River water quality management considering agricultural return flows: application of a nonlinear two-stage stochastic fuzzy programming

Abstract

In this paper, a new fuzzy methodology is developed to optimize water and waste load allocation (WWLA) in rivers under uncertainty. An interactive two-stage stochastic fuzzy programming (ITSFP) method is utilized to handle parameter uncertainties, which are expressed as fuzzy boundary intervals. An iterative linear programming (ILP) is also used for solving the nonlinear optimization model. To accurately consider the impacts of the water and waste load allocation strategies on the river water quality, a calibrated QUAL2Kw model is linked with the WWLA optimization model. The soil, water, atmosphere, and plant (SWAP) simulation model is utilized to determine the quantity and quality of each agricultural return flow. To control pollution loads of agricultural networks, it is assumed that a part of each agricultural return flow can be diverted to an evaporation pond and also another part of it can be stored in a detention pond. In detention ponds, contaminated water is exposed to solar radiation for disinfecting pathogens. Results of applying the proposed methodology to the Dez River system in the southwestern region of Iran illustrate its effectiveness and applicability for water and waste load allocation in rivers. In the planning phase, this methodology can be used for estimating the capacities of return flow diversion system and evaporation and detention ponds.

Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty

“…where the solution is constrained by and must adhere to quality targets [17,42,91]). The mathematical programming techniques applied in this research include linear programming [80,103,178,197], nonlinear programming [17,91,121,150,155,206], dynamic programming [138,174,241], stochastic programming [33,42,70,99,128,139,141,187,207,208,224,225,240], and quadratic programming [86,113].…”

“…Marinoni et al [140] propose a framework for planning major investment decisions and apply this to the case of a water quality enhancement program in a river catchment in Brisbane, Australia. Compromise programming is first used to score the options [42,87,118,121,126,132,139,150,174,176,208,213,224] Storm water [17] Wastewater [1,33,65,80,86,98,106,113,129,139,141,169,187,197,206,219,238] Water allocation [172,230,233] Water trading [224] Water treatment [33,206] Wetlands [39,207,225] for pollution reduction at various sites and the optimal investment problem is then formulated as a multicriteria knapsack problem. In some cases, legislation needs to be considered alongside other management strategies.…”

A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty

“…For example, Liu et al [16] improved a two-stage fuzzy robust programming model for water pollution control to address fuzzy parameters, which were represented by possibility distributions on the left-and right-hand sides of the constraints. Tavakoli et al [17] developed an interactive two-stage stochastic fuzzy programming method to handle uncertainties expressed as fuzzy boundary intervals (i.e., the lowerand upper-bounds of intervals are presented as possibility distributions). Ji et al [18] enhanced an inexact left-hand-side chance-constrained fuzzy multi-objective programming approach to cope with fuzziness in the constraints and objectives.…”

A Semi-Infinite Interval-Stochastic Risk Management Model for River Water Pollution Control under Uncertainty

“…It was applicable to problems characterized by uncertainty in unobservable parameters; meanwhile, some problems were resolved upon observation of the outcome of the first-stage decision. Tavakoli [24] proposed a nonlinear two-stage stochastic fuzzy programming to tackle uncertainties described as fuzzy boundary intervals and probability distributions in decision making of optimal water allocation and pollutant load policies. Hu et al [25] proposed a Bayesian-based two-stage inexact optimization method for supporting water pollution control under uncertainty; optimal production patterns of economic activities under different pollutant discharge allowance scenarios were generated.…”