The Dynamical Characteristics and Wave Structure of ...

ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 26, NO. 3, 2009, 523–542

The Dynamical Characteristics and Wave Structure

of Typhoon Rananim (2004)

MING Jie∗1 (� �), NI Yunqi2 (��), and SHEN Xinyong3 (��)

1Department of Atmospheric Sciences, Nanjing University, Nanjing 210093

2State Key Laboratory of Sever Weather, Chinese Academy of Meteorological Sciences, Beijing 100081

3Key Laboratory of Meteorological Disaster of Ministry of Education,

Nanjing University of Information Science and Technology, Nanjing 210044

(Received 18 March 2008; revised 24 November 2008)

ABSTRACT

Typhoon Rananim (2004) was one of the severest typhoons landfalling the Chinese mainland from 1996to 2004. It brought serious damage and induced prodigious economical loss. Using a new generation ofmesoscale model, named the Weather Research and Forecasting (WRF) modeling system, with 1.667 kmgrid horizontal spacing on the finest nested mesh, Rananim was successfully simulated in terms of track,intensity, eye, eyewall, and spiral rainbands. We compared the structures of Rananim to those of hurricanes inprevious studies and observations to assess the validity of simulation. The three-dimensional (3D) dynamicand thermal structures of eye and eyewall were studied based on the simulated results. The focus wasinvestigation of the characteristics of the vortex Rossby waves in the inner-core region. We found thatthe Rossby vortex waves propagate azimuthally upwind against the azimuthal mean tangential flow aroundthe eyewall, and their period was longer than that of an air parcel moving within the azimuthal meantangential flow. They also propagated outward against the boundary layer inflow of the azimuthal meanvortex. Futhermore, we studied the connection between the spiral potential vorticity (PV) bands and spiralrainbands, and found that the vortex Rossby waves played an important role in the formation process ofspiral rainbands.

Key words: dynamical structure, vortex Rossby wave, spiral rainband, typhoon

Citation: Ming, J., Y. Q. Ni, and X. Y. Shen, 2009: The dynamical characteristics and wave structure ofTyphoon Rananim (2004). Adv. Atmos. Sci., 26(3), 523–542, doi: 10.1007/s00376-009-0523-0.

1. Introduction

Tropical cyclones (TCs) are one of the most de-structive natural disasters in the world. LandfallingTCs induce not only strong winds and storm surges,but also heavy precipitation, which usually causesfloods and waterlogging. These damages are charac-terized by strong paroxysmal and destructive power.China is one of the countries seriously affected by TCs.On average, about 7 or 8 typhoons make landfall inChina each year.

The horizontal extent of TCs is typically severalhundred to a thousand kilometers, and the life cycleis several tens of hours. But the range of strong con-vective systems is only a few kilometers across. Previ-

ous observations have revealed that the following con-ditions are necessary for tropical cyclogenesis (Gray,1979; Anthes, 1982): (1) an underlying large-area ofwarm water with sea-surface temperature (SST) of atleast 26◦C; (2) a pre-existing lower-level disturbance;(3) weak vertical shear; (4) favorable larger-scale meanflow, including a tropical upper tropospheric trough(TUTT); (5) a moist lower to middle troposphere. Be-cause of the spatial and temporal limitation of obser-vations, numerical simulations provide us a tool forresearching multiscale interaction in the inner-core oftyphoons.

Numerical studies of tropical cyclones began inthe 1960s with axisymmetric models, in which theflow variations in the azimuthal direction were ignored

∗Corresponding author: MING Jie, [email protected]

524 DYNAMICAL CHARACTERISTICS AND WAVE STRUCTURE OF RANANIM VOL. 26

(Kasahara, 1961; Ooyama, 1969). Since the 1970s, nu-merical models simulating tropical cyclones can be di-vided into two branches. The first branch was modelswith a grid resolution of 20–100 km; the second branchincludes cloud resoloving models with high resolution.Following the initial development of models, a three-dimensional model was used to study more realisticdevelopment of typhoons. The first simulation wasachieved by Anthes (1972), in which a three-level hy-drostatic model with 30-km horizontal grid resolutionwas used. That simulation captured the structuresof asymmetric outflows and spiral rainbands. Jones(1977) used a triply nested model to simulate an asym-metric ring of maximum wind speed and the spiralconvergent flow.

Over the past three decades, notable progress hasbeen made in TC simulation and prediction with therapid development in computing ability. By usinga nested grid model with an inner resolution of 5km, Kurihara and Bender (1982) simulated the de-tailed eye structure of an intense hurricane. Tripoli(1992) carried out a nonhydrostatic simulation andcaptured more realistic structure of hurricane rain-bands. The work of Bender et al. (1993) showedthat the Geophysical Fluid Dynamics Laboratory(GFDL) hurricane model had some skill in predict-ing the development of hurricanes. Liu et al. (1997,1999) showed a successful simulation of HurricaneAndrew using the fifth-generation Pennsylvania StateUniversity-National Center for Atmospheric Research(PSU-NCAR) Mesoscale model (MM5) with the finestmesh size of 6 km. They presented some detailed 3Dstructures in the storm core region and analyzed thekinematics and inner core structures.

Parallel to the considerable progress in numeri-cal models, various theoretical investigations based onnumerical models were used to explain multiple as-pects of hurricane dynamics. Examples are studieson the secondary circulation (Willoughby, 1979; Schu-bert and Hack, 1982), concentric eyewall and eyewallcontraction (Shapiro and Willoughby, 1982), air-seainteraction (Emanuel, 1986), balanced flows (Shapiroand Montgomery, 1993), the dynamics of the eye(Willoughby, 1979; Smith, 1980; Emanuel, 1997), andspiral rainbands (Willoughby, 1979; Guinn and Schu-bert, 1993).

Spiral rainbands, a unique feature of TCs, are madeup of several strong convective cells. They may pro-duce severe rainfall outside the eyewall and play animportant role in TC structure and intensity changes.Although spiral rainbands were detected in the earliestradar observations, their formation and their dynamiceffect in TCs was still unresolved for many years.Most earlier theories of spiral rainbands were based

on inertia-gravity waves (Kurihara, 1976; Willoughby,1978; Lewis and Hawkins, 1982). With a differ-ent view, MacDonald (1968) hypothesized that thespiral rainbands are induced by Rossby-type waves.This theory has been known for long time, but itwas not recognized until more recently that vortexRossby waves can exist in a storm’s core and mayplay important roles in structure and intensity changes(Guinn and Schubert, 1993; Montgomery and Kallen-bach, 1997; Montgomery and Enagonio, 1998; Kuo etal., 1999; Moller and Montgomery, 1999, 2000; Rea-sor and Montgomery, 2000; Wang, 2001; Shen et al.,2007).

