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Effect of evapotranspiration underprediction on irrigation scheduling and yield of corn: a simulation study
Agricultural Water Management, 19 ( 1991 ) 167-179
167
Elsevier Science Publishers B.V., Amsterdam
Effect of evapotranspiration underprediction on irrigation scheduling and yield of corn: a simulation study Claudio O. Stockle a, Larry G. James a, Day L. Bassett a and Keith E. Saxton b %lgricultural Engineering Department, Washington State U'niversiO', Pulhnan. B~4, UX4 bUSDA/ARS, Pullman, I~;4, US.4 (Accepted 3 September 1990 )
ABSTRACT Stockle, C.O., James, L.G., Bassett, D.L. and Saxton, K.E., 1991. Effect of evapotranspiration underprediction on irrigation scheduling and yield of corn: a simulation study. Agric. Water Manage.. 19: 167-179. Underprediction of evapotranspiration (ET) introduces inaccuracies in water balance-based irrigation scheduling procedures. This may reduce crop yield. A simulation study was performed to evaluate sprinkler irrigated corn yield as affected by irrigation schedules resulting from three levels of ET underprediction. Four irrigation uniformity treatments, two soil types, and two weather scenarios in central Washington were also considered. Yield reductions ranging from 1 to 7% and from 8 to 27% were predicted when daily ET was underpredicted by 15% and 30%, respectively. Implications of underpredicting ET in water balance-based irrigation scheduling techniques are discussed.
INTRODUCTION
Prediction of evapotranspiration (ET) is an important component of many irrigation scheduling techniques. ET estimates are, however, subject to errors, which may result in erroneous irrigation schedules and reduced crop yield. Some of these errors are associated with the method used to predict ET. Others are the result of inaccurate input data and spatial variations in climate, soil, and crop (Jensen, 1974; Doorenbos and Pruitt, 1977; Sharma, 1985 ). ET underprediction results in underestimating the rate of soil water depletion between irrigations. Irrigations scheduled on the basis of this information are often late and applications too small to replenish the root zone. Use of underpredicted ET for irrigation scheduling increases the potential for crop water stress and yield reductions. It has been reported, however, that seasonal ET underprediction ranging from 11 to 16% did not affect the yield of corn due to erroneous irrigation scheduling (Braunworth and Mack, 1987), suggesting that a reasonable margin of tolerance to ET underprediction may exist.
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C.O. STOCKLE ET AL.
The magnitude of this margin is probably related to the water holding capacity of the soil, the magnitude of the actual ET rate, and irrigation system uniformity. When irrigation is delayed as a result of ET underprediction, soils with high water holding capacity are able to supply the crop water requirement for some period of time before the onset of severe water stress. This period is shorter for soils of lower water holding capacity. The length of the period will also depend on the magnitude of the actual ET rate. The higher ET. the shorter the period. The Christiansen uniformity coefficient (Christiansen, 1942) with which sprinkler systems apply water normally ranges from 60 to 99% (Pair et al., 1975; Addink et al., 1980). Uniformities in the upper end of the range are unlikely to be economically feasible. A uniformity less than 100% means that some fraction of the area receives less than the specified average irrigation depth, while other parts of the field receive more. Therefore, the potential for crop water stress and yield reductions from ET underprediction will fluctuate across the field. The Soil Conservation Service of the United States Department of Agriculture (USDA/SCS, 1983) indicates that, for uniformity coefficients between 80% and 90%, 99% of m a x i m u m yield may be obtained by increasing the irrigation depth to adequately irrigate at least 90% of the area. This extra amount of water will also provide some margin of tolerance to ET underprediction. The objective of this work was to evaluate sprinkler irrigated corn yield as affected by irrigation schedules resulting from three levels of ET underprediction. Four irrigation uniformity treatments, two soil types, and two weather scenarios in central Washington were included in the analysis. A computer simulation approach was used to estimate corn grain yield as a function of soil water availability. METHODOLOGY
The growth and yield of sprinkler irrigated corn at Prosser, WA for two weather scenarios was simulated. A planting date of April 25 was used for both weather scenarios. The irrigation strategy was full irrigation, although water deficits eventually resulted from ET underprediction. Corn growth and yield response to water were simulated with a model developed by Stockle and Campbell ( 1985 ). This model simulates water transport in the soil-plant-atmosphere system, linked with photosynthesis and crop growth. It includes a soil water balance which is based on a finite difference solution of the differential equation describing water flow and storage in the soil (Campbell, 1985 ). Plant water uptake is regulated by an interaction between atmospheric demand, soil and plant water potentials, and stomatal resistance. The photosynthesis simulation includes environmental factors such
EFFECT
OF IRRIGATION
169
UNDERPREDICTION
as photosynthetically active radiation, temperature, and atmospheric CO2 concentration as well as plant factors including canopy structure, leaf area, and internal CO2 concentration. Inputs to the model include daily climatic variables (solar radiation, maximum and m i n i m u m temperatures and precipitation), soil hydraulic properties, initial water content, amount and time of irrigations, latitude, and planting date. The model was calibrated for Davis, CA and validated with independent data collected at Davis and Fort Collins, CO (Fig. 1 ). Buttler ( 1989 ) tested the applicability of the model to the savanna region of Central Brazil, concluding that predicted leaf area development and dry matter accumulation over time compared well with measured data under a range of irrigation water treatments. Two sets of synthetic daily weather data, developed from a 30-year record ( 1950-1979 ) for Prosser, WA, were used in the current simulations. One of these sets was developed using, for each month of the growing season, the daily weather data from the year with m a x i m u m pan evaporation for that month. Thus, the data for each month could have been from a different year of the 30-year record. This set will be referred hereafter as the envelope year. The other synthetic data set, referred as the average year, was obtained similarly, but using the daily weather data from the year with monthly pan evaporation nearest the 30-year average. Two soil types were considered, a silt loam and a loamy sand, with water holding capacities of 210 and 130 mm, respectively for a 1.2 m soil profile. Daily values of m a x i m u m vx (ETmax) for the two weather scenarios and soil r--,
