OpenIFS/IFS 43r3 introduced the so-called cubic reduced Gaussian grid (with spectral truncation denoted by TC) instead of the current linear reduced Gaussian grid (denoted by TL) where the shortest wave is represented by four rather than two grid points. By increasing the number of grid points used to represent the shortest wave, more resolution is added in grid-point space while keeping the spectral truncation constant,
To reduce further the computational cost, the new IFS cycle implements a modification to the grid, the octahedral reduced Gaussian grid (with spectral truncation denoted by TCO). The octahedral grid is a form of the reduced Gaussian grid but applying a new rule for computing the number of points per latitude circle.
In this page, we refer to the reduced Gaussian grid as described by Hortal and Simmons (Use of Reduced Gaussian Grids in Spectral Models; ECMWF Tech. Memo. 168, 1990 - see also Hortal M., and A.J. Simmons, 1991, Mon. Wea. Rev. 119 1057-1074) and used by the IFS up to cycle 41r1 as the original reduced Gaussian grid. The new octahedral form of the reduced Gaussian grid is described in this page.
What is the octahedral grid ?
The octahedral grid has been inspired by the Collignon Projection of the sphere onto an octahedron.
It is a form of reduced Gaussian grid with the same number of latitude lines located at the same latitude values as those of a original Gaussian grid but with the number of longitude points at each latitude circle between the pole and equator computed according to the formula:
\[ \begin{equation*} \mbox{N}_{lat_i} = 4 \times i + 16 \mbox{ for } i = 1, \ldots, \mbox{N} \end{equation*} \]In other words:
- there are 20 longitude points at the latitude circle closest to the poles;
- the number of points increases by 4 at each latitude line from the pole towards the equator.
This is in contrast to the original reduced Gaussian grid where there are 'jumps' between blocks of latitudes with a constant number of longitude points (a restriction imposed by the Fast Fourier Transform routines being used up to IFS cycle 41r1).
As a consequence, the zonal resolution of the octahedral grid varies more with latitude than for the original reduced Gaussian grid. This can be seen in the figures to the right.
Note in particular that the octahedral grid has 4N + 16 longitude points at the latitude circle closest to the equator whereas the original reduced Gaussian grid has 4N longitude points at the latitude circle closest to the equator.
There are also fewer total grid points in the octahedral grid compared to the original reduced Gaussian grid. For example, the O1280 octahedral grid has about 20% fewer grid points than the equivalent N1280 original reduced grid. Generally, an octahedral grid with N latitude lines between the pole and equator has 4xNx(N+9) grid points.
The octahedral grid has been shown to improve the calculation of local derivatives in grid point space.
Comparison of the resolution variation with latitude for the reduced Gaussian grids
Variation of the resolution (characteristic length scale) with latitude for the reduced Gaussian grids. The red curve shows the resolution for the original reduced Gaussian grid at N1280 (TC1279). Note that the resolution remains more or less constant at 8km as the latitude varies. The corresponding curve for the O1280 (TCO1279) octahedral grid is shown by the blue curve. The resolution for the O1280 octahedral grid varies from about 8 km at the equator, increasing to about 10 km at 70oN and 70oS before decreasing again towards the poles. The resolution of the N640 original reduced Gaussian grid used for HRES at IFS cycle 41r1 is at about 16 km. Also shown is the regular Gaussian grid at F1280 (black curve).
Comparison of the zonal variation in resolution between original reduced and octahedral grids
Comparison of the zonal variation in resolution for the N1280 original reduced Gaussian grid (left) with the corresponding O1280 octahedral grid (right) on the surface of the sphere.
Further information
For further background information see:
See also:
- Malardel S., et al. 2016: "A new grid for the IFS", ECMWF Newsletter No.146 - Winter 2015/16 (pages 23-28).
- Wedi N.P., 2014: Increasing the horizontal resolution resolution in numerical weather prediction and climate simulations: illusion or panacea ?" Phil. Trans. R.Soc.A, 372, doi: 10.1098/rsta.2013.0289.
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