A Numerical Investigation of the Eyewall Evolution in a Landfalling Typhoon
CHUN-CHIEHWU ANDHSIU-JU CHENG
Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan
YUQINGWANG
International Pacific Research Center and Department of Meteorology, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, Hawaii
KUN-HSUANCHOU
Department of Atmospheric Sciences, Chinese Culture University, Taipei, Taiwan
(Manuscript received 9 January 2008, in final form 27 June 2008) ABSTRACT
An interesting eyewall evolution occurred in Typhoon Zeb (1998) when it devastated Luzon. The eyewall of Zeb contracted before landfall and broke down and weakened after landfall; then a much larger new eyewall formed and strengthened as it left Luzon and reentered the ocean. The fifth-generation Pennsyl-vania State University–NCAR Mesoscale Model (MM5) with four nested domains was used to perform numerical experiments to understand the effects of terrain and land surface variation on the observed eyewall evolution. Results show that the presence of Luzon plays a critical role in the observed eyewall evolution. Quite different from the conventional concentric eyewall replacement, the eyewall replacement that occurred in Typhoon Zeb was triggered by the mesoscale landmass and terrain variation with a horizontal scale similar to the core of the typhoon. In Typhoon Zeb, the original eyewall contracted and broke down because of enhanced surface friction after landfall. The outer eyewall was triggered by con-vective rainbands near the western coastal region of Luzon and formed as a result of axisymmetrization well after the dissipation of the inner eyewall convection.
Several sensitivity experiments were conducted to elucidate the roles of both condensation heating and planetary boundary layer processes in the evolution of the typhoon eyewall. It is found that although condensational heating is the key to the maintenance of the annular potential vorticity (PV) structure, surface friction plays dual roles. Although friction is a sink to PV and thus dissipates PV in the eyewall, it helps keep the PV annulus narrow by enhancing the stretching deformation in the lower troposphere when condensational heating is present. In the absence of condensational heating, however, surface friction enhances the inward PV mixing by boundary layer frictional inflow and thus destroys the PV annulus.
1. Introduction
The evolution of the eyewall in tropical cyclones (TCs) has always been an intriguing issue in TC ther-modynamics and dynamics (Wang and Wu 2004). The variability in the eyewall structure also plays a very important role in TC intensity change. The intensifica-tion of a TC is usually accompanied by eyewall con-traction, which can be explained easily by the simple
Sawyer–Eliassen model of the response of a balanced vortex to convective heating in the eyewall (Shapiro and Willoughby 1982; Schubert and Hack 1982). When concentric eyewalls are present, the amplification and inward propagation of the outer eyewall usually sup-presses and eventually kills the convection in the inner eyewall, leading to an eyewall replacement (loughby et al. 1982; Wil(loughby 1990; Black and Wil-loughby 1992; WilWil-loughby and Black 1996). A similar eyewall replacement process has been recently identi-fied by Wang (2008a) in the formation of annular hur-ricanes but with no secondary wind maximum associ-ated with the outer convective ring because of its prox-imity to the primary eyewall. Recent studies attributed
Corresponding author address: Dr. Chun-Chieh Wu, Dept. of
Atmospheric Sciences, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10673, Taiwan.
E-mail: cwu@typhoon.as.ntu.edu.tw
JANUARY2009 W U E T A L . 21
DOI: 10.1175/2008MWR2516.1
© 2009 American Meteorological Society
polygonal eyewalls and eyewall mesovortices to baro-tropic instability and the resultant asymmetric mixing processes (Schubert et al. 1999; Reasor et al. 2000). It was also found that the asymmetric vorticity mixing between the eye and eyewall of a TC could lead to pressure falls in the TC core (Schubert et al. 1999; Kossin and Eastin 2001; Kossin and Schubert 2001). Other studies also suggested that the interaction of the vorticity asymmetries and mean vortex could either spin up the mean vortex through the vortex Rossby
wave–mean flow interaction (Montgomery and Kallen-bach 1997; Montgomery and Enagonio 1998) or limit the maximum intensity of a TC by spinning down the maximum tangential wind through eddy diffusion (Wu and Braun 2004; Yang et al. 2007). Furthermore, it has been shown in Emanuel (1997) that the maintenance of a narrow annulus of the inner-core eyewall is frontoge-netic by nature and would naturally tend toward an infinitely narrow annulus with infinite vorticity (i.e., a circular vortex sheet).
FIG. 1. The Geostationary Meteorological Satellite-5 (GMS-5) visible images for Typhoon Zeb (1998): (a) 0732 UTC 13 Oct; (b) 0032 UTC 14 Oct; (c) 0832 UTC 14 Oct; and (d) 0232 UTC 15 Oct.
