II. “II I I I. I “I. III III I.“ III IIIIIIIII" ”Ctr—‘1‘ II III; I II I 'II'r-IIIIII'." II I III fIIII‘II IIIIIIIIIIIIIIIIIIIIIIIII 'II III "II II IIIII‘III' III'I‘I III I III II‘IIIIII II III‘ IIIIJI III III III III IIIIIIIII IIIIIIIIIIIII III IIIIIII IIIIIII II . WWII ° II'IIIIII II II III I II III IIIIIIII II'III IIIId IIIIIIIII IIIII'TII I I F ‘9. .. a . - ~....¢M‘-' cot,‘ .— o—«QaA . -; -l , gm I {III II LII“ I I III. , III}! , v . , '. . . o > , . - 0" . .. ”p.-~‘ _ .. u ‘ - ~ .A‘-.'—‘~— ” . _ V A r~ . - . ~— p...- . c .. 23-— ' ———--.- ‘ .‘ "2H .' ” I‘IIIIIII II; ILI - . .4..." - —. f, n v .I v ‘- _ \ I ’ '- fl _ o u.” . V . - _ _ .t. a" ‘ an - ‘- - . . Jr... 2 - m, .4.-. - ....-A— mw“ . -‘ - d A.-. . ‘ , o I - ... .t 0“ LIBRARY Michigan State University This is to certify that the thesis entitled AN ANALYSIS OF IRRIGATION UNIFORMITY AND SCHEDULING EFFECTS ON SIMULATED MAIZE YIELD IN HUMID REGIONS presented by SALLY L. WALLACE has been accepted towards fulfillment of the requirements for Master of Science Ag. Eng. Technology degree in 1 Major professor Date Aug. 6, 1987 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution _._—_v . ____ ._ . ,7 7 , ... __ ____ _ _. MSU LIBRARIES m \— RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES wiii be charged if book is returned after the date stamped beiow. AN ANALYSIS OF IRRIGATION UNIFORMITY AND SCHEDULING EFFECTS ON SIMULATED MAIZE YIELD IN HUMID REGIONS BY SALLY L. WALLACE A THESIS Submitted to MICHIGAN STATE UNIVERSITY in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Agricultural Engineering Technology Department of Agricultural Engineering 1987 ABSTRACT AN ANALYSIS OF IRRIGATION UNIFORMITY AND SCHEDULING EFFECTS ON SIMULATED MAIZE YIELD IN HUMID REGIONS BY Sally L. Wallace The objective of irrigation in humid regions is to supply sufficient water to meet crop requirements during short-term droughts. In addition to supplying an adequate volume of water, an irrigation system should distribute this water uniformly. Uniformity is an index inversely related to the variance of irrigation depth. In some cases where uniformity is sub-Optimal, adverse yield effects may be lessened through more frequent water application. Most research into the relationship between uniformity, scheduling and yield has been of a theoretical nature, thus the first objective of this research was to determine, using a crop model and irrigation scheduling program, the effects of irrigation uniformity and scheduling on maize yield. Irrigation uniformity is commonly measured using evenly spaced collectors over which the irrigation system is operated. This method of assessment only considers an Sally L. Wallace initial level of uniformity as applied by the irrigation technology. Several factors, such as uniform rainfall during the growing season, may serve to mitigate the effects of non-uniform irrigation. The second objective of this research was to assess the effects of rainfall on overall water application uniformity and efficiency. The third objective of this research was to analyze and discuss these new insights into irrigation uniformity with respect to economics and farm management. The results of this research have shown that there is a relationship between irrigation uniformity , yield uniformity and mean yield. In addition, rainfall is an important factor in improving overall uniformity in humid regions. The use of a coefficient of variation adjusted for rainfall leads to more accurate assessments of yield losses due to non-uniformity. Economic analysis showed that irrigation scheduling at a higher available water content is not beneficial in humid regions; however is appropriate in arid areas if water and energy costs are low. Substantial rainfall inputs also influence farm management, especially in decisions concerning irrigation technology selection and improvement. To Geech, who lay at my feet through the worst of it all. ii ACKNOWLEDGEMENTS The author wishes to sincerely thank Dr. John Gerrish, Mr. Alan Herceg, Dr. Joe Ritchie and especially Dr. Vincent Bralts for their contributions to, and support of this research. Special thanks go to Ken Algozin and Ed Martin for their invaluable assistance in data presentation and analysis. iii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . vi LIST OF FIGURES. . . . . . . . . . . . . . . . . .vii I. INTRODUCTION . . . . . . . . . . . . . . . . . l A. Background . . . . . . . . . . . . . . . . 4 B. Justification . . . . . . . . . . . . . . . 7 C. Objectives. . . . . . . . . . .1. . . . . . 9 II. LITERATURE REVIEW. . . . . . . . . . . . . . .10 A. Irrigation Uniformity Concepts . . . . . .10 8. Application Efficiency Concepts and Theory . . . . . . . . . . . . . . . .20 C. Irrigation Uniformity and Yield . . . . . .28 D. Computer Modeling of Maize Growth and water use 0 O O O O O O O O O O O O O .34 E. Summary . . . . . . . . . . . . . . . . . .39 I I I 0 METHODS O O O O O O O O O O O O O O O O O O O 41 .42 A. Research Approach 3. ResearCh MethOds O O O O O O O O O O O O .45 C. Analysis Techniques . . . . . . . . . . . .61 iv IV. RESULTS, ANALYSIS AND DISCUSSION . . A. Irrigation Uniformity, Scheduling and Yield 0 O O I O O O O O O O O B. Verification of Adjusted Coefficient of Variation . . . . . C. Irrigation Uniformity and Rainfall Effects on Economics and Management Decision Making . . . . . . . . . . V. CONCLUSIONS AND RECOMMENDATIONS . . . APPENDIX A: SCS Center Pivot Evaluation Procedure . . . . . . . . . . APPENDIX B: CERES-Maize and SCHEDULER Information. . . . . . . . . . APPENDIX C: Additional Information . . . . REFERENCES 0 O O O O O O O O O O O O O O O 63 63 .80 .93 100 103 107 113 162 10. 11. LIST OF TABLES Spinks Series Soil Characteristics . . . . Irrigation Scheduling and Crop Growth Summary (With Rainfall) . . . . . . . . . , Average ET Estimates from SCHEDULER and CERES-Maize Compared to ET Measured by LYSimeter O O O O O O O I O O O O O O O Irrigation Scheduling and Crop Growth Summary (Without Rainfall). . . . ,., . . . Irrigation Uniformity and Yield for 40% 50% and 60% Depletion Schedules (With Rainfall) O O O O O O O O O O O O O O Irrigation Uniformity and Yield for 40% and 50% Depletion Schedules (Without Rainfall). 'Adjusted Coefficient of Variation for 1984 Rainfall I O O O I O O O O I O I O O I I 0 Water Application CV Changes Over Time. . . Potential Seasonal Irrigation Requirements for Corn in Nine Michigan Districts . . . . Irrigation Scheduling Costs (With Rainfall) Irrigation Scheduling Costs (Without Rainfall) . . . . . . . . . . . . vi Page 47 49 51 59 64 74 81 84 88 93 96 Figure 11. 12. 13. 14. 15. LIST OF FIGURES Center Pivot System Design . Application Efficiency Under Sprinkler Irrigation . . . . . . . . . Deficit Irrigation for 100% Efficiency Application Efficiency Relationships . Application Efficiency, Coefficient of Variation and Percent Deficit Relationships. Sample Input for Scheduler . . . Irrigation Scheduling Summary Graph (With Rainfall) o o o o o o o 0 Sample Input for CERES-Maize . _Sample Output from CERES-Maize . Irrigation Scheduling Summary Graph (Without Rainfall) . . . . . . . CV of Irrigation and CV of Yield (40% Depletion Schedule) . . . . CV of Irrigation and CV of Yield (50% Depletion Schedule) . . . . CV of Irrigation and CV of Yield (60% Depletion Schedule) . . . . CV of Irrigation and Mean Yield (40% Depletion Schedule) . . . . CV of Irrigation and Mean Yield (50% Depletion Schedule) . . . vii Page .23 .24 .25 .27 .48 .50 .53 .54 .60 .65 .66 .67 .68 .69 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. CV of Irrigation and Mean Yield (60% Depletion Schedule) . . . . . . . . . . .70 CV of Irrigation and Mean Yield: 40%, 50% and 60% Depletion Scheduling Comparison . . . . .71 Parabolic Production Function Example. . . . .73 CV of Irrigation and CV of Yield Without Rainfall (40% Depletion Schedule). . . . . . .75 CV of Irrigation and CV of Yield Without Rainfall (50% Depletion Schedule). . . . . . .76 CV of Irrigation and Mean Yield Without Rainfall (40% Depletion Schedule). . . . . . .77 (CV of Irrigation and Mean Yield Without Rainfall (40% Depletion Schedule). . . . . . .78 CV of Irrigation and Mean Yield Without Rainfall: 40% and 50% Depletion Scheduling Comparison. .79 Graphical Validation of Adjusted CV. . . . . .83 CV of Water Application Changes over Time (1984) O O O O O O O O O O O O O .85 Nomograph for Estimating Adjusted CV . . . . .87 ‘Cumulative Frequency Distribution for a CV of .4 (Not Adjusted for Rainfall) . . . . .91 Application Efficiency Comparisons Between Original and Adjusted CVs . . . . . .92 Income Loss Under Different Irrigation Schedules (With Rainfall) . . . . . . . . . .94 Income Loss Under Different Irrigation Schedules (Without Rainfall) . . . . . . . . .95 Comparison of Income Loss in Humid vs. Dry Locations . . . . . . . . . . . . . .98 viii I. INTRODUCTION Irrigation in the engineering sense, is the application of water by artificial means (i.e. via some technology) for agricultural or horticultural crop growth. In very arid regions, irrigationis often the only way to meet crop water requirements and insure yield. Hence irrigation has been practiced in many of these areas for centuries. In humid locations, supplemental irrigation is a fairly recent though rapidly expanding phenomenon. In Michigan, 3% of the total cropland was irrigated as of 1978 (ERS, 1984). In 1980, a Cooperative Extension survey reported that Michigan's irrigated land area comprised over 400,000 acres, a 200% increase since 1975. Although the rapid expansion of irrigated cropland has slowed somewhat in recent years, irrigation will continue to be an important technology on many Michigan farms. The objective of irrigation in humid regions such as Michigan, is to provide sufficient water to meet crap demands during short term drought periods. The extent to which this objective is met by an irrigation system is dependent upon both design and management factors. Design factors include the proper selection of irrigation ' system and pumping station components to insure adequate capacity for water delivery to the crop. Management factors include the accurate assessment of crop water requirements and subsequent scheduling of irrigations to meet these requirements. Irrigation scheduling may be accomplished with varying degrees of success by many different means including : (a) direct or indirect assessment of soil water status, (b) evaluation of plant stress, and (c) estimate of evapotranspiration and soil water status through the use of climate and water balance numerical models. One of the most widely accepted and successful methods of irrigation scheduling is through the use of numerical models which estimate ET and calculate soil water status. With the advent of microcomputers and the development of irrigation scheduling software such as SCHEDULER (Driscoll and Bralts, 1986), extension services, agricultural consultants and irrigators themselves, are now able to solve the necessary equations with a microcomputer and schedule irrigation in a matter of minutes. Irrigation uniformity is a measure of the variability of the application of water to an irrigated area. The degree of irrigation uniformity also depends on technology design and management and is related to crop yield through the effects of over and under watering. In non-uniform irrigation situations, deficit areas exhibit yield loss due to plant stress. Areas where excess water has been applied may also show decreased yield because of nutrient leaching and reduced root aeration. Even with a good design, all irrigation systems exhibit some degree of non-uniformity. If an irrigation system is to be properly managed to minimize the costs of yield and nutrient loss associated with the system's non-uniformity, an appropriate irrigation schedule must be found. In the case of a poor design or a loss irrigation system uniformity over time, management through scheduling may also be important. There is some level however, where the cost of non-uniformity exceeds the cost of improving the irrigation technology, regardless of the irrigation schedule. The availability of sophisticated crop models such as the CERES-Maize corn model (Jones and Kiniry, 1986) allow for accurate estimates of the yield effects of excess and deficit water on a crop. As Dent and Blackie (1979) have .noted, there are distinct advantages to using simulation models over fieldbased experimentation. These advantages include: (1) total control over the experimental environment and treatment; (2) time constraints are reduced to that required for computer operations; and (3) treatments are evaluated sequentially as opposed to simultaneously in actual field experiments. One of the objectives of this research then, will be to use the standard version of the CERES-Maize model to analyze the effects of different center-pivot irrigation uniformity levels and scheduling strategies on maize yield. Uniformity of center pivot irrigation is commonly measured using collectors of equal size placed at constant intervals along the radius of the pivot. The pivot is turned on and allowed to pass over the collectors. The volume of water in each can is then meaSured and uniformity is calculated. This method of measurement only considers an initial uniformity of water as it is applied by the irrigation system. Several other factors, however may influence the final level of water uniformity in the field. On an instantaneous basis (i.e. after one irrigation event) lateral movement of water in the soil may significantly increase the final uniformity of soil water. Over an entire season, uniform application of water through periodic rainfall will affect the overall seasonal uniformity of water applied to an irrigated area. A second major objective of this research will be to determine the effect of rainfall on uniformity of water application. The third objective of this research will be to analyze and discuss these new insights into irrigation uniformity with respect to economics and farm management decision making. A. Background There are numerous methods available for irrigation water application. These methods may be divided into four general categories: (a) subsurface (b) surface (c) drip/ trickle, and (d) above ground sprinkler. Above ground sprinkler is by far the most prevalent irrigation method in humid regions including Michigan. The most commonly used sprinkler irrigation technologies are center pivot and big gun. Solid set and hand move sprinklers are also used to irrigate high value horticultural crops. System expense, however prohibits their use in field crops. Sprinkler irrigation, particularly center pivot and big gun systems are popular primarily because of their relatively low per acre cost and their versatility. Sprinkler irrigation is appropriate for a wide range of topographies, soils and crops. Because of the importance of center pivot sprinkler irrigation in Michigan and other humid areas, this work will focus on uniformity under center pivot sprinkler systems. Figure l on the following page is a schematic diagram of center pivot operation. The previously noted irrigation system categories may also be differentiated by cost and by application efficiency characteristics. Generally, drip irrigation is more efficient (and expensive) than sprinkler irrigation which in turn, is more efficient (and expensive) than surface irrigation. It should be noted that many different efficiency concepts exist and are widely used. Care must be taken to determine the precise definition of a particular concept and all terms which are included in it. In this study, irrigation efficiency refers to a ratio of Underground mainline or well in center \ source . Lateral Figure 1. Center Pivot system design (Kay, 1983). beneficially used water to total water applied. "Beneficial use" is a cloudy and often subjective term which may lead to over or under estimation of the efficiency of a given system or systems. Application efficiency, in contrast to irrigation efficiency, is the ratio of water stored in the root zone to total water applied. These two definitions are most likely to differ when leaching water is required. Although this water is not stored in the rootzone, it is generally considered beneficially used. Consequently, when leaching water is required in a system, the calculated irrigation efficiency will be higher than the application efficiency. In Michigan, where high precipitation alleviates the need for leaching water, irrigation efficiency is synonymous with application efficiency. B. Justification In 1983, Michigan State University in cooperation with the St. Joseph County Cooperative Extension Service and Soil Conservation Service developed a program for local irrigators which included an irrigation system evaluation service. See Appendix A for an overview of the evaluation method used for center pivot irrigation. During the past three years, SCS has evaluated over seventy center pivot systems and has found coefficient of variation uniformities ranging from .11 to .50 . The acceptable uniformity standard for sprinkler irrigation is found to have sub-standard uniformities. The application of water by any irrigation system is inherently non-uniform to some degree. In addition, the level of uniformity which can be achieved by any irrigation system at the onset or when the system is improved is generally dictated by the level of capital investment. Assuming that a farmer's objective is to maximize profit, the optimization of irrigation technology is probably not economical unless water costs and/or energy costs are very high. In addition, factors such as frequent rainfall may serve to mitigate the effects of non-uniform irrigation. Thus, in some situations, low uniformities may be quite acceptable. The body of work that deals with the issue of non-uniformity and yield is primarily of a theoretical nature. The empirical relationship between irrigation uniformity and yield uniformity to be better understood. The development of sophisticated crop models such as CERES-Maize can allow for the evaluation of these theoretical principles in on- farm irrigation situations. C. Objectives The effects such as regions The overall goal of this research is to determine the of irrigation uniformity and mitigating factors rainfall on the economics of irrigation in humid like Michigan. specific objectives of this research are: To evaluate the mean and variance of maize yield with respect to high, medium, and low center pivot irrigation system uniformities. To determine the effect of rainfall on the uniformity of irrigation systems and on the uniformity of crop yield. To analyze and discuss these new insights into irrigation uniformity with respect to economics and farm management decision making. I I . LITERATURE REVIEW To adequately address the issue of irrigation uniformity as it relates to scheduling, yield and rainfall some knowledge of (a) irrigation uniformity concepts, (b) application efficiency concepts and theory, (c) uniformity and yield relationships and (d) computer modeling of crop growth and water use is required. This section provides a review of the more pertinent literature and theory associated with these topics. A. Irrigation Uniformity Concepts 1. Distribution Models In sprinkler irrigation, a wide range of statistical models have been used to describe uniformity. The normal distribution has been considered by Elliott at. al.