Singular Vectors, Metrics, and Adaptive Observations.

TLDR: In this paper, a third use of singular vectors is proposed as part of a strategy to target adaptive observations to “sensitive” parts of the atmosphere using unmanned aircraft, though calculations in this paper are motivated by the upstream component of the Fronts and Atlantic Storm-Track Experiment.

Abstract: Singular vectors of the linearized equations of motion have been used to study the instability properties of the atmosphere–ocean system and its related predictability. A third use of these singular vectors is proposed here: as part of a strategy to target adaptive observations to “sensitive” parts of the atmosphere. Such observations could be made using unmanned aircraft, though calculations in this paper are motivated by the upstream component of the Fronts and Atlantic Storm-Track Experiment. Oceanic applications are also discussed. In defining this strategy, it is shown that there is, in principle, no freedom in the choice of inner product or metric for the singular vector calculation. However, the correct metric is dependent on the purpose for making the targeted observations (to study precursor developments or to improve forecast initial conditions). It is argued that for predictability studies, where both the dynamical instability properties of the system and the specification of the opera...