INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely afreet reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information C om pany 300 North Z ee b Road. Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Num ber 9303001 The development of a framework for m anaging w ater resources: Irrigation development in Saginaw Bay, Michigan He, Chan Sheng, Ph.D. Michigan State University, 1992 UMI 300 N. ZeebRd. Ann Arbor, MI 48106 THE DEVELOPMENT OF A FRAMEWORK FOR MANAGING WATER RESOURCES: IRRIGATION DEVELOPMENT IN SAGINAW BAY, MICHIGAN By Chan Sheng He A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Resource Development 1992 ABSTRACT THE DEVELOPMENT OF A FRAMEWORK FOR MANAGING WATER RESOURCES: IRRIGATION DEVELOPMENT IN SAGINAW BAY, MICHIGAN By Chan Sheng He This study develops a framework for use by decision makers in the water resource management irrigation development in the area. It focuses on Saginaw Bay area of Michigan. The components of the framework include the: (1) estimation of crop irrigation requirements, (2 ) evaluation of groundwater sustainability for irrigation, capacity for irrigation, (4) (3) assessment of streamflow optimization of expected irrigation returns, and (5) spatial distribution of irrigation development. Crop growth simulation models are used to simulate yields and irrigation water requirements of corn, soybeans, dry beans, and sugarbeets based on 30-year data on weather, soil, and management practices. A hydrologic budget equation, well log records, and partial chemistry data were used to evaluate the sustainability of groundwater and streamflow for irrigation supply. Optimization models, which incorporate the simulated crop yields, irrigation requirements, and streamflow availability, were established to develop spatially-oriented irrigation scenarios. The results indicate that irrigation may of increase yields corn, soybeans, dry beans and sugarbeets by a large margin over non-irrigated identical plantings in the study area. The available streamflow may be sufficient to supply a maximum irrigation acreage of 44,000 acres, which is only 2 percent of the total agricultural land in the study area. Use of groundwater for irrigation should be practiced cautiously since continuous pumping would reduce discharge to streamflow and also induce upward movement of brine from deeper aquifers. Currently, there is increasing evidence that growers and decision makers will apply pressure to greatly exceed the available irrigation acreage. This study demonstrates such an expansion is not sustainable and could lead to the degradation and depletion of groundwater and streamflow and to the destruction of fisheries habitat. optimal irrigation scenarios, given the The assumptions of linearity and uniformity employed in this study, indicate that acreage of corn may be expanded and that irrigation priority be given to dry beans. Computer simulation and optimization models and Geographic Information Systems are shown to be useful tools in supporting decision making for water resource management. The framework established in this study demonstrates the viability of using simulation models for policy aides. It also shows that models, to be used in irrigation planning, should have a sound physical basis and should first be validated in the field. To my wife, Zhizhen, and my son, Bo. iv ACKNOWLEDGMENTS I would like to extend my sincere appreciation to many people who have endeavor. his in different stages of this I am indebted to my advisor, Dr. Jon Bartholic, for guidance research, assisted me and support. He not but also taught me skills integration, and management. only guided me in my in conceptualization, Having him as a mentor will certainly enhance my professional development for many years to come. I would especially like to thank the other members of my graduate committee: Dr. Thomas Edens, Dr. Roger Wallace, and Dr. Baxter Vieux. In addition to serving as principal investigator on three grants which lead to the completion of this endeavor, Dr. Edens spent much of his time with me in finalizing this work. His support and dedication to this work are greatly appreciated. Dr. Wallace, despite his extremely busy schedule, guided me in the hydrogeologic analysis of this research. Finally, Dr. Vieux continued to serve as my graduate committee member even after he left Michigan State University. Working with the three of them was intellectually stimulating and rewarding. v Special thanks also go to my host family, Mr. and Mrs. Jack Bails. Their encouragement, care, and warm friendship have added much joy and happiness to my stay in the United States. I am also thankful to Dr. Frank D'ltri for his help and support in my research. From him, I learned a great deal about project management and administration. I wish to thank the United States Department of Agriculture Soil Conservation Service and the Michigan State University Institute of Water Research for providing financial support for this research. Without their support, this research would not have been possible. I would also like to extend my gratitude to my colleagues for their technical assistance in this work. First, I would like to recognize the help of Todd Zahniser for his editorial assistance and his help in producing many graphics for this work. Additionally, I thank Mark Phillips for reviewing this work and James Riggs for assistance in the preparation of some of the graphics in this work. Finally, I am grateful to my parents for their encouragement and support. I especially appreciate the values and beliefs they taught me during my growth, which laid the foundation for my development. Thanks also go to my little boy, Bo, whom I had not seen for four years during my study in the United States. He has given me much joy and happiness since he came to the United States in 1990. Lastly, special thanks go to my wife, Zhizhen, for her dedication, encouragement, and support. While working on her M.S. degree in Civil Engineering, she has sacrificed so much to help me complete this work. I attribute many of my achievements to her, my wonderful partner. TABLE OF CONTENTS Page List of Tables xiii List of Figures xvi Chapter Is INTRODUCTION ------------------------------ 1 Chapter 2: PROBLEM STATEMENT AND RESEARCH DESIGN ------- 8 1. Background 8 2. Problem 3. Research Design 11 ------------------------------ 11 3.1 Description of Irrigation System 3.2 Flowchart and Scope of Work — 4. System Modeling -------- 11 -- ------— 15 — --- — ■--17 4.1 Estimation of Irrigation W a t e r ----------- 17 Requirement 4.2 Evaluation of Groundwater Sustainability for Irrigation — -— — -- 18 4.3 Assessment of Streamflow Capacity -----for Irrigation 19 4.4 Maximizing Expected Water Use Returns 19 4.5 Spatial Distribution of Irrigation --- — Expansion 20 5. Assumptions 21 viii Chapter 3: LITERATURE REVIEW 22 1. Estimating Irrigation Water Requirement --- 22 2. Estimating Groundwater Recharge -------- 27 3. Evaluation of Streamflow Capacity -------- 33 4. Use of Optimization Techniques f o r ---------- 36 Water Resource Management 5. Use of Geographic Information System in ---Water Resource Management Chapter 4: 39 PHYSICAL AND SOCIO-ECONOMIC CONTEXT ------OF IRRIGATION DEVELOPMENT IN THE SAGINAW BAY AREA 41 1. Climate 41 2. Crop Mix in the Study Area 43 3. Crop Yield Variability 46 4. Soil Suitability for Irrigation Expansion Chapter 5: I. --------- MASS BALANCE OF IRRIGATION REQUIREMENTS AND AVAILABLE WATER RESOURCES 49 53 Crop Irrigation Water Requirements -------- 53 1. Description of the Irrigation System ---- 54 2. Simulation of the Irrigation System ----- 58 2.1 Description of the Simulation Models ------ 58 ---------- 60 3. Simulation Results and Discussion ------- 62 3.1 Irrigation Water Requirements ------per acre of Land 62 3.2 Total Irrigation Water Requirements — in the Cass River Watershed 71 2.2 Model Inputs and Outputs 4. Total Irrigation Water Requirements in --- 71 the Saginaw Bay Area 5. Limitations of the Simulation Models II. The Sustainability of Groundwater Resources for Irrigation Development ---- 74 ----- 82 1. Hydrogeologic Setting 82 ------ 84 3. Recharge and Discharge----------- -------- 88 3.1 Estimate of Groundwater------ -------Recharge Rates 88 ------ 99 2. The Availability of Groundwater 3.2 Direction of Groundwater Plow 4. Salinity Level in Groundwater 104 5. Sustained Groundwater Yield 110 6 . Potential Irrigation ExpansionArea 7. Summary -— - 112 -------- 114 III. Capacity of Streamflow for Irrigation ---- 117 Development 1. Introduction ------— — 2. Streamflow During the Irrigation Season --- 117 ---- 117 3. Capacity of Streamflow for Irrigation --- 119 Expansion in the Cass River Watershed 3.1 Methods -------- 119 3.2 Maximum Irrigation Acreage in the ---- 125 Cass River Watershed 4. Maximum Irrigation Acreage in the Saginaw Bay Area ----- 128 IV. Summary 131 1. Introduction 136 — 2. Optimization Model - Chapter 6 . DEVELOPMENT OP OPTIMAL IRRIGATION SCENARIOS 136 137 x 2.1 Objective Function 2.2 Resource Constraints 138 -------------- 141 — — — — ------ 142 3.1 LP Model Output with Streamflow-----at the 75 and 50 Percent Exceedence Levels 142 3.2 Sensitivity Analysis of the Model ----Output with the Streamflow at 75 Percent Exceedence Level 148 3.3 Verification of the LP Model Output with Streamflow at 75 Percent Exceedence Level 150 3. Results and Discussions ------ 3.4 LP Model Output with Unlimited Streamflow Supply ----- 152 3.5 Irrigation Expansion and Associated Risk 157 4. Summary 159 Chapter 7. SUMMARY AND CONCLUSIONS 161 1. Summary 161 — — ---- 167 Chapter 8 . RECOMMENDATIONS FOR FUTURE STUDIES -------- 171 Appendix A. Groundwater Recharge and Discharge ------Rates Estimated by the Computer Program by Pettyjohn and Henning 174 for Cass River — 177 Appendix C. Linear Programming Model Output for Cass River Watershed Crop Mix with the Parameters at 75 Percent Confidence Level Appendix D. Linear Programming Model for Cass River Watershed Crop Mix with the Parameters at Mean Level xi Output - Appendix B. Linear Programming Model Watershed Crop Mix with the Parameters at 75 Percent Confidence Level 180 - 2. Conclusions 187 Appendix E. Linear Programming Model Output for Cass River Watershed Crop Mix with Unlimited Streamflow Supply ---- 194 Appendix F. Linear Programming Model Output for the Cass River Watershed Crop Mix Using Actual Crop Yields ---- 200 Bibliography ------------------------------------------ xii 204 LIST OF TABLES Page Table 1. Growing Season Length, Temperature, and Precipitation in the Saginaw Bay Area (1951-1980). ------ 42 Table 2. Average Crop Yields and Coefficients ---of Variation over the Period 1959-1989. 47 Table 3. Correlation Coefficients between Crop Climatic Yields and Precipitation and Temperature. 48 Table 4. Agricultural Land Soil Suitability for Subsurface Irrigation in the Saginaw Bay Area. ---- 50 Table 5. Soil Associations in the Cass River Watershed. ----- 58 Table 6 .Simulated Average Irrigation Water Requirements (mm) at the 75th Percentile. ----- 65 Table 7. Simulated Average Irrigation Water Requirements (mm) at the Mean Level. ----- 66 Table 8 .Simulated Average Crop Yields at the 25th Percentile. ----- 67 Table 9. Simulated Average Crop Yields at the Mean Level. Table 10. Total Irrigation Water Requirement for the 392,713 Acres of Agricultural Land in the Cass River Watershed (If a Single Crop were Planted to the Total Acreage). xiii 68 ----- 72 Table 11. Total Irrigation Water Requirement for the 1,971,933 acres of Agricultural Land in the Saginaw Bay Area (If a Single Crop were Planted to the Total Acreage). 72 Table 12. Correlation Analysis between the Simulated Non-Irrigated Crop Yields in the Cass River Watershed and the Actual Crop Yields (1959-1980) in Tuscola County 76 Table 13. Comparison of Sub-Irrigated and Non-Subirrigated Crop Yields in Huron County 78 --Table 14. Comparison of the Mean Simulated Irrigated Crop Yields in the Cass River Watershed (1951-1980) with the Mean Actual Subsurface Irrigated Crop Yields (1987-1990) in Huron County 79 Table 15. Estimates of Recharge and Discharge in the Saginaw Bay Area of Michigan (Based on Weather Data from 1951-1980 and 30-78 Years of Streamflow Data). 93 Table 16. Seasonal Cumulative ET (May through September) Estimated by the CERES-MAIZE model for Non-irrigated Corn in the Cass River Watershed (Based on Weather Data from 1951-1980). 95 Table 17. Acreage of Potential Sub-Irrigation Expansion Area with Suitable Groundwater Supply. 114 — Table 18. Maximum Irrigation Acreage Supported by Cass River Streamflow (based on Irrigation Requirements of Corn at the 75th Percentile). 126 Table 19. Maximum Irrigation Acreage Supported by July 75 Percent Exceedence Streamflow in the Saginaw Bay Area (Based on the July Irrigation Requirement of Corn at the 75th Percentile). 130 Table 20. Output Summary of the LP Model with the Parameters at 75 Percent Confidence Level. 143 xiv Table 21. Output Summary of the LP Model with All the Parameters at Mean Level. ------- 144 Table 22. Output Summary of the LP Model with ------Streamflow at 75 Percent Exceedence Level. The Objective Function Coefficients were Derived from the Actual Crop Yields in Tuscola and Huron Counties. 152 Table 23. Output Summary of the LP Model with -----All the Parameters at 75 Percent Confidence Level (Assuming Unlimited Streamflow Supply). 153 Table 24. Soybean Gross Margins (Actual Yields in Tuscola County) (Prices and Variable Costs Comparable on the Basis of 1982-1984 Values = 100). ----- 156 Table 25. Dry Bean Gross Margins (Actual Yields ----in Tuscola County) (Prices and Variable Costs Comparable on the Basis of 1982-1984 Values = 100). 156 xv LIST OF FIGURES Page ------- 4 Figure 1. The Saginaw Bay Watershed Boundary Figure 2. The SaginawBay Study Area 13 Figure 3. Land Use inthe Saginaw Bay Area of -------Michigan 14 Figure 4. Flowchart of Water Resource Management System for Irrigation Development Figure 5. Mean Monthly Precipitation in Caro, Michigan (1951-1980) 16 --— — 44 Acreage of Corn, Soybeans, ----Sugarbeets, and Dry Beans as a Percentage of the Total Crop Acreage Harvested in the Five-County Area 45 Soil Suitability for Subsurface Irrigation ------ 51 . The Cass River Watershed Boundary ------ 55 Land Use in the Cass River Watershed ----- 56 Figure 6 .Harvested Figure 7. Figure 8 Figure 9. Figure 10. Soil Associations in the Cass River Watershed ----- 57 Figure 11. Simulated Irrigation Water Requirements -at the 75th Percentile (June through August) 69 Figure 12. Comparison of Simulated Irrigated and Non-irrigated Crop Yields in the Cass River Watershed --- 70 xvi Figure 13. Total Irrigation Water Requirements -----in July at the 75th Percentile for Selected Crops Grown in the Saginaw Bay Area 73 Figure 14. Bedrock Geology of the Saginaw Bay Area --- 83 Figure 15. The Availability of Groundwater----- -----in Glacial Deposits (Twenter, 1966a) 85 Figure 16. The Availability and Quality of----- -----Groundwater in Bedrock Deposits (Twenter, 1966b) 86 Figure 17. Conceptual Model of Groundwater Recharge — 90 Figure 18. Location of the Drift Wells Figure 19. Location of the Bedrock Wells -------------— --- Figure 20. Potentiometric Surface (Feet ------— above Sea Level) of Drift Aquifer 100 101 — 102 ------ 103 Figure 22. Residual Surface Obtained by -----------Subtracting the Bedrock Aquifer Potentiometric Surface from the Drift Surface 105 Figure 23. Location of the Wells Sampled for Partial Chemistry Analysis 107 Figure 24. Concentrations of Chloride in Groundwater Figure 25. Concentrations of Sodium in Groundwater -- Figure 21. Potentiometric Surface of Bedrock Aquifers Figure 26. Potential Subsurface Irrigation Expansion Areas -------------- -— 108 109 115 Figure 27. Exceedence Flow in the Cass R i v e r --------at the Frankenmuth Station (1936-1985) 118 Figure 28. Exceedence Flow in the Cass River -------at the Cass City Station (1948-1985) 120 Figure 29. Exceedence Flow in the Cass River -------at the Wahjamega Station (1969-1985) 121 xvii Figure 30. Exceedence Flow in the Cass River at the — Frankenmuth Station (June through August) (1936-1985) 122 Figure 31. Watersheds in the Saginaw Bay Area ------- 129 Figure 32. Maximum Irrigation Acreage Supported -----by Groundwater and Streamflow in the Saginaw Bay Area 134 Figure 33. Seasonal Average Crop Prices in --------Michigan (Real Value, 1982-1984=100) 140 Figure 34. Spatial Distribution of the LP Model ----Output with the Parameters at 75 Percent Confidence Level 145 Figure 35. Spatial Distribution of LP Model---------Output with the Parameters at Mean Level 146 Figure 36. Spatial Distribution of LP Model ------- — Output with the Parameters at 75 Percent Confidence Level, While Assuming Unlimited Streamflow Supply 154 Figure 37. 158 Expected Crop Gross Margins overa ------Range of Irrigation Acreage and Streamflow Exceedence Levels xviii CHAPTER 1 INTRODUCTION Management of limited water resources is one of the most important challenges in modern society as multiple demands have been placed on water for food production, industrial development, hydropower generation, transportation, waste disposal, recreation and maintenance of the ecosystem. These competing uses must be examined against the available sources to avoid over-withdrawal of these precious water supplies. This study develops a framework for an adaptive water resource management system to estimate crop irrigation requirements and to examine the availability of water resources for irrigation supply to support the wise use of the available water resources in humid and semi-humid areas. An adequate supply of water is essential to ensure the success of agricultural production. One important way by which crops obtain water is through irrigation. Irrigated land accounts for 16 percent of the world's total cultivated area (Mather, 1984). In the United States, irrigation has become a crucial factor in the nation's agricultural output. It accounts for 13 percent of the nation's harvested cropland and contributes approximately 30 percent of the 1 2 value of agricultural production (Negri and Hanchar, 1989). The total acreage of irrigated land, which has tripled since 1940, is still increasing in the United States (Gibbons, 1986}. Irrigated agriculture consumes the largest portion of the United States' water resources. In 1985, total freshwater consumption in the United States was estimated at 103 million acre-feet, of which irrigation accounted for approximately 83 percent 1 (Negri and Hanchar, 1989). Irrigated agriculture faces competition from alternative uses of water resources. First, as the population expands and industry grows, the demand for water for municipal supply, industrial development, waste disposal, navigation, and hydroelectricity increases. Second, over the past two decades, an increasing environmental awareness and the desire for outdoor recreation have also resulted in higher nonuser values for the instream use of water resources. Of particular importance is the growing recognition that instream water has value for water quality improvement, fish propagation, recreation and the maintenance of wildlife habitat. Due to the uneven distribution of water resources, these competing demands have led to significant over­ development of existing water supplies in many areas, including the "mining" of streams and aquifers, the loss of ‘One acre-foot is the amount of water needed to cover an acre of land to a depth of 1 foot. 3 wetlands, and the destruction of fisheries and wildlife habitat (Mather, 1984). The development of irrigation remains vital to the western United States, although the region will not experience a continuous growth of irrigated agriculture due to the limits established by the available water supply. The potential for agricultural irrigation expansion lies in humid and semi-humid areas of the country (Mather, 1984). Thus, it is anticipated that there will be a shift of new irrigation enterprises from the drier states to the humid or semi-humid regions (Mather, 1984). Unlike irrigated agriculture in arid or semiarid areas where no profit can exist without irrigation, irrigation in humid areas supplements precipitation. The timing and quantity of irrigation must be carefully scheduled in humid areas to maximize the profitability of crop production. As irrigation expands in humid areas, the availability of irrigation water must be examined in the context of multiple demands for water and alternative allocation methods to ensure sustainable use of the available water resources. The Saginaw Bay Watershed, located in the east central portion of Michigan's lower peninsula, is the largest watershed in Michigan and covers a land area of approximately 8,072 square miles (Figure 1). The watershed provides a variety of recreational and industrial opportunities and many services for Michigan residents. 