VOLUME 70 JOURNAL OF THE ATMOSPHERIC SCIENCES MARCH 2013

Vortex–Vortex Interactions for the Maintenance of Blocking. Part I: The Selective Absorption Mechanism and a Case Study

AKIRA YAMAZAKI* AND HISANORI ITOH Earth and Planetary Sciences, Kyushu University, Fukuoka, Japan

(Manuscript received 1 November 2011, in final form 11 July 2012)

ABSTRACT

A new block maintenance mechanism, the selective absorption mechanism (SAM), is proposed. According to this mechanism, which is based on vortex–vortex interactions (i.e., the interactions between a blocking and synoptic eddies with the same polarity), a blocking anticyclone actively and selectively ab- sorbs synoptic (strictly, air parcels with low potential vorticity). The blocking anticyclone, which is thus supplied with low potential vorticity of the synoptic anticyclones, can subsist for a prolonged period, withstanding dissipation. The SAM was verified in a case study through trajectory analysis. Ten actual cases of blocking were ex- amined. Trajectories were calculated by tracing parcels originating from synoptic anticyclones and located upstream of the blocking. Parcels starting from anticyclones were attracted to and absorbed by the blocking anticyclone, whereas parcels from cyclones were repelled by the blocking anticyclone and attracted to the blocking , if one was present. The results show that the SAM is effective in the maintenance of observed cases of blocking. In addition, the uniqueness and distinction of the SAM from other previously proposed maintenance mechanisms are discussed.

1. Introduction These blocks literally ‘‘block’’ the eastward progression of synoptic eddies drifting from upstream. Atmospheric blocking is a quasi-stationary pattern As the anomalous pattern of blocking persists for persisting for about 1 week or more, characterized by a prolonged period, blocks are related to various a pronounced meandering of the middle-latitude west- weather extremes and hence to various natural disasters. erly toward high latitudes or by a split of the A typical example of such a disaster was the record- westerly jet stream into two distinct currents. The pat- breaking summer of 2010 in western Russia and Asia. A tern is accompanied by a large-amplitude anticyclone blocking anomaly persisted over western Russia from with an equivalent-barotropic structure on its poleward July through mid-August, causing an extreme heat wave side. The anticyclone is often V shaped in a synoptic field. in western Russia and flooding in Pakistan and north- Another type of quasi-stationary pattern also sometimes western India (Dole et al. 2011; Hong et al. 2011). appears, consisting of a dipole structure with a cyclone on The recognition of blocking phenomena is also critical the equatorial side. We call the former an V-type block for medium-range weather forecasting; at present, block- and the latter a dipole-type block, and refer to the anti- ing is not accurately reproduced by numerical models, cyclones (cyclones) as blocking anticyclones (cyclones). even using advanced modeling techniques (Kimoto et al. 1992; Pelly and Hoskins 2003a). Moreover, because the occurrence and persistence of blocks can strongly in- fluence seasonal climate patterns, it is important to de- * Current affiliation: Earth Simulator Center, JAMSTEC, velop climate models that can successfully reproduce Yokohama, Japan. blocking. However, we still lack the ability to model and reproduce blocking phenomena (e.g., D’Andrea et al. Corresponding author address: Dr. Akira Yamazaki, Earth 1998; Matsueda et al. 2009; Scaife et al. 2010). Simulator Center, Japan Agency for Marine-Earth Science and Technology, 3173-25, Showa-machi, Kanazawa-ku, Yokohama, Blocking has generated considerable scientific in- Kanagawa 236-0001, Japan. terest, and has received attention in a broad spectrum of E-mail: [email protected] disciplines and approaches. It has been the subject of

DOI: 10.1175/JAS-D-11-0295.1

Ó 2013 American Meteorological Society 725 Unauthenticated | Downloaded 09/29/21 04:20 PM UTC 726 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 70 numerous studies since Garriott first discovered the In addition, blocking influences the synoptic eddies. phenomenon in 1904 (Rex 1950). In particular, the Thus, the synoptic eddies and the blocking interact with mechanism of blocking remains a central and critical one another; the interaction mechanism, referred to as issue in atmospheric research, despite the fact that 100 the eddy-feedback mechanism, has been supported by years have elapsed since its discovery. There can be no numerous studies, some of which are cited above. We doubt that an understanding of the blocking mechanism believe that there may be no other way to systematically is key for improved forecasts of blocking and the pre- and continuously maintain blocking other than the vention or mitigation of natural disasters associated with eddy-feedback mechanism, aside from the development blocking. of accidental or fortuitous circumstances. Thus, the To clarify the mechanism of blocking, it is important maintenance mechanism proposed here is developed on to explicitly distinguish between the two mechanisms of the basis of the eddy-feedback mechanism framework. formation and maintenance (also see Mullen 1987), as The eddy-feedback mechanism has been developed the time scale for the formation of blocking is different by Shutts (1983, hereafter S83) in his milestone publi- from that of its maintenance. The time scale of forma- cation on blocking theory. S83 proposed a well-known tion is approximately 1–2 days, while that of mainte- blocking maintenance mechanism, the eddy straining nance is longer than the typical time scale for the mechanism (ESM), as a physical eddy-feedback entity. persistence of synoptic eddies. This implies that even Using numerical experiments based on a linearized one instantaneous event, such as single wave breaking or model, he demonstrated how the behavior of eddies su- a strong synoptic eddy, can cause the onset of blocking, perimposed on uniform zonal , combined with whereas maintenance requires a continuous or periodic blocking flow, can reinforce the blocking flow. Based on source to counterbalance dissipation. Several theories his results, he suggested that synoptic eddies strained in the have been proposed for the blocking mechanism, including north–south direction by the blocking provide negative theories of local nonlinear resonance (Pierrehumbert (positive) vorticity forcing to the blocking anticyclone and Malguzzi 1984) and the breaking of local Rossby (cyclone); this vorticity forcing (i.e., a second-order in- waves propagating from outside (H. Nakamura 1994; duced flow) maintains the blocking dipole structure and Naoe and Matsuda 2002). However, these theories are counteracts dissipation. Eddy straining in the diffluent appropriate for the formation of blocking but not its region of blocks has been observed in many case studies maintenance, as resonance alone cannot sustain and and climatological ones, and has been reproduced in nu- maintain blocking (in the absence of a source), and merical experiments (Hoskins et al. 1983; Nakamura and Rossby wave breaking does not repeatedly occur in Wallace 1993; Luo 2005; and many others). From a blocking regions during the period of the block main- theoretical viewpoint, M. Nakamura (1994) presented tenance (in the absence of a continuous source). Thus, evidence for eddy straining in a region of jet splitting these theories are insufficient to account for blocking that mimicked blocking flow using contour dynamics maintenance. The aim of this study, unlike those men- principles. tioned above, is to propose a new and explicit mecha- S83 suggested that in the ESM, the basic flow pattern, nism for the maintenance of blocking. While the including that of the blocking flow, determines the ef- mechanism of blocking formation merits detailed in- fectiveness of the eddy-feedback mechanism; using vestigation, this topic will be addressed in a future work. a linearized model, he showed that different basic flows One achievement of long-term studies on the main- cause drastic variations in second-order flow patterns. tenance mechanism of blocking is the finding that syn- Thus, when basic flows satisfy the proper conditions, optic eddies obstructed by blocking actually enhance the blocking can be maintained by the eddy feedback. blocking (e.g., Green 1977; Shutts 1983, 1986; Mullen S83 also supported the ESM using an analytical ap- 1986, 1987; Nakamura and Wallace 1993; Nakamura proach. Supposing the existence of an area bounded by an et al. 1997). Synoptic eddies (synoptic cyclones and isopleth of eddy enstrophy just upstream of blocking, and anticyclones)1 are ubiquitous around blocking and integrating the eddy enstrophy equation for eddy straining therefore can be a continuous source for maintenance. over this area, he showed a balance between the terms for equatorward eddy vorticity flux and dissipation: ð ð 0 0 02 1 z $ z 1 52E z In this paper, synoptic cyclones (anticyclones) exclusively V ( f ) dSens dSens , (1) S S mean migratory ones. Since those interacting blocking are treated, ens ens they are usually upper-level ones. Therefore, they and synoptic upper-level troughs (ridges) are interchangeably used. Moreover, where Sens denotes the area bounded by the isopleth of both are referred to collectively as synoptic eddies. eddy enstrophy; z and f are the relative and planetary

