Optimal estimation of suspended‐sediment concentrations in streams

Abstract

AbstractOptimal estimators are developed for computation of suspended‐sediment concentrations in streams. The estimators are a function of parameters, computed by use of generalized least squares, which simultaneously account for effects of streamflow, seasonal variations in average sediment concentrations, a dynamic error component, and the uncertainty in concentration measurements. The parameters are used in a Kalman filter for on‐line estimation and an associated smoother for off‐line estimation of suspended‐sediment concentrations. The accuracies of the optimal estimators are compared with alternative time‐averaging interpolators and flow‐weighting regression estimators by use of long‐term daily‐mean suspended‐sediment concentration and streamflow data from 10 sites within the United States. For sampling intervals from 3 to 48 days, the standard errors of on‐line and off‐line optimal estimators ranged from 52·7 to 107%, and from 39·5 to 93·0%, respectively. The corresponding standard errors of linear and cubic‐spline interpolators ranged from 48·8 to 158%, and from 50·6 to 176%, respectively. The standard errors of simple and multiple regression estimators, which did not vary with the sampling interval, were 124 and 105%, respectively. Thus, the optimal off‐line estimator (Kalman smoother) had the lowest error characteristics of those evaluated. Because suspended‐sediment concentrations are typically measured at less than 3‐day intervals, use of optimal estimators will likely result in significant improvements in the accuracy of continuous suspended‐sediment concentration records. Additional research on the integration of direct suspended‐sediment concentration measurements and optimal estimators applied at hourly or shorter intervals is needed. Published in 2001 by John Wiley & Sons, Ltd.