall and global radiation. Daily values of maximum and
minimum temperature, maximum vapor pressure deficit, and average wind speed were
Fig. 1. The average daily evapotranspiration rate over the maize growing season during 1988±1996. Error bars
denote standard error, and the labels 1, 2, 3, 4 express well watered, mild water deficit, inter-medium deficit and
severe water deficit treatments, respectively.
Fig. 2. The average total evapotranspiration in whole growing season of the five replicates during 1988±1996.
Labels (1, 2, 3, 4) inside figure express well watered, mild water deficit, inter-medium deficit and severe water
deficit treatments, respectively. Error bars indicate standard error.
K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
5
also recorded, a E601 evaporation pan (round with a diameter of 601 mm) as located at
the experiment station.
Leaf water potential was measured on fully expanded leaves facing the sun. Leaves
were detached, placed immediately in a plastic bag and inserted into a pressure chamber.
Measurement of leaf water potential at 09:30 hours was taken during several days in
growing season. Diurnal measurement of leaf water potential was taken on some special
days. Diurnal measurements started at 07:00 hours and ended at 19:00 hours. Before each
measurement of leaf water potential, stomatal conductance was measured using a
portable photosynthesis system (LI-6200, Li-Cor, USA). The same leaves were used for
stomatal conductance and leaf water potential measurements. Each time, measurements
were taken from the three plants of each replicate.
Data was analyzed for statistical significance using the general linear model (GLM)
procedure. Duncan's multiple range test was used to compare treatments.
2.4. Estimation of soil moisture adjustment coefficient
The actual evapotranspiration was calculated as follows:
ETa Ks Kc ET0
(1)
where Ks is the soil moisture adjustment coefficient, Kc is the crop coefficient, ET0 and
ETa are the reference crop evapotranspiration and actual evapotranspiration in soil water
deficit condition.
Doorenbos and Pruitt (1977) defined the reference crop evapotranspiration rate as `the
rate of evapotranspiration from an extensive surface of 8 to 15 cm tall, green grass cover
of uniform height, actively growing, completely shading the ground and not short of
water'. In an FAO manual, Doorenbos and Pruitt (1977) developed methods of estimating
reference crop evapotranspiration for a region using relationships involving the physical
parameters involved in the evapotranspiration process. The resulting procedures involve
using one of three equations: the Blaney±Criddle equation (Blaney and Criddle, 1950),
the radiation equation (Makkink, 1957), and the Penman equation (Penman, 1948), or a
fourth method that is based on pan evaporation information. When sufficient data are
available, Doorenbos and Pruitt (1977) recommended the use of the Penman equation
because it includes a great deal of the important meteorological parameters in the
relationship, and is likely to provide the best results. In addition, they suggested that a
modified Penman equation be used to determine ET0. The modified Penman equation that
involves a revised wind function term and an adjustment coefficient dependent upon the
day to night distribution of wind, maximum relative humidity, and daytime wind speed if
this additional information is available. ET0 was calculated using the Penman±Monteith
equation for ET as given by Allen et al. (1989), and it was the top ranked equation in a
comparison of 19 equations for estimating ET0 (Jensen et al., 1990). Kang et al. (1992)
and Chen et al. (1995) compared these methods based on the measured data at more
than 100 stations in China, and the results showed that the Penman equation gave
the best estimation, and the precision of the equation can be improved by an air
pressure correction in the weighting factor. Therefore, in this study ET0 can be
calculated according to the Penman formula, and an air pressure correction factor
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
included, as follows
ET0
ÿ
p
P0 =P D=
1ÿ QA a b n=N ÿTk4 0:56ÿ0:079 ea 0:1 0:9n=N 0:26 es ÿea 1 Cu2
P0 =P D=
1
(2)
in which P and P0 are air pressure and the standard air pressure at the sea level respectively;
is the slope of the saturation vapor pressure curve;
is the psychrometric constant; is
the reflection ratio of reference crop and usually equals to 0.25; QA is the extra terrestrial
radiation in equivalent evaporation units (mm/day); is a constant equal to 2.01 10ÿ9
when the extra terrestrial radiation QA and ET0 are in equivalent evaporation units (mm/
day); n and N are actual sunshine hours and potential sunshine hours, respectively; Tk is
air temperature (K); es and ea are the saturation vapor pressure at the current air
temperature and actual vapor pressure of the air; u2 is the wind speed at 2 m height; C is
the modification coefficient of wind speed; a and b are the empirical coefficients of net
radiation calculation based on the ratio of actual sunshine hours and potential sunshine
hours, 0.2048 and 0.4325, respectively, based on solar radiation measurements at Xian,
Shaanxi, China, which are significantly different from that reported by Doorenbos and
Pruitt (1977) and Abdulmumin and Misari (1990), suggesting regional difference.
More reports on crop coefficient estimates are becoming available (e.g. Doorenbos and
Pruitt, 1977; Pruitt et al., 1987; Snyder et al., 1987). Summaries of crop coefficients are
given for grass reference by Doorenbos and Kassam (1979) and for alfalfa reference by
Jensen et al. (1990). Crop coefficients may be varied with the regional condition. Kang et
al. (1992) estimated crop coefficients (Kc) for maize at 10 stations in Shaanxi Province,
and developed a crop coefficient curve was developed for the local growing season based
on calculated reference crop evapotranspiration and measured potential evapotranspiration during 1982±1990, when soil moisture was sufficient for crop's needs (at soil water
tensions up to 0.1 MPa). Kc values at the experiment station for every 10 days are given in
Table 2. The values in August were higher than that given by Doorenbos and Pruitt
(1977), but they are not significantly different from the results reported by Doorenbos and
Kassam (1979). It was possibly caused by the large leaf area index of maize in this period
and the large leaf transpiration as a result.
