Aeolian dust from arid and semi-arid areas contributes significantly to the global atmospheric aerosol mass and is expected to impact the climate system by direct and indirect effects. The project Saharan Mineral dust experiment (SAMUM) aims at investigating the properties of Saharan dust. Within this framework, a new regional model system was developed for simulations of the Saharan dust cycle and radiative effects. The model performance is tested for two Saharan dust outbreaks directed to Europe in August and October 2001.The importance of dispersion modelling in low wind conditions lies in the fact that such conditions occur frequently and are crucial for air pollution episodes. The classical approach based on conventional models, such as Gaussian plume or the K-theory with suitable assumptions, are known to work reasonably well during most meteorological regimes, except for weak wind conditions.A steady-state mathematical model for dispersion of contaminants in low wind conditions that takes into account the along-wind diffusion is proposed. The solution of the advection–diffusion equation for these conditions is obtained applying the Laplace transform, considering the planetary boundary layer (PBL) as a multilayer system. The eddy diffusivities used in the K-diffusion model were derived from the local similarity and Taylor's diffusion theory. The eddy diffusivities are functions of distance from the source and correctly represent the near-source diffusion in weak winds.