Hybrid vertical coordinates

[milankl]

Most atmospheric models use hybrid sigma-pressure coordinates, this could be one way of defining them easily

pref = 1013

# sigma coordinates
nlev = 8
σ_half = range(0,1,length=nlev+1)
p_σ = σ_half*ps'

# hybrid coordinates
γ(σ) = @. σ
A,B = σ_half.*(1 .- γ(σ_half)),σ_half.*γ(σ_half)
p_h = A*(pref*ones(n))' .+ B*ps'

(green) sigma-pressure coordinates (black) sigma coordinates

[milankl]

Following

and

from the GFDL spectral model documentation.

[milankl]

Currently going rather the other direction with #409 as I don't see a good argument yet that a more sophisticated vertical coordinate is essential

[milankl]

With NeuralGCM basically beating all other weather forecasts I'm tempted to postpone the idea of hybrid coordinates for now, as I don't see a big urgency for these.