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

Abstract

UNCERTAINTY AND SENSITIVITY IN A BANK STABILITY MODEL: IMPLICATIONS FOR ESTIMATING PHOSPHORUS LOADINGEutrophication 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, ii 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.iii ACKNOWLEDGEMENTS

Application of a simple headcut advance model for gullies

“…Recent work on slope stability by Samadi et al (2009) indicates that parameter uncertainties in bank stability models, similar in mechanics to headcut failures, are high enough that the likelihood of generating unreliable predictions is very high (>80%) for predictions requiring an accuracy of <15%. Similar arguments are made by Parker et al (2008) and, in an exhaustive survey of bank stability models, by Lammers et al (2016). Daly et al (2015a, b) demonstrate the difficulty in predicting soil erosion rates for concentrated flow erosion.…”

Influence of Catchment and Stream Characteristics on Suspended Solids and Phosphorus Concentrations Across an agriculturally Intensive Watershed in Southern Ontario

“…Bank erosion is often cited as a major source of sediments and nutrients in lotic systems (Allmanová and Jakubis, 2016;Kronvang et al, 1997;Lammers et al, 2017;McMillan et al, 2018). Stream bank erosion can be caused by two major factors: hydraulic/gravitation forces and bank erodibility potential (Janes et al, 2018;Prosdocimi et al, 2015;Rosgen, 2001).…”

“…Streambank erosion is often cited as a major source of sediments and nutrients in lotic systems (Allmanová and Jakubis, 2016;Kronvang et al, 1997;Lammers et al, 2017;McMillan et al, 2018).…”

A network scale, intermediate complexity model for simulating channel evolution over years to decades

“…BSTEM accounts for several processes that increase or decrease bank strength, including: (1) water pressure in soil pores (positive pressure decreasing stability and negative pressure increasing stability); (2) confining pressure of the streamflow; and (3) increased soil cohesion from plant roots. Although the simplified version of BSTEM accounts for the first two processes, we exclude vegetation effects since they have a negligible effect on BSTEM output in sensitivity analyses (Lammers et al, 2017) and increase computation time and data requirements. This gives the following factor of safety equation:…”

“…REM is designed primarily for modeling channel evolution in smaller watersheds (i.e. 10s -100s km 2 ) with cohesive banks, integrating a bank stability model based on Lammers et al (2017) with novel stream power based sediment transport equations (Lammers and Bledsoe, 2018). Unfortunately, watershed-scale data on channel response are rarely available for these types of systems.…”