Optimal Allocation and Scheduling of Irrigation Water for Cotton and Soybeans

Transcription

1 University of Arkansas, Fayetteville Technical Reports Arkansas Water Resources Center Optimal Allocation and Scheduling of Irrigation Water for Cotton and Soybeans M. J. Cochran University of Arkansas, Fayetteville L. D. Parsch University of Arkansas, Fayetteville J. M. Redfern University of Arkansas, Fayetteville H. D. Scott University of Arkansas, Fayetteville Follow this and additional works at: Part of the Fresh Water Studies Commons, and the Water Resource Management Commons Recommended Citation Cochran, M. J.; Parsch, L. D.; Redfern, J. M.; and Scott, H. D Optimal Allocation and Scheduling of Irrigation Water for Cotton and Soybeans. Arkansas Water Resources Center, Fayetteville, AR. PUB This Technical Report is brought to you for free and open access by the Arkansas Water Resources Center at It has been accepted for inclusion in Technical Reports by an authorized administrator of For more information, please contact

2 OPTIMAL ALLOCATION AND SCHEDULING OF IRRIGATION WATER FOR COTTON AND SOYBEANS M. J. Cochran, L. D. Parsch, J. M. Redfern and H. D. Scott Departments of Agricultural Economics and Agronomy University of Arkansas Fayetteville, Arkansas Publication No. 116 September, 1985 Technical Completion Report Research Project G Arkansas Water Resources Research Center University of Arkansas Fayetteville, Arkansas AW RRC Arkansas W ater Resources Research Center Prepared for United States Department of the Interior

3 OPTIMAL ALLOCATION AND SCHEDULING OF IRRIGATION WATER FOR COTTON AND SOYBEANS M. J. Cochran, L. D. Parsch, J. M. Redfern and H. D. Scott Departments o f A g ric u ltu ra l Economics and Agronomy U n iversity o f Arkansas F a y e tte v ille, AR Research P roject Technical Completion Report P roject G The research on which th is re p o rt is based was financed in p a rt by the United States Department o f the In te r io r as authorized by the Water Research and Development A ct o f 1978, (P.L ). Arkansas Water Resources Research Center U n iversity o f Arkansas 223 Ozark H all F a y e tte v ille, Arkansas P ublica tion No. 116 September, 1985 Contents o f th is p u b lica tio n do not necessarily r e fle c t the views and p o lic ie s o f the U.S. Department o f the In te r io r, nor does mention o f trade names o r commercial products c o n s titu te th e ir endorsement or recommendation fo r use by the U.S. Government. The U n iversity o f Arkansas, in compliance w ith federal and sta te laws and regulations governing a ffirm a tiv e action and nondiscrim ination, does not discrim inate in the re cruitm e nt, admission and employment o f students, fa c u lty and s ta f f in the operation o f any o f it s educational programs and a c tiv itie s as defined by law. A ccordingly, nothing in th is p u b lica tio n should be viewed as d ir e c tly o r in d ir e c tly expressing any lim ita tio n, s p e c ific a tio n o r d is c rim in a tio n as to race, re lig io n, co lo r or national o rig in ; or to handicap, age, sex, o r status as a d is abled Vietnam-era vete ran, except as provided by law. In q u irie s concerning th is p o licy may be d ire cted to the A ffirm a tiv e Action O ffic e r.

4 A B S T R A C T OPTIMAL ALLOCATION AND SCHEDULING OF IRRIGATION WATER FOR COTTON AND SOYBEANS This study evaluated a lte r n a tiv e ir r ig a t io n scheduling s t r a t e gies f o r c o tto n and soybean p ro d u ctio n on Sharkey c la y s o ils in southeast Arkansas. S tra te g ie s were ranked on the basis o f two basic c r it e r i a : expected net revenue and r is k e ffic ie n c y. Risk e ffic ie n c y was d efin ed f o r d iffe r e n t r is k preferences using s to c h a s tic dominance techniques. P re fe rre d s tra te g ie s f o r c o tto n employed te n sio m e te r th re sh o ld s between atm and atm. Risk e f f ic ie n t soybean i r r ig a tio n s tra te g ie s v a rie d w ith the degree o f r is k aversion--m ore r is k averse d e c is io n makers p re fe r s tra te g ie s w ith low er th re s h o ld s. M.J. Cochran, L.D. Parsch, J.M. Redfern and H.D. S c o tt Completion Report to the U.S. Department o f the I n t e r io r, Washington, D.C., September, Keywords - - C o tto n /S o y b e a n s /Irrig a tio n P ractices/s cheduling/c om puter M odel/s toch astic Model i

5 TABLE OF CONTENTS Page A b stra ct... L is t o f T ables/f ig ures... Acknowledgements... In tro d u c tio n... A. Purpose and O b je ctive s... B. Related Research or A c t iv itie s... Methods and Procedures... A. Soybean Model... B. Soybean I r r ig a tio n S tra te g ie s... C. Cotton Model... D. Timing o f A p p lic a tio n s -- Cotton I r r ig a tio n S tra te g ie s... E. Amount o f Water A p p lie d -- Cotton I r r ig a tio n S tra te g ie s... i i i i iv P rin c ip a l Findings and T h e ir S ig n ific a n c e A. Soybean R esults... S t a t is t ic a l T estin g.... Risk A n alysis... B. Cotton R esults... Center P iv o t System... Furrow System... P ric e U n c e rta in ty... Center P ivo t System... Furrow System... Model E rro rs and the E stim ation o f the P r o b a b ility D is trib u tio n s... Conclusion L ite r a tu r e C ited i i

6 LIST OF TABLES Page Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Table 11 Table 12 Table 13 Table 14 Table 15 Soybean Irrig a tio n Strategy Descriptions... Strategy Cotton Irrig a tio n Descriptions... ASICM Model Output of Soybean Irrig a tio n Strategies. Duncan M u ltiple Range Test fo r Differences In Mean Net Revenues: Soybean Irrig a tio n Strategies... Preference Inte rvals Used to Define Groups of Decision Makers... Risk E ffic ie n t Soybean Irrig a tio n Strategies fo r D iffe re n t Groups of Decision Makers... COTCROP-A Model Results fo r Cotton Irrig a tio n Strategies: Center Pivot System... Risk E fficie n cy Rankings fo r Cotton Irrig a tio n S trategies: Center Pivot System... COTCROP-A Model Results fo r Cotton Irrig a tio n S trategies: Furrow System... Risk E fficie ncy Rankings fo r Cotton Irrig a tio n Strategies: Furrow System... COTCROP-A Model Results fo r Selected Cotton Irrig a tio n Strategies Under Uncertainty... Cotton Water Stress Tables... Years Non-Irrigated Cotton Yields Exceeded Irrig a te d Strategy Yields: Center Pivot System... Years Non-Irrigated Cotton Yields Exceeded Irrig a te d Strategy Yields: Furrow System... Seasonal Summaries of Solar Radiation and P re cip ita tio n from the S tone ville Weather F ile LIST OF FIGURES Figure 1 SICM - Subroutine Flow Chart... Figure 2 Flow Chart of COTCROP Cycles Once Per Day 8 15 i i i

7 ACKNOWLEDGEMENTS The p rin c ip a l in v e s tig a to rs o f th is p ro je c t wish to acknowledge the fo llo w in g : 1. Mary P r ic k e tt and Caren Harp. This re p o rt in te g ra te s the research and work contained in t h e ir re s p e c tiv e Masters o f Science th e s e s - - " Ir r ig a tio n Scheduling f o r Arkansas Soybean P ro d u ctio n " and "R isk E f f ic ie n t Cotton I r r ig a t io n S tra te g ie s f o r A rkansas." 2. Rob Raskin. Much o f the programming and v a lid a tio n work w ith the COTCROP-A, the c o tto n crop growth s im u la tio n model, was perform ed by Mr. R askin. 3. Dr. T e rry C. K e is lin g, Extension A gronom ist. Dr. K e is lin g c o lla b o ra te d on the v a lid a tio n o f ASICM and the re w ritin g o f the soybean phenology. 4. U.S. Department o f the I n t e r io r, G eological Survey and the Arkansas Water Resources Research Center who f in a n c ia lly supported th is research. iv

8 INTRODUCTION The purpose of th is study is to determine the optimal a lloca tion and tim ing o f ir rig a tio n water fo r soybeans and cotton fo r Southeast Arkansas. O ptim ality is f i r s t defined in terms of economic e ffic ie n cy, then in terms of ris k e ffic ie n c y. A lte rn a tive solutions are compared fo r the two c r ite r ia and contrasted w ith engineering e ffic ie n c y and y ie ld maximization. Bio-physical, computer sim ulation models were used to evaluate the various ir r ig a tio n scheduling strategies. This study, although sp e cific to Arkansas, addresses a problem that a ll farmers who use ir rig a tio n must consider. In e ffic ie n t a llo cation and tim ing of irrig a tio n applications can prevent farmers from re a lizin g the f u ll potential of th e ir ir r ig a tio n investments. This can re s u lt in lower expected y ie ld s, increased production risks through v a r ia b ility in yie lds and lower farm incomes. Scheduling and e f f i cie nt water use is also important given the rapid growth in ir r ig a tio n in the state. From 1975 to 1980, the irrig a te d acreage in Arkansas increased by 50 percent. Three crops (ric e, cotton and soybeans) accounted fo r 90 percent o f the increase. In th a t tim e, soybean i r r i gated acreage increased by over 100 percent and in 1980, s lig h tly under 20 percent of a ll soybean acreage was irrig a te d (USDA, 1983). Irrig a tio n scheduling may have impacts at both the farm level and at the aggregate demand level as w e ll. This study w ill focus on only the farm level inputs. In e ffic ie n t a lloca tion and tim ing of water applications is partic u la r ly relevant to Arkansas because the irre g u la r ra in fa ll patterns 1