A number of studies have investigated the evolution of landfalling TCs (Brand and Blelloch 1973, 1974; Yeh and Elsberry 1993a,b; Wu and Kuo 1999; Wu 2001; Wu et al. 2002; Chen and Yau 2003). Whereas most of the above studies focused on investigating the impact of Taiwan terrain, Brand and Blelloch (1973) were the first to document the effect of the Philippine Islands on the changes of track, eye diameter, storm intensity, and size for TCs during 1960–70 based on the annual ty-phoon reports of the Joint Tyty-phoon Warning Center (with aircraft reconnaissance available during that pe-riod). It was indicated that the frictional effect of the landmass and the reduction in heat and moisture supply from the ocean are the primary causes of the above changes, although no specific analyses were conducted to assess the physical mechanisms involved. In general, there have been few studies focusing on the eyewall dynamics of typhoons making landfall on the Philippine Islands, which have terrain features with horizontal scales similar to the size of a TC. Wu et al. (2003a) conducted an observational and modeling study to document the eyewall evolution of Typhoon Zeb (1998) when Zeb interacted with the terrain of Luzon. As an extension of the study by Wu et al. (2003a), this study further examines the roles of landmass and the terrain of Luzon in producing the interesting eye-wall evolution of Typhoon Zeb (1998) before, during, and after its landfall. As we can see from the satellite images given in Fig. 1, the eyewall of Zeb contracted before landfall and broke down and dissipated after
landfall; then a new and much larger eyewall formed as Zeb left Luzon and reentered the ocean. The new eye-wall contracted again but remained large as Zeb moved along the east coast of Taiwan. Similar features have also been observed in other TCs, such as Typhoon Melor (2003) over Luzon and Hurricane Wilma (2005) over the Yucatan Peninsula, but these special eyewall evolutions have never been investigated in detail in the literature.
The objectives of this study are twofold: (i) to inves-tigate the effects of terrain, land surface, and ocean on the evolution of the eyewall of Typhoon Zeb and (ii) to understand the dynamics of the eyewall evolution and the associated intensity change of a landfalling ty-phoon. Several sensitivity experiments are also con-ducted to explore the effects of moist convection, sur-face heat flux, and sursur-face friction on the maintenance of the narrow potential vorticity (PV) annulus in the new large eyewall. The experimental design is de-scribed in section 2. Results from full-physics simula-tions and from several sensitivity experiments are dis-cussed in sections 3 and 4, respectively. The major find-ings are summarized in the last section.
2. Experimental design
The numerical simulations are conducted with the fifth-generation Penn State University–National Center for Atmospheric Research (NCAR) Mesoscale Model (MM5; Grell et al. 1995). The nonhydrostatic MM5 FIG. 2. (a) The four nested domains in the three major experiments. (b) The model’s terrain height (contour interval of 500 m) of
Luzon within the third mesh in CTL.
with four nested domains (Fig. 2a) is used to perform 72-h simulations, starting from 0000 UTC 13 October 1998. The model was run with 23 vertical levels (0.025, 0.075, 0.125, 0.175, 0.225, 0.275, 0.325, 0.375, 0.425, 0.475, 0.525, 0.575, 0.625, 0.675, 0.725, 0.775, 0.825, 0.87, 0.91, 0.945, 0.97, 0.985, and 0.995) in the terrain-following coordinate [ ⫽ (p ⫺ pt)/( ps⫺ pt), where p
is the pressure, psthe surface pressure, and ptthe
con-stant top pressure of 10 hPa]. The horizontal grid spac-ings of the four domains are 54 km (the first mesh, 95⫻ 109 grid points), 18 km (the second mesh, 142 ⫻ 139 grid points), 6 km (the third mesh, 226 ⫻ 178 grid points), and 2 km (the fourth mesh, 487 ⫻ 409 grid points). The initial and lateral boundary conditions are based on the European Centre for Medium-Range Weather Forecasts (ECMWF) advanced global analy-sis. The model initialization and vortex bogusing are based on the method described in Wu et al. (2002). The planetary boundary layer (PBL) scheme used in the model is the Blackadar formula (Blackadar 1976, 1979;
Zhang and Anthes 1982). In the two coarser meshes (with 54- and 18-km horizontal grid spacings), cumulus convection is parameterized with the Betts–Miller scheme (Betts and Miller 1986). The explicit cloud mi-crophysics scheme of Reisner et al. (1998) is used for all meshes.