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Fig. 1. Comparison of measured corn grain yield ( M g / h a ) and predicted yield using a simulation model. (Adapted from the validation test presented by Stockle and Campbell, 1985. )
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EFFECT OF IRRIGATION UNDERPREDICTION
17 [
types were obtained by simulating well-watered corn growth. These values constituted the 0% (no error) level of ET underprediction (0% ETU). Using ETmax as reference, two other levels of ET underprediction were defined: fifteen percent ( 15% ETU ) and thirty percent underprediction (30% ETU ), with predicted ET equal to 0.85 and 0.70 of ETmax respectively. ET underprediction was assumed to occur each day of the growing season. A computerized scheduling procedure, based on a checkbook type of soil water balance (Lundstrom et al., 1981 ), was used to determine the irrigation amount and timing information needed as input to the crop growth model. In this scheduling procedure, the soil profile was assumed to be at field capacity at planting, and irrigations were scheduled whenever 60% of the plant available soil water (PAW) was depleted. Precipitation was assumed negligible. Irrigation schedules for both the envelope and average weather scenarios, using 0, 15, and 30 percent ET underprediction, were determined for each soil. Prior to their use in the crop growth model, the scheduled irrigation depths for each soil were adjusted for system non-uniformity using the depth distribution curves in Fig. 2. The irrigated field was subdivided into 14 zones, each with its own irrigation depth. The irrigation depth for a zone was calculated by multiplying the scheduled depth by the zone's fractional depth from one of the curves in Fig. 2. Crop yield was then simulated for each zone and the yields for the 14 zones s u m m e d to obtained the yield for the field. A total of 48 cases (fields) were simulated, one for each combination of weather scenario, soil type, ET prediction level, and irrigation uniformity treatment. The four uniformity treatments in Fig. 2 included: (a) Irrigation applied with 90% Christiansen uniformity coefficient and enough water to supply 90% of the field at least the scheduled depth of irrigation (CU90E). (b) Irrigations applied with 80% Christiansen uniformity coefficient and enough water to supply 90% of the field at least the scheduled depth of irrigation (CUSOE). (c) Irrigation applied with 90% Christiansen uniformity coefficient and enough water to supply 50% of the field at least the scheduled depth of irrigation (CU90). (d) Irrigations applied with 80% Christiansen uniformity coefficient and enough water to supply 50% of the field at least the scheduled depth of irrigation (CU80). In uniformity treatments CU90E and CU80E, the depth of irrigation was increased as recommended by USDA/SCS ( 1983 ) to compensate for non-uniform application, and to achieve 99% of m a x i m u m yield. RESULTS
AND DISCUSSION
Simulated yields for the 48 combinations of soil type, weather, irrigation uniformity, and ET underprediction fluctuated from 7.3 to 11.4 M g / h a (Ta-
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('.O. STOCKLE ET AL.
ble 1 ). Yields were higher for the envelope than for the average year due to high radiation. For all combinations, the addition of extra water to compensate for non-uniformity (the CU90E and CU80E treatments ) resulted in larger yields. This result is consistent with the recommendation of the U S D A / S C S ( 1983 ), which calls for an increase of irrigation depths to preserve yields with non-uniform irrigations. The maximum simulated yields across soil types and weather years were obtained with 0% ETU and irrigation uniformity treatments CU90E and CU80E, with only a slight advantage for the better uniformity. As the ET underprediction level increased, CU80E was superior to CU90E because the larger amount of water added to have 90% of the field with at least the scheduled irrigation depth resulted in lower soil water deficits in a larger portion of the field than the CU90E treatment. CU90 was superior to CU80 across soil types, weather years, and 0% and 15% of ET underprediction, showing the advantage of a better uniformity. With 30% ETU, simulated yields for the TABLE 1
Average yield (Mg/ha) for 48 combinations of soil, weather scenario, irrigation uniformity Ireatmcnt, and ET underprediction (ETU) level. Silt loam soil
Loamy sand soil
Envelope year
Average )'ear
Envelope year
CU90 a 0%ETU 15% ETU 30% ETU
11.0 10.5 8.5
9.8 9.4 7.9
11.2 10.5 8.3
9.8 9.1 7.3
CU90E a 0% ETU 15% ETU 30% ETU
11.2 11.0 9.5
9.9 9.7 8.6
I 1.4 9.5
10.0 9.8 8.3
CU80 a 0% ETU 15% ETU 30% ETU
10.9 10.4 8.7
9.6 9.3 8.1
10.9 10.4 8.7
9.6 9.0 7.6
11.2 11.0 10.0
9.9 9.8 9.0
11.4 11.2 10.3
10.0 9.8 9.0
11.2
Average year
CU80E a 0% ETU 15% ETU 30% ETU :'CU80 CU90 CU80E CU90E
= 80% =90% = 80% = 90%
coefficient of uniformity.
coefficient of uniformity. coefficient of uniformity and extra water added to adequately irrigate 90% of the field. coefficient of uniformity and extra water added to adequately irrigate 90% of the field.
EFFECT OF IRRIGATION UNDERPREDICTION
173
CUB0 treatment were slightly higher than for the CU90 because its larger yield in the areas of the field where percolation occurred (see Fig. 2) compensated for the larger decline in areas with low soil water contents. When the two soil types considered in the study were compared (Table 2 ), yields with 0% ETU were slightly larger for the loamy sand than the silt loam soil, as indicated by the negative percents. Due to more frequent irrigations and higher water potential at 60% PAW depletion (threshold value used to schedule irrigations), the simulation model predicted a higher average soil water potential through the season, and therefore, more favorable growth conditions for the loamy sand soil. When ET was underpredicted, the comparative yield between the two soils fluctuated, depending primarily on irrigation uniformity treatment. For treatments without extra water addition (CU 80 and CU90 ), the simulated yields of the silt loam soil were higher than those of the loamy sand soil (positive percent) for both, 15% and 30% ETU, due to its larger water holding capacity. The soil water potential decreased rapidly for the loamy sand soil after 60% PAw depletion, generating condiTABLE 2 P e r c e n t difference a of silt loam and loamy sand soils average yields for 24 combinations of weather sccnario, irrigation uniformity treatment, and ET underprediction (ETU) level.
Envelope year
Average y e a r
CU90 u 0 % ETU 15% ETIJ 3 0 % ETI~
-- 1.7 +0.2 +2.1
--0.8 +3.1 +8.2
CU90E u 0%} ETU 15% ETU 30°/6 ETU
--2.2 --2.4 0.5
-- 1.2 --0.5 + 3.7
--0.8 +0.5 +0.1
--0.2 +2.8 + 5.9
--2.2 --2.0 2.7
-- 1.2 --0.5 + 0.4
-
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CU80 b 0 % E-IU I 5% ETtJ 3 0 % ETU CU80E b
0% ETU 15% ETt; 3 0 % ETU
-
-
5,[ ( yield silt loam - yield loamy sand ) ) / y i el d silt loam ] × 100. b C U 8 0 = 8 0 % coefficient of uniformity. C U 9 0 = 9 0 % c o e f f i c i e n t o f uniformity. C U 8 0 E = 8 0 % coefficient o f uniformity and extra water added to adequately irrigate 90% o f the field. CI J90E = 90% coefficient of uniformity and extra water added to adequately irrigate 90% of the field.