(l979,l980), English and Nuss (1982), Hart et.al. (1980) Hart and Reynolds (1965) Hill and Keller (1980) Karmeli (1978) Peri et.al. (1979) Seniwongse et.a1. (1972) Su (1979), and Walker (1979) Elliott et al. (1979,1980,) have reported on the use of the beta distribution. Gamma distributions in sprinkler irrigation have been researched by Chaudry (1976,1978), Seniwongse et.al. (1972) and Su (1979). 10 11 a. Linear Model The use of the linear or cumulative linear (uniform) models for sprinkler irrigation has been found primarily in the works of Karmeli (1977 and 1978) and Elliott et. al. (1978 and 1980). Karmeli tested 36 sets of sprinkler data with a linear model with coefficients of variation ranging from .38 to .62. He concluded that the linear model supplied a good estimate (compared with normal estimates) for higher uniformities and a superior estimate for low uniformities (UCC < 55%). Elliott et.a1. (1979 and 1980) also used linear regression to estimate the cumulative distribution function for sprinkler irrigation. In contrast to Karmeli's work, they found that the linear model was only superior to the normal for low uniformities. The linear regression function (Y = a + bx) when used with low uniformity sprinklers can supply information as to the areas of deficit, surplus and adequate irrigation as well as area depth in deficit and surplus areas. b. Beta Distribution Elliott et.a1. (1980) used the beta statistical distribution to describe sprinkler irrigation distribution patterns. Fitting the linear, normal and beta distributions to 2,450 overlapped sprinkler patterns with widely varying uniformities, they concluded that the beta distribution was the superior model at all 12 uniformities, especially low ones. Although the beta distribution is quite flexible a major drawback to its use is its complexity. c. Gamma Distribution Chaudry (1978 and 1980) , Seniwongse et.al. (1972) and Su (1979) have all explored the gamma distribution as a method of characterization of irrigation patterns. Chaudry's work is theoretical and does not consider how well the gamma distribution represents real data. However his work is justified in that asymmetry or skewness characteristics are common in sprinkler irrigation distribution patterns. The gamma distribution can be used to account for this skewness. In addition, the normal distribution does allow for negative irrigation depths and the gamma distribution has the advantage of eliminating these. Seniwongse et.a1. (1972) found that the gamma distribution was representative of most high uniformity data, but was only moderate for medium and unacceptable for low uniformities. Su (1979) using uniformity ranges from 60 to 90% found that the gamma distribution fit his data no better than the normal distribution. 13 d. Normal Distribution The normal distribution is most often used to describe sprinkler irrigation uniformities and has been found by most authors to be an acceptable representation of irrigation distribution. A major advantage of the normal distribution model is its simplicity. Only two moments, mean and standard deviation, are required to describe the distribution. Too, the normal distribution is reported to provide an adequate representation over a wide range of uniformities, sprinkler sizes and spacings (Hart and Reynolds 1965, Seniwongse et.a1. 1972, Karmeli 1978). e. Other Distribution Models Childs and Hanks (1975) used the parabolic model to Adescribe sprinkler pattern distributions. Although this model has some advantages in that it does not predict negative or infinite irrigation depths, it has only been used with high uniformity sprinkler patterns. Seniwongse, Wu and Reynolds attempted representing sprinkler patterns with the poisson and exponential models but generally found that acceptable fits were not possible. Karmeli (1977) tried modeling the cumulative distribution function for sprinkler data with a variety of exponential models and found that the approach was far more complex and the results were no better than with the linear model . 14 2. Uniformity Measures Uniformity measures are calculations based on estimates of irrigation depths at various locations in an irrigated area. Based on these depths, a single number is produced which may be used as an indicator of uniformity. Uniformity measures are only a function of the variation in irrigation depth, although weighting factors may be used to express a greater degree of significance of some (usually lesser) depths. a. Christiansen's Coefficient (UCC) The first and to this day most widely used expression of sprinkler uniformity was reported by J.E. Christiansen in 1942. This coefficient, commonly referred to as Christiansen's Coefficient symbolized by UCC or CU is ex- pressed as a percentage and defined by the following equation: UCC = 100 ( 1.0 - ) mn in which x is the sum of the absolute deviations of individual observations from the mean value m (i.e. x = [xi - m1) and n is the number of observations. If the irrigation system is completely uniform, then all xi = m and UCC = 100%. Heerman and Hein have mpdified the above equation for use with center pivot systems such that each observation represents a different area of the field. 15 The resulting number contains the weighted value of the observations: 55 as -( D5 SS ) Ss UCC = 100 ( 1.0 - ) Ds Ss where D5 is the depth applied at a catch can and SS is the distance to equally spaced collectors. Despite its popularity, presumably due to its simplicity, Christiansen's Coefficient has been criticized extensively over its 40 year existence. Benami and Hore (1964) questioned Christiansen's assumption that the average deviation is a satisfactory measure of performance. They present an hypothetical example wherein two systems are measured and twelve readings are taken of each. In the first case, all readings deviate by +/- 20 and in the second case, eight readings deviate by +15, two readings by -15, and two reading deviate by -45 percent from the mean. In each case, the average deviation equals 20 and both systems have the same uniformity coefficient (80%). Clearly however, the first system is more uniformly distributed than the secOnd. Benami and Hore's argument would be far more compelling if the coefficient that they present as an alternative were not subject to the same problem of arbitrariness as the UCC (Solomon, 1983). Norum (1961 cited in Solomon 1983 and 1966) also 16 criticized the UCC as lacking "pertinent physical significance" and as "incomplete" and "arbitrary". By this, Norum means the lack of a connection between capital cost of a system and irrigation efficiency as characterized by the UCC. At the time that Norum made these comments and continuing today, most systems are selected so that they can provide an adequate mean application with a Christiansen's Uniformity Coefficient deemed "acceptable" (generally 80% or greater). Even if a system exhibits a uniformity which is less than optimal, investment in and utilization of such a system may still be economically justifiable if water and energy costs are sufficiently inexpensive. b. Wilcox and Swailes Coefficient (UCW) In 1947, another uniformity coefficient was introduced by J.C. Wilcox and G.E. Swailes. Wilcox and Swailes evaluated the efficiency of several sprinkler models at different spacings. The sprinkler types are real, however the spacing assessments are purely theoretical. The authors evaluated the catch from a single sprinkler in evenly spaced cans. Then assuming that the pattern and catch would be the same for another sprinkler of the same type, the uniformity is calculated. The Wilcox and Swailes coefficient (UCW) is defined as: l7 UCW = 100 (1 - ) i Where S is the standard deviation of the catch can values and i is the mean. The Wilcox and Swailes coefficient of uniformity is also called the coefficient of variability or variation and the statistical uniformity. Wilcox and Swailes as well as others have noted that because the squares of the deviations from the mean are used rather than the deviations themselves, larger deviations are given more weight. Thus, UCW is generally lower than UCC for the same system. Dabbous ( 1962 as reported in Solomon 1983) and Tezer (1971) both found a strong linear relationship between UCC and UCW which is generally expressed as follows: ucc = 100( 1- .798 5/2) The Wilcox and Swailes coefficient or coefficient of variation has become widely used in the assessment of drip irrigation uniformity ( Wu and Gitlin, 1981, Bralts and Kesner, 1983). As Wu and Gitlin note (1981) the coefficient of variation can be used to determine the average depth of deficit in the deficit area of the field. This in turn may be used to schedule irrigation in such a way that yield losses may be minimized in drip irrigated fields. 18 c. Hart and Reynolds Coefficient (UCH) In 1965, Hart and Reynolds proposed another uniformity coefficient which essentially utilizes the same statistical parameters as the UCC and UCW. Assuming that non-uniform sprinkler distributions are normally distributed and since the mean deviation of normally distributed values is equal to (JZ/n) times the standard deviation of those values they proposed: UCH = l - [/(2/n ) ] (S/Y) The UCH incorporates the standard deviation to mean ratio and produces the same value as Christiansen's when irrigation depths are normally distributed. d. Benami and Hore's Coefficient In 1964, Benami and Hore presented what they considered to be a favorable alternative to Christiansen's coefficient. As mentioned above, the authors criticized the UCC for its arbitrary performance measurement. In addition they state that although the UCW is a somewhat better representation, it too is insufficiently sensitive to differentiate between satisfactory and unsatisfactory sprinkler performance. The Benami and Hore coefficient (UCA) is a radical departure from the previously discussed methods in that the approach is not simply a statistical evaluation of a 19 technology irrespective of crop needs. As Solomon (1983) notes, " The significance of UCA is in the fact that the authors constructed it with a particular interpretation in mind. It was not merely a measure which varied with the degree of uniformity. It was intended to vary with the physical significance of uniformity... UCA incorporates not only a measure of uniformity, but a value system appropriate to the context within which uniformity measurements are used.” The UCA is based on a consideration of the deviations from the mean of a group of readings below the mean and a group above the mean: UCA = Cl/Cz where [xlb C1 = Mb - Nb and [X13 C2 = Ma + Na Ma is the mean of a group of readings above the general mean, Mb is the mean of a group of readings below the general mean, Na and Nb are the number of readings . above and below the mean respectively. [xla is the absolute deviation from Ma for the group of readings above the mean and [xlb is the sum of the absolute deviations from Mb for the group of readings below the mean. 20 The ratio of means and deviations devised by Benami and Hore tend to stress the deviations below the general mean on the assumption that yield losses due to drought stress are more significant with respect to yield and economics than are losses due to inundation. e. SCS Pattern Efficiency (PE) The On-Farm Irrigation Committee of the ASCE defines pattern efficiency proposed by the SCS as the ratio of the average low quarter depth of irrigation water infiltrated and stored in the rootzone to the average depth of irrigation water applied. Because of this reference to the low quarter applied, pattern efficiency is also called the application efficiency of the low quarter or AELQ. B. Application Efficiency Concepts and Theory As noted previously irrigation efficiency generally refers to the ratio of water which is beneficially used to total water applied. Irrigation efficiency (sometimes called water use efficiency) is defined by the equation (Israelsen and Hansen, 1962) wu Eu = 100 wd Where Eu is the water use efficiency, Wu is the water which is beneficially used and Wd is water which is delivered to the farm or irrigation system. 21 Another widely used efficiency concept is water application efficiency, the ratio of water stored in the rootzone to total water applied. Water application efficiency is defined by the equation Ws wf Where Ea is the water application efficiency, W5 is water stored in the root zone during irrigation and Wf is the water delivered to the farm or irrigation system. The most common sources of loss of irrigation water during water application include surface runoff (Rf) and deep percolation below the root zone (Df) (Israelsen and Hansen, 1962). Therefore, Wf = Ws + Rf + Dr and Ea may then be defined as Wf - (Rf + Df) Ea = 100 , Wf The definitions of application efficiency and water use efficiency are most likely to differ when leaching water is required. Although this water is not stored in the rootzone, it is generally considered beneficially used. Consequently, when leaching water is required in a system, the calculated irrigation efficiency will be 22 higher than the application efficiency. Irrigation and/or application efficiency give no indication of irrigation uniformity or adequacy. Figure 2 shows a common application efficiency found under sprinkler irrigation. In Figure 2, area A is adequately irrigated, area B is in deficit and area C has been excessively irrigated. Using these areas, application efficiency may be calculated as A / A + C. Figure 3 shows how, with deficit irrigation, application efficiencies of 100% may be achieved (Wu and Gitlin, 1981). For drip irrigation, Wu and Gitlin (1983) and Bralts (1984) have defined the application efficiency as Vr(l-PD) Vr(l-PD) Ea = 100 ( ) = 100 ( va 3600QaT Where Vr is the amount of water applied, PD is the irrigation deficit expressed as a decimal, Va is the irrigation volume required, Qa is the actual discharge to the submain per second and T is the irrigation time in hours. The above relationship is illustrated in Figure 4 (Wu and Gitlin, 1981). In the special case where the irrigation volume applied is equal to the irrigation volume required, the irrigation deficit is equal to 0.4 times the coefficient of variation. (Bralts,1984) In this case, application efficiency can be determined by the equation 23 Figure 2. Application Efficiency Under Sprinkler Irrigation 24 Figure 3. Deficit Irrigation for 100% Efficiency RATIO OF DEPTH. Xi/X 25 FRACTION OF AREA, a,% 0 20 40 60 80 100 I I f I _ A 0.5 r- L. r 1.0 Coefficient of Variation of Emitter Flow (total), Vq = 0.10 1.5 A a Water stored in root zone B a Water lost due to deep seepage C - Deficit G - Ratio of the required irri etion depth Xi to the mean irrigation gepth X X = Mean irrigation depth 2.0 (Figure 4. Application Efficiency Relationships (Bralts, 1984) 26 Vr( l'PD) Ea = 100 ( ) = 100 (1 - 0.4 cv) if Va = Vr This relationship between application efficiency, percent deficit, and coefficient of variation is based on probability and normal statistical distribution and is demonstrated in Figure 5 (Wu and Gitlin, 1983). Hart and Reynolds (1964) used the coefficient of variation for analytical irrigation system design purposes. Assuming that the standard deviation and mean calculated from a population sample adequately reflect the actual mean and variance of the total population then the equation for the normal probability density function may be written as Nq - i } s/Zn where N is the number of observations, q is the class interval, x is the value of an occurance , E is the mean of the sample and s is its standard deviation. If the distribution is continuous, it is then possible to determine the fraction of the total number of observations falling between two points with the equation APPLICATION EFFICIENCY. E, S 27 80 ’ Vq' Coefficient of variation at emitter flow (total) 70 V 00 50 f L P g 4 L n L L e n e n e n 0 2 O 8 10 12 14 16 18 20 22 24 2' 28 rtnceur or omen. Po. 1. Figure 5. Application Efficiency, Coefficient of Variation and Percent Deficit Relationships (Bralts, 1984) 28 s/2n a Substitution into this equation allows the definition of a distribution coefficient. Replacing Ay with a, a with xHa and B with a, the equation becomes EH3 where a is the fraction under a normal curve from x = EH3 to x =o, xHa is the minimum application on the area a, and Ha is the fraction of the mean application (I) equaled or exceeded over the area a. This equation thus may be used to determine the fraction of irrigated area in excess or deficit. C. Irrigation Uniformity and Yield Irrigation uniformity is related to crop yield through the effects of over and under watering. Insufficient water leads to high soil moisture tension, plant stress and reduced yields. Excess water may also reduce crop yields due to nutrient leaching and lack of root aeration. 