A MODEL FOR ESTIMATING PREMIUMS TO REDUCE IRRIGATION ON FARMS

Abstract This paper aims to determine the minimum agri‐environmental premium per hectare that farmers should receive to reduce crop irrigation. To this end, the authors develop a mixed‐integer quadratic model using a new methodology based on traditional positive mathematical programming, which allows the inclusion in the model of crop variants that are not present in the baseline situation of the farms. What is shown is that the results obtained with this new methodology, using the cost average approach of calibration, are the same as those obtained with an empirical method, when there is no change of crop distribution after the changeover from irrigated to nonirrigated farms. The theoretical results are compared with those obtained using the calibration with exogenous elasticities and are illustrated numerically for a representative farm of an area around Spain's Tablas de Daimiel in which the use of groundwater for crop irrigation has led to the ongoing deterioration of wetlands that depend on the same source of water, endangering the region's environmental sustainability.     

A decision tool for optimal irrigated crop planning and water resources sustainability

In the present study, the conjunctive use policies of surface and ground water resources are developed for minimizing water shortage in an irrigation district subject to constraints on groundwater withdrawals and crop planning capacities. An integrated soil water balance algorithm is coupled to a non-linear optimization model in order to carry out water allocation planning in complex deficit agricultural water resources systems based on an economic efficiency criterion. Various options of conjunctive use water resources along with current and proposed cropping patterns have been explored by Koohdasht Irrigation District (KID), a semi-arid region in I.R. Iran. The analysis provides various scenarios, which can help managers in decision-making for the optimum allocation plans of water resources within the irrigation area. The results reveal that the proposed model, as a decision tool for optimal irrigated crop planning and water resources sustainability, may be used for maximizing the overall net benefits and global water productivity of an irrigation district considering an allowable annual recharge of groundwater. Findings indicate the importance of the conjunctive water management modeling, which can be easily implemented and would enhance the overall benefits from cropping activities in the study area.     

春小麦水分敏感指数与有限水量生育期的最优分配

通过不同的受旱处理，确定了Jensen模型中的春小麦水分敏感指数。介绍了运用生态规划模型实现有限水量生育期最优分配的方法与步骤，并以辽西地区春小麦为例，确定了不同初始含水量和生育期可利用灌溉水量下的最优分配决策。     

Simulation and optimization for crop water allocation based on crop water production functions and climate factor under uncertainty

In this paper, the uncertainty methods of interval and functional interval are introduced in the research of the uncertainty of crop water production function itself and optimal allocation of water resources in the irrigation area. The crop water production functions in the whole growth period under uncertainty and the optimal allocation of water resources model in the irrigation area under uncertainty are established, and the meteorological factor is considered in the model. It can promote the practical application of the uncertain methods, reflect the complexity and uncertainty of the actual situation, and provide more reliable scientific basis for using water resources economically, fully improving irrigation efficiency, and keeping the sustainable development of the irrigated area. This approach has important value on theoretical and practical for the optimal irrigation schedule, and has very broad prospects for research and development to other related agriculture water management.     

Optimal cropping patterns under water deficits

A mathematical programming model is proposed for optimal cropping patterns under water deficits in dry regions. Crops may be deliberately under-irrigated in order to increase the total irrigated area and possibly the profit. An operating policy will identify both the total area and the irrigation level allocated to a given selected crop taking into account the possible successors and predecessors of this crop. Both annual and seasonal crops are examined in the same study. The model starts by identifying the optimal operating policy for each grower in the region having a given stock of irrigation water. Then, in order to allocate water efficiently among growers, the model determines the global optimal cropping plan of the entire region. To solve efficiently the problem, a decomposition algorithm is developed. Also some useful economic interpretations are given.     

DEVELOPMENT OF AN OPTIMAL WATER ALLOCATION DECISION TOOL FOR THE MAJOR CROPS DURING THE WATER DEFICIT PERIOD IN THE SOUTHEAST UNITED STATES

ABSTRACT. We developed a dynamic economic model to optimize irrigation water allocations during water deficit periods for three major crops grown in the humid southeastern United States. Analysis involved the use of crop simulation models to capture (a) the yield water relationship and (b) soil moisture dynamics from one week to another week. A hy‐drological model was used to find the water supply; combinations of hydrological and simulation models were used to find the optimal water allocation during each week in corn, cotton and peanuts. Results indicated that farmers should irrigate the most valuable crop first (peanuts) before applying water to other crops (corn and cotton). Results also showed that, because of restriction on total water supply, an increase in crop acreage did not increase the net revenue of the farm in a proportionate amount. Results should provide guidelines to water managers, engineers, policy makers, and farmers regarding an optimal amount of water allocation that will maximize net returns when water shortage is a serious concern.     