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C.O. STOCKLE ET AL.
tions for crop water stress. When extra water was added to compensate for non-uniformity (i.e., treatments CU80E and CU90E), the water holding capacity advantage of the silt loam soil was overidden, except for the 30% ETUaverage year combination. The percent difference of simulated average yields between the silt loam and loamy sand soil (Table 2) became either less negative or more positive with the average year compared to the envelope year. The lower ET of the average year reduced the irrigation frequency, and therefore the relative advantage of the loamy sand soil as discussed above. In addition, the effect on growth of differences in soil water potential become less important with lower ET.
Table 3 presents relative yields expressed as percent of the yield without underprediction (0% ETU ), for each combination of soil type, weather year, and irrigation uniformity treatment. Yields were reduced due to water stress as the ET underprediction level increased. A continuous underprediction of TABLE 3
Relative yield expressed as percent of the yield with 0% ET underprediction (0% ETU) for each comb i n a t i o n of soil, weather scenario, and irrigation uniformit~ treatment. Silt loam soil
Loamy sand soil
Envelope year
Average year
Envelope year
),ear
Average
C U 9 0 ,~ 0% ETI! 15% ETi! 30% ETU
100.0 95.3 76.9
100.0 95.3 81.2
100.0 93.5 74.0
100.0 92.6 72.9
CU90E a 0% ETU 15% EvtJ 30% ETIJ
100.0 98.0 84.8
100.0 98.4 87.4
100.0 98.2 83.5
100.0 97.6 83.2
15% ETt; 30% ETU
100.0 95.9 80.4
100.0 96.7 84.5
100.0 94.7 79.7
100.0 93.8 79.3
CU80 ~ 0% ETI; 15% ETLI 30% ETU
100.0 98.6 90.3
100.0 98.9 91.9
100.0 98.4 90.8
100.0 98.2 90.4
CU80 a
0% Err'
aCU80 CU90 CU80E CU90E
= = = =
80% 90% 80% 90%
coefficient of uniformity. coefficient of uniformity.
coefficient of uniformity and extra water added to adequately irrigate 90% of the field. coefficient of uniformity and extra water added to adequately irrigate 90% of the field.
EFFECT OF IRRIGATION UNDERPREDICTION
175
ET by 15% only reduced yields by 3 to 7% for uniformity treatments CU80 and CU90, depending on soil type and weather year. Yields for 30% ETU were reduced by 15 to 27%. Irrigation uniformity treatments CU90E and CU80E presented a lower yield decline with increased ET underprediction. Yield reduction was minimal ( 1 to 2%) with 15% ETU, and it ranged from 8 to 17% with 30% ETU. Predicted yield reductions were less than a 1 : 1 correspondence to the level of ET underprediction, i.e., yield reductions for 15 and 30% ET underprediction were less than 15 and 30%, respectively. This was a consequence of ( 1 ) predicted biomass production being maintained at near o p t i m u m for a few days after the 60% PAW depletion threshold was reached, (2) intrafield differences in application depths due to non-uniform irrigation, and (3) increased application depths to compensate for non-uniformity. Irrigations were delayed and reduced with ET underprediction. Thus, simulated PAW was sometimes below the 60% depletion threshold for triggering irrigations, providing potential conditions for crop water stress. However, the magnitude of the predicted stress was not necessarily significant for a few days after 60% depletion. As simulated by the model, the onset of crop water stress depends on the balance between supply and demand of water to the crop. The ability of the soil/root system to meet the atmospheric evaporative demand increases as the root system grows, decreases as the soil dries, and fluctuates during and between days with variables demands. As the soil drying continues, water stress is unavoidable, even for small demands. The specification of a PAW threshold to trigger irrigations, usually 40 to 60% depletion (James et al., 1982), is somewhat arbitrary, and must be conservative to avoid undesired stress if the d e m a n d becomes large. Stegman ( 1982 ), working with corn in North Dakota, concluded that irrigations could possibly by delayed in certain growth stages until as much as 90-95% of the plant available water was depleted, and the resulting yield would remain near maximum. Intrafield variations in application depths due to non-uniform irrigation contributed to the moderation of yield reductions. When ET is underpredicted, all parts of a field receive less water because application depths are low. This results in crop stress and yield reduction in many areas of the field, especially those areas receiving less than the scheduled irrigation depth (see Fig. 2). In the remainder of the field, however, some of the water that would be lost as deep percolation during full irrigations remains in the root zone and available to the crop. Crop yields remain at near m a x i m u m levels in these areas even though there may be significant yield reduction in other parts of the field. When irrigation depth is increased to compensate for non-uniform irrigations, the amount and areas of percolation in the field increase and the moderating effect of intrafield variation in application depth also increases. For additional analysis of the interactions involved in the simulated yield
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C.O. STOCKLE ET AL
response to the different conditions imposed, the seasonal soil water balance for the envelope year and silt loam soil is presented in Table 4. Similar trends in the seasonal water balance were obtained for other combinations of soil and weather scenario. Data in Table 4 indicate that, as the level of ET underprediction increased, predicted evaporation and percolation losses decreased and the depletion of the soil water storage increased (except for 30% ETU), all these factors contributing to increase the availability of water for transpiration (and plant growth). Depletion for 30% ETU did not increase because a late irrigation recharged the soil profile with no significant effect on yields. The larger irrigation amount applied to CU90E and CU80E treatments resulted in a more favorable soil water balance and a lower reduction of the amount of transpiration when ET was underpredicted. The factors moderating the effect on yield of ET underprediction discussed might explain why many investigators have found little or no difference of corn yield when different irrigation scheduling methods have been tested in the field (e.g., Stegman and Ness, 1974; Lundstrom et al., 1981; Fischbach, TABLE 4
Seasonal soil water balance and yield for the envelope year and silt loam soil, for 12 combinations of irrigation uniformity treatment and ET underprediction ( ETU ) level. Irrigation
Transpiration
( mm )
(mm)
Soil evaporation
Deep percolation
Soil water depletion
(mm)
(mm)
(ram)
Yield ( Mg/ha )
CU90 a 0% ETW 15% ETt~ 30% ETt~
490 398 386
477 454 412
162 140 133
18 16 13
167 212 172
11.0 10.5 8.5
CU90E a 0% ETU 15% ETU 30% ETtT
556 452 438
485 472 438
177 152 143
21 17 13
127 189 156
11.2 11.0 9.5
CU80 a 0% ETtJ 15% ETU 30% ETU
490 398 386
466 445 408
160 139 130
22 16 13
158 202 165
10.9 10.4 8.7
CU80E" 0% ETU 15% crt, 30% ETU
607 493 478
484 474 440
180 160 148
45 26 18
102 167 128
11.2 11.0 10.1
