Source terms for shallow water on the sphere

The shallow water equations on the sphere involve some geometric source terms that are currently missing from GeoClaw. Experiments during initial develpment of GeoClaw seemed to indicate that they were not important, but more recently it has been found that at least the source term in the mass equation can be quite important for properly modeling waves moving between the tropics and polar regions due to the variation in cell size with latitude.

As of v5.9.1, these source terms have been added to $CLAW/geoclaw/src/2d/shallow/src2.f90. In v5.9.1 these terms are turned off by default for backward compatibility but to allow for further testing by turning them on and recompiling. As of v5.9.2, there is a setrun.py parameter rundata.geo_data.sphere_source that can be set to 0 (default) for no source terms, 1 to add the source term only in the mass equation, or 2 to add source terms in the momentum equations too. In the future the default value will probably be 1, to add the source term in mass.

A document is in preparation to describe these source terms and show some examples of the impact they have. A draft can be viewed at https://faculty.washington.edu/rjl/misc/spherical_swe_2023-10-27.pdf