Parameter Estimation of Dispersion Models

Mixing and transportation process of water quality in river flow is usually predicted by dispersion models which describe concentration distribution of contaminants. The application of the nonlinear least squares method to the parameter of one of dispersion models, namely storage zone or dead water zone model, is developed in this paper. Though parameters of storage zone model can not be estimated directly because of the unstable condition of numerical calculations, Marquardt's method is applicable by the modification of the combination of parameters as given by eq.(9) andeq. (1O). Applying Marquardt's al gorithm, four parameters of storage zone model are estimated by the use of observed concentration distribution which is obtained from experiments carried out in the flow over rough beds. It is found that the solution of Laplace transform domain of the storage zone model is well fitted to the numerical Laplace transform of the observed concentration distribution. However, the physical meaning of estimated parameters is not definite. The comparison of temporal moments of storage zone model with those of observed data is presented in fig.10, for the statistical variance and in fig.11, for the skewness factor. The gamma distribution approximation of the concentration distribution based on the storage zone model is presented in fig.13 and fig.14. In these fiqures; the results of the well known Taylor's model are also presented. The observed concentration distribution is well described by the storage zone model when the density of the boundary roughness element is high. On the contrary, the model fitness to the observed data is not good when the roughness density is low