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Structure and Maintenance Mechanism of Long-Lived Concentric Eyewalls Associated with Simulated Typhoon Bolaven (2012)

SATOKI TSUJINO Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japan

KAZUHISA TSUBOKI Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, and Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

HUNG-CHI KUO Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan

(Manuscript received 9 August 2016, in ﬁnal form 23 July 2017)

ABSTRACT

Typhoons with long-lived concentric eyewalls (CEs) are more intense than those with short-lived CEs. It is important for more accurate prediction of typhoon intensity to understand the maintenance mechanism of the long-lived CEs. To study the mechanism of the long-term maintenance of CEs, a numerical experiment of Typhoon Bolaven (2012) is performed using a nonhydrostatic model with full physics. Two aspects of the maintenance of simulated CEs are investigated: the maintenance of the inner eyewall and the contraction of the outer eyewall. To examine the maintenance of the inner eyewall, the equivalent potential temperature budget and air parcel trajectories of the simulated inner eyewall are calculated. The results show that the entropy supply to the inner eyewall is sufficient to maintain the inner eyewall after secondary eyewall formation (SEF). During the early period after SEF, entropy is supplied by an axisymmetric inflow, and later it is supplied by nonaxisymmetric flows of the outer eyewall. To examine the contraction of the outer eyewall, the potential vorticity (PV) budget of the outer eyewall is diagnosed. The result reveals that the negative contribution to the contraction of the outer PV peak (i.e., the outer eyewall) in the early period is the negative PV generation due to axisymmetric advection and diabatic heating just inside of the outer PV peak. In the later period, the negative PV generation due to nonaxisymmetric structure is important for the prevention of contraction. The present study reveals that the structure of the outer eyewall plays important roles in the maintenance of long-lived CEs.

1. Introduction field in both eyewalls, and then the maximum wind peak shifted from the inner eyewall to the outer eyewall, and Tropical cyclones (TCs) often have several distinct the radius of maximum wind increased during the ERC. concentric eyewalls (CEs). Some TCs with CEs undergo During an ERC, the rapid changes that occur in a TC an eyewall replacement cycle (ERC), a phenomenon intensity and wind field influence the accuracy of TC whereby the outer eyewall contracts after secondary eyewall formation (SEF) and the inner eyewall gradually prediction. However, an ERC does not always occur after dissipates. TCs undergoing an ERC exhibit rapid intensity SEF. Yang et al. (2013, 2014), who used satellite data to changes. On the basis of aircraft observations, Black and study the characteristics of typhoons with CEs in the Willoughby (1992), reported that Hurricane Gilbert western North Pacific from 1997 to 2011, indicated that (1988) had two clear CEs with peaks in the tangential wind 23% of typhoons with CEs did not undergo an ERC; moreover, the intensity of these typhoons was higher than that of typhoons that experienced an ERC. Therefore, it is Denotes content that is immediately available upon publica- important for more accurate prediction of TC intensity tion as open access. changes to understand not only the mechanisms of SEF and ERCs but also the mechanism by which long-lived Corresponding author: Satoki Tsujino, [email protected] CEs are maintained by some TCs.

DOI: 10.1175/JAS-D-16-0236.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 10/06/21 08:39 AM UTC 3610 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 74

