How to initialize an atmosphere in (discrete) hydrostatic balance?

[ali-ramadhan]

I tried solving for pressure and density profiles that would satisfy the discrete form of hydrostatic balance but I still get transient acoustic waves when running the model.

Not super high priority but might be good to figure out how to do this to avoid transient acoustic waves.

Currently I just put a strong damping sponge layer at the top and all the acoustic waves are damped after ~500 seconds then I turn off the sponge layer.

Sandbox script: https://github.com/thabbott/JULES.jl/blob/master/sandbox/solve_for_hydrostatic_profiles.jl