Evolution of Dipole-Type Blocking Life Cycles: Analytical Diagnoses and Observations

52 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 64

FEI HUANG Department of Physics, Shanghai Jiao Tong University, Shanghai, and Physical Oceanography Laboratory, Department of Marine Meteorology, Ocean University of China, Qingdao, and Center of Nonlinear Science, Ningbo University, Ningbo, China

XIAOYAN TANG AND S. Y. LOU Department of Physics, Shanghai Jiao Tong University, Shanghai, and Center of Nonlinear Science, Ningbo University, Ningbo, China

CUIHUA LU Weather Bureau of Zaozhuang, Zaozhuang, China

(Manuscript received 13 October 2005, in final form 20 April 2006)

ABSTRACT

A variable coefficient Korteweg–de Vries (VCKdV) system is derived by considering the time-dependent background flow and boundary conditions from a nonlinear, inviscid, nondissipative, and equivalent barotropic vorticity equation in a beta plane. One analytical solution obtained from the VCKdV equation can be successfully used to explain the evolution of atmospheric dipole-type blocking (DB) life cycles. Ana- lytical diagnoses show that the background mean westerlies have great influence on evolution of DB during its life cycle. A weak westerly is necessary for blocking development and the blocking life period shortens, accompanied with the enhanced westerlies. The shear of the background westerlies also plays an important role in the evolution of blocking. The cyclonic shear is preferable for the development of blocking but when the cyclonic shear increases, the intensity of blocking decreases and the life period of DB becomes shorter. Weak anticyclonic shear below a critical threshold is also favorable for DB formation. Time-dependent background westerly (TDW) in the life cycle of DB has some modulations on the blocking life period and intensity due to the behavior of the mean westerlies. Statistical analysis regarding the climatological features of observed DB is also investigated. Observational results show that the Pacific is a preferred region for DB, especially at high latitudes. These features may associate with the weakest westerlies and the particular westerly shear structure over the northwestern Pacific.

1. Introduction term climate anomalies. Hence, the prediction for atmospheric blocking plays a significant role in regional Atmospheric blocking is an important large-scale midterm weather forecast and short-term climate trend weather phenomena in mid–high latitudes in the atmo- prediction. Because of the needs of midterm weather sphere that has a profound effect on local and regional forecasts, there has been a lot of research on dynamics climates in the immediate blocking domain (Rex of blocking. However, the physical mechanism leading 1950a,b; Illari 1984) as well as in regions upstream and/ to blocking formation remains unclear, which may re- or downstream of the blocking event (Quiroz 1984; sult in the difficulty of blocking onset prediction using White and Clark 1975). Therefore, it has long been of general circulation models (Tracton et al. 1989; Tibaldi interest to synoptic and dynamical meteorologists. The and Molteni 1990). formation, maintenance, and collapse of atmospheric Theoretical (Long 1964; Charney and DeVore 1979; blocking always causes large-scale weather or short- Tung and Linzen 1979; McWilliams 1980; Malguzzi and Malanotte-Rizzoli 1984; Haines and Marshall 1987; Butchart et al. 1989; Michelangeli and Vautard 1998; Corresponding author address: Fei Huang, Department of Ma- rine Meteorology, Ocean University of China, 238 Songling Rd., Haines and Holland 1998; Luo 2000; Luo et al. 2001), Qingdao 266100, China. observational (Rex 1950a,b; Colucci and Alberta 1996; E-mail: [email protected] Berggren et al. 1949; Illari 1984; Quiroz 1984; White

DOI: 10.1175/JAS3819.1

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JAS3819 JANUARY 2007 HUANG ET AL. 53 and Clark 1975; Dole and Gordon 1983; Dole 1986, an approximate equation valid in a certain asymptotic 1989; Lejenäs and Økland 1983; Lupo and Smith sense. Taking account of additional physical factors, 1995a), and numerical (Tanaka 1991, 1998; Luo et al. one may also obtain various KdV-type equations. For 2002; D’Andrea et al. 1998; Ji and Tibaldi 1983; Chen instance, a variable coefficient KdV-type (VCKdV) and Juang 1992; Colucci and Baumhefner 1998) studies equation with conditions given at the inflow site was on atmospheric blocking systems have undergone sub- derived as governing the spatial dynamics in a simpli- stantial and extensive development over the past sev- fied one-dimensional model for pulse wave propagation eral decades. Usually an atmospheric blocking anticy- through fluid-filled tubes with elastic walls (Cascaval clone has three types of patterns: monopole-type block- 2003). From the discussion below of a problem on the ing (or ⍀-type blocking), dipole-type blocking dynamics of atmospheric blocking, it will be seen that (McWilliams 1980; Malguzzi and Malanotte-Rizzoli the VCKdV equation is fairly universal and useful to 1984; Luo and Ji 1991), and multipole-type blocking explain the lifetime of the atmospheric blocking sys- (Berggren et al. 1949; Luo 2000). The setup of the two tems. latter patterns are usually due to the strong nonlinear One important fact is that in the usual treatment of interaction between upstream high frequency synoptic- deriving either KdV- or NLS-type equations in the scale transient eddies and planetary-scale waves in ex- study of atmospheric blocking dynamics, one always citing blocking circulation (Hansen and Chen 1982; separates the background flow, assumed to linearly de- Shutts 1983, 1986; Ji and Tibaldi 1983; Illari and Mar- pend on y only, and takes zero boundary values. None- shall 1983; Illari 1984; Hoskins et al. 1985; Egger et al. theless, in reality, the background westerly changes 1986; Mullen 1987; Holopainen and Fortelius 1987; with time as well as the shear type, which is something Haines and Marshall 1987; Vautard and Legras 1988; that has not yet been considered. Therefore, in this Vautard et al. 1988; Chen and Juang 1992; Tanaka 1991; paper, we are motivated to introduce time into the Lupo and Smith 1995b; Lupo 1997; Lupo and Smith background flow and boundary conditions to reinvesti- 1998; Haines and Holland 1998; Luo 2000, 2005a,b). gate the Rossby KdV theory for atmospheric blocking However, the nature of the planetary–synoptic scale systems. interaction has yet to be clarified theoretically (Colucci The term “blocking” denotes a breakdown in the 1985, 1987). prevailing tropospheric westerly flow at midlatitudes, Atmospheric blocking events, mainly located in the often associated with a split in the zonal jet and with mid–high latitudes and usually over the ocean, were persistent ridging at higher latitudes (Rex 1950a,b; Illari first discovered as a dipole pattern by Rex (1950a,b). 1984). Therefore, the basic pattern of blocking is dipole Later, Malguzzi and Malanotte-Rizzoli (1984) first type and it always occurs under weak background west- found the dipole-type blocking from the Korteweg–de erlies (Shutts 1983; Luo and Ji 1991; Luo 1994; Luo et Vries (KdV) Rossby soliton theory. However, their al. 2001; Luo 2005b). Weak background westerlies as a analytical results cannot explain the onset, developing, precondition for block onset were first noted by Shutts and decay of a blocking system. Recently, Luo et al. (1983), who found that the block does not occur for (2001) proposed the envelope Rossby soliton theory more rapid flows in which a stationary free state cannot based on the deduced nonlinear Schrödinger (NLS) be excited. However, Tsou and Smith (1990) and type equations to explain the blocking life cycle. How- Colucci and Alberta (1996) suggested that the precon- ever, they obtained their solutions of the NLS type ditioned planetary-scale ridge (incipient blocking ridge) equations numerically instead of analytically. may be another necessary condition for block onset in In 1895, the KdV equation was first derived in the addition to the weak planetary-scale westerly flow. classic paper of Korteweg and de Vries (1895) as a Although previous theoretical analyses have shown fundamental equation governing propagation of waves that the weaker background westerlies were prevailing in shallow water. After that, much progress has been for the onset of DB rather than that of ⍀-type blocking made on this equation in both mathematics and physics. (Luo 1994), the role of the weak westerlies on the evo- Now, physical applications of the KdV equation have lution of DB life cycles is still unclear. Further, how been seen in a number of problems such as plasmas variations of the time-dependent background westerlies (Zabusky and Kruskal 1965; Rao et al. 1990), quasi- influence the evolution of DB during its life period is one-dimensional solid-state physics (Flytzanis et al. also an interesting problem, since the real-time wester- 1985), nonlinear transmission lines (Yoshinaga and lies vary with time. Shear in the background westerlies Kakutani 1984), and so on. was always introduced into theoretical models (Tung In all these applications, the KdV equation arises as and Linzen 1979; McWilliams 1980; Malguzzi and Ma-