4 Figure 1. The Saginaw Bay Watershed Boundary (Shaded Area) Water from Saginaw Bay supplies 45 drinking water distribution systems serving over 300,000 people. The Bay also supports commercial and recreational fisheries and other types of recreation. Nearly 50 percent of Michigan's 750,000 registered boats are located within 100 miles of Saginaw Bay, and 80 percent of Michigan's population lives within one hour's driving time. The watershed assimilates the flows of 67 municipal waste-water treatment facilities as well as hundreds of industrial waste treatment systems. In addition, the Bay is valuable to wildlife as a major fish spawning and nursery area, and it provides shelter and food for waterfowl on a major migratory flyway (Michigan Department of Natural Resources, 1988; Michigan Sea Grant College Program, 1990). The Saginaw Bay Watershed is also one of the most productive agricultural regions in Michigan. Agriculture is a major contributor to the region's economy. In recent years, agricultural irrigation has rapidly expanded in the region. However, due to increasing demands for water for municipal uses, industrial development, waste disposal, aesthetic and recreational use, and fisheries and wildlife habitat protection, agricultural irrigation faces ever increasing competition for the available water resources. Without an overall management system, these competing demands may lead to over-development of the existing water resources. As a result, the depletion of streams and 6 aquifers and the destruction of fisheries and wildlife habitat will likely occur. To assure sound economic development and sustainable use of the existing water resources, a systems approach2 must be taken to assess the multiple demands for existing water resources to establish a balance between the various competing demands for water. This study takes a systems approach to develop a framework for managing water resources for irrigation development in humid and semi-humid areas. The components of the framework to be developed include (1 ) examination of the complex relationships of crop irrigation water requirements and climate, soils, land use, and crop management, (2 ) evaluation of the water resources available for irrigation supply using a mass balance approach3, and (3) development of optimal irrigation scenarios for sustainable use of the available water resources. The Saginaw Bay Watershed is chosen as the study area of this research. Once a framework for water resource management has been developed, there is a good chance that wise resource use 2The systems approach assumes the holistic investigation of objects as a whole but also their separation into subsystems and elements, which facilitates the investigation of the structure, organization and functional behavior of an object (Votruba et al., 1988). 3The mass balance approach or mass budget method is based on the principle of conservation of mass applied to some part of the hydrologic cycle. Conservation of mass, formulated as a mass budget equation, requires that for any given control volume, the inflow rate minus the outflow rate equals the rate of change of the water stored. decisions will be made to ensure sound economic development along with the sustainable use of the available water resources. The framework developed from this study in the Saginaw Bay area of Michigan may also be applicable to practices of irrigation in other humid and semi-humid regions around the country. CHAPTER 2 PROBLEM STATEMENT AND RESEARCH DESIGN 1. BACKGROUND The Saginaw Bay Watershed is chosen as the study area to develop a framework for managing water resources for irrigation development. The watershed, located in the eastcentral portion of the lower peninsula of Michigan, is one of the most important resources in Michigan. It covers a land area of 8,709 square miles (22,557 km2 ) and accounts for 15% of Michigan's total land area. The watershed includes portions of 22 of Michigan's 83 counties and supports a population of 1.5 million people. There is a diversified industrial infrastructure in the watershed, ranging from automobile manufacturing to food processing. The watershed contains the largest coastal wetland complex in Michigan and provides an outstanding habitat for fisheries and wildlife. Over 90 fish and 259 vertebrate species have been recorded in Saginaw Bay, and more than 20 species of waterfowl use Saginaw Bay habitats during the breeding and migration season (Michigan department of Natural Resources, 1988). The watershed also offers 8 excellent recreational opportunities. The total value of the Bay sport fishery alone is estimated at several millions of dollars annually. In addition, the watershed is used for commercial navigation and waste disposal. Commercial freight traffic in the Saginaw River alone totals over 2 million tons per year. Currently, 211 industrial and municipal facilities discharge their waste waters into the watershed (Michigan Department of Natural Resources, 1988). Agriculture is the most extensive single category of land use in the Saginaw Bay Watershed. A recent survey by He et al. (1992) indicates that agriculture is perceived as the most important sector in the region's economy. Cropland, totaling 3,300,000 acres, accounts for 59 percent of the total land area in the watershed. In recent years, the watershed has been targeted for irrigation expansion based on soil properties. There are a potential 1.67 million acres of land suitable for subsurface irrigation expansion. The water management system, formerly used exclusively for drainage, is now being used for irrigation as well. At the same time, local and regional communities are undergoing major economic readjustments in response to the recent decline in automobile manufacturing and associated businesses. These communities are moving rapidly to enhance tourism and light industries to take advantage of the water resources in the region. Environmental groups are also actively promoting the instream uses of water for recreation 10 and aesthetics, and for fisheries and wildlife habitat. Unfortunately, these water uses compete with each other. As population grows, the need for water for enhanced food production, industrial development, hydropower generation, navigation, aesthetic and recreational uses, and ecosystem maintenance will increase. There is already increasing concern that inland water resources may not be sufficient to support these competing demands. Over-withdrawal of streamflow or groundwater may lead to their depletion as well as to degradation of water guality and destruction of fisheries and wildlife habitats. A framework must be developed to examine the inter-relationships of these competing demands and the available water resources to avoid adverse human, physical and ecological impacts resulting from over-withdrawal of the water resources. This research develops a framework for an adaptive water resource management system. The framework will examine the complex inter-relationships among irrigation water reguirements, climate, soils, land use, and available water resources as part of a systems approach. Once this framework has been developed, the reguirements for available water resources for irrigation, the alternative crop mixes and the optimal acreage of irrigation can be evaluated prior to extensive investment in irrigation. In this manner, land and water resources can be better utilized, and over-development of irrigation can be avoided. 11 2. PROBLEM Inland water resources in the Saginaw Bay area do not appear sufficient to support the potential increases in irrigation supplied by groundwater and streamflow. There is evidence that potential use significantly exceeds water availability (He et al., 1990 and Sweat, 1992). In order to address this type of problem, it is first necessary to establish several related parameters. These include: A. Irrigation water requirements, B. Groundwater sustainability for irrigation, C. Streamflow capacity for irrigation, D. Optimal crop mix for maximizing expected water use returns, and E. Spatial distribution of irrigation expansion. This study develops a framework for addressing this class of water resource problems. Although it will not provide a definitive answer for the case study chosen here, it will serve to provide an exportable template which can be used to resolve these types of water resource issues. 3. RESEARCH DESIGN 3.1 Description of the Irrigation System The irrigation system examined in this study is an agricultural crop production system in the Saginaw Bay 12 Watershed, Michigan. The study area encompasses Bay, Huron, Saginaw, Sanilac, and Tuscola Counties4(Figure 2). This area is being targeted for irrigation expansion, especially for subsurface irrigation. The five county irrigated acreage has expanded from 8,460 acres in 1978 to 15,035 acres in 1987 (Bureau of the Census, 1984 and 1989). Based on soil suitability, the potential exists for as many as 1,667,000 acres of subsurface irrigation expansion, which accounts for 85 percent of the total agricultural land in the five county area (Kittleson et al., 1987). Agriculture and forestry are two major land uses in the study area, accounting for 79 and 14 percent of the total land area (2,500,000 acres), respectively (Figure 3). Soils in the study area consist mainly of loam, silty clays and sandy loam, and are poorly drained in much of the area. Crops being studied include corn, soybeans, dry beans, and sugarbeets. The harvested acreage of each of the four crops accounts for 33.5, 19.4, 17.2, and 9.3 percent, respectively, of the total crop acreage harvested between 1985 and 1989 (Michigan Department of Agriculture, 1986-1990). The irrigation season typically runs from June through August. 4The five county study area is a portion of Bay Watershed, which includes 22 counties. The corresponds to the USDA Soil Conservation Service Subirrigation and Drainage Project Area. The five in this paper is referred to as the "Saginaw Bay the Saginaw study area Saginaw Bay county area area." 13 Study Area Q(NK< an Figure 2. The Saginaw Bay Study Area RTs] Agrlcullura B i Urban and Barrtn |§13 Daclduou* Foraats B88 Inland Watan V77X Watlands Figure 3. Land Use in the Saginaw Bay Area of Michigan 15 3.2 Flowchart and Seopa of Vork Figure 4 illustrates the design of this study. It represents the integration of the five crop simulation and optimization models, along with the mass balance equation for assessing the capacity of groundwater and streamflow for irrigation. Four simulation models are used to estimate the evapotranspiration rates, irrigation water requirements and yields of corn, dry beans, soybeans and sugarbeets. Spatial and temporal variations in weather and soils are considered in estimating these parameters on the regional scale. The sustainability of groundwater for irrigation supply is evaluated in this study by examining the groundwater recharge rate, flow direction and quality. The capacity of streamflow for irrigation supply is evaluated in the mass balance equation to determine if the available water resources are sufficient to meet the crops' irrigation water requirements. Optimization models are developed to optimize the crop mixes for maximizing the expected returns from irrigation. Geographic Information Systems (GIS) are used in this study to process and analyze the data sets of land use, soils, and hydrogeology to provide inputs to the simulation and optimization models. Spatial distribution of the simulated results are processed by GIS at the watershed scale. The scope of this study is the integration of the crop simulation and optimization models along with the mass 16 Input Data Sets P r e c i p . , Temp., S olis, Land Use, M anagement Crop M odels C E R E S - M A IZ E SOYGRO BEANGRO YIELD YES END MASS BALA N C E Ground Water Stream flow NO Optimization Model Economic Info. Optimal Irrig. S c e n a rio s C ro p p in g Mix Irrigation A c r e a g e Figure 4. Flow chart of W ater R esource M anagem ent System for Irrigation D evelopm ent 17 balance equation for evaluating the availability of water resources for irrigation supply at the regional level. On- farm allocation and operation of irrigation is beyond the scope of this study. In addition, detailed hydrogeologic or geophysical investigations are not the subject of this study. Likewise, the quality of streamflow for the purpose of irrigation is not evaluated in this study, since the streamflow in the study area is generally of good quality for agricultural irrigation. 4. SYSTEM MODELING The major components of system modeling in the framework are described below: 4.1 Estimation of Irrigation Water Requirement The requirement for irrigation, which is the difference between the crop need and the amount of available soil moisture, is first estimated. Factors affecting the irrigation water requirement are considered, which include temperature, precipitation, solar radiation, soil texture and depth, land use activities, and management practices. Data sets of weather, soils, and management factors were acquired from the Michigan Department of Agriculture Climatology Program; the Michigan State University Nowlin Chair's Office and the USDA Soil Conservation Service; and the Huron County Cooperative Extension Service, 18 respectively. These data sets were used in the crop simulation models to estimate irrigation water requirements for corn, soybeans, dry beans, and sugarbeets. The crop growth simulation models used in this study include CERES-MAIZE (Ritchie et al., 1989) for corn, S0Y6R0 (Jones et al., 1989) for soybeans, and BEANGRO (Hoogenboom et al., 1990) for dry beans. They use daily weather data, soil characteristics, and management information to estimate crop yields and irrigation reguirements. The YIELD model (Schultink et al., 1989) is used to estimate the yield and irrigation water requirement of sugarbeets. It is based on one of the FAO's methods for estimating the potential crop yield, evapotranspiration rate, and irrigation requirement (Doorenbos and Kassam, 1979). Inputs to the model include daily or monthly mean temperature, precipitation, solar radiation, wind speed (at 2 m height), and relative humidity. 4.2 Evaluation of Groundwater Sustainability for Irrigation Groundwater is used for domestic use and agricultural irrigation in the Saginaw Bay area. The sustainability of groundwater for irrigation is evaluated in this study by examining the groundwater recharge and discharge rates, flow direction and quality. A hydrologic budget is used to estimate the groundwater recharge and discharge rates in the 19 study area. Well log records are used to derive the potentiometric surfaces of water in drift and bedrock aquifers to determine the direction of groundwater flow. Concentrations of dissolved solids, chloride and sodium are used to evaluate the quality of groundwater for irrigation. 4.3 Assessment of Streamflow Capacity for Irrigation Use of surface water may increase the available water supply for agricultural irrigation. However, since the withdrawal of water from the Great Lakes for irrigation is legally restricted, streamflow availability needs to be examined in evaluating irrigation expansion. This study uses a mass balance approach to compute the streamflow available for irrigation and the maximum irrigation acreage that streamflow can sustain at the 90, 75 and 50 percent exceedence flow levels .3 4.4 Maximising Expected Water Use Returns Allocating limited water resources among different crops for irrigation is a typical resource use decision. Decision makers must determine which crops to irrigate, where to irrigate, and how much land to irrigate. The use of optimization techniques can help decision makers achieve the 5The exceedence flow indicates the probability level at which streamflow will exceed or equal the specified value. 20 most satisfactory results while meeting resource and activity constraints. In this study, linear programming models are developed to generate irrigation scenarios for use by decision makers as part of the basis for making resource use decisions. The models incorporate irrigation water reguirements, available water resources, simulated crop yields, and expected returns to maximize total expected economic returns from the crops in the study area. 4.5 Spatial Distribution of Irrigation Expansion Spatial distribution of irrigation expansion in the Saginaw Bay area is essential information to decision makers in water resource planning and management. Geographic Information Systems6 are used in this study to derive inputs from the data sets of land use, soil associations, watershed boundaries, well log records, and hydrogeologic settings of the study area, to the simulation and optimization models as well as the water balance equation. The spatial distribution of the simulated irrigation reguirements, potential irrigation expansion areas, and 6A Geographic Information System (GIS) is a system of computer hardware, software, and procedures designed to support the capture, management, manipulation, analysis, medullary and display of spatially referenced data for solving complex planning and management problems (Antenucci et al., 1991). 21 optimal crop mixes is processed by GIS at the watershed scale for display. 5. ASSUMPTIONS It is assumed in the four simulation models that the four crops are not affected by pests and diseases. In addition, the irrigation requirement of crops does not include the loss of water during the delivery process. This loss should be considered in designing the irrigation pipe system. Furthermore, it is assumed that no advection exists since irrigation in a small scale would not result in the significant modification of the air movement. Thus, the irrigation water requirement per acre of land for the same crop on the same soil association is assumed the same regardless of the field size. In other words, uniformity and linearity are assumed for the same soil association. Precipitation is assumed to be the only input to a watershed in estimating the groundwater recharge rate. Streamflow available for irrigation withdrawal is assumed to be the amount of water above the 95 percent exceedence flow level set by the National Pollutant Discharge Elimination System (NPDES). Linearity is assumed in developing irrigation scenarios. That is, the expected returns from the crops increase linearly with the expansion in crop acreage. No economy of scale is considered in this study. CHAPTER 3 LITERATURE REVIEW 1. ESTIMATING IRRIGATION WATER REQUIREMENTS The requirement for irrigation is defined as the difference between the water needs of the disease-free crop and available soil moisture and effective precipitation7 (Bartholic et al., 1983). Data on soil moisture and precipitation can be readily acquired from government agencies such as the U.S. Department of Agriculture Soil Conservation Service and the National Weather Service. The regional water requirements for each crop, however, are not readily available from government agencies or research institutions. They have to be calculated by determining the evapotranspiration rates of each crop assuming that they are grown in large fields under optimal soil conditions. Evaporation is defined as the removal of water from soil or water surface by the conversion of liquid into vapor. The vaporization of water through the stomata of living plants is called transpiration. Since over-land transpiration from vegetation and direct evaporation from the soil are Effective precipitation = total precipitation - surface runoff - deep percolation 22 23 difficult to separate, they are often combined together and are referred to as evapotranspiration which is defined as the total amount of water lost to the atmosphere through transpiration, plus the evaporation of water from the surrounding soil surface. Potential evapotranspiration is defined as the evapotranspiration rate of a disease-free crop growing in large fields under optimal soil conditions, including sufficient water and fertility and achieving full production potential under the given growing environment (Doorenbos and Pruitt, 1977). Many methods have been developed to estimate the evapotranspiration rate of plants (Bowen, 1926; Blaney and Criddle, 1950; Makkink, 1957; Van Bavel, 1966; Fuchs and Tanner, 1967; Bartholic et al., 1970; Camillo et al., 1983; and Shayya and Bralts, 1989). A classic work by Penman (1948) combined aerodynamic heat and water vapor transport equations with the energy balance approach8 to estimate evaporation from open water. Inputs to Penman's equations include the mean surface temperature, air temperature, mean dew point temperature, mean wind velocity, and the mean duration of sunshine. 8The energy balance for a given system at the earth's surface is expressed as: Rn = LE + H + G where Rn is the specific flux of net incoming radiation, L the latent heat of evaporation, E the rate of evaporation, H the specific flux of sensible heat into the atmosphere and 6 the specific flux of heat conducted into the earth, assuming that the effects of unsteadiness, ice melt, photosynthesis and lateral advection can be neglected. 24 Doorenbos and Pruitt (1977) modified the Penman method to take into account the effect of crop characteristics (via crop coefficients), including growth stages, on the potential evapotranspiration rate of the crop. Based on the modified Penman method, Doorenbos and Kassam (1979) integrated the relationships between crop, climate, water and soil to quantify maximum and actual crop yields, maximum and actual evapotranspiration, and irrigation water reguirements. The maximum yield of a particular crop is defined as the harvested yield of a high producing variety that is well adapted to the given growing environment, under conditions where water, nutrients, pests and diseases do not limit yield. These methods (Doorenbos and Pruitt, 1977; and Doorenbos and Kassam, 1979) have been used in many regions throughout the world for irrigation planning and management. Bartholic et al. (1983) used the Doorenbos and Pruitt (1977) method to assess the water requirements of major field crops grown in Michigan. Terjung et al. (1984) modified the method of Doorenbos and Pruitt (1977) to estimate the water requirements of rainfed and irrigated winter wheat in China. However, these two models (Doorenbos and Pruitt, 1977; Doorenbos and Kassam, 1979) do not take into account the effect of crop genetics and management practices, such as plant population and fertilization levels, on the evapotranspiration rate of crops. 