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ECONOMIC APPROACH ON ALLOCATION OF IRRIGATION WATER UNDER SALINITY BASED ON DIFFERENT SOILS FOR POTENTIAL IRRIGATED AGRICULTURE USING EPIC CROP MODEL By JONGSAN CHOI Bachelor of Science in Agricultural Economics Kangwon National University Chuncheon, South Korea 2000 Master of Science in Agricultural Economics Kangwon National University Chuncheon, South Korea 2002 Submitted to the Faculty of the Graduate College of the Oklahoma State University In partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 2011 ii ECONOMIC APPROACH ON ALLOCATION OF IRRIGATION WATER UNDER SALINITY BASED ON DIFFERENT SOILS FOR POTENTIAL IRRIGATED AGRICULTURE USING THE EPIC CROP MODEL Dissertation Approved: Dr. Arthur Stoecker Dissertation Adviser Dr. Francis Epplin Dr. Jeffrey Vitale Dr. Dan Storm Outside Committee Member Dr. Sheryl A. Tucker Dean of the Graduate College iii TABLE OF CONTENTS Chapter Page I. INTRODUCTION ......................................................................................................1 Problem Statement ...................................................................................................1 Objectives ................................................................................................................4 II. REVIEW OF LITERATURE....................................................................................5 Crop Simulation with Salinity .................................................................................5 Experiment with Salinity .........................................................................................6 III. METHODOLOGY ................................................................................................10 Conceptual Framework ..........................................................................................10 Data and Procedure ................................................................................................12 GIS Analysis ....................................................................................................14 EPIC Simulation ..............................................................................................17 Weather Data Generation .........................................................................17 Soil Data...................................................................................................21 Crop Management Data ...........................................................................24 Model Evaluation ...................................................................................................25 Simulation Design and Process ..............................................................................34 Dynamic Optimization ...........................................................................................38 IV. RESULTS OF SIMULATION, REGRESSION AND OPTIMIZATION BY SOIL TYPE .....................................................................44 Tipton Loam Soil, 01% Slope .............................................................................53 EPIC Output Data ...........................................................................................53 Econometric Estimation ..................................................................................56 Dynamic Optimization ....................................................................................67 Madge Fine Sandy Loam and Madge Loam Soil, 23% Slope.............................73 EPIC Output Data ...........................................................................................73 iv Econometric Estimation ..................................................................................76 Dynamic Optimization ....................................................................................86 Roark Loam Soil, 01% Slope ...............................................................................92 EPIC Output Data ...........................................................................................92 Econometric Estimation ..................................................................................95 Dynamic Optimization ..................................................................................105 Spur Loam Soil, 01% Slope, occasionally flooded ...........................................111 EPIC Output Data .........................................................................................111 Econometric Estimation ................................................................................114 Dynamic Optimization ..................................................................................124 Spur Clay Loam Soil, 01% Slope, occasionally and rarely flooded...................130 EPIC Output Data .........................................................................................130 Econometric Estimation ................................................................................133 Dynamic Optimization ..................................................................................143 Tillman Clay Loam Soil, 13% Slope ..................................................................149 EPIC Output Data .........................................................................................149 Econometric Estimation ................................................................................152 Dynamic Optimization ..................................................................................162 Frankirk Loam Soil, 13% Slope .........................................................................168 EPIC Output Data .........................................................................................168 Econometric Estimation ................................................................................171 Dynamic Optimization ..................................................................................181 Hardeman Fine Sandy Loam Soil, 01% Slop .....................................................187 EPIC Output Data .........................................................................................187 Econometric Estimation ................................................................................190 Dynamic Optimization ..................................................................................200 Lawton Loam Soil, 01% Slope ...........................................................................206 EPIC Output Data .........................................................................................206 Econometric Estimation ................................................................................209 Dynamic Optimization ..................................................................................219 Westill Clay Loam Soil, 13% Slope .................................................................. 225 EPIC Output Data .........................................................................................225 Econometric Estimation ................................................................................228 Dynamic Optimization ..................................................................................238 Abilene Loam Soil, 01% Slope ..........................................................................244 EPIC Output Data .........................................................................................244 Econometric Estimation ................................................................................247 Dynamic Optimization ..................................................................................257 v Burford Loam Soil, 13% Slope ..........................................................................263 EPIC Output Data .........................................................................................263 Econometric Estimation ................................................................................266 Dynamic Optimization ..................................................................................276 Carey Silt Loam Soil, 13% Slope .......................................................................282 EPIC Output Data .........................................................................................282 Econometric Estimation ................................................................................285 Dynamic Optimization ..................................................................................295 Grandfield Fine Sandy Loam Soil, 13% Slope...................................................301 EPIC Output Data .........................................................................................301 Econometric Estimation ................................................................................304 Dynamic Optimization ..................................................................................314 Tipton Fine Sandy Loam Soil, 01% Slope .........................................................320 EPIC Output Data .........................................................................................320 Econometric Estimation ................................................................................323 Dynamic Optimization ..................................................................................333 V. CONCLUSION AND APPLICATIONS .............................................................339 REFERENCES ..........................................................................................................346 APPENDICES ...........................................................................................................350vi LIST OF TABLES Table Page Table 1. Monthly Statistical Properties of the Daily Historical Weather Data at Altus Station, OK from years 1950 to 2006...............................................20 Table 2. Tipton Soil Input Data for EPIC Model.........................................................21 Table 3. Tested and Collected Irrigable Soil Samples .................................................23 Table 4. Summary of Crop Operation Data in EPIC Model ........................................24 Table 5. Parameters related to Cotton Yield in EPIC Model .......................................25 Table 6. Holister Silty Clay Loam Soil Properties used in EPIC calibration for Jackson County Cotton Yield ..................................................................27 Table 7. Results of Paired ttest for the mean of Observed and Simulated of Irrigated Cotton Yields in Jackson County ..............................29 Table 8. Results of EPIC Model Calibration for Irrigation Cotton Yield in Jackson County for the Period from 2000 to 2006 .....................................................30 Table 9. Results of Paired ttest for the mean of Observed and Simulated of Dryland Cotton Yields in Jackson County ........................32 Table 10. Results of EPIC Model Validation for Dryland Cotton Yield in Jackson County for the Period from 2000 to 2006 .....................................................33 Table 11. EPIC Output File Variable Definition and Unit Conversion .......................37 Table 11. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Tipton Loam Soil ..................................................................................53 Table 12. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Tipton Loam Soil ................................................................54 Table 13. Result of Likelihood Ratio Test for the Tipton Loam Soil. .......................56 vii Table Page Table 14. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Tipton Loam Soil ............................................................57 Table 15. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Tipton Loam Soil ........................64 Table 16. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Tipton Loam Soil ............................................................................65 Table 17. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Tipton Loam Soil .............................................................................66 Table 18. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Tipton Loam Soil ............................................................................72 Table 21. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Madge Fine Sandy Loam and Madge Loam Soil ................................73 Table 22. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Madge Fine Sandy Loam and Madge Loam Soil ...............74 Table 23. Result of Likelihood Ratio Test for the Madge Fine Sandy Loam and Madge Loam Soil. ................................................................................76 Table 24. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Madge Fine Sandy Loam and Madge Loam Soil............77 Table 25. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Madge Fine Sandy Loam and Madge Loam Soil ...........................84 Table 26. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Madge Fine Sandy Loam and Madge Loam Soil ...........................85 Table 27. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Madge Fine Sandy Loam and Madge Loam Soil ............................85 Table 28. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Madge Fine Sandy Loam and Madge Loam Soil ...........................91 viii Table Page Table 31. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Roark Loam Soil ..................................................................................92 Table 32. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Roark Loam Soil .................................................................93 Table 33. Result of Likelihood Ratio Test for the Roark Loam Soil .........................95 Table 34. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Roark Loam Soil .............................................................96 Table 35. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Roark Loam Soil .......................103 Table 36. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Roark Loam Soil ..........................................................................104 Table 37. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Roark Loam Soil ...........................................................................104 Table 38. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Roark Loam Soil ...........................................................................110 Table 41. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Spur Loam Soil ..................................................................................111 Table 42. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Spur Loam Soil .................................................................112 Table 43. Result of Likelihood Ratio Test for the Spur Loam Soil ..........................114 Table 44. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Spur Loam Soil .............................................................115 Table 45. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Spur Loam Soil ..........................122 Table 46. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Spur Loam Soil .............................................................................123 ix Table Page Table 47. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Spur Loam Soil ..............................................................................123 Table 48. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Spur Loam Soil .............................................................................129 Table 51. Initial EPIC Soil Salinity Input Data based on Soil Samples of Spur Clay Loam Soil ................................................................................130 Table 52. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Spur Clay Loam Soil .........................................................131 Table 53. Result of Likelihood Ratio Test for the Spur Clay Loam Soil .................133 Table 54. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Spur Clay Loam Soil .....................................................134 Table 55. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Spur Clay Loam Soil ................141 Table 56. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Spur Clay Loam Soil .....................................................................142 Table 57. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Spur Clay Loam Soil ....................................................................142 Table 58. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Spur Clay Loam Soil .....................................................................148 Table 61. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Tillman Clay Loam Soil .....................................................................149 Table 62. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Tillman Clay Loam Soil ....................................................150 Table 63. Result of Likelihood Ratio Test for the Tillman Clay Loam Soil ............152 Table 64. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Tillman Clay Loam Soil......................153 x Table Page Table 65. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Tillman Clay Loam Soil ...........160 Table 66. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Tillman Clay Loam Soil ..............................................................161 Table 67. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Tillman Clay Loam Soil ................................................................161 Table 68. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Tillman Clay Loam Soil ...............................................................167 Table 71. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Frankirk Loam Soil ............................................................................168 Table 72. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Frankirk Loam Soil ...........................................................169 Table 73. Result of Likelihood Ratio Test for the Frankirk Loam Soil ...................171 Table 74. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Frankirk Loam Soil .......................................................172 Table 75. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Frankirk Loam Soil ..................179 Table 76. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Frankirk Loam Soil ......................................................................180 Table 77. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Frankirk Loam Soil ......................................................................180 Table 78. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Frankirk Loam Soil ........................................................................186 Table 81. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Hardeman Fine Sandy Loam Soil ......................................................187 xi Table Page Table 82. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Hardeman Fine Sandy Loam Soil .....................................188 Table 83. Result of Likelihood Ratio Test for the Hardeman Fine Sandy Loam Soil ................................................190 Table 84. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Hardeman Fine Sandy Loam Soil .................................191 Table 85. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Hardeman Fine Sandy Loam Soil ................................................198 Table 86. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Hardeman Fine Sandy Loam Soil .................................................199 Table 87. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Hardeman Fine Sandy Loam Soil .................................................199 Table 88. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer .............205 Table 91. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Lawton Loam Soil ..............................................................................206 Table 92. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Lawton Loam Soil .............................................................207 Table 93. Result of Likelihood Ratio Test for the Lawton Loam Soil .....................209 Table 94. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Lawton Loam Soil .........................................................210 Table 95. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Lawton Loam Soil ....................217 Table 96. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Lawton Loam Soil ........................................................................218 Table 97. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Lawton Loam Soil .........................................................................218 xii Table Page Table 98. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Lawton Loam Soil ........................................................................224 Table 101. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Westill Clay Loam Soil .....................................................................225 Table 102. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Westill Clay Loam Soil ....................................................226 Table 103. Result of Likelihood Ratio Test for the Westill Clay Loam Soil ...........228 Table 10 4. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Westill Clay Loam Soil ...............................................229 Table 105. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Westill Clay Loam Soil ...........236 Table 106. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Westill Clay Loam Soil ..............................................................237 Table 107. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Westill Clay Loam Soil ...............................................................237 Table 108. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Westill Clay Loam Soil ...............................................................243 Table 111. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Abilene Loam Soil ...........................................................................244 Table 112. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Abilene Loam Soil ..........................................................245 Table 113. Result of Likelihood Ratio Test for the Abilene Loam Soil ..................247 Table 114. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Abilene Loam Soil ......................................................248 Table 115. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Abilene Loam Soil..................255 xiii Table Page Table 116. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Abilene Loam Soil......................................................................256 Table 117. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Abilene Loam Soil......................................................................256 Table 118. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Abilene Loam Soil.......................................................................262 Table 121. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Burford Loam Soil ...........................................................................263 Table 122. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Burford Loam Soil ..........................................................264 Table 123. Result of Likelihood Ratio Test for the Burford Loam Soil ..................266 Table 124. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Burford Loam Soil ......................................................267 Table 125. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Burford Loam Soil ...................274 Table 126. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Burford Loam Soil......................................................................275 Table 127. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Burford Loam Soil......................................................................275 Table 128. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Burford Loam Soil.......................................................................281 Table 131. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Carey Silt Loam Soil ........................................................................282 Table 132. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Carey Silt Loam Soil .............................................................283 xiv Table Page Table 133. Result of Likelihood Ratio Test for the Carey Silt Loam Soil ...............285 Table 134. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Carey Silt Loam Soil ...................................................286 Table 135. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Carey Silt Loam Soil ..............293 Table 136. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Carey Silt Loam Soil ..................................................................294 Table 137. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Carey Silt Loam Soil ...................................................................294 Table 138. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Carey Silt Loam Soil ...................................................................300 Table 141. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Grandfield Fine Sandy Loam Soil ....................................................301 Table 142. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Grandfield Fine Sandy Loam Soil ..................................302 Table 143. Result of Likelihood Ratio Test for the Grandfield Fine Sandy Loam Soil .............................................304 Table 144. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Grandfield Fine Sandy Loam Soil ...............................305 Table 145. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Grandfield Fine Sandy Loam Soil ..............................................312 Table 146. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Grandfield Fine Sandy Loam Soil ..............................................313 Table 147. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Grandfield Fine Sandy Loam Soil ..............................................313 xv Table Page Table 148. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Grandfield Fine Sandy Loam Soil ...............................................319 Table 151. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Tipton Fine Sandy Loam Soil ...........................................................320 Table 152. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Tipton Fine Sandy Loam Soil .........................................321 Table 153. Result of Likelihood Ratio Test for the Tipton Fine Sandy Loam Soil ....................................................323 Table 154. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Tipton Fine Sandy Loam Soil .....................................324 Table 155. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Tipton Fine Sandy Loam Soil ....................................................331 Table 156. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Tipton Fine Sandy Loam Soil ....................................................332 Table 157. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Tipton Fine Sandy Loam Soil ....................................................332 Table 158. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Tipton Fine Sandy Loam Soil ....................................................338 Table 16. Optimal Irrigation Water and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer with 1,280 p.p.m (ECw=2) of Salt Concentration by Soil Texture and Type ......................................343 xvi LIST OF FIGURES Figure Page Figure 1. Study Area ......................................................................................................2 Figure 2. Study Procedure............................................................................................13 Figure 3. Irrigable Soil Area by Soil Type along the Elm and North Fork after Elimination of Soils with 10meter Slopes Greater than Three Percent .......16 Figure 4. Weather Data Generating Process ................................................................18 Figure 5. Soil Sample Points Collected in the Study Area (Source: Oklahoma State University Experiment Station) .....................................................................22 Figure 6. Comparison of the Simulated and Observed Irrigated Cotton Yields for Jackson County Obtained from National Agricultural Statistics Service (NASS) .........................................28 Figure 7. Difference between Observed and Simulated Irrigated Cotton Yield for Jackson County ......................................................................................28 Figure 8. Comparison of the Simulated and Observed Dryland Cotton Yields for Jackson County Obtained from National Agricultural Statistics Service (NASS) .........................................31 Figure 9. Difference between Observed and Simulated Dryland Cotton Yield for Jackson County ......................................................................................32 Figure 10. Environmental Factors Affecting Yield .....................................................36 Figure 11. Statistics and Histogram with the Fitted Gamma Distribution for Growing and NonGrowing Season Rainfall Used in EPIC Simulation ...........................................................................51 Figure 12. Statistics and Histogram with the Fitted Gamma Distribution for Growing and NonGrowing Season Rainfall randomly Generated based on Gamma distribution in Figure 12 for 50 years Planning Horizon of Dynamic Optimization Model ..................................................51 xvii Figure Page Figure 13. Distribution of Growing Season Rainfall and Precipitation of NonGrowing Season Generated based on Gamma Distribution over 50 years ..............................................................................................52 Figure 11. Fiftyyear Average EPIC Simulated Yield Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Tipton Loam Soil ................................................55 Figure 12. Marginal Product of Irrigation Water and Salt Concentration for the Tipton Loam Soil ...........................................................................58 Figure 13. 3D Surface of Crop Response Function versus Responsible Variables for the Tipton Loam Soil ...........................................................................62 Figure 14. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Tipton Loam Soil ...........................................................................68 Figure 15. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Tipton Loam Soil ...........................................................................70 Figure 16. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Tipton Loam Soil ...........................................................................71 Figure 21. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Madge Fine Sandy Loam and Madge Loam Soil ....................................................................................................................75 Figure 22. Marginal Product of Irrigation Water and Salt Concentration for the Madge Fine Sandy Loam and Madge Loam Soil ..........................78 Figure 23. 3D Surface of Crop Response Function versus Responsible Variables for the Madge Fine Sandy Loam and Madge Loam Soil ..........................82 Figure 24. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Madge Fine Sandy Loam and Madge Loam Soil ..........................87 xviii Figure Page Figure 25. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Madge Fine Sandy Loam and Madge Loam Soil ..........................89 Figure 26. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Madge Fine Sandy Loam and Madge Loam Soil ..........................90 Figure 31. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Roark Loam Soil................................................94 Figure 32. Marginal Product of Irrigation Water and Salt Concentration for the Roark Loam Soil ...........................................................................97 Figure 33. 3D Surface of Crop Response Function versus Responsible Variables for the Roark Loam Soil .........................................................................101 Figure 34. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Roark Loam Soil .........................................................................106 Figure 35. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Roark Loam Soil .........................................................................108 Figure 36. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Roark Loam Soil .........................................................................109 Figure 41. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Spur Loam Soil ................................................113 Figure 42. Marginal Product of Irrigation Water and Salt Concentration for the Spur Loam Soil ............................................................................116 Figure 43. 3D Surface of Crop Response Function versus Responsible Variables for the Spur Loam Soil ............................................................................120 xix Figure Page Figure 44. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation and Risk Aversion for the Spur Loam Soil ............................................................................125 Figure 45. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Spur Loam Soil ............................................................................127 Figure 46. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Spur Loam Soil ............................................................................128 Figure 51. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Spur Clay Loam Soil .......................................132 Figure 52. Marginal Product of Irrigation Water and Salt Concentration for the Spur Clay Loam Soil ...................................................................135 Figure 53. 3D Surface of Crop Response Function versus Responsible Variables for the Spur Clay Loam Soil ...................................................................139 Figure 54. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Spur Clay Loam Soil ...................................................................144 Figure 55. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Spur Clay Loam Soil ...................................................................146 Figure 56. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Spur Clay Loam Soil ...................................................................147 Figure 61. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Tillman Clay Loam Soil ..................................151 xx Figure Page Figure 62. Marginal Product of Irrigation Water and Salt Concentration for the Tillman Clay Loam Soil ..............................................................154 Figure 63. 3D Surface of Crop Response Function versus Responsible Variables for the Tillman Clay Loam Soil ..............................................................158 Figure 64. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Tillman Clay Loam Soil ..............................................................163 Figure 65. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Tillman Clay Loam Soil ..............................................................165 Figure 66. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Tillman Clay Loam Soil ..............................................................166 Figure 71. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Frankirk Loam Soil ..........................................170 Figure 72. Marginal Product of Irrigation Water and Salt Concentration for the Frankirk Loam Soil .....................................................................173 Figure 73. 3D Surface of Crop Response Function versus Responsible Variables for the Frankirk Loam Soil .....................................................................177 Figure 74. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Frankirk Loam Soil .....................................................................182 Figure 75. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Frankirk Loam Soil .....................................................................184 Figure 76. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Frankirk Loam Soil .....................................................................185 xxi Figure Page Figure 81. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Hardeman Fine Sandy Loam Soil .................187 Figure 82. Marginal Product of Irrigation Water and Salt Concentration for the Hardeman Fine Sandy Loam Soil ...............................................192 Figure 83. 3D Surface of Crop Response Function versus Responsible Variables for the Hardeman Fine Sandy Loam Soil ...............................................196 Figure 84. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Hardeman Fine Sandy Loam Soil ...............................................201 Figure 85. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Hardeman Fine Sandy Loam Soil ...............................................203 Figure 86. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Hardeman Fine Sandy Loam Soil ...............................................204 Figure 91. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Lawton Loam Soil ...........................................208 Figure 92. Marginal Product of Irrigation Water and Salt Concentration for the Lawton Loam Soil .......................................................................211 Figure 93. 3D Surface of Crop Response Function versus Responsible Variables for the Lawton Loam Soil .......................................................................215 Figure 94. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Lawton Loam Soil .......................................................................220 Figure 95. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Lawton Loam Soil .......................................................................222 xxii Figure Page Figure 96. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Lawton Loam Soil .......................................................................223 Figure 101. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm)of Salt Concentration of Irrigation Water for the Westill Clay Loam Soil .................................227 Figure 102. Marginal Product of Irrigation Water and Salt Concentration for the Westill Clay Loam Soil .............................................................230 Figure 103. 3D Surface of Crop Response Function versus Responsible Variables for the Westill Clay Loam Soil .............................................................234 Figure 104. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Westill Clay Loam Soil .............................................................239 Figure 105. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Westill Clay Loam Soil .............................................................241 Figure 106. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Westill Clay Loam Soil .............................................................242 Figure 111. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Abilene Loam Soil ....................................246 Figure 112. Marginal Product of Irrigation Water and Salt Concentration for the Abilene Loam Soil.....................................................................249 Figure 113. 3D Surface of Crop Response Function versus Responsible Variables for the Abilene Loam Soil.....................................................................253 Figure 114. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Abilene Loam Soil.....................................................................258 xxiii Figure Page Figure 115. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Abilene Loam Soil.....................................................................260 Figure 116. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Abilene Loam Soil.....................................................................261 Figure 121. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Burford Loam Soil ....................................265 Figure 122. Marginal Product of Irrigation Water and Salt Concentration for the Burford Loam Soil.....................................................................268 Figure 123. 3D Surface of Crop Response Function versus Responsible Variables for the Burford Loam Soil.....................................................................272 Figure 124. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Burford Loam Soil.....................................................................277 Figure 125. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Burford Loam Soil.....................................................................279 Figure 126. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Burford Loam Soil.....................................................................280 Figure 131. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Carey Silt Loam Soil ................................284 Figure 132. Marginal Product of Irrigation Water and Salt Concentration for the Carey Silt Loam Soil ...................................................................287 Figure 133. 3D Surface of Crop Response Function versus Responsible Variables for the Carey Silt Loam Soil .................................................................291 xxiv Figure Page Figure 134. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Carey Silt Loam Soil .................................................................296 Figure 135. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.2 m for the Carey Silt Loam Soil .................................................................298 Figure 136. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Carey Silt Loam Soil .................................................................299 Figure 141. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Grandfield Fine Sandy Loam Soil .............303 Figure 142. Marginal Product of Irrigation Water and Salt Concentration for the Grandfield Fine Sandy Loam Soil .............................................306 Figure 143. 3D Surface of Crop Response Function versus Responsible Variables for the Grandfield Fine Sandy Loam Soil .............................................310 Figure 144. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Grandfield Fine Sandy Loam Soil .............................................315 Figure 145. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Grandfield Fine Sandy Loam Soil .............................................317 Figure 146. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Grandfield Fine Sandy Loam Soil .............................................318 Figure 151. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Tipton Fine Sandy Loam Soil ...................322 xxv Figure Page Figure 152. Marginal Product of Irrigation Water and Salt Concentration for the Tipton Fine Sandy Loam Soil ...................................................325 Figure 153. 3D Surface of Crop Response Function versus Responsible Variables for the Tipton Fine Sandy Loam Soil ....................................................329 Figure 154. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Tipton Fine Sandy Loam Soil ...................................................334 Figure 155. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Tipton Fine Sandy Loam Soil ...................................................336 Figure 156. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Tipton Fine Sandy Loam Soil ...................................................337 1 CHAPTER I INTRODUCTION Problem Statement The United States Army Corps of Engineers (USACE) has asked Oklahoma State University to estimate the net agricultural benefits from reducing the salt loading into the Elm Fork of the Red River just west of the highway 30 bridge in Harmon County. Saline soils and waters contain excessive amounts of soluble salts which preclude the practical and normal production of most agricultural crops. They have been a potential threat for agriculture in a study area. The study area is located along Elm and North Forks of the Red River in Greer, Harmon, Jackson and Tillman Counties of Oklahoma. A major source of the salt is a series of three canyons, which join the Elm Fork in Harmon County. The control point in this area contributes some 510 tons per day of chlorides in Elm and North Fork (Red River Chloride Control Project, 2010). If we use water from the Elm and/or the North Fork as irrigation water, it would quickly increase soil salinity and depress crop yield. Irrigated agriculture depends on adequate and highquality water supplies. As the level of salinity increases in irrigation source, the quality of that water for plant growth decreases. 2 Currently, the USACE is investigating the potential benefits from irrigation if the source of chloride contamination were cut off at the control point. The specific area is defined by sections of land that either transverse or are adjacent to sections transverse by the Elm and North Forks of the Red River. This area is shown in Figure 1. Figure 1. Study Area 3 Although salinity currently precludes irrigation, it is expected the irrigated area would increase rapidly in the study area. However, we do not know the relationship between yield, quality of irrigation water, soil containing salinity and the volume of irrigation water directly. Before applying irrigation in the study area, we need to determine how much of the shaded area in Figure 1 might be economically irrigated, how much salinity affects a cotton yield, and how much irrigation is required under salinity. To assess the relationship between cotton yield, quantity and quality of irrigation water, and soil salinity, the Erosion Productivity Impact Calculator (Williams et al, 1990) crop model simulation will be used. The EPIC simulation model is a research tool usually that is commonly used to determine the response of crop yields to environmental factors. For the purpose of this study, the EPIC will be used to determine potential crop yields for cotton subject to the salinity of surface water and soil salinity with different levels of irrigation water for next 50 years. 4 Objectives The development of irrigable land is one of the fundamental measures for increasing agricultural production. However, the study area is a nonirrigable because of a lack of sufficient ground water for irrigation and the salt load from the chloride control point. If irrigation is expanded along the alluvial plain the Elm and North Fork Rivers, it is important to understand the long term effect of using irrigation water with various levels of salinity on cotton yield based on the different soil types in the study area. The objectives of this study are to 1) estimate the potential cotton response for each soil type to irrigation water and salinity content, 2) estimate the economic viability of establishing irrigation systems to irrigate potentially irrigable soils in the study area along the Elm and North Fork rivers, 3) estimate dynamic soil salinity changes in response to the amount of irrigation water, the salinity of irrigation water, and the soil salinity of the previous year, 4) determine that temporal use of water with the given levels of salt concentration that maximizes the Net Present Value (NPV) from irrigation for each soil type. 5 CHAPTER II REVIEW OF LITERATURE Crop simulation models have some ability to extend the results of crop experiments. The process of the actual experiment such as designing, building, and testing can be expensive and consequently is limited to select area. Simulation models are generally based on experiments covered over a broad geographical area and covers many years. However, crop simulation models can generate the level of detail that we cannot find in actual experiments. It also can be set to run for as many time steps we desire. After proper validation, it can be used to predict the crop yield under environmental changes and expand the results of actual experiments (Jame et al, 1996) Crop simulation with salinity Beginning in 1981, a mathematical model called the EPIC model was developed to determine the relation between soil erosion and soil productivity throughout the U.S.A (Williams, 1990). The EPIC is a field scale and daily time step model composed by soil and crop processes such as an erosion, nutrient balance, and related process. The EPIC crop model has been successfully applied in the study of erosion, water pollution, and 6 crop growth and production. However, there is little literature on crop simulation with salinity. Tayfur et al (1996) provides useful evidence on the salinity effect on decreasing crop yields. They extended the EPIC to consider the effects of root zone salinity in alfalfa production on a field scale under optimal and under water stress or limited irrigation conditions. The revised model was calibrated and validated with field data. The results suggest that an increase in salt concentration in applied irrigation water would dramatically decrease the total alfalfa yield under irrigation treatments. Experiment with salinity Salinity problems occur because irrigation water contains some amount of soluble salts. Evaporation and transpiration by plants leave these salts in the soil. These salts accumulate over time in soil and affect the crop yields. The matter of soil salinity and the use of irrigation water containing soluble salts is one of the major considerations when irrigation is used in the study area. The response function of the crop yield to salinity is an important factor in an economic model. There is considerable literature available on crop yield response to irrigation water and salinity with experimental data. Yaron and Bresler (1970) determined the efficient combination of water quantity and quality in irrigation under specific field conditions. They used to a linear programming model to derive the optimal quantityquality combinations under different levels of irrigation water and initial soil salinity. The authors used a leaching model to trace the salt distribution in the soil profile and restrictions on the chloride concentration in the soil solution. They compared the 7 empirical estimates of the marginal rate of substitution of water salinity for quality with the cost of the water quantity and quality ratio. Unfortunately, information on the cost did not exist at that time. However, in the empirical estimates from the linear programming model, they found that as the quantity of irrigation water applied increases, the maximum permissible chloride concentration in irrigation water also increases. Dinar and Knapp (1986) provide econometric estimates of yield response and salt accumulation in the soil under saline conditions with experimental data for alfalfa and cotton. They estimated to log and quadratic functions of yield and soil salinity. The dependent variables of crop yield and soil salinity at the end of the growing season were regressed on quantity of rainfall and applied irrigation water during the growing season, salt concentration of the irrigation water, soil salinity of the root zone at planting time, and pan evaporation during the growing season. The log yield response functions and the log soil salinity relations moved for alfalfa and cotton as they expected. The crop yield increases as water quantity increases, salt concentration decreases and soil salinity decreases. The quadratic yield function showed unexpected patterns. The crop yield generally increases as the quantity of water increases. However, when the quantity of water is held constant, the yield increases as initial soil salinity increases. The log soil salinity relations also exhibit for alfalfa and cotton as they expected. Ending soil salinity decreases as water quantity increases, salt concentration decreases. The quadratic soil salinity relations also did not behave as they expected. Ending salinity decreases as initial soil salinity increases, holding water quantity constant. They added the pan evaporation variable on the log and quadratic functions of yield and soil salinity. Its coefficient was a negative in yield response functions and a positive in soil salinity relations indicating the 8 crop yield decreases and soil salinity increases as the pan evaporation decreases. In addition, they combined the estimated response functions and dynamic soil salt relations with an economic decision model to determine water applications for any give prices and initial soil salinity which maximize the net present value of profits. Profits increase as crop prices increase, decrease as irrigation water prices increase, and decrease as initial soil salinity increases. Contrary to their expectation, they found that profits increase as the initial soil salinity increase with a range of salinity EC levels from 4 to7 for alfalfa. Dinar et al (1991) provided statistical estimates of cropwater response functions with various levels of salinity. They estimated the quadratic and loglog response function of yield, soil salinity and drainage volume for wheat, sorghum and wheatgrass in terms of the quantity and quality of the applied irrigation water and the initial level of root zone salinity at the beginning of the growing season. Their data came from a fouryear lysimeter experiment. Coefficients from SAS Proc Mixed for the quadratic function were statistically significant and the function described the relative effects of input water quality and quantity on yield, soil salinity, and drainage volume for three crops. In case of the loglog response function, the estimated coefficients for water quantity were greater than or close to 1 for wheat and wheatgrass. This indicates that any increase in water quantity would increase yield with all other variables being constant. They found that final soil salinity increased with small amounts of irrigation water and then decreased with larger amounts of irrigation water. They also found that amount of and/or requirement for drainage increased as applied irrigation water increased, as the level of initial soil salinity increased, and as the salt concentration in irrigation water increased for three crops. 9 Feinerman (1994) estimates the response function to soil salinity of a given crop (potatoes) in a singlefarm framework. He uses a switching regression to estimate a piecewise linear response function. Crop yield is dependent of average soil salinity below a certain critical threshold, and thereafter decreases linearly. Datta et al (1998) estimate a set of production functions relating wheat yield to initial soil salinity and water quantity and quality. They used the functions to find optimal water application for given irrigation water quality, reuse of drainage water, reduction in income from using saline drainage waters mixed at various rates with good quality water. Crop yield response functions fitted to experimental data were quadratic, CobbDouglas and linear. They found that the quadratic function provided a better fit to the data for the response of cotton yield to selected variables than did the linear or CobbDouglas functions. They suggest that yield is not simply related to the average initial soil salinity but also to the salinity in irrigation water applied. Kiani and Abbasi (2009) used experimental data to investigate crop response to both soil water content and soil salinity. They estimated linear, CobbDouglas, quadratic, and transcendental functions. They compared the various production functions in terms of their Fvalue, R2, standard error (SE), and relative error (RE). They found the quadratic and transcendental functions predicted yield response very well. They also found that both soil water content and soil salinity affected the variation of yield. The effect of soil salinity on yield increases as soil water content is increased. 