EMC Targetting Obs Project
During the FASTEX field experiments in January-February 1997, NCEP provides experimental guidance for upstream observations. In order to improve 36-60 hours weather forecasts over the main observing area (also called verification area, 20-0W, 45-55N), sensitivity calculations are carried out to identify upstream areas where extra observations prior to initial time can have a beneficial impact on the quality of forecasts at final time in the verification area. So that the sensitivity calculations can be used in real time they must be prepared at least 24 hours in advance.
At NCEP, a singular value decomposition (SVD) technique is used for the sensitivity calculations (Bishop and Toth, 1996) . This technique is based on an ensemble of nonlinear forecasts. The SVD is carried out in the subspace of the 14 NCEP ensemble forecasts, given at the targeting time (usually at 24-hour lead time, also called initial time level) and at verification time (usually somewhere between 36 and 96 hours, also called final time level). For the computations, the 850, 500 and 250 hPa streamfunction field is used. Linear combinations of the ensemble perturbations are sought that maximize the perturbaions at verification time while keeping the initial perturbations fixed at an estimated level of analysis uncertainty. The square root of the eigenvalue of the above calculation is the amplification marked on the sensitivity maps.
To find the most sensitive upstream area, we perform a series of SVD calculations where we reduce the initial perturbations in a 225 km radius "observing" area to a low level (smallest estimated uncertainty on the earth) to see how much (if any) the final perturbation amplitudes are affected. A new SVD is carried out every 10 degrees latutide and longitude and the eigenvalues (normalized by the background amplification) are plotted as sensitivity fields. For further details, click here.
Sensitivity field (contour lines). The numbers (X) at any gridpoint show the following: if, due to extra observations taken at targeting time in the 1000 km radius of the gridpoint, the initial error is reduced to the lowest analysis error level on the earth, the final expected error variance in the verification region is reduced to the X fraction of the value expected without having the extra observations.
Tendency in sensitivity (color shades overlaid on sensitivity charts). The shades at any grid point indicate the change in sensitivity over a 24-hour period centered at targeting time.
Ensemble mean forecast (contour lines). An unweighted mean of the 17-member NCEP
Ensemble spread (color shades overlaid on ensemble mean forecasts). The numbers show the standard deviation around the ensemble mean in the 17-member NCEP ensemble.
An advantage of the SVD technique is that it is performed in the subspace of the ensemble forecasts, which represent realistic perturbations (expected errors). A potential disadvantage is, however, that the number of perturbations is very limited (7 pairs of forecasts currently at NCEP). In a limited sample, from time to time far-field correlations among the perturbations may show up by chance, that in turn may lead to spurious areas of sensitivity, far from the real sensitive area. In our limited experience, this may happen when the amplification (indicated in title of sensitivity maps) is relatively low and no large errors develop in the verification region - a case when sensitivity calculations would not be used anyway.
By inspection of a series of sensitivity charts one can usually identify an area of sensitivity (a local minimum) that with targeting time shifting closer to verification time, reaches the vicinity of the verification area. This area can be considered as a real sensitive region. The tendency charts (in color) overlaid upon the sensitivity maps can help to identify this region: one can usually see a deepening tendency (yellow/red/white colors) associated with the movement and development of this sensitivite area with shifting targeting time. Potentially spurious areas of sensitivity do not exhibit continuous deepening/development into the direction of the verification region.
These products have been developed in collaboration with Craig Bishop (Penn State University), Chris Snyder (NCAR/MMM) and Kerry Emanuel (MIT).
Istvan Szunyogh at firstname.lastname@example.org or
Zoltan Toth at Zoltan.Toth@noaa.gov
Timothy Marchok at email@example.com