Unauthenticated | Downloaded 09/29/21 04:20 PM UTC MARCH 2013 Y A M A Z A K I A N D I T O H 727 vorticity, respectively; V is the horizontal wind vector; E similar but slightly different patterns of eddy flux di- 0 is the Ekman friction coefficient; and ()and() are the vergence and convergence, characterized by north–south time-averaged field and the deviation from it, re- dipole structures, induce drastically different patterns of spectively. Equation (1) shows that the net equatorward second-order flows in the framework of the ESM eddy vorticity flux, or its divergence (convergence) on (AM02). In some cases, equatorward eddy vorticity flux the poleward (equatorward) side just upstream of the works to destroy basic blocking patterns. Therefore, diffluent blocking region, counterbalances dissipation these problems suggest that the equatorward eddy vor- (S83, his section 2b). He further showed that the net ticity flux does not represent the ESM. equatorward vorticity (or potential vorticity) flux cor- Lupo and Smith (1995) proposed another blocking responds to the pattern of eddy straining upstream of the maintenance mechanism associated with synoptic eddies. jet splitting. The eddy flux pattern was observed in case They showed the importance of the rapid development studies by Illari (1984) and Shutts (1986) and in nu- of an intense short (synoptic cyclone) upstream merical simulations by S83, Haines and Marshall (1987), of a block; the trough advects subtropical air into the and Arai and Mukougawa (2002, hereafter AM02). blocking . This mechanism, however, does not es- More detailed and quantitative analyses of the eddy- tablish an obvious causal relationship between the rapid feedback effect were conducted by Mullen (1986, 1987); troughing and the existence of blocking, and the main- through investigation of the eddy-feedback budgets of tenance of the blocking is attributed to chance. The re- composited blocks in the output of a general circulation lationship between rapid troughing and blocking most model and observational data, he concluded that eddy likely establishes a mechanism for reintensification of vorticity flux patterns observed in both the model and blocking as well as initial formation. In terms of blocking the data are consistent with those predicted by the ESM, formation, the rapid troughing mechanism must be re- and that this eddy forcing is the main contributor to lated to ‘‘explosive cyclogenesis,’’ as identified by Colucci blocking maintenance. He also observed that the eddy (1985), who concluded that blocking formation is pre- feedback can counteract not only dissipation but also the ceded by rapid cyclogenesis. However, the role of syn- advective effect of background westerlies (downstream optic cyclones in the maintenance stage is different than advection of blocks). their role in the formation stage (Mullen 1987). Some recent studies, however, have suggested that the Here, we propose a general maintenance mechanism ESM cannot fully explain the maintenance of blocking of blocking. This is a comprehensive and detailed ver- in real situations; the ESM shows a strong sensitivity to sion of Yamazaki and Itoh (2009). This paper is orga- storm-track conditions, and these conditions vary con- nized as follows. In section 2, we propose a general siderably in real situations. Using an approach similar to maintenance mechanism of blocking. The difference S83, AM02 demonstrated that patterns of second-order between this mechanism and the ESM is explained in induced flow that intensify the blocking pattern are easily section 3. In section 4, the proposed mechanism is cor- lost by meridional shifts (as small as about 400 km) of roborated by observational datasets, using trajectory wavemakers (i.e., storm tracks) or small changes in the analyses of 10 blocking events in winter. Related issues sizes of eddies. This result is adverse to the maintenance are discussed in section 5. Finally, section 6 presents a of real blocking because the relative positions of a block summary and suggestions for future work. Quantification and a storm track fluctuate largely from one case to the of the mechanism will be demonstrated in Yamazaki and next; the center positions of a block and a storm track Itoh (2013, hereafter Part II) using numerical experiments. are not necessarily in the same latitudinal band. More- over, amplitudes and sizes of synoptic eddies are not 2. The selective absorption mechanism constant in real situations. Maeda et al. (2000) also showed that a zonal shift of wavemakers disrupts the Before proposing the maintenance mechanism, the ESM. Therefore, the fact that the ESM has a strong premise of quasi stationarity should be explained, as it is sensitivity to storm tracks is a weak point in the eddy- essential to an understanding of block maintenance. feedback model. Without the quasi-stationary nature, blocking would In addition, the use of the equatorward eddy vorticity easily move here and there, and the eddy feedback flux as an indicator of the ESM presents two problems. would not effectively work, because migratory blocking The first problem is related to the assumption that the could not well interact with synoptic eddies drifting from isopleth of eddy enstrophy is closed, which is a necessary upstream. However, the nature of the quasi stationarity condition for Eq. (1); however, closed isopleths in the has not been enough considered in previous studies. region of the equatorward flux are not present in S83’s Then, we mention this nature in the following. We hy- results (S83, his Fig. 4d). The second problem is that pothesize that blocking is a phenomenon around a

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FIG. 1. Conceptual diagrams of vortex–vortex interactions between (a) two anticyclones and (b) an anticyclone and a cyclone. Vortex A represents a blocking anticyclone (high) and vortex B represents anticyclonic and cyclonic eddies in (a) and (b), respectively. The vorticity distribution of vortex A, represented schematically below each plate, shows that the vorticity of vortex A extends beyond the circle of A and encompasses vortex B. The sizes of the gray-shaded circles qualitatively represent absolute values of vorticity magnitudes. See text for details. quasi-stationary solution in phase space. Here, a quasi- its own longevity; this process occurs because binary stationary solution means that local time change terms vortices with the same polarities attract and merge with of governing equations are small as compared with other one another, as will be shown later. Thus, according to the dominant terms, so that blocking can persist over a fixed second principle, the eddy-feedback mechanism is re- region provided there is no damping. A simple analysis garded as a vortex–vortex interaction, involving a block- to prove this hypothesis is presented in the appendix, ing anticyclone and synoptic anticyclones. This interaction while a more thorough investigation, which includes the also includes the effects of repulsion of binary vortices trajectory and separatrix in phase space, will be de- with opposite polarities, such that a blocking anticyclone scribed in a subsequent paper. The result outlined in the repels synoptic cyclones with high PV. The vortex–vortex appendix indicates that a blocking anticyclone has interactions necessarily cause an asymmetry between a quasi-stationary nature in high-latitude regions, where synoptic anticyclones and cyclones, which are attracted background westerlies are weak. and repelled, respectively, by a blocking anticyclone. The proposed maintenance mechanism is now ex- The attraction and repulsion between binary vortices plained. The mechanism consists of the following two is qualitatively described in Fig. 1 [for similar inter- foundational principles, both related to potential vorticity pretations, see Cushman-Roisin and Beckers (2011), (PV; e.g., Hoskins et al. 1985), which is a conservative their chapter 18]. First, consider two anticyclones (vor- quantity characterizing blocking. In a PV perspective, tices A and B) on a barotropic f plane, as depicted in Fig. blocking and synoptic anticyclones are characterized by 1a; vortex A is relatively large and strong (representing low PV on an isentropic surface. The first principle re- a blocking anticyclone) and vortex B is relatively small gards the maintenance mechanism in terms of low PV and weak (representing a synoptic anticyclone). The supply to a blocking anticyclone. In order for a blocking vorticity of vortex A is not, however, confined to the anticyclone to persist for 1 week or more, the low PV circle representing the vortex, but extends outward to must be supplied to it, which thus diminishes the tendency encompass vortex B. The vorticity of vortex B, on the for dissipation. The necessity of this supply mechanism other hand, is assumed to be restricted to the small circle condition is likely not controversial. Given this condition, representing the vortex. the question arises: how is low PV supplied to the block? In this model, vorticity z is conserved on the f plane, The answer to this question is the basis for the second according to principle of our maintenance mechanism. A blocking anticyclone can attract and absorb synoptic anticyclones ›z 52J(c, z), (2) with low PV, thus incorporating low PV and extending ›t

