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The planned horizontal resolution upgrade planned at IFS cycle 41r2 employs the so-called cubic Gaussian grid (with spectral truncation denoted by TC) instead of the current linear 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 41r2 implements a modification to the grid, the spectral octahedral grid (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 implementation of 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. Information about the new octahedral form of the reduced Gaussian grid is provided in this page.

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Section
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What is the octahedral grid ?

The octahedral grid has been inspired by the Collignon Projection of the sphere onto an octahedron.

 

Projection of the sphere onto an octahedronImage Added

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 computed according to the formula:

Mathdisplay
\begin{eqnarray*}
\mbox{N}_{lat}(lat_N) & = & 20 \\
\mbox{N}_{lat}(lat_i) & = & \mbox{N}_{lat}(lat_{i+1}) + 4,  \mbox{ for } i=\mbox{N} - 1,\ldots,1
\end{eqnarray*}

In other words, there are 20 longitude points at the latitude circle closest to the poles with the number of points increasing continuously by 4 at each latitude 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 prior to IFS cycle 41r2).

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 N1280 octahedral grid has about 20% fewer grid points than the equivalent N1280 linear grid. Generally, an octahedral grid of resolution N has 4xNx(N+8) grid points.

The octahedral grid has been shown to improve the calculation of local derivatives in grid point space.

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Comparison of the resolution variation with latitude for the reduced Gaussian grids

Variation of resolution with latitude for the reduced Gaussian grids.  The full red and yellow curves show the resolution for the original reduced Gaussian grids at N1024 and N1280 (TC1023 and TC1279, respectively).  Note that the resolution remains more or less constant at 10km and 8km, respectively, as the latitude varies.  The corresponding curves for the N1024 (TCO1023) and N1280 (TCO1279) octahedral grids are shown by the dashed and full blue lines, respectively.  The resolution for the N1280 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 are the regular Gaussian grids at N1024 (black dashed line) and N1280 (black full line).

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 octahedral grid (right) on the surface of the sphere

 

 

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Section

Gaussian grid descriptions

Descriptions of the Gaussian grids introduced for the planned horizontal resolution upgrade at IFS cy41r2 and used for HRES and ENS are available:

The descriptions provide the latitude values and the number of longitude points at each latitude for both the original and octahedral reduced Gaussian grids.

The number of points at each latitude is encoded as the PL array in the Grid description section of the GRIB header of a grid point field.  This is accessible with grib_api as the pl key.

 As of grib_api 1.14.0, a new computed key isOctahedral is introduced which allows users to query the grid type. For an octahedral grid, isOctahedral=1; otherwise, isOctahedral=0.

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Section

Background

Spectral representation of the IFS

The IFS uses a spectral transform method to solve numerically the equations governing the spatial and temporal evolution of the atmosphere.  The idea is to fit a discrete representation of a field on a grid by a continuous function.  This is achieved by expressing the function as a truncated series of spherical harmonics:

Mathdisplay
\begin{equationeqnarray*}
A(\lambda,\mu,\eta,t) & = & \sum_{l=0}^{\mbox{T}} \sum_{|m|\leq l}^{\mbox{T}}  \psi_{lm}(\eta,t) Y_{lm}(\lambda,\mu)
\end{equation*} & = &  \sum_{l=0}^{\mbox{T}} \sum_{|m|\leq l}^{\mbox{T}}  \psi_{lm}(\eta,t) P_{l}^{m}(\mu) e^{im\lambda}
 \end{eqnarray*}

where μ = sinθ with λ  the where μ = sinθ with λ  the longitude and θ the latitude of the grid point, T is the spectral truncation number and Y lm are the spherical harmonic functionstruncation number and Y lm are the spherical harmonic functions which are products of the associated Legendre polynomials,

Mathinline
P_{l}^{m}(\mu)
and the Fourier functions,
Mathinline
e^{im\lambda}.
The spectral coefficients ψlm are computed from the discrete values known at each point of a Gaussian grid on the sphere by

  • a Fast Fourier Transform in the zonal direction followed by
  • a slow/fast Legendre transform in the meridional direction.

At each time step in the IFS:

  • derivatives, semi-implicit correction and horizontal diffusion are computed in spectral space;
  • explicit dynamics, semi-Lagrangian advection and physical parametrizations are computed in grid point space.

The representation in grid point space is on the Gaussian grid.  The grid point resolution is determined by the spectral truncation number, T.

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Section

Relationship between spectral truncation and grid point resolution - linear, quadratic and cubic grids

The relationship between the spectral resolution, governed by the truncation number T, and the grid resolution depends on the number of points on the grid at the equator, 4N, at which the shortest wavelength field is represented:

linear grid:  each wavelength is represented by 2 grid points → 4N

Mathinline
\simeq
 2(TL + 1)

quadratic grid: each wavelength is represented by 3 grid points → 4N 

Mathinline
\simeq
3(TQ + 1)

cubic grid: each wavelength is represented by 4 grid points → 4N 

Mathinline
\simeq
4(TC + 1)

Until the implementation of IFS cycle 18r5 on 1 April 1998, the IFS used a quadratic grid. The introduction of the two-time level semi-Lagrangian numerical scheme at IFS cycle 18r5 made possible the use of a linear Gaussian grid reflected by the TL notation.  The linear grid has been used since then, up to and including IFS cycle 41r1. At IFS cycle 41r2  For the planned resolution upgrade, the cubic representation is used with the notation TC used to indicate the spectral truncation.

