Least Squares Estimation of Mixing Coefficients

The principle of least squares estimation of nonlinear parameters as a general tool in mathematical modeling can be shown to be applicable to many common problems in sanitary engineering. A digital computer program for accomplishing this procedure is explained, and the results are illustrated for the example of estimating mixing coefficients and mean travel times for measured time-concentration curves. A critical examination of existing estimation procedures shows them to be inaccurate and unreliable. The results of comparative fit of several methods to several hundred curves are presented. If a digital computer is not available, a simple, quick, trial-and-error procedure—outlined in the paper—can be used to produce results more reliable than those given by presently used methods.