Impact of vertical velocity damping on the numerical stability and atmospheric representation in ICON

The upper portion of atmospheric models typically employ a damping (sponge) layer to absorb upward-propagating wave energy, thereby preventing spurious wave reflections from the rigid model top. In the Icosahedral Nonhydrostatic Weather and Climate Model (ICON), implicit Rayleigh damping is applied on the vertical velocity following the approach of Klemp et al., 2008. In high-resolution simulations, the waves resolved in the model can increase substantially. Insufficient damping leads to more frequent model crashes due to numerical instability. While increasing the amount of damping might be a simple and intuitive adjustment, excessive damping can also induce back reflections from the damping layer itself, causing spurious standing oscillations. It is therefore crucial to carefully adjust the damping settings with sensitivity experiments. 

We analyze a set of ICON simulations with different damping settings. These are 1-month simulations with a horizontal resolution of 10 km. The goal is to provide insights into the optimal damping settings that can improve numerical stability in high-resolution simulations without compromising the atmospheric representation. Evaluation of the mean wind field outside of the damping layer shows no significant changes across different damping settings. However, spurious standing oscillations are observed in the tropical stratosphere. Further examination demonstrates that these oscillations align with the vertical grids, an indication that they can possibly be caused by vertical discretization error rather than back reflections from the damping layer. Investigation of Eliassen-Palm (EP) flux using Transformed Eulerian Mean (TEM) analysis also shows no significant change in the mean EP flux at the damping layer height due to changing damping coefficient. This suggests no major change in back reflections from the damping layer. Overall, our current results show that increasing the amount of damping could improve numerical stability with no indication of severely altered atmospheric representation over the 1-month time frame. Further analysis through long-term simulations will be necessary to assess the possible impact on longer timescales. 

References
Klemp, J. B., Dudhia, J., and Hassiotis, A. D. (2008). An Upper Gravity-wave Absorbing Layer for NWP Applications. Mon. Wea. Rev., 136(10), 3987–4004. doi: 10.1175/2008MWR2596.1