Development of a Three Dimensional Numerical Water Quality Model for Estuary and Continental Shelf Applications

A model to predict the distribution of water quality parameters in three dimensions has been developed, and applied to several theoretical and real problems. The mass transport equation is solved using a non-dimensional vertical axis and an alternating direction implicit finite different technique. The reaction kinetics of the constituents are incorporated into a matrix method which permits computation of the interactions of multiple constituents. Extensive literature reviews were made to determine the most appropriate methods available for the computation of dispersion coefficients and coliform bacteria decay rates. Numerical investigations of dispersive and dissipative effects showed that the three-dimensional model performed as predicted by the analysis of simpler cases. The mass transport was then linked to a two-dimensional vertically averaged tidal dynamics model for the Providence River. A uniform field was simulated, indicating mass conservation errors of less than 0.1%. Modeling coliform concentrations in the area revealed a mass conservation error of as much as 3.5%, due to an extrapolated, time-varying boundary condition. However, the model compared quite closely to a set of field data when no decay was specified. Additional effort was devoted to the extension of the model to a steady-state application, by replacing the time step with an iteration sequence. This was verified by comparison to analytical solutions, and demonstrated by application to a river confluence situation. Another application of the time-varying model was to point sources in Block Island Sound. A two-dimensional model prediction was compared to the three-dimensional distribution for the vertically well-mixed case, and found very similar after several tidal cycles