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Water scarcity, the intensification of agricultural nonpoint pollution, and continuous deterioration of the ecosystem are serious problems in arid areas. Optimal allocation of water resources is the key way to achieve sustainable and efficient development of irrigated agriculture. An integrated multiobjective optimization model considering water-balance processes was developed under shallow groundwater environments to enhance comprehensive objectives and obtain optimal irrigation solutions. A simulation module of the physical processes of water movement among crop root zones, soil water, and groundwater aquifers, and a multiobjective optimization module of irrigation water allocation were incorporated into a general framework. It has the following advantages in terms of (1) illustrating variations of agricultural hydrological parameters (e.g., soil water content, groundwater depth, groundwater-based evaporation, and so on) in water movement processes; (2) obtaining a set of noninferior decision-making solutions through a modified nondominated sorting genetic algorithm (NSGA-II), which can maximize the interests for multiple parties; and (3) generating optimal solutions of irrigation water allocation and alleviating water scarcity, improving irrigation water productivity, and reducing negative environmental effects. To demonstrate its applicability, it was applied to optimize irrigation water allocation in the Jiefangzha Irrigation Subarea (JIS), China. It was firstly split into 44 irrigation subsystems, and each subsystem was assumed to be a homogeneous unit in meteorology, soil texture, and groundwater. Under the water competition between subsystems and rigid constraints of water availability, optimized results enhanced net economic benefits by 14.7%, saved 7.74% of irrigation water amount, and improved irrigation water productivity by 13% compared with status quo. Meanwhile, it can reduce graywater footprint of grain production by 58% compared with the average level of Hetao Irrigation District, China. [ABSTRACT FROM AUTHOR]

Due to the complex feedback cycle relationship among water resources, energy, and food, the agricultural water management mode and concept with a single object or two objects as the core can no longer meet the inherent requirements of the coordinated, sustained, and healthy development of economy and society. A two-stage multiobjective decision-making method based on a θ -dominance evolutionary algorithm (θ -DEA) is proposed for the optimization of agricultural systems with a water-energy-food nexus. First, the Pareto noninferior solution set of the model is obtained by the evolutionary algorithm based on θ -DEA. Then, the economic benefit and carbon emission of each solution are evaluated, and the optimal solution is selected by using the multiobjective decision-making method based on interval-valued hesitant fuzzy sets and the technique for order preference by similarity to ideal solution (TOPSIS). Through a case study of the Hetao Irrigation District (HID), the best optimization results are obtained when the carbon footprint is 4.16×109 kg CO2 eq, and the economic benefit is 8.09×109 yuan. The example shows that the model can well select the optimal allocation solution of water resources, which not only has high economic benefits and low pollution discharge but also meets the subjective wishes of decision-makers. The model has good practicability and stability. [ABSTRACT FROM AUTHOR]

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]

Nonlinear and conflicting objectives as well as complex uncertainties are commonly encountered by irrigation-water managers. To address such problems, an interval nonlinear multiobjective programming model with fuzzy-interval credibility constraint (FIC-INMP) is proposed for crop water allocation. The FIC-INMP model integrating interval programming, nonlinear multiobjective programming and fuzzy-interval credibility-constrained programming could address not only the conflicts of multiple nonlinear objectives under interval uncertainty, but also the fuzziness expressed as fuzzy-interval membership function. Moreover, an interval fuzzy weighted (IFW) method is proposed to solve developed model by integrating fuzzy weighted programming approach and interval Zimmermann fuzzy method. The FIC-INMP and IFW are applied to Yingke Irrigation District to plan crop monthly water allocation and demonstrate their applicability. By fully considering the main factors in allocation, including concerns of different decision makers, normal growth of crops, local water balance and uncertainties existing in allocation, optimal crop water-allocation schemes can be obtained via the FIC-INMP and IFW. The optimal results offer abundant schemes to decision makers by trading off benefit and risk. In addition, from the comparison between single objective and multiobjective model, the multiobjective model shows better practicality due to more reasonable water allocation in critical water demand period of crops. These results can effectively contribute to the local irrigation water management and ecological restoration. [ABSTRACT FROM AUTHOR]

