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Relationship between spectral and grid resolution

IFS is a model of two resolutions: the spectral resolution determining the number of retained waves and the corresponding grid onto which these waves can be transformed. A greater spectral resolution can improve the forecast quality whilst reduced Gaussian grid resolutions can improve the efficiency of the model.

IFS model grids

IFS can make use of different latitude-longitude grids for the same spectral resolution. Each grid type offers different advantages and disadvantages.  A 'reduced' grid is one in which the number of gridpoints around each latitude circle is reduced as the poles are approached. A full grid, or 'regular' grid, has the same number of points around each latitude circle. The terms 'linear', 'quadratic' and 'cubic' refer to the number of gridpoints used to describe the shortest waves retained in spectral space. For example, linear grids use two gridpoints to describe the shortest wave, and so on.

A linear grid allows a higher spectral truncation for the same number of gridpoints as a quadratic or cubic grid. Linear and quadratic in this sense means enough gridpoints are available to compute the linear and quadratic terms in the equations respectively. Likewise a cubic grid has more gridpoints per spectral wavenumber and provides more gridpoints to describe the highest wavenumbers. However, aliassing of the quadratic (and cubic) terms in the model equations can result from using linear grids, which needs to be compensated for in the model formulation. A cubic grid removes aliassing and the need for additional filters.

For more information about IFS grids please see: OpenIFS: Gaussian grids and OpenIFS: Octahedral grid in the OpenIFS User Guide.

The following table describes the different grid types together with the filename extension used in the ifsdata filesnames (see: Download OpenIFS).

Linear reduced and Cubic Octahedral are by far the most commonly used, with cubic octahedral grids typically used for the higher resolutions.

Info

The cubic grids are only available in OpenIFS 43r3 and later. They were introduced in the IFS at cycle 41r2, operational March 2016.

Model timestep

The timestep depends on the horizontal resolution and the choice of the grid. ECMWF typically use a long a timestep as possible for efficiency reasons. However, there are times when this may result in some of the semi-Lagrangian trajectories going underground (messages can be seen in the model logfile), though generally this is not a problem.

Recommended maximum timesteps are given in the table below. Shorter timesteps can be used, though note that the model will not produce the exact same result between two forecasts with different timesteps.

Wave model grids

The ECMWF Wave Model, a component of IFS, uses a different grid to the atmospheric grid in IFS.

The wave model uses an irregular latitude-longitude grid. For such grids the distance between latitudes is set to a certain resolution in degrees, where the number of grid points per latitude is adjusted so that the actual distance between points on each latitude is roughly the same as the one between 2 consecutive latitudes.

There is an approximate match between the number of latitudes in the atmospheric grid and the wave model grid, it is still a good approximation to run the wave model on a slightly coarser grid in order to save overall cost during operational forecasts. Future developments of IFS will include a wave model grid that matches the IFS.

The table below summarises the wave model recommended grid (as used by ECMWF) for each atmospheric resolution. This is for information only, the wave initial files provided by ECMWF will already have this taken into account for the requested resolutions.


Supported spectral and horizontal grid resolutions

The table below summarizes the supported configurations of the IFS and the relationship between spectral truncation, atmosphere and wave model grids and the recommended timestep for optimum performance.


Info

Click in the column header to display the table according to that column.



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pageGrid and Resolution




Spectral truncationGrid
(lats pole to eq)		Grid typeResolution at equator
(npts at eq. / spacing)		Wave model
latitude spacing		Recommended
timestep (mins)

Application

Tco1279O1280cubic oct / _45136 / 8km / 0.070o0.125o7.5Operational forecast resolution (43r3)
Tl1279N640linear reduced / l_22560 / 16km / 0.141o0.25o10Operational forecast resolution (40r1)

Tl1023

N512linear reduced / l_22048 / 20km / 0.176o0.25o10-
Tco799O800cubic oct / _43216 / 12.5km / 0.112o0.125o12-
Tl799N400linear reduced / l_21600 / 25km / 0.225o0.36o12-
Tco639O640cubic oct / _42576 / 16km / 0.140o0.25o12Operational ensemble resolution (43r3)
Tl639N320linear reduced / l_21280 / 31km / 0.281o0.36o15ERA-5 high resolution
Tl511N256linear reduced / l_21024 / 39km / 0.352o0.50o15-
Tco399O400cubic oct / _41616 / 25km / 0.223o0.36o15-
Tl399N200linear reduced / l_2800 / 50km / 0.45o1.0o20Operational ensemble resolution (40r1)
Tco319O320cubic oct / _41296 / 31km / 0.278o0.36o15Seasonal system 5
Tl319N160linear reduced / l_2640 / 63km / 0.563o1.0o20ERA-5 ensemble
Tco255O256cubic oct / _41040 / 39km / 0.346o
0.50o20-
Tl255N128linear reduced / l_2512 / 78km / 0.703o1.0o45ERA-Interim; Seasonal system 4
Tq213

