Stratus over rolling terrain: Large‐eddy simulation reference and sensitivity to grid spacing and numerics

Abstract

AbstractThe formation of low stratus cloud over idealized hills is investigated using numerical model simulations. The main driver for the cloud formation is radiative cooling due to outgoing longwave radiation. Despite a purely horizontal flow, the advection terms in the prognostic equations for heat and moisture produce vertical mixing across the upper cloud edge, leading to a loss of cloud water content. This behavior is depicted via a budget analysis. More precisely, this spurious mixing is caused by the diffusive error of the advection scheme in regions where the sloping surfaces of the terrain‐following vertical coordinate intersect the cloud top. This study shows that the intensity of the (spurious) numerical diffusion depends strongly on the horizontal resolution, the order of the advection schemes, and the choice of scalar advection scheme. A large‐eddy simulation with 4‐ horizontal resolution serves as a reference. For horizontal resolutions of a few hundred meters and simulations carried out with a model setup as used in numerical weather prediction, a strong reduction of the simulated liquid‐water path is observed. In order to keep the (spurious) numerical diffusion at coarser resolutions small, at least a fifth‐order advection scheme should be used. In the present case, a weighted essentially nonoscillatory scalar advection scheme turns out to increase the numerical diffusion along a sharp cloud edge compared with an upwind scheme. Furthermore, the choice of vertical coordinate has a strong impact on the simulated liquid‐water path over orography. With a modified definition of the sigma coordinate, it is possible to produce cloud water where the classical sigma coordinate does not allow any cloud formation.