25 Furthermore, the models do not differentiate the effects of soil profile characteristics such as soil texture, porosity, thickness of the soil layer, and organic matter content on evapotranspiration rates at the soil association level. In addition, these models require intensive climatic data, including air and surface temperature, wind velocity, and net radiation. In some locations, data concerning wind velocity and surface temperature are often not available. In these cases, the applicability of the models is limited. Ritchie et al. (1989) developed a computer simulation model, CERES-MAIZE. The model simulates the effects of particular cultivars, planting density, weather, soil water, and nitrogen on the growth, development, and yield of corn. It takes into account phenological development, extension growth (of leaves, stems, and roots), biomass accumulation and partitioning, soil water balance and water use by the crop. It also takes into account soil nitrogen transformations, uptake by the crop, and partitioning among plant parts in simulating maize growth and yield. The model uses readily available data sets of precipitation and air temperature, soil characteristics, and management practices to estimate potential and actual crop evapotranspiration rates. In computing the soil water balance, the model incorporates the effects of precipitation, runoff, infiltration, drainage, crop developmental stages and 26 irrigation efficiency9 on irrigation amounts. Outputs of the model include the corn evapotranspiration rate, irrigation dates and amounts, and yield. Similar simulation models were developed for other crops, such as S0Y6R0 for soybeans (Jones et al., 1989) and BEANGRO for dry beans (Hoogenboom et al., 1990). These models have been tested and used in many areas of the U.S. and other countries, and in numerous instances satisfactory results have been obtained (Jones and Kiniry, 1986). These simulation models can be used to estimate irrigation water reguirements and to develop management decisions in large areas. He et al. (1990) obtained satisfactory results when using the CERES-MAIZE model to estimate the yield and irrigation water reguirements of corn on a 30-year basis in the Cass River Watershed of Michigan. In this study, the simulation models — SOYGRO, and BEANGRO — CERES-Maize, are used at the soil association level to estimate the irrigation water reguirements and yields of corn, soybeans, and dry beans in the study area. In addition, the FAO YIELD model (Doorenbos and Kassam, 1979) is used to estimate the irrigation water reguirements and yield of sugarbeets in the study area. ’irrigation efficiency is the ratio of average depth of water which is used to satisfy soil moisture demands to the depth of applied water. 27 2. ESTIMATING GROUNDWATER RECHARGE Recharge 10 and discharge rates of groundwater are essential knowledge for achieving sustainable use of groundwater resources. Under natural conditions, recharge is balanced by discharge from the aquifer, and the effects of groundwater development are superimposed upon these conditions. The magnitude of sustained groundwater development generally depends on how much of the natural discharge can be captured by the cone of depression 11 (Bredehoeft et al., 1982). Assuming an equilibrium condition between recharge and discharge, changes in groundwater recharge and discharge rates can be used to indicate how much water might be pumped before the aquifer system reaches a new steady state. Many methods are available to estimate groundwater recharge. Walton (1970) stated that, for a given period of time, precipitation reaching the water table (groundwater recharge) is balanced by groundwater runoff, underflow, and evapotranspiration, plus or minus changes in groundwater 10Recharge is the process by which water infiltrates the unsaturated zone and is added to the zone of saturation. It is also the quantity of water added to the zone of saturation. Major sources of recharge to drift aquifers include infiltration of precipitation, natural or induced infiltration from surface water, and upward leakage from underlying till or bedrock. uThe cone of depression is the cone-shaped geometric solid formed, after a well has begun discharging, between the water table (or other potentiometric surface) and the original position of the water table (Morrissey, 1989). 28 storage. This balance can be expressed as a groundwater budget: P, = R, + ET, + U ± AS, where P, is groundwater recharge, R, is groundwater runoff, ET, is groundwater evapotranspiration, U is subsurface underflow, and aS, is change in groundwater storage. Groundwater runoff may be estimated by separating the streamflow hydrograph 12 into surface runoff and groundwater runoff. Groundwater evapotranspiration can be estimated from rating curves13 of mean groundwater stage versus groundwater runoff. The difference in groundwater runoff between the curve for the period April through October and the curve for the period November through March is the approximate groundwater evapotranspiration. Subsurface underflow can be estimated from Darcy's equation14. Changes in groundwater storage can be estimated by the change in the mean water table during an inventory period. 12A streamflow hydrograph is a graph or table showing the flow rate as a function of time at a given location on the stream. 13The rating curve is developed using a set of measurements of groundwater discharge and water table height in a well over a period of months or years so as to obtain a relationship between the groundwater discharge and the gage height in the gaging well. 14Darcy's equation is: Q=KAI, where Q is the quantity of water per unit of time; K is the hydraulic conductivity; A is the cross-sectional area, at a right angle to the flow direction, through which the flow occurs; and I is the hydraulic gradient. 29 Allen et al. (1973) evaluated the availability of groundwater in Kalamazoo County, Michigan. Using a groundwater budget similar to Walton's, they estimated that the mean annual groundwater recharge in the Kalamazoo River basin during the 34-year period (1933-66) was about 9 inches. Groundwater runoff contributed about 65 to 80 percent of the stream's total flow. The relationships between groundwater and surface water were discussed by Pettyjohn and Henning (1979). They pointed out that, over a long period of time, the average annual groundwater runoff is equal to the effective recharge 15 to the aquifer .16 Therefore, the replenishment of groundwater in a river basin can be estimated by determining the groundwater component of runoff by stream hydrograph separation. Pettyjohn and Henning (1979) considered the effect of geologic framework on groundwater runoff and developed a computer model to estimate groundwater runoff by hydrograph separation. They ran the computer program for a number of river basins in Ohio and demonstrated that groundwater runoff contributed approximately 30 to 51 percent of the total streamflow in the study area. ISEffective groundwater recharge is defined as the total quantity of water that originates from downward infiltration to the water table and upward leakage from deeper zones to the surficial aquifer and eventually reaches a nearby stream. The volume of effective recharge is smaller than the total annual quantity of recharge due to evapotranspiration. 16An aquifer is a saturated permeable geologic unit that can yield water in a usable quantity to wells and springs. 30 Petrie (1984) used different methods of hydrograph separation described by Pettyjohn and Henning (1979) and flow duration ratios (QkW O=(Q10/Q9o)1/2 and Qior Q251 Q75 112> where and Q9Q are the discharges equalled or exceeded 10, 25, 75 and 90 percent of the time, respectively), to estimate the recharge of the aquifer system of Michigan's Upper Grand River Basin. The resulting annual recharge values range from 3.95 to 5.5 inches for a water year of almost normal precipitation, and from 2.10 to 8.32 inches for yearly extremes. Dugan and Peckenpaugh (1985) examined the climate, vegetation, and soil factors that affect consumptive water use and recharge to the groundwater system. They developed a soil-moisture computer program to estimate the recharge to the Central Midwest regional aquifer system. Their equation for computing groundwater recharge was stated as follows: R = (S + P - O - E ) - C where R is recharge (deep percolation), S is antecedent soil moisture, P is precipitation, 0 is surface runoff, E is actual evapotranspiration (AET), and C is moisture storage capacity of the soil zone. Their results demonstrated that mean annual recharge averaged slightly more than 4.5 inches for the entire study area, although the results ranged from less than 0.10 inch in eastern Colorado to slightly more than 15 inches in Arkansas. Patterns of annual recharge closely paralleled yearly and cool season precipitation 31 (October through March). They concluded that climatic effects dominate overall regional recharge patterns in the study area, and that local variations result from differences in vegetation and soil. Sophocleous and McAllister (1987) developed a detailed but simple hydrologic budget to characterize the spatial distribution of the hydrologic components of the water balance for the entire Rattlesnake Creek Basin in southcentral Kansas. The hydrologic balance equation that they used is : DR = PCP + SD - AE - RO where DR is deep drainage, PCP is precipitation, SD is soil moisture deficit, AE is actual evapotranspiration, and RO is surface runoff. By using minimal daily weather input data and the soil-plant-water system analysis methodology, they showed that, in addition to climatic controls, soil, vegetation, and land use factors also exert a considerable influence on the water balance of the study area. Precipitation is the principal natural water supply, while evapotranspiration is the major water depletion process. The available water capacity of soil profiles plays a dominant role in soil water deficit development and deep drainage (potential groundwater recharge). Vegetation and dryland or irrigated farming particularly affect the evapotranspiration (ET) components, with ET from irrigated corn and alfalfa being two to three times that from wheat. Deep drainage from 32 irrigated wheat fields was significantly higher than that from grassland and dryland wheat, while deep drainage from alfalfa is practically non-existent. In evaluating the effects of irrigation withdrawal on streamflow reduction, Wallace et al. (1987b) estimated recharge for a surface aquifer in southeastern Michigan using a water budget approach. While assuming negligible movement of water across the lateral and lower boundary of the aquifer, the recharge rate was estimated by the following equation: R = De + D, + AS Where R is the recharge from infiltration and surface water bodies, De is the discharge by evapotranspiration, D, is the discharge to surface water bodies, and groundwater storage. aS is the change in The results indicate that the annual net recharge (R„ = R - De) rate ranged from 4.8 to 9.5 inches during the period from 1971 to 1976. During the summer months of June through August, virtually no infiltrated water reached the water table. If aquifer withdrawal for irrigation had continued for a period of time, groundwater discharge to the stream would have been reduced. The full effect of aquifer withdrawal on reduction in streamflow may not show up for many years. 33 Groundwater recharge in this study is estimated using a hydrologic budget approach17, while taking into account the effects of soils, land use, crop characteristics and management practices on evapotranspiration rates of crops. Surface runoff is estimated by separating the streamflow hydrograph into surface runoff and groundwater runoff using a hydrograph separation method described by Freeze and Cherry (1979) and a computer program by Pettyjohn and Henning (1979). Evapotranspiration rates for corn, soybeans, dry beans, and sugarbeets are estimated by the computer simulations models, CERES-MAIZE, SOYGRO, BEANGRO, and YIELD. The major advantages of the hydrologic budget approach used in this study are: (1 ) ease of use, (2 ) minimal data requirements with respect to climate, soils, and the management of crops, and (3) incorporation of the effects of climate, soils, crops, and management factors on groundwater recharge (via estimation of evapotranspiration rates). 3. EVALUATION OF STREAMFLOW CAPACITY Evaluation of streamflow capacity must consider quantity, variability, and quality of streamflow over a period of time. In humid regions, problems associated with water quantity are often caused by the variability of flow 17Hydrologic budget equation and water balance equation are identical concept and are used inter-changeable in this work. 34 rather than by the lack of water. The variability of flow in a watershed can be reflected to some degree by minimum, mean, median, and maximum flows over a month or year. However, to best characterize the variability of flow, probability (i.e. the likelihood of a particular flow event) must be used. For irrigation planning, which requires adequate water supply during the irrigation season, the duration of low flows in the driest season (the percentage of time that a flow rate is equaled or exceeded) is the governing factor. Wallace and Annable (1987a) used the August Drought Flow, the discharge that was equaled or exceeded 95 percent of the time in August, to evaluate the availability of surface waters in Michigan. Wallace (1984) used a water budget approach to evaluate the impact of withdrawing streamflow for agricultural irrigation in Fish Creek in south central Michigan. July exceedence flows of 50 and 90 percent were used to compute the streamflow reduction caused by irrigation. The results indicate that, if all the irrigable land were irrigated by streamflow, July streamflow reduction would range from 50 to 80 percent, and zero flows would occur about 10 percent of the time. A study by Fulcher et al. (1986) illustrated that the July drought flows at 50 and 95 percent exceedence levels were reduced by 30 to 84 percent due to the consumptive water uses along the River Raisin in southeastern Michigan. 35 They recommended that the drought flows used in the National Pollutant Discharge Elimination System 18 (NPDES) be reduced to reflect consumptive water uses, and that current waste load allocations be re-evaluated in the watershed. In a similar study, Wallace et al. (1987b) evaluated the impacts of agricultural irrigation on streamflow in southeastern Michigan. They indicated that if all the currently irrigated land were irrigated by streamflow, the stream would be reduced to zero flow in 4 out of 6 years, for periods of time lasting as long as two months. If the stream was used to irrigate a portion of the irrigated land, flow in the river would be reduced below the 95 percent August low flow. If the flow drops below this level, there is increased risk that the water quality would become unacceptable. This study assumes that streamflow available for irrigation withdrawal is the amount of water above the 95 percent exceedence flow level set by the National Pollutant Discharge Elimination System (NPDES). The 95 percent exceedence flow is used here as the lower threshold for the purpose of estimating the amount of water for irrigation. 18The NPDES permit process controls the discharge of pollutants into surface waters by imposing effluent limitations to protect the environment. Monthly 95% exceedence flow is used in setting effluent limits. If the discharge of effluents to surface water exceeds the NPDES limit, there is increased risk that the quality of water would be degraded. The lower the value of the 95% exceedence flow in a stream, the less the amount of pollutants that can be discharged into the stream. 36 The 90, 75, and 50 percent exceedence flows in the irrigation season are used as the upper threshold for computing the maximum irrigation acreage that streamflow can support without degrading water quality. 4. USE 07 OPTIMIZATION TECHNIQUES FOR NATER RESOURCE MANAGEMENT Optimization techniques have been used in many studies of water resource management, either to attain a maximum (minimum) objective function with the given resources, or to meet the given goal with a minimum of resources. Gisser (1970) applied parametric linear programming methods to estimate the agricultural production function for imported irrigation water for corn, barley, sorghum, and alfalfa in the Pecos River Basin, New Mexico. The study showed the expected quantities of imported irrigation water that would be demanded at different prices and under a variety of constraints. Gisser et al. (1979) developed linear programming models to estimate the impact of shifting water from agriculture to the electric generating sector on the regional income of New Mexico. A study by Bras and Cordova (1981) optimized the temporal allocation of irrigation water for corn while talcing into consideration the intraseasonal stochastic variation of the crop water requirements and the dynamics of the soil moisture depletion process. Bredehoeft and Young (1983) coupled a stream aquifer simulation model 37 to a linear programming model to optimize the groundwater pumping capacity for irrigating all the available acreage of crop land in the South Platte Valley of Colorado. They concluded that under the given economic conditions in the South Platte Valley of Colorado, the most reasonable groundwater capacity would be a total capacity capable of irrigating the entire 65,500 acres of crop land with groundwater. Installing sufficient pumping capacity to totally discount surface water for irrigating all available acreage would maximize the expected net benefit and minimize the variance in expected income. Schmidt and Plate (1983) developed a stochastic optimization model to optimize the size of the irrigation area and the operation schedule of a reservoir delivering irrigation water for maximizing the crop production return in the Arabian Peninsula. They concluded that, with all of the water available in the Peninsula, the optimal irrigation design area was 1,500 hectares (3,675 acres). Singh et al. (1987) used linear and goal programming models to optimize the irrigation water supply for winter crops such as wheat, oilseeds and potatoes in Assam, India, while meeting the constraints of land, water, and protein requirements. Ponnambalam and Adams (1987) used a stochastic dynamic programming model to optimize the reservoir water supply for irrigation in India. Based on a single crop irrigation scheduling model, Rao et al. (1990) developed linear 38 programming and dynamic programming models to generate optimal weekly irrigation schedules of sorghum and cotton in India. These optimization studies considered the average economic coefficients (average gross income or net income per unit of land), crop areas, and crop growth stages to some degree. However, the effects of soil variations on crop irrigation requirements and yields were not considered in these studies. This study attempts to optimize the mix of multiple crops (i.e. corn, dry beans, soybeans, and sugarbeets) in the Cass River Watershed of the Saginaw Bay area to maximize the expected returns of irrigation. Simulation models of corn, dry beans, soybeans, and sugarbeets, and streamflow supply equations are integrated with linear programming models to optimize the expected irrigation returns under different water supply conditions. Effects of soil characteristics, climate, crop growth stages and genotypes, management practices such as fertilization and plant population, and crop budgets on irrigation water requirements and crop yields are considered over a 30-year period at the soil association level. In computing the economic coefficient (the expected gross margins per acre of land) for each of the four crops, the seasonal average value and 25th percentile 19 value of crop prices are used in the 19The 25th percentile value of crop prices indicates that crop prices in a particular year will be greater than the specified price 75 percent of the time. 39 study to avoid the overstatement of the expected returns of the optimal crop mix. 5. USE or GEOGRAPHIC INFORMATION SYSTEMS IN WATER RESOURCE MANAGEMENT A Geographic Information System (GIS) is a system of computer hardware, software, and procedures designed to support the capture, management, manipulation, analysis, medullary and display of spatially referenced data for solving complex planning and management problems (Antenucci et al., 1991). In recent years, GIS has been used more widely to improve water resource management. Many government agencies (e.g., U.S. Army Corps of Engineers, Oak Ridge National Laboratory, Tennessee Valley Authority, and agencies in Colorado, Maryland, Michigan, Minnesota, Nebraska, North Carolina, Pennsylvania, and Texas) have been using GIS in water resource management and planning (Lindhult et al., 1988). Applications include mapping land use/land cover, delineating watershed boundaries, conducting soil surveys and stream and lake inventories, monitoring and remediating surface water and groundwater contamination, evaluating water supplies, and analyzing water use impacts. GIS is also used in modeling activities. Soloman et al. (1968) used a grid system to estimate precipitation, temperature, and runoff in a 43,000 square mile area. Based on soil and agricultural capability survey data, Nagpal et 40 al. (1986) mapped Irrigation water requirements using a vector GIS and water requirement model in Vancouver Island, British Columbia. He et al. (1987) integrated a raster GIS and remote sensing data with evapotranspiration models to evaluate the impacts of human activity on changes in the surface conditions of the earth. Harris et al. (1989) combined a vector GIS with a three-dimensional finite element model to simulate groundwater flow in San Gabriel Basin, California. GIS was used in their study to process and manage the hydrogeologic data sets, to provide the input parameters to the finite element model, and to display the simulated results. Hamlett and Petersen (1992) incorporated data sets of watershed boundaries, land use, animal density, topography, soils, precipitation, and rainfall-runoff factors into a GIS-modeling system to rank the agricultural nonpoint pollution potential of 104 watersheds in Pennsylvania. In this study, GIS is used to store, process, and analyze the data sets of land use, soil associations, watershed boundaries, well log records, and geology to provide input parameters to the simulation and optimization models as well as the water balance equation for estimating irrigation requirements, evaluating the availability of groundwater and streamflow for irrigation, and developing optimal crop mixes. Simulated results are processed and displayed using GIS at the watershed scale. CHAPTER 4 PHYSICAL AMD SOCIO-ECONOMIC CONTEXT OF IRRIGATION DEVELOPMENT IN THE SAGINAW BAY AREA 1. CLIMATE Michigan is located in the heart of the Great Lakes region and consists of two large peninsulas. The lower peninsula comprises approximately 70 percent of Michigan's total land area. It extends northward nearly 300 miles from the Indiana-Ohio border (42°N latitude) to the Straits of Mackinac (46°N latitude). The Great Lakes surround Michigan and strongly influence the state's climate. For example, the lake waters' slow response to temperature changes and the dominating westerly winds retard the arrival of both summer and winter. In the spring, cool temperatures within a few miles of the shoreline slow the development of vegetation and reduce the danger of frost. In the fall, warm lake waters temper the first outbreaks of cold air and allow additional time for crops to mature or reach a stage less vulnerable to frost damage (Nurnberger, 1985). The Saginaw Bay Watershed is located in the east central portion of the lower peninsula and is surrounded by the Saginaw Bay of Lake Huron in the east. 41 The mean annual 42 temperature in the study area ranges between 46 - 47 °F. Due to the close proximity of the lake, the latitude and the local topography, the growing season20 ranges from 154 days in Saginaw County (Saginaw Consumer Power station), to 147 days in Sanilac County (Sandusky station), 144 days in Huron County (Bad Axe station), and 122 days in Tuscola County (Caro station). The seasonal (March - October) growing degree days from 1951-1980 averaged between 2,382 and 2,758 °F (see Table l)21. Table 1. Growing season length, temperature, and precipitation in the Saginaw Bay Area _________ (1951-1980)_____________________________ Station Growing Season (Days) Annual Mean T. (•F) Degree days-50 <°F) Annual Precip. (inches) Seasonal Precip. (Apr-Sep) Bad Axe 144 46.0 2,382.4 29.35 16.74 Caro 122 46.8 2,556.0 28.22 17.02 Saginaw C.P. 154 47.7 2,758.1 28.95 17.44 Sandusky 147 46.7 2,496.9 27.96 16.47 Source: Mich.Lgan Department of Agricu lture Climatology Program. Annual mean precipitation in the study area ranges between 28 and 29 inches. While there are no pronounced wet or dry periods, the mean precipitation during the growing 20The growing season is defined as the number of days between the last spring 32°F on or before July 31 and the first fall 32°F temperature after July 31. 