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Conservative cascade interpolation on the sphere: An intercomparison of various non‐oscillatory reconstructions
Author(s) -
Norman Matthew R.,
Semazzi Fredrick H. M.,
Nair Ramachandran D.
Publication year - 2009
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.402
Subject(s) - piecewise , mathematics , interpolation (computer graphics) , grid , polynomial , mathematical analysis , harmonic , cascade , geometry , computer science , physics , animation , chemistry , computer graphics (images) , chromatography , quantum mechanics
Various new polynomial and non‐polynomial approximations to a subgrid distribution have been adapted for use in the conservative cascade scheme (CCS) and applied to conservative grid‐to‐grid interpolation on a latitude‐‐longitude grid. These approximations include the following: piecewise parabolic method (PPM), piecewise hyperbolic method (PHM), piecewise double hyperbolic method (PDHM), power‐limited piecewise parabolic method (P‐PPM), piecewise rational method (PRM), third‐order weighted essentially non‐oscillatory (WENO23), fifth‐order weighted essentially non‐oscillatory (WENO35), and a modified piecewise parabolic method (M‐PPM). A series of test cases are performed in which initial gridded data are interpolated between T 42 and 2° grids and compared against analytical values. Four initial data profiles are used: smooth harmonic, high‐frequency harmonic, quasi‐polar vortex data and slotted cylinder data. In general, PDHM (WENO35) had the lowest error norms of the three‐(five‐)cell stencil methods. Quite often, M‐PPM gave accuracy comparable to WENO35 at significantly lower cost. Monotonicity violations generally only occurred when interpolating to a finer grid with a maximum violation of 1.8% of the data range. Copyright © 2009 Royal Meteorological Society