In this study, a simulation-based multi-objective two-level optimization decision-making approach is developed for optimal irrigation water allocation, improving irrigation water productivity and controlling regional accumulated salts. Techniques of multi-objective programming, two-level programming and simulation model of water and salt physical movement process are incorporated into the modeling framework. The simulated processes are parameterized and calibrated with field experimental data while the optimization model is used to generate optimal solutions though predefined objectives and the associated constraints. This model is applied to a case study on irrigation water allocation in the Jiefangzha Irrigation Subarea in Hetao Irrigation District, Northwest China. Firstly, the study area is delineated into several homogeneous irrigation decision-making units (IDMUs) for better characterizing their spatial variability because it's spatially heterogeneous. Afterwards, decomposition-coordination algorithm is introduced to solve such an integrated simulation-based multi-objective two-level optimization model. Finally, optimal solutions of irrigation water allocation for different crops during crop growth periods in different IDMUs can be obtained for supporting sustainable strategies of irrigation. The results can achieve balanced tradeoffs between different stakeholders (i.e., the upper-level decision-makers and the lower-level farmers) and between conflicting economic objectives and environmental objectives. Moreover, optimal solutions have a slight increase in economic returns over the baseline scenario (i.e., status quo), but the irrigation water productivity is increased by nearly 60% due to less irrigation water used. Regional accumulated salts can be controlled because the soil salinity is constrained within the predetermined salt accumulation constraint. Therefore, these findings can provide evidence for efficient use of irrigation water resources and further support of sustainable irrigated agriculture. • A simulation-based multi-objective two-level optimization model is developed. • This study addresses three objectives, and reflects sequential decisions. • An efficient algorithm is introduced to solve such an integrated model. • The study area is delineated into several irrigation decision-making units. • The results balance tradeoffs between economic and environmental objectives. [ABSTRACT FROM AUTHOR]

This study presents an interval multi-objective fuzzy-interval credibility-constrained nonlinear programming (IMFICNP) model combined with spatial water requirement of ecological vegetation (SEWR) estimation for solving the problem of allocation of agricultural and ecological water in irrigation districts under uncertainties. Through techniques of remote sensing (RS) and geographic information system (GIS), the ecological vegetation is subdivided into three types including forest land, grassland and shrubland and the water requirement of ecological vegetation is extended from site-specific sample to spatial decision-making unit (DMU), which provides a set of spatial data for input parameters of constraints. The IMFICNP model can be formulated through combination of interval parameter programming, multi-objective programming and fuzzy-interval credibility-constrained programming, which can handle the conflicts of multiple objectives under uncertainties such as single uncertainty (interval and fuzzy parameters) and dual-uncertainties (fuzzy-interval sets), and finally generate optimal water allocation schemes for crop and ecological vegetation under different credibility levels. The interval quadratic crop water production functions (IQCWPFs) are introduced to express the nonlinear relationships between crop yield and irrigation amount. Then, this model is applied to a case study of Huangyang Irrigation District (HID) in Shiyang River Basin to demonstrate its applicability. The results indicate that a higher credibility level is accompanied by less amount of water allocation and lower system benefit. The amount of water allocation at the DMU is dominated by planting area of crops and ecological vegetation, but there are few exceptions that optimal solutions are determined by the economic value. In addition, SEWR enables to reflect spatial heterogeneity of the DMU at a larger scale. IMFICNP model can coordinate conflicts among multiple objectives and it can tackle the violation of system constraints with fuzzy-interval sets. Therefore, these results can effectively balance the agricultural and ecological water management in irrigation districts, and provide valuable basis for the sustainable development of arid and semi-arid areas. • Tackle single uncertainty, dual-uncertainties and violation risk by optimization model. • Generate optimal solutions for agricultural and ecological water allocation. • A novel spatial method for estimating water requirement of ecological vegetation. • Balance agricultural and ecological water management in HID in Shiyang River Basin. [ABSTRACT FROM AUTHOR]

[Display omitted] • A novel w ater-f o od-carbo n -lan d - e cology-nut r ient (WONDER) nexus in an arid area is proposed. • The irrigation priority ranking of different decision-making units is calculated based on GEE platform. • The ecological satisfaction degree is proposed to characterize the degree of achieving the pre-given ecological objectives. • A fuzzy-interval credibility-constrained bi-level multi-objective programming model is developed. • The findings can provide decision support for balancing conflicts and preferences in agricultural and ecological water management. Multiple subsystems such as water, food, land, carbon, ecology, and nutrition are closely intertwined, and the resulting complexity and uncertainty pose challenges to water resource management. This study proposes an optimization framework from a novel w ater-f o od-carbo n -lan d - e cology-nut r ition (WONDER) nexus perspective for the integrated management of agricultural and ecological water resources. Firstly, the irrigation priority ranking of decision-making units (DMU) is obtained based on the remote sensing indices from the Google Earth Engine (GEE) platform. Secondly, the ecological satisfaction degree, which aggregates carbon sink satisfaction degree and ecological water demand satisfaction degree, is proposed to characterize the degree of achieving the pre-given ecological objectives. Then, the above two indicators (i.e., the irrigation priority ranking and the ecological satisfaction degree) are integrated with a fuzzy-interval credibility-constrained bi-level multi-objective programming model to realize: (1) reconciling conflicts in food nutrition, food security, economic development, and ecological conservation; (2) making trade-offs among the positions and preferences of different decision-makers; (3) dealing with the dual uncertainties of fuzzy-interval parameters; (4) obtaining optimal agricultural and ecological water allocation schemes. The applicability of the model is verified by taking Hongyashan Irrigation District of Minqin County as an example. The results show that: (1) the irrigation priority ranking for the DMUs is: DMU 10 > DMU 9 > DMU 4 > DMU 5 > DMU 1 > DMU 11 > DMU 6 > DMU 8 > DMU 7 > DMU 2 > DMU 3; (2) the ratio of agricultural to ecological water allocation in the irrigation district is about 3:1, which is consistent with the water use characteristics of this area; (3) the total water allocation during the whole growth period for different crops is mainly determined by planting area, and the ranking of the water allocation is: sunflower > maize > wheat > seed melon. Moreover, compared with the single-level models, the inexact bi-level multi-objective model can well coordinate the upper and lower decision-makers and the multiple decision objectives under the WONDER nexus. Therefore, the proposed framework can provide the scientific basis for balancing agricultural and ecological water management and conflicting objectives in similar irrigation districts through involving multiple subsystems and perspectives. [ABSTRACT FROM AUTHOR]

