Estimation of maize evapotranspiration under
water deficits in a semiarid region
Kang Shaozhong
a,b,*, Cai Huanjie
a, Zhang Jianhua
c aInstitute of Agricultural Soil and Water Engineering, Northwest Agricultural University,Yangling, Shaanxi, PR China
bInstitute of Soil and Water Conservation, Chinese Academy of Sciences
and Ministry of Water Resources, Yangling, Shaanxi, PR China cDepartment 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 ofKstoCsand lpeaked at 09:30 hours,
and then decreased, indicating that landCsat 09:30 hours were better predictors of plant water
status. The correlations ofKsto relative leaf water potential ( l/ lm) and relative leaf stomatal
conductance (Cs/Csm) were better than that of Ksto l andCsdirectly.Kswas also significantly
related to soil water availability (Aw). Correlation withKswas 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 withKsfunction based on the relative
stomatal conductance, and at least in the case of maize that the soil water adjustment coefficientKs
based on relative stomatal conductanceCs/Csmprovided 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)
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 ET0andKc. The applica-tion of the popular method has been successful to many crops and locaapplica-tions. Also several different versions ofKs were studied, and straight line, cosine, and logarithmic functions, with and without threshold soil water depletion values, were used to provided adjustments representing Ksversus 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 measure-ments. The number of required measurements is particularly large under interval furrow irrigation, wide-spaced furrow irrigation and drip irrigation, where two- or three-dimensional 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.
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 348200N, 1088240E, 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 cm20 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 Growth stages
Seedling Jointing Grain-filling Maturing
Well watered 65 70 70 65
Mild water deficit 50±50 55±60 55±60 50±55
Inter-medium deficit 45±50 50±55 50±55 45±50
Severe water deficit 40±45 40±45 40±45 35±40
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.
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:
ETaKsKcET0 (1)
whereKsis the soil moisture adjustment coefficient,Kcis the crop coefficient, ET0and ETaare the reference crop evapotranspiration and actual evapotranspiration in soil water deficit condition.
(2)
in whichPandP0are 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;QAis the extra terrestrial radiation in equivalent evaporation units (mm/day);is a constant equal to 2.0110ÿ9 when the extra terrestrial radiationQAand ET0are in equivalent evaporation units (mm/ day);nandNare actual sunshine hours and potential sunshine hours, respectively;Tkis air temperature (K); es and ea are the saturation vapor pressure at the current air temperature and actual vapor pressure of the air;u2is the wind speed at 2 m height;Cis the modification coefficient of wind speed;a andbare 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 evapotranspira-tion during 1982±1990, when soil moisture was sufficient for crop's needs (at soil water tensions up to 0.1 MPa).Kcvalues 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 coefficientKs is 1 unless soil water is depleted sufficiently to limit evapotranspiration.Kscan be determined by rearranging Eq. (1) with the result
Ks
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) June July August September
5 15 25 5 15 25 5 15 25 5 15 25
where ETpis the potential evapotranspiration when soil moisture, at soil water tensions less than 0.1 MPa, is sufficient for maize's needs.
Ksis 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 whereKs1.0 and a soil moisture stress phase whereKsdecreases 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 ofKsunder 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 ofKsand found that the logarithmic function was more suitable in our region.
For different soil moisture treatments,Ksin different stages can be obtained by Eq. (3). Moreover, it can be estimated from the relationships ofKs 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 Fig. 3. The average soil water adjustment coefficientKsover the maize growing season during 1988±1996.
(Fig. 4). However, diurnal leaf water potential ( l) measurements showed that both had a similar leaf water potential at the midday time (Fig. 5). TheCsof both treatments peaked at 09:30 hours and then decreased. The decline ofCsin 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), thatCsand lat 09:30 hours are two better indicators of plant water status and can respond to the changes in soil moisture availability.
The correlation coefficient betweenKsandCs, 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.
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.
3.2. Comparison of the relationships of Ksto soil water availability, Cs andy1
According to our earlier research (Kang, 1986), the correlation coefficient ofKs and relative soil water availability (Aw) is higher than that ofKsto soil water contents directly. Awwas calculated as
Aw
aÿwp
fÿwp
in whichais the average soil water contents in the layer for water balance estimation, andf is the field capacity, wpis 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 ofKsand l,Csare 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 ofKs to relative stomatal conductanceCs/Csmand relative leaf water potential l/ lm, were plotted according to the experimental data in 1988±1992 for improving ET estimation, landCswere the average values of leaf water potential and stomatal conductance in this period under soil water deficit conditions, and lmandCsmwere the average values for well watered condition at the same period. The results showed that Ks was highly correlated (r20.9047, significance at P0.001) 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 ofKs 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/Csmmay have an advantage over the use of soil water contents or matric potential as an indicator for estimatingKs.
The high correlation betweenKsandCs/Csmmay be explained by the control ofCsby root signals which are known to be affected by soil moisture (Davies and Zhang, 1991). Table 3
Coefficient of determination (r2) and significance level (p) for the correlation betweenKsand leaf stomatal
conductance (Cs), leaf water potential ( l) at different hours in August 1991a
Indicators Coefficients Local time (hours)
07:30 09:30 11:30 14:00 15:30
Cs r2 0.6203 0.7053 0.6815 0.6504 0.6318
p 0.02 0.001 0.01 0.02 0.02
l r2 0.5037 0.6154 0.5918 0.4801 0.4125
p 0.05 0.02 0.02 0.05 0.100
aThe results based on the 5 time measurements in August 1991 for different soil water deficits treatments,
Fig. 6. The relationship of soil water adjustment coefficient (Ks) to relative leaf stomatal conductance (Cs/Csm), CsandCsmare 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([(aÿwp)/(fÿwp)]) is considered as the indicator of relative soil water availability, in whichais average
soil water contents in the layer for water balance estimation, andfis field capacity,wpis soil water contents at
the wilting point.
Table 4
Empirical equation ofKsas 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 correlationR2 Significance level
Aw Ks0.5716 ln(Aw)0.9859 0.7230 0.01
Cs/Csm Ks0.9149Cs/Csm0.0712 0.9047 0.001
l/ lm Ks ÿ0.7615 ln( l/ lm)0.9193 0.6850 0.02
aThe results based on the measured data during 1988±1992, the empirical equations were obtained by Eq.
(3) calculatingKsbased on every 10 days potential evapotranspiration when soil water suction was less than
The lower correlation between Ksand l/ lmhas 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 KstoAwis lower than that ofKstoCs/Csmis 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. Ks1.0, 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 ETaestimation 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 variousKs 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 Fig. 8. The relationship of soil water adjustment coefficient to relative leaf water potential ( l/ lm), land lm
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 coefficientKsfunctions, gave the satisfactory results when compared with field observa-tions. The best estimation ofKs function is based on the relative stomatal conductance 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 14.48 17.92 15.59
Aw 19.36 21.81 23.04
l/ lm 22.95 26.77 29.21
1.0 25.36 30.18 34.59
aRelative error is equal to [(estimated ET
ÿmeasured ET)/measured ET]100%, and the average relative error is equal toP
relative error2i= nÿ1
1=2,nis 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 Deficit treatment 2 Deficit treatment 3
Average
Aw 442.72 28.34 363.50 23.66 301.48 35.47
l/ lm 442.72 43.69 363.50 48.71 301.48 50.82
1.0 442.72 98.42 363.50 92.53 301.48 98.22
aStandard errors (SEE) were calculated as Xn
iÿ1
Estimated ET-Measured ET2i= n
" #1=2
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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