15 JANUARY 2012 Z H A O E T A L . 447 Coupling Modes among Action Centers of Wave–Mean Flow Interaction and Their Association with the AO/NAM NAN ZHAO AND SUJIE LIANG State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China YIHUI DING National Climate Center, Beijing, China (Manuscript received 2 December 2010, in final form 29 June 2011) ABSTRACT The Arctic Oscillation/Northern Hemisphere annular mode (AO/NAM) is attributed to wave–mean flow interaction over the extratropical region of the Northern Hemisphere. This wave–mean flow interaction is closely related to three atmospheric centers of action, corresponding to three regional oscillations: the NAO, the PNA, and the stratosphere polar vortex (SPV), respectively. It is then natural to infer that local wave– mean flow interactions at these three centers of action are dynamically coupled to each other and can thus explain the main aspects of the three-dimensional coherent structure of the annular mode, which also pro- vides a possible way to understand how the local NAO–PNA–SPV perspective and the hemispheric AO/NAM perspective are interrelated. By using a linear stochastic model of coupled oscillators, this study suggests that two coupling modes among the PNA, NAO, and SPV are related to the two-dimensional pattern in sea level pressure of the AO. Although both of them may contribute to the AO/NAM, only one is related to the three- dimensional equivalent barotropic structure of the NAM, while the other one is mainly restricted to the troposphere. So the equivalent barotropic structure of the NAM, as usually revealed by the regression of the zonal wind against the AO index, is the manifestation of just one coupling mode. Another coupled mode is a baroclinic mode that resembles the NAM only in the troposphere. However, this similarity in spatial structures does not imply that the total variability of the AO/NAM index can be explained by those of the NAO–PNA–SPV or their coupling modes, because of the existence of the variability that may contribute to the AO/NAM, produced outside of these three regions. It is estimated that the coupling modes can jointly explain 44% of the variance of the AO/NAM index. 1. Introduction and cause the fluctuation of 10–20 and 30–60 days to the AO/NAM, respectively. Particularly, this wave–mean The Arctic Oscillation (AO) (see Thompson and flow interaction is concentrated on three regional centers: Wallace 1998, 2000; Wallace 2000), also known as the 1) the interaction between a synoptic eddy and the North Northern Hemisphere annular mode (NAM), is usu- Atlantic jet stream in the troposphere, which in recent ally regarded as a result of wave–mean flow interaction years is known to be characterized by the anticyclonic/ (Limpasuvan and Hartmann 1999, 2000; DeWeaver and cyclonic synoptic wave breaking; 2) that between syn- Nigam 2000; Eichelberger and Holton 2002; Lorenz and optic eddy and the Northern Pacific jet stream; and 3) the Hartmann 2003; Vallis et al. 2004; Riviere and Orlanski interaction between upward propagating quasi-stationary 2007; Benedict et al. 2004; Franzke et al. 2004; Feldstein waves and the polar vortex in the stratosphere. On these 2003; Feldstein and Franzke 2006). Researchers suggest issues, one can refer to a review by Thompson et al. that synoptic eddy and quasi-stationary waves can inter- (2002). In general, the AO represented by the leading act with zonal flow in the troposphere and stratosphere empirical orthogonal function (EOF) of monthly mean sea level pressure (SLP) has also three centers of action over both oceanic basins and the Arctic region, coinciding Corresponding author address: Dr. Nan Zhao, Chinese Academy of Meteorological Sciences, No. 46, South Zhongguancun Ave., with those of wave–mean flow interaction. However, due Beijing 100081, China. to the following facts of 1) the weak correlation between E-mail: [email protected] the SLP in the two centers of the Atlantic and the Pacific DOI: 10.1175/2011JCLI4240.1 Ó 2012 American Meteorological Society Unauthenticated | Downloaded 09/26/21 12:34 PM UTC 448 JOURNAL OF CLIMATE VOLUME 25 and 2) that the AO pattern cannot be identified in principal component analysis (PCA) methods or other a physically consistent way in EOF analysis applied to purely statistical tools, some dynamical model is neces- various fields of the whole Northern Hemisphere, the sary in the data analysis and mode recognition. For this dynamical relevance of the AO/NAM has been ques- purpose, in this paper we will develop a coupled linear tioned by many researchers (Deser 2000; Ambaum et al. oscillator model with random forcing and thus seek for 2001; Wallace and Thompson 2002;Dommenget and coupling modes related to the AO/NAM from this model. Latif 2002; Christiansen 2002a,b). In fact, these doubts