Untill now, the vortex Rossby waves in TCs hadbeen studied by using both observation data and sim-plified numerical models. Using the data obtianedfrom airborne dual-Doppler radar with 30-min timeresolution for Hurricane Olivia (1994), Reasor andMontgomery (2000) examined the low-wavenumberasymmetric structure and evolution of the inner core.They found that an azimuthal wavenumber 2 fea-ture, which dominated the asymmetry in the innercore region, showed some consistency with vortexRossby waves. Guinn and Schubert (1993) identifiedan axisymmetric vortex in a shallow-water model, andthey studied the connection between potential vor-ticity (PV) or vortex Rossby waves and spiral rain-bands. Based on a two-dimensional non-divergent in-viscid flow, Montgomery and Kallenbach (1997) fur-ther developed the theory for vortex Rossby waves andexamined the structure of radially and azimuthallypropagating Rossby waves. They connected the vortexRossby wave dynamics to the axisymmetrization pro-cess. To further understand the physics of vortex ax-isymmetrization, a 3D quasi-geostrophic model (Mont-gomery and Enagonio, 1998), a barotropic asymmetricbalance model (Moller and Montgomery, 1999), anda 3D asymmetric balance model (Moller and Mont-gomery, 2000) were used. Their results indicatedthat an initial barotropic or baroclinic vortex couldbe intensified by vortex Rossby wave-mean flow andwave-wave interactions. In recent numerical study,Chen and Yau (2001) simulated Hurricane Andrewusing MM5 with modified initial conditions, and in-vestigated the characteristics of the vortex Rossbywaves propagaton. Based on a 3D tropical cyclonemodel, Wang (2001, 2002a,b) verified and studied vor-tex Rossby waves in a simulated storm and found thatthe asymmetric structures were dominated by the vor-tex Rossby waves with low azimuthal wave numbers.They discussed the complex interactions and feedbacksbetween vortex Rossby waves and eyewall convection,and their role in structure and intensity changes ofsimulated TC.

NO. 3 MING ET AL. 525

Although these recent studies have revealed manycharacteristics of vortex Rossby waves and their im-portant roles in the life cycle of typhoons and hurri-canes, there are still many insufficiencies. Examplesare the lack of observational data, the approximationsused in the simplified models, the idealized initial con-ditions, and so on. Untill now there have been veryfew studies about vortex Rossby waves using high res-olution and full physical model simulations, and it isthe purpose of this paper to fill that gap. In this study,we investigate the features of vortex Rossby waves inTyphoon Rananim using the new generation of theWeather Research and Forecasting (WRF) model withthe finest grid length of 1.667 km and realistic ini-tial and boundary conditions. Furthermore, we exam-ine the relationship between the vortex Rossby wavesand the mesoscale convective system in the spiral rain-bands.

In this study, we mainly focus on: (1) the structureof Typhoon Rananim (2004), especially in the innercore region; (2) mesoscale features in the eye, eyewall,and spiral rainbands; and (3) the characteristics of thevortex Rossby waves, and their connection to heavyrainfall. In section 2 we give an overview of TyphoonRananim (2004). Sections 3 and 4 introduce the WRFmodel, the numerical experiment, and the initial fields.We provide verification of the simulation against ob-servations and previous studies, and present the struc-ture and evolution of Typhoon Rananim (2004) in sec-tion 5. Section 6 shows the structure and propagationcharacteristics of the vortex Rossby waves. Finally,the conclusions and discussions are given in section 7.

2. A brief overview of Typhoon Rananim(2004)

Typhoon Rananim (2004) originated from a tropi-cal depression near the east Philippine Sea on 8 August2004. It was facing toward the East China Sea andmoving northwestward. Rananim intensified quicklyand reached typhoon intensity by 1200 UTC 10 Au-gust, with a central location of 22.4◦N, 127.4◦E anda maximum wind speed of 34 m s−1. Subsequently,Rananim landed in Wenlin of Zhejiang Province onthe east coast of China at 1200 UTC 12 August, andthen moved westward and passed through the southernparts of Taizhou and the northern parts of Wenzhou.It reduced to tropical storm intensity within Quzhouof Zhejiang Province by 12 hours later. Finally, itweakened to a depression in Nanchang.

When Rananim landed in Zhejiang Province, itattained an intensity with a minimum central pres-sure of 950 hPa and a maximum surface wind speedof 45 m s−1. It was one of the severest typhoons

landfalling the Chinese mainland from 1996 to 2004.Typhoon Rananim ripped through East China’s Zhe-jiang, Jiangxi, Hubei, and Hunan Provinces, causingwidespread destruction. This typhoon affected 18 mil-lion people, killed 192 persons, and ruined 70 thou-sands hectares of farmland. The strong winds andheavy rainfall caused direct economic losses of 21.04billion Yuan (U.S. $2.53 billion). Because of the hugelosses, “Rananim” is retired from typhoon naming inthe future and became the specified name of the ty-phoon No. 14 in 2004.

The Geostationary Operational EnvironmentalSatellite 9 (GOES9) infrared brightness temperatureobservations (Fig. 1) revealed the primary evolutionof Typhoon Rananim (2004). When Rananim waslocated at 24.5◦N, 125.0◦E, the outward convectivecloud bands spiraled towards the center and the eye-wall did not take shape. The cloud bands divided intotwo parts, one located on the northeastern quarter,and the other in the southern quarters. Six hours later,the spiral cloud bands rotated cyclonically around thecenter and began to take the shape of an eye and eye-wall. Following the development of Rananim, the eye-wall became more circular and the small eye becamemore clear. The convective systems in the eyewallspread outward and demonstrated asymmetry.

3. Model description and experimental design

3.1 Model description

The WRF modeling system is a multi-agency ef-fort intended to provide a next-generation mesoscaleforecast model and data assimilation system that willadvance both the understanding and prediction ofmesoscale weather and accelerate the transfer of re-search advances into operations. There are two dy-namics solvers in the WRF Software Framework: theAdvanced Research WRF (ARW) solver (originally re-ferred to as the Eulerian mass or “em” solver) devel-oped primarily at NCAR, and the NMM (Nonhydro-static Mesoscale Model) solver developed at NCEP,which will be documented and supported to the com-munity by the Developmental Testbed Center (DTC).

We use the ARW system that consists of the ARWdynamics solver together with other components of theWRF system. The ARW system uses Eulerian finitedifferencing to integrate the fully compressible nonhy-drostatic equations in mass-coordinate, scalar conserv-ing flux form using a time-split small step for acousticmodes. Large time steps utilize a third-order Runge-Kutta technique. The horizontal staggering is anArakawa-C grid, and the vertical coordinate is terrain-following hydrostatic pressure. The system supportsone-way, two-way, and moving nests. The physical pro-


(a)

(b)

(c)

Fig. 1. The observed GOES9 cloud brightness temper-ature for Rananim at (a) 1300 UTC, (b) 2200 UTC on11 August, and (c) 0600 UTC on 12 August 2004, atintervals of 5◦C.

forreal data mesoscale forecasts include selectionscesses of explicit microphysics schemes, cumulus con-vective parameterizations, surface schemes, planetaryboundary layer (PBL) parameterizations, and atmo-spheric radiation schemes.

3.2 Experimental design

In this paper, we use the WRF model in version

D01

D02

D03

Fig. 2. The design of model domains and tracks of Ty-phoon Rananim from the best track analysis (every 6-h)by JTWC (2004) and the model output (every 6-h) from0000 UTC 10 August to 0000 UTC 13 August 2004.

