Momentum Transports Associated with Tropical Cyclone Recurvature

Transcription

1 1021 Momentum Transports Associated with Tropical Cyclone Recurvature Y. S. LIANDJOHNNY C. L. CHAN Department of Physics and Materials Science, City University of Hong Kong, Kowloon, Hong Kong, China (Manuscript received 4 September 1997, in final form 9 June 1998) ABSTRACT This study attempts to investigate the linear momentum budget responsible for tropical cyclone (TC) recurvature. Using the operational analyses from the U.K. Meteorological Office global model, the environmental flow associated with recurving TCs over the western North Pacific for the years is composited. In general, the dominant features include an eastward-retreating subtropical ridge (STR) and an approaching westerly trough during the recurvature. While the southeasterly flow associated with the STR changes to southerly in the northeast quadrant of the TC in the mid- to upper troposphere, the southwesterly flow associated with the trough penetrates into the northwest quadrant of the TC, especially in the upper troposphere. These changes of the environmental flow throughout the recurvature alter the linear momentum of the TC from southeasterly to southwesterly. To understand the dynamical processes responsible for the linear momentum changes, individual momentum tendency terms are calculated. In the zonal direction, throughout the recurvature, the southerly component from the environment is found to play an important role for the increase of the net zonal momentum tendency through the earth momentum advection and the zonal component of the Coriolis force. The contribution of the environmental westerlies through the advection of westerly momentum is very small and is eventually cancelled by the negative advection associated with the southerly flow. The net positive meridional force appears to be the main contributor of the meridional tendency component. The negative meridional momentum advection term during and after recurvature only weakens the net meridional momentum tendency at the later stage. 1. Introduction Tropical cyclone (TC) recurvature is an important issue in the study of TC motion. Synoptically, the approach of a westerly trough and eastward retreat of the subtropical ridge (STR) are found to be favorable conditions for recurvature (e.g., Riehl and Shafer 1944; Dong et al. 1991). More quantitatively, George and Gray (1977) pointed out that prior to recurvature, the 200- hpa flow north of the TC is significantly stronger. This feature was also identified by Chan et al. (1980). Hodanish and Gray (1993) further found that the environmental zonal winds in the mid- and upper troposphere at 6 and 8 lat radii north, northwest, and west are critical for predicting TC recurvature empirically. In addition to observational studies, barotropic (e.g., Evans et al. 1991) and baroclinic (e.g., Holland and Wang 1995) models have been applied to simulate TC recurvature under idealized environmental conditions (such as a westerly shear). Based on the vorticity advection analyses, the asymmetric gyres of the TC cir- Corresponding author address: Dr. Johnny C. Chan, Department of Physics and Materials Science, City University of Hong Kong, 83 Tat Chee Ave., Kowloon, Hong Kong, China. Johnny.Chan@cityu.edu.hk culation [proposed by Elsberry (1990) to explain the deviation of TC motion from the steering concept] in the models are found to be distorted and thus modify the vortex motion to produce recurvature. Instead of idealized conditions, Krishnamurti et al. (1992) examined a real case of successful typhoon recurvature track forecast from a high-resolution global spectral model. They determined that in forward and right quadrants of a TC center, the tropospheric mean divergence and vorticity advection change significantly during recurvature. More recently, based on the analyses of the TCM-90 [Tropical Cyclone Motion Experiment in 1990 (Rogers et al. 1993)], Chan and Cheung (1998) found that during TC recurvature, the wavenumber 2 (WN-2) of the asymmetric circulation is dominant. Kinetic energy is transferred from the environment, symmetric, and WN-1 components to WN-2. In this research, we also intend to utilize observational data to study the physics of TC recurvature. In previous dynamical studies, the concept of vorticity advection is generally used to explain TC motion, including recurvature. Here, we propose that an exchange of linear momentum between a TC and its environment provides a straightforward explanation of TC recurvature. This research therefore attempts to study the linear momentum budget of a TC throughout recurvature. Although the vertically integrated linear momentum of a 1999 American Meteorological Society

