Optimal Wasteload Allocation Procedure for Achieving Dissolved Oxygen Water Quality Objectives. I: Sensitivity Analysis

A method is presented to compute sensitivities of in-stream dissolved oxygen (DO) with respect to perturbations in the load vector and the reaction coefficients that make up the eutrophication cycle. It is shown that the direct sensitivity method, i.e., the repetitive solution of the direct problem, produces the desired information, however at a large computational cost. The utilization of the adjoint sensitivity method proves to be a much more efficient way to compute these sensitivities as large subsets of the sensitivity information domain can be easily extracted with just a few runs. It is found that for the given problem setup, in-stream DO is most sensitive to ammonia, effluent DO, algae, and carbonaceous biochemical oxygen demand (CBOD) loads. Additionally, the computed sensitivities vary considerably in their general trend over the simulation time. Sensitivities also are computed with respect to the reaction coefficients (26 total) that govern the interdependency of all constituents. Sediment oxygen demand proves to be the coefficient with the highest influence that is three orders of magnitude higher than the next set of coefficients comprised of reaeration, CBOD degradation, nitrification, and denitrification. All other coefficients have a negligible influence on DO concentrations. Computations are carried out using a two-dimensional model formulation applied to a long rectangular channel with varying width and slope and periodic but unsteady flow conditions.