Control of Contaminant Releases in Rivers. I: Adjoint Sensitivity Analysis

A mathematical method that determines the sensitivity of solute concentration to real-time changes of the loading intensity at a remote source is developed here. The hydrodynamic and mass transport conditions correspond to flow in rivers and shallow estuaries and numerical simulations are performed by a two-dimensional finite-element model. The sensitivities are evaluated by solution of the adjoint equation of the fate and transport problem, which is shown to produce accurate results with increased efficiency when compared to equivalent perturbations of the loading intensity of the contaminant source. The corresponding reduction in computational effort allows the real-time optimal control of a contaminant release, which cannot be accomplished otherwise. The method is validated by comparisons with perturbation solutions in channels of simple geometry. Results are also presented for a practical application corresponding to the upper Potomac estuary.