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A New Look at the Binary Interaction: Potential Vorticity Diagnosis of The JULY 2003 WU ET AL. 1289 A New Look at the Binary Interaction: Potential Vorticity Diagnosis of the Unusual Southward Movement of Tropical Storm Bopha (2000) and Its Interaction with Supertyphoon Saomai (2000) CHUN-CHIEH WU,TRENG-SHI HUANG,WEI-PENG HUANG, AND KUN-HSUAN CHOU Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan (Manuscript received 28 June 2002, in ®nal form 22 November 2002) ABSTRACT Tropical Storm Bopha (2000) showed a very unusual southward course parallel to the east coast of Taiwan, mainly steered by the circulation associated with Supertyphoon Saomai (2000) to Bopha's east. The binary interaction between the two typhoons is well demonstrated by the potential vorticity (PV) diagnosis. With the use of the piecewise PV inversion, this paper quantitatively evaluates how Bopha moved southward due to the binary interaction with Saomai. A newly proposed centroid-relative track, with the position weighting based on the steering ¯ow induced by the PV anomaly associated with the other storm, is plotted to highlight such binary interaction processes. Note that the above analysis can be well used to understand the more complicated vortex merging and interacting processes between tropical cyclones either from observational data or numerical ex- periments. The results also shed some light on the prediction of nearby tropical cyclones. 1. Introduction localized vortical disturbances. The mutual rotation of interacting hurricanes was qualitatively demonstrated. The concept of binary interaction has been well de- Observational evidences (Brand 1970) suggested that scribed by tank experiments (Fujiwhara 1921, 1923, there is a correlation between the separation distance 1931), observations (Brand 1970; Dong and Neumann and the angular rotation rate of two tropical cyclones. 1983; Lander and Holland 1993; Carr et al. 1997; Carr Brand also showed that the effect of such a binary in- and Elsberry 1998), and modeling studies (Chang 1983, teraction depends on differences in storm size and in- 1984; DeMaria and Chan 1984; Ritchie and Holland tensity, and on variations in the currents within which 1993; Holland and Dietachmayer 1993; Wang and Hol- the tropical storm systems are imbedded. Speci®cally, land 1995), all indicating that two tropical cyclones can Brand showed that when the distance of two tropical interact and then develop mutual orbiting and possible cyclones is under 750 nm (nautical miles), they begin approaching, merging, and escaping processes (Lander to circle around each other; as the distance is less than and Holland 1993). The binary interaction is not only 400 nm, they apparently attract each other. an interesting and fundamental problem in ¯uid me- Dong and Neumann (1983) analyzed the best-track chanics and vortex dynamics, but also of practical con- data from 1946 through 1981 and showed that the annual cern in improving the forecast accuracy of multiple trop- frequency of binary interaction is higher (1.5 times) in ical cyclones in close vicinity. the western North Paci®c than that (0.33 times) in the Early laboratory experiments by Fujiwhara (1921, Atlantic. Dong and Neumann veri®ed mutual interaction 1931) studied the interaction of binary vortex systems. of spatially proximate tropical cyclones according to the In addition to the mutual rotational effect, Fujiwhara Fujiwhara expectation, although in some exceptional also detected a tendency for an attraction between vor- cases such an effect tends to be masked by other en- tices having the same sense of rotation. A close mete- vironmental currents. orological analogy to these laboratory vortices occurs Lander and Holland (1993) performed a more detailed when two tropical cyclones are close suf®ciently for analysis based on 44-yr data from 1945 through 1988 mutual interaction. An analytical model by Gryanik to observe the behavior of interacting tropical-cyclone- (1983) used singular geostrophic vortices to represent scale vortices in the western North Paci®c. Lander and Holland showed that rarely does the interaction of cy- clones follow the classic Fujiwhara model. Instead, a Corresponding author address: Dr. Chun-Chieh Wu, Dept. of At- mospheric Sciences, National Taiwan University, 61, Ln. 144, Sec. series of interactions may occur, including capturing, 4, Keelung Rd., Taipei 106, Taiwan. stable cyclonic orbiting, and cyclone merging and es- E-mail: [email protected] caping. q 2003 American Meteorological Society Unauthenticated | Downloaded 09/24/21 04:30 PM UTC 1290 MONTHLY WEATHER REVIEW VOLUME 131 Many of the above processes have also been closely can quantitatively identify the balanced ¯ow associated examined from numerical studies of Ritchie and Holland with each individual PV anomaly. Therefore, in this (1993), Holland and Dietachmayer (1993), and Wang paper we shall quantitatively investigate the movement and Holland (1995). Interestingly, a