Eutrophication Model Calibration as a Coupled Inverse Problem

摘要

An inverse algorithm was integrated into a real time, vertical, two-dimensional eutrophication model to assist in calibrating of the model kinetic parameters. The problem of the eutrophication model calibration was posed as a coupled inverse problem in a framework of multiobjective optimization. The solution was found by minimizing a global objective function, which was a weighted least-square of residuals between modeled water quality state variables and their corresponding observed values. Both conjugate gradient and modified Gauss-Newton methods were used to update unknown parameter values. The gradient vectors of the objective function, with respect to the model parameters, and the sensitivity coefficient matrix used to estimate the Hessian matrix were obtained by using the variational method and the influence coefficient method, respectively. In comparison to the variational method, using the influence coefficient method to calculate the sensitivity matrix provides an alternate way to estimate the Hessian matrix and Gauss-Newton direction. It requires much less effort in coding and is very efficient for estimating limited parameters. Because the sensitivity matrix is calculated during the iteration process, the convergence speed of the inverse model is improved. The quick convergence compensates for the time consumed in computing the sensitivity matrix. A series of model experiments with a real time eutrophication model of the tidal Rappahannock River were conducted. The results of the numerical experiments demonstrate the efficiency and accuracy of the inverse model. Thirteen unknown kinetic parameters were calibrated with hypothetical data sets generated by the forward model. Both data sets, with and without random errors, were used to test the inverse model. The results of model calibration demonstrate that the invarse model is capable of conducting model calibration. With the use of the inverse model, the unknown parameters can be estimated satisfactorily.