10 CHAPTER III METHODOLOGY Conceptual Framework The response function of a crop yield to soil salinity is an important factor in an optimization model concerning irrigation or irrigation systems with water salinity (Feinerman, 1993). In this study, the specific yield response function will be estimated from the EPIC simulation results. The EPIC model will be used to simulate the yield of cotton on the soil types in the study area. The simulation will use different levels of irrigation, water salinity, and soil salinity. The results will indicate the changes in yield over time to soil salinity for each soil type in the study area. This approach has assumptions that the given crop was directly affected by irrigation water, water salinity, soil salinity and other possible factors (Datta, 1998). These functions were measured by Dinar and Knapp (1986), Dinar et al (1991), Datta (1998) and Kiani and Abbasi (2009). The general relationships of the factors for an individual soil type are specified as follows: 11 where Y is a crop yield per unit area, Irr is a quantity of irrigation water applied in acrefeet, WS is the dissolved salts in irrigation water, SS is the salt in the soil profile, X is a vector of all other factors affecting the crop yield and t is the simulation year. The estimated crop response function and the dynamic soil salinity function can be incorporated into an economic decision model to determine optimal level of irrigation levels maximizing the net present value of profits. The dynamic programming optimization for individual soil types in the study area is constructed as follows: subject to where Py is the price of cotton ($/lb), Yt is the cotton yield function (lbs/acre), is the quantity of irrigation water applied (acrefeet), is the irrigation cost ($/acrefeet), and is total costs except for the irrigation cost. 12 Data and Procedure In this study, it is necessary to complete the following steps to estimate the net agricultural benefits from reducing salt loading and expanding irrigation along the Elm and North Fork of the Red River. These steps include: 1) Determine the location and area of potentially irrigable soils along the Elm and North Forks 2) Establish soil parameters by depth for each of the irrigable soil types to be simulated 3) Establish crop management data and enterprise budgets for cotton 4) Use the EPIC model to simulate cotton yield and soil salinity for each of the major irrigable soil types identified in step 1 5) Calibrate the EPIC simulation model to conditions in Jackson County 6) Generate fifty years of daily maximum/minimum temperature, precipitation and solar radiation 7) Simulate and estimate the crop response functions and dynamic soil salinity functions for each soil type with randomly generated weather data 8) Set up and solve the necessary dynamic optimization models 13 Figure 2 represents the different implementation and solution steps graphically. Figure 2. Study Procedure The procedure consists of several different steps to achieve the academic purpose. It also includes applications of the Geographic Information System (GIS) technology and Historical Weather Data Stochastic weather Input Data Soil Input Data Crop management Input Data a EPIC Run & Calibration Simulation of Yield and Soil salinity with irrigation water and water salinity Yield Response Function and Soil Salinity Dynamics Nonlinear Dynamic Programming to Determine Maximum Potential Profit from Irrigation GIS Analysis 14 Erosion Productivity Impact Calculator (EPIC) crop simulation model. GIS is used to capture the potentially irrigable soil types in the study area. It allows us to view, understand and visualize soil data. The EPIC model is able to utilize the soil data, plant parameters, and weather conditions to more accurately predict crop response yield to environmental factors in agriculture. This approach will offer the decision maker opportunities to have a crop management tool with economic considerations under the limitation of environmental conditions. 1. GIS Analysis Irrigation is one of the major measures for increasing the production of agriculture. It can be seen that the development of irrigable land is one of the fundamental measures for increasing agricultural production, but not all soil types are suitable for irrigation. Finding the area of irrigable soil types will be the first step for making group of soil for their sustained use under irrigation. GIS technology is a very useful tool to locate and determine the extension of irrigable soil in the study area. The study area consists of sections of land which are transversed by or are adjacent to sections that are transversed by the Elm and North Forks. The study area is made up of 339 640acre sections. The approximate coordinates for latitude and longitude of Chloride Control Point are 35.0 N and 99.9 W respectively. The original soil map of the study area contains various types of soils. Each soil type map has a land capability classification. To find irrigable soil types, we use the land 15 capability classification obtained from SSURGO (Soil Survey Geographic database) soil data provided by the Natural Resource Conservation Service (NRCS). The land capability classification means the land categories according to the suitability of soil quality for the potential agricultural output. The National Soil Survey Handbook provides the definition of the land capability classification. Class codes I, II, III, IV, V, VI, VII, and VIII are used to represent land capability classes. Class codes I to VIII indicate progressively greater limitations and narrower choices for agriculture. Class I and Class II (2e and 2w) are chosen as irrigated land capability class for determining the most productive soils to irrigate. By definition, Class I soils have few limitations that restrict their use. Class II soils have moderate limitations that reduce the choice of plants or require moderate conservation practices. The land capability classification includes the capability subclass. The capability subclass is the second category in the land capability classification system. Class codes e, w, s, and c are used for land capability subclasses. Briefly, e, w, s and c are related with erosion problems, wetness problems, root zone limitations, and climatic limitations respectively. Subclass e and w are chosen for defining irrigable soil types. Land capability classification is made by adding the subclass e, w, s and c to class codes. I, IIe and IIw classes as the potential irrigated soil class are used in this study (National Soil Survey Handbook, USDA). The irrigable soil areas that satisfy conditions of the land capability classification (I, IIe, and IIw) are found in Figure 5. Many types of irrigable soils still remain in the study area. The major irrigable soil types having the largest areas were selected to collect soil samples from actual fields. Potential major irrigable soil types found will be used as an individual soil input data for the EPIC simulation. 16 Figure 3. Irrigable Soil Area by Soil Type along the Elm and North Fork after Elimination of Soils with 10meter Slopes Greater than Three Percent 17 2. EPIC Simulation The Erosion Productivity Impact Calculator (EPIC) is a crop simulation model that can be used to assess the impact of weather, soil, water resources, and management strategies on agricultural production. It is useful as both a decisionmaking tool from the farm level to the national level and as a research tool. It can simulate alternative management strategies and develop, test and refine model components for simulating various physical and chemical processes (Williams et al, 1990). The potential cotton yield in response to soil salinity, response to irrigation water, response to salinity in irrigation water will be simulated using the EPIC version 0509. EPIC simulations will be used to estimate cotton yields based on daily estimates of soil salinity, rainfall and temperature for next 50 years. Input data for the EPIC include weather, soil, crop management, and specific site information. It also includes parameter data files for major crops, fertilizers, and tillage practices (Cabelguenne et al, 1990). Weather Data Generation The EPIC simulation runs on a daily time step requiring the input of daily weather data. Minimum input requirements to set up weather data are daily precipitation and minimum and maximum temperature and latitude and longitude for the specific weather station. Historical daily weather data can be directly used in the EPIC simulation when the length of historical daily weather is the same as the simulation period. It is also used to generate monthly weather statistics using the WXPM 3020 (Williams et al, 2006) weather simulator (ftp://ftp.brc.tamus.edu/pub/epic/wxparm/). 18 The EPIC program can simulate daily weather with the aid of a stochastic weather generator called the WXGEN (ftp://ftp.brc.tamus.edu/pub/epic/wxgen/) (Liu et al, 2009). The WXGEN can generate daily weather based on the monthly input statistics. A stochastic weather generator produces artificial daily time series of weather data based on the statistical characteristics of historical or observed weather at a specific location. Figure 4 represents the weather data generating process with the WXPM3020 program and stochastic weather generator the WXGEN. Figure 4. Weather Data Generating Process The historical daily weather data for precipitation and minimum/max temperature from 1950 to 2006 at Jackson country obtained from National Climatic Data Center were used as the baseline weather data. The monthly weather statistics can be generated from Historical Weather Data from1950 to 2006 Monthly Weather Statistics using WXPM3020 Random Daily Weather Data for the years 2011 to 2060 using WXGEN 10 Random Daily Weather Data Sets for EPIC Run (by Aaron Mittelstet) 19 the historical daily data by using the WXPM 3020 program. When the monthly weather statistics is available, the WXGEN is a useful tool in generating daily weather data (Liu et al, 2009). The WXGEN was used to randomly generate daily solar radiation, precipitation and minimum/max temperature for the years 2011 to 2060 based on the means, standard errors, and skew coefficients in the monthly weather statistics of the baseline weather data. 10 Random Daily Weather Data Sets for EPIC Run were generated by Aaron Mittelstet who is a research engineer of Biosystems and Agricultural Engineering in Oklahoma State University. Table 1 shows the monthly statistics of the baseline weather data from years 1950 to 2006. 20 Table 1. Monthly Statistical Properties of the Daily Historical Weather Data at Altus Station, OK from years 1950 to 2006 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TMX 12.04 15.55 20.13 25.92 30.40 34.62 36.21 34.13 29.77 23.93 16.21 12.21 TMN 2.57 0.33 4.55 10.43 15.62 19.95 21.48 19.57 15.02 8.60 1.99 1.83 SDMX 7.95 8.21 8.21 6.72 4.95 4.05 3.71 6.06 5.82 6.65 7.17 7.24 SDMN 5.25 5.45 5.41 5.26 4.36 3.11 2.22 3.61 5.25 5.74 5.51 4.90 PRCP 25.01 30.73 43.33 57.99 115.00 83.12 57.05 61.50 72.71 61.31 28.80 25.33 SDRF 9.43 10.93 11.42 13.16 17.64 19.25 13.15 17.70 18.04 19.43 9.02 9.16 SKRF 2.37 4.09 2.45 2.09 2.23 2.93 2.20 3.49 3.05 3.99 1.78 2.21 PWD 0.08 0.10 0.12 0.13 0.20 0.14 0.12 0.13 0.12 0.11 0.08 0.08 PWW 0.28 0.32 0.31 0.34 0.34 0.35 0.35 0.35 0.46 0.37 0.35 0.32 DAYP 3.05 3.70 4.54 4.95 7.32 5.18 4.82 5.18 5.35 4.61 3.35 3.21 Note: Variable definitions are as below. TMX: Maximum daily air temperature (Â°C) TMN: Minimum daily air temperature (Â°C) SDMX: Monthly average standard deviation of daily maximum air temperature (Â°C) SDMN: Monthly average standard deviation of daily minimum air temperature (Â°C) PRCP: Precipitation (mm) SDRF: Monthly standard deviation of daily precipitation (mm) SKRF: Monthly skew coefficient for daily precipitation (mm) PWD: Monthly probability of wet day after dry day PWW: Monthly probability of wet day after wet day DAYP: Number of days with precipitation 21 Soil Data Soil is one of the important input components. Soil parameters should be prepared for the EPIC run. Soil data are composed of relevant physical and chemical parameters. Although up to ten soil layer parameters can be input into the EPIC, five or six soil layers were used to in this study set up soil input data. The following minimum parameter set was used on all soil types: soil albedo, soil hydrologic group, depth to bottom of layer, bulk density, percentage of sand, percentage of silt, soil pH, cation exchange capacity and electrical conductivity (EC). Table 2 shows the example of one of the irrigable soil types (Tipton Loam soil) used in the EPIC simulation as soil input data. Table2. Tipton Loam Soil Input Data for EPIC Model Tipton Loam Soil (Albedo =0.09, hydrologic group = B) Soil layers 1 2 3 4 5 6 Depth(m) 0.15 0.3 0.6 0.9 1.2 1.5 Bulk Density(t/m3) 1.43 1.43 1.5 1.5 1.5 1.5 Sand (%) 43.2 43.2 33.5 34.4 34.4 34.4 Silt (%) 38.8 38.8 36.5 37.6 37.6 37.6 Soil PH 6.7 7.5 7.8 7.9 8 8.1 Cation Exchange Capacity (cmol/Kg) 12.8 12.8 17 17 17 15.3 Electrical Conductivity (mmho/cm) 0.78 1.08 1.47 1.17 1.33 2 Values of soil pH and EC at different depths in the soil profile were obtained from the soil test conducted by the Oklahoma State University (OSU) Experiment Station 22 (Zhang et al, 2011). Other values are obtained from Soil Survey Geographic (SSURGO) Database in Natural Resource Conservation Service (NRCS). The OSU Experiment Station collected samples of potentially irrigable soil affected by chloride loading at the control point along the Elm and North Fork of the Red river. The collected soil samples were located based on the result of GIS analysis. Figure 5 shows that 37 samples were collected along the Elm Fork across Greer County and 26 along the North Fork across Jackson, Kiowa and Tillman County. All 63 soil samples are classified into 15 soil types. Table 3 lists the soil samples along the Elm and North Fork rivers. Figure 5. Soil Sample Points Collected in the Study Area (Source: Oklahoma State University Experiment Station, 2009) ^!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(HarmonJacksonKiowaTillman23 Table 3. Tested and Collected Irrigable Soil Samples Tested soil group Collected soil group County Samples Abilene loam Abilene loam, 01% slopes Tillman 1 Burford loam Burford loam, 13% slopes Tillman 1 Carey silt loam Carey silt loam, 13% slopes Kiowa 1 Frankirk loam Frankirk loam, 1 3 % slopes Greer 2 Grandfield fine sandy loam Grandfield fine sandy loam, 13% slopes Jackson 1 Hardeman fine sandy loam Hardeman fine sandy loam, 01% slopes Jackson 1 Hardeman fine sandy loam, 13% slopes Jackson 2 Lawton loam Lawton loam, 01% slopes Greer 2 Madge loam and Madge fine sandy loam Madge fine sandy loam, 13% slopes Greer 3 Madge loam, 1 3% slopes Greer 2 Madge loam, 13% slopes Jackson 1 Roark loam Roark loam, 0 1% slopes Greer 6 Roark loam, 01% slopes Jackson 2 Spur clay loam Spur clay loam, 0 1% slopes, occasionally flooded Greer 4 Spur clay loam, 01% slopes, occasionally flooded Jackson 1 Spur clay loam, 01% slopes, rarely flooded Greer 2 spur loam Spur loam, 0 1% slopes, occasionally flooded Greer 6 Tillman clay loam Tillman clay loam, 13% slopes Kiowa 1 Tillman clay loam, 13% slopes Jackson 3 Tipton fine sandy loam Tipton fine sandy loam, 01% slopes Tillman 1 Tipton fine sandy loam, 01% slopes Jackson 1 Tipton loam Tipton loam, 0 1% slopes Jackson 5 Tipton loam, 0 1% slopes Tillman 3 Tipton loam, 01% slopes Greer 8 Tipton loam, 13% slopes Tillman 1 Westil clay loam Westill clay loam, 13% slopes Greer 2 Source: Oklahoma State University Experiment Station, 2009 24 Crop Management Data The EPIC simulation program also requires data on the details of farm operations such as planting and harvesting timing, plant population, type and amounts of fertilizer and pesticides applied, potential heat units and others for the specific crop cultivating in the study area. Since the EPIC model simulates the potential cotton yield for next 50 years, actual information of crop operation schedule is not fully available. Most of the economic data were obtained from the cotton budget (Oklahoma State University Extension, 2011). We assume that the farmers in the study area follow this crop operation schedule. Table 4. Summary of Crop Operation Data in EPIC Model Month Cropping Practice Dryland Irrigation April Bedder Tillage, Dry Fertilizer and Pesticide Bedder Tillage, Dry Fertilizer and Pesticide May Planting and Row Cultivation Planting and Row Cultivation June Pesticide Pesticide and Irrigation July Irrigation August Pesticide Pesticide and Irrigation October Harvest Ginning, Bagging and Ties Pesticide, Harvest Ginning, Bagging and Ties November Kill and Shredder Tillage Kill and Shredder Tillage December Field Cultivation Field Cultivation Source: OSU Enterprise Budget Software, 2011 25 Usual planting dates for cotton in Oklahoma are from May second until June eighteenth and harvesting dates are from October fourth through December twenty fourth (Usual Planting and Harvesting Dates for U.S. Field Crops, 2010). The duration of growing season used for the EPIC simulations was 160 days from May sixth to October twelfth. Dry fertilizer, Vydate LV, Pix, Roundup Max, Pix 8, Prep and Def 6 for pesticide were assumed to be applied in the study area during the crop growing season. Model Evaluation To validate the estimated crop response function, it is necessary that the EPIC simulation accurately predicts the observed yield. The evaluation is generally reported as a comparison of simulated and observed variables. It can be expected the simulated cotton yields will be overestimated because the EPIC model does not consider disease, insects and severe weather conditions such as hail. The parameters used to calibrate the EPIC model are shown in Table 5. Table 5. Parameters related to Cotton Yield in EPIC Model Crop Parameters Symbol* Parameters Used Initial Parameters BiomassEnergy Ratio WA 20 20 Harvest Index HI 0.5 0.55 Potential Heat Unit PHU** 1760 1200 ~2400 Plant Population (plants/m2) 8.5 7.41 ~ 12.35 Note : (*) Symbols of parameters are used in the EPIC model. (**) Range of PHU for South and East Texas is from 1200 to 2400 which was defined by Ko et al (2009) and Wang et al (2005) respectively. 26 The parameters varied to calibrate the EPIC model were the Biomass Energy Ratio (WA), Harvest Index (HI), Potential Heat Unit (PHU) and Plant Population. The values used were based on literature and researcherâ€™s knowledge. According to the EPIC user guide for version 0509 (Williams et al 2006), the BiomassEnergy Ratio (WA) is the potential growth rate per unit of intercepted photosynthetically active radiation. Harvest Index (HI) is the percent of economic yield to the above ground biomass. The Potential Heat Unit (PHU) is the number of heat units expected for a typical growing season from plant to maturity. The optimal plant population for cotton has a wide range from 30,000 to 50,000 plants per acre, which can be converted into 7.41 to 12.35 plants per m2 (Hake et al, 1996). These parameters were adjusted up or down until the simulated yield matched the 7year observed yield of Jackson County. The cotton yield at the county level was used to calibrate and validate the EPIC model. The EPIC model performance is evaluated by the paired ttes for mean. It is used to investigate the relationship between two groups when each data point in one group corresponds to matching data point in the other group. It starts with comparing the means of each group of observations and simulations in this study. The observed variables for evaluation of the EPIC model are the dryland and irrigated cotton yields (lb/acre) of Jackson County obtained from National Agricultural Statistics Service (NASS) from years 2000 to 2006. The LugertAltus Irrigation District in Jackson County covers approximately 48,000 acres and the annual irrigation delivery from Lake Altus for irrigation has varied from a low of 13,600 acrefeet in 1953 to a high of 106,542 acrefeet in 1998 (W.C. 27 Austin Project, 2005). The district supplies more than 85,000 acft/acre of irrigation water to about 300 cotton farms in the area every year (Bimonthly Newsletter of OWRB, 2000). Salinity levels in the reservoir ranged from 1.8 to 2.4 EC levels (Oklahoma's Beneficial Use Monitoring ProgramLakes Sampling, 2009). For the model evaluation, it was assumed that approximately 1.64 acft/acre per acre of irrigation water with an EC level of 2 from the LugertAltus Reservoir is applied for each simulation year. The Holister Silty Clay Loam soil, which is a predominant soil type in the LugertAltus Irrigation District was used in Jackson County. Some of the more important properties of Holister Silty Clay Loam soil are shown Table 6. Table 6. Holister Silty Clay Loam Soil Properties used in EPIC calibration for Jackson County Cotton Yield Holister Silty Clay Loam (Albedo =0.16, hydrologic group = D) Soil layers 1 2 3 4 5 6 Depth(m) 0.15 0.3 0.6 0.9 1.2 1.5 Bulk Density(t/m3) 1.4 1.48 1.48 1.48 1.48 1.48 Sand (%) 10 22.5 22.5 22.5 22.5 22.5 Silt (%) 56.5 32.5 32.5 32.5 32.5 36.5 Soil pH 7.74 7.65 7.66 7.82 7.9 7.88 Cation Exchange Capacity (cmol/Kg) 22.5 27.5 27.5 27.5 27.5 27.5 Electrical Conductivity (mmho/cm) 1.92 7.29 8.85 8.4 7.64 7.95 An Oklahoma State University (OSU) Experiment Station soil sampling study provided data on Soil pH and EC levels at different depths in the soil profile (Zhang et al, 2011). Other Data were obtained from the Soil Survey Geographic (SSURGO) Database in Natural Resource Conservation Service (NRCS). 28 Figure 6 shows the comparison between the observed and simulated cotton yield with irrigation levels of 1.64 acft/acre with a salinity level EC of 2. The paired ttest for mean was used to test the null hypothesis of no difference between simulated and observed cotton yield. Figure 7 shows the difference two groups (Observed cotton yield  Simulated cotton yield) for irrigation. Figure 6. Comparison of the Simulated and Observed Irrigated Cotton Yields for Jackson County Obtained from National Agricultural Statistics Service (NASS) Figure 7. Difference between Observed and Simulated Irrigated Cotton Yield for Jackson County 0 200 400 600 800 1000 1200 2000 2001 2002 2003 2004 2005 2006 Yield (lb/acre) Years Observed Cotton Yield Simulated Cotton Yield 200 100 0 100 200 2000 2001 2002 2003 2004 2005 2006 Yield (lb/acre) Years Observed  Simulated Yield 29 If a statistical tvalue is less than a critical tvalue or pvalue is larger than a significant level , we fail to reject the null hypothesis. Therefore, we conclude that there is no evidence of statistically significant difference between the two groups. Table 7 shows the results of the paired t test using the SAS program. Table 7. Results of Paired ttest for the mean of Observed and Simulated of Irrigated Cotton Yields in Jackson County Observed Yield (lb/acre) Simulated Yield (lb/acre) Mean of each group 1025 985 Observations 7 7 Mean Difference in Yields 40 Standard Deviation of Difference 119 Statistical t value* 0.89 pvalue 0.41 Critical tvalue 2.45 Note: (*) indicates statistical tvalue is defined as where is a mean difference of yields of two group, is a standard deviation of difference and n is observations. Since the statistical tvalue (= ) is less than the critical tvalue (=2.45) and pvalue (=0.41) is larger than the significant level , we fail to reject the null hypothesis. We conclude that there is no statistical difference at the 95% confidence level between the observed cotton yield group and simulated cotton yield group. Table 8 shows the summary statistics of relative error, NashSutcliffe efficiency and coefficient of determination (R2) for observed and simulated irrigation cotton yield after calibration. 30 Table 8. Results of Yearly EPIC Model Calibration for Irrigation Cotton Yield in Jackson County for the Period from 2000 to 2006 Mean of Observed Yield (lb/acre) Mean of Simulated Yield (lb/acre) Relative Error* NashSutcliffe Efficiency** Coefficient of Determination (R2)*** 1025 985 4% 0.01 0.68 Note: (*) Relative Error is defined as R.E = â€“. (**) NashSutcliffe Efficiency is defined as E = with O observed and S simulated Yield. (***) Coefficient of Determination (R2) is obtained from outputs of linear regression. Relative Error is generally represented as percentage of the absolute error of simulated value minus observed value divided by observed value to assess the error between two models. NashSutcliffe efficiency and coefficient of determination (R2) are used to assess how well EPIC simulated cotton yield fits the observed cotton yield. NashSutcliffe efficiency is defined as one minus of the absolute squared difference between the observed and simulated values divided by the variance of the observed values for 7 target year. The range of NashSutcliffe efficiency is between  âˆž to 1. The efficiency of 1 means the simulated data perfectly fits the observed data. The efficiency of 0 indicates that the simulated model predictions are as accurate as the mean of the observed data, whereas the efficiency of lower than zero indicates that the mean of the observed data is a better predictor than the simulated model. Coefficient of determination (R2) can be obtained from outcomes of linear regression of two data. R2 is generally used as a measure of goodnessoffit of linear regression which the range of R2 is between 0 and 1. The R2 values of 1 means observed data perfectly fits simulated data whereas the R2 values of 0 means observed data does not fit any simulated data. Generally, if 31 Relative Error is within 5%, NashSutcliffe efficiency is larger than 0.4 and Coefficient of determination (R2) is larger than 0.6, the simulated model well performed with prediction of observed cotton yield (Wang et al, 2006). Relative Error between the observed and simulated mean of irrigation cotton yield is less than 5%. NashSutcliffe Efficiency is close to zero indicating the simulated model predictions are as accurate as the mean of the observed data. Coefficient of Determination (R2) is 0.68 indicating simulated model well explains the variation of observed data. To ensure the reliability of the parameters used in the calibration for the irrigation system, the parameters were also applied to dry land (nonirrigation). Figures 8 and 9 show the comparison of the observed and the simulated dryland cotton yields between the years 2000 and 2006. Figure 8. Comparison of the Simulated and Observed Dryland Cotton Yields for Jackson County Obtained from National Agricultural Statistics Service (NASS) 0 100 200 300 400 500 600 700 800 2000 2001 2002 2003 2004 2005 2006 Yield (lb/acre) Years Observed Cotton Yield Simulated Cotton Yield 32 Figure 9. Difference between Observed and Simulated Dryland Cotton Yield for Jackson County Results of paired ttest for the mean of observed and simulated dryland yield using SAS program are shown in Table 10. Table 9. Results of Paired ttest for the mean of Observed and Simulated of Dryland Cotton Yields in Jackson County Observed Yield (lb/acre) Simulated Yield (lb/acre) Mean of each group 375 426 Observations 7 7 Mean Difference in Yields 51 Standard Deviation of Difference 125 Statistical t value 1.07 pvalue 0.32 Critical tvalue 2.45 Note: (*) indicates statistical tvalue is defined as where is a mean difference of yields of two group, is a standard deviation of difference and n is observations. 