Applying horizontal diffusion on pressure surface to mesoscale models on terrain-following coordinates

The National Centers for Environmental Prediction regional spectral model and mesoscale spectral model (NCEP RSM/MSM) use a spectral computation on perturbation. The perturbation is defined as a deviation between RSM/MSM forecast value and their outer model or analysis value on model sigma-coordinate surfaces. The horizontal diffusion used in the models applies perturbation diffusion in spectral space on model sigma-coordinate surfaces. However, because of the large difference between RSM/MSM and their outer model or analysis terrains, the perturbation on sigma surfaces could be large over steep mountain areas as horizontal resolution increases. This large perturbation could introduce systematical error due to artificial vertical mixing from horizontal diffusion on sigma surface for variables with strong vertical stratification, such as temperature and humidity. This nonnegligible error would eventually ruin the forecast and simulation results over mountain areas in high-resolution modeling. To avoid the erroneous vertical mixing on the systematic perturbation, a coordinate transformation is applied in deriving a horizontal diffusion on pressure surface from the variables provided on terrain-following sigma coordinates. Three cases are selected to illustrate the impact of the horizontal diffusion on pressure surfaces, which reduces or eliminates numerical errors of mesoscale modeling over mountain areas. These cases address concerns from all aspects, including unstable and stable synoptic conditions, moist and dry atmospheric settings, weather and climate integrations, hydrostatic and nonhydrostatic modeling, and island and continental orography. After im plementing the horizontal diffusion on pressure surfaces for temperature and humidity, the results show better rainfall and flow pattern simulations when compared to observations. Horizontal diffusion corrects the warming, moistening, excessive rainfall, and convergent flow patterns around high mountains under unstable and moist synoptic conditions and corrects the cooling, drying, and divergent flow patterns under stable and dry synoptic settings.