Estimation of maize evapotranspiration under water deficits in a semiarid region

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1 Agricultural Water Management 43 (2000) 1±14 Estimation of maize evapotranspiration under water deficits in a semiarid region Kang Shaozhong a,b,*, Cai Huanjie a, Zhang Jianhua c 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 (C s ) of maize crop to soil water availability, and to test and compare the soil water adjustment coefficient (K s ) functions for estimation of actual evapotranspiration (ET) under water deficits. The results showed that correlation coefficients of K s to C s and l peaked at 09:30 hours, and then decreased, indicating that l and C s at 09:30 hours were better predictors of plant water status. The correlations of K s to relative leaf water potential ( l / lm ) and relative leaf stomatal conductance (C s /C sm ) were better than that of K s to l and C s directly. K s was also significantly related to soil water availability (A w ). Correlation with K s was reduced in the following order: C s / C sm > A w > l / lm. The procedure was used that reference crop evapotranspiration (ET 0 ) was estimated by the modified Penman formula and with a crop coefficient (K c ) and different K s functions. The results showed that it was the best estimation with K s function based on the relative stomatal conductance, and at least in the case of maize that the soil water adjustment coefficient K s based on relative stomatal conductance C s /C sm 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.: ; fax: address: kangshaozhong@163.net (K. Shaozhong) /00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S (99)

2 2 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 (ET 0 ), and crop coefficient (K c ) as well as soil moisture adjustment coefficient (K s ) (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 ET 0 and K c. The application of the popular method has been successful to many crops and locations. Also several different versions of K s were studied, and straight line, cosine, and logarithmic functions, with and without threshold soil water depletion values, were used to provided adjustments representing K s 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.

3 K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14 3 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/cm 3. The experimental site was located at N, 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 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 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 treatments a Treatments Growth stages Seedling Jointing Grain-filling Maturing Well watered 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 a Soil moisture contents is the percent of field capacity (23.5% of dry soil weights) in the soil layer irrigated.

4 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.

5 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 Estimation of soil moisture adjustment coefficient The actual evapotranspiration was calculated as follows: ET a ˆ K s K c ET 0 (1) where K s is the soil moisture adjustment coefficient, K c is the crop coefficient, ET 0 and ET a 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 ET 0. 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. ET 0 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 ET 0 (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 ET 0 can be calculated according to the Penman formula, and an air pressure correction factor

6 6 K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14 included, as follows ET 0 ˆ P0=P D= 1 Q A a b n=n Tk 4 p 0:56 0:079 e a 0:1 0:9n=N 0:26 es e a 1 Cu 2 P 0 =P D= 1 (2) in which P and P 0 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; Q A is the extra terrestrial radiation in equivalent evaporation units (mm/day); is a constant equal to when the extra terrestrial radiation Q A and ET 0 are in equivalent evaporation units (mm/ day); n and N are actual sunshine hours and potential sunshine hours, respectively; T k is air temperature (K); e s and e a are the saturation vapor pressure at the current air temperature and actual vapor pressure of the air; u 2 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, and , 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 (K c ) 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). K c 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 K s is 1 unless soil water is depleted sufficiently to limit evapotranspiration. K s can be determined by rearranging Eq. (1) with the result K s ˆ ET a K c ET 0 ˆ ET a (3) ET p 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) June July August September K c

7 K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14 7 Fig. 3. The average soil water adjustment coefficient K s 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 ET p is the potential evapotranspiration when soil moisture, at soil water tensions less than 0.1 MPa, is sufficient for maize's needs. K s 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 K s ˆ 1.0 and a soil moisture stress phase where K s 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 K s 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 K s and found that the logarithmic function was more suitable in our region. For different soil moisture treatments, K s in different stages can be obtained by Eq. (3). Moreover, it can be estimated from the relationships of K s 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 (C s ) of well watered treatment was higher than that of the severe deficit treatment (3) throughout the day

8 8 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 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 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 C s of both treatments peaked at 09:30 hours and then decreased. The decline of C s 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 C s 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 K s and C s, 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.

9 K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14 9 Table 3 Coefficient of determination (r 2 ) and significance level (p) for the correlation between K s and leaf stomatal conductance (C s ), leaf water potential ( l ) at different hours in August 1991 a Indicators Coefficients Local time (hours) 07:30 09:30 11:30 14:00 15:30 C s r p l r p 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 Comparison of the relationships of K s to soil water availability, C s and y 1 According to our earlier research (Kang, 1986), the correlation coefficient of K s and relative soil water availability (A w ) is higher than that of K s to soil water contents directly. A w was calculated as A w ˆ a wp f wp 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 K s and C s, l were not very high (Table 3), if the empirical function of K s and l, C s 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 K s to relative stomatal conductance C s /C sm and relative leaf water potential l / lm, were plotted according to the experimental data in 1988±1992 for improving ET estimation, l and C s were the average values of leaf water potential and stomatal conductance in this period under soil water deficit conditions, and lm and C sm were the average values for well watered condition at the same period. The results showed that K s was highly correlated (r 2 ˆ , significance at P ˆ 0.001) with the average relative stomatal conductance C s /C sm measured at 09:30 hours (Fig. 6) and the correlation coefficient of K s with C s /C sm is higher than that of K s with relative soil water availability (A w ) and relative leaf water potential ( l / lm ) (Figs. 7 and 8). Table 4 compares the degree of correlation between K s 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, C s /C sm may have an advantage over the use of soil water contents or matric potential as an indicator for estimating K s. The high correlation between K s and C s /C sm may be explained by the control of C s by root signals which are known to be affected by soil moisture (Davies and Zhang, 1991).

