A recourse-based nonlinear programming model for stream water quality management

Abstract

A recourse-based nonlinear programming (RBNP) method is developed for stream water quality management under uncertainty. It can not only reflect uncertainties expressed as interval values and probability distributions but also address nonlinearity in the objective function. A 0-1 piecewise linearization approach and an interactive algorithm are advanced for solving the RBNP model. The RBNP is applied to a case of planning stream water quality management. The RBNP modeling system can provide an effective linkage between environmental regulations and economic implications expressed as penalties or opportunity losses caused by improper policies. The solutions can be used for generating a variety of alternatives under different combinations of pre-regulated targets, which are also associated with different water-quality-violation risk levels and varied potential economic penalty or loss values.

Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty

“…However, for a particular water source, water quality typically involves the measurement of components, such as total phosphorus and total nitrogen [129], biological oxygen demand [33,42,129], chemical oxygen demand [132,139,141], dissolved oxygen [139] and Escherichia coli [33]. The impacts of pollution on water sources have been modelled by tools, such as the Streeter-Phelps equation [121] and the Soil and Water Assessment Tool (SWAT) [63]. For example, the SWAT has been used to obtain protocols for water quality [235], and to explore the impacts of nitrogen runoff, fertiliser application rates and crop yields [241].…”

“…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].…”

“…The highly interconnected and interdependent nature of hydrological systems, the desire to balance social, economic and environmental factors and the inherent uncertainty associated with such systems, often lead to complex models [121,213]. The implementation of long-term models, particularly those which are nonlinear and include uncertainty can be limited by the computational burden associated with solving such models [150].…”

Mathematical Modeling for Water Quality Management under Interval and Fuzzy Uncertainties

“…The objective is to maximize the net system benefit subject to the environmental requirements under uncertainty over the planning horizon. Policies in terms of the related human activities (i.e., industrial, municipal, and agricultural activities) and the pollutant discharges (from fifteen point and four nonpoint sources) are critical for ensuring a maximum system benefit and a safe water quality [24]. Based on field investigations and related literatures, biological oxygen demand (BOD), total nitrogen (TN), and total phosphorus (TP) are selected as water quality indicators [1,25].…”

A Physically Based Runoff Model Analysis of the Querétaro River Basin

“…In Mendoza et al [6], the implications for land-use and land cover changes are soil erosion and degradation that disturbs the ecosystem capability to provide the natural benefits such as superficial and underground water retention; 2 Journal of Applied Mathematics nevertheless it is considered a distributed model that considers the runoff as a function of biophysical characteristics and not based on the physical basin variables. With the product of this research, as mentioned in Li and Huang, 2012 [7], a linkage can be applied among environmental regulations and economic implications with the use of informatics tools; finally through numerical modeling and applied research an environmental linkage can be carried out that involves the law and the economic implications [7].…”