Parameter estimation and uncertainty analysis for a watershed model

Abstract

Where numerical models are employed as an aid to environmental management, the uncertainty associated with predictions made by such models must be assessed. A number of different methods are available to make such an assessment. This paper explores the use of three such methods, and compares their performance when used in conjunction with a lumped parameter model for surface water flow (HSPF) in a large watershed. Linear (or first-order) uncertainty analysis has the advantage that it can be implemented with virtually no computational burden. While the results of such an analysis can be extremely useful for assessing parameter uncertainty in a relative sense, and ascertaining the degree of correlation between model parameters, its use in analyzing predictive uncertainty is often limited. Markov Chain Monte Carlo (MCMC) methods are far more robust, and can produce reliable estimates of parameter and predictive uncertainty. As well as this, they can provide the modeler with valuable qualitative information on the shape of parameter and predictive probability distributions; these shapes can be quite complex, especially where local objective function optima lie within those parts of parameter space that are considered probable after calibration has been undertaken. Nonlinear calibration-constrained optimization can also provide good estimates of parameter and predictive uncertainty, even in situations where the objective function surface is complex. Furthermore, they can achieve these estimates using far fewer model runs than MCMC methods. However, they do not provide the same amount of qualitative information on the probability structure of parameter space as do MCMC methods, a situation that can be partially rectified by combining their use with an efficient gradient-based search method that is specifically designed to locate different local optima. All methods of parameter and predictive uncertainty analysis discussed herein are implemented using freely-available software. Hence similar studies, or extensions of the present study, can be easily undertaken in other modeling contexts by other modelers.