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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. 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.
The table below summarizes the relationship between spectral resolution, gridpoint resolution and the recommended timestep for optimum performance.
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\begin{table}[t]
\caption{Spectral and grid horizontal resolutions with recommended timestep}\label{tab:spectral_res}
% this should match the resolutions of the climate data provided by OpenIFS.
% see bin/gaussgr for further definitions of the grids.
% 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):
% 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.
\begin{center}
\begin{tabular}{lllcl}
\tophline
Truncation & Grid & Spacing at Eq. & Timestep (mins) & Application \\
\middlehline
T$_l$1279 & N640 & 16km / 0.1406$\degree$ & 10 & Operational forecast resolution \\
T$_l$1023 & N512 & 20km / 0.1758$\degree$ & 10 & - \\
T$_l$799 & N400 & 25km / 0.225$\degree$ & 12 & - \\
T$_l$639 & N320 & 31km / 0.28125$\degree$ & 15 & ERA 5 high resolution \\
T$_l$511 & N256 & 39km / 0.352$\degree$ & 15 & - \\
T$_l$399 & N200 & 50km / 0.45$\degree$ & 20 & Operational ensemble resolution (day 1-9) \\
T$_l$319 & N160 & 63km / 0.5625$\degree$ & 20 & Operational ensemble resolution (day 10 on); ERA 5 ensemble \\
T$_l$255 & N128 & 78km / 0.703$\degree$ & 45 & ERA Interim \\
T$_q$213 & N160 & 63km / 0.5625$\degree$ & 20 & - \\
T$_l$159 & N80 & 125km / 1.125$\degree$ & 60 & ERA 40 \\
T$_q$106 & N80 & 125km / 1.125$\degree$ & 60 & - \\
T$_l$95 & N48 & 209km / 1.875$\degree$ & 60 & - \\
T$_q$63 & N48 & 209km / 1.875$\degree$ & 60 & - \\
T$_q$42 & N32 & 310km / 2.813$\degree$ & 30 & - \\
T$_q$21 & N16 & 626km / 5.625$\degree$ & 30 & Development/testing only \\
\bottomhline
\end{tabular}
\end{center}
\belowtable{N.B. T21 and T42 use the Eulerian dynamical core and a regular Gaussian grid. T63 and above use the reduced Gaussian grid. T$_l$ denotes a linear grid, T$_q$ denotes a quadratic grid.} % table footnotes
\end{table} |
| Truncation | Grid | Spacing at Equator | Recommended timestep (min) | Application |
|---|---|---|---|---|
| Tl1279 | N640 | 16km / 0.1406o | 10 | Operational forecast resolution (40r1) |
Tl1023 | N512 | 20km / 0.1758o | 10 | - |
| Tl799 | N400 | 25km / 0.225o | 12 | - |
| Tl639 | N320 | 31km / 0.28125o | 15 | ERA-5 high resolution |
| Tl511 | N256 | 39km / 0.352o | 15 | - |
| Tl399 | N200 | 50km / 0.45o | 20 | Operational ensemble resolution |
| Tl319 | N160 | 63km / 0.5625o | 20 | ERA-5 ensemble |
| Tl255 | N128 | 78km / 0.703o | 45 | ERA-Interim |
| Tq213 | N160 | 63km / 0.5625o | 20 | - |
| Tl159 | N80 | 125km / 1.125o | 60 | ERA-40 |
| Tq106 | N80 | 125km / 1.125o | 60 | - |
| Tl95 | N48 | 209km / 1.875o | 60 | - |
| Tq63 | N48 | 209km / 1.875o | 60 | - |
| Tq42 | N32 | 310km / 2.813o | 30 | Development/testing only |
| Tq21 | N16 | 626km / 5.625o | 30 | Development/testing only |
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Note that a linear grid allows a higher spectral truncation for the same number of gridpoints as a quadratic grid. Linear and quadratic in this sense means enough gridpoints are available to compute the linear and quadratic terms in the equations respectively.
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this table is taken from the OpenIFS 40r1 paper. | ||
\begin{table}[t] \caption{Spectral and grid horizontal resolutions with recommended timestep}\label{tab:spectral_res} % this should match the resolutions of the climate data provided by OpenIFS. % see bin/gaussgr for further definitions of the grids. % 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): % 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. \begin{center} \begin{tabular}{lllcl} \tophline Truncation & Grid & Spacing at Eq. & Timestep (mins) & Application \\ \middlehline T$_l$1279 & N640 & 16km / 0.1406$\degree$ & 10 & Operational forecast resolution \\ T$_l$1023 & N512 & 20km / 0.1758$\degree$ & 10 & - \\ T$_l$799 & N400 & 25km / 0.225$\degree$ & 12 & - \\ T$_l$639 & N320 & 31km / 0.28125$\degree$ & 15 & ERA 5 high resolution \\ T$_l$511 & N256 & 39km / 0.352$\degree$ & 15 & - \\ T$_l$399 & N200 & 50km / 0.45$\degree$ & 20 & Operational ensemble resolution (day 1-9) \\ T$_l$319 & N160 & 63km / 0.5625$\degree$ & 20 & Operational ensemble resolution (day 10 on); ERA 5 ensemble \\ T$_l$255 & N128 & 78km / 0.703$\degree$ & 45 & ERA Interim \\ T$_q$213 & N160 & 63km / 0.5625$\degree$ & 20 & - \\ T$_l$159 & N80 & 125km / 1.125$\degree$ & 60 & ERA 40 \\ T$_q$106 & N80 & 125km / 1.125$\degree$ & 60 & - \\ T$_l$95 & N48 & 209km / 1.875$\degree$ & 60 & - \\ T$_q$63 & N48 & 209km / 1.875$\degree$ & 60 & - \\ T$_q$42 & N32 & 310km / 2.813$\degree$ & 30 & - \\ T$_q$21 & N16 & 626km / 5.625$\degree$ & 30 & Development/testing only \\ \bottomhline \end{tabular} \end{center} \belowtable{N.B. T21 and T42 use the Eulerian dynamical core and a regular Gaussian grid. T63 and above use the reduced Gaussian grid. T$_l$ denotes a linear grid, T$_q$ denotes a quadratic grid.} % table footnotes \end{table} |
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