Uncertainty of Predicted In-stream Fecal Coliform Concentration for TMDL Development using HSPF: Markov Chain Monte Carlo Approach

Abstract

Developing TMDLs can be an intensive, expensive undertaking with potentially far reaching consequences. Quantification of uncertainty in water quality model output can allow decision makers and stakeholders to assess the probability of achieving water quality standards and meeting a TMDL. Hydrological Simulation Program – FORTRAN (HSPF) is commonly used for developing TMDLs for waterbodies impaired with fecal coliform (FC). HSPF, however, is often used without any quantification of uncertainty in predicted in-stream FC concentration. This study quantifies the uncertainty associated with predicted in-stream FC concentrations simulated using HSPF for a watershed model. To estimate the uncertainty, MCMC was used as a Bayesian technique to estimate probability distributions of input parameters using prior knowledge and observed data. Posterior input parameter distributions were used to estimate predictive uncertainty in simulated FC concentration for two alternative pollutant load allocation scenarios developed for the bacteria impairment TMDL for Mossy Creek in Virginia. The percentage of violations of instantaneous FC water quality criterion resulting from the daily average time series for both the allocation scenarios were very similar and were approximately 1%. The percentage of criterion violation incidences for the 80 and 95% probability intervals for the two allocation scenarios were also similar, although the allocation scenario that permitted greater FC loading by cattle via direct deposit in the streams yielded greater uncertainty than the scenario that restricted cattle via direct deposit. The type of uncertainty estimation information presented here and the implicit information related to the uncertainty of meeting a water quality criterion can be used by decision makers and stakeholders to select among alternative TMDL allocation scenarios, to set realistic targets for water quality achievements, and to prioritize implementation efforts