The moments of the concentration distribution obtained using a recent analytical solution of the steady-state two-dimensional advection–diffusion equation are presented. The solving methodology is the Generalized Integral Laplace Transform Technique, which allows obtaining a reliable solution of the advection–diffusion equation without any restrictive assumption about the eddy diffusivity coefficients and wind speed profiles. The first four moments and value and position of maximum ground level concentration are calculated. The concentration standard deviation is compared against the semi-empirical ones used in operative Gaussian models.