9 in th is region complicate scheduling decisions. Arkansas farmers also have a tendency to re ly on th e ir experience and observations o f the crop to schedule irrig a tio n s. Water applications made a fte r the crop has incurred drought stress are not as e ffe c tiv e as possible because y ie ld loss has already occurred. The use o f tensiometers and oth er s o il m oisture m onitoring devices is the recommended practic e, but only a small percentage o f the farmers a c tu a lly use any o f these instrum ents1. Due to the uncertainty introduced by the irre g u la r r a in f a ll, farmers' a ttitu d e s toward ris k must be considered. E ffic ie n t scheduling can reduce the impacts o f weather uncertainty but perhaps only by adopting strategies w ith lower expected returns. However, some growers may p refer the v a r ia b ility in returns to the reduction in the expected re tu rn. A. Purpose and Objectives This study hopes to provide inform ation on the e f f ic ie n t a llo cation and tim ing o f irrig a tio n water, thus encouraging farmers to adopt production practices which reduce ris k, increase farm incomes and p o te n tia lly decrease the a g ric u ltu ra l water demand on the current base o f irrig a te d acres. The overall objectives o f th is paper are divided in to three s p e c ific parts. They are: 1) to id e n tify the y ie ld changes under 1Based on a 1983 survey o f cotton growers p a rtic ip a tin g in B o llworm Management Communities, only 25 percent o f the cotton growers who irrig a te use tensiometers. 2

10 selected conditions o f various soybean and cotton ir r ig a t io n schedules, s o il types and v a rie tie s ; 2) to evaluate the combinations o f these a lte rn a tiv e stra tegie s w ith the c r ite r ia o f economic e ffic ie n c y and ris k e ffic ie n c y ; and 3) to compare and to contrast the re su lts using the a lte rn a tiv e c r ite r ia o f engineering e ffic ie n c y and maximum y ie ld. For the purpose o f th is paper, engineering e ffic ie n c y is defined as the average physical product and is calculated as the to ta l y ie ld divided by the to ta l amount o f ir rig a tio n water applied to the crop. Economic e ffic ie n c y is defined as the highest average net re turns and ris k e ffic ie n c y is based upon u t i l i t y maximization. Risk e ffic ie n c y is evaluated w ith stochastic dominance w ith re spect to a fu n ctio n, SDWRF (Meyer, 1977) and re su lts in e ffic ie n t sets o f strategies th a t are consistent w ith the ris k preferences o f specified groups o f decision makers. D iffe re n t ir r ig a tio n scheduling strategies w ill be id e n tifie d in th is paper fo r fo u r classes o f decision makers w ith varying ris k a ttitu d e s. These classes w ill in clude: 1) groups who are u n w illin g to bear r is k ; 2) groups who are w illin g to bear small amounts o f ris k ; 3) groups who are ris k n e u tra l; and 4) groups who are w illin g to bear substantial ris k to increase expected net re tu rn s. B. Related Research o r A c tiv itie s E ffic ie n t scheduling o f water applicatio n allows the farmer to increase the in te n s ity o f land use, raises a g ric u ltu ra l p ro d u c tiv ity and can lower per u n it cost o f production (Bajwa, e t a l., 1983). The farmer in humid regions, ty p ic a lly aided by s p e c ia lis ts, estimates 3

11 water requirements in advance of production and develops plans fo r an ir r ig a tio n water supply system. This system represents a subs ta n tia l long-term capita l investment. Mederski and Jeffe rs (1972) point out th a t in the absence of ir r ig a tio n, s o il moisture levels or p o te n tia ls, except follow ing a r a in f a ll, "are seldom high enough to ensure the optimum plant water potential required maximum y ie ld." There is substantial lite ra tu re available to support the assertio n that ir r ig a tio n scheduling is c r it ic a l to crop performance (Lambert et a l., 1981; Hammond et a l., 1981; Spooner et a l., 1958). The assumptions made regarding the importance of the water supply to crops, the use o f sim ulation models in place of fie ld experiments and ris k as related to ir r ig a tio n are v a lid and well documented. Musser and Tew (1984), in th e ir a r tic le on the applications of sim ulation models, point out that use of bio-physical sim ulation models can be e ffic ie n t and expedient a lte rn a tive s to fie ld experiments when evaluating certain production problems in a g ric u ltu re, especially those th a t contain an element of ris k. There have been many studies done in recent years that incorporate th is methodology (Yaron and Dinar, 1982; G ille y et a l., 1980; Yar, 1980; Feddes et a l., 1978; and Mapp and Eidman, 1975; Boggess, et a l., 1983; and Lynne et a l., 1984). In a study conducted at the U niversity of New Mexico, Lansford et a l. (1984) used two irrig a tio n scheduling models to demonstrate the increases in yie ld s and net return possible with irrig a tio n scheduling. The models used were a dynamic programming model and 4

12 a bio-physical sim ulation model. The p r o fit maximizing, dynamic programming model considered p rice before making an ir r ig a tio n app lic a tio n and then only added water when the value o f the a d d itio n al water exceeded the cost. The bio-physical model chose to irrig a te when the s o il moisture reached a predetermined level as defined by the percentage o f the ra tio between fie ld capacity and permanent w iltin g point. The results from Lansford's, th is study showed th a t the dynamic programming model produced higher yie ld s and net returns fo r each of the crops simulated ( a lfa lfa, corn and sorghum). The net returns fo r sorghum were higher w ith the bio-physical model at the 40 percent s o il moisture le v e l, implying th a t sorghum can to le ra te some drought stress during the growing season. In e ith e r case, y ie ld s and net returns were higher than those reported in the New Mexico State Univ e rs ity crop budgets fo r typica l farms. Risk e ffic ie n c y was not considered in the study. Uncertain weather patterns, seasonality o f production and the nature o f a g ric u ltu ra l commodities make ris k an inescapable feature o f a g ric u ltu ra l production. Farmers' a ttitu d e s toward ris k a ffe c t th e ir management and investment decisions on a ll le ve ls. Management decisions ranging from what crop to plant to s p e c ific production practices are affected by producers' preferences or aversion to ris k. Risk e ffic ie n c y considers both the average net revenue and the v a r i a b ilit y in th a t net revenue which may occur through a series o f growing seasons. I t ranks a lte rn a tiv e management s tra te g ie s consistent 5

13 w ith the w illingness o f the producers to bear ris k. Two recent studies incorporate ris k e ffic ie n c y and irrig a tio n scheduling. Boggess e t a l. (1983) from F lo rid a, demonstrated th a t the p r o fit maximizing strategies were those th a t called fo r frequent applications a t sm aller rates and incomplete w etting o f the s o il prof i l e. They also showed th a t when price v a r ia b ility was introduced, risk-averse decision makers chose to ir r ig a te less fre quently but at higher rates than th a t prescribed by the maximum net returns s t r a t egy. This demonstrates th a t ris k preferences do a ffe c t management decisions. H a rris, Mapp and Stone (1983) used stochastic e ffic ie n c y c r i te ria and optimal control theory to develop irrig a tio n strategies designed to reduce the water demand from the Oklahoma panhandle re gion o f the O g a lla lla a q u ife r. They found th a t fo r risk-averse decisio n makers, schedules th a t include ir rig a tio n during growth stage 4 ( a n tith e s is to ph ysiological m a tu rity) were dominant over the contemporary s tra te g ie s based on calendar dates. METHODS AND PROCEDURES To research soybean and cotton growth and water response fo r Arkansas, two b io-ph ysica l crop growth sim ulation models were modifie d fo r th is experiment. The crop growth models were used to simula te the performance o f a series o f ir rig a tio n strategies fo r both crops. From these sim ulations, several performance variables were monitored i.e. (y ie ld s, net re turn s, number o f applications and to ta l water applied) and p ro b a b ility d is trib u tio n s o f net revenues were 6

14 developed. Expected values fo r the performance varia bles were compared and the p ro b a b ility d is trib u tio n s were analyzed w ith Stochast ic Dominance With Respect to a Function (Meyer, 1977; King and Robison, 1981; Cochran, e t. a l., 1984) to determine ris k e ffic ie n c y. A. Soybean Model Soybean Integrated Crop Management (SICM) was the model adapted fo r the soybean analysis. I t was developed at the U niversity of F lo rid a, G ain esville, Florida by Wilkerson, et a l. (1981). The development o f the model was an in te rd is c ip lin a ry e ffo r t by the a g ric u ltu ra l engineers, agronomists, entomologists and a g ric u ltu ra l economists. The model contains components o f crop, s o il, in se ct, ta c tic s (p esticide and ir rig a tio n applicatio ns) and economics. SICM is designed to study various soybean in se ct pest and ir r ig a t io n management strategies during a season fo r systems consisting o f d iffe re n t weather regimes soybean v a rie tie s, irrig a tio n systems and insect in fe s ta tio n s. The model is w ritte n in FORTRAN, using a modular subroutin e stru ctu re. SICM is broken in to fo u r main sectio ns: 1) p la n t process growth, 2) s o il moisture, 3) irrig a tio n and 4) economic factors o f seasonal soybean growth. A simple flow chart o f the model is presented in Figure 1. Each o f the four main sections o f SICM had to be modified to simulate soybean growth fo r Arkansas. The Florida weather data file s were replaced by the S to n e ville, M ississippi weather data. The Florida s o il is sandy, therefore, the s o il moisture section o f SICM 7