2.1.1 (WRFv2.1.1) with a two-way interactive, mov-able, triply nested grid technique. Figure 2 shows thethree model domains that consist of a 15-km grid witha 341×251 mesh (D01), a 5-km grid with a 211×211mesh (D02), and a 1.667-km grid with a 421×421 mesh(D03), respectively. The outermost domain D01 isfixed and it is used to simulate the synoptic-scale en-vironment of Rananim. The size of this domain is bigenough to reduce the influence of the lateral boundaryconditions (LBCs) around the evolution of Rananim.The inner domains D02 and D03 are automatic vortex-following moving nested grids. The top of the model isat 50 hPa and all the domains have 31 levels in the ver-tical direction. The description of all three domains’physical parameterization schemes is in Table 1.

4. Initial conditions and methodology

The coarse domain (D01) is initialized at 0000 UTC10 August 2004 and integrated for 84 h, with initialconditions (ICs) and LBC interpolated from a 6-hourlyglobal analysis of the National Centers for Environ-mental Prediction (NCEP) with horizontal resolutionof 1◦×1◦. The ICs of the finer domains (i.e., D02 andD03) are always interpolated from the coarser-meshdata. The hourly outputs of the coarse domain pro-vide the LBCs for the inner domains. To reduce thecomputational cost, D02 and D03 are activated after15-h integration of D01 (see Fig. 3). However, the1◦ × 1◦ NCEP AVN analysis is too coarse to capturethe right scale and intensity of the tropical storm, re-sulting in a failure of the simulation. Therefore, it isnecessary to append a realistic vortex with the rightsize and intensity into the initial conditions. Kuriharaet al. (1993, 1995) have used this method to improve


Fig. 3. The schematic diagram of model integration.

the first 24- to 48-h forecast of the track and intensityof hurricanes. For this reason, we design an exper-iment to insert a vortex into the ICs (see Fig. 3).Firstly, we run D01 with full physical processes from0600 UTC 8 August to 0000 UTC 10 August, untillthe model generates a vortex whose minimum centralpressure is similar to the best analysis at the initialtime. We extract the 3D vortex and merge it into theICs with the location of the center consistent with thatin the best track. We set up our new initial conditionsfollowing the method used similarly by Kwon et al.(2002) in the form:

Xn = Xvw + (1 − w)Xo , (1)

where the weighting coefficient w is defined as,

w=

⎧⎪⎪⎨

⎪⎪⎩

1 r�R/2 ,

exp

[

−4(

r−R/2R/2

)2]

R/2< r�R .(2)

Here, R is the calculated radius of the vortex, Xo isthe former initial condition, Xv is the new vortex wewant to merge into the former condition, and Xn isthe new initial condition. In this case, we used R=570km. Note that Xo, Xv and Xn are functions of thefollowing variables: U, V, W, T , PH, PHB, P , PB,and QV, where U is x-wind component, V is y-windcomponent, W is z-wind component, T is perturbationpotential temperature, PH is perturbation geopoten-tial, PHB is base-state geopotential, P is perturbation

pressure, PB is base state pressure, and QV is watervapor mixing ratio. The inner radius for the vortexshifting is r � 285 km, and the bending radius is 285km< r �570 km, which is the smoothing field betweenthe former one and the new vortex.

We designed this method based on the followingreasons: (1) the track of Rananim is not westward ifwe integrate from the initial time backwards, and thechanges in the Coriolis parameter are big, so we inte-grate the model 42-h ahead. Although the location ofthe vortex center is not identical with the best trackat initial time, the latitudinal errors are very small,and there are little changes in the Coriolis parame-ter. This eliminates the limitation mentioned in Yauet al. (2004). (2) We also thought about extracting thevortex at the initial time, to ensure the vortex is rel-atively uniform with the background field. However,after smoothing the discontinuity between the vortexand the environment, one cannot figure out where thevortex boundary is. Furthermore, the vortex gener-ated by the model tends to be more compatible withthe model dynamics and ICs than the case of a bogusvortex.

5. Model verification and distribution of vari-ables

5.1 Model verification

In this section, we compare the results of the sim-ulation, especially from D02 and D03, against variousavailable observations, and show the overall structureof Rananim.

First of all, the simulated track is compared to ob-servations. Figure 2 also depicts the 6-h best trackanalysis obtained from Joint Typhoon Warning Center(JTWC) and the track simulated by the model from0000 UTC 10 August to 0000 UTC 13 August. The ob-served storm moved north-northwestward in the first6-h, then turned nearly northwestward; whereas thesimulated one propagated northwestward first and

Table 1. The model design and physical parameterization schemes.

Domain

Parameters D01 D02 D03

Dimensions 341×251 211×211 421×421Grid size 15 km 5 km 1.667 kmVertical levels 31 31 31Cumulus parameterization schemes KF scheme No NoMicrophysics Thompson scheme Thompson scheme Thompson schemeLand surface model Noah LSM Noah LSM Noah LSMPlanetary boundary layer YSU PBL YSU PBL YSU PBLShortwave radiation scheme Dudhia scheme Dudhia scheme Dudhia schemeLongwave radiation scheme RRTM scheme RRTM scheme RRTM scheme


Fig. 4. Time series of simulated (a) minimum centralpressure (hPa) and (b) the maximum surface wind speed(m s−1) of Rananim from 1200 UTC 10 August to 1800UTC 12 August 2004 (solid line) and the correspondingbest analysis by JTWC (dashed line).

moved faster than the observed storm. The error inthe beginning period may be caused by the incorpo-ration of the vortex into the IC. This may bring someinteraction between the vortex and the synoptic-scaleenvironment. However, after 18-h spin up, the simu-lated track is closer to the best one little by little andthe error between them becomes smaller and smaller.At last, the deviation in track decreases to nearly zerobefore landfall. In a word, the simulation of the trackis successful.

Secondly, we compare the simulated minimum cen-tral pressure and maximum surface wind speed to thebest analysis in Fig. 4. They are in general agreementbut differ in the details during the 56-hour period. Forinstance, they have the same deepening trend of cen-tral pressure during the beginning period, but have

relative big error from 34-h to 54-h. After landfall,both of them have same ascending trend. The stormreaches a minimum central pressure of 954 hPa andthe model produces a value of 950 hPa. Moreover, theerror of the maximum surface wind speed is relativelybig in the first half of the simulation and relativelysmall in the second half. Especially during landfall,the error reduces to zero and the model also mimicsvery well the abrupt decrease of the maximum surfacewind speed. Here we must mention that if we do notincorporate the vortex generated by the model intothe ICs, the difference of intensity between simulatedand the best analysis is very big, and the numericalsimulation of typhoon is unsuccessful.

