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Tropical Cyclone Motion in Response to Land Surface Friction MARTIN L. M. WONG

AND

JOHNNY C. L. CHAN

Laboratory for Atmospheric Research, Department of Physics and Materials Science, City University of Hong Kong, Kowloon, Hong Kong, China (Manuscript received 12 January 2005, in final form 25 July 2005) ABSTRACT Numerical experiments are performed with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) to study the effects of surface-moisture flux and friction over land on the movement of tropical cyclones (TCs). On an f plane, the TCs are initially placed 150 km due east of a north–south-oriented coastline in an atmosphere at rest. It is found that a TC could drift toward land when the roughness length is 0.5 m over land, with an average drift speed of ⬃1 m s⫺1. Friction, but not surface-moisture flux over land, is apparently essential for the movement toward land. The friction-induced asymmetry in the large-scale flow is the primary mechanism responsible for causing the TC drift. The mechanism responsible for the development of the large-scale asymmetric flow over the lower to midtroposphere (⬃900–600 hPa) appears to be the creation of asymmetric vorticity by the divergence term in the vorticity equation. Horizontal advection then rotates the asymmetric vorticity to give a northeasterly flow in the TC periphery (⬃500–1000 km from the TC center). The flow near the TC center has a more northerly component because of the stronger rotation by the tangential wind of the TC at inner radii. However, the TC does not move with the large-scale asymmetric flow. Potential vorticity budget calculations indicate that while the horizontal advection term is basically due to the effect of advection by the large-scale asymmetric flow, the diabatic heating and vertical advection terms have to be considered in determining the vortex landward drift, because of the strong asymmetry in vertical motion. Two mechanisms could induce the asymmetry in vertical motion and cause a deviation of the TC track from the horizontal asymmetric flow. First, the large-scale asymmetric flow in the upper troposphere differs from that in the lower troposphere, both in magnitude and direction, which results in a vertical shear that could force the asymmetry. A vertical tilt of the vortex axis is also found that is consistent with the direction of shear and also the asymmetry in rainfall and vertical motion. Second, asymmetric boundary layer convergence that results from the internal boundary layer could also force an asymmetry in vertical motion.

1. Introduction The understanding of tropical cyclone (TC) motion has improved significantly during the last two decades. Regarding a TC as an area of positive relative vorticity, Chan (1984) studied the processes that can lead to a local change of relative vorticity, and hence TC motion. In recent years, this concept is refined to incorporate the effect of diabatic heating explicitly, by treating the TC as an area of positive potential vorticity (PV) instead of relative vorticity, and using the PV equation instead of the vorticity equation (e.g., Wu and Wang 2000; Chan et al. 2002). Track prediction is then equiva-

Corresponding author address: Johnny Chan, Dept. of Physics and Materials Science, City University of Hong Kong, Tat Chee Ave., Kowloon, Hong Kong, China. Email: [email protected]

© 2006 American Meteorological Society

lent to finding the processes (including but not limited to steering and ␤ effect) that can create an (axially) asymmetric PV tendency. Massive destruction of life, property, and infrastructure occurs when a TC is near a densely populated region. The movement of a TC near such a region is therefore of more social and economic interests than when it is in the open sea. Significant track deflection can occur when a TC interacts with topography. More complicated cases, such as discontinuous tracks or formation of secondary lows, are also observed over the island of Taiwan (e.g., Shieh et al. 1998). Possible mechanisms leading to track changes due to topographic effects have recently been reviewed and investigated further by Kuo et al. (2001). When a TC is close to a coast, the boundary layer winds over land are weaker than those over water because of the different surface properties between land

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and sea. Strong asymmetries in the surface fluxes of heat, moisture, and momentum are also created. Intuitively, one would not expect these near-surface asymmetries to have large effects on TC motion as compared with steering, ␤ effect, or topographic effect. Nevertheless, the development of considerable convective asymmetries due to asymmetric surface fluxes is found in the idealized TC-landfall modeling studies of Tuleya and Kurihara (1978), Tuleya et al. (1984), and Chan and Liang (2003). Chan et al. (2004) also found strong convective asymmetries for four TCs that made landfall over Hong Kong. Such asymmetries could give rise to asymmetric PV tendencies and thus affect vortex motion. The objective of the current study is therefore to investigate the possible vortex motion associated with the different surface fluxes between land and sea, and to examine the physics responsible for such motion. Idealized numerical experiments are performed with the fifth-generation Pennsylvania State University– National Center for Atmospheric Research Mesoscale Model (MM5). In section 2, the numerical model and the experimental design are described. The results, including the asymmetric structure of the TCs and PV budget calculations, are presented in section 3. Results of some complementary experiments are shown in section 4. Further discussion and concluding comments appear in section 5.