15 FIGURE 1 SI CM - Subroutine Flow Chart 1. MAIN Program 2. In ita liz a tio n of daily variables 3. D aily plant growth 4. End o f the season report 8

16 was changed to represent more closely Arkansas' s ilt y and clayey s o ils. The plant process growth section was modified to represent the Arkansas v a rie tie s o f soybean and th e ir phenological development. The economic c a lc u la tio n s were changed to r e fle c t those used in Arkansas. L a stly, the irrig a tio n component was expanded to include the 37 proposed irrig a tio n stra te g ie s. The F lo rid a weather f ile s contain d a ily measurements fo r temperature, r a in f a l l, pan-evaporation (the maximum leve l o f evapora tio n ), PAR (p hotosynthetically active ra d ia tio n ), times o f sunrise and sunset and to ta l sola r ra diatio n (langleys). They were replaced by 23 years o f d a ily records from S to n e ville, M ississippi fo r the years 1960 to S to n e ville, M ississippi is located across the M ississippi River on Arkansas' southeastern border. This weather data f i l e was selected because o f the large number o f data years a va ila b le and because so la r ra d ia tio n and pan-evaporation was recorded, which had not been done in Arkansas. The S toneville weather file s contain the follow ing e n trie s: d a ily amounts o f ra in fa ll (cm), d a ily pan-evaporation, to ta l d a ily solar ra diatio n (langleys) and the d a ily maximum and minimum a ir temperatures ( C ). A procedure to convert d a ily temperature values to hourly values was developed to allow the model to approximate more closely actual weather conditions. This was done w ith a sine curve using the maximum and minimum values as anchors. The s o il water component has been changed to represent the Crowley s o il conditions in the southern d e lta o f Arkansas. The 9

17 Crowley s o il is composed o f a surface layer o f s i l t loam about 37 centimeters deep over a th ic k layer o f clay. The s o il is subdivided in to seven v e rtic a l zones, each one o f which contains it s own s o il water and ro o t length d e n s ity. The water content o f each zone varied between a lower and upper lim it ; these lim its were changed to more close ly approximate Arkansas s o il conditions. The weighting fa c to r (WR) which determines the new root growth d is trib u tio n s fo r each s o il level was calculated in the subroutine SOILRI to more close ly represent the Crowley s o il. These data were determined from Scott e t a l. (1985). The phenological subroutine PHEN1, where the ten pla nt growth stages are calculated, has been changed to represent the e a rlie r harvest dates, d iffe re n t soybean v a rie tie s and shorter growing season in Arkansas as compared w ith F lo rid a. The production costs fo r th is study were taken from the Arkansas Soybean Budgets. Both v a ria b le and fix e d production costs were in cluded. The variable costs fo r seasonal production and harvest are $93.60 per acre. These costs were converted from per bushel basis to a per acre basis as a s im p lific a tio n to re fle c t the fa c t th a t many o f these a c tiv itie s are performed at the same level regardless o f the y ie ld expectations. The fixed costs, which included machinery and overhead, are $53.40 per acre. Therefore, the to ta l production cost was estimated a t $ per acre in 1984 d o lla rs. Irrig a tio n costs were handled separately from these fig u re s. The cost o f irrig a tio n was m odified to represent a 300 acre center p iv o t system. 10

18 There are several assumptions rele van t to both ir r ig a tio n systems present in the calcu la tions. The well depth fo r both systems is estimated to be 90 fe e t w ith 10 fe e t o f draw down. These numbers represent the average depth and draw down o f 60 wells in Arkansas County. The in te re s t rate is set at 13 percent and the tax rate at one percent o f the to ta l investment. The s tra ig h t lin e method is used to depreciate the machinery over it s estimated l i f e and an in surance ra te o f.6 percent o f the equipment investment is assumed. Irrig a tio n costs were estimated on a variable per acre inch and fixe d per acre basis. operate a center p iv o t. Minimal labor is a ll th a t is required to Based on Arkansas Soybean Budget estim ates, 0.05 hours per acre inch is the amount o f labor used and a wage rate o f $4.50 per hour was assumed. The fixe d ir rig a tio n costs were $47.67 per acre and the va ria b le ir r ig a tio n costs equaled $2.59 per acre inch. The subroutine IRRIG2 is where the decision to ir r ig a te was made and i t was modified to include the 37 proposed irrig a tio n scheduling stra te g ie s. The irrig a tio n strategies used in th is paper were developed by consulting agronomists and the soybean lite ra tu r e. The 37 irrig a tio n strategies include applications by a mixture o f growth stage inform ation, tensiometer readings and the capacity o f e x tra c t- able w ater. Tensiometer stra te g ie s using bar readings were combinations o f d iffe re n t thresholds values and three d iffe re n t reading depths o f 15cm, 30 cm,and 60 cm. To d istin g u ish the o rig in a l Florida version o f the SICM model from the version adapted to Arkansas cond itio n s, we have designated the la t t e r as ASICM. 11

19 B. Soybean Irrig a tio n Strategies Table 1 lis t s the irrig a tio n strategies th a t are to be used in th is paper. The strategies f a ll in to fiv e main categories: (a) non- irrig a te d ; (b) s ta tic, tensiometer stra te g ie s; (c) dynamic tensiometer stra te g ie s; (d) s ta tic capacity o f extractable water stra te g ie s; and (e) dynamic capacity o f extractable water stra te g ie s. To make the irrig a tio n strategy names in th is paper understandable, the follow ing code has been used: 1) A ll S ta tic tensiometer strategies begin with the le tte r ' T' followed by the bar reading ( i. e. -04 fo r -0.4bars) and then the depth in cm o f the s o il where the tensiometer is placed. 2) A ll the dynamic tensiometer strategies begin with ' R', the growth stage, followed by the weeks before R1 when irrig a tio n water is f i r s t applied, la s tly the threshold bar reading fo r ir rig a tio n a fte r R1 is given ( i. e. 05 fo r -0.5 b a rs). 3) For the s ta tic capacity o f extractable water approach the word 'Cap' begins each strategy name followed by the percent o f water in the s o il p ro file which trig g e rs irrig a tio n. 4) The dynamic capacity o f extractable water strategies begin w ith 'Cap' also, followed by the percent o f water which trig g e rs irrig a tio n u n til growth stage R2 and then the percent o f water which trig g e rs. C. Cotton Model A b io -physica l, crop growth model fo r cotton, COTCROP, developed by Brown et a l. was adapted to Arkansas conditions fo r th is portion 12

20 Table 1: Soybean Irrig a tio n Strategy Descriptions Strategy Name Description N on-irrig Tensiometer Strategies T T T T T T T T T T T T T T Non-Irrigated soybeans -0.1 bars placed at 15 cm -0.3 bars placed at 15 cm -0.4 bars placed at 15 cm -0.5 bars placed at 15 cm -0.8 bars placed at 15 cm -1.0 bars placed at 15 cm -4.0 bars placed at 15 cm -0.1 bars placed at 30 cm -0.3 bars placed at 30 cm -0.4 bars placed at 30 cm -0.5 bars placed at 30 cm -0.8 bars placed at 30 cm -1.0 bars placed at 30 cm -4.0 bars placed at 30 cm T bars placed at 60 cm T bars placed at 60 cm T bars placed at 60 cm T bars placed at 60 cm T bars placed at 60 cm T bars placed at 60 cm T bars placed at 60 cm Rl one application at R1 and then -0.5 bars u n til R6 Rl one application one week before R1 and then -0.5 bars u n til R6 Rl one application two weeks before R1 and then -0.5 bars u n til R6 Capacity of Extractable Water Strategies Cap-10 water applied when RATIO =.10 Cap-20 water applied when RATIO =.20 Cap-25 water applied when RATIO =.25 Cap-30 water applied when RATIO =.30 Cap-40 water applied when RATIO =.40 Cap-50 water applied when RATIO =.50 Cap-60 water applied when RATIO =.60 Cap-70 water applied when RATIO =.70 Cap-80 water applied when RATIO =.80 Cap80-70 water applied a t RATIO =.80 u n til R2 and then at RATIO =.70 Cap75-65 water applied at RATIO =.75 u n til R2 and then at RATIO =.65 Cap70-60 water applied at RATIO =.70 u n til R2 and then at RATIO =.60 Ratio = Actual Water Storage/Potential Water Storage 13

21 o f the study. This model is w ritte n in FORTRAN. COTCROP calculates plant growth by sim ulating carbohydrate, nitrogen and water balances fo r the plant. Nitrogen and water balances are approximated fo r the so il root zone, specified by the user. Plant growth is a function not only of the three balances but o f the weather factors of d a ily solar ra dia tion (la n g le ys), d a ily maximum and minimum temperatures ( F ), d a ily pan evaporation (inches) and d a ily ra in fa ll (inches). Daily temperature values were converted to hourly values w ith a sine curve anchored by the maximum and minimum observations. In COTCROP, the state o f the crop is defined by vectors fo r each organ class o f f r u i t, stems and leaves. In each vector there are elements which specify the number, weight and nitrogen content fo r plant organs o f d iffe re n t ages. Leaf areas o f d iffe re n t ages are also maintained. These variables are continuous but time and age are handled in a discrete manner in the model. The in te g ra tio n of the plant processes are managed by d a ily time steps. A s im p lifie d flow chart fo r COTCROP appears in Figure 2. To designate the version of COTCROP which was adapted to southeast Arkansas conditions from the o rig in a l, the label COTCROP-A was selected. Most of the changes involved resetting in it ia liz a t io n values fo r user supplied variables. However, some s tru c tu ra l changes to the program were implemented. COTCROP-A is divided in to several modules. They are WEATHER, SOIL, PLANT, WORM, WEEVIL and SPRAY, which contain the s c ie n tific subroutines th a t implement the sim ulation. Other modules are: MAIN, which contains the main c o n tro llin g program 14

