Optimal perturbations (also referred to as singular vectors; SV's) are those disturbances which amplify most rapidly on a given basic state over a finite time interval. SV's of linearized numerical weather prediction (NWP) models have been used to study the both amplification and predictability of midlatitude weather systems (e.g. SV's are used to determine sets of perturbations for initialization of ensemble forecasts). In addition, SV's have been used to identify data collection regions for the purposes of targetting adaptive observations.
Amplification of SV's is measured with respect to a predefined norm: the most commonly chosen norms have been streamfunction variance, total energy, kinetic energy, and enstrophy. Because the calculation of SV's is dependent on the choice of norm, different initial structures and subsequent evolutions are observed for different norms: For the Eady model, the initial structures for the total energy and streamfunction variance norms are characterized by highly tilted PV anomalies in the Eady model "troposphere." These structures are at odds with the observed distribution of PV in the troposphere - suggesting that these may be inapproproiate norms for the purposes of selecting ensemble perturbations for NWP models.
In this presentation, SV's for the Eady model are calculated and compared for the norms identified above. The evolutions of the streamfunction, potential vorticity, and perturbation wave activity fluxes are used to diagnose development. An interpretation of these varying structures and evolution is framed from the perspective of PV thinking. In addition alternative norms are proposed which yield more realistic initial structures.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics