Parameter Uncertainty Analysis for the Annual Phosphorus Loss Estimator (APLE) Model.

Models are often used to predict phosphorus (P) loss from agricultural fields. While it is commonly recognized that model predictions are inherently uncertain, few studies have addressed prediction uncertainties using P loss models. In this study, we conduct an uncertainty analysis for the Annual P Loss Estimator (APLE) model by estimating the model parameter uncertainty associated with five regression equations used to calculate four of the model variables in APLE. Specifically, we estimate the parameter uncertainties associated with the regression equations used to estimate total soil P from measurements of soil clay content, organic matter, and labile P; the P enrichment ratio from erosion rates; concentration of P in runoff due to labile soil P; and partitioning of P between runoff and infiltration from applied manures and fertilizers. Our analysis included calculating both confidence and prediction intervals. We then calculated predictions of P loss using the APLE model while including uncertainties in both model parameters and model inputs and compared the relative magnitude of these sources of uncertainty to the overall uncertainty associated with predictions of P loss. We also demonstrate how the estimation of model parameter uncertainty can identify model limitations. This work builds on our previous study where we evaluated the effects of model input error on APLE model predictions.