22 FIGURE 2 FLOW CHART OF COTCROP CYCLES ONCE PER DAY Yes INITLZ DRAININ RICHIE RUNOFF TRANS SWDIST INFIL NO BLMDRP LINT ABSC PLTNUM VBRNUM CDEM CARBO * NITDEM ** PLTNUM NDIST PLTWT CARBO LFAREA STRESS * CYCLES UNTIL CARBOHYDRATE IS BALANCED ** CYCLES UNTIL NITROGEN IS BALANCED 15

23 and in it ia liz a t io n subroutines; STRAG, which contains the predefined ir rig a tio n and pest control stra te g ie s; and OUTPUT, which prin ts the output tables. The weather values used in the study sim ulations were actual d a ily records from S to n e ville, across the M ississippi River, from Southeast Arkansas. These records were judged to be representative of southeastern Arkansas, which had only incomplete weather data a v a ilable. Production and harvest cost data fo r th is study have come p r i m arily from the 1984 Arkansas Cotton Budgets published by the Cooperative Extension Service. These budget estimates are reported on a per acre basis and assess cotton production on sandy or s i l t loam s o ils in the South Delta region of Arkansas. The inform ation in the budgets is divided in to pre-harvest and harvest variable costs and pre-harvest and harvest fixe d costs. The variable ir r ig a tio n costs are calculated on a per application and per acre inch basis to allow fo r comparisons between the ir r ig a tio n s tr a t egies. The calculations fo r irrig a tio n costs are taken from a v a rie ty of sources including the U niversity of Minnesota A g ricu ltu ra l Experiment Station th ird DISC re p o rt, the 1984 Arkansas Cotton Budgets and an American Association fo r Vocational Instruction al M aterials (AAVIM) publication. There are several assumptions relevant to both ir r ig a tio n systems present in the ca lcu la tio n s. The well depth fo r both systems is e s timated to be 90 fe e t w ith 10 feet of draw down. These numbers represent 16

24 the average depth and draw down o f 60 wells in Arkansas County. The in te re s t rate is set a t 13 percent and the tax rate at one percent of the to ta l investment. The s tra ig h t lin e method is used to depreciate the machinery over it s estimated l i f e and an insurance rate o f.6 percent o f the equipment investment is assumed. The center p iv o t system represented in th is study is a s e lf-p ro pelled u n it with a diesel engine and turbine drive u n it designed to irrig a te 300 acres. The in it ia l investment costs fo r the system are estimated at $5000 fo r the w e ll, $8714 fo r the power u n it, $8300 fo r the pump and gearhead and $57,000 fo r the d is tr ib u tio n system. There is a minimal amount o f lab or required to operate th is system and based on the Arkansas Cotton Budget estim ates,.05 hours per acre inch is the value used to calculate labor costs. A wage rate of $4.50 per hour is assumed. The furrow irrig a tio n system represented in th is study uses gated pipe and is designed to irrig a te 160 acres. The in it ia l investment costs fo r the system are estimated a t $5000 fo r the w e ll, $5999 fo r the power u n it, $8300 fo r the pump and gearhead and $17,600 fo r the d is trib u tio n system. The variable labor requirement fo r a furrow system is greater than fo r a center pivo t system. The value used to calculate labor fo r th is system is.54 hours per a p p lica tio n. This value f a lls w ith in the range suggested by the AAVIM publication and is taken from the Arkansas Cotton Budget estimates. Additional labor and tra c to r costs are the two elements o f the fix e d cost per a p p lic a tio n 17

25 c a lc u la tio n. These elements re fle c t the costs th a t remain constant regardless o f the number o f a p p lic a tio n s o r the amount applied. In addition to costs and weather parameters, COTCROP-A requires input data in several other areas. Management practices such as planting and harvest dates, plant density, pesticide a p p lica tio n s, irrig a tio n schedules and f e r t iliz e r applications must be sp e cifie d. COTCROP-A id e n tifie s emergence date ra ther than planting date and approximates upland v a rie tie s which mature and are harvested 150 days follo w in g emergence. For th is study, pests were not considered in the sim ulations. The values used fo r the management variables are as follo w s: emergence date-may 5; plant density-40,0000 plants per acre harvest date-october 2; and nitrogen fe r tiliz a tio n -4 0 lb s. preplant, 30 lb s. at f i r s t square and 30 lb s. at f i r s t bloom. D. Timing o f A pplica tions - Cotton Ir r ig a tio n S trategies The irrig a tio n strategies evaluated in th is study were developed with input from several agronomists and represent a wide v a rie ty o f scheduling options. Calendar dates, growth stage inform ation and tensiometer readings were used in d iv id u a lly and in combination to create eight strategies fo r a center pivo t system and ten strategies fo r a furrow system. The strategies based sole ly on calendar dates or tensiometer readings re fle c t some o f the current fie ld practices o f Arkansas cotton producers. The strategies th a t incorporate growth stage inform ation represent a future d ire ctio n fo r ir rig a tio n schedu lin g. These strategies are more easily explained i f viewed in two separate groups. 18

26 The f i r s t group of strategies are referred to as s ta tic because the water application decision rule does not change throughout the growing season. This group includes: 1. one irrig a tio n three weeks a fte r f i r s t bloom 2. tensiometer readings (one threshold level employed throughout the growing season, i. e. each threshold defines a d is tin c t strategy) -.45 atm -.65 atm -.50 atm -.70 atm -.55 atm -.75 atm -.60 atm The recommended practice is to have applications occurring at -.55 atm. The second group of strategies are considered dynamic because the water applications are based on tensiometer readings and growth stage in form ation, thus implying changes in the decision rule as the growing season progresses. This group includes: atm to -.45 atm from f i r s t square to eight weeks past f i r s t bloom atm to -.45 atm from f i r s t square to six weeks past f i r s t bloom, followed by -.46 atm to -.55 atm during the six to eight week period past f i r s t bloom atm to -.45 atm from f i r s t square to three weeks past f i r s t bloom, followed by -.46 atm to -.55 atm during the four to eight week period past f i r s t bloom. The depth of the tensiometer is important in measuring the so il moisture. A tensiometer depth of 12 inches (30 cm) is the common f ie ld practice. E. Amount of Water Applied - Cotton Irrig a tio n Strategies These strategies were simulated fo r a center pivot irrig a tio n system and a furrow ir r ig a tio n system. Gated pipe was used in the 19

27 furrow system. The center p ivo t system applied three quarters o f an inch o f water a t each a p p lic a tio n, w hile the furrow system applied two inches o f water on each a p p lic a tio n. The sim ulation model in cluded an e ffic ie n c y fa c to r fo r each system. The center p ivo t system was assumed to be 90 percent e ffic ie n t and the furrow system was assumed to be 60 percent e ffic ie n t. These e ffic ie n c y values represent the percentage o f applied water th a t is a c tu a lly available fo r plant use. Y ield was also estimated w ith no water applications to demonstrate the increase in y ie ld s possible w ith irrig a tio n (see Table 2 fo r stra te g y names). PRINCIPAL FINDINGS AND THEIR SIGNIFICANCE A. Soybean Results A ll 37 o f the irrig a tio n strategies were simulated w ith the center p ivo t ir rig a tio n system. The Arkansas version o f SICM used 23 years o f weather data from 1960 to The Forrest v a rie ty o f soybean was simulated and ASICM calculated y ie ld s, net revenue and irrig a tio n amounts fo r each o f the 23 years. The amount o f water applied fo r a ll irrig a tio n strategies was one acre inch. The re su lts fo r three o f the fo u r c r ite r ia are presented in Table 3. I t can be seen th a t the strategies which are ranked highest fo r economic e ffic ie n c y are T and Cap The strategies th a t maximized expected y ie ld s are T and T Expected y ie ld s decreased s ig n ific a n tly when evaluating i r r i gation e ffic ie n y (average y ie ld per average inches o f water applied). T re sulted in the sm allest use o f water per acre when using a 20

28 TABLE 2 Strategy Cotton Irrig a tio n Descriptions* Center Pivot CALCP = one irrig a tio n 3 weeks a fte r f i r s t bloom TENSCP45 == -.45 atm from f i r s t square to 8 weeks past f i r s t bloom TENSCP50 = -.50 atm from f i r s t square to 8 weeks past f i r s t bloom TENSCP55 =: -.55 atm from f i r s t square to 8 weeks past f i r s t bloom TENSCP60 =: -.60 atm from f i r s t square to 8 weeks past f i r s t bloom TENSCP65 = -.65 atm from f i r s t square to 8 weeks past f i r s t bloom DYNCP1 DYNCP2 DYMCP3 NOIRR = -.3 atm to -.45 atm from f i r s t square to 8 weeks past f i r s t bloom = -.3 atm to -.45 atm from f i r s t square to 6 weeks past f i r s t bloom, followed by -.46 atm to -.55 atm during the 6 to 8 week period past f i r s t bloom = -.3 atm to -.45 atm from f i r s t square to 3 weeks past f i r s t bloom, followed by -.46 atm to -.55 atm during the 4 to 8 week period past f i r s t bloom = no irrig a tio n Furrow System CALF TENSF45 TENSF50 TENSF55 TENSF60 TENSF65 = one application 3 weeks past f i r s t bloom ;= -.45 atm from f i r s t square to 8 weeks past f i r s t bloom = -.50 atm from f i r s t square to 8 weeks past f i r s t bloom = -.55 atm from f i r s t square to 8 weeks past f i r s t bloom = -.60 atm from f i r s t square to 8 weeks past f i r s t bloom = -.65 atm from f i r s t square to 8 weeks past f i r s t bloom 21