Proposed mechanisms of SEF include purely barotropic CEM type is least common among typhoons with CEs, vorticity dynamics (Kuo et al. 2004, 2008), b-skirt axisym- the intensity of CEM typhoons is higher than that of ERC metrization (Terwey and Montgomery 2008), a super- and NRC typhoons (see Yang et al. 2013, their Fig. 4). gradient wind effect in the planetary boundary layer Thus, the type should be taken into account for more (PBL) (Huang et al. 2012; Abarca and Montgomery 2013), accurate predictions of TC intensity changes. Yang et al. persistent rainband convection (e.g., Wang 2009; Judt and (2013) proposed that barotropic stability of core and Chen 2010; Moon and Nolan 2010; Rozoff et al. 2012), and ring vortices (Kossin et al. 2000) is a possible mechanism an unbalanced eddy process as a spinup mechanism of the of CE maintenance. Kossin et al. (2000) performed a outer eyewall within the PBL in particular (Wang et al. stability analysis with a nondivergent barotropic model 2016). Studies of the ERC mechanisms have focused and proposed that outer eyewall contraction and inner mainly on the dissipation of the inner eyewall. Rozoff et al. eyewall dissipation occur as a result of barotropic in- (2008) studied the analytical profiles of diabatic heating stability caused by the interaction of a core vortex (i.e., and tangential winds using a balanced vortex model and inner eyewall) with a ring vortex (i.e., outer eyewall). indicated that diabatic heating in the outer eyewall region Indeed, Zhou and Wang (2011) indicated that barotropic statically stabilizes the inner eyewall region, allowing up- instability between the inner and outer eyewalls acted drafts associated with the inner eyewall to gradually during the ERC. Yang et al. (2013) proposed that CEs weaken. This result suggests that the inner eyewall does not of CEM typhoons can be maintained for a long time if decay as a direct result of subsidence associated with the barotropic instability does not arise between the CEs outer eyewall; instead, the mechanism is indirect warming (i.e., the core and ring vortices) after SEF. However, the due to diabatic heating in the outer eyewall. On the basis of model proposed by Kossin et al. (2000) does not include any radar observations of Hurricane Rita (2005), which had diabatic heating or variations with height of the dynamic clear CEs, Houze et al. (2007) reported that, after the outer and thermodynamic fields. In real TCs, temporal variations eyewall forms, it chokes the inner eyewall by blocking the of the storm are dominated by processes, such as acceler- entropy supply to the inner eyewall. Zhou and Wang ation of tangential winds due to diabatic heating (e.g., (2011) used a three-dimensional, nonhydrostatic, full- Shapiro and Willoughby 1982) and strong inflow in the PBL physics model and showed that the high entropy supply (e.g., Huang et al. 2012). It is difficult, however, to obtain to the inner eyewall is cut off in the PBL below the outer information about such processes from satellite and radar eyewall. They also reported that more time is required for observations. To investigate the maintenance mechanism the ERC when the radius at which the outer eyewall forms of long-lived CEs, therefore, it is necessary to use a three- is larger. This finding suggests that the time required for dimensional full-physics atmospheric model to perform the ERC is determined by the radius of the outer eyewall numerical simulations of real TCs with long-lived CE. and that the contraction of the outer eyewall controls the Typhoon Bolaven (2012) is one example of a typhoon dissipation of the inner eyewall. Kepert (2013) showed by with long-lived CEs. Because the CEs were maintained for using boundary layer models and an imposed gradient more than one day, Bolaven was a CEM-type typhoon wind field that a small perturbation in vorticity outside of (Yang et al. 2013). The operational radars of the Japan the primary radius of maximum wind results in a relatively Meteorological Agency (JMA 2002) observed Bolaven and strong updraft, which, through feedbacks between the its CEs as the typhoon passed over the Okinawa islands. updraft, convection, and vorticity, can lead to formation The purpose of the present study is to propose a possible and intensification of a secondary eyewall. Kepert and maintenance mechanism of long-lived CEs through di- Nolan (2014) found by using boundary layer models and agnostic analyses of a numerical simulation of Typhoon the gradient wind field based on a numerical simula- Bolaven (2012) with a three-dimensional nonhydrostatic tion that the vertical velocity field can largely be repro- full-physics model. To examine the maintenance mecha- duced as the frictional response to the gradient wind field. nism, we focus on 1) maintenance of the inner eyewall and The maintenance mechanism of long-lived CEs, how- 2) contraction of the outer eyewall. We investigate the first ever, is not well studied. Yang et al. (2013) classified ty- by an entropy budget and backward trajectory analysis of phoons with CEs into three types: 1) an ERC type, in the inner eyewall and the second by diagnosis of the po- which the inner eyewall dissipates less than 20 h after tential vorticity (PV) budget. In section 2, the configuration SEF; 2) a no replacement cycle (NRC) type, in which the of our numerical experiment is documented. Section 3 is an outer eyewall dissipates less than 20 h after SEF; and 3) a overview of Bolaven based on JMA’s operational obser- CE maintenance (CEM) type, in which CEs are main- vations. Section 4 is an overview of the simulated Bolaven tained for more than 20 h. They reported that the ERC, and its CEs. We discuss the maintenance of the inner NRC, and CEM types comprise 53%, 24%, and 23%, eyewall in section 5 and contraction of the outer eyewall in respectively, of all typhoons with CEs. Although the section 6. Finally, we present our conclusions regarding the

