A Methodology for Robust Total Maximum Daily Load Allocations

The determination of how pollutant loads should be distributed among different pollutant sources in the watershed, which is known as pollutant load allocation, 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 the watershed simulation model predicts that water quality standards will be met given a Margin of Safety. Unfortunately, because there may be many feasible combinations of load reductions and/or significant uncertainties, it is difficult and time-consuming to compare different 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 is used to explicitly address the uncertainty of a watershed simulation model, Hydrological Simulation Program — Fortran. 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 on 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 USEPA. The results show that the optimized load reduction scenario requires 30% less load reductions than the scenario approved by the USEPA at the same reliability level.