The Boundary Layer Dispersion and Footprint Model: A fast numerical solver of the Eulerian steady-state advection-diffusion equation

Abstract. Understanding how greenhouse gases and pollutants move through the atmosphere is essential for predicting and mitigating their effects. We present a novel atmospheric dispersion and footprint model: the Boundary Layer Dispersion and Footprint Model (BLDFM), which solves the three-dimensional steady-state advection-diffusion equation in Eulerian form using a numerical approach based on the Fourier method, the linear shooting method and the exponential integrator method. In contrast to analytical Gaussian plume or stochastic Lagrangian models, this novel numerical approach proves beneficial as it does not rely on any asymptotic assumptions or estimates. Furthermore, it is fully modular, allowing for the use of a variety of turbulence closure models in its implementation or direct usage of measured or simulated wind profiles. The model is designed to be flexible and can be used for a wide range of applications, including climate impact studies, industrial emissions monitoring and spatial flux attribution. We validate the model using an analytical test case. The numerical results show excellent agreement with the analytical solution. We also compare the model with the well-established Kormann and Meixner (Boundary-Layer Meteorology, 2001) footprint model (FKM) which is based on the analytical Gaussian plume. The results show overall good agreement but some differences in the fetch of the footprints, which are attributed to the neglect of streamwise turbulent mixing – being one of the aforementioned asymptotic assumptions – in the FKM model. Our results demonstrate the potential of the BLDFM model as a useful tool for atmospheric scientists, biogeochemists, ecologists, and engineers.