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In this study, a fuzzy dependent-chance interval multi-objective stochastic expected value programming model is developed for irrigation water resources management under uncertainties. It incorporates fuzzy dependent-chance programming, stochastic expected value programming, interval programming into multi-objective programming. Compared with conventional programming methods, it can quantify the relationship between the expected values of stochastic variables and the fuzzy goals of expected values set by decision-makers through the satisfactory degrees, and trade-off the relationship amid multiple satisfactory degrees selected as objective functions. Besides, it can cope with uncertainties expressed as interval numbers, fuzzy numbers, and stochastic variables. Moreover, the fairness of water allocation constraints formulated by the GINI coefficient can achieve the interactions between fair water allocation and satisfactory degrees. The model is applied to a real case study of irrigation water resources management of different water types (i.e., surface water and groundwater) under different water flow levels (high, medium, and low flow levels) in the midstream region of the Heihe River basin, northwest China. The results reveal that: (1) maximum water demands of wheat and economic crop are satisfied while that of corn is not met under three flow levels; (2) the expected economic benefit and water shortages of crops have positive relationships with water allocation while the expected canal water loss has a negative relationship with water allocation; (3) the bigger expected economic benefit results in the higher satisfactory degree of the expected economic benefit while the lower expected water shortage and canal water loss lead to higher satisfactory degrees of expected water shortage and canal water loss. It shows that the developed model can overcome the disadvantages of the single-objective programming of putting attention to the satisfactory degree of a kind of expected value, and neglecting the satisfactory degree of other associated expected benefit. It also can overwhelm the drawbacks of the two-objective programming model of more focus on the satisfactory degree of the expected canal water loss. The results can provide different water allocation schemes for decision-makers. [ABSTRACT FROM AUTHOR]

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Due to the widespread uncertainties in agricultural water resources systems and climate change projections, the traditional optimization methods for agricultural water management may have difficulties in generating rational and effective optimal decisions. In order to get optimal future agricultural water allocation schemes for arid areas with consideration of climate change conditions, the model framework established in this paper integrates a statistical downscaling model, back propagation neural networks, and an evapotranspiration model (the Hargreaves model) with inexact irrigation water allocation optimization model under future climate change scenarios. The model framework, which integrates simulation models and optimization models, considers the interactions and uncertainties of parameters, thereby reflecting the realities more accurately. It is applied to the Yingke Irrigation Area in the midstream area of the Heihe River Basin in Zhangye city, Gansu Province, northwest China. Then, water allocation schemes in planning year (2047) under multiple future Representative Concentration Pathways (RCP) scenarios and the status quo (2016) are compared, in order to evaluate the practicability of generated water allocation schemes. The results show that the water shortages of economic crops are improved compared with the status quo under all RCP scenarios while those of the grain crops present opposite results. Meanwhile, the economic benefits decrease from the status quo to planning year under all future scenarios. This phenomenon is directly related to the amount of irrigation water allocation and is indirectly related to the changes of meteorological conditions. The model framework can reveal the regular pattern of hydro-meteorological elements with the impact of climate change. Meanwhile, it can generate irrigation water allocation schemes under various RCPs scenarios which could provide valuable decision support for water resources managers. [ABSTRACT FROM AUTHOR]

In this study, a fuzzy linear fractional programming (FLFP) approach with double-sided fuzziness is developed for optimal irrigation water allocation under uncertainty. The FLFP model can be derived from incorporating double-sided fuzzy chance-constrained programming (DFCCP) into linear fractional programming (LFP) optimization framework. The developed model can deal with uncertainty presented as fuzziness in both right-hand and left-hand sides of constraints. Moreover, it has advantages in: (1) addressing two objectives directly without considering subjective factors, (2) effectively reflecting economic water productivity between total system economic benefit and total irrigation water use, (3) introducing the concept of confidence levels of fuzzy constraints-satisfaction under both the minimum and maximum reliabilities to generate more flexible solutions and (4) facilitating in-depth analysis of interrelationships among economic water productivity, system benefits and varying confidence levels. The model is applied to a case study of irrigation water allocation in the middle reaches of Heihe River Basin, northwest China. The optimal irrigation water allocation solutions from the FLFP model can be obtained. These results can provide decision-support when deciding on selecting reasonable irrigation water resources management and agricultural production. [ABSTRACT FROM AUTHOR]

The vague and fuzzy parametric information is a challenging issue in irrigation water management problems. In response to this problem, a generalized fuzzy credibility-constrained linear fractional programming (GFCCFP) model is developed for optimal irrigation water allocation under uncertainty. The model can be derived from integrating generalized fuzzy credibility-constrained programming (GFCCP) into a linear fractional programming (LFP) optimization framework. Therefore, it can solve ratio optimization problems associated with fuzzy parameters, and examine the variation of results under different credibility levels and weight coefficients of possibility and necessary. It has advantages in: (1) balancing the economic and resources objectives directly; (2) analyzing system efficiency; (3) generating more flexible decision solutions by giving different credibility levels and weight coefficients of possibility and (4) supporting in-depth analysis of the interrelationships among system efficiency, credibility level and weight coefficient. The model is applied to a case study of irrigation water allocation in the middle reaches of Heihe River Basin, northwest China. Therefore, optimal irrigation water allocation solutions from the GFCCFP model can be obtained. Moreover, factorial analysis on the two parameters (i.e. λ and γ ) indicates that the weight coefficient is a main factor compared with credibility level for system efficiency. These results can be effective for support reasonable irrigation water resources management and agricultural production. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

An interval linear fractional irrigation water allocation (ILFIWA) model is developed in response to the complexity of errors in estimating crop yields, fluctuating hydrological elements as well as varying economic profits in an irrigation system. The model is capable of quantitatively solving multi-objective problems, i.e. to obtain the maximum system net benefit and the minimum irrigation water use. Particularly, it can handle multi-objective functions expressed as ratios, such as irrigation water productivity. Moreover, it can reflect the uncertainties of the variables/parameters and functions involved. The potential of the developed model is shown by applying to a case study in northwest China. Results of the model can help make irrigation water allocation decisions for different time periods under varying flow levels. Comparison between ILFIWA model and ordinary interval linear programming model shows that the developed model is conducive to improving irrigation water productivity and saving irrigation water, and helping decision makers formulate desired irrigation water resources management policies under uncertainty. [ABSTRACT FROM AUTHOR]

In this study, the multi-dimensional critical regulation control (MCRC) modes and water allocation for irrigation system were studied in the middle reaches of Heihe River basin, China, to coordinate the water contradiction of agricultural irrigation and ecological irrigation. Based on the key indexes of five dimensions, including water resources, ecological environment, society, economy and water-saving measures, 320 schemes of three regulation control levels were generated and analyzed, then the optimal modes were obtained by introducing entropy theory and synergetic theory, thus the corresponding thresholds were obtained meanwhile. Based on the parameters of the most optimal irrigation system regulation control modes, an inexact multi-stage stochastic programming (IMSP) model for water resources optimal allocation of the 12 major irrigation districts in the middle reaches of Heihe River basin was developed and the corresponding results were obtained. This paper gives the optimal MRCR modes and water resources allocation plans from a different perspective by considering the ecological environment protection and agricultural water-saving. The results can help decision makers to develop a more sustainable water resources planning program in study areas and similar areas. [ABSTRACT FROM AUTHOR]