2 1022 MONTHLY WEATHER REVIEW VOLUME 127 FIG. 1. Best tracks of the eight selected TCs. Each TC track is drawn relative to the point of recurvature (T) located at (0, 0). The recurving time of each TC is given in parentheses next to the TC name and labeled as yymmddhh, where yy is the year, mm the month, dd the day, and hh the UTC time. TC may be interpreted to be equivalent to the deeplayer mean steering flow, the emphasis of this study is not simply an analysis of the momentum itself. Rather, the rate of the local change of the linear momentum throughout recurvature is examined to understand the dynamical role (beyond the steering) of the wind flows on recurvature. However, the mutual interaction between the environment and the vortex will not be investigated; it will be the subject of a subsequent study. The operational analyses of the U.K. Meteorological Office (UKMO) global model for the years over the western North Pacific (WNP) form the database of this study (section 2). The definition of the point of recurvature and the criteria for the selection of recurving TCs are also given in this section. Since the TC domain is one of the parameters in calculating the momentum budget, vortex specification is necessary. The methodologies to calculate the momentum budget of the individual recurving TCs and to composite the results of the selected TCs are also presented in section 2. The composite synoptic wind flow patterns are then examined in section 3. Full analyses of the linear momentum transports to elucidate the recurvature dynamics are presented in section 4. The results are then summarized and discussed in section Data and methodology a. Data The operational analyses of the UKMO global model for the years are employed in the study. The data have a 2 2 lat rectangular grid resolution at 0000 and 1200 UTC, in the area of 50 N 40 S and 30 E 180. Parameters to be examined (wind and geopotential height) are available at 950-, 850-, 700-, 500-, 400-, 300-, 200-, and 100-hPa. Details of the UKMO model can be found in Cullen (1993). Furthermore, the 6-hourly best-track TC positions from the Annual Tropical Cyclone Reports published by the Joint Typhoon Warning Center in Guam (JTWC ) are used to identify the recurving TCs over the WNP. b. Selection of recurving TCs The TC recurvature is formally defined as the turning of a TC from an initial path west and poleward to

3 1023 FIG. 2. (a) The movement of the STR at 500 hpa represented by the composite 5880-m geopotential height and (b) the movement of the westerly trough at 500 hpa represented by the composite 5850-m geopotential height. The dot is the relative TC center among the eight composite TCs. east and poleward by the JTWC. The location where the TC track first takes on an eastward component of motion is called the point of recurvature. In this study, similar to the above definition, the recurving time (T) is defined as either the 0000 or 1200 UTC nearest the 6-h interval (best-track positions) at which the TC first reached the westernmost position. Eight recurving TCs with a time span of nine time periods [72 h before (T 72) and 24 h after (T 24) recurvature] are considered (Fig. 1) in this study. Each TC is selected according to the following criteria: 1) The track of the TC possesses a northwestward to northeastward turning. 2) Throughout the TC recurvature, an eastward-retreating STR and an approaching westerly trough can be identified. The movements of these two systems throughout the recurvature can be clearly identified from the displacements of the 5880-m and 5850-m geopotential height at 500 hpa, respectively (Figs. 2a and 2b). 3) At each time period, enough data are available in the UKMO dataset ( 20 lat from the TC center). 4) The intensity of the TC at each time period is 35 kt. 5) The TC consists of a well-defined TC circulation throughout the study time periods. c. Vortex specification Since the best-track TC center usually does not coincide with the grid points of the analysis fields of the UKMO data, a readjustment of the TC center is necessary. A well-defined TC domain is also required for the calculations of the momentum budgets. A vortex specification on individual TCs in this study is therefore required. For simplicity, the readjusted TC center and the TC domain are assumed to be independent of height. The best-track positions of the TC are used primarily as a reference to extract the portion of the analyses that covered the TC within a 20 lat square at all available pressure levels. As the resolution of the UKMO data is as low as 2 2 lat, interpolation of the dataset to 1 lat resolution within a 15 lat square is then carried out. The interpolated wind fields from 850 to 300 hpa are pressure-weighted to form a deep-layer-mean for the determination of the readjusted TC center and the TC domain. The results are then applied to all individual levels in the momentum budget calculations. Note that the interpolated wind fields at individual levels are also used in the momentum budget calculations. In this study, the algorithm of the filtering scheme of Kurihara et al. (1995) is adopted in positioning the readjusted TC center and determining the TC domain [for details, please refer to Kurihara et al. (1995)]. Here we briefly describe the algorithm. First, the total wind field is separated into the basic flow and the disturbance field. A first-guess position of the TC center is then set to the location of the centroid of the disturbance wind speed within the TC region. For each grid point within a 7 7 lat area centered at the grid point nearest the firstguess position, the azimuthally averaged tangential component of the disturbance wind is computed at 0.2 lat radial intervals out to a distance of 6 lat. The grid point associated with the tangential wind profile containing the largest maximum value is regarded as the readjusted TC center. To determine the TC domain, the disturbance flow is bilinearly interpolated to a polar grid centered on the readjusted TC center with 1 lat radius 15 azimuth resolution. Along each of the 24 radial directions, the extent of the domain is determined by testing the radial profile of the tangential component of the disturbance wind, such that the tangential wind speed at each specified direction is less than 6 m s 1 and the radial gradient of the tangential wind is less than s 1. Note that the domain of the TC may not be a circle.

