I would like to use Laplacian, Div, and Grad in geophysical spherical coordinates rather than the usual spherical coordinates. The difference is that standard spherical coordinates uses the polar angle, θp, the angle from the North Pole with southwards being positive, while in geophysics it is standard to use latitude, θ, the angle from the Equator with northwards being positive. The transformation is relatively simple, θp = π/2 - θ.

Does Mathematica have this as a defined coordinate system? If not, can I define a new coordinate system that will work with Laplacian, Div, and Grad?