Predictive Uncertainty in Water-Quality Modeling

A general and integrated approach to parameter identification, model calibration, and estimation of predictive uncertainty in water-quality models is proposed and validated. The proposed approach determines the maximal conditional likelihood functions of each of the model parameters using a transformation that forces the model errors to be normally distributed, with predictive uncertainty characterized by random normally distributed and homoscedastic model errors in the transform space. The proposed approach is demonstrated using a watershed-scale model to predict the fecal coliform levels in a third-order stream within the Little River Experimental Watershed in Georgia. Maximal conditional likelihood functions were identified for all parameters in the log, square root, and no-transformation cases. The key results are: (1) the number of sensitive parameters and the optimal parameter values can depend on the transformation; (2) only in the case of the log-transformation are the errors normally distributed and consistent with the assumed Gaussian likelihood function; (3) the standard error in the model is least for the no-transform case and highest for the log-transform case; and (4) the observed model errors are most predictable using the log-transform and least predictable using the no-transform approach.