Lat-Lon Finite Differences about xinvert HOT 4 CLOSED

Hi, thanks for your interests. This is just a simple centered finite difference for lat-lon grids. I guess you can find the differential operators in spherical coordinates in a textbook like dynamic meteorology or geophysical fluid dynamics. I had a clip for your convenience:

• For a scalar, its meridional gradient (second line) does not need the cosine weighting;
• For a vector, its meridional divergence (third line) does require cosine weighting.

from xinvert.

Thank you very much!

I have a quick question about the formulation: why is the wikipedia article consistently have a sin instead of a cos? Is this because of the typical bounds? Or am I missing something more fundamental and/or subtle? Perhaps the bounds?

from xinvert.

My theta is latitude, and I guess its theta is co-latitude (i.e., 90 - my theta). You can check that.

from xinvert.

Close this now and feel free to re-open it in any case.

from xinvert.