29 TABLE 2 Continued TENSF70 TENSF75 DYNF1 DYNF2 DYNF3 NOIRR = -.70 atm from f i r s t square to 8 weeks past f i r s t bloom** = -.75 atm from f i r s t square to 8 weeks past f i r s t bloom** = -.3 atm to -.45 atm from f i r s t square to 8 weeks past f i r s t bloom = -.3 atm to -.45 atm from f i r s t square to 6 weeks past f i r s t bloom, followed by -.46 atm to -.55 atm during the 6 to 8 week period past f i r s t bloom = -.3 atm to -.45 atm from f i r s t square to 3 weeks past f i r s t bloom, followed by -.46 atm to -.55 atm during the 4 to 8 week period past f i r s t bloom = no irrig a tio n * atm = atmospheres of pressure; 1 atm = bars on a tensiometer **These strategies do not appear in the group of center pivot strategies because prelim inary results demonstrated that the center pivot s tra te gies w ith thresholds higher than -.65 atm were in Stage I I I of the pro duction fu n ctio n, in d ica tin g an irra tio n a l range o f input use. 22

30 Table 3 ASICM Model Output of Soybean Irrig a tio n Strategies Strategy Average Yield Bushels Average Net Returns in Dollars Std. Dev. in Net Returns Average Water Applied in inches Irrig a tio n E fficie ncy bu/in N on-irrig T T T T T T T T T T T T T T T T T T T T T Rl Rl R Cap Cap Cap Cap Cap Cap Cap Cap Cap Cap Cap Cap

31 tensiometer. T had an e ffic ie n t value of bushels per inch of water applied. Strategy T allowed the tensiometer to reach -4.0 bars before any ir r ig a tio n water was applied. T used an average o f 2.2 inches o f ir r ig a tio n water per season, re s u lting in an average y ie ld o f bushels per acre and an average p r o fit of $77.58 per acre. Cap-20 had the lowest y ie ld of 29.3 bushels per acre while having the highest ir r ig a tio n e ffic ie n c y compared with a ll other capacity stra te g ie s. S ta tis tic a l Testing The Duncan M u ltip le Range te s t was calculated fo r the seven preferred strategies lis te d in Table 3 (T-05-30, Rl-02-05, Cap75-65, T-04-15, T-05-15, T-03-30, T-04-30, T-05-30). The te s t indicated that none o f the expected net returns were s ig n ific a n tly d iffe re n t at an a =.05. One explanation fo r th is outcome is that a ll of the seven preferred strategies are basica lly variatio ns of the same irrig a tio n technique, which is ir r ig a tio n applied by the tensiometer placed in the top layer (37 cm ) of s o il when the tensiometer readings are bet- tween -.3 to -.5 bars. Also, the slope of the water retention curve is low in th is region. The Duncan M ultiple Range te s t was also calculated fo r the complete set of 37 ir r ig a tio n strategies (Table 4). Stochastic dominance is not based on expected net revenue calculations but on expected u t i l i t y which re fle c ts the e n tire cumulative d is trib u tio n function. There are nine groups of strategies with s ig n ific a n tly d iffe re n t expected net revenues. The group A, which includes the seven 24

32 Table 4 Duncan M u ltip le Range Test For D ifferences in Mean Net Revenues: Soybean Irrig a tio n Strategies Strategy Name Mean Net Revenue Duncan Grouping1 Doll ars T A T A Cap A T A T A B Cap A B Cap A B Cap A B C T A B C T A B C T A B C Cap A B C T A B C T A B C D T A B C D T A B C D R A B C D R A B C D T A B C D Cap A B C D Rl A B C D T A B C D T A B C D T B C D E T B C D E T C D E T D E Cap E F T G F T G H F Cap G H T H I Cap H I Cap I Cap I Cap I N on-irrig I 1(Means with the same le tte r are not s ig n ific a n tly d iffe re n t; a =.05) 25

33 strategies preferred by a ll decision makers from ris k -p re fe rrin g to strongly risk-averse groups, also includes 16 other irrig a tio n s tr a t egies. The Duncan M u ltip le Range te s t can only give a rough estimate of the significa nce when applying stochastic dominance. Differences in mean y ie ld s are neither necessary nor s u ffic ie n t conditions fo r the differences in expected u t i l i t y. However, to-date there is no procedure to s ta tis tic a lly te s t the significance o f re su lts when using ris k in te rvals w ith stochastic dominance. Another note o f caution must be exercised, Duncan's M u ltip le Range Test assumes th a t normal d is trib u tio n s are being examined. An SAS U nivariate Normal te s t was used to check i f each ir rig a tio n s tr a t egy's yearly net return followed a normal d is trib u tio n a t a =.05. Only seven of the 37 irrig a tio n strategies f i t the normal curve. They were: Cap-80, T-01-15, T-03-15, T-08-15, T-03-30, T and R Only T and T were included in one o f the four e ffic ie n t sets. Y e t, f o r lack o f a better te s t at th is tim e, the Duncan M u ltip le Range te st shows th a t a ll seven o f the e ffic ie n t strategies have no s ta tis tic a l difference in mean net revenue at =.05. Risk Analysis Risk e ffic ie n c y can only be defined fo r specified ranges o f ris k preferences. This study has used four d iffe re n t sets o f preferences, each representing a d iffe re n t class o f decision makers. By comparing the e ffic ie n t sets id e n tifie d fo r each set o f preferences, inferences can be made as to the influ ence th a t r is k preferences can have on the 26

34 re la tiv e rankings o f the stra te g ie s; The preferences and the e f f i cie n t sets derived w ith stochastic dominance w ith respect to a function are displayed in Table 5. The preferences are expressed in in te rvals w ith bounds measured w ith P ratt risk-aversion c o e fficie n ts. The outcome variables were scaled to re fle c t the average soybean component o f farms in southeast Arkansas. This was accomplish e d by m u ltip ly in g the per acre returns by 300. Table 5 Preference Interva ls Used to Define Groups o f Decision Makers Group o f Decision Makers P ratt/a rrow Risk C o e ffic ie n t1 ris k p referring to approaching r is k neutral to.0001 s lig h tly ris k averse.0001 to.0004 stro n g ly r is k averse.0004 to.001 1The in te rvals are defined based upon em pirical work (Cochran, Robison and Lodwick). The e ffic ie n t set id e n tifie d fo r the group o f ris k -p re fe rrin g decision makers contained strategies th a t used a tensiometer placed at 30 cm in the s o il. T and R were the two preferred s tra te g ie s, both have large ranges in net returns (Table 6). S tra te gies T and Rl have s lig h tly lower average net returns than the p r o fit or y ie ld maximizing strategies o f T and T-03-15, re spective ly, although the differences were n o n -sig n ifica n t. 27

35 Table 6 Risk E ffic ie n t Soybean Irrig a tio n Strategies fo r D iffe re n t Groups of Decision Makers Average Minimum Maximum Average Net Net Net Water Returns Returns1 Returns Applied (in ) Risk P referring ( to ) T R Approaching Risk Neutral ( to.0001) Cap T T T T T S lig h tly Risk Averse (.0001 to.0004) T T S trongly Risk Averse (.0004 to.001) T T A ll of the minimum returns occurred in the extremely dry year

36 The group of decision makers defined as approaching ris k neutral had an e ffic ie n t set of six ir r ig a tio n strategies. The group included one dynamic capacity strategy, Cap75-65, two s ta tic strategies where the tensiometer was placed at 15 cm, T and T and three s ta tic stra te g ie s, T-03-30, T and T-05-30, where the tensiometer was placed at 30 cm. Risk-neutral decision makers want the highest return fo r th e ir d o lla rs invested and as the stochastic dominance model predicted, these six strategies produce the highest returns over the 23 years of sim ulation. The s lig h tly risk-averse and strongly risk-averse decision makers preferred the same two stra te g ie s, T and T (Table 5). Strategy T had an average net return o f $210 per acre and a standard deviation of $32.03 per acre. Strategy T had an average net return of $ per acre and a standard deviation of $29.85 per acre. Risk-averse decision makers put more emphasis on the low income years and, hence, are interested in the poorest outcomes or net returns in th is study. For example, strategies T and T each have the highest incomes in 1980 of $ and $153.75, respective ly, over a ll of the other ir r ig a tio n strategies in the group of seven picked by a ll decision makers. This performance in the worst income year re s u lted in these strategies being ris k e ffic ie n t fo r these decision makers. The results of th is analysis went as expected at the beginning of th is study. I t was assumed at the s ta rt of th is paper th a t irrig a tio n water could be used as a risk-reducing in p u t, therefore, decision makers 29

