Analytical solution of the advection-diffusion equation with nonlocal closure of the turbulent diffusion

In this work we consider the nonlocal closure of the turbulent diffusion in the advection-diffusion equation. Accounting for the current knowledge on the Convective Boundary Layer structure and characteristics, we obtain an expression for the advection-diffusion equation depending on eddy diffusivity, skewness, Lagrangian time scale and vertical turbulent velocity. This expression is solved analytically using the Laplace transform technique. The present study shows that the inclusion of the countergradient term modifies the maximum concentration which is one of the most important parameters in air-quality applicative context.