TABLE 1. Roughness length and moisture availability of land in the four numerical experiments. The labels of the experiments are smooth wet land (SW), rough wet land (RW), rough dry land (RD), and smooth dry land (SD).

Expt

Roughness length (m)

Moisture availability (%)

SW (CTRL) RW RD SD

As at sea 0.5 0.5 As at sea

100 100 5 5

RL and the moisture availability MA of the surface are modified. Four experiments are performed with the respective combinations of RL and MA (experiment names are defined in Table 1): 1) SW: RL as at sea and MA ⫽ 100%, 2) RW: RL ⫽ 0.5 m and MA ⫽ 100%, 3) RD: RL ⫽ 0.5 m and MA ⫽ 5%, and 4) SD: RL as at sea and MA ⫽ 5%. The first experiment SW simply considers a sea surface over the entire domain, and is therefore regarded as the control (CTRL). All the experiments begin with a very intense TC (minimum sea level pressure ⬃888 hPa) embedded in an atmosphere that is at rest. The TC is placed over the center of the domains and the north–south-oriented coast is 150 km west of the TC. The surface temperature over land and sea is fixed at 28.5°C in all the experiments.

3. Results 2. Model and experimental design

a. Track and intensity

The MM5 model used in the current study has nested domains of 45-, 15-, and 5-km grid sizes and 26 layers. The square domains have lengths of 6750, 2250, and 1200 km, respectively, and their centers coincide. The methods of creating the base state of the atmosphere and the initial/boundary atmospheric conditions of the experiments follow those in Wong and Chan (2004). The specified vortex, which includes the horizontal variation of the tangential wind profile first used by Wang and Li (1992), is also the same except that the radius at which the tangential wind drops to zero is 3000 km instead of 900 km and there is no vertical variation of the tangential wind below 850 hPa. The simulations are carried out on an f plane, with the Coriolis parameter set to that at 15°N. An explicit moisture prediction scheme (Dudhia 1989) is used for all of the domains, but the Betts and Miller (1986) cumulus parameterization is also used in the 45- and 15-km domains. The surface fluxes and vertical diffusion are determined from a modified Mellor–Yamada level-2.5 planetary boundary layer scheme (Janjic´ 1994). To simulate the effect of land, the roughness length

The position of the minimum pressure is used to define the TC center at the various model levels. Bicubic interpolation is performed in order to determine the position. The TCs (surface center) in the CTRL and SD cases remain quasi-stationary during the six-day (144 h) simulation (Figs. 1a,d, respectively). For the RW and RD cases, the TCs drift toward the southwest and reached the land surface (Figs. 1b,c, respectively). The TC in the RD case is apparently accelerating, with an average drift speed of ⬃1 m s⫺1 during the sixth day (t ⫽ 120 h to t ⫽ 144 h). This contribution to TC movement may not be considered negligible when steering and topographic effects are not dominant, or as compared with the ␤ drift of ⬃2–3 m s⫺1 (Chan and Williams 1987). The different results between the rough (RW/RD) and smooth (SW/SD) cases suggest increased friction over land is playing the dominant role in the TC drift. In fact, the drift of the TCs in the RW and RD cases are very similar, which also suggests that the MA does not play an important role in the TC drift. The reduced MA over land, however, has influence on the TC intensity. The TC in the RD case is weaker

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FIG. 1. Track of the TC surface center in the (a) SW (CTRL), (b) RW, (c) RD, and (d) SD experiments. The dots denote 12-hourly TC positions. The origin is the location of the domain center.