CONTROLLING GROUNDWATER QUALITY WITH ENDOGENOUS REGULATORY INSTRUMENTS

ABSTRACT. This research presents a competitive dynamic model that endogenously evaluates the economics of regulatory tax-policy options. This model is then applied to an irrigated corn production area west of Kearney, Nebraska, where the average groundwater contamination level from nitrates is reported to be 8.7 parts per million (ppm). Results indicate that no regulatory policies are necessary for maintaining potable groundwater quality with either a surge-flow irrigation system or a sprinkler irrigation system. In areas where conventional furrow irrigation technology is being used, higher net economic benefits result from the adoption of a variable-tax on nitrogen fertilizer use, followed by a constant-unit tax and a pollution tax.     

A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin’s irrigation areas, Gansu Province, China. In this study, the irrigation areas’ economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties.     

GLOBAL WARMING,IMPACT ON AGRICULTURE AND ADAPTATION STRATEGY

Abstract Sensitivity of the Southeastern US agriculture sector to temperature increases will be based largely on accompanying changes in precipitation, extent of the warming, and relative impact on competing crops grown in the area. The impact of climate change in 10 Southeastern US counties was investigated under three different climate scenarios for two different reference years (2030 and 2090). Seven major crops grown in the area were selected to study the impact on crop yield, irrigation acreage, and optimal choice of crops in a representative farm in each of the southeastern states. If warming is moderate and also brings a considerable increase in precipitation—as indicated by the Hadley model—then, the effect on yields, water use, and income will be mostly benign. If warming is moderate without increased precipitation and the water for irrigation is available, then the effects on the agriculture sector are still mostly negligible. If warming is not moderate and no increased precipitation materializes, farmers could realize quite dramatic negative consequences for row crop agriculture in the Southeastern United States.     

A Decision Support System for Micro-Watershed Management in India

The improvement of economic conditions in developing countries like India is crucially dependent on improvement in agriculture. Crop production depends on the volume of irrigation water and its temporal distribution, water quality, solar radiation, precipitation and a host of soil properties. All these factors vary from crop to crop. In view of the above it is imperative for increasing agricultural production that scarce water resources should have efficient management. It is necessary to evolve an innovative approach for water distribution and management. This paper presents an integrated DSS model for a Micro-Watershed Management System (MWMS) for generating alternative water allocation and agricultural production scenarios for a semi-arid region. The model is tested with data from the Radharamanpur micro-watershed (364 Ha. area) in the Bankura district of West Bengal state in India.     

IMPACTS OF WATER SUPPLY UNCERTAINTY AND STORAGE ON EFFICIENT IRRIGATION TECHNOLOGY ADOPTION

In the framework of a stochastic dynamic programming model, the paper investigates the impact of water supply uncertainty and storage at farm level on adoption of efficient irrigation technologies under a flexible water price regime. We find that even a flexible water pricing cannot guarantee higher adoption of efficient irrigation technology in all cases. Results of the paper indicate that if a farmer invests in water storage capacity, then the value of efficient usage of water increases, and the rate of adoption of efficient irrigation technology will be higher. It establishes a complementarity relationship between investments in storage capacity and adoption of efficient irrigation technology. The relationship becomes stronger with increasing variance in water supply. In a situation without any option to store water at the farm level, we find a negative relationship between investment in efficient irrigation technology and water variability. However, numerical analysis results suggest that a risk averse farmer may invest more in efficient irrigation only if the variance in water supply is very high.     

Applying stochastic goal programming: A case study on water use planning

A decision support model to help public water agencies allocate surface water among farmers and authorize the use of groundwater for irrigation (especially in Mediterranean dry regions) is developed. This is a stochastic goal programming approach with two goals, the first concerning farm management while the other concerns environmental impact. Targets for both goals are established by the agency. This model yields three reduction factors to decide the different reductions in available surface water, standard groundwater and complementary groundwater that the agency should grant/authorize for irrigation, this depending on if it is a dry or wet year. In drought periods, the model recommends using more groundwater (in percentage) than in wet periods. A case study using year-to-year statistical information on available water over the period 1941–2005 is developed through numerical tables. A step-by-step computational process is presented in detail.     

基金最佳使用计划的线性规划模型

给出了基金存款策略的线性规划模型 .对基金 M使用 n年的情形 ,只需比较银行存款税后年利率 ,初步确定 n年内的一切可能有的基金存款方式及其到期本利率 ,通过基金流转分析 ,即可建立以最大奖金数为目标的线性规划模型 ( LP1 ) n;问题二则需先分析 n年内一切可行的存款和购国库卷的组合方式及其到期的最佳本利率 ,然后调整模型 ( LP1 ) .中有关的系数 ,即可得到模型 ( LP2 ) n,调整模型 ( LP1 ) n与 ( LP2 ) n中第三年的奖金 y的系数 ,即可得到问题三的线性规划模型 .本文用 SAS/OR软件求解上述模型 ,得到在 n=1 0 ,M=5 0 0 0的情形下 ,使每年奖金数为最大的各种问题的基金的最佳使用策略 .     

