An inverse problem approach to modelling coastal effluent plumes

Formulated as an inverse problem, the diffusion parameters associated with length-scale dependent eddy diffusivities can be viewed as the unknowns in the mass conservation equation for coastal zone transport problems. The values of the diffusion parameters can be optimized according to an error function incorporated with observed concentration data. Examples are given for the Fickian, shear diffusion and inertial subrange diffusion models. Based on a new set of dye-plume data collected in the coastal zone off Bronte, Lake Ontario, it is shown that the predictions of turbulence closure models can be evaluated for different flow conditions. The choice of computational schemes for this diagnostic approach is based on tests with analytic solutions and observed data. It is found that the optimized shear diffusion model produced a better agreement with observations for both high and low advective flows than, e.g., the unoptimized semi-empirical model, K-y = 0.075 sigma(1.2)(y), described by Murthy and Kenney.