37 would choose to apply more water as they become more ris k averse. This condition was observed by the re su lts. The data in Table 6 summarizes the four groups of decision makers and th e ir re su ltin g e ffic ie n t sets. The ris k -n e u tra l decision makers favored an average of three inches additional ir r ig a tio n water than the ris k -p re fe rrin g decision makers. The risk-averse decision makers favored an average of fiv e additional inches of ir r ig a tio n water per season over the ris k -p re fe rrin g group. The re s u lts, therefo re, give v a lid ity to the hypothesis that ir r ig a tio n is an important risk-reducing input to Arkansas soybean farmers in the short run. Further discussion of the re sults and ASICM may be found in P ricke tt (1985). B. Cotton Results Each of the 12 strategies was simulated with the center pivot and furrow ir rig a tio n systems. The model incorporated 23 years of weather data, from 1960 through Based on the assumptions that farmers are committed to an ir rig a tio n system already in place and there are no differences between systems i f used properly, no comparisons of the strategies were made across the two systems. The analysis begins with the center pivot system. Center Pivot System P ro fit maximization and y ie ld maximization were used in the evaluation of economic e ffic ie n c y. The p r o fit maximizing strategy on the center pivot system came from the dynamic group of strategies that combined growth stage inform ation with tensiometer readings. 30

38 DYNCP2 resulted in an average y ie ld o f pounds o f l i n t per acre w ith average net returns o f $ per acre. The net returns are only above irrig a tio n costs. This strategy called fo r an average o f 5.9 inches o f water to be applied each growing season (Table 7). There is a major improvement in both expected net returns and yie ld s associated w ith the tensiometer stra te g ie s. Net returns are increased on average by about $130 per acre over the non-irrig a te d strategy. CALCP did re s u lt in a higher mean y ie ld, but w ith a cotton price o f 65 per pound, the expected net returns were a ctu a lly lower than the n o n-irrigate d strategy. These re sults support the notion th a t the use o f tensiometers is economical. S ta tis tic a l tests based on Duncan's M u ltip le Range te s t indicate th a t there was not much difference in expected y ie ld s and net returns between any o f the tensiometer s t r a t egies. The y ie ld maximizing strategy fo r the center pivo t system was also DYNCP2. With an average y ie ld of pounds o f l i n t per acre, th is strategy produced approximately 1.9 pounds per acre more than TENSCP50, the next highest strategy, and two to four pounds per acre more than any o f the strategies based sole ly on tensiometer readings (Table 7). In terms o f irrig a tio n e ffic ie n c y (average yield/average inches o f water applied), TENSCP65 resulted in the most e ffic ie n t use of irrig a tio n water fo r the center pivo t system. With an e ffic ie n c y value o f pounds o f l i n t per inch o f water applied, TENSCP65 allowed the tensiometer reading to reach -.65 atm before applying 31

39 Table 7 COTCROP-A Model Results fo r Cotton Irrig a tio n Strategies: Center P ivot System CENTER AVERAGE AVERAGE AVERAGE IRRIGATION PIVOT YIELD NET RETURNS WATER EFFICIENCY STRATEGIES LINT1,2 IN DOLLARS 1,2,3 IN INCHES CALCP (8) b (8) b.8 TENSCP (4) a (5) a (7) TENSCP (2) a (2) a (6) TENSCP (5) a (4) a (3) TENSCP (6) a (6) a (2) TENSCP (7) a (7) a (1) DYNCP1 same as TENSCP45 DYNCP (1) a (1) a (5) DYNCP (3) a (3 ) a (4) NOIRR (9) b (9) b numbers in parenthesis represent rank from high to low 2 Duncan's m u ltip le range te s t was used to determine differences between y ie ld and net returns. Means w ithin groups id e n tifie d by "a" and "b" are not s ta tis tic a lly s ig n ific a n tly d iffe re n t at an a = Net returns are above ir r ig a tio n costs only. 32

40 water. With th is strategy, an average of 5.1 inches o f water was applied re su ltin g in an average y ie ld o f pounds per acre. The p r o fit and y ie ld maximizing strategy, DYNCP2, called fo r an average o f 5.9 inches of water to produce an average y ie ld of pounds per acre but produced only pounds per inch o f ir r ig a tio n water. The calcula tion fo r ir r ig a tio n e ffic ie n c y is the same as that fo r Average Physical Product. TENSCP65, with an average of 5.1 inches of water applied, approximates the beginning of Stage I I of productio n. At th is po in t, Average Physical Product is maximized and is equal to Marginal Physical Product (Table 7). Stochastic dominance with respect to a function was used to evaluate the strategies fo r ris k e ffic ie n c y. R is k -e ffic ie n t strategies were determined fo r four groups of decision makers. A ll outcomes variables were scaled to approximate the average cotton component of farm operations in southeast Arkansas. This was achieved by m u ltiplyin g the per acre returns by 300. For th is study, the preference in te rva ls defining the decision groups are as follow s: ris k preferring to approaching ris k neutral to.0001 s lig h tly ris k averse.0001 to.0004 strongly ris k averse.0004 to.001 The most e ffic ie n t strategy fo r ris k -p re fe rrin g decision makers was TENSCP50, followed by DYNCP2, TENSCP60, TENSCP55 and DYNCP3 (Table 8). DYNCP2, the p r o fit and y ie ld maximizing strategy, was 33

41 Table 8 Risk E ffic ie n c y Rankings f o r Cotton I r r ig a t io n S tra te g ie s : Center P iv o t System RISK PREFERRING ( to ) AVERAGE MINIMUM MAXIMUM NET NET NET RANK RETURNS RETURNS RETURNS TENSCP DYNCP TENSCP TENSCP DYNCP APPROACHING RISK NEUTRAL ( to.0001) SLIGHTLY RISK AVERSE (.0001 to.0004) STRONGLY RISK AVERSE (.0004 to.001) DYNCP TENSCP DYNCP TENSCP TENSPC TENSPC TENSPC TENSCP TENSCP DYNCP DYNCP TENSCP TENSCP TENSCP DYNCP DYNCP

42 determined to be not as ris k e ffic ie n t as TENSCP50 fo r ris k -p re fe rrin g decision makers. This was expected since ris k -p re fe rrin g farmers place more emphasis on the p ro b a b ility o f high net returns than they do on low net returns. The highest net return fo r TENSCP50 was $10 an acre greater than th a t fo r DYNCP2. The group o f decision makers, defined as approaching ris k neut r a l, had six strategies which were ris k e ffic ie n t. DYNCP2, TENSCP50, DYNCP3, TENSCP55, TENSCP60 and TENSCP65 a ll appear in the e ffic ie n t set. The size o f th is e ffic ie n t set re fle c ts the fa c t th a t the performance o f these strategies were very s im ila r due to the retention chara cte ristics o f the s o il. The Duncan M u ltip le Range te st indicated th a t none o f the expected yie ld s or net returns o f the tensiometer strategies were s ta tis tic a lly s ig n ific a n tly d iffe re n t at a = The rankings o f the top strategies fo r the s lig h tly risk-averse and stro n g ly risk-a ve rse groups o f decision makers were id e n tic a l. The preferred strategy was TENSCP65, followed by TENSCP60, TENSCP5, DYNCP3 and DYNCP2. I t appears th a t at the cotton price o f 65 per pound, the higher thresholds maximize u t i l i t y. Due to the in a b ility of stochastic dominance techniques to te s t fo r s ta tis tic a l differences in expected u t i l i t y and strong s im ila ritie s in the p ro b a b ility d is t r i butions, caution must be exercised before the conclusion th a t i r r i g a tio n is not a risk-re d u cin g inp ut is reached. TENSCP50 produced the second highest average net returns and average y ie ld but was less irrig a tio n e ffic ie n t than DYNCP2 with 35

43 the same amount of water applied. This demonstrates the importance of tim ing water applications with growth stage information to insure maximum output fo r each u n it of water applied. The two groups of ris k-a v e rs e decision makers showed no preference between TENSCP50 and DYNCP3 once DYNCP2 was eliminated from the e ffic ie n t set. DYNCP3 called fo r s lig h tly less water applied and resulted in only 1/2 pound of lin t less in average y ie ld and only 21 cents less in average net returns. I t was s lig h tly more irrig a tio n e ffic ie n t producing pounds per inch of water, whereas TENSCP50 produced pounds per inch o f water. I t is reasonable fo r the s tro n g ly ris k-a v e rs e decision makers to be ambiguous between these stra te g ie s since they are very s im ila r in nature. TENSCP50 called fo r a threshold o f -.50 atm throughout the growing season, while DYNCP3 maintained a -.45 atm threshold u n til three weeks past f i r s t bloom, then went to a -.55 atm th re s hold through four to eight weeks past f i r s t bloom. Given that the difference in average water applied between the two strategies is only.10 o f an inch over 23 years, i t is possible th a t the preference in te rv a ls are not se n sitive enough to pick up such a n e g lig ib le difference. Furrow System The p r o fit maximizing strategy fo r the furrow irrig a tio n system came from the group of stra tegie s based sole ly on tensiometer readings. TENSF70 allowed the tensiometer reading to reach -.70 atm before adding w ater. This resulted in an average y ie ld o f pounds 36

