Water quality modeling under hydrologic variability and parameter uncertainty using erosion-scaled export coefficients

Water quality modeling is important to assess the health of a watershed and to make necessary management decisions to control existing and future pollution of receiving water bodies. The existing export coefficient approach is attractive due to minimum data requirements; however, this method does not account for hydrologic variability. In this paper, an erosion-scaled export coefficient approach is proposed that can model and explain the hydrologic variability in predicting the annual phosphorus (P) loading to the receiving stream. Here sediment discharge was introduced into the export coefficient model as a surrogate for hydrologic variability. Application of this approach to model P in the Fishtrap Creek of Washington State showed the superiority of this approach compared to the traditional export coefficient approach, while maintaining its simplicity and low data requirement characteristics. In addition, a Bayesian framework is proposed to assess the parameter uncertainty of the export coefficient method instead of subjective assignment of uncertainty. This work also showed through a joint variability-uncertainty analysis the importance of separate consideration of hydrologic variability and parameter uncertainty, as these represent two independent and important characteristics of the overall model uncertainty. The paper also recommends the use of a longitudinal data collection scheme to reduce the uncertainty in export coefficients.