Nonlinear Interval Parameter Programming Combined with Cooperative Games: a Tool for Addressing Uncertainty in Water Allocation Using Water Diplomacy Framework

Water Resources Management - This paper shows the utility of a new interval cooperative game theory as an effective water diplomacy tool to resolve competing and conflicting needs of water users...     

A Hybrid Dynamic Dual Interval Programming for Irrigation Water Allocation under Uncertainty

Along with the economic development in Canada, the shortage of irrigation water has become a serious concern (Bouwer 1993; Hennessy 1993). In this study, a model of Dynamic Dual Interval Programming (DDIP) is developed and applied to the irrigation water allocation systems with uncertainty. DDIP method improves the existing dynamics interval programming by explicitly addressing the system uncertainties with a dual interval that had higher system reliability. The solution of DDIP is computationally effective, and its decision variables are incorporated into the solutions for final decision. In order to obtain the optimal allocation schemes in a dynamic process, the developed DDIP was applied to an irrigation water system. The results from this case study revealed that optimal solution can be obtained through the DDIP approach from the agriculture water management activities for feasible decisions. These decisions reflect the high uncertainty of the information in the boundaries of dual intervals. The solution presents a maximum benefit under limited yearly uncertain natural resources. Furthermore, the information obtained though this model may help the authority to make optimal decisions and to reduce the risk for uncertain situations.     

Interval-parameter Two-stage Stochastic Nonlinear Programming for Water Resources Management under Uncertainty

Over the past decades, controversial and conflict-laden water allocation issues among competing interests have raised increasing concerns. In this research, an interval-parameter two-stage stochastic nonlinear programming (ITNP) method is developed for supporting decisions of water-resources allocation within a multi-reservoir system. The ITNP can handle uncertainties expressed as both probability distributions and discrete intervals. It can also be used for analyzing various policy scenarios that are associated with different levels of economic consequences when the promised allocation targets are violated. Moreover, it can deal with nonlinearities in the objective function such that the economies-of-scale effects in the stochastic program can be quantified. The proposed method is applied to a case study of water-resources allocation within a multi-user, multi-region and multi-reservoir context for demonstrating its applicability. The results indicate that reasonable solutions have been generated, which present as combined interval and distributional information. They provide desired water allocation plans with a maximized economic benefit and a minimized system-disruption risk. The results also demonstrate that a proper policy for water allocation can help not only mitigate the penalty due to insufficient supply but also reduce the waste of water resources.     

An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem

In this study, an improved single-step method (SSM) is developed based on two-step method (TSM) to solve the interval-parameter linear programming (ILP) model of which the right-hand sides are highly uncertain. Two numerical examples are presented to ascertain appropriate value of λ in SSM. The risk preference degree of λ could be 0.8 for maximum objective function type. To demonstrate the applicability of the developed method, an agricultural water management problem has been provided in the case study section. The results show that SSM is more effective than TSM for complete solutions. There is only partial solution obtained from the first submodel of TSM, because the right-hand side of the wheat output constraint is highly uncertain. Finally, local farmers’ net benefit reaches to [8.949, 12.442]?×?10⁸ RMB (the unit of Chinese currency). The priority order of crops that are needed to be irrigated by surface water is maize > wheat > cotton.     

Evaluating and Calibrating Reference Evapotranspiration Models Using Water Balance under Hyper-Arid Environment

This research investigates five reference evapotranspiration models (one combined model, one temperature-based model, and three radiation-based models) under hyper-arid environmental conditions at the operational field level. These models were evaluated and calibrated using the weekly water balance of alfalfa by EnviroSCAN to calculate crop evapotranspiration (ET_c). Calibration models were evaluated and validated using wheat and potatoes, respectively, on the basis of weekly water balance. Based on the results and discussion, the FAO-56 Penman-Monteith model proved to be superior in estimating ET_c with a slight underestimation of 2 %. Meanwhile, the Hargreaves-Samani (HS) model (temperature-based) underestimated ET_c by 20 % and the Priestley-Taylor (PT) and Makkink (MK) models (radiation-based) had similar performances underestimating by up to 35 % of the measured ET_c. The Turc (TR) model had the lowest performance compared with other models, demonstrating values underestimated by up to 60 % of the measured ET_c. Local calibration based on alfalfa evapotranspiration measurements was used to rectify these underestimations. The surprisingly good performance of the calibrated simple HS model, with a new coefficient 0.0029, demonstrated its favorable potential to improve irrigation scheduling. The MK and PT models were in third and fourth rank, respectively, reflecting minor differences between one another. The new coefficients obtained for the MK and PT models were 1.99 and 0.963, respectively. One important observation was that the calibrated TR model performed poorly, with an increase in its coefficient from 0.013 to 0.034 to account for hyper-arid environmental conditions; moreover, it required additional seasonal calibration to adequately improve its performance.     