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lanotte-Rizzoli 1984; Haines and Marshall 1987; Butch- dimensionless streamfunction, u and ␷ are components ϭ 2 2 art et al. 1989; Luo 1994; Haines and Holland 1998; Luo of the dimensionless velocity, F L /R 0 is the square et al. 2001) in the study of blocking, while Luo (1995) of the ratio of the characteristic horizontal length scale ␤ ϭ ␤ 2 revealed that dipole structure of solitary Rossby waves L to the Rossby deformation radius R0, 0(L /U), ␤ ␤ ϭ ␻ ␾ ␻ excited by the parameter could be obtained excluding 0 (2 0/a0) cos 0, in which a0 is the earth’s radius, 0 ␾ the effect of shearing basic-state flow. In addition, the is the angular frequency of the earth’s rotation, 0 is the role of anticyclonic shear of basic-state flow on DB was latitude, and U is the characteristic velocity scale. The emphasized (Luo 1994). In contrast, Luo et al. (2001) characteristic horizontal length scale can be L ϭ 106 m found that the cyclonic shear of the background west- and the characteristic horizontal velocity scale is taken erly wind at the beginning of block onset was a favor- as U ϭ 1msϪ1. able preblock environment, which increased the Similar to the usual treatments, we rewrite the ␺ ϭ ␺ ϩ ␺Ј ␺ strength of the precursor blocking ridge, but the anti- streamfunction as 0(y, t) where 0 means the cyclonic shear weakened the precursor blocking ridge background flow term, and introduce the stretched ␰ ϭ ⑀ Ϫ ␶ ϭ ⑀ 3 considerably. Recently, Luo (2005b) also found that the variables (x c0t), t,(c0 is a constant). In the ␺ asymmetry, intensity, and persistence of dipole block previous studies, the background field 0 is often taken depend strongly upon the horizontal shear of the basic- only as a linear function of y, and in most cases one ␺Јϭ͚ϱ ⑀ n␺Ј ␰ ␶ state flow prior to block onset. Then there arises an- simply makes the expansion nϭ1 n( , y, ). other question: what does the role of cyclonic/anticy- However, here we also have the expansion for the back- ␺ ϭ ϩ͚ϱ ⑀ n ␶ clonic shear of the background westerlies play in the ground flow term as 0 U0(y) nϭ1 Un(y, ). evolution of DB during different stages of its life cycle? Then, again similarly, substitute the expansions into (1) In this paper, we will focus on two questions men- and set the coefficient of each order of ⑀ equal to zero. tioned above by diagnosing the analytical solution ob- For notation simplicity, the primes are dropped out in tained from a VCKdV equation derived from the at- the remainder of this paper. In the first order of ⑀,we mospheric nonlinear, inviscid, nondissipative, and obtain equivalent barotropic vorticity equation in a beta plane ␺ ϭ A͑␰, ␶͒G͑y, ␶͒, considering the time-dependent background flow and 1 boundary conditions. The paper is organized as follows. where G is determined by Section 2 introduces the derivation of the VCKdV ͑ ϩ ͒ Ϫ ͑ 2 ϩ ␤ ϩ ͒ ϭ equation and its analytical solution. Analytical diag- U0y c0 Gyy F c0 U0yyy G 0. noses of background westerly variations (including the In the second order, we have variation of mean flow, the westerly shears, and the ␺ ϭ ͑␰ ␶͒ ͑ ␶͒ ϩ 2͑␰ ␶͒ ͑ ␶͒ time-dependent background flow) on the evolution of 2 A , G1 y, A , G2 y, , DB during its life cycle are investigated in section 3. In where G satisfies the following section, some statistical observational re- 1 ͑ ϩ ͒2 Ϫ ͑ ϩ ͒͑ 2 ϩ ϩ ␤͒ sults about DB in the Northern Hemisphere are given U0y c0 G1yy U0y c0 F c0 U0yyy G1 and possible interpretations from above theoretical Ϫ ͓͑ ϩ ͒ Ϫ ͑ 2 ϩ ϩ ␤͒ ͔ ϭ model are demonstrated. Section 5 will outline our con- U0y c0 U1yyy F c0 U0yyy U1y G 0, clusions. and G2 satisfies ͑ ϩ ͒2͓͑ ϩ ͒ Ϫ ͑ 2 ϩ ϩ ␤͒ ͔ 2 U0y c0 U0y c0 G2yy F c0 U0yyy G2 2. Theoretical model ϩ ͓͑ 2 ϩ ϩ ␤͒ F c0 U0yyy U0yy a. Derivation of the VCKdV equation Ϫ ͑ ϩ ͒ ͔ 2 ϭ U0y c0 U0yyyy G 0. Our starting model is the atmospheric nonlinear, inviscid, nondissipative, and equivalent barotropic vortic- Substituting the solutions obtained from the previous ␺ ϭ ity equation in a beta-plane channel (Pedlosky 1979; two orders and 3 0 into the coefficient of the third Luo 2001, 2005a): order of ⑀, then integrating the result with respect to y from 0 to y0 as in the usual treatments of the oceanic ͑Ѩ ϩ Ѩ ϩ ␷Ѩ ͒͑␷ Ϫ Ϫ ␺͒ ϩ ␤␺ ϭ ͑ ͒ and atmospheric dynamics, yield the modified VCKdV t u x y x uy F x 0, 1 ϭ equation (e2 0) and/or VCKdV equation (e2 0):

which is well known and one of the most important 2 e A␰␰␰ ϩ ͑e A ϩ e A ϩ e ͒A␰ ϩ ͑e A͒␶ ϩ e ϭ 0, models in the study of atmospheric and oceanic dy- 1 2 3 4 5 6 ϭϪ␺ ␷ ϭ ␺ ␺ ͑ ͒ namical systems. In Eq. (1), u y, x, is the 2

