Some Applications of Optimization Techniques to Water Quality Modeling and Control

Dynamic water quality modeling methodology is presented along with a number of applications of optimization theory to deterministic water quality modeling and control. Two of the applications are basically parameter estimation problems. The first involves the generation of a dynamic model for the behavior of coliform bacteria in Grand Traverse Bay, while the second is concerned with the estimation of parameters in an existing model for the growth of bacteria in organic carbon limited media. The third application utilizes the proposition that the laws of nature are in some sense optimal to aid in the characterization of an algae inhibition function. The basic problem involves the development of a model of phytoplankton succession in lakes involving two species of algae and two nutrients. An unknown algal inhibition function is treated as an unknown control that is to be determined to minimize the loss of nutrients from the system, which is considered as an approximate optimality principle for the system. The resultant solution possesses an optimal singular subarc that has an interesting ecological interpretation. An active control application utilizing the same model is also presented.