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2. Numerical model, experimental design, and analysis method The Typhoon Bolaven numerical experiment was conducted with the Cloud Resolving Storm Simulator (CReSS 3.4.2), which is a three-dimensional, regional, compressible nonhydrostatic model (Tsuboki and Sakakibara 2002). This numerical model uses a Car- tesian horizontal coordinate system with a Lambert conical projection and a terrain-following coordinate with stretching. It solves 15 prognostic variables: three-dimensional wind velocities, pressure perturbation, potential temperature perturbation, turbulent kinetic energy (TKE), mixing ratios of water vapor, cloud water, rain, cloud ice, snow, and graupel, and number densities of cloud ice, snow, and graupel. The CReSS model has been used to study many aspects of TCs (e.g., Akter and Tsuboki 2012; Wang et al. 2012; FIG. 1. Model domains and Typhoon Bolaven’s track. Domains Tsuboki et al. 2015). 1, 2, and 3 are the areas enclosed by the solid line, the short- The cloud physics scheme was an explicit bulk cold dashed line, and the long-dashed line, respectively. The simulated rain scheme, which is a double moment for ice, snow, track in domain 3 is shown by dots, and the observed track is shown by cross marks. Open circles and squares show the location and graupel, based on Murakami (1990), Ikawa and of Bolaven along each track at the initial time of 1200 UTC 24 Aug Saito (1991),andMurakami et al. (1994). Cumulus and the end time of 0600 UTC 27 Aug 2012 in domain 3. parameterization was not utilized in this model. Subgrid- scale turbulent mixing was parameterized using 1.5- order closure with TKE prediction (Deardorff 1980). resolution (domain 2), and the finest domain was Momentum and energy fluxes at the surface were for- 1200 km 3 1500 km with a 1-km resolution (domain 3). mulated according to Kondo (1975) for ocean and Louis The detailed configuration of the numerical model in et al. (1981) for land. No atmospheric radiation scheme each domain is summarized in Table 1. There were 45 was included because the sensitivity of the atmospheric vertical levels, the lowest grid interval was 200 m, and and cloud radiation processes on the intensity and track the upper boundary condition was a rigid lid. To prevent was not significant when a simulation with radiation for reflection of vertically propagating waves, a sponge only domain 2 was performed as a sensitivity test. layer was applied from a height of 17 km to the top of To simulate a realistic CE structure, the horizontal each calculation domain. The model tops of domains 1, grid spacing of a numerical model must be less than 2 km 2, and 3 were at 25, 22.5, and 20 km, respectively. The (e.g., Wang et al. 2013). In general, to save numerical initialization times of domains 1, 2, and 3 were 0000 resources, two-way nesting methods are used in a ty- UTC 22 August, 0600 UTC 23 August, and 1200 phoon simulation with high resolution. Use of the two- UTC 24 August 2012, respectively. The ending time of way nesting can change an environmental field in which integration of all experiments was 0600 UTC 27 August the storm is embedded because of interactive commu- 2012. The sea surface temperature (SST) was calculated nication of the two-way nesting between the fine- by using a one-dimensional, vertical heat diffusion resolution and coarse-resolution domains. Two-way equation (Segami et al. 1989). The SST calculation did nesting is not supported in our model, and a one-way not take account of cooling due to vertical mixing or nesting method was used in our simulation with three Ekman upwelling processes (e.g., Yablonsky and Ginis computational domains (Fig. 1). Note that the influence 2009), although in strong typhoons, SST cooling due to of the storm-induced circulation on the environmental these processes can be large (Lin et al. 2008). Typhoon field cannot be estimated in our numerical simulation. Bolaven was a category 3 typhoon, and the magnitude of The area of the outermost domain was 2140 km 3 2390 km SST cooling during its passage was about 1 K, based on with a horizontal grid spacing of 5 km (domain 1), the the JMA’s Merged Satellite and In Situ Data Global middle domain was 1700 km 3 1800 km with a 2.5-km Daily SST (MGDSST) dataset (JMA 1996). Thus, we