The value of the coefficient Ks is 1 unless soil water is depleted sufficiently to limit
evapotranspiration. Ks can be determined by rearranging Eq. (1) with the result
Ks
ETa
ETa
Kc ET0 ETp
(3)
Table 2
Average crop coefficients for every 10 days of a maize growing season during 1982±1990, based on calculated
reference crop evapotranspiration and measured potential evapotranspiration when soil moisture suction was less
than 0.1 MPa
Data (M/d)
Kc
June
July
August
September
5
15
25
5
15
25
5
15
25
5
15
25
0.4
0.51
0.69
0.87
1.05
1.18
1.30
1.43
1.38
1.33
1.28
1.23
K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
7
Fig. 3. The average soil water adjustment coefficient Ks over the maize growing season during 1988±1996.
Error bars denote standard error, and the labels 1, 2, 3, 4 express well watered, mild water deficit, inter-medium
deficit and severe water deficit treatments, respectively.
where ETp is the potential evapotranspiration when soil moisture, at soil water tensions
less than 0.1 MPa, is sufficient for maize's needs.
Ks is a dimensionless coefficient dependent on available soil water and crop rooting
characteristics, and is under increasing soil moisture depletion characterized by two
distinct phases: an energy limiting phase where Ks 1.0 and a soil moisture stress phase
where Ks decreases with decreasing soil moisture. The critical value where soil moisture
stress occurs has been reported (e.g. Doorenbos and Pruitt, 1977; Doorenbos and Kassam,
1979; Robinson and Hubbard, 1990). Doorenbos and Pruitt (1977) considered that the
critical value is at soil water tensions up to one atmosphere pressure corresponding
approximately to 30 vol.% of available soil water for clay, 40 vol.% for loam, 50 vol.%
for sandy and 60 vol.% for loamy sand. Robinson and Hubbard (1990) found the
threshold was 60% soil water depletion for several crops in the High Plains Region. We
analysed the critical value and it was found that it was about 0.1 MPa in maize growing
season in our region. Therefore we calculated the values of Ks under different soil water
treatments during 1986±1994. The average values over the growing season in the 9-year
study are shown in Fig. 3. We compared the different versions of Ks and found that the
logarithmic function was more suitable in our region.
For different soil moisture treatments, Ks in different stages can be obtained by Eq. (3).
Moreover, it can be estimated from the relationships of Ks to soil moisture availability,
leaf conductance and leaf water potential.
3. Results and discussion
3.1. Diurnal changes of leaf water potential and stomatal conductance
Figs. 4 and 5 show the diurnal changes of leaf water potential and stomatal
conductance for two soil moisture treatments. Stomatal conductance (Cs) of well watered
treatment was higher than that of the severe deficit treatment (3) throughout the day
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Fig. 4. Diurnal measurements on 6 August 1990 of leaf stomatal conductance of maize plants with sufficient
water supply (*) and soil water deficit (&). The average soil water contents in 100 cm layer were 19.97 and
14.1% for these two soil water treatments, respectively. Error bars denote standard error.
Fig. 5. Diurnal measurements on 6 August 1990 of leaf water potential of maize plants with sufficient water
supply (*) and soil water deficit (&). The average soil water contents in 100 cm layer were 19.97 and 14.1%
for these two soil water treatments, respectively. Error bars denote standard error.
(Fig. 4). However, diurnal leaf water potential ( l) measurements showed that both had a
similar leaf water potential at the midday time (Fig. 5). The Cs of both treatments peaked
at 09:30 hours and then decreased. The decline of Cs in the well watered treatment may
indicate that some stress existed even in soil with high moisture contents because of the
hot and dry weather. These findings are in agreement with other reports (Denmead and
Millar, 1976; Jarvis, 1976; Liang et al., 1995), that Cs and l at 09:30 hours are two better
indicators of plant water status and can respond to the changes in soil moisture
availability.
The correlation coefficient between Ks and Cs, l, was calculated for different hours in
a day and showed its peak at 09:30 hours with some decline at the afternoon (Table 3).
This might be related to the non-steady flow of water in the soil toward plant roots. Such
non-steady water flow may reduce the uniformity in soil water contents or matric
potential at the root zone and the degree of which buck soil water contents represents the
soil water availability.
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Table 3
Coefficient of determination (r2) and significance level (p) for the correlation between Ks and leaf stomatal
conductance (Cs), leaf water potential ( l) at different hours in August 1991a
Indicators
Coefficients
2
Cs
r
p
r2
p
l
Local time (hours)
07:30
09:30
11:30
14:00
15:30
0.6203
0.02
0.5037
0.05
0.7053
0.001
0.6154
0.02
0.6815
0.01
0.5918
0.02
0.6504
0.02
0.4801
0.05
0.6318
0.02
0.4125
0.100
a
The results based on the 5 time measurements in August 1991 for different soil water deficits treatments,
the parameters are averaged over 5 days.
3.2. Comparison of the relationships of Ks to soil water availability, Cs and y1
According to our earlier research (Kang, 1986), the correlation coefficient of Ks and
relative soil water availability (Aw) is higher than that of Ks to soil water contents directly.
Aw was calculated as
Aw
a ÿwp
f ÿwp
in which a is the average soil water contents in the layer for water balance estimation,
and f is the field capacity, wp is the soil water contents at the wilting point. As the
correlation coefficients between Ks and Cs, l were not very high (Table 3), if the
empirical function of Ks and l, Cs are used directly for estimating ET, there would be
great errors because of the great changes of stomatal conductance and leaf water potential
in different meteorological conditions. Thus the relationships of Ks to relative stomatal
conductance Cs/Csm and relative leaf water potential l/ lm, were plotted according to the
experimental data in 1988±1992 for improving ET estimation, l and Cs were the average
values of leaf water potential and stomatal conductance in this period under soil water
deficit conditions, and lm and Csm were the average values for well watered condition at
the same period. The results showed that Ks was highly correlated (r2 0.9047,
significance at P 0.001) with the average relative stomatal conductance Cs/Csm
measured at 09:30 hours (Fig. 6) and the correlation coefficient of Ks with Cs/Csm is
higher than that of Ks with relative soil water availability (Aw) and relative leaf water
potential ( l/ lm) (Figs. 7 and 8).
Table 4 compares the degree of correlation between Ks and these water status
indicators and gives the best-fit curves. It should be noted that the location of the TDR
sensors in the soil is usually determined arbitrarily. Therefore, with similar plant water
status, the value of soil water contents can differ in response to different soil hydraulic
properties and root distribution. As hydraulic properties and root distribution are difficult
to be determined in the field, Cs/Csm may have an advantage over the use of soil water
contents or matric potential as an indicator for estimating Ks.
