Horizontal grids for global weather and climate prediction models: a review

Abstract

AbstractA latitude–longitude grid is used by almost all operational atmospheric forecast models, and many research models. However, it is expected that the advantages of a latitude–longitude grid will become outweighed on massively parallel computers by data‐communication bottlenecks. There is therefore renewed interest in quasi‐uniform alternatives. This review surveys and assesses previously proposed horizontal grids for modelling the atmosphere over the sphere. Aspects of numerical accuracy likely to be affected by grid structure are discussed; particular attention is paid to computational modes and grid imprinting. Computational modes are potentially very serious, since they may be excited in realistic applications by boundary conditions, nonlinearity, physical forcing, and data assimilation. The geometry of polyhedra is reviewed due to its relation to numerical degrees of freedom, and hence to numerical wave dispersion and the possible existence of computational modes.All grids proposed to date have known problems or issues that merit further investigation. Orthogonal logically rectangular grids may be generated using conformal maps, but these suffer from singularities and resolution clustering. Resolution clustering may be avoided by using overset grids, but there are potential issues associated with the overlap regions. Alternatively, resolution clustering may be avoided, whilst retaining a logically rectangular grid, by giving up orthogonality; however, existing numerical schemes exploit orthogonality to obtain various properties thought to be important for accuracy, and it is not yet known whether these can also be obtained on non‐orthogonal grids. Quasi‐uniformity and orthogonality can be obtained without resolution clustering or overlaps by using non‐quadrilateral grid cells, such as triangles, or pentagons and hexagons. However, when a staggered placement of variables is used to minimise dispersion errors for fast waves, non‐quadrilateral grids support computational modes.In view of the lack of a single ideal grid, several topics meriting further investigation are identified. Copyright © 2011 Royal Meteorological Society and British Crown Copyright, the Met Office