Unauthenticated | Downloaded 09/29/21 04:20 PM UTC MARCH 2013 Y A M A Z A K I A N D I T O H 729 where c is streamfunction. Now, the vorticity and stream- The mechanism is essentially the same as that of a b function of vortex A (B) are represented as zA (zB)and gyre (or b drift); the result is the meridional drift of c A (c B), respectively, so that Eq. (2) can be rewritten as tropical cyclones or isolated cyclonic eddies in the ocean toward the polar side, where planetary vorticity is ›z 52J(cA, zA) 2 J(c B, zB) 2 J(c A, zB) 2 J(cB, zA). greater in the (Fujiwhara 1923; ›t Rhines and Holland 1979; DeMaria and Chan 1984; Ito (3) and Kubokawa 2003). In other words, ‘‘a huge cyclonic vortex’’ of the earth attracts smaller cyclonic vortices. Among the terms on the right-hand side, the net effect of We name this mechanism the selective absorption the first and second terms is zero (if the vortices are mechanism (SAM), distinguishing it from the ESM. In the precise circles), as they represent the self-advection ef- SAM, a blocking anticyclone selectively absorbs synoptic fect. The third term represents the anticyclonic rotation anticyclones and excludes synoptic cyclones (Fig. 2a). effect on vortex B around A, caused by winds induced by Large-scale conditions are favorable for the operation of vortex A (black arrows around A). The fourth term also the SAM, as synoptic eddies are ‘‘naturally’’ transported has the corresponding anticyclonic rotation effect on downstream through the jet upstream of blocking, which vortex A by winds induced by vortex B. However, this acts as a waveguide. The low PV thus supplied by synoptic effect is almost negligible, since winds induced by B are eddies extends the longevity of the blocking. The above very small around the center of A. The main effect of interpretation applies specifically to V-type blocking, but this term is an attraction of vortex B toward vortex A it can also be applied to dipole-type blocking, because (represented by the dashed outline arrow in vortex B in a dipole-type blocking cyclone selectively absorbs synop- Fig. 1a), because the vorticity of A around B is advected tic cyclones (Fig. 2b). In both situations, synoptic eddies by the rotational flow by B, as described below. approach the blocking following the jet (waveguide)— As defined above, vortex A is larger and stronger than a condition that is favorable for vortex–vortex interaction. vortex B, and the vorticity distribution of vortex A ex- Although we have indicated that a blocking anticy- tends radially and increases monotonically with distance clone absorbs synoptic anticyclones, strictly speaking, it from the vortex center, as shown in the bottom panel of absorbs air parcels with negative vorticity on an f plane Fig. 1a; therefore, the vorticity associated with vortex A or low potential vorticity in a baroclinic atmosphere. (gray-shaded circles) is higher (lower) on the left (right) This is because synoptic anticyclones are strongly dis- side of vortex B than that on the right (left) side. This torted and then seem to disappear in the process of ab- right (left) side vorticity is then advected clockwise by sorption. In more complicated real situations, air parcels the flow induced by vortex B (black arrows on vortex B originating from a synoptic anticyclone may separate in Fig. 1a). The result is that the ambient vorticity on the from the original anticyclone. bottom (top) side is relatively smaller (larger) than the In general, the stronger (larger amplitude and/or size ambient vorticity attributed to vortex A; the vorticity on of) a blocking anticyclone becomes, the more effectively the bottom (top) side induces a strong (weak) anticy- the SAM works. This is because the vortex–vortex in- clonic flow (light-shaded arrows) on the bottom (top) teractions become stronger as PV gradients in the block- side ambient vorticity. These flows generate the differ- ing anticyclone become steeper or as the region of these ential advection (dashed outline arrow), which causes gradients more expands (curves in the bottom panel of vortex B to drift toward vortex A. Fig. 1). Thus, the effectiveness of the SAM is dependent Then, consider the case that vortex B is a cyclone (Fig. 1b) on the strength of blocking; when the amplitude and/or and A is also larger and stronger vorticity anomaly (as the size of a blocking vortex is larger, it attracts synoptic eddies absolute values) than B. In this situation, the same rationale ofthesamepolaritymorestrongly(increaseofthePV- can be adopted as Fig. 1a except for the opposite rotation supply rate). Also, it becomes more stationary (strength- by the flow associated with vortex B. Thus, in the same ening of the phase lock of blocking), since the increase of way, vortex B tends to drift away from vortex A, as repre- the PV-supply rate delays the decrease of the amplitude of sented by the dashed outline arrow in vortex B in Fig. 1b. blocking against dissipation; when the amplitude of block- This process is referred to as the selective absorption ing is weak, blocking is easily advected downstream (see and exclusion of synoptic eddies by a blocking anticy- Part II). This is nothing but the view of the eddy-feedback clone, alternatively referred to as the asymmetry between mechanism, which is a self-organizing system. From this anticyclonic and cyclonic eddies. The same explanation viewpoint, blocking governs its own maintenance, so as given above for relative vorticity can be given for absolute to be ‘‘actively’’ (but not ‘‘passively’’) maintained. vorticity on a barotropic b plane and PV in a baroclinic Although the SAM and the ESM are both eddy- atmosphere. feedback mechanisms, the two mechanisms are different.

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FIG. 2. Conceptual diagrams illustrating the SAM. (a) For an V-type block, when synoptic eddies propagating along a waveguide approach a blocking anticyclone, synoptic anticyclones (H) are selectively absorbed by the blocking anticyclone, while synoptic cyclones (L) are repelled and drift downstream. (b) As in (a), but for a dipole- type block.