Integrated Water Resources Management and the Hydrosocial Balance

Abstract

During the last seven years, the author has developed a new analytic framework for the understanding of out-stream flows in any catchment or region. This is termed the area's “hydrosocial balance” because the flows from which it is constructed are hydrosocial rather than hydrological. Until now this meta-theory has been limited to flow quantities. The present paper extends the scope of the hydrosocial balance to issues of water qualities. The conjoint framework is then applied to a case-study of an island in the English Channel—Jersey—well known for its agricultural outputs, its financial services sector, and its tourist industry. The paper shows how general lessons for integrated water resources management can be drawn from the Jersey fieldwork: a world in a grain of sand.     

Optimization of Nebhana Reservoir Water Allocation by Stochastic Dynamic Programming

This study is devoted to the identification of an optimal rule that would permit to improve the water resources management of dam in arid condition. The Nebhana dam is considered in this study as a representative of a set dams situated in such condition. The water storage is used for irrigation purpose. The identification of an optimal rule is based on two opposite objectives: the satisfaction of the irrigation water demand and the safeguard of a minimal water storage in the dam. By considering different weights for these objectives, the stochastic dynamic programming technique was lead to various optimal rules for the water resources management of the Nebhana dam. This technique takes into account the variability of the volume of water inflow to the dam on the basis of their occurrence probability; the water losses by means of forecasting models and the water resources goals using weight coefficients. The identified optimal rule would permit to estimate the necessary water release volume for irrigation by considering the water storage and the decision period.     

IB-ICCMSP: An Integrated Irrigation Water Optimal Allocation and Planning Model Based on Inventory Theory under Uncertainty

In this study, an inventory-theory-based inexact chance-constrained multi-stage stochastic programming (IB-ICCMSP) model under multi-uncertainties is developed. IB-ICCMSP integrates inventory theory into an inexact chance-constrained multi-stage stochastic optimization framework. This method can not only effectively address system multiple uncertainties (e.g. discrete intervals and probability density functions) and dynamic features, but also provide water transferring and allocating schemes among multiple stages. The developed model is applied to irrigation water allocation optimization system in Zhangye City, Gansu province, China. Based on the runoff simulation prediction of Yingluo Gorge and water supply–demand balance analysis of the 12 irrigation areas in Zhangye City, different optimal irrigation water measures are generated under different flow levels and different probabilities in the planning year. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identifying desired water-allocation plans for irrigation under multi-uncertainties.     

A Compromise Programming Model to Integrated Urban Water Management

Integrated urban water management is an important and critical matter in every city and country. Many objectives and criteria such as satisfaction of the urban water consumers, the national benefits and social hazards must be considered in the integrated urban water management. So the integrated urban water management can be considered as a multi-objective problem. In this paper, a mathematical model which uses the compromise programming model is presented to optimize this multi-objective problem. Three famous objectives involving water distribution cost, leakage water and social satisfaction level are considered. To evaluate the performance and efficiency of the proposed model, Hamedan potable water network is chosen as a case study. Results show that the proposed model is capable to present effective solutions for the considered problem. So the proposed mathematical model can be used as an efficient tool for the integrated urban water management in every urban area.     

区域水土资源联合优化配置理论框架体系探讨

以区域水土资源联合优化配置的多学科综合与新技术的应用成果相结合,探讨了区域水土资源联合优化配置的内涵及其体系的主要构成要素。将涉及水土资源联合优化配置的所有要素与社会、经济、环境系统耦合成一个复杂的水–土–社会经济–生态系统的模拟系统,研究在社会、经济和自然等因素的共同作用下区域水资源与土地资源配置的相互作用趋势。基于多级递阶结构的分解协调方法,讨论了水土资源联合配置的递阶结构及求解思路,提出了基于"压力–状态–响应"概念框架的区域水土资源联合优化配置的系统动力学仿真模型体系的设计方法,建立了区域水土资源联合优化配置系统的理论框架体系。     

Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games

In recent years, uneven distribution of available water resources as well as increasing water demands and overexploiting the water resources have brought severe need for transferring water from basins having sufficient water to basins facing water shortages. Therefore, optimal allocation of shared water resources in water transfer projects, considering the utilities of different stakeholders, physical limitations of the system and socioeconomic criteria is an important task. In this paper, a new methodology based on crisp and fuzzy Shapley games is developed for optimal allocation of inter-basin water resources. In the proposed methodology, initial water allocations are obtained using an optimization model considering an equity criterion. In the second step, the stakeholders form crisp coalitions to increase the total net benefit of the system as well as their own benefits and a crisp Shapley Value game is used to reallocate the benefits produced in the crisp coalitions. Lastly, to provide maximum total net benefit, fuzzy coalitions are constituted and the participation rates of water users to fuzzy coalitions are optimized. Then, the total net benefit is reallocated to water users in a rational and equitable way using Fuzzy Shapley Value game. The effectiveness of this method is examined by applying it to a large scale case study of water transfer from the Karoon river basin in southern Iran to the Rafsanjan plain in central Iran.     

A Nonlinear Interval Model for Water and Waste Load Allocation in River Basins

In this paper, a new methodology is proposed for simultaneous allocation of water and waste load in river basins. A nonlinear interval number optimization model is used to incorporate the uncertainties of model inputs and parameters. In this methodology, the bounds of the uncertain inputs are only required, not necessarily knowing their probability density or fuzzy membership functions. In the proposed model, the existing uncertainties in water demands and monthly available water are considered in the optimization model. Also the economic and environmental impacts of water allocation to the agricultural water users are taken into account. To have an equitable water and waste load allocation, benefits are reallocated to water users using some solution concepts of the cooperative game theory. Results of applying the methodology to the Dez river system in south-western part of Iran show its effectiveness and applicability for water and waste load allocation in an uncertain environment.     

基于多目标规划的杨凌示范区水资源优化配置

介绍了水资源优化配置理论,在分析杨凌示范区供用水现状基础上,全面考虑该区社会、经济与环境协调发展的实际情况,建立以经济、社会、环境综合效益最大为目标的多目标优化模型;采用目标逼近法,并结合大系统总体优化对所建立的模型进行求解,得到了杨凌示范区不同规划水平年(2010、2020)、不同设计保证率(50%、75%)条件下的水资源优化配置结果;通过对该优化配置结果的分析与讨论,提出了相应的保障措施及对策.     

Optimization of Irrigation Scheduling Using Soil Water Balance and Genetic Algorithms

In arid and semi-arid countries, the use of irrigation is essential to ensure agricultural production. Irrigation water use is expected to increase in the near future due to several factors such as the growing demand of food and biofuel under a probable climate change scenario. For this reason, the improvement of irrigation water use efficiency has been one of the main drivers of the upgrading process of irrigation systems in countries like Spain, where irrigation water use is around 70 % of its total water use. Pressurized networks have replaced the obsolete open-channel distribution systems and on farm irrigation systems have been also upgraded incorporating more efficient water emitters like drippers or sprinklers. Although pressurized networks have significant energy requirements, increasing operational costs. In these circumstances farmers may be unable to afford such expense if their production is devoted to low-value crops. Thus, in this work, a new approach of sustainable management of pressurized irrigation networks has been developed using multiobjective genetic algorithms. The model establishes the optimal sectoring operation during the irrigation season that maximize farmer’s profit and minimize energy cost at the pumping station whilst satisfying water demand of crops at hydrant level taking into account the soil water balance at farm scale. This methodology has been applied to a real irrigation network in Southern Spain. The results show that it is possible to reduce energy cost and improve water use efficiency simultaneously by a comprehensive irrigation management leading, in the studied case, to energy cost savings close to 15 % without significant reduction of crop yield.     

Estimation of the Interaction Between Groundwater and Surface Water Based on Flow Routing Using an Improved Nonlinear Muskingum-Cunge Method

Water Resources Management - The interaction between groundwater (GW) and surface water (SW) not only sustains runoff in dry seasons but also plays an important role in river floods. Lateral inflow...     

对长江和黄淮海水资源统一配置的认识

黄淮海平原的发展受到水资源短缺的制约,在南水北调工程逐步实施后,可以与长江流域水资源通盘考虑.要进行统一的水资源配置规划,要充分考虑发展华北农业、农业用水和节水、长江河口水量分配、平原蓄水等因素.     

