84th AMS Annual Meeting

Wednesday, 14 January 2004: 9:15 AM
Analysis errors decomposed into singular vectors
Room 6A
C. Snyder, NCAR, Boulder, CO; and G. Hakim
Singular vectors (SVs), particluarly those based on the energy norm, are used both in initializing ensemble forecasts and in predictability studies. Ideally, the calculation of the SVs would employ the analysis error covariance norm at the initial time but the energy norm is often used as a more practical substitute.

In the simple context of the Eady model, we consider a classical cyclogenetic perturbation, consisting of an upper-level wave with no potential vorticity perturbation in the troposphere, as a typical analysis error that may then be decomposed by its projection onto each energy SV. Viewed in terms of the energy SVs, the smooth vertical structure of this perturbation, as well as its evolution, results from strong cancellation between the growing and decaying SVs, both of which are highly structured and tilted in the vertical.

This result may be understood by noting that the use of the energy norm implicitly assumes initial perturbations with second-order statistics given by the covariance matrix whose inverse defines the energy norm. Unlike the "typical" perturbation we chose above, perturbations with those statistics have large variance of potential vorticity in the troposphere and have fine vertical structure. We will also present evidence from analysis differences and from experiments with an ensemble Kalman filter in a simple GCM, that the "typical" perturbation is, in fact, broadly representative of analysis errors.

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