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ϵ ␶ ϭ 2 ϩ with ei ei ( ), with time-dependent coefficients; that is, U1 a2y ϩ y0 a3y a4 with a2, a3, a4 all time-dependent functions. ϭ ͵ Ϫ ͑ ϩ ͒ The higher orders are all taken as zero, namely U ϭ 0 e1 G U0y c0 dy, n 0 for n Ն 2 so as to simplify the problem. In this case, the y0 background flow is similar to the cases in Gottwald and ϭ ͵ ͑ Ϫ ͒ ϩ Ϫ e2 2 GyyyG2 GyG2yy GG2yyy GyyG2y dy, Grimshaw (1999) except that the mean flow configura- 0 tions are time-varying instead of stable. It is noted that y0 ⑀a ϭ ͵ Ϫ ϩ Ϫ ͑ ͒ the quantity 2 plays the role of the shear of the back- e3 2U1yyyG2 2U1yG2yy GyyyG1 GyG1y y 0 ground flow, and the background westerly wind is determined by a ϩ ⑀a . Apparently, both the shear and ϩ 1 3 GG1yyy dy, the background westerlies vary with time. After these y0 selections, G, G , and G can be easily solved as ϭ ͵ Ϫ ϩ Ϫ 1 2 e4 U1yyyG1 GyyU2y GU2yyy U1yG1yy dy, 0 ϭ ͑ ϩ ͒ G F1 sin My F2 , y0 ϭ ͵ Ϫ 2 ͑F 2 ϩ M2͒F e G F Gdy, 1 5 yy G ϭ F sin͑My ϩ F ͒ ϩ 0 1 5 6 ͑ 2 Ϫ ␤͒ 4M a1F y0 ϭ ͵ ͑ Ϫ 2 ͒ ϫ ͓ ͑ ϩ ͒ ͑ ϩ ͒ e6 U1yy F U1 ␶ dy. M 2a2y a3 sin My F2 0 Ϫ ͑ 2 2 ϩ 2 Ϫ ͒ ͑ ϩ ͔͒ 2a2M y 2a3M y a2 cos My F2 , b. Exact solution of the VCKdV equation G ϭ F sin͑My ϩ F ͒, Obviously, in the above derivation of the VCKdV 2 3 4 ϭϪ 2 ϩ ␤ 2 ϩ 2 ϳ equation, the background flow is left as an arbitrary where c0 (a1M /F M ). Also, F1 F6 and function of {y, t}. For the sake of obtaining meaningful all functions with respect to time should be determined analytical solutions to the VCKdV equation, we have to by the boundary conditions. No constraints are made fix its variable coefficients further. In the expansion of on these functions because in the following, we will ␺ ϭ Ն the background flow term 0,ifUn 0 for n 1, it focus on the behavior of the VCKdV equation with becomes a function of y as usual. Therefore, the higher- different values for the parameters appeared in the order items Un can be viewed as higher-order correc- background flow so as to investigate what effect of the tions to the lowest one, U0. Because of this, we also take background can make on the possible coherent struc- ϭ ϩ U0 as a linear function of y; that is, U0 a1y a0 with ture; that is, the soliton solution. a0, a1 constant, and for the next higher order, as men- With the above selections and results, we can finally tioned before, it is chosen as a quadratic function of y write down an exact solution to the VCKdV equation as

␰ Ϫ ͑ 2 Ϫ ␤͒1ր3 3 3 Ϫ C2 H F a1 C4 8K C3C7 2KC4 A ϭ ϩ ͭ ϩ 12C K2C2ր3sech2ͫ ϩ KC ͌Ϫ ϩ ␶ ͑ 2 ϩ 2͒2ր3͌Ϫ ϩ ␶ 2 1ր3 3 7 ͌Ϫ ϩ ␶ 5 2C3e6 C1 C2 e6 F M C1 C2 C3C7 C2 C1 C2 1ր3͑ 2 ϩ 2͒2ր3 ␰ ͌Ϫ ϩ ␶ KC3C7 F M 2 H e4 C1 C2 Ϫ 4K3C ϩ ͩ ϩ ͵ d␶ͪͬͮ Ϫ , ͑3͒ 6 ͑ 2 Ϫ ␤͒1ր3 ͌Ϫ ϩ ␶ ͑Ϫ ϩ ␶͒3ր2 2 2 F a1 C1 C2 C1 C2 C3e6 where

͑ Ϫ ␶͒͑ Ϫ ͒ 2 C1 C2 e4e6␶ e4␶e6 e4C2 H ϭ ͵ ϩ 2e C ͌C Ϫ C ␶ Ϫ d␶, 2 7 3 2 1 e e6 6

ϭ ͓ ͑ ϩ ͒ Ϫ ͑ ͒ Ϫ ͑ ϩ ͒ ͑ ϩ ͒ ϩ ͑ ͔͒ e4 2a2 sin My0 F6 2a2 sin F6 M 2a2y0 a3 cos My0 F6 Ma3 cos F6 F5 ͑ 2 ϩ 2͒ F M F1 Ϫ ͕a a sin͑F ͒M Ϫ ͑M2a2 ϩ 2a2͓͒cos͑My ϩ F ͒ Ϫ cos͑F ͔͒ ͑ 2 Ϫ ␤͒ 2 3 2 3 2 0 2 2 4 F a1 M ϩ ͑ ϩ ͒͑ 2 2 ϩ 2 Ϫ ͒ ͑ ϩ ͖͒ M 2a2y0 a3 2M a2y0 2M a3y0 a2 sin My0 F2 ,

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͑ 2 ϩ 2͒ F1 M F e ϭϪ ͓cos͑F ͒ Ϫ cos͑My ϩ F ͔͒, 6 M 2 0 2

y0 2 2 2 2 e ϭϪ ͓͑2y F Ϫ 12͒a ␶ ϩ 3y F a ␶ ϩ 6F a ␶͔, 7 6 0 2 0 3 4

ϭ ϳ and M, K, Ci,(i 1,2,...,7)arearbitrary constants. There is also a necessary relation between F2 F4:

͕ 2͑␭ 2 Ϫ ␤͒͌Ϫ ϩ ␶͓ ͑ ͒ Ϫ ͑ ϩ ͒ Ϫ ͑ ͒ ϩ ͑ ϩ ͒ ͑ ϩ ͔͖͒ F3 2M 0 a1 C1 C2 2a2 sin F4 2a2 sin My0 F4 a3M cos F4 M 2y0a2 a3 cos My0 F4 Ϫ 2͑ 2 ϩ 2͕͒ 3͌Ϫ ϩ ␶ ϫ ͓ ͑ ͒ ͑ ͒ Ϫ ͑ ϩ ͒ ͑ ϩ ͒ ϩ ͔ F 1 F M a2M C1 C2 cos F2 sin F2 cos My0 F2 sin My0 F2 My0 Ϫ ͑ 2 Ϫ ␤͒͑ 2 ϩ 2͓͒ ͑ ͒ Ϫ ͑ ϩ ͔͒2͖ ϭ C3 F a1 F M cos F2 cos My0 F2 0.