2lThe growing degree day is the average daily temperature above a selected base temperature. The base temperature used here is 50 °F. 43 season (April - September) is between 16 and 17 inches and accounts for about 60 percent of the annual total precipitation. The monthly distribution of precipitation is shown in Figure 5. 2. CROP NIX IN THE STUDY AREA The Saginaw Bay area comprises one of the most productive farmlands in Michigan. The production of field crops for food and livestock feed plays a leading role in the region's economy. Major field crops in the study area include corn, soybeans, dry beans, and sugarbeets. Production of these crops in the study area accounted for 20.1, 23.7, 63.6, and 80.8 percent, respectively, of the total production in the State of Michigan in 1989 (Michigan Department of Agriculture, 1990). The harvested acreage of the four crops collectively accounted for 80 percent of the total harvested crop acreage in the five county area (Bay, Huron, Saginaw, Sanilac, and Tuscola). Percentage of harvested acreage of the four crops to the total harvested crop acreage over the period from 1959-1988 is shown in Figure 6. Of the five counties in the study area, Huron County is ranked first in the state in the production of corn, dry beans and barley, Saginaw County is ranked first in the state in soybean production, and Sanilac County is ranked first in the state in the production of wheat and oats. 4.0 3.5 - 3.0 — Inches 2.5 2.0 - 1.5 — 1.0 - 0.5 — 0.0 Jan Feb M ar Jun M o n th Figure 5. M ean Monthly Precipitation (inches) in C aro, M ichigan (1951-1980) 60 Crops 96 C o r n 50 h “f~ S o y b e a n s ■*“ S u g a r B e e ts _E1' Dry B e a n s percent 40 — 30 H •t* U 1 CO CO > 05 in co CO • co CO r^. ■ 05 CO CO 1^1 r ^- co CO • CO CO CF> ■ * 3 " CO r^~ CD CO a Years Figure 6. H arvested A creag e of Corn, S o y b e a n s, S u g a r B eets, a n d Dry B e a n s a s a P e rc e n ta g e of th e Total C rop A creag e H arvested in th e Five C ounty A rea (B ased on Five Year Intervals) 46 As seen in Figure 6, there have been some changes in the crop mix between the periods of 1959-63 and 1984-88. The percentage share of corn and soybeans compared to the total harvested acreage of field crops increased from 16.5 and 2.8 percent during 1959-1963 to 34.3 and 18.7 percent, respectively, during 1984-1988. During the same period, the percentage of sugarbeets was relatively stable. However, the percentage acreage share of dry beans decreased from 35.5 to 17.9 percent. These changes may be due to: (1) progress in crop breeding and the management of high yield corn and soybean cultivars that have been bred to adapt to the climate of the Saginaw Bay Watershed in areas where they would not have been grown during the 1960's; (2) compared to corn and soybeans, dry bean production is labor intensive; (3) the rotation of corn and soybeans improves yield and soil organic matter content; and (4) the production of sugarbeets is limited by the sugar processing capacity of the companies that manufacture sugar (Michigan Department of Agriculture, 1959-1990; Christenson, 1991; LeCureux, 1992; and Rouget, 1992, personal communication). 3. CROP YIELD VARIABILITY The average yields of the four crops grown in the five county area between 1959 and 1989 are: 85.3 bushels per acre (5,346 kg/ha) for corn, 24.6 bushels per acre (1,654 kg/ha) for soybeans, 12.0 cwt (hundred weight) per acre (220 kg/ha) 47 for dry beans, and 17.7 short tons22 per acre (39,678 kg/ha) for sugarbeets (Table 2). The coefficients of variation23 for the four crops over the period 1959-1989 are: 0.198 for corn, 0.253 for soybeans, 0.146 for dry beans, and 0.112 for sugarbeets. A comparison of these coefficients indicates that dry beans and sugarbeets had relatively stable yields during the period of 1959-1989 while the yield variations of corn and soybeans were relatively greater. Table 2. Average Crop Yields and Coefficient of Variation over the Period 1959-1989 Period 1959-1989 Corn (bu/a) 85.3 Soybean (bu/a) 24.6 Drybean (cwt/a) 12.0 Sugarbeet (ton/a) 17.7 0.198 Coef. Var. 0.253 0.146 0.112 Source: Michigan Agricultural Statistics, 1959-1990. The variations in the production of corn, soybeans, dry beans, and sugarbeets were affected by multiple factors including weather, soils, and management practices. Correlation analysis between the crop climatic yields24 and the monthly mean precipitation and temperature reveals that M1 short ton = 2,000 lbs “The coefficient of variation is the ratio of standard deviation to the mean of the sample. It measures the relative magnitude of variation. ^Crop climatic yield is defined here as the difference between the actual yield and the three year moving average yield. The assumption was that technology would remain the same during a three-year period and the changes in crop yield during this period were caused by fluctuation of climate. 48 the production of corn was positively related to the amount of precipitation during June through August. Soybean production was positively related to the July mean temperature and the amount of precipitation during July through August. The production of dry beans was inversely related to the mean temperatures between May and June (see Table 3). Table 3. Correlation Coefficients between Crop Climatic Yields and Precipitation and Temperature. Crop Precipitation Period r Corn Jun. - Aug. 0.648 ** Soybeans Jul. - Aug. 0.612 ** Temperature Period r July 0.442* Drybeans May - June -0.489* Note: Crop yields of Tuscola County and weather data (19511980) from the Caro Station were used in this analysis. The correlation analysis indicates that the period from June through August is a critical period for managing corn and soybean production (grain forming and filling period) . Irrigation may be needed during this period to ensure an adequate water supply for plant growth. Similarly, drybeans are sensitive to the mean temperature during May and June, and appropriate planting dates should be determined to ensure that adequate yields are obtained. 49 4. SOIL SUITABILITY FOR IRRIGATION EXPANSION The soils in the Saginaw Bay area are mainly loamy and silty clays on nearly level to gently sloping topography, and are poorly drained in much of the area. They have moderate to high available water capacity and slow to very slow permeability (Michigan State University, 1981). A compact layer is present within 6 feet of the surface in a majority of the area. Based on soil properties (which include slope, texture, permeability, and natural drainage), Kittleson et al. (1987) evaluated the suitability of soils for subsurface irrigation in the Saginaw Bay area. The most important factors used in classifying the suitability of soils for subsurface irrigation were the presence or absence of a barrier layer within 6 feet of the surface as well as the drainage and slope characteristics of the soil. First, if a barrier layer with low permeability (less than 0.02 inch/hr) is present between 40 - 60 inches of the surface in a very flat (slope less than 1%) and poorly drained soil association, this association was believed to be highly suitable for subsurface irrigation. Second, soil associations which have a moderately low permeability (between 0.02 and 0.06 inch/hr) layer within 40-60 inches of the surface and are both flat (slope between 1 - 2 %) and moderately well drained were classified as less suitable (i.e. medium suitability) for subsurface irrigation. Third, associations which are well drained and have a layer with a 50 permeability greater than 0.06 inch/hr which lies between 40 and 60 inches of the surface were grouped as not suitable for subsurface irrigation. Considering all of the factors (which include presence of a barrier layer within 40-60 inches of surface, slope, texture, and natural drainage characteristics), Kittleson et al. (1987) derived a soil suitability map for subsurface irrigation in the Saginaw Bay area. Their results indicate that 85 percent (1,667,000 acres) of the total agricultural land in the study area would be suitable for subsurface irrigation (see Table 4 and Figure 7). Thus, there is a great potential for subsurface irrigation expansion in the Saginaw Bay area. Table 4. Agricultural Land Soil Suitability for Subsurface _________ Irrigation in the Saginaw Bay Area_______________ Soil Suitability Highly Suitable Less Suitable (Medium) Not Suitable (Low) Total Acres % 437,582 22.2 1,229,414 62.3 304,937 15.5 1,971,933 100.0 In summary, annual mean temperature and precipitation in the Saginaw Bay area average around 47 °F and 29 inches, respectively. The four major field crops in the region are corn (34.3 percent of the total harvested acreage of all field crops), soybeans (18.7 percent), dry beans (17.9 percent), and sugarbeets (8.6 percent). These crops 51 I I N on-A grleultural Land ■ I High Sultablllly jH U Uidlum Suitability Lo* Suitability Figure 7. Soil Suitability for Subsurface Irrigation 52 collectively account for about 80 percent of the total harvested crop acreage. The production of corn and soybeans are positively related to the amount of precipitation during the period from June through August. Appropriate crop management during this period is critical. Based on the suitability of soils, the potential exists for as many as 1,667,000 acres of subsurface irrigation expansion in the Saginaw Bay area. CHAPTER 5 MASS BALANCE 07 IRRIGATION WATER REQUIREMENTS AND AVAILABLE WATER RESOURCES Streamflow and groundwater are used for agricultural irrigation and domestic uses in parts of the Saginaw Bay area. The currently irrigated crop land in the Saginaw Bay five-county area25 is 15,035 acres (Bureau of the Census, 1989). However, the potential exists to irrigate as many as 1.67 million acres using subsurface irrigation based on the suitability of soils. To assure an adequate water supply for the potential expansion of irrigation, the irrigation requirements and the availability of groundwater and streamflow must be evaluated before large investment is committed to irrigation expansion. I. CROP IRRIGATION WATER REQUIREMENTS The irrigation water requirement of a crop is the difference between its water need and available soil moisture and effective precipitation26 (Bartholic et a l ., “The Saginaw Bay five-county area refers to Bay, Huron, Saginaw, Sanilac and Tuscola counties. “Effective precipitation = total precipitation - surface runoff - deep percolation 54 1983). In this study, simulation models are used to estimate the irrigation water requirements for corn, soybeans, dry beans and sugarbeets. 1. DESCRIPTION OF THE IRRIGATION SYSTEM The irrigation system examined in this study is an agricultural crop production system in the Saginaw Bay Watershed, Michigan. The Cass River Watershed, a subwatershed, was chosen as a pilot study area to estimate the crop requirements for irrigation. The watershed runs across Huron, Sanilac, Tuscola, Lapeer, Genesee and Saginaw Counties, and has a drainage area of 841 square miles (Figure 8). Agriculture, the major land use in the Cass River Watershed, accounts for 67 percent of the total land area (Figure 9). Soils in the watershed consist mainly of loamy and silty clays and sands, and are poorly drained in much of the area. The spatial distribution of 12 soil associations in the Cass River Watershed is shown in Figure 10 and Table 5. The predominant associations are Marlette-Capac, CapacParkhill, Pipestone-Kingsville-Saugatuck-Wixom, Metamora-Blount-Pewamo, and Boyer-Wasepi, which collectively account for 77 percent of the total land area. The four crops being studied are corn, soybeans, dry beans, and sugarbeets. They collectively accounted for approximately 80 percent of the total harvested acreage 55 a a BAOAXE SAGINAWCP SANDUSKY WAHJAMEGA * Waafher sta tio n Figure 8. a Gaging station The Cass River Watershed Boundary 56 Urban ond Built-Up Agriculture Deciduous F o re st Wetland Figure 9. Land Use in the Cass River Watershed 57 ■ 1 n 40. O akvIIU -P loin-Sptnks □ 51. P ip it lo n s - K ln g s v lllt- E lc . 41. M orl*M *-Copae fu m 64. M e ta m c r a - B la u n l- P m m a 42. Capac-Parkhlll E S 69. T apan-Londs 70. Tappan-Londo-Po$*yvIII» P JT JB 11 i i 11 43. H o u g h ton -P alm s-S Ioa n I" 1* T ' H 46. B o y ir -W a s tp ! w 73. San ilac-B ach 48. L e n a v t« -T o le d o -D « l Ray 8888888 74. Sh ib ion -K llm an agh m l Figure 10. Soil Associations in the Cass River Watershed 58 between 1985 and 1989 in the Saginaw Bay five-county area (Michigan Department of Agriculture, 1986-1990). Table 5. Soil Associations in the Cass River ftWatershed Soil No. Soil Association Acres 40 Oakville-Plainfield-Spinks 35,355 6.1 41 Marlette-Capac 153,105 26.3 42 Capac-Parkhi11 91,798 15.8 43 Houghton-Palms-Sloan 24,714 4.2 46 Boyer-Wasepi 56,788 9.8 48 Lenawee-Toledo-Del Rey 7,812 1.3 51 Pipestone-KingsvilleSaugatuck-Wixom 76,846 13.2 64 Metamora-Blount-Pewamo 71,671 12.3 69 Tappan-Londo 20,508 3.5 70 Tappan-Londo-Poseyville 19,549 3.4 73 Sanilac-Bach 21,146 3.6 74 Shebeon-Kilmanagh 2,945 0.5 582,237 100.0 Total % 2. SIMULATION 07 THE IRRIGATION SYSTEM 2.1 Description of the simulation Models The irrigated crop production system in this study consists of three components: the crops, the soil, and the inland water resources. Inputs to the system include precipitation, solar radiation and management practices. Outputs of the system include grains, beets, nutrients and 59 runoff. Computer models are used to simulate the interactions between the three components to estimate evapotranspiration, irrigation water requirements, and the yields of corn, soybeans, dry beans, and sugarbeets. The computer models used include WGEN, CERES-MAIZE, SOYGRO, BEANGRO and YIELD. WGEN is a weather simulation program developed by Richardson and Wright (1984). It generates solar radiation estimates from precipitation and maximum and minimum temperature data for use in the CERES-MAIZE, SOYGRO, BEANGRO, and YIELD models. CERES-MAIZE (Ritchie et al., 1989), SOYGRO (Jones et al., 1989), and BEANGRO (Hoogenboom et al., 1990) are crop growth simulation models for corn, soybeans, and dry beans, respectively. They use daily weather data, soil characteristics, and management information to estimate crop yields and irrigation water requirements. YIELD is a computer model (Schultink et al., 1989) based on a method developed by FAO27 (Doorenbos and Kassam, 1979) and is used to estimate crop yield, evapotranspiration, and irrigation requirements. The FAO method was modified in the computer model to incorporate slope, soil water content and fertilizer usage information. Inputs to the model include ^This method was developed to estimate the production potential of many crops based mainly on the climatic conditions. It does not take into account the effects of crop genetics, soil profile characteristics, and management practices on evapotranspiration rate and yield. 60 daily or monthly mean temperature, precipitation, solar radiation, wind speed (at 2 m height), and relative humidity. The YIELD model is used in this study to estimate the yield and irrigation water requirement of sugarbeets. 2.2 Model Inputs and Outputs A. Climatic Data Daily minimum and maximum temperature in °F and precipitation in inches are required to run the WGEN and CERES-MAIZE, SOYGRO, and BEANGRO models. Thirty year climatic data (1951-1980) for the Bad Axe, Caro, Flint, Saginaw Consumer Power, and Sandusky weather stations were obtained from the Michigan Department of Agriculture Climatology Program. The locations of these weather stations are shown in Fig. 8. The data sets from these weather stations were entered into the WGEN model to generate solar radiation estimates for use in the simulation models. Monthly mean temperature, precipitation, duration of sunshine (%), wind speed (in m/s at 2 m height) and relative humidity data obtained from the Flint weather station (located in Genesee County, south of the study area) were used in the YIELD model to estimate yield and irrigation requirement of sugarbeets. 61 B. soil Data Soil characteristics data are also required to run the CERES-MAIZE, SOYGRO, and BEANGRO models. The necessary data set includes the following parameters: soil type, classification, bare soil albedo, porosity, SCS runoff curve number, thickness of the soil layer, lower limit of plant extractable soil water, drained upper limit of soil water content, saturated water content, moist bulk density, and organic carbon concentration in the soil layer (Jones and Kiniry, 1986). The soil characteristics for the study area were obtained from the Michigan State University Nowlin Chair's Office and the U.S. Department of Agriculture Soil Conservation Service. C. Management Information Management inputs to the simulation models include crop varieties and their genetic coefficient data, planting and harvest dates, plant population, row spacing, and type and amount of fertilizer to be used. Management data in this study were acquired from the Huron County Cooperative Extension Service Office (LeCureux, 1988a, 1988b, 1990a) and the Saginaw Valley Bean and Beet Research Farm (Christenson et al., 1986, 1987, 1988, and 1989). 62 D. Modal outputs The model outputs used in this study include crop development stages, leaf area index, ground biomass (g/m2), root weight (g/plant), root depth (cm) and root length density (cm root/cm3); organic nitrogen content (kg/ha) and elemental nitrogen as nitrate (N03, kg/ha) and ammonium (NH4) in the soil profile, total nitrification (kg/ha), leaching of nitrate (kg/ha) and total plant nitrogen uptake (kg/ha); cumulative evapotranspiration (ET, mm), precipitation (mm), irrigation water requirements (in mm), irrigation date, plant-extractable soil water in the soil profile (in cm); grain number (grains/m2), dry single kernel weight (g/kernel), and grain yields (in kg/ha, bu/acre, cwt/acre, or short ton/acre). 