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

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 nonoscillatory (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.