A Local Terrain Smoothing Approach for Stabilizing Microscale and High-Resolution Mesoscale Simulations: Application to FastEddy® and WRF

High-resolution simulations, both at mesoscale and microscale, have become increasingly prevalent, often leveraging high-resolution terrain datasets. However, terrain-following coordinate models can encounter numerical instabilities in regions where terrain slopes exceed critical thresholds, generally around 35º. To address this issue, terrain smoothing is typically required. Current approaches usually involve applying global smoothing methods across the entire domain, which inevitably results in a loss of terrain detail and resolution to prevent numerical instabilities in regions where it is not necessary. Moreover, as the model resolution increases, the number of grid points with steep slopes grows, underscoring the need for alternative terrain smoothing strategies.

This study presents the development and implementation of a local terrain smoothing approach designed to mitigate numerical instabilities in a mesoscale model (the WRF model) and a microscale model (NCAR-RAL’s GPU-accelerated FastEddy^® LES model). Various smoothing techniques were evaluated, including both simultaneous and sequential approaches. Following a thorough performance analysis—considering the number of iterations required for convergence, computational cost, and, most importantly, the degree of terrain distortion—the most effective method was selected and implemented. The final approach applies a Gaussian filter (σ = 25) over a 3x3 grid centered on each steep-slope point, with a blending factor of 0.2 at the edges. This ensures that the central point is smoothed while the surrounding points retain 80% of their original terrain characteristics. Each steep slope is addressed individually but processed simultaneously across iterations. A higher blending factor results in greater terrain distortion, while a lower blending factor significantly increases computational time, often preventing convergence within the imposed iteration limit.

This terrain smoothing method has been fully implemented in FastEddy^® and is now used operationally and routinely within the model. This implementation will be made publicly available in the next release of FastEddy^®, hosted on GitHub (https:// github.com/NCAR/FastEddy-model, starting with version 3.0). For WRF, the method has been integrated as an additional step in the WPS workflow, following the execution of the geogrid program. The proposed local smoothing approach helps preventing the occurrence of CFL errors in high-resolution simulations over complex terrain without relying on excessively high values of the time off-centering parameter (epssm) to dampen vertically propagating sound waves, which can lead to excessive high-frequency damping, negatively impacting the accuracy of the simulations.

In conclusion, this study presents a simple yet effective method for avoiding terrain-driven numerical instabilities in high-resolution simulations, ensuring the maximal preservation of terrain resolution in both microscale and mesoscale models. This approach can be easily applied to other models, offering a straightforward solution to enhance numerical stability while maintaining high-resolution terrain features in diverse simulation environments.

Acknowledgements: The authors acknowledge the ECCE project (PID2020-115693RB-I00) of the Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación (MCIN/AEI/10.13039/501100011033). ERL thanks her predoctoral contract FPU (FPU21/02464) to the Ministerio de Universidades of Spain.