Thedifferencebetweenthemisinthenatureofthe where  is an expansion parameter ( 1). Here, q and c vortex–vortex interactions, or the asymmetry between represent the perturbation from a constant westerly, anticyclonic and cyclonic eddies. On the basis of this na- using the relationship ture, we investigated the SAM by first showing the differ- ences between the SAM and the ESM. Then, we verified q 5 $2c 2 g2c, (5) the SAM by examining the evidence for selective absorp- tion in real datasets, and by investigating how blocking 2 5 2 where g 1/Ld and Ld denotes the Rossby de- counteracts dissipation using numerical experiments. formation radius. Equation (4) is substituted into the equivalent-barotropic PV anomaly equation: 3. The eddy straining mechanism versus › › ›c the selective absorption mechanism 1 U q 1 J(c, q) 1 b 5 F 2 D(c), (6) ›t ›x *›x The most important difference between the ESM and the SAM is whether the feedback effects of synoptic where U is the basic westerly, b 5 b 1 UL22, b is the eddies are symmetric or asymmetric with respect to their * D Rossby parameter, L is the Rossby deformation radius polarities, as described below. The essence of the SAM D of the background (zonal) field, F is a forcing term, D is is a vortex–vortex interaction that causes an asymmetry a dissipation term (related, for example, to Ekman between synoptic eddies possessing different polarities; friction or numerical diffusion; a single-valued function that is, the behaviors of synoptic anticyclones and syn- of c), and J is the Jacobian operator. The following optic cyclones with respect to a blocking anticyclone are equations are obtained: different. On the other hand, as eddy straining is the essence of the ESM, there is a symmetry with respect to ›q ›c O(1): U 0 1 J(c , q ) 1 b 0 5 F 2 D(c ), (7) the polarity of synoptic eddies; the roles of synoptic ›x 0 0 * ›x 0 0 anticyclones and synoptic cyclones in blocking mainte- nance are not distinguishable. S83 thus does not con- › › ›c O(): 1 U q 1 J(c , q ) 1 J(c , q ) 1 b 1 sider the asymmetry between anticyclonic and cyclonic ›t ›x 1 1 0 0 1 * ›x eddies, which is the foundation of the SAM, in his 5 F 2 D(c ), and (8) equations proving the ESM. S83 formulated a linearized 1 1 equivalent-barotropic quasigeostrophic PV equation as › › ›c O(2): 1 U q 1 J(c , q ) 1 J(c , q ) 1 b 2 follows. He expanded the PV q and the streamfunction c ›t ›x 2 0 2 2 0 * ›x in a perturbation series as 52 2 D J(c1, q1) (c2), (9) 5 1  1 2 q(x, y, t) q0(x, y) q1(x, y, t) q2(x, y, t), where the forcing term F is also expanded in a pertur- 5 1  1 2 c(x, y, t) c0(x, y) c1(x, y, t) c2(x, y, t), (4) bation series. Thus, the nonlinear equation (6) is separated

Unauthenticated | Downloaded 09/29/21 04:20 PM UTC MARCH 2013 Y A M A Z A K I A N D I T O H 731 into the O(1), O(), and O(2) quasi-linear equations frequent (e.g., Pelly and Hoskins 2003b; Schwierz et al. governing, respectively, the stationary blocking flow, the 2004; Barriopedro et al. 2006). eddy flow, and the second-order induced flow that is the The analysis was conducted using Ertel’s PV and feedback effect of the eddy flow on the blocking flow. a wind with a horizontal resolution of approximately Although this quasi-linearized system can extract the 1.125831.1258 (320 3 160 Gaussian grids) and a time essence of the eddy-feedback effect by eddy straining, resolution of 6 h. The data are from the Japanese 25-yr the asymmetry between cyclonic and anticyclonic eddies Reanalysis dataset (JRA-25; Onogi et al. 2007) and the is lost; the O() equation is insensitive to the polarities Japan Meteorological Agency Climate Data Assimila- of eddies (i.e., the signs of c1 and q1), while the eddy tion System (JCDAS). 2 forcing J(c1, q1)intheO( ) equation is symmetric with The PV and wind quantities were decomposed into respect to eddy polarities. This means that the advec- synoptic-eddy and blocking components using a Lanc- tion patterns of eddies are insensitive to their polarities zos time filter with a cutoff period of 8 days; the high- [O() equation] and that synoptic anticyclones and and low-frequency components correspond to synoptic synoptic cyclones contribute to blocking maintenance eddies and blocking flow, respectively. Blocking and its in the same way [O(2) equation]. Thus, the ESM does duration were defined by our own procedure (PV not include the asymmetry between synoptic anticyclones based), which is essentially the same as that of Pelly and and cyclones. Hoskins (2003b) (potential temperature based). This is We think that the asymmetry of synoptic eddies is an based on the fact that blocking is characterized by a re- important factor for the maintenance mechanism of versal of the usual meridional PV gradient (Fig. 3a). blocking. A consideration of the asymmetry can lead to In this paper, blocking is said to occur when the fol- the interpretation that a blocking anticyclone (cyclone) lowing conditions are satisfied (Fig. 3b). The blocking selectively attracts and absorbs synoptic anticyclones index B defining the reversal at longitude l0 is (cyclones) (Fig. 2). Because of this effect, blocking can ð ð f f 1Df/2 attract synoptic eddies even from storm tracks far from 2 0 2 0 B [ Pdf 2 Pdf the blocking center as long as the synoptic eddies are Df 2D Df f0 f/2 f0 trapped within the region of the PV gradient associated f 5 f (l) 1D, D508, 648, (10) with blocking. Although S83 also mentions the PV-supply 0 c mechanism in his conclusion, he does not consider the where P represents the PV at 320 K, f is the latitude, Df 5 effects of attraction due to vortex–vortex interactions 308,andf (l) is the central blocking latitude. The mathematically or physically in the framework of the c blocking index B becomes positive for at least contin- ESM. Thus, the SAM provides a robust explanation for uous 158 of longitude in each sector (Dl . 158), which is the displacements of storm tracks and the sizes, ampli- characteristic of a large-scale reversal of the mid- tudes, and phases of eddies, whereas the ESM cannot latitude PV gradient; this is one of the features of adequately explain these phenomena, as shown in AM02 blocking. The Pacific sector is defined as 1608E–1358W and Maeda et al. (2000). or 958–1608W2 and the Atlantic sector as 208W–258E. The central blocking latitude at each longitude is de- 4. Case study: Trajectory analysis fined as the latitude at which the variance of the high- frequency winter-averaged (November–April, 1981–2005) A trajectory analysis demonstrates how air parcels PV at 320 K is a maximum in the Northern Hemisphere behave in a Lagrangian manner during blocking main- (Fig. 3c). The parameter D defines the modification of the tenance. Although some previous studies are based on central blocking latitude at each longitude. This modifi- trajectory analyses (Crum and Stevens 1988; Croci- cation is necessary because of interannual variabilities, Maspoli and Davies 2009), they have all been conducted such as the North Atlantic Oscillation, the Pacific–North to analyze blocking formation (onset)—that is, the in- American pattern, and El Nin˜ o–Southern Oscillation vestigation of the origins of air in blocking anticyclones. (Pelly and Hoskins 2003b). The largest value of B among In this study, trajectories originating from synoptic an- ticyclones and synoptic cyclones upstream of blocks were calculated to investigate the interactions between synoptic eddies and blocking. 2 We found two kinds of Pacific blocking in the course of the Ten wintertime (November–April) blocking events study: one persists over the Aleutian region (drifting upstream), while the other persists over western America (drifting down- were selected from the period 1990–2005. Five blocking stream). Schwierz et al. (2004) actually showed two peaks in the events each were chosen from the eastern Pacific (PAC) blocking-frequency distribution just upstream and downstream of and Atlantic (ATL) regions, where blocks are most the eastern Pacific.

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FIG. 3. (a) The PV distribution of an ATL block (on the 320-K isentropic surface at 1200 UTC 7 Feb 1993). The unit of PV is PVU.