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TABLE 1. Speciﬁcations of the numerical experiment in each calculation domain. The variable Dz denotes the averaged value on the stretched grid spacings.

Domain 1 Domain 2 Domain 3 Domain size 2140 km 3 2390 km 3 25 km 1700 km 3 1800 km 3 22.5 km 1200 km 3 1500 km 3 20 km Number of grids 428 3 478 3 45 680 3 720 3 45 1200 3 1500 3 45 Grid spacing Dx 5 5 km, Dz 5 550 m Dx 5 2.5 km, Dz 5 500 m Dx 5 1 km, Dz 5 450 m Initial data GSM by the JMA Domain 1 output Domain 2 output Initial time 0000 UTC 22 Aug 2012 0600 UTC 23 Aug 2012 1200 UTC 24 Aug 2012 SST date 22 Aug 2012 23 Aug 2012 24 Aug 2012

considered SST cooling due to mixing and upwelling to 3. Overview of Typhoon Bolaven be small in this case. For the initial SSTs, the MGDSST Typhoon Bolaven formed in the western North Pacific dataset, which has a 0.258 resolution, was used. The (14.18N, 142.18E) on 19 August 2012. It slowly moved lateral boundary conditions were wave radiating with northwestward and passed over Okinawa Island on constant phase velocity (e.g., Klemp and Wilhelmson 26 August 2012 (Fig. 1). Bolaven made landfall on the 1978). In the experiment, 6-hourly Global Spectral coast of North Korea on 28 August 2012 and changed to Model (GSM; JMA 2007) output data (horizontal res- an extratropical cyclone on 29 August 2012. The life- olution, 0.5830.58) provided by JMA (2002) were used time maximum wind speed and minimum central for the initial atmospheric and boundary conditions of 2 pressure of Bolaven of 100 kt (1 kt 5 0.51 m s 1)and domain 1 (Davies 1983). Shuttle Radar Topography 910 hPa, respectively (i.e., category 3), were estimated Mission data with a horizontal resolution of 30 s from the at 1200 UTC 25 August 2012, before the TC passed U.S. National Aeronautics and Space Administration over the Okinawa Islands. The estimation is based on were used for the terrain (U.S. Geological Survey 2005). the JMA best-track data (i.e., the maximum wind No data assimilation was performed in our experiment. speed is the 10-min average value). On the other hand, The best-track data were used for comparing the simu- estimation of the maximum wind speed and minimum lated and observed tracks of Bolaven. central pressure based on the JTWC best-track data is 125 kt A backward trajectory analysis of air parcels car- (1-min average) and 929 hPa at 1800 UTC 24 August 2012, rying entropy supply to the inner eyewall was used to respectively. investigate paths of the air parcels. An equation to To check the eyewall structure observed in Bolaven, calculate the backward trajectory is expressed as microwave imagery provided by the Naval Research follows: Laboratory (NRL; https://www.nrlmry.navy.mil/TC. 5 2 d html) Marine Meteorology Division in Monterey, Cal- xt2dt xt U(xt) t. (1) ifornia (Hawkins et al. 2001), is shown in Fig. 2.As Here, xt indicates the location of the parcel at time t,and shown in Fig. 2b, Typhoon Bolaven qualitatively had U(xt) indicates wind velocities at xt. The parameter U(xt) triple eyewalls (McNoldy 2004; Zhao et al. 2016), al- was calculated with wind velocities output in domain 3. though the innermost eyewall was very small and The time interval of model output in domain 3 was 1 min enclosed a pinhole eye (e.g., McNoldy 2004). Yang et al. for more accurate estimation of the trajectory analysis (2013) developed an objective method to detect CEs of (described below). Then, linear interpolation in space typhoons using microwave imagery, and Abarca et al. and time was used to obtain U(xt). The time interval dt (2014) modified the method so that it could be used for for the integration was 1 s. A fourth-order Runge–Kutta the detection of triple eyewalls. These methods were scheme was used for the time integration scheme. Tra- used to examine the maintenance period of Bolaven’s jectory parcels were located at heights of 200, 300, 400, triple eyewalls. In a typhoon with triple eyewalls, for- 500, 600, 700, and 800 m. At each level, 50 parcels were mation of the secondary eyewall is defined by Abarca arranged at equal intervals around a circle with a radius of et al. (2014) as the secondary minimum (#230 K) of the 60 km from the center of the TC. This radius corre- brightness temperature, but its dissipation is not defined, sponded to the lateral boundary of the cylinder used in unlike in the case of a typhoon with double eyewall. the equivalent potential temperature budget analysis. Thus, in the present study, the dissipation of the sec- The levels at which the parcels were located are included ondary eyewall was defined as the dissipation of the in the azimuthal-mean inflow layer at the radius of 60 km secondary minimum of the brightness temperature, at the start times of the backward trajectory calculation. similar to Yang et al. (2013). As shown in the right

