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A cubic spline Galerkin scheme for the vertical discretization of atmospheric models
Author(s) -
Steppeler J.
Publication year - 1988
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.49711448410
Subject(s) - discretization , galerkin method , basis function , mathematics , collocation (remote sensing) , grid , finite element method , basis (linear algebra) , discontinuous galerkin method , mathematical analysis , spline (mechanical) , geometry , computer science , physics , thermodynamics , machine learning
A Galerkin finite element discretization for the vertical coordinate using high‐order basis functions is introduced. The basis functions are cubic splines, assuming continuity of the spline and its first and second derivatives. Locality of the scheme is required, allowing each basis function to be different from zero on four grid intervals only. An efficient solution of the resulting Galerkin finite element equations is achieved by introducing a collocation grid. A number of test integrations were done using the ECMWF spectral model with resolution T63 for horizontal discretization. The scheme was also used in a data assimilation experiment where it reduced the first guess error.