29 Irrigation uniformity is also related to the efficient use of agricultural resources. Over watering implies the wasting of the energy used to power the pump and used to manufacture the chemicals which are leached below the rootzone. In deficit water areas, the inability to achieve potential crop yields results in the waste of agricultural inputs applied in anticipation of maximum yield (Gurovich et. al. 1983). Howell (1964) showed that for theoretical cases when determining the relationship between non-uniformity and yield, if the yield relationship can be expressed as a polynomial function of application depth, the relevant characteristics are the moments of the distribution taken to the order of the polynomial. If the yield relationship is parabolic, only the mean and standard deviation are required to estimate total yield. ,If the relationship is cubic, then mean, standard deviation and skewness are required. If quartic, the mean, standard deviation, skewness and kurtosis are all required. Varlev (1976) following the work of Howell, described a coefficient of non-uniformity which characterizes both non-uniformity and the yield depression caused by it. ' This coefficient can be used to in comparing the Quality of different technologies for irrigation with respect to non-uniformity. He notes that in a large number of cases, the relationship of infiltrated water-yield can be expressed as a second degree polynomial. The coefficient 30 of non-uniformity relates linearly for the absolute and relative yield loss due to the non-uniform distribution_ of the same amount of water. Stern and Bresler (1983) investigated the relationship between crop yield and uniformity of water application. The relationship between uniformity of water applied by sprinklers, variability of soil of soil water content after irrigation and its effect on yield was studied and the yield response of sweet corn on two plots was quantitatively evaluated. The relationships among net water application, seasonal average soil water contents (before and after irrigation), depth of water measured in cans during four different irrigations and three different yield components were obtained by calculating the correlation coefficients between each pair of variables. Using normal distributions to characterize the probability density function of water application and Christiansen's coefficient to express uniformity, relative crop yield was expressed as a function of CU and total amount of irrigation water. Seigner (1978) proposed a method of calculating the mean yield of a non-uniformly irrigated field and then illustrated the effect of non-uniform water application and the price of water on farm profits. Using cotton as an example with varying uniformities and water prices, two regions are identified. The first is associated with low water prices and high uniformities. Within this 31 region, a reduction in uniformity justifies increased water application. Within region two, associated with high water prices and low uniformities, the opposite is trUE. Amir and Seigner (1985) quantified the benefits to a producer from improved trickle irrigation emitter uniformity. The general approach is the same as that proposed by Seigner (1983). By determining the optimal seasonal water application depth and evaluating net income per unit area for a given crop, the value of improved emitter uniformity can be assessed. Feinerman et. al. (1983) evaluated the economic implications of non—uniform water application. Two different water production functions, one for crops sensitive to excess water and the other for crops which are not sensitive to water applications greater than that required for maximum yield, are linked to a simplified water balance equation and to an economic optimization model. In the case of crops which are sensitive to excess water, productivity and optimal levels of water application are lower in non-uniform fields than in uniform fields. Where crops are not sensitive to excess water, the outcome depends on the price of water relative to crop income. Letey et. al. (1984) describe a methodology for analyzing the effects of infiltration uniformity on crop yield, optimum application depth and profit. The 32 relationships between corn grain yield and average applied water were presented for various uniformities of water. Generally, production at almost any water application rate was found to decrease with decreasing uniformity. Because of the nature of the crop production for corn (i.e. corn seems to be insensitive to excess water application) increased water application may substitute for uniformity. If sufficient water is applied, maximum yields may be achieved even at very low uniformity levels. However, it should be noted that the study does not account for cost associated with nutrient leaching when, excess water is applied. Solomon (1983) provides a paradigm for uniformity and yield study. He notes that most common uniformity and efficiency measures are imbued with some degree of physical significance and the steps used in calculating these measures to some extent parallel those used to calculate yield. Solomon advocates the use of distribution models rather than simply working with raw uniformity data, for reasons of generalization, and ease of estimation and computation. In selecting the proper distribution model, statistical moments must be considered the key characteristics of that distribution. Thus moment matching is the proper approaCh for model selection. For polynomial yield functions, crop yields are completely determined by the moments of the irrigation distribution. Thus distribution models should 33 be fitted to empirical sprinkler data by choosing parameter values that cause the moments of the model to match the moments of the data. Although somewhat complex, Solomon recommends the use of the beta distribution model which allows the matching of the mean, standard deviation, skewness and kurtosis statistical moments. For some distributions, the first two moments may be sufficient. However, sprinkler distribution skewness and kurtosis may have a sizable effect on yield. Guronovich and Duke (1984) provide a methodology for assessing the economic implications of improving center pivot uniformities. Using a geostatistical approach to characterize uniformity, results were then applied to the PLANTGRO simulation model developed by Hanks (1974). Because PLANTGRO only accounts for yield loss due to insufficient water, the authors assumed that each cm. of water applied over the requirement leached 13 kg./ha. below the rootzone reducing yield by 170 kg./ha. The authors conclude that the cost of installing pressure regulators at each sprinkler nozzle may be more than offset by increased uniformity and resultant increased yields. Solomon (1984) proposed that in some special cases, irrigation uniformity measures which are generally considered quantitative indices without physical significance, may be used to determine relative yields. In situations where effective rainfall exceeds the water 34 requirement threshhold, the Christiansen's Uniformity Coefficient appears to be the lower bound on the relative yield. D. Computer Modeling of Maize Growth and Water Use 1. Maize Growth Simulation Models Maize growth simulation models rely on the principle that plant growth is a response to various environmental factors. These factors and associated responses may be stated in mathmatical language. Plant growth results from the influence of various daily inputs into a system (i.e. the plant) which itself is continuously changing. The process of computer simulation is essentially estimating these daily inputs and modeling the plant growth response according to empirically derived rules. Crop growth simulation models generally fall into two categories, incremental and decremental. Incremental models estimate crap growth from germination forward over the growing season. Decremental models begin with an optimum curve and estimate decreased production according to type, timing and duration of various stresses. Crop growth simulation models have proven very useful in the evaluation of water management strategies. A properly formulated and validated crop mpdel allows for testing and experimentation with irrigation depth and scheduling strategies which could take years to accomplish 35 in the field. Many growth simulation models have been developed and used to evaluate different farm management strategies. The purpose of this section is to provide an overview of some of the more important maize growth simulation models. SIMAIZ developed by Duncan (1975) simulates the growth, development and final grain yield of maize over a growing season. The required initial inputs to the SIMAIZ model include certain known or inferred characteristics of the corn variety being grown, soil moisture characteristics, and management details such as planting rate, irrigation dates and amounts. Daily inputs to the model include solar radiation, maximum and minimum temperature, pan evaporation and rainfall. SIMAIZ estimates growth by modeling photosynthesis and the quantity and partitioning of the net photosynthate produced each day. Childs et. a1. (1977) developed the maize growth model CORNGRO which was later modified by Tscheschke and Gilley (1979). CORNGRO simulates maize growth and yield as affected by water stress. The major process simulated by CORNGRO are soil water movement, photosynthesis, and respiration. The PLANTGRO model was developed by Hanks in 1974. PLANTGRO assumes that the ratio of actual to potential dry matter yield is directly related to the ratio of actual to potential transpiration. PLANTGRO is simple and inexpensive to run on a computer to determine seasonal 36 yields as influenced by irrigation, rainfall and soil water storage. CERES-Maize is a daily incrementing simulation model of maize growth, development and yield. CERES—maize is available in two versions; the standard, which simulates the effects of genotype, soil properties and weather on growth and in a nitrogen version which models the growth and yield effects of soil and plant nitrogen on the crop. In order to accurately determine maize growth, development and yield, the model simulates such physical and biological processes as phenological development, growth of leaves and stems, biomass accumulation and partitioning, soil water balance and plant water use, and soil nitrogen transformations. See Appendix B. for more information on file structure and validation of CERES-Maize. 2.. Computer Modeling of Crop Water Use The amount of irrigation water required by a crop is influenced by several factors, the most important of which include (1) climate, (2) available water supply or soil moisture, (3) plant growth characteristics, and (4) cultural practices (Bureau of Reclamation). The' purpose of this section is to provide a brief overview of direct and indirect methods of estimating crop water use for irrigation scheduling. 37 a. Direct Methods Direct methods for determining soil wetness and timing of irrigation include (1) gravimetric sampling, (2) neutron scattering, and (3) tensiometer. Gravimetric sampling involves the removal of a sample by augering into the soil, weighing the moist sample, drying and then reweighing. Soil moisture content is calculated as (Hillel, 1982). wet weight - dry weight dry weight Neutron scattering was developed in the 1950's and has gained widespread acceptance as method of soil moisture determination which is less laborious, more rapid and less destructive than gravimetric sampling. Neutron scattering operates by inserting a probe into a vertical access tube in the soil. The probe contains both a source of fast neutrons and a detector of slow neutrons. As these fast neutrons collide with hydrogen atoms from water in the soil they are slowed. The slow neutrons are counted and soil water content is determined by matching this reading to a calibration curve. Although neutron scattering is a convenient way of making soil water determinations, it has some disadvantages including high initial instrument cost and danger associated with exposure to neutron radiation. 38 The tensiometer is comprised of a porous ceramic cup, filled with water and connected to a manometer. As the cup encounters the surrounding soil, the water inside tends to equilibrate with the surrounding soil water. As the water is drawn out of the cup by soil matric forces, a drop in hydrostatic pressure occurs which is indicated by the manometer reading. b. Indirect Estimates of Soil Water The principal techniques used to estimate ET or water use, are based completely or in part on measurements of (1) solar radiation (2) wind (3) temperature, and (4) humidity. The best known ET estimation method requiring only temperature data is the Blaney-Criddle equation (1950). This equation, although easy to solve, Idoes not work well in humid regions. Jensen and Haise (1963) developed an equation which estimates ET based on inputs for both temperature and radiation. This equation has been found to work well in the central 0.8, however it does not correlate well in other regions. The Penman equation (1948) combines net radiation terms with advective energy transfer effects on crop use into one equation. The Penman equation, modified for estimating alfalfa based reference ET, is 39 Y Etr = (Rn + G) + 15.36 Wf (ea — ed) where Etr = reference crop ET in cal/cm2*d; A is the slope of the vapor pressure - temperature curve in mb/deg. C; y is the psychrometer constant in mb/deg. C; Rn is net radiation in cal/cm2*d; G is soil heat flux to the surface in cal/cm2*d; Wf is the wind function (dimensionless); (ea - ed) is the mean daily vapor pressure deficit in mb; and 15.36 is a proportionality constant in cal/cm2*d*mb. The Penman equation has been found to be very accurate for ET estimation in a wide variety of climatic conditions (Jensen, 1983) c. Computerized Irrigation Scheduling The purpose of irrigation scheduling is to provide farm managers with accurate information on soil water status. With this information, irrigators are able to make better decisions as to the timing and volume of irrigation water application. SCHEDULER (Driscoll and Bralts, 1986), like most scheduling software, uses a "checkbook" accounting system. Climatic data, antecedent soil moisture, rainfall, and irrigation are entered into the program on a weekly basis. SCHEDULER then uses the Penman equation to calculate ET and subtract these losses from the initial soil moisture. Irrigation and rainfall 40 volumes are added to this value so that a new soil moisture content is calculated. See Appendix B. for additional information on SCHEDULER. E. Summary 1. The definition of irrigation uniformity may be approached from either a distribution modeling perspective or by a uniformity definition. Although distribution models may in some cases be more representative of system uniformity, their complexity makes them quite difficult to implement in an on-farm evaluation procedure. Christiansen's Uniformity Coefficient is the most popular expression of sprinkler uniformity, however it has been justly criticized as arbitrary. Therefore in the interest of simplicity and accuracy, the Wilcox and Swailes coefficient (coefficient of variation) will be used in this report, to express uniformity of irrigation and yield. 2. Most of the work on the relationship between irrigation uniformity and yield has been of a theoretical nature. There is a need for a better understanding of how irrigation uniformity affects yield and how mitigating factors such as seasonal rainfall may influence seasonal uniformity. 3. Several maize growth models are presently available and could possibly be used in the type of analysis proposed here. The CERES-Maize growth simulation model in the 41 standard and nitrogen version is more encompassing than some of the other models reviewed, requires easily attainable input information, and has been validated in a variety of climates. (Jones and Kiniry, 1986). Thus the CERES-Maize model will be used in this study. 4. Computerized irrigation scheduling with software such as SCHEDULER facilitates accurate estimation of soil moisture status and allows for better decision making in timing and volume of irrigation application. Thus, SCHEDULER will be used in this study, for determining the effect of irrigation scheduling and uniformity on yield. I I I . METHODS The review of literature has shown that a large body of theoretical work exists dealing with the issues of irrigation uniformity and crop yield. There is, however, a lack of empirical research in this area. In addition, previous research has not effectively focused on how rainfall affects the seasonal uniformity of water application. More accurate estimates of the effects of irrigation uniformity on crop yield and better understanding of seasonal water application uniformity when rainfall is considered may aid irrigators in making more economically sound management decisions where irrigation is concerned. A. Research Approach Based upon the need to gain further insight into irrigation uniformity as it affects irrigators in humid regions, the following approaches are proposed to achieve the stated research objectives. 