Irrigation Water Allocation Using an Inexact Two‐Stage Quadratic Programming with Fuzzy Input under Climate Change

Agricultural irrigation accounts for nearly 70% of the total water use around the world. Uncertainties and climate change together exacerbate the complexity of optimal allocation of water resources for irrigation. An interval‐fuzzy two‐stage stochastic quadratic programming model is developed for determining the plans for water allocation for irrigation with maximum benefits. The model is shown to be applicable when inputs are expressed as discrete, fuzzy or random. In order to reflect the effect of marginal utility on benefit and cost, the model can also deal with nonlinearities in the objective function. Results from applying the model to a case study in the middle reaches of the Heihe River basin, China, show schemes for water allocation for irrigation of different crops in every month of the crop growth period under various flow levels are effective for achieving high economic benefits. Different climate change scenarios are used to analyze the impact of changing water requirement and water availability on irrigation water allocation. The proposed model can aid the decision maker in formulating desired irrigation water management policies in the wake of uncertainties and changing environment.     

POTENTIAL WATER USE AND AGRICULTURAL PRODUCTION PATTERNS UNDER ALTERNATIVE WATER PRICES1

Out study deals with the demand for water and alternative agricultural production and land use patterns under varying prices for both surface and ground water. We derive irrigation water demands for both the United States and regions of it. Not only is a different amount of water used at each set of water prices but also a different mix of crops, livestock, and production technology develops among the different regions. Under the highest set of prices used, more than fourteen million acres are converted into dryland farming. Total irrigated water use decreases by more than 25 million acre-feet. Irrigated crop yields are reduced and cropping patterns shift away from irrigation. Commodity shadow prices increase as much as 15 percent under high prices for both surface and ground water. A redistribution of farm income occurs between irrigated and dryland regions.     

GROUND WATER MANAGEMENT OPTIMIZATION USING GENETIC ALGORITHMS AND SIMULATED ANNEALING: FORMULATION AND COMPARISON1

ABSTRACT: Genetic algorithms (GA) and simulated annealing (SA), two global search techniques, are coupled with MODFLOW, a commonly used groundwater flow simulation code, for optimal management of ground water resources under general conditions. The coupled simulation-optimization models allow for multiple management periods in which optimal pumping rates vary with time to reflect the changing flow conditions. The objective functions of the management models are of a very general nature, incorporating multiple cost terms such as the drilling cost, the installation cost, and the pumping cost. The models are first applied to two-dimensional maximum yield and minimum cost water supply problems with a single management period, and then to a multiple management period problem. The strengths and limitations of the GA and SA based models are evaluated by comparing the results with those obtained using linear programming, nonlinear programming, and differential dynamic programming. For the three example problems examined in this study, the GA and SA based models yield nearly identical or better solutions than the various programming methods. While SA tends to outperform GA in terms of the number of forward simulations needed, it uses more empirical control parameters which have significant impact on solution efficiency but are difficult to determine.     

Using system dynamics to model water-reallocation

Improving the efficiency of water allocation has long been recognised as a key problem for the water resources management decision-makers. However, assessing the efficacy of management decision is difficult due to the complexity and interconnectivity of water resource systems. For this reason, it is vital that robust modelling approaches are employed to deal with the feedback loops inherent in the water resource systems. Whilst many studies have applied modelling to various aspects of water resource management, little attention has been given to innovations in modelling approaches to deal with the modelling challenges associated with improving decision-making. The aim of this study is to apply a System Dynamics modelling approach to improve the efficiency of water allocation incorporating a myriad of irrigation system constraints. The system dynamic approach allows the different system components to be organised as a collection of discrete objects that incorporate data, structure and function to generate complex system behaviour. Through the application of a system dynamic approach, a robust model (named the Economical Reallocating Water Model (ERWM)) was developed which was used to examine the options of re-allocating water resources that minimize the water cost all over an irrigated agricultural area. The EWRM incorporated a wide range of complexities likely to be encountered in water resource management: surface and ground water sources, water trading between sources, system constraint such as maximum ground water pumping, rates, maximum possible trading volumes and differential water resource prices. Two hypothetical systems have been presented here as an example. The results show that the System Dynamics approach has a significant advantages in estimating and assessing the outcomes of alternative water management strategies through time and space.     