(b) Schematic representation of the relevant parameters for the blocking index B at longitude l0. This panel is a modified version of Fig. 2 in Pelly and Hoskins (2003b). See text for details. (c) Distributions of storm tracks and central blocking latitudes fc. The white plus signs show central blocking latitudes; shaded areas represent the variance of high-frequency PV (PVU2).

D50, 4, or 24 was adopted at each longitude. The du- (event P-1996) indicates that the maximum difference ration was defined as the number of consecutive days for between the PV values of blocked longitudes (1608– which the above definition was continuously satisfied in 1208W) and other longitudes occurs at 320 K (Fig. 4); each sector. Also, the onset was defined as the first day that is, the amplitude of blocking is a maximum on the of a sequence of consecutive days. We used the two re- 320-K surface. This feature is typical of winter blocking. gions, ATL and PAC, to detect blocking events because Therefore, an isentropic surface at 320 K is used for the the frequency of blocking in these regions is high. As the analysis. aim of this study was to clarify the general mechanism of The method for calculating trajectories is the same as blocking, we did not focus on the differences in blocking that of Yamazaki and Itoh (2009). Parcels placed on dynamics as related to different geographical regions. synoptic eddies upstream of blocking are traced around A total of 10 events, consisting of 5 PAC blocks and 5 blocks. Parcel positions are calculated using the fourth- ATL blocks, were chosen somewhat subjectively (Table order Runge–Kutta scheme; the integration time step 1). However, all blocks have large amplitudes and du- and period are 10 min and 5 days, respectively, and the rations of greater than 8 days, according to the above wind (raw wind; i.e., the unfiltered wind) advecting definition; that is, B becomes positive over Dl . 158 in parcels is interpolated linearly in time and by a cubic each sector. spline in space. It has been shown that trajectories of Since the amplitude of blocking shows a maximum in parcels on an isentropic surface in the upper troposphere the upper troposphere (Dole 1986), the supply of PV (selective absorption) there is important. In fact, the potential temperature–longitude cross section of a block

TABLE 1. Regions, event names, periods, and durations of the 10 blocking events selected for this study. Event names reference the region (A: Atlantic; P: Pacific) and the year of occurrence.

Period of Region Event name blocking Duration (days) PAC P-1991 25 Feb–4 Mar 1991 8 P-1996 27 Feb–12 Mar 1996 15 P-1997 9–16 Nov 1997 8 P-2002 3–11 Nov 2002 9 P-2003 3–17 Mar 2003 15 ATL A-1993 4–18 Feb 1993 15 A-1996 6–27 Mar 1996 22 A-2001 9–17 Dec 2001 9 FIG. 4. Potential temperature (K)–longitude cross section of A-2003 6 Feb–5 Mar 2003 28 potential vorticity anomaly (PVU) from the zonal mean at 608Nat A-2005 14 Feb–7 Mar 2005 22 0000 UTC 1 Mar 1996 (P-1996). Data for white regions are missing.

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FIG. 5. Snapshots of blocking flows represented by the low-frequency PV (colored regions; PVU) and parcel isentropic trajectories from synoptic anticyclones (blue) and cyclones (red) in events (a) P-1996 and (b) A-1996 on the 320-K isentropic surface. Details about blocking flows and synoptic eddies are described in the text and in Table 2. Eight other events are also shown: (c) P-1991, (d) P-1997, (e) P-2002, (f) P-2003, (g) A-1993, (h) A-2001, (i) A-2003, and (j) A-2005. represent actual tracks of air over a period of approxi- described in Part II, section 5a. The dates for the mately 1 week (M. Nakamura 1994; Appenzeller et al. placements of the parcels and the numbers of parcels 1996; Peters and Waugh 1996). Of course, the same must placed are listed in Table 2. hold for periods of blocking maintenance. Figure 5 shows the trajectories (i.e., behaviors) of We next describe the initial condition for the place- parcels originating from synoptic anticyclones/cyclones ment of air parcels. At time zero, parcels originating from around maintained blocks. Hereafter, parcels originating a synoptic anticyclone (cyclone) were placed upstream of from synoptic anticyclones (cyclones) are referred to blocks on a grid on which the values of the high-frequency simply as anticyclonic (cyclonic) parcels because they PV component are #23.0 (.3.0) PV units (PVU) and approximately conserve their original PV within the the values of the raw PV component are #0.50 (.8.0) analysis period. At first, results for the P-1996 and A-1996 PVU. The parcels were placed considerably upstream events are explained. The P-1996 event shows trajecto- of blocking (Fig. 5) to enable observation of the true ries from a synoptic anticyclone (cyclone) located near behaviors of synoptic eddies around blocking. This is the Korean Peninsula at 1800 UTC 28 February (0600 UTC because we found that synoptic eddies viewed in high- 27 February) (Fig. 5a). Only parcels from the synoptic pass-filtered fields sometimes show apparent move- anticyclone were absorbed into the blocking anticyclone ments near blocking because of time filters; the detail is (near the Gulf of Alaska), which is displayed by a

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TABLE 2. Information of the 10 selected blocking events: event names (based on region and year of occurrence), dates of placement of synoptic anticyclonic parcels and numbers of parcels placed, and dates of placement of synoptic cyclonic parcels and numbers of parcels placed; dates of the low-frequency PV displayed in Fig. 5. Note that variations in the numbers of parcels for different events vary because of our unified definitions of the PV-based thresholds for anticyclones and cyclones. See text for more details.

Date (number of parcels) Date (number of parcels) Event name for synoptic anticyclone for synoptic cyclone Displayed date of the blocking flow P-1991 0000 UTC 2 Mar (5) 1200 UTC 28 Feb (3) 0000 UTC 3 Mar P-1996 1800 UTC 28 Feb (11) 0600 UTC 27 Feb (3) 0000 UTC 1 Mar P-1997 1200 UTC 12 Nov (21) 0000 UTC 10 Nov (23) 0000 UTC 13 Nov P-2002 0000 UTC 7 Nov (16) 0000 UTC 4 Nov (21) 0000 UTC 7 Nov P-2003 1200 UTC 5 Mar (24) 1200 UTC 9 Mar (32) 0000 UTC 9 Mar A-1993 0600 UTC 13 Feb (8) 0600 UTC 7 Feb (3) 0000 UTC 13 Feb A-1996 0000 UTC 5 Mar (20) 0000 UTC 9 Mar (10) 0000 UTC 9 Mar A-2001 1200 UTC 10 Dec (13) 0000 UTC 9 Dec (27) 0000 UTC 13 Dec A-2003 1200 UTC 16 Feb (13) 1800 UTC 13 Feb (14) 0000 UTC 18 Feb A-2005 0600 UTC 26 Feb (17) 1200 UTC 23 Feb (13) 0000 UTC 26 Feb

