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Water Balance Irrigation Scheduling: Comparing Crop Curve Accuracies and Determining the Frequency of Corrections to Soil Moisture Estimates

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Water Balance Irrigation Scheduling: Comparing Crop Curve Accuracies and Determining the Frequency of Corrections to Soil Moisture Estimates WATER BALANCE IRRIGATION SCHEDULING: COMPARING CROP CURVE ACCURACIES AND DETERMINING THE FREQUENCY OF CORRECTIONS TO SOIL MOISTURE ESTIMATES D. D. Steele, T. F. Scherer, L. D. Prunty, E. C. Stegman ABSTRACT. Water balance methods are commonly used to schedule irrigations and use evapotranspiration (ET) functions and crop curves to estimate crop ET (ETc). Because the methods may over or underestimate ETc, field-measured values of available soil moisture content (SMC) are often used to correct or adjust estimates of soil moisture during the growing season. This study was conducted to (1) compare the accuracies of four crop curves, based on the Jensen-Haise reference ET method, for corn in the northern Great Plains, and (2) determine the need for and frequency of in-season corrections to SMC estimates. The comparisons were based on differences between estimated and measured SMC for the 1990, 1991, 1992, and 1994 seasons using nonweighing lysimeters near Oakes, North Dakota. The SMC data were compared to estimates using bias and absolute errors, r2, Friedman Rank Sums, and sign distributions. The SMC estimates were corrected to measured values at three frequencies: start of season only, approximately monthly, and approximately semi- monthly. The crop curve based on days past planting was generally the most accurate, followed by the crop curve based on cumulative growing degree days. All of the methods tended to overestimate ETc. Selection of a correction frequency is more important than selection of a particular independent variable—days or weeks past emergence, days past planting, or cumulative growing degree days since planting—for a crop curve. For the crop curves, soil types, and climatic conditions of this study, none of the crop curves should be used without in-season SMC corrections on at least a monthly frequency, and semi-monthly corrections are preferred. The methods employed in this study can be transferred to other sites, climates, and crops. Keywords. Error analysis, Lysimeters, Soil moisture, Maize, Northern Great Plains. ater balance irrigation scheduling methods Water balance algorithms use ETc estimates to indicate are more likely to be used when producers when irrigations should be scheduled. Stegman and Coe are confident of the methods’ accuracies and (1984) presented irrigation scheduling software based on when the methods are easy to use. Because the unmodified Jensen-Haise (1963) equation: Wwater balance techniques for irrigation scheduling may over- or under-predict crop evapotranspiration (ETc), ETr = 0.0102 (Tm + 3.36) Rs (1) corrections or adjustments should be used to correct or –1 “reset” a water balance to accurately reflect field where ETr is the reference evapotranspiration (mm d ); conditions during the growing season (Lundstrom and Tm is the average daily temperature (°C), and is given by Stegman, 1988). Accurate predictions of ETc are necessary Tm = (Tmin + Tmax) / 2; and Rs is the solar radiation for efficient use of irrigation water. Efficient use of (MJ m–2 d–1). Jensen and Haise (1963) used the term irrigation water not only assists with maximized returns, “potential evapotranspiration” for their equation, although but also helps to minimize losses of chemicals to ground equation 1 was based on data from alfalfa, cotton, oats, and water through excessive leaching of water through the soil. winter wheat. Here we employ the more commonly Estimates of ETc are commonly made available to referenced “alfalfa-based ET” (ETr) term, distinct from producers. For example, Enz et al. (1995) presented “grass-based ET” (ETo) terminology. Crop ET was computerized, on-line, real-time ETc estimates for computed by the equation: producers that are available through the North Dakota Agricultural Weather Network (NDAWN). Forty-eight ETc = KcETr (2) weather stations throughout North Dakota allow users to estimate local ETc for alfalfa, turf grass, corn, potatoes, where Kc is a dimensionless crop coefficient given by: wheat, barley, dry beans, and sugarbeets. Kc = KcoKa + Ks (3) Article was submitted for publication in June 1996; reviewed and In equation 3, the factor K represents the basal crop curve approved for publication by the Soil & Water Div. of ASAE in May 1997. co The authors are Dean D. Steele, ASAE Member Engineer, Associate calibrated to the reference crop, i.e., a non-water-stressed Professor, Thomas F. Scherer, ASAE Member Engineer, Extension condition with minimal evaporation from the soil surface. Irrigation Engineer, and Earl C. Stegman, ASAE Member Engineer, The factor Ka represents a reduced-ET condition when Professor and Chair, Agricultural and Biosystems Engineering plant-available