Now let us shift our attention to the verificationof the system scale features, such as the rainfall andcloud fields. Figures 5a and 5b compare the AMSR-E89-GHz composite microwave imagery and simulatedhourly rainrate at 1800 UTC 11 August. The modelsimulates the main structure of Rananim as a whole,and reproduces a distinct eye, asymmetrical eyewall,and several spiral rainbands in the outer region. Onthe other hand, compare the observed and simulatedradar reflectivity. Figure 5c depicts the reflectivityimage captured by the Wenzhou radar at 1100 UTC12 August. For the purposes of verification, the sim-ulated radar reflectivity is calculated using the Read-Interpolate-Plot (RIP) program developed by the Uni-versity of Washington (Stoelinga, 2003). The formulaof RIP is:

RF =10lgmax{1, [(ρqr)1.75 × 3.630803× 10−9+

(ρqs)1.75 × 2.185 × 10−10+

(ρqg)1.75 × 1.033267× 10−9] × 1018} , (3)

where ρ is the density of atmosphere,

ρ =p

RdTv. (4)

Here p is pressure, Rd=287.04 J kg−1 K−1, Tv is vir-tual temperature, and qr, qs, and qg are rainwater,snow, and graupel mixing ratios, respectively.

The model reproduces very well the echo-free eye,the asymmetrical eyewall with several high reflectiv-ity bands (>55 dBZ), and intense convective regionsaround them. We can see that high reflectivity re-gions exist in the north part of eyewall, several spiralmesoscale high reflectivity bands are outside them, andthere is a low reflectivity area between them. Thereis an echo-free region in the southwstern quarter anda series of spiral rainbands outside the eyewall. Thesefeatures agree with observations of Typhoon Rananim.For example, based on a complete set of the DopplerRadar data, Xue et al. (2006) conclude that the scope


(a)

(c)

(b)

(d)

Fig. 5. (a) The AMSR-E 89-GHz composite microwave imagery and (b) simulated hourly rainrateat 1800 UTC 11 August 2004 (units: mm h−1). (c) Observed radar reflectivity from Wenzhou and(d) the simulated radar reflectivity at 1100 UTC 12 August 2004 (units: dBZ). The star representsthe location of Wenzhou, and the thick circle represents the range of radar.

of the outer spiral echo reaches over 700 km, the inten-sity exceeds 45 dBZ and the height of the echo reaches15 km. The spiral echo regions are close-grained andcentralize around the eyewall. After filtering 35-dBZecho, the main structure looks like a typical figureshape of a “9”. Nevertheless, we found that the sim-ulated reflectivity seems to be systematically strongthan the observed, roughly by 5–10 dBZ, and the rea-sons for this need further research.

In summary, the model reproduces reasonable sim-ulations of the intensity, the track, the eye, the eye-wall, the spiral rainbands, and the landfall of TyphoonRananim compared to observations. Despite some de-ficiencies with the simulation, these structures com-pare favorably with observations. The high spatio-temporal resolution and four dimensionally dynami-cally consistent model output provides us an oppor-

tunity to study the detailed structures and mesoscalesystems of Rananim.

5.2 Distribution of variables

In this part, we investigate the distribution of vari-ables in the inner core region, and analyze the struc-ture of the simulated Rananim, focusing on the stageover the ocean. Because of the limitation and lack ofmaritime observations, we compare the structure toprevious studies of hurricanes to assess the validity ofthe simulation.

First of all, we compare the vertical structure ofthe simulated Rananim to that of the simulated Hur-ricane Andrew. For the sake of convenient comparison,we use the output of D02 with 5 km horizontal reso-lution. Figure 6a shows a vertical cross-section of theequivalent potential temperature (θe), along the lati-


Interval: 2.0K

H

(b)

H

L

(a)

L L

L

L L

Pressure (hPa)

Pressure (hPa)

H

L

Fig. 6. (a) Vertical cross-section of equivalent potentialtemperature (K) at 0000 UTC 12 August 2004, along thelatitude of 27◦N. The thick dashed lines show the eyewallas defined by the radar reflectivity of 10 dBZ. (b) As inFig. 6a but for the temperature deviation (K) and thelongitude from 121◦E to 128.5◦E. The simulated radar re-flectivity is superposed with shading and the thick solidline denotes the 0◦C isotherm.

tude of 27◦N. Comparing Fig. 6a and the verticalcross-section of θe of Andrew at 2000 UTC 23 August1992 (from Liu et al., 1997), several similarities can benoted. In the PBL, an air parcel flows inward fromthe outer high pressure region, and its θe increasesrapidly resulting from the upward transport of sensi-ble and latent heat fluxes from the underlying warmocean. Intense vertical gradients of θe occur at thetop of the boundary layer, and the value of θe reduceswith height in this region. There are several minimumθe values between 600 hPa and 700 hPa. These struc-tures tend to produce potentially unstable conditionsfor development of deep convection. In low levels ofthe eye, we find the high θe center, and a narrow highθe dip marked by a thick dashed line in the inner edge

of the eyewall. This suggests the presence of strongdescending motion near the edge. In the marked nar-row zone, the high θe air above 400 hPa appears todescend from the tropopause. Furthermore, we com-pare the differences between the cases. Firstly, themaximum value of the high θe center in the bottomof the eye is smaller than that of Andrew, resultingfrom the fact that the intensity of Rananim is weakerthan that of Andrew. According to empirical estima-tions of hurricane intensity (Malkus and Riehl, 1960):Psea−1000 = −2.5(θe,max−350), when Psea=950 hPa,and then θemax ≈370 K, which is close to our simula-tion. Secondly, the radial increment of θe is smaller,because of the range of Rananim is big and the inten-sity is weak. Thirdly, there is no uniform or clear lowθe center in the eye, but rather it is divided into twoparts. This may be due to the weak convective systemin the eye. Due to the convection, the high θe trans-port upward results in two parts of the low θe centerand high θe tongue in the low levels of the eye.

A vertical cross section of temperature deviationis shown in the Fig. 6b. The deviation temperatureis obtained by subtracting the pressure-level averagetemperature. We find evidence of warm-core struc-ture from the boundary layer to the tropopause inthe eye region. The horizontal extent of the warmanomaly expands along with height, with a small ther-mal gradient in the upper-level outflow region. Themaximum anomaly is 5◦C near 600 hPa. Below thewarm core, the stratification is relative stable. It couldsuppress the development of vertical motion and deepconvection, and allow the formation of weak convec-tion. The warm temperature anomaly in the eye isdue to adiabatic warming associated with subsidence.There is positive feedback between the low pressureand the warm core. The warm core induced by adi-abatic warming can produce a low pressure perturba-tion. The perturbation can accelerate the inflow ofmoist air and increase the release of latent heat. Thestronger vertical and tangential circulation around theeye can produces greater subsidence. It can bring thewarm core to the lower levels and produce a low pres-sure perturbation again to maintain the intensity oftyphoon. Willoughby (1998) suggests when the con-vection is intense, net flux from the eye lowers the in-version and promotes descent above the inversion, withwarming and drying the eye. When the convectionweakens, net frictional inflows and mixing raise theinversion, cooling the eye and filling it with cloud. Hisinterpretations also support our results. Compared tothe temperature deviation of Andrew (Liu et al., 1997),the magnitudes of the warm-core are different and themaximum anomaly of Andrew is 16◦C. This is relatedto the size of the eye and the intensity of the typhoon.