44 per acre and average net returns o f $ per acre. This strategy ca lle d fo r an average o f 7.8 inches o f water to be applied each growing season (Table 9). A s im ila r pattern as found w ith the center pivo t results surfaced in the analysis o f the furrow system. The Duncan M u ltip le Range te st fa ile d to uncover any s ig n ific a n t differences between the expected yie ld s and net returns fo r any o f the tensiometer stra te g ie s. However, there was a s ig n ific a n t difference between the average net returns fo r th a t group and the n o n-irrigate d and calendar stra te g ie s. Expected net returns were increased by more than $80 per acre by the use o f tensiometers. In th is case, the calendar strategy had both a higher expected net return and y ie ld than the n o n-irrigate d strategy. The s im ila ritie s in the re su lts fo r the tensiometer strategies can lik e ly be a ttrib u ta b le to the moisture retention ch a ra cte ristics o f the s o il examined. The y ie ld maximizing strategy fo r the furrow system also came from the group o f strategies based on tensiometer readings. TENSF60 allowed the tensiometer reading to reach -.60 atm before applying water and th is resulted in the maximum average y ie ld o f pounds per acre. TENSF60 produced approximately 3.1 pounds per acre more than the p r o fit maximizing strategy and applied an average o f 1.1 inches o f water more per season than the p r o f it maximizing stra te g y (Table 9). In terms o f irrig a tio n e ffic ie n c y, TENSF70, the p r o fit maximizing strategy, resulted in the most e ffic ie n t use o f irrig a tio n water on the furrow system. With an average y ie ld o f pounds per acre and 37

45 Table 9 COTCROP-A Model Results fo r Cotton Ir r ig a tio n S trategie s: Furrow System FURROW SYSTEM STRATEGIES AVERAGE YIELD # LINT1 2 AVERAGE NET RETURNS IN DOLLARS1 2 3 AVERAGE WATER IN INCHES IRRIGATION EFFICIENCY CALF (10) b (10) b TENSF (9) a (9) a TENSF (5) a (6) a TENSF (4) a (4) a TENSF (1) a (3) a TENSF (2) a (2) a TENSF (3) a (1) a TENSF (7) a (4) a DYNF1 same as TENSF45 DYNF (8) a (8) a DYNF (6) a (7) a NOIRR (11) b (11) b Numbers in parenthesis represent rank from high to low. 2 Duncan's m u ltip le range te s t was used to determine differences between y ie ld and net returns. Means w ithin groups id e n tifie d by "a" and "b" are not s ta tis tic a lly s ig n ific a n tly d iffe re n t at a = Net returns are above ir r ig a tio n costs only. 38

46 an average of 7.8 inches of water applied per year, TENSF70 produced an average of pounds per inch of water over the 23 years of weather data. Although TENSF60, the y ie ld maximizing strategy, applied more water, i t only produced pounds per inch of water. This demonstrates the economic p rin c ip le of diminishing marginal returns. At the point where 7.8 inches of water was applied, the farmer realized maximum output per u n it of variable input. A fte r th a t point, although to ta l y ie ld continued to increase, the returns to each additional u n it o f water decreased (Table 9). At the maximum y ie ld of pounds per acre, 8.9 inches o f water represents the maximum amount of water th a t can be applied without decreasing y ie ld. The results from the other strategies bears th is out. TENSF55 applied an average of 9.4 inches o f water fo r an average y ie ld of pounds per acre. TENSF45 applied 10.2 inches and produced an average y ie ld of pounds per acre. Risk e ffic ie n t strategies were determined fo r the four groups of decision makers (Table 10). Once again, d iffe re n t rankings of s tra tegies were produced fo r the d iffe re n t decision makers. The ris k - preferring group ranked DYNF2 as the strategy which maximized u t i l i t y. The s lig h tly risk-averse and strongly risk-averse groups preferred TENSF75. Of the e ntire set of tensiometer strategies, only TENSF45 could be rejected as in e ffic ie n t fo r the risk-n e u tra l group. The in f e r io r it y of the calendar and non-irrigated strategies is once again apparent. I t is surprising, though, to note that as ris k aversion was increased, strategies which apply less water were preferred. 39

47 Table 10 Risk E fficie n cy Rankings fo r Cotton Irrig a tio n S trategies: Furrow System RISK PREFERRING ( to ) RANK AVERAGE NET RETURNS MINIMUM NET RETURNS MAXIMUM NET RETURNS DYNF TENSF DYNF TENSF TENSF TENSF APPROACHING RISK NEUTRAL ( to.0001) DYNF DYNF TENSF TENSF TENSF TENSF TENSF TENSF SLIGHTLY RISK AVERSE (.0001 to.0004) TENSF TENSF TENSF TENSF TENSF STRONGLY RISK AVERSE (.0004 to.001) TENSF TENSF TENSF TENSF TENSF

48 The ris k -p re fe rrin g group that chose DYNF2 to TENSF75 applied an average o f 10.0 inches o f water fo r an average y ie ld o f pounds per acre. Those decision makers who preferred TENSF75 chose to apply an average o f 7.8 inches o f water to produce pounds per acre. The net returns fo r these two strategies d iffe re d by $8.50 per acre. The risk-averse group o f decision makers chose the higher threshold strategy, TENSF75, and applied less water. This was not expected since irrig a tio n water is usually considered to be a ris k - reducing input. The lower threshold strategy, TENSF55, should have resulted in a lower p ro b a b ility o f low incomes, but due to the weather conditions in the low y ie ld years, the low threshold stra teg y re sulted in a higher p ro b a b ility o f low incomes. Since risk-averse decision makers are more concerned with low y ie ld years, they chose the higher threshold strategy to decrease the p ro b a b ility o f low in comes. Price U ncertainty The introduction o f price uncertainty in to the decision problem can influence the stra te g ie s preferred by each group o f decision makers. Boggess et a l. (1983) demonstrated th is by introducing soybean price v a r ia b ility to a risk-averse group o f decision makers in a Florida study. They found th a t under price uncertainty, risk-averse farmers chose to irrig a te less frequently and w ith larg er amounts of water than th a t ca lle d fo r by the maximum net returns stra teg y (Boggess et a l., 1983). For th is study, price uncerta inty was introduced through the use 41

49 of h is to ric a l prices. Each of the 23 yie ld s per strategy was m u ltiplied by the real price of cotton fo r that year. untrended and were converted to constant d o lla rs. These prices were The Index of Prices Received By Farmers in 1982 was used to deflate the price series. The average real price received by farmers in 1982 dolla rs was 58 cents per pound. This is su b sta n tia lly lower than the 65 cents per pound price used to calculate net returns fo r th is study. changed the net return rankings fo r the strategies. The lower price This deflated price does not include deficiency payments. Once again, the strategies were analyzed re la tiv e to the two ir r ig a tio n systems. There were no comparisons made between the systems. Center Pivot System With the in trodu ction of price uncertainty, the e ffic ie n t set changed fo r each group of decision makers. TENSCP45, with average net returns of $ per acre, was the e ffic ie n t strategy fo r a ll four decision groups. TENSCP45 was the p r o fit maximizing strategy, and as such, i t was not expected to be the e ffic ie n t strategy fo r the ris k - averse decision makers. Under conditions of price uncertainty, most risk-averse decision makers move away from the p r o fit maximizing s tr a t egy in an attempt to decrease the p ro b a b ility of low net returns (Table 11) Furrow System The results fo r the furrow system conformed more closely to expectations. The decision groups ranging from ris k preferring to s lig h tly ris k averse found the p r o fit maximizing strategy to be the only strategy in each of th e ir respective e ffic ie n t sets. TENSF60, with average net returns of $469.39, was the r is k - e ffic ie n t strategy 42

50 Table 11 COTCROP-A Model Results fo r Selected Cotton Irrig a tio n S trategies Linder U ncertainty1 CENTER PIVOT STRATEGIES AVERAGE YIELD AVERAGE NET RETURNS TENSCP45 TENSCP50 TENSCP55 TENSCP60 DYNCP2 DYNCP (1) (3) (5) (6) (2) (4) FURROW SYSTEM STRATEGIES AVERAGE YIELD AVERAGE NET RETURNS TENSF60 TENSF65 TENSF (1) (3) (2) 1 Price uncertainty was only introduced to the strategies whose net returns were w ith in a three d o lla r range of each other. 43

51 fo r the ris k -p re fe rrin g, approaching risk-n e u tra l and s lig h tly ris k - averse decision groups (Table 11). The strongly risk-averse decision group found TENSF70 to be the r is k - e ffic ie n t strategy under price uncertainty. This ir r ig a tio n schedule produced an average net y ie ld of 809 pounds per acre, with average net returns of $ per acre. Model Errors and the Estimation of the P ro b a b ility D istrib u tio n s U t ilit y functions are estimated with one va ria b le, income, and are assumed to be represented by an in te rva l rather than a precise measurement. Each of the ir rig a tio n strategies produced a p ro b a b ility d is trib u tio n of net returns. Unlike the u t i l i t y functions used in the stochastic dominance analysis, i t is assumed that the p ro b a b ility d is trib u tio n s are measured accurately. With u t i l i t y functions, the re la tiv e sizes of the preference in te rva ls allow two types of errors to occur. A Type I erro r results when a preferred action choice is omitted from the e ffic ie n t set. A Type I I erro r results when a non-preferred action choice is included in the e ffic ie n t set. The p ro b a b ility of incurring a Type I erro r can be reduced by increasing the p ro b a b ility of a Type I I e rro r, and vice versa, by adjusting the size of the preference in te rv a l. Since the p ro b a b ility d is trib u tio n s are assumed to be accurate, i. e. they are not represented by in te rv a ls, the opportunity to adjust a p a rtic u la r type of erro r does not e x is t. With these d is trib u tio n s, Type I errors are the concern and they occur through measurement e r rors in the model. In the process of adapting COTCROP to re fle c t Arkansas growing 44