2 Ϫ 2 ϭ 3. Analytical diagnosis on DB evolution [(2/F ) (y0 /3)]a2 (and then e6 0). Hence, one possible approximate solution to (1) is in the form of In this section we analyze a DB evolution case under ϭ ϭϪ ϩ certain parameters. Set e4 0 and a4 (y0 /2)a3

y 2 y2 sin͑My ϩ F ͒⑀M ␺ Ϸ ⑀ 2 ϩ ͑ ϩ ⑀ ͒ ϩ Ϫ 0 ⑀ ϩ Ϫ 0 ⑀ Ϫ 2 a2 y a1 a3 y a0 a3 ͩ ͪ a2 2 F 2 3 ͓ ͑ ͒ Ϫ ͑ ϩ ͔͒͑ 2 ϩ 2͒͌Ϫ ϩ ⑀3 cos F2 cos My0 F2 M F C1 C2t ⑀C C M K ⑀C C1ր3 8K2C3C Ϫ 2C ϫ 2 ͑ Ϫ ͒ ϩ 4 1 ϩ 2 2ր3 2 3 7 ͑ Ϫ ͒ ϩ 3 7 4 ͩ x c0t ր 12C3M1K C7 sech ͭ ͫ x c0t ͬ 2 1 3 2C3 C C ͌Ϫ ϩ ⑀3 M1 C2 3 7 C1 C2t

ϩ ͑ Ϫ 2 ͒ ͑ ͒ K C5 4K C6 ͮͪ, 4

ϭ 2 Ϫ ␤ 1/3 2 ϩ 2 2/3 with M1 [(F a1 ) /(F M ) ]. maintenance, and decay processes—a whole life cycle From the analytical solution of streamfunction ␺ of a dipole-type blocking event. The streamlines are it is easy to derive the background westerly flow u ϭ gradually deformed and split into two branches at the ⑀ ϭ ϩ ␦ ϭϪ ϩ ץ ␺ץ Ϫ ( 0/ y) u0 y, where u0 [a1 a3(t)] and second day, with the anticyclonic high in the north de- ␦ ϭϪ ⑀ 2 a2(t). As we know, the weather or climate pe- veloping first (Fig. 1a). Then the cutoff low develops riodically changes on either large or small scales. Thus, south of the high, forming a pair of high–low dipole it is reasonable to choose the time-dependent unknown patterns where the center of the high is located at the functions in the background flow as periodic, so here higher latitude than that of the low (Fig. 1b). They are ϭϪ the sine function is in use. Thus we choose a2(t) a20 strengthened daily. At around the sixth day (Fig. 1c), ϭϪ sin(K2t), a3(t) a30 sin(K3t). The basic-state wester- they are at their strongest stage and then become ␦ Ͻ Ͼ lies have cyclonic shear when 0ora20 0, but weaker and eventually disappear after the eleventh day correspond to anticyclonic westerly shear when ␦ Ͼ 0or (Figs. 1d–f). Obviously, Fig. 1 possesses the phenom- Ͻ ␾ ϭ a20 0. Here we consider 0 60°N in that the block- enon’s salient features including their spatial-scale and ing systems are mainly situated in the mid–high lati- structure, amplitude, life cycle, and duration. There- tudes. For example, when we take the functions and fore, Fig. 1 is a very typical dipole-type blocking epi- ϭ parameters in our analytical solution (4) as a20 0.1, sode. More importantly, it corresponds quite well to a ϭ ϭ ϭ ϭ ϭ ϭ k2 2.1, a30 0.5, k3 k2 2.1, y0 6, F2 real observational blocking case (Fig. 2) that happened Ϫ8 Ϫ ⑀ ϭ ϭ arccos[10 cosh(0.75t 4.5)], 0.1, a0 2, over the Pacific during 2–12 January 1996, which is ob- ϭϪ ϭϪ ϭ ϭϪ ϭϪ a1 0.2, C1 30, C2 0.1, C3 10, C4 16, tained from the National Centers for Environmental ϭ ϭϪ ϭ ϭ ϭ ϭ ␲ C5 4, C6 7, C7 0.1, K 0.2, F 64, M /6, Prediction–National Center for Atmospheric Research a dipole-type blocking life cycle appears and is shown in (NCEP–NCAR) reanalysis data. Because blocking is a Fig. 1. large-scale atmospheric phenomenon, the geopotential Figure 1 clearly reveals the onset, development, height fields in Fig. 2 were filtered by preserving wave-

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ϭϪ ϭϪ ⑀ ϭ FIG. 1. A dipole blocking life cycle from the theoretical solution (4) with a2 0.1 sin(2.1t), a3 0.5 sin(2.1t), 0.1, ϭϪ ϭ a1 0.2. The contour interval (CI) 0.2. numbers 0–4 in a harmonic analysis around latitudes in ground westerlies in the DB evolution is not clear in a order to filter high-frequency synoptic-scale perturba- VCKdV soliton system, while the typical KdV Rossby tions. soliton can only represent a steady-state DB pattern It is easily found in Fig. 2 that the life cycle of this instead of an evolution of DB life cycles. To simplify blocking lasts almost 10 days, experiencing three stages: the question, here only variation of the mean flow is ϭ onset (2–5 January 1996), maturity (7–9 January 1996), considered without the westerly shear [a2(t) 0] and ϭ and decay (10–12 January 1996). This blocking event time-dependent background westerly term [a3 (t) 0]. developed within an atmospheric long Rossby wave Only the parameter a1 varies in different constants in- ridge extending northwestward and an upstream cutoff dicating the variation of the mean background wester- low moving southeastward (Figs. 2a,b). With the lies. The evolutions of DB life cycles under different strengthening of the blocking high and the cutoff low, mean background westerlies are shown in Fig. 3. two closed centers of high and low appeared forming a It is shown in Fig. 3 that the intensity, zonal and north–south dipole-like pattern with the closed high in meridional scales, position, and period of DB during its the north and the closed low in the south during the life episode alter with increasing mean background mature stage (Figs. 2c,d). Then the high center decayed ϭϪ westerlies. Under the weak mean westerly a1 0.2 and vanished first, as well as the cutoff low decayed condition (Fig. 3a), the DB period is about 10 days from subsequently (Figs. 2e,f). At last the block became a t ϭ 1tot ϭ 10, consistent with typical period of block- traveling Rossby wave ridge and moved eastward (fig- ing observed (Rex 1950b; White and Clark 1975; ure omitted). Lejenäs and Økland 1983; Dole 1989; Luo and Ji 1991; Huang 2002). At time t ϭ 2 an incipient dipole-like a. Effect of the mean background westerlies envelope Rossby soliton pattern appears and begins to Previous research showed that the background west- enhance, forming closed high and low centers at t ϭ 4. erlies are a necessary precondition for the onset of an- Then the high and low centers strengthen dramatically ticyclonic blocking and they also played an important from t ϭ 4tot ϭ 6 and reach their peaks at t ϭ 6. role in the blocking life cycle (Shutts 1983, 1986; Luo Subsequently, the high and low centers in DB decrease and Ji 1991; Luo 1994; Luo et al. 2001). For DB evolu- gradually from t ϭ 7tot ϭ 10. The meridional scale of tion during its life cycle, the role of the mean back- DB (distance between the high and low centers) in-