4 1024 MONTHLY WEATHER REVIEW VOLUME 127 FIG. 3. The composite wind flow patterns in the hPa layer at (a) T 72, (b) T 48, (c) T 24, (d) T, and (e) T 24. The contours indicate the steadiness of the wind flow. Only contours of 90% and 95% are shown. The dot is the relative TC center. d. Linear momentum budget calculations For individual TCs, the relative momentum vector over a vortex column M r in an Eulerian cylindrical coordinate system can be calculated as 1 Mr Vr dp da, (2.1) g where V r ui j is the relative wind vector, g the gravity, p the pressure, and A the horizontal area of the vortex. The zonal wind u and meridional wind components at each pressure level are interpolated onto a 1 lat 15 azimuth polar grid so that the integration within the irregular TC domain at that pressure level can be calculated. The vertical extent of the cyclone at each time period is assumed to be constant and hence the integration goes from 950 to 100 hpa. Note that since each TC domain as defined by the previous sub-

5 1025 FIG. 4. As in Fig. 3 except for the hPa layer. section is different, the composite of the relative momentum vector among the eight selected TCs is obtained by simply taking the averages of the individual ones. Again, for individual TCs, at a given pressure level and grid point, the absolute momentum vector per unit mass M is given by M V r V E, where V E (a cos )i is the earth s rotational speed, a the earth radius, the earth angular velocity, and the latitude. The absolute momentum equation in Cartesian, isobaric coordinates is then given by M V r M f k V r p t Residual, (2.2) where f is the Coriolis parameter and the geopotential. The residual consists largely of the frictional term. Because our interest is in the main dynamical terms,

6 1026 MONTHLY WEATHER REVIEW VOLUME 127 FIG. 5. The time variation of the relative linear momentum averaged among the eight composite TCs. The error bars indicate the standard errors. (Unit: kgms 1.) this residual will not be explicitly included in subsequent equations. It will be discussed when comparing the momentum tendency with the sum of all the other terms. The zonal and meridional components of (2.2) at individual grid points are calculated separately. The absolute zonal momentum tendency (AZM tendency) is the sum of the relative zonal momentum advection (RZadv), the earth momentum advection (Eadv), and the net force along the x direction (F x ). It can be written as (u a cos ) u u u t x y (a cos ) f, y x (AZM tendency) (RZadvZ) (RZadvM) (EadvM) (CO x) (GGF x). (2.2a) The first and second terms represent the RZadv by the zonal (labeled by RZadvZ) and meridional (RZadvM) winds, respectively. The third term is the Eadv by the meridional wind (EadvM), which is equal to Eadv. The fourth and fifth terms represent the zonal component of the Coriolis force (CO x ) and the geopotential gradient force in the x direction (GGF x ), respectively. Note that because the vertical p-velocity is relatively small, the advection of the zonal momentum by the vertical wind is insignificant. Similarly, the absolute meridional momentum tendency (AMM tendency) is the sum of the relative meridional momentum advection (RMadv) and the net force along the y direction (F y ). The AMM tendency is written as u fu, t x y y (AMM tendency) (RMadvZ) (RMadvM) (CO y) (GGF y ). (2.2b) The first and second terms represent the RMadv by the zonal (RMadvZ) and meridional (RMadvM) winds, respectively. The third and fourth terms represent the meridional component of the Coriolis force (CO y ) and the geopotential gradient force in the y direction (GGF y ), respectively. The volume integrations of the above momentum ten- TABLE 1. Student s t-test statistic on the difference between two means along the times series of the relative linear momentum averaged among the eight composite TCs. Relative momentum component Zonal Meridional Student s t-test statistic on the difference between two means that are 24 h apart T 72 T 48 T 48 T 24 T 24 T T T

7 1027 FIG. 6. Time changes of the AZM tendency and the individual terms averaged among the eight composite TCs. Note that the solid and the empty symbols represent the cases in which the means are significantly different from and close to zero at the 95% level (based on the t test), respectively. The table in the figure is the Student s t-test statistic on the difference between two means that are 24 h apart. (Unit: N.) dency terms for individual TCs are calculated separately over their corresponding TC domain [similar to the calculation in (2.1)]. The results of the individual terms among the eight selected TCs are then averaged for the composite analyses. Notice that this study is performed in an Eulerian frame. Although studying in a Lagrangian frame can elucidate the momentum transports of a TC following the motion, it may underestimate the mechanisms associated with the steering flow on recurvature. 3. Synoptic wind flow patterns As mentioned in section 2b, the eight composite TCs are selected such that they consist of an approaching trough and an eastward-retreating STR during recurvature. Here we examine the synoptic wind flow patterns associated with these two systems in terms of steadiness. The steadiness of the wind vector at each grid point is defined as the percentage of the ratio of the magnitude FIG. 7. Vertical variations of the AZM tendency and the individual tendency terms at T 72, T 48, T 24, T, and T 24, averaged among the eight composite TCs. The dots indicate that at these levels, the specified term is significantly different from zero at the 95% level (based on the t-test). (Unit: 10 6 NPa 1.)

