Examination of targeting methods in a simplified setting

The effectiveness of 2 methods for targeting observations is examined using a T21 L3 QG modelin a perfect model context. Target gridpoints are chosen using the pseudo-inverse (the inversecomposed of the first three singular vectors only) and the quasi-inverse or backward integration(running the tangent equations with a negative time-step). The effectiveness of a target is measuredby setting the analysis error to zero in a region surrounding the target and noting theimpact on the forecast error in the verification region. In a post-time setting, when the targetsare based on forecast errors that are known exactly, both methods provide targets that aresignificantly better than targets chosen at random within a broad region upstream of theverification region. When uncertainty is added to the verifying analysis such that the forecasterror is known inexactly, the pseudo-inverse targets still perform very well, while the backwardintegration targets are degraded. This degradation due to forecast uncertainty is especiallysignificant when the targets are a function of height as well as horizontal position. When anensemble-forecast difference is used in place of the inexact forecast error, the backward integrationtargets may be improved considerably. However, this significant improvement depends onthe characteristics of the initial-time ensemble perturbation. Pseudo-inverse targets based onensemble forecast differences are comparable to pseudo-inverse targets based on exact forecasterrors. Targets based on the largest analysis error are also found to be considerably moreeffective than random targets. The collocation of the backward integration and pseudo-inversetargets appears to be a good indicator of target skill.

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