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FIG. 2. (left) Color-enhanced microwave (89-GHz band) CE imageries of Typhoon Bolaven provided by the NRL website. (right) The averaged brightness temperature TBB proﬁles of eight radial directions, which are deﬁned in Yang et al. (2013), are as follows: SSE (dashed–dotted yellow), SSW (solid yellow), WSW (dashed–dotted blue), WNW (solid blue), NNW (dashed–dotted green), NNE (solid green), ENE (dashed– dotted red), and ESE (solid red).

Unauthenticated | Downloaded 10/06/21 08:39 AM UTC 3614 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 74 panels of Fig. 2, the triple-eyewall structure can also be detected quantitatively. In particular, the triple eyewalls were clearly formed at 1100 UTC 25 August (Figs. 2a,b). They continued to be maintained at 0800 UTC 26 August (Fig. 2c), but by 2000 UTC 26 August they had collapsed (Fig. 2d). Thus, the triple eyewalls were maintained for at least 20 h. Thus, in the classifica- tion of Yang et al. (2013), Bolaven was a CEM typhoon. The secondary eyewall had significant asymmetry, however, and the asymmetry had a linkage with the tertiary eyewall (left panel of Fig. 2c). Radar observations made as Bolaven passed through the Okinawa region revealed a multiple-ring shaped precipitation pattern (Fig. 3), which in this study is interpreted as CEs. The horizontal resolution of the JMA radar observation network is 1 km, and its temporal resolution is 10 min. Bolaven’s CEs had already formed before the typhoon came into the JMA radar range, so the SEF was not observed by the radar (Fig. 3a). Con- sistent with the microwave imagery in Fig. 2, the JMA radar observations showed that Bolaven had three eyewalls (Fig. 3b). The eyewall distribution of precipitation associated with Bolaven persisted until 1800 UTC 26 August (Fig. 3c), except for asymmetry of the primary and secondary eyewalls. Although the primary and secondary precipitation corresponding to the eyewalls have the asymmetry, the triple eyewall structure does not collapse. It is consistent with the microwave imagery (Fig. 2d). In addition, the outermost eyewall and the inner or middle eyewall still remain at 0700 UTC 27 August based on satellite observations (not shown). Thus, the JMA radar observations showed that the CEs of Bolaven were maintained for at least one day. Precipitation intensity was azimuthally averaged at each time from Ts 5 30 h (1800 UTC 25 August) to Ts 5 54 h (1800 UTC 26 August), using the center of Bolaven that was determined by the best-track data of the JMA (Fig. 4). In this paper, Ts is used as a relative time in comparing simulation with observation, and Ts 5 0 h corresponds to the initialization time of domain 3 (i.e., 1200 UTC 24 August 2012). The middle and outermost eyewalls moved inward very slowly from Ts 5 30 to 46 h, a period defined as period of observation 1 (PO1), and they maintained their position from Ts 5 46 to 54 h, a period defined as PO2. Thus, Bolaven’s CEs were maintained for at least one day, and an ERC was not observed. The innermost, middle, and outermost eyewalls, which were subjectively determined on the basis of azimuthal-mean of precipitation rate esti- 21 mated by the radar observation, were at radii of about FIG. 3. Distribution of precipitation intensity (color scale; mm h ) 5 estimated from radar reflectivity, observed by the JMA radar network 20, 60, and 120 km at Ts 42 h (Fig. 4), respectively, and in the Okinawa region at (a) 1800 UTC 25 Aug, (b) 0600 UTC 26 Aug, they were approximately 10, 20, and 60 km wide, re- and (c) 1800 UTC 26 Aug 2012. The Okinawa Main Island is located in spectively. The inner moat (i.e., the area of weak or no the center of each panel.

