Approaches to Evaluate Water Quality Model Parameter Uncertainty for Adaptive TMDL Implementation1

Abstract:  The National Research Council recommended Adaptive Total Maximum Daily Load implementation with the recognition that the predictive uncertainty of water quality models can be high. Quantifying predictive uncertainty provides important information for model selection and decision-making. We review five methods that have been used with water quality models to evaluate model parameter and predictive uncertainty. These methods (1) Regionalized Sensitivity Analysis, (2) Generalized Likelihood Uncertainty Estimation, (3) Bayesian Monte Carlo, (4) Importance Sampling, and (5) Markov Chain Monte Carlo (MCMC) are based on similar concepts; their development over time was facilitated by the increasing availability of fast, cheap computers. Using a Streeter-Phelps model as an example we show that, applied consistently, these methods give compatible results. Thus, all of these methods can, in principle, provide useful sets of parameter values that can be used to evaluate model predictive uncertainty, though, in practice, some are quickly limited by the “curse of dimensionality” or may have difficulty evaluating irregularly shaped parameter spaces. Adaptive implementation invites model updating, as new data become available reflecting water-body responses to pollutant load reductions, and a Bayesian approach using MCMC is particularly handy for that task.