Optimal Wasteload Allocation Procedure for Achieving Dissolved Oxygen Water Quality Objectives. II: Optimal Load Control

This paper presents the development of an efficient strategy for achieving in-stream dissolved oxygen (DO) water quality standards (WQSs) via optimized point-load control strategies using the adjoint method. To this end, a least-squares-type objective function is formulated that measures the difference between desired (WQSs) and current DO concentrations at strategically selected monitoring points in the domain. The goal is to minimize the difference between actual DO concentration and the WQS, hence allowing time-variant loadings to utilize the assimilative capacity of the receiving water body at an optimal level. Time-variant discharge rates for a number of discharge locations are considered as control parameters, while different zone-specific critical DO levels are imposed as constraints. The selection of the control is kept flexible and a number of different scenarios are tested. First, only carbonaceous biochemical oxygen demand is used, which allows for a reduction of the number of equations that need to be solved. In the other tests, all constituents are switched on and different variables at each load node are selected as a control by first varying the concentrations individually, and then linking them through control of the volumetric flow rate. Optimization is achieved using a conjugate gradient search method, for which the gradients are computed through the solution of both the direct and adjoint problems. It is shown that the large amount of gradient information (parameter space has a dimension of several thousands) can be computed very efficiently using the adjoint, and that optimized results are achieved after only a few iterations irrespective of the initial guess. Computations are carried out using both two-dimensional model formulation applied to a long rectangular channel with varying width and slope and a model for the upper Potomac River estuary.