The high correlation between Ks and Cs/Csm may be explained by the control of Cs by
root signals which are known to be affected by soil moisture (Davies and Zhang, 1991).
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Fig. 6. The relationship of soil water adjustment coefficient (Ks) to relative leaf stomatal conductance (Cs/Csm),
Cs and Csm are the stomatal conductance in deficient water supply and deficit water treatments, respectively.
Fig. 7. The relationship of soil water adjustment coefficient (Ks) to relative soil water availability (Aw).
Aw([(a ÿ wp)/(f ÿ wp)]) is considered as the indicator of relative soil water availability, in which a is average
soil water contents in the layer for water balance estimation, and f is field capacity, wp is soil water contents at
the wilting point.
Table 4
Empirical equation of Ks as a function of relative soil moisture availability (Aw), relative stomatal conductance
(Cs/Csm), relative leaf water potential ( l/ lm)a
Indicators
Empirical equation
Coefficient of correlation R2
Significance level
Aw
Cs/Csm
l/ lm
Ks 0.5716 ln(Aw) 0.9859
Ks 0.9149Cs/Csm 0.0712
Ks ÿ0.7615 ln( l/ lm) 0.9193
0.7230
0.9047
0.6850
0.01
0.001
0.02
a
The results based on the measured data during 1988±1992, the empirical equations were obtained by Eq.
(3) calculating Ks based on every 10 days potential evapotranspiration when soil water suction was less than
0.1 MPa, and measured actual maize evapotranspiration under soil water deficits, with the measured soil water
content, stomatal conductance and leaf water potential in the corresponding periods.
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Fig. 8. The relationship of soil water adjustment coefficient to relative leaf water potential ( l/
are the leaf water potential in deficit water supply and sufficient water treatment, respectively.
lm),
l
and
lm
The lower correlation between Ks and l/ lm has been shown by several studies in the
past 15 years (Bates and Hall, 1982; Gollan et al., 1985; Naor and Wample, 1994; Naor
et al., 1995) and suggests that stomatal conductance is better correlated with soil water
potential or soil water availability than leaf water potential. The result that correlation of
Ks to Aw is lower than that of Ks to Cs/Csm is probably due to the spatial variability of the
soil water contents and hydraulic properties under a same soil moisture treatment
(Warrick and Nielsen, 1980).
3.3. Estimated maize evapotranspiration using various Ks functions
Reference crop evapotranspiration (ET0) was estimated using Eq. (2) with input data
for periods when the soil water measurement data were obtained. The potential maize
evapotranspiration (ETp), estimated as a product of ET0 and the appropriate crop
coefficients (Kc) shown in Table 2, were then adjusted using three kinds of soil water
adjustment coefficients based on the above discussed field measurements, i.e. the soil
water contents, leaf water potential and stomatal conductance during 1988±1992. A
maximum soil water adjustment coefficient Ks, i.e. Ks 1.0, was also used for
comparison. These estimations were performed to test the applicability of these soil water
adjustment coefficients for the actual evapotranspiration (ETa) estimation under different
soil water status, and to compare the errors of ETa estimation with and without the soil
water adjustment coefficient. The measured ETa in the whole growing season was
calculated by a sum of evapotranspiration in the calculation period. Estimated and
measured ET values were compared for monthly values during 1993±1996 in Table 5.
The comparison of estimated and measured actual ET in whole growing season with
different soil water deficits was also conducted during 1993±1996. The results are shown
in Table 6. The various Ks functions have been ranked from best to worst performance
based on the average relative errors and the standard errors of estimate, with low values
associated with the Ks function based on the relative stomatal conductance. If the soil
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Table 5
The average relative errors as a percent of the estimated monthly actual ET during 1993±1996 with different soil
water adjustment functiona
Ks
Mild water deficit
Inter-medium deficit
Severe water deficit
Cs/Csm
Aw
l/ lm
1.0
14.48
19.36
22.95
25.36
17.92
21.81
26.77
30.18
15.59
23.04
29.21
34.59
a
Relative errorPis equal to [(estimated ET ÿ measured ET)/measured ET] 100%, and the average relative
error is equal to relative error2i = nÿ11=2 , n is the number of samples, the soil water contents ranges of
different deficit treatments were same as Table 1.
Table 6
Standard errors for the estimation of the total ET in the whole growing season with different soil water
adjustment coefficients (Ks)a
Ks
Deficit treatment 1
Cs/Csm
Aw
l/ lm
1.0
Deficit treatment 2
Deficit treatment 3
Average
measured
ET (mm)
SEE
(mm)
Average
measured
ET (mm)
SEE
(mm)
Average
measured
ET (mm)
SEE
(mm)
442.72
442.72
442.72
442.72
21.87
28.34
43.69
98.42
363.50
363.50
363.50
363.50
18.49
23.66
48.71
92.53
301.48
301.48
301.48
301.48
#1=2
20.04
35.47
50.82
98.22
a
Standard errors (SEE) were calculated as
number of samples.
"
n
X
iÿ1
Estimated ET-Measured ET2i = n
, where n is the
water adjustment was not considered, the estimation of ET could have greater error in
conditions of variable soil moistures. The results obtained herein indicate that at least in
the case of summer maize, the soil water adjustment coefficient Ks based on relative
stomatal conductance Cs/Csm, provides a means to predict required adjustments in ET
estimates for different soil water status.
4. Conclusions
Results of this study show that the correlations of soil water adjustment coefficient (Ks)
to relative leaf water potential ( l/ lm), relative leaf stomatal conductance (Cs/Csm) and
relative soil water availability (Aw), was reduced in the following order: Cs/Csm > Aw > l/
lm, and that the actual evapotranspiration (ET) estimation under water deficits in the
semiarid region, based on reference crop evapotranspiration (ET0) by the modified
Penman formula and with a crop coefficient (Kc) and a suitable soil water adjustment
coefficient Ks functions, gave the satisfactory results when compared with field observations. The best estimation of Ks function is based on the relative stomatal conductance
K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
13
Cs/Csm, and at least in the case of maize that it provided a means of predicting required
adjustments in ET estimation for different soil water status. In practice, the stomatal
conductance can be measured by the porometer, and also the equation to predict leaf
stomatal conductance in this procedure may be established in the future.
