Quantifying the Eddy Feedback and the Persistence of the Zonal Index in an Idealized Atmospheric Model

Abstract

An idealized atmospheric model is employed to quantify the strength of the eddy feedback and the persistence of the zonal index. The strength of the surface frictional damping on the zonal index is varied, and an external zonal momentum forcing is included to compensate for the momentum change associated with the friction change such that the climatological jet latitude and shape are unchanged.The model can generate a nearly identical climatology and leading mode of the zonal mean zonal wind for different frictional damping rates, except when the jet undergoes a regime transition. For those experiments without a regime transition, as the surface friction is increased, the strength of eddy feedback is enhanced but the zonal index becomes less persistent. A simple feedback model suggests that the e-folding decorrelation time scale of the zonal index can be determined by the frictional damping rate and the strength of eddy feedback. The strength of eddy feedback is found to be related to the instantaneous vertical wind shears near the surface controlled by the frictional damping. Furthermore, the climate response to an external zonal torque is proportional to the decorrelation time scale, although the simple prediction used here overestimates the climate response by a factor of 2.

The Impact of Baroclinic Eddy Feedback on the Persistence of Jet Variability in the Two-Layer Model

“…2b) is nearly indistinguishable from that of the simulated z. This is consistent with the findings of Chen and Plumb (2009), who showed that frictional damping of the zonal index is well captured in an idealized model by projecting the annular mode/ zonal index pattern onto the lower-layer friction.…”

“…These modes are associated with a mass exchange between middle and high latitudes, producing a meridional seesaw in sea level pressure and a north-south displacement of the eddy-driven jet and extratropical storm tracks. Similar variability patterns are also found in a variety of atmospheric models, ranging from quasigeostrophic models (Lee and Feldstein 1996;Zhang et al 2012) to idealized primitive equation models (Gerber and Vallis 2007;Chen and Plumb 2009) to comprehensive general circulation models (Gerber et al 2008). It has also been noted that the atmospheric response to external forcing projects strongly on this mode of variability for many types of forcing (Yin 2005;Son et al 2008b).…”

“…Gerber et al (2008) showed that the coupled general circulation models used in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) report are too persistent compared with observations in both hemispheres and seasons. Some studies have addressed the sensitivity of zonal index persistence on external parameters using idealized models (Gerber and Vallis 2007;Son et al 2008a), but results must be interpreted with caution because changes in persistence when parameters are varied might be due to changes in the mean state rather than to changes in the feedback mechanism (Chen and Plumb 2009).…”

“…Barotropic mechanisms attribute the sensitivity of the eddy momentum forcing when the mean state changes to anomalous wave propagation at upper levels resulting from changes in the refraction index and/or critical layer shifts (Simmons and Hoskins 1978;Hartmann and Zuercher 1998;Chen and Zurita-Gotor 2008;Lorenz 2013, personal communication). In contrast, baroclinic mechanisms rely on changes in the wave source, as it is well known that baroclinic eddies tend to produce a westerly acceleration as they propagate away from the latitudes at which they are generated (Vallis 2006).…”

Propagating Annular Modes: Empirical Orthogonal Functions, Principal Oscillation Patterns, and Time Scales

“…One consequence of this is that the autocorrelations of the leading principal components (PCs) corresponding to the individual EOFs do not decay exponentially but show some oscillatory characteristics. This behavior, in turn, cautions against using simple paradigms based on stochastically forced, single component, systems as a basis for estimating eddy feedback strength (e.g., Lorenz andHartmann 2001, 2003;Watterson 2007;Chen and Plumb 2009) or for estimating the sensitivity of the system to climate perturbations (Gerber et al 2008;Ring and Plumb 2008). Such questions are addressed here by application of theory to results from a dry, dynamical core, global model run in a simplified solsticial configuration.…”