"CU80 = 80% coefficient CU90 =90%coefficient CU 80E = 80% coefficient C U 9 0 E = 90% coefficient
of uniformity. of uniformity. of uniformity and extra water added to adequately irrigate 90% of the field. of uniformity and extra water added to adequately irrigate 90% of the field
EFFECT OF IRRIGATION UNDERPREDICTION
177
1981; Camp et al., 1985 ). In this simulation study, continuous underprediction of ET was found not to have a major effect on yield due to erroneous irrigation scheduling. This supports the view that a reasonable margin of tolerance to ET prediction errors exists for irrigation scheduling. This is consistent with the results of a two-year field study conducted by Braunworth and Mack (1987), in which corn was grown in a high water holding capacity soil in western Oregon. They observed that underprediction of seasonal ET ranging from 11 to 16% did not affect the yield. Furthermore, based on calculations using yield-water production functions, they concluded that up to a 25% underprediction of ET, if used to schedule irrigations, would not be expected to cause significant yield reduction. Because 15% continuous ET underprediction did not cause a significant reduction on simulated yield (Table 3), this study seems to indicate that some of the more accurate methods available to predict evapotranspiration, including Penman and some radiation methods, are probably adequate for irrigation scheduling without local calibration. This statement applies with an increasing degree of reliability if: ( 1 ) the soil is close to field capacity at planting time, (2) the soil water holding capacity is not restricted (e.g., limited soil depth, sandy soils), and (3) irrigation depths are increased to compensate for non-uniform irrigations. In principle, it would seem that uniformities less than 80% - the lower value considered in this study - could further minimize the effect on yield of erroneous irrigation scheduling due to ET underprediction. This is because a larger amount of extra water would be applied to adequately irrigate 90% of the field. However, the expected benefits would be accomplished with a dramatic increase in water use and irrigation costs, and the potential for yield reductions due to over irrigation would also increase. Finally, results presented (Table 1 ) seem to indicate that a decrease in irrigation uniformity from 90 to 80% would not affect yields significantly. This is consistent with data reported by Stern and Bresler ( 1983 ) showing little differences in yield of crops irrigated with uniformities between 85% and 100%. CONCLUSIONS
A simulation study was performed to evaluate sprinkle irrigated corn yield as affected by irrigation schedules resulting from three levels OfET underprediction. Four irrigation uniformity treatments, two soil types, and two weather scenarios in central Washington were included in the analysis, the main conclusions of this study were: (a) Fifteen percent continuous underprediction of daily ET through the entire growing season reduced simulated corn yield from 1 to 7%, depending on irrigation uniformity treatment (80 and 90% uniformity, with and without increase of the irrigation depth to adequately irrigate 90% of the area), soil
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C.O. STOCKLE ET AL.
water holding capacity, and atmospheric evaporative demand. Thirty percent continuous underprediction of daily ET reduced simulated crop yield from 8 to 27%. These reductions resulted from delayed and insufficient irrigations. (b) Yield reductions were less than a 1 : 1 correspondence with the levels of ET underprediction due to some compensatory factors. Intrafield differences in application depths due to non-uniform irrigation, especially when irrigation depths were increased to compensate for non-uniformity, reduced the effect on yield. Another moderating effect was the ability of the soil to maintain some water supply to the crop after the 60% PAW depletion threshold to schedule irrigations was reached. (c) A reasonable margin of tolerance to VT prediction errors seems to exist for irrigation scheduling. This result is consistent with findings from field studies. This suggests that relatively accurate ET prediction methods like Penman and some radiation methods may be adequate for irrigation scheduling without the need for local calibrations.
REFERENCES Addink, J.W., Keller, J., Pair, C.H., Sneed, R.E. and Wolfe, J.W., 1980. Design and operation of sprinkler systems. In: M.E. Jensen (Editor), Design and Operation of Farm Irrigation Systems. ASAE Monograph No. 3, pp. 621-660. Braunworth, W.S. and Mack, H.J., 1987. Evapotranspiration and yield comparisons among soilwater-balance and climate-based equations for irrigation scheduling of sweet corn. Agron. J., 79: 837-841. Buttler, I.W., 1989. Predicting water constraints to productivity of corn using plant-environmental simulation models. Ph.D. dissertation, Cornell University, 237 pp. Camp, C.R., Karlen, D.L. and Lambert, J.R., 1985. Irrigation scheduling and row crop configurations for corn in the southeastern coastal plain. Trans. ASAE, 28:1159-1165. Campbell, G.S., 1985. Soil Physics with BASI~'.Elsevier, Amsterdam, 150 pp. Christiansen, J.E., 1942. Irrigation by sprinkling. Bull. 670, Univ. of California, Berkeley, CA. Doorenbos, J. and Pruitt, W.O., 1977. Crop water requirements. Irrigation and Drainage Paper No. 24. FAO, Rome. Fischbach, P.E., 1981. A comparison of various irrigation scheduling procedures with corn. In: Irrigation Scheduling for Water and energy Conservation in the 80"s. proc. ASAE Irrigation Scheduling Conf. Chicago, I, pp. 166-170. James, L.G., Erpenbeck, J.M., Bassett, D.L. and Middleton, J.E., 1982. Irrigation requirements for Washington. Estimates and methodology. Res. Bull. XB925, Agricultural Research Center. Washington State University. Jensen, M.E. (Editor), 1974. Consumptive Use of Water and irrigation Water Requirements. Rep. tech. Comm. on Irrig. Water Requirements, Am. Soc. Cir. Eng., Irrig. Drain. Div. Lundstromn, D.R., Stegman E.C. and Werner, H.D., 1981. Irrigation scheduling by the checkbook method. InL Irrigation Scheduling for Water and Energy Conservation in the 80"s. Proc. ASAE Irrigation Scheduling Conf. Chicago, IL, pp. 187-193. Pair, C.H., Hinz, W.H., Frost, K.R., Sneed, R.E. and Schiltz, T.J. (Editors), 1975. Irrigation. the Irrigation Association. Silver Spring, MD, 615 pp. Sharma, M.L., 1985. Estimating evapotranspiration. Adv. Irrig. 3:213-281.
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Stegman, E.C. and Ness, L.D., 1974. Evaluation of alternative scheduling schemes for center point sprinkler systems. North Dakota Agric. Exp. Stn. Res. Rep., 48. Stcgman, E.C., 1982. Corn grain yield as influenced by timing of evapotranspiration deficits. lrrig. Sci., 3: 75-87. Stern, J. and Bresler, E., 1983. Non-uniform sprinkler irrigation and crop yield, lrrig. Sci., 4: 17-29. Stockle, C.O. and Campbell, G.S., 1985. A simulation model for predicting effect of water stress on yield: an example using corn. In: D. Hillel (Editor), Adv. Irrig. 3:283-311. USDA/SCS, 1983. Sprinkle Irrigation. National Engineering Handbook, Section 15, Chapter 11.