ALLOCATION MODEL FOR IRRIGATION WATER COST: CASE STUDY OF THE NILE VALLEY IN EGYPT1

ABSTRACT: An allocation model for irrigation water cost, based on the Use of Facilities method, is presented. The model is developed for large-scale irrigation systems which may include multipurpose reservoirs, irrigation control works, pump stations and irrigation canals of various orders. The model accounts for the water conveyance losses as well as the water gains in the irrigation canals, and their effects on irrigation cost. It is applied to the irrigation distribution system of the Nile Valley in Egypt, which contains the High Aswan Dam, 16 irrigation structures, 12 pump stations, and numerous irrigation canals. The irrigation water cost at 29 areas representing the Nile Valley is determined.     

Surface Water Seepage Effects on Shallow Ground‐Water Quality Along the Rio Grande in Northern New Mexico1

Abstract: Interactions between surface irrigation water, shallow ground water, and river water may have effects on water quality that are important for both drinking water supplies and the ecological function of rivers and floodplains. We investigated water quality in surface water and ground water, and how water quality is influenced by surface water inputs from an unlined irrigation system in the Alcalde Valley of the Rio Grande in northern New Mexico. From August 2005 to July 2006, we sampled ground water and surface water monthly and analyzed for concentrations of major cations and anions, specific conductance, pH, dissolved oxygen, and water levels. Results indicate that irrigation ditch seepage caused an increase in ground water levels and that the Rio Grande is a gaining stream in this region. Temporal and spatial differences were found in ion concentrations in shallow ground water as it flowed from under the ditch toward the river. Ground‐water ion concentrations were higher when the ditch was not flowing compared with periods during peak irrigation season when the ditch was flowing. Ditch inputs diluted ion concentrations in shallow ground water at well positions near the ditch. Specifically, lower ion concentrations were detected in ground water at well positions located near the ditch and river compared with well positions located in the middle of an agricultural field. Results from this project showed that ditch inputs influenced ion concentrations and were associated with ground‐water recharge. In arid region river valleys, careful consideration should be given to management scenarios that change seepage from irrigation systems, because in some situations reduced seepage could negatively affect ground‐water recharge and water quality.     

LINEAR PROGRAMMING USE FOR EVALUATING WATER RESOURCES AND COST AND BENEFIT ALLOCATION1

ABSTRACT A linear programming model for a river basin was developed to include almost all water-related economic activity both for consumers and producers. The model was so designated that the entire basin or basin sub-division could be analyzed. The model included seven sectors, nine objective function criteria, and three river-flow levels. Economic basis for conflicts among sectors over incidence of cost allocation and level of economic activity can be traced to some chosen objective. The disposal of untreated household waste water, particularly from the rural household, directly into the river was consistent with maximizing net benefits and minimizing costs. The optimum resource allocation, water-treatment plants, farms and industry activities would change with flow level. For each of the three industries analyzed separately, paper, wool and tanning, public treatment of industrial waste water was the optimal treatment process in one or more of the solutions. Lake shoreline was the dominant feature determining lake-resource valuation. Implied capital value varied from $126 per shoreline foot to over $250 depending on discount rate. Implied prices on lake surface ranged from $42 to $147 per acre. Strong economic forces encouraged small lot sizes for vacation cottages.     

THE ECONOMIC VALUE OF GROUND WATER RECHARGE FOR IRRIGATION USE1

ABSTRACT: Artificial recharge as a means of augmenting water sup plies for irrigation is a management alternative which policy makers in ground water decline areas are beginning to consider seriously. A conceptual model is developed to evaluate the economic benefits from ground water recharge under conditions where the major water use is irrigation. The methodology presented separates recharge benefits into two components: pumping cost savings and aquifer extension benefits. This model is then applied to a Nebraska case to approximate the value of recharge benefits as a function of aquifer response. discount rate, and commodity prices. It was found that recharge benefits vary from less than $2 to over $6 an acre foot recharged.     

