ANALYSIS OF PARAMETER UNCERTAINTY INCONCEPTUAL CATCHMENT MODELS USING MONTE CARLO TECHNIQUES

Abstract

Two methods for assessing the uncertainty of parameters in complicated hydrologic models are discussed, both of which make use of the Monte Carlo method. To begin, the GLUE framework developed by Beven and Binley employs a technique called significance sampling, which is meant to mitigate bias when approximating unknown values. The Metropolis approach uses a random walk rather than significance sampling to account for parameter uncertainty, which has a non-normal probability distribution. Three examples are provided to illustrate the use of these Monte Carlo techniques. In the first, we take into account a straightforward water balance model for which we already know the solutions. The Metropolis sampling approach has been shown to be more effective than the importance sampling strategy. If insufficiently random samples are collected, results from significance sampling might be quite misleading. In the second and third examples, we use a more catchment model to show what insights can be obtained using the Metropolis approach. Specifically, they explain how to evaluate correlations for split-sample tests, how to
use prior data, and how to measure reliability for hydrological responses not involved in the calibration process. The Metropolis method outperforms more traditional assumptions as a first-order method of
estimation when dealing with uncertainties in water samples.