Ensemble Adaptive Data Assimilation Techniques Applied to Land-Falling North American Cyclones - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 558

Fig. 23.6 Value of maximum variance reduction of the response function normalized by the
response function variance for all cyclones for observations of ( a ) temperature, ( b ) pressure,
( c ) zonal wind, and ( d ) meridional wind
It is also useful to describe targeting impacts in terms of the estimated variance
reduction relative to the response function variance. This can be done by dividing
the maximum variance reduction values by the original response function variance
resulting in what is referred to here as normalized variance reduction. In this
way, it is possible to reveal cases where observations might reduce a substantial
fraction of the original response function variance even if the actual variance
reduction values themselves (as shown in Fig. 23.5 ) are quite small. Figure 23.6
shows the normalized maximum values of estimated variance reduction, and reveals
the percentage of response function variance that could be reduced through the
assimilation of observations. In general, pressure observations show an estimated
34 % variance reduction averaged over all cyclones, which is larger than both wind
(23 %) and temperature (12 %). As with the absolute values in Fig. 23.5 ,thetrend
among all variables remains the same. Figure 23.7 depicts both the normalized and
absolute maximum values of variance reduction with regard to temperature for all
cyclones. The trend for both the normalized and absolute values is generally similar
for all cyclones, although there are localized differences in the plots. For example,
the peaks in the normalized and non-normalized values between cyclone number 30