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filtered out. The equations that resulted from Charney's filtering approximations
were essentially those of the quasi-geostrophic model. Thus, Charney's approach
utilized the conservative properties of potential vorticity. A special case of this
model, the
equivalent barotropic model
, was used in 1950 to make the first suc-
cessful numerical forecast.
This model provided forecasts of the geopotential near 500 hPa. Thus, it did not
forecast “weather” in the usual sense. It could, however, be used by forecasters as
an aid in predicting the local weather associated with large-scale circulations. Later
multilevel versions of the quasi-geostrophic model provided explicit predictions
of the surface pressure and temperature distributions, but the accuracy of such pre-
dictions was limited due to the approximations inherent in the quasi-geostrophic
model.
With the development of vastly more powerful computers and more sophis-
ticated modeling techniques, numerical forecasting has now returned to models
that are quite similar to Richardson's formulation, and are far more accurate than
quasi-geostrophic models. Nevertheless, it is still worth considering the simplest
filtered model, the barotropic vorticity equation, to illustrate some of the technical
aspects of numerical prediction in a simple context.
13.2
FILTERING METEOROLOGICAL NOISE
One difficulty in directly applying the unsimplified equations of motion to the
prediction problem is that meteorologically important motions are easily lost in
the noise introduced by large-amplitude sound and gravity waves, which may arise
as a result of errors in the initial data, and then can spuriously amplify to dominate
the forecast fields. As an example of how this problem might arise, consider the
pressure and density fields. On the synoptic scale these are in hydrostatic balance to
a very good approximation. As a consequence, vertical accelerations are extremely
small. However, if the pressure and density fields were determined independently
by observations, as would be the case if the complete dynamical equations were
used, small errors in the observed fields would lead to large errors in the computed
vertical acceleration simply because the vertical acceleration is the very small
difference between two large forces (the vertical pressure gradient and buoyancy).
Such spurious accelerations would appear in the computed solutions as high-speed
sound waves of very large amplitude. In a similar fashion, errors in the initial
horizontal velocity and pressure fields would lead to spuriously large horizontal
accelerations, as horizontal acceleration results from the small difference between
Coriolis and pressure gradient forces. Such spurious horizontal accelerations would
excite both sound and gravity waves.
In order to overcome this problem, either the “observed” fields must be modified
systematically to remove unrealistic force imbalances or the prediction equations