0.2 0.3

1.1

0.8

0.8 1.2

3.5 3.2

2.5

5.5

(a)

(b)

(c)

Pressure (hPa)

Pressure (hPa)

Pressure (hPa)

Fig. 7. As in Fig. 6a but for the mixing ratios of(a) cloud water/ice (solid/dashed), (b) rainwater/snow(solid/dashed), (c) graupel at isopleths of 0.1, 0.2 , 0.4,0.8, 1.6, 3.2, and 6.4 g kg−1. The simulated radar reflec-tivity is superposed with shading and the thick solid linedenotes the 0◦C isotherm.

Rananim has a bigger eye, so any increment of thewarm anomaly needs more energy. On the other hand,the intensity of Rananim is weaker, so the warm-corecould not reach the extent of Andrew. In the figureof time-height cross section for temperature anomaly

in Liu et al. (1999), when the central minimum pres-sure reaches 955 hPa, the warm anomaly is 7◦C. Thisindirectly suggests out our simulation is correct.

To examine the microphysical structure of the eye-wall, we plot the vertical cross section of different cloudmicrophysical quantities including cloud water, rain-water, cloud ice, snow, and graupel, also comparing tothe structure of Andrew (Liu et al., 1997). One maynote that most of the cloud water develops near the800 hPa level, where tremendous condensation occursin the eyewall. The cloud water centers almost in theeyewall and near the 0◦C isotherm because of the mi-crophysics scheme which includes supercooled water,and a majority of coagulation occurs in the eyewall.The rainwater distributes below the 0◦C isotherm orthe melting/freezing level, owing to fact that the pre-cipitation centers in the lower region of the eyewall.Cloud ice is initiated through freezing of supercooledwater, and it develops upward following vertical mo-tion. Snow forms as cloud ice reaches a critical size,and it grows following the continual aggregation of thecloud ice. The centers for snow are higher than thoseof cloud ice. When the size of snow exceeds a criticalvalue, snow converts to graupel. Graupel grows veryfast by collecting liquid and solid particles near themelting/freezing level, and then melts into rain as itfalls through the level. Compared to the microphys-ical structure of Andrew (Liu et al., 1997), there aresome differences between the storms. The values ofcloud water and cloud ice in the lower level are rela-tively small, but for snow the value is big. We thinkthat this is because of choosing different microphysicsschemes. However, the other distribution character-istics seem to have common features, indicating thatwe successfully simulate the microphysical structure ofRananim. No matter if it is a typhoon in the WesternPacific or a hurricane in the Atlantic, they have thesame essence of microphysical process.

For the purposes of further understanding the dy-namical and thermal characteristics, we calculate themean axisymmetric structures of variables to study theaxisymmetric characteristics. We choose a 10-h pe-riod of the mature stage, from 1800 UTC 11 Augustto 0300 UTC 12 August. For the purposes of reduc-ing the transient and smaller-scale signals, we performspatial azimuthal and temporal averages that will bet-ter retain the persistent and organized features.

Figure 8a shows the mean azimuthal fields of radarreflectivity and vertical motion vectors, and we can seea clear eye and eyewall with sharp gradient at the in-ner edge, and weak convective systems in the eye. Thevectors show the ascending region in the eyewall anda distinct descending airflow in the upper eye. Then,the mean azimuthal tangential and radial flow is in


0o

C

H

Height (km)

Height (km)

Radius (km)

H

H

H

L

L

(a)

Height (km)

(b)

(c)

Fig. 8. Radius-height cross-sections of azimuthally andtemporally averaged fields of Rananim for (a) radar re-flectivity (dBZ), (b) tangential winds (m s−1), and (c)radial winds (m s−1). The thick solid lines denote theinner edge of the eyewall by the 25-dBZ contours, andthe radius of the maximum wind.

Figs. 8b and 8c. The mean axisymmetric tangential

flow represents the primary circulation of a typhoon.The intense tangential flow is in a radius of about 130km and 1 km above the surface, with a maximum windspeed of 41 m s−1. Extremely large vertical shears arepresent in the boundary layer, especially in the eye-wall, because of surface friction. The radius of themaximum wind has little slope outward below the 6-km level, and is almost vertical to the surface abovethat level. The mean radial flow represents the featureof the intense inflow below 2 km with the maximumvalue of up to 10 m s−1 located at the surface out-side of the eyewall. The main outflow is above 11 km,with a maximum value of 15 m s−1. There are weakradial flows between these two layers. Two importantairflows are worth mentioning. One is the outflow cen-ter at the 2-km level, and the other one is the returninflow in the higher region of eye. These two airflowsplay an important role in the development of typhoons.The first outflow initiates the bottom of the eye, andslopes into the eyewall. It can draw air out of theeye to reduce the central pressure, and transport highθe air from the bottom of the eye to partially sup-port eyewall convection. The second return inflow is apart of the upper divergent outflow. It is a supplyingsource of the penetrative downdrafts at the inner edgeof the eyewall. Next we compare the differences of themean axisymmetric structures between Rananim andAndrew (Liu et al., 1999). Firstly, there is weak echoin the eye region in our result, relative to the free echoin the eye of Andrew. The reason may be that therange of Rananim is bigger than Andrew, so shallowconvection could form in the eye region. Secondly, thetop of radar reflectivity is higher than that of Andrew.We use the microphysical variables to calculate theradar reflectivity. In the upper layer, the distributionof snow and graupel decide the top of radar reflectivity.Although the intensities of Rananim and Andrew aredifferent, the magnitude of radar reflectivity is similar.This is because the distribution of microphysical vari-ables is similar. Thirdly, the discrepancy of intensitycauses the difference of tangential speed and radiusof maximum wind. The radius of maximum wind ofRananim is 125 km. It is two times larger than that ofAndrew. Due to the weaker tangential flow, the radialflow of Rananim at the lower levels is weaker than thatof Andrew. But the radial flow in the upper levels isstronger. The reasons for that need further research.

To show the transient features of the eye, we plotthe azimuthal mean field of vertical motion. We choosethe hourly model output from 2200 UTC 11 Augustto 0100 UTC 12 August (Fig. 9). Our results indicatepronounced fluctuations and mixtures of vertical mo-tion in the eye and strong descent at the inner edge ofthe eyewall. Particularly, a deep layer of upward mo-


Height (km)

Height (km)

Radius (km) Radius (km)

(a) (b)

(c) (d)

Fig. 9. Radial-height cross-sections of azimuthally averaged vertical velocity with contours at (±)0.01, (±) 0.02, (±) 0.05, (±) 0.08, (±) 0.1, (±) 0.2, and (±) 0.5, at (a) 2200 UTC, (b) 2300 UTC11 August 2004 and (c) 0000 UTC, (d) 0001 UTC 12 August 2004.

tion sometimes appears at the center of the eye. Thisfinding is at odds with the traditional concept of down-ward motion in the eye region. However, the upwardmotion must be transitory; otherwise the warm corecannot be maintained. These results are similar withthe structure of Andrew (Liu et al., 1999), but theyalso have some differences. In the eye of Andrew, thewarm core is strong and there is an inversion below it.The inversion acts as a “lid” to suppress deep convec-tion and vertical motion, and divide the air into twoparts. Below the inversion, there is always upwardmotion; above it, there are fluctuations of upward anddownward motions. In our model output, the warmcore is relatively weak and the inversion is not strong.So the air in the eye could not divide into two parts,and the fluctuations exist in all regions of the eye.

