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

TL;DR

This paper introduces a new spherical grid system compatible with spectral and multigrid methods, utilizing Clenshaw-Curtis quadrature for exact spectral transforms and demonstrated through tests on weather modeling components.

Contribution

The paper presents a novel, nestable grid on a sphere that simplifies implementation of spectral and multigrid methods using Clenshaw-Curtis quadrature, with minimal code modifications.

Findings

Spectral transforms are exact within machine precision with the new grid.

Integration results are nearly identical to those with Gaussian quadrature.

Minor code changes suffice to adapt existing models to the new quadrature.

Abstract

A new grid system on a sphere is proposed that allows for straight-forward 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 the 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 Gaussian grid. Only minor code changes are required to any Gaussian-based spectral models to employ the proposed quadrature.