10 10 K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14 Fig. 6. The relationship of soil water adjustment coefficient (K s ) to relative leaf stomatal conductance (C s /C sm ), C s and C sm are the stomatal conductance in deficient water supply and deficit water treatments, respectively. Fig. 7. The relationship of soil water adjustment coefficient (K s ) to relative soil water availability (A w ). A w ([( a wp )/( f 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 K s as a function of relative soil moisture availability (A w ), relative stomatal conductance (C s /C sm ), relative leaf water potential ( l / lm ) a Indicators Empirical equation Coefficient of correlation R 2 Significance level A w K s ˆ ln(a w ) C s /C sm K s ˆ C s /C sm l/ lm K s ˆ ln( l / lm ) a The results based on the measured data during 1988±1992, the empirical equations were obtained by Eq. (3) calculating K s 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.

11 K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14 11 Fig. 8. The relationship of soil water adjustment coefficient to relative leaf water potential ( l / lm ), l and lm are the leaf water potential in deficit water supply and sufficient water treatment, respectively. The lower correlation between K s 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 K s to A w is lower than that of K s to C s /C sm 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) Estimated maize evapotranspiration using various K s functions Reference crop evapotranspiration (ET 0 ) was estimated using Eq. (2) with input data for periods when the soil water measurement data were obtained. The potential maize evapotranspiration (ET p ), estimated as a product of ET 0 and the appropriate crop coefficients (K c ) 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 K s, i.e. K s ˆ 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 (ET a ) estimation under different soil water status, and to compare the errors of ET a estimation with and without the soil water adjustment coefficient. The measured ET a 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 K s 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 K s function based on the relative stomatal conductance. If the soil

12 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 function a K s Mild water deficit Inter-medium deficit Severe water deficit C s /C sm A w l/ lm a Relative error is equal to [(estimated ET measured ET)/measured ET] 100%, and the average relative error is equal to P relative error 2 i = n 1 Š1=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 (K s ) a K s Deficit treatment 1 Deficit treatment 2 Deficit treatment 3 Average measured ET (mm) SEE (mm) Average measured ET (mm) SEE (mm) Average measured ET (mm) SEE (mm) C s /C sm A w l/ lm " X n a Standard errors (SEE) were calculated as Estimated ET-Measured ET 2 i = n number of samples. i 1 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 K s based on relative stomatal conductance C s /C sm, 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 (K s ) to relative leaf water potential ( l / lm ), relative leaf stomatal conductance (C s /C sm ) and relative soil water availability (A w ), was reduced in the following order: C s /C sm > A w > l / lm, and that the actual evapotranspiration (ET) estimation under water deficits in the semiarid region, based on reference crop evapotranspiration (ET 0 ) by the modified Penman formula and with a crop coefficient (K c ) and a suitable soil water adjustment coefficient K s functions, gave the satisfactory results when compared with field observations. The best estimation of K s function is based on the relative stomatal conductance

13 K. Shaozhong et al. / Agricultural Water Management 43 (2000) 1±14 13 C s /C sm, 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. References Abdulmumin, S., Misari, S.M., Crop coefficients of some major crops of the Nigerian semi-arid tropics. Agric. Water Management 18, 159±171. Allen, R.G., Jensen, M.E., Wright, J.L., Burman, R.D., Operational estimates of reference evapotranspiration. Agron. J. 81, 650±662. Bates, L.M., Hall, A.E., Diurnal and seasonal responses of stomatal conductance for cowpea plants subjected to different levels of environmental drought. Oecologia 54, 304±308. Blaney, H.F., Criddle, W.D., Determining water requirements in irrigated areas from climatological and irrigation data. TP-96, Soil Conservation Service, U.S. Dept. of Agriculture, Washington, DC. Boonyathorobol, W., Walker, W.R., Evapotranspiration under depleting soil moisture. J. Irrig. Drain. Div. ASCE 105, 391±402. Chen Yumin, Guo Guoshuang, Wang Tongxing, Kang Shaozhong, Main crops water requirements and irrigation in China. Chinese Hydraulic and Hydro-power Press, 376 p. Davies, W.J., Zhang, J., Root signals and the regulation of growth and development of plants in drying soil. Annu. Rev. Plant Physoil. Plant Mol. Biol. 1991(42), 55±76. Denmead, O.T., Millar, B.D., Field studies of the conductance of wheat leaves and transpiration. Agron. J. 68, 305±311. Doorenbos, J., Pruitt, W.O., 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., 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., The response of stomata and leaf gas exchange to vapor pressure deficits and soil water content. 3. In the sclerophyllous woody species. Nerium oleander. Oecologia 65, 356± 362. Hill, R.W., Hanks, R.J., Wright, J.L., Crop yield models adapted to irrigation scheduling. Utah Agric. Exp. Stn. Rep. 99, Utah State University, Logan, Utah, 198 p. Jarvis, P.G., 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. Jensen, M.E., Consumptive use of water and irrigation water requirements. Irrig. Drain. Div. Am. Soc. Civ. Eng., New York. Jensen, M.E., Robb, D.C.N., Franzoy, C.E., Scheduling irrigations using climate-crop-soil data. J. Irrig. Drain. Div. ASCE 96, 25±28. Jensen, M.E., Wright, J.L., Pratt, B.J., Estimating soil moisture depletion from climate crop and soil data. Trans. ASCE 14, 954±959. Jensen, M.E., Consumptive use of water and irrigation water requirements, Irrig. Drain. Div. Am. Soc. Civ. Eng., New York. Jensen, M.E., Burman, R.D., Alllen, R.G., Evapotranspiration and irrigation water requirements. A 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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