Acknowledgements
KS is supported by National Excellent Young Scientist Fund, P.R. China.
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irrigation in China. Chinese Hydraulic and Hydro-power Press, 376 p.
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68, 305±311.
Doorenbos, J., Pruitt, W.O., 1977. Crop water requirement. Food and Agricultural Organization of the United
Nations. FAO Irrigation and Drainage Paper 24, revised 1977, Rome, 144 p.
Doorenbos, J., Kassam, A.H., 1979. Yield response to water. Food and Agriculture Organization of the United
Nations. FAO Irrigation and Drainage Paper 33, revised 1986, Rome, 193 p.
Gollan, T., Turner, N.C., Schulze, E.D., 1985. The response of stomata and leaf gas exchange to vapor pressure
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Stn. Rep. 99, Utah State University, Logan, Utah, 198 p.
Jarvis, P.G., 1976. The interpretation of the variations in leaf water potential and stomatal conductance found in
canopies in the field. Philos. Trans. R. Soc. London Ser. B. 273, 593±610.
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Eng., New York.
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Drain. Div. ASCE 96, 25±28.
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Trans. ASCE 14, 954±959.
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Eng., New York.
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manual prepared by the committee on irrigation and drainage division of the American Society of Civil
Engineers. ASCE, New York, 332 p.
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Kang, S.Z., 1986. Calculation and prediction of actual winter wheat evapotranspiration in condition of soil water
deficit (in Chinese). Acta Univ. Agric. Boreali-Occidentalis 14(1), 93±102.
Kang, S.Z., He, Z.Z., Zhang, X., 1992. Crop water requirement and irrigation models in Shaanxi Province.
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application. Chinese Hydraulic and Hydro-power Press, Beijing, 228 p.
Kerr, G., Pochop, L., Fornstrom, K.J., Krall, J.M., Brown, D., 1993. Soil water and ET estimates for a wide range
of rainfed and irrigated conditions. Agric. Water Management 24, 147±159.
Liang, Z.S., Kang, S.Z., Li, X.Y., 1995. The effect of limited water supply on the yield and water use efficiency
of summer corn. Acta Bot. Boreal.-Occident. Sin. 15(1), 26±31.
Makkink, G.F., 1957. Testing the Penman formula by means of lysimeters. J. Inst. Water Eng. 11, 277±288.
Naor, A., Klein, I., Doron, I., 1995. Stem water potential and apple size. J. Am. Soc. Hort. Sci. 120(4), 577±582.
Naor, A., Wample, R.L., 1994. Gas exchange and water relations of field-grown concord (vitis labruscana
bailey) grapevines. Am. J. Enol. Vitic. 45(3), 333±337.
Penman, H.L., 1948. Natural evaporation from open water, bare soil, bare soil and grass. Proc. R. Soc. London
Ser. A 193, 120±146.
Pruitt, W.O., Fereres, E., Kaita, K., Snyder, R.L., 1987. Reference evapotranspiration (ET0) for California, Agr.
Exp. Sta. Bull. 1922, University Of California. 16 p. and 12 maps.
Robinson, J.M., Hubbard, K.G., 1990. Soil water assessment model for several crops in the High Plains. Agron.
J. 82, 1141±1148.
Snyder, R.L., Lanini, B.J., Shaw, D.A., Pruitt, W.O., 1987. University Of California. Div. of Agric. and Natural
Resour. Leaflet 21427, 12.
Warrick, A.W., Nielsen, D.R., 1980. Spatial variability of soil physical properties in the field. In: Hillel, D. (Ed.),
Applications of Soil Physics, Academic Press, New York, p. 319±344.
Wright, J.L., 1982. New evapotranspiration crop coefficients. J. Irrig. Drain. Div. ASCE 108, 57±74.
Estimation of maize evapotranspiration under
water deficits in a semiarid region
Kang Shaozhonga,b,*, Cai Huanjiea, Zhang Jianhuac
a
Institute of Agricultural Soil and Water Engineering, Northwest Agricultural University,
Yangling, Shaanxi, PR China
b
Institute of Soil and Water Conservation, Chinese Academy of Sciences
and Ministry of Water Resources, Yangling, Shaanxi, PR China
c
Department of Biology, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Accepted 18 June 1999
Abstract
A field study was conducted to investigate the response of leaf water potentials ( l) and stomatal
conductance (Cs) of maize crop to soil water availability, and to test and compare the soil water
adjustment coefficient (Ks) functions for estimation of actual evapotranspiration (ET) under water
deficits. The results showed that correlation coefficients of Ks to Cs and l peaked at 09:30 hours,
and then decreased, indicating that l and Cs at 09:30 hours were better predictors of plant water
status. The correlations of Ks to relative leaf water potential ( l/ lm) and relative leaf stomatal
conductance (Cs/Csm) were better than that of Ks to l and Cs directly. Kswas also significantly
related to soil water availability (Aw). Correlation with Ks was reduced in the following order: Cs/
Csm > Aw > l/ lm. The procedure was used that reference crop evapotranspiration (ET0) was
estimated by the modified Penman formula and with a crop coefficient (Kc) and different Ks
functions. The results showed that it was the best estimation with Ks function based on the relative
stomatal conductance, and at least in the case of maize that the soil water adjustment coefficient Ks
based on relative stomatal conductance Cs/Csm provided a means of predicting required adjustments
in ET estimation for different soil water status. # 2000 Elsevier Science B.V. All rights reserved.
Keywords: Evapotranspiration estimation; Water deficits; Stomatal conductance; Soil water adjustment
coefficient; Maize (Zea mays)
*
Corresponding author. Tel.: 86-910-7092942; fax: 86-910-7012559.
