A model for regional optimal allocation of irrigation water resources under deficit irrigation and its applications

It is important to promote efficient use of water through better management of water resources, for social and economical sustainability in arid and semi-arid areas, under the conditions of severe water shortage. Based on the developments in deficit irrigation research, a recurrence control model for regional optimal allocation of irrigation water resources, aiming at overall maximum efficiency, is presented, with decomposition-harmonization principles of large systems. The model consists of three levels (layers). The first level involves dynamic programming (DP) for optimization of crop irrigation scheduling. The second level deals with optimal allocation of water resources among various crops. The last level concerns optimal allocation of water resources among different sub-regions. As a test, this model was applied to the combined optimal allocation of multiple water resources (surface, ground and in-take from the Weihe river) of Yangling, a semi-arid region on the Loess Plateau, China. Exemplary computation showed that not only are the results rational, but the method can also effectively overcome possible “dimensional obstacles” in dynamic programming of multiple dimensions. Furthermore, each sub-model is relatively independent by using various optimization methods. The model represents a new approach for improving irrigation efficiency, implementing water-saving irrigation, and solving the problem of water shortage in the region studied. The model can be extended in arid and semi-arid areas for better water management.     

An inexact two-stage water management model for planning agricultural irrigation under uncertainty

In this study, an inexact two-stage water management (ITWM) model is developed for planning agricultural irrigation in the Zhangweinan River Basin, China. The ITWM model is derived from the incorporation of interval-parameter programming (IPP) within a two-stage stochastic programming (TSP) framework. It can reflect not only uncertainties expressed as probability distributions but also interval numbers. Moreover, it can provide an effective linkage between conflicting economic benefits and the associated penalties attributed to the violation of the predefined policies. Four decision scenarios associated with different water-resources management policies are examined. Targeted incomes, recourse costs, and net system benefits under different scenarios are analyzed, which indicates that different policies for agricultural irrigation targets correspond to different water shortages and surplus, and thus lead to varied system benefit and system-failure risk. The results are valuable for supporting the adjustment or justification of the existing irrigation patterns and identify a desired water-allocation plan for agricultural irrigation under uncertainty.     

Evolving strategies for crop planning and operation of irrigation reservoir system using multi-objective differential evolution

In this paper multi-objective differential evolution (MODE) approach is proposed for the simultaneous evolution of optimal cropping pattern and operation policies for a multi-crop irrigation reservoir system. In general, farming community wants to maximize total net benefits by irrigating high economic value crops over larger area, which may also include water-intensive crops and longer duration crops. This poses a serious problem under water-scarce conditions and often results in crop failure. Under varying hydrological conditions, the fixed cropping pattern with conventional operating rule curve policies may not yield economically good results. To provide flexible policies, a nonlinear multi-objective optimization model is formulated. To achieve robust performance by handling interdependent relationships among the decision variables of the model, the recent MODE technique is adopted to solve the multi-objective problem. The developed model is applied for ten-daily reservoir operation to a case study in India. The model results suggest that changes in the hydrologic conditions over a season have considerable impact on the cropping pattern and net benefits from the irrigation system. Towards this purpose, the proposed MODE model can be used to evolve different strategies for irrigation planning and reservoir operation policies, and to select the best possible solution appropriate to the forecasted hydrologic condition.     

A real-time water allocation model for large irrigation systems

In this study a simulation model for real-time irrigation scheduling of water deliveries at the tertiary and secondary canal levels of large irrigation systems has been developed. The model is responsive to current season changes in weather and other variables. The irrigation scheduling of the subsequent week is found out at the end of each week by updating the status of the system with real time data up to that week and then by solving the model for the new conditions. The model is based on water balance approach for lowland paddy and a soil moisture simulation approach for determining the irrigation requirements of upland crops. Expected rainfall at different probability levels during the irrigation season was used based on past rain fall data and Leaky law. The model was applied to an irrigation system in Thailand for determining the required irrigation deliveries. Result of the application indicate that the model can be used for determining water deliveries in a real-time basis.     