200 100 0 100 200 2000 2001 2002 2003 2004 2005 2006 Yield (lb/acre) Years Observed  Simulated Yield 33 Since the statistical tvalue (= ) is less than the critical tvalue of 2.45 and the pvalue of 0.32 is larger than significant level , we fail to reject the null hypothesis. We conclude that there is no statistical difference at the 95% confidence level between the observed cotton yield group and simulated cotton yield group. Table 11 shows the summary statistics of relative error, NashSutcliffe efficiency and coefficient of determination (R2) for observed and simulated dryland cotton yield after calibration. Table 10. Results of Yearly EPIC Model Validation for Dryland Cotton Yield in Jackson County for the Period from 2000 to 2006 Observed Yield (lb/acre) Simulated Yield (lb/acre) Relative Error NashSutcliffe Efficiency Coefficient of Determination (R2) 375 426 14% 0.61 0.69 Note: (*) Relative Error is defined as R.E = . (**) NashSutcliffe Efficiency is defined as E = with O observed and S simulated Yield. (***) Coefficient of Determination (R2) is obtained from outputs of linear regression. Relative Error between the observed and simulated mean of irrigation cotton yield is larger than 5% indicating that there are some deviation between mean of observed and simulated dryland cotton yield. However, NashSutcliffe Efficiency is 0.61 indicating the simulated data well fits the observed data. Coefficient of Determination (R2) is 0.69 indicating simulated model well explains the variation of observed data. 34 The results of calibration and validation process indicate the EPIC simulated yields matched observed yields for the 7target year. The calibrated and validated parameters related to cotton yield were used to simulate the potential cotton yield and soil salinity with different levels of irrigation water and water salinity for the next 50 years. Simulation Design and process After setting up the input data, the EPIC program was used to simulate the cotton yield, soil salinity and other variables for next 50 years. A simulation design is much like that of an agronomic field experiment. The designed simulation is applied with combinations of three different levels of plant water stress, three different levels of salt concentration of irrigation water and 10 stochastic weather scenarios over a 50year period. EPIC offers two options for irrigation. Sprinkler or furrow irrigation can be simulated by fixed or automatic option. The fixed option requires that application dates and amounts be specified in advance by the EPIC users. With the automatic option, the model decides when and how much water to apply. The user must input the plant water stress level to trigger automatic irrigation, the maximum volume applied per growing season, and the minimum time interval between applications (Williams, 1990). The automatic irrigation option was selected for use for this study to represent a more realistic irrigation practice. Plant water stress factors to trigger automatic irrigation were set at 0.1, 0.5 and 0.9. This factor ranges from zero (high stress) to one (no stress) and is computed 35 as the ratio of actual plant water use to potential water use (Easterling et al, 1992). When plant water stress factor was set at 0.1, a total irrigation application is applied under 200 mm and the range of an amount of water for single application was limited to 50 mm. Similarly, when plant water stress factor was set at 0.5 and 0.9, a total irrigation application is applied under 800 mm and the range of an amount of water for single application was limited to 200 mm. The minimum interval between irrigations was set at 20 days during the growing season. The three levels of salt concentration of irrigation water represent 0, 1,280, and 2,560 p.p.m (parts per millions). Salt concentration in p.p.m can be generally expressed in terms of Electrical Conductivity (EC). It is assumed that 1 EC (mmhos/cm) in irrigation water is equal to 640 p.p.m. These units of measurement can be converted to tons of salt per acre foot as follows (Agriculture Handbook No. 60, USDA): 640 p.p.m = 1 EC mmhos/cm 1 p.p.m Ã— 0.00136 = Tons per AcreFoot For example, 0, 1,280 and 2,560 p.p.m of salt concentration can be converted to 0, 2 and 4 of EC and 0, 1.74 and 3.48 tons/acft. In addition, 1,280 p.p.m of the salt concentration are equal to 2 mmhos/cm of EC or 1.74 tons of salt for every foot of irrigation water applied. If during the growing season, 400mm (1.3 acft) of irrigation water is applied, the amount of salt in irrigation water is approximately 2.263 tons/acre (1,280 ppm Ã— 0.00136 Ã— 1.3). From this example, we can expect that the amount of salts in irrigation water can quickly increase the salinity level in the soil. 36 Based on the simulation design, a total of 90 simulations (3Ã—3Ã—10) were conducted for each soil type in the study area. The variables we need to estimate cotton yield and soil salinity response functions were taken from EPIC output. Figure 10 illustrates how cotton yield and soil salinity are affected by environmental factors. During and before the growing season, cotton yield is affected by irrigation water applied, rainfall, soil salinity at planting, salinity in irrigation water. Total water used in the field is equal to irrigation water applied plus rainfall. Total salinity is equal to soil salinity at planting plus the amount of salt in irrigation water. From irrigation water, salts accumulate in the root zone. Soil salinity at harvest assumes to be affected by irrigation water, rainfall, soil salinity at planting and the amount of salt in irrigation water. Soil salinity at planting is assumed to be affected by nongrowing season rainfall and soil salinity at harvest on the previous year. Figure 10. Environmental Factors Affecting Yield Irrigation, Rainfall Soil Salinity at plant, Salinity in Irrigation water Rainfall Planting day May, next year Harvesting day October Planting day May NonGrowing Season Growing Season 37 The simulated cotton yields, irrigation water and growing season rainfall can be selected from the annual crop yield output file (*.ACY). In case of soil salinity levels at planting and harvest, they can be found in the Daily Soil Table output file (*.DSL) which is generated on a daily basis for each soil layer. Nongrowing season rainfall was calculated by subtracting growing season rainfall from the sum of the monthly precipitation in Monthly Flipsim output file (*.MFS). The variables, descriptions and their unit conversions are shown in Table 9. Data selected from the EPIC output file are used to estimate cotton and dynamic soil salinity response function. Table 11. EPIC Output File Variable Definition and Unit Conversion EPIC Output File Variable Description Unit Conversion *.ACY YLDG Yield (Ton/Ha) 1 metric ton/Ha = 892 lbs/acre *.ACY IRGA Irrigation Volume Applied (mm) 100mm = 0.328 feet *.ACY CRF Growing season Rainfall (mm) 100mm = 0.328 feet *.DSL WLST Salt Content in Soil (Kg/Ha) 1 kg/ha = 0.446Ã—103 tons/acre *.MFS PRCP Precipitation (mm) 100mm = 0.328 feet 38 Dynamic Optimization The outputs of the EPIC simulations were used to estimate the cotton yield and soil salinity response functions. The estimated response functions for each soil type can be incorporated into an economic decision model to determine the optimal level of irrigation for any given level of salt concentration of irrigation water maximizing the net present value (NPV) of expected utility. Since crop yield and risk are generally influenced by fluctuations in weather conditions, uncertainty or risk exists in the agricultural production. The NPV of expected utility of profit instead of the NPV of profit is expressed as: The von NeumannMorgenstern utility function is used to maximize the expected value of profit. MeanVariance (EV) is incorporated to express expected utility (Hazell and Norton, 1986). Expected utility is represented as follows: where is the von NeumannMorgenstern utility function with and , is the absolute ArrowPratt risk aversion coefficient, defined as â€“. 39 Expected utility can be transformed with respected to EV of crop yield taking risk aversion as follows: = where is the expected yield, is the variance of yield derived from the equation (Coyle, 1999). The level of risk of a producer is directly related to variances of crop yield. The variance of the crop yield is evaluated as the effect of risk factors in the agricultural production. The final dynamic programming model maximizing the expected utility of profit for individual soil types in the study area is constructed as: subject to 40 where P is the price of cotton ($/lb), E(Y) is the expected cotton yield response function (lbs/acre) to quantity of total water applied and total salinity in soil, TW is the total quantity of water which is the sum of irrigation water and rainfall during the growing season. Irr is the quantity of irrigation water applied (acft/acre), is the quantity of rainfall in feet, TS is the total quantity of salinity in soil which is the sum of total dissolved salt in irrigation water and soil salinity at planting, WS is the amount of salt in irrigation water (tons/acft) which is the salt concentration (p.p.m) multiplied by the quantity of irrigation water, SSHA and SSPL is the quantity of soil salinity at harvest and planting (tons/acre) during the growing season respectively, RainG is the growing season rainfall (acft), is the quantity of soil salinity at harvest of the previous year, RainNG is rainfall received during the nongrowing season (acft), is the irrigation cost ($/acrefeet), is the operation cost and is the fixed cost, r is discount rate. The simulation design was conducted as a full factorial with three levels of irrigation water stress and three levels of irrigation water salinity, and 10 random weather data sets of 50year. A modified quadratic yield response function of cotton for the individual soil type in the study area was specified as follows: for weather scenarios for water stress factor 0.1, 0.5 and 0.9 respectively for salt concentration 0, 1280 and 2560 ppm respectively for simulation years 41 where are the parameters to be estimated, is the simulated cotton yield for a soil with the level of a water stress factor and the level of salt concentration of irrigation water in year t under the weather scenario. is the total water from irrigation water applied ( and the growing season rainfall (, is the nongrowing season rainfall. is the total salinity which is the sum of the amount of salt in irrigation water ( ) and soil salinity at planting (). The interaction term, is the total salinity divided by total water, is a random effect of weather, and are assumed to be the independent and normal distributed error terms, and ), respectively. In crop yield response function, the specification of the interaction term does not follow the standard practice of being a product of the two linear variables. This term was formulated as a ratio because more water serves to increase the yield while more salt tends to decrease the yield. When specified as a ratio (total salt/total water), the two variables work in the same direction. The soil salinity response functions at planting and harvest were also estimated for the individual soil type. The soil salinity function at harvest is assumed to be affected by irrigation water applied, dissolved salt in irrigation water and growing season rainfall. It can be constructed as follows: where are the parameters to be estimated, is the soil salinity at harvest which is simulated from a set of combinations of the soil condition having the water 42 stress factor and the level of salt concentration in year with a weather scenario . is the quantity of irrigation water applied, is the amount of salt in irrigation water, is the soil salinity at planting, is the growing season rainfall in weather scenario and year , is a random effect of weather, and are assumed to be the independent and normal distributed error terms, and ), respectively. To estimate the dynamic soil salinity function at planting, we assumed that the amount of soil salinity at planting in the current year will be determined by soil salinity level at harvest in the previous year and non growing season rainfall. The dynamic soil salinity function at planting is defined as: where and are the parameters to be estimated, is the soil salinity at planting given the water stress factor, the level of salt concentration in year t with a weather scenario , is the soil salinity at harvest in the previous year, is nongrowing season rainfall in weather scenario and year t, is a random effect of weather, and are assumed to be the independent and normally distributed error terms, and (0, , respectively. The yield variance function is expressed as the squared residuals of the estimated yield response function. It is expressed as the linear function of the irrigation and growing season rainfall which mainly affect crop yield and yield variability (risk), i.e., 43 where , and are the parameters to be estimated, is a random effect of weather, and are assumed to be the independent and identical error terms, and (0, , respectively. The coefficients of and represent the influence of irrigation water and growing season rainfall on yield variability (risk). The input variable is riskreducing if and riskincreasing if , respectively (Finger and Schmid, 2007). 44 CHAPTER IV RESULTS OF SIMULATION, REGRESSION AND OPTIMIZATION BY SOIL TYPE SAS PROC MIXED is a powerful procedure for a wide variety of statistical analyses with both fixed and random effect in research situations. In this study, the fixed and random effects model was applied to EPIC data. Since we selected 10 random weather scenarios, weather is considered as the random effect in the model. Since data selected from EPIC simulations with different inputs are in the form of panel data, autocorrelation and heteroskedasticity may occur in the model. Models to describe the variance as a function of independent variables in a regression model can be fitted to data where the variance increases or decreases as the values of the independent variables change. One of the great advantages of the likelihoodbased estimation approach to mixed models is the ability to fit a variety of covariance structures (Littell et al, 2006). To fit a model with autocorrelation and heterogeneous variances, the model can be specified in PROC MIXED by using the REPEATED statement with the AR(1) for autocorrelation and GROUP = option for heterogeneous variances. The REPEATED statement specifies the covariance structures of the error term. The AR(1) models may adequately describe the autocorrelation and assumes a homogeneous variance and error correlations that decline exponentially with distance. Group = option defines an effect specifying heteroscedasticity in the covariance structure. Each new level of the GROUP 45 effect produces a new set of covariance parameters with the same structures as the original group (SAS Institute Inc, 2008). In this study, GROUP = option specifies a different residual variance for each weather scenario. The fitted models should be compared with model with an assumption without autocorrelation and heteroscedasticity to draw accurate conclusions from data. The Likelihood Ratio Test (LRT) is used to determine the better fitted model. PROC MIXED model is based on Maximum Likelihood Estimation (MLE) which maximizes the likelihood function with/without imposing any restrictions. The LR test requires estimating two models and comparing them. The LR test statistic is calculated in the following way (Johnston & DiNardo, 1997): LR = where L and l are the likelihood and log likelihood of the respective model. Since the PROC MIXED model directly provides the 2 loglikelihood statistic, we can compare with the difference in the 2 loglikelihood of the restricted and unrestricted model for the LR test. The LR statistics follows a chisquare distribution with degrees of freedom equal to the difference in the number of degrees of freedom between the two models. By using the 1 PROBCHI function in SAS, which returns the value of the function of the chisquare distribution, SAS will compute the test statistic and its pvalue from the 2 loglikelihood values (SAS Institute Inc, 2008). If the pvalue is less than the critical value, we reject the null hypothesis of no difference between two models. 46 To determine if the estimated crop response function is concave with respect to variables we used in the regression, the second derivative test is examined by algebraically or numerically checking the signs of the secondorder conditions of the variables (Beattie & Taylor, 1985). From the yield response function, the first order and second order conditions are derived. Given a modified quadratic functional form, y = f(TW, TS, RainNG) is represented as the equation below: Given the functional form y = f(TW, TS, RainNG), this function can be extended with respect to the specified individual variables. The extended functional form y = f(x1, x2, x3, x4, x5) is represented as the equation below: where x1 is irrigation water applied (acrefeet), x2 is the growing season rainfall (feet), x3 is the salt concentration of irrigation water (tons/acft), therefore, x1Â· x3 is the amount of salt in irrigation water (tons/acre) which is the product of salt concentration and irrigation water, x4 is the salinity in the soil (tons/acre), x5 is the nongrowing season rainfall (feet). The firstorder conditions (F.O.C) with respect to the individual variable are 47 The secondorder conditions (S.O.C) for variables except for are The determinants derived from S.O.C is used to examine that the crop response function has a maximum yield with respect to irrigation water and salt concentration in irrigation water(, irrigation water ( and soil salinity (, and salt concentration in irrigation water () and soil salinity (, respectively. The Hessian matrix of second derivatives at the critical point is represented as the follows: 48 For maximization problem, must be negative definite or negative semidefinite. If and only if or , is negative definite or negative semidefinite, respectively. Hence, the determinants should be all negative, the determinants should be positive, the determinat should be negative, and the determinant is positive. The determinants are the diagonal elements of , , , , and which are 210.9, 200, 11.5 and 2.9. The order 4 determinant ( ) is formed by the 44 matrix as the above hessian matrix. The determinant is expanded into four 33 submatrices (and ) along the diagonal elements in the Hessian matrix as follows: The determinants of and should be negative so that the determinant should be positive. The determinant of and can again 49 be expanded into three 2Ã—2 submatrices (), respectively, along their diagonal elements as follows: , , , and All determinants of the 2Ã—2 matrix ( ) should be positive so that the determinants of and are negative. If the determinants of the respective orders have the indicated signs, , , , and , the matrix is negative definite. Therefore we conclude that the modified crop response function is concave and has a local maximum. The dynamic optimization procedure for the economic decision model was performed by GAMS IDE. To solve the dynamic optimization problem, we need to know the cotton price, irrigation cost, operating cost, and fixed cost. The irrigated and dryland cotton budgets were revised from the OSU cotton budget for the surfacefurrow irrigation system provided by Oklahoma State University Extension. We assumed that the farms in the study area follow this cotton budget. From APPENDIX A for the irrigated cotton, the cost of irrigation water is 28.89$/acft and total cost is 677.37 $/acre. From APPENDIX B for the dryland cotton, total cost is 312.29$/acft. We also suppose that 1) cotton price is fixed at 0.6 $/lbs for irrigation and dryland over 50 years planning horizon 2) discount rate is 4.125 percent for Federal water resources planning for fiscal year 2011 50 (http://www.economics.nrcs.usda.gov/cost/priceindexes/rates.html), 3) the available irrigation water is 2.62 acft (800mm) or less, 4) one of risk neutrality and two levels of risk aversion coefficient are used in this analysis: 0, 0.025 and 0.05 which are used in the literature for irrigated producers (Johnson and Blackshear, 2004 and Wojciechowski et al, 2000), 5) dryland producers are riskneutral since they are indifferent to the risk such as a big rainfall and drought and are concerned about expected profit, 6) the growing season and nongrowing season rainfall is randomly generated based on the gamma distribution over the 50 years planning horizon. Rainfall in the EPIC simulation is determined by generating from a skewed normal daily precipitation (Williams et al, 1992). The generated yearly rainfall and precipitation have a skewed distribution. The data that are skewed to the right are adequately modeled by a gamma density function (Wackerly et al, 2002). PROC UNIVARIATE with the HISTOGRAM statement is used to determine if the gamma distribution fits a data distribution used in the EPIC simulation. SAS output provides three goodnessoffit tests which are the KolmogrovSmirnov, Cramervon Mises and AndersonDarling test (SAS Institute Inc., 2010). The pvalues of all tests for growing and nongrowing season rainfall are larger than 0.25. Since pvalues are larger than significant value . We conclude that we fail to reject the null hypothesis of the gamma distribution and the fitted gamma distribution provides an appropriate model for distribution of generated growing and nongrowing season rainfall. Figure 12 and 13 represent the fitted gamma distribution curve on the histogram and displays the mean, standard deviation, skewness and kurtosis of growing and nongrowing season rainfall used in EPIC and dynamic optimization model, respectively. 51 Figure 11. Statistics and Histogram with the Fitted Gamma Distribution for Growing and NonGrowing Season Rainfall used in EPIC Figure 12. Statistics and Histogram with the Fitted Gamma Distribution for Growing and NonGrowing Season Rainfall randomly Generated based on Gamma distribution in Figure 12 for 50 years Planning Horizon of Dynamic Optimization Model 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 Percent Summary Statistics N 500 Mean 1.389 Std Dev 0.397 Skewness 0.426 Kurtosis .058 Growing_Season_Rainfall 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 5 10 15 20 25 30 35 40 Percent Summary Statistics N 490 Mean 0.652 Std Dev 0.228 Skewness 0.503 Kurtosis .068 Non_Growing_Season_Rainfall 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0 5 10 15 20 25 30 35 40 Percent Summary Statistics N 50 Mean 1.294 Std Dev 0.213 Skewness 0.528 Kurtosis .475 Growing_Season_Rainfall 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 10 20 30 40 50 60 70 Percent Summary Statistics N 50 Mean 0.579 Std Dev 0.132 Skewness 0.525 Kurtosis .617 Non_Growing_Season_Rainfall 52 For the dynamic programming, the growing season rainfall and nongrowing season rainfall are randomly generated for the 50 years planning horizon based on the gamma distribution. The pvalues of KolmogrovSmirnov, Cramervon Mises and AndersonDarling test for rainfall are 0.068, 0.181 and 0.204, respectively. The pvalues of their tests for nongrowing season rainfall are 0.25, 0.191 and 0.18, respectively. Since their pvalues are larger than significant value . Therefore, we conclude that we fail to reject the null hypothesis of the gamma distribution and the data are appropriately generated based on the gamma distribution in Figure 12. The generated random growing season rainfall and nongrowing season rainfall are combined with the dynamic optimization model maximizing the net present value of expected utility for all soil types. Figure 13 shows the growing season and nongrowing season rainfall based on the gamma distribution are distributed over 50 years. Figure 13. Distribution of Growing Season and Non Growing Season Rainfall Generated based on Gamma Distribution over 50 years 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 8 15 22 29 36 43 50 Rainfall (feet) Year Growing Season Rainfall NonGrowing Season Rainfall 53 Tipton Loam Soil, 01% Slope EPIC Output Data The quantity of salt in the soil at each depth in the EPIC *DSL output file is calculated by EPIC based on the initial EC values (mmho/cm) in the soil input file. Table 11 presents the calculated quantity of soil salinity based on the sampled data for the Tipton Loam soil at the start of the simulation. In EPIC, WSLT (Kg/ha) is automatically simulated at each depth on a daily basis for 50 years and the total value of them is also automatically calculated. It can be converted to tons per acre. Table 11. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Tipton Loam Soil 1* 1 2 3 4 5 6 TOTAL DEPTH(m) 0.01 0.15 0.3 0.6 0.9 1.2 1.5 ECND(mmho/cm) 1.07 0.78 1.08 1.47 1.17 1.33 2 WSLT(kg/ha)* 9 103 153 587 444 504 756 2,555 Salinity(tons/acre) 1.14** Source: Zhang et al, Oklahoma Soil Test Laboratory, 2011. Note: (*) indicates layer 1 and WSLT are simulated by EPIC. (**) indicates the value is calculated by the conversion (1 kg/ha = 0.446Ã—103 tons/acre). The total salt in the 1.5 meter profile was calculated as 1.14 tons/acre on the first day of simulation. This will be used as the initial soil salinity in the dynamic programming. The level of soil salinity at the day of planting and harvest in each year 54 can be selected from *DSL file. The cotton yield, irrigation water, growing season rainfall and nongrowing season rainfall are also obtained from the EPIC output file. The range of the simulated output variables which are used in the model are summarized in Table 12. Table 12. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Tipton Loam Soil Variable Symbol (Unit) Range Mean Cotton Yield Y (lbs/acre) 33 ~1,857 1,071 Irrigation Water Irr (acft/acre) 0.16 ~ 2.62 1.28 Soil Salinity at Planting SSPL (tons/acre) 0 ~ 24.65 8.61 Soil Salinity at Harvest SSHA (tons/acre) 0 ~ 27.34 9.39 Growing Season Rainfall RainG (feet) 0.47 ~ 2.61 1.39 NonGrowing Season Rainfall RainNG (feet) 0.06 ~ 1.64 0.66 Salt Concentration of Irrigation Water* (tons/acft) 0, 1.74 and 3.48 1.74 Note: (*) indicates the input variable to run EPIC. Ten sets of 50year cotton yield and irrigation applications were simulated by EPIC given three levels of salt concentration of irrigation water and three levels of water stress to trigger irrigation from 50 mm to 800 mm. When we use irrigation water containing a high salt concentration on the crop land, the salts accumulate in the root zone. Saline soils have a very limited agricultural production. The range of data for the simulated yield and soil salinity at harvest with given levels of the salt concentration are shown on a box plot in Figure 11. 55 Figure 11. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying irrigation water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Tipton Loam Soil A box plot visually provides a summary of simulated data. The box extends from the first quartile which is defined as the 25th percentile of the data to the third quartile which is defined as the 75th percentile of the data. The bottom and top are the minimum and maximum value of the data, respectively. The median is shown as a line across the box. The diamond sign is the average values of the simulated data at given levels of the salt concentration. As the salt concentration of irrigation water increases, the mean of simulated yield data decreases and the mean of simulated soil salinity increases. In addition, the mean of yield data decreases as the mean of soil salinity increases. The high 0 500 1000 1500 2000 Yield (lbs/acre) 0 10 20 30 0 2 4 Soil Salinity at Harvest (tons/acre) EC (mmhos/cm) Mean 0 1,280 2,560 P.P.M. 56 level of salt concentration of irrigation water causes salts to accumulate in the soil. It is expected that the accumulated salts affect the reduction of crop yields. Econometric Estimation The SAS PROC MIXED procedure with the REPEATED statement with Type=AR(1) and GROUP = weather was used to estimate the parameters of the modified quadratic yield function with autocorrelation and/or heterogeneous variances. The Likelihood Ratio Test was used to determine the appropriate error function for the model. The results of the LR test are shown in Table 13. Table 13. Result of Likelihood Ratio Test for the Tipton Loam Soil Model 2LogLikelihood pvalue LR Test Without Autocorrelation and Heteroscedasticity 56754 < 0.0001 Reject Ho With Autocorrelation and Heteroscedasticity 56628 Because the value of 2LogLikelihood with the distribution with 19 degrees of freedom has a pvalue of less than 0.01, we reject the null hypothesis of no difference between two models. It indicates that the model fitted with autocorrelation and heteroscedasticity is more appropriate (SAS Institute Inc, 2008). The procedure of fitting a model with autocorrelation and heterogeneous variance reports parameter estimates along with standard errors. The results of cotton response function are shown in Table 14. 57 Table 14. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Tipton Loam Soil Variable Symbol Parameter Estimates Standard Errors Intercept 524.38* 42.1649 Total Water Applied 940.09* 30.0577 Total Salinity 1.6022 1.3225 NonGrowing Season Rainfall 112.39* 9.7781 (Total Water Applied)2 101.98* 5.3211 (Total Salinity)2 1.4344* 0.0393 (Total Salinity / Total Water Applied) 7.3683* 2.5073 Note: Total Water Applied is the sum of irrigation water and growing season rainfall. Total Salinity is the sum of the amount of salt (irrigation wa
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Title  Economic Approach on Allocation of Irrigation Water under Salinity Based on Different Soils for Potential Irrigated Agriculture Using the Epic Crop Model 
Date  20111201 
Author  Choi, Jongsan 
Keywords  Cotton, Economics, EPIC, Irrigation, Salinity, Soils 
Department  Agricultural Economics 
Document Type  
Full Text Type  Open Access 
Abstract  The objective of this study was to understand the long term effect of using irrigation water with water and soil salinity on cotton yield based on the 15 soil types along the Elm and North Fork of the Red River. The specific aims were to 1) estimate the potential cotton response for each soil type to irrigation water and salinity, 2) estimate the economic viability of establishing irrigation systems, 3) estimate dynamic soil salinity changes in response to irrigation water, the salinity of irrigation water, and the soil salinity of the previous year, 4) determine that temporal use of water with the given levels of salt concentration that maximizes the Net Present Value (NPV) of the expected utility from irrigation for each soil type. To assess the econometric relationships between cotton yield, quantity and quality of irrigation water, and soil salinity, the EPIC simulation model was used. The estimated crop yield response function, two soil salinity functions and yield variance function are incorporated in an economic decision model to find the optimal level of irrigation water maximizing NPV of the expected utility with different salt concentrations of irrigation water and three levels of risk. The dynamic optimization procedure for the economic decision model was performed by GAMS IDE. The results of crop response functions for the individual soil types indicate that the cotton yield increases as irrigation water and rainfall increase, and it decreases as the amount of salts in irrigation water which is the product of irrigation and salt concentration and soil salinity increase. The soil salinity response functions at planting and harvest have a negative sign on irrigation water, growing season rainfall and nongrowing season rainfall indicating the level of soil salinity decreases as the variables related with water increase. The yield variance function has a negative sign on irrigation water which is riskreducing factor and a positive on the growing season rainfall which is riskincreasing. From the EPIC and dynamic optimization model, when irrigation water with a high salt concentration with or above 1280 p.p.m (ECw =2) is permitted from the salt control point in the study area, NPV of expected utility is negative and less than NPV of the dryland. The irrigation water containing salts should be controlled less than or equal to 1,280 p.p.m for sustainable irrigation. 