8 1028 MONTHLY WEATHER REVIEW VOLUME 127 FIG. 8. Earth momentum advection (EadvM) distribution of TC Yuri in the hPa layer at (a) (T 72) and (b) (T). The closed, bold dashed line is the TC boundary and the dot is the readjusted TC center. (Unit: 10 4 ms 2.) of the averaged wind vector among the eight composite TCs to the average speed of the wind vectors at the same grid point without regard to direction for all individual TCs. The greater the value of the steadiness, the more persistent the wind flow (direction) is among the composite TCs. For convenience, wind fields within the hPa and the hPa layers are averaged (pressure-weighted) to see the general flow patterns at the mid- and the upper troposphere, respectively. Three to two days prior to recurvature (T 72 and T 48), the midtropospheric flow around the composite TC center was most steady (Figs. 3a,b, with steadiness 95%). If we assumed the cyclonic flow of the vortex was largely symmetric, the stronger easterly (southeasterly) flow to the north (northeast) of the TC center was the environmental flow associated with the STR located north of the TC. As the STR shifted eastward, a larger area of southeasterlies associated with the STR can be seen to the northeast of the TC center at T 24 (Fig. 3c). Note that the southwesterlies with steadiness 90% northwest of the TC center was consistent with the location of the flow associated with the westerly trough. During recurvature (Fig. 3d), although the flow associated with the trough dominated beyond 5 lat northwest of the TC (with steadiness 90%), the southerly flow of the retreating STR near the TC center was more steady (with steadiness 95%). After recurvature, the TC was embedded in the cyclonic flow of the westerly trough (Fig. 3e). The combined flow associated with the approaching trough and the eastward-retreating STR northeast of the TC center gave a steady southerly (southwesterly) flow to the east (northeast) of the TC center. Note that the winds to the northwest of the TC were weak and variable. In the upper troposphere, the presence of an area with wind steadiness over 90% beyond 10 lat northwest of the TC suggests that 3 days prior to recurvature, the southwesterly flow associated with the westerly trough was already present (Fig. 4a). However, it was far away from the TC center. The broad area of easterlies south of the TC is the climatological feature present in the upper troposphere in the Tropics. The horizontal extent of the southwesterlies over the northern quadrant of the TC then increased with time (Figs. 4b e). The steadiness of the winds in that quadrant ( 95%) further reveals that the southwesterly flow associated with the approaching trough significantly penetrated into the TC throughout the recurvature. Notice also that especially during and after recurvature, the steady wind flow near the TC center was partially due to the anticyclonic flow of the STR. To summarize, the steadiness values demonstrate the consistency among the eight composite TCs so that the results should be valid for individual cases. For these TCs, the approaching westerly trough provided strong southwesterlies to the northern side of the TC, especially in the upper troposphere, while the retreating STR gave strong southerlies (southwesterlies) near the TC center at the mid- (upper) troposphere. 4. Momentum budgets The previous section has identified those components of the wind flow associated with the STR and the trough that were present throughout the recurving process. The question is, to what extent did the environmental flow cause the TC to recurve? In the following analysis, the

9 1029 FIG. 9. As in Fig. 8 except for the hPa layer. contributions of momentum transports to TC recurvature are examined. a. Time variation of the relative momentum The time series of the relative linear momentum over hpa averaged among the eight composite TCs shows that the relative linear momentum is highly correlated with the moving speed of the TC (Fig. 5). The sign change of the zonal momentum from negative to positive is consistent with the changing direction of the zonal motion of the TC. In other words, the recurving TC either received westerly momentum or exported easterly momentum during recurvature. Since the verification times in this study are in 12-h increments, the change of the relative zonal momentum occurring any time between T 12 and T is acceptable. For the meridional component, a positive momentum is observed and this maintained the poleward motion of the TC. To determine whether the variations along the time series are statistically significant, the Student s t-test is employed. Because only nine consecutive time periods from T 72 to T 24 are available, the test focuses on the difference between two means that are 24 h apart.