Performance based irrigation planning under water shortage

A linear programming (LP) based optimization model and a simulation model are developed and applied in a typical diversion type irrigation system for land and water allocation during the dry season. Optimum cropping patterns for different management strategies are obtained by the LP model for different irrigation efficiencies and water availability scenarios. The simulation model yields the risk-related irrigation system performance measures (i.e. reliability, resiliency and vulnerability) for the management policies defined by the optimization model. The alternative strategies are evaluated in terms of all performance criteria (i.e. net economic benefit, equity and reliability) simultaneously through a trade-off analysis using a multi-criteria decision making method (compromise programming). For the case study of the Kankai irrigation system in Nepal, with equal preference to the objectives, a management strategy with equal share of water among the project subareas appears to be the most satisfactory alternative under water shortage conditions. The existing water allocation policy is not economically efficient. Deficit irrigation in Early paddy appears attractive under favorable hydrologic scenario, particularly if accompanied by measures to improve existing irrigation system efficiency.     

Effect of brackish water irrigation and straw mulching on soil salinity and crop yields under monsoonal climatic conditions

Fresh water shortages are severally restricting sustainable agriculture development in the North China Plain. The scarcity of fresh water has forced farmers to use brackish water from shallow underground sources, which helps to overcome drought and increase crop yields but also increases the risk of soil salinization. To identify safe and effective ways of using brackish water in this region, field experiments were conducted to evaluate the effect of brackish water irrigation and straw mulching on soil salinity and crop yield in a winter wheat-summer maize double cropping system. The experiment was in a split-plot design. Six rates of straw mulching (0, 4.5, 6.0, 7.5, 15.0 and 30.0 Mg/ha) were assigned to the main plots and two irrigation water qualities (i.e. brackish water with salt content of 3.0-5.0 g/L and fresh water with only 1.27 g salt/L) were applied to subplots. The brackish water irrigation significantly increased the salt content at different soil depths in the upper 1 m soil layer during the two growing seasons. Straw mulching affected the vertical distribution of salt in the brackish water irrigation plots and the average salt content of straw mulch treatments (4.5, 6.0, 7.5, 15.0 and 30.0 Mg/ha) within the 0-20, 20-40 and 0-100 cm soil depths was 10.2, 14.0 and 1.8% lower than that without straw mulch (A₀). No salt accumulation occurred to a depth of 1 m in the brackish water irrigation plots and there was no correlation between the value of SAS (salt accumulated in 1 m of soil) and straw mulch rate. In 2000 and 2001, the salt content within the 0-40 cm soil layer in brackish water irrigation plots increased due to high evaporation rates during April-June, and then decreased up to September as salts were leached by rain. For the fresh water irrigation plots, the salt content remained relatively stable. Straw mulching affected the salt content in the 0-40 cm soil layer in brackish water irrigation plots in different periods of 2000 and 2001, but no correlation between salt content and straw mulch rates was observed except in September of 2000. Unlike for wheat, the yield of maize increased as the straw mulch rate increased according to the equation, y = 0.1589x + 5.3432 (R² = 0.6506). Our results would be helpful in adopting brackish water irrigation and straw mulching in ways that enhance crop yields and reduce the risk of soil salinization. However, long-term effects of brackish water irrigation and straw mulching on soil salinity and crop yield need to be further evaluated for sustainability of the system.     

Optimal irrigation planning model for an existing storage based irrigation system in India

A weekly irrigation planning LP model is formulated for determining the optimal cropping pattern and reservoir water allocation for an existing storage based irrigation system in India. Objective of the model is maximization of net annual benefit from the project. In an irrigation planning of a storage based irrigation system, initial storage of the reservoir at the beginning of the reservoir operation, expected inflows into the reservoir during each intraseasonal period, capacity of channels, crop calendar and yield response to water deficit in each growth stage of crop play a vital role in deciding acreage and water allocation to each crop. The planning model takes into account yield response to water deficit in each intraseasonal period of the crop, expected weekly inflows entering into the reservoir, storage continuity of reservoir, land and water availability, equity of water allocation among sub areas and proportionate downstream river release. One year comprising of 52 weeks is considered as planning horizon. To account for uncertainty in water resources availability, the model is solved for four levels of reliability of weekly inflows entering into the reservoir (90%, 85%, 80% and 75%). Alternative optimal cropping patterns and weekly releases to crops grown in each sub area under each main canal are obtained for various states of initial storage at the beginning of reservoir operation and for various levels of weekly inflows into the reservoir. Results reveal the importance of initial state of reservoir storage for feasible solution and shows the impact on cropping pattern with the change in initial storage of reservoir for different levels of reliability of weekly inflows.     