than that in the RW case because of the reduced moisture supply (Fig. 2). Moreover, while the TCs in the SD and CTRL cases remained intense, the TCs in the RD and RW cases weakened significantly because of their drifts toward land. The tracks of the TCs are not smooth. Looping/ oscillatory motions are clearly seen even in the CTRL experiment. Computation errors could contribute to the looping/oscillatory motion. However, as will be shown in section 3c, maximum rainfall and vertical motion in the RD and RW experiments occur in preferred directions so that such asymmetries are likely to be real. Previous numerical and observational studies (e.g., Chan and Liang 2003; Chan et al. 2004) have also shown the development of asymmetric convection associated with TC landfall. Thus, the looping/oscillatory motions in the RW/RD experiments do not merely result from computation/systematic errors because the asymmetric convergence/divergence associated with

the asymmetric convective activities could induce a trochoidal motion (Willoughby 1988). In the following subsections, the asymmetric structures of the TCs are presented. The possible role in the motion and the effects of friction in creating them are discussed. Physical reasons are given to support that the TC drifts are real. Most of the discussion will focus on the RD experiment because it represents more typical land surface conditions and the results for the RW experiment are similar.

b. Horizontal flow asymmetries As pointed out in the introduction, the TC drifts in the RW and RD experiments should be accompanied by (axially) asymmetric changes of PV that could result from advection or convective activity (i.e., diabatic heating). Although no environmental flow exists in the initial condition of the experiments, an asymmetric flow

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FIG. 2. Minimum sea level pressure of the TC in the SW (CTRL; boldface solid), RW (solid), RD (dashed), and SD (dotted) experiments.

develops not only within the boundary layer, but throughout much of the troposphere. In the current study, the asymmetric flow is obtained by subtracting the symmetric wind field, with respect to the center of the layer in question, from the total wind field. The layer-average of a variable g(␴) between two (reference) model “full levels” ␴m, ␴n (␴m ⬎ ␴n) is computed as 1 ␴m ⫺ ␴n

兺 g冉

m⫺1

k⫽n

冊

␴k⫹1 ⫹ ␴k 共␴k⫹1 ⫺ ␴k兲, 2

共3.1兲

and the values of g are taken at model “half levels” (␴k⫹1 ⫹ ␴k)/2. The center of the layer is taken to be the position of the minimum pressure at ␴ ⫽ (␴m ⫹ ␴n)/2. For the sake of brevity, the layers with 1.0 ⱖ ␴ ⱖ 0.9 (⬃1010–914 hPa), 0.9 ⱖ ␴ ⱖ 0.55 (⬃914–578 hPa), and 0.55 ⱖ ␴ ⱖ 0.25 (⬃578–290 hPa) are referred to as the boundary layer (BL), lower layer (LL), and upper layer (UL), respectively. Because the main interest here is on the average TC movement but not the looping/ oscillatory motion, daily composites are obtained from the hourly model output. For the RD case, the LL asymmetric flow develops gradually during the first two days (Figs. 3a,b). Convergent (divergent) flow to the south (north) appears to be a response to the frictioninduced divergence (convergence) to the south (north) within the BL (not shown). Northeasterly flow persists in the periphery (⬃500–1000 km from the TC center) during the next four days (Figs. 3c–f). Within the UL, asymmetric flow also develops gradually though it appears to be smaller in magnitude than