A Stochastic Non-linear Programming Model for a Multi-period Water Resource Allocation with Multiple Objectives

A rapid increase in demand and severe droughts in recent years has increased the pressure on water supplies throughout most parts of Australia. This has resulted in the need for tools to allocate limited water across users in different regions, and explore scenarios so as to achieve economic, social and environmental benefits. A major challenge in water resource allocation is dealing with the uncertainty in the system, particularly with respect to reservoir inflow. Stochastic non-linear programming is applied to water resource allocation to accommodate this uncertainty across the time periods of the planning horizon. A large range of solutions is produced representing the distributions of uncertainty in reservoir inflow. These solutions are used in a Monte Carlo simulation to estimate the trade-off in amounts of water allocated versus risk of not achieving minimal reservoir levels. The methodology is applied to a case study in South East Queensland in Australia, a region which is currently facing a severe water shortage over the next 3 years. A new water supply initiative that the Queensland State Government is considering to overcome the water crisis is assessed using the methodology.     

Exploring Future Water Shortage for Large River Basins under Different Water Allocation Strategies

Climate change and socio-economic development increase variations in water availability and water use in the Pearl River Basin (PRB), China. This can potentially result in conflicts over water resources between water users, and cause water shortage in the dry season. To assess and manage water shortage in the PRB, we first explored two water availability and three water use scenarios. Next, four different strategies to allocate water were defined. These water allocation strategies prioritized upstream water use, Pearl River Delta water use, irrigation water use, and manufacturing water use, respectively. The impact of the four strategies on water use and related economic output was assessed under different water availability and water use scenarios. Results show that almost all the regions in the PRB are likely to face water shortage under the four strategies. The increasing water demand contributes twice as much as the decreasing water availability to water shortage. All four water allocation strategies are insufficient to solve the water scarcity in the PRB. The economic losses differ greatly under the four water allocation strategies. Prioritizing the delta region or manufacturing production would result in lower economic losses than the other two strategies. However, all of them are rather extreme strategies. Development of water resources management strategies requires a compromise between different water users.     

Leakage Detection Using Smart Water System: Combination of Water Balance and Automated Minimum Night Flow

This paper presents a methodology for the application of the Smart Water technology to detect water leakage. This methodology consists in the use of the traditional water balance method together with the minimum night flow approach. This procedure has been applied to a large-scale pilot project conducted at the Scientific Campus of the University of Lille, which is the size of a small town. The water network of the campus is monitored by a set of sensors that record and transmit, in real-time, the hydraulic parameters of the water system. Analysis of real-time data has allowed the verification of water balance and the estimation of water losses level in the network. The paper presents an improvement of the application of the minimum night flow method, which is based on the determination of flow thresholds. A leak alarm is generated if the night flow exceeds the thresholds. This data analysis methodology provides the capability to detect the pipe bursts quickly, thereby reducing the runtime of leakage. The application of the improved method allowed the detection of 25 unreported leaks and decreased the Non-Revenue Water (NRW) level by 36%.     

Agricultural Multi-Water Source Allocation Model Based on Interval Two-Stage Stochastic Robust Programming under Uncertainty

Numerous uncertainties and complexities exist in the agricultural irrigation water allocation system, that must be considered in the optimization of water resources allocation. In this paper, an agricultural multi-water source allocation model, consisting of stochastic robust programming and two-stage random programming and introducing interval numbers and random variables to represent the uncertainties, was proposed for the optimization of irrigation water allocation in Jiamusi City of Heilongjiang Province, China. The model could optimize the water allocaton to different crops of groundwater and surface water. Then, the optimal target value and the optimal water allocation of different water sources distributed to different crops could be obtained. The model optimized the economic benefits and stability of the agricultural irrigation water allocation system via the introduction of a the penalty cost variable measurement to the objective function. The results revealed that the total water shortage changed from [18.6, 32.3]?×?10⁸ m³ to [15.7, 26.2]?×?10⁸ m³ at a risk level ω from zero to five, indicating that the water shortage decreased and the reliability improved in the agricultural irrigation water allocation system. Additionally, the net economic benefits of irrigation changed from [287.21, 357.86]?×?10⁸ yuan to [253.23, 301.32]?×?10⁸ yuan, indicating that the economic benefit difference was reduced. Therefore, the model can be used by decision makers to develop appropriate water distribution schemes based on the rational consideration of the economic benefit, stability and risk of the agricultural irrigation water allocation system.