E-mail address: kangshaozhong@163.net (K. Shaozhong)
0378-3774/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 3 7 7 4 ( 9 9 ) 0 0 0 6 3 - 3
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
1. Introduction
Evapotranspiration is a very important parameter in irrigation management and is
usually estimated by a reference crop evapotranspiration (ET0), and crop coefficient
(Kc) as well as soil moisture adjustment coefficient (Ks) (Doorenbos and Pruitt, 1977;
Kang, 1986, 1992; Kerr et al., 1993). Reference crop evapotranspiration can be
estimated by many methods (Jensen, 1974; Hill et al., 1985; Kang et al., 1994), but
the most popular one is the Penman equation and the modified Penman formula
(Doorenbos and Pruitt, 1977). Crop coefficient changes with growing stages and can
be determined by dividing measured potential evapotranspiration with a reference crop
evapotranspiration. Soil moisture adjustment coefficient changes with soil water
availability and usually can be calculated by an empirical formula based on soil
moisture contents and matric potential or relative soil available water contents (Jensen
et al., 1970, 1971; Boonyathorobol and Walker, 1979; Wright, 1982; Kang, 1986).
Much work has been done to develop methods for estimating ET0 and Kc. The application of the popular method has been successful to many crops and locations. Also
several different versions of Ks were studied, and straight line, cosine, and logarithmic
functions, with and without threshold soil water depletion values, were used to provided
adjustments representing Ks versus soil water depletion curves with various slopes and
shapes (Kerr et al., 1993).
However, the soil moisture adjustment coefficient is mainly estimated by a relationship
to the average soil moisture contents or matric potential in a soil layer. Since water uptake
by roots is not the same in different soil layers, the treatment of the soil profile as a single
layer is inaccurate. Moreover, measurements of soil water status have been widely used
for calculating evapotranspiration. However, determination of soil water availability
requires numerous discrete spatial measurements and an integration of such measurements. The number of required measurements is particularly large under interval furrow
irrigation, wide-spaced furrow irrigation and drip irrigation, where two- or threedimensional gradients of water content exist. Furthermore, measurements across the
furrow or around many emitters are needed to average soil water contents in fields
because of spatial variability of soil hydraulic parameters.
Transpiration accounts about 60±70% of evapotranspiration (Kang et al., 1994), and is
related to leaf stomatal conductance and water potential. Leaf water potential is a better
indicator than soil moisture content or matric potential because plant water status is an
function of soil water availability, hydraulic resistance along the water flow, plant water
capacitance, and meteorological conditions that determine atmospheric evaporative
demand. Rapid changes in climatic conditions may cause abrupt changes in plant water
status. The required threshold level of available soil water for crop under variable
climatic conditions may change because of the nonsteady water flow in the soil±plantatmosphere continuum. The difficulties encountered in determining soil water availability
make it desirable to use plant water status as an additional tool for soil water adjustment
estimation. Predawn and midday leaf water potential, leaf stomatal conductance have
been found to be in correlation with soil water content and closely represent soil water
availability. In this study we have selected these parameters for estimation of soil water
adjustment coefficient.
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
The objectives of the present investigation therefore are to study the relations of leaf
water potentials and stomatal conductance to soil water availability in a maize field and to
test and compare the soil water adjustment coefficient functions for estimating actual ET
in conditions of variable soil moistures.
2. Materials and methods
2.1. Experimental site
The experiment was conducted in 20 lysimeters during 1988±1996 at the Irrigation
Experiment Station, Northwest Agricultural University, Yangling, Shaanxi, China, on a
loess loam soil. The soil field capacity was about 23.5%, and the bulk density was about
1.35 g/cm3. The experimental site was located at 348200 N, 1088240 E, in a semiarid zone,
521 m above sea level. Average annual rainfall is about 630 mm, and groundwater table
lower than 50 m beneath soil surface. The size of lysimeters is 3 m long, 2 m wide and
2 m deep. Mobile rainproof shelter above the lysimeters was installed to control soil
water status. Planting and all the other field managements in all lysimeters were the same.
2.2. Experimental treatments
Maize plants were planted, at density of 40 cm 20 cm apart. Four soil water
treatments were designed with five replicates using a randomized block design. Each
replicate consisted of 36 plants. Each treatment was controlled by a pre-designed lower
limit of soil water contents. When soil moisture contents in lysimeters dropped to the
lower limits, the lysimeters were irrigated to 90% of their field capacity. Total water
use was calculated on the measured soil layer, 45 cm deep in vegetative period and
60 cm in reproductive period. The lower limit of water content for each treatment is
shown in Table 1.
2.3. Measurements and statistical analysis
Soil water content was measured with Time-Domain-Reflectometry (TDR, Trase
system, Soil Moisture Equipment). Seven waveguides were installed in the center at each
Table 1
The lower limit of soil moisture contents in different treatmentsa
Treatments
Well watered
Mild water deficit
Inter-medium deficit
Severe water deficit
a
Growth stages
Seedling
Jointing
Grain-filling
Maturing
65
50±50
45±50
40±45
70
55±60
50±55
40±45
70
55±60
50±55
40±45
65
50±55
45±50
35±40
Soil moisture contents is the percent of field capacity (23.5% of dry soil weights) in the soil layer irrigated.
4
K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
20 cm depth in the soil profile in different lysimeters, and measurements were taken once
every 5 days at 8:00 a.m. Three readings were obtained for a waveguide each time.
Readings at each lysimeter were averaged. The measured actual evapotranspiration in
each lysimeter was calculated by the water balance equation based on soil moisture
content measurements. Evapotranspiration changes over the growing season and the nine
years study as well as the variability of values are in Figs. 1 and 2.
Meteorological data were measured in a standard weather station located in the
experiment station. Parameters measured included air temperature, air humidity, wind
speed at 2 m above ground, rainfall and global radiation. Daily values of maximum and
minimum temperature, maximum vapor pressure deficit, and average wind speed were
Fig. 1. The average daily evapotranspiration rate over the maize growing season during 1988±1996. Error bars
denote standard error, and the labels 1, 2, 3, 4 express well watered, mild water deficit, inter-medium deficit and
severe water deficit treatments, respectively.
Fig. 2. The average total evapotranspiration in whole growing season of the five replicates during 1988±1996.