snapshot of low-frequency PV at 0000 UTC 1 March. The relationship between anticyclonic parcels and an Note that trajectories of synoptic anticyclones seem to associated migratory ridge (i.e., a synoptic anticyclone separate to two courses just southwest of the blocking in terms of the raw PV field) is noteworthy because anticyclone (near 1608W); most parcels take a northerly these two do not accompany each other through the trajectory and are absorbed into the blocking anticy- time when the parcels or the ridge approach blocking. clone. However, only three anticyclonic parcels are di- Figure6showsthetimesequenceofanticyclonicpar- rected southward and eastward. It should be noted that cels, PV, and the Montgomery streamfunction in the trajectories of synoptic cyclones appear to be passing P-2002 event. The Montgomery streamfunction on isen- through the northern side of the blocking anticyclone. tropic surfaces corresponds to the geopotential height on However, these parcels are at some distance from the isobaric surfaces. At the starting time for the trajectory blocking anticyclone, as the anticyclone was actually lo- calculation (Fig. 6a), anticyclonic parcels were located in cated farther south of the displayed position at the time ridge A, and were traveling at the same speed as the when the cyclonic parcels passed by. For event A-1996, ridge until 2 days later (Figs. 6a–c). However, 12 h later trajectories from synoptic anticyclones and cyclones (Fig. 6d), the parcels had moved into the subtropics, were passing near the Great Lakes, , at south of the high PV air (trough B) and southwest of 0000 UTC 5 March and 0000 UTC 9 March, respec- the blocking anticyclone; simultaneously, ridge A seems tively (Fig. 5b). Only anticyclonic parcels were at- to disappear. Thus, ridge A and the anticyclonic parcels tracted toward the V-shaped blocking region over the moves at different speeds (Figs. 6e and f). eastern Atlantic (shown by the low-frequency PV field The reason why the anticyclonic parcels moved south at 0000 UTC 9 March), and several remained trapped is clearly due to the flow field associated with the trough inside the anticyclone. On the other hand, cyclonic eddies (label B in Fig. 6) and the interaction with it (recall that were repelled by the blocking anticyclone and contin- anticyclonic parcels are repelled by troughs). Other events ued to drift downstream. These two events (P-1996 and in addition to event P-2002 also show such movements A-1996) show the selective absorption of synoptic anti- of anticyclonic parcels around troughs (high-PV air) up- cyclones and the asymmetry between the trajectories of stream of blocks (not shown, but we can infer this be- synoptic anticyclones and synoptic cyclones. The other havior from Fig. 5). The reason that ridge A disappeared eight events displayed in Figs. 5c–j also showed selective may be explained in a similar way; it was also pushed into absorption and similar asymmetries. the subtropics, where PV is as low as that of ridge A. Thus, In some events, such as event A-2005 (Fig. 5j), cyclonic ridge A cannot be distinguished from the surroundings. parcels were absorbed into blocking cyclones. Further- Since trough B is located southwest of a blocking more, in most V-shaped blocks (except in A-2005), anticyclone, its rotational flow leads to the SE–NW blocking cyclones were temporarily formed (for approx- (southeast–northwest) oriented absorption of anticyclonic imately 1/2–2 days) on the equatorward side, although parcels into blocking anticyclones (Figs. 6e and f). This is they are not expressed in the low-frequency PV fields; it is related to overturning of a PV contour and thus cyclonic possible that these blocking cyclones absorbed synoptic wave breaking (Thorncroft et al. 1993) of the trough. This cyclonic parcels (e.g., P-2003 and A-2001). result is consistent with the favored orientation of the

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FIG. 6. Snapshots of synoptic anticyclonic parcels (black circles), raw PV (shaded regions; PVU), and Montgomery streamfunction (contours; m2 s2) on the 320-K isentropic surface for event P-2002 for the period from 0000 UTC 7 Nov to 1200 UTC 10 Nov 2002 at intervals of 12 h or 1 day. A ridge in (a) and (d), and a trough in (d), are labeled ‘‘A’’ and ‘‘B,’’ respectively. wave breaking around blocking shown by Altenhoff The PV supply on lower isentropic surfaces is not as et al. (2008). important to block maintenance as is the supply on the In some events (e.g., P-1996, A-1993, A-1996, and 320-K surface, as already stated. However, as these is- A-2003), there were large differences between the me- entropic surfaces are steeply inclined in midlatitude re- ridional tracks of parcels originating upstream of blocks gions, it is interesting to note from which route low PV is from synoptic anticyclones and synoptic cyclones. The supplied to blocking anticyclones. Figure 7 shows the differences would have been caused by effects of the b trajectories of the A-2005 event in Fig. 5 but for the 300-K gyre: i.e., the polar region acting as a massive cyclone isentropic surface. The anticyclonic (cyclonic) parcels at repels (attracts) anticyclonic (cyclonic) parcels to the 300 K were placed at the same starting dates as those on south (north) by vortex–vortex interaction mechanisms, the 320-K surface and on grids with high-frequency PV rather than by shifts of the westerly jet; this is because values #21.0 (.1.0) PVU; the parcels were within 88 of the tracks of synoptic anticyclones (cyclones) system- longitude and latitude of the parcels placed on the 320-K atically shift southward (northward), and jet patterns do surface. The altitude of the 300-K surface varies greatly not show considerable changes between two dates on with latitude, and roughly corresponds to the 700-hPa which parcels are placed on the synoptic anticyclone and surface in the subtropics, the 500-hPa surface at mid- synoptic cyclone in each event. In other words, wave- latitudes, and the 300-hPa surface at high latitudes. Even guides may not be well formed during an interval be- on the 300-K surface, the selective absorption of a syn- tween the two dates. Such differences can also be optic anticyclone into a blocking anticyclone can be ob- observed in results of numerical experiments in which served. Moreover, anticyclonic parcels were observed to the jet is absent (see Part II). move from lower altitudes (3500 m) in the western

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FIG. 7. As in Fig. 5, but for the 300-K isentropic surface of event A-2005. Contours show time- averaged height (m) on the 300-K surface from the date at which the anticyclonic parcels were placed to 5 days after.

Atlantic to higher altitudes (8500 m) over eastern anticyclones (not shown), in accordance with Fig. 5. In the . This indicates that anticyclonic parcels in the A-1993 event, although many parcels seem to come from lower troposphere ascend along the isentropic surface the subtropics, it is superficial; since a trough southwest of and are absorbed into the blocking anticyclone in the the blocking anticyclone extended to the subtropics, upper troposphere. parcels entering the blocking region had to move around We have investigated so far that low PV originating the trough. We confirmed the midlatitude origin of all from synoptic anticyclones in midlatitudes is supplied to parcels (not shown). Noting that parcels designated with blocking anticyclones. However, low PV from other the plus signs in each blocking anticyclone are those phenomena or regions may be simultaneously supplied. continuing to stay within it from the block onset, almost If the latter dominates the former, we cannot say that all original parcels at the onset time were replaced by low PV supply from synoptic anticyclones is the cause of ‘‘fresh’’ parcels during the 6 days. Comments should be block maintenance. Then, we examined the origin of low given for the two exceptions. In P-1991, many parcels PV air within maintained blocking anticyclones by the seem to be transported from downstream regions; this is backward trajectory analysis. How to calculate the tra- because the blocking anticyclone moved west in this pe- jectory is the same as the forward trajectory analysis ex- riod. Therefore, many parcels were within the blocking cept that the time integration is backward. The backward anticyclone even at that time. In P-1997, many parcels still time integration is carried out for 6 days from 6 days after stayed within the blocking anticyclone. Although several the block onsets (Table 1). Parcels are placed on grids parcels are placed just south of the blocking anticyclone, where the values of raw PV are # 2.0 PVU over latitudes it can be recognized that they came from the west along whose zonally averaged PV is . 4.0 PVU. The latter storm-track regions, when the time integration is carried condition is to restrict parcels within high latitudes. farther back. The longevities of these two events were as The result is shown in Fig. 8. Except for P-1991 (Fig. 8a) short as 8 days, which may be related to the above- and P-1997 (Fig. 8c), it is commonly found that almost mentioned feature that anticyclonic parcels absorbed by all parcels entered blocking regions from midlatitudes. the blocking anticyclones were not so many. Thus, over- Also, we find these parcels originating from synoptic all, a significant number of parcels within maintained

