Editorial Type:
Article
Article Type:
Research Article

Comparative Analysis of Conformal Mappings Used in Limited-Area Models of Numerical Weather Prediction

Andrei Bourchtein Department of Mathematics, Pelotas State University, Pelotas, Brazil

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Ludmila Bourchtein Department of Mathematics, Pelotas State University, Pelotas, Brazil

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Print Publication:
01 Aug 2003
DOI:
https://doi.org/10.1175//2560.1
Page(s):
1759–1768
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Abstract

Conformal separable projections from a sphere onto a plane are introduced to generalize the concept of conformal stereographic, conic, and cylindrical projections. The concept of equivalence of projections is used for partition of all considered projections into equivalence classes. The variation coefficient is defined as the ratio between maximum and minimum mesh sizes of numerical grids. The problem of minimization of this coefficient inside each equivalence class is studied. The obtained variation coefficients from all classes are compared and the principal relation among stereographic, cylindrical, and conic projections is established. The stereographic conformal projection is indicated as that which generates the “best” numerical grids for numerical weather prediction limited-area models.

Corresponding author address: Dr. Andrei Bourchtein, Rua Anchieta 4715 bloco K, Ap. 304, 96020-250 Pelotas, Brazil. Email: burstein@terra.com.br

Abstract

Conformal separable projections from a sphere onto a plane are introduced to generalize the concept of conformal stereographic, conic, and cylindrical projections. The concept of equivalence of projections is used for partition of all considered projections into equivalence classes. The variation coefficient is defined as the ratio between maximum and minimum mesh sizes of numerical grids. The problem of minimization of this coefficient inside each equivalence class is studied. The obtained variation coefficients from all classes are compared and the principal relation among stereographic, cylindrical, and conic projections is established. The stereographic conformal projection is indicated as that which generates the “best” numerical grids for numerical weather prediction limited-area models.

Corresponding author address: Dr. Andrei Bourchtein, Rua Anchieta 4715 bloco K, Ap. 304, 96020-250 Pelotas, Brazil. Email: burstein@terra.com.br

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