Labels (1, 2, 3, 4) inside figure express well watered, mild water deficit, inter-medium deficit and severe water
deficit treatments, respectively. Error bars indicate standard error.
K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
5
also recorded, a E601 evaporation pan (round with a diameter of 601 mm) as located at
the experiment station.
Leaf water potential was measured on fully expanded leaves facing the sun. Leaves
were detached, placed immediately in a plastic bag and inserted into a pressure chamber.
Measurement of leaf water potential at 09:30 hours was taken during several days in
growing season. Diurnal measurement of leaf water potential was taken on some special
days. Diurnal measurements started at 07:00 hours and ended at 19:00 hours. Before each
measurement of leaf water potential, stomatal conductance was measured using a
portable photosynthesis system (LI-6200, Li-Cor, USA). The same leaves were used for
stomatal conductance and leaf water potential measurements. Each time, measurements
were taken from the three plants of each replicate.
Data was analyzed for statistical significance using the general linear model (GLM)
procedure. Duncan's multiple range test was used to compare treatments.
2.4. Estimation of soil moisture adjustment coefficient
The actual evapotranspiration was calculated as follows:
ETa Ks Kc ET0
(1)
where Ks is the soil moisture adjustment coefficient, Kc is the crop coefficient, ET0 and
ETa are the reference crop evapotranspiration and actual evapotranspiration in soil water
deficit condition.
Doorenbos and Pruitt (1977) defined the reference crop evapotranspiration rate as `the
rate of evapotranspiration from an extensive surface of 8 to 15 cm tall, green grass cover
of uniform height, actively growing, completely shading the ground and not short of
water'. In an FAO manual, Doorenbos and Pruitt (1977) developed methods of estimating
reference crop evapotranspiration for a region using relationships involving the physical
parameters involved in the evapotranspiration process. The resulting procedures involve
using one of three equations: the Blaney±Criddle equation (Blaney and Criddle, 1950),
the radiation equation (Makkink, 1957), and the Penman equation (Penman, 1948), or a
fourth method that is based on pan evaporation information. When sufficient data are
available, Doorenbos and Pruitt (1977) recommended the use of the Penman equation
because it includes a great deal of the important meteorological parameters in the
relationship, and is likely to provide the best results. In addition, they suggested that a
modified Penman equation be used to determine ET0. The modified Penman equation that
involves a revised wind function term and an adjustment coefficient dependent upon the
day to night distribution of wind, maximum relative humidity, and daytime wind speed if
this additional information is available. ET0 was calculated using the Penman±Monteith
equation for ET as given by Allen et al. (1989), and it was the top ranked equation in a
comparison of 19 equations for estimating ET0 (Jensen et al., 1990). Kang et al. (1992)
and Chen et al. (1995) compared these methods based on the measured data at more
than 100 stations in China, and the results showed that the Penman equation gave
the best estimation, and the precision of the equation can be improved by an air
pressure correction in the weighting factor. Therefore, in this study ET0 can be
calculated according to the Penman formula, and an air pressure correction factor
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
included, as follows
ET0
ÿ
p
P0 =P D=
1ÿ QA a b n=N ÿTk4 0:56ÿ0:079 ea 0:1 0:9n=N 0:26 es ÿea 1 Cu2
P0 =P D=
1
(2)
in which P and P0 are air pressure and the standard air pressure at the sea level respectively;
is the slope of the saturation vapor pressure curve;
is the psychrometric constant; is
the reflection ratio of reference crop and usually equals to 0.25; QA is the extra terrestrial
radiation in equivalent evaporation units (mm/day); is a constant equal to 2.01 10ÿ9
when the extra terrestrial radiation QA and ET0 are in equivalent evaporation units (mm/
day); n and N are actual sunshine hours and potential sunshine hours, respectively; Tk is
air temperature (K); es and ea are the saturation vapor pressure at the current air
temperature and actual vapor pressure of the air; u2 is the wind speed at 2 m height; C is
the modification coefficient of wind speed; a and b are the empirical coefficients of net
radiation calculation based on the ratio of actual sunshine hours and potential sunshine
hours, 0.2048 and 0.4325, respectively, based on solar radiation measurements at Xian,
Shaanxi, China, which are significantly different from that reported by Doorenbos and
Pruitt (1977) and Abdulmumin and Misari (1990), suggesting regional difference.
More reports on crop coefficient estimates are becoming available (e.g. Doorenbos and
Pruitt, 1977; Pruitt et al., 1987; Snyder et al., 1987). Summaries of crop coefficients are
given for grass reference by Doorenbos and Kassam (1979) and for alfalfa reference by
Jensen et al. (1990). Crop coefficients may be varied with the regional condition. Kang et
al. (1992) estimated crop coefficients (Kc) for maize at 10 stations in Shaanxi Province,
and developed a crop coefficient curve was developed for the local growing season based
on calculated reference crop evapotranspiration and measured potential evapotranspiration during 1982±1990, when soil moisture was sufficient for crop's needs (at soil water
tensions up to 0.1 MPa). Kc values at the experiment station for every 10 days are given in
Table 2. The values in August were higher than that given by Doorenbos and Pruitt
(1977), but they are not significantly different from the results reported by Doorenbos and
Kassam (1979). It was possibly caused by the large leaf area index of maize in this period
and the large leaf transpiration as a result.
The value of the coefficient Ks is 1 unless soil water is depleted sufficiently to limit
evapotranspiration. Ks can be determined by rearranging Eq. (1) with the result
Ks
ETa
ETa
Kc ET0 ETp
(3)
Table 2
Average crop coefficients for every 10 days of a maize growing season during 1982±1990, based on calculated
reference crop evapotranspiration and measured potential evapotranspiration when soil moisture suction was less
than 0.1 MPa
Data (M/d)
Kc
June
July
August
September
5
15
25
5
15
25
5
15
25
5
15
25
0.4
0.51
0.69
0.87
1.05
1.18
1.30
1.43
1.38
1.33
1.28
1.23
K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
7
Fig. 3. The average soil water adjustment coefficient Ks over the maize growing season during 1988±1996.
