Conservative cascade interpolation on the sphere: An intercomparison of various non‐oscillatory reconstructions

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 135; no. 640; pp. 795 - 805
• Main Authors: Norman, Matthew R., Semazzi, Fredrick H. M., Nair, Ramachandran D.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.04.2009; Wiley
• Subjects: conservative cascade scheme; conservative interpolation; Earth, ocean, space; Exact sciences and technology; External geophysics; Meteorology; non‐oscillatory; Physics of the high neutral atmosphere; spherical; WENO; Sphere; Polar vortex; interpolation; non-oscillatory; Polynomial approximation; conservative cascade scheme; WENO; spherical; conservative interpolation
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.402

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 T42 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