Based on the above results, we summarize a con-ceptual model of the axisymmetric structures in theinner core region in Fig. 10. This model includes the

basic flows and circulations. The 1, 2, and 3 airflowscompose the secondary circulation, which plays an im-portant role in the development process of typhoons.The main inflow originates from the far outer regions.Its speed reaches a maximum value outside the radiusof the maximum wind and decreases rapidly towardsthe center of the typhoon. It feed the high θe air andangular momentum to the eyewall convection. Then,it cooperates with the outflow in the upper layer, andthey provide the energy and dynamical source for theupdrafts. The number 4 and 5 airstreams constitutethe local vertical circulation. The return airflow abovethe eyewall falls into three parts. One part directlypours into the eyewall, another part pours into theeye, and the third part forms the main downdraftsand becomes the mass source of the downward motionin the eye. The part pouring into the eye and the weakconvective system at the bottom of the eye composethe vertical fluctuations and mixtures. There is a re-


Fig. 10. A schematic axisymmetric conceptual model ofa mature typhoon in the inner-core region. The grayishareas indicate the clouds and precipitation. The darkgray areas represent the eyewall and spiral rainbands.The dark hatched region above the 0◦C isotherm repre-sents the low zone. The light hatched region at the bot-tom of the eye represents the weak convective systems,and the hatched regions in the lower eyewall representthe main inflow zones. The flows marked number 1 aremain inflows in the boundary layer, those marked num-ber 2 are main outflows in the upper troposphere, and 3are the updrafts in the eyewall and spiral rainbands. Theflows marked number 4 are the return inflows above theeyewall, and 5, 6, and 7 respectively represent the maindowndrafts in the inner edge of eyewall, the part pouringinto the eye of the return inflows, and the part pour-ing into the eyewall of the downdrafts. The flow markednumber 8 is the return flow pouring into the eyewall atthe bottom of the eye; number 9 is the part pouring intothe eye of the downdraft. The number 10 represents thevertical fluctuations and mixtures, and the number 11represents the lateral mixing and turbulent exchange.

turn outflow at the bottom layer of the eye, where itcan transport the high air from the bottom of the eyeto the eyewall and reduce the pressure of the typhoon.The lateral mixing and turbulent exchange happensat the inner edge of the eyewall. This exchanges en-ergy, momentum, and mass between the eye and theeyewall. We see differences between our conceptualmodel and the conceptual model of Andrew (Liu etal., 1999). Firstly, there is weak inversion in the eyefor our results, due to fact that the magnitude of thewarm core is not as big. So, the vertical fluctuationsand mixtures exist in all regions of the eye, and are dif-fer from the motion dividing flow into two parts in theeye of Andrew. Secondly, there are weak convective

systems in the lower levels of the eye, but no verticalcirculation below the inversion of Andrew. Thirdly,our low zone has higher height and smaller range.

5.3 Mesoscale characteristics

Now let us change our focus to the result with1.667-km horizontal resolution, to see some detailedstructures and investigate the mesoscale characteris-tics of Rananim.

Figure 11 shows the field of wind at 0.5-km heightat 0000UTC 12 August 2004. One can see the windstreaks which exist in the eyewall, marked by S1and S2. The magnitudes of the streaks are 10–15 ms−1 bigger relative to the surrounding areas, and thewidths are about several ten kilometers and the az-imuthal lengths are about a few hundreds kilometers.They always exist in the lower layer of the eyewallacross the whole life of the typhoon. The character-istics of our results are coincident with the simula-tion of Andrew using 2-km spacing (Yau et al., 2004).Owing to the discrepancy of intensity, the simulatedwind speed of Rananim is smaller than that of An-drew. These small but intense wind streaks bring se-rious wind disasters and have been reported by ob-servations and damage analysis mentioned in Yau etal. (2004). Comparing with the hourly rainfall (figurenot shown), we find the wind streaks correspond to theheavy rainfall areas. They cooperate with each other,and cause various nature disasters.

Figure 12a displays the simulated vertical velocityvalid at 0000 UTC 12 August 2004 at 850 hPa. Thevertical motion in the core region is composed of small-scale spiral bands, which are about 5–15-km wide and

S1

S2

Fig. 11. The distribution of wind at 0.5-km height at0000 UTC 12 August 2004 (units: m s−1).


(a) (b)

Fig. 12. (a) Vertical velocity valid at 0000 UTC 12 August 2004 at 850 hPa (units: m s−1). (b)PV valid at 0000 UTC 12 August 2004 at 850 hPa (units: PVU).

5m/s

50m/s

Height (km)

Radius (km)

Fig. 13. Radial-height section of the azimuthally aver-aged field of vertical velocity at 0000 UTC 12 August2004 (units: m s−1).

50–150-km long. Every spiral band exhibits a wavypattern with interweaving ascending and descendingzones. In the radial direction, the bands also present awavy pattern, and the dominant descending zones ap-pear between the bands. Corresponding to the radarreflectivity, the strong ascending center combines to aring in the eyewall. Furthermore, the spiral verticalmotion bands coincide with the spiral rainbands oneby one. Because of the spiral bands, the whole struc-ture presents strong asymmetries. Downdrafts are alsocommon in the eyewall, but they are fewer in numberand weaker in intensity than updrafts. Compared to

the results of Andrew with 2-km spacing (Yau et al.,2004), our simulation displays a more distinct wavypattern and the upward speed centers have the char-acteristics of individual nuclei which are different fromthe zonation seen of Andrew.

Figure 12b displays the horizontal distribution ofPV at 0000 UTC 12 August at 850 hPa. It is ob-vious that PV is not of a uniformally high value inthe core region but is marked by a ring-like structure.The ring of maximum PV corresponds to the regionsof maximum upward motion in the eyewall. The outerregion of the ring is characterized by numerous small-scale patches of positive and negative PV. Like the spi-ral rainbands, these patches rotate cyclonically aroundthe center and are sheared by the tangential flow intothe shape of spirals. In the inner region of the ring,patches of high PV are mixed and transported into theeye. The distribution of PV is similar with that of An-drew (Yau et al., 2004) in the outer spiral regions, butdifferent in the inner core region. The ring of maxi-mum PV is not tight, but incompact. This is becausethe intensity of Rananim is weak and its range is big.

Next we examine the azimuthal mean fields of ver-tical velocity at 0000 UTC 12 August 2004 (Fig. 13).The upward motion is slightly slantwise, with the av-erage peak of 1 m s−1 in the middle and upper levels,and the upwardmotion is relative weak in the outerspiral regions. The intense updraft in the eyewall isrooted in the boundary layer, with the mass and en-ergy fed by the strong convergence of the lower levelair. The upper level outflow represents a sink of airparcels for the upward motion. The upward motion


plays an important role in ventilating the mass andmomentum to the eyewall. At the top of the eyewall,some air parcels return to the eye. The returned airsinks in a narrow zone at the inner edge of the eyewalland some reenters the eyewall. Compared to the az-imuthal mean field of Andrew (Yau et al., 2004), wefind some differences. In the eyewall, there are twohigh value centers: one is at 5-km height, the otheris at 11-km, but there is only one in Andrew. Thisdifference confirms the stronger outflow in the upperlayer of Rananim.