Error bars denote standard error, and the labels 1, 2, 3, 4 express well watered, mild water deficit, inter-medium
deficit and severe water deficit treatments, respectively.
where ETp is the potential evapotranspiration when soil moisture, at soil water tensions
less than 0.1 MPa, is sufficient for maize's needs.
Ks is a dimensionless coefficient dependent on available soil water and crop rooting
characteristics, and is under increasing soil moisture depletion characterized by two
distinct phases: an energy limiting phase where Ks 1.0 and a soil moisture stress phase
where Ks decreases with decreasing soil moisture. The critical value where soil moisture
stress occurs has been reported (e.g. Doorenbos and Pruitt, 1977; Doorenbos and Kassam,
1979; Robinson and Hubbard, 1990). Doorenbos and Pruitt (1977) considered that the
critical value is at soil water tensions up to one atmosphere pressure corresponding
approximately to 30 vol.% of available soil water for clay, 40 vol.% for loam, 50 vol.%
for sandy and 60 vol.% for loamy sand. Robinson and Hubbard (1990) found the
threshold was 60% soil water depletion for several crops in the High Plains Region. We
analysed the critical value and it was found that it was about 0.1 MPa in maize growing
season in our region. Therefore we calculated the values of Ks under different soil water
treatments during 1986±1994. The average values over the growing season in the 9-year
study are shown in Fig. 3. We compared the different versions of Ks and found that the
logarithmic function was more suitable in our region.
For different soil moisture treatments, Ks in different stages can be obtained by Eq. (3).
Moreover, it can be estimated from the relationships of Ks to soil moisture availability,
leaf conductance and leaf water potential.
3. Results and discussion
3.1. Diurnal changes of leaf water potential and stomatal conductance
Figs. 4 and 5 show the diurnal changes of leaf water potential and stomatal
conductance for two soil moisture treatments. Stomatal conductance (Cs) of well watered
treatment was higher than that of the severe deficit treatment (3) throughout the day
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Fig. 4. Diurnal measurements on 6 August 1990 of leaf stomatal conductance of maize plants with sufficient
water supply (*) and soil water deficit (&). The average soil water contents in 100 cm layer were 19.97 and
14.1% for these two soil water treatments, respectively. Error bars denote standard error.
Fig. 5. Diurnal measurements on 6 August 1990 of leaf water potential of maize plants with sufficient water
supply (*) and soil water deficit (&). The average soil water contents in 100 cm layer were 19.97 and 14.1%
for these two soil water treatments, respectively. Error bars denote standard error.
(Fig. 4). However, diurnal leaf water potential ( l) measurements showed that both had a
similar leaf water potential at the midday time (Fig. 5). The Cs of both treatments peaked
at 09:30 hours and then decreased. The decline of Cs in the well watered treatment may
indicate that some stress existed even in soil with high moisture contents because of the
hot and dry weather. These findings are in agreement with other reports (Denmead and
Millar, 1976; Jarvis, 1976; Liang et al., 1995), that Cs and l at 09:30 hours are two better
indicators of plant water status and can respond to the changes in soil moisture
availability.
The correlation coefficient between Ks and Cs, l, was calculated for different hours in
a day and showed its peak at 09:30 hours with some decline at the afternoon (Table 3).
This might be related to the non-steady flow of water in the soil toward plant roots. Such
non-steady water flow may reduce the uniformity in soil water contents or matric
potential at the root zone and the degree of which buck soil water contents represents the
soil water availability.
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Table 3
Coefficient of determination (r2) and significance level (p) for the correlation between Ks and leaf stomatal
conductance (Cs), leaf water potential ( l) at different hours in August 1991a
Indicators
Coefficients
2
Cs
r
p
r2
p
l
Local time (hours)
07:30
09:30
11:30
14:00
15:30
0.6203
0.02
0.5037
0.05
0.7053
0.001
0.6154
0.02
0.6815
0.01
0.5918
0.02
0.6504
0.02
0.4801
0.05
0.6318
0.02
0.4125
0.100
a
The results based on the 5 time measurements in August 1991 for different soil water deficits treatments,
the parameters are averaged over 5 days.
3.2. Comparison of the relationships of Ks to soil water availability, Cs and y1
According to our earlier research (Kang, 1986), the correlation coefficient of Ks and
relative soil water availability (Aw) is higher than that of Ks to soil water contents directly.
Aw was calculated as
Aw
a ÿwp
f ÿwp
in which a is the average soil water contents in the layer for water balance estimation,
and f is the field capacity, wp is the soil water contents at the wilting point. As the
correlation coefficients between Ks and Cs, l were not very high (Table 3), if the
empirical function of Ks and l, Cs are used directly for estimating ET, there would be
great errors because of the great changes of stomatal conductance and leaf water potential
in different meteorological conditions. Thus the relationships of Ks to relative stomatal
conductance Cs/Csm and relative leaf water potential l/ lm, were plotted according to the
experimental data in 1988±1992 for improving ET estimation, l and Cs were the average
values of leaf water potential and stomatal conductance in this period under soil water
deficit conditions, and lm and Csm were the average values for well watered condition at
the same period. The results showed that Ks was highly correlated (r2 0.9047,
significance at P 0.001) with the average relative stomatal conductance Cs/Csm
measured at 09:30 hours (Fig. 6) and the correlation coefficient of Ks with Cs/Csm is
higher than that of Ks with relative soil water availability (Aw) and relative leaf water
potential ( l/ lm) (Figs. 7 and 8).
Table 4 compares the degree of correlation between Ks and these water status
indicators and gives the best-fit curves. It should be noted that the location of the TDR
sensors in the soil is usually determined arbitrarily. Therefore, with similar plant water
status, the value of soil water contents can differ in response to different soil hydraulic
properties and root distribution. As hydraulic properties and root distribution are difficult
to be determined in the field, Cs/Csm may have an advantage over the use of soil water
contents or matric potential as an indicator for estimating Ks.
The high correlation between Ks and Cs/Csm may be explained by the control of Cs by
root signals which are known to be affected by soil moisture (Davies and Zhang, 1991).
