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A comparison of spectral and finite‐difference simulations of a growing baroclinic wave
Author(s) -
Simmons A. J.,
Hoskins B. J.
Publication year - 1975
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49710142912
Subject(s) - baroclinity , truncation (statistics) , amplitude , finite difference , mathematics , finite difference method , spectral method , perturbation (astronomy) , finite difference coefficient , wavenumber , mathematical analysis , physics , mechanics , finite element method , optics , quantum mechanics , statistics , mixed finite element method , thermodynamics
A comparison is made of integrations of the primitive equations on the sphere using a second‐order finite‐difference model, and spectral models with both triangular and rhomboidal truncation. The initial conditions comprise a baroclinically unstable mid‐latitude jet, and a perturbation of small amplitude. Increasing the resolution in each model gives a good estimate of the exact solution, and thus of the errors involved in each integration. No one method has a superiority in all respects. Spectral integrations with truncations at zonal wave‐number 16 give a more accurate description of amplitudes and phases in the growing wave than does a finite‐difference integration using a 5° × 3° grid, but a much poorer description of the fronts that form as the disturbance approaches maturity. Large‐scale changes to the zonal‐mean state are predicted to greater accuracy using the spectral models, but smaller‐scale changes are resolved better by the finite‐difference model. The spectral models require less computing time, and less storage. For these experiments, rhomboidal truncation is favoured.