TL;DR about spherical harmonics: It is what you use instead of Fourier transforms if what you transform is on the surface of a sphere. My experience is from co

TL;DR about spherical harmonics: It is what you use instead of Fourier transforms if what you transform is on the surface of a sphere. My experience is from cosmology (CMB) where they are heavily used just like Fourier transforms, I think they are also used in meteorology.