Singular vectors (SVs) have been applied to cyclogenesis, to initializing ensemble forecasts, and in predictability studies. Ideally, the calculation of the SVs would employ the analysis error covariance norm at the initial time or, in the case of cyclogenesis, a norm based on the statistics of initial perturbations, but the energy norm is often used as a more practical substitute. To illustrate the role of the choice of norm, an upper-level wave with no potential vorticity perturbation in the troposphere is considered as a "typical" cyclogenetic perturbation or analysis error, and this perturbation is then decomposed by its projection onto each energy SV. All calculations are made, for simplicity, in the context of the quasigeostrophic Eady model (that is, for a background flow with constant vertical shear and horizontal temperature gradient). Viewed in terms of the energy SVs, the smooth vertical structure of the typical 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. A simpler picture, involving less cancellation, follows from decomposition of the typical perturbation into SVs based an alternative initial norm, which is developed using the relation between initial norms and the statistics of initial perturbations and the assumption that the initial perturbations are not dominated by interior potential vorticity. These results 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, perturbations with those statistics have large variance of potential vorticity in the troposphere and have fine vertical structure. Evidence from from dynamical influences on perturbations, from observations of cyclogenesis, and from data assimilation results all suggest the upper wave chosen as a typical perturbation is plausible both as a cyclogenetic perturbation and as an analysis error.

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