The accuracy of sediment loads when log-transformation produces nonlinear sediment load-discharge relationships

Most sediment loads are estimated from sediment-rating curves created by performing a linear least-square regression on log-transformed sediment load-discharge data. When log-transformed sediment load-discharge data plots result in concave or convex curves, such regressions under- or overestimate sediment loads. Conflicting results exist regarding the accuracy/utility of using nonlinear regression to estimate loads. A nonlinear regression technique (optimized/constrained two different ways) was compared with the linear regression method at 26 United States Geological Survey gaging stations throughout the Upper Mississippi River basin. Sensitivity analyses were conducted at two stations, one having a concave sediment load-discharge plot and one having a convex sediment load-discharge plot, to determine each rating curve's ability, based on varying amounts of data, to predict annual and cumulative suspended sediment yields. With a 5-year calibration dataset, a nonlinear maximized r² statistic curve produced the best estimates for a station with a convex sediment load-discharge relationship, while a nonlinear load-constrained curve produced the best estimates for a station with a concave sediment load-discharge relationship. At both stations (using 5-year calibration datasets), annual yield errors ranged from -54% to 112%, while 15- and 18-year cumulative yield errors ranged from about -21% to 13%.