Examination of targeting methods in a simplified setting

The effectiveness of 2 methods for targeting observations is examined using a T21 L3 QG model in a perfect model context. Target gridpoints are chosen using the pseudo-inverse (the inverse composed of the first three singular vectors only) and the quasi-inverse or backward integration (running the t angent equations with a negative lime-step). The effectiveness of a target is measured by setting the analysis error to zero in a region surrounding t he target and noting the impact on the forecast error in the verification r egion. In a post-time setting, when the targets are based on forecast error s that are known exactly, both methods provide targets that are significant ly better than targets chosen at random within a broad region upstream of t he verification region. When uncertainty is added to the verifying analysis such that the forecast error is known inexactly, the pseudo-inverse target s still perform Very well, while the backward integration targets are degra ded. This degradation due to forecast uncertainty is especially significant when the targets are a function of height as well as horizontal position. When an ensemble-forecast difference is used in place of the inexact foreca st error, the backward integration targets may be improved considerably. Ho wever, this significant improvement depends on the characteristics of the i nitial-time ensemble perturbation. Pseudo-inverse targets based on ensemble forecast differences are comparable to pseudo-inverse targets based on exa ct forecast errors. Targets based on the largest analysis error are also fo und to be considerably more effective than random targets. The collocation of the backward integration and pseudo-inverse targets appears to be a good indicator of target skill.