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Fig. 6. The relationship of soil water adjustment coefficient (Ks) to relative leaf stomatal conductance (Cs/Csm),
Cs and Csm are the stomatal conductance in deficient water supply and deficit water treatments, respectively.
Fig. 7. The relationship of soil water adjustment coefficient (Ks) to relative soil water availability (Aw).
Aw([(a ÿ wp)/(f ÿ wp)]) is considered as the indicator of relative soil water availability, in which a is average
soil water contents in the layer for water balance estimation, and f is field capacity, wp is soil water contents at
the wilting point.
Table 4
Empirical equation of Ks as a function of relative soil moisture availability (Aw), relative stomatal conductance
(Cs/Csm), relative leaf water potential ( l/ lm)a
Indicators
Empirical equation
Coefficient of correlation R2
Significance level
Aw
Cs/Csm
l/ lm
Ks 0.5716 ln(Aw) 0.9859
Ks 0.9149Cs/Csm 0.0712
Ks ÿ0.7615 ln( l/ lm) 0.9193
0.7230
0.9047
0.6850
0.01
0.001
0.02
a
The results based on the measured data during 1988±1992, the empirical equations were obtained by Eq.
(3) calculating Ks based on every 10 days potential evapotranspiration when soil water suction was less than
0.1 MPa, and measured actual maize evapotranspiration under soil water deficits, with the measured soil water
content, stomatal conductance and leaf water potential in the corresponding periods.
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K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Fig. 8. The relationship of soil water adjustment coefficient to relative leaf water potential ( l/
are the leaf water potential in deficit water supply and sufficient water treatment, respectively.
lm),
l
and
lm
The lower correlation between Ks and l/ lm has been shown by several studies in the
past 15 years (Bates and Hall, 1982; Gollan et al., 1985; Naor and Wample, 1994; Naor
et al., 1995) and suggests that stomatal conductance is better correlated with soil water
potential or soil water availability than leaf water potential. The result that correlation of
Ks to Aw is lower than that of Ks to Cs/Csm is probably due to the spatial variability of the
soil water contents and hydraulic properties under a same soil moisture treatment
(Warrick and Nielsen, 1980).
3.3. Estimated maize evapotranspiration using various Ks functions
Reference crop evapotranspiration (ET0) was estimated using Eq. (2) with input data
for periods when the soil water measurement data were obtained. The potential maize
evapotranspiration (ETp), estimated as a product of ET0 and the appropriate crop
coefficients (Kc) shown in Table 2, were then adjusted using three kinds of soil water
adjustment coefficients based on the above discussed field measurements, i.e. the soil
water contents, leaf water potential and stomatal conductance during 1988±1992. A
maximum soil water adjustment coefficient Ks, i.e. Ks 1.0, was also used for
comparison. These estimations were performed to test the applicability of these soil water
adjustment coefficients for the actual evapotranspiration (ETa) estimation under different
soil water status, and to compare the errors of ETa estimation with and without the soil
water adjustment coefficient. The measured ETa in the whole growing season was
calculated by a sum of evapotranspiration in the calculation period. Estimated and
measured ET values were compared for monthly values during 1993±1996 in Table 5.
The comparison of estimated and measured actual ET in whole growing season with
different soil water deficits was also conducted during 1993±1996. The results are shown
in Table 6. The various Ks functions have been ranked from best to worst performance
based on the average relative errors and the standard errors of estimate, with low values
associated with the Ks function based on the relative stomatal conductance. If the soil
12
K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
Table 5
The average relative errors as a percent of the estimated monthly actual ET during 1993±1996 with different soil
water adjustment functiona
Ks
Mild water deficit
Inter-medium deficit
Severe water deficit
Cs/Csm
Aw
l/ lm
1.0
14.48
19.36
22.95
25.36
17.92
21.81
26.77
30.18
15.59
23.04
29.21
34.59
a
Relative errorPis equal to [(estimated ET ÿ measured ET)/measured ET] 100%, and the average relative
error is equal to relative error2i = nÿ11=2 , n is the number of samples, the soil water contents ranges of
different deficit treatments were same as Table 1.
Table 6
Standard errors for the estimation of the total ET in the whole growing season with different soil water
adjustment coefficients (Ks)a
Ks
Deficit treatment 1
Cs/Csm
Aw
l/ lm
1.0
Deficit treatment 2
Deficit treatment 3
Average
measured
ET (mm)
SEE
(mm)
Average
measured
ET (mm)
SEE
(mm)
Average
measured
ET (mm)
SEE
(mm)
442.72
442.72
442.72
442.72
21.87
28.34
43.69
98.42
363.50
363.50
363.50
363.50
18.49
23.66
48.71
92.53
301.48
301.48
301.48
301.48
#1=2
20.04
35.47
50.82
98.22
a
Standard errors (SEE) were calculated as
number of samples.
"
n
X
iÿ1
Estimated ET-Measured ET2i = n
, where n is the
water adjustment was not considered, the estimation of ET could have greater error in
conditions of variable soil moistures. The results obtained herein indicate that at least in
the case of summer maize, the soil water adjustment coefficient Ks based on relative
stomatal conductance Cs/Csm, provides a means to predict required adjustments in ET
estimates for different soil water status.
4. Conclusions
Results of this study show that the correlations of soil water adjustment coefficient (Ks)
to relative leaf water potential ( l/ lm), relative leaf stomatal conductance (Cs/Csm) and
relative soil water availability (Aw), was reduced in the following order: Cs/Csm > Aw > l/
lm, and that the actual evapotranspiration (ET) estimation under water deficits in the
semiarid region, based on reference crop evapotranspiration (ET0) by the modified
Penman formula and with a crop coefficient (Kc) and a suitable soil water adjustment
coefficient Ks functions, gave the satisfactory results when compared with field observations. The best estimation of Ks function is based on the relative stomatal conductance
K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14
13
Cs/Csm, and at least in the case of maize that it provided a means of predicting required
adjustments in ET estimation for different soil water status. In practice, the stomatal
conductance can be measured by the porometer, and also the equation to predict leaf
stomatal conductance in this procedure may be established in the future.
Acknowledgements
KS is supported by National Excellent Young Scientist Fund, P.R. China.
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