3. SIMULATION RESULTS AND DISCUSSION 3.1 Irrigation Water Requirements Per Acre of Land The irrigation water requirements of corn, soybeans, and dry beans were estimated for 25 to 30 years by performing simulations that rely on data obtained from the weather stations at Bad Axe, Caro, Saginaw Consumer Power, and Sandusky for each of the 12 soil associations in the Cass River Watershed. The locations of these four weather stations and the 12 soil associations were digitized using 63 C-Map and PC ARC/INFO28, and are shown in Figures 8 and 10, respectively. The irrigation requirement of sugarbeets was simulated for all soils for 32 years by using the YIELD model based on the weather data from the Flint weather station in Genesee County. Distinctions of irrigation requirements and yields for sugarbeets between soil associations were not made because of limitations in the YIELD model and the lack of wind speed data. The CERES-MAIZE, SOYGRO, BEANGRO, and YIELD models were run over 2,200 times to estimate irrigation requirements and yields of corn, soybeans, dry beans, and sugarbeets for different soil associations and weather stations. The outputs of these 2,200 simulations are statistically divided into two groups: mean and 25th or 75th percentile. The summary values at the mean level are just simple, arithmetically averaged values. The summary values at the 25th percentile (used for crop yields) indicate that the crop yield in an individual year will be smaller than the specified yield 25 percent of the time, and will exceed or equal the specified yield 75 percent of the time. For irrigation water requirements, the value at the 75th percentile indicates that the requirement for irrigation in 28C-MAP is a geographic information system developed at the Michigan State University Center for Remote Sensing, East Lansing, MI. ARC/INFO is a trademark of Environmental Systems Research Institute, Inc., Redlands, CA. 64 a particular year will be smaller than the specified value 75 percent of the time.29 The output summaries of the simulations are listed in Tables 6-9. The irrigation requirements are greatest in July when the four crops are at their critical development stage (silking or blossoming and starting grain filling for corn, dry beans and soybeans, and the rapid development period of roots for sugarbeets) and need adequate soil moisture to obtain high yields. Irrigation requirements at the mean level average 77 mm (3.03 inches) for corn, 105 mm (4.13 inches) for soybeans, 102 mm (4.02 inches) for dry beans, and 69 mm (2.72 inches) for sugarbeets. Irrigation requirements at the 75th percentile average 108 mm (4.25 inches) for corn, 140 mm (5.51 inches) for soybeans, 130 mm (5.12 inches) for dry beans, and 96 mm (3.78 inches) for sugarbeets (Figure 11). Irrigation may increase yields of corn, soybeans, dry beans and sugarbeets by a large margin over non-irrigated identical plantings in the simulated study area (Figure 12). wIt is not sufficient to consider how crops respond to the average characteristics of the environmental inputs. The use of statistical values at the 25th or 75th percentile will better represent the historical trends of the crops' responses to the environmental variables and will be less subject to overstatement. Table 6. Simulated Average Irrigation Water Requirements (mm) at the 75th Percentile Corn Soybean Location Period Soil # June July Aug June Bad Axe 30 40 43 129 86 30 41 53 107 30 74 54 25 41 25 Caro Sandusky Saginaw Sugarbeet* Drybean July Aug June 0 129 132 54 51 156 109 58 46 55 107 55 46 53 106 25 51 38 25 70 30 July Aug June July Aug 0 130 90 24 96 71 109 51 145 105 24 96 71 154 113 0 142 109 24 96 71 52 160 107 48 154 104 24 96 71 54 0 142 106 0 143 86 24 96 71 105 73 34 141 116 35 141 71 24 96 71 53 109 105 0 112 109 0 109 56 24 96 71 42 0 105 53 0 151 107 0 138 . 102 24 96 71 30 43 0 95 97 0 97 97 0 94 93 24 96 71 30 64 47 98 96 0 142 125 0 145 97 24 96 71 25 48 56 110 57 54 118 111 51 116 57 24 96 71 25 69 56 110 58 53 159 114 0 114 107 24 96 71 25 70 54 108 105 0 140 109 0 135 96 24 96 71 25 73 60 117 60 57 155 117 54 120 60 24 96 71 44 108 Mean 72 25 140 112 17 130 88 96 24 71 * Note: For sugarbeets the values are the same for all soils and all stations due to the limitation of the YIELD model and availability of the weather data. Table 7. Simulated Average Irrigation Water Requirements (mm) at the Mean Level Corn Soybean Location Period Soil / June July Aug June Bad Axe 30 40 23 96 60 30 41 30 82 30 74 23 25 41 25 Caro Sandusky Saginaw Sugarbeet* Drybean July Aug June July Aug June 1 92 98 0 105 66 11 69 50 54 17 117 91 16 106 63 11 69 50 85 53 12 109 95 11 105 58 11 69 50 38 82 53 26 123 79 16 110 63 11 69 50 46 33 84 57 0 101 88 0 103 59 11 69 50 25 51 33 79 58 17 115 91 12 115 56 11 69 50 25 70 20 83 56 4 108 87 0 103 54 11 69 50 30 42 8 69 50 2 94 92 2 95 58 11 69 50 30 43 0 37 45 0 60 75 0 51 48 11 69 50 30 64 19 74 57 0 91 93 0 99 58 11 69 50 25 48 28 70 49 18 107 73 13 104 48 11 69 50 25 69 28 83 60 13 120 86 7 108 60 11 69 50 25 70 25 79 60 4 113 89 2 110 53 11 69 50 25 73 34 75 53 25 116 87 14 113 49 11 69 50 July Aug 24 55 105 Mean 77 10 87 7 102 69 57 11 50 * Note: For sugarbeets the values are the same for all soils and all stations due to the limitation of the YIELD model and availability of the weather data. Table 8. Simulated Average Crop Yields at the 25th Percentile Locetion 1 r r i fl Period (yrs.l Soil # Bad Axe 30 30 30 40 41 74 6437 7035 7105 102.5 112.0 113.1 Caro 25 25 25 25 30 30 30 41 46 51 70 10830 10024 10100 11151 172.4 159.6 160.8 177.6 42 43 64 48 69 70 73 . 9755 9823 9697 11065 11060 11034 10298 9672 155.3 156.4 154.4 2713 3367 3918 3941 3299 2283 4914 4 3.2 5 3.6 6 2.4 62.7 5 2.5 3 6.3 7 8.3 4000 9823 3693 4609 5082 4685 4939 4376 63.7 156.4 58.8 7 3 .4 80.9 7 4 .6 7 8 .6 69.7 Sandusky a t e Saginaw d 25 25 25 25 Mean N 0 Bad Axe 30 30 30 Caro 25 25 25 25 40 41 74 41 46 51 70 Sandusky 30 30 30 25 25 25 25 42 43 64 48 69 70 73 n i r r i g a Saginaw t e d Mean * Note : the values lor s kg/ha Corn | bu/ac 176.2 176.1 175.7 164.0 154.0 Soybean | kg/ha | bu/ac | 2059 30.6 2619 39.0 2627 39.1 3085 45.9 2289 34.1 2840 42.3 2683 39.9 2661 39 .6 3028 45.1 2105 31.3 2729 40 .6 2625 39.1 2617 39 .0 3089 46.0 2647 39 .4 400 5.9 737 11.0 640 9.5 795 11.8 758 11.3 455 6.8 769 11.4 761 11.3 2752 4 1.0 564 8 .4 776 11.6 773 11.5 776 11.6 . 855 12.7 844 12.6 nrj ■■j .. . 1 L _ 1!— !__• -- r- Drybean kg/ha 1 Ibs/ac 1 1 ■I... kg/ha Sugarbeet * 1 tons/ac 4618 4756 4758 4122.0 4245.1 4246.5 67380 67380 67380 27.3 27.3 27.3 4543 4418 4526 4432 4428 4429 4361 4 054.4 3 943.2 4039.4 3956.1 67380 67380 67380 67380 3 951.8 3953.1 3892.6 67380 67380 67380 4159 4140 4030 4238 4417 621 1474 1333 1323 1302 7 50 1626 3 711.7 3 695.4 3 5 9 7 .4 3 782.4 3 942.2 67380 67380 67380 67380 67380 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 554.0 1315.4 1189.5 1180.9 1162.3 669.3 1451.6 58150 58150 58150 23.5 23.5 23.5 58150 58150 58150 58150 23.5 23.5 23.5 23.5 1489 4372 1125 1655 1455 1447 1554 1538 1329.0 3 9 0 2 .0 1004.3 58150 58150 58150 23.5 23.5 23.5 1477.4 1299.0 1291.7 1386.7 1372.4 58150 58150 58150 58150 58150 23.5 23.5 23.5 23.5 23.5 model and availability of the weather data. cn -j Table 9. Simulated Average Crop Yields at the Mean Level Location 1 Period (yrs.) Soil # Bad Axe 30 30 30 40 41 74 Caro 25 25 25 25 41 46 51 70 Sandusky 30 30 30 42 43 64 Saginaw 25 25 25 25 48 69 70 73 11656 11554 11424 10845 10909 30 30 30 40 41 74 5267 6512 6862 185.5 183.9 181.9 172.7 173.7 83.8 103.6 109.2 25 25 25 25 41 46 51 70 6661 5104 4252 7467 106.0 8 1.2 67.7 118.9 r r i g a t e d Mean Bad Axe N o n i r r i g a t e d Caro Corn kg/ha | bu/ac 9531 151.7 10279 164.0 10488 167.0 11261 179.3 10510 167.3 10684 170.1 11612 184.9 10720 170.7 11407 181.6 10756 171.2 Soybean kg/ha 2428 2912 2892 | Drybean bu/ac 36.1 43.3 43.1 kg/ha 3263 2696 3087 2960 2840 3154 2473 3101 3048 2979 3255 2935 | Sugarbeet11 Ibs/ac kg/ha 5012 5100 5098 4473.2 4551.6 4 550.6 69210 69210 69210 tons/ac 28.0 28.0 28.0 48.6 40.1 4 6.0 44.1 4787 4705 4746 4721 4273.0 4 199.4 4236.3 4213.3 69210 69210 69210 69210 28.0 28.0 28.0 28.0 42.3 46.9 36.8 4795 4815 4729 4 280.0 4 297.6 4 220.5 28.0 28.0 28.0 4 6 .2 4 5 .4 44 .3 4 8 .4 4 3.7 4527 4477 4456 4539 4751 4040.9 3995.1 3977.1 4 051.2 4 240.0 69210 69210 69210 69210 69210 69210 69210 69210 766 1149 1078 11.4 17.1 16.0 1306.3 2241.7 2145.9 61382 61382 61382 1200 1067 708 1183 17.9 15.9 10.5 17.6 1464 2512 2404 2196 2106 1406 2271 1 1 28.0 28.0 28.0 28.0 28.0 24.9 24.9 24.9 24.9 24.9 24.9 24.9 1959.7 61382 1879.6 61382 1255.2 61382 2027.1 61382 Sandusky 30 42 8148 129.7 1200 17.9 2404 2146.1 61382 24.9 30 43 10976 174.7 2969 4 4 .2 4637 4 138.5 61382 24.9 30 64 6440 102.5 io io 15.0 2133 1904.2 61382 24.9 Saginaw 25 48 7705 122.6 1377 20.5 2334 2083.3 61382 24.9 25 69 7499 119.4 1302 19.4 2141 1910.9 61382 24.9 25 70 7174 114.2 1269 18.9 2091 1866.7 61382 24.9 25 73 7250 115.4 1371 2 0.4 2252 2009.8 61382 24.9 Mean 6951 110.6 1261 18.8 2311 2062.5 61382 24.9 ** Note : The values lor « Note: The values lor sugarbaets are the same lor all soils and for all stations due to the limitation of the YIELD model and availability of the weather data.' 180 Note -- For sugarbeets, th e values are the sam e for all soils and for all w eather stations d ue to limitations of th e YIELD model and th e availability of w eather data. E lJu ly . . . EH A u g u s t 150 Irrigation Water Requirement (mm) Month E3 J u n e 120 90 60 30 C o rn Soybeans D ry B e a n s S u g a rb e e ts Crop Figure 11. S im ulated Irrigation W ater R eq u irem en ts a t th e 75th P ercentile (Ju n e th ro u g h A ugust) 180 S 3 I r rig a te d 03 N o n - l r r ig a t e d 150 Units: Corn and S oybeans (bu/ac), Dry B eans (cwt/ac), S ugar B eets (tons/ac) Yield 120 90 60 30 C o rn Soybeans D ry B e a n s S u g a r B e ets C ro p Figure 12. C o m p ariso n of S im u lated Irrigated a n d N on-lrrigated C rop Y ields in th e C a s s River W ate rsh e d 71 3.2 Total irrigation Watar Requirements in tha Casa Rivar Watarstaad The average values of the irrigation requirements in July at the 75th percentile for each of the four crops (Table 6 ) were multiplied by the total acreage of agricultural land to derive the total irrigation requirements for the Cass River Watershed (Table 10). The results indicate that sugarbeets only require (at the 75th percentile) about 124,000 acre-feet of water for irrigation in July, which is the least amount among the four crops. That is, if all 392,713 acres of the total agricultural land in the Cass River Watershed were planted in sugarbeets, the minimum amount of water that would be needed in July to satisfy the irrigation need would be about 124,000 acrefeet. If any other single crop or combination of the four crops were planted in all the agricultural land in the watershed, a greater amount of water would be needed in July to meet the irrigation requirements. 4. TOTAL IRRIGATION WATER REQUIREMENTS IN THE SAGINAW BAY AREA The total irrigation requirements at the 75th percentile for the entire Saginaw Bay five-county area were determined by multiplying the total acreage of agricultural land by the per acre irrigation water requirements. shown in Table 11 and Figure 13. The results are If all 2 million Table 10. Total Irrigation Water Requirement for the 392,713 acres of Agricultural Land in the Cass River Watershed (If A Single Crop were __________ Planted to the Total Acreage)__________________________________________ Item Irrigation Demand in July at 75th Percentile Corn Acreage Planted Irrigation Demand in inches per acre Total Irrigation Demand in acrefeet Soybeans Dry Beans | Sugarbeets 392,713 392,713 392,713 392,713 4.25 5.51 5.12 3.78 139,090 180,320 167,560 123,700 Total Irrigation Demand in cfs 2,263 2,934 2,726 2,012 * One acre-foot is the amount of water needed to cover an acre of land to a depth of 1 foot. Table 11. Total Irrigation Water Requirement for the 1,971,933 acres of Agricultural Land in the Saginaw Bay Area (If A Single Crop were Planted __________ to the Total Acreage)______________________________________________________ Item Irrigation Demand in July at 75th Percentile Soybeans Dry Beans Sugarbeets I 1,971,933 1,971,933 1,971,933 1,971,933 I 4.25 5.51 5.12 3.78 1 698,390 905,450 841,360 621,160 1 11,360 14,730 13,680 10,100 I Corn Acreage Planted 1 Irrigation Demand in inches per acre Total Irrigation Demand in acrefeet 1 Total Irrigation Demand in cfs | 16 Irrigation Demand in cfs (Thousands) 14 12 10 C o rn Soybeans Dry B e a n s S u g a r B e e ts Crop Figure 13. Total Irrigation W ater R equirem ent in July at th e 75th Percentile for S elected C rops Grown in the Saginaw Bay Area 74 acres of existing agricultural land were irrigated and planted in sugarbeets (the least water consumptive of the four crops), a total volume of about 621,000 acre-feet (or a flow rate of 10,000 cfs) of water would be needed in July in order to meet the irrigation requirement. If soybeans (the most water consumptive of the four crops) were planted and irrigated over the entire agricultural land area, a total volume of approximately 910,000 acre-feet of water would be required in July to meet the irrigation need. The total irrigation requirements for corn and dry beans in July over the entire agricultural land area are 7000,000 and 841,000 acre-feet, respectively. Greater July irrigation requirements for soybeans and dry beans, as compared to those for corn and sugarbeets, may indicate more frequent irrigation applications are needed for soybeans and dry beans in July. These simulated results need to be validated in the field in the Saginaw Bay area to avoid over- or under-statement. 5. LIMITATIONS OF THE SIMULATION MODELS A simulation model is a mathematical representation of the physical system that has been chosen for study. Conceptually, it includes only those important, quantifiable factors and excludes factors that are difficult to quantify or less important. Since it only incorporates a portion of 75 the factors that affect the physical system to be studied, even a validated simulation model has its limitations. The four simulation models used in this study do not include the effects of diseases and pests on the development of the crops. The effects of nutrients deficiency (except nitrogen) on the growth of crops are not considered either. Thus, it is inevitable that differences exist between simulated and actually measured results. For the CERES-MAIZE model, after being evaluated in numerous locations, it has been reported that the model produced estimates of grain yields that had highly significant correlations with measured values (r2= 0.52 -0.87). The measured data accounted for 52 to 87 percent of the variations found in the simulated data (Kiniry and Jones, 1986). The comparison of the simulated non-irrigated crop yields in the Cass River Watershed with actual crop yields (1959-1980) in Tuscola County is shown in Table 12. The simulated yields of corn, soybeans and sugarbeets had highly significant correlations with the actual crop yields (a=0 . 0 1 for corn, at-0.05 for soybeans and sugarbeets). However, the actual crop yields only accounted for less than 40 percent of the variations in the simulated data. A large portion of the variations (up to 80 percent) found in the simulated yields was caused by errors. The simulated dry bean yields were poorly correlated with the actual yields from the period 1959-1980. Of the four simulation models, the CERES 76 MAIZE produced relatively accurate estimates of corn yield when compared to the actual corn yield. Table 12. Correlation Analysis between the Simulated Nonlrrigated Crop Yields in the Cass River Watershed and the Actual Crop Yields (1959-1980) in Tuscola County_____________________________________________ Crop Regression Equation Corn Y = 26.66 + 1.10 x 0.36** Dry Beans Y = 14.93 + 0.54 X 0.03 Soybeans Y = X 0 .2 0 * 6.24 + 0.60 r2 Sugarbeets Y = 15.70 + 0.64 X 0.25* Actual Yield Source: Michigan Department of Agriculture, 1959-1989. The discrepancies between the simulated yields and actual yields may be partly attributed to the specifications of some of the input parameters. During the simulation, the soil conditions, planting dates, plant population, and fertilizer levels were fixed for all four crops over the period 1951-1980 because information on these parameters in each individual year was not available. Thus, the effects of chronology, soils, and management on crop yields may not be fully considered in some years. In addition, the simulated yields do not take into account the effects of pests and diseases on crop yields. Moreover, the simulated yields are at the watershed scale, whereas the actual crop yields were aggregated over the entire Tuscola County. This scale difference affects the comparability of the simulated yields and the actual county-wide data. 77 Table 13 shows the comparison of subsurface irrigated and non-irrigated crop yields in Huron County from the period 1987-1990 (LeCureux and Booms, 1987; 1988a, 1988b; LeCureux, 1989; 1990b). The results represent four years' study of corn, one year study of soybeans, two years' study of dry beans, and three years' study of sugarbeets. Subsurface irrigation increased corn yields by 6 . 6 percent in 1990 (a wet year) and by 78.9 percent in 1988 (a drought year). There was no difference between subsurface irrigated and non-irrigated soybean yields in 1989. For dry beans, subsurface irrigation did not result in increased yield in 1989 but increased the yield by 27.7 percent in 1990. Application of subsurface irrigation for sugarbeets increased yields by 6.9 percent in 1990 and by 38.9 percent in 1988. The amount of irrigation water applied for the four crops during the entire growing season ranged from 3.1 inches for dry beans, to 4.3 inches for soybeans and 6 inches for corn and sugarbeets. It should be noted that the effects of subsurface irrigation on crop yields and irrigation water requirements may be different from those of other irrigation techniques such as flood irrigation or sprinkler irrigation. Thus, although application of subsurface irrigation did not result in an increase in soybean yield in 1989, application of other irrigation techniques may increase soybean yield. Table 13. Comparison of Sub-Irrigated and Non-Subirrigated __________ Crop Yields in Huron County____________________ Year 1987 Item Corn Nonlrrg. 115 Irrig. 164 Diff. (%) Irrig. Amount (") Nonlrrg. Irrig. 1988 Diff. (%) Irrig. Amount (") 1989 Sugar Beets 42.6 4.5 90 18 161 25 78.9 38.9 6.5 4.8 160 39 21.6 22.5 Irrig. 175 39 20.8 24.0 9.4 0 -3.7 6.7 7.9 4.3 4.3 8.1 Diff. (%) Nonlrrg. 147 18.8 26.2 Irrig. 157 24.0 28.0 6.6 27.7 6.9 5.5 1.8 5.0 Diff. (%) Irrig. Amount (") Mean Drybean Nonlrrg. Irrig. Amount (") 1990 Soybean Nonlrrg. 128 39 20.2 22.2 Irrig. 164 39 22.4 25.7 0 10.9 15.6 3.1 6.0 Diff. (%) Irrig. Amount (") 28.1 6.1 4.3 79 Table 14 lists the mean simulated irrigated (1951-1980) crop yields and irrigation water requirements in the Cass River Watershed and the mean actual subsurface irrigated crop yields and irrigation requirements in Huron County (1987-1990). Information on the actual subsurface irrigated crop yields and amount of irrigation water applied is only available for up to 4 years (for corn) (LeCureux and Booms, 1987; 1988a, 1988b; LeCureux, 1989, 1990b). It is used here for reference since no long term records on subsurface irrigated crop yields is available. Table 14. Comparison of the Mean Simulated Irrigated Crop Yields in the Cass River Watershed (1951-1980) with the Actual Subsurface Irrigated Crop Yields (1987-1990) in Huron County______________________ Item Yields Irrig. Applied Corn Soybean Drybean Sugar Beets Actual 164.0 39.0 22.4 25.7 simulat. 173.7 43.7 42.4 28.0 Diff.(%) 5.9 12.1 89.3 8.9 Actual 6.1 4.3 3.1 6.0 Simulat. 6.1 8.0 6.5 5.1 Diff.(%) 0.7 84.9 111.0 -14.7 It can be seen from Table 14 that based on the limited information, the simulation models seemed to have produced relatively accurate estimates of the yields and irrigation water requirements of corn and sugarbeets but over-estimated the yield of dry beans by 89.3 percent. The irrigation water 80 requirements of soybeans and dry beans were over-estimated by 85 and 111 percent, respectively. be related to the following factors: These differences may (1 ) long term subsurface irrigated crop records were not available; (2 ) effects of pests and diseases on crop yields and irrigation water requirements were not incorporated in the simulation models; (3) effects of subsurface irrigation techniques on crop yields and irrigation water requirements were not considered in the models; and (4) automatic irrigation was used in the simulation models during the simulation. That is, whenever there was a need for irrigation, the models adopted automatic irrigation so as to timely meet the irrigation water requirements of the crops. However, in the field operation, there may exist a time lag between the time when crops need water and the time that application of irrigation starts. This delay may result in physiological stress of the crops and eventually affect the crop yields. In summary, like any other simulation models, the four simulation models used in this study have their limitations. The models yielded relatively accurate estimates of the yields and irrigation water requirements for corn and sugrbeets but overestimated yields and irrigation requirements for soybeans and dry beans by a large margin. Of the four simulation models used in this study, when compared to the actual yields and amount of irrigation water applied, the CERES MAIZE produced better accurate estimates 81 of the corn yields and irrigation water requirements. To improve accuracy of the simulated yields and irrigation requirements in the study area, long term field experiments, beyond the scope of this study, must be conducted to verify the input parameters in the simulation models. This effort may well take up to several decades if a thorough field validation is desirable. The four simulation models used in this study were to demonstrate how they can be used in developing a framework for irrigation development. If the simulated results are to be used for decision making, errors associated with the simulated results must be considered. In addition, validation of the models in the field is strongly recommended. Subsequent studies which are oriented to decision making must carefully verify the models and collect better data sets so as to reduce the difference between simulated and observed crop yields and irrigation requirements. 