# Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis

## Abstract

The dissertation examines spectral transform algorithms for the solution of the shallow water equations on the sphere and studies their implementation and performance on shared memory vector multiprocessors. Beginning with the standard spectral transform algorithm in vorticity divergence form and its implementation in the Fortran based parallel programming language Force, two modifications are researched. First, the transforms and matrices associated with the meridional derivatives of the associated Legendre functions are replaced by corresponding operations with the spherical harmonic coefficients. Second, based on the fast Fourier transform and the fast multipole method, a lower complexity algorithm is derived that uses fast transformations between Legendre and interior Fourier nodes, fast surface spherical truncation and a fast spherical Helmholz solver. Because the global shallow water equations are similar to the horizontal dynamical component of general circulation models, the results can be applied to spectral transform numerical weather prediction and climate models. In general, the derived algorithms may speed up the solution of time dependent partial differential equations in spherical geometry.

- Authors:

- Publication Date:

- Research Org.:
- National Center for Atmospheric Research, Boulder, CO (United States)

- OSTI Identifier:
- 5479370

- Alternate Identifier(s):
- OSTI ID: 5479370

- Report Number(s):
- PB-94-115029/XAB; NCAR/CT--144

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Doctoral thesis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54 ENVIRONMENTAL SCIENCES; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; AIR-WATER INTERACTIONS; CLIMATE MODELS; ATMOSPHERIC CIRCULATION; COMPUTERIZED SIMULATION; MATHEMATICAL MODELS; SIMULATION 540120* -- Environment, Atmospheric-- Chemicals Monitoring & Transport-- (1990-); 990200 -- Mathematics & Computers

### Citation Formats

```
Jakob, R.
```*Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis*. United States: N. p., 1993.
Web.

```
Jakob, R.
```*Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis*. United States.

```
Jakob, R. Fri .
"Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis". United States.
doi:.
```

```
@article{osti_5479370,
```

title = {Fast and parallel spectral transform algorithms for global shallow water models. Doctoral thesis},

author = {Jakob, R.},

abstractNote = {The dissertation examines spectral transform algorithms for the solution of the shallow water equations on the sphere and studies their implementation and performance on shared memory vector multiprocessors. Beginning with the standard spectral transform algorithm in vorticity divergence form and its implementation in the Fortran based parallel programming language Force, two modifications are researched. First, the transforms and matrices associated with the meridional derivatives of the associated Legendre functions are replaced by corresponding operations with the spherical harmonic coefficients. Second, based on the fast Fourier transform and the fast multipole method, a lower complexity algorithm is derived that uses fast transformations between Legendre and interior Fourier nodes, fast surface spherical truncation and a fast spherical Helmholz solver. Because the global shallow water equations are similar to the horizontal dynamical component of general circulation models, the results can be applied to spectral transform numerical weather prediction and climate models. In general, the derived algorithms may speed up the solution of time dependent partial differential equations in spherical geometry.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Jan 01 00:00:00 EST 1993},

month = {Fri Jan 01 00:00:00 EST 1993}

}