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that in the LL (Fig. 4). The flow has an easterly component that seems to agree with the direction of movement. For the RW case, the development of the asymmetric flow within the LL and UL is similar (not shown). On the other hand, such a distinct asymmetric flow does not develop in either the CTRL or the SD case (not shown). The development of the asymmetric flow within the LL/UL in the RD and RW cases is apparently related to the friction-induced asymmetric vorticity above the BL. For example, during the first day, the wavenumber-1 (WN1) component of the LL vorticity change (following the TC) in the RD case (Fig. 5a) is mainly determined from the horizontal advection term and the divergence term in the vorticity equation. The WN1 component of the divergence term (Fig. 5b) has, except for small bands of the opposite sign, a north–southoriented vorticity dipole indicating strong asymmetric convergence (divergence) to the south (north). The WN1 component of the horizontal advection term (Fig. 5c) indicates rotation of the vorticity maximum toward the east. The resultant vorticity increases in the southeast (Fig. 5a) are consistent with the northeasterly peripheral flow shown in Fig. 3. Such a flow is not observed in the CTRL and SD cases (not shown), which again suggests that friction is essential in the development of this asymmetric flow. In summary, differential friction between land and sea generates a north–south asymmetry of vorticity within the LL through the divergence term. Near the TC center, the asymmetric flow actually has a more northerly component than the flow in the periphery (see Fig. 3), which is apparently consistent with the faster rotation of the asymmetric vorticity by the stronger symmetric wind of the TC at inner radii. However, this northerly asymmetric flow does not appear to drive the TC toward the coast. On the other hand, the asymmetric flow within the UL is different from that within the LL and has smaller magnitude. The divergence and the horizontal advection terms within the UL are also different (not shown). The different flow directions within the LL and UL imply a vertical shear between these two layers. Moreover, as time is required for the asymmetric vorticity (and the asymmetric flow) to develop, the TCs in the RD and RW cases move slowly during the first two days. Because horizontal advection cannot explain the TC drift, the possible contribution of convective asymmetries near the TC to the drift must be considered.

c. Rainfall and vertical motion asymmetries For the RD case, rainfall is found to be larger to the south (Fig. 6a) within 100 km from the TC surface cen-

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FIG. 3. Time composite of the asymmetric component of the LL (0.9 ⱖ ␴ ⱖ 0.55) flow for the RD experiment on the (a) first, (b) second, (c) third, (d) fourth, (e) fifth, and (f) sixth days. Results are shown within 1500 km from the TC center (marked by a dot at the origin). The big arrow, magnified by a factor of 10 such that a length that reads 1000 km on the horizontal axis represents an actual distance of 100 km, indicates the overall movement of the center during that day.

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FIG. 4. As in Fig. 3, but for the UL (0.55 ⱖ ␴ ⱖ 0.25).

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ter. However, the rainfall averaged over a distance of 300 km is different (Fig. 6b), with maximum rainfall west of the TC, then gradually becomes northwest. The figures indicate that rainfall over the south is small at 100–300 km from the TC surface center. Asymmetry in rainfall in the RW case is similar but no persistent asymmetries occur in the CTRL and SD cases (not shown). Rainfall should be strongly related to vertical motion. The first thing to note from the vertical motion within 100 km from the TC (surface) center at the lowest model level (␴ ⫽ 0.995) is the rapid change near the time of landfall in the RD case (Fig. 7a). An area of maximum rising motion rotates from the northwest to the northeast around t ⫽ 122 h when the TC is very close to the coast. At the same time, an area of sinking motion can be found to the south. Obviously these are due to the friction-induced convergence (divergence). Before landfall, rainfall has been persistently larger in the west. Similar patterns can be found in the RW case (not shown) when the TC gets very close to the coast but not for TCs that maintain a distance from the coast (CTRL and SD cases). The vertical motion within 100 km just above the boundary layer (␴ ⫽ 0.9) and at midlevel (␴ ⫽ 0.55) are similar with larger values to the west, although the large north–south asymmetry during landfall is no longer significant (see Figs. 7b,c). We could observe that the slight shift of the maximum vertical motion to the northwest is related to landfall. This shift is similar to the rainfall pattern averaged within 300 km (Fig. 6b) but not the rainfall pattern averaged within 100 km (Fig. 6a). At inner radii, the rain has been advected counterclockwise by the strong tangential wind during its fall toward the surface, so that rainfall is larger to the south. One possible reason for the larger vertical motion to the west is a vertical shear of the asymmetric flow. Under even very small vertical shear (e.g., 2 m s⫺1 between 850 and 200 hPa), considerable asymmetry of vertical motion could develop (Wong and Chan 2004). This can occur without a significant tilt of the vortex axis. If the shear is strong enough so that a tilt develops, vertical motion tends to be strongest ahead of the direction of tilt as found in previous numerical studies (e.g., Frank and Ritchie 1999; Wong and Chan 2004). For the RD case, it could be observed that the average vertical shear between the LL and the UL is south← FIG. 5. Wavenumber-1 component of the time composite of the LL (0.9 ⱖ ␴ ⱖ 0.55) average of the different terms in the vorticity equation for the RD experiment on the first day: (a) sum of the

terms (friction term neglected), (b) divergence term, and (c) horizontal advection term. The results are shown within 1500 km of the center (marked by a dot at the origin). The positive values are shaded.

