Robust optimization for total maximum daily load allocations

Abstract

[1] The determination of the pollutant load distribution among different pollutant sources in a watershed is a critical step in total maximum daily load (TMDL) development. Under current TMDL practices, TMDL allocations are typically determined through a trial-and-error approach of reducing pollutant loadings until a watershed simulation model predicts that water quality standards will be met given a margin of safety. Unfortunately, many feasible combinations of load reductions and significant uncertainties may exist. Therefore it is difficult and time-consuming to compare various allocation scenarios using a trial-and-error approach. A robust optimization model is developed in this study to incorporate the uncertainty of water quality predictions and to minimize pollutant load reductions given various levels of reliability with respect to the water quality standards. The generalized likelihood uncertainty estimation approach is used to explicitly address the uncertainty of a watershed simulation model, the Hydrological Simulation ProgramFortran. The uncertainty is integrated into TMDL allocations using a robust genetic algorithm model linked with a response matrix approach. The developed robust optimization model is demonstrated using a case study based on the Moore's Creek fecal coliform TMDL study. The trade-offs between reliability levels and total load reductions of allocation scenarios are evaluated, and the optimized load reduction scenarios are compared with the scenario generated by a trial-and-error approach and approved by the U.S. Environmental Protection Agency. The results show that the optimized load reduction scenario requires 30% less load reductions than the scenario approved by the U.S. Environmental Protection Agency at the same reliability level.

Quantifying soil hydraulic properties and their uncertainties by modified GLUE method

“…So, in order to reach a balance between the sample size and computational efficiency, in the following study of sensitivity of GLUE simulations we adopt the sample size equal to 15 000 for a (loamy sand) and 25 000 for b (sandy loam) and c (sandy clay loam). The number of sample simulations for van Genuchten-Mualem model in our research is quite a low as compared to McMichael et al (2006), Li et al (2010) and Jia and Culver (2012). They all use Monte Carlo assessment or GLUE for much more complicated models, such as conceptual catchment models and watershed models.…”

An Indirect Simulation-Optimization Model for Determining Optimal TMDL Allocation under Uncertainty

“…Based on the experience of TMDL in the United States [1], the objective function Z ± is usually defined as an acceptable measure of economic efficiency, reliability and equity. When detailed cost information is not available, minimizing load reduction could be used as an alternative to maximize the economic efficiency, since we would at least expect increased system costs for a given pollution source following increased load reduction [2]. The objective function used in this study was eventually used to determine the required minimum total load reductions; the system constraints in Equation (1) were to bring a watershed system in compliance with water-quality criteria…”

“…TMDL refers to the maximum loading rates of a pollutant that a water body receives to ensure compliance with water-quality standards and allocates pollutant loadings among point and nonpoint sources at different risk levels [1,2]. In most TMDL allocation analyses, load reduction scenarios are generated through trial-and-error (TAE) simulation [2], which involves repeatedly running process-oriented simulation models to derive the pollutant loadings to meet water-quality standards and allocation criteria in the water body [3,4]. However, the TAE simulation method does not necessarily generate the most cost-effective and reliable load allocations [5].…”

Siting and sizing the components of a regional wastewater system: a multiobjective approach

“…A new global search algorithm developed recently, the Probabilistic Global Search Lausanne, was used to solve the model. Jia and Culver [9] applied a robust genetic algorithm to total maximum daily load allocations.…”