10 1030 MONTHLY WEATHER REVIEW VOLUME 127 FIG. 10. Vertical variations of (a) CO x and (b) GGF x averaged among the composite TCs. The dots indicate that at these levels, the specified term is significantly different from zero at the 95% level (based on the t-test). (Unit: 10 6 NPa 1.) Note that since the samples within 24 h may be dependent, the test gives only an indication of the difference between the two means. A larger value of the statistic implies a larger difference between the two means. As seen from Table 1, the test statistic suggests that the increase of the zonal momentum was obviously significant from T 24. This implies that the tendency of the TC to recurve should be noticeable 1 day prior to recurvature. On the other hand, the increase of the meridional momentum was relatively small throughout the recurvature. b. Absolute zonal momentum (AZM) tendency An import of zonal momentum can directly decelerate a westward-moving cyclone or change the direction of motion of the cyclone. In this subsection, the contribution of each term in (2.2a) to the local change in AZM is identified. 1) CONTRIBUTION OF THE ZONAL COMPONENTS Figure 6 shows that the average of the net AZM tendency over the vortex column ( hpa) among the eight composite TCs was positive throughout the study period. The variation between two 24-h consecutive time periods further suggests that the AZM tendency increased sharply from T 48 to T. Since the relative zonal momentum at around 2 days prior to recurvature was nearly constant (Table 1), the nonzero AZM tendency before T 48 (Fig. 6) was probably to cancel the negative frictional force. For the individual tendency terms, the contribution of the EadvM to the AZM tendency was the largest (Fig. 6). In fact, the test statistics for the period T 48 to T were comparable for both terms. Even though the net zonal force (F x ) shows an obvious increase from T 24 to T, its magnitude was smaller than that of the EadvM. On the other hand, the RZadv decreased with time and thus did not favor an increase of the AZM. Although the decreasing tendency of the RZadv between two 24-h consecutive time periods is not obvious, the RZadv differed significantly from zero (95% significant) from T 36 on. The vertical variations of the AZM tendency terms from T 72 to T 24 are given in Fig. 7. Throughout the recurvature, the EadvM was significantly positive over the whole vortex column. The contribution of the F x is also noticeable. In addition, it is found that throughout the recurvature, the RZadv gave only a negative tendency to the TC at the upper levels. In the following subsection, one of the composite TCs (Yuri in 1991) is selected randomly as an example to discuss the horizontal distributions of the individual tendency terms within a specified TC domain at the mid- and the upper troposphere. 2) THE EARTH MOMENTUM ADVECTION At the midtroposphere ( hPa average), in general, a dipole can be seen near the TC center due to the cyclonic flow of the TC (e.g., Figs. 8a,b). However, the dipole is asymmetric. The positive area of the EadvM covered the eastern half of the TC and gradually extended toward the western part along the northern TC boundary throughout the recurvature (cf. Figs. 8a,b). Since EadvM is governed by the meridional flow, this positive advection was mainly due to the increasing southerly component of the retreating STR to the northeast of the TC as discussed in section 3. Similar to the situation at the midtroposphere, the EadvM pattern in the upper troposphere also followed

11 1031 Here, CO x and GGF x are the two components of F x. As expected, they were generally out of phase and of similar magnitude (Figs. 10a,b). The CO x had an increasing tendency over the whole vortex column, while the opposite was true for the GGF x term. However, the magnitude of the CO x was larger so that the sum of these two components gave a positive net zonal force acting on the TC. At the midtroposphere, the horizontal distribution of the CO x term (not shown) was similar to that of the EadvM term since both terms were mainly governed by the meridional flow. For the GGF x term, apart from a dipole with a positive on the left and a negative on the right of the TC center, a negative area to the north of the TC was observed and extended toward the west of the TC, especially during and after recurvature (not shown). This result was consistent with the increasing geopotential gradient set up by the higher geopotential associated with the STR and the lower geopotential associated with the trough along the x direction. However, the sum of the two forces, as in the example of Yuri at time T (Fig. 11a), shows that the GGF x was dominant near the TC center while the CO x was dominant in the outer region. And indeed, the positive CO x along the northeastern boundary of the TC became very significant during and after recurvature. Patterns of the net force at the upper troposphere were slightly different from that in the midtroposphere (Fig. 11b). Since the southerly component of both the trough and the STR in the upper troposphere was very significant (see Fig. 4), the horizontal distribution of the net F x at that layer was similar to that of CO x, which consisted of a larger positive area (eastward force) to the north of the TC (not shown). FIG. 11. The net F x distribution of TC Yuri in (a) the hPa layer and (b) the hPa layer at time T. The closed, bold dashed line is the TC boundary and the dot is the readjusted TC center. (Unit: 10 4 ms 2.) the meridional flow (Fig. 9). The distribution was mainly dominated by the increasing southerly and southwesterly of the STR and the trough throughout the recurvature. 3) THE NET ZONAL FORCE 4) THE RELATIVE ZONAL MOMENTUM ADVECTION As seen from Fig. 7, RZadv was negative especially at the upper levels. A breakdown of the RZadv into the RZadvZ and the RZadvM components further demonstrates that the latter was the main contributor (cf. Figs. 12a,b). At the midtroposphere, the RZadv pattern shows an asymmetry with a larger positive area to the east of the TC (Fig. 13a) due to the poleward advection of the westerly momentum (associated with cyclonic flow) by the southerly component of the STR east of the TC center. On the other hand, the retreating STR and the encroaching trough during recurvature provided a strong southerly flow at the northeastern boundary of the TC so that the westerly momentum was exported from the TC, and hence there was negative advection. However, the net RZadv within the TC domain at this layer was negligible. Note a very weak positive advection at the northwest boundary of the TC that resulted from the import of the westerly momentum by the westerly flow of the trough. The horizontal distribution of the RZadv at the upper troposphere was also dominated by that of the RZadvM (Fig. 13b). Although the approach of the westerly trough provided a westerly component for the import of the westerly momentum near the western and northwestern