Integrated decision making for reservoir,irrigation, and crop management

An integrated approach to reservoir, irrigation, and cropping management which links four different models—a hydrologic model (PRMS), a crop growth simulation model (EPIC), an economic model based on linear programming, and a dynamic programming model—is developed and demonstrated. The demonstration is based on an irrigation district located in a subhumid climate with an irrigation reservoir large enough for over-year storage. The model is used to make repeated simulations for various planning horizons. Two different types of results are presented. The first provides the probability that each of the various farm plans (land/crop/water allocation) will be chosen as the optimum in the first year of the planning horizon. The second approach provides probability distributions of accumulated revenues over a chosen length of planning horizon. Each distribution is associated with an initial reservoir level and a particular farm plan in the first year of the planning horizon. The consequence of selecting certain farm plans at the beginning of a specified planning horizon is therefore quantified in a probabilistic way. Based on families of probability–revenue curves, an irrigation manager can simultaneously evaluate crop, irrigation, and reservoir management options.     

A model for optimal allocation of canal water based on crop production functions

A model for optimal distribution of water in the canal command areas has been developed. Water production functions in the form of polynomial expressions were developed from existing experimental information. Using the production functions, water distribution is indicated in order to obtain maximum returns. It has been shown that higher returns can be obtained from canal command areas by a suitable modification of the existing water release pattern at the outlet.     

Optimal allocation of water from a single purpose reservoir to an irrigation project with pre-determined multiple cropping patterns

A model for optimal allocation of water from a single-purpose reservoir to an irrigation project with pre-determined multiple cropping patterns was developed. The model consisted of two modules: (I) the intra-seasonal allocation model (non-linear programming) which is used for allocation of water among different crops for a definite combination of state variables (inflow class, rainfall class, reservoir storage classes at the beginning and at the end of the season) for the non-dormant season to maximize total farm income; and (II) the seasonal allocation model (stochastic-dynamic programming) which is used for the convergent operating policy over seasons for optimal expected farm income over a year. The model was applied to Ardak reservoir dam (I.R. Iran) in an arid region. Low river inflow in the dormant season at the study area could not admit the reservoir class changes for specific combinations of state variables, and therefore resulted in a non-usable result. Imposing a fictitious positive relative net benefit for all possible combinations of reservoir class changes eliminated this problem. It was also shown that rainfall did not play a marked role in the study area, which is an arid region, and its stochastic nature can be removed from the model.     

Simulated crop production under saline high water table conditions

Summary Many irrigated lands in semi-arid regions of the world are underlain with saline high water tables. Water management is critical to maintain crop productivity under these conditions. A multi-seasonal, transient state model was used to simulate cotton and alfalfa production under various irrigation management regimes. The variables included in-season water application of 1.0 or 0.6 potential evapotranspiration (PET), and 18 or 33 cm pre-irrigation amounts for cotton. The water table was initially at a 1.5m depth and a 9 dS/m salinity. A impermeable lower boundary at 2.5 m depth was imposed. Irrigation water salinity was 0.4 dS/m. Climatic conditions typical to the San Joaquin Valley of California were used for PET and precipitation values. The simulations were for no-lateral flow and also lateral flow whereby the water table was raised to its initial level prior to each irrigation event. Uniform application of 1.0 PET provided for relative cotton lint yields and alfalfa yields of 95% or more for at least 4 years. In-season irrigation of cotton with 0.6 PET had higher yields when associated with a 33 cm rather than an 18 cm pre-irrigation. Lateral flow provided for higher cotton lint yields production than the no-lateral flow case for each pre-irrigation treatment. The beneficial effects of lateral flow diminished with time because of the additional salt which accumulated and became detrimental to crop production. Substantial alfalfa yield reductions occurred after the first year when irrigation was set at 0.6 PET regardless of other conditions. Evaporation losses from the soil during the cotton fallow season were higher when the soil water content entering the fallow season were higher.Research was supported by the University of California Salinity/ Drainage Task Force     