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FIG. 6. Temporal variations of the rainfall rate averaged within (a) 100 and (b) 300 km from the TC surface center at each azimuth for the RD experiment. The abscissa gives the azimuth relative to east with the four cardinal directions (E, S, W, N) indicated on top of each panel. The dashed horizontal line marks the landfall time of the TC surface center.

southeasterly (strong northerly flow in LL, weak easterly flow in UL, see Figs. 3 and 4). The variation of the asymmetric wind with height in the TC core (100 km within TC center) is, however, more complicated (Fig. 8). Although the average zonal wind component within the LL is small in comparison to the average meridional wind component, the variation of the zonal wind within

FIG. 7. Temporal variations of the vertical motion averaged within 100 km from the TC center at each azimuth for the RD experiment: (a) ␴ ⫽ 0.995, (b) ␴ ⫽ 0.9, and (c) ␴ ⫽ 0.55. The dashed horizontal line marks the landfall time of the TC surface center.

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FIG. 8. Zonal and meridional winds averaged within 100 km from the TC center at each sigma level for the RD experiment.

the LL is large with significant easterly shear. From the zonal wind distribution (boldface solid and boldface dash in Fig. 8), we could see a deep relative (to the movement) easterly flow below and westerly flow above ␴ ⬇ 0.75. For the meridional wind distribution (solid and dash in Fig. 8), significant northerly relative flow is present only within the LL while southerly relative flow occurs within the BL. Overall, relative westsouthwesterly flow occurs within the BL, which is consistent with the inner-core rainfall being located to the south of the TC (see Fig. 6a). Because the TC weakens with time, an axis tilt might have developed. For the RD case, the tilt of the vortex axis with height is, however, not significant (Fig. 9). The tilt becomes larger toward the end of the simulation, with the center at ␴ ⫽ 0.2 located 16 km west-northwest of the center at ␴ ⫽ 0.995 at t ⫽ 144 h. The configuration of the tilt would give stronger vertical motion to the west-northwest of the TC, which is again fairly consistent with the results shown in Fig. 7c. The tilt in the meridional direction is less significant. As found in Wong and Chan (2004), the vortex tilt would be on the left of the shear vector. The axis tilt for the RD case is therefore consistent with the average south-southeasterly shear of the asymmetric flow. For the SW, RW, and SD cases, the vortex axis tilt is negligibly small. With such an asymmetry in vertical motion, the TC movement should be strongly modified by the effect of vertical advection and diabatic heating, and would not simply follow the advection by the asymmetric flow. In the next section, the movement of the TCs will be in-

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FIG. 9. Zonal and meridional positions of the minimum pressure at each sigma level for the RD experiment, relative to that at ␴ ⫽ 0.995.

vestigated by computing the PV tendency due to the various effects.

d. Potential vorticity tendency Schubert et al. (2001) derived a generalized form of Ertel’s PV equation (Ertel 1942), and takes into account the effects of moisture and rainfall. For simplicity, however, Ertel’s equation is used in the current study. Within the LL and UL (where the effect of friction can be neglected), the three terms that contribute to the local rate of change of PV are the horizontal advection (HA) term, the vertical advection (VA) term, and the diabatic heating (DH) term. The DH term is computed as DH ⫽

1 ␳

冋冉

冊 冉 册

⭸w ⭸␷ ⫺ ⭸y ⭸z

⫹ 共␨ ⫹ f 兲

⭸␪˙ , ⭸z

⭸␪˙ ⫹ ⭸x

⭸u ⭸w ⫺ ⭸z ⭸x

冊

⭸␪˙ ⭸y 共3.2兲

where the symbols carry their usual meaning and ␪˙ is the rate of change of potential temperature. The WN1 component of the PV tendency obtained by adding HA, VA, and DH gives results fairly consistent with the movement of the TCs when the TC drift is significant. For example, during the sixth day in the RD case, the WN1 PV tendency on the LL has positive (negative) values southwest (northeast) of the TC, which is consistent with the southwestward movement of the TC (Fig. 10a). As seen in Fig. 3f, the asymmetric

