Analytical Solution of the advection diffusion equation using Fourier and square complement methods and comparing with Gaussian model

Two approaches have been used to solve the two-dimensional atmospheric diffusion problem analytically. First, the integration has been solved using the separation of variables, Fourier transform, and square complement methods. Next, the normalized cross-wind integrated concentration of pollutants at the earth's surface with variable eddy diffusivity and wind speed with power in vertical height and downwind distance has been obtained using the Gaussian plume model. creating a Gaussian plume model by using the dispersion parameters of Briggs and Brookhaven National Laboratories. Sulfur Hexafluoride (SF6) tracer data sets from the northern portion of Copenhagen, Denmark, and Iodine-135 data sets under unstable conditions, are used to validate the current and Gaussian models.