Performance of bed-load transport equations relative to geomorphic significance: Predicting effective discharge and its transport rate

Previous studies assessing the accuracy of bed-load transport equations have considered equation performance statistically based on paired observations of measured and predicted bed-load transport rates. However, transport measurements were typically taken during low flows, biasing the assessment of equation performance toward low discharges, and because equation performance can vary with discharge, it is unclear whether previous assessments of performance apply to higher, geomorphically significant flows (e.g., the bankfull or effective discharges). Nor is it clear whether these equations can predict the effective discharge, which depends on the accuracy of the bed-load transport equation across a range of flows. Prediction of the effective discharge is particularly important in stream restoration projects, as it is frequently used as an index value for scaling channel dimensions and for designing dynamically stable channels. In this study, we consider the geomorphic performance of five bed-load transport equations at 22 gravel-bed rivers in mountain basins of the western United States. Performance is assessed in terms of the accuracy with which the equations are able to predict the effective discharge and its bed-load transport rate. We find that the median error in predicting effective discharge is near zero for all equations, indicating that effective discharge predictions may not be particularly sensitive to one's choice of bed-load transport equation. However, the standard deviation of the prediction error differs between equations (ranging from 10% to 60%), as does their ability to predict the transport rate at the effective discharge (median errors of less than I to almost 2.5 orders of magnitude). A framework is presented for standardizing the transport equations to explain observed differences in performance and to explore sensitivity of effective discharge predictions.