OPTIMIZING NONPOINT SOURCE CONTROLS IN WATER QUALITY REGULATION1

ABSTRACT: A stochastic programming framework is developed to evaluate the economic implications of reliability criteria and multiple effluent controls on nonpoint source pollution. An integrated watershed simulation model is used to generate probability distributions for agricultural effluents in surface and ground water resulting from agricultural practices. Results from the planning model indicate that reliability and multiple effluent constraints significantly increase the cost of nonpoint controls but the effects vary by control alternative. The analysis indicates that an evaluation of multiple water quality objectives can be an important planning tool for designing nonpoint source controls for innovative programs to promote cost-effective water quality regulation.     

IRRIGATION METHODS AND TRANSPORT OF IMAZAMETHABENZ‐METHYL TO GROUND WATER: GREENFIELDS BENCH,MONTANA1

ABSTRACT: A series of gravel terraces support a shallow aquifer that is the sole source of drinking water for three public water supplies and more than 400 private wells on the Greenfields Bench in west‐central Montana. Farming practices on the Greenfields Bench include irrigation of malting barley and the yearly application of herbicides for the control of weeds. The most commonly used herbicide (imazamethabenz‐methyl, U.S. trade name Assert®) has been found in the ground water on the Greenfields Bench. An experiment was conducted in 2000 and 2001 to characterize the transport of Assert and its acid metabolite to ground water under three irrigation methods: flood, wheel line sprinkler, and center pivot sprinkler. Results show that Assert concentrations in ground water are controlled by hydraulic loading rates of each irrigation method, Assert persistence in soil, hydraulic characteristics of the aquifer, and adsorption/desorption of Assert onto clay particles and organic matter.     

FARM INCOME AND GROUND WATER QUALITY IMPLICATIONS FROM REDUCING SURFACE WATER SEDIMENT DELWERIES1

ABSTRACT: The potential surface water and ground water quality tradeoff implications from the nonpoint source provisions of the 1987 Water Quality Act are investigated in this paper using a national linear programming model developed at Iowa State University and modified by the Economic Research Service and the Leaching Evaluation of Agricultural Chemicals (LEACH) Handbook developed by the U.S. Environmental Protection Agency. The linear programming model is used to maximize net farm revenue using optimal combinations of crop rotations and tillage practices for each region of the United States given natural resource constraints. The LEACH handbook is used to determine the relative potential for pesticides to leach below the root zone for different soil types, hydrologic conditions, pesticides used, and tillage practices. The results indicate that imposing a surface water quality erosion constraint aimed at reducing sediment concentrations results in a larger decrease in farm income than imposing a uniform 5 ton per acre per year erosion constraint. Both constraints could result in regional improvement in ground water quality in some regions of the country while decreasing ground water quality in other regions.     

A CONCEPTUAL FRAMEWORK FOR EVALUATING AGRICULTURAL WATER CONSERVATION POTENTIALS1

ABSTRACT: This paper defines types of water losses in irrigated agriculture and outlines potentials for water conservation. Recoverable water “losses” (seepage, leakage, and spillage during storage and conveyance, and surface runoff and deep percolation during irrigation) and irrecoverable losses (evaporation from water and soil surfaces and transpiration from plants) are described and illustrated. Some conservation terms are defined, particularly the distinction between on-farm irrigation efficiency and areawide efficiency. Briefly reviewed are agricultural water conservation technologies and their applicability. The biggest untapped potential for water conservation may be a reduction in irrecoverable losses, especially evapotranspiration. The advantages and disadvantages of reducing recoverable and irrecoverable water losses are described, including possible effects on ground water, energy, salinity, crops, wildlife, and in-stream uses. Such information may be useful in several policy and management issues, e.g., ground water overdraft and possible constraints on crops and sites to be irrigated.     