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and middle eyewalls was 10 km, whereas on the north side it was 10 and 6 km, respectively. The echo-top height did not decrease with time during the passage of the TC over the Okinawa region (not shown). Yang et al. (2013) indicated that convective activity (CA), deﬁned by the brightness temperature of microwave images observed by satellites, in the inner eyewall of a CEM typhoon does not change drastically with time after SEF, so the characteristics of the echo-top height of the innermost and middle eyewalls of Bolaven were consistent with those of a CEM typhoon (Yang et al. 2013). Moreover, the echo-top height of the outermost eyewall (8 km on the south side and 6 km on the north side) also did not decrease with time (not shown). This behavior of the echo-top height is consistent with the temporal variation of precipitation intensity shown in Fig. 4. The characteristics of time variations of echo-top height and precipitation intensity are consistent with that of CA deﬁned by Yang et al. (2013). FIG. 4. Time–radius cross section of the azimuthal mean of pre- 2 cipitation intensity (color scale; mm h 1) observed by the JMA ra- 5 dars from Ts 30 to 54 h. The outer eyewalls move inward during 4. Results PO1 (period below the dashed line) and were mostly stationary during PO2 (above the dashed line). The dashed line is at Ts 5 46 h. a. Track and intensity of simulated Typhoon Bolaven In this paper, only the results of the domain 3 precipitation between the innermost and middle eyewalls) simulation are presented. The time length of in- was 20–30 km wide, whereas the outer moat was 40– tegration is 66 h. The simulated track (Fig. 1)isesti-

60 km wide at Ts 5 30 h. At Ts 5 42 h, the widths of the mated by the method of Braun (2002), which calculates inner and outer moats decreased to 10 and 20 km with the azimuthal variance of sea level pressure for 50 radii contraction of each eyewall, respectively. between 1 and 50 km at each grid point within a radius The three-dimensional structure of Bolaven’s ob- of 65 km from the minimum sea level pressure grid served CEs was revealed by Constant Altitude Plan and searches for the point of minimum variance. Position Indicator radar reﬂectivity data obtained by the This method is often used to determine TC centers in

JMA radar on Okinawa Main Island. At Ts 5 42 h simulations performed with a high-resolution non- (Figs. 3b and 5), the echo-top height, deﬁned here by the hydrostatic model (e.g., Mashiko 2005). The root- 20-dBZ contour, on the south side of both the innermost mean-square error of the simulated track to the

FIG. 5. Latitude (from south to north) and vertical cross section of radar reﬂectivity (color scale; dBZ), observed by the JMA radar on Okinawa Main Island, through the center of Bolaven at Ts 5 42 h. The black contour indicates a radar reﬂectivity of 20 dBZ. The vertical black line denotes the storm center.