• A full fuzzy-interval credibility-constrained nonlinear programming (FFICNP) model is proposed under uncertainty. • This approach is applied to a case study for planning irrigation water allocation in the Zhanghe Irrigation District. • A lower credibility level corresponds to higher net system benefit and system efficiency. • The results support in-depth analysis of interrelationships among water allocation schemes, system benefits, and credibility levels. To address the water shortage caused by various natural conditions and ineffective irrigation water management in the Zhanghe Irrigation District (ZID) of the Yangtze River basin in China, a full fuzzy-interval credibility-constrained nonlinear programming (FFICNP) model is developed under uncertainty. Derived through incorporating fuzzy credibility constrained programming into the Jensen model optimization framework, FFICNP can not only address intervals (single uncertainty) and fuzzy-interval sets (dual uncertainties) in the model objectives and double-sided constraints, but also reflect nonlinear responsive relationships between the crop yields and irrigation levels by introducing the crop water production functions (CWPFs) under different growth stages. Moreover, an expected-value-based (EVB) approach is introduced to solve the FFICNP model. The FFICNP model is then applied to the case study of irrigation water allocation in the ZID for demonstrating its applicability. Optimal solutions can be generated from the FFICNP model for solving the irrigation water allocation problem under uncertainty. The results indicate that a lower credibility level corresponds to a higher level of system benefits and system efficiency. The system benefits of ZID in a wet year are [17.72, 24.23] × 109 CNY when λ = 1.0 and [17.79, 25.03] × 109 CNY when λ = 0.6. These findings from the FFICNP model can support in-depth analysis of interrelationships among irrigation water allocation schemes, system benefits, and credibility levels, and thus contribute to the effectiveness of irrigation water management under various inflow levels and complex uncertainties. [ABSTRACT FROM AUTHOR]

• An interval multiobjective multi-stage stochastic programming (IMMSP) model is proposed. • A modified minimum deviation (MMD) method was proposed for solving IMMSP. • The developed approach is applied to a case study for planning seasonal irrigation water-storage scale and allocation. • The results guide local water managers identify the optimal management strategies and project construction scale of water conservancy. Water managers in arid and semi-arid areas must allocate limited irrigation water to different water use sectors considering the conflicting objectives, seasonal runoff inflow, and multiple uncertainties. To deal with these problems, an interval multiobjective multi-stage stochastic programming (IMMSP) model was proposed for finding reasonable water-storage scale and optimizing limited irrigation-water resources. Key factors in planning irrigation-water resources, such as random seasonal runoff, interval uncertainty in data collection, economic benefits, water leakage loss, and water deficit, were fully considered in the IMMSP model. Additionally, as an important indicator to describe the seasonal water supply capability of local water supply project, including reservoirs, agricultural ponds and etc., the water-storage scale, defined as the ratio of water storage capacity over total streamflow, is proposed to obtain the quantitative relationship between this indicator and objective of IMMSP. This study attempted to obtain the relationship between water-storage scale and objective of IMMSP as well as provide a reference of determining water-storage scale from the perspective of optimization. In addition, to solve the IMMSP model, a modified minimum deviation (MMD) method was proposed for dealing with uncertainties, making tradeoff among conflicting objectives, and reflecting the different importance of objectives. Both the IMMSP model and MMD method were applied to a real-world water-allocation problem in the middle reaches of the Heihe River basin for verifying its validity. The solutions generate a set of decision alternatives under different seasonal runoff scenarios and further guide local water managers identify the optimal management strategies and project construction scale of water conservancy. Moreover, a sound discussion of contribution to water-storage scale planning is made and the comparisons between IMMSP and each single-objective model (economic benefits, water leakage loss, and water deficit) in this study demonstrate that the results obtained by the proposed approach are more practical than a single objective with the same constraints. These results can not only effectively contribute to local irrigation water management and ecological restoration, but also provide more information to plan regional water-storage scale values. [ABSTRACT FROM AUTHOR]