12 1032 MONTHLY WEATHER REVIEW VOLUME 127 FIG. 12. Vertical variations of (a) RZadvZ and (b) RZadvM averaged among the composite TCs. Note that the x axis in (a) is an order of magnitude less than that in (b). The dots indicate that at these levels, the specified term is significantly different from zero at the 95% level (based on the t-test). (Unit: 10 6 NPa 1.) boundaries, the southerly component of the trough and the STR advected the westerly momentum out of the TC through the RZadvM process over most of the northern part of the TC. Note that the small positive area near the TC center was due to the weak cyclonic flow of Yuri in the upper troposphere. 5) SUMMARY In general, the pattern of the horizontal distribution of the AZM tendency (not shown) is similar to that of the EadvM term. Prior to recurvature, the AZM tendency was mainly contributed by the EadvM, which resulted from southeasterly flow of the STR in the midtroposphere and the southwesterly flow of the trough in the upper troposphere. In addition, the sum of CO x and GGF x provided a small positive AZM tendency to the northeast of the TC. During and after recurvature, the westerly trough amplified and the STR shifted to the east of the TC. These two environmental features combined to give a strong southerly (southwesterly) flow in the mid- (upper) troposphere for the transport of the earth s momentum from a lower latitude to a higher latitude. The CO x component also became much larger than GGF x, which resulted in a net eastward force acting on the TC. Although the westerly component of the trough brought westerly momentum into the TC at the upper levels, the southerly component of the environment transported the westerly momentum out of the TC and resulted in a negative advection. Nevertheless, the contribution of this advection was relatively small, so that a positive and increasing net AZM tendency was still observed throughout the recurving period. c. Absolute meridional momentum (AMM) tendency Recall from Fig. 5 that the relative meridional momentum was positive and increased very slightly with time. This result is consistent with the relatively small positive AMM tendency throughout the recurving period (Fig. 14). Indeed, the change of the AMM tendency was similar to that of the F y (sum of CO y and GGF y ) from the time period T 72 to T 24, in which their test statistics on the difference between two 24-h consecutive time periods were comparable. An abrupt decrease in RMadv occurred from T 24. Since the RMadv was significantly different from zero during and after recurvature, the decrease in AMM tendency after recurvature probably resulted from changes in RMadv. For the vertical variations, prior to recurvature, the RMadv was nearly negligible and the AMM tendency followed much of the F y term. Then, the upper-level RMadv became negative (95% significant) and reduced the net AMM tendency (e.g., Fig. 15). 1) THE NET MERIDIONAL FORCE Figure 16a shows the horizontal distribution of the net meridional force F y of Yuri at time T in the midtroposphere. Generally speaking, the CO y and GGF y patterns were out of phase (not shown). However, the magnitude of the CO y was relatively smaller and the net F y pattern mostly followed the GGF y pattern. The dipole in Fig. 16a was due to the lower geopotential associated with the TC. Notice the weak positive area located at the northern boundary. In fact, this positive area increased and extended southward throughout the recurvature (not shown) due to the increasing geopotential

