A two-dimensional solution of the advection-diffusion equation with dry deposition to the ground

A mathematical scheme is developed to simulate the vertical turbulent dispersion of air pollution that is absorbed or deposited to the ground. The scheme is an exact analytical solution of the atmospheric diffusion equation, without any restriction to the vertical profile of wind speed and eddy diffusivities, and taking into account the dry deposition by a boundary condition of a nonzero flux to the ground. The performances of the solution, with a proper parameterization of the vertical profiles of the wind and eddy diffusivities, were evaluated against the dataset from the Hanford (Washington) diffusion experiment, in which two tracers (one depositing and one nondepositing) were released simultaneously. In addition, the solution derived in this work is compared with four different models, with deposition at the ground, found in the literature.