SPHEREPACK 3.0: A model development facility

SPHEREPACK 3.0 is a collection of FORTRAN programs that facilitates compute r modeling of geophysical processes. The package contains programs for comp uting certain common differential operators including divergence, vorticity , gradients, and the Laplacian of both scalar and vector functions. Program s are also available for inverting these operators. For example, given dive rgence and vorticity, the package can be used to compute the velocity compo nents. The Laplacian can also be inverted and therefore the package can be used to solve both the scalar and vector Helmholtz equations. Use of the pa ckage is illustrated by three sample programs that solve the scalar Helmhol tz equation, the time-dependent linear advection equation, and the time-dep endent nonlinear shallow-water equations. Accurate solutions are obtained v ia the spectral method that uses both scalar and vector spherical harmonic transforms that are available to the user. The package also contains utilit y programs for computing the associated Legendre functions, Gauss points an d weights, and multiple fast Fourier transforms. Programs are provided for both equally spaced and Gauss distributed latitudinal points as well as pro grams that transfer data between these grids.