Intelligent gradient search in linear programming

The simplex algorithm is still the best known and most frequently used way to solve LP problems. Khachian has suggested a method to solve these problems in polynomial time. The average behaviour of his method, however, is still inferior to the modern simplex based LP codes. A new gradient based approach which also has polynomial worst-case behaviour has been suggested by Karmarkar. This method was modified, programmed and compared with other available LP codes. It is shown that the numerical efficiency of Karmarkar's method compares favourably with other LP codes, particularly for problems with high numbers of variables and few constraints.     

A Mixed Linear Programme for Short-term Irrigation Scheduling

For farmers in the UK who use hosereel-raingun irrigation systems, irrigation scheduling requires that three questions be answered: (i) when should each field be irrigated; (ii) how much water should be applied; and (iii) which field should be irrigated first on a particular day? A mixed linear programme has been built to produce optimum irrigation schedules. The objective function maximizes the financial return from irrigation over the short term (typically 7 days). The constraints are equipment, labour and water availability. Use of the mixed linear programme is illustrated with a typical situation faced by a UK farmer.     

Finding all Solutions of Systems of Nonlinear Equations Using the Dual Simplex Method

An efficient algorithm is proposed for finding all solutions of nonlinear equations using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations in a given region. In the conventional LP test, the system of nonlinear equations is transformed into an LP problem, to which the simplex method is applied. However, although the LP test is very powerful, it requires many pivotings for each region. In this paper, we use the dual simplex method in the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm can find all solutions of systems of 200 nonlinear equations in practical computation time.     

A mathematical programming model applied to the study of water markets within the Spanish agricultural sector

Spanish irrigated agriculture uses about 80% of all the nation's available water resources. The need to increase the economic efficiency of current uses of water in the agricultural sector is perceived as the top priority of the country's national water policy. In Spain surface water is centrally allocated among competing users based on allocation criteria dictated by the Water Law. The complete absence of price or market signals is a major obstacle to induce irrigators to use water more efficiently. Water markets within the agricultural sector is a promising, though scarcely analyzed in Spain, solution to increase its economic efficiency. This research is an attempt to evaluate probable water transfers among farmers and irrigation districts as well as water price equilibria resulting from different water market arrangements. Three interconnected mathematical programming models permit the simulation of water use at the farm level and water market arrangements in the Guadalquivir Valley (Spain). Results show that water markets would be highly dependent on the level of transaction costs and on the relative reductions of water allotments due to nonoverlapping drought cycles among water districts.     

Analysis of lettuce evapotranspiration across soil water

In this study, we evaluated the lettuce accumulated evapotranspiration (ET) across four levels of irrigation, using a nonlinear mixed‐effects model. The plants were grown in protected environments and monitored over 23 consecutive days. When the moisture of the substrate in the vessels reached 50% of their maximum retention capacity, the water levels were elevated according to four treatments: , , , and . The model appeared to provide a good fit to the data and showed that the estimates of the maximum amount of accumulated ET were similar for the three treatments with soil water deficit and lower for . The results of the study supported the idea that optimization of the ET of lettuce plants could be achieved through irrigation with deficit, also indicating that the economical use of water was the most efficient way to boost agricultural production. Recommendations for resource managers

• The continued growth of the world population will result in a decrease of quality and availability of water and also an increase in demand for food. Therefore, sustainability will depend on high agricultural productivity with rational use of water.
• Considered the most efficient technology for boosting agricultural productivity, irrigation is also the largest water consumer in the world. With any kind of irrigation in the vegetable production area, the water intake for the plants must be treated with great caution.
• Both a lack or excess in water can decrease plant productivity. The amount of water available in the soil should be enough to maximize production. It is shown that high levels of irrigation are not necessary for this.
• It is important to balance the amount of irrigated water for an optimal level, in order that the production has its the production is maximized and valuable water resources are not wasted.

     

Analysing production and environmental risks in arable farming systems: A mathematical approach

In response to a growing environmental concern in Dutch society, sustainable production systems in arable farming have been developed. Amongst other things, a reduction of the dependency on chemical inputs is attempted. This paper addresses the role of risk in the adoption by farmers of new systems by means of a model that determines differences in production risks between conventional and sustainable farming systems (CAFS and IAFS).Timing of activities – setting out a management track – is particularly important in sustainable arable farming systems. Resource requirements of crop husbandry activities mainly depend on weather conditions. To assess risks caused by weather conditions, the major aspects of crop husbandry in various crops have been modelled. Using tactics in crop husbandry (decision rules) and weather uncertainty as input, crop husbandry models (HMs) calculate management tracks that require resources. The value distributions of resource requirements of crop husbandry according to different farming systems is calculated in different HMs represented by stochastic dynamic directed networks. Hence, production risks of CAFS and IAFS can be compared.On a farm, all the aspects of crop husbandry in the various crops are to be taken into account. Given the weather conditions, tactics for all the aspects are combined in an LP model of the whole farm where they compete for limited resources. In the LP model, tactics are re-assessed by means of the HMS, using information of the LP solution. This iterative procedure enables production risks of CAFS and IAFS to be compared, considering fixed, allocatable resources for the whole farm firm.