Contents:
Computing on the sphere - P. N. Swarztrauber
Real spherical harmonics - SHTOOLS
Python notebooks - examples and tutorials - SHTOOLS
A New Recurrence Formula for Efficient Computation of Spherical Harmonic Transform - K. Ishioka
Spherical harmonics
Vector spherical harmonics
Quickstart Guide: Idealized Global Atmospheric Models with Spectral Dynamics - GFDL/NOAA Alternate link from web archive.
Initial-value problem for testing shallow water models - Galewsky et al.