42 43 Objective 1: To evaluate the mean and variance of maize yield with respect to high, medium and low center pivot irrigation system uniformities. Approach Eight center pivot irrigation systems, exhibiting a range of uniformities, which either have been evaluated by SCS in St. Joseph County, or which have been generated will be selected for yield and uniformity evaluation. Usinghistorical weather data from 1984 collected at the Kellogg biological station, in Kalamazoo, Michigan, a mean application rate of 19.00 mm (.75 in) will be scheduled with the SCS SCHEDULER software program. Three schedules will be generated with irrigations beginning at 40, 50, and 60 percent soil moisture depletion. Collector data from the SCS evaluations will be adjusted so that the mean application rate will equal 19 mm as specified by the schedule. After the collector values are adjusted, each of these values for each system will be entered into the CERES- Maize irrigation file for an individual run. All other inputs (i.e. soil type, corn variety, weather, planting date etc.) except depth of water applied at each irrigation will be kept constant. Mean, standard deviation and coefficient of variation will be calculated for the water distributions and resultant yields as estimated by CERES-Maize. Coefficient of variation of 44 yield and mean yield will be analyzed with respect to irrigation water applied and gross water applied. The effect of scheduling on irrigation water requirement and yield will also be analyzed. Objective 2: To determine the effect of rainfall on the uniformity of irrigation systems and on the uniformity of crop yield. Approach During this stage of the analysis, the procedure outlined in objective 1 will be followed, except rainfall will be eliminated from the weather data. In addition, a theoretical basis will be presented for the determination of an adjusted coefficient of variation considering rainfall. The resultant uniformities in crop .yield’will be compared with those generated under rainfall and the adjusted coefficient of variation will be verified. Objective 3: To analyze and discuss the effects of these new insights into irrigation uniformity on economics and management decisions. Approach Costs of irrigation (water and energy) and yield loss, will be found or estimated and used to analyze and discuss the economic effects of irrigation non-uniformity. 45 Specific issues to be addressed are: l. The costs and returns of different scheduling strategies for varying uniformity levels. ,2. The effects that substantial amounts of seasonal rainfall may have on the decisions to improve or replace center pivot irrigation systems. 8. Research Methods 1. Objective 1. Method Eight center pivot uniformities, with CVs ranging from 0 to .58 were evaluated. Five of these uniformities were based on actual center pivot evaluations carried out from 41983-86 by the Soil Conservation Service in St. Joseph County, Michigan. See Appendix A for the center pivot evaluation procedure used by SCS. The collector values for three of the evaluations were generated using a random number generation procedure. Generated uniformities were necessary in order to evaluate a complete range of CVs. Once actual and generated catch can data were assembled, , each evaluation was entered into a short Turbo-Pascal program written by the author. Given inputs for the can weighting factor and the depth of water in the can in mm, the program calculates values for mean depth of application, variance of application depth, coefficient of 46 variation and Christiansen's Uniformity Coefficient. See Appendix C for the listing of this program. It was decided that irrigation would be scheduled based on a mean application depth of 19.00 mm (.75 in). In order to avoid generating an irrigation schedule for each system, catch can values were adjusted so that the CV remained the same for the system but mean depth of application was equal to 19.00 mm. The adjustment was made using the following equation 19.00 * original depth / original mean - adjusted depth. After the adjusted catch can values were calculated, the system evaluation data were again entered into the computer program to verify that the adjustments were correct (i.e. that the new mean = 19.00 mm and that the adjusted CV = the original CV). Irrigation scheduling was accomplished with the SCHEDULER software program using 1984 weather data collected at the Kellogg Biological Station near Kalamazoo, Michigan. Sample input for the SCHEDULER program is presented in Figure 6 . The soil type used in both SCHEDULER and CERES-Maize was a Spinks Loamy Sand soil. This soil was selected because it is one which is commonly irrigated in the state of Michigan and because, given its coarse texture, lateral water movement is minimal. Characteristics of the Spinks soil series are presented in Table l . 47 Table l . Spinks Series Soil Characteristics Depthmm (in) USDA Texture AWC mm/mm (in/in) 0 - 254 ( 0-10) loamy sand .11 (.11) 254 - 660 (lo-26) loamy sand .11 (.11) 660 - 1524 (26-60) sand .07 (.07) Rootzone 914 mm (36 in) 88.90 mm (3.5 in) Pioneer commercial corn variety 3780 was selected for the CERES-maize analysis. It was determined that this variety had an approximately 120 day growing season. This value was then used as input for SCHEDULER. Three different schedules were generated with the SCHEDULER program. The first schedule initiated irrigation when 40% of the available water was depleted; the second, when 50% of the water was depleted and the third when 60% of the available water was depleted from the soil profile. It should be noted here that the crop rooting depth was assumed to be .91 m (3 ft.) for scheduling and for the analysis with CERES - Maize. A summary of these irrigation schedules is presented in Table 2 and graphically in Figure 7. 48 01. COUNTY? ST. JO 02. FARM NAME? SALLY 1 03. CROP TYPE? CORN 04. GROWING SEASON (DAYS) ? 120 05. SOIL MOIST. HOLDING CAPACITIES (IN/FT) FOR 1 FOOT ? 1.32 FOR 2 FOOT ? 1.32 FOR 3 FOOT ? .84 06. MINIMUM SOIL MOISTURE BEFORE IRRIGATION EXPRESSED AS A PERCENTAGE OF AVAILABLE PROFILE CONTENT? 50 07. DATE OF PROFILE MOISTURE CONTENT 5.24 08. PROFILE MOISTURE CONTENT ESTIMATE (PERCENT) ON 5.24? 85 09. RAIN SINCE 5.24 (IN) :5.27 0.01 :5.29 0.10 :0.00 0.00 :0.00 0.00 :0.00 0.00 10. IRRIGATION WATER SINCE 5.24 :0.00 0.00 :0.00 0.00 :0.00 0.00 :0.00 0.00 :0.00 0.00 11. EMERGENCE DATE 5.10 12. NET WATER PER IRRIGATION CYCLE (INCHES) .75 13. TYPE IN DATE DESIRED As MO.DY.YR 5.30.84 Figure 6. Sample Input for Scheduler (49 AZ" oo.m v 23 oo.oo~ n MJDOmrum zonhqumo 800 AZH mh.m u I! oo.moN manomrum zospmuamo Rom Azn om.o_. :2 oo.von u manomrum zoapuaamo Roe zo~hca. __ 5.. __ _ v.0 _. a. __ _ _ 1. _ _.,u_ -.v___m_ _ __ _ o. o... _ __ oucoaL65m_ _ o— _ acute new. __ _ __ _ Q. ~__ _ o.. __ _ _ m _ _ v_.m __ a. _ __ _ __ _ __ _ . m _ _ __ m__ __ m__ __ oaeum _ m._ ._ _ _ s _ _ mm. __m. _ __ _ o.m __ .>55 new . __ _ . m _ _ __ _ __m_ . __ _ mu. __ _ _ m _ _ m.n ____,4 c.ato_ __ a. _ m“. __ _ __ _ _ e _ _ __ c.aoo_ ._ _ __ _ __ _ _ n _ _ .m. __ a. _ ._ m._ __ _ __ _ _ N _ _ so.s __m_ m__ __ _ __ _ __ _ _ _ «om om ov_ __oo an ac. __oo an ac. __ cm on ow. __oo om ov— _ ms425 __ mzaw __ >LmEE3m Cusoco nocu nce oc._3uocum covuea.ctu .N o.noh 50 man we Irene muck.- swam caoe. com: D 32%: / 34% mm»: m: came Pivor ma non 0 summer we 5/10 E WEE {KW mommsmom :20 ms 5.00 -pAEBQEECE mm 4.00 - Hm Mm; gg 13945. 5 100 ’3 3 l U, I b u :1: «2) 200 - ‘ __ _ _ wwm- L]. M “t _. A..- i IE9. :__o.7 _ A 7' f M 0-00 l I ' ' I ' ’ l r ’ r T T ' r 5112 5/25 5/00 5/23 7/07 7/21 a/04 we 9/01 DATE (sun - SAT) (with Rainfall) Figure 7. Irrigation Scheduling Summary Graph 1“ 15 PERCENT 51 The irrigation dates generated by SCHEDULER were entered into three separate irrigation files in the standard version of the CERES-Maize corn model. See Appendix B for information on inputs and file structures for CERES-Maize. The same weather data (1984 KBS) were entered into the CERES-Maize weather files. It should be noted here that the CERES—Maize model calculates ET using daily climatological inputs of maximum temperature, minimum temperature, total solar radiation and rainfall. In addition to these inputs, SCHEDULER requires inputs for maximum and minimum relative humidity , night time wind speed and average wind speed. Despite these differences, Bralts and Algozin (1985) have found that the ET estimates for the two methods are quite similar. Table 3 presents a comparison of lysimeter, SCHEDULER, and CERES-Maize evapotranspiration estimates. Table 3 . Average ET Estimates from SCHEDULER and CERES-Maize Compared to ET Measured by Lysimeter Period Lysimeter SCHEDULER Ceres-Maize (1985) (mm/day) (mm/day) (mm/day) 6/10 - 7/10 3.91 4.83 3.83 8/04 - 8/18 4.06 3.35 3.25 Average . 3.99 4.09 3.53 (Bralts and Algozin, 1985) 52 After irrigation scheduling was completed and other parameters for CERES-Maize were determined, each irrigation depth at each Observation point was entered into the irrigation files for the model. See Figure 8 for sample input for, and Figure 9 for sample output from CERES-Maize. When the model runs were completed, coefficient of variation of yield and mean yield for each uniformity were determined. See Appendix C for the yield results for each uniformity evaluation. 2. Objective 2. Method a. Theoretical Development As noted in the review of literature, the normal dis- tribution has been considered by a large number of researchers. Most authors have found that this distribution provides an adequate representation of irrigation data over a wide range Of uniformities, sprinkler sizes and spacings. Another advantage of using the normal distribution is its simplicity. Only two statistical moments, mean and standard deviation, are required to describe the distribution. Uniformity measures are calculations based on estimates of irrigation depths at various locations in an irrigated area. Using these depths, a single number is produced which may serve as an indicator of uniformity of water applied by an irrigation system. Uniformity 53 PLEASE INFUT THE NUMBER CORRESPONDING ENTER ZERO (0) IF NONE. . WEATHER FILE = HBSWET.DAT GENETICS FILE a CGENET SOILS FILE = SOIL.JOE . IRRIGATION DATA (Y/N/A) a Y . IRRIGATION FILE = CIRRIB.DAT . INITIAL SN FILE 3 SWATER 7. DIOMASS OUTPUT FILE 3 BOCORN 8. WATER OUTPUT FILE = WACORN 9. FREQUENCY OF OUTPUT = 10 10. THE CROP VARIETY a 24 11. THE SOIL NUMBER = 166 2. THE LATITUDE i 42.0 0‘ Cl .5 lL-i a“) *‘ TO THE PARAMETER YOU WISH TO 13. 14. 15. 16. 17. 18. '19. 20. 21. 22. 23. 24. INITIAL SW CONDITION = DATE OF SOWING = 115 O SOWING DEPTH a 5.0 FLANTS/M**2 B 7.2 DATE OF SILKING a 0 DATE OF MATURITY a 0 BRAIN YIELD (KG/HA) = GRAIN WIEGHT (DRY) = GRAINS/Mii2 8 0. GRAINS/EAR I 0. MAXIMUM LAI = .0 BIOMASS (GRAMS/M**2) a Figure 8. Sample Input for CERES-Maize CHANGE. .9 O. 54 VARIETY NUMBER 24 VARIETY NAME PIO 3780 LAT ”42.0 , SUNING DEPTH 5 5.0 CM , PLANT FOP = 7.2 FLANTS/M**2 GENETIC CONSTANTS Pl =170. P2 =3.76 FS=685. GB #600. 53 =10. SOIL ALBEDO= .14 U= 6.0 SNCON= .90 RUNOFF CURVE NO.=67. SOIL NO.=166 JULIAN DAY IRRIGATION 160 23. 174 23. 178 23. 183 23. 188 23. 208 23. 214 23. 219 23. 227 23. 237 23. DEPTH«CM Low LIM UP LIM SAT 3w EXT SN INIT SN wR 0.~ 10. .059 .171 .221 .112 .160 1.000 10.“ 30. .059 .171 .221 .112 .160 .800 30.» 45. .061 .173 .223 .112 .162 .300 45.— 61. .056 .168 .218 .112 .157 .090 61.~ 76. .056 .127 . .177 .071 .120 .040 76.“ 91. .041 .112 .162 .071 .105 .009 91.4 5.1 14.0 18.6 9.0 13.1 TOTAL PROFILE THE PROGRAM STARTED ON JULIAN DATE 92 JUL CUM wATER BALANCE COMPONENTS DAY DAY DTT PHENOLOGICAL STAGE CUMULATIVE AFTER GERMINATION 4/24/ 0 115 0. SOWING BIOMASS LAI C501 ET PREC PESN 4/25/ 0 116 3. GERMINATION 25. 40. 8.1 5/10/ 0 131 47. EMERGENCE 22. 15. 7.1 6/ 6/ 0 158 182. END JUVENILE STAGE 11. .26 .00 73. 88. 6.8 6/13/ 0 165 289. TASSEL INITIATION 46. .83 .00 94. 92. 4.0 7/21/ 0 203 764. SILKING, LNO= 19.0 1054. 4.95 .00 271. 279. 5.0 8/ 3/ 0 216 934. BEGIN GRAIN FILL 1399. 4.57 .00 322. .33. 5.2 9/ 8/ 0 252 1420. END FILL, GPP=452. 2645. 1.16 .00 502. 504. 4.2 9/10/ 0 254 1444. PHYSIO MATURITY 2645. 1.16 PREDICTED VALUES MEASURED VALUES SILHING JD 203 1) MATURITY JD 254 0 GRAIN YIELD KG/HA (15) 12691. 0. KERNEL WEIGHT 6 (DRY) .32 3 .0000 FINAL GPSM 5256. 0. GRAINS/EAR 452. Cu MAX. LAI 4.95 .00 BIOMASS G/SM ‘ 2645. Ch Figure 9. Sample Output from CERES-Maize 55 measures are only a function of the variation of irrigation depth, although weighting factors are sometimes used to express a greater degree of significance of some (usually lesser) depths. Statistical Parameters Several different measures have been used to describe the uniformity of irrigation application including Christiansen's Uniformity Coefficient (CU) and the Wilcox and Swailes Coefficient or Coefficient of Variation (CV). CV was introduced as a method of uniformity evaluation by Wilcox and Swailes in 1947. CV, which assumes that the distribution of irrigation water is normal, uses common statistical paramenters, mean and standard deviation, to estimate uniformity. The equation for CV is defined as CV = XI where CV is the coefficient of variation, S is the standard deviation of the distribution of water, and i is the mean of the distribution of water measured. In the case of center pivot uniformity evaluation, the mean is defined as the sum of the values for each observation (i.e. volume of water in each can) divided by the number of observations (number of cans). In center pivot irrigation, each can represents a different portion 56 of the irrigated area, therefore a weight is assigned to each can volume. Thus the equation for the mean becomes wi Yi Xw= wi where Xw is the weighted mean water application for the system, wi is the weight value for each observation, and yi is the value measured at each observation. Standard deviation is defined as As Marek et.al. (1986) have shown, in a situation where obsevations are weighted and where the observation spacing is constant, the equation becomes (w°y°2) 2' 1 1 - (ZWiYi)2 S = (21:11 - 1.0) ) .5 Zwi (Zwi - 1.0) where all terms are as previously defined. 57 Addition of a Constant When a constant (C) is added to a distribution, the statistical moments of mean and standard deviation are affected such that 2 becomes Y + C. Standard deviation however remains unchanged. For example, in the series of numbers 3,4,5,7,5,2, the mean is calculated as 4.33 and the standard deviation is 1.75. If a C equal to 3 is added to each of the numbers in the series, the new mean is 7.33 which equals i + C. The standard deviation remains the same. The effect of the addition of a constant to a distribution is to increase the mean by the value of that constant while leaving the standard deviation unaffected. The coefficient of variation (S/i) then, is effectively decreased due to the increase in the denominator. Theoretical Application to Irrigation Uniformity In arid regions where most if not all water is supplied by irrigation, a high degree of uniformity, represented by a low CV, is desirable to insure adequate crop growth over an entire irrigated area. As previously noted, rainfall is often the major source for crop water requirements in humid regions and should be taken into consideration in the evaluation the uniformity of a given irrigation system. If rainfall is assumed to be 100% uniform over an irrigated area it then represents a constant value which may be added to the mean value of 58 the irrigation distribution. For example, if a center pivot irrigation system has a measured mean application rate of 19 mm, a standard deviation of 5.7 mm and a CV of .30 and if 50% of the seasonal water requirement is supplied by rainfall then the CV considering rainfall would be or approximately l/Z of the originally measured CV. 3. Verification Approach During this stage of the analysis, the procedure outlined above for objective 1 was followed, except that rainfall and pre-season soil water were eliminated from the analysis. In order to allow germination to occur, the irrigation system was operated four times immediately prior to the date of planting. The irrigation schedule summary is presented in Table 4 and graphically in Figure 10. Because there was no difference in total irrigation requirement for the 50% and 60% depletion schedules, only the 40% and 50% depletion schedules were evaluated. Again, uniformity of yield and mean yield will be calculated for each irrigation system. The results of the evaluations without rainfall approximate the expected yields based on simply evaluating the uniformity of the center pivot 59 Azu m~.h—V 23 hoe Azu oo.m—v 28 omc mJDOMIum zonhMJauo 80m n NJDowrum ZOHHNJQMQ 89¢ ZO~h433 cm 0? co'uao.LL~ uznfi an ac covuuowctn mk(3 .__uyc_nz unocu.sv >coesam nuxoco nocu uco oc._:uocum coFuuu.LL~ .c o_noh INCHES OF WATER 60 man ease LEGEND PM". WEI RAN [NM CROP: corm 1] mm / om mmnou we; coma PNOT :0 non 51:0 mtncmcz one 5/10 8 fig X 0A A 030mm $9504 :20 ms .m-mmflwg *flfifl 4.00 ~ fEuLQEEEDL_JA££!m§L_. 3.00 - 2.00 ~ ‘ L‘ t ,'I ‘1 ~' ‘ ' LL‘ *4 _ _ .- 100 - .. : : : I a .4 ’1 j H S S a 000 I ‘ 7 r 7 I l , n , , u , I * u . T 5/12 5&5 6/09 6/21 7/07 7/21 8/0‘ U" °/°' Figure 10. DATE (SJN - SAT) Irrigation Scheduling Summary Graph (without Rainfall) 15 PERCENT 61 system, without considering the addition of rainfall. In order to test the validity of an adjusted CV, the volume of effective rainfall (including initial soil moisture) from 1984 has been calculated . This value has been used to estimate the constant added to the mean of the systems tested. If the adjusted CV theory is indeed valid, then when the rainfall constant is added to the system CV (without rainfall) the adjusted CV should more closely express the yield CV with rainfall. C. Analysis Techniques Coefficient of variation of yield, mean yield and percent decrease in yield will be calculated for all schedules and uniformities. Data analysis and representation will be performed using the Plot-it statistical package. Linear regression analysis will be performed to determine the correlation between CV of yield and CV of the irrigation system application (for all schedules, with and without rainfall), mean yield and CV of the irrigation systems and percent decrease in yield and CV of the irrigation systems. The three irrigation scheduling strategies will be compared under rainfall and dry conditions. To determine the validity of the adjustment to CV considering rainfall, the volume and percent of effective rainfall for 1984 will be calculated. This value will then be used to adjust the CV for each system. 