Semi-analytical solution of the steady three-dimensional advection-diffusion equation in the planetari boundary layer

We present a three-dimensional solution of the steady-state advection-diffusion equation considering a vertically inhomogeneous Planetary Boundary Layer (PBL). We reach this goal applying the GITT (Generalized Integral Transform Technique), a hybrid method that had solved a wide class of direct and inverse problems mainly in the area of Heat Transfer and Fluid Mechanics. The transformed problem is solved by the ADMM (Advection-Diffusion Multilayer Model) method, a semi-analytical solution based on a discretization of the PBL in sub-layers where the advection-diffusion equation is solved by the Laplace transform technique. Numerical simulations are presented and the performances of the solution are compared against field experiments data.