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Elsevier Science Publishers B.V., Amsterdam
Effect of evapotranspiration underprediction on irrigation scheduling and yield of corn: a simulation study Claudio O. Stockle a, Larry G. James a, Day L. Bassett a and Keith E. Saxton b %lgricultural Engineering Department, Washington State U'niversiO', Pulhnan. B~4, UX4 bUSDA/ARS, Pullman, I~;4, US.4 (Accepted 3 September 1990 )
ABSTRACT Stockle, C.O., James, L.G., Bassett, D.L. and Saxton, K.E., 1991. Effect of evapotranspiration underprediction on irrigation scheduling and yield of corn: a simulation study. Agric. Water Manage.. 19: 167-179. Underprediction of evapotranspiration (ET) introduces inaccuracies in water balance-based irrigation scheduling procedures. This may reduce crop yield. A simulation study was performed to evaluate sprinkler irrigated corn yield as affected by irrigation schedules resulting from three levels of ET underprediction. Four irrigation uniformity treatments, two soil types, and two weather scenarios in central Washington were also considered. Yield reductions ranging from 1 to 7% and from 8 to 27% were predicted when daily ET was underpredicted by 15% and 30%, respectively. Implications of underpredicting ET in water balance-based irrigation scheduling techniques are discussed.
INTRODUCTION
Prediction of evapotranspiration (ET) is an important component of many irrigation scheduling techniques. ET estimates are, however, subject to errors, which may result in erroneous irrigation schedules and reduced crop yield. Some of these errors are associated with the method used to predict ET. Others are the result of inaccurate input data and spatial variations in climate, soil, and crop (Jensen, 1974; Doorenbos and Pruitt, 1977; Sharma, 1985 ). ET underprediction results in underestimating the rate of soil water depletion between irrigations. Irrigations scheduled on the basis of this information are often late and applications too small to replenish the root zone. Use of underpredicted ET for irrigation scheduling increases the potential for crop water stress and yield reductions. It has been reported, however, that seasonal ET underprediction ranging from 11 to 16% did not affect the yield of corn due to erroneous irrigation scheduling (Braunworth and Mack, 1987), suggesting that a reasonable margin of tolerance to ET underprediction may exist.
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The magnitude of this margin is probably related to the water holding capacity of the soil, the magnitude of the actual ET rate, and irrigation system uniformity. When irrigation is delayed as a result of ET underprediction, soils with high water holding capacity are able to supply the crop water requirement for some period of time before the onset of severe water stress. This period is shorter for soils of lower water holding capacity. The length of the period will also depend on the magnitude of the actual ET rate. The higher ET. the shorter the period. The Christiansen uniformity coefficient (Christiansen, 1942) with which sprinkler systems apply water normally ranges from 60 to 99% (Pair et al., 1975; Addink et al., 1980). Uniformities in the upper end of the range are unlikely to be economically feasible. A uniformity less than 100% means that some fraction of the area receives less than the specified average irrigation depth, while other parts of the field receive more. Therefore, the potential for crop water stress and yield reductions from ET underprediction will fluctuate across the field. The Soil Conservation Service of the United States Department of Agriculture (USDA/SCS, 1983) indicates that, for uniformity coefficients between 80% and 90%, 99% of m a x i m u m yield may be obtained by increasing the irrigation depth to adequately irrigate at least 90% of the area. This extra amount of water will also provide some margin of tolerance to ET underprediction. The objective of this work was to evaluate sprinkler irrigated corn yield as affected by irrigation schedules resulting from three levels of ET underprediction. Four irrigation uniformity treatments, two soil types, and two weather scenarios in central Washington were included in the analysis. A computer simulation approach was used to estimate corn grain yield as a function of soil water availability. METHODOLOGY
The growth and yield of sprinkler irrigated corn at Prosser, WA for two weather scenarios was simulated. A planting date of April 25 was used for both weather scenarios. The irrigation strategy was full irrigation, although water deficits eventually resulted from ET underprediction. Corn growth and yield response to water were simulated with a model developed by Stockle and Campbell ( 1985 ). This model simulates water transport in the soil-plant-atmosphere system, linked with photosynthesis and crop growth. It includes a soil water balance which is based on a finite difference solution of the differential equation describing water flow and storage in the soil (Campbell, 1985 ). Plant water uptake is regulated by an interaction between atmospheric demand, soil and plant water potentials, and stomatal resistance. The photosynthesis simulation includes environmental factors such
EFFECT
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169
UNDERPREDICTION
as photosynthetically active radiation, temperature, and atmospheric CO2 concentration as well as plant factors including canopy structure, leaf area, and internal CO2 concentration. Inputs to the model include daily climatic variables (solar radiation, maximum and m i n i m u m temperatures and precipitation), soil hydraulic properties, initial water content, amount and time of irrigations, latitude, and planting date. The model was calibrated for Davis, CA and validated with independent data collected at Davis and Fort Collins, CO (Fig. 1 ). Buttler ( 1989 ) tested the applicability of the model to the savanna region of Central Brazil, concluding that predicted leaf area development and dry matter accumulation over time compared well with measured data under a range of irrigation water treatments. Two sets of synthetic daily weather data, developed from a 30-year record ( 1950-1979 ) for Prosser, WA, were used in the current simulations. One of these sets was developed using, for each month of the growing season, the daily weather data from the year with m a x i m u m pan evaporation for that month. Thus, the data for each month could have been from a different year of the 30-year record. This set will be referred hereafter as the envelope year. The other synthetic data set, referred as the average year, was obtained similarly, but using the daily weather data from the year with monthly pan evaporation nearest the 30-year average. Two soil types were considered, a silt loam and a loamy sand, with water holding capacities of 210 and 130 mm, respectively for a 1.2 m soil profile. Daily values of m a x i m u m vx (ETmax) for the two weather scenarios and soil r--,
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EFFECT OF IRRIGATION UNDERPREDICTION
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types were obtained by simulating well-watered corn growth. These values constituted the 0% (no error) level of ET underprediction (0% ETU). Using ETmax as reference, two other levels of ET underprediction were defined: fifteen percent ( 15% ETU ) and thirty percent underprediction (30% ETU ), with predicted ET equal to 0.85 and 0.70 of ETmax respectively. ET underprediction was assumed to occur each day of the growing season. A computerized scheduling procedure, based on a checkbook type of soil water balance (Lundstrom et al., 1981 ), was used to determine the irrigation amount and timing information needed as input to the crop growth model. In this scheduling procedure, the soil profile was assumed to be at field capacity at planting, and irrigations were scheduled whenever 60% of the plant available soil water (PAW) was depleted. Precipitation was assumed negligible. Irrigation schedules for both the envelope and average weather scenarios, using 0, 15, and 30 percent ET underprediction, were determined for each soil. Prior to their use in the crop growth model, the scheduled irrigation depths for each soil were adjusted for system non-uniformity using the depth distribution curves in Fig. 2. The irrigated field was subdivided into 14 zones, each with its own irrigation depth. The irrigation depth for a zone was calculated by multiplying the scheduled depth by the zone's fractional depth from one of the curves in Fig. 2. Crop yield was then simulated for each zone and the yields for the 14 zones s u m m e d to obtained the yield for the field. A total of 48 cases (fields) were simulated, one for each combination of weather scenario, soil type, ET prediction level, and irrigation uniformity treatment. The four uniformity treatments in Fig. 2 included: (a) Irrigation applied with 90% Christiansen uniformity coefficient and enough water to supply 90% of the field at least the scheduled depth of irrigation (CU90E). (b) Irrigations applied with 80% Christiansen uniformity coefficient and enough water to supply 90% of the field at least the scheduled depth of irrigation (CUSOE). (c) Irrigation applied with 90% Christiansen uniformity coefficient and enough water to supply 50% of the field at least the scheduled depth of irrigation (CU90). (d) Irrigations applied with 80% Christiansen uniformity coefficient and enough water to supply 50% of the field at least the scheduled depth of irrigation (CU80). In uniformity treatments CU90E and CU80E, the depth of irrigation was increased as recommended by USDA/SCS ( 1983 ) to compensate for non-uniform application, and to achieve 99% of m a x i m u m yield. RESULTS
AND DISCUSSION
Simulated yields for the 48 combinations of soil type, weather, irrigation uniformity, and ET underprediction fluctuated from 7.3 to 11.4 M g / h a (Ta-
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('.O. STOCKLE ET AL.
