Fibonacci grids: A novel approach to global modelling

Abstract

SUMMARYRecent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges); (iv) ease of parallelization.One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as 'Fibonacci grids'. These grids possess virtually uniform and isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of this type of grid in shallow-water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional weather prediction or climate models.

Synoptic Composites of Tornadic and Nontornadic Outbreaks

“…To eliminate this issue, an equally spaced hemispheric grid is applied. Swinbank and Purser (2006) define a Fibonacci grid (Fig. 2b), which uses the Golden ratio [F 5 (1 1 ffiffi ffi 5 p )/2] and a predetermined number of grid points N to compute an equally spaced hemispheric grid.…”

The ICON-1.2 hydrostatic atmospheric dynamical core on triangular grids – Part 1: Formulation and performance of the baseline version

“…The efforts of Heikes and Randall (1995a,b), Ringler and Randall (2002), Majewski et al (2002), Tomita and Satoh (2004) and Giraldo and Rosmond (2004) are examples that developed models on icosahedral grids. Other grid configurations such as the cubed sphere (e.g., McGregor, 1996;Giraldo et al, 2003;Putman and Lin, 2007), Yin-Yang grid (e.g., Kageyama and Sato, 2004;Qaddouri et al, 2008;Li et al, 2007), and Fibonacci grid (Swinbank and Purser, 2006), have also been investigated. The numerical discretizations applied in these models include not only finite-difference and finite-volume schemes (e.g., Heikes and Randall, 1995a;Putman and Lin, 2007), but also modern techniques such as high-order continuous and discontinuous Galerkin methods (e.g.…”

The Evolution of Dynamical Cores for Global Atmospheric Models

“…Fibonacci grids Swinbank and Purser (2006) developed a spherical grid which is virtually uniform and highly isotropic, mimicking forms found in nature. They describe them as ''mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples'' for example.…”