SPHEREPACK 3.0: A Model Development Facility

John C. Adams National Center for Atmospheric Research, * Boulder, Colorado

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Paul N. Swarztrauber National Center for Atmospheric Research, * Boulder, Colorado

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Abstract

SPHEREPACK 3.0 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 Helmholtz equations. Use of the package is illustrated by three sample programs that solve the scalar Helmholtz equation, the time-dependent linear advection equation, and the time-dependent nonlinear 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.

Corresponding author address: Dr. John C. Adams, NCAR, P.O. Box 3000, Boulder, CO 80307.

Email: pauls@ucar.edu

Abstract

SPHEREPACK 3.0 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 Helmholtz equations. Use of the package is illustrated by three sample programs that solve the scalar Helmholtz equation, the time-dependent linear advection equation, and the time-dependent nonlinear 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.

Corresponding author address: Dr. John C. Adams, NCAR, P.O. Box 3000, Boulder, CO 80307.

Email: pauls@ucar.edu

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  • Adams, J. C., 1991: Recent enhancements in MUDPACK: A multigrid package for elliptic partial differential equations. Appl. Math. Comput.,43, 79–94.

  • ——, and P. N. Swarztrauber, 1997: SPHEREPACK 2.0: A model development facility. NCAR Tech. Note NCAR/TN-436-STR, 62 pp. [Available from NCAR, P.O. Box 3000, Boulder, CO 80307-3000.].

  • ——, ——, and R. A. Sweet, 1981: Efficient FORTRAN subprograms for the solution of elliptic partial differential equations. Elliptic Problem Solvers, M. H. Schultz, Ed., Academic Press, 187–190.

  • Swarztrauber, P. N., 1979: On the spectral approximation of discrete scalar and vector functions on the sphere. SIAM J. Numer. Anal.,16, 934–949.

  • ——, 1993: The vector harmonic transform method for solving partial differential equations in spherical geometry. Mon. Wea. Rev.,121, 3415–3437.

  • ——, 1996: Spectral transform methods for solving the shallow-water equations on the sphere. Mon. Wea. Rev.,124, 730–744.

  • Temperton, C., 1991: On scalar and vector transform methods for global spectral methods. Mon. Wea. Rev.,119, 1303–1307.

  • Williamson, D. L., J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992: A standard test set for numerical approximations to the shallow-water equations in spherical geometry. J. Comput. Phys.,102, 211–224.

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