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.