In this work, we present an analytical solution for the nonstationary two-dimensional advection–diffusion equation to simulate the pollutant dispersion in the planetary boundary layer. In this method the advection–diffusion equation is solved by the application of the Laplace transform technique and the solution of the resulting stationary problem by the generalised integral Laplace transform technique (GILTT). We also report numerical simulations and statistical comparison with experimental data available in the literature.