52 conditions, several problems were discovered. The s o il component and the irrig a tio n component o f the model presented the greatest d iffic u ltie s. The water stress table in the s o il component adjusts plant growth to re fle c t the s o il moisture status (Table 12). The relationships presented in the o rig in a l documentation stated th a t when the tensiometer reading was at 0.0 atm, 100 percent o f p la n t growth was re a liz e d. This obviously is not corre ct. With a tensiometer reading o f 0.0 atm, the s o il is completely saturated, the plant receives no oxygen and growth is in h ib ite d. Some crude ca lib ra tio n s were made in an attempt to correct the s o il m oisture/plant growth relationships represented in Table 12. These c a lib ra tio n s may be one source o f measurement e rro r. This model also assumes a uniform s o il p r o file which is not re presentative o f many Arkansas s o ils. The nonuniform s o il p ro file s c h a ra te ris tic o f th is study area were unable to be incorporated in to the model, therefore, the plant growth measurements may be inaccurate. These measurement e rro rs may have affected y ie ld estim ates. Another problem observed in the s o il water balance portion o f the model had to do w ith the drainage o f the s o il. In some cases, rather than being drained from the s o il p r o file, water was a ctu a lly pulled up from the water ta b le. Although th is weeping s o il is observed in some parts o f Arkansas, the model was not designed to capture th is a c tiv ity. The program should have kept water constant a t the end o f each day, or allowed i t to decrease. On the days when no ra in fa ll occurred, water was drawn from the water ta b le. This weeping s o il 45

53 O rig in a l Documentation (COTCROP) Table 12 Cotton Water Stress Tables Tensiometer Reading Percentage of P ote ntial Growth 0.0 atm atm atm atm atm atm 5 Revised Table (COTCROP-A) Tensiometer Reading Percentage of P otential Growth 0.0 atm atm atm atm atm atm 0 46

54 a c tiv ity may be reflected in the y ie ld estimates. Other observations stemming from the weeping so il problem were evident when s e n s itiv ity analysis was conducted in an attempt to validate the model. In a day-by-day comparison of one irrig a tio n strategy to the no ir rig a tio n strategy, results showed th a t three days a fte r the irrig a tio n a p p lica tio n, more water was present in the so il p ro file of the dryland production run than in the irrig a te d run, even a fte r no ra in fa ll was recorded. This same problem may be reflected in another in te re stin g phenomenon observed among the strategies. In certain years, the non- irrig a te d yie lds exceeded the irrig a te d yie ld s. This occurs most regula r ly in 1961, 1969, 1976, 1979 and 1982 (see Tables 13 and 14). For some of the irrig a tio n stra te g ie s, in the years 1961 and 1979, the non -irrig ate d yie ld s t ie the estimated yie lds o f the irrig a te d s tra tegies. According to the weather data, 1961 and 1979 were very wet years with good su n lig h t. Both 1969 and 1976 were f a ir ly wet years with moderate sunlight and 1982 was an extremely dry year with moderate sunlight (Table 15). There does not appear to be a sp e cific type of weather year that causes non -irrig ate d yie ld s to exceed irrig a te d y ie ld s. These problems re q uire that the results be interpreted with caution. I t is unclear how sensitive the rankings o f the strategies by e ith e r c r ite r ia ( p r o fit maximization or ris k e fficie n cy) w ill be to the model errors. Additional work is now underway to correct COTCROP-A. Further discussion of the results and model may be found in Harp (1985). 47

55 Table 13 Years N on-lrrigated Cotton Yields Exceeded Irrig a te d Strategy Yields: Center P ivot System TENSCP45 TENSCP50 TENSCP55 TENSCP60 TENSCP65 DYNCP2 DYNCP3 CALCP * 1961* * * *yie lds fo r n o n -irrig a te d sim ulations were equal to y ie ld s fo r the spe c ifie d irrig a tio n strategy Table 14 Years N on-lrrigated Cotton Yields Exceeded Irrig a te d Strategy Yields: Furrow System TENSF 45 TENSF50 TENSF55 TENSF60 TENSF65 TENSF70 TENSF75 DYNF2 DYNF3 CALF * 1961* 1961* 1961* 1961* * *yie lds fo r non-irrig a te d sim ulations were equal to yie ld s fo r the spec ifie d irrig a tio n strategy 48

56 Table 15 Seasonal Summaries of Solar Radiation and P re cip ita tio n from the S to n e ville Weather F ile Year Solar R adiation1 P re c ip ita tio n Solar Radiation reported in Langleys fo r the length of the growing season. 2 P re cip ita tio n reported in to ta ls inches fo r the growing season. Growing season extended from May 5 through October 2. 49

57 CONCLUSION The re sults from the two b io -p h ysica l, crop growth models, ASICM and COTCROP-A, demonstrate the s u p e rio rity o f current scheduling stra te g ie s which employ s o il moisture m onitoring. In both crops, s ig n ific a n t differences in expected y ie ld s and net return were observed between these strategies and the non-irrig a te d stra te g ie s. In no case were the calendar or non-irrig a te d strategies ever ris k e ffic ie n t. The s o il monitoring strategies produced higher expected y ie ld s, achieved greater average net returns and were r is k e f f ic ie n t. However, diffe re n ce s between the s o il moisture m onitoring s tra tegies were d if f ic u lt to detect. Soil water re tentio n c h a ra cte ristics o f the Crowley Soil can probably explain th is re s u lt. In the soybean analysis, only strategies w ith e ith e r very high or very low thresholds could be e a sily distinguished. Examples would include: (1) tensiometer thresholds o f -.80 bars or -4.0 bars and (2) capacity thresholds o f 50 percent o f extractable water. In the cotton analysis, no tensiometer strategies had mean net returns th a t d iffe re d from any other. The ranking o f the strategies by ris k e ffic ie n c y varied by degree o f ris k aversion. As ris k aversion increased soybean strategies moni- ito rin g the only top 15 cm o f the s o il p ro file became preferred. Tensiometer thresholds in the range o f -.40 and -.50 bars seem to be most commonly preferred values. On the cotton side, d iffe re n t re sults were observed fo r the two irrig a tio n systems. For the center pivo t system, the more risk-a verse decision makers would have a preference 50

58 fo r the tensiometer strategy using a threshold o f -.65 bars. The ris k -p re fe rrin g group would select the threshold o f -.50 bars. For the furrow system, due p rim a rily to the la rg e r ap plicatio ns, s lig h tly d iffe re n t re sults were produced but the same general pattern prevailed. The more risk-a verse groups preferred the tensiometer stra teg y employing a threshold o f -.75 bars. For the ris k - p re fe rrin g group, the dynamic strategy, DYNF2 (-.45 bars from f i r s t square to six weeks past f i r s t bloom followed by -.55 bars during the eight weeks a fte r f i r s t bloom) maximized expected u t i l i t y. In both models, enhancements to th e ir sim ulative c a p a b ilitie s can be made and work is underway to achieve such improvements. Additional c a lib ra tio n to Arkansas growing conditions w ill be necessary before the models can successfully make the tra n s itio n from research to management uses. 51

59 LITERATURE CITED American Association For Vocational In stru ctio n a l M aterials, (in cooperation w ith the Soil Conservation Service, USDA) Planning fo r an ir r ig a tio n system. Engineering Center, Athens, GA Arkansas Soybean Association Soybean ir r ig a tio n -- m ulti state Bajwa, B ia jin d a r S., Crosswhite, W illiam M. and Gadsby, Dwight M Consumptive use of water and supplemental ir r ig a tio n needs fo r selected crops and locations in the southeastern United States. Boggess, W.G., Lynne, G.D., Jones, J.W. and Swaney, D.P Riskreturn assessment of ir r ig a tio n decisions in humid regions. Southern Journal of A g ric u ltu ra l Economics, V o l. 15 (1 ), pp Brown, L.G., Jones, J.W., Hesketh, J.D., Hartsog, J.D., W hisler, F.D. and H a rris, F.A COTCROP: Computer sim ulation of cotton growth and y ie ld. User's Manual. Cochran, Mark, Lodwich, Weldon and Raskin, Rob The implementa tio n of convex set stochastic dominance fo r applied ris k analysis Risk analysis fo r a g ric u ltu ra l production firm s: concepts, in formation requirements and policy issues. AE-4575 Department of A g ric u ltu ra l Economics. Univ, of I llin o is at Urbana-Champaign, A g ric u ltu ra l Experiment S tation. G ille y, James R., M artin, Derrel L. and S p lin te r, W illiam E A pplication o f a sim ulation model o f corn growth to ir r ig a tio n management decisions. Operations research in a g ric u ltu re and water resources. D. Yaron and C. Tapiero (E ditors) North Holland Publishing Company, Ifo rs. Hammond, L.C., Campbell, R.B. and T h re a d g ill, E.D Irrig a tio n management strategies fo r humid regions. Irrig a tio n scheduling fo r water and energy conservation in the 8 0 's. Proceedings of the American Society of A g ric u ltu ra l Engineers Irrig a tio n Scheduling Conference, pp Hansford, Robert et a l Irrig a tio n scheduling models: an economic analysis. Journal o f Farm Managers and Rural Appraisers. 48: Harp, Caren Risk e ffic ie n t cotton ir r ig a tio n strategies fo r Arkansas. Unpublished Master's th e sis. Department o f A g ric u l tu ra l Economics and Rural Sociology. U niversity of Arkansas. 52