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FIG. 8. Backward trajectories on the 320-K isentropic surface in events (a) P-1991, (b) P-1996, (c) P-1997, (d) P-2002, (e) P-2003, (f) A-1993, (g) A-1996, (h) A-2001, (i) A-2003, and (j) A-2005. Black lines show trajectories of parcels initially placed on positions of the circles. The initial date is 6 days after the onset of each event, and the backward integration is carried out for 6 days. The plus signs indicate the positions of these parcels at 6 days before the initial dates. The shading shows the low-frequency PV (PVU) on the initial dates. blocking anticyclones have synoptic anticyclone origins. amplitude of blocking; in the former events the values This further supports that the SAM is the block mainte- of low-frequency PV are low in the raw PV field (large nance mechanism. amplitude) whereas those of the latter are relatively high (small amplitude). The most typical events 5. Discussion exhibiting these differences are events P-1996 (Fig. 5a) and A-2003 (Fig. 5i). In event P-1996, a large area of a. Two types of absorption low-frequency PV less than 1.5 PVU was present, Although anticyclonic parcels were absorbed into whereas this region was absent in event A-2003. The blocking anticyclones in all the events studied, they amplitude of troughs just downstream of blocking may seemed to be absorbed in two different ways: (i) they also be related to these two patterns; for example, were absorbed into and then remained within a blocking a high-PV trough east of the blocking anticyclone oc- anticyclone, and (ii) they passed through the inside of curred in event A-1996, whereas such a trough did not a blocking anticyclone, and then drifted downstream. intrude into midlatitudes from high latitudes in event Examples of the former occurred in events P-1996, P-1991. The troughs can also restrict the trajectories of A-1996, and P-2003, while examples of the latter oc- anticyclonic parcels. Thus, behaviors of synoptic eddies curred in events P-1991 and A-2003. The difference can change on account of the strength of blocking and between the two patterns may be related to the the presence of a downstream trough.

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When we focus on the strength of blocking, the dif- ference between the two patterns is thought to depend on amplitudes of maintained blocking anticyclones via the strength of the vortex–vortex interaction. As for pattern (i), because the vortex–vortex interaction is strong, parcels originating from synoptic anticyclones absorbed by a blocking anticyclone remain strongly trapped within it. On the other hand, in pattern (ii), anticyclonic parcels attracted by blocking anticyclones remain on the north side of the block, and then drift downstream. Therefore, these differences may cause differences in the momentum and mass transport of parcels from middle to polar latitudes or influence re- FIG. 9. Conceptual diagram illustrating the relationship between gions downstream of blocking. blocking and a southwest-side trough. The trough (gray-shaded b. Troughs southwest of blocking anticyclones circle) attracts and absorbs cyclonic parcels (triangles) originating from a synoptic cyclone (L), advecting anticyclonic parcels (dots) and their relationship to the SAM in a synoptic anticyclone (H) toward a blocking anticyclone. The As shown in Fig. 6, anticyclonic parcels are trans- black arrow shows the trajectories of cyclonic parcels before (solid) and after (dashed) being absorbed by the southwest-side trough. ported into high latitudes by the trough located south- The gray arrow is a flow induced by the trough. west of the blocking anticyclone (hereafter, referred to as southwest-side trough), then being absorbed by the However, we still hesitate to include the southwest-side blocking anticyclone in event P-2002. In the other nine trough in the general block maintenance mechanism. events, anticyclonic parcels always reached blocking This is because blocking can be maintained without it, anticyclones along the flow associated with southwest- aswillbeshownintheb-plane, barotropic models in side troughs. Part II. Therefore, even real blocking that is formed Then, we consider the role of the southwest-side in relatively low latitudes may be maintained without trough in the block maintenance. All the blocking an- the southwest-side trough. We have no answer about it at ticyclones analyzed in this study are located in high present, because all the blocking anticyclones that we have latitudes, which are far from midlatitudes, where anti- analyzed are formed in high latitudes. It is an interesting cyclonic parcels (i.e., origins of low PV) are generated. and important future work whether or not blocking Thus, a route for the supply of low PV from mid- formed in relatively low latitudes still needs the south- latitudes to high latitudes is necessary, as mentioned in west-side trough in its maintenance, and is now under the appendix. The southwest-side trough is just what to way. Also, it is necessary to investigate whether the build this route. Without this route, the SAM may not southwest-side trough is indispensable for the mainte- effectively work because the PV gradient associated nance of all blocking formed in high latitudes. with blocking anticyclones does not have influence on anticyclonic parcels in midlatitudes. In this respect, the c. Diabatic effect southwest-side trough may be an important ingredient The effects of diabatic heating were not considered in in the block maintenance. this study, although some previous studies suggested The southwest-side trough itself may also be main- that the cloud-diabatic effect contributes to the onset of tained by synoptic cyclones through vortex–vortex in- blocking in some events (Altenhoff et al. 2008; Croci- teractions. Figure 9 shows a conceptual diagram of the Maspoli and Davies 2009). However, we think that the interaction between this trough and synoptic cyclones. adiabatic condition of the upper and middle troposphere When blocking is maintained, the southwest-side trough is nearly satisfied in the situations that we studied, as we attracts and absorbs cyclonic parcels, being maintained investigated the maintenance process and not the process or even intensified by the SAM. In fact, we can see that of blocking formation. all trajectories of cyclonic parcels pass through regions of southwest-side troughs (Fig. 5); cyclonic parcels seem 6. Summary to be more effectively attracted than anticyclonic par- cels. This may be explained that cyclonic parcels tend to In a study of blocking maintenance, we investigated the move higher latitudes owing to the b gyre, which is interaction mechanism between synoptic (high-frequency a favorable condition for the southwest-side trough to transient) eddies and blocking. The selective absorption attract cyclonic parcels. mechanism (SAM), in which a blocking anticyclone