82 II. THE SUSTAINABILITY 07 GROUNDWATER RESOURCES 70R IRRIGATION DEVELOPMENT 1. HYDROGEOLOGIC SETTING Glacial deposits in the study area have a thickness of 10 to 130 feet and are primarily clay underlain in places by sand and gravel. In some places, the clay extends from the land surface to the bedrock surface; while in other places, sand and gravel beds ranging in thickness from a few feet to 60 feet occur in the lower part of the glacial deposits. Clay yields little or no water to wells, whereas sand and gravel beds yield sufficient water to some wells for domestic needs (Davis, 1909; Twenter and Cummings, 1985; Sweat, 1992). Bedrock units in the study area include the Saginaw Formation, the Bayport Limestone, the Michigan Formation, the Marshall Formation, and the Coldwater Shale (Figure 14). The Saginaw Formation was deposited during the Pennsylvanian Period; the other four bedrock units were deposited during the Mississippian Period. The Saginaw Formation is the first unit encountered below the glacial drift in the western part of the study area. It has a thickness of 100-300 feet and consists primarily of shale and siltyshale (Twenter and Cummings, 1985). Underlying the Saginaw Formation is the Bayport Limestone, which is principally a fossiliferous, cherty limestone, often intermixed with L \ 1 R td b id i E S3 Soglnav Form allin 1 ^ Boyporl L lm u lo n i P 7 1 Ulchlgan Formation V/A U anhall Sandilono W& C oldvalir Shall I F P Sunbury Shall llftjl B aria S andilom TOM B idlord Shall Figure 14. Bedrock Geology of the Saginaw Bay Area 84 sandstone (Sweat, 1992). Underlying the Bayport Limestone is the 130-foot thick Michigan Formation. mainly a sandstone (Long et al., 1988). This unit is Below the Michigan Formation lies the Marshall Formation, which consists of 70-120 feet of sandstone with some interbedded shale lenses. The Marshall Formation, locally and elsewhere in the State where not deeply buried, is a good producer of potable water (Layne Northern Company, 1984b). Formation is the Coldwater Shale. Underlying the Marshall Outcroppings of the Coldwater Shale occur along the east shoreline of Lake Huron (Gordon, 1990). 2. THE AVAILABILITY OF GROUNDWATER The availability of groundwater in the glacial deposits of the Saginaw Bay five county area is shown in Figure 15 (Twenter, 1966a). Statistical analysis using PC ARC/INFO reveals that wells in the glacial deposits may yield less than 10 gallons of water per minute (GPM) in 55 percent of the area, 10 - 100 GPM in 39 percent of the area, and 100 500 GPM in 6 percent of the area. This result, in terms of having sufficient groundwater to support expanded irrigation, is not promising. The general availability and quality of groundwater in the bedrock deposits is shown in Figure 16 (Twenter, 1966b). GIS statistical analysis indicates that wells in bedrock layers may yield water at a rate of less than 10 GPM in 17 K N L tis Than 10 GPU 10-100 GPU Figure 15. The Availability of Groundwater in the Glacial Deposits 1X3 Lain Than 10 6PII g g l 10-100 CPU H 100—500 GPU P71 Dlssohrod Solids Uoro Than 1000 ppm Figure 16. The Availability and Quality of Groundwater in the Bedrock Deposits 87 percent of the area, 10 - 100 GPM in 46 percent of the area, and 100 - 500 GPM in 37 percent of the area. However, in over 52 percent of the area, groundwater in the bedrock deposits is highly mineralized and has a dissolved solids content of more than 1 , 0 0 0 ppm (parts per million, equivalent to milligrams per liter, mg/L). There exist great variations in the availability of groundwater in each individual bedrock unit. The Saginaw Formation is a poor source with respect to water supply. Although small quantities of water can be withdrawn from sandstone and siltstone beds, the water generally is highly mineralized in areas where the formation is in contact with sand and gravel glacial deposits. Under pumping conditions, more highly mineralized water would flow to the glacial deposits from the bedrock. Statewide, the mean dissolved solids concentration in water from the Saginaw Formation is about 1,629 mg/L (Twenter and Cummings, 1985). Water from the Michigan Formation is generally saline and unsuitable for use. Because of high dissolved solids concentrations, water from the Michigan Formation is a potential source of elevated dissolved solids to the underlying Marshall Formation (Sweat, 1992). The uppermost sandstone of the Marshall Formation is a good source of water for irrigation and domestic uses (Sweat, 1992). Yields of wells tapping this formation vary from 10 to 500 GPM (Twenter, 1966b). The dissolved solids 88 concentration of water in this formation ranges from 181 to 2,440 mg/L (Sweat, 1992). Wells tapping the Coldwater Shale yield small quantities of water with dissolved solids concentrations greater than 20,000 mg/L. Water in this formation is considered brackish and suitable only for livestock (Gordon, 1900; Sweat, 1992). Water from the Coldwater Shale may also be a source of dissolved solids to overlying sandstones in the lower part of the Marshall Formation, where pumping draws saline water upward from the shales (Sweat, 1992). 3. RECHARGE AND DISCHARGE Recharge and discharge rates are essential information for evaluating the sustainability of groundwater for irrigation. Estimates of the recharge and discharge rates in the study area are described below: 3.1 Estimate of Groundwater Recharge Rate A. Equations Groundwater recharge is the process by which water infiltrates the unsaturated zone and is added to the zone of saturation. Major sources of recharge to drift aquifers include infiltration of precipitation, natural or induced infiltration from surface waters, and upward leakage from underlying till or bedrock (Morrissey, 1989). In this study, precipitation is assumed to be the only source of 89 groundwater recharge for estimating the recharge rate. Figure 17 shows the process of groundwater recharge from precipitation in a watershed. As shown by Figure 17, after dropping to the ground, a portion of the precipitation infiltrates into the soil, and a portion of it becomes surface runoff when the rainfall rate exceeds the soil infiltration rate. Infiltrated water supplements soil moisture lost from soil evaporation and plant transpiration (ET). When the soil moisture content reaches the field capacity (i.e. the maximum amount of water the soil can hold), deep percolation, or recharge (RJ , occurs. In other words, the excess soil water reaches the water table and becomes stored in the aquifer. The deeply percolating precipitation enters the groundwater reservoir. At the same time, a portion of the aquifer water, known as baseflow, discharges into streams and lakes. If infiltration causes the water table to rise, groundwater discharge into nearby streams will also increase. According to the laws of mass conservation, the following equation is valid: P = R„ + ET + D + a S, + ASg (1) where P is precipitation, R,, is surface runoff, ET is evapotranspiration, D is groundwater discharge (i.e. baseflow to a stream), a S, is change in soil moisture E v a p o tr a n s p ir a tio n P r e c ip ita tio n (E T ) (P) Surface R unoff (Ro) Ground Surface Infiltration Soil M oisture Storage Field Capacity Unsaturated zone (Recharge) Deep Percolation (Re) W ater Table Saturated zone i Groundwater Storage (Sgw) Channel Storage Baseflow (D) Stream flow Figure 17. Conceptual Model of Groundwater Recharge ► 91 content in the unsaturated zone, and a S, is change in groundwater storage. Soil moisture is near field capacity during the winter and early spring of most years, and annual change in be assumed to be negligible. a S, can By rearrangement, Equation (1) becomes: P - R„ - ET = D + a S, Since Re = P - R„ - ET (2) (3), then Equation (2) becomes Re - D = AS, (4) Equation (3) can be used to estimate the groundwater recharge rate for a relatively long period of time by assuming that precipitation is the only input to the watershed30. Equation (4) shows that groundwater storage is dependent upon groundwater recharge and discharge. When groundwater recharge (Re) equals discharge (D), groundwater storage is at equilibrium and a S, = 0. If Re is smaller than D, groundwater storage will decline and reach a new equilibrium at a lower level. If too much water is withdrawn from the aquifer via pumping, groundwater discharge (D) will decrease and eventually reach zero. ^Equation 3 is only used to estimate the groundwater recharge rate in watersheds where precipitation is the only input. In areas where regional flow, infiltration of surface water, and upward leakage from underlying layers exist, Equation 3 should incorporate these factors. 92 B. Estimates of Recharge and Discharge Precipitation data sets for the years 1951-1980 were acquired from the Michigan Department of Agriculture Climatology Program for the Bad Axe, Caro, Flint, Midland, Saint Johns, and Sandusky weather stations. Mean annual precipitation over the period of 1951-1980 for each of the watersheds is shown in Table 15. Streamflow data for as many as 78 years were obtained from the U.S. Geological Survey for the Cass River at the Frankenmuth gage station, the Black River near the Fargo gage station, the Flint River near the Fosters gage station, the Pigeon River near the Owendale gage station, the Shiawassee River at the Owosso gage station, and the Tittabawassee River at the Midland gage station (see Figure 31). Stream hydrographs were derived from the acquired streamflow data and were separated into the components of baseflow (D) and surface runoff ( R J . This was accomplished by using a hydrograph separation method described by Freeze and Cherry (1979). The evapotranspiration rate (ET) was estimated by using CERES-MAIZE, a corn growth simulation model, and pan evaporation data from both the Michigan State University Saginaw Valley Beet and Bean Research Farm and the East Lansing Weather Station. It was assumed that the annual ET in the study area approximately equals the ET rate during the period of April through October. The amount of ET Table 15 . Estimates of Recharge and Discharge in The Saginaw Bay Area of Michigan (Based on Weather Data from 1951-1980 and 30-78 years of Streamflow Data ____________ (inches/yr))_____ ________________________________________________________ Watershed P - ET - Ro = Re P ET Re - D = ASg Ro Re D a ( Q 25/Q 7 5 ) 1/2 Sg Black River 27.96 22.47 3.58 1.91 4.72 -2.81 2.76 Cass River 28.22 22.47 3.37 2.38 5.01 -2.63 2.48 Flint River 29.19 22.47 3.18 3.54 5.29 -1.75 2.07 Pigeon River 29.35 22.47 3.94 2.94 4.30 -1.36 2.48 Shiawassee River 30.09 22.47 3.03 4.59 5.25 -0.66 1.98 Tittabawassee 28.71 22.47 3.10 3.14 -2 . 8 8 6.02 1.86 Note: P=precipitation, ET=evapotranspiratxon, Ro=surface runoff, Re=recharge, D=baseflow, aSg=change in groundwater storage, and are exceedence flows at the 25 and 75 percent level, respectively, and (Q25/Q75)1/2 is a flow ratio. A low flow ratio is an indication of a permeable basin that has a large storage capacity. 94 during periods of freezing temperatures (November through March) is negligible. The mean ET estimate of 19.30 inches between May and September was derived by computing the average value of simulated ET rates of non-irrigated corn in all 12 soil associations in the Cass River Watershed over the period of 1951-1980 (see Table 16). The monthly ET rates for April (1.89 inches) and October (1.28 inches) were estimated by multiplying the Class A Pan evaporation values for April and October that were measured on the Saginaw Valley Beet and Bean Research Farm during the period of 1986 to 1989, by 0.5 (Doorenbos and Pruitt, 1977). It was found that the mean annual ET estimate for the Cass River Watershed is 22.47 inches .31 Table 15 shows groundwater recharge and discharge rates and changes in storage. The annual groundwater recharge rates due to precipitation range between 1.91 and 4.59 inches. The lowest recharge rate of 1.91 inches is in the Black River Watershed near Fargo, where the bedrock formation is Coldwater Shale which yields small quantities 31ET may be the most difficult variable to estimate in the equation. Although there are always errors associated with ET estimates, the annual ET of 22.47 inches is believed to be a reliable estimate since (1) the mean ET value of simulated irrigated corn in all the 12 soil associations in the Cass River Watershed during the period of 1951-1980 is 21.87 inches, and (2) the crop reference ET (ETo), derived by multiplying the mean Class A Pan evaporation value of April through October during the period of 1949-1980 (from the East Lansing weather station) by 0.7, is 27.31 inches. Thus, annual ET rate in the study area should range between 22 and 27 inches. Error in the annual ET estimate of 22.47 inches may range between 2 and 2 0 percent. 95 Table 16. Seasonal Cumulative ET (May though September) Estimated by the CERES-MAXZE Model for Non­ irrigated Corn in the Cass River Watershed (Based on Weather Data from 1951-1980)__________________ Weather Station Period (yrs.) Soil Association ET (inches) Bad Axe 30 40 16.77 30 41 19.21 30 73 19.92 30 74 19.45 18.86 Mean Caro 25 41 18.82 25 42 19.06 25 43 21.77 25 46 17.32 25 51 15.79 25 64 18.78 25 70 19.09 Mean Sandusky 18.66 30 42 22.24 30 43 21.57 30 64 18.70 Mean Saginaw C.P. 20.83 25 48 19.06 25 69 18.90 25 70 18.62 25 73 18.86 Mean 18.86 Note: The mean seasonal ET for the entire Cass River Watershed is 19.30 inches. 96 of water with highly dissolved solids concentrations to wells. The flow duration ratio32 of (Q25/Q7J)1/2 is 2.76 in the Black River Watershed, which is the highest of all 6 watersheds, and indicates a low storage capacity in the watershed (Pettyjohn and Henning, 1979). The highest recharge rate of 4.59 inches is in the Shiawassee River Watershed, and the flow duration ratio is 1.98, which suggests a greater storage capacity in the river basin. Annual baseflow (groundwater discharge) in the study area ranges between 4 and 6 inches, with the minimum occurring in the Pigeon River Watershed and the maximum occurring in the Tittabawassee River Watershed. It accounts for between 52 percent and 66 percent of the total streamflow. Of the six watersheds, Pigeon River has the lowest groundwater discharge rate (4.30 inches per year, accounting for 52 percent of the total flow). It was dry on several days each year over the period of 1986-1989 (U.S. Geological Survey Water Resources Data: Michigan, 19861989). 32The shape of the flow duration curve is an index of the natural storage within a basin. During dry weather, the flow of streams is almost entirely from groundwater sources. The lower ends of duration curves indicate in a general way the characteristics of the shallow groundwater bodies in the drainage basin. When plotted on logarithmic probability paper, the more nearly horizontal the curve, the greater is the effect of groundwater storage. Similarly, the lower the flow ratio, the larger the capacity of the basin to store groundwater (Pettyjohn and Henning, 1979). 97 Groundwater recharge and discharge rates were also estimated using daily streamflow data for 1961 and from 1985 to 1989 for all six watersheds using the computer program developed by Pettyjohn and Henning (1979). Two methods, Local Minima and Sliding Interval, were used to estimate annual groundwater recharge and discharge rates. The results indicate that, during the periods of 1961 and from 1985 to 1989, the mean annual recharge rates estimated by the Local Minima method ranged between 2.80 and 5.51 inches, with the minimum occurring in the Black River Watershed (2.80 inches) and the maximum occurring in the Shiawassee River Watershed (5.51 inches) (Appendix A). During the same period, the mean annual recharge rates estimated by the Sliding Interval method ranged between 3.61 and 6.64 inches, with the minimum recharge rate occurring in the Pigeon River and the maximum recharge rate in the Flint River Watershed. The mean groundwater discharge rates varied between 3.32 and 6.38 inches (using the Local Minima method). The mean percentage of the groundwater discharge rate to the total streamflow (by using the Local Minima method) ranged between 40 and 67 percent, with the lowest (40%) in the Black River Watershed and the highest (67%) in the Shiawassee River Watershed. The mean recharge and discharge rates estimated by using the Sliding Interval method showed (Appendix A ) . similar results These estimates are very similar to the estimates in Table 15. 98 Change rates in groundwater storage (a Ss) are all negative numbers, which may indicate that the amount of water being added to the zone of saturation from precipitation is smaller than the baseflow (i.e. the amount of water flowing out of the aquifer to the stream). It may also suggest the existence of flowing wells in some areas. A study by Allen (1974) points out that flowing wells exist in the Saginaw Formation and Marshall Formation in the Saginaw Bay area. In either case, negative storage change rates serve as a signal that the aquifer water supply may be declining. A study by Sweat (1992) also indicates that there is a net discharge of groundwater from the aquifers into the streams of Huron County. It should be noted that errors exist in estimating annual ET rates, which could lead to errors in estimates of recharge and change in groundwater storage (see Equations 3 and 4). In addition, changes in recharge (R,) and storage change (a S8) due to infiltration from surface waters and upward leakage from underlying bedrock were not considered in this study. 99 3.2 Direction of Groundwater Flow Well log records that cover the period from 1969-1986 were obtained for Huron, Sanilac and Tuscola Counties33 from the Michigan Department of Natural Resources Geological Survey Division, and were digitized using C-MAP. Static water elevations (above mean sea level) of the 218 drift wells and 1,157 bedrock wells were entered into SURFER, a computer graphic package for generating topographic surfaces, to derive the potentiometric surfaces of water in the drift and bedrock aquifers (Figures 18 and 19). The hydraulic heads are similar in both the drift and bedrock aquifers of Huron, Sanilac and Tuscola Counties (Figures 20 and 21). They are higher in the south and central areas and decrease toward the west and east. Thus, groundwater flows east toward Lake Huron and west toward Saginaw Bay, from the central areas of Huron, Sanilac and Tuscola Counties. In Bay County, groundwater flow in both the drift and bedrock aquifers is toward Saginaw Bay (Long et al., 1988). The relative head between the drift and bedrock aquifers can indicate the direction of leakage. If the head in the overlying aquifer is less than the head below it, leakage is from the deeper aquifer to the overlying aquifer. In this case, the leakage is from the bedrock to the drift aquifer. 33No well log records were collected for Bay and Saginaw Counties where the Saginaw Formation underlies based on the suggestion of the Saginaw Bay Subirrigation Project Groundwater Advisory Committee that generally, these is not much water available in the Saginaw Formation. Figure 18. Locations of the Drift Wells Figure 19. Location of the Bedrock Wells Figure 20. Potentiometric Surface (Feet above Sea Level) Drift Aquifer Figure 21. Potentiometric Surface of Bedrock Aquifers 104 This was determined by subtracting the bedrock potentiometric surface from the drift potentiometric surface (Long et al., 1988). The residual surface (Figure 22) shows that in the eastern and southwestern parts of the three county area, the bedrock aquifer has a higher head than does the drift aquifer, which indicates potential upward leakage from the bedrock to the drift aquifer (The presence of the flowing wells in this area has been reported by Allen (1974)). In the central and western parts of the three county area, the bedrock potentiometric surface is lower than the drift potentiometric surface. There is potential vertical flow from the drift aquifer to the bedrock aquifer. Hence, this area may be a groundwater recharging area, as high hydraulic head areas are recharge areas and low hydraulic head areas are discharge areas (Freeze and Cherry, 1979) (Figure 22). 4. SALINITY LEVEL IN GROUNDWATER Partial chemical records covering the period from 1988 1989 were collected from the Health Departments of Huron, Sanilac and Tuscola Counties to evaluate the quality of groundwater. Unfortunately, of the 464 partial chemical records collected, only 129 of them could be located on the Land Atlas and Plat Books of the above three counties because no specific addresses were shown on the rest of the records. The 129 partial chemical records were digitized Area Where the Potentiometric Surface of the Drift Aquifer is: Lower than the Bedrock Rotentiometrix: Surface Higher than the Bedrock Potentio­ metric Surface. Figure 22. Residual Surface Obtained by Subtracting the Bedrock Aquifer Potentiometric Surface from the Drift Surface 106 using C-MAP and their locations are shown in Figure 23. Concentrations of chloride and sodium were chosen as indicators of brine levels in groundwater. Distributions (surfacing) of chloride and sodium concentrations were processed by SURFER. The results are shown in Figures 24 and 25. As shown by Figures 24 and 25, concentrations of chloride and sodium in groundwater had a similar spatial distribution: they ranged between 100 and 400 mg/L along the eastern coast line where outcroppings of the Coldwater Shale occur. In addition, concentrations of the dissolved solids in this area exceed 1,000 mg/L. Concentrations of chloride and sodium varied between 100 and 400 mg/L in the northwestern corner, and were less than 100 mg/L in the central and western parts of the three-county area. The lower concentrations of chloride and sodium in groundwater in the central and western parts of the three-county area seemed to confirm that those areas where the bedrock potentiometric surface is lower than the drift potentiometric surface may be the recharge area. If crops such as soybeans and dry beans, which have a low tolerance to salinity, are irrigated by groundwater with a chloride level greater than 142 mg/L or a sodium level greater than 69 mg/L, yield reduction and quality problems may occur. Severe problems may occur if the chloride level in irrigation water exceeds 355 mg/L (Bouwer, 1978). Thus, 107 Figure 23. Location of Wells Sampled for Partial Chemistry Analysis S 108 Figure 24 . Concentrations of Chloride in Groundwater (Dashed Lines Represent the Michigan, Marshall, and Coldwater Formations, from Left to Right) \(g!