Weather Regimes, Low-Frequency Oscillations, and Principal Patterns of Variability: A Perspective of Extratropical Low-Frequency Variability

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Abstract
The dynamical basis of extratropical low-frequency variability (LFV) is investigated using a quasigeostrophic model on a sphere with realistic Northern Hemisphere topography. The model is driven by Newtonian relaxation to an axisymmetric radiative equilibrium temperature. Two versions of the model are used: one with two vertical levels and horizontal T15 resolution and the other with five levels and T21 resolution. In previous investigations, by the authors, the former model has been found to possess multiple attractors in a stable range of the model parameters and to wander irregularly among attractor ruins for unstable parameter sets. A similar behavior is found for the higher-resolution model as well. Three aspects of LFV are considered in this paper. The first two are intermittent appearances of quasi-stationary weather regimes and low-frequency oscillations. The third is the dominance of a few principal patterns of variability that show red noise–like temporal behavior. In the real atmosphere, the first two can be found by careful examinations in the general predominance of the last aspect. The model is able to simulate these aspects with a certain level of realism. It is found that the first two are associated with the existence of multiple attractors and oscillations intrinsic to them. As for the two-level model, attractors that used to be confined to small regions in phase space correspond to quasi-stationary weather regimes and those located in regions where the phase space structure is flat support the oscillations with sizable amplitudes at a more turbulent stage. The five-level model shows a more complicated behavior, but the relevance of multiple attractors and associated oscillations has been confirmed as well. It is found in the realistic range of parameters that singular modes of linearized equations with time-mean basic states form the basis of principal spatial patterns for which low-frequency temporal variations dominate. The singular vector with the smallest singular value roughly coincides with the first mode of empirical orthogonal function (EOF) for the lower-resolution model. The smallness of the singular value guarantees the small rate of time change so that the system spends a long time along the linear axis in phase space. The singular vector is found to be relatively insensitive to the changes in the basic state for the linearization. The relevance of the singular vector is more controversial in the higher-resolution model. The similarity with the leading EOFs is lost considerably. However, it is found that leading singular vectors still play a role in determining a low-dimensional linear subspace with which most of the low-frequency variance is associated. The interaction between singular modes and forcing due to transients is suggested to be responsible for the deviation of the principal patterns from singular modes.

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