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FIG. 10. Wavenumber-1 component of the time composite of the LL (0.9 ⱖ ␴ ⱖ 0.55) average of the terms in the Ertel’s potential vorticity equation for the RD experiment on the fourth day: (a) sum of the terms (friction term neglected), (b) horizontal advection term, (c) vertical advection term, and (d) diabatic heating term. Positive values are shaded. The big arrow indicates the overall movement of the center during that period. (Unit is 104 PVU s⫺1.)

flow does not agree with the movement of the TC in the RD case. In fact, the HA term is mainly due to the advection of symmetric PV by the asymmetric wind, and would tend to drive the TC toward the south (Fig. 10b). The DH term has opposite phase (Fig. 10d) and tends to cancel the HA term. Although the WN1 component of the VA term has smaller magnitude than the HA and DH terms (Fig. 10c), it cannot be neglected because the sum of HA and DH does not agree with the moving direction. Since heating is strongest at midlevels, the stronger vertical motion west of the TC gives larger DH within the LL due to the third term in (3.2).

However, the first and second terms are not negligible (not shown). In the UL, the contribution to the PV tendency is much different than that in the LL. During the sixth day, the sum of the terms agrees fairly well with the moving direction (Fig. 11a). The HA would tend to drive the TC toward the west (Fig. 11b) while DH tends to cancel the HA term (Fig. 11d). Again, the VA term cannot be neglected though it has a smaller magnitude (Fig. 11c). Similar patterns of the PV tendency, HA, VA, and DH terms are observed on the other days within the LL

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FIG. 11. As in Fig. 10, but for the UL (0.55 ⱖ ␴ ⱖ 0.25).

and UL. The results for the RW case are also similar. Overall, all three have to be taken into account in determining the PV tendency, although the HA appears to align with the moving direction. Results in this subsection are also consistent with those of Chan et al. (2002) that the effects other than HA cannot be overlooked when the movement (direction and speed) of the TC is not steady. The vertical coupling effect found in Wu and Wang (2001) is not evident.

4. Complementary experiments It is shown in the previous section that the TC drifts are related to the development of the asymmetric vor-

ticity. The asymmetric vorticity (and the asymmetric flow) can be enhanced by extracting energy from the symmetric circulation of the TCs (barotropic instability). This occurs when the tangential wind decreases fast enough with radius, so that the radial (absolute) vorticity gradient changes sign. The vortex profile used in this study has a cutoff radius that determines where the circulation of the TC goes to zero. The large cutoff radius of 3000 km virtually reduces the equation of the vortex profile to the form used in some previous studies (e.g., Chan and Williams 1987), and suppresses the effect of barotropic energy transfer in the vicinity of the TCs. However, it is still possible that other factors affect-