A LINEAR ANALYSIS OF AN URBAN WATER SUPPLY SYSTEM1

The use of linear programming as a planning tool for determining the optimal long-range development of an urban water supply system was explored. A stochastic trace of water demand was synthesized and used as an input to the model. This permitted evaluating the feasibility of imposing demand restrictions as an effective cost reduction mechanism. The City of Lincoln, Nebraska, was used as the urban model. The fundamental problem was to allocate limited water supplies from several sources to an urban load center to minimize costs and comply with system constraints. The study period covered twenty years, and findings indicate the planning direction for stage development during this period. Sensitivity analyses were performed on cost coefficients and demands. Thirteen sources were included in the initial computations. Conclusions were that linear programming and generated demand traces are useful tools for both short- and long-term urban water supply planning. Lowering peak demands results in long-range development of fewer sources of supply and more economic and efficient use of the supplies developed.     

Evidence Supporting Cap and Trade as a Groundwater Policy Option for Reducing Irrigation Consumptive Use1

Thompson, Christopher L., Raymond J. Supalla, Derrel L. Martin, and Brian P. McMullen, 2009. Evidence Supporting Cap and Trade as a Groundwater Policy Option for Reducing Irrigation Consumptive Use. Journal of the American Water Resources Association (JAWRA) 45(6):1508‐1518. Abstract: In the American West water is becoming an increasingly scarce resource. Obligations to bordering states, endangered species protection, and long‐term resource sustainability objectives have created a need for most western states to reduce the consumption of irrigation water. In Nebraska specifically, the Nebraska Department of Natural Resources (NDNR) and local Natural Resource Districts (NRDs) are meeting a large part of this need by using a regulatory approach, commonly called groundwater allocation. The cost of allocation, which occurs in the form of reduced economic returns to irrigation, could be greatly reduced by using an integrated cap and trade approach. Much like environmental cap and trade programs which are used to reduce the cost of limiting environmental pollution, the trading of capped groundwater allocations can reduce the cost of limiting water use. In an analysis of a typical case in the Nebraska Republican Basin, we found that the impact of a water market to trade groundwater allocations depended on the size of the allocation and on the characteristics of the land and irrigation systems involved in the trade. Potential economic benefits from trade ranged from US$0 to US$120 per 1,000 cubic meters traded, from US$25 to US$250 per 1,000 cubic meters of reduction in consumptive use, and from US$16 to US$50 per hectare of irrigated land in the region. The highest benefits occurred at relatively high allocations, which capped withdrawals at 65‐75% of the expected unrestricted pumping level. These gains from trade would be split between buyers and sellers based on the negotiated selling price.     

Analysis of irrigation systems using sustainability-related criteria

Sustainable agricultural development as a desired goal in irrigation management is a result of recent public awareness of the scarcity of water for food production. In order to incorporate sustainability-related criteria in the analysis of irrigation systems, the present study aims at introducing environmental indices that represent irrigation water conservation and satisfactory production and income for farmers under stress conditions. An experiment was conducted in Chania, Greece, during the irrigation periods of 1989 and 1990. The irrigation water delivered to 40 experimental plots and the relevant soil moisture content at the root zone were recorded. The data, collected in real time, were used for the calculation of the corresponding environmental indices. The variation of indices in time and space was high, and demonstrated that up to 13% of water was delivered to crops, 82% was yield loss, and 84% was economic return. The study indicated that environmental indices could be easily computed by means of routinely collected data, and could also be incorporated into decision-making approaches, such as compromise programming, in order to develop policies for irrigation water allocation.     

Optimal Location and Management of Waste Disposal Facilities Affecting Ground Water Quality1

ABSTRACT: Numerical simulation of ground water solute transport is combined with linear programming to optimize waste disposal. A discretized form of the equation governing solute transport is included as a set of constraints in a linear program. Two problems are described. First, the management model is used to maximize ground water waste disposal. The model constrains disposal activities so that the quality of local ground water supplies is protected. Parametric programming is shown to be important in evaluating waste disposal tradeoffs at the various facilities. Changes in the velocity field induced by waste water injection cause a nonlinearity in the solute transport equation which is dealt with by employing an iterative procedure. The second problem is aimed at identifying all sites which are suitable for waste disposal in the subsurface. The management model is manipulated so that the optimal value of the dual variables are “unit source impact indicators.” This physical interpretation is valuable in identifying feasible disposal sites. The joint simulation and optimization approach permits the management of complex ground water systems where the aquifer is used simultaneously for waste disposal and water supply.     

