Spherical coordinates Earth science convention

Question

Earth science often uses a different convention for spherical coordinates than the spherical coordinates Mathematica defines by "Spherical". "Spherical" uses (radius, colatitude, longitude). The common Earth science convention is (radius, latitude, longitude). Colatitude is the angle from the North Pole, latitude is the angle from the Equator with positive being north, and latitude = pi/2 - colatitude.

Is there a name like "Spherical" that I can use to work with the Earth science convention? If not, can I define a new coordinate system that I can use everywhere I use coordinate transforms like "Spherical", in coordinate transforms, Laplacians, etc?

More detail added:

Let's call this new coordinate system "GeoSpherical", with coordinates {radius, latitude, longitude}. Suppose I have a function in these coordinates F[r, latitude, longitude]. I want to do vector calculus in these coordinates, taking the Laplacian, Curl, Div, and Grad of F using the same syntax as other coordinate systems. The Laplacian would then be

Laplacian[F[r, latitude, longitude],{r, latitude, longitude},"GeoSpherical"]

I also want to transform a function, say 8 x y z, using

TransformedField["Cartesian" -> "GeoSpherical", 8 x y z, {x, y,z} -> {r, latitude, longitude}]

CoordinateChartData[] gives a list of coordinate systems but it doesn't look like any of them are what I want. I would be happy if I was wrong and the coordinate system is already predefined.

The transformation from "Spherical" to "GeoSpherical" is mathematically simple, just latitude = pi/2 - colatitude. If I knew the syntax I could calculate and define all the data CoordinateChartData needs to define a coordinate system.

Answer 1

Is the answer to this question perhaps what you're looking for?

geoSphericalPatch = 
  SymbolicTensors`ScaleFactorGeometryPatch[{1, r, r Sin[π/2 - θ]}, {r, θ, φ}];

Simplify[Laplacian[u @@ {r, θ, ϕ}, {r, θ, ϕ}, geoSphericalPatch], r > 0]

Note this won't work for TransformedField though.