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ing the development of the asymmetric vorticity could influence the drift. This includes: 1) the vortex size, if the vortex is very small, there would be no interaction with the land surface, and 2) the roughness of the land surface. The RL of 0.5 m would seem to be large when compared with previous studies (e.g., Tuleya and Kurihara 1978; Chan and Liang 2003), although an even larger value of 0.8 m has recently been adopted for the “urban and built-up land” category in MM5 to make better representation of the effects of buildings, 3) effects of sensible heat over land. The effect has to be tested although previous studies (e.g., Chan and Liang 2003) found little association of the sensible heat flux over land with the rainfall asymmetry, and 4) boundary layer parameterization. If the results depend on the boundary layer parameterization then it is likely to be not physical. Additional experiments are carried out with the same conditions as in the RD experiment except: 1) a smaller vortex was used, 2) an RL of 0.05 m instead of 0.5 m was used over land, 3) a land surface temperature of 26.5° and 30.5°C, respectively, was used, and 4) the Blackadar boundary layer scheme (Blackadar 1979) was used. The drifts for experiments 1 and 2 are smaller than RD while there is little difference in the tracks between experiment 3 and RD (not shown). Therefore the drift is sensitive to the vortex size and the roughness over land, but not the sensible heat flux over land. Using the Blackadar boundary layer scheme in experiment 4 also results in a landward drift (not shown). The influence of the coast extends away from the coast as it takes time for the flow within the boundary layer to adjust to the land. It is worthwhile to investigate how such an adjustment could affect the inner core (asymmetric) structure of the TC. For this purpose, some other experiments are performed with simpler physics. Moisture and latent heating are excluded in these runs. An initially symmetric TC with an intensity of ⬃976 hPa is placed directly at the coastline and at locations 50, 100, and 150 km to the east and west of the coastline, respectively. The mass fields (i.e., temperature, pressure) are not allowed to change with time during the 48-h simulation, while the three-dimensional winds are allowed to adjust to the mass fields and the drag from the surface. The BL convergence within 100 km from the TC center or the vertical velocity at ␴ ⫽ 0.9 could be used to indicate the asymmetry forced by the surface. When the TC is placed at 50, 100, and 150 km east of the coast, BL convergence is much stronger west of the TC, though the averaging area covers the sea only for the TCs placed 100 and 150 km east of the coast (Fig. 12a). There is also a small tendency for the asymmetry to

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FIG. 12. Boundary layer (1.0 ⱖ ␴ ⱖ 0.9) convergence averaged within 100 km at each azimuth for the experiments where the mass fields of the TC are fixed: (a) results for TCs located at 50 (solid), 100 (dashed), and 150 km (dotted) east of the coast, and (b) results for TCs located at 50 (solid), 100 (dashed), and 150 km (dotted) west of the coast. The boldface solid line corresponds to the case where the TC is located at the coast.

rotate slightly anticyclonically as the vortex “edges closer” to the coast, from 150 to 50 km (dotted and solid lines, respectively, in Fig. 12a). These results seem to be consistent with the asymmetry in rainfall and vertical motion. When the TC is placed at the coast or west of the coast, the asymmetry diminishes (Fig. 12b). However, it could be observed that when the TC is 50 km

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west of the coast, BL convergence is smaller east of the TC. Thus, the asymmetry in vertical motion, rainfall, and TC drift are strongly modified by this effect. The study of the adjustment of wind to a surface of different properties is the subject of the internal boundary layer. While previous studies focused on the adjustment of the onshore wind to the land surface, the results here demonstrate that the adjustment of the offshore wind to the sea surface may have a stronger effect on the convection distribution of the TC core, especially when the TC is still over the sea and is about to make landfall.

5. Summary and discussion Numerical experiments are performed with the MM5 to study the effects of surface-moisture flux and friction over land on the movement of TCs. On an f plane, the TCs are initially placed 150 km due east of a north– south-oriented coastline in an atmosphere at rest. It is found that a TC could drift toward land when the RL is 0.5 m over land, with an average drift speed of ⬃1 m s⫺1. Friction, but not surface-moisture flux over land, is essential for the movement toward land. The presence of the rough land surface forces an asymmetry of the near-surface wind in two ways. First, as is well known, wind over land is reduced so that there is a large-scale asymmetric convergence/divergence along the coast. Second, air flowing offshore needs time to adjust to the sea surface, and vice versa. As shown in Fig. 12, this affects the asymmetric structure of the TC core. These two mechanisms, which depend on the roughness contrast between land and sea, are hypothesized to be the cause of the TC drift, since they could modify the PV tendency. For the first mechanism, the large-scale BL asymmetric divergence could induce an asymmetry in vertical motion. An asymmetric flow also develops in the LL because of the creation of asymmetric vorticity by the divergence term in the vorticity equation. Horizontal advection then rotates the asymmetric vorticity to give a northeasterly flow in the TC periphery (⬃500–1000 km from the TC center). The flow near the TC center has a more northerly component as a result of the stronger rotation by the tangential wind of the TC at inner radii. This asymmetric flow has an advective effect on the vortex (Figs. 10b and 11b). However, there is a vertical shear of this large-scale asymmetric flow. The magnitude of the flow is much stronger in the LL than in the UL, and there is also a difference in the flow direction. This represents a creation of an asymmetry in vertical motion, and a deviation of the TC motion from the HA. Potential vorticity budget calculations indicate

