A Stochastic Method to Characterize Model Uncertainty for a Nutrient TMDL

Abstract

The U.S. EPA's Total Maximum Daily Load (TMDL) program has encountered hindrances in its implementation partly because of its strong dependence on mathematical models to set limitations on the release of impairing substances. The uncertainty associated with predictions of such models is often not scientifically quantified and typically assigned as an arbitrary margin of safety (MOS) in the TMDL allocation. The Soil Water Assessment Tool (SWAT) model was evaluated to determine its applicability to identify the impairment status and tabulate a nutrient TMDL for a waterbody located in the Piedmont physiographic region of Maryland. The methodology for tabulating the nutrient TMDL is an enhancement over current methods used in Maryland. The mean-value first-order reliability method (MFORM) was paired with a stochastic approach to tabulate a science-based estimate of model uncertainty and MOS for the TMDL approach. Monthly streamflow estimates were quite good, with Nash-Sutcliffe efficiency (NSE) coefficients of 0.75 and 0.70 for the calibration and validation phases, respectively. Sediment and nutrients were not estimated as well as streamflow on a monthly basis; however, large improvements in model estimation were observed on an annual time scale. MOS was determined based on the desired level of confidence in meeting the water quality standard. The water quality standard was met at 20% nitrate reduction (9.9 kg N d-1) with a 37.5% level of confidence. The water quality goal was met by a 30% reduction in nitrate load (8.6 kg N d-1), in which case there was a 75% chance of meeting the water quality standard. Therefore, the MOS load (the difference between the standard and the goal) was 1.3 kg N d-1 or 10% of the baseline load. These results indicate that SWAT is a suitable model for use in TMDL assessments of impaired water bodies, especially assessments based on long-term simulations. In addition, the stochastic method used to quantify MOS for a nitrate TMDL is an improvement over current methods because it provides a formal, scientifically derived measure of model uncertainty.