A Dual Monte Carlo Approach to Estimate Model Uncertainty and its Application to the Rangeland Hydrology and Erosion Model

Abstract

Natural resources models serve as important tools to support decision making by predicting environmental indicators. All model predictions have uncertainty associated with them. Model predictive uncertainty, often expressed as the confidence interval around a model prediction value, may serve as important supplementary information for assisting decision making processes. In this article, we describe a new method called Dual Monte Carlo (DMC) to calculate model predictive uncertainty based on input parameter uncertainty. DMC uses two Monte Carlo sampling loops, which enable model users to not only calculate the model predictive uncertainty for selected input parameter sets of particular interest, but also to examine the predictive uncertainty as a function of model inputs across the full range of parameter space. We illustrate the application of DMC to the process-based, rainfall event-driven Rangeland Hydrology and Erosion Model (RHEM). The results demonstrate that DMC effectively generated model predictive uncertainty from input parameter uncertainty and provided information that could be useful for decision making. We found that for the model RHEM, the uncertainty intervals were strongly correlated to specific model input and output parameter values, yielding regression relationships (r2 > 0.97) that enable accurate estimation of the uncertainty interval for any point in the input parameter space without the need to run the Monte Carlo simulations each time the model is used. Soil loss predictions and their associated uncertainty intervals for three example storms and three site conditions are used to illustrate how DMC can be a useful tool for directing decision making.