Overall, the objective of this research is to examine can be attributed to one question of how wave–mean how local wave–mean flow interaction at different centers flow interactions localized to three regional centers can of action can dynamically form the three-dimensional be coordinated to form one three-dimensional coherent coherent structure of the annular mode so as to better structure of the AO/NAM, even if the mechanisms, the understand how the local NAO–PNA–SPV perspective phases, and time scales of the interactions in these cen- and the hemispheric AO/NAM perspective are inter- ters are rather different. related to each other. In section 2, we establish such On the other hand, the local eddy–jet interaction in a model and discuss its theoretical aspects. In section 3, the two basins can be reflected well by the North At- coupling modes of this model and their physical nature lantic Oscillation (NAO) and the Pacific–North Ameri- are derived and discussed. The last section gives a sum- can pattern (PNA) (Walker and Bliss 1932; Wallace and mary and further discussion on related issues. Gutzler 1981), two regional modes confined to the Euro- Atlantic and the Pacific sectors, respectively, and found 2. Stochastic model of coupled oscillators much earlier than the AO. Both phases of the NAO and PNA are associated with basinwide changes in the The description of the coordinated behavior of the strength and location of the North Atlantic/Pacific jet above three regional oscillations resulting from local stream and storm track. So, unlike the AO, the NAO wave–mean flow interactions needs a well-designed cou- and PNA patterns are physical modes rather than sta- pled dynamical model. Such a model can only be obtained tistical artifacts. In addition, the fluctuation of the strato- statistically from the observed data. Traditional multi- sphere polar vortex (SPV), induced also by wave–mean variate statistical tools like PCA or EOF yields only flow interaction, is an observable physical entity and is statistical modes in context of the optimal variance con- surely another physical mode that must be incorporated tribution and need not be explained as physical modes. into the understanding of this issues as well. In a point Consequently, it is of key importance to construct em- of view of synoptic wave breaking over the Atlantic, pirically from observed datasets a dynamical model that is Feldstein and Franzke (2006) suggests that the NAO and able to depict the coupling dynamics of these oscillations. AO/NAM are indistinguishable in a statistical sense and a. Regional oscillators and the coupling among them offers a somewhat different perspective on the role of the NAO in the formation of the AO/NAM. However, As mentioned above, the centers of action of wave– this may be true only at the time scale of 10–20 days, mean flow interaction in the troposphere are situated at or the life cycle of synoptic wave breaking over the At- two jet streams over the two basins of the Atlantic and lantic. Contributions from the other two regional oscil- the Pacific and represented by the NAO and the PNA. lations to the AO/NAM, such as the fluctuation of the The positive and negative phases of the NAO are found SPV at 30–60 days, cannot be completely ignored. All of to correspond to a meridional shift of the jet stream these naturally raise another question as to how the local caused by the anticyclonic and cyclonic synoptic wave NAO–PNA–SPV perspective and the hemispheric AO/ breaking over the Atlantic, respectively (Riviere and NAM perspectives are interrelated to each other. Orlanski 2007; Benedict et al. 2004; Franzke et al. 2004, As the regional wave–mean flow interactions can be Feldstein 2003). The positive phase of the PNA is asso- reflected by the NAO, PNA, and SPV, it can be inferred ciated with an enhanced Pacific jet stream and an east- that an appropriate combination of the NAO, PNA, and ward shift in the jet exit region, while the negative phase SPV may be well enough to depict the three-dimensional is associated with a westward retraction of that jet stream. quasi-zonally symmetric variability like the AO/NAM, Another center is on the stratospheric polar vortex. In which is regarded as the result of hemispheric scale wave– midlatitudes, upward propagating Rossby waves are re- mean flow interaction, as long as this quasi-zonal sym- fracted by the SPV more or less strongly toward the metric variability does exist. The question is what kind of tropics, depending on the strength of the SPV. If the polar combination of these three regional oscillations can rep- vortex is weak, more waves are refracted into it. When resent the physical ways of the coupling among them and these waves break they decelerate the vortex signifi- give rise to physically relevant modes.