Cooperative Water Resources Allocation among Competing Users

Abstract

A comprehensive model named the Cooperative Water Allocation Model (CWAM) is developed for modeling equitable and efficient water allocation among competing users at the basin scale, based on a multiperiod node-link river basin network. The model integrates water rights allocation, efficient water allocation and equitable income distribution subject to hydrologic constraints comprising both water quantity and quality considerations. CWAM allocates water resources in two steps: initial water rights are firstly allocated to water uses based on legal rights systems or agreements, and then water is reallocated to achieve efficient use of water through water transfers. The associated net benefits of stakeholders participating in a coalition are allocated by using cooperative game theoretical approaches. <br /><br /> The first phase of the CWAM methodology includes three methods for deriving initial water rights allocation among competing water uses, namely the priority-based multiperiod maximal network flow (PMMNF) programming, modified riparian water rights allocation (MRWRA) and lexicographic minimax water shortage ratios (LMWSR) methods. PMMNF is a very flexible approach and is applicable under prior, riparian and public water rights systems with priorities determined by different criteria. MRWRA is essentially a special form of PMMNF adapted for allocation under the riparian regime. LMWSR is designed for application under a public water rights system, which adopts the lexicographic minimax fairness concept. The second step comprises three sub-models: the irrigation water planning model (IWPM) is a model for deriving benefit functions of irrigation water; the hydrologic-economic river basin model (HERBM) is the core component of the coalition analysis, which searches for the values of various coalitions of stakeholders and corresponding optimal water allocation schemes, based on initial water rights, monthly net benefit functions of demand sites and the ownership of water uses; the sub-model cooperative reallocation game (CRG) of the net benefit of the grand coalition adopts cooperative game solution concepts, including the nucleolus, weak nucleolus, proportional nucleolus, normalized nucleolus and Shapley value, to perform equitable reallocation of the net benefits of stakeholders participating in the grand coalition. The economically efficient use of water under the grand coalition is achieved through water transfers based on initial water rights. <br /><br /> Sequential and iterative solution algorithms utilizing the primal simplex method are developed to solve the linear PMMNF and LMWSR problems, respectively, which only include linear water quantity constraints. Algorithms for nonlinear PMMNF and LMWSR problems adopt a two-stage approach, which allow nonlinear reservoir area- and elevation-storage relations, and may include nonlinear water quality constraints. In the first stage, the corresponding linear problems, excluding nonlinear constraints, are solved by a sequential or iterative algorithm. The global optimal solution obtained by the linear programming is then combined together with estimated initial values of pollutant concentrations to be used as the starting point for the sequential or iterative nonlinear programs of the nonlinear PMMNF or LMWSR problem. As HERBM adopts constant price-elasticity water demand functions to derive the net benefit functions of municipal and industrial demand sites and hydropower stations, and quadratic gross benefit functions to find the net benefit functions of agriculture water uses, stream flow demands and reservoir storages, it is a large scale nonlinear optimization problem even when the water quality constraints are not included. An efficient algorithm is built for coalition analysis, utilizing a combination of the multistart global optimization technique and gradient-based nonlinear programming method to solve a HERBM for each possible coalition. <br /><br /> Throughout the study, both the feasibility and the effectiveness of incorporating equity concepts into conventional economic optimal water resources management modeling are addressed. The applications of CWAM to the Amu Darya River Basin in Central Asia and the South Saskatchewan River Basin in western Canada demonstrate the applicability of the model. It is argued that CWAM can be utilized as a tool for promoting the understanding and cooperation of water users to achieve maximum welfare in a river basin and minimize the damage caused by water shortages, through water rights allocation, and water and net benefit transfers among water users under the regulated water market or administrative allocation mechanism.