Wave Reflection Caused by Sponge Layer Configuration

It is well known that sponge-layer upper boundary condition serves as an effective way in damping upward propagating waves from a numerical model and hence, preventing spurious wave reflections and instabilities from the model top. In practice, it is recommended that sponge layers be sufficiently thick to encompass one vertical wavelength of the wave passing through and to have sufficient vertical levels to resolve said wave. However, in this study, thorough testing with the models WRF and CM1 have shown that setting up the sponge layer solely on this fact is not sufficient. The tests performed use a two-dimensional grid with a bell-shaped mountain of 2500 m high in a uniform flow of 20 ms^-1 with constant Brunt-Väisälä frequency of 0.01 s^-1. The model top is specified at 33 km and the sponge layer depth is varied between 18 km to 8 km from the model top. Results of these experiments show wave reflection occurring at the bottom of the sponge layer except when the depth was set to 18 km.  The same results were also evidenced when using a two-layer structured atmosphere. It is found that using the guideline of setting the sponge layer at 1.7λ_z, where λ_z is the vertical wavelength of the fluid, and the model top at 3.4λ_z also results in reflection from the sponge layer. Recommendations to avoid these problems from the sponge layer setup will also be provided.