water (AW) in the root zone is limited and Department, and Lyle D. Prunty, Professor, Soil Science Department; North Dakota State University, Fargo, N. Dak. Corresponding author: is given by Ka = 1 if AW > 50% and Ka = AW/50 if AW < Dean D. Steele, Room 103 Agric. and Biosystems Engineering Bldg., 50%. The factor Ks represents conditions with incomplete North Dakota State University, Fargo, ND 58105-5626; tel.: (701) 231- crop cover (Kco < 0.9) and when the soil surface is wet, 7268; fax: (701) 231-1008; e-mail: <[email protected]>. and is given by: Applied Engineering in Agriculture VOL. 13(5):593-599 © 1997 American Society of Agricultural Engineers 0883-8542 / 97 / 1305-593 593 K = 0.8(0.9 – K ) (4) Table 1. Corn crop curve polynomials based on days past planting, s co cumulative growing degree days, and days past emergence on the day of rain or irrigation Coefficient Values Coefficient DPP Base* CGDD Base* DPE Base† K = 0.5(0.9 – K ) (5) s co C1 0.17549 0.24738 0.1814466119 –4 C2 0.0017287 –0.0014929 –1.877271 × 10 –4 –5 –4 on the first day after rain or irrigation C3 –1.7684 × 10 1.6737 × 10 7.004694 × 10 –5 –8 –6 C4 1.3588 × 10 –3.1877 × 10 –9.3707 × 10 –7 –11 –8 C5 –1.7126 × 10 2.2973 × 10 3.12 × 10 Ks = 0.3(0.9 – Kco) (6) –10 –15 C6 5.9329 × 10 –5.8428 × 10 - R2 0.679 0.544 (Not reported) on the second day after rain or irrigation SEKc 0.21 0.25 (Not reported) N 73 73 (Not reported) and Ks = 0 for other times or when Kco > 0.9. * The coefficients C1, C2, . C6 are used in the equation Kc = C1 + 2 3 4 5 Crop coefficients for Stegman and Coe’s (1984) C2 X + C3 X + C4 X + C5 X + C6 X , where Kc is the crop publication were based on earlier work (Stegman et al., coefficient and X is the time base (days past planting or cumulative 1977) and used days past emergence (DPE) as the growing degree days since planting); SEKc is the standard error of the Kc estimates; and N is the number of data points (Steele et al., 1996). independent variable (table 1). In addition to the inputs Time base abbreviations: DPP = Days Past Planting, CGDD = required for ETr computation, the method requires rainfall Cumulative Growing Degree Days since planting. The CGDD values and irrigation data, crop type and emergence date, soil root use a 10°C base and no upper limit. The Kc values are used in the zone depth, and soil water holding capacity. equation ETc = KcETr, where ETc is the crop ET and ETr is the Jensen-Haise (1963) reference ET equation. Lundstrom and Stegman (1988) presented a simplified † The coefficients C1, C2, . C5 are used in the equation Kco = C1 + 2 3 4 checkbook irrigation scheduling method that uses daily C2DPP + C3DPP + C4DPP + C5DPP , where Kco is the basal crop Tmax as the only climatological input. The checkbook coefficient and DPP is the time base days past emergence (Stegman and Coe, 1984). method contains ETc tables derived from the earlier crop curves of Stegman et al. (1977) and long-term weather records for North Dakota. Their corn water use values are by their method. Whether producers routinely monitor soil shown in table 2. The checkbook method has gained moisture every two weeks is uncertain, and the acceptance in the northern U.S., as evidenced by Wright consequences for less frequent corrections is unknown. If and Bergsrud’s (1991) adaptation of the checkbook method the irrigation scheduling methods over predict ETc, for use in Minnesota and Werner’s (1996) development of producers will over-irrigate. Consequences include similar checkbook tables for South Dakota based on possible yield reductions, excessive pumping costs, and climatic data. leached agricultural crop chemicals. Conversely, Steele et al. (1996) presented crop curves for corn underprediction of ETc will result in under-irrigation and (table 1) based on days past planting and cumulative probable yield reductions. growing degree days since planting for use with Jensen- Comparisons between model estimates and measured Haise (1963) ETr computations. Their crop curve values of ETc and/or soil moisture content (SMC) are too polynomials were developed for use in equation 2 and numerous to review here. However, a few examples include time periods or conditions in which transpiration illustrate the variety of statistics that can be applied. Linear may have been limited, the soil surface was wet, and/or regression of model estimates of ET versus measured ET crop cover was incomplete. That is, they developed crop values has been used to evaluate the accuracy of ET curves for Kc, not Kco, and they did not employ equations models (e.g., Farahani and Bausch, 1995; Abtew and 3 through 6. In the data sets used to construct the crop Obeysekera, 1995). Mahdian and Gallichand (1995) used curves, periods of limited transpiration did not cause yield- mean bias error, mean absolute error, root mean square reducing stresses (Steele et al., 1996). error, and a coefficient of efficiency to compare model Lundstrom and Stegman (1988) recommended soil estimates and measured values of soil moisture.
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