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FIG. 2. Filtered geopotential height at 500-hPa pressure level of a blocking case during 2–11 Jan 1996. Contour interval is 4 gpdm. The x axis is longitude, and the y axis is latitude. creases during the developing period (t ϭ 1tot ϭ 6) of out the period of DB life cycles. Nevertheless, the be- DB life cycle and decreases during the decay process haviors of the high and low centers appear inconsistent (t ϭ 7tot ϭ 10). It is noticeable that the high and low during the different developing stages of DB life epi- centers in the DB streamlines pattern seem antisym- sode. That is, the high center (Fig. 4a) decreases greatly metric along the north–south direction as well as the during the onset (t ϭ 1tot ϭ 4) and decay (t ϭ 8to evolution process is symmetric with respect to the ma- t ϭ 11) stages of DB life episode, and decreases slowly ture phase of DB at t ϭ 6 under the highly idealized in the DB mature phase (t ϭ 5tot ϭ 7). On the con- theoretical solution. However, the main characteristics trary, the low center (Fig. 4b) deepens greatly during of the DB streamlines pattern and its evolution, includ- the mature stage of DB life cycle, but strengthens rela- ing the onset, development, mature, and decay pro- tively slightly at the onset and decay stages. cesses, are well captured. To see more clearly the movement of DB high center Comparing the DB evolution processes under differ- with respect to time t, Fig. 5 shows space–time (x–t or ent mean westerlies (Figs. 3b–d), it is easily found that y–t) cross sections crossing the high center. From the the incipient dipole-like envelope at time t ϭ 3 weakens x–t cross section (Fig. 5a) it is found that the blocking with the mean westerly increasing. The closed stream- high moves westward and the zonal scale of DB en- lines of high and low centers in DB under weak west- larges with the strengthening of the mean westerlies. erly conditions (Figs. 3a,b) at t ϭ 4 disappear and are This feature can also be identified in Fig. 3. For the y–t replaced by the gradually decreasing envelope stream- cross section crossing the high center (Fig. 5b), the me- line pattern (Figs. 3c,d) when the parameter a1 varies ridional scale of the DB shortens and the evolution ϭϪ ϭϪ from a1 0.8 to a1 1.0. That means the period of crossing the dipole high/low center with respect to t the DB life cycle shortens when the mean westerlies displays a shrinking dipole-like pattern, suggesting increase. At time t ϭ 4ort ϭ 8, it is very clear that the shortening of DB period of life cycles under the condi- DB intensity represented by values of the DB high and tion of the mean westerlies increasing. This result im- low centers also weakens with the mean flow increas- plies that the DB could not maintain stationary long ing. This feature is also clearly seen in Fig. 4, showing time in the strong westerlies (Shutts 1983). the intensity of DB high (Fig. 4a) and low (Fig. 4b) b. Effect of the background westerly shear center varying with respect to time t. It is obvious that the high center of DB weakens while the low center In this section effects of the westerly shears including strengthens when the mean westerlies increase through- cyclonic shear and anticyclonic shear on evolution of

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ϭϪ ϭϪ ϭϪ FIG. 3. The evolutions of DB life cycle under different background westerlies (a) a1 0.2, (b) a1 0.5, (c) a1 0.8, ϭϪ ϭ (d) a1 1.0 (CI 0.4).

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FIG. 4. The intensity of the DB (a) high and (b) low center varying with respect to time t.

DB are investigated. As mentioned above, the westerly 0.45, and 0.6, corresponding to 1%, 5%, 10%, 15%, and ␦ ␦ ϭϪ ⑀ ␦ Ͻ shear parameter is expressed as 2 a2(t); 0or 20% of the mean westerlies u0, are investigated respec- Ͼ a2(t) 0 denotes the cyclonic background westerly tively in Fig. 6. Results show that weak CWS is favor- ␦ Ͼ Ͻ shear, and 0ora2(t) 0 represents the anticyclonic able for the onset of DB, similar to the conclusion by shear. As we know, a2(t) is a function with respect to Luo et al. (2001), Luo (2005b), and Dong and Colucci time t. To simplify the question, here a2 is assumed to (2005). However, the DB life period shortens and the be a small constant, suggesting a time-independent DB high/low centers weaken simultaneously when the weak linear shear superposed on the background mean weak CWS enhances during the evolution of the DB flow. The mean westerlies without the time-dependent episode (Figs. 7a,c). The intensity variation of the low ϭ term [a3(t) 0] is also assumed. Consequently, the center appears to have different behaviors, considering ϭ ϩ ␦ background westerly with linear shear is u u0 y, the CWS comparisons with and without shear (Fig. 4). ϭϪ ϭ where the mean flow u0 a1 0.6. That is, the low weakens along with increasing CWS (Fig. 7c), and strengthens with increasing background 1) THE CYCLONIC WESTERLY SHEAR mean westerlies without shear (Fig. 4b). A noticeable phenomenon is that the CWS destroys the antisymmet- The background westerly shear is always introduced ric structure of the DB high/low poles. The low devel- into a theoretical model (Tung and Linzen 1979; ops more slowly than the high at the DB onset stage McWilliams 1980; Malguzzi and Malanotte-Rizzoli (t ϭ 4), while it trails off faster than the high during the 1984; Haines and Marshall 1987; Butchart et al. 1989; decay period (t ϭ 8) with the CWS increasing (Fig. 6). Luo 1994; Haines and Holland 1998; Luo et al. 2001; This feature is also indicated in Figs. 7a,c. Luo 2005b) in the study of blocking, but the role of the cyclonic westerly shear (CWS) in evolution of DB dur- 2) THE ANTICYCLONIC WESTERLY SHEAR ing its life cycle is not clear, although Luo et al. (2001) and Luo (2005b) emphasized the important role of the Luo (1994) revealed that strong anticyclonic westerly cyclonic shear of background westerly wind in block shear (AWS) was disadvantageous for establishment of onset. Recently, Dong and Colucci (2005) also demon- dipole-type blocking, but his solution could not inter- strated the important effect of cyclonically sheared flow pret the onset and decay process of DB. Recently, Luo on forcing weakening westerlies associated with the et al. (2001) and Luo (2005b) also pointed out that the Southern Hemisphere blocking onset. To compare the anticyclonic background westerly shear weakened the influence of different cyclonic shear on a DB episode, precursor blocking ridge considerably; therefore, the ϭ the DB evolutions at parameter a2 0.03, 0.15, 0.3, formation of a blocking anticyclone was difficult. How-

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FIG. 5. The space–time (a) x–t and (b) y–t cross sections crossing the high center of DB under different basic mean westerlies; CI ϭ 0.2.

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ϭ FIG. 6. The streamfunction patterns of DB evolution under different cyclonic westerly shears: (a) a2 0.03; ϭ ϭ ϭ ϭ ϭ (b) a2 0.15; (c) a2 0.3; (d) a2 0.45; (e) a2 0.6 (CI 0.4).