An econometric irrigated crop allocation model for analyzing the impact of water restriction policies

The objective of the Spanish government-funded GESMO project is to research on new water policy evaluation and monitoring tools, applied to aquifer 8/23 in the Eastern Mancha, which covers one of the most important areas under the charge of the Júcar Catchment Confederation. The project is to output two types of end products: Decision Support Systems for defining water use policies, including economic impact and environmental simulators within a single multi-criteria decision-making environment and Measure Monitoring and Control Systems employing tele-detection and simulation of crop water needs. The Decision Support Systems will include three, highly complex, theoretical models in a single information technology product: a three-dimensional aquifer 8/23 behavior simulation model, an econometric model to predict crop allocation depending on the economic environment, water availabilities, etc., and an automatic alternative generation and evaluation system based on a multi-criteria methodology. The objective of the system is to advise on possible water policies and how they would materialize into spatially and temporally distributed water quotas (m³/ha) with the objective of both safeguarding the aquifer in the medium and long term and increasing the economic profitability of regional agriculture. In this paper, a regional econometric model is presented for studying the impact of water use quotas on the main irrigated crops allocation in the region.     

Optimisation model for water allocation in deficit irrigation systems: I. Description of the model

In this paper, an economic optimisation model for hydrologic planning in deficit irrigation systems is proposed. Irrigation water allocation between agricultural demands is carried out following an economic efficiency criterion with the aim of maximising the overall economic benefits obtained, allocating available water to each user as a function of the water’s profit margin. Water resources constraints in the system are considered. Aggregated economic functions for each irrigation district are generated optimising the water used for the cropping pattern. Stochastic nature of water availability and irrigation requirements have been taken into account.Due to the complexity of the system, the problem has been broken down into three independent optimisation sub-problems that perform hierarchically. Each of these sub models takes into account a different resolution level of the system: crop, irrigation district and the whole basin.The proposed model has been used in a subsequent paper to optimise water allocation planning in a small basin in southern Spain; the Bembézar system.     

Evaporation and drift losses from sprinkler irrigation systems under various operating conditions

Quantitative determinations of evaporation and drift losses from sprinkler systems were carried out under different operating conditions.Evaporation losses determined by an electrical-conductivity method ranged from 1.5 to 16.8% of the total sprinkled volume. Wind velocity and vapor pressure deficit were the most significant factors affecting the evaporation losses. Exponential relationships between the evaporation losses and both wind velocity and vapor pressure deficit have been found. For the operating pressures used in this study the least effect on evaporation was found.Drift losses measured by the magnesium-oxide method varied from 1.5 to 15.1%. Drift losses increased with the second power of the wind velocity, and decreased with increasing distance in the downwind direction.Combined losses from a sprinkler system for a given set of operating conditions have been estimated by using the results obtained from the experiments. Combined losses ranged from 1.7 to 30.7% of the applied water.     

考虑气象因子的不确定性灌溉水资源优化配置

基于不确定性区间作物水分生产函数,选取春小麦、玉米、棉花和白兰瓜这4种典型作物,建立不确定性条件下灌溉水资源优化配置模型,并将气象因子(蒸发蒸腾量和相对湿度)的不确定性引入其中,以反映气候变化对灌区配水的影响.结果表明,在石羊河流域民勤地区,玉米单方水经济效益较低,故其优化灌溉定额相比现状灌溉定额变化较大.棉花是单方水经济效益最大的作物,其次是白兰瓜,所以当可用水量短缺时,在确保粮食安全的前提下,为降低因灌溉缺水而带来的经济损失,要优先保证棉花和白兰瓜灌溉用水.引入气象因子的灌区水资源优化配置模型区间优化配水定额范围更广,反映出气象因子对灌区配水的影响.本研究验证了不确定性方法在实际应用的可行性,可为灌区水资源合理分配提供更可靠的科学依据.     

