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SPHEREPACK 2.0 is a collection of FORTRAN programs that facilitates computer modeling of geophysical processes. The package contains programs for computing certain common differential operators including divergence, vorticity, gradients, and the Laplacian of both scalar and vector functions. Programs are also available for inverting these operators. For example, given divergence and vorticity, the package can be used to compute the velocity components. The Laplacian can also be inverted and therefore the package can be used to solve both the scalar and vector Poisson equations. In addition, the package can be used to compute a scalar function with a specified gradient. Its use in model development is demonstrated by a sample program that solves the time-dependent non-linear shallow-water equations. Accurate solutions are obtained via the spectral method that uses both scalar and vector spherical harmonic transforms that are available to the user. The package also contains utility programs for computing the associated Legendre functions, Gauss points and weights, and multiple fast Fourier transforms. Programs are provided for both equally-spaced and Gauss distributed latitudinal points as well as programs that transfer data between these grids.
Adams et al. (Sun,) studied this question.