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Title:   Author  item
                                            Bolster, Carlitem
                                            Vadas, Peter
  Submitted to: Journal of Environmental Quality
                                    Publication Type: Peer Reviewed Journal
                                    Publication Acceptance Date: 5/2/2013
                                    Publication  Date: 6/15/2013
                                    Citation: Bolster, C.H., Vadas, P.A. 2013. Sensitivity and uncertainty analysis for the annual phosphorus loss estimator model. Journal of Environmental Quality. 42:1109-1118.Interpretive Summary: Models are often used to predict phosphorus (P) loss from agricultural fields, and when properly used they can be useful tools for evaluating the potential impacts of various P management strategies on P loss. While it is commonly recognized that there are inherent uncertainties with model predictions due to various sources of error, many P loss models provide only a single output value for a given set of input variables with no estimate of the uncertainty in model predictions. Such models may give the false impression that the model output is known more accurately than what it really is. This can lead to skepticism of modeling results by the public, regulators, and the scientific community.  In this study we assess the effect of model input error on predictions of annual P loss by the Annual P Loss Estimator (APLE) model, an empirically-based spreadsheet model developed to describe annual, field-scale P loss when surface runoff is the dominant loss pathway. A sensitivity analysis for all APLE input variables was conducted to determine which variables the model is most sensitive to. Predictions of P loss using APLE were then evaluated against a large and diverse measured P loss data set, accounting for errors in both the model input variables and the observed data. The estimated uncertainties in APLE predictions based on assumed errors in the input variables ranged from ± 2 to 64% of the predicted value. Incorporating uncertainties in both measured data and model predictions improved model performance. Results from this study highlight the importance of including reasonable estimates of model uncertainty when using models to predict P loss.
                                Technical Abstract: Models are often used to predict phosphorus (P) loss from agricultural fields. While it is commonly recognized that there are inherent uncertainties with model predictions, limited studies have addressed model prediction uncertainty. In this study we assess the effect of model input error on predictions of annual P loss by the Annual P Loss Estimator (APLE) model, an empirically-based spreadsheet model developed to describe field-scale P loss from surface runoff. A sensitivity analysis for all APLE input variables was conducted to determine which variables the model is most sensitive to. Two methods – first-order approximation (FOA) and Monte Carlo (MC) simulation – were compared to determine whether the FOA method is appropriate for estimating uncertainties with APLE. APLE predictions were then evaluated against measured P loss data accounting for errors in both the model input variables and the observed data. Results showed that for low to moderate uncertainties in APLE input variables, the FOA method yields reasonable estimates of model prediction uncertainties, though for cases where manure solid content is ~ 15%, the FOA method may not be as accurate as the MC method due to an artifact in APLE. The estimated uncertainties in APLE predictions based on assumed errors in the input variables ranged from ± 2 to 64% of the predicted value. Incorporating uncertainties in both measured data and model predictions improved model performance. Results from this study highlight the importance of including reasonable estimates of model uncertainty when using models to predict P loss.


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