Kalman filtering in water quality modeling: Theory vs. practice

Kalman filtering is a statistical technique for computing minimum-uncertainty estimates of the states in linear uncertain dynamic systems. Filtering theory is qualitatively described. Potential applications to water quality modeling are discussed for state and parameter estimation, and model identification. Literature is reviewed on filtering applications to modeling receiving water quality. Several characteristics of environmental modeling problems are identified which may limit the filter's applicability. A case study is presented of optimal filtering applied to hydrothermal model development for a coastal power plant discharge. A simple model structure is proposed, for which 33 parameters are estimated using full-information maximum-likelihood methods with filtering. Discrepancies in model performance are highlighted, which typify the difficulties of a filtering approach to water quality model development. The theoretical advantages of filtering, and its practical limitations, are summarized for water quality applications. It is concluded that filtering techniques offer valuable organizing concepts, and are themselves a valuable tool when dynamic quantification of the variance in state estimates is required. Filtering is most applicable when dealing with a low-dimensional system with a well-known model and dense data base, for which highly accurate short-term forecasts are required. However, less accurate models and estimation techniques may provide more cost-effective solutions to many water quality problems.