Three full-physics numerical experiments with differ-ent underlying surface conditions are conducted to in-vestigate the effects of the terrain of Luzon, the land surface, and the ocean on the evolution of the eyewall of Zeb. The control experiment (CTL; see Table 1 for descriptions of all experiments) retains all the model-resolved terrain in the model domain. In the second experiment (NLT), the mountains of Luzon (with a maximum height of 2125 m in the third mesh; Fig. 2b) are flattened. In the third experiment (SEA), the land of Luzon is totally replaced with the ocean, where the “sea” surface temperature over Luzon is interpolated from the boundary value around the replaced area. To save computing time, each of the three simulations is
FIG. 3. (a) Best track of CWB and model tracks of all experiments; (b) minimum sea level pressure of Typhoon Zeb. The left (right) vertical dashed line indicates the time when Zeb made landfall at (exited from) Luzon.
TABLE1. Summary of all experiments. Expt
name Luzon terrain Moisture
Surface heat flux
Surface friction
Simulation
period Eyewall evolution during 54–72h
CTL Full Yes Yes Yes 0–72 h (MSLP⫽ 962–954 hPa) PV ring
NLT Flat Yes Yes Yes 0–72 h
SEA Virtual ocean Yes Yes Yes 0–72 h
DFL Full No No No 54–72 h (MSLP⫽ 962–971 hPa) Mixing and dissipating
DRY Full No Yes Yes 54–72 h (MSLP⫽ 962–991 hPa) Rapid dissipating
NHF Full Yes No Yes 54–72 h (MSLP⫽ 962–973 hPa) Rapid mixing
FL Full Yes No No 54–72 h (MSLP⫽ 962–952 hPa) Distorted PV ring with mesovortices
FIG. 4. Radius–time Hovmöller diagram of azimuthally averaged tangential wind (m s⫺1) at 925 hPa for (a) CTL, (b) NLT, and (c)
SEA. The lower (upper) horizontal long-dashed line indicates the time when Zeb made landfall at (exited from) Luzon.
FIG. 5. The low-level (⫽ 0.91) radar reflectivity (dBZ) in CTL at (a) 18, (b) 24, (c) 30, (d) 36, (e) 42, (f) 48, (g) 54, (h) 60, and (i) 66 h.
first performed with the two outer meshes only. The simulation on the third mesh is started at t⫽ 4 h. The initial field of the third mesh, except for the terrain height, is interpolated from the output of the second mesh at t⫽ 4 h as well. At t ⫽ 12 h, the fourth mesh is activated with the initial field interpolated from the output of the third mesh. Most of the results shown in the following sections are from the fourth domain. Re-sults from these full-physics simulations are discussed in section 3.
To further understand the physical processes respon-sible for the maintenance of the eyewall PV annulus of the simulated Zeb, we have performed four sensitivity experiments with varying model physics (see Table 1). All sensitivity experiments are initialized with the out-put of the CTL experiment at 54 h and integrated for 18 h with the lateral boundary conditions from the 54–72-h output of the CTL experiment. In the first sensitivity
experiment (DFL), the MM5 is integrated with neither moist processes nor the PBL scheme; that is, the ex-periment is dry, frictionless, and without the surface sensible and latent heat fluxes. In the second sensitivity experiment (DRY), the moist processes are turned off but the PBL scheme is retained. The third sensitivity experiment (NHF) is similar to the CTL experiment but with the surface heat fluxes turned off. The final sensitivity experiment (FL) is the same as CTL but without the PBL scheme. Results from these sensitivity experiments are discussed in section 4. Note that some level of imbalance is introduced in these sensitivity ex-periments because of the inconsistencies in the model physics with both the initial and lateral boundary con-ditions. Nevertheless, these imbalance and inconsisten-cies are expected not to overtake the actual physics that we intend to explore, although the results should be explained with caution.
FIG. 6. As in Fig. 5, but for NLT.
3. The effects of terrain and land surface of Luzon
Except for some slight northward deflection of Zeb’s track in the initial 24 h and an eastward deflection after 48 h, the simulated tracks (the location of the storm is defined as the center of the minimum sea level pressure here)1of all the three full-physics experiments (Fig. 3a)
are in general agreement with the best-track analysis of Zeb from the Central Weather Bureau (CWB) of Tai-wan. The evolution of the minimum sea level pressure (MSLP) is also well simulated in CTL (Fig. 3b). NLT shows a MSLP evolution similar to that in CTL, espe-cially the filling after landfall at Luzon. The similar filling rates of MSLP in both NLT and CTL, as
com-pared to the continuous strengthening of the storm in SEA, suggest that the weakening of Zeb after landfall is mainly due to the great reduction of heat fluxes from the underlying surface. Note that the storm intensity after landfall in CTL, although weaker than observed, is generally about 10–15 hPa weaker than that in NLT, indicating that the terrain over Luzon plays a role in weakening the storm. We find that in the presence of terrain, convection outside the eyewall is triggered ear-lier after the landfall of Zeb. This results in strong sup-pression and rapid dissipation of the eyewall convec-tion, and thus the weakening of the storm.
