A Dual-Monte-Carlo Approach to Estimate Model Uncertainty and its Application to the Rangeland Hydrology and Erosion Model 1914

Authors: WEI, H. - UNIVERSITY OF ARIZONA; Nearing, Mark; Stone, Jeffry; BRESHEARS, D. - UNIVERSITY OF ARIZONA

Submitted to: Transactions of the ASABE
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/1/2008
Publication Date: 3/8/2008
Citation: Wei, H., Nearing, M.A., Stone, J.J., Breshears, D.P. 2008. A dual-monte-carlo approach to estimate model uncertainty and its application to the rangeland hydrology and erosion model. Trans. Am. Soc. Agric. Bio. Eng. 51(2): 515-520.

Interpretive Summary: Natural resource models are developed to quantitatively predict important environmental indicators based on model user input for assessing environmental issues and directing decision making. However, all model predictions involve a certain level of uncertainty, which is called model predictive uncertainty, because we generally ignore the uncertainty associated with input parameters due to spatial heterogeneity and measurement errors. Model predictive uncertainty describes the confidence of a model prediction, often expressed as the confidence interval around a model prediction. The ability for numerical models to assist natural resources management would be improved if they included estimated of model uncertainty because model users would be able to answer questions such as how much better one conservation practice is than another. This paper describes a new method called “Dual-Monte-Carlo” (DMC), which calculates model predictive uncertainty for any input parameter set based on input parameter uncertainty. The Rangeland Hydrology and Erosion Model (RHEM) was used as a case study. DMC gave reasonable results on model predictive uncertainty for RHEM compared to the natural variations associated with measured erosion plot data. Results from DMC for RHEM were applied to different erosional conditions to illustrate how model predictive uncertainty varies with different situations and how DMC can be used to assist conservation practice management. This new tool will improve our ability to make natural resource decisions across the United States.

Technical Abstract: Natural resources models serve as important tools to support decision making by simulating and predicting natural processes. All model predictions have uncertainty associated with them. The quantification of model predictive uncertainty, particularly when expressed as the confidence interval around a model prediction value, may serve as important supplementary information for assisting the decision making process. In this paper, 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 to not only calculate predictive uncertainty for one input parameter set, but also examine the predictive uncertainty as a function of model inputs across the full range of parameter space. The process-based, rainfall event-driven Rangeland Hydrology and Erosion Model (RHEM) was used as an example. The results showed that DMC was an effective method for calculating the predictive uncertainty for this model. To evaluate the uncertainty results for RHEM, we compared the calculated uncertainty intervals with the natural variation associated with measured erosion plot data. Both datasets showed a similar relationship between the variation of soil loss and the magnitude soil loss. We also found that the uncertainty intervals were strongly related to specific model input and output values, thus regression relationships (R2>0.97) were developed that enable the 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 3 example storms and 3 site conditions were used to illustrate how DMC can be a useful tool for directing decision making.