In a word, there are many similarities about thedynamic and thermodynamic structures between theTyphoon Rananim and Hurricane Andrew, but theystill have some differences. In forthcoming articles,we will study the strengthening mechanisms and themesoscale characteristics after landing, furthermoreattempting to find the essential reasons for the dif-ferences between these typhoons and hurricanes.

6. Verification and characteristics of vortexRossby waves

6.1 Verification of vortex Rossby wave

To verify whether vortex Rossby waves exist nearthe eyewall, as suggested by Montgomery and Kallen-bach (1997), we plot the temporal evolution of thewavenumber 1 relative vorticity along the 150-km ra-dius at 850 hPa from 1600 UTC 10 to 1200 UTC 13August 2004 in Fig. 14a. Wavenumber-1 disturbanceshave big amplitudes, whereas the higher wavenumberdisturbances have even smaller amplitudes with no ob-vious dynamical importance. The wave moves cycloni-cally along the eyewall and the period is about 15-h atthe mature stages of Rananim. This period is muchlonger than that of a parcel moving along the eyewallwith the local mean tangential flow for one circle. Thetangential wind along R=150 km is about 40 m s−1 at850 hPa, and the period of the parcel moving one circleis 6.5-h. This period is about a half of that of the wave,and is consistent with the results of Wang (2001).Compared to inertia-gravity waves, the phase speeds ofvortex Rossby waves are still within the “slow” regimeas defined by Montgomery and Lu (1997), whereasinertia-gravity waves belong to the “fast” regime andhave a freguency between the Brunt-Vaisala frequencyand the local inertial frequency, implying that inertia-gravity waves must either propagate upwind so rapidlythat they are nearly stationary or propagate downwindmuch faster than the azimuthal wind of the mean cy-clone (Willoughby, 1978). In addition, vortex Rossbywaves are regarded as PV waves, and they are verifiednear the eyewall where there is a relatively big PV gra-dient, but the PV gradient is not a necessary condition

for inertia-gravity waves.The phase speed of the wave is much slower than

the local mean tangential flow,indicating thatthe wave

Fig. 14. (a) Azimuthal-time section of wavenumber-1relative vorticity (with positive vorticity shaded) arounda radius of 150-km from the center at 850 hPa from 16-hto 84-h of simulation (units: 10−4 s−1). (b) and (c) are asin (a) but for hourly rain rate (units: mm h−1) and ob-served GOES9 cloud brightness temperature (units: ◦C).The thick solid lines 1, and 2 (in a) label the division be-tween the trough and ridge of the wave; lines 3 and 4 (inb) label the temporal evolution of heavy rainfall centers;lines 5 and 6 (in c) label the low temperature zone of thecloud brightness temperature.


Fig. 15. (a) Radius-time section of wavenumber-1 relative vorticity(with positive vorticity shaded)from the center to 300-km to east at 850 hPa from 16-h to 84-h of simulation (units: 10−4 s−1).(b) as in (a) but for hourly rain rate (units: mm h−1).

Fig. 16. (a) Wavenumber-1 component of relative vorticity, (b) wavenumber-1 component of hor-izontal divergence, (c) wavenumber-2 component of relative vorticity, and (d) wavenumber-2 com-ponent of horizontal divergence at 850 hPa valid at 1800 UTC 11 August 2004 (units: 10−4 s−1).


(a) (b)

(c) (d)

Pressure (hPa)

Pressure (hPa)

Azimuth Azimuth

Fig. 17. The azimuthal-vertical cross sections of (a) wavenumber-1 component of relative vorticity,(b) wavenumber-1 component of vertical motion, (c) wavenumber-2 component of relative vortic-ity, (d) wavenumber-2 component of vertical motion around 135-km radius circle at 1800 UTC 11August 2004. Regions with positive relative vorticity and upward motion are shaded (units: 10−4

s−1 and 10−1 m s−1).

propagates anticyclonically relative to the tangentialflow of the primary cyclone. The vorticity decreaseswith radius in the radial direction, according to vortexwave theory (Zhang et al., 2005), and the wave shouldpropagate outward. Figure 15a shows the temporalevolution of the wavenumber 1 relative vorticity fromthe center to 420-km to the east at 850 hPa from 1600UTC 10 to 1200 UTC 13 August 2004. The wave haslargest amplitude near the eyewall and seems to formjust inside the eyewall, and then propgate outward,consistent with the above-cited theory. Although thewave propgates outward against the main inflow ofRananim, the wave energy seems to propagate to thecenter from 1600 UTC 10 to 1200 UTC 13 August2004. For example, there are three maximum ampli-tudes of the wave at R=70 km, 105 km, and 125 km,at 1700 UTC 11 August 2004. With the passage oftime, the three centers of maximum amplitude moveslowly towards the center. This inward energy prop-agation is consistent with the results of Wang (2001).He also points out that PV has a maximum just insidethe radius of maximum wind in his simulated tropical

cyclone. This inversed PV gradient in the eyewall maybe responsible for the inward energy dispersion.

Figures 14b and 15b show the temporal evolutionof hourly rainrate at the same radius and directionfrom 1600 UTC 10 to 1200 UTC 13 August. We alsoplot the observed GOES9 cloud brightness tempera-ture for the same time period in Fig. 14c, to verify oursimulated vortex Rossby wave. We compare simulatedhourly rainfall to the figures of wavenumber-1 relativevorticity, and find that the heavy rainfall center is nearthe positive perturbation of relative vorticity. First ofall, we compare the temporal evolution of rainfall tothe observations. Although there is some difference,the main features are the same. The heavy rainfallcenters match the low cloud brightness temperaturezone. Then we can see the heavy rainfall centers agreewith the division between the trough and ridge of thewave, consistent with the classic synoptic theory, anddemonstrating that the rainfall area always appearsahead of the trough and behind the ridge. The flowis anticlockwise in the typhoon circumfluence, so theflow in Fig. 14a should be from right to left. Firstly,


a parcel should pass though the positive vorticity per-turbation. Then it arrives at the division between thetrough and the ridge. The movement creates positivevorticity advection, and causes this area to be favor-able for upward motion and rainfall. With time, theheavy rainfall centers forms in the division betweenthe trough and ridge of the wave.

After analyzing and verifying the above, we affirmthat the wave is consistent with characteristics of thevortex Rossby wave. Furthermore, we see the relation-ship between the wave and rainfall. Next we continueinvestgating the structure and propgation characteris-tics of vortex Rossby waves.

