Cartesian to Spherical coordinates

[fxgiraldo]

Just wanted to pass it by everyone to see if this is the sort of map that you all need to go from Cartesian to Spherical. You can find the code here: https://github.com/fxgiraldo/CLIMA/blob/5b181c1e7802cc9107cd0f2c533e373a65f72548/src/DGmethods/test/Advection/advection_sphere.jl#L33-L67

The code here runs advection on the full 3D sphere. It is the first test of CLIMA on the sphere.

Before committing it to CLIMA, we would like feedback on the following:

• where should these type of functions go (e.g., a MOD_Utilities is what we do in NUMA)?

• Is this what you need? Do you need a specific (prime) meridian so that we can adjust this as needed?

Here is what the snippet of code looks like:

#{{{ Cartesian->Spherical
@inline function cartesian_to_spherical(x,y,z,format)
#Conversion Constants
if format == "degrees"
c=180/π
elseif format == "radians"
c=1.0
end
λ_max=2πc
λ_min=0c
ϕ_max=+0.5πc
ϕ_min=-0.5πc

#Conversion functions
r = hypot(x,y,z)
λ=atan(y,x)*c
ϕ=asin(z/r)*c

#Stay within bounds

#= if (λ < λ_min)
λ = λ + λ_max
end
if (λ > λ_max)
λ = λ - λ_max
end
if (ϕ < ϕ_min)
ϕ = ϕ + ϕ_max
end
if (ϕ > ϕ_max)
ϕ = ϕ - ϕ_max
end
=#
return r, λ, ϕ
end
#}}} Cartesian->Spherical

[simonbyrne]

cross ref: #179

One thing we should consider is using types to convey semantic meaning:

struct XYZCoord{T}
    x::T
    y::T
    z::T
end

struct LatLongAltCoord{T}
    latitude::T
    longitude::T
    altitude::T
end

[tapios]

• It seems natural to me to put these functions in the CLIMA/src/Mesh directory, though Utilities would also work.
• I suggest format to be defined in PlanetParameters (and have a more descriptive name, e.g., AngleUnits)
• In the end (when we have topography), we need to fix a prime meridian, and also need the inverse of these functions so that we can read topography files in lat, lon, alt coordinates.