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FIG. 7. The intensity of the DB (a), (b) high and (c), (d) low center varying with respect to time t under different conditions of westerly shears; cyclonic shear is shown in (a) and (c), and anticyclonic shear is shown in (b) and (d). ever, the role of the AWS on DB life cycles is not clear. (decays) earlier (later) with the increasing of the AWS ␦ Ͼ ␦ In our model, the influence of different weak AWS on (Figs. 8a–c). For c, the dipole-like circulation can ϭϪ Ϫ Ϫ DB episode with parameters a2 0.03, 0.15, 0.3, still develop, but never be a blocking pattern splitting Ϫ0.45, and Ϫ0.6, respectively, are compared with each the westerlies into two northward and southward other in Fig. 8. Results show that only very weak anti- branches (Figs. 8d,e). Instead, the separate northward cyclonic shear is more preferable for the onset and westerlies around the high disappear and the developed maintenance of DB, resulting in longer life of DB (Figs. high in the dipole comes from the most northern

8a–c). There exists a threshold value of a2 limiting the boundary, which indicates a cutoff high from the North anticyclonic shear that controls the appearance of DB Pole region moving southward, forming the dipole cir- ϭ streamline patterns. Under the mean westerlies u0 culation together with the low in the south. Actually, in Ϫ 0.6, the threshold of a2 is about 0.45, or the threshold a daily synoptic chart, the cutoff high from the North ␦ ϭ Ϫ shear c 0.09, denoting the slope of lines on the (u0 Pole region is often seen moving southward. The y) plane. This means the DB is easily established under threshold value of the AWS decreases along with de- ␦ Ͻ ␦ ␦ Ͻ ␦ weak AWS condition when c. For c, the DB creasing of the mean background westerlies u0. life period is prolonged obviously and DB establishes It is also obvious that the AWS induces the asym-

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FIG. 8. The streamfunction patterns of DB evolution under different anticyclonic westerly shears: ϭϪ ϭϪ ϭϪ ϭϪ ϭϪ ϭ (a) a2 0.03; (b) a2 0.15; (c) a2 0.3; (d) a2 0.45; (e) a2 0.6 (CI 0.4).

Unauthenticated | Downloaded 10/07/21 10:49 AM UTC JANUARY 2007 HUANG ET AL. 65 metric development of the high/low centers in DB during different stages of its life cycle (Fig. 8). Espe- cially at DB onset (t ϭ 3, 4) and decay (t ϭ 8, 9) phases, the high center is apparently stronger than the low center, and the high/low center tends to strengthen along with the strengthening of the AWS. The DB high/low center strengthens simultaneously when the AWS stengthens during the evolution of the DB episode (Figs. 7b,d), which appears to have opposite behavior than that with CWS (Fig. 7a,c). In addition, the intensity of the DB dipole centers with AWS is stronger than that of CWS. c. Effect of the time-dependent background westerlies In the real atmospheric circulation, the background westerly is not always a constant during the life period of blocking. Actually there is interaction between blocking and the background westerlies; that is, the weak background westerlies modulated by transient eddies are a precondition for the onset of blocking; mean- while, after the blocking is established, it prevents the westerlies passing through as a result of a weakened FIG. 9. Different types of TDW profiles during the DB life westerly (Berggren et al. 1949; Elliott and Smith 1949; cycle. The x axis is time t in DB life episode and y axis denotes ϭ Ϫ Egger et al. 1986; Mullen 1987; Long 1964; Shutts 1983; u. Case 1 represents u 0.5 0.3 cos(0.26t), case 2 denotes u ϭ 0.5 Ϫ 0.3 cos[0.52(t Ϫ 6)], and case 3 denotes u ϭ 0.5 Ϫ 0.3 Colucci 1985; Holopainen and Fortelius 1987; Dole cos[0.37(t Ϫ 6)]. 1989; Luo et al. 2001). Therefore, the background westerlies may be a time-dependent function during the episode interacting with blocking. For simplification, the ϭ ens the intensity of the DB. Tests changing slopes of the westerly shear (a2 0) is not considered here, so the ϭ Ϫ ⑀ ϭϪ ϭ (u Ϫ t) profiles indicate that the variation rate of the background flow, u u0 a3(t), here is u0 a1 background westerlies during the DB episode does not 0.5. Several types of a3(t) profiles shown in Fig. 9 are attempts to investigate the influence of time-dependent act as an influence on the DB evolution (not shown). background westerlies (TDW) on DB evolution. Case 1 This result implies that the time-dependent westerlies indicates the condition that the background westerlies varying accordingly before and after the DB reaches its become weakest at DB onset stage and increase gradu- peak phase play a similar role in the DB evolution. For ally throughout the block life cycle. It is found that the the TDW reflecting interaction between blocking and variations of the curve slope do not impact the evolu- background flow in case 2, the evolution of DB has tion of DB in case 1. Cases 2 and 3 show the westerly been considerably impacted. The most noticeable fea- profiles reflecting the interaction between the back- ture is that the time of the DB onset and decay lags that ground westerlies and blocking with the westerlies de- without the TDW term, either for the high (Fig. 10a) or creasing during the developing period before the DB for the low center (Fig. 10b) in the dipole structure. The peak at t ϭ 6 and increasing throughout the decay stage decay process from the peak phase of DB to its disap- after the DB peak. The latter is conceptually consistent pearance is longer than the DB developing process with the actual variation of the westerlies during a from the onset of DB to its peak phase, resulting in the blocking evolution (Elliott and Smith 1949). asymmetric evolution of the DB during its life episode. Figure 10 presents the intensity of the DB high (Fig. In addition, the intensity of the DB high/low centers at 10a) and low (Fig. 10b) center varying with respect to its peak phase strengthens slightly. However, the inten- time t under different types of TDW as shown in Fig. 9 sity of DB depends on the slope of the profile. For during the DB life cycle. For case 1, the TDW varying example, when the slope is not so sharp (case 3 in Fig. from the weakest to the strongest stage during the DB 9) as in case 2, the high (low) peak drops down (goes life cycle, shortens the life period of the DB and weak- up) indicating the weakening of the DB (dot–dashed

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FIG. 10. The intensity of the DB (a) high and (b) low center varying with respect to time t under different types of TDW as shown in Fig. 9 during the DB life cycle. Label “Ctrl” means the case of background westerly u without ϭ time-dependent term a3(t) 0. line in Fig. 10), but the lag and asymmetric character- 4. Observational features of DB in the Northern istics are not changed. Hemisphere The detailed evolutions of DB impacted by TDW are presented in Fig. 11. For case 1 (Fig. 11a), the DB evo- a. Data and the DB definition lution process is similar to that without the TDW term The data source in this study is the NCEP–NCAR in Fig. 3b, exhibiting a symmetric feature about the reanalysis data from January 1958 to December 1997, peak phase in the evolution of the DB episode. The which uses a state-of-the-art global data assimilation most differences between Fig. 3b and Fig. 11a are in the system (Kalnay et al. 1996). The variables used in this different intensity of DB at any phase during the DB study are daily mean geopotential height at 1000 and life cycle and the zonal and meridional scales. The high/ 500 hPa and the west–east wind component at 500 hPa, low intensity weakens in case 1 and the zonal and me- on a 2.5° latitude ϫ 2.5° longitude grid, from 20° to ridional scales of DB all lessens a little, suggesting the 90°N around the Northern Hemisphere. DB period shortens, which is coherent with the results Although the blocking phenomenon is well known in discussed above from Fig. 10. For case 2 the developing the meteorological community, there is no generally process from the onset (t ϭ 3) of DB to its peak phase accepted definition of a blocking event (Lejenäs and (t ϭ 6) resembles that in case 1, but the decay process Økland 1983). Commonly used definitions can be di- from the DB peak phase to the blocking vanishing (t ϭ vided into four categories of methods to identify block- 10) appears very different. Compared to the DB evo- ing. The first is a subjective technique first put forward lution process without TDW (Fig. 3b), the dipole center by Rex (1950a,b) in the 1950s. This was then inherited of the blocking in case 2 is stronger than that in Fig. 3b and modified by Sumner (1954) and White and Clark at the beginning decay stage (t ϭ 7, 8). At t ϭ 9 the (1975). They identified the blocking events subjectively dipole-like pattern with closed high/low centers still by visual inspection and then used semiobjective crite- maintains although the streamlines become sparser in ria to determine the exact dates of initiation and dura- case 2, while it disappears and only shows a dipolelike tion of blocking based on examination of the daily envelope in Fig. 3b. At t ϭ 10 the almost straight weather charts. The second category uses objective cri- streamlines in Fig. 3b are instead of dipolelike envelope teria first used by Elliott and Smith (1949) based on in Fig. 11b with sparser streamlines. Above all, the ef- magnitude and persistence of pressure anomalies. fect of the TDW on evolution of DB is owing to altering Later, Hartman and Ghan (1980), Dole and Gordon the DB life period and leading to the asymmetry of the (1983), Dole (1986, 1989), Shukla and Mo (1983), DB life cycle evolution with respect to its peak phase. Huang (2002), and Huang et al. (2002b) extended the