Note  Dissertation 
Rights  Â© Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  ECONOMIC APPROACH ON ALLOCATION OF IRRIGATION WATER UNDER SALINITY BASED ON DIFFERENT SOILS FOR POTENTIAL IRRIGATED AGRICULTURE USING EPIC CROP MODEL By JONGSAN CHOI Bachelor of Science in Agricultural Economics Kangwon National University Chuncheon, South Korea 2000 Master of Science in Agricultural Economics Kangwon National University Chuncheon, South Korea 2002 Submitted to the Faculty of the Graduate College of the Oklahoma State University In partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 2011 ii ECONOMIC APPROACH ON ALLOCATION OF IRRIGATION WATER UNDER SALINITY BASED ON DIFFERENT SOILS FOR POTENTIAL IRRIGATED AGRICULTURE USING THE EPIC CROP MODEL Dissertation Approved: Dr. Arthur Stoecker Dissertation Adviser Dr. Francis Epplin Dr. Jeffrey Vitale Dr. Dan Storm Outside Committee Member Dr. Sheryl A. Tucker Dean of the Graduate College iii TABLE OF CONTENTS Chapter Page I. INTRODUCTION ......................................................................................................1 Problem Statement ...................................................................................................1 Objectives ................................................................................................................4 II. REVIEW OF LITERATURE....................................................................................5 Crop Simulation with Salinity .................................................................................5 Experiment with Salinity .........................................................................................6 III. METHODOLOGY ................................................................................................10 Conceptual Framework ..........................................................................................10 Data and Procedure ................................................................................................12 GIS Analysis ....................................................................................................14 EPIC Simulation ..............................................................................................17 Weather Data Generation .........................................................................17 Soil Data...................................................................................................21 Crop Management Data ...........................................................................24 Model Evaluation ...................................................................................................25 Simulation Design and Process ..............................................................................34 Dynamic Optimization ...........................................................................................38 IV. RESULTS OF SIMULATION, REGRESSION AND OPTIMIZATION BY SOIL TYPE .....................................................................44 Tipton Loam Soil, 01% Slope .............................................................................53 EPIC Output Data ...........................................................................................53 Econometric Estimation ..................................................................................56 Dynamic Optimization ....................................................................................67 Madge Fine Sandy Loam and Madge Loam Soil, 23% Slope.............................73 EPIC Output Data ...........................................................................................73 iv Econometric Estimation ..................................................................................76 Dynamic Optimization ....................................................................................86 Roark Loam Soil, 01% Slope ...............................................................................92 EPIC Output Data ...........................................................................................92 Econometric Estimation ..................................................................................95 Dynamic Optimization ..................................................................................105 Spur Loam Soil, 01% Slope, occasionally flooded ...........................................111 EPIC Output Data .........................................................................................111 Econometric Estimation ................................................................................114 Dynamic Optimization ..................................................................................124 Spur Clay Loam Soil, 01% Slope, occasionally and rarely flooded...................130 EPIC Output Data .........................................................................................130 Econometric Estimation ................................................................................133 Dynamic Optimization ..................................................................................143 Tillman Clay Loam Soil, 13% Slope ..................................................................149 EPIC Output Data .........................................................................................149 Econometric Estimation ................................................................................152 Dynamic Optimization ..................................................................................162 Frankirk Loam Soil, 13% Slope .........................................................................168 EPIC Output Data .........................................................................................168 Econometric Estimation ................................................................................171 Dynamic Optimization ..................................................................................181 Hardeman Fine Sandy Loam Soil, 01% Slop .....................................................187 EPIC Output Data .........................................................................................187 Econometric Estimation ................................................................................190 Dynamic Optimization ..................................................................................200 Lawton Loam Soil, 01% Slope ...........................................................................206 EPIC Output Data .........................................................................................206 Econometric Estimation ................................................................................209 Dynamic Optimization ..................................................................................219 Westill Clay Loam Soil, 13% Slope .................................................................. 225 EPIC Output Data .........................................................................................225 Econometric Estimation ................................................................................228 Dynamic Optimization ..................................................................................238 Abilene Loam Soil, 01% Slope ..........................................................................244 EPIC Output Data .........................................................................................244 Econometric Estimation ................................................................................247 Dynamic Optimization ..................................................................................257 v Burford Loam Soil, 13% Slope ..........................................................................263 EPIC Output Data .........................................................................................263 Econometric Estimation ................................................................................266 Dynamic Optimization ..................................................................................276 Carey Silt Loam Soil, 13% Slope .......................................................................282 EPIC Output Data .........................................................................................282 Econometric Estimation ................................................................................285 Dynamic Optimization ..................................................................................295 Grandfield Fine Sandy Loam Soil, 13% Slope...................................................301 EPIC Output Data .........................................................................................301 Econometric Estimation ................................................................................304 Dynamic Optimization ..................................................................................314 Tipton Fine Sandy Loam Soil, 01% Slope .........................................................320 EPIC Output Data .........................................................................................320 Econometric Estimation ................................................................................323 Dynamic Optimization ..................................................................................333 V. CONCLUSION AND APPLICATIONS .............................................................339 REFERENCES ..........................................................................................................346 APPENDICES ...........................................................................................................350vi LIST OF TABLES Table Page Table 1. Monthly Statistical Properties of the Daily Historical Weather Data at Altus Station, OK from years 1950 to 2006...............................................20 Table 2. Tipton Soil Input Data for EPIC Model.........................................................21 Table 3. Tested and Collected Irrigable Soil Samples .................................................23 Table 4. Summary of Crop Operation Data in EPIC Model ........................................24 Table 5. Parameters related to Cotton Yield in EPIC Model .......................................25 Table 6. Holister Silty Clay Loam Soil Properties used in EPIC calibration for Jackson County Cotton Yield ..................................................................27 Table 7. Results of Paired ttest for the mean of Observed and Simulated of Irrigated Cotton Yields in Jackson County ..............................29 Table 8. Results of EPIC Model Calibration for Irrigation Cotton Yield in Jackson County for the Period from 2000 to 2006 .....................................................30 Table 9. Results of Paired ttest for the mean of Observed and Simulated of Dryland Cotton Yields in Jackson County ........................32 Table 10. Results of EPIC Model Validation for Dryland Cotton Yield in Jackson County for the Period from 2000 to 2006 .....................................................33 Table 11. EPIC Output File Variable Definition and Unit Conversion .......................37 Table 11. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Tipton Loam Soil ..................................................................................53 Table 12. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Tipton Loam Soil ................................................................54 Table 13. Result of Likelihood Ratio Test for the Tipton Loam Soil. .......................56 vii Table Page Table 14. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Tipton Loam Soil ............................................................57 Table 15. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Tipton Loam Soil ........................64 Table 16. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Tipton Loam Soil ............................................................................65 Table 17. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Tipton Loam Soil .............................................................................66 Table 18. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Tipton Loam Soil ............................................................................72 Table 21. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Madge Fine Sandy Loam and Madge Loam Soil ................................73 Table 22. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Madge Fine Sandy Loam and Madge Loam Soil ...............74 Table 23. Result of Likelihood Ratio Test for the Madge Fine Sandy Loam and Madge Loam Soil. ................................................................................76 Table 24. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Madge Fine Sandy Loam and Madge Loam Soil............77 Table 25. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Madge Fine Sandy Loam and Madge Loam Soil ...........................84 Table 26. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Madge Fine Sandy Loam and Madge Loam Soil ...........................85 Table 27. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Madge Fine Sandy Loam and Madge Loam Soil ............................85 Table 28. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Madge Fine Sandy Loam and Madge Loam Soil ...........................91 viii Table Page Table 31. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Roark Loam Soil ..................................................................................92 Table 32. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Roark Loam Soil .................................................................93 Table 33. Result of Likelihood Ratio Test for the Roark Loam Soil .........................95 Table 34. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Roark Loam Soil .............................................................96 Table 35. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Roark Loam Soil .......................103 Table 36. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Roark Loam Soil ..........................................................................104 Table 37. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Roark Loam Soil ...........................................................................104 Table 38. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Roark Loam Soil ...........................................................................110 Table 41. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Spur Loam Soil ..................................................................................111 Table 42. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Spur Loam Soil .................................................................112 Table 43. Result of Likelihood Ratio Test for the Spur Loam Soil ..........................114 Table 44. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Spur Loam Soil .............................................................115 Table 45. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Spur Loam Soil ..........................122 Table 46. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Spur Loam Soil .............................................................................123 ix Table Page Table 47. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Spur Loam Soil ..............................................................................123 Table 48. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Spur Loam Soil .............................................................................129 Table 51. Initial EPIC Soil Salinity Input Data based on Soil Samples of Spur Clay Loam Soil ................................................................................130 Table 52. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Spur Clay Loam Soil .........................................................131 Table 53. Result of Likelihood Ratio Test for the Spur Clay Loam Soil .................133 Table 54. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Spur Clay Loam Soil .....................................................134 Table 55. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Spur Clay Loam Soil ................141 Table 56. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Spur Clay Loam Soil .....................................................................142 Table 57. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Spur Clay Loam Soil ....................................................................142 Table 58. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Spur Clay Loam Soil .....................................................................148 Table 61. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Tillman Clay Loam Soil .....................................................................149 Table 62. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Tillman Clay Loam Soil ....................................................150 Table 63. Result of Likelihood Ratio Test for the Tillman Clay Loam Soil ............152 Table 64. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Tillman Clay Loam Soil......................153 x Table Page Table 65. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Tillman Clay Loam Soil ...........160 Table 66. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Tillman Clay Loam Soil ..............................................................161 Table 67. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Tillman Clay Loam Soil ................................................................161 Table 68. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Tillman Clay Loam Soil ...............................................................167 Table 71. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Frankirk Loam Soil ............................................................................168 Table 72. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Frankirk Loam Soil ...........................................................169 Table 73. Result of Likelihood Ratio Test for the Frankirk Loam Soil ...................171 Table 74. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Frankirk Loam Soil .......................................................172 Table 75. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Frankirk Loam Soil ..................179 Table 76. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Frankirk Loam Soil ......................................................................180 Table 77. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Frankirk Loam Soil ......................................................................180 Table 78. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Frankirk Loam Soil ........................................................................186 Table 81. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Hardeman Fine Sandy Loam Soil ......................................................187 xi Table Page Table 82. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Hardeman Fine Sandy Loam Soil .....................................188 Table 83. Result of Likelihood Ratio Test for the Hardeman Fine Sandy Loam Soil ................................................190 Table 84. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Hardeman Fine Sandy Loam Soil .................................191 Table 85. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Hardeman Fine Sandy Loam Soil ................................................198 Table 86. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Hardeman Fine Sandy Loam Soil .................................................199 Table 87. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Hardeman Fine Sandy Loam Soil .................................................199 Table 88. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer .............205 Table 91. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Lawton Loam Soil ..............................................................................206 Table 92. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Lawton Loam Soil .............................................................207 Table 93. Result of Likelihood Ratio Test for the Lawton Loam Soil .....................209 Table 94. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Lawton Loam Soil .........................................................210 Table 95. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Lawton Loam Soil ....................217 Table 96. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Lawton Loam Soil ........................................................................218 Table 97. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Lawton Loam Soil .........................................................................218 xii Table Page Table 98. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Lawton Loam Soil ........................................................................224 Table 101. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Westill Clay Loam Soil .....................................................................225 Table 102. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Westill Clay Loam Soil ....................................................226 Table 103. Result of Likelihood Ratio Test for the Westill Clay Loam Soil ...........228 Table 10 4. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Westill Clay Loam Soil ...............................................229 Table 105. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Westill Clay Loam Soil ...........236 Table 106. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Westill Clay Loam Soil ..............................................................237 Table 107. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Westill Clay Loam Soil ...............................................................237 Table 108. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Westill Clay Loam Soil ...............................................................243 Table 111. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Abilene Loam Soil ...........................................................................244 Table 112. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Abilene Loam Soil ..........................................................245 Table 113. Result of Likelihood Ratio Test for the Abilene Loam Soil ..................247 Table 114. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Abilene Loam Soil ......................................................248 Table 115. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Abilene Loam Soil..................255 xiii Table Page Table 116. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Abilene Loam Soil......................................................................256 Table 117. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Abilene Loam Soil......................................................................256 Table 118. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Abilene Loam Soil.......................................................................262 Table 121. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Burford Loam Soil ...........................................................................263 Table 122. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Burford Loam Soil ..........................................................264 Table 123. Result of Likelihood Ratio Test for the Burford Loam Soil ..................266 Table 124. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Burford Loam Soil ......................................................267 Table 125. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Burford Loam Soil ...................274 Table 126. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Burford Loam Soil......................................................................275 Table 127. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Burford Loam Soil......................................................................275 Table 128. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Burford Loam Soil.......................................................................281 Table 131. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Carey Silt Loam Soil ........................................................................282 Table 132. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Carey Silt Loam Soil .............................................................283 xiv Table Page Table 133. Result of Likelihood Ratio Test for the Carey Silt Loam Soil ...............285 Table 134. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Carey Silt Loam Soil ...................................................286 Table 135. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Carey Silt Loam Soil ..............293 Table 136. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Carey Silt Loam Soil ..................................................................294 Table 137. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Carey Silt Loam Soil ...................................................................294 Table 138. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Carey Silt Loam Soil ...................................................................300 Table 141. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Grandfield Fine Sandy Loam Soil ....................................................301 Table 142. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Grandfield Fine Sandy Loam Soil ..................................302 Table 143. Result of Likelihood Ratio Test for the Grandfield Fine Sandy Loam Soil .............................................304 Table 144. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Grandfield Fine Sandy Loam Soil ...............................305 Table 145. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Grandfield Fine Sandy Loam Soil ..............................................312 Table 146. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Grandfield Fine Sandy Loam Soil ..............................................313 Table 147. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Grandfield Fine Sandy Loam Soil ..............................................313 xv Table Page Table 148. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Grandfield Fine Sandy Loam Soil ...............................................319 Table 151. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Tipton Fine Sandy Loam Soil ...........................................................320 Table 152. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Tipton Fine Sandy Loam Soil .........................................321 Table 153. Result of Likelihood Ratio Test for the Tipton Fine Sandy Loam Soil ....................................................323 Table 154. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Tipton Fine Sandy Loam Soil .....................................324 Table 155. Coefficients from SAS Proc Mixed for Dynamic Soil Salinity Levels at Harvest from EPIC Simulations for the Tipton Fine Sandy Loam Soil ....................................................331 Table 156. Coefficients from SAS Proc Mixed of Changes in Soil Salinity from Harvest to Planting from EPIC Simulations for the Tipton Fine Sandy Loam Soil ....................................................332 Table 157. Coefficients from SAS Proc Mixed for Yield Variance ( Function for the Tipton Fine Sandy Loam Soil ....................................................332 Table 158. NPV of Given Salt Concentration and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer for the Tipton Fine Sandy Loam Soil ....................................................338 Table 16. Optimal Irrigation Water and Difference between NPV of Irrigated and Dryland Production for RiskNeutral Producer with 1,280 p.p.m (ECw=2) of Salt Concentration by Soil Texture and Type ......................................343 xvi LIST OF FIGURES Figure Page Figure 1. Study Area ......................................................................................................2 Figure 2. Study Procedure............................................................................................13 Figure 3. Irrigable Soil Area by Soil Type along the Elm and North Fork after Elimination of Soils with 10meter Slopes Greater than Three Percent .......16 Figure 4. Weather Data Generating Process ................................................................18 Figure 5. Soil Sample Points Collected in the Study Area (Source: Oklahoma State University Experiment Station) .....................................................................22 Figure 6. Comparison of the Simulated and Observed Irrigated Cotton Yields for Jackson County Obtained from National Agricultural Statistics Service (NASS) .........................................28 Figure 7. Difference between Observed and Simulated Irrigated Cotton Yield for Jackson County ......................................................................................28 Figure 8. Comparison of the Simulated and Observed Dryland Cotton Yields for Jackson County Obtained from National Agricultural Statistics Service (NASS) .........................................31 Figure 9. Difference between Observed and Simulated Dryland Cotton Yield for Jackson County ......................................................................................32 Figure 10. Environmental Factors Affecting Yield .....................................................36 Figure 11. Statistics and Histogram with the Fitted Gamma Distribution for Growing and NonGrowing Season Rainfall Used in EPIC Simulation ...........................................................................51 Figure 12. Statistics and Histogram with the Fitted Gamma Distribution for Growing and NonGrowing Season Rainfall randomly Generated based on Gamma distribution in Figure 12 for 50 years Planning Horizon of Dynamic Optimization Model ..................................................51 xvii Figure Page Figure 13. Distribution of Growing Season Rainfall and Precipitation of NonGrowing Season Generated based on Gamma Distribution over 50 years ..............................................................................................52 Figure 11. Fiftyyear Average EPIC Simulated Yield Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Tipton Loam Soil ................................................55 Figure 12. Marginal Product of Irrigation Water and Salt Concentration for the Tipton Loam Soil ...........................................................................58 Figure 13. 3D Surface of Crop Response Function versus Responsible Variables for the Tipton Loam Soil ...........................................................................62 Figure 14. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Tipton Loam Soil ...........................................................................68 Figure 15. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Tipton Loam Soil ...........................................................................70 Figure 16. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Tipton Loam Soil ...........................................................................71 Figure 21. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Madge Fine Sandy Loam and Madge Loam Soil ....................................................................................................................75 Figure 22. Marginal Product of Irrigation Water and Salt Concentration for the Madge Fine Sandy Loam and Madge Loam Soil ..........................78 Figure 23. 3D Surface of Crop Response Function versus Responsible Variables for the Madge Fine Sandy Loam and Madge Loam Soil ..........................82 Figure 24. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Madge Fine Sandy Loam and Madge Loam Soil ..........................87 xviii Figure Page Figure 25. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Madge Fine Sandy Loam and Madge Loam Soil ..........................89 Figure 26. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Madge Fine Sandy Loam and Madge Loam Soil ..........................90 Figure 31. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Roark Loam Soil................................................94 Figure 32. Marginal Product of Irrigation Water and Salt Concentration for the Roark Loam Soil ...........................................................................97 Figure 33. 3D Surface of Crop Response Function versus Responsible Variables for the Roark Loam Soil .........................................................................101 Figure 34. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Roark Loam Soil .........................................................................106 Figure 35. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Roark Loam Soil .........................................................................108 Figure 36. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Roark Loam Soil .........................................................................109 Figure 41. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Spur Loam Soil ................................................113 Figure 42. Marginal Product of Irrigation Water and Salt Concentration for the Spur Loam Soil ............................................................................116 Figure 43. 3D Surface of Crop Response Function versus Responsible Variables for the Spur Loam Soil ............................................................................120 xix Figure Page Figure 44. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation and Risk Aversion for the Spur Loam Soil ............................................................................125 Figure 45. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Spur Loam Soil ............................................................................127 Figure 46. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Spur Loam Soil ............................................................................128 Figure 51. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Spur Clay Loam Soil .......................................132 Figure 52. Marginal Product of Irrigation Water and Salt Concentration for the Spur Clay Loam Soil ...................................................................135 Figure 53. 3D Surface of Crop Response Function versus Responsible Variables for the Spur Clay Loam Soil ...................................................................139 Figure 54. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Spur Clay Loam Soil ...................................................................144 Figure 55. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Spur Clay Loam Soil ...................................................................146 Figure 56. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Spur Clay Loam Soil ...................................................................147 Figure 61. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Tillman Clay Loam Soil ..................................151 xx Figure Page Figure 62. Marginal Product of Irrigation Water and Salt Concentration for the Tillman Clay Loam Soil ..............................................................154 Figure 63. 3D Surface of Crop Response Function versus Responsible Variables for the Tillman Clay Loam Soil ..............................................................158 Figure 64. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Tillman Clay Loam Soil ..............................................................163 Figure 65. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Tillman Clay Loam Soil ..............................................................165 Figure 66. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Tillman Clay Loam Soil ..............................................................166 Figure 71. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Frankirk Loam Soil ..........................................170 Figure 72. Marginal Product of Irrigation Water and Salt Concentration for the Frankirk Loam Soil .....................................................................173 Figure 73. 3D Surface of Crop Response Function versus Responsible Variables for the Frankirk Loam Soil .....................................................................177 Figure 74. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Frankirk Loam Soil .....................................................................182 Figure 75. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Frankirk Loam Soil .....................................................................184 Figure 76. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Frankirk Loam Soil .....................................................................185 xxi Figure Page Figure 81. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Hardeman Fine Sandy Loam Soil .................187 Figure 82. Marginal Product of Irrigation Water and Salt Concentration for the Hardeman Fine Sandy Loam Soil ...............................................192 Figure 83. 3D Surface of Crop Response Function versus Responsible Variables for the Hardeman Fine Sandy Loam Soil ...............................................196 Figure 84. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Hardeman Fine Sandy Loam Soil ...............................................201 Figure 85. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Hardeman Fine Sandy Loam Soil ...............................................203 Figure 86. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Hardeman Fine Sandy Loam Soil ...............................................204 Figure 91. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Lawton Loam Soil ...........................................208 Figure 92. Marginal Product of Irrigation Water and Salt Concentration for the Lawton Loam Soil .......................................................................211 Figure 93. 3D Surface of Crop Response Function versus Responsible Variables for the Lawton Loam Soil .......................................................................215 Figure 94. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Lawton Loam Soil .......................................................................220 Figure 95. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Lawton Loam Soil .......................................................................222 xxii Figure Page Figure 96. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Lawton Loam Soil .......................................................................223 Figure 101. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm)of Salt Concentration of Irrigation Water for the Westill Clay Loam Soil .................................227 Figure 102. Marginal Product of Irrigation Water and Salt Concentration for the Westill Clay Loam Soil .............................................................230 Figure 103. 3D Surface of Crop Response Function versus Responsible Variables for the Westill Clay Loam Soil .............................................................234 Figure 104. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Westill Clay Loam Soil .............................................................239 Figure 105. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Westill Clay Loam Soil .............................................................241 Figure 106. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Westill Clay Loam Soil .............................................................242 Figure 111. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Abilene Loam Soil ....................................246 Figure 112. Marginal Product of Irrigation Water and Salt Concentration for the Abilene Loam Soil.....................................................................249 Figure 113. 3D Surface of Crop Response Function versus Responsible Variables for the Abilene Loam Soil.....................................................................253 Figure 114. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Abilene Loam Soil.....................................................................258 xxiii Figure Page Figure 115. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Abilene Loam Soil.....................................................................260 Figure 116. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Abilene Loam Soil.....................................................................261 Figure 121. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Burford Loam Soil ....................................265 Figure 122. Marginal Product of Irrigation Water and Salt Concentration for the Burford Loam Soil.....................................................................268 Figure 123. 3D Surface of Crop Response Function versus Responsible Variables for the Burford Loam Soil.....................................................................272 Figure 124. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Burford Loam Soil.....................................................................277 Figure 125. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Burford Loam Soil.....................................................................279 Figure 126. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Burford Loam Soil.....................................................................280 Figure 131. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Carey Silt Loam Soil ................................284 Figure 132. Marginal Product of Irrigation Water and Salt Concentration for the Carey Silt Loam Soil ...................................................................287 Figure 133. 3D Surface of Crop Response Function versus Responsible Variables for the Carey Silt Loam Soil .................................................................291 xxiv Figure Page Figure 134. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Carey Silt Loam Soil .................................................................296 Figure 135. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.2 m for the Carey Silt Loam Soil .................................................................298 Figure 136. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Carey Silt Loam Soil .................................................................299 Figure 141. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Grandfield Fine Sandy Loam Soil .............303 Figure 142. Marginal Product of Irrigation Water and Salt Concentration for the Grandfield Fine Sandy Loam Soil .............................................306 Figure 143. 3D Surface of Crop Response Function versus Responsible Variables for the Grandfield Fine Sandy Loam Soil .............................................310 Figure 144. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Grandfield Fine Sandy Loam Soil .............................................315 Figure 145. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Grandfield Fine Sandy Loam Soil .............................................317 Figure 146. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Grandfield Fine Sandy Loam Soil .............................................318 Figure 151. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying Irrigation Water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Tipton Fine Sandy Loam Soil ...................322 xxv Figure Page Figure 152. Marginal Product of Irrigation Water and Salt Concentration for the Tipton Fine Sandy Loam Soil ...................................................325 Figure 153. 3D Surface of Crop Response Function versus Responsible Variables for the Tipton Fine Sandy Loam Soil ....................................................329 Figure 154. Average Optimal Application of Irrigation Water and Resulting Cotton Yield from 50year Planning Horizon with Three Levels of Salinity in Irrigation Water and Risk Aversion for the Tipton Fine Sandy Loam Soil ...................................................334 Figure 155. Changes of Quantity of Soil Salinity at Planting and Cotton Yield over 50 years Planning Horizon in case of Absolute Risk Aversion = 0.025 and Soil Depth = 1.5 m for the Tipton Fine Sandy Loam Soil ...................................................336 Figure 156. Net Present Value of Expected Utility of Optimal level of irrigation with Given Levels of Salt Concentration and Absolute Risk Aversion for the Tipton Fine Sandy Loam Soil ...................................................337 1 CHAPTER I INTRODUCTION Problem Statement The United States Army Corps of Engineers (USACE) has asked Oklahoma State University to estimate the net agricultural benefits from reducing the salt loading into the Elm Fork of the Red River just west of the highway 30 bridge in Harmon County. Saline soils and waters contain excessive amounts of soluble salts which preclude the practical and normal production of most agricultural crops. They have been a potential threat for agriculture in a study area. The study area is located along Elm and North Forks of the Red River in Greer, Harmon, Jackson and Tillman Counties of Oklahoma. A major source of the salt is a series of three canyons, which join the Elm Fork in Harmon County. The control point in this area contributes some 510 tons per day of chlorides in Elm and North Fork (Red River Chloride Control Project, 2010). If we use water from the Elm and/or the North Fork as irrigation water, it would quickly increase soil salinity and depress crop yield. Irrigated agriculture depends on adequate and highquality water supplies. As the level of salinity increases in irrigation source, the quality of that water for plant growth decreases. 2 Currently, the USACE is investigating the potential benefits from irrigation if the source of chloride contamination were cut off at the control point. The specific area is defined by sections of land that either transverse or are adjacent to sections transverse by the Elm and North Forks of the Red River. This area is shown in Figure 1. Figure 1. Study Area 3 Although salinity currently precludes irrigation, it is expected the irrigated area would increase rapidly in the study area. However, we do not know the relationship between yield, quality of irrigation water, soil containing salinity and the volume of irrigation water directly. Before applying irrigation in the study area, we need to determine how much of the shaded area in Figure 1 might be economically irrigated, how much salinity affects a cotton yield, and how much irrigation is required under salinity. To assess the relationship between cotton yield, quantity and quality of irrigation water, and soil salinity, the Erosion Productivity Impact Calculator (Williams et al, 1990) crop model simulation will be used. The EPIC simulation model is a research tool usually that is commonly used to determine the response of crop yields to environmental factors. For the purpose of this study, the EPIC will be used to determine potential crop yields for cotton subject to the salinity of surface water and soil salinity with different levels of irrigation water for next 50 years. 4 Objectives The development of irrigable land is one of the fundamental measures for increasing agricultural production. However, the study area is a nonirrigable because of a lack of sufficient ground water for irrigation and the salt load from the chloride control point. If irrigation is expanded along the alluvial plain the Elm and North Fork Rivers, it is important to understand the long term effect of using irrigation water with various levels of salinity on cotton yield based on the different soil types in the study area. The objectives of this study are to 1) estimate the potential cotton response for each soil type to irrigation water and salinity content, 2) estimate the economic viability of establishing irrigation systems to irrigate potentially irrigable soils in the study area along the Elm and North Fork rivers, 3) estimate dynamic soil salinity changes in response to the amount of irrigation water, the salinity of irrigation water, and the soil salinity of the previous year, 4) determine that temporal use of water with the given levels of salt concentration that maximizes the Net Present Value (NPV) from irrigation for each soil type. 5 CHAPTER II REVIEW OF LITERATURE Crop simulation models have some ability to extend the results of crop experiments. The process of the actual experiment such as designing, building, and testing can be expensive and consequently is limited to select area. Simulation models are generally based on experiments covered over a broad geographical area and covers many years. However, crop simulation models can generate the level of detail that we cannot find in actual experiments. It also can be set to run for as many time steps we desire. After proper validation, it can be used to predict the crop yield under environmental changes and expand the results of actual experiments (Jame et al, 1996) Crop simulation with salinity Beginning in 1981, a mathematical model called the EPIC model was developed to determine the relation between soil erosion and soil productivity throughout the U.S.A (Williams, 1990). The EPIC is a field scale and daily time step model composed by soil and crop processes such as an erosion, nutrient balance, and related process. The EPIC crop model has been successfully applied in the study of erosion, water pollution, and 6 crop growth and production. However, there is little literature on crop simulation with salinity. Tayfur et al (1996) provides useful evidence on the salinity effect on decreasing crop yields. They extended the EPIC to consider the effects of root zone salinity in alfalfa production on a field scale under optimal and under water stress or limited irrigation conditions. The revised model was calibrated and validated with field data. The results suggest that an increase in salt concentration in applied irrigation water would dramatically decrease the total alfalfa yield under irrigation treatments. Experiment with salinity Salinity problems occur because irrigation water contains some amount of soluble salts. Evaporation and transpiration by plants leave these salts in the soil. These salts accumulate over time in soil and affect the crop yields. The matter of soil salinity and the use of irrigation water containing soluble salts is one of the major considerations when irrigation is used in the study area. The response function of the crop yield to salinity is an important factor in an economic model. There is considerable literature available on crop yield response to irrigation water and salinity with experimental data. Yaron and Bresler (1970) determined the efficient combination of water quantity and quality in irrigation under specific field conditions. They used to a linear programming model to derive the optimal quantityquality combinations under different levels of irrigation water and initial soil salinity. The authors used a leaching model to trace the salt distribution in the soil profile and restrictions on the chloride concentration in the soil solution. They compared the 7 empirical estimates of the marginal rate of substitution of water salinity for quality with the cost of the water quantity and quality ratio. Unfortunately, information on the cost did not exist at that time. However, in the empirical estimates from the linear programming model, they found that as the quantity of irrigation water applied increases, the maximum permissible chloride concentration in irrigation water also increases. Dinar and Knapp (1986) provide econometric estimates of yield response and salt accumulation in the soil under saline conditions with experimental data for alfalfa and cotton. They estimated to log and quadratic functions of yield and soil salinity. The dependent variables of crop yield and soil salinity at the end of the growing season were regressed on quantity of rainfall and applied irrigation water during the growing season, salt concentration of the irrigation water, soil salinity of the root zone at planting time, and pan evaporation during the growing season. The log yield response functions and the log soil salinity relations moved for alfalfa and cotton as they expected. The crop yield increases as water quantity increases, salt concentration decreases and soil salinity decreases. The quadratic yield function showed unexpected patterns. The crop yield generally increases as the quantity of water increases. However, when the quantity of water is held constant, the yield increases as initial soil salinity increases. The log soil salinity relations also exhibit for alfalfa and cotton as they expected. Ending soil salinity decreases as water quantity increases, salt concentration decreases. The quadratic soil salinity relations also did not behave as they expected. Ending salinity decreases as initial soil salinity increases, holding water quantity constant. They added the pan evaporation variable on the log and quadratic functions of yield and soil salinity. Its coefficient was a negative in yield response functions and a positive in soil salinity relations indicating the 8 crop yield decreases and soil salinity increases as the pan evaporation decreases. In addition, they combined the estimated response functions and dynamic soil salt relations with an economic decision model to determine water applications for any give prices and initial soil salinity which maximize the net present value of profits. Profits increase as crop prices increase, decrease as irrigation water prices increase, and decrease as initial soil salinity increases. Contrary to their expectation, they found that profits increase as the initial soil salinity increase with a range of salinity EC levels from 4 to7 for alfalfa. Dinar et al (1991) provided statistical estimates of cropwater response functions with various levels of salinity. They estimated the quadratic and loglog response function of yield, soil salinity and drainage volume for wheat, sorghum and wheatgrass in terms of the quantity and quality of the applied irrigation water and the initial level of root zone salinity at the beginning of the growing season. Their data came from a fouryear lysimeter experiment. Coefficients from SAS Proc Mixed for the quadratic function were statistically significant and the function described the relative effects of input water quality and quantity on yield, soil salinity, and drainage volume for three crops. In case of the loglog response function, the estimated coefficients for water quantity were greater than or close to 1 for wheat and wheatgrass. This indicates that any increase in water quantity would increase yield with all other variables being constant. They found that final soil salinity increased with small amounts of irrigation water and then decreased with larger amounts of irrigation water. They also found that amount of and/or requirement for drainage increased as applied irrigation water increased, as the level of initial soil salinity increased, and as the salt concentration in irrigation water increased for three crops. 9 Feinerman (1994) estimates the response function to soil salinity of a given crop (potatoes) in a singlefarm framework. He uses a switching regression to estimate a piecewise linear response function. Crop yield is dependent of average soil salinity below a certain critical threshold, and thereafter decreases linearly. Datta et al (1998) estimate a set of production functions relating wheat yield to initial soil salinity and water quantity and quality. They used the functions to find optimal water application for given irrigation water quality, reuse of drainage water, reduction in income from using saline drainage waters mixed at various rates with good quality water. Crop yield response functions fitted to experimental data were quadratic, CobbDouglas and linear. They found that the quadratic function provided a better fit to the data for the response of cotton yield to selected variables than did the linear or CobbDouglas functions. They suggest that yield is not simply related to the average initial soil salinity but also to the salinity in irrigation water applied. Kiani and Abbasi (2009) used experimental data to investigate crop response to both soil water content and soil salinity. They estimated linear, CobbDouglas, quadratic, and transcendental functions. They compared the various production functions in terms of their Fvalue, R2, standard error (SE), and relative error (RE). They found the quadratic and transcendental functions predicted yield response very well. They also found that both soil water content and soil salinity affected the variation of yield. The effect of soil salinity on yield increases as soil water content is increased. 