Convergence analysis: The DWD model GME



Test design
Zonal wind
Eddy heat flux
Eddy momentum flux
Eddy kinetic energy

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  Test design

The current global weather prediction model GME of the German Weather Service (DWD, Offenbach, Germany) is based on a spherical icosahedral grid structure. This grid consists of a specific number of triangles which is listed in the table below. The grid points (as well as all model variables, Arakawa-A grid) are located at the vertices of each triangle so that the actual number of grid points per model level is shown in column 2. The corresponding grid point distances are indicated in column 4 and 5.
Resolution ni
# Grid points per level
# Triangles per level
Minimum grid point distance
Maximum grid point distance
Time step
ni = 24
294 km
347 km
1100 s
ni = 32
220 km
263 km
800 s
ni = 48
147 km
174 km
550 s
ni = 64
110 km
132 km
400 s
Characteristic features of the DWD model GME.
Four GME dynamical core runs at four different horizontal resolutions have been performed to test the model's sensitivity to an increased model resolution. Each model run covers a time period of 1440 days. A 900-day sequence taken during this time period has been used to compute the time-mean values which are good representatives of the model's climate. In addition to the time average, the data are zonally averaged (over one latitude). This extracts the meridional (north-south) oriented model circulation.

Some of the model results are shown below. The results indicate that the model GME is sensitive to an increased horizontal resolution but seems to converge at high resolutions. The next section discusses this model behavior in greater detail. There, the time-mean zonal-mean zonal wind, the Eddy heat flux, the Eddy momentum flux and the Eddy kinetic energy are presented. Each figure is linked to an underlying figure that is bigger in size and can be used to examine the structures more detailed.

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  GME convergence analysis with respect to the horizontal resolution

  Zonal wind [u]

The figures below show the time-mean zonal-mean zonal wind patterns at four different horizontal resolutions (as indicated). The zonal wind structures reveal that the wind pattern is sensitive to an increased resolution. This becomes obvious when looking at the upper atmosphere near the equator and the shape of the jet streams in the midlatitudes. With an increased resolution the jets are slightly shifted to the poles and become narrower whereas the strength of the jets nearly remain constant. In addition, the wind pattern in the equatorial stratosphere varies with resolution. The typical band of easterlies extends with increased resolution and reaches wind speeds up to -30m/s at GME (ni=48) and GME (ni=64) resolution. This indicates that the zonal wind pattern seems to converge when the resolution becomes fine enough.
Zonal wind (m/s), GME (ni=24)Zonal wind (m/s), GME (ni=32)
Zonal wind (m/s), GME (ni=48)Zonal wind (m/s), GME (ni=64)
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  Eddy heat flux [v'T']

The Eddy heat flux demonstrates one of the important energy transport mechanisms that establish the global model circulation. This co-variance term indicates that heat is transported from the equatorial heat surplus regions to the poles where the heat budget becomes negative. As can be seen in the figures below the heat transfer increases with increased resolution. Especially the two transport maxima in the upper and lower atmosphere in midlatitudes become stronger and converge at high resolutions.

Eddyy heat flux (Km/s), GME (ni=24)Eddy heat flux (Km/s), GME (ni=32)
Eddy heat fleux (Km/s), GME (ni=48)Eddy heat flux (Km/s), GME (ni=64)
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  Eddy momentum flux [u'v']

In addition to the Eddy heat flux, the Eddy momentum flux is the second energy transfer mechanism that establishes the model circulation. This co-variance term describes to which degree zonal momentum gets transported by the meridional (north-south) wind in order to fulfill the global momentum balance. The momentum flux is characterized by one maximum in each hemisphere that lies close to the flux convergence zone around 50 degrees north and south. The momentum transport only shows little sensitivity to an increased resolution. The strength of the fluxes remains almost constant and the maxima are slightly shifted towards the poles with increased resolution.
Eddy momentum flux, GME (ni=24)Eddy momentum flux, GME (ni=32)
Eddy momentum flux, GME (ni=32)Eddy momentum flux, GME (ni=64)
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  Eddy kinetic energy [u'2+v'2]

In contrast to the Eddy momentum flux, the Eddy kinetic energy depends strongly on the horizontal resolution which is displayed in the figures below. The amount of kinetic energy increases a great deal with increased resolution and almost doubles when comparing the GME (ni=24) and the GME (ni=64) model run. The kinetic energy represents the wave activity in the model. Higher kinetic energy values demonstrate that more intense high and low pressure systems travel along the typical wave paths in the midlatitudes. The kinetic energy pattern has not yet converged at the resolutions shown below but the differences tend to become less significant when comparing the two finest model resolutions GME (ni=48) and GME (ni=64).
Eddy kinetic energy, GME (ni=24)Eddy kinetic energy, GME (ni=32)
Eddy kinetic energy, GME (ni=48)Eddy kinetic energy, GME (ni=64)
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