Energy balance and crop water stress in winter maize under phenology-based irrigation scheduling

In eastern India, cultivation of winter maize is getting popular after rainy season rice and farmers practice irrigation scheduling of this crop based on critical phenological stages. In this study, crop water stress index of winter maize at different critical stages wase determined to investigate if phenology-based irrigation scheduling could be optimized further. The components of the energy budget of the crop stand were computed. The stressed and non-stressed base lines were also developed (between canopy temperature and vapor pressure deficit) and with the help of base line equation, [(T _c − T _a) = −1.102 VPD − 3.772], crop water stress index (CWSI) was determined from the canopy-air temperature data collected frequently throughout the growing season. The values of CWSI (varied between 0.42 and 0.67) were noted just before the irrigations were applied at critical phenological stages. The soil moisture depletion was also measured throughout the crop growing period and plotted with CWSI at different stages. Study revealed that at one stage (silking), CWSI was much lower (0.42–0.48) than that of recommended CWSI (0.60) for irrigation scheduling. Therefore, more research is required to further optimize the phenology-based irrigation scheduling of winter maize in the region. This method is being used now by local producers. The intercepted photosynthetically active radiation and normalized difference vegetation index over the canopy of the crop were also measured and were found to correlate better with leaf area index.     

Contribution to irrigation from shallow water table under field conditions

The mathematical model SWBACROS was applied to estimate the contribution of a shallow groundwater to the water needs of a maize crop. The model was applied with the top and boundary conditions defined by the observed irrigation/rainfall events and the observed water table depth. The simulated water contents of the top zone were very close to the observed values. Furthermore the model was applied with an assumed free drainage bottom boundary condition. The difference of the computed water content profiles under the presence and absence of the water table gave a very good estimate of the capillary rise. It was found that under the specific field conditions about 3.6 mm/day of the water in the root zone originated from the shallow water table, which amounts to about 18% of the water, which was transpired by the maize crop.     

Proposal for equitable water allocation for rotational irrigation in Pakistan

A rotational water supply system is designed to deliver a constant flow of water among irrigators along a tertiary canal. Under the existing rotational system in Pakistan transmission losses along the canal are not considered. A constant time per unit irrigated area is allocated to all the farmers regardless of their location along the canal. This results in decreasing volumes of water delivered to downstream farmers. A variable time model is developed which allocates more time to the downstream farmers to deliver a constant volume of water per unit area to all the farmers in the command area of a tertiary unit.     

MOPECO: an economic optimization model for irrigation water management

Water is a natural, sometimes scarce, and fundamental resource for life, essential both for agriculture in many regions of the world and also to achieve sustainability in production systems. Maximizing net returns with the available resources is of the utmost importance, but doing so is a complex problem, owing to the many factors that affect this process (e.g. climatic variability, irrigation system configuration, production costs, subsidy policies). The MOPECO model is a tool for identifying optimal production plans, and water irrigation management strategies. The model estimates crop yield, production and gross margin as a function of the irrigation depth. Finally, these gross margin functions are used to determine an optimum cropping pattern and irrigation strategy to maximize the gross margin on a farm in a specific scenario. Since the relationships between the variables are generally non-linear and the number of alternative strategies is quite large, the optimum process is complex and computationally intensive. Genetic algorithms are therefore used to identify optimal strategies. This paper describes the MOPECO model, which comprises three computing modules: (1) estimation of net water requirements; (2) derivation of the relationship between gross margin and irrigation depth; and (3) identification of the crop planning and the water volumes to be applied. The results obtained by applying the MOPECO model to a specific irrigable area in a semi-arid area of Spain, with great deficits and high water costs, are also included and discussed. These results usually show that the irrigation depth for maximum benefits is lower than that necessary to obtain maximum production. In some areas of Spain, horticultural crops are nearly always part of the optimum alternative. The crops that become part of the optimum alternative are mainly horticultural crops with a high gross margin and low water requirements. The irrigation depths selected for the ideal crop rotation are included among the irrigation depth of maximum economic efficiency and the maximum gross margin irrigation depth. Both are lower than that necessary for the maximum yield. This model helps farmers, extension services, and other agents to analyse, make decisions and optimize water management.Communicated by A. Kassam