Unauthenticated | Downloaded 09/29/21 04:20 PM UTC MARCH 2013 Y A M A Z A K I A N D I T O H 739 selectively attracts and absorbs synoptic anticyclones We thank Drs. H. Mukougawa, H. Nakamura, M. Kimoto, and extends the lifetime, is proposed for the mainte- A. Kubokawa, K. Nakajima, R. Kato, S. Miyahara, T. nance of blocks. The SAM is a new maintenance Hirooka, T. Kawano, K. Iga, M. Watanabe, M. Mori, K. mechanism based on vortex–vortex interactions. Takaya, M. Nakamura, W. Yanase, D. G. Andrews, H.-C. The SAM is a variety of the eddy-feedback mechanism. Kuo, T. Horinouchi, M. Inatsu, H. Mitsudera, B. Taguchi, In this sense, it is similar to the eddy straining mechanism and O. Martius for stimulating discussions and helpful (ESM). However, the SAM explicitly accounts for vortex– comments. Professor P. B. Rhines and an anonymous re- vortex interactions, whereas the ESM does not. Eddy ab- viewer gave us critical and constructive comments, which sorption is the essence of the SAM, whereas this is not led to substantial improvements of the paper. The first and considered in the straining mechanism. Furthermore, the second authors were supported by, respectively, a grant SAM focuses on the nature of PV, not only as a conser- from the Research Fellowship of the Japan Society for the vative property of blocking, but also as being representa- Promotion of Science for Young Scientists and a Grant- tive of a ‘‘vortex.’’ In this respect, the SAM is distinguished in-Aid for Scientific Research from the Japanese Min- from other eddy-feedback mechanisms. We clarified that istry of Education, Science, Sports and Culture. The dataset the ESM does not include an asymmetry between synoptic used in this study was provided by the cooperative research anticyclones and synoptic cyclones, or vortex–vortex in- project of the JRA-25 long-term reanalysis dataset of the teraction, which is essential for the SAM. Japan Meteorological Agency and the Central Research We investigated the SAM in the context of observed Institute of the Electric Power Industry. An original block maintenance events in case studies of 10 events. code for the trajectory analysis was kindly provided by The different behaviors of synoptic anticyclones and Dr. K. Shimose. The figures were produced by GrADs. synoptic cyclones around blocks were observed by tracking parcels originating from each. Our observations APPENDIX indicate that synoptic anticyclones are absorbed into blocking anticyclones, while synoptic cyclones are re- Quasi Stationarity of Blocking pelled by blocking anticyclones and continue drifting downstream of the block, or are attracted by blocking This appendix provides an understanding of the quasi cyclones, if they exist. stationarity of blocking. As already stated, our hy- Several directions for future research are suggested by pothesis is that blocking is a fluctuation around a quasi- our findings. Croci-Maspoli and Davies (2009) demon- stationary solution in phase space; that is, blocking strated that distributions of sea surface temperature satisfies J(c, q) ’ 0, where c is streamfunction, q is (SST) over the North Atlantic drastically change the (quasigeostrophic) potential vorticity, and J is the Jaco- amplitudes of blocks. Also, Ha¨kkinen et al. (2011) re- bian operator. Starting from the same hypothesis, cently argued that Atlantic blocking is strongly corre- Butchart et al. (1989) tried to prove J(c, q) ’ 0usingreal lated with decadal-scale variability of North Atlantic data. However, because real data contain large-ampli- SSTs. Although these studies do not directly address tude disturbances, there were several problems to blocking maintenance, SSTs may also influence main- overcome in demonstrating that J(c, q) ’ 0 in real tenance mechanisms. For example, strong SST gradients blocking flows. We adopted a different approach than and/or strong diabatic heating associated with warm that used by Butchart et al. (1989): we sought a quasi- SSTs may intensify synoptic anticyclones in the lower stationary solution near the blocking in phase space by troposphere at storm-track regions, which in turn effec- making an initial guess about the timing and location at tively supply low PV to blocking anticyclones through an which real blocking appears. We consider that our hy- adiabatic process of the SAM in the middle or upper pothesis is proven if a quasi-stationary solution can be one. The influence of SSTs on block maintenance has yet successfully obtained. to be studied. We first identified an appropriate model. Ideal models In this study, we only investigated blocks in winter are baroclinic; however, they necessarily involve complex when the activities of synoptic disturbances are the computations and the calculations are time consuming. greatest. However, the SAM could be applied to blocks in Thus, we will use baroclinic models in a subsequent anal- other seasons. We found, for example, that the SAM ef- ysis. Here, we adopt a simple model using a basic equation fectively explains a Russian blocking event in the summer that is an equivalent-barotropic, quasigeostrophic PV of 2010. This result will be published in the near future. equation. Adoption of this model is based on the fact that blocking has an equivalent-barotropic nature (see Fig. 4). Acknowledgments. This work represents a portion of This model is also used in Part II. If there is no damping, the first author’s Ph.D. dissertation at Kyushu University. the equation can be written as

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FIG. A1. Snapshots of the streamfunction at 250 hPa at (a) 1200 UTC 28 Feb 1996 and (b) 0000 UTC 8 Mar 1996. (c),(d) Quasi-stationary solutions obtained from the initial guesses for (a) and (b), respectively. The midpoint of each side of the panel borders is at 208N.

›q Rossby deformation radius. An L 5 822 km is adopted 1 J(c, q) 5 0, (A1) d ›t in this model, as in Part II, although results are not sensitive to this value. Using a spectral method, based on where spherical harmonic functions, Eq. (A1) is expanded to

2 1 ›q q 5 f 1 $ c 2 c, (A2) m,n 2 1 [J(c,q)] 5 0, (A3) Ld ›t m,n and where t represents time, f is the Coriolis parameter, where m is the zonal wavenumber and n is the total

= is the two-dimensional nabla operator, and Ld is the wavenumber. Next, F is defined as

Unauthenticated | Downloaded 09/29/21 04:20 PM UTC MARCH 2013 Y A M A Z A K I A N D I T O H 741 N M ›q 2 REFERENCES F [ å å m,n , (A4) n51 m51 ›t Altenhoff, A. M., O. Martius, M. Croci-Maspoli, C. Schwierz, and H. C. Davies, 2008: Linkage of atmospheric blocks and synoptic- where M and N are the zonal and total truncation scale Rossby waves: A climatological analysis. Tellus, 60A, 1053–1063. wavenumbers, respectively (the norm is omitted in this Appenzeller, C., H. C. Davies, and W. A. Norton, 1996: Frag- expression). The truncation is triangular with a maxi- mentation of stratospheric intrusions. J. Geophys. Res., 101 mum wavenumber of 31. The solution is quasi stationary (D1), 1435–1456. if the value of F is very small. Usually, an algorithm to Arai, M., and H. Mukougawa, 2002: On the effectiveness of the minimize the sum of squares of nonlinear functions is eddy straining mechanism for the maintenance of blocking flows. J. Meteor. Soc. Japan, 80, 1089–1102. used to obtain quasi-stationary solutions. Specifically, Barriopedro, D., R. Garcı´a-Herrera, A. R. Lupo, and E. Herna´ndez, we used the revised Marquardt method, and the crite- 2006: A climatology of Northern Hemisphere blocking. 2 rion of a very small value of F was taken as 10 4 of the J. Climate, 19, 1042–1063. original F. Butchart, N., K. Haines, and J. C. Marshall, 1989: A theoretical and The isobaric surface for application of the equiva- diagnostic study of solitary waves and atmospheric blocking. J. Atmos. Sci., 46, 2063–2078. lent-barotropic model is at 250 hPa. This level almost Colucci, S. J., 1985: Explosive cyclogenesis and large-scale circu- corresponds to the 320-K isentropic surface at high lation changes: Implications for atmospheric blocking. J. At- latitudes. Calculations were performed for two typical mos. Sci., 42, 2701–2717. blocking events, one each in the Pacific and Atlantic Croci-Maspoli, M., and H. C. Davies, 2009: Key dynamical features regions. We adopted the Pacific blocking pattern of the 2005/06 European winter. Mon. Wea. Rev., 137, 664– 678. in event P-1996 at 1200 UTC 28 February 1996 Crum, F. X., and D. E. Stevens, 1988: A case study of atmospheric (Fig. A1a) and the Atlantic blocking pattern in event blocking using isentropic analysis. Mon. Wea. Rev., 116, 223– A-1996 at 0000 UTC 8 March 1996 (Fig. A1b). Results 241. are not particularly sensitive to initial guesses, as long as Cushman-Roisin, B., and J.-M. Beckers, 2011: Introduction to some previous or later timings for initial guesses are Geophysical Fluid Dynamics. 2nd ed. International Geo- physics Series, Vol. 101, Academic Press, 828 pp. adopted. D’Andrea, F., and Coauthors, 1998: Northern Hemisphere atmo- Results are shown in Figs. A1c and d. The blocking spheric blocking as simulated by 15 atmospheric general cir- anticyclones clearly remain in their original locations as culation models in the period 1979–1988. 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