The radius–time Hovmöller diagrams of the azimuth-ally averaged tangential wind from the three full-physics experiments (Fig. 4) indicate that the break-down and reformation of the eyewall of Zeb are closely related to the influence of the different underlying sur-faces. The main features of the eyewall contraction, breakdown, and reformation processes during the pe-1The typhoon center in the later discussion is defined as the
PV-weighted center, leading to a more accurate circulation center, especially after the formation of the large eye.
FIG. 7. Surface latent heat flux (W m⫺2) in CTL at (a) 18, (b) 24, (c) 30, (d) 36, (e) 42, (f) 48, (g) 54, (h) 60, and (i) 66 h. The typhoon symbol indicates the location of MSLP.
riod when Zeb is near Luzon are well captured in CTL. The eyewall contracts before landfall and breaks down and dissipates over land, and a large, new eyewall forms as Zeb leaves Luzon and reenters the ocean. The con-traction of the eyewall before landfall is likely en-hanced by the orographic effect of Luzon because the contraction is not significant in NLT (i.e., without terrain). Despite a slight decrease of maximum wind between about 20 and 40 h, the simulated storm in SEA intensifies from the beginning of the integration until 50 h (Fig. 3) with nearly constant eyewall size (Fig. 4c).
The evolution of the simulated radar reflectivity at a low model level ( ⫽ 0.91; Fig. 5) in CTL shows a remarkable weakening of convection in the eyewall af-ter the landfall of Zeb. In the first few hours afaf-ter land-fall, the radius of maximum azimuthal mean tangential wind (RMTW) in the boundary layer decreases as the storm weakens. The RMTW at 925 hPa reduces from
40 km at 25 h (when Zeb makes landfall) to 18 km at 33 h (Fig. 4). The eyewall convection continues to weaken as the storm moves inland, whereas the cyclonic circula-tion beyond a radius of 150 km strengthens (Fig. 4) with the radius of the wind speed⬎15 m s⫺1increasing. It is not until the eyewall dissipates that an outer convective rainband is organized to form a circular convective ring outside the original eyewall. A secondary wind maxi-mum associated with the outer convective ring occurs at a radius of about 120 km at 32 h. The original eyewall breaks down about 12 h after landfall. As the original eyewall convection continues to weaken and the maxi-mum wind decreases, the outer convective ring strength-ens and the secondary maximum wind increases. The outer eyewall develops more rapidly after the storm reenters the ocean, and the storm then continues to reintensify. The convection in the original eyewall de-cays and a larger new eyewall appears at around 52 h (figure not shown). Our results indicate that the for-FIG. 8. As in Fig. 7, but for surface sensible heat flux.
mation of the larger new eyewall of Zeb is due to the weakening and dissipation of the original eyewall and the development of the outer eyewall.
With the terrain removed in NLT, the eyewall does not contract before landfall (Fig. 4b), although its breakdown and reformation processes resemble those in CTL. In NLT, the maximum tangential wind de-creases after landfall, with the RMTW increasing at the same time (Fig. 4b), in contrast to the RMTW decrease in CTL. However, similar to what happens in CTL, a larger, new eyewall appears several hours after the storm reenters the ocean (Fig. 6), but the radius of the new eyewall in NLT is smaller than that in CTL.
The different eyewall evolution in the three full-physics experiments indicates that the interesting eye-wall evolution of Zeb is closely associated with the landfall of Zeb and its interaction with the terrain of Luzon. Moreover, the radius of the eyewall increases gradually in NLT and more abruptly in CTL. The for-mation of the outer eyewall in both CTL and NLT is associated with the development and organization of the outer spiral rainbands. The mountains of Luzon play an important role in enhancing the convection in
the outer rainbands such that the new eyewall forms more rapidly in CTL than in NLT.
The distribution of the surface sensible and latent heat fluxes shows that the maximum surface heat fluxes are located underneath the eyewall before Zeb makes landfall (Figs. 7 and 8). The surface heat fluxes under the eyewall decrease remarkably as Zeb moves inland. The decrease of the low-level equivalent potential tem-perature (Fig. 9) indicates that the air in the PBL in the eye cools and dries significantly after Zeb makes land-fall. As a result, the convection in the eyewall is greatly suppressed. On the other hand, although the surface sensible and latent heat fluxes from the underlying sur-face under the eyewall are reduced, those outside the core remain large because of the maintenance of the outer circulation of the storm. Moreover, in CTL, the low-level convergence along the western coast is hanced by the mountain of Luzon initiating and/or en-hancing convective rainbands to the west coast of Lu-zon (Fig. 5). The rainbands are later axisymmetrized to form an outer convective ring. In such an eyewall evo-lution process, the dissipation of the original eyewall that occurs prior to the formation of the new outer FIG. 9. The azimuthal mean equivalent potential temperature (contour interval of 4 K) profile in CTL at (a) 24, (b) 30, (c) 36, and
(d) 42 h.
eyewall is triggered by the landfall, whereas the avail-ability of the surface sensible and latent heat fluxes plays a critical role in the formation of the new large eyewall.