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Section

Increasing the horizontal resolution

The relationship between the spectral truncation, T, the number of grid points used to represent the shortest wave (i.e. linear, quadratic or cubic) and the grid point resolution, N, allows for three possible approaches for increasing the horizontal resolution:

  1. increase the number of wave numbers in the spectral representation but keep the same Gaussian grid by reducing the number of grid points used to represent the shortest wave (i.e., increase T with TQ →TL keeping N constant);
  2. increase the number of wave numbers in the spectral representation and the Gaussian grid resolution but keep the number of grid points used to represent the shortest wave constant (i.e. increase T and increase N).
  3. keep the number of wave numbers in the spectral representation constant and increase the Gaussian grid resolution by increasing the number of grid points used to represent the shortest wave (i.e., TL →TC, and increase N).
Note
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The planned horizontal resolution upgrade at IFS cycle 41r2 is achieved by:

  • increasing the Gaussian grid resolution by keeping the spectral truncation constant but representing the shortest wave by four grid points (use the cubic representation);
  • introducing a new form of the reduced Gaussian grid - the octahedral grid.

The notation TCO (CO - Cubic Octahedral)is used to indicate the corresponding spectral truncation.

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Section

Frequently asked questions

Will the change to the octahedral grid affect me if I use regular lat-lon data ?

No, users of regular lat-lon data will be unaffected by the change of model grid.  They will, however, benefit from the increase of the model horizontal resolution.

Will ECMWF make data available on the original regular and reduced Gaussian grids ?

Yes, users will still be able to request data, both in dissemination and MARS, of the original regular and reduced Gaussian grids. Note, however, that this will be interpolated from the values on the original model grid.See also I make computations involving flux parameters or accumulated fields (for example, to de-accumulate precipitation) and am advised to work on the model grid: which grid should I use ?

I use point data (e.g., for meteograms, vertical profiles, etc) - what do I need to do ?

Users of point data should note that the coordinates of the nearest grid point will have changed.  Users should take particular care for coastal points for which the nearest grid point may have changed from a land point to a sea point or vice versa.

Are the new land-sea mask and orography for the octahedral grid available ?

Yes, the new land-sea masks and orography fields for HRES at TCO1279 (N1280), ENS Leg A at TCO639 (N640) and ENS Leg B TCO319 (N320) are available for download:

I use the orography in spectral representation - will I be affected ?

Although the spectral resolution for HRES remains constant, the spectral orography has changed.  If you have this as a static file then this should be updated with the new version.

Do I need to upgrade the version of GRIB API I use in order to decode data on the octahedral grid ?

Version 1.12.3 of grib_api can decode fields on the octahedral grid correctly.  As of grib_api 1.14.0, a new computed key isOctahedral is introduced which allows the grid type to be queried. For the octahedral grid, isOctahedral=1; otherwise, isOctahedral=0.

Can GRIBEX decode data on the octahedral grid ?

GRIBEX is no longer supported by ECMWF and will therefore not be upgraded to support the octahedral grid.

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I make computations involving flux parameters or accumulated fields (for example, to de-accumulate precipitation) and am advised to work on the model grid:  which grid should I use ?

For performing computations with accumulated fields, users are advised to request data on the octahedral grid.

Is there any change to the vertical resolution

at IFS cycle 41r2

as part of the planned resolution upgrade ?

No, only the horizontal resolution is increased.  The vertical resolution remains at L137 for HRES and L91 for ENS.

What will happen if I retrieve

IFS cycle 41r2

data from MARS using grid=av ?

Users retrieving data from MARS with the keyword, grid=av ("archived value") will retrieve data on the model grid.  For data from IFS cycle 41r2 the upgraded model this will be the octahedral grid.

What will happen if I retrieve

IFS cycle 41r2

data from MARS using grid=1280 ?

This behaviour is unchanged. By default, users retrieving data from MARS with the keyword, grid=1280 will retrieve data on the regular N=1280 Gaussian grid. 

Will ERA-Interim fields also use the cubic octahedral grid ?

No, the horizontal resolution upgrade applies only to ECMWF HRES and ENS operational forecasts, including the monthly extension. It will affect the additional runs in support of the Optional Programme for Boundary Conditions (BC).

Will the ECMWF System 4 Seasonal Forecasts (SEAS) also use the octahedral grid ?

No, the horizontal resolution upgrade applies only to ECMWF HRES and ENS operational forecasts, including the monthly extension.