# Estimation of suspended-sediment rating curves and mean suspended-sediment loads

January 1, 1991

Suspended-sediment loads are often estimated from an empirical relation between suspended-sediment load (L) and streamflow (S). This relation is usually defined as a power function, L = aSh, and is referred to as a suspended-sediment rating curve. This function can be formulated as either a linear or non-linear model to find the solution of the rating-curve parameters (a and b). Formulation of the power function as a linear model requires a logarithmic transformation to linearize the function and a subsequent correction for transformation bias. Rating-curve parameter estimates for both the bias-corrected, transformed-linear or non-linear models can be obtained by the method of least squares.

Each model has distinct advantages and disadvantages. A unique solution of the parameters of the transformed-linear model may be obtained algebraically. These parameter estimates have some optimal properties when certain attainable conditions are met. However, the parameter estimates must be corrected for transformation bias when obtained this way. Parameter estimates obtained for the non-linear model do not require a correction for transformation bias. However, these estimates must be obtained by iterative methods which do not always converge to a solution. In addition, the residual errors of the non-linear model typically are not identically distributed throughout the range of streamflow values. This problem adversely affects the precision of the parameter estimates. Weighted non-linear least squares can be used to improve the parameter estimates for the non-linear model, but the weights must be approximated and their appropriate form may be difficult to determine.

A simulation study was done to evaluate: (1) the accuracy and precision of parameter estimates for the bias-corrected, transformed-linear and non-linear models obtained by the method of least squares; (2) the accuracy of mean suspended-sediment loads calculated by the flow-duration, rating-curve method using model parameters obtained by the alternative methods. Parameter estimates obtained by least squares for the bias-corrected, transformed-linear model were considerably more precise than those obtained for the non-linear or weighted non-linear model. The accuracy of parameter estimates obtained for the biascorrected, transformed-linear and weighted non-linear model was similar and was much greater than the accuracy obtained by non-linear least squares. The improved parameter estimates obtained by the biascorrected, transformed-linear or weighted non-linear model yield estimates of mean suspended-sediment load calculated by the flow-duration, rating-curve method that are more accurate and precise than those obtained for the non-linear model.

## Citation Information

Publication Year 1991 Estimation of suspended-sediment rating curves and mean suspended-sediment loads 10.1016/0022-1694(91)90057-O Charles G. Crawford Article Journal Article Journal of Hydrology 70015019 USGS Publications Warehouse Indiana Water Science Center