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that while the HA term is basically due to the largescale asymmetric flow, the DH and VA terms have to be considered in determining the vortex landward drift. For the second mechanism, additional experiments in which the mass fields are fixed in time are performed to allow the initially axisymmetric wind fields to adjust to the surface, in order to see the asymmetry produced. The results show that boundary layer convergence is much stronger west of the TC when the TC is east of the coast (before landfall). This mechanism could increase the westerly relative flow in the BL and the asymmetry in vertical motion. This also modifies the PV tendency and therefore the drift. However, the results are based on the assumption that the mass fields remain symmetric and the wind fields adjust to it. The mass fields would be strongly distorted from symmetry in reality. Additional work is under way to study the wind fields near the coast, to validate and understand the asymmetric convergence when the TC is near the coast. These two mechanisms differ from the results found in Chan and Liang (2003), where the asymmetry in vertical motion was found to be sensitive to the latent heat flux over land. Without using the 5-km domain, it is found that the results greatly depend on whether the cumulus parameterization is used. For the smooth and dry land conditions (as in the SD), there is a large difference in the parameterized rainfall between the land and the sea. The core resolvable-scale rainfall is also asymmetric and a drift is found. However, not using the cumulus parameterization does not result in an asymmetric and drift, similar to the results obtained in the SD experiment here using the 5-km domain with explicit cumulus physics. The direction of the shear is shown to be consistent with the asymmetry in vertical motion. The vertical tilt of the vortex axis, though small, is found to be consistent with previous results that vertical motion is strongest in the direction of tilt. With the ␤ effect or a significant background flow, the TC drift due to the differential friction between land and sea would likely be less important. However, for slow-moving TCs (e.g., with moving speed less than 10 km h⫺1) near a long, straight coastline, it would be of scientific interest to conduct some observational studies to see whether such an effect is taking place. Moreover, a larger contribution to TC motion does not necessarily imply a larger contribution to the asymmetry in vertical motion and rainfall. In other words, the vertical shears of the ␤ effect or the background flow may not be strong enough to mask the asymmetry in vertical motion and rainfall due to the shear caused by the largescale asymmetric flow induced by the land–sea inter-

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face or the frictional convergence. Inclusion of the ␤ effect or/and a background flow in future numerical studies would be beneficial for a better understanding of the complex, and not always consistent, rainfall distribution of landfalling TCs in the real world. Acknowledgments. This research is sponsored by the Research Grants Council of the Hong Kong Special Administrative Region, China Grant CityU 100203. REFERENCES Betts, A. K., and M. Miller, 1986: A new convective adjustment scheme. Part II: Single column tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets. Quart. J. Roy. Meteor. Soc., 112, 693–709. Blackadar, A. K., 1979: High resolution models of the planetary boundary layer. Advances in Environmental Science and Engineering, Vol. 1, J. Pfaffilin and E. Ziegler, Eds., Gordon and Briech, 50–85. Chan, J. C. L., 1984: An observational study of the physical processes responsible for tropical cyclone motion. J. Atmos. Sci., 41, 1036–1048. ——, and R. T. Williams, 1987: Analytical and numerical studies of the beta-effect in tropical cyclone motion. Part I: Zero mean flow. J. Atmos. Sci., 44, 1257–1265. ——, and X. Liang, 2003: Convective asymmetries associated with tropical cyclone landfall. Part I: f-plane simulations. J. Atmos. Sci., 60, 1560–1576. ——, F. M. F. Ko, and Y. M. Lei, 2002: Relationship between potential vorticity tendency and tropical cyclone motion. J. Atmos. Sci., 59, 1317–1336. ——, K. S. Liu, S. E. Ching, and E. S. T. Lai, 2004: Asymmetric distribution of convection associated with tropical cyclone making landfall along the south China coast. Mon. Wea. Rev., 132, 2410–2420. Dudhia, J., 1989: Numerical study of convection observed during

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