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In-Depth Information
x
obs
J
o
analysis
J
o
obs
corrected
forecast
J
o
x
b
obs
J
b
x
a
previous
forecast
J
o
obs
3z
6z
9z
12z
16z
time
assimilation window
Fig. 13.8
The ECMWF data assimilation process. Vertical axis indicates the value of an atmospheric
field variable. The curve labeled x
b
is the first guess or “background” field, and x
a
is the
analysis field. J
b
indicates the misfit between the background and analysis fields. Stars
indicate the observations, and J
0
designates the “cost function,” a measure of the misfit
between the observations and the analysis, which along with J
b
is minimized to produce
the best estimate of the state of the atmosphere at the analysis time (Courtesy ECMWF.)
13.8
PREDICTABILITY AND ENSEMBLE PREDICTION SYSTEMS
For short-range forecasts (1 or 2 days) of the midlatitude 500-hPa flow, it is possible
to neglect diabatic heating and frictional dissipation. It is important, however, to
have good initial data in the region of interest because on this short time scale
forecasting ability depends primarily on the proper advection of the initial vorticity
field. As the length of the forecast period increases, the effects of propagation of
influences from other regions and changes due to various sources and sinks of
momentum and energy become increasingly important. Therefore, the flow at a
point in the middle-latitude troposphere will depend on initial conditions for an
increasing domain and on accurate representation of various physical processes
as the period of the forecast is extended. In fact, according to the estimate of
Smagorinsky shown in Fig. 13.9, for periods greater than 1 week it is necessary to
know the initial state of the entire global atmosphere from the stratosphere to the
surface, as well as the state of the upper layers of the oceans.
However, even if an ideal data network were available to specify the initial
state on a global scale, there still would be a time limit beyond which a useful
