Parameter Identification in Transverse Mixing Models of Rivers – an Inverse Problem for a Parabolic Equation

Abstract

AbstractThe basic equation of transverse mixing in rivers and streams is given. A simple analytical solution (Gaussian distribution) is derived, firstly, assuming uniform transverse distributions of longitudinal flow velocity, depth, and transverse mixing coefficient. Using a modified linear regression technique, the cross sectional average of the transverse mixing coefficient is determined. Then, to get an estimate of the cross sectional distribution of the mixing coefficient, a finite difference scheme was applied in order to solve the mixing equation numerically, and the identification of the mixing coefficient was carried out by a nonlinear least squares technique, combining several minimization methods. The numerical methods described were successfully applied to experimental data of the Elbe river and led to certain crossmixing models. In applications, these models may save measurement expense and serve as scientific tools to predict the influence of large waste water treatment plants on water quality in the longitudinal and transversal coordinate of the river.