ble 1 ). Yields were higher for the envelope than for the average year due to high radiation. For all combinations, the addition of extra water to compensate for non-uniformity (the CU90E and CU80E treatments ) resulted in larger yields. This result is consistent with the recommendation of the U S D A / S C S ( 1983 ), which calls for an increase of irrigation depths to preserve yields with non-uniform irrigations. The maximum simulated yields across soil types and weather years were obtained with 0% ETU and irrigation uniformity treatments CU90E and CU80E, with only a slight advantage for the better uniformity. As the ET underprediction level increased, CU80E was superior to CU90E because the larger amount of water added to have 90% of the field with at least the scheduled irrigation depth resulted in lower soil water deficits in a larger portion of the field than the CU90E treatment. CU90 was superior to CU80 across soil types, weather years, and 0% and 15% of ET underprediction, showing the advantage of a better uniformity. With 30% ETU, simulated yields for the TABLE 1
Average yield (Mg/ha) for 48 combinations of soil, weather scenario, irrigation uniformity Ireatmcnt, and ET underprediction (ETU) level. Silt loam soil
Loamy sand soil
Envelope year
Average )'ear
Envelope year
CU90 a 0%ETU 15% ETU 30% ETU
11.0 10.5 8.5
9.8 9.4 7.9
11.2 10.5 8.3
9.8 9.1 7.3
CU90E a 0% ETU 15% ETU 30% ETU
11.2 11.0 9.5
9.9 9.7 8.6
I 1.4 9.5
10.0 9.8 8.3
CU80 a 0% ETU 15% ETU 30% ETU
10.9 10.4 8.7
9.6 9.3 8.1
10.9 10.4 8.7
9.6 9.0 7.6
11.2 11.0 10.0
9.9 9.8 9.0
11.4 11.2 10.3
10.0 9.8 9.0
11.2
Average year
CU80E a 0% ETU 15% ETU 30% ETU :'CU80 CU90 CU80E CU90E
= 80% =90% = 80% = 90%
coefficient of uniformity.
coefficient of uniformity. coefficient of uniformity and extra water added to adequately irrigate 90% of the field. coefficient of uniformity and extra water added to adequately irrigate 90% of the field.
EFFECT OF IRRIGATION UNDERPREDICTION
173
CUB0 treatment were slightly higher than for the CU90 because its larger yield in the areas of the field where percolation occurred (see Fig. 2) compensated for the larger decline in areas with low soil water contents. When the two soil types considered in the study were compared (Table 2 ), yields with 0% ETU were slightly larger for the loamy sand than the silt loam soil, as indicated by the negative percents. Due to more frequent irrigations and higher water potential at 60% PAW depletion (threshold value used to schedule irrigations), the simulation model predicted a higher average soil water potential through the season, and therefore, more favorable growth conditions for the loamy sand soil. When ET was underpredicted, the comparative yield between the two soils fluctuated, depending primarily on irrigation uniformity treatment. For treatments without extra water addition (CU 80 and CU90 ), the simulated yields of the silt loam soil were higher than those of the loamy sand soil (positive percent) for both, 15% and 30% ETU, due to its larger water holding capacity. The soil water potential decreased rapidly for the loamy sand soil after 60% PAw depletion, generating condiTABLE 2 P e r c e n t difference a of silt loam and loamy sand soils average yields for 24 combinations of weather sccnario, irrigation uniformity treatment, and ET underprediction (ETU) level.
Envelope year
Average y e a r
CU90 u 0 % ETU 15% ETIJ 3 0 % ETI~
-- 1.7 +0.2 +2.1
--0.8 +3.1 +8.2
CU90E u 0%} ETU 15% ETU 30°/6 ETU
--2.2 --2.4 0.5
-- 1.2 --0.5 + 3.7
--0.8 +0.5 +0.1
--0.2 +2.8 + 5.9
--2.2 --2.0 2.7
-- 1.2 --0.5 + 0.4
-
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CU80 b 0 % E-IU I 5% ETtJ 3 0 % ETU CU80E b
0% ETU 15% ETt; 3 0 % ETU
-
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5,[ ( yield silt loam - yield loamy sand ) ) / y i el d silt loam ] × 100. b C U 8 0 = 8 0 % coefficient of uniformity. C U 9 0 = 9 0 % c o e f f i c i e n t o f uniformity. C U 8 0 E = 8 0 % coefficient o f uniformity and extra water added to adequately irrigate 90% o f the field. CI J90E = 90% coefficient of uniformity and extra water added to adequately irrigate 90% of the field.
