Atmospheric Regimes: The Link between Weather and the Large Scale Circulation

The theme of recurrent structures in the circulation of the atmosphere is woven into many aspects of atmospheric science. Weather forecasters in any region are familiar with a set of weather patterns or types that a?ect their area, and through experience can forecast their likely propagation characteristics. This has led to various definitions of "weather types" and motivated the development of the field of synoptic climatology. A very early example of empirically defined weather types is the grosswetterlagen, a catalogue of central European weather types maintained by the German Weather Service for over 70 years. This e?ort, as well as other early classifications of daily circulation patterns over Europe, is well described in James (2006). A recent upsurge of interest in weather classifications has been motivated by their relationship to larger scale patterns of variability (Coleman and Rogers, 2007). Related to weather types, recent work has focused on the e?ects of European weather patterns on African rainfall (Polo et al., 2011), and on the longer term forcing of the ocean (Cassou et al., 2011). Preferred circulation patterns on larger spatial and longer time scales have also had a long history. The so-called index cycle describing the variability of the latitude of maxima in the zonal wind (jets) on the planetary scale was systematically described by Namias (1940). It has since been recognized that the "cycle" is not periodic but occurs over a broad range of intra-seasonal (and inter-annual) time scales. The circulation patterns associated with the extremes of the cycle, e.g. strong blocking and meanderings of the polar vortex in the low-index phase, have been very relevant for recent extreme winters. Along the same lines, 1 strong correlations of geopotential height anomalies between remote points that occur on monthly and longer time scales were distilled into teleconnection patterns by Wallace and Gutzler (1981), whose approach helped to catalog previously known correlation patterns and highlight new ones. A limitation of this approach, and of the related approach of principal component analysis, is that a particular anomaly field (pattern) and the one of opposite sign appear on an equal footing. Thus such patterns may be considered to be linear perturbations about a (presumably unstable) equilibrium state, and might represent instabilities or neutral waves. This unstable equilibrium is often associated with the time mean state of the atmosphere. In contrast, a decidedly non-linear explanation of the index cycle was sought by J. G. Charney, who posited the existence of more than one unstable equilibrium state or atmo- spheric oscillation (Charney and Devore, 1979; Charney and Straus, 1980). In particular this work sought to dispel the notion that distinct weather and circulation types originate from instabilities about a single large-scale equilibrium. The results obtained in the above cited papers using highly truncated barotropic and baroclinic models suggest a " ...multiplicity of stationary or oscillatory states, each presumably with its own class of smaller scale insta- bilities and each presumably capable of undergoing transition with the aid of instabilities from one to another" (Charney and Devore, 1979). This work was extended by Reinhold and Pierrehumbert (1982) who showed that multiple unstable, wavy steady states could be stabilized in a statistical sense by the fluxes of heat and momentum that their instabilities generated. 2 These early ideas stimulated an intensive theoretical e?ort to extend the multiple equilib- rium theory to more sophisticated models and to understand the nature of the instabilities. Although evidence for the existence of multiple unstable equilibrium atmospheric states has remained elusive, a great deal of subsequent work has been done identifying atmospheric states that are in some sense preferred. If preferred states are not only recurrent but also persistent, they represent a source of predictability. The methods used to identify these states di?er on how they treat the relationship between recurrent and persistence, as this chapter will show. Readers should also consult the review of Ghil and Robertson (2002). Two basic techniques for finding such atmospheric states are reviewed in detail in this chap- ter, providing the conceptual background for exploring the more advanced (and modern) techniques which are introduced, albeit more briefly. The techniques are: (i) the detailed ex- amination of low dimensional probability distribution functions of measures of the strength of the observed planetary waves; and (ii) a systematic approach using cluster techniques in a low-dimensional space defined by principal components (Cheng and Wallace, 1993; Ki- moto and Ghil, 1993a,b; Michelangeli et al., 1995; Straus et al., 2007). Examples of both basic techniques are given in some detail, including both original work of the authors and calculations presented in the literature. Some more technical matters are discussed in the Appendix.