13 1033 2) THE RELATIVE MERIDIONAL MOMENTUM ADVECTION Similar to the result in section 4b, the advection term tends to inhibit the positive absolute momentum tendency during and after recurvature. Prior to recurvature, the RMadv distribution in the midtroposphere consists of an asymmetric dipole with a larger positive area to the north of the TC (not shown). This is due to the easterly (southeasterly) flow of the STR north (northeast) of the TC that advected the southerly momentum from the environment to the TC through the RMadvZ process. However, during and after recurvature, since the southerly component of the environment at the northern boundary of the TC strengthened, the export of the southerly momentum by the RMadvM process became important. Thus, the magnitude of the positive area decreased and a region of negative advection was formed at the northern boundary of the TC (e.g., Fig. 17a). Indeed, the RMadv distribution seems to be reflected by the RMadvZ distribution, especially in the upper troposphere. Since the southerly components associated with the trough and the STR combined together near the northern edge of the TC, a southerly maximum was found in that region. The advection by the westerly flow resulted in a negative (positive) RMadvZ in the northwest (northeast) quadrant of the TC. The net RMadv distribution followed this pattern (Fig. 17b). Nevertheless, the vertically integrated RMadv was dominated by the RMadvM component. FIG. 13. As in Fig. 11 except for the RZadv distribution. gradient associated with the trough, the STR, and the vortex along the y direction. In the upper troposphere, since the CO y was mainly contributed by the strong westerly component of the approaching trough, a southward force at the north edge of the TC was found (not shown). However, the geopotential gradient of the extended trough began to strengthen at that layer so that the poleward GGF y in the northern quadrant became significant and prevailed over the CO y. The net F y distribution (Fig. 16b) was therefore positive throughout much of the vortex domain. 3) SUMMARY Since the F y and the RMadv were opposite in sign, they generally cancelled each other, so that the net AMM tendency did not have well-defined patterns. However, the integrated result of the net AMM tendency over the TC domain shows that the F y term is the principal component. A breakdown of the F y indicates that the GGF y was significant, especially during recurvature. In contrast to the contribution of the F y, the RMadv produced a negative tendency during and after recurvature. On the whole, the net AMM tendency was positive throughout the recurving process and decreased only at the later stage. 5. Summary and discussion a. Summary With the use of the UKMO operational analyses for the years , eight recurving TCs associated with an approaching westerly trough and an eastward-retreating STR are chosen in this study. Before and during recurvature, these two features, with the trough being most prevalent in the upper troposphere and the STR dominant in the mid- to upper troposphere, are found to modify the TC circulation. Strong southwesterlies

14 1034 MONTHLY WEATHER REVIEW VOLUME 127 FIG. 14. Time changes of the AMM tendency and the individual terms averaged among the composite TCs. Note that the solid and the empty symbols represent the cases in which the means are significantly different from and close to zero at the 95% level (based on the t-test), respectively. The table in the figure is the Student s t-test statistic on the difference between two means that are 24 h apart. (Unit: N.) (southerlies and southwesterlies) appeared in the upper (mid-) troposphere within the TC domain. These two synoptic-scale systems also strengthened the zonal geopotential gradient. The relative momentum of a recurving TC is found to change from southeasterly to southwesterly during recurvature. This change in sign of the relative linear zonal momentum of a recurving TC resulted from a positive AZM tendency. Although the westerly component of the environmental flow resulted in westerly momentum advection, the increasing environmental southerly flow transferred the westerly momentum away from the TC. The advection of relative zonal momentum was therefore negative and decreasing, especially during and after recurvature. Meanwhile, the increasing southerly flow transported the earth (westerly) momentum from a lower latitude to a higher latitude and hence modified the TC momentum significantly. Furthermore, because of the strong southerly flow, the zonal component of the Coriolis force also prevailed over that of the geopotential gradient force, so that an eastward force F x continuously acted on the TC throughout the recurvature. As a result, the net AZM tendency was positive and increased with time, which caused the easterly relative zonal momentum of the TC to decrease with time and eventually become westerly. Although frictional force is not treated explicitly in the present momentum budget calculations, it is treated as a residual that can be associated with the nonzero AZM tendency (when the relative zonal momentum of the TC is constant). For the meridional motion of the TC, the net meridional force (F y ) provided the necessary meridional momentum for the TC to keep its poleward motion throughout recurvature. On the other hand, the meridional momentum advection reduced the increasing southerly momentum (due to an increase in F y ) of the TC in order to give a very small increase in the poleward motion of the TC during recurvature. b. Discussion Previous studies (such as Hodanish and Gray 1993) have shown that TC recurvature is characterized by the penetration of the westerlies from the environment (especially from an approaching westerly trough) into the TC in the mid- and upper troposphere. In other words, based on the linear momentum concept, the enhanced westerly flow changes the relative zonal momentum of the TC from easterly to westerly to produce recurvature. While we have found that the penetration of the westerly flow of the trough can bring westerly momentum from the environment to the TC, the southerly flow of the environment actually advects the westerly momentum away from the TC. The net result of such a momentum transport is negligible so that the westerly flow cannot be responsible for TC recurvature. Instead, the increase of the southerly component from the approaching trough and the retreating STR during the recurvature process causes the earth momentum advection by the meridional flow and the zonal component of the Coriolis