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C.O. STOCKLE ET AL.
tions for crop water stress. When extra water was added to compensate for non-uniformity (i.e., treatments CU80E and CU90E), the water holding capacity advantage of the silt loam soil was overidden, except for the 30% ETUaverage year combination. The percent difference of simulated average yields between the silt loam and loamy sand soil (Table 2) became either less negative or more positive with the average year compared to the envelope year. The lower ET of the average year reduced the irrigation frequency, and therefore the relative advantage of the loamy sand soil as discussed above. In addition, the effect on growth of differences in soil water potential become less important with lower ET.
Table 3 presents relative yields expressed as percent of the yield without underprediction (0% ETU ), for each combination of soil type, weather year, and irrigation uniformity treatment. Yields were reduced due to water stress as the ET underprediction level increased. A continuous underprediction of TABLE 3
Relative yield expressed as percent of the yield with 0% ET underprediction (0% ETU) for each comb i n a t i o n of soil, weather scenario, and irrigation uniformit~ treatment. Silt loam soil
Loamy sand soil
Envelope year
Average year
Envelope year
),ear
Average
C U 9 0 ,~ 0% ETI! 15% ETi! 30% ETU
100.0 95.3 76.9
100.0 95.3 81.2
100.0 93.5 74.0
100.0 92.6 72.9
CU90E a 0% ETU 15% EvtJ 30% ETIJ
100.0 98.0 84.8
100.0 98.4 87.4
100.0 98.2 83.5
100.0 97.6 83.2
15% ETt; 30% ETU
100.0 95.9 80.4
100.0 96.7 84.5
100.0 94.7 79.7
100.0 93.8 79.3
CU80 ~ 0% ETI; 15% ETLI 30% ETU
100.0 98.6 90.3
100.0 98.9 91.9
100.0 98.4 90.8
100.0 98.2 90.4
CU80 a
0% Err'
aCU80 CU90 CU80E CU90E
= = = =
80% 90% 80% 90%
coefficient of uniformity. coefficient of uniformity.
coefficient of uniformity and extra water added to adequately irrigate 90% of the field. coefficient of uniformity and extra water added to adequately irrigate 90% of the field.
EFFECT OF IRRIGATION UNDERPREDICTION
175
ET by 15% only reduced yields by 3 to 7% for uniformity treatments CU80 and CU90, depending on soil type and weather year. Yields for 30% ETU were reduced by 15 to 27%. Irrigation uniformity treatments CU90E and CU80E presented a lower yield decline with increased ET underprediction. Yield reduction was minimal ( 1 to 2%) with 15% ETU, and it ranged from 8 to 17% with 30% ETU. Predicted yield reductions were less than a 1 : 1 correspondence to the level of ET underprediction, i.e., yield reductions for 15 and 30% ET underprediction were less than 15 and 30%, respectively. This was a consequence of ( 1 ) predicted biomass production being maintained at near o p t i m u m for a few days after the 60% PAW depletion threshold was reached, (2) intrafield differences in application depths due to non-uniform irrigation, and (3) increased application depths to compensate for non-uniformity. Irrigations were delayed and reduced with ET underprediction. Thus, simulated PAW was sometimes below the 60% depletion threshold for triggering irrigations, providing potential conditions for crop water stress. However, the magnitude of the predicted stress was not necessarily significant for a few days after 60% depletion. As simulated by the model, the onset of crop water stress depends on the balance between supply and demand of water to the crop. The ability of the soil/root system to meet the atmospheric evaporative demand increases as the root system grows, decreases as the soil dries, and fluctuates during and between days with variables demands. As the soil drying continues, water stress is unavoidable, even for small demands. The specification of a PAW threshold to trigger irrigations, usually 40 to 60% depletion (James et al., 1982), is somewhat arbitrary, and must be conservative to avoid undesired stress if the d e m a n d becomes large. Stegman ( 1982 ), working with corn in North Dakota, concluded that irrigations could possibly by delayed in certain growth stages until as much as 90-95% of the plant available water was depleted, and the resulting yield would remain near maximum. Intrafield variations in application depths due to non-uniform irrigation contributed to the moderation of yield reductions. When ET is underpredicted, all parts of a field receive less water because application depths are low. This results in crop stress and yield reduction in many areas of the field, especially those areas receiving less than the scheduled irrigation depth (see Fig. 2). In the remainder of the field, however, some of the water that would be lost as deep percolation during full irrigations remains in the root zone and available to the crop. Crop yields remain at near m a x i m u m levels in these areas even though there may be significant yield reduction in other parts of the field. When irrigation depth is increased to compensate for non-uniform irrigations, the amount and areas of percolation in the field increase and the moderating effect of intrafield variation in application depth also increases. For additional analysis of the interactions involved in the simulated yield
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C.O. STOCKLE ET AL
response to the different conditions imposed, the seasonal soil water balance for the envelope year and silt loam soil is presented in Table 4. Similar trends in the seasonal water balance were obtained for other combinations of soil and weather scenario. Data in Table 4 indicate that, as the level of ET underprediction increased, predicted evaporation and percolation losses decreased and the depletion of the soil water storage increased (except for 30% ETU), all these factors contributing to increase the availability of water for transpiration (and plant growth). Depletion for 30% ETU did not increase because a late irrigation recharged the soil profile with no significant effect on yields. The larger irrigation amount applied to CU90E and CU80E treatments resulted in a more favorable soil water balance and a lower reduction of the amount of transpiration when ET was underpredicted. The factors moderating the effect on yield of ET underprediction discussed might explain why many investigators have found little or no difference of corn yield when different irrigation scheduling methods have been tested in the field (e.g., Stegman and Ness, 1974; Lundstrom et al., 1981; Fischbach, TABLE 4
Seasonal soil water balance and yield for the envelope year and silt loam soil, for 12 combinations of irrigation uniformity treatment and ET underprediction ( ETU ) level. Irrigation
Transpiration
( mm )
(mm)
Soil evaporation
Deep percolation
Soil water depletion
(mm)
(mm)
(ram)
Yield ( Mg/ha )
CU90 a 0% ETW 15% ETt~ 30% ETt~
490 398 386
477 454 412
162 140 133
18 16 13
167 212 172
11.0 10.5 8.5
CU90E a 0% ETU 15% ETU 30% ETtT
556 452 438
485 472 438
177 152 143
21 17 13
127 189 156
11.2 11.0 9.5
CU80 a 0% ETtJ 15% ETU 30% ETU
490 398 386
466 445 408
160 139 130
22 16 13
158 202 165
10.9 10.4 8.7
CU80E" 0% ETU 15% crt, 30% ETU
607 493 478
484 474 440
180 160 148
45 26 18
102 167 128
11.2 11.0 10.1
"CU80 = 80% coefficient CU90 =90%coefficient CU 80E = 80% coefficient C U 9 0 E = 90% coefficient
