Forecasting fog and low stratus (FLS) accurately poses a challenge to current numerical weather prediction models, despite many advancements in recent years. We present a novel method to quantify FLS extent bias by comparing forecasts with satellite observations. Evaluating a four‐month period, we show that COSMO‐1, the MeteoSwiss high‐resolution operational model, exhibits a considerable negative FLS bias during wintertime. To study the cause, we conduct a series of sensitivity experiments for a representative case study, where COSMO‐1 dissipated extensive FLS erroneously. Replacing the one‐moment bulk microphysics parameterisation scheme by a two‐moment scheme, as well as increasing the number of vertical levels, did not show any improvements. The FLS dissipation was delayed (but not prevented) by decreasing the lower bound imposed on the turbulent diffusion coefficients from 0.4  to 0.01 m2·s−1, or by reducing horizontal grid spacing from 1.1 km to 550 m. Additionally, simulations at 1.1‐km grid spacing with smoothed orography led to more extensive FLS than the same simulations without smoothed orography. An analysis of the cloud water budget revealed that the model's advection scheme is causing a loss of liquid water content near the cloud top. A simulation with an alternative terrain‐following coordinate system, in which the vertical coordinates are quasihorizontal near the cloud top, reduced the loss of cloud water through advection and improved the evolution of FLS in the case study. In combination, our findings suggest that the advection scheme exhibits numerical diffusion, which promotes spurious mixing in the vertical of cloudy and adjacent cloud‐free grid cells in terrain‐following vertical coordinates; this process can become the root cause for too rapid dissipation of FLS during nighttime in complex terrain.

Many numerical weather prediction models employ terrain‐following vertical coordinates. As a consequence, over orography, flat tops of stratus clouds are intersected by the vertical coordinate surfaces. We conduct idealised two‐dimensional simulations of a stratus cloud with the COSMO model to study the effect of such sloping vertical coordinate surfaces. The evolution of the stratus cloud above a flat surface within a horizontally homogeneous atmosphere serves as a reference. During night‐time, the cloud thickens, driven by radiative cooling at the cloud top. Adding a sinusoidal perturbation to the vertical coordinate surfaces reduces the growth of the stratus cloud. With strong perturbations, the cloud starts to dissipate. The physical processes in the two simulations are identical, hence this behaviour is purely driven by numerical diffusion. The cloud is similarly thinned when sinusoidal orographic features are introduced. The reduction depends on the amplitude and wavelength of the perturbations and hills. Increasing the horizontal resolution partly mitigates the numerical diffusion. However, this is a very costly measure for an operational weather model. We suggest conducting further research on a new vertical coordinate with additional local smoothing of the orographic signal.

To our knowledge, no study on FLS modeling has yet addressed the choice of the vertical coordinate transformation. Most operational NWP models employ a terrain-following vertical coordinate system. One of the first was developed by Phillips (1957); he introduced the  -coordinate with   p p s / , p being the pressure and s p the surface pressure. Similarly, Gal-Chen and Somerville (1975) proposed a terrain-following coordinate based on height. Terrain-following coordinate systems have the advantages that the wind component perpendicular to the model level vanishes at the bottom of the atmosphere and that the coupling to column-based physical parameterizations is straightforward.So-called hybrid coordinate systems change from one coordinate transformation to another to retain advantages of both. Bleck (1978) was the first to use a hybrid coordinate, combining a terrain-following  -coordinate in the boundary layer with an isentropic coordinate aloft. A challenging aspect of hybrid