10 CHAPTER III METHODOLOGY Conceptual Framework The response function of a crop yield to soil salinity is an important factor in an optimization model concerning irrigation or irrigation systems with water salinity (Feinerman, 1993). In this study, the specific yield response function will be estimated from the EPIC simulation results. The EPIC model will be used to simulate the yield of cotton on the soil types in the study area. The simulation will use different levels of irrigation, water salinity, and soil salinity. The results will indicate the changes in yield over time to soil salinity for each soil type in the study area. This approach has assumptions that the given crop was directly affected by irrigation water, water salinity, soil salinity and other possible factors (Datta, 1998). These functions were measured by Dinar and Knapp (1986), Dinar et al (1991), Datta (1998) and Kiani and Abbasi (2009). The general relationships of the factors for an individual soil type are specified as follows: 11 where Y is a crop yield per unit area, Irr is a quantity of irrigation water applied in acrefeet, WS is the dissolved salts in irrigation water, SS is the salt in the soil profile, X is a vector of all other factors affecting the crop yield and t is the simulation year. The estimated crop response function and the dynamic soil salinity function can be incorporated into an economic decision model to determine optimal level of irrigation levels maximizing the net present value of profits. The dynamic programming optimization for individual soil types in the study area is constructed as follows: subject to where Py is the price of cotton ($/lb), Yt is the cotton yield function (lbs/acre), is the quantity of irrigation water applied (acrefeet), is the irrigation cost ($/acrefeet), and is total costs except for the irrigation cost. 12 Data and Procedure In this study, it is necessary to complete the following steps to estimate the net agricultural benefits from reducing salt loading and expanding irrigation along the Elm and North Fork of the Red River. These steps include: 1) Determine the location and area of potentially irrigable soils along the Elm and North Forks 2) Establish soil parameters by depth for each of the irrigable soil types to be simulated 3) Establish crop management data and enterprise budgets for cotton 4) Use the EPIC model to simulate cotton yield and soil salinity for each of the major irrigable soil types identified in step 1 5) Calibrate the EPIC simulation model to conditions in Jackson County 6) Generate fifty years of daily maximum/minimum temperature, precipitation and solar radiation 7) Simulate and estimate the crop response functions and dynamic soil salinity functions for each soil type with randomly generated weather data 8) Set up and solve the necessary dynamic optimization models 13 Figure 2 represents the different implementation and solution steps graphically. Figure 2. Study Procedure The procedure consists of several different steps to achieve the academic purpose. It also includes applications of the Geographic Information System (GIS) technology and Historical Weather Data Stochastic weather Input Data Soil Input Data Crop management Input Data a EPIC Run & Calibration Simulation of Yield and Soil salinity with irrigation water and water salinity Yield Response Function and Soil Salinity Dynamics Nonlinear Dynamic Programming to Determine Maximum Potential Profit from Irrigation GIS Analysis 14 Erosion Productivity Impact Calculator (EPIC) crop simulation model. GIS is used to capture the potentially irrigable soil types in the study area. It allows us to view, understand and visualize soil data. The EPIC model is able to utilize the soil data, plant parameters, and weather conditions to more accurately predict crop response yield to environmental factors in agriculture. This approach will offer the decision maker opportunities to have a crop management tool with economic considerations under the limitation of environmental conditions. 1. GIS Analysis Irrigation is one of the major measures for increasing the production of agriculture. It can be seen that the development of irrigable land is one of the fundamental measures for increasing agricultural production, but not all soil types are suitable for irrigation. Finding the area of irrigable soil types will be the first step for making group of soil for their sustained use under irrigation. GIS technology is a very useful tool to locate and determine the extension of irrigable soil in the study area. The study area consists of sections of land which are transversed by or are adjacent to sections that are transversed by the Elm and North Forks. The study area is made up of 339 640acre sections. The approximate coordinates for latitude and longitude of Chloride Control Point are 35.0 N and 99.9 W respectively. The original soil map of the study area contains various types of soils. Each soil type map has a land capability classification. To find irrigable soil types, we use the land 15 capability classification obtained from SSURGO (Soil Survey Geographic database) soil data provided by the Natural Resource Conservation Service (NRCS). The land capability classification means the land categories according to the suitability of soil quality for the potential agricultural output. The National Soil Survey Handbook provides the definition of the land capability classification. Class codes I, II, III, IV, V, VI, VII, and VIII are used to represent land capability classes. Class codes I to VIII indicate progressively greater limitations and narrower choices for agriculture. Class I and Class II (2e and 2w) are chosen as irrigated land capability class for determining the most productive soils to irrigate. By definition, Class I soils have few limitations that restrict their use. Class II soils have moderate limitations that reduce the choice of plants or require moderate conservation practices. The land capability classification includes the capability subclass. The capability subclass is the second category in the land capability classification system. Class codes e, w, s, and c are used for land capability subclasses. Briefly, e, w, s and c are related with erosion problems, wetness problems, root zone limitations, and climatic limitations respectively. Subclass e and w are chosen for defining irrigable soil types. Land capability classification is made by adding the subclass e, w, s and c to class codes. I, IIe and IIw classes as the potential irrigated soil class are used in this study (National Soil Survey Handbook, USDA). The irrigable soil areas that satisfy conditions of the land capability classification (I, IIe, and IIw) are found in Figure 5. Many types of irrigable soils still remain in the study area. The major irrigable soil types having the largest areas were selected to collect soil samples from actual fields. Potential major irrigable soil types found will be used as an individual soil input data for the EPIC simulation. 16 Figure 3. Irrigable Soil Area by Soil Type along the Elm and North Fork after Elimination of Soils with 10meter Slopes Greater than Three Percent 17 2. EPIC Simulation The Erosion Productivity Impact Calculator (EPIC) is a crop simulation model that can be used to assess the impact of weather, soil, water resources, and management strategies on agricultural production. It is useful as both a decisionmaking tool from the farm level to the national level and as a research tool. It can simulate alternative management strategies and develop, test and refine model components for simulating various physical and chemical processes (Williams et al, 1990). The potential cotton yield in response to soil salinity, response to irrigation water, response to salinity in irrigation water will be simulated using the EPIC version 0509. EPIC simulations will be used to estimate cotton yields based on daily estimates of soil salinity, rainfall and temperature for next 50 years. Input data for the EPIC include weather, soil, crop management, and specific site information. It also includes parameter data files for major crops, fertilizers, and tillage practices (Cabelguenne et al, 1990). Weather Data Generation The EPIC simulation runs on a daily time step requiring the input of daily weather data. Minimum input requirements to set up weather data are daily precipitation and minimum and maximum temperature and latitude and longitude for the specific weather station. Historical daily weather data can be directly used in the EPIC simulation when the length of historical daily weather is the same as the simulation period. It is also used to generate monthly weather statistics using the WXPM 3020 (Williams et al, 2006) weather simulator (ftp://ftp.brc.tamus.edu/pub/epic/wxparm/). 18 The EPIC program can simulate daily weather with the aid of a stochastic weather generator called the WXGEN (ftp://ftp.brc.tamus.edu/pub/epic/wxgen/) (Liu et al, 2009). The WXGEN can generate daily weather based on the monthly input statistics. A stochastic weather generator produces artificial daily time series of weather data based on the statistical characteristics of historical or observed weather at a specific location. Figure 4 represents the weather data generating process with the WXPM3020 program and stochastic weather generator the WXGEN. Figure 4. Weather Data Generating Process The historical daily weather data for precipitation and minimum/max temperature from 1950 to 2006 at Jackson country obtained from National Climatic Data Center were used as the baseline weather data. The monthly weather statistics can be generated from Historical Weather Data from1950 to 2006 Monthly Weather Statistics using WXPM3020 Random Daily Weather Data for the years 2011 to 2060 using WXGEN 10 Random Daily Weather Data Sets for EPIC Run (by Aaron Mittelstet) 19 the historical daily data by using the WXPM 3020 program. When the monthly weather statistics is available, the WXGEN is a useful tool in generating daily weather data (Liu et al, 2009). The WXGEN was used to randomly generate daily solar radiation, precipitation and minimum/max temperature for the years 2011 to 2060 based on the means, standard errors, and skew coefficients in the monthly weather statistics of the baseline weather data. 10 Random Daily Weather Data Sets for EPIC Run were generated by Aaron Mittelstet who is a research engineer of Biosystems and Agricultural Engineering in Oklahoma State University. Table 1 shows the monthly statistics of the baseline weather data from years 1950 to 2006. 20 Table 1. Monthly Statistical Properties of the Daily Historical Weather Data at Altus Station, OK from years 1950 to 2006 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TMX 12.04 15.55 20.13 25.92 30.40 34.62 36.21 34.13 29.77 23.93 16.21 12.21 TMN 2.57 0.33 4.55 10.43 15.62 19.95 21.48 19.57 15.02 8.60 1.99 1.83 SDMX 7.95 8.21 8.21 6.72 4.95 4.05 3.71 6.06 5.82 6.65 7.17 7.24 SDMN 5.25 5.45 5.41 5.26 4.36 3.11 2.22 3.61 5.25 5.74 5.51 4.90 PRCP 25.01 30.73 43.33 57.99 115.00 83.12 57.05 61.50 72.71 61.31 28.80 25.33 SDRF 9.43 10.93 11.42 13.16 17.64 19.25 13.15 17.70 18.04 19.43 9.02 9.16 SKRF 2.37 4.09 2.45 2.09 2.23 2.93 2.20 3.49 3.05 3.99 1.78 2.21 PWD 0.08 0.10 0.12 0.13 0.20 0.14 0.12 0.13 0.12 0.11 0.08 0.08 PWW 0.28 0.32 0.31 0.34 0.34 0.35 0.35 0.35 0.46 0.37 0.35 0.32 DAYP 3.05 3.70 4.54 4.95 7.32 5.18 4.82 5.18 5.35 4.61 3.35 3.21 Note: Variable definitions are as below. TMX: Maximum daily air temperature (Â°C) TMN: Minimum daily air temperature (Â°C) SDMX: Monthly average standard deviation of daily maximum air temperature (Â°C) SDMN: Monthly average standard deviation of daily minimum air temperature (Â°C) PRCP: Precipitation (mm) SDRF: Monthly standard deviation of daily precipitation (mm) SKRF: Monthly skew coefficient for daily precipitation (mm) PWD: Monthly probability of wet day after dry day PWW: Monthly probability of wet day after wet day DAYP: Number of days with precipitation 21 Soil Data Soil is one of the important input components. Soil parameters should be prepared for the EPIC run. Soil data are composed of relevant physical and chemical parameters. Although up to ten soil layer parameters can be input into the EPIC, five or six soil layers were used to in this study set up soil input data. The following minimum parameter set was used on all soil types: soil albedo, soil hydrologic group, depth to bottom of layer, bulk density, percentage of sand, percentage of silt, soil pH, cation exchange capacity and electrical conductivity (EC). Table 2 shows the example of one of the irrigable soil types (Tipton Loam soil) used in the EPIC simulation as soil input data. Table2. Tipton Loam Soil Input Data for EPIC Model Tipton Loam Soil (Albedo =0.09, hydrologic group = B) Soil layers 1 2 3 4 5 6 Depth(m) 0.15 0.3 0.6 0.9 1.2 1.5 Bulk Density(t/m3) 1.43 1.43 1.5 1.5 1.5 1.5 Sand (%) 43.2 43.2 33.5 34.4 34.4 34.4 Silt (%) 38.8 38.8 36.5 37.6 37.6 37.6 Soil PH 6.7 7.5 7.8 7.9 8 8.1 Cation Exchange Capacity (cmol/Kg) 12.8 12.8 17 17 17 15.3 Electrical Conductivity (mmho/cm) 0.78 1.08 1.47 1.17 1.33 2 Values of soil pH and EC at different depths in the soil profile were obtained from the soil test conducted by the Oklahoma State University (OSU) Experiment Station 22 (Zhang et al, 2011). Other values are obtained from Soil Survey Geographic (SSURGO) Database in Natural Resource Conservation Service (NRCS). The OSU Experiment Station collected samples of potentially irrigable soil affected by chloride loading at the control point along the Elm and North Fork of the Red river. The collected soil samples were located based on the result of GIS analysis. Figure 5 shows that 37 samples were collected along the Elm Fork across Greer County and 26 along the North Fork across Jackson, Kiowa and Tillman County. All 63 soil samples are classified into 15 soil types. Table 3 lists the soil samples along the Elm and North Fork rivers. Figure 5. Soil Sample Points Collected in the Study Area (Source: Oklahoma State University Experiment Station, 2009) ^!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(!(HarmonJacksonKiowaTillman23 Table 3. Tested and Collected Irrigable Soil Samples Tested soil group Collected soil group County Samples Abilene loam Abilene loam, 01% slopes Tillman 1 Burford loam Burford loam, 13% slopes Tillman 1 Carey silt loam Carey silt loam, 13% slopes Kiowa 1 Frankirk loam Frankirk loam, 1 3 % slopes Greer 2 Grandfield fine sandy loam Grandfield fine sandy loam, 13% slopes Jackson 1 Hardeman fine sandy loam Hardeman fine sandy loam, 01% slopes Jackson 1 Hardeman fine sandy loam, 13% slopes Jackson 2 Lawton loam Lawton loam, 01% slopes Greer 2 Madge loam and Madge fine sandy loam Madge fine sandy loam, 13% slopes Greer 3 Madge loam, 1 3% slopes Greer 2 Madge loam, 13% slopes Jackson 1 Roark loam Roark loam, 0 1% slopes Greer 6 Roark loam, 01% slopes Jackson 2 Spur clay loam Spur clay loam, 0 1% slopes, occasionally flooded Greer 4 Spur clay loam, 01% slopes, occasionally flooded Jackson 1 Spur clay loam, 01% slopes, rarely flooded Greer 2 spur loam Spur loam, 0 1% slopes, occasionally flooded Greer 6 Tillman clay loam Tillman clay loam, 13% slopes Kiowa 1 Tillman clay loam, 13% slopes Jackson 3 Tipton fine sandy loam Tipton fine sandy loam, 01% slopes Tillman 1 Tipton fine sandy loam, 01% slopes Jackson 1 Tipton loam Tipton loam, 0 1% slopes Jackson 5 Tipton loam, 0 1% slopes Tillman 3 Tipton loam, 01% slopes Greer 8 Tipton loam, 13% slopes Tillman 1 Westil clay loam Westill clay loam, 13% slopes Greer 2 Source: Oklahoma State University Experiment Station, 2009 24 Crop Management Data The EPIC simulation program also requires data on the details of farm operations such as planting and harvesting timing, plant population, type and amounts of fertilizer and pesticides applied, potential heat units and others for the specific crop cultivating in the study area. Since the EPIC model simulates the potential cotton yield for next 50 years, actual information of crop operation schedule is not fully available. Most of the economic data were obtained from the cotton budget (Oklahoma State University Extension, 2011). We assume that the farmers in the study area follow this crop operation schedule. Table 4. Summary of Crop Operation Data in EPIC Model Month Cropping Practice Dryland Irrigation April Bedder Tillage, Dry Fertilizer and Pesticide Bedder Tillage, Dry Fertilizer and Pesticide May Planting and Row Cultivation Planting and Row Cultivation June Pesticide Pesticide and Irrigation July Irrigation August Pesticide Pesticide and Irrigation October Harvest Ginning, Bagging and Ties Pesticide, Harvest Ginning, Bagging and Ties November Kill and Shredder Tillage Kill and Shredder Tillage December Field Cultivation Field Cultivation Source: OSU Enterprise Budget Software, 2011 25 Usual planting dates for cotton in Oklahoma are from May second until June eighteenth and harvesting dates are from October fourth through December twenty fourth (Usual Planting and Harvesting Dates for U.S. Field Crops, 2010). The duration of growing season used for the EPIC simulations was 160 days from May sixth to October twelfth. Dry fertilizer, Vydate LV, Pix, Roundup Max, Pix 8, Prep and Def 6 for pesticide were assumed to be applied in the study area during the crop growing season. Model Evaluation To validate the estimated crop response function, it is necessary that the EPIC simulation accurately predicts the observed yield. The evaluation is generally reported as a comparison of simulated and observed variables. It can be expected the simulated cotton yields will be overestimated because the EPIC model does not consider disease, insects and severe weather conditions such as hail. The parameters used to calibrate the EPIC model are shown in Table 5. Table 5. Parameters related to Cotton Yield in EPIC Model Crop Parameters Symbol* Parameters Used Initial Parameters BiomassEnergy Ratio WA 20 20 Harvest Index HI 0.5 0.55 Potential Heat Unit PHU** 1760 1200 ~2400 Plant Population (plants/m2) 8.5 7.41 ~ 12.35 Note : (*) Symbols of parameters are used in the EPIC model. (**) Range of PHU for South and East Texas is from 1200 to 2400 which was defined by Ko et al (2009) and Wang et al (2005) respectively. 26 The parameters varied to calibrate the EPIC model were the Biomass Energy Ratio (WA), Harvest Index (HI), Potential Heat Unit (PHU) and Plant Population. The values used were based on literature and researcherâ€™s knowledge. According to the EPIC user guide for version 0509 (Williams et al 2006), the BiomassEnergy Ratio (WA) is the potential growth rate per unit of intercepted photosynthetically active radiation. Harvest Index (HI) is the percent of economic yield to the above ground biomass. The Potential Heat Unit (PHU) is the number of heat units expected for a typical growing season from plant to maturity. The optimal plant population for cotton has a wide range from 30,000 to 50,000 plants per acre, which can be converted into 7.41 to 12.35 plants per m2 (Hake et al, 1996). These parameters were adjusted up or down until the simulated yield matched the 7year observed yield of Jackson County. The cotton yield at the county level was used to calibrate and validate the EPIC model. The EPIC model performance is evaluated by the paired ttes for mean. It is used to investigate the relationship between two groups when each data point in one group corresponds to matching data point in the other group. It starts with comparing the means of each group of observations and simulations in this study. The observed variables for evaluation of the EPIC model are the dryland and irrigated cotton yields (lb/acre) of Jackson County obtained from National Agricultural Statistics Service (NASS) from years 2000 to 2006. The LugertAltus Irrigation District in Jackson County covers approximately 48,000 acres and the annual irrigation delivery from Lake Altus for irrigation has varied from a low of 13,600 acrefeet in 1953 to a high of 106,542 acrefeet in 1998 (W.C. 27 Austin Project, 2005). The district supplies more than 85,000 acft/acre of irrigation water to about 300 cotton farms in the area every year (Bimonthly Newsletter of OWRB, 2000). Salinity levels in the reservoir ranged from 1.8 to 2.4 EC levels (Oklahoma's Beneficial Use Monitoring ProgramLakes Sampling, 2009). For the model evaluation, it was assumed that approximately 1.64 acft/acre per acre of irrigation water with an EC level of 2 from the LugertAltus Reservoir is applied for each simulation year. The Holister Silty Clay Loam soil, which is a predominant soil type in the LugertAltus Irrigation District was used in Jackson County. Some of the more important properties of Holister Silty Clay Loam soil are shown Table 6. Table 6. Holister Silty Clay Loam Soil Properties used in EPIC calibration for Jackson County Cotton Yield Holister Silty Clay Loam (Albedo =0.16, hydrologic group = D) Soil layers 1 2 3 4 5 6 Depth(m) 0.15 0.3 0.6 0.9 1.2 1.5 Bulk Density(t/m3) 1.4 1.48 1.48 1.48 1.48 1.48 Sand (%) 10 22.5 22.5 22.5 22.5 22.5 Silt (%) 56.5 32.5 32.5 32.5 32.5 36.5 Soil pH 7.74 7.65 7.66 7.82 7.9 7.88 Cation Exchange Capacity (cmol/Kg) 22.5 27.5 27.5 27.5 27.5 27.5 Electrical Conductivity (mmho/cm) 1.92 7.29 8.85 8.4 7.64 7.95 An Oklahoma State University (OSU) Experiment Station soil sampling study provided data on Soil pH and EC levels at different depths in the soil profile (Zhang et al, 2011). Other Data were obtained from the Soil Survey Geographic (SSURGO) Database in Natural Resource Conservation Service (NRCS). 28 Figure 6 shows the comparison between the observed and simulated cotton yield with irrigation levels of 1.64 acft/acre with a salinity level EC of 2. The paired ttest for mean was used to test the null hypothesis of no difference between simulated and observed cotton yield. Figure 7 shows the difference two groups (Observed cotton yield  Simulated cotton yield) for irrigation. Figure 6. Comparison of the Simulated and Observed Irrigated Cotton Yields for Jackson County Obtained from National Agricultural Statistics Service (NASS) Figure 7. Difference between Observed and Simulated Irrigated Cotton Yield for Jackson County 0 200 400 600 800 1000 1200 2000 2001 2002 2003 2004 2005 2006 Yield (lb/acre) Years Observed Cotton Yield Simulated Cotton Yield 200 100 0 100 200 2000 2001 2002 2003 2004 2005 2006 Yield (lb/acre) Years Observed  Simulated Yield 29 If a statistical tvalue is less than a critical tvalue or pvalue is larger than a significant level , we fail to reject the null hypothesis. Therefore, we conclude that there is no evidence of statistically significant difference between the two groups. Table 7 shows the results of the paired t test using the SAS program. Table 7. Results of Paired ttest for the mean of Observed and Simulated of Irrigated Cotton Yields in Jackson County Observed Yield (lb/acre) Simulated Yield (lb/acre) Mean of each group 1025 985 Observations 7 7 Mean Difference in Yields 40 Standard Deviation of Difference 119 Statistical t value* 0.89 pvalue 0.41 Critical tvalue 2.45 Note: (*) indicates statistical tvalue is defined as where is a mean difference of yields of two group, is a standard deviation of difference and n is observations. Since the statistical tvalue (= ) is less than the critical tvalue (=2.45) and pvalue (=0.41) is larger than the significant level , we fail to reject the null hypothesis. We conclude that there is no statistical difference at the 95% confidence level between the observed cotton yield group and simulated cotton yield group. Table 8 shows the summary statistics of relative error, NashSutcliffe efficiency and coefficient of determination (R2) for observed and simulated irrigation cotton yield after calibration. 30 Table 8. Results of Yearly EPIC Model Calibration for Irrigation Cotton Yield in Jackson County for the Period from 2000 to 2006 Mean of Observed Yield (lb/acre) Mean of Simulated Yield (lb/acre) Relative Error* NashSutcliffe Efficiency** Coefficient of Determination (R2)*** 1025 985 4% 0.01 0.68 Note: (*) Relative Error is defined as R.E = â€“. (**) NashSutcliffe Efficiency is defined as E = with O observed and S simulated Yield. (***) Coefficient of Determination (R2) is obtained from outputs of linear regression. Relative Error is generally represented as percentage of the absolute error of simulated value minus observed value divided by observed value to assess the error between two models. NashSutcliffe efficiency and coefficient of determination (R2) are used to assess how well EPIC simulated cotton yield fits the observed cotton yield. NashSutcliffe efficiency is defined as one minus of the absolute squared difference between the observed and simulated values divided by the variance of the observed values for 7 target year. The range of NashSutcliffe efficiency is between  âˆž to 1. The efficiency of 1 means the simulated data perfectly fits the observed data. The efficiency of 0 indicates that the simulated model predictions are as accurate as the mean of the observed data, whereas the efficiency of lower than zero indicates that the mean of the observed data is a better predictor than the simulated model. Coefficient of determination (R2) can be obtained from outcomes of linear regression of two data. R2 is generally used as a measure of goodnessoffit of linear regression which the range of R2 is between 0 and 1. The R2 values of 1 means observed data perfectly fits simulated data whereas the R2 values of 0 means observed data does not fit any simulated data. Generally, if 31 Relative Error is within 5%, NashSutcliffe efficiency is larger than 0.4 and Coefficient of determination (R2) is larger than 0.6, the simulated model well performed with prediction of observed cotton yield (Wang et al, 2006). Relative Error between the observed and simulated mean of irrigation cotton yield is less than 5%. NashSutcliffe Efficiency is close to zero indicating the simulated model predictions are as accurate as the mean of the observed data. Coefficient of Determination (R2) is 0.68 indicating simulated model well explains the variation of observed data. To ensure the reliability of the parameters used in the calibration for the irrigation system, the parameters were also applied to dry land (nonirrigation). Figures 8 and 9 show the comparison of the observed and the simulated dryland cotton yields between the years 2000 and 2006. Figure 8. Comparison of the Simulated and Observed Dryland Cotton Yields for Jackson County Obtained from National Agricultural Statistics Service (NASS) 0 100 200 300 400 500 600 700 800 2000 2001 2002 2003 2004 2005 2006 Yield (lb/acre) Years Observed Cotton Yield Simulated Cotton Yield 32 Figure 9. Difference between Observed and Simulated Dryland Cotton Yield for Jackson County Results of paired ttest for the mean of observed and simulated dryland yield using SAS program are shown in Table 10. Table 9. Results of Paired ttest for the mean of Observed and Simulated of Dryland Cotton Yields in Jackson County Observed Yield (lb/acre) Simulated Yield (lb/acre) Mean of each group 375 426 Observations 7 7 Mean Difference in Yields 51 Standard Deviation of Difference 125 Statistical t value 1.07 pvalue 0.32 Critical tvalue 2.45 Note: (*) indicates statistical tvalue is defined as where is a mean difference of yields of two group, is a standard deviation of difference and n is observations. 