Spectral methods for limited area models
| dc.contributor.author | Fulton, Scott R., author | |
| dc.contributor.author | Schubert, Wayne H., advisor | |
| dc.contributor.author | Taylor, Gerald D., committee member | |
| dc.contributor.author | Krueger, David A., committee member | |
| dc.contributor.author | Stevens, Duane E., committee member | |
| dc.contributor.author | Johnson, Richard H. (Richard Harlan), committee member | |
| dc.date.accessioned | 2016-12-19T17:41:17Z | |
| dc.date.available | 2016-12-19T17:41:17Z | |
| dc.date.issued | 1984 | |
| dc.description.abstract | This study investigates the usefulness of Chebyshev spectral methods in limited area atmospheric modeling. Basic concepts of spectral methods and properties of Chebyshev polynomials are reviewed. Chebyshev spectral methods are illustrated by applying them to the linear advection equation in one dimension. Numerical results demonstrate the high accuracy obtained compared to finite difference methods. The nonlinear shallow water equations on a bounded domain in two dimensions are then considered as a more realistic prototype model. Characteristic boundary conditions based on Reimann invariants are developed, and contrasted with wall conditions and boundary conditions based on the assumption of balanced flow. Chebyshev tau and collocation methods are developed for this model. Results from one-dimensional tests show the superiority of the characteristic conditions in most situations. Results from two-dimensional tests are also presented. Comparison of the tau and collocation methods shows that each has its own advantages and both are practical. Time differencing schemes for Chebyshev spectral methods are studied. The stability condition obtained with explicit time differencing, often thought to be "severe", is shown to be less severe than the corresponding condition for finite difference methods. Numerical results and asymptotic estimates show that time steps may in fact be limited by accuracy rather than stability, in which case simple explicit time differencing is practical and efficient. Two modified explicit schemes are reviewed, and implicit time differencing is also discussed. A Chebyshev spectral method is also used to solve the vertical structure problem associated with vertical normal mode transforms in a hydrostatic atmosphere. Numerical results demonstrate the accuracy of the method, and illustrate the aliasing which can occur unless the vertical levels at which data is supplied are carefully chosen. Vertical transforms of observed forcings of tropical wind and mass fields are presented. The results of this study indicate that Chebyshev spectral methods are a practical alternative to finite difference methods for limited area modeling, especially when high accuracy is desired. Spectral methods require less storage than finite difference methods, are more efficient when high enough accuracy is desired, and are at least as easy to program. | |
| dc.description.sponsorship | Supported by the National Science Foundation - ATM-8207563. | |
| dc.description.sponsorship | Supported by the Office of Naval Research - N00014-84-C-0591. | |
| dc.description.sponsorship | Acknowledgment to the National Center for Atmospheric Research, sponsored by the National Science Foundation, for computer time. | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier.uri | http://hdl.handle.net/10217/178747 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation | Catalog record number (MMS ID): 991006716349703361 | |
| dc.relation | QC996.F85 1984 | |
| dc.relation.hasversion | Fulton, Scott R. and Schubert, Wayne H. Spectral methods for limited area models. Atmospheric science paper, no. 384. Colorado State University. Department of Atmospheric Science, 1984. | |
| dc.relation.ispartof | 1980-1999 | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.subject.lcsh | Meteorology -- Mathematical models | |
| dc.subject.lcsh | Numerical weather forecasting | |
| dc.subject.lcsh | Chebyshev polynomials | |
| dc.title | Spectral methods for limited area models | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Atmospheric Science | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
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