62 Regression lines for irrigation CV measured vs yield with rainfall, irrigation CV measured vs yield without rain and adjusted irrigation CV vs expected yield will be compared. Economic analysis will be carried out by estimating costs (i.e. due to yield loss) of non-uniform irrigation under different irrigation requirements. In addition, cost analysis of different scheduling strategies will be compared to determine optimal scheduling strategy with increasing irrigation costs. IV. RESULTS, ANALYSIS AND DISCUSSION A. Irrigation Uniformity, Yield and Scheduling 1. With Rainfall In this part of the analysis, the CERES-Maize corn model was run under eight different irrigation uniformities (for the 40% and 60% depletion schedules) and eleven different uniformities for the 50% depletion schedule. The objective was to determine the effect of irrigation uniformity and schedule on yield uniformity and mean yield under typical rainfall conditions. Except for water applied to each sector of the field and timing of water application, all other parameters such as weather, rainfall, soil water holding capacity and maize variety have been kept constant. It was assumed in the analysis that the model provided accurate yield values for each irrigation depth and schedule. Irrigation uniformities as expressed by CV are compared with CV of maize yield and mean yield under the three different scheduling strategies. The results for each schedule are presented in Table 5. Figures 11 through 17 show the relationships graphically. 63 64 Table 5 Irrigation Uniformity and Yield for 40% 50% and 60% Depletion Schedules (With Rainfall) CV | cv I MEAN OF IRRIG.| OF YIELD I YIELD : . : (KG/HA) l % Depletion I % Depletion IScheduling Strategyl Scheduling Strategy I 40 50 60 I 40 50 60 : : 0.00 I 0 0 0 I 12692 12692 12692 I .17 : 0 0 0 I 12691 12688 12688 I I I .26 :.07 .06 .09 : 12486 12386 12360 .29 I.02 .02 .04 I 12635 12564 12454 I | .33 I - .11 - I - 12075 - ‘ l | .39 I.11 .12 .13 I 12116 12029 11926 I | .42 I - .18 - I - 11724 - I | .44 I.l6 .18 .17 : 12080 11933 11823 I .52 I.20 .20 .21 I 11786 11677 11584 | | .58 :.20 .20 .21 : 11800 11735 11532 COEFFICIENT OF VARIATION OF'YIELD WITH RAINFALL 0.40 - 0.30 — 0.20 - 0.10- 65 0 R2 8 .85 Y a .4IX - .041 0.00 0.00 L f I I R I I I 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 40% DEPLETION SCHEDULE Figure 11. CV of Irrigation and CV of Yield (40% Depletion Schedule) COEFFICIENT OF VARIATION OF'YIELD WITH RAINFALL 0.40 - 0.30 - 0.20 - 0.10-I O R2= 66 .84 Y I .42X - .032 0.00 0.00 I T I I I “I 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 50% DEPLEHON SCHEDULE Figure 12. CV of Irrigation and CV of Yield (50% Depletion Schedule) COEFFICIENT OF VARIATION OF YIELD WITH RAINFALL 0.40--I 0.30 - 0.20 -I 0.10- 0.00 67 0 R2 I .89 Y - .43X - .034 0.00 I T I r I r —l 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 60% DEPLETION SCHEDULE Figure 13. CV of Irrigation and CV of Yield (60% Depletion Schedule) MEAN YIELD KG\HA X 1000 “NHIIUHNFAZL 68 13-1 10- ! R2 :- .84 Y - 4863 X +12904 I I I I I 0.00 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 40% DEPLEHON SCHEDULE Figure 14. CV of Irrigation and Mean Yield (40% Depletion Schedule) AINFA MEAN YIELD (QKG\HA2 X 1000 WITH L 11.. 1o- 69 0 R2 - .83 Y - -2150 X + 12884 I T T I I *I 0.00 0.10 0.20 . 0.30 0.40 0.50 0.60 COEFFICIENT 0F VARIATION OF IRRIGATION 50% DEPLET ION SCHEDULE Figure 15. CV of Irrigation and Mean Yield (50% Depletion Schedule) 131 121 11— 10- MEAN YIELD KG HA X 1000 “WHITUMNFABL 8 0.00 Figure 70 0 R2 - .90 Y - -2363 x +12916 I r 1’ I I —I 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 60%IDEPLEHON SCHEDULE 16. CV of Irrigation and Mean Yield (60% Depletion Schedule) 71 II- 10- MEAN YIELD $506M) x 1000 WITH AI FALL . o 60% DEPLEI'ION SCHEDULE 1 50% DEPLETION SCHEDULE :1 40% DEPLEI'ION SCHEDULE I I I I ’fi fi 0.00 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 40%, 50%, AND 60% DEPLEI'ION SCHEDULES Figure 17. CV of Irrigation and Mean Yield : 40%, 50% and 60% Depletion Scheduling Comparison 72 From Table 5. and Figure 17, it can be seen that under the rainfall conditions analyzed here (40% of crop water requirement provided by rainfall) there is little effect on CV of yield or mean yield among the different scheduling strategies. This would then suggest that under conditions where rainfall provides more than 40% of the crop water requirement during a growing season, a conservative scheduling strategy (i.e. irrigation when 60% of the water is depleted rather than when only 40% or 50% of the available water is used) is appropriate. It should also be noted that the data and figures suggest that at very high uniformities (CV <.l7) CV of yield is virtually 0, with little effect on mean yield compared with the maximum expected yield. This is probably due to the fact that at high uniformities, only the top of the parabolic maize-water production function curve is being analysed. Figure 18 (Kramer and Jensen, 1979) on the following page is an example of a production function curve relating a single input and output. 2. Without Rainfall The results of the CERES-Maize yield analysis performed without rainfall are presented in Table 6 and Figures 19 through 23 . 73 9(1)— .1". 800— I.’—‘ /. ./|AY'43 [w— 1 DJ L 1.; an to can no x,1x,. . . x. Figure 18. Parabolic Production Function Example 74 Table 6 . Irrigation Uniformity and Yield for 40 and 50% Depletion Schedules (Without Rainfall) ............................ f-_-___------__---_____--__ CV CV MEAN OF IRRIG. OF YIELD YIELD (KG/HA) % Depletion Scheduling Strategy 50 r I I | I I I I I I I I 40 I 40 50 I I 0.00 : 0 0 I 12692 12690 I .17 I .04 .06 I 12440 12278 I I .22 I - .32 I - 11194 I I .26 I .26 .26 I 11570 11396 | I .29 : .28 .29 : 10896 10709 .33 : - .45 I - 9997 .39 I .46 .47 : 9820 9602 I .42 I - .55 : - 9176 I .44 : .49 .49 I 9392 9268 .52 I .53 .52 : 9080 9058 .58 I .54 .55 : 9097 8959 l 0.60- 0.50 .1 0.40 - 0.30 - 0.20 J COEFFICIENT OF VARIATION OF YIELD WITHOUT RAINFALL 0.10-I 75 o R2-.93 Y- I.09X-.037 0.00 0.00 T Ti T I— I fil 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 40% DEPLETION SCHEDULE Figure 19. CV of Irrigation and CV of Yield Without Rainfall (40% Depletion Schedule) COEFFICIENT OF VARIATION OF Y~IELD 0.60 - o 0.50 - 0.40 - 0.30 - 0.20 ‘ WITHOUT RAINFALL 0.10-I 76 R2=.86 Y= I.08X+.006 0.00 0.00 Figure 20. I I I I I 0.10 0.20 0.30 0.40 0.50 COEFFICIENT OF VARIATION OF IRRIGATION 50% DEPLEHON SCHEDULE CV of Irrigation and CV of Yield Without Rainfall (50% Depletion Schedule) 11- 10-I MEAN YIELD sKG\HA'-) X 1000 WITHOU RAIN ALL 0.00 Figure 21. 77 v R2 II .92 Y I -7995 X '+ 13209 fl T_ F I I j 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 40% DEPLETION SCHEDULE CV of Irrigation and Mean Yield Without Rainfall (40% Depletion Schedule) 12- 11¢ 10% MEAN YIELD $KG\HA}) X 1000 WITHOU RAIN ALL 9.. 8 0.00 78 A R2 - .91 Y :- -7732 X + 12943 I I I I I 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 50% DEPLETION SCHEDULE Figure 22. CV of Irrigation and Mean Yield Without Rainfall (50% Depletion Schedule) MEAN YIELD (“AHA") X 1000 WITHOU RAIN ALL 0.00 Figure 23. 79 A 50% DEPLETION SCHEDULE 0 40% DEPLETION SCHEDULE I fl I I I fl 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF IRRIGATION 40% AND 50% DEPLETION SCHEDULES CV of Irrigation and Mean Yield Without Rainfall: 40% and 50% Depletion Scheduling Comparison 0 80 Figure 20 shows the relationship between CV of irrigation and CV of yield without rainfall. As can be seen from the regression line and equation (y = 1.08x + .006 ) , the relationship between CV of irrigation and CV of yield is very close to l : l. Essentially, in a situation where all of the crop water requirement is supplied by rainfall, CV of the irrigation system will approximately equal the CV of the maize yield. From Figure 22, one can see that in a situation where no rainfall occurs, or when CV of irrigation is adjusted to account for all rainfall, there is a decrease in yield of about 750 kg/ha or about 6% for every 10% decrease in irrigation uniformity. In this case, irrigation scheduling strategy is more critical than in a situation where rainfall occurs. But scheduling still does not have a significant effect on CV of yield or mean yield. 8. Verification of Adjusted Coefficient of Variation The uniformity of center pivot irrigation is commonly measured using containers spaced at equal intervals along the pivot radius. The pivot is allowed to pass over the cans and the resulting depths of water are measured. This procedure, however, only measures an initial uniformity of irrigation water applied without consideriing the effect of additional uniform water application through rainfall. The theoretical 81 been presented in the Methods section. The purpose of this analysis is to determine whether or not this proposed adjustment is valid. Assuming an initial soil water content of 85% (75.1 mm), adding the effective rainfall from 1984, and subtracting the water remaining in the soil profile at harvest, a total rainfall volume of 158.8 mm was calculated. This rainfall was assumed to be uniform over the entire field area. Under the 50% depletion scheduling strategy, 247.0 mm of water was applied by irrigation. Thus, irrigation supplied 60 % of the total crOp water requirement. Using the equation for adjusted CV presented in the Methods section, the CV of each irrigation system has been altered to reflect the addition of this rainfall. Original CVs and adjusted CVs _are presented below in Table 7 Table 7 . Adjusted CV for 1984 Rainfall ORIGINAL CV ADJUSTED CV 0.00 0.00 .17 .10 .22 .13 .26 .16 .29 .17 .33 .20 .39 .23 .42 .25 .44 .26 .52 .31 .58 .35 82 The relationship between mean yield with rainfall (based on measured CV), mean yield without rainfall and mean yield based on adjusted CV is presented in Figure 25. In theory, the CV adjusted vs mean yield line should lie exactly over the CV without rainfall line . As can be seen in Figure 24, there was movement toward the CV without rainfall line, however the shift is not complete. This is most likely due to the fact that the adjusted CV only reflects the CV of water application weighted by volume. But CV of water application under humid conditions is not a static parameter over time. With additions of 100% uniform rainfall occurring periodically throughout the ' growing season, CV changes. This is reflected in Table 8. and Figure 25 for a system with a measured CV of .52 (adjusted CV =.3l) under 1984 rainfall conditions. 83 CV ADJUSTED FOR RAINFALL AND TIME CV ADJUSTED FOR RAINFALL CV WITH RAINFALI. CV WITHOUT RAINFALL 13— II <3 0 12“ <3 ‘x A < 11— I’ ./ (9 .x V 53104 IE >— :Z :5 .2 9‘ I O A 8 D 000 Figure 25. I I I I I 1 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT OF VARIATION OF WATER APPLICATION 50% DEPLEHON SCHEDULE Graphical Validation of Adjusted CV 84 Table 8. Water Application CV Changes Over Time (1984) DATE RAIN (TO DATE) IRRIGATION (TO DATE) CV MM MM ' 5/10-6/13 54.10 0 0 6/14-6/19 54.36 19 .14 6/20-6/23 55.12 38 .21 6/24-6/28 56.13 57 .26 6/29-7/03 56.13 76 .29 7/04-7/18 112.52 95 .24 7/18-7/28 134.37 114 .24 7/29-8/01 134.37 133 .26 8/02-8/07 134.37 152 .28 8/08-8/11 134.37 171 .29 8/12-8/16 134.37 190 .29 8/17-8/21 134.37 209 .32 8/22-8/26 134.37 228 .31 8/27-9/10 158.75 247 .30 85 4'. _III I J O O O W 4 I. 3- s 4 3. 2 O O 0 20:3??? ”.33; mo ZOZSK<> no bzuwCCquU 3.3 8:82 5:; 0 7/ Hum, 9 HI QJIHIIJIFIIIFIIOJIIIV ‘ f- 1! IIIIIIIIIIIIIIII 2 / 8 1r lllllllllllllllllll iilflllildHlHHfFfH w T/ 1 IIIIIIIIIIIIIIIII 8 illi‘lliiiP iiiii t HHIJVIFFVJIIIIAAMMIFIF 7 2 1 v/ 7 1| -Ifl#“j HHHHHHHHHHH 3 cl 1/ II 7 HI niVflfliiiIldiflllfHfil 9 HXIJIIHI iiiiiiiiiiiiii E 2 N D W LO iJHHIHIIIHHHHHIFHf L...“ D A NIAIAII HHHHHHHHHHHHHHHHH NI 5 II AR jdlfi IIIIIIIIIIII ‘I Rm nu W D U 3 cl m _ 3 . 3 _ 6 0 O 5 O 5 0 3 2 1 1 TIME Coefficient of Variation of Water Application Changes Over Time Figure 26. 86 Table 8 and Figure 26 give some insight into why the adjusted CV tends to give a conservative estimate of mean yield. Although the adjusted CV of .31 reflects the uniformity of water application over the entire season, in fact, the CV is at .31 for less than one quarter of the total growing season. If each uniformity in Table 8 is weighted by the number of days over which it occured and a seasonal mean CV is calculated, then the coefficient of variation for the system is adjusted downward again to .16 . When this point is plotted in Figure 25, the adjustment is a more accurate estimate of expected yield. It should also be noted that crop sensitivity to non-uniform water application changes over the course of the season. The relationship between measured CV and adjusted CV based on percentage of crop water requirement supplied by rainfall is shown below in Figure 27 . This relationship was developed using the equations proposed in the Methods section. By finding CV measured on the horizontal axis and drawing a line upward to the line which indicates percentage of effective rainfall (i.e. rain which does not runoff or deep percolate) and then over to the vertical axis, adjusted CV may be estimated. Table 9 from Bartholic et.al. presented below, estimates potential yearly irrigation requirements for all regions in Michigan. Employing an irrigation requirement value ADJUSTED COEFFICIENT OE VARIATION 87 I00 _ PERCENTAGE OF SEASONAL WATER SUPPLIED BY 75 IRRIGATION 50 25 ID I 2 .3 4 .S COEFFICIENT OF VARIATION MEASURED Figure 27. Nomograph for Estimating Adjusted CV 88 from Table 9 and estimating total crop water requirement, one may then determine the percentage of effective rainfall and the adjusted CV. Table 9. Potential Seasonal Irrigation Requirements for Corn in Nine Michigan Districts Potential Irrigation Requirement (mm)* District Corn Soybeans Dry Beans Upper Penninsula 47.2 33.8 22.3 Northwest 137.9 110.2 95.3 Northeast 104.4 81.0 66.5 West Central 176.5 138.4 114.3 Central 188.0 161.0 135.6 East Central 190.0 162.3 133.9 Southwest 229.7 201.4 141.5 South Central 215.6 184.9 133.6 Southeast 236.7 206.8 149.9 A. Irrigation requirment based on an estimated efficiency of 85%. As noted above, the adjustment to the CV proposed here does give a conservative estimate of yield effect. The adjusted CV, however, is a more accurate expression of the effect of irrigation non-uniformity on yield in humid regions than is the traditionally measured CV. In addition, the adjusted CV may be determined prior to the growing season based on historical weather data. The most important advantage to CV adjustment for rainfall is in the standardization of uniformity recommendations. Presently, the recommended uniformity level for center pivot irrigation is .15 or less. (SCS). This recommendation is based on the assumption that most if not all of the crop 89 water requirement is supplied by irrigation. In regions where much of the crop water is supplied by rainfall, a much lower level of irrigation uniformity may be supported. 2. Application Efficiency Considerations The application efficiency of an irrigation system is defined as the percentage of water applied that is actually stored in the rootzone compared to the total water applied (Hanson et. al. 1979). When the rootzone is not fully irrigated the application efficiency has been defined by Wu and Gitlin (1981) as Vr (1 " PD) Ea = 100 ( va where Ea is the application efficiency, Vr is the volume of water required to fill the rootzone, PD is the percent of deficit, and Va is the volume of water applied. The relationship between the coefficient of variation, irrigation deficit and application efficiency is based on probability and normal distribution function. In the case where irrigation volume applied is equal to the irrigation volume required, the irrigation deficit is equal to approximately .4 times the coefficient of variation for the center pivot system (Bralts,1986,) . In this instance, the application efficiency can be determined by the equation ' 90 Vr (l ‘ PD) _Ea = 100 ( ) = 100 (1 - 0.4 cv) _ Va A dimensionless plot of the cumulative frequency curve is given in Figure 28 which shows the required irrigation depth in the rootzone for a CV of .4 and an application efficiency of approximateley 84%. When rainfall is considered in determining application efficiency over an entire season, both the degree of deficit and excess are reduced. Using Figure 28 as an example, if the seasonal crop water requirement is 250 mm (10 in.) and if 50 % of this requirement is met by rainfall, then the area of the field receiving 0 mm from irrigation will have received 125 mm from rainfall which reduces the deficit by half. Conversely, the area which would have received 500 mm from irrigation will receive 250 mm from irrigation and 125 mm from rainfall decreasing the maximum excess application from 500 mm to 375 mm. Figure 29 presents the original system CV shown in Figure 28 compared to the application efficiency after rainfall is considered. 91 Fraction“ Area. It 0 0.2 0.4 0.5 0.6 0.0 1.0 0 I I I I I I ' Dimensionless Applied Depth. Y Figure 28. Cumulative Frequency Distribution for a CV of .4 (Not Adjusted for Rainfall) 92 Fractional Area, I: 0 0.2 0.4 0.5 0.6 0.0 1.0 I I l l l l I l I ' ‘0.6 - Y=yli 0.8 - 1.0 01 ."‘ r I Dimensionless Applied Depth. 3 I 1.8 2.0 Figure 29. Application Efficiency Comparison Between Original and Adjusted CVs 93 C. Irrigation Uniformity Effects on Economics and Management l.‘ Irrigation Scheduling Figures 29 and 30 present the income loss per 40.5 ha (100 ac) associated with different irrigation scheduling strategies under humid and dry conditions. The 30 year average cost per 19.0 mm irrigation per 40.5 ha for Michigan, Spinks sandy loam soil has been determined by Algozin (1986) to be $392.00 . Table 10 below shows the cost per season of total irrigation for the three different strategies under humid conditions compared with the average I benefit for increased yield (based on $2.00/bushel profit for each additional bushel of maize produced). Table 10. Irrigation Scheduling Costs (With Rainfall) I TREATMENT I I 40% 50% 60% I NO. OF 19 MM I APPLICATIONS I REQUIRED I 14 13 12 I TOTAL COST OF I IRRIGATION /40.5 I HA (1984) I $5488 $5096 $4704 I BENEFIT/COST I .68 .71 - I 94 12- x 40% DEPLETION SCHEDULE . o 50% DEPLETION SCHEDULE 0 60% DEPLETION SCHEDULE , 10— 40.5 HA) X 1000 1 WITH( IéINI-‘ALL ‘I’ I2 0 4- _I w . 5 o 2‘ Z O 1., - 5 I I I I fl 0.00 0.10 0.20 0.30 0.40 0.50 0.60 COEFFICIENT 0F VARIATION OF IRRIGATION Figure 30. Income Loss Under Different Irrigation Schedules (With Rainfall) 95 v 40% DEPLEDON SCHEDULE 0 50% DEPLETION SCHEDULE ° 12? c3 . C) 53 10— >< . 23 3 IE “XE ‘ O< <4! 