A nestable, multigrid‐friendly grid on a sphere for global spectral models based on Clenshaw–Curtis quadrature

Abstract

A new grid system on a sphere is proposed which allows for straightforward implementation of both spherical-harmonics-based spectral methods and gridpoint-based multigrid methods. The latitudinal gridpoints in the new grid are equidistant and spectral transforms in the latitudinal direction are performed using Clenshaw-Curtis quadrature. The spectral transforms with this new grid and quadrature are shown to be exact within machine precision provided that the grid truncation is such that there are at least 2N + 1 latitudinal gridpoints for the total truncation wavenumber of N. The new grid and quadrature is implemented and tested on a shallow-water equations model and the hydrostatic dry dynamical core of the global NWP model JMA-GSM. The integration results obtained with the new quadrature are shown to be almost identical to those obtained with the conventional Gaussian quadrature on a Gaussian grid. Only minor code changes are required to adapt any Gaussian-based spectral models to employ the proposed quadrature. KEYWORDS Clenshaw-Curtis quadrature, Fejér quadrature, global spectral model, Legendre transform, multigrid 1 Q J R Meteorol Soc. 2018;144:1382-1397.wileyonlinelibrary.com/journal/qj

Elimination of spectral blocking by ensuring rotation‐free property of discretized pressure gradient within a spectral semi‐implicit semi‐Lagrangian global atmospheric model

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“…Given the current trend of high‐performance computing where growth of computing capacity relies increasingly on massive parallelism, spectral models are predicted to face serious scalability issues, and many centres, including JMA, are exploring transition to (or have already transitioned to) a grid‐based model with better data locality (e.g. Hotta and Ujiie, ; Kühnlein et al ., ). The lesson that we learned here will serve nicely as a guiding principle in deciding which discretization to use out of many possibilities.…”

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Noniterative Computation of Gauss--Jacobi Quadrature

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