15 1035 FIG. 15. Vertical variations of the AMM tendency and the individual tendency terms at time T, averaged among the eight composite TCs. The dots indicate that at these levels, the specified term is significantly different from zero at the 95% level (based on the t- test). (Unit: 10 6 NPa 1.) force to increase. The absolute zonal momentum tendency then becomes positive and changes the zonal direction of the TC significantly. This result highlights an important point; although intuitively the westerlies appear to be the largest contributor toward the recurvature process (as suggested from previous research), the increasing southerly flow from the environment actually plays the major role. Note that although the present momentum budget is calculated from the total wind field, the involvement of the environmental flows toward the TC recurvature is remarkable. Of course, a separation of the environmental flows from the TC vortex in future studies can provide more detailed information on the interaction between the environment and the vortex during recuvature. Since the synoptic-scale features of the eight composite TCs in the present study are very clear, the mechanisms associated with the TC recurvature can easily be identified. However, other effects, such as orographic influence [e.g., Abe in 1990 hit the coast of Zhejiang FIG. 16. The net F y distribution of TC Yuri in (a) the hPa layer and (b) the hPa layer at time T. The closed, bold dashed line is the TC boundary and the dot is the readjusted TC center. (Unit: 10 4 ms 2.) Province prior to its recurvature (ESCAP/WMO 1990)] and binary interaction between TCs [e.g., Brian in 1994 underwent recurvature when Colleen was located on its west side (JTWC 1994)], may also cause a TC to recurve. The processes responsible for the momentum transports associated with these effects may be different. Besides comparing recurving TCs, which resulted from different environmental effects, analyses of the momentum budgets of nonrecurving TCs will also help

16 1036 MONTHLY WEATHER REVIEW VOLUME 127 zonal momentum tendency of Flo throughout the recurvature is larger when compared with the composite case of Dot, their difference is relatively small especially prior to recurvature. The higher recurving potential of Flo is due to its smaller initial westward momentum. However, when comparing the relative importance of their tendency terms, it is found that none of the terms is significant in the nonrecurving Dot. To conclude, this study represents an attempt to identify the absolute momentum tendency terms responsible for recurvature. Although the sample size of this study is small, the results are generally consistent with our initial single case study of Flo, which came from a different dataset. They provide another viewpoint in understanding the role of the environmental flow toward TC recurvature. However, further exploration is needed for possible applications to TC track forecasting. Acknowledgments. The authors would like to thank the Hong Kong Observatory and the U.K. Meteorological Office for providing the best-track data and the analyses data, respectively. Programming assistance from Mr. Kevin Cheung is also appreciated. Thanks are also extended to the reviewers for giving many constructive comments on the manuscript. This study was partially supported by U.S. Office of Naval Research Grant N REFERENCES FIG. 17. As in Fig. 16 except for the RMadv distribution. to identify the significant mechanisms related to recurvature. However, comparisons between recurving TCs and nonrecurvers must be made carefully. For example, even if two TCs (a recurving and a nonrecurving one) have the same momentum tendency, their subsequent motion may be different because of their different relative linear momentum (which is highly correlated with the moving speed) at the initial time period. In an initial study of this research (Li and Chan 1997), zonal momentum transports associated with a typical right-turning TC (Flo) and a straight-moving TC (Dot) that occurred during TCM-90 are compared. Although the net Chan, J. C. L., and K. K. W. Cheung, 1998: Characteristics of the asymmetric circulation associated with TC motion. Meteor. Atmos. Phys., 65, , W. M. Gray, and S. Q. Kidder, 1980: Forecasting tropical cyclone turning motion from surrounding wind and temperature fields. Mon. Wea. Rev., 108, Cullen, M. J. P., 1993: The unified forecast/climate model. Meteor. Mag., 122, Dong, K. Q., G. J. Holland, and B. C. Diehl, 1991: Typhoon recurvature and environmental circulation features. WMO/TD-No. 472, World Meteorological Organization, Geneva, Switzerland, Elsberry, R. L., 1990: International experiments to study tropical cyclones in the western North Pacific. Bull. Amer. Meteor. Soc., 71, ESCAP/WMO, 1990: Typhoon Committee Annual Review ES- CAP/WMO, 152 pp. Evans, J. L., G. J. Holland, and R. L. Elsberry, 1991: Interactions between a barotropic vortex and an idealized subtropical ridge. Part I: Vortex motion. J. Atmos. Sci., 48, George, J. E., and W. M. Gray, 1977: Tropical cyclone recurvature and nonrecurvature as related to surrounding wind-height fields. J. Appl. Meteor., 16, Hodanish, S., and W. M. Gray, 1993: An observational analysis of tropical cyclone recurvature. Mon. Wea. Rev., 121, Holland, G. J., and Y. Wang, 1995: Baroclinic dynamics of simulated tropical cyclone recurvature. J. Atmos. Sci., 52, JTWC, 1991: Annual tropical cyclone report Joint Typhoon Warning Center, Guam, 238 pp. [Available from J. C. L. Chan, Department of Physics and Materials Science, City University of Hong Kong, 83 Tat Chee Ave., Kowloon, Hong Kong, China.], 1992: Annual tropical cyclone report Joint Typhoon Warning Center, Guam, 269 pp. [Available from J. C. L. Chan,

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