6- 39' O 4 at: 8: 4... _3; LIJ d 5 a) 2‘ Z? 0 000 Figure 0.l10 0.20 0.130 0.40 0.80 0.160 COEFFICIENT OF VARIATION OF IRRIGATION 31. Income Loss Under Different Irrigation Schedules (Without Rainfall) 96 Table 11 below presents costs and benefits of different irrigation scheduling strategies under conditions without rainfall. Table 11. Irrigation Scheduling Costs (Without Rainfall) I TREATMENT I I 40% 50% I NO. OF 19 MM I APPLICATIONS I 24 23 REQUIRED l I TOTAL COST OF I IRRIGATION /40.5 I $9408 $9016 HA (1984) I I BENEFIT/COST I 1.43 —-- From Table 10 and Figure 29 , it can be seen that the average benefit cost ratio for the more conservative scheduling regimes is less than one. This indicates that under rainfall conditions, scheduling irrigation at higher levels of soil moisture depletion is a more economically sound strategy except at very high levels of non- uniformity. Figure 30 and Table 11 indicate that under conditions where no rainfall occurs, there is some benefit to scheduling irrigation at a higher moisture content. It should be noted, however, that the cost per irrigation 97 estimate used in this analysis is the same as that used for the analysis with rainfall ($392.00/40.5 ha). In reality, an irrigated area where no rainfall occurs would be likely to have a much lower water table and substantially higher pumping costs than those found in Michigan. 2. Effect of Rainfall on Economics of Irrigation Uniformity Figure 31 shows income loss per 40.5 ha (100 ac) in humid and dry irrigation situations. As can be seen from this figure, income loss under the rainfall conditions analyzed here (1984) are insignificant except at very low levels of uniformity. Conversely, under the scenario where no rainfall has occurred, income loss is significant even at moderate levels of non-uniformity. This situation may have some important effects on farm management decision making. In terms of technology selection, farmers in humid regions are able to select irrigation technologies which are less uniform and less expensive, such as big gun rather than center pivot systems. A survey carried out among St. Joseph County irrigators by the author in 1986 indicates that this is true. The survey showed that more than half of the irrigation in the county was done with less expensive big gun irrigation than with center pivot. Improvement of existing technology is also greatly 98 17 WITH RAINFALL .I o WITHOUT RAINFALL INCOME LOSS (S/40.5 HA.) X 1000 0’ I V? 0.00 8'10 o.'20 0.30 0.5.0 also 0.80 COEFFICIENT OF VARIATION OF IRRIGATION Figure 31. Income Losses Associated with Non-Uniform Irrigation: Humid vs Dry Conditions 99 influenced by the proportion of seasonal water supplied by precipitation. As noted previously, SCS in St. Joseph County has evaluated more than 90 irrigation systems over the past four years. Most of these systems have been found to have sub-standard uniformities, yet few if any of the irrigators have improved their irrigation systems. If the CVs of these systems are adjusted to reflect the addition of uniform rainfall to the irrigated area (approximately 45% of the crOp water requirement for corn is supplied by rainfall) then a system CV as low as .30 has an adjusted CV of .16, a nearly acceptable value. v. CONCLUSIONS AND RECOMMENDATIONS The objectives of the proposed research have been addressed in full. The effect of irrigation uniformity on coefficient of variation of yield and mean yield has been evaluated for both humid and dry conditions through the use of a simulation model. In addition, the theoretical basis for and practical applications of an adjusted coefficient of variation considering rainfall have been presented. This adjusted CV has also been verified. Economic analysis with respect to the effects of non- uniformity and rainfall on scheduling and technology management has been carried out. The specific conclusions of this research are: 1. The coefficient of variation of yield and mean yield are related to coefficient of variation for an irrigation system. In an environment where 100% of the crop water requirement is supplied by irrigation, or if CV of irrigation is adjusted to account for volume and weighted to account for timing of rainfall, then the expected CV of yield is approximately that of the irrigation system. In addition, yield decrease is approximately 6% for every 10% increase in coefficient of variation of irrigation. 100 Rainfall is an important mitigating factor in uniformity of water application in humid regions. An adjustment to the CV of an irrigation system reflecting the percentage of seasonal crop water supplied by precipitation allows for a more accurate estimate of non-uniformity effects on application efficiency and crop yield than the traditionally measured CV. When the average seasonal uniformity is weighted to express the length of time over which each different uniformity level occurs, a very accurate estimate of yield reduction due to non-uniform irrigation can be made. Irrigation scheduling at higher available water contents in humid regions (i.e. scheduling irrigation when only 40% of available water is depleted rather than waiting until 50% or 60% of the available soil water is depleted) is not economically sound except at very low levels of uniformity. The practice of scheduling in this manner may be feasible in arid regions provided that water and energy costs are low. 101 Because of the existence of relatively substantial rainfall inputs, irrigation non-uniformity is not as important an economic issue in humid areas as it is in arid regions. This applies particularly with regard to irrigation technology selection and irrigation system repair Recommendations for further research include: 1. Analysis of other environmental factors such as Spatial variability of soil types, which may also affect irrigation uniformity. Historical analysis of seasonal timing and volume of rainfall related to crop growth stages to further refine adjustments to CV. ' Validation of adjustments to CV with other soils and crops. Analysis of yield loss due to nitrate leaching at higher application levels in non-uniform irrigation as well as post season nitrate loss in areas where irrigation deficits have occured. 102 APPEND I X A SCS Center Pivot Evaluation Procedure SCS Center Pivot Evaluation Procedure Uniformity estimates used in this work are based on actual system evaluations performed by the St. Joseph County Soil Conservation District on center pivot irrigation systems in the St. Joseph area. These evaluations have been performed during the summers from 1983 through 1985. The following is an overview of the SCS uniformity evaluation procedure for center pivot irrigation systems. Evaluations of irrigation systems are performed to determine adequacy of irrigation water management. The major factors which must be considered in making this determination are uniformity, total depth of application and maximum application rate. Irrigation water application should be as uniform as possible for maximum efficiency. The total depth of water applied should be sufficient to meet crop needs but should not exceed the water holding capacity of the soil to the bottom of the rootzone. The maximum application rate should not exceed the infiltration rate of the soil so that runoff and erosion do not occur. A center pivot irrigation system operates by moving a lateral sprinkler line in a circle around a stationary central pivot point. The lateral is supported by self propelling towers mounted on wheels. The speed at which 103 104 the system moves is controlled by the speed of the end (farthest from the pivot) tower. Generally, the lateral irrigates a circular area. See Figure 1 for a schematic drawing of center pivot Sprinkler operation. The attachment of a big gun or cornering attachment allows the irrigation of a square area. The big gun or cornering attachment only operates part of the time and consequently large changes in the uniformity of a system may be observed when the gun is off versus when it is on. The SCS recommended procedure for estimating irrigation uniformity for a center pivot system is first to set cans in a line along the radius of the lateral. Normally, quart ' oil cans with the tops removed are used for catching preci- pitation. Cans may be set on (or slightly imbedded in) the ground if the crop is small enough to permit unobstructed catches. If not, cans should be attached to stakes which hold them above the vegetation. The catch cans should be placed at a uniform interval, usually 30 feet, beginning this distance from the pivot and extending to a point beyond the wetted area. After the system has passed the can line, the depth of water in each can is measured and recorded. In a center pivot evaluation each can, providing that the distance between the cans is constant, represents a different area. Therefore, in calculating the uniformity of the system, a weighting factor for each can must be calculated. When cans are set at a uniform spacing the area weighted factor 105 is equal to the can number. The first can is set 30 feet from the pivot and represents an area from 15 feet to 45 feet from the pivot. The second can is set 60 feet from the pivot and 30 feet from the first can. It represents an area from 45 feet to 75 feet from the pivot and so on. The area of a Circle is equal to pi times the square of the radius or the distance to the furthest point from the pivot represented by that catch can. The area represented by can 1: 3.1416 * 4s2 - 3.1416 * 152 5654.88 sq. ft. The area represented by can 2: = 3.1416 * 752 - 3.1416 * 452 = 11309.76 ft. sq. The area represented by can 3: a 3.1416 * 1052 - 3.1416 * 752 = 16964.54 sq. ft. The weighting factor for can 1 is the ratio of its area to itself or: 1 5654.88 / 5654.88 The weighting factor for can 2 is the ratio of its area to the area of can 1: 11309.76 /5654.88 2 And the weighting factor for can 3 is the ratio of its area 106 to can 1: 16964.54 / 5654.88 = 3 This procedure may be followed for determining the weighting factors of all cans along the radius. APPENDIX B CERES - Maize and SCHEDULER Information I. CERES-Maize Model 1. Introduction CERES-Maize is a daily incrementing simulation model of maize growth, development and yield. CERES-maize is available in two versions; the standard, which simulates the effects of genotype, soil properties and weather on growth and in a nitrogen version which models the growth and yield effects of soil and plant nitrogen on the crop. In order to accurately determine maize growth, development and yield, the model simulates such physical and biological processes as phenological development, growth of leaves and stems, biomass accumulation and partitioning, soil water balance and plant water use, and soil nitrogen transformations. The CERES-Maize model is appropriate for use on most IBM compatible microcomputers with at least 256K of memory and Microsoft DOS operating systems (version 2.0 or higher). 2. Input Files The input requirements for the CERES-maize model are contained in four files. Most of the required parameters are readily available or may be easily estimated. This section will discuss each of the files and parameters. 107 108 a. Climate File The Climate file requires daily inputs of solar radia- tion, maximum and minimum temperature and precipitation. This information is used to estimate evapotranspiration and to track soil mosture status. b. Soil Water File The following inputs are required for the soil water file: Soil Albedo or soil reflectivity. Values range from sandy soils. Stage 1 soil evaporation coefficient This coefficient varies from 6 mm in sands and heavy clays to 9 mm in loams and 12 mm in clay loams. Whole profile drainage rate coefficient This coefficient is used to estimate drainage from the whole soil profile. The drainage coefficient is calculated for each layer and the minimum layer value is used as the coefficient for the whole profile. Runoff curve number This number is derived from SCS runoff estimates for different hydrological soil groups. Soil layer thickness Up to 10 soil layers may be identified as model inputs. To insure accurate water balance estimates, the minimum pedon depth should be 2.0 m, within 30 cm of the soil surface, no layer should be 109 thicker than 15 cm, and below 30 cm of the soil surface no soil layer should be thicker than 30 cm. Lower limit of plant extractable water Estimates are available for some representative soils or the value can be calulated from sand, silt clay and organic carbon contents of the soil, and bulk density. Drained ppper limit See above. Saturation water content Once the drained upper limit is calculated, the saturation water content may be estimated based on that value and the soil porosity. Root distribution weighting factor This factor is used to estimate the relative root growth in all soil layers where root growth actually occurs. In the case of physical or chemical constraints to growth, the weighing factor should be reduced accordingly. C. Genetic File The genetic inputs to the CERES-Maize model include growing degree days (from seedling emergence to end of juvenile phase and from silking to physiological maturity), photoperiod sensitivity, potential kernal number and potential kernal growth rate. At present, CERES-Maize documentation contains genetic input values for several commonly grown commercial corn varieties. For other cultivars, these genetic input values may be estimated or easily measured. 110 d. Irrigation File The irrigation file contains inputs for date of irrigation and amount of application. 3. Model Operation The biological processes modeled by CERES-Maize are soil water balance, phenological development and crop growth. Soil water balance is evaluated using inputs for rainfall and irrigation. The model determines distribution and movement of water through each layer in the soil profile. Soil water redistribution and drainage are then calculated establishing conditions from which potential and actual ET are determined. The crop phenological development parameters are used by the model to determine the dates and duration of each 'growth stage of the crop. The occurance of these growing stages are dependant upon temperature, photoperiod, and genetic Characteristics of the crop, all of which are required inputs to the model. The growth of the crop (i.e. the accumulation and partitioning of biomass within the plant) is based upon water and temperature stresses primarily. The model calculates potential dry matter production and actual production. 111 4. Model Validation The CERES-Maize model has been evaluated at a number of different locations under a variety of growing conditions. The results of these evaluations are discussed in Jones and Kiniry (1986). Generally, CERES-Maize has been found to be sensitive to input data particularly with regard to soil water information. Thus, the accuracy of CERES-Maize is highly dependant on the quality of input data. The model has performed accurately, especially in estimating maximum leaf area index, maximum above-ground biomass and grain yield. Although CERES-Maize has been evaluated in many areas where rainfed agricultural production is common, there has been at present little validation in southern Michigan. The necessary inputs for the model, however, are available and preliminary investigations suggest that CERES—Maize is valid for this region as well. II. SCHEDULER ‘The MSU microcomputer irrigation SCHEDULER program is an interactive program designed for use by Agricultural Extension Agents and Soil Conservation Districts. SCHEDULER may be operated using actual weather data obtained from a weather Station, or may be used to schedule irrigation based on historical weather information. 112 At present, SCHEDULER supports three crops; corn, soybeans and potatoes. The primary use of SCHEDULER to date has been in irrigation scheduling for corn. SCEEDULER operates by employing user prompted inputs for weather (maximum temperature, minimum temperature, windspeed, humidity, total and net solar radiation) rainfall and irrigation to calculate soil moisture status. Beginning with an assumed or measured soil moisture, SCHEDULER calculates ET based on the weather (actual or historical). This water is subtracted from the soil profile. Then using the inputs for rainfall and irrigation, SCHEDULER adds this water to the profile and generates a new soil moisture estimate. Scheduler has been in operation in St. Joseph County since 1983. Although comprehensive validation of the SCHEDULER algorithms is not completed, initial results are favorable. It should be noted that SCHEDULER has performed particularly well during dry years. APPENDIX C Additional Information 113 TURBO-PASCAL PROGRAM FOR CV CALCULATION PROGRAM uniformity (INPUT,OUTPUT); VAR a,b,c,d,e,f,g,h,i,j,k,l :REAL; {This is a program to calculate the coefficient of variation for a center pivot irrigation system. The values input are a can weighting factor and a water quantity for each catch can. The output includes a calculation of the weighted mean application and the coefficient of variation} BEGIN C :=0.0; {sum of the weights} d :=0.0; {sum of the catch can values} 9 :=0.0; {sum of the weighted values} h :=0.0; {sum of the weighted values squared} REPEAT WRITELN ('Enter multiplier factor 'I; READLN (a): IF a <>0 THEN BEGIN WRITELN ('Enter amount of water in catch can '); READLN (b); c+a; {this adds up the values of the weights} d+b; {this adds up the values of the catch cans} a*b; {this calculates the weighted value for each can} SQR(b)*a;{this squares the weighted value} g+e; {this sums the weighted values} h+f; {this sums the weighted values squared} 0 d e f 9 h ND 1* END IF *) NT L a = 0: ' g/C; {this calculates the weighted mean} (h/(c-l.0)) - SQR(g)/(C*(c-l.0)): SQRT(j)/i: = 100 * (1.0 - (0.798 * k)); WRITELN ('The weighted mean value is ', i : 4:2); WRITELN ('The the variance for this system is ', j : 2:3): WRITELN ('The coefficient of variation for this system is ', k : 1:4); WRITELN ('Christiansens uniformity coefficient is ', 1:2:1); 62m II II II H HX‘U-H END. 114 40% DEPLETION SCHEDULE SYSTEM CV .1681 FACTOR ACTUAL CATCH ADJ.CATCH YIELD YIELD ' (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 65.71 48.90 12692 12692 2 61.29 45.61 12692 12692 3 40.31 30.00 12692 12692 4 34.80 25.90 12692 12692 5 34.80 25.90 12692 12692 6 34.80 25.90 12692 12692 7 33.10 24.63 12692 12692 8 32.03 23.84 12692 12692 9 25.90 19.27 12692 12692 10 29.82 22.19 12692 12692 11 27.10 20.17 12692 12692 12 28.16 20.98 12692 12692 13 25.90 19.27 12692 12692 14 25.40 18.90 12692 12692 15 25.40 18.90 12692 12692 16 24.30 18.08 12692 12683 17 25.90 19.27 12692 12692 18 25.90 19.27 12692 12692 19 25.90 19.27 12692 12692 20 23.74 17.68 12692 12568 21 24.85 18.49 12692 12690 11 5 22 24.85 18.49 12692 12690 23 24.80 18.46 12692 12690 24 22.09 16.44 12690 11455 25 22.64 16.85 12691 12141 26 23.74 17.67 12692 12565 27 22.64 16.85 12691 12141 28 21.53 16.02 12689 10816 29 24.85 18.49 12692 12690 30 25.40 18.90 12692 12692 ACTUAL CATCH ADJUSTED CATCH MEAN = 25.53 MEAN = 19.00 ST.DEV = 4.29 ST.DEV = 3.19 CV = .1681 CV = .1681 CU = 86.6% CU = 86.6% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 12691 MEAN = 12440 .0001 CV = .0413 MEAN CV 116 40% DEPLETION SCHEDULE SYSTEM CV .2643 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) l 35.40 29.56 12692 12692 2 42.50 35.49 12692 12692 3 50.20 41.92 12692 12692 4 28.10 23.47 12692 12692 5 16.80 14.03 12673 7369 6 17.20 14.36 12676 8029 7 21.30 17.79 12692 12596 8 21.30 17.79 12692 12596 9 21.30 17.79 12692 12596 10 23.50 19.63 12692 12692 11 22.20 18.54 12692 12690 12 18.60 15.53 12686 9839 13 19.50 16.29 12689 11389 14 19.50 16.29 12689 11389 15 19.50 16.29 12689 11389 16 19.50 16.29 12689 11389 17 20.40 17.04 12692 12404 18 20.40 17.04 12692 12404 19 21.30 17.79 12692 12596 20 22.20 18.54 12692 12690 117 21 24.50 20.46 12692 12692 22 25.20 21.05 12692 12692 23 20.30 21.96 12692 12692 24 21.30 17.79 12692 12596 25 22.20 18.54 12692 12690 26 30.20 25.22 12692 12692 27 9.10 7.60 8646 85 28 21.90 18.29 12692 12692 29 35.80 29.90 12692 12692 30 22.60 18.87 12692 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 22.75 MEAN = 19.00 ST.DEV = 6.01 ST.DEV = 5.02 cv = .2643 cv = .2643 CU = 78.9% CU = 78.9% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 11570 .2593 12486 MEAN .0760 CV H E 118 40% DEPLETION SCHEDULE SYSTEM CV .2908 20 25.91 18.88 12692 FACTOR ACTUAL CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 22.35 16.28 12689 11387 2 53.08 38.67 12692 12692 3 23.62 17.21 12692 12448 4 20.07 14.62 12678 8497 5 18.80 13.70 12671 6922 6 20.32 14.80 12680 8657 7 22.35 16.28 12689 11387 8 19.56 14.25 12675 7778 9 20.07 14.62 12678 8947 - 10 19.81 14.43 12676 8147 11 22.35 16.28 12689 11387 12 24.13 17.58 12692 12543 13 21.08 15.36 12684 9739 14 45.72 33.31 12692 12692 15 19.05 13.88 12672 7144 16 18.29 13.32 12688 6305 17 27.43 19.98 12692 12692 18 23.37 17.03 12692 12402 19 20.57 14.99 12682 8842 12692 119 21 28.70 20.91 12692 12692 22 27.69 20.17 12692 12692 23 26.92 19.61 12692 12692 24 26.42 19.25 12692 12692 25. 