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The figure at left is the
anomaly correlation of the surface
pressure maps as a function of time since the model was initialized
with the Gaussian bump (not with any additional random number) to the
otherwise balaned velocity field. The 0.5 degree resolution integration
is taken as the "truth" at left. Hence the integrations at each of the
other resolutions are compared to the half degree integration. The maps
above illustrate how resolution sharpens the high and low pressure
centers. The Anomaly
Correlation is a measure of how well the patterns match. In time, we
expect the models to diverge from one another because the solutions to
the model equations are unstable. The anomaly correlation gives us one
measure of how long it takes for the information contained in the
initial conditions to be forgotten. Here where we compare lower
resolution to higher resolution integrations, we also see how errors
from failing to capture the finest scales also reduces our
predictability. It appears that there is still predictability after 30
days, which surprisingly long. I think this is because the Gaussian
bump was quite small and was not a fast growing mode. The figures below at left is the anomaly correlation of the 850hPa temperature and at right is the 500hPa height. All maps had the zonal mean removed first, which was not that important for the surface pressure, but was critical for the other two fields. |
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| The 226 hPa wind ensemble mean
of all 9 ensemble members at 2 deg resolution that Cecilia ran in
advance is shown below at left for day 20. The black lines mark the
northern hemisphere jet maximum along latitudes in the northern
hemisphere. The dark red filled region is above 60m/s and the contour
inteval is 10m/s. The figure below is of the individual ensemble
members. Note where the black lines lie on top of one another and where
they are widely seperated. This indicates how large magnitude events
are generally more predictable than flimsy ones. |
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The figures at left are the
anomaly correlation of the 226 hPa zonal wind (with zonal mean removed)
for the 14 ensemble members at 2 deg resolution that we ran as a class.
Each ensemble member is made distinct by initialzing with the Gaussian
bump plus a small random number. The upper figure has the "truth" equal
to
the 0.5 deg integration and the lower has the truth equal to the 2
deg run with no random number added to it. Note that the anomaly
correlation tends to be larger in the latter because the error does not
include errors associated with failing to resolve the fine scales. The
red line in either case is the average (ensemble mean) of the blue
lines. The black dashed line is the anomaly correlation of the average
(ensemble mean) taken first before correlating with the "truth". Hence
in the former the correlation is taken 14 times and then averaged and
in the former the average is taken first and then one correlation is
computed. This shows the ensemble mean has less error usually than
individual members. The figures below are the standard deviation with everything else as in the previous two panels. The left one is compared to 0.5 deg and the right is compared to 2 deg. |
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