Below are plots of the virtual temperature observation increment and analysis increment. These are the observation-first guess differences and analysis-first guess differences, interpolated to the horizontal and vertical location of the observation. The observation increments show that the observations are six to eight degrees colder than the guess in the rain band and mostly one to three degrees colder south of the rain band. The analysis increments show that the analysis is around four to five degrees cooler than the first guess along most of the approach. Thus the analysis moved more than halfway toward the coldest aircraft observations despite having the good radiosonde data. This is because there were a large number of aircraft observations pulling the analysis toward colder temperatures and because the observations corroborated each other enough to avoid being treated as bad data.
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The variation of analysis increments shown is mostly due to altitude. The analysis increments are nearly uniform on horizontal slices covering the area on these plots, but are smaller (less negative) at levels below 700 hPa. Recall from the flight tracks that the planes descended after turning towards the south.
Why are the analysis increments so smooth while the data clearly show a sharp gradient?
Because 3D-VAR analyses assume that when the analysis corrects the first guess, that correction applies
over a broad region. The idea is that if the forecast serving as the first guess has an error in one place,
then it probably has a similar error in another place some distance away. Statistics of forecast error or
forecast uncertainty are generally used to determine the distance through which these corrections are
correlated in the analysis and also the shape of that influence. In the Eta model, 700 hPa temperatures
have a correlation length of 160 km, meaning observations influence the analysis over a circle around
160 km. This is more than seven times the model grid spacing, ensuring a smooth analysis the model
can handle. The correlation length is different for different variables and at different levels, but it
is assumed essentially uniform in all directions. The technical jargon for this is "isotropic background
error covariances". The primary practical effect is to smear mesoscale features in all directions. In this
case it resulted in a large cold blob in the analysis.
What can be done to make an analysis now like 
into an analysis more like 
?
Allowing the observation influence to extend a long distance parallel to
a feature's orientation and only a short distance across its short axis could
enable the analysis to more realistically capture features only partially sampled
by observations. For instance, what if the observation increments in this case
were spread only in the direction parallel to the radar echoes? The NCEP Environmental
Modeling Center is developing a method like this. The idea is to allow observation
increments to spread their influence mostly along instead of across isentropes
and/or streamlines. Other criteria will be tested too. It probably won't be
ready until at least late 2002. Other adaptive methods are being developed elsewhere.
One method made the cover of the recent Weather Analysis and Forecasting conference
preprint volume, showing one observation causing the analysis to shift the location
of a front instead of smearing the change uniformly. It used ensembles, allowing
greater analysis changes in regions of higher forecast spread.
Ultimately, the ability to make good model objective analyses of mesoscale features will depend on the success of these efforts. Even then there will be shortcomings and limitations, leaving room for the attentive and knowledgable human forecaster to improve on the model.