24.64 17.95 12692 12676 26 27.18 19.80 12692 12692 27 28.19 20.54 12692 12692 28 27.69 20.17 12692 12692 29 45.72 33.31 12692 12692 30 15.49 11.28 11867 2265 ACTUAL CATCH ADJUSTED CATCH MEAN = 26.08 MEAN = 19.00 ST.DEV = 7.58 ST.DEV = 5.53 CV = .2908 CV = .2908 CU = 76.8% CU = 76.8% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL MEAN = 10896 .2761 12635 .0160 CV = MEAN CV 120 40% DEPLETION SCHEDULE SYSTEM CV .3891 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 36.90 29.91 12692 12692 2 63.20 51.23 12692 12692 3 56.80 46.04 12692 12692 4 42.60 34.53 12692 12692 5 38.30 31.04 12692 12692 6 35.20 28.53 12692 12692 7 25.40 20.59 12692 12692 8 28.60 23.18 12692 12692 9 29.30 23.75 12692 12692 10 9.20 7.46 8414 78 11 11.60 9.40 9661 585 12 12.70 10.29 10528 1365 13 21.50 17.43 12692 12505 14 21.50 17.43 12692 12505 15 21.50 17.43 12692 12505 16 18.40 14.91 12681 8759 17 19.60 15.89 12688 10303 18 20.20 16.37 12690 11419 19 20.20 16.37 12690 11419 20 26.30 21.32 12692 12692 121 21 24.50 19.86 12692 12692 22 24.50 19.86 12692 12692 23 23.80 19.29 12692 12692 24 19.40 15.72 12687 10196 25 12.30 9.97 10283 1071 26 9.70 7.86 8663 97 27 18.50 15.00 12682 8850 28 30.40 24.64 12692 12692 29 40.20 32.58 12692 12692 30 33.50 27.15 12692 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 23.44 MEAN = 19.00 ST.DEV = 9.12 ST.DEV = 7.39 CV = .3891 CV = .3891 CU = 68.9% CU = 68.9% YIELD WITHOUT RAINFALL 9820 .4574 YIELD WITH RAINFALL 12116 MEAN .1052 CV MEAN CV 122 40% DEPLETION SCHEDULE SYSTEM CV .4430 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 33.10 28.72 12692 12692 2 48.20 41.82 12692 12692 3 52.50 45.55 12692 12692 4 8.40 7.29 8324 69 5 6.30 5.47 5563 0 6 28.60 24.81 12692 12692 7 13.20 11.45 12077 2470 8 16.80 14.57 12678 8251 9 16.80 14.57 12678 8251 10 15.90 13.79 12671 7025 11 0.00 0.00 2859 0 12 24.90 21.60 12692 12692 13 23.20 20.13 12692 12692 14 26.70 23.16 12692 12692 15 18.80 16.31 12690 11168 16 13.60 11.80 12453 2868 17 19.50 16.92 12692 12373 18 19.50 16.92 12692 12373 19 20.10 17.44 12692 12508 20 20.10 17.44 12692 12508 123 21 13.80 11.97 12543 3223 22 14.60 12.66 12607 4277 23 25.30 21.95 12692 12692 24 26.20 22.73 12692 12692 25 15.40 13.36 12668 6350 26 23.40 20.30 12692 12692 27 8.70 7.55 8651 82 28 42.60 36.96 12692 12692 30 35.20 30.54 12692 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 21.90 MEAN = 19.00 ST.DEV = 9.70 ST.DEV = 8.41 CV = .4430 CV = .4430 CU = 64.4% CU = 64.4% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 9392 .4895 ‘MEAN = 12080 MEAN CV = .1568 CV 124 40% DEPLETION SCHEDULE SYSTEM CV .5175 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 1.30 1.12 3109 0 2 9.20 7.96 8709 109 3 13.50 11.69 12297 2691 4 25.70 22.25 12692 12692 5 14.30 12.38 12580 3667 6 14.30 12.38 12580 3667 7 12.00 10.39 10569 1372 8 19.10 16.53 12690 11542 9 14.50 12.55 12597 4051 10 17.80 15.41 12685 9767 11 21.50 18.61 12692 12691 12 0.00 0.00 2859 0 13 14.80 12.81 12622 4448 14 18.00 15.58 12686 9868 15 19.10 16.53 12690 11542 16 27.70 23.98 12692 12692 17 22.40 19.39 12692 12692 18 14.20 12.29 12572 3578 19 14.90 12.90 12632 5621 20 22.40 19.39 12692 12692 125 21 23.40 20.26 12692 12692 22 28.20 24.41 12692 12692 23 6.30 5.45 5563 0 24 22.40 19.39 12692 12692 25 18.00 15.58 12686 9868 26 26.70 23.11 12692 12692 27 9.20 7.96 8709 109 28 36.10 31.25 12692 12692 29 26.50 22.94 12692 12692 30 53.20 46.05 12692 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 21.95 MEAN = 19.00 ST.DEV = 11.36 ST.DEV = 9.81 CV = .5175 CV = .5175 CU = 58.7% CU = 58.7% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 9080 .5324 11786 MEAN .1979 CV 55 E 126 40% DEPLETION SCHEDULE SYSTEM CV .5802 FACTOR ACTUAL CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 1.27 1.01 3091 0 2 9.14 7.26 8307 68 3 13.46 10.69 10890 1686 4 25.65 20.37 12692 12692 5 14.48 11.50 12149 2526 6 14.48 11.50 12149 2526 7 11.94 9.48 9698 587 8 19.05 15.12 12683 9340 9 14.48 11.50 12149 2526 10 17.78 14.12 12674 7711 11 21.59 17.14 12692 12430 12 0.00 0.00 2859 0 13 14.73 11.69 12297 2691 14 18.03 14.31 12675 7832 15 19.05 15.12 12683 9340 16 23.37 18.55 12692 12690 17 19.05 15.12 12683 9340 18 27.69 21.98 12692 12692 19 22.35 17.74 12692 12583 20 14.22 11.29 11869 2332 127 21 4.83 3.83 4596 O 22 22.35 17.74 12692 12583 23 23.37 18.55 12692 12690 24 28.19 22.38 12692 12692 25 28.96 22.99 12692 12692 26 26.67 21.17 12692 12692‘ 27 13.46 10.69 10890 1686 28 36.07 28.64 12692 12692 29 26.42 20.98 12692 12692 30 67.56 53.64 12692 12692 ACTUAL CATCH ADJUSTEDCATCH MEAN = 23.93 MEAN = 19.00 ST.DEV = 13.89 ST.DEV = 11.03 CV = .5802 CV = .5802 CU = 53.7% CU = 53.7% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 9097 .5350 11800 MEAN .1959 CV MEAN CV 128 50% DEPLETION SCHEDULE SYSTEM CV .1681 FACTOR ACTUAL CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 65.71 48.90 12692 12692 2 61.29 45.61 12692 12692 3 40.31 30.00 12692 12692 4 34.80 25.90 12692 12692 5 34.80 25.90 12692 12692 6 34.80 25.90 12692 12692 7 33.10 24.63 12692 12692 8 32.03 23.84 12692 12692 9 25.90 19.27 12692 12690 10 29.82 22.19 12692 12692 11 27.10 20.17 12692 12692 12 28.16 20.98 12692 12692 13 25.90 19.27 12692 12690 14 25.40 18.90 12692 12690 15 25.40 18.90 12692 12690 16 24.30 18.08 12692 12673 17 25.90 19.27 12692 12690 18 25.90 19.27 12692 12690 19 25.90 19.27 12692 12690 N O 23.74 17.68 12689 12468 12 9 21 24.85 18.49 12692 12687 22 24.85 18.49 12692 12687 23 24.80 18.46 12692 12686 24 22.09 16.44 12681 10659 25' 22.64 16.85 12685 11363 26 23.74 17.67 12689 12646 27 22.64 16.85 12685 11363 28 21.53 16.02 12645 10143 29 24.85 18.49 12692 12687 30 25.40 18.90 12692 12690 ‘ ACTUAL CATCH ADJUSTED CATCH MEAN = 25.53 MEAN = 19.00 ST.DEV = 4.29 ST.DEV = 3.19 CV = .1681 CV = .1681 CU = 86.6% CU = 86.6% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 12278 .0648 MEAN = 12688 MEAN CV 3 .0009 CV 130 50% DEPLETION SCHEDULE SYSTEM CV .2246 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 20.30 20.37 12692 12692 2 19.60 19.67 12692 12692 3 19.60 19.67 12692 12692 4 17.40 17.46 12688 12359 5 18.50 18.93 12692 12688 6 20.20 20.27 12692 12692 7 20.20 20.27 12692 12692 8 9.60 9.63 9944 695 9 8.30 8.33 8500 103 10 10.90 10.94 11101 1590 11 15.40 15.46 12594 9152 12 19.60 19.67 12692 12692 13 19.60 19.67 12692 12692 14 20.30 20.37 12692 12692 15 25.20 25.29 12692 12692 16 18.90 18.97 12692 12689 17 18.20 18.27 12691 12678 18 17.80 17.87 12690 12666 19 17.80 17.87 12690 12666 20 17.80 17.87 12690 12666 13 l 21 15.30 15.36 12586 8865 22 10.40 10.44 10689 1185 23 20.10 20.17 12692 12692 24 19.80 19.87 12692 12692 25 19.70 19.77 12692 12692 26 20.60 20.68 12692 12692 27 18.40 18.47 12692 12687 28 18.40 18.47 12692 12687 29 28.20 28.30 12692 12692 30 23.50 23.59 12692 12692 ACTUAL CATCH ADJUSTED CATCH MEAN = 18.93 MEAN = 19.00 ST.DEV = 4.25 ST.DEV = 4.27 CV = .2246 CV = .2246 CU = 82.3% CU = 82.3% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL = 11194 .3246 12427 MEAN .0647 CV = 2’ 132 50% DEPLETION SCHEDULE SYSTEM CV .2643 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 35.40 29.56 12692 12692 2 42.50 35.49 12692 12692 3 50.20 41.92 12692 12692 4 28.10 23.47 12692 12692 5 16.80 14.03 12420 7065 6 17.20 14.36 12458 7496 7 21.30 17.79 12690 12663 8 21.30 17.79 12690 12663 9 21.30 17.79 12690 12663 10 23.50 19.63 12692 12692 11 22.20 18.54 12692 12687 12 18.60 15.53 12600 9196 13 19.50 16.29 12671 10594 14 19.50 16.29 12671 10594 15 19.50 16.29 12671 10594 16 19.50 16.29 12671 10594 17 20.40 17.04 12686 11651 18 20.40 17.04 12686 11651 19 21.30 17.79 12690 12663 20 22.20 18.54 12692 12687 13 3 21 24.50 20.46 12692 12692 22 25.20 21.05 12692 12692 23 20.30 21.96 12692 12692 24 21.30 17.79 12690 12663 25 22.20 18.54 12692 12687 26 30.20 25.22 12692 12692 27 9.10 7.60 7620 85 28 21.90 18.29 12692 12679 29 35.80 29.90 12692 12692 30 22.60 18.87 12692 12690 GENERATED CATCH ADJUSTED CATCH MEAN = 22.75 MEAN = 19.00 ST.DEV = 6.01 ST.DEV = 5.02 CV = .2643 CV = .2643 CU = 78.9% CU = 78.9% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 11396 .2662 12386 MEAN .0957 CV MEAN CV 134 50% DEPLETION SCHEDULE SYSTEM CV .2908 FACTOR ACTUAL CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 22.35 16.28 12670 10589 2 53.08 38.67 12692 12692 3 23.62 17.21 12687 11975 4 20.07 14.62 12490 7880 5 18.80 13.70 12392 6905 6 20.32 14.80 12512 7998 7 22.35 16.28 12671 10589 8 19.56 14.25 12445 7424 9 20.07 14.62 12490 7880 10 19.81 14.43 12467 7527 11 22.35 16.28 12670 10589 12 24.13 17.58 12689 12384 13 21.08 15.36 12586 8865 14 45.72 33.31 12692 12692 15 19.05 13.88 12405 6981 16 18.29 13.32 12367 5971 17 27.43 19.98 12692 12692 18 23.37 17.03 12686 11649 19 20.57 14.99 12536 8380 20 25.91 18.88 12692 12690 135 21 28.70 20.91 12692 12692 22 27.69 20.17 12692 12692 23 26.92 19.61 12692 12692 24 26.42 19.25 12692 12691 25 24.64 17.95 12690 12669 26 27.18 19.80 12692 12692 27 28.19 20.54 12692 12692 28 27.69 20.17 12692 12692 29 45.72 33.31 12692 12692 30 15.49 11.28 11514 2082 ACTUAL CATCH . ADJUSTED CATCH MEAN = 26.08 MEAN = 19.00 ST.DEV = 7.58 ST.DEV = 5.53 CV = .2908 CV = .2908 CU = 76.8% CU = 76.8% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 10709 .2908 MEAN 8 12564 MEAN .0233 CV 136 50% DEPLETION SCHEDULE SYSTEM CV .3323 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 24.60 25.69 12692 12692 2 30.10 31.44 12692 12692 3 15.90 16.61 12683 11023 4 14.30 14.94 12529 8082 5 7.60 7.94 7844 97 6 8.20 8.56 8676 109 7 24.60 25.69 12692 12692 8 20.30 21.24 12692 12692 9 21.90 22.87 12692 12692 10 9.60 10.03 10262 932 11 8.30 8.67 8227 114 12 18.70 19.53 12692 12692 13 19.50 20.37 12692 12692 14 19.50 20.37 12692 12692 15 14.40 15.04 12543 8412 16 14.30 14.94 12529 8082 17 23.60 24.65 12692 12692 18 23.00 24.02 12692 12692 19 23.60 24.65 12692 12692 N O 17.50 18.28 12691 12678 13 7 21 17.60 18.38 12691 '12681 22 18.40 19.22 12692 12690 23 8.30 8.67 8727 114 24 9.22 9.61 9935 683 25 15.30 15.98 12641 10122 26 15.60 16.29 12671 10594 27 25.60 26.74 12692 12692 28 119.60 20.47 12692 12692 29 17.40 18.17 12691 12675 30 31.10 32.48 12692 12692 ACTUAL CATCH ADJUSTED CATCH MEAN = 18.19 MEAN = 19.00 ST.DEV = 6.04 ST.DEV = 6.31 CV = .3323 CV = .3323 CU = 73.6% CU = 73.6% YIELD WITHOUT RAINFALL 9997 .4544 YIELD WITH RAINFALL 12075 MEAN .1128 CV 138 50% DEPLETION SCHEDULE SYSTEM CV .3891 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) .W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 36.90 29.91 12692 12692 2 63.20 51.23 12692 12692 3 56.80 46.04 12692 12692 4 42.60 34.53 12692 12692 5 38.30 31.04 12692 12692 6 35.20 28.53 12692 12692 7 25.40 20.59 12692 12692 8 28.60 23.18 12692 12692 9 29.30 23.75 12692 12692 10 9.20 7.46 7580 76 11 11.60 9.40 9517 596 12 12.70 10.29 10646 1107 13 21.50 17.43 12688 12266 14 21.50 17.43 12688 12266 15 21.50 17.43 12688 12266 16 18.40 14.91 12525 8063 17 19.60 15.89 12632 9840 18 20.20 16.37 12680 10629 19 20.20 16.37 12680 10629 20 26.30 21.32 12692 12692 13 9 21 24.50 19.86 12692 12692 22 24.50 19.86 12692 12692 23 23.80 19.29 12692 12691 24 19.40 15.72 12616 9536 25 12.30 9.97 10266 895 26 9.70 7.86 7822 90 27 18.50 15.00 12537 8130 28 30.40 24.64 12692 12692 29 40.20 32.58 12692 12692 30 33.50 27.15 12692 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 23.44 MEAN = 19.00 ST.DEV = 9.12 ST.DEV = 7.39 CV = .3891 CV = .3891 CU = 68.9% CU = 68.9% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 9602 .4694 12029 MEAN .1210 CV MEAN CV 140 50% DEPLETION SCHEDULE SYSTEM CV .4177 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 3.40 3.87 4869 0 2 5.60 6.38 6517 0 3 23.10 26.31 12692 12692 4 19.30 21.98 12692 12692 5 18.30 20.84 12692 12692 6 18.40 20.96 12692 12692 7 17.20 19.59 12692 12692 8 17.20 19.59 12692 12692 9 20.60 23.46 12692 12692 10 8.20 9.34 9475 547 11 8.20 9.34 9475 547 12 0.00 0.00 2859 0 13 12.00 13.67 12389 6845 14 19.30 21.98 12692 12692 15 25.00 28.48 12692 12692 16 10.70 12.19 12227 3493 17 11.20 12.76 12298 5160 18 14.20 16.17 12659 10515 19 10.80 12.30 12245 4506 20 26.10 29.73 12692 12692 14 1 21 20.00 22.78 12692 12692 22 16.50 18.79 12692 12692 23 19.20 21.87 12692 12692 24 20.60 23.46 12692 12692 25' 6.30 7.18 7359 68 26 8.20 9.34 9475 547 27 15.40 17.54 12688 12375 28 19.00 21.64 12692 12692 29 28.00 31.89 12692 12692 30 26.10 29.73 12692 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 16.68 MEAN = 19.00 ST.DEV = 6.97 ST.DEV = 7.93 CV = .4854 CV = .4854 CU = 61.1% CU = 61.1% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 11724 MEAN = .1802 CV = 142 50% DEPLETION SCHEDULE SYSTEM CV .4430 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 33.10 28.72 12692 12692 2 48.20 41.82 12692 12692 3 52.50 45.55 12692 12692 4 8.40 7.29 7488 71 5 6.30 5.47 6008 0 6 28.60 24.81 12692 12692 7 13.20 11.45 11776 2383 8 16.80 14.57 12483 7611 9 16.80 14.57 12483 7611 10 15.90 13.79 12399 6950 11 0.00 0.00 2859 0 12 24.90 21.60 12692 12692 13 23.20 20.13 12692 12692 14 26.70 23.16 12692 12692 15 18.80 16.31 12673 10602 16 13.60 11.80 11949 2808 17 19.50 16.92 12685 11621 18 19.50 16.92 12685 11621 19 20.10 17.44 12688 12268 20 20.10 17.44 12688 12268 14 3 21 13.80 11.97 12182 3038 22 14.60 12.66 12285 5022 23 25.30 21.95 12692 12692 24 26.20 22.73 12692 12692 25 15.40 13.36 12371 6003 26 23.40 20.30 12692 12692 27 8.70 7.55 7599 83 28 42.60 36.96 12692 12692 29 30.40 26.37 12692. 12692 30 35.20 30.54 12692 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 21.90 MEAN = 19.00 ST.DEV = 9.70 ST.DEV = 8.41 CV = .4430 CV = .4430 CU = 64.4% CU = 64.4% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 9268 .4911 11933 MEAN .1676 CV MEAN CV 144 50% DEPLETION SCHEDULE SYSTEM CV .5175 FACTOR GENER. CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 1.30 1.12 3121 0 2 9.20 7.96 7852 97 3 13.50 11.69 11921 2658 4 25.70 22.25 12692 12692 5 14.30 12.38. 12255 4612 6 14.30 12.38 12255 4612 7 12.00 10.39 10674 1148 8 19.10 16.53 12682 10987 9 14.50 12.55 12272 4913 10 17.80 15.41 12590 8901 11 21.50 18.61 12692 12688. 