_ BOO Figure 25. \P Concentrations of Sodium in Groundwater 110 groundwater along the eastern coastline and In the northwestern corner of the three county area should not be withdrawn for irrigation. 5. SUSTAINED GROUNDWATER YIELD The magnitude of groundwater development depends on both the manner in which the effects of withdrawal are transmitted through the aquifer system and the changes in rates of groundwater recharge and discharge induced by the withdrawals. Over a sufficiently long period of time (prior to the start of withdrawals), an aquifer is in a state of equilibrium, and recharge (Re) is balanced by discharge (D) from the aquifer, Rg - D = 0. Discharge from wells (i.e. pumping, represented by Q) superimposes a new discharge onto a previously stable system. The new discharge must be balanced by an increase in the recharge (RJ of the aquifer, or by a decrease in the natural discharge (D), or by loss of storage in the aquifer (a S8) , or by a combination of these. This relationship can be expressed as: Q = Rj - D ± a S, (Bredehoeft, et al. 1982) (5) This equation indicates that water pumped from wells will be derived from (1) storage in the aquifer, (2) reduction of groundwater flow to nearby streams or lakes, and (3) possibly induced infiltration from streams or deeper aquifers (Morrissey, 1989). If the cone of depression ceases to expand, the rate of withdrawal is balanced by an Ill increase in the rate of recharge or by a reduction in groundwater discharge to nearby streams or lakes. Under this condition: Q = aD + aR (6) Changes in recharge and discharge rates as a result of pumping can be referred to as capture, and the sustained yield of groundwater is limited by capture. Estimates of capture are important to groundwater planning for long term water supplies. In the Saginaw Bay area, the Marshall Formation is the only good source of water for irrigation and domestic use. If pumping for irrigation continues on a relatively large scale, highly mineralized water would be induced either to move upward from the underlying Coldwater Shale or to move downward from the overlying Saginaw and Michigan Formations into the Marshall Formation. This would probably occur even before the reduction in the discharge rate can take place. In addition, more highly mineralized water would also flow from the Saginaw Formation to the glacial deposits in areas where the formation is in contact with sand and gravel deposits (Twenter and Cummings, 1985; Long et al., 1988; Sweat, 1992.). This indicates that aR (the induced recharge), although not zero, can not be used for irrigation. If the groundwater discharge rate does decrease, the maximum amount of reduction (the worst consequence) would 112 result in total depletion of the discharge, which would dry up many streams in the summer and lead to the destruction of valuable fisheries habitat. Thus, aD could be as much as the natural discharge rate, D, with the consequence of degradation of water quality and destruction of aquatic habitats. 6. POTENTIAL IRRIGATION EXPANSION AREA The expansion of irrigation requires an adequate water supply. The above analysis indicates that water in the Saginaw Formation, Michigan Formation, and the Coldwater Shale is too highly mineralized, as these formations have dissolved solids concentrations greater than 1,000 mg/L, which exceed the U.S. Environmental Protection Agency's (EPA) drinking water maximum of 500 mg/L (Sweat, 1992). In addition, the salinity level (indicated by chloride and sodium concentrations) is high in these formations. If water with a high salinity level is used to irrigate crops that have a low tolerance for salinity, yield reduction and quality problems may occur (Bouwer, 1978). Thus, the Saginaw and Michigan Formations and the Coldwater Shale are not potential sources of irrigation water. The Marshall Formation is the only good source of water available for irrigation and domestic use (Sweat, 1992). However, continuous pumping of water for irrigation from this formation would induce highly mineralized water either to 113 move upward from the underlying Coldwater Shale or to move downward from the overlying Saginaw and Michigan Formations to the Marshall Formation. Therefore, the withdrawal of groundwater for irrigation should be practiced cautiously in the Saginaw Bay area. To be on the conservative side, this study assumes that the potential expansion of subsurface irrigation by groundwater lies in the areas where the soils are suitable (high and medium), the wells yield suitable water at the rate of 100 - 500 6PM and the concentration of dissolved solids is less than 1,000 mg/L. Based on this assumption, the general availability and quality of groundwater in the bedrock (Twenter, 1966b, Figure 16) is first superimposed on the bedrock geology map (Figure 14) to derive the general availability and quality of groundwater in the Marshall Formation. The resulting map is then superimposed on the map of soil suitability for subsurface irrigation (Figure 7) in order to estimate the maximum irrigation acreage that might be supported by groundwater in the Marshall Formation. The results are shown in Table 17 and Figure 26. As shown by Table 17, groundwater with a yield of 100 500 GPM may be able to supply 160,000 acres of subsurface irrigable land, which represents 8.1 percent of the 2 million acres of the total agricultural land in the Saginaw Bay five-county area. The expansion, however, should proceed cautiously since the recharge of groundwater from 114 precipitation is low in the study area, and since brine in the deep aquifer may move upward due to the large withdrawal of groundwater. Table 17. Acreage of Potential Subsurface Irrigation Expansion Area with Suitable Groundwater Supply Soil Suitability High Medium Low (Not Suitable) Total Groundwater Yield ( 100-500 GPM) Total (%) 15,541 8.6 144,177 80.2 20,181 11.2 179,899 100.0 7. SUMMARY The above results indicate that: 1) Recharge due to precipitation, less surface runoff and evapotranspiration, ranges between 2 and 4.6 inches annually in the Saginaw Bay area. 2) Baseflow, resulting from discharges from groundwater storage, varies between 4.3 and 6.02 inches per year. Annual groundwater discharge accounts for between 52 and 66 percent of the total streamflow. 3) The difference between recharge and baseflow is assumed to be the change in groundwater storage. Negative values indicate the depletion of the regional groundwater storage. They may also indicate upward movement of groundwater from bedrock aquifers, such as occurs with Lov S u itab ility and 10-100 GPU Uadlum and 1 0 0 -5 0 0 GPU High and 10 -1 00 GPU 35 High and 1 0 0 -5 0 0 GPU 115 Figure 26. Potential Subsurface Irrigation Expansion Areas 116 artesian wells reported by Allen (1974). Uncertainty associated with the annual ET estimate may affect the estimates of recharge and change in groundwater storage. 4) Central Huron County, western Sanilac County, and eastern Tuscola County may be recharging areas based on well yields, water quality and hydraulic heads of aquifers. 5) Total dissolved solids concentrations and salinity levels (indicated by chloride and sodium concentrations) are lower in the potential recharging areas in these counties. 6) Potential subsurface irrigation development supplied by groundwater may lie in parts of central Huron County, southwestern Sanilac County and northeastern Tuscola County. The maximum irrigation acreage by groundwater supply could be 160,000 acres. However, use of groundwater for irrigation should be practiced cautiously since continuous pumping of groundwater would reduce the baseflow and induce the upward movement of brine from the deeper aquifer. 117 III. CAPACITY OF STREAMFLOW FOR IRRIGATION DEVELOPMENT 1. INTRODUCTION As discussed above, the amount of groundwater available for irrigation in the Saginaw Bay area is limited; only 160,000 acres (8 percent of 2 million acres of the total agricultural land) may be subsurface irrigated with groundwater. Surface water may be used to increase the water available for irrigation expansion in the study area. However, since the withdrawal of water for irrigation from the Great Lakes is legally restricted, the availability of streamflow must be examined as a source of water for irrigation expansion. The Cass River Watershed (Figure 8) was chosen as a pilot study area to evaluate streamflow capacity for irrigation. 2. STREAMFLOW DURING THE IRRIGATION SEASON In Michigan, the requirement for irrigation water is greatest in July and August when streamflow is at its lowest (Figure 27). Thus, the low flow period of July and August was chosen as the critical period. The flow rates of the Cass River were acquired from the U.S. Geological Survey for three gage stations: the Cass City Station on the upper stream, the Wahjamega Station on the middle stream, and the Frankenmuth Station at the mouth of the stream (Figure 8). The locations of the Cass City, Wahjamega and Frankenmuth 2000 S tation ID: 04151500 1750 - ■^mean (cfs) 1250 - Streamflow 1500 - 1000 + p = 75% — p = 90% p = 95% - 750 - 500 ~ 250 Oct Nov Dec Jan Feb Mar Apr M ay Jun Jul Aug Sep Month Figure 27. E xceedence Streamflow in the C ass River at th e Frankenm uth Station (1936-1985) 119 gage stations were digitized using C-MAP and PC ARC/INFO. The exceedence flow rates of the Cass River at the three gage stations are shown in Figures 28, 29, and 30, respectively.34 Spatial analysis using ERDAS, a Geographic Information System, shows that 50.8 percent of the potentially irrigable agricultural land is within one kilometer (0.62 mile) of the Cass River. This indicates that it is likely to be technically feasible to withdraw water from the Cass River for irrigation expansion. Whether or not this would translate into economic viability cannot be assumed and is beyond the scope of this project. 3. CAPACITY OF STREAMFLOW FOR IRRIGATION EXPANSION IN THE CASS RIVER WATERSHED 3.1 Methods Streamflow at 95, 90, 75 and 50 percent exceedence levels is used in this study to estimate the capacity of streamflow available for irrigation water supply. A computer program, BALANCE, was developed in this study to compute the amount of streamflow for irrigation and the maximum irrigation acreage that the streamflow can sustain. ^The exceedence flow indicates the probability level at which streamflow is exceeded or equaled. For example, P75 ~ 57.4 cfs indicates that the streamflow would exceed or equal 57.4 cfs 75 percent of the time. 120 S tation ID: 04150500 100 mean i J P = .50 80 P = .75 P = .90 60 O p 40 20 Jun Jul Au g Month Figure 28. E xceedence Streamflow in th e C ass River at th e C a ss City Station (1948-1985) = .95 250 S tation ID: 04150800 200 I - El mean ED 7 a - = .50 ESI P = .75 150 - - 100 p H p = .90 O p = .95 - 7a 7 a Va 7 a 7 a 7 a Va z 7 a 7 a Figure 29. E xceedence Streamflow in the C ass River at th e W ahjam ega Station (1969-1985) 350 S tation ID: 04151500 300 mean 250 P = .50 P = .75 200 P = .90 o O P = .95 150 100 50 Jun Ju l A ug Month Figure 30. E xceedence Streamflow in the C ass River at th e Frankenm uth Station (1936-1985) 123 Equations used in the program are described below: where V = volume of water available for irrigation withdrawal in ft3; Q = streamflow in cubic feet per second (cfs) at an exceedence level; Q9S5(=streamflow at 95 percent exceedence level in cfs; and Tt/ T2 = starting and ending time in seconds, respectively. It is assumed in Equation (7) that streamflow available for irrigation withdrawal is the amount of water above the 95 percent exceedence flow level set by the National Pollutant Discharge Elimination System (NPDES). The 95 percent exceedence flow is used for the NPDES program in setting effluent limits. It is used here as the lower threshold for the purpose of estimating the amount of water available for irrigation. It should be noted, however, that any withdrawals that would deplete the flow to the 95 percent exceedence level on a regular basis would seriously degrade the quality of the stream. If water is withdrawn for irrigation upstream, the amount of water available downstream will be reduced. The amount of water for irrigation downstream is computed as follows: 124 (8) where Vd- volume of water available for irrigation at the downstream location in ft3; and Wu = withdrawal rate at upper stream location(s) in cfs. The irrigation requirements for corn, soybeans, dry beans, and sugarbeets are estimated by using the CERESMAIZE, S0Y6R0, BEANGRO, and YIELD models at a fixed irrigation efficiency of 75 percent. The total irrigation water requirement is computed by Equation (9). (9) (10 ) where A = irrigation acreage, A, and A 2 are lower and upper limits of irrigation acreage, respectively; I = irrigation water requirement in mm per acre, estimated by the simulation models; E = irrigation efficiency (percentage); Vj = volume of irrigation water requirement in ft3; Vr = volume of the remaining streamflow after irrigation withdrawal in ft3; and V = volume of streamflow before irrigation in ft3. 125 The amount of streamflow available for irrigation is compared with the irrigation requirement in Equation (10). If the irrigation requirement is smaller than the streamflow supply, irrigation is expandable. Conversely, if the irrigation requirement is greater than the streamflow supply, the stream is unable to sustain the irrigation expansion. Irrigation expansion is thus limited by the maximum acreage that the stream can sustain. Attempts to expand irrigation beyond this limit would lead to streamflow depletion and fisheries habitat destruction. 3.2 Maximum Irrigation Acreage in the Cass River Watershed As shown by Table 10, a minimum streamflow of 2,000 cfs is needed to irrigate all 392,713 acres of the total agricultural land (assuming it is planted only in sugarbeets) in July at a confidence level of 75 percent. Streamflow during the same period at the Frankenmuth gage station is only 57.4 cfs at the 75 percent exceedence level (Figure 27), which is far less than the total irrigation requirement of 2,000 cfs. This indicates that streamflow can only irrigate a small portion of the total agricultural land in the Cass River Watershed, especially if it is planted with crops that have greater irrigation requirements. To compute the maximum irrigation acreage that the streamflow can support without depleting the stream, the 126 irrigation requirements of corn (the major crop in the region) in July and August at the 75th percentile, and exceedence streamflow rates at the 50, 75, 90 and 95 percent levels, were entered into the BALANCE model. The simulation was run for the Cass City, Wahjamega, and Frankenmuth gage stations. The results are shown in Table 18. It should be noted that the Frankenmuth gage station is located at the mouth of the Cass River. Streamflow at this station includes the contribution of the upper and middle drainage areas (i.e. Cass City and Wahjamega). Thus, the maximum irrigation acreage derived at the Frankenmuth station represents the total irrigation acreage that the entire Cass River can sustain. Table 18. Maximum Irrigation Acreage Supported by Cass River Streamflow (Based on Irrigation Requirements of . Corn at the 75th Percentile)_______________________ Location Exceedence Flow in July Pso P75 Exceedence Flow in August P90 P50 P75 P90 Cass City 2,600 885 243 2,420 910 310 Wahjamega 5,920 2,310 640 7,310 2,500 910 10,520 5,030 1,460 10,620 5,130 1,850 Frankenmuth ♦Assuming an irrigation efficiency of 75% The maximum irrigation acreage for the entire irrigation season at an exceedence flow level is determined by choosing the minimum value between maximum July and August irrigation acreage, i.e., max A = min ( Max A 7, Max A8) . The results 127 show that, given an irrigation efficiency of 75 percent, the maximum irrigation acreage that the Cass River can support at the exceedence flow of 75 percent, without falling below the NPDES 95 percent exceedence flow limit, is 5,030 acres, which accounts for only 1.3 percent of the total agricultural land.35 Irrigation could expand to 10,520 acres at an exceedence flow of 50 percent. If the upper stream portion of the watershed (the Cass City gage station) is evaluated separately, at the 75 percent exceedence flow level, it is capable of supplying water to only 885 acres of corn while maintaining a minimum 95 percent exceedence flow in the upper stream. If, at the same time, the middle stream (at the Wahjamega station) and the lower stream (at the Frankenmuth station) are being used for maximum irrigation, they can sustain 1,420 and 2,720 acres of irrigated corn, respectively. It should be noted that the maximum irrigation acreage shown in Table 18 is derived by assuming that the streamflow is withdrawn down to the 95 percent exceedence level. If a higher exceedence flow level (e.g., 90%) was set, then even fewer acres could be irrigated. 3SNote that this estimate rests on the assumption that all available agricultural land is planted in corn. Any combination of the four major crops will further reduce irrigable acreage. 128 4. MAXIMUM IRRIGATION ACREAGE IN THE SAGINAW BAY AREA The maximum acreage of corn (the major crop) that can be supported by streamflow irrigation in other major watersheds (Figure 31) in the Saginaw Bay area was computed the same way as that shown above for the Cass River Watershed. results are shown in Table 19. The The total irrigation requirement for each of the watersheds was derived by multiplying the acreage of total agricultural land in each watershed by the July irrigation water requirement of corn at the 75th percentile. If all 2 million acres of currently existing agricultural land were irrigated and planted in corn, a total streamflow of 11,362 cfs in all watersheds would be needed in July in order to meet the irrigation requirement. While assuming available streamflow for irrigation is the volume of water above the NPDES 95 percent exceedence flow level, the maximum acreage of land irrigable by streamflow in all gaged watersheds totals about 44,000 acres (assuming all acreage is in corn). This accounts for only about 2 percent of the total agricultural land in the Saginaw Bay five-county area. It should be noted that agricultural irrigation is subject to the Riparian Rights Doctrine. This doctrine grants a riparian (i.e. landowner of property adjacent to a water body) the right to a reasonable use of that water on riparian land. However, one cannot interfere with another riparian's right of reasonable use including activities 129 P lg io n Rlvor Plnnobog Rivir Saginaw River C a n River Black River Flint River Not C onsidered Figure 31. Watersheds in the Saginaw Bay Area 130 ranging from non-consumptive navigational and aesthetic uses to water supply and heavily consumptive agricultural irrigation. According to this doctrine, only riparian lands in the Saginaw Bay five-county area have a right to the use of streamflow for irrigation, and that right is limited to a reasonable use. That is, use of streamflow for riparian land irrigation should not adversely impact uses of the streamflow for other activities such as aesthetic enjoyment and maintenance of the ecosystem. Table 19. Maximum Irrigation Acreage Supported by July 75 Percent Exceedence Streamflow in the Saginaw Bay Area (Based on the July Irrigation Requirement of Corn at the 75th Percentile)__________________ Watershed Ag. Land (Acres) Irrig Demand (cfs) Avail. Flow for Irrig. (cfs) Maximum Irrig Land (acres) Black 215,373 1,241 8.5 1,475 Cass 392,713 2,263 29.0 5,030 Flint 60,488 348 64.0 11,120 Pigeon 76,111 439 2.1 360 Pinnebog 87,643 505 N.A. N.A. Saginaw 104,611 603 N.A. N.A. Sebewaing 60,927 351 N.A. N.A. Shiawassee 179,706 1,035 34.2 5,940 35,310 203 116.0 20,180 759,051 4,374 N.A. N.A. Tittabawassee Others Total 1,971,933 11,362 *Note: N.A. means no streamflow data were available. 131 IV. SUMMARY A framework was developed in this study for managing water resources for irrigation development in the Saginaw Bay area. Crop growth simulation models and Geographic Information Systems (GIS) were used in this study to simulate the yields and irrigation requirements for corn, soybeans, dry beans, and sugarbeets. A hydrologic budget equation, well log records, and partial chemistry data were used to evaluate the sustainability of groundwater and streamflow for irrigation in the Saginaw Bay five-county area. The results indicate that: 1. Irrigation may increase the yields of corn, soybeans, dry beans, and sugarbeets by a large margin over non­ irrigated identical plantings in the Cass River Watershed. The requirement for irrigation water is greatest in July and at the mean level averages 77 mm (3.03 inches) for corn, 105 mm (4.13 inches) for soybeans, 102 mm (4.02 inches) for dry beans, and 69 mm (2.72 inches) for sugarbeets. The irrigation requirement in July at the 75th percentile averages 108 mm (4.25 inches) for corn, 140 mm (5.51 inches) for soybeans, 130 mm (5.12 inches) for dry beans, and 96 mm (3.78 inches) for sugarbeets. 2. A minimum flow of 2,000 cfs is needed to satisfy the irrigation requirement if all 392,713 acres of agricultural land in the Cass River Watershed were irrigated for sugarbeet production (the least water-consumptive of the 132 crop alternatives). If all 2 million acres of the currently existing agricultural land in the Saginaw Bay five-county area were irrigated and planted with corn (the major crop in the region), a minimum flow of 11,400 cfs in all watersheds would be needed in July to meet the irrigation requirement. 