of uniformity. of uniformity. of uniformity and extra water added to adequately irrigate 90% of the field. of uniformity and extra water added to adequately irrigate 90% of the field
EFFECT OF IRRIGATION UNDERPREDICTION
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1981; Camp et al., 1985 ). In this simulation study, continuous underprediction of ET was found not to have a major effect on yield due to erroneous irrigation scheduling. This supports the view that a reasonable margin of tolerance to ET prediction errors exists for irrigation scheduling. This is consistent with the results of a two-year field study conducted by Braunworth and Mack (1987), in which corn was grown in a high water holding capacity soil in western Oregon. They observed that underprediction of seasonal ET ranging from 11 to 16% did not affect the yield. Furthermore, based on calculations using yield-water production functions, they concluded that up to a 25% underprediction of ET, if used to schedule irrigations, would not be expected to cause significant yield reduction. Because 15% continuous ET underprediction did not cause a significant reduction on simulated yield (Table 3), this study seems to indicate that some of the more accurate methods available to predict evapotranspiration, including Penman and some radiation methods, are probably adequate for irrigation scheduling without local calibration. This statement applies with an increasing degree of reliability if: ( 1 ) the soil is close to field capacity at planting time, (2) the soil water holding capacity is not restricted (e.g., limited soil depth, sandy soils), and (3) irrigation depths are increased to compensate for non-uniform irrigations. In principle, it would seem that uniformities less than 80% - the lower value considered in this study - could further minimize the effect on yield of erroneous irrigation scheduling due to ET underprediction. This is because a larger amount of extra water would be applied to adequately irrigate 90% of the field. However, the expected benefits would be accomplished with a dramatic increase in water use and irrigation costs, and the potential for yield reductions due to over irrigation would also increase. Finally, results presented (Table 1 ) seem to indicate that a decrease in irrigation uniformity from 90 to 80% would not affect yields significantly. This is consistent with data reported by Stern and Bresler ( 1983 ) showing little differences in yield of crops irrigated with uniformities between 85% and 100%. CONCLUSIONS
A simulation study was performed to evaluate sprinkle irrigated corn yield as affected by irrigation schedules resulting from three levels OfET underprediction. Four irrigation uniformity treatments, two soil types, and two weather scenarios in central Washington were included in the analysis, the main conclusions of this study were: (a) Fifteen percent continuous underprediction of daily ET through the entire growing season reduced simulated corn yield from 1 to 7%, depending on irrigation uniformity treatment (80 and 90% uniformity, with and without increase of the irrigation depth to adequately irrigate 90% of the area), soil
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C.O. STOCKLE ET AL.
water holding capacity, and atmospheric evaporative demand. Thirty percent continuous underprediction of daily ET reduced simulated crop yield from 8 to 27%. These reductions resulted from delayed and insufficient irrigations. (b) Yield reductions were less than a 1 : 1 correspondence with the levels of ET underprediction due to some compensatory factors. Intrafield differences in application depths due to non-uniform irrigation, especially when irrigation depths were increased to compensate for non-uniformity, reduced the effect on yield. Another moderating effect was the ability of the soil to maintain some water supply to the crop after the 60% PAW depletion threshold to schedule irrigations was reached. (c) A reasonable margin of tolerance to VT prediction errors seems to exist for irrigation scheduling. This result is consistent with findings from field studies. This suggests that relatively accurate ET prediction methods like Penman and some radiation methods may be adequate for irrigation scheduling without the need for local calibrations.
REFERENCES Addink, J.W., Keller, J., Pair, C.H., Sneed, R.E. and Wolfe, J.W., 1980. Design and operation of sprinkler systems. In: M.E. Jensen (Editor), Design and Operation of Farm Irrigation Systems. ASAE Monograph No. 3, pp. 621-660. Braunworth, W.S. and Mack, H.J., 1987. Evapotranspiration and yield comparisons among soilwater-balance and climate-based equations for irrigation scheduling of sweet corn. Agron. J., 79: 837-841. Buttler, I.W., 1989. Predicting water constraints to productivity of corn using plant-environmental simulation models. Ph.D. dissertation, Cornell University, 237 pp. Camp, C.R., Karlen, D.L. and Lambert, J.R., 1985. Irrigation scheduling and row crop configurations for corn in the southeastern coastal plain. Trans. ASAE, 28:1159-1165. Campbell, G.S., 1985. Soil Physics with BASI~'.Elsevier, Amsterdam, 150 pp. Christiansen, J.E., 1942. Irrigation by sprinkling. Bull. 670, Univ. of California, Berkeley, CA. Doorenbos, J. and Pruitt, W.O., 1977. Crop water requirements. Irrigation and Drainage Paper No. 24. FAO, Rome. Fischbach, P.E., 1981. A comparison of various irrigation scheduling procedures with corn. In: Irrigation Scheduling for Water and energy Conservation in the 80"s. proc. ASAE Irrigation Scheduling Conf. Chicago, I, pp. 166-170. James, L.G., Erpenbeck, J.M., Bassett, D.L. and Middleton, J.E., 1982. Irrigation requirements for Washington. Estimates and methodology. Res. Bull. XB925, Agricultural Research Center. Washington State University. Jensen, M.E. (Editor), 1974. Consumptive Use of Water and irrigation Water Requirements. Rep. tech. Comm. on Irrig. Water Requirements, Am. Soc. Cir. Eng., Irrig. Drain. Div. Lundstromn, D.R., Stegman E.C. and Werner, H.D., 1981. Irrigation scheduling by the checkbook method. InL Irrigation Scheduling for Water and Energy Conservation in the 80"s. Proc. ASAE Irrigation Scheduling Conf. Chicago, IL, pp. 187-193. Pair, C.H., Hinz, W.H., Frost, K.R., Sneed, R.E. and Schiltz, T.J. (Editors), 1975. Irrigation. the Irrigation Association. Silver Spring, MD, 615 pp. Sharma, M.L., 1985. Estimating evapotranspiration. Adv. Irrig. 3:213-281.
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Stegman, E.C. and Ness, L.D., 1974. Evaluation of alternative scheduling schemes for center point sprinkler systems. North Dakota Agric. Exp. Stn. Res. Rep., 48. Stcgman, E.C., 1982. Corn grain yield as influenced by timing of evapotranspiration deficits. lrrig. Sci., 3: 75-87. Stern, J. and Bresler, E., 1983. Non-uniform sprinkler irrigation and crop yield, lrrig. Sci., 4: 17-29. Stockle, C.O. and Campbell, G.S., 1985. A simulation model for predicting effect of water stress on yield: an example using corn. In: D. Hillel (Editor), Adv. Irrig. 3:283-311. USDA/SCS, 1983. Sprinkle Irrigation. National Engineering Handbook, Section 15, Chapter 11.