Uncertainty and sensitivity in a bank stability model: implications for estimating phosphorus loading

Abstract

Eutrophication of aquatic ecosystems is one of the most pressing water quality concerns in the U.S. and around the world. Bank erosion has been largely overlooked as a source of nutrient loading, despite field studies demonstrating that this source can account for the majority of the total phosphorus budget of a watershed. Substantial effort has been made to develop mechanistic models to predict bank erosion and instability in stream systems; however, these models do not account for inherent natural variability in input values. Providing only single output values with no quantification of associated uncertainty can complicate management decisions focused on reducing bank erosion and nutrient loading to streams. To address this issue, uncertainty and sensitivity analyses were performed on the Bank Stability and Toe Erosion Model (BSTEM), a mechanistic model developed by the USDA-ARS that simulates both mass wasting (stability) and fluvial erosion of streambanks. Sensitivity analysis results indicate that variable influence on model output can vary depending on assumed input distributions. Generally, bank height, soil cohesion, and plant species were found to be most influential in determining stability of clay (cohesive) banks. In addition to these three inputs, groundwater elevation, stream stage, and bank angle were also identified as important in sand (non-cohesive) banks. Slope and bank height are the dominant variables in fluvial erosion modeling, while erodibility and critical shear stress are relatively unimportant. However, the threshold effect of critical shear stress (determining whether erosion occurs) was not explicitly accounted for, possibly explaining the relatively low sensitivity indices for this variable. Model output distributions of sediment and phosphorus loading rates corresponded well to ranges published in the literature, helping validate both model performance and selected ranges of input values. In addition, a probabilistic modeling approach was applied to data from a watershed-scale sediment and phosphorus loading study on the Missisquoi River, Vermont to quantify uncertainty associated with these published results. While our estimates indicated that bank erosion was likely a significant source of sediment and phosphorus to the watershed in question, the uncertainty associated with these predictions indicates that they should probably be considered order of magnitude estimates only.