THE IMPORTANCE OF INSTITUTIONAL STRUCTURE IN CONTROLLING AGRICULTURAL RUNOFF1

Abstract: Agricultural runoff, such as dissolved mineral salts and selenium, creates pronounced downstream impacts to agricultural producers and to wildlife. The ability to manage these problems efficiently depends critically on the institutional pricing structure of irrigation water delivery agencies. An important characteristic of irrigation water delivery is whether irrigators pay per unit of water received or make one payment regardless of the quantity of water received. In this study we compare the effectiveness of agricultural runoff reduction policies in two regions that employ these different water pricing structures. We find that reduction policy is more effective and can be achieved at a lower cost when water is priced on a per unit basis and that growers have greater incentive to act on their own to reduce runoff problems. Operating under a per unit pricing system encourages water conservation and runoff reduction, which creates public benefits that are not achieved under the single-payment, fixed allotment method of irrigation water delivery.     

Farm-level irrigation and the marginal cost of water use: evidence from Georgia

We create a proxy for the cost of irrigation water in Georgia from a sample of Georgia irrigators by investigating the marginal cost of pumping groundwater. We then combine this proxy with agronomic and climatic variables to estimate the response of agricultural water use to differences in the marginal cost of irrigation. The results show that pumping costs are a significant determinant of water use, and imply that agricultural water use would be moderately affected by institutional changes that would explicitly price water.     

REUSE OF POWER PLANT COOLING WATER FOR IRRIGATION1

ABSTRACT: Current water quality policies in California require disposal of saline blowdown waters from power plants in sealed evaporation ponds to avoid degradation of ground waters. This policy highlights the conflict between increased energy demands, increasing scarcity of water, and environmental priorities. Saline blowdown waters can be used for the irrigation of salt tolerant crops, albeit with some reduction in yields. The results of experiments intended to specify these yield reductions are reported. If such irrigation is carefully managed, the soil profile can be used to store residual salts and ground water degradation will be avoided, provided that irrigation ceases before the salts are leached to the ground water. An analysis of discharge below a carefully managed irrigation project shows that the downward movement of salts below the root zone is no worse than with conventional methods of disposal. Thus, irrigation reuse with blowdown water is shown to be a viable means of saline water disposal while maintaining existing standards of ground water quality protection. Further analysis demonstrates the economic feasibility of such irrigation reuse by showing that it is significantly less costly than the evaporation pond alternative.     

Regional Blue and Green Water Balances and Use by Selected Crops in the U.S.

The availability of freshwater is a prerequisite for municipal development and agricultural production, especially in the arid and semiarid portions of the western United States (U.S.). Agriculture is the leading user of water in the U.S. Agricultural water use can be partitioned into green (derived from rainfall) and blue water (irrigation). Blue water can be further subdivided by source. In this research, we develop a hydrologic balance by 8‐Digit Hydrologic Unit Code using a combination of Soil and Water Assessment Tool simulations and available human water use estimates. These data are used to partition agricultural groundwater usage by sustainability and surface water usage by local source or importation. These predictions coupled with reported agricultural yield data are used to predict the virtual water contained in each ton of corn, wheat, sorghum, and soybeans produced and its source. We estimate that these four crops consume 480 km³ of green water annually and 23 km³ of blue water, 12 km³ of which is from groundwater withdrawal. Regional trends in blue water use from groundwater depletion highlight heavy usage in the High Plains, and small pockets throughout the western U.S. This information is presented to inform water resources debate by estimating the cost of agricultural production in terms of water regionally. This research illustrates the variable water content of the crops we consume and export, and the source of that water.