200 100 0 100 200 2000 2001 2002 2003 2004 2005 2006 Yield (lb/acre) Years Observed  Simulated Yield 33 Since the statistical tvalue (= ) is less than the critical tvalue of 2.45 and the pvalue of 0.32 is larger than significant level , we fail to reject the null hypothesis. We conclude that there is no statistical difference at the 95% confidence level between the observed cotton yield group and simulated cotton yield group. Table 11 shows the summary statistics of relative error, NashSutcliffe efficiency and coefficient of determination (R2) for observed and simulated dryland cotton yield after calibration. Table 10. Results of Yearly EPIC Model Validation for Dryland Cotton Yield in Jackson County for the Period from 2000 to 2006 Observed Yield (lb/acre) Simulated Yield (lb/acre) Relative Error NashSutcliffe Efficiency Coefficient of Determination (R2) 375 426 14% 0.61 0.69 Note: (*) Relative Error is defined as R.E = . (**) NashSutcliffe Efficiency is defined as E = with O observed and S simulated Yield. (***) Coefficient of Determination (R2) is obtained from outputs of linear regression. Relative Error between the observed and simulated mean of irrigation cotton yield is larger than 5% indicating that there are some deviation between mean of observed and simulated dryland cotton yield. However, NashSutcliffe Efficiency is 0.61 indicating the simulated data well fits the observed data. Coefficient of Determination (R2) is 0.69 indicating simulated model well explains the variation of observed data. 34 The results of calibration and validation process indicate the EPIC simulated yields matched observed yields for the 7target year. The calibrated and validated parameters related to cotton yield were used to simulate the potential cotton yield and soil salinity with different levels of irrigation water and water salinity for the next 50 years. Simulation Design and process After setting up the input data, the EPIC program was used to simulate the cotton yield, soil salinity and other variables for next 50 years. A simulation design is much like that of an agronomic field experiment. The designed simulation is applied with combinations of three different levels of plant water stress, three different levels of salt concentration of irrigation water and 10 stochastic weather scenarios over a 50year period. EPIC offers two options for irrigation. Sprinkler or furrow irrigation can be simulated by fixed or automatic option. The fixed option requires that application dates and amounts be specified in advance by the EPIC users. With the automatic option, the model decides when and how much water to apply. The user must input the plant water stress level to trigger automatic irrigation, the maximum volume applied per growing season, and the minimum time interval between applications (Williams, 1990). The automatic irrigation option was selected for use for this study to represent a more realistic irrigation practice. Plant water stress factors to trigger automatic irrigation were set at 0.1, 0.5 and 0.9. This factor ranges from zero (high stress) to one (no stress) and is computed 35 as the ratio of actual plant water use to potential water use (Easterling et al, 1992). When plant water stress factor was set at 0.1, a total irrigation application is applied under 200 mm and the range of an amount of water for single application was limited to 50 mm. Similarly, when plant water stress factor was set at 0.5 and 0.9, a total irrigation application is applied under 800 mm and the range of an amount of water for single application was limited to 200 mm. The minimum interval between irrigations was set at 20 days during the growing season. The three levels of salt concentration of irrigation water represent 0, 1,280, and 2,560 p.p.m (parts per millions). Salt concentration in p.p.m can be generally expressed in terms of Electrical Conductivity (EC). It is assumed that 1 EC (mmhos/cm) in irrigation water is equal to 640 p.p.m. These units of measurement can be converted to tons of salt per acre foot as follows (Agriculture Handbook No. 60, USDA): 640 p.p.m = 1 EC mmhos/cm 1 p.p.m Ã— 0.00136 = Tons per AcreFoot For example, 0, 1,280 and 2,560 p.p.m of salt concentration can be converted to 0, 2 and 4 of EC and 0, 1.74 and 3.48 tons/acft. In addition, 1,280 p.p.m of the salt concentration are equal to 2 mmhos/cm of EC or 1.74 tons of salt for every foot of irrigation water applied. If during the growing season, 400mm (1.3 acft) of irrigation water is applied, the amount of salt in irrigation water is approximately 2.263 tons/acre (1,280 ppm Ã— 0.00136 Ã— 1.3). From this example, we can expect that the amount of salts in irrigation water can quickly increase the salinity level in the soil. 36 Based on the simulation design, a total of 90 simulations (3Ã—3Ã—10) were conducted for each soil type in the study area. The variables we need to estimate cotton yield and soil salinity response functions were taken from EPIC output. Figure 10 illustrates how cotton yield and soil salinity are affected by environmental factors. During and before the growing season, cotton yield is affected by irrigation water applied, rainfall, soil salinity at planting, salinity in irrigation water. Total water used in the field is equal to irrigation water applied plus rainfall. Total salinity is equal to soil salinity at planting plus the amount of salt in irrigation water. From irrigation water, salts accumulate in the root zone. Soil salinity at harvest assumes to be affected by irrigation water, rainfall, soil salinity at planting and the amount of salt in irrigation water. Soil salinity at planting is assumed to be affected by nongrowing season rainfall and soil salinity at harvest on the previous year. Figure 10. Environmental Factors Affecting Yield Irrigation, Rainfall Soil Salinity at plant, Salinity in Irrigation water Rainfall Planting day May, next year Harvesting day October Planting day May NonGrowing Season Growing Season 37 The simulated cotton yields, irrigation water and growing season rainfall can be selected from the annual crop yield output file (*.ACY). In case of soil salinity levels at planting and harvest, they can be found in the Daily Soil Table output file (*.DSL) which is generated on a daily basis for each soil layer. Nongrowing season rainfall was calculated by subtracting growing season rainfall from the sum of the monthly precipitation in Monthly Flipsim output file (*.MFS). The variables, descriptions and their unit conversions are shown in Table 9. Data selected from the EPIC output file are used to estimate cotton and dynamic soil salinity response function. Table 11. EPIC Output File Variable Definition and Unit Conversion EPIC Output File Variable Description Unit Conversion *.ACY YLDG Yield (Ton/Ha) 1 metric ton/Ha = 892 lbs/acre *.ACY IRGA Irrigation Volume Applied (mm) 100mm = 0.328 feet *.ACY CRF Growing season Rainfall (mm) 100mm = 0.328 feet *.DSL WLST Salt Content in Soil (Kg/Ha) 1 kg/ha = 0.446Ã—103 tons/acre *.MFS PRCP Precipitation (mm) 100mm = 0.328 feet 38 Dynamic Optimization The outputs of the EPIC simulations were used to estimate the cotton yield and soil salinity response functions. The estimated response functions for each soil type can be incorporated into an economic decision model to determine the optimal level of irrigation for any given level of salt concentration of irrigation water maximizing the net present value (NPV) of expected utility. Since crop yield and risk are generally influenced by fluctuations in weather conditions, uncertainty or risk exists in the agricultural production. The NPV of expected utility of profit instead of the NPV of profit is expressed as: The von NeumannMorgenstern utility function is used to maximize the expected value of profit. MeanVariance (EV) is incorporated to express expected utility (Hazell and Norton, 1986). Expected utility is represented as follows: where is the von NeumannMorgenstern utility function with and , is the absolute ArrowPratt risk aversion coefficient, defined as â€“. 39 Expected utility can be transformed with respected to EV of crop yield taking risk aversion as follows: = where is the expected yield, is the variance of yield derived from the equation (Coyle, 1999). The level of risk of a producer is directly related to variances of crop yield. The variance of the crop yield is evaluated as the effect of risk factors in the agricultural production. The final dynamic programming model maximizing the expected utility of profit for individual soil types in the study area is constructed as: subject to 40 where P is the price of cotton ($/lb), E(Y) is the expected cotton yield response function (lbs/acre) to quantity of total water applied and total salinity in soil, TW is the total quantity of water which is the sum of irrigation water and rainfall during the growing season. Irr is the quantity of irrigation water applied (acft/acre), is the quantity of rainfall in feet, TS is the total quantity of salinity in soil which is the sum of total dissolved salt in irrigation water and soil salinity at planting, WS is the amount of salt in irrigation water (tons/acft) which is the salt concentration (p.p.m) multiplied by the quantity of irrigation water, SSHA and SSPL is the quantity of soil salinity at harvest and planting (tons/acre) during the growing season respectively, RainG is the growing season rainfall (acft), is the quantity of soil salinity at harvest of the previous year, RainNG is rainfall received during the nongrowing season (acft), is the irrigation cost ($/acrefeet), is the operation cost and is the fixed cost, r is discount rate. The simulation design was conducted as a full factorial with three levels of irrigation water stress and three levels of irrigation water salinity, and 10 random weather data sets of 50year. A modified quadratic yield response function of cotton for the individual soil type in the study area was specified as follows: for weather scenarios for water stress factor 0.1, 0.5 and 0.9 respectively for salt concentration 0, 1280 and 2560 ppm respectively for simulation years 41 where are the parameters to be estimated, is the simulated cotton yield for a soil with the level of a water stress factor and the level of salt concentration of irrigation water in year t under the weather scenario. is the total water from irrigation water applied ( and the growing season rainfall (, is the nongrowing season rainfall. is the total salinity which is the sum of the amount of salt in irrigation water ( ) and soil salinity at planting (). The interaction term, is the total salinity divided by total water, is a random effect of weather, and are assumed to be the independent and normal distributed error terms, and ), respectively. In crop yield response function, the specification of the interaction term does not follow the standard practice of being a product of the two linear variables. This term was formulated as a ratio because more water serves to increase the yield while more salt tends to decrease the yield. When specified as a ratio (total salt/total water), the two variables work in the same direction. The soil salinity response functions at planting and harvest were also estimated for the individual soil type. The soil salinity function at harvest is assumed to be affected by irrigation water applied, dissolved salt in irrigation water and growing season rainfall. It can be constructed as follows: where are the parameters to be estimated, is the soil salinity at harvest which is simulated from a set of combinations of the soil condition having the water 42 stress factor and the level of salt concentration in year with a weather scenario . is the quantity of irrigation water applied, is the amount of salt in irrigation water, is the soil salinity at planting, is the growing season rainfall in weather scenario and year , is a random effect of weather, and are assumed to be the independent and normal distributed error terms, and ), respectively. To estimate the dynamic soil salinity function at planting, we assumed that the amount of soil salinity at planting in the current year will be determined by soil salinity level at harvest in the previous year and non growing season rainfall. The dynamic soil salinity function at planting is defined as: where and are the parameters to be estimated, is the soil salinity at planting given the water stress factor, the level of salt concentration in year t with a weather scenario , is the soil salinity at harvest in the previous year, is nongrowing season rainfall in weather scenario and year t, is a random effect of weather, and are assumed to be the independent and normally distributed error terms, and (0, , respectively. The yield variance function is expressed as the squared residuals of the estimated yield response function. It is expressed as the linear function of the irrigation and growing season rainfall which mainly affect crop yield and yield variability (risk), i.e., 43 where , and are the parameters to be estimated, is a random effect of weather, and are assumed to be the independent and identical error terms, and (0, , respectively. The coefficients of and represent the influence of irrigation water and growing season rainfall on yield variability (risk). The input variable is riskreducing if and riskincreasing if , respectively (Finger and Schmid, 2007). 44 CHAPTER IV RESULTS OF SIMULATION, REGRESSION AND OPTIMIZATION BY SOIL TYPE SAS PROC MIXED is a powerful procedure for a wide variety of statistical analyses with both fixed and random effect in research situations. In this study, the fixed and random effects model was applied to EPIC data. Since we selected 10 random weather scenarios, weather is considered as the random effect in the model. Since data selected from EPIC simulations with different inputs are in the form of panel data, autocorrelation and heteroskedasticity may occur in the model. Models to describe the variance as a function of independent variables in a regression model can be fitted to data where the variance increases or decreases as the values of the independent variables change. One of the great advantages of the likelihoodbased estimation approach to mixed models is the ability to fit a variety of covariance structures (Littell et al, 2006). To fit a model with autocorrelation and heterogeneous variances, the model can be specified in PROC MIXED by using the REPEATED statement with the AR(1) for autocorrelation and GROUP = option for heterogeneous variances. The REPEATED statement specifies the covariance structures of the error term. The AR(1) models may adequately describe the autocorrelation and assumes a homogeneous variance and error correlations that decline exponentially with distance. Group = option defines an effect specifying heteroscedasticity in the covariance structure. Each new level of the GROUP 45 effect produces a new set of covariance parameters with the same structures as the original group (SAS Institute Inc, 2008). In this study, GROUP = option specifies a different residual variance for each weather scenario. The fitted models should be compared with model with an assumption without autocorrelation and heteroscedasticity to draw accurate conclusions from data. The Likelihood Ratio Test (LRT) is used to determine the better fitted model. PROC MIXED model is based on Maximum Likelihood Estimation (MLE) which maximizes the likelihood function with/without imposing any restrictions. The LR test requires estimating two models and comparing them. The LR test statistic is calculated in the following way (Johnston & DiNardo, 1997): LR = where L and l are the likelihood and log likelihood of the respective model. Since the PROC MIXED model directly provides the 2 loglikelihood statistic, we can compare with the difference in the 2 loglikelihood of the restricted and unrestricted model for the LR test. The LR statistics follows a chisquare distribution with degrees of freedom equal to the difference in the number of degrees of freedom between the two models. By using the 1 PROBCHI function in SAS, which returns the value of the function of the chisquare distribution, SAS will compute the test statistic and its pvalue from the 2 loglikelihood values (SAS Institute Inc, 2008). If the pvalue is less than the critical value, we reject the null hypothesis of no difference between two models. 46 To determine if the estimated crop response function is concave with respect to variables we used in the regression, the second derivative test is examined by algebraically or numerically checking the signs of the secondorder conditions of the variables (Beattie & Taylor, 1985). From the yield response function, the first order and second order conditions are derived. Given a modified quadratic functional form, y = f(TW, TS, RainNG) is represented as the equation below: Given the functional form y = f(TW, TS, RainNG), this function can be extended with respect to the specified individual variables. The extended functional form y = f(x1, x2, x3, x4, x5) is represented as the equation below: where x1 is irrigation water applied (acrefeet), x2 is the growing season rainfall (feet), x3 is the salt concentration of irrigation water (tons/acft), therefore, x1Â· x3 is the amount of salt in irrigation water (tons/acre) which is the product of salt concentration and irrigation water, x4 is the salinity in the soil (tons/acre), x5 is the nongrowing season rainfall (feet). The firstorder conditions (F.O.C) with respect to the individual variable are 47 The secondorder conditions (S.O.C) for variables except for are The determinants derived from S.O.C is used to examine that the crop response function has a maximum yield with respect to irrigation water and salt concentration in irrigation water(, irrigation water ( and soil salinity (, and salt concentration in irrigation water () and soil salinity (, respectively. The Hessian matrix of second derivatives at the critical point is represented as the follows: 48 For maximization problem, must be negative definite or negative semidefinite. If and only if or , is negative definite or negative semidefinite, respectively. Hence, the determinants should be all negative, the determinants should be positive, the determinat should be negative, and the determinant is positive. The determinants are the diagonal elements of , , , , and which are 210.9, 200, 11.5 and 2.9. The order 4 determinant ( ) is formed by the 44 matrix as the above hessian matrix. The determinant is expanded into four 33 submatrices (and ) along the diagonal elements in the Hessian matrix as follows: The determinants of and should be negative so that the determinant should be positive. The determinant of and can again 49 be expanded into three 2Ã—2 submatrices (), respectively, along their diagonal elements as follows: , , , and All determinants of the 2Ã—2 matrix ( ) should be positive so that the determinants of and are negative. If the determinants of the respective orders have the indicated signs, , , , and , the matrix is negative definite. Therefore we conclude that the modified crop response function is concave and has a local maximum. The dynamic optimization procedure for the economic decision model was performed by GAMS IDE. To solve the dynamic optimization problem, we need to know the cotton price, irrigation cost, operating cost, and fixed cost. The irrigated and dryland cotton budgets were revised from the OSU cotton budget for the surfacefurrow irrigation system provided by Oklahoma State University Extension. We assumed that the farms in the study area follow this cotton budget. From APPENDIX A for the irrigated cotton, the cost of irrigation water is 28.89$/acft and total cost is 677.37 $/acre. From APPENDIX B for the dryland cotton, total cost is 312.29$/acft. We also suppose that 1) cotton price is fixed at 0.6 $/lbs for irrigation and dryland over 50 years planning horizon 2) discount rate is 4.125 percent for Federal water resources planning for fiscal year 2011 50 (http://www.economics.nrcs.usda.gov/cost/priceindexes/rates.html), 3) the available irrigation water is 2.62 acft (800mm) or less, 4) one of risk neutrality and two levels of risk aversion coefficient are used in this analysis: 0, 0.025 and 0.05 which are used in the literature for irrigated producers (Johnson and Blackshear, 2004 and Wojciechowski et al, 2000), 5) dryland producers are riskneutral since they are indifferent to the risk such as a big rainfall and drought and are concerned about expected profit, 6) the growing season and nongrowing season rainfall is randomly generated based on the gamma distribution over the 50 years planning horizon. Rainfall in the EPIC simulation is determined by generating from a skewed normal daily precipitation (Williams et al, 1992). The generated yearly rainfall and precipitation have a skewed distribution. The data that are skewed to the right are adequately modeled by a gamma density function (Wackerly et al, 2002). PROC UNIVARIATE with the HISTOGRAM statement is used to determine if the gamma distribution fits a data distribution used in the EPIC simulation. SAS output provides three goodnessoffit tests which are the KolmogrovSmirnov, Cramervon Mises and AndersonDarling test (SAS Institute Inc., 2010). The pvalues of all tests for growing and nongrowing season rainfall are larger than 0.25. Since pvalues are larger than significant value . We conclude that we fail to reject the null hypothesis of the gamma distribution and the fitted gamma distribution provides an appropriate model for distribution of generated growing and nongrowing season rainfall. Figure 12 and 13 represent the fitted gamma distribution curve on the histogram and displays the mean, standard deviation, skewness and kurtosis of growing and nongrowing season rainfall used in EPIC and dynamic optimization model, respectively. 51 Figure 11. Statistics and Histogram with the Fitted Gamma Distribution for Growing and NonGrowing Season Rainfall used in EPIC Figure 12. Statistics and Histogram with the Fitted Gamma Distribution for Growing and NonGrowing Season Rainfall randomly Generated based on Gamma distribution in Figure 12 for 50 years Planning Horizon of Dynamic Optimization Model 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 Percent Summary Statistics N 500 Mean 1.389 Std Dev 0.397 Skewness 0.426 Kurtosis .058 Growing_Season_Rainfall 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 5 10 15 20 25 30 35 40 Percent Summary Statistics N 490 Mean 0.652 Std Dev 0.228 Skewness 0.503 Kurtosis .068 Non_Growing_Season_Rainfall 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0 5 10 15 20 25 30 35 40 Percent Summary Statistics N 50 Mean 1.294 Std Dev 0.213 Skewness 0.528 Kurtosis .475 Growing_Season_Rainfall 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 10 20 30 40 50 60 70 Percent Summary Statistics N 50 Mean 0.579 Std Dev 0.132 Skewness 0.525 Kurtosis .617 Non_Growing_Season_Rainfall 52 For the dynamic programming, the growing season rainfall and nongrowing season rainfall are randomly generated for the 50 years planning horizon based on the gamma distribution. The pvalues of KolmogrovSmirnov, Cramervon Mises and AndersonDarling test for rainfall are 0.068, 0.181 and 0.204, respectively. The pvalues of their tests for nongrowing season rainfall are 0.25, 0.191 and 0.18, respectively. Since their pvalues are larger than significant value . Therefore, we conclude that we fail to reject the null hypothesis of the gamma distribution and the data are appropriately generated based on the gamma distribution in Figure 12. The generated random growing season rainfall and nongrowing season rainfall are combined with the dynamic optimization model maximizing the net present value of expected utility for all soil types. Figure 13 shows the growing season and nongrowing season rainfall based on the gamma distribution are distributed over 50 years. Figure 13. Distribution of Growing Season and Non Growing Season Rainfall Generated based on Gamma Distribution over 50 years 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 8 15 22 29 36 43 50 Rainfall (feet) Year Growing Season Rainfall NonGrowing Season Rainfall 53 Tipton Loam Soil, 01% Slope EPIC Output Data The quantity of salt in the soil at each depth in the EPIC *DSL output file is calculated by EPIC based on the initial EC values (mmho/cm) in the soil input file. Table 11 presents the calculated quantity of soil salinity based on the sampled data for the Tipton Loam soil at the start of the simulation. In EPIC, WSLT (Kg/ha) is automatically simulated at each depth on a daily basis for 50 years and the total value of them is also automatically calculated. It can be converted to tons per acre. Table 11. Initial EPIC Soil Salinity Input Data based on Soil Samples of the Tipton Loam Soil 1* 1 2 3 4 5 6 TOTAL DEPTH(m) 0.01 0.15 0.3 0.6 0.9 1.2 1.5 ECND(mmho/cm) 1.07 0.78 1.08 1.47 1.17 1.33 2 WSLT(kg/ha)* 9 103 153 587 444 504 756 2,555 Salinity(tons/acre) 1.14** Source: Zhang et al, Oklahoma Soil Test Laboratory, 2011. Note: (*) indicates layer 1 and WSLT are simulated by EPIC. (**) indicates the value is calculated by the conversion (1 kg/ha = 0.446Ã—103 tons/acre). The total salt in the 1.5 meter profile was calculated as 1.14 tons/acre on the first day of simulation. This will be used as the initial soil salinity in the dynamic programming. The level of soil salinity at the day of planting and harvest in each year 54 can be selected from *DSL file. The cotton yield, irrigation water, growing season rainfall and nongrowing season rainfall are also obtained from the EPIC output file. The range of the simulated output variables which are used in the model are summarized in Table 12. Table 12. Range and Mean of the Input and Output Variables Simulated from EPIC model for the Tipton Loam Soil Variable Symbol (Unit) Range Mean Cotton Yield Y (lbs/acre) 33 ~1,857 1,071 Irrigation Water Irr (acft/acre) 0.16 ~ 2.62 1.28 Soil Salinity at Planting SSPL (tons/acre) 0 ~ 24.65 8.61 Soil Salinity at Harvest SSHA (tons/acre) 0 ~ 27.34 9.39 Growing Season Rainfall RainG (feet) 0.47 ~ 2.61 1.39 NonGrowing Season Rainfall RainNG (feet) 0.06 ~ 1.64 0.66 Salt Concentration of Irrigation Water* (tons/acft) 0, 1.74 and 3.48 1.74 Note: (*) indicates the input variable to run EPIC. Ten sets of 50year cotton yield and irrigation applications were simulated by EPIC given three levels of salt concentration of irrigation water and three levels of water stress to trigger irrigation from 50 mm to 800 mm. When we use irrigation water containing a high salt concentration on the crop land, the salts accumulate in the root zone. Saline soils have a very limited agricultural production. The range of data for the simulated yield and soil salinity at harvest with given levels of the salt concentration are shown on a box plot in Figure 11. 55 Figure 11. Fiftyyear Average EPIC Simulated Yield and Soil Salinity after applying irrigation water with EC of 0, 2 and 4 (mmhos/cm) of Salt Concentration of Irrigation Water for the Tipton Loam Soil A box plot visually provides a summary of simulated data. The box extends from the first quartile which is defined as the 25th percentile of the data to the third quartile which is defined as the 75th percentile of the data. The bottom and top are the minimum and maximum value of the data, respectively. The median is shown as a line across the box. The diamond sign is the average values of the simulated data at given levels of the salt concentration. As the salt concentration of irrigation water increases, the mean of simulated yield data decreases and the mean of simulated soil salinity increases. In addition, the mean of yield data decreases as the mean of soil salinity increases. The high 0 500 1000 1500 2000 Yield (lbs/acre) 0 10 20 30 0 2 4 Soil Salinity at Harvest (tons/acre) EC (mmhos/cm) Mean 0 1,280 2,560 P.P.M. 56 level of salt concentration of irrigation water causes salts to accumulate in the soil. It is expected that the accumulated salts affect the reduction of crop yields. Econometric Estimation The SAS PROC MIXED procedure with the REPEATED statement with Type=AR(1) and GROUP = weather was used to estimate the parameters of the modified quadratic yield function with autocorrelation and/or heterogeneous variances. The Likelihood Ratio Test was used to determine the appropriate error function for the model. The results of the LR test are shown in Table 13. Table 13. Result of Likelihood Ratio Test for the Tipton Loam Soil Model 2LogLikelihood pvalue LR Test Without Autocorrelation and Heteroscedasticity 56754 < 0.0001 Reject Ho With Autocorrelation and Heteroscedasticity 56628 Because the value of 2LogLikelihood with the distribution with 19 degrees of freedom has a pvalue of less than 0.01, we reject the null hypothesis of no difference between two models. It indicates that the model fitted with autocorrelation and heteroscedasticity is more appropriate (SAS Institute Inc, 2008). The procedure of fitting a model with autocorrelation and heterogeneous variance reports parameter estimates along with standard errors. The results of cotton response function are shown in Table 14. 57 Table 14. Coefficient Estimates from SAS Proc Mixed for the Yield Response Function for the Tipton Loam Soil Variable Symbol Parameter Estimates Standard Errors Intercept 524.38* 42.1649 Total Water Applied 940.09* 30.0577 Total Salinity 1.6022 1.3225 NonGrowing Season Rainfall 112.39* 9.7781 (Total Water Applied)2 101.98* 5.3211 (Total Salinity)2 1.4344* 0.0393 (Total Salinity / Total Water Applied) 7.3683* 2.5073 Note: Total Water Applied is the sum of irrigation water and growing season rainfall. Total Salinity is the sum of the amount of salt (irrigation wa 



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