Construction of Orthogonal Basis Functions with Non-Divergent Barotropic Rossby-Haurwitz Waves

서지정보

· 발행기관 : 한국지구과학회
· 수록지 정보 : 한국지구과학회지 / 35권 / 5호
· 저자명 : Cheong, Hyeong-Bin, Jeong, Hanbyeol, Kim, Wonho

목차

Abstracts
Introduction
Non-divergent Barotropic Rossby-Haurwitz Waves and Legendre Functions
Evaluation of the basis functions
Summary and Conclusion
Acknowledgments
References

영어초록

A new set of basis functions was constructed using the Rossby-Haurwitz waves, which are the eigenfunctions of nondivergent barotropic vorticity equations on the sphere. The basis functions were designed to be non-separable, that is, not factored into functions of either the longitude or the latitude. Due to this property, the nodal lines of the functions are aligned neither along with the meridian nor the parallel. The basis functions can be categorized into groups of which members have the same degree or the total wavenumber-like index on the sphere. The orthonormality of the basis functions were found to be close to the machine roundoffs, giving the error of O(10-15) or O(10-16) for double-precision computation (64 bit arithmetic). It was demonstrated through time-stepping procedure that the basis functions were also the eigenfunctions of the non-divergent barotropic vorticity equations. The projection of the basis functions was carried out onto the low-resolution geopotential field of Gaussian bell, and compared with the theory. The same projections were performed for the observed atmospheric-geopotential height field of 500 hPa surface to demonstrate decomposition into the fields that contain disturbance of certain range of horizontal scales. The usefulness of the new basis functions was thus addressed for application to the eigenmode analysis of the atmospheric motions on the global domain.

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