A Bayesian approach for evaluation of the effect of water quality model parameter uncertainty on TMDLs: A case study of Miyun Reservoir

Facing increasingly serious water pollution, the Chinese government is changing the environmental management strategy from solely pollutant concentration control to a Total Maximum Daily Load (TMDL) program, and water quality models are increasingly being applied to determine the allowable pollutant load in the TMDL. Despite the frequent use of models, few studies have focused on how parameter uncertainty in water quality models affect the allowable pollutant loads in the TMDL program, particularly for complicated and high-dimension water quality models. Uncertainty analysis for such models is limited by time-consuming simulation and high-dimensionality and nonlinearity in parameter spaces. In this study, an allowable pollutant load calculation platform was established using the Environmental Fluid Dynamics Code (EFDC), which is a widely applied hydrodynamic-water quality model. A Bayesian approach, i.e. the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm, which is a high-efficiency, multi-chain Markov Chain Monte Carlo (MCMC) method, was applied to assess the effects of parameter uncertainty on the water quality model simulations and its influence on the allowable pollutant load calculation in the TMDL program. Miyun Reservoir, which is the most important surface drinking water source for Beijing, suffers from eutrophication and was selected as a case study. The relations between pollutant loads and water quality indicators are obtained through a graphical method in the simulation platform. Ranges of allowable pollutant loads were obtained according to the results of parameter uncertainty analysis, i.e. Total Organic Carbon (TOC): 581.5-1030.6 t·yr^-1; Total Phosphorus (TP): 23.3-31.0 t·yr^-1; and Total Nitrogen (TN): 480-1918.0 t·yr^-1. The wide ranges of allowable pollutant loads reveal the importance of parameter uncertainty analysis in a TMDL program for allowable pollutant load calculation and margin of safety (MOS) determination. The sources of uncertainty are discussed and ways to reduce the uncertainties are proposed.