6.2 Structure and characteristics of vortexRossby waves

Because vortex Rossby waves are vortex waves,we focus on the vorticity and divergence structureof the waves. Figure 16 shows the relative vorticityand horizontal divergence fields of wavenumber-1 andwavenumber-2 at 850 hPa, valid at 1800 UTC 11 Au-gust. We can see that the wavenumber-1 structurespirals cyclonically inward in the vorticity field, andoutward in the divergence field, and there are severalcenters in the radial direction. This structure of vortic-ity indicates an outward propgation and a cyclonic ro-tation around the eyewall. The wavenumber-2 vortexRossby wave has a much more complicated horizontalstructure than the wavenumber-1 wave.

To give a three-dimension view of the vortexRossby waves, we show the vertical structure ofwavenumber-1 and wavenumber-2 relative vorticityand vertical motion along a 105-km radius, validat 1800 UTC 11 August 2004 (Fig. 17). Thewavenumber-1 wave tilts upwind azimuthally withheight below about 450 hPa and then downwind abovein the relative vorticity field, but both wavenumberstilt upwind in the vertical motion field. A similar fea-ture of the two fields in the mid-lower levels is thatthe positive relative vorticity disturbances are coupledwith upward motion below 400 hPa. This implies somerelationship between vortex Rossby waves and convec-tion systems in the eyewall, and a detailed study ofthis relationship will occur in future research. Thewavenumber-2 waves tilt downwind azimuthally at thelower and upper levels in relative vorticity, contrarilyto the waves tilt downwind below 300 hPa and up-wind above in the vertical motion field. The relativevorticity leads vertical motion by about one quarterwavelength above 250 hPa, and they have the samephase below 500 hPa.

6.3 Vortex Rossby waves and spiral rainbands

To elucidate some important aspects of the spiralrainbands, we plot the time series of PV at 850 hPa

at 1-h intervals from 0000 UTC to 0800 UTC 12 Au-gust 2004 in Fig. 18. At 0000 UTC, two PV bandsmarked ABC and DE, which are characterized by nu-merous small-scale patches of positive and negativePV, are located cyclonical around the positive PVring. The PV band DE is formed just outside theeyewall. Corresponding to the radar reflectivity (notshown), the rainbands are associated with the spiralPV bands, in agreement with the former studies (Mayet al., 1994; Zhang et al., 2005). From 0100 UTC to0300 UTC, the spiral PV bands propagate outside anda new PV band is formed in upstream. Given the factthat the typhoon is close to the land, the PV bandABC landfalls earlier than the typhoon, and the prop-agation speed is obviously slower. The PV bands DEand FG strengthen and a new band forms upstream.Because of friction, the PV band ABC tends towardsstationary. The band DE catches up with ABC, and itis replaced/overlaid by band DE. The bands FG andHI continue to rotate cyclonically with the mean tan-gential flow. Owing to the combination of bands ABCand DE, they could not propgate, and result is thatthere are no PV bands in the forward left quarter of thedirection of typhoon propgation. Furthermore, radarreflectivity displays the same features of the spiral PVbands. There are echo-free zone in the forward left ofthe typhoon at 0800 UTC 12 August 2004.

As we have already analyzed, the spiral PV bandsand spiral rainbands have the same features. Thesefeatures indicate that there are some dynamic andthermodynamic factors to assist the spiral bands indeveloping. In particular, the propagation of spiralPV bands around the PV ring has a compact relation-ship with the theory of vortex Rossby waves. So thevortex Rossby waves must play an important role inthe formation of the spiral rainbands.

7. Summary

In this paper, the WRF modeling system is usedto simulate almost the whole life cycle of TyphoonRananim (2004) with the finest grid size of 1.667 km.The model is initialized with the NCEP AVN analysiswith incorporation of a model-generated vortex at theinitial time. After verifying against various observa-tions and earlier studies of hurricanes and typhoons,the main findings are as follows:

(1) Typhoon Rananim (2004) is successfully simu-lated in terms of eye, eyewall, and spiral rainbands.The results are verified to observations and formerstudies.

(2) It is found that Typhoon Rananim (2004) ischaracterized by a shallow layer of intense inflows inthe boundary layer and intense outflows above 300hPa,with weak radial flows between them.The inflows


(a) (b)

(d) (e) (f)

(h) (i)

(c)

(g)

A

B

C D

E

A

B

C D

E

A

B

C D

E

A

B

C D E

F

G

B

C

D E

F

G

B

C

D E

F

G

B

C

D E

F

G

H I

B C

F

G D

E

H

I

D

E F G

H

I

Fig. 18. Model-simulated PV at 850 hPa valid at (a) 0000 UTC, (b) 0100 UTC, (c) 0200 UTC,(d) 0300 UTC, (e) 0400 UTC, (f) 0500 UTC, (g) 0600 UTC, (h) 0700 UTC, and (i) 0800 UTC 12August 2004. Red (blue) lines are for the positive (negative) PV (units: PVU).

can transport the high-θe air from the underlyingwarm ocean to the eyewall and provide enough mois-ture for vertical motion and the development of con-vection. After azimuthal averaging, we could see themaximum upward motion region is just outside the ra-dius of the maximum wind, and the range of distinctdownward motion is in the inner edge of the eyewall.

(3) Compared to the simulation of Hurricane An-drew (1992) in Liu et al. (1997, 1999) and Yau etal. (2004), we could see some similarities between Ty-phoon Rananim and Hurricane Andrew. However, thedifferences are summarized as follow: (a) there is aweak inversion in the lower level of eye, due to thefact that the magnitude of the warm core is small.The temperature difference from surface to the center

of the warm core is just 3◦C, but in Andrew it is about14◦C. So, vertical fluctuations and mixtures exist in allregions of the eye. (b) There are weak convective sys-tems in the lower levels of the eye and a low θe zoneat the higher heights, but it is not distinct. Becausethe inversion is weak, it can not divide the eye intotwo regions and suppress the development of shallowconvection in the lower level. (c) There are two centersof upward motion in the eyewall, and the outflows arebigger than that of Andrew in the upper levels.

(4) We verify the existence of vortex Rossby wavesin our full-physics simulation. The vortex Rossbywaves propagate azimuthally upwind against the az-imuthal mean tangential flow around the eyewall, andhave a longer period than the period of a parcel mov-


ing with the azimuthal mean tangential flow. Theyalso propagate both in the radial and vertical direc-tions. Furthermore, the heavy rainfall centers form inthe division between the trough and ridge of wave.

(5) We analyze the relationship of the spiral PVbands and spiral rainbands, and find that the vortexRossby waves might play an important role in the for-mation process of spiral rainbands.

In this study, we mainly analyzed the 3D dynamicand thermal structures in the inner core region and thecharacteristics of the vortex Rossby waves. We alsocompared the similarities and differences of the innercore structures between Typhoon Rananim and thatof Hurricane Andrew. In the forthcoming articles, wewill study the complicated interactions and feedbacksbetween the vortex Rossby waves and the convectivesystems in the eyewall, mechanisms of intensification,and the mesoscale characteristics after landfalling.

Acknowledgements. This research was supported

by the National Key Basic Research and Develop-

ment Project of China (Grant Nos. 2004CB418301,

2009CB421503); National Natural Science Foundation of

China (Grant No. 40775033); the Chinese Special Sci-

entific Research Project for Public Interest (Grant No.

GYHY200806009).

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