3. Annual groundwater recharge from precipitation less surface runoff and evapotranspiration ranges between 2 to 4.6 inches. The annual baseflow resulting from discharges from the groundwater storage varies between 4.3 and 6.0 inches. The negative differences between recharge and baseflow indicate depletion of groundwater storage. They may also indicate upward movement of groundwater from bedrock aquifers, such as artesian wells reported by Allen (1974). Uncertainty associated with the estimates of annual ET could affect the estimates of recharge and groundwater storage change. 4. Central Huron County, western Sanilac County, and eastern Tuscola County may be recharge areas based on well yields, water quality and hydraulic heads of aquifers. 5. Total dissolved solids concentrations and salinity levels (indicated by chloride and sodium concentrations) are lower in the potential recharge areas in these counties. 6. The Marshall Formation in the Saginaw Bay area is a source of water suitable for irrigation and domestic use. The maximum irrigation acreage that might be supported with groundwater is 160,000 acres, which accounts for 8 percent 133 of the total agricultural land in the Saginaw Bay area. Potential subsurface irrigation expansion areas may lie in parts of central Huron County, southwestern Sanilac County, and northeastern Tuscola County. 7. streamflow in the Cass River is lowest in July. Assuming that the stream is withdrawn down to the 95 percent exceedence level, the maximum irrigation acreage that the entire Cass River Watershed can sustain at the 75 percent exceedence flow level is 5,000 acres. This is approximately 1 percent of the total agricultural land in the watershed. The maximum irrigation acreage that the streamflow can support in all gaged watersheds in the Saginaw Bay fivecounty area totals 44,000 acres (assuming all acreage is in corn), which accounts for only 2 percent of the total agricultural land in the Saginaw Bay area. If a higher level was set as the lower threshold for estimating the amount of water available for irrigation, even fewer acres could be irrigated. 8. If available groundwater and streamflow are combined to supply irrigation, the maximum irrigation acreage might be as many as 200,000 acres, which is 10 percent of the total agricultural land in the Saginaw Bay five-county area (Figure 32). However, withdrawal of groundwater for irrigation should be practiced cautiously since continuous pumping of groundwater would decrease the discharge to streams and also induce the upward movement of brine from Expressed a s a percentage of total agricultural land 8.1 % G roundw ater 2.2 % Stream flow Total Agricultural Land = 1,971,933 a c re s Figure 32. Maximum Irrigation A c re a g e S u p p o rte d b y G ro u n d w ater a n d Stream flow (C om bined) in th e S ag in aw Bay A rea 135 the deeper aquifers. Moreover, reduction in the groundwater discharge due to irrigation could lead to the degradation and depletion of streamflow and the destruction of fisheries habitats. 9. Agricultural irrigation is subject to the Riparian Rights Doctrine. Only owners of riparian lands (i.e. lands adjacent to a water body) have a right to the use of the water and that right is limited to a reasonable use. That is, withdrawal of streamflow for riparian land irrigation should not adversely impact uses of the streamflow for other activities such as wetland protection, maintenance of fisheries habitats, and aesthetic enjoyment. 10. Simulation models are useful tools in aiding management of water resources for irrigation development. However, limitations of these models should be recognized when the model outputs are used for decision making. Of the four simulation models used in this study, the CERES MAIZE produced relatively accurate estimates of the corn yield and irrigation water requirements when compared to the actual data. The simulated dry bean yields were poorly correlated with the actual yields. To improve the reliability of the simulated yields and irrigation water requirements, long term field experiments must be conducted to validate the simulation models. CHAPTER 6 DEVELOPMENT OF OPTIMAL IRRIGATION SCENARIOS 1. INTRODUCTION Streamflow in the Cass River at the 75 percent exceedence level can, at most, support only 1 percent of the total available agricultural land (392,713 acres) for irrigation in the entire watershed. The four major crops (i.e. corn, soybeans, dry beans, and sugarbeets) are competing for the use of the limited groundwater and streamflow available for irrigation. Decision makers must determine which crops to irrigate, where to irrigate, and how much land to irrigate. Ignorance on the part of individual growers could lead to water extraction plans that are unsustainable and damage the watershed. With better information, public decision makers can effectively deal with these complicated issues. This study uses optimization techniques to determine the optimal crop mixes in order to maximize the total economic returns of irrigation while meeting the constraints of resources and activities. outputs of the optimization models provide information regarding which crops to irrigate, how many acres to irrigate, and which soil association(s) to irrigate. 136 The 137 2. OPTIMIZATION MODEL Linear programming (LP) models were developed to generate irrigation scenarios. The LP model is of the following form: 74 Maxf(x) CjX* (1 1 ) £ ayx^bj (12 ) ^2:0 (13) where Xj is a set of decision variables, as is the resource consumption coefficient for each decision variable, Cj is the objective coefficient for each decision variable, and bj is a set of available resources. Equation (11) is the objective function, Equation (12) is a set of resource constraints, and Equation (13) represents the non-negative requirements of decision variables. In this study, x; represents acreage of non-irrigated and irrigated corn, soybeans, and dry beans in each of the 12 soil associations, and non-irrigated and irrigated sugarbeets in all soils. Model restrictions and data availability did not allow yield and irrigation requirement of sugarbeets to be linked to soil associations. Thus, there are 74 decision variables in the models (3 crops, 2 irrigation types (irrigated vs. non-irrigated), 12 soil 138 associations, and irrigated and non-irrigated sugarbeets, yielding 3*2*12 + 2 = 74 variables). ay represents the coefficient in constraint j of variable i. For example, 129 mm (5.08 inches) of water is needed in July at the 75th percentile (i.e. 75% confidence level) to irrigate an acre of corn in the OakvillePlainfield-Spinks soil association (soil #40) (constraint 2 of variable 2, see Appendix B). bj represents the available resources. For example, the total agricultural land in the entire Cass River Watershed is 392,713 acres. 2.1 Objective Function The objective function of the LP model in this study is to maximize expected gross margins. In this study, C represents expected gross margins36 for each of the decision variables (Ferris, 1990). For irrigated corn in the Oakville-Plainfield-Spinks soil association (#40), for example, the gross margin at the 75 percent confidence level is $90.70 per acre of land. Gross margin in this study was calculated from the following equation: Expected Gross Margins/acre = Gross Returns/acre - Variable Costs/acre MGross margin equals the gross variable costs per acre. returns (14) in excess of 139 where Gross Returns = Prices/unit * yields/acre (simulated) and Variable costs include variable cash expenses plus an allocation for returns to operating capital and unpaid labor (Ferris, 1991). Two values for per unit prices (per bushel for corn and soybeans, per hundred weight (cwt) for dry beans, and per ton for sugarbeets) were used in Equation (14): seasonal average value and the 25th percentile value. Seasonal average value is the average of the prices at real value (1982 - 1984 price = 100) over the period of 1960-1990. Seasonal average crop prices for 1960-1990 are shown in Figure 33 (Ferris, 1991). Crop prices at the 25th percentile indicate that crop prices in a particular year would be greater than the specified prices 75 percent of the time. The 25th percentile values represent the crop prices during the worst years over the period of 1960 - 1990. The estimates of gross margins at the 25th percentile are lower than the average level, and hence are conservative and less subject to overstatement. Seasonal prices and variable costs at real value (average values of prices and variable costs between 1982 and 1984 = 100) for non-irrigated corn, dry beans, soybeans and sugarbeets in Michigan were obtained from Ferris (1991) for the period from 1960-1990. Additional variable costs associated with subsurface irrigated corn, dry beans, 120 Units: $/bu (Corn & Soybeans), $/ton (Sugar Beets), $/cwl (Dry Beans) C o rn + Soybeans 100 ^ S u g a r B e e ts ^ Dry B e a n s 80 60 20i 1960 1965 1970 1975 1980 1985 Year Figure 33. S e a s o n a l A verage C rop P rices in M ichigan (Real Value, 1982-1 9 8 4 = 1 0 0 ) S o u rce: J.W . Ferris, 1991. M ichigan S ta te U niversity 1990 141 soybeans and sugarbeets were obtained from LeCureux and Booms (1987, 1988a, 1988b). 2.2 Resource Constraints The resource constraints considered in this study include: 1) Agricultural land acreage limit: the total acreage of crops shall not exceed the total acreage of the currently existing agricultural land. 2) Water resource constraint: the total requirement for irrigation shall not exceed the amount of streamflow available for irrigation at the 75 percent exceedence level. The available streamflow for irrigation was computed from the BALANCE model, assuming that it is the amount of water above the 95 percent exceedence flow level set by the NPDES (National Pollutant Discharge Elimination System). July was chosen as the critical period for irrigation since irrigation demand is greatest in July when streamflow is lowest. 3) Agricultural land constraint in each of the 12 soil associations: the total acreage of crops in each soil association shall not exceed the total acreage of each soil association. The agricultural land acreage in each of the 12 soil associations was derived by superimposing the land use map on the soil association map using ARC/INFO, a Geographic Information System (GIS). 142 4) Current crop mix constraint: the total acreage of sugarbeets shall not exceed the contract acreage set by the processing capacity of the sugar manufacturing companies. Acreage of dry beans has been declining since 1970s and may stay at the current level to keep the balance of the current crop production system. Two LP models were developed in this study— one with the model parameters at the mean level and the other with the model parameters at the 75 percent confidence level. The LP model for the Cass River Watershed crop mix at the 75 percent confidence level is listed in Appendix B. 3. RESULTS AND DISCUSSIONS 3.1 LP Model Outputs with Streamflow at the 75 and 50 Percent Exceedence Levels The two LP models were run on the IBM 3090 (a mainframe computer) using LINDO (Linear, INteractive, and Discrete Optimizer) which is an interactive linear, quadratic, and integer programming system (Schrage, 1989). listed in Appendices C and D. output summary. The outputs are Tables 20 and 21 show the Spatial distribution of the outputs is shown in Figures 34 and 35. Table 20. Output Summary of the LP Model with the Parameters at 75 Percent Confidence Level Soil Association Corn (acres) Irrig. Nonlr. 40 18,185 41 84,910 42 46,328 Soybeans (acres) Irrig. Nonlr. Dry Beans (acres) Irrig. Nonlr. 37,833 20,713 24,506 48 4,034 51 4,548 64 57,902 69 16,191 70 16,274 73 14,939 74 2,898 Total Irrig. 4,181 43 46 Nonlr. |{ Sugarbeets (acres) 286,681 39,271 4,181 62,580 simulated yields are all at the 75 percent probability level) 39,271 Table 21. Output Summary of the LP Model with All the Parameters at Mean Level Soil Association Corn (acres) Irrig. Soybeans (acres) Nonlr. 40 11,550 41 74,184 42 84,161 Irrig. Nonlr. Dry Beans (acres) Irrig. Nonlr. 46 24,506 51 4,548 64 57,902 69 16,191 70 16,274 73 14,939 74 2,898 Total 286,681 39,271 10,816 55,945 (Expected Gross P[argins) = §1 3 9 , 3 7 5 ,280 * Objective Function Value simulated yields are all average values) Nonlr. 10,726 20,713 4,034 Irrig. 10,816 43 48 Sugarbeets (acres) 39,271 (PrjLees and ( 4 145 Soil A s s o c i a t i o n s 4 0 . Corn (N) + Dr'/ Bean (I) [\\| 64. Corn (N) 41. Corn (N) g g 69. Corn (N) 4 2. Corn (N) + Dry Bean (N) El 7fllCornM 43. Dry Bean (N) [\^ \j 73. Corn (N) 46. Corn (N) fc\j 74. Corn (N) 48. Dry B ean (N) 51. Corn (N) + S u g a r b e e l (N) Figure 34. Non-agricullural (N) - N o n i r r i g a t e d (I) - I r r i g a t e d Spatial Distribution of the LP Model Output with the Parameters at 75 Percent Confidence Level 146 Soil A s s o c ia t io n s ^ 40. Corn (N) + Dry 3 s s n (I) 41. Corn (N) f Dry Been (N) 64. Corn (N) S3 69. Corn (N) ESI 70. Corn (N) (ggg) 43. Dry Boan (N) S3 73. Corn (N) ggfl 46. Dry Bean (N) S3 74. Corn (N) (\\| 48. Corn (N) ■ Non -a g r ic u lt u r a l |\\1 42- Corn (N) MMI SI. Corn (N) + S u g a r b e a t (N) Figure 35. (N) - No n irrigated (I) - I r r i g a t e d Spatial Distribution of the LP Model Output with the Parameters at Mean Level 147 As shown in Tables 20 and 21, and Figures 34 and 35, the model outputs indicate that the acreage of corn may be expanded to 286,681 acres, which accounts for 73 percent of the total agricultural land in the Cass River Watershed. Sugarbeets are limited to 39,271 acres by the sugar manufacturing companies' processing capacity. Irrigation priority may be given to dry beans in the OakvillePlainfield-Spinks soil association (#40). At the 75 percent exceedence level, streamflow in the Cass River in July may irrigate 4,181 acres of dry beans. Total expected gross margins (similar to net income but do not subtract fixed costs such as taxes and interests) of the four crops in the entire watershed is up to $40,197,504, with a confidence level of 75 percent. At the 50 percent exceedence level, streamflow in the Cass River can irrigate 10,816 acres of dry beans (with irrigation water requirements all at the mean level over the period of 1951-1980)(Table 21). Total expected gross margins of the four crops in the watershed may reach $139,375,280 (note that crop prices, variable costs, and simulated yields are all average values over the 30 year period), a 247 percent increase over the total expected gross margins at the 75 percent confidence level. The confidence level for the expected gross margins, however, is only 50 percent. 148 All the soybean variables were dropped out in the model outputs due to their low objective function coefficients (low gross margins per acre of land). 3.2 Sensitivity Analysis of the Model Output with the Streamflow at the 75 Percent Exceedence Level The solution of the LP model with the streamflow at the 75 percent exceedence level is listed in Appendix C and Table 20. Appendix C also lists information on the sensitivity of the solution to the model, which is the impact of changing the value of a parameter (one at a time) on the solution of the model. This section discusses the amount that a parameter must change before the optimal solution changes. As shown in Appendix C, if the optimal variable value is zero, the reduced cost is the amount that variable's objective function coefficient must improve before it is worthwhile for that variable to become positive. In the optimal solution of the model the values of all the soybean variables are zero. The reduced cost of these variables ranges from $12.44 to $824.76, which indicates that the objective function coefficient (gross margins per acre) of one of the soybean variables (changing one parameter at a time) must increase by the minimum amount of $12.44 to $824.76 in order to make the soybean variables positive. That is, assuming the unchanged price, the simulated soybean 149 yields must increase by a large amount to make up the needed additional gross margin in order to make the soybean variables a favorable choice. The dual price of a constraint in Appendix C is the objective function value's rate of improvement due to per unit change in its right hand side constraint, given that the set of positive variables does not change. The dual prices for Rows 3, 4 and 17 (constraints of streamflow, sugarbeet acreage and dry bean acreage) are $4.47, $401.37 and $126.30, respectively, which indicates that if streamflow available for irrigation is increased by one acre-mm (acre-millimeter), the gross margins of crops would be increased by $4.47. Similarly, if acreage of sugarbeets (dry beans) is expanded by one more acre, the gross margins of crops would be increased by $401.37 ($126.30). The maximum allowable increase for streamflow is 2,364,090 acre-mms. That is, the available streamflow for irrigation can be increased from the current amount of 543,489 acre-mms to 2,907,579 acre-mms (an increase of 435%) without changing the current optimal solution basis. If change in the streamflow constraint exceeds the allowable range, the current optimal solution would be changed and the model needs to be re-run to obtain a new optimal solution. The maximum allowable increase for sugarbeet acreage is 4,548 acres, an increase of 11.6 percent (46,327 acres for dry beans, an increase of 69 percent). These changes, if 150 within the allowable range, would not alter the optimal solution basis if they take place one at a time. Otherwise, the optimal solution basis would be changed and the model needs to be re-run. The dual price of agricultural land constraint is $49.55, indicating that if agricultural land is increased by one more acre, the objective function value (gross margin) would be reduced by $49.55. This is because the equality constraint requires that all the agricultural land be planted in crops including some crops such as non-irrigated corn in soil association #40 (CORN40NO) which have a negative gross margin. If the equality constraint is changed to "smaller than (<)" constraint, the optimal solution would be different and the dual price of the agricultural land constraint would become positive. 3.3 Verification of the LP Model output with Streamflow at the 75 Percent Exceedence Level The objective function coefficients (gross margins) in the two LP models were derived by multiplying simulated yields by crop prices and then subtracting variable costs per acre of land (see Equation 14). To verify the model output, a new LP model was developed (see Appendix F), which used actual non-irrigated crop yields at the 25th percentile in Tuscola County and actual irrigated crop yields in Huron County to derive the objective function 151 coefficients. Four constraints used in the model include agricultural land acreage, streamflow at the 75 percent exceedence level, and sugarbeet and dry bean acreage limits. It was not possible to link the crop yields to the soil associations due to the availability of crop data. Summary of the model output is listed in Table 22. The model output, given the assumptions of linearity and uniformity employed in the study, indicates the optimal crop mix as: corn, 73 percent; sugarbeets, 10 percent; and dry beans, 17 percent. Soybean variables were dropped out in the solution due to their low gross margins per acre of land. This result is essentially the same as the result obtained from the first LP model which used simulated crop yields to derive model parameters. The reduced cost of non-irrigated and irrigated soybeans is $32.85 and $227.76, respectively, which indicates that the objective function coefficient (gross margins) of nonirrigated soybeans must increase by a minimum amount of $32.85 ($227.76 for irrigated soybeans) in order to make the non-irrigated soybean variable (irrigated soybeans variable) positive. The dual price of the streamflow constraint is about $2.64, which suggests that if available streamflow increases by one acre-mm, the objective function value would increase by $2.64. The streamflow available for irrigation may be increased by 846 percent without changing the optimal solution basis. 152 Table 22. Output Summary of the LP Model with Streamflow at 75 Percent Exceedence Level. The Objective Function Coefficients were derived from Actual __________ Crop Yields in Tuscola and Huron Counties. Variable Non-irrigated corn Acres 286,681 Irrigated corn 0 Non-irrigated soybeans 0 Irrigated soybeans 0 Non-irrigated dry beans Irrigated dry beans Non-irrigated sugarbeets Irrigated Sugarbeets 59,703 7,058 39,271 0 Total 392,713 * Objective Function Value (Expected gross margins) =$27,322,832 The result of the LP model using actual crop yields agreed with the LP model output derived from the simulated crop yields. Thus, it is feasible to incorporate simulation models into optimization models to provide useful information for decision making. 3.4 LP Model Output with Unlimited streamflow Supply While assuming unlimited streamflow supply, the output of the LP model with crop prices and simulated yields all at the 75 percent confidence level shows that irrigable acreage in the Cass River Watershed is up to 372,000 acres, which is approximately 94.7 percent of the total agricultural land (Table 23, Figure 36, and Appendix E). The expected gross Table 23. Output Summary of the LP Model with All the Parameter at 75 Percent Confidence Level (Assuming Unlimited Streamflow supply) Soil Corn (acres) Association Irrig. Nonlr. Soybeans (acres) Irrig. Nonlr. Dry Beans (acres) Irrig. 40 41 4,142 42 84,161 Nonlr. 63,863 16,905 20,713 46 24,506 48 4,034 51 43,819 64 57,902 69 16,191 70 16,274 73 14,939 I I 74 Total Irrig. 22,366 43 1 Nonlr. Sugarbe S. and J.T. Ritchie. 1985. 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