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FIG. 11. The streamfunction patterns of DB evolution under different time-dependent westerly profiles in Fig. 9: (a) case 1, (b) case 2 (CI ϭ 0.4). analysis from sea level pressure departure to the occur- do not wholly address DB, so new criteria for identify- rence of persistent positive geopotential height anoma- ing DB have to be established. In this study the DB is lies at the upper level. The useful objective criteria for distinguished by the following criteria. identifying blocking events were designed by Lejenäs 1) At least one pair of closed high/low contours ap- and Økland (1983), using the north–south geopotential pears simultaneously at 4 (2.5) geopotential deca- height gradient based on the coherence between the meters (dam) contour interval at 500 hPa (1000 occurrence of persistent anomalous midlatitude east- hPa), with the distance between the high and low erly flow and blocking. The advantage of this objective centers is no larger than 30 longitudes. method is its simplicity for automatic calculation, and it 2) The westerlies must split into two branches at 500 has therefore been used widely (Tibaldi and Molteni hPa, and the distance between the divarication point 1990; D’Andrea et al. 1998; Huang et al. 2002a). Re- and the meeting point is no less than 45 longitudes. cently, Pelly and Hoskins (2003a,b) constructed a new 3) The closed high or low center lasts at least 5 days. dynamical blocking index using a meridional ␪ differ- 4) The moving speed of the blocking does not exceed ence on a potential vorticity (PV) surface. They reveal ten degrees of longitude per day. that their PV–␪ index is better able to detect ⍀ blocking 5) The high center is located at least north of 40°N. than conventional height field indices. Since we are fo- Ϫ 6) The blocking index (BI) is no less than 20 m s 1. cusing on dipole-type blocking, the newest PV–␪ index ϭ Ϫ ϫ Ϫ1 is not suitable for us in this study. The BI is calculated as BI UWM 3 UEM ms , All of the definitions of blocking mentioned above where UEM is the maximum of the 20-point running

Unauthenticated | Downloaded 10/07/21 10:49 AM UTC 68 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 64 mean of geostrophic easterlies bounded by 20 degrees of longitude in the east and west of the high center, respectively, and 30 degrees of latitude south of the high center; UWM is the maximum of the westerlies south of the UEM position bounded by 30 degrees of latitude. Because the easterlies south of the blocking anticyclone are usually about 3 times less than the westerlies, 3 times UEM is calculated in BI. The geostrophic -y (f is the Coץ/zץ( wind U is calculated as U ϭϪ(g/f riolis parameter, g is the gravitational acceleration, and z is the geopotential height at 500 hPa). The latitude FIG. 12. The latitudinal distribution of DB over the three and longitude of the high center denote the position of favorable regions. the high, which is prescribed similarly to that of Dole (1986) as persistent positive anomalies (with respect to latitude mean) greater than 70 gpm at 500 hPa. The Smith (1949) and Rex (1950b), which were published number of times that dipole-type blocking appears is within a year of each other, gave contradictory results counted and the latitude where the high center of a on the relative frequency of blocking in the Atlantic dipole block is located is regarded as the meridional and Pacific. White and Clark (1975), however, obtained position of the DB. a result that was not in agreement with Rex (1950b). In the research of Elliott and Smith (1949), they found b. Climatological features of DB and possible that the total number of blocking days in central Pacific reasons is 4 times of that in the northeastern Atlantic. Notice Many studies have derived a comprehensive set of that the previous results did not distinguish the DB or climatological statistical characteristics of blocking an- monopole blocking, Elliott and Smith’s (1949) results ticyclones using subjective or objective techniques, in- might include more DBs, while the statistics of Rex cluding location, frequency, duration, intensity, size, (1950b) may include more monopole blocks since they and distribution (Elliott and Smith 1949; Rex 1950a,b; used different data in different periods of time or their White and Clark 1975; Lupo and Smith 1995a; Lejenäs definitions of blocking may not be exactly the same. and Økland 1983; Huang et al. 2002a; Huang 2002). The latitudinal distribution of DB over the three fa- Preferred Northern Hemisphere locations for blocking vorable regions is displayed in Fig. 12. It is shown that are the northeastern boundaries of the Pacific and At- the latitude of DB over the Pacific is mostly concen- lantic Oceans and the Ural area (Elliott and Smith trated at 65°–80°N, while the DB over Atlantic focuses 1949; Rex 1950b; Lejenäs and Økland 1983; Dole and at 55°–65°N, about 10° southward from that in the Pa- Gordon 1983; Shukla and Mo 1983; Huang 2002). For cific. The Ural area has the least DB, mainly at 60°– the statistical characteristics of DB, only Luo and Ji 70°N, and it is also more southward than that over the (1991) performed an observational study of dipole-type Pacific. blocking in the atmosphere during 1969–84. However, From the statistics above it is found that the Pacific is the time series are too short to include the interdecadal the most favorable place for DB occurrence, but fewer variability of blocking (Huang et al. 2002b). The avail- blocking events (include DB and ⍀ blocking) occurred ability of the NCEP–NCAR reanalysis data (Kalnay et over the Pacific compared to the Atlantic and Ural ar- al. 1996) includes a considerably long time series, and eas (see Huang 2002). Why does DB seem to prefer the so provides a solid basis for understanding behavior of Pacific? This is really a puzzling question. According to the atmospheric midlatitude blocking. the analysis in section 3, we know the intensity of the In this paper, statistical features of DB in the North- background mean westerlies is associated with the DB ern Hemisphere are investigated based on a 40-yr pe- development. Therefore, the observational westerlies riod data spanning from 1958–97. Results show that are examined first. Figure 13 displays the climatological there are three preferable regions: the northwestern seasonal cycle of the westerlies averaged in the high Pacific, the Atlantic, and the Ural area, where DB fre- latitudes (55°–80°N) for the Northern Hemispheric DB quently occurred, agreement with the results of Luo preferable latitudes at 500 hPa and annual mean west- and Ji (1991). The Pacific is the most preferable region, erly profiles with respect to latitudes averaged over where a total of 1982 days of DB occurred, far more three favorable regions for DB occurrence: the Pacific than the Atlantic (848 days) and Ural areas (533 days). (120°E–150°W), the Atlantic (60°W–30°E), and the It is interesting to note that the papers by Elliott and Ural (30°–90°E) areas, respectively. It is noticeable