PV is a quantity useful for understanding many as-pects of inner core dynamics of TCs (e.g., Wang 2002a,b). Ertel’s PV is approximated (ignoring the hori-zontal gradient of the vertical velocity in the definition of horizontal vorticity; Wu et al. 2003b, 2004) as
q⫽ ⫺g p
冉
⭸ ⭸ ⫺ 1 a cos ⭸ ⭸ ⭸ ⭸ ⫹ 1 a ⭸u ⭸ ⭸ ⭸冊
, where ⫽ Rd/Cp; u and are the storm-relative radialand tangential winds, respectively; denotes the verti-cal component of the absolute vorticity; the vertiverti-cal
coordinate is the Exner function [ ⫽ Cp( p/p0)]; and
and g denote the potential temperature and gravita-tional acceleration, respectively.
The PV evolution in the two landfall experiments suggests that the increased surface friction and the re-duced surface sensible and latent heat fluxes could both disrupt the maintenance of the annular PV structure of the eyewall over land. As shown in Figs. 10 and 11, before Zeb makes landfall, the maximum PV is located just inside the RMTW. The small high-PV annulus col-lapses (Fig. 10a) after Zeb makes landfall. The PV an-nulus evolves into a monopole in the 12 h after landfall (Figs. 10d and 11). Similar evolution occurs in NLT (Fig. 12). In the two landfall experiments, the low-level PV evolution after Zeb makes landfall resembles the PV mixing between the eye and the eyewall described FIG. 10. The PV (PVU; 1 PVU⫽ 1 ⫻ 10⫺6m2s⫺1K kg⫺1) at 875 hPa in CTL at (a) 18, (b) 24, (c) 30, (d) 36, (e) 42, (f) 48, (g) 54,
(h) 60, and (i) 66 h. The typhoon symbol indicates the location of MSLP.
in the observational study of Kossin and Eastin (2001) and the theoretical study of Schubert et al. (1999) based on an unforced barotropic model. However, in our case, it seems that either the reduced moist convection or the increased surface friction or both after landfall could lead to the enhanced PV mixing between the eye and the eyewall. The annular nature of the eyewall PV is easily maintained over the ocean, whereas a monopo-lar PV structure dominates over land. The relative roles of moist processes and surface friction in the mainte-nance of the large outer PV annulus will be further discussed in the next section through several sensitivity experiments with varying model physics.
In CTL, the new large PV annulus associated with the outer eyewall forms before Zeb reenters the ocean and becomes well organized after Zeb reenters the ocean (Figs. 10e,f). When the new outer eyewall is en-FIG. 11. The azimuthal mean PV (PVU) at 875 hPa at different
stages in CTL.
FIG. 12. As in Fig. 10, but for NLT.
tirely over the ocean, the high-PV annulus exhibits a distinct wavelike asymmetric structure, evolving into different polygonal patterns (Fig. 13). The polygonal patterns, as well as the location of the MSLP (shown with a typhoon symbol), rotate cyclonically around the low-level PV-weighted center (shown with a triangle). At the same time, the central monopolar PV patch weakens and migrates toward the outer PV annulus (Fig. 12h) and then orbits along the inner edge of the outer high-PV annulus (Fig. 13). Eventually, the mono-polar PV patch is distorted and merges into the new eyewall PV annulus.
To further examine the mechanism of the outer eye-wall development, PV budget analyses are carried out. The local PV change,
⭸q ⭸t ⫽ ⫺h⭈ q ⫺* ⭸q ⭸ ⫺g p
冋
⭈ 冉
d dt冊
⫹ ⭈ ⫻ F册
(as in Wu and Kurihara 1996), is governed by the hori-zontal and vertical advection of PV (where* ⫽ d/dt), diabatic heating (d/dt, including the condensational and radiative heating), and friction.
