An analytical footprint model for non-neutral stratification

We propose an analytical model for the so-called footprint of scalar fluxes in the atmospheric boundary layer. It is the generalization of formulations already given in the literature, which allows to account for thermal stability. Our model is only marginally more complicated than these, and it is therefore simple enough to be applicable for a routine footprint analysis within long-term measurements. The mathematical framework of our model is a stationary gradient diffusion formulation with height-independent crosswind dispersion. It uses the solution of the resulting two-dimensional advection - diffusion equation for power law profiles of the mean wind velocity and the eddy diffusivity. To find the adjoint Monin-Obukhov similarity profile, we propose two different approaches, a purely analytical one and a simple numerical error minimalization.