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FIG. 13. Climatological seasonal cycle of the westerlies averaged in the high latitudes (55°–80°N) at (a) 500 hPa and (b) annual mean westerly profiles with respect to latitude averaged over Pacific (PAC or WPAC, 120°E– 150°W), Atlantic (ATL, 60°W–30°E), and Ural (URL, 30°–90°E) areas. Label “EPAC” denotes the eastern Pacific averaged over 180°–90°W, and “GLB” is the mean of PAC, ATL, and URL. that the westerlies where the high center of DB locates sponding to the latitudinal distribution of the DB preferably over the high latitudes of the Pacific region shown in Fig. 12. are almost all less than that over the Atlantic and Ural Observational studies also give the seasonal variabil- areas (Fig. 13a). The climatological annual mean west- ity of global DB as shown in Fig. 14a. The numbers of erly over the Pacific is about 3.25 m sϪ1, not reaching DB decrease from winter (December to February) to half of that over the Atlantic (7.35 m sϪ1) or Ural areas spring (March to May), summer (June to August), and (7.77 m sϪ1). Hence it is not strange that many more autumn (September to November) successively. Winter DBs occurred over the Pacific than over the Atlantic is the most favorable season for DB producing, consis- and Ural regions. From a climatological point of view, tent with the results for total blocking by White and the weak westerlies are one of the most important fac- Clark (1975), Lejenäs and Økland (1983), Shukla and tors that impact the DB occurrence. Mo (1983), and Huang (2002), but contradictory to re- However, the weak westerly is a precondition for sults by Rex (1950a); while autumn is the quiet season onset of blocking, including DB and monopole blocks for DB onset, which disagrees with the common statis- (Shutts 1983, 1986; Luo and Ji 1991; Luo 1994; Luo et tical results for total blocking (White and Clark 1975; al. 2001). The inconsistency between DB (the most lo- Lejenäs and Økland 1983; Shukla and Mo 1983; Huang cated at northwestern Pacific) and total blockings (the 2002). The mean westerlies averaged over the three least occurred at northeastern Pacific) implies that the preferable DB regions in each season (Fig. 14b) indi- weak westerly is a necessary condition for blocks, but cate that the autumn westerlies are the strongest, and not a sufficient condition for DB onset. Since the west- are associated with the least DB occurring in autumn erly shears play a considerably important role in DB according to the theory discussed above. The summer evolution, the annual mean westerly profiles with re- westerly is weakest, but does not correspond to the spect to latitudes averaged over the three DB prefer- largest DB frequency in summer. Nevertheless, the sea- able regions are also studied (Fig. 13b). The figure re- sonal variability of the background westerlies over the veals that westerly profile over the global DB regions Pacific region (120°E ϳ 150°W) in Fig. 14c appears to appears to be a weak cyclonic westerly shear from 40° have a completely negative correlation to the seasonal to 80°N, which is advantageous for DB establishment at cycle of the global DB occurrence in Fig. 14a. This these latitudes. The Pacific has the strongest CWS from suggests that the seasonal variation of the global DB is 40° to 60°N and a considerably weak AWS from 60° to mostly due to the seasonal cycle of the Pacific DB, 80°N, which favors more DB produced at higher lati- which is mostly determined by the mean background tudes and less DB reduced at lower latitudes, corre- westerlies over the Pacific. For the Atlantic and Ural

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FIG. 14. Seasonal variations of (a) the number of DB days, (b) the mean westerlies averaged over the three DB preferable regions, (c) westerlies averaged over the Pacific (120°E–150°W), and (d) seasonal mean westerly profiles with respect to latitude averaged over the Pacific. Label “Win” denotes winter season (December to February), “Sum” denotes summer (June to August), “Spr” denotes spring (March to May), and “Aut” denotes autumn (September to November).

DB, the seasonal variability of the mean westerlies may time-dependent background flow and boundary condi- play important but indecisive role in the DB seasonal tions from the nonlinear, inviscid, nondissipative, and cycle. The seasonal westerly profiles with respect to equivalent barotropic vorticity equation in a beta-plane latitudes over the Pacific region of DB (Fig. 14d) show channel. The analytical solution obtained from the that the westerly shears are very favorable for DB es- VCKdV equation can be successfully used to explain tablishment in winter, spring, and autumn, with a CWS the evolution of atmospheric dipole-type blocking life at 45°–60°N and very weak AWS at higher latitudes, cycle. Analytical diagnoses are analyzed and three fac- while in summer the AWS at 60°–75°N seems too tors that may influence the evolution of atmospheric strong to be unfavorable for DB pattern developing. It DB are investigated. is remarkable that among the very weak AWSs in win- Theoretical results show that the background mean ter, spring, and autumn, the AWS in winter is the rela- westerlies have great influence on the evolution of DB tively strongest one, which is favorable for strong DB during its life episode. Weak westerlies are necessary development, and results in the most DB occurring in for blocking development and the high/low centers of winter. Therefore, the intensity of the background blocking decrease and move southward and westward, mean westerlies and their shear structures closely asso- the horizontal scale enlarges and meridional span re- ciate with the establishment of DB, leading to the duces, as well as the blocking life period shortens with northwestern Pacific being the most preferable region respect to the enhanced westerly. for DB and its seasonal variability. Shear of the background westerlies also plays an important role in the evolution of DB. The CWS is pref- 5. Concluding remarks erable for the development of DB, which agrees with the recent result from Luo (2005b). When the cyclonic In this paper, a variable coefficient Korteweg de shear increases, the intensity of DB decreases and its Vries (VCKdV) system is derived by considering the life period becomes shorter. Weak AWS is also favor-

Unauthenticated | Downloaded 10/07/21 10:49 AM UTC JANUARY 2007 HUANG ET AL. 71 able for DB formation, but a critical threshold shear ated with the climatological features of the DB in the exists, beyond which a cutoff anticyclone from the Northern Hemisphere, which may play crucial role in North Pole region develops dramatically instead of an the DB life cycles. The type of TDW could also impact envelope Rossby soliton forming the high anticyclone the DB life episode concluded from analytical resolu- center of DB. Inside the critical threshold of the anti- tion, but it is yet to be demonstrated from the obser- cyclonic shear, the intensity of DB increases and the life vational studies in the future. period of DB prolongs when the anticyclonic shear increases. For the role of CWS in DB evolution, our Acknowledgments. The work was supported by the result is inconsistent with that of Luo (2005b), who National Natural Science Foundation of China (Grants revealed that an isolated vortex pair block excited 40305009, 10475055, 10547124, and 90203001), Program resonantly by synoptic-scale eddies is more likely sup- for New Century Excellent Talents in University pressed in an anticyclonic shear environment. The dif- (NCET-05-0591), Program 973 (No. 2005CB422301), ference may lie on different nonlinear systems consid- and Shanghai Post-Doctoral Foundation. ered by Luo (2005b) and us. That is, Luo (2005b) considered an eddy-forced nonlinear Schrödinger Rossby REFERENCES soliton system in the atmosphere, while we established Berggren, R., B. Bolin, and C. G. Rossby, 1949: An aerological a nonlinear system based on a nonlinear KdV equation study of zonal motion, its perturbations and breakdown. 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