Control of Contaminant Releases in Rivers. II: Optimal Design

Abstract

A numerical method is developed for the optimal design of contaminant releases in shallow rivers and estuaries. The algorithm is based on the hypothesis that the control action, at one or more points of release, can be discretized in time so each of the individual loads can be uniquely identified in an optimal fashion. A finite-element solution of the adjoint equation to the fate and transport problem yields the gradient information necessary for the optimization process, which permits accurate and efficient determination of the mass loading at the sources. The optimization is based on the cumulative effects of the contaminant at one or more targets and is achieved by a Gauss-Newton iteration procedure. The adjoint model is driven by the dynamic difference between the computed and desired concentration at the target nodes and incorporates all physical constraints of the problem. The validity of the model is demonstrated by convergence to a unique control action from different starting vectors. The procedure also provides estimates of the uncertainty associated with operator or mechanical device error, which defines the likelihood of success of the suggested dynamic changes. Practical applications are presented for Fox River and the upper Potomac Estuary.