Smooth Operator: Using Spectral Filtering Techniques to Modify Terrain in WRF-ARW

Forecasting in areas of complex terrain have proved to be a challenge for numerical weather prediction (NWP) models. Horizontal grid spacings in places like British Columbia (BC) are typically courser than individual terrain features such as valleys and mountain peaks. To avoid aliasing issues, models such as the Weather Research Forecast (WRF) model employ terrain smoothing to eliminate problematic wavelengths and retain model stability. The consequences of this process are the loss of amplitude in terrain. Namely, mountain ranges are modeled too low, and valleys too high.

This study investigates an alternate way of performing terrain smoothing using Fourier Transforms, eliminating problematic wavelengths while maintaining prominent terrain features throughout the domain. A Von Neumann stability analysis is done for the Runge-Kutta 3^rd order in time 5^th order in space scheme, as used in WRF, to uncover problematic wavelengths in the model. Using this analysis, select wavelengths that are considered stable but smoothed by default are amplified by 1.5 times their original value. The result is a terrain dataset that is both numerically stable for the given differencing method and retains prominent features that contribute to important meteorological conditions including but not limited to: terrain blocking, channeling, cold pooling, and orographic convection. Results are compared to an identical run using the default smoothing method provided by the WRF Preprocessing System (WPS), reanalysis data, and observations.