Two-phase Uncertainty Analysis: An Example Using the Universal Soil Loss Equation

Hydrologic and water quality (H/WQ) models are important tools for environmental assessment and management. Model simulations are often performed deterministically, which results in a single estimate of the output while ignoring the natural variability of the modeled system and other knowledge uncertainties. We present a two-phase Monte Carlo method that provides for the evaluation and propagation of natural stochastic variability and knowledge uncertainty separately in H/WQ modeling efforts. The Universal Soil Loss Equation (USLE) and experimental plot data were used to present the methods and to illustrate the value of incorporating uncertainty analysis into modeling investigations. In addition, we demonstrated that, when using Monte Carlo techniques, output variance is reduced as the level of discretization increases in spatially distributed modeling. This reduction is due to the mathematics of the underlying statistics if the parameters of the discrete units are not perfectly correlated across the units. Landscapes are often represented as a collection of discrete subunits in distributed parameter H/WQ models. Therefore, model output uncertainty can be underestimated due to discretization rather than due to increased confidence in parameter estimates or model improvements if the correlation structure among the discrete units is not considered. Additional work is needed to develop and test procedures for determining and using the correlation structure among parameters of the discrete units to accurately present output variability and uncertainty for distributed H/WQ models using Monte Carlo analysis techniques.