Watershed-scale hydrologic and nonpoint-source pollution models: review of mathematical bases

A clear understanding of a model is important for its appropriate use. In this article, eleven watershed scale hydrologic and nonpoint-source pollution models are reviewed: AGNPS, AnnAGNPS, ANSWERS, ANSWERS-Continuous, CASC2D, DWSM, HSPF, KINEROS, MIKE SHE, PRMS, and SWAT. AnnAGNPS, ANSWERS-Continuous, HSPF, and SWAT are continuous simulation models useful for analyzing long-term effects of hydrological changes and watershed management practices, especially agricultural practices. AGNPS, ANSWERS, DWSM, and KINEROS are single rainfall event models useful for analyzing severe actual or design single-event storms and evaluating watershed management practices, especially structural practices. CASC2D, MIKE SHE, and PRMS have both long-term and single-event simulation capabilities. Mathematical bases, the most important and critical elements of these mathematical models, were identified and compiled. In this article, a comprehensive summary of the compilation is presented in tabular form. The flow-governing equations and their solution methods used in each of the eleven models are discussed. The compilation of the mathematical bases of these models would be useful to determine the problems, situations, or conditions for which the models are most suitable, the accuracies and uncertainties expected, their full potential uses and limitations, and directions for their enhancements or new developments. AGNPS, AnnAGNPS, DWSM, HSPF, MIKE SHE, and SWAT were found to have all the three major components (hydrology, sediment, and chemical) applicable to watershed-scale catchments. SWAT is a promising model for continuous simulations in predominantly agricultural watersheds, and HSPF is promising for mixed agricultural and urban watersheds. Among the single-event models, DWSM provides a balance between the simple but approximate and the computationally intensive models and, therefore, is a promising storm event model for agricultural watersheds.