N160

quadratic reduced / _2640 / 63km / 0.563o1.0o20-
Tco199O200cubic oct / _4816 / 49km / 0.44o1.0o20-
Tco159O160cubic oct / _4656 / 61km / 0.55o1.0o20-
Tl159N80linear reduced / l_2320 / 125km / 1.125o1.5o60ERA-40
Tq106F80quadratic reduced / _2320 / 125km / 1.125o1.5o60-
Tco95O96cubic oct / _4400 / 100km / 0.9o1.0o30-
Tl95N48linear reduced / l_2192 / 209km / 1.875o3.0o60-
Tq63F48quadratic reduced / _2192 / 209km / 1.875o3.0o60-
Tq42F32quadratic regular / _full128 / 313km / 2.813o3.0o30Development/testing only
Tq21F16quadratic regular / _full64 / 626km / 5.625o3.0o30Development/testing only








Info
  • Grid type suffix refers to the file suffix used at the end of filenames for the OpenIFS/IFS climatology files. It is also used as an argument to the 'gaussgr' command, see 5 OpenIFS: Grid tools.
  • The 'cubic' grid rather than 'cubic octahedral' is not listed here as it's infrequently used, the suffix for these files is '_3'.
  • T21 and T42 use the Eulerian dynamical core and a regular Gaussian grid.
  • Tco denotes cubic octahedral grid, Tl denotes a linear grid, Tq denotes a quadratic grid.
  • Other resolutions not listed here may be provided with the OpenIFS climatology files.





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% this should match the resolutions of the climate data provided by OpenIFS.
% see  bin/gaussgr for further definitions of the grids.
% the wave model resolutions come from the prepIFS checks (see: fc.check)

% for resolution information, look at prepIFS defaults in:
% ~rdx/prepIFS.defaults/current/40r1/setup_fc/resolution
% gives (ignoring some resolutions, only including those for which we have climate files):

Look in /home/rd/rdx/data/ifs/rtable* to confirm no. of long pts at lats closest to eq (see Paul's message below).

%  T21,  _full, Eulerian dyn., 1800sec, 32x64
%  T42,  _full, Eul          , 1800sec, 64x128
%  T63,  _2   , Semi Lagr.   , 3600   , 96x192
%  T95,  l_2  , SL           , 3600   , 96x192
%  T106, _2   , SL?          , 3600   , 160x320 (LSLAG not set by 106.setup.save?)
%  T159, l_2  , SL           , 3600   , 160x320
%  T213, _2   , SL           , 1200   , 320x640
%  T255, l_2  , SL           , 2700   , 256x512
%  T319, l_2  , SL           , 1200   , 320x640
%  T399, l_2  , SL           , 1200   , 400x800
%  T511, l_2  , SL           , 900    , 512x1024
%  T639, l_2  , SL           , 900    , 640x1280
%  T799, l_2  , SL           , 720    , 800x1600
%  T1023, l_2 , SL           , 600    , 1024x2048
%  T1279, l_2 , SL           , 600    , 1280x2560
%
% _full, etc refer to the suffix on the model climate files, where _full mean regular (quadratic) Gaussian grid
% _2 means reduced regular grid, l_2 means reduced linear grid.

FOr 43r3, also look in the prepIFS default directory.
However, there is a discrepancy between the namfpd@NLON values in those files and the
formula on the octahedral grid page: Nlat = 4 x i + 16  where i=1,.. N.
For an O1280 grid (Tco1279) -> Nlat = 4 x 1280 + 16 = 5136. This doesn't match namfpd@NLON = 5120.
I've used the 4i+16 formula in working out the NLONeq values above for Tco grids.

Checking with Paul Dando (the oracle of all things grids...)

The formula for the number of longitude lines at latitude=i = 4*i + 16 (starting with i=1 nearest the pole) is definitely correct.  So the latitude nearest the equator for the O1280 grid has 4*1280 + 16 = 5136 longitude points.

In fact, you can check this in the NAMGRI namelist (read from, e.g. /home/rd/rdx/data/ifs/rtable_41279).  Here you will see that line nearest the pole has 20 points and those nearest the equator have 5136 points

My conclusion is, therefore, that namfpd has the wrong number for the octahedral grids.

Of course, I don't know what namfpd@NLON refers to in fullpos.  It could be that this is the number of longituide points on the full Gaussian grid (which is always 4*N) ?

Or perhaps it's just not been updated and still refers to the old-style reduced grids which did have 5120 points at the latitudes nearest the equator.

I hope that helps.







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