The PV budget analyses at 700 hPa at 38 h (Fig. 14) indicate that diabatic (condensation) heating contrib-utes to the production of high PV in the outer eyewall, especially in the lower levels (figures not shown). The redistribution of the high PV is accomplished through the cyclonic advection by the swirling flow of the storm FIG. 13. The PV (PVU) at 875 hPa in CTL at (a) 63 h, (b) 63 h 20 min, (c) 63 h 40 min, (d) 64 h, (e) 64 h 20 min, (f) 64 h 40 min, (g) 65 h, (h) 65 h 20 min, and (i) 65 h 40 min. The typhoon symbol indicates the location of MSLP; the triangle indicates the low-level PV-weighted center.
in the lower-middle troposphere (especially between 700–500 hPa; Fig. 14). Therefore, PV in the rainbands intensifies as a result of enhanced moist convection and is axisymmetrized by the lower-to-midlevel shear de-formation flow of the storm and organized into a new convective eyewall with elevated PV (Wang 2008b). When the inner eyewall finally dissipates, the larger eyewall appears. As shown in the PV budget analyses at 925 hPa at 54 h (Fig. 15), the diabatic heating is the leading factor contributing to the PV generation in the lower troposphere when the storm is located over the open ocean. Again, this analysis highlights the impor-tance of the PV source from diabatic processes in the full-physics simulation. In CTL, the outer PV annulus forms slightly before the appearance of the larger eye-wall in the wind field (Figs. 4a and 10). In NLT, the formation of the complete outer PV annulus appears
after the formation of the larger eyewall in the wind field (Figs. 4b and 12). Therefore, the mountains of Luzon hasten the weakening of the original eyewall and the development of the new large outer eyewall.
4. Maintenance of the eyewall PV annulus
The evolution of PV in the eyewall is highly influ-enced by the effects of surface friction and diabatic heating. Therefore, moist convection and friction must be important to the evolution of the PV annulus in the full-physics simulations discussed in section 3. The large PV annulus satisfies the necessary condition for baro-tropic instability. Such instability was studied by Schu-bert et al. (1999) and Kossin and SchuSchu-bert (2001) using a barotropic model (in which vorticity evolution is stud-FIG. 14. The local changes of PV (as scaled by the upper color bar; PVU h⫺1) at 38 h, 700 hPa in CTL due to the horizontal (HADV) and vertical (VADV) advection of PV, diabatic heating (DIAB, including the condensational and radiative heating), and friction (FRIC); D⫹ F denotes the sum of diabatic heating and friction and PV denotes the potential vorticity (as scaled by the lower color bar; PVU).
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ied instead of PV). They showed that depending on the ratio of the width of the vorticity annulus to the radius of the annulus at the initial state, the end state due to the release of the instability is either vorticity crystals [see Fig. 4 of Kossin and Schubert (2001), in which several patches of high-vorticity blobs are present] or a monopole. Therefore, without moist and frictional pro-cesses, a narrow large-PV annulus cannot maintain it-self, and it breaks down into PV crystals (dynamically equivalent to vorticity crystals in the barotropic model as mentioned above) or evolves into monopole. To bet-ter understand the roles of the moist and frictional pro-cesses in the maintenance of the new eyewall PV an-nulus, several sensitivity experiments are conducted with or without moist processes, PBL processes, or sur-face heat flux (Table 1). All the sensitivity experiments start with a PV annulus with a large radius and a small PV patch in the center of the annulus, taken from the output of CTL at 54 h (Fig. 10g), and are integrated
with the lateral boundary condition from the 54–72-h output of CTL. Each sensitivity experiment is inte-grated for 18 h on domain 4 (with 2-km horizontal grid spacing). As noted in section 2, in these sensitivity ex-periments some level of imbalance is introduced be-cause of the inconsistencies in the model physics with both the initial and lateral boundary conditions. Nev-ertheless, these imbalances and inconsistencies are ex-pected not to overtake the actual physics that we intend to explore within the relatively short integration time examined.
Without the moist and frictional processes in experi-ment DFL (dry and frictionless; Fig. 16), the high-PV annulus breaks down to form several small PV patches of different sizes and strengths within 1 h of integration (cf. Figs. 10g and 16a). The central high-PV patch mi-grates toward the inner edge of the annulus in the fol-lowing hours and then orbits cyclonically with the other PV patches (Figs. 16b–d). The original central PV patch FIG. 15. As in Fig. 14, but for 925 hPa at 54 h.
34 M O N T H L Y W E A T H E R R E V I E W VOLUME137
decays while orbiting. At t ⫽ 9 h, the PV patch and other mesovortices on the annulus have merged with one another to form larger mesovortices that are con-nected to PV filaments (figure not shown). Subse-quently, only two major mesovortices remain at t⫽ 18 h. The central pressure fills from 962 to 971 hPa throughout the 18-h integration. The distinctively dif-ferent eyewall PV evolution in CTL and DFL demon-strates that the behavior of the eyewall evolution, which involves moist and frictional processes, could dif-fer significantly from the unforced barotropic advective process.
