Low-Frequency Variability in a BaroclinicβChannel with Land–Sea Contrast*

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Abstract
Atmospheric low-frequency variability (LFV) is studied in a two-layer quasigeostrophic model. The model geometry is a periodic β channel with flat bottom and zonally inhomogeneous thermal forcing. As a result of the idealized land–sea contrast, the model produces a zonally modulated climatological jet with realistic amplitude. The model's LFV is equivalent barotropic; principal component analysis reveals that it consists of (i) dominant stationary patterns with red-noise-like temporal behavior and (ii) propagating waves with periods of 37 and 50 days superimposed on the former. The vorticity forcing due to synoptic eddies is dominated by self-interaction of high-pass filtered model fields. Applying a phase-randomized, stochastic analog of this forcing to a version of the full model in which fast baroclinic instability and, therefore, synoptic eddies are suppressed, produces a climatology and LFV that are very similar to those in the full model. Synoptic eddies are solely represented in the simplified model version by means of stochastic forcing that is independent of the low-frequency flow. It follows that, while fast synoptic eddies are modulated in the full model by the LFV, this modulation is fairly passive: anomalous generation of the synoptic eddies in the course of the full system's low-frequency evolution, the so-called synoptic-eddy feedback, is not essential in selecting the system's low-frequency modes; the main role of synoptic eddies is to supply energy to these modes. Further analysis indicates that the LFV in this thermally driven model originates from the barotropic mode's dynamics. The baroclinic mode passively follows, to first order, the low-frequency changes in the barotropic mode. The latter changes are due to stochastically excited, weakly damped linear eigenmodes of the barotropic-mode equation. Two distinct stationary eigenmodes, as well as two pairs of propagating modes with periods of 27 and 36 days, respectively, dominate the low-frequency behavior. The leading empirical orthogonal functions in this model are associated with these six particular eigenmodes. The latter are not well separated, however, from the other eigenmodes in terms of damping time scale, and it is the barotropic nonlinearity that selects the six dynamically important modes over the others. Interactions between these six modes also result in the occurrence of probability density maxima in two-dimensional subspaces of the model's phase space.

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