recent observational of Bopha, as affected by the presence of Saomai, from case study from Kuo et al. (2000) clearly documented the PV diagnosis. The minor steering effect of Typhoon a case of interaction and merger of Supertyphoon Zeb Wukong on Bopha, as well as Bopha on Saomai, is also and Tropical Storm Alex (1998). It is shown that the discussed. two storms rotated around each other when they were within about 850 km, and then the weaker Alex was sheared into a potential vorticity ®lament by the stronger 2. Data and methodology circulation associated with Zeb, absorbed into Zeb as a a. Data rainband. Concerning the more complicated and realistic ¯ow The data used in this study are based on the analysis patterns surrounding tropical cyclones, recent work ®elds of the Global Forecast System (GFS) from the from Carr et al. (1997) and Carr and Elsberry (1998) Central Weather Bureau (CWB) in Taiwan, which has has proposed detailed conceptual models to categorize a horizontal resolution of 2.5832.58, and 16-vertical- the binary interaction processes, namely, 1) the direct layer on standard pressure surfaces. The GFS (Liou et tropical cyclone (TC) interaction with one-way in¯u- al. 1997) is a T79 primitive equation model with 18 ence, mutual interaction, or merger of the two TCs; 2) sigma levels. The observational data is assimilated into the semidirect TC interaction involving another TC and the GFS by the optimal interpolation, while the nonlin- an adjacent subtropical anticyclone; and 3) the indirect ear normal-mode initialization was adopted for the ini- TC interaction involving the anticyclone between the tialization of the GFS. Parameterization processes in- two TCs. In spite of their successful rate of 80% in clude the 1.5-order eddy-mixing parameterization, shal- distinguishing the modes of the binary interactions from low convection parameterization, and Arakawa±Schu- analyses of 8-yr samples of western North Paci®c TCs, bert Cumulus parameterization (Arakawa and Schubert it remained unsolved how to quantify the binary inter- 1974). In addition, the grid-scale latent heating and the action of TCs. radiation of both long- and shortwaves related to clouds Meanwhile, studies (Chan and Gray 1982) have clear- are also taken into account. ly shown that tropical cyclone motion is mainly gov- erned by the tropospheric average steering ¯ow, gen- erally de®ned as the weighted vertical average of the b. Methodology ¯ow in the troposphere. As an example, during the sum- 1) CONCEPT OF THE PV INVERSION mer and early autumn seasons tropical cyclones in the western North Paci®c generally move westward, north- The use of PV for understanding the evolution of the westward, or northward, mainly driven by the ¯ow as- dynamical system in the atmosphere has been well re- sociated with the dominant Paci®c High to the east or viewed in Hoskins et al. (1985). Such merit is partic- northeast of these storms. Curious enough, Tropical ularly enhanced with its inversion characteristics. The Storm Bopha (2000) moved westward from 7 to 9 Sep- PV invertibility principle states that given a distribution tember, then had a dramatic southward turn on 9 Sep- of PV, a prescribed balanced condition, and boundary tember, and ®nally continued its unusual southward conditions, the balanced mass and wind ®elds can be course parallel to the east coast of Taiwan until 11 Sep- recovered. The use of the inversion of the quasigeo- tember when it dissipated near the east coast of the strophic PV is limited to ¯uids with a low Rossby num- Philippines. ber. Using the nonlinear balanced condition (Charney It is interesting to ask what led to such an atypical 1955) to invert the Ertel PV, Davis and Emanuel (1991), southward track of Bopha. The answer appears empir- and Wu and Emanuel (1995a,b) were able to quantita- ically and intuitively clear, that is, such motion was tively examine extratropical cyclogenesis and the steer- likely to be steered by the circulation attributed to Su- ing of tropical cyclones, individually. Formulated on the k pertyphoon Saomai (2000) to Bopha's east. In other p[p 5 CP(p/p 0) ] coordinate and spherical coordinates, words, the mechanism of the Fujiwhara effect (Fuji- the two equations to be solved are whara 1923) or binary interaction may be the dominant driving force. However, the question is how we can gkp ]F2221 ]C ]F q 5 ( f 1¹C2 ) 2 quantify such an effect. As shown by Dong and Neu- p [ ]p222a cos f ]l]p ]l]p mann (1983), the effects from the environmental ¯ow need to be ®ltered out before the real Fujiwhara effect 1 ]C22 ]F 2 , and (1) can be determined. With the successful development and a2 ]f]p ]f]p] application of the piecewise potential vorticity (PV) in- 2 ](]C/]l, ]C/]f) version (Davis and Emanuel 1991; Wu and Emanuel ¹F52 = ´(f =C) 1 , (2) 1995a,b; Shapiro 1996; Shapiro and Franklin 1999), one a42cos f ](l, f) Unauthenticated | Downloaded 09/24/21 04:30 PM UTC JULY 2003 WU ET AL.
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