Mean square error of regression‐based constituent transport estimates

Abstract

Estimates of long‐term transport of constituents commonly are obtained by summing retransformed estimates from regressions of logarithmically transformed response variables. Typical explanatory variables for these regressions include functions of flow, change in flow, time, and time of year. The mean and mean square error of four estimators of long‐term transport at periodically measured stations are presented as a function of the observed values of the explanatory variables from the long‐term record and summary statistics of the regression data. Estimates of the mean square errors can be used in designing sampling strategies to attempt to minimize the uncertainty in the estimation of long‐term transport subject to a constraint on the number of samples to be taken. This uncertainty is expressed in terms of the explanatory variables in the long‐term record, the regression coefficients and standard error of the regression and the mean and covariance structure of the explanatory variables used in the regression.