Retaining PBL processes but excluding condensation heating in experiment DRY, the PV annulus exhibits a more rapid weakening (Fig. 17). The annulus is quickly distorted and rolls up into a number of small vortices in the first hour of integration (cf. Figs. 10g and 17a). As in DFL, the central high-PV patch migrates toward the proximity of the eyewall PV annulus and orbits cycloni-cally along the inner edge of the annulus. Merging and dissipation occur rapidly in the following hours. At t⫽ 6 h, three major mesovortices and one weak mesovor-tex remain, which continue to dissipate and merge.
Fi-nally, the mesovortices merge to form a monopole, which continues weakening throughout the end of the integration. The final central pressure is 991 hPa, 29 hPa higher than the central pressure of the initial vor-tex. Results from DFL and DRY thus indicate that the eyewall annulus cannot sustain itself without conden-sation heating and that surface friction is a sink to PV; it enhances the inward PV mixing by the boundary layer frictional inflow in the absence of condensation heating.
In experiment NHF (retaining both moist and fric-tional processes but with the surface heat fluxes turned off), the PV annulus is complete and undistorted in the first hour of integration (cf. Figs. 10g and 18a). The central high-PV patch orbits cyclonically along the in-ner edge of the annulus whereas the annulus starts to weaken and break down in the following hours (Fig. 18). The central PV patch collects high PV and strengthens while orbiting and the eyewall PV annulus weakens at the same time. It is not until the whole annulus disappears that the PV patch starts to weaken (Fig. 18c). By t ⫽ 18 h, an approximate monopole forms; it has much larger central PV than in DRY but FIG. 16. PV (PVU) at⫽ 0.875 in DFL at (a) 1, (b) 6, (c) 12, and (d) 18 h.
much smaller PV than in the eyewall in CTL. In NHF, although moist processes are retained, diabatic heating is much smaller than in CTL because of the lack of moisture supply from the ocean underlying the eyewall. Diabatic heating in NHF is mainly associated with the moisture supply from the large-scale moisture conver-gence in the lower troposphere and acts as source of additional PV compared to DRY. The central pressure increases by 11 hPa in the 18-h integration.
If only the PBL process is turned off in the model (FL), a nearly complete PV annulus exists with a weak PV patch near the center at t⫽ 1 h (cf. Figs. 10g and 19a). In the following hours, the annulus breaks down into small mesovortices and the central PV patch is advected along the inner edge of the annulus. Then the small mesovortices merge to form larger mesovortices, and each larger mesovortex is connected to filaments of high PV (Fig. 19). At t⫽ 15 h, three major mesovortices coexist with some small PV patches and PV filaments (figure not shown). The three mesovortices do not merge throughout the remaining integration. The final central pressure is 952 hPa, 10 hPa lower than the initial central pressure because of the lack of any dissipation
in this run. Comparing the PV evolution in CTL and FL, we can see that frictional processes play a role in narrowing the eyewall PV annulus and allowing the mesovortices to escape from merging with their neigh-bors in the presence of strong eyewall convection. This can be explained by the fact that friction is responsible for the low-level convergence in the eyewall. This fric-tional convergence serves as a stretching deformation and narrows the eyewall ascent and vorticity ring, thus maintaining the eyewall PV annulus.
The results presented in this section demonstrate that both surface friction and diabatic heating play quite important roles in the evolution of the typhoon eyewall. The convective heating is strongly coupled with the cy-clonic PV anomalies. In our sensitivity experiments, the monopolar structure is most likely to appear in the ab-sence of the moist process or the surface heat fluxes. These results also support the idea that the surface fric-tion enhances the inward PV mixing by the fricfric-tionally induced boundary layer inflow. With full moist pro-cesses included, the eyewall PV appears to maintain an annular structure. In other words, the heating from moist convection would prevent the eyewall annulus FIG. 17. As in Fig. 16, but for DRY.
from breaking down because of the barotropic instabil-ity regardless of the presence of friction.
It should be noted that the MM5 model employs the diffusion terms in both momentum (horizontal and ver-tical) and thermodynamic equations. One may ask whether the diffusion in the current model is much larger than that in the barotropic model, thus providing an unfair comparison. It is believed that the diffusion should not be the major reason for the differences be-tween the barotropic experiment and the full-physics experiment. Even if the same diffusion were used in the barotropic model as in MM5, the PV ring still could not be maintained because of the intrinsic instability and lack of a PV source to enhance the PV ring. As in the experiments without condensation heating (i.e., DFL and DRY), the PV ring is no longer maintained and disintegrates.
However, if the sensible and latent heat fluxes from the underlying surface (i.e., the fuel for moist convec-tion) are turned off, barotropic instability of the eye-wall may ruin the PV annulus quickly and result in the formation of a monopolar PV structure. Therefore,
moist convection in the eyewall is critical for the main-tenance of the eyewall PV annulus. Our results support the notion of Schecter and Montgomery (2007), who show that moist processes may play a role in stabilizing the TC vortex by suppressing the growth rate of un-forced unstable modes.
