An examination of existing shoreline fumigation models and formulation of an improved model

We test assumptions and approximations used in existing coastal fumigation models of varying complexity. Several fumigation cases involving typical values of entrainment rate and plume spread at the interface of the plume and the thermal internal boundary layer (TIBL) are considered. It is observed that, when compared with the results from a physically more realistic Lagrangian stochastic model, many existing models that assume uniform and/or instantaneous vertical mixing in the TIBL give inaccurate results for large entrainment rate and/or small vertical plume spread at the plume-TIBL interface. We develop an improved analytical fumigation model based on a probability density function (PDF) approach, with its parameters calculated using results from a stochastic model for the horizontally homogeneous convective boundary layer. The new model is general and is capable of better representing the fumigation process than the existing analytical models. A limited number of field data support the model simulations for analogous input conditions.