12 0.00 0.00 2859 0 13 14.80 12.81 12304 5216 14 18.00 15.58 12605 9229 15 19.10 16.53 12682 10987 16 27.70 23.98 12692 12692 17 22.40 19.39 12692 12691 18 14.20 12.29 12244 4495 19 14.90 12.90 12315 5293 20 22.40 19.39 12692 12691 14 5 21 23.40 20.26 12692 12692 22 28.20 24.41 12692 12692 23 6.30 5.45 5999 0 24 22.40 19.39 12692 12691 25 18.00 15.58 12605 9229 26 26.70 23.11 12692 12692 27 9.20 7.96 7852 97 28 36.10 31.25 12692 12692 29 26.50 22.94 12692 12692 30 53.20 46.05 12692 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 21.95 MEAN = 19.00 ST.DEV = 11.36 ST.DEV = 9.81 CV = .5175 CV = .5175 CU = 58.7% CU = 58.7% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 9058 .5230 MEAN = CV = 11677 .1998 MEAN = CV = 146 50% DEPLETION SCHEDULE SYSTEM CV .5175 FACTOR ACTUAL CATCH ADJ.CATCH YIELD YIELD (MM) (MM) W/RAIN W/O RAIN (KG/HA) (KG/HA) 1 1.27 1.01 3088 o 2 9.14 7.26 7417 71 3 13.46 10.69 10752 1378 4 25.65 20.37 12692 12692 5 14.48 11.50 11788 2476 6 14.48 11.50 11788 2476 7 11.94 9.48 9765 556 8 19.05 15.12 12554 8464 9 14.48 11.50 11788 2476 10 17.78 14.12 12430 7313 11 21.59 17.14 12686 11677 12 0.00 0.00 2859 o 13 14.73 11.69 11921 2658 14 18.03 14.31 12452 7433 15 19.05 15.12 12554 8464 16 23.37 18.55 12692 12687 17 19.05 15.12 12554 8464 18 27.69 21.98 12692 12692 19 22.35 17.74 12689 12661 20 14.22 11.29 11516 2163 l4 7 21 4.83 3.83 4581 0 22 22.35 17.74 12689 12661 23 23.37 18.55 12692 12687 24 28.19 22.38 12692 12692 25 28.96 22.99 12692 12692 26 26.67 21.17 12692 12692 27 13.46 10.69 10752 1378 28 36.07 28.64 12692 12692 29 26.42 20.98 12692 12692 30 67.56 53.64 12692 12692 ACTUAL CATCH ADJUSTED CATCH MEAN = 23.93 MEAN = 19.00 ST.DEV = 13.89 ST.DEV = 11.03 CV = .5802 CV = .5802 CU = 53.7% CU = 53.7% YIELD WITH RAINFALL YIELD WITHOUT RAINFALL 11735 MEAN MEAN : .1938 CV = .5484 CV 148 60% DEPLETION SCHEDULE SYSTEM CV .1681 FACTOR ACTUAL CATCH ADJ.CATCH YIELD (MM) (MM) W/RAIN (KG/HA) 1 65.71 48.90 12692 2 61.29 45.61 12692 3 40.31 30.00 12692 4 34.80 25.90 12692 5 34.80 25.90 12692 6 34.80 25.90 12692 7 33.10 24.63 12692 8 32.03 23.84 12692 9 25.90 19.27 12689 10 29.82 22.19 12691 11 27.10 20.17 12690 12 28.16 20.98 12690 13 25.90 19.27 12689 14 25.40 18.90 12688 15 25.40 18.90 12688 16 24.30 18.08 12685 17 25.90 19.27 12689 18 25.9 19.27 12689 19 25.90 19.27 12689 20 23.74 17.68 12683 149 21 24.85 18.49 12686 22 24.85 18.49 12686 23 24.80 18.46 12686 24 22.09 16.44 12596 25 22.64 16.85 12640 26 23.74 17.67 12683 27 22.64 16.85 12640 28 21.53 16.02 12535 29 24.85 18.49 12686 30 25.40 18.90 12688 ACTUAL CATCH ADJUSTED CATCH MEAN = 25.53 MEAN = 19.00 ST.DEV = 4.29 ST.DEV = 3.19 CV = .1681 CV = .1681 CU = 86.6% CU = 86.6% YIELD WITH RAINFALL 12688 .0033 MEAN CV 150 60% DEPLETION SCHEDULE SYSTEM CV .2643 FACTOR GENER. CATCH ADJ.CATCH YIELD (MM) (MM) W/RAIN (KG/HA) 1 35.4 29.56 12692 2 42.50 35.49 12692 3 50.20 41.92 12692 4 28.1 23.47 12692 5 16.80 14.03 12183 6 17.20 14.36 12247 7 21.30 17.79 12684 8 21.30 17.79 12684 9 21.30 17.79 12684 10 23.50 19.63 12689 11 22.2 18.54 12689 12 18.6 15.53 12453 13 19.50 16.29 12576 14 19.50 16.29 12576 15 19.50 16.29 12576 16 19.50 16.29 12576 17 20.40 17.04 12645 18 20.40 17.04 12645 19 21.30 17.79 12684 20 22.20 18.54 12687 151 21 24.50 20.46 12690 22 25.20 21.05 12690 23 26.3 17.79 12684 24 21.30 17.79 12684 25' 22.20 18.54 12687 26 30.20 25.22 12692 27 9.1 7.6 7642 28 21.9 18.29 12686 29 35.8 29.90 12692 30 22.60 18.87 12687 ACTUAL CATCH ADJUSTED CATCH MEAN = 22.75 MEAN = 19.00 ST.DEV = 6.01 ST.DEV = 5.02 CV = .2643 CV = .2643 CU = 78.9% CU = 78.9% YIELD WITH RAINFALL 12360 .0951 MEAN CV 152 60% DEPLETION SCHEDULE SYSTEM CV .2908 FACTOR GENER. CATCH ADJ.CATCH YIELD (MM) (MM) W/RAIN (KG/HA) 1 22.35 16.28 12575 2 53.08 38.67 12692 23.62 17.21 12271 4 20.07 14.62 12290 5 18.80 13.70 12121 6 20.32 14.80 12330 7 22.35 16.28 12575 8 19.56 14.25 12226 9 20.07 14.62 12290 10 19.81 14.43 12260 11 22.35 16.28 12575 12 24.13 17.58 12683 13 21.08 15.36 12426 14 45.72 33.31 12692 15 19.05 13.88 12154 16 18.29 13.32 12060 17 27.43 19.98 12689 18 23.37 17.03 12653 19 20.57 14.99 12371 20 25.91 18.88 12688 153 21 28.70 20.91 12690 22 27.69 20.17 12690 23 26.92 19.61 12689 24 26.42 19.25 12689 25 24.64 17.95 12685 26 27.18 19.80 12689 27 28.19 20.54 12690 28 27.69 20.17 12690 29 45.72 33.31 12692 30 15.49 11.28 10706 ACTUAL CATCH ADJUSTED CATCH MEAN = 26.08 MEAN = 19.00 ST.DEV = 7.58 ST.DEV = 5.53 CV = .2908 CV = .2908 CU = 76.8% CU = 76.8% YIELD WITH RAINFALL MEAN = 12484 CV = .0399 154 60% DEPLETION SCHEDULE SYSTEM CV .3891 FACTOR GENER. CATCH ADJ.CATCH YIELD (MM) (MM) W/RAIN (KG/HA) 1 36.90 29.91 12692 2 63.20 51.23 12692 3 56.80 46.04 12692 4 42.60 34.53 12692 5 38.30 31.04 12692 6 35.20 28.53 12692 7 25.40 20.59 12690 8 28.60 23.18 12692 9 29.30 23.75 12692 10 9.20 7.46 7595 11 11.60 9.40 8877 12 12.70 10.29 9779 13 21.50 17.43 12682 14 21.50 17.43 12682 15 21.50 17.43 12682 16 18.40 14.91 12356 17 19.60 15.89 12513 18 20.20 16.37 12586 19 20.20 16.37 12586 20 26.30 21.32 12691 155 21 24.50 19.86 12689 22 24.50 19.86 12689 23 23.80 19.29 12689 24 19.40 15.72 12484 25 12.30 9.97 9717 26 9.70 7.86 7879 27 18.50 15.00 12372 28 30.40 24.64 12692 29 40.20 32.58 12692 30 33.50 27.15 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 23.44 MEAN = 19.00 ST.DEV = 9.12 ST.DEV = 7.39 CV = .3891 CV = .3891 CU = 68.9% CU = 68.9% YIELD WITH RAINFALL 11926 .1282 MEAN CV 156 60% DEPLETION SCHEDULE SYSTEM CV .4430 FACTOR GENER. CATCH ADJ.CATCH YIELD (MM) (MM) W/RAIN (KG/HA) 1 33.10 28.72 12692 2 48.20 41.82 12692 3 52.50 45-55 12692 4 8.40 7.29 7298 5 6.30 5.47 5367 6 28.60 24.81 12692 7 13.20 11.45 10735 8 16.80 14.57 12284 9 16.80 14.57 12284 10 15.90 13.79 12138 11 0.00 0.00 2859 12 24.90 21.60 12691 13 23.20 20.13 12690 14 26.70 23.16 12692 15 18.80 16.31 12578 16 13.60 11.80 11619 17 19.50 16.92 12646 18 19.50 16.92 12646 19 20.10 17.44 12682 20 20.10 17.44 12682 157 21 13.80 11.97 11648 22 14.60 12.66 11961 23 25.30 21.95 12691 24 26.20 22.73 12691 25 15.40 13.36 12066 26 23.40 20.30 12690 27 8.70 7.55 7616 28 42.60 36.96 12692 29 30.40 26.37 12692 30 35.20 30.54 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 21.90 MEAN = 19.00 ST.DEV = 9.70 ST.DEV = 8.41 CV = .4430 CV = .4430 CU = 64.4% CU = 64.4% YIELD WITH RAINFALL 11823 .1706 MEAN = CV = 158 60% DEPLETION SCHEDULE SYSTEM CV .2643 FACTOR GENER. CATCH ADJ.CATCH YIELD (MM) (MM) W/RAIN (KG/HA) 1 1.30 1.12 3098 2 9.20 7.96 7933 3 13.50 11.69 11450 4 25.70 22.25 12691 5 14.30 12.38 11911 6 14.30 12.38 11911 7 12.00 10.39 9777 8 19.10 16.53 12609 9 14.50 12.55 11942 10 17.80 15.41 12434 11 21.50 18.61 12687 12 0.00 0.00 2859 13 14.80 12.81 11983 14 18.00 15.58 12461 15 19.10 16.53 12609 16 27.70 23.98 12692 17 22.40 19.39 12689 18 14.20 12.29 11895 19 14.90 12.90 11994 20 22.40 . 19.39 12689 159 21 23.40 20.26 12690 22 28.20 24.41 12692 23 6.30 5.45 5357 24 22.40 19.39 12689 25 18.00 15.58 12461 26 26.70 23.11 12692 27 9.20 7.96 7933 28 36.10 31.25 12692 29 26.50 22.94 12691 30 53.20 46.05 12692 GENERATED CATCH ADJUSTED CATCH MEAN = 21.95 MEAN = 19.00 ST.DEV = 11.36 ST.DEV 8 9.81 CV = .5175 CV 8 .5175 CU = 58.7% CU = 58.7% YIELD WITH RAINFALL 11584 .2073 160 60% DEPLETION SCHEDULE SYSTEM CV .5802 FACTOR GENER. CATCH ADJ.CATCH YIELD (MM) (MM) W/RAIN (KG/HA) 1 1.27 1.01 3044 2 9.14 7.26 7349 3 13.46 10.69 10056 4 25.65 20.37 12690 5 14.48 11.50 11037 6 14.48 11.50 11037 7 11.94 9.48 8901 8 19.05 15.12 12389 9 14.48 11.50 11037 10 17.78 14.12 12201 11 21.59 17.14 12664 12 0.00 0.00 2859 13 14.73 11.69 11450 14 18.03 14.31 12238 15 19.05 15.12 12389 16 23.37 18.55 12687 17 19.05 15.12 12389 18 27.69 21.98 12691 19 22.35 17.74 12684 20 14.22 11.29 10707 161 21 4.83 3.83 4013 22 22.35 17.74 12684 23 23.37 18.55 12687 24 28.19 22.38 12691 25' 28.96 22.99 12691 26 26.67 21.17 12691 27 13.46 10.69 10056 28 36.07 28.64 12692 29 26.42 20.98 12690 30 67.56 53.64 12692 ACTUAL CATCH ADJUSTED CATCH MEAN = 23.93 MEAN = 19.00 ST.DEV = 13.89 ST.DEV = 11.03 ,CV = .5802 CV = .5802 CU = 53.7% CU = 53.7% YIELD WITH RAINFALL 11532 .2106 REFERENCES Bartholic, J.F. ed. 1983. Impact Evaluation of Increased Water Use by Agriculture in Michigan. MSU Ag. Expt. Sta. Research Report No. 449. East Lansing, MI. Benami, A. and F. R. Hore. 1964. A New Irrigation Sprinkler Distribution Coefficient. Transactions of the ASAE 7:157- 158. Blaney, H.F. and W.D. Criddle. 1950. A Method of Estimating Water Requirements in Irrigated Areas from Climatological DAta. USDA-SCS mimeo. Bralts, Vincent F. and Charles D. Kesner. 1983. Drip Irrigation Field Uniformity Estimation. Transactions of the ASAE Vol. 26:1369-1374. Bralts, V.F. and K.A. Algozin. 1985. Report of Results for Irrigation System Evaluation and Demonstration Project. USDA. Bralts, V.F. and Wu I. .1986. Drip Irrigation Design and Evaluation Based on the Statistical uniformity Concept. in: Advances in Irrigation Vol IV. D. Hillel ed. Academic Press, Orlando, FLA. Bralts, V.F. 1897. Personal Communication. Bresler E., G. Dagen and J. Hanks. 1982. Statistical Analysis of Crop Yield under Controlled Line Source Irrigation. Soil Science Society of America Journal 4. Chang, A.C., R.W. Skaggs, L.F. Hermsmeir and W.R. Johnston .1983. Evaluation of a Water Management Model for Irrigated Agriculture. Transactions of the ASAE 26:2. Chaudry, F.H. 1976. Sprinkler Uniformity Measures and Skewness. Journal of Irrigation and Drainage Division ASCE 102 (Ir4) Chaudry, F.H. 1978. Nonuniform Sprinkler Application Efficiency. Journal Of Irrigation and Drainage Division ASCE 104 (1R2) Childs, S.W. and R.J. Hanks. 1975. Model of Soil Salinity Effects on Crop Growth. Proc. Soil Sci. SOC. Am. 39:617- 622. ' 162 163 Childs, S.W., J.R. Gilley and W.E. Splinter. 1977. A Simplified Model of Corn Growth Under Moisture Stress. Transactions Of the ASAE 20(5):858-865. Christiansen, J.E. 1912. Irrigation by Sprinkling. CalifOrnia Agricultural Expt. Sta. Bulletin 670, Univ. of Calif., Berkeley, CA. Dabbous, B.J. 1962. A Study of Sprinkler Uniformity Evaluation Methods. Thesis submitted in partial fulfillment Of the requirements for the degree of Master of Science, Utah State Univ., Logan, Utah. Dent, J.B. and M.J. Blackie. 1979. Systems Simulation in Agriculture. Applied Science Publishers Ltd., Essex, G.B. Doorenbos, J. and A. H. Kassam. 1979. Yield Response to Water. FAO Irrigation and Drainage Paper NO. 33. FAQ, Rome, Italy. Doorenbos, J. and W.O. Pruitt. 1977. Crop Water Requirements FAO Irrigation and Drainage Paper 24. FAQ, Rome, Italy. Driscoll, M.A., and V.F. Bralts. 1986. Report of Results for Irrigation System Evaluation and Scheduling Demonstration Project. USDA. Duncan, W.G. 1975. MAIZE in: Crop Physiology. L.T. Evans, ed. Cambridge University Press, London, G.B. Elliott, R.L., J.D. Nelson, J.C. Loftis and W.E. Hart. 1979. Statistical Distributions of Sprinkler Application Depths. ASAE paper No. 79-2081, ASAE, St. Joseph, Mi. Elliott, R.L., J.D. Nelson, J.C. Loftis and W.E. Hart. 1980. Comparison of Sprinkler Uniformity Models. Journal of Irrigation and Drainage Division ASCE 106(IR4) . English, M.J. 1981. The Uncertainty of Crop Models in Irrigation Optimization. Transactions of the ASAE 24:4. English, M.J. and 6.5. Nuss 1982. Designing for Deficit Irrigation. Journal of Irrigation and Drainage Division ASCE 108 (1R2) English, M.J., L.D. James, D.J. Hunsaker, and R.J. McKusick 1985. A practical View of Deficit Irrigation. ASAE Paper NO. 85-2595. ASAE, St. Joseph, MI. (1983) Estimating Agricultural Crop Water Requirements. Technical Guideline for the Bureau of Reclamation. Division of Planning and Technical Services Hydrology Branch Water Utilization Section, Engineering and Research Center, Denver, CO. 164 Feinerman, E., J. Letey and H.J. Vaux Jr. 1983. The Economics of Irrigation with Nonuniform Infiltration. Water Resources Research 19:6. Fienerman, E., K.C. Knapp and J. Letey. 1984. Salinity and Uniformity of Water Infiltration as Factors in Yield and Economically Optimal Water Application. Soil Science Society of America Journal Vol.48:477-481. Gurovich, L.A. 1979. Effects of Improved Field Practice on Crop Yield, Water Use and Profitability of Irrigation in Central Chile. Irrigation Science 1. Gurovich, L.A. and H.R. Duke. 1984. Economic Effects of Spatial Distribution Patterns for Water Application Under Center Pivot Systems. ASAE Paper No. 84-2584. Hanks, R.J. 1974. Model for Predicting Yield as Influenced by Water Use. Agronomy Journal Vol. 66:660-664. Hanson, B.R. and W.W. Wallender. 1985. Bidirectional Uniformity Of Water Applied by Continuous Move Sprinkler Machines. ASAE. Paper NO. 85-2572 ASAE, St. Joseph, MI. Hardjoamidjojo, S. R.W. Skaggs and G.O. Schwab. 1982. Corn Yield Response to Excessive Soil Water Conditions. Transactions of the ASAE Vol. 25:922-927. Hart, W.E. 1961. Overhead Irrigation Pattern Parameters. Agricultural Engineering. 42:354-355. ‘Hart,W.E., G. Peri and G.V. Skogerboe .1979. Irrigation Performance: An Evaluation. Journal of the Irrigation and Drainage Division of the ASCE. Hart, W.E. D.I. Norum and G. Peri. 1980. Optimal Seasonal Irrigation Application Analysis. Journal Of Irrigation and Drainage Division ASCE 106(IR3) Hart, W.E. and W.N. Reynolds. 1965. Analytical Design of Sprinkler Systems. Transactions of the ASAE 8(1):83-85,89. Heerman,D.F. and P.R. Hein. 1968. Performance Characteristics of Self Propelled Center Pivot Sprinkler Systems. Transactions of the ASAE 11(1):11-15. Heerman, D.F. and D.L. Swedensky. 1984. Simulation Analysis of Center Pivot Sprinkler Uniformity. ASAE Paper No. 84-2582. ASAE, St. Joseph, MI. Hillel, Daniel and Y. Guron. 1973. Relation Between Evapotranspiration Rate and Maize Yield. Water Resources Research 9:3. 165 Hillel, D. Fundamentals of Soil Physics. 1980. Academic Press Inc., London, G.B. Hill, R.W. and J. Keller. 1980. Irrigation System Selection for Maximum Crop Profit. Transactions of the ASAE 23(2):366—372. Howell, D.T. 1964. Sprinkler Non-uniformity Characteristics and Yield. Journal of Irrigayion and Drainage Division ASCE 90(IR3) Israelsen, O.W. and V.E. Hansen. 1962. Irrigation Principles and Practices. John Wiley and Sons, New York. Jensen, M.E. D.C.N. Robb and G.E. Franzoy. 1970. Scheduling Irrigation Using Crop-Soil Data. Journal of the Irrigation and Drainage Division ASCE 96(IR1). Jones, C.A. and J.R. Kiniry. 1986. CERES-Maize A Simulation of Maize Growth and Development. Texas A&M Univ. Press, College Station, TX. Karmeli, D. 1977. Water Distribution Patterns for Sprinkler. and Surface Irrigation Systems. Proc. National Conf. on Irrig. Return Flow Quality Management, Colo. State Univ, Fort Collins, Colorado, May 16-19, 1977 Karmeli, David (1978) Estimating Sprinkler Distribution Patterns Using Linear Regression. Transactions of the ASAE 21 (3)682-686. Karmeli, D., L.J. Salazar and W.R. Walker. 1978. Assessing the Spatial Variability of Irrigation Water Applications. Document No. EPA-600/2-78-041, U.S. Environ. Prot. Agency, ADA, OK. Karmeli,D. G. Peri and M. Todes. 1985. Irrigation Systems: Design and Operation. Oxford University Press, Cape Town. Kay, M. 1983. Sprinkler Irrigation Equipment and Practice. Batsford Academic and Educational Ltd., London, G.B. Kruse, E.G. 1978. Describing Irrigation Efficiency and Uniformity. Journal of the Irrigation and Drainage Division ASCE 104(IR1). Letey, J., H.J. Vaux Jr., and E. Fienerman 1984. Optimum Crop Water Application as Affected by Uniformity of Water Infiltration. Agronomy Journal 76: May-June. Lynne, G.D. and R.R. Carriker. 1979. Crop Response Information for Water Institutions. Journal of Irrigation and Drainage Division ASCE 105 (IR3) 166 Marek, T.H., D.J. Undersander, and L.L. Ebeling. 1986. An Areal-Weighted Uniformity Coefficient for Center Pivot Irrigation Systems. Transactions of the ASAE 29(6):1665- 1668. Martin, D.L., D.G. Watts and J.R. Gilley. 1984. Model and Production Functions for Irrigation Management. Journal of Irrigation and Drainage Division ASCE 110 (1R2). Morey, R.V., J.R. Gilley, F. G. Bergsrud and L.R. Dirkzwager 1980. Yield Response of Corn Related to Soil Moisture. Transactions of the ASAE 23:5. Musick, J.T. and D.A. Dusek. 1980. Irrigated Corn Yield Response to Water. Transactions of the ASAE 23:1. Norum, E.M. 1961. A Method of Evaluating the Adequacy and Efficiency of Overhead Irrigation Systems. ASAE Paper NO. 61-206, ASAE, St. Joseph, MI. Norum, Donald 1., G. Peri and W.E. Hart. 1979. Application of System Optimal Depth Concept. Journal of the Irrigation and Drainage Division of the ASAE. On-Farm Irrigation Committee of the Irrigation and Drainage Division, ASCE. 1978. Describing irrigation efficiency and uniformity. Journal of the Irrigation and Drainage Division of the ASCE. Penman, H.L. 1948. Natural Evaporation from Open Water, Bare Soil and Grass. Proc. from the Royal Soc. Series A. Peri, G., W.E. Hart and D.I. Norum. 1979. Optimal Irrigation Depths - a Method of Analysis. Journal Of Irrigation and Drainage Division ASCE 105(IR4) Seigner, Ido. 1978. A Note on the Economic Significance of Uniform Water Application. Irrigation Science 1. Seigner, I. 1979. Irrigation Uniformity Related to Horizontal Extent of Root Zones Irrigation Science 1:89-96. Seniwongse, C., 1. Wu and W.N. Reynolds. 1972. The Effects of Skewness and Kurtosis on the Uniformity Coefficient and their Applications to Sprinkler Irrigation Design. Transactions of the ASAE 15(2):266-271. Slabbers, P.J. v.5. Herrendorf and M. Stapper. 1979. Evaluation Of Simplified Water-crop Yield Models. Agricultural Water Management 2:2 Solomon, Ken and Malcolm Kodoma. 1978. Center Pivot End Sprinkler Pattern Analysis and Selection. Transactions of the ASAE : 167 Solomon, Ken (1979) Variability of Sprinkler Coefficient of Uniformity Test Results. Transactions of the ASAE Solomon, K.H. 1983. Irrigation Uniformity and Yield Theory. PhD DiSsertation. Agricultural & Engineering Dept. Utah State Univ., Logan, Utah. Solomon, K.H. 1984. Yield Related Interpretations of Irrigation Uniformity and Efficiency Measures. Irrigation Science Solomon, Kenneth H. 1985. Typical CrOp Water Production Functions. ASAE Paper No. 85-2596 ASAE, St. Joseph, MI. Stegman, E.C. L.H. Schiele and A. Bauer. 1976. Plant Water Stress Criteria for Irrigation Scheduling Transactions of the ASAE 19:5 Stern, Jack and Eshel Bresler. 1983. Nonuniform Sprinkler Irrigation and Crop Yield. Irrigation Science 4: 17-29 Su, M . 1979. Comparative Evaluation of Irrigation Uniformity Indices. Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, Utah State Univ. Logan, Utah. Tezar, E. 1971. Investigation into Distribution Uniformity Of Water from Sprinkler Heads. Yearbook of the Fac. Of Ag., Adana, Univ. of Ankara, Turkey, 1(1):63-87. Tscheschke, P.D. and J.R. Gilley. 1979. Status and Verification of Nebraska's Corn Growth Model - CORNGRO. Transactions of the ASAE 22:1329-37 USDA-SCS 1982. South National Technical Center Note No. 707. USDA Soil Conservation Service, Fort Worth, TX. Walker, W.R. 1979. Explicit Sprinkler Irrigation Uniformity: Efficiency Model. J. Irrig. and Drain. Div. ASCE 105(IR2):129-136. Wilcox, J.C. and G.E. Swailes. 1947. Uniformity Of Water Distribution by Some Under-Tree Orchard Sprinklers. Scientific Agriculture 27(11)565-583. Varlev, I. 1976. Evaluation of Nonuniformity and Irrigation Yield. Irrigation and Drainage Division Journal ASCE 102(IR1). von Bernuth, R.D. 1983. Nozzling Considerations for Center Pivots With End Guns. Transactions of the ASAE 26:419-422. Warrick A.W. and W.R. Gardner. 1983. Crop Yield as Affected by Spatial Variations Of Soil and Irrigation. Water Resources Research 19. 168 Wu, I.P. and H.M. Gitlin. 1983. Drip Irrigation Application Efficiency and Schedules. Transactions of the ASAE Vol 26:92-99. Zaslavasky, D. and N Buras. 1967. Crop Response to Uniform Application of Irrigation Water. Transactions of the ASAE 10:96. “(WWIIIRIMI11(11):)((1111:)ES 177 9659