For a landfalling TC, the sensible and latent heat fluxes from the underlying surface decrease tremen-dously, resulting in the weakening of the eyewall con-vection and diminishing the PV anomaly production from condensation. Moreover, the increased surface friction acts to enhance the inward PV mixing in the absence of strong eyewall convection. As a result, the eyewall PV annulus of a landfalling typhoon tends to be destroyed, and then the enhanced mixing between the eyewall and the eye contributes to the formation of the monopole. However, in the presence of strong eyewall convection, as seen in CTL, frictional processes can help narrow the PV annulus and contribute to the maintenance of the PV annulus of the large eyewall. Therefore, frictional processes play a complicated (dual) role in affecting the evolution of eyewall PV. FIG. 18. As in Fig. 16, but for NHF.
5. Conclusions
It is found that the breakdown and reformation of the eyewall of Zeb are largely controlled by the under-lying surface. In the eyewall replacement process of Zeb, both the breakdown and reformation of the eye-wall are closely related to the availability of the surface heat and moisture fluxes from the lower boundary.
The large eye occurs as inner eyewall dissipates and the outer eyewall intensifies. However, the eyewall re-placement of Zeb is quite different from the conven-tional concentric eyewall replacement of Willoughby et al. (1982). In our case, the landfall of the eyewall trig-gers the particular eyewall replacement process. The weakening of the original eyewall convection is initi-ated by the reduction of surface moisture and heat fluxes after landfall rather than by the cutoff of mois-ture fluxes due to the development of the outer eyewall. The outer eyewall, developed over the ocean from outer spiral rainbands, intensifies because the moisture and heat fluxes from the underlying ocean are available for the outer circulation. Therefore, the presence of Luzon plays the key role in the eyewall evolution in this
case. The mountain plays an extra role in the weaken-ing and dissipation of the original eyewall and the early formation of a large outer eyewall by triggering strong outer spiral rainbands offshore.
It is believed that similar eyewall evolution may often occur when a typhoon encounters terrain of a size com-parable to the size of the storm circulation. For ex-ample, when Hurricane Wilma (2005) encountered the Yucatán Peninsula, a large eyewall occurred when Wilma reentered the Caribbean Sea. The radar images show that the large eye appeared while the inner eye-wall dissipated because of the landfall process. The in-tensity and size of the storm and the height and size of the terrain are all important factors that affect the eye-wall evolution of landfalling typhoons.
It is also found that surface friction both acts to en-hance the inward PV mixing by the frictionally induced boundary layer inflow in the absence of diabatic heat-ing and also narrows the PV annulus through stretchheat-ing deformation in the presence of strong eyewall convec-tion. Diabatic heating is the PV source and acts to en-hance the PV annulus. It is suggested that if the rate of PV production in the eyewall is more efficient than the FIG. 19. As in Fig. 16, but for FL.
rate at which the PV is advected or mixed away from the eyewall, the high-PV annulus can be maintained. In contrast to the results presented in Schubert et al. (1999) and Kossin and Schubert (2001), the very nar-row high-PV annulus in our control full-physics experi-ment maintains its annular structure to the end of simu-lation. Results of sensitivity experiments indicate the importance of moist processes and the underlying sur-face conditions in the evolution of the typhoon eyewall. There are many factors affecting the evolution of the eyewall, including the internal dynamics and environ-mental conditions (such as sea surface temperature, friction, environmental vertical shear, environmental heat or momentum sources, etc.). The numerical results in this study indicate that the availability of sensible and latent heat from the underlying surface is crucial for the eyewall and intensity evolution of a landfalling ty-phoon. Our results suggest that the presence of diabatic heating and friction lead to qualitatively quite different behaviors as compared to those based on purely advec-tive dynamics. However, the detailed mechanism in-volved in the processes requires further investigation through more specifically designed numerical experi-ments. For example, how do friction, terrain, latent heat, and sensible heat interact with each other in the storm core and what is their relative importance in the eyewall evolution? What determines the efficiency of the symmetrization process? It is expected that a suite of idealized model simulations with full physics could be used to gain more physical insights into these inter-esting issues.
Acknowledgments. The leading author is supported
by NSC94-2119-M-002-006-AP1, NSC95-2119-M-002-039-MY2, and NTU-97R0302. YW has been supported in part by NSF Grants 0427128 and ATM-0754039 and ONR Grant N00014-06-10303. The au-thors wish to thank Jim Kossin, Chris Davis, and the anonymous reviewers for their valuable comments.
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