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b. Distribution and lifetime of precipitation

At Ts 5 15 h (Fig. 7a), the inner precipitation ring of simulated Bolaven had already formed, but the outer precipitation band was still a spiral rainband. By around

Ts 5 24 h, precipitation in the outer eyewall of simulated Bolaven was distributed in a clear ring (Fig. 7b); therefore, we determined that SEF occurred at that time. At

Ts 5 48 h (Fig. 7c), simulated Bolaven continued to maintain the CE distribution. In the outer region, strong precipitation was simulated southeast of the center, and weak precipitation was simulated northwest of the center. This asymmetric distribution of the simulated precipitation in the outer region was consistent with the FIG. 6. Time series of (a) central pressure and (b) maximum wind speed of Bolaven in the best-track data of the JMA (red dots) and radar observations (Fig. 3). in the simulation by the CReSS model (black lines). The simulation The axisymmetric distribution of the simulated CEs 5 time Ts is shown on the horizontal axis; Ts 0 at 1200 UTC 24 Aug and its time variation can be shown by a radius–time 2012. The best-track data are not only every 6 h but also include an cross section of the azimuthally averaged precipitation additional estimation every 3 h, which is done for typhoons approaching Japan. The simulated intensity is plotted every 1 h. The intensity (Fig. 8). Two peaks of intense precipitation maximum wind in the simulation is the maximum of azimuthally were simulated: one between radii of 40 and 60 km and averaged surface wind speed within a radius of 100 km from the the other between 100 and 160 km. The width of the storm center. simulated moat was about 40 km. The simulated inner eyewall was located at mostly the same position as the observed track was 168 km. In Fig. 1,thewesternbias observed middle eyewall, and the simulated outer of simulated Bolaven (i.e., the error in the initial lo- eyewall was at the same position as the observed out- cation on domain 3) was mainly influenced by the error ermost eyewall. In the numerical experiment, the pre- of the track arising from the simulations of domain cipitation peak associated with the innermost eyewall 1 and domain 2 (not shown). In the domain 1 simula- of observed Bolaven was not simulated. However, the tion, another typhoon, Tembin, was present over the two simulated precipitation peaks were maintained 5 sea to the east of Taiwan, and the track of simulated from Ts 24 to 50 h. Bolaven in domain 1 was influenced by the wind field of The radius of the simulated outer eyewall gradually 5 typhoon Tembin through vortex–vortex interaction decreased from Ts 24 to 40 h [period of simulation 1 (e.g., Fujiwhara effect). However, the simulated track (PS1) in Fig. 8] and was approximately steady from 5 of Bolaven was nearly parallel to the observed track Ts 40 to 50 h (PS2 in Fig. 8). The observed CEs of (Fig. 1). The time series of central pressure of the JMA Bolaven exhibited the same characteristics. Thus, on the best track and simulated Bolaven (Fig. 6a) showed that basis of the simulated precipitation distribution and the simulated central pressure was 926 hPa when the lifetime, simulated Bolaven is classified as a CEM-type minimum central pressure of 910 hPa was estimated on typhoon according to the criteria of Yang et al. (2013). the basis of satellite observations. For the time series of c. Vertical structure of the CEs wind speed, the simulated wind speed was about 2 2 40 m s 1 during the maximum wind speed of 47.5 m s 1 To compare the structure of radar reflectivity between estimated by satellites. The intensification rates of the observed and simulated Bolaven, we estimate the sim- simulated central pressure and wind speed are different ulated radar reflectivity by the method of Murakami from the estimated pressure and wind speed in the best (1990) from the simulated mixing ratios of liquid and ice 5 track during Ts 5 10–24 h. On the other hand, the hydrometeors. At Ts 30 h, a region with low relative simulated pressure and wind speed are nearly flat, humidity (RH) and no echo within the radius of 30 km similar to the estimation in the best track during corresponded to the eye of simulated Bolaven (Fig. 9).

Ts 5 27–45 h at least. However, after Ts 5 50 h (i.e., Another low-RH region between radii of 80 and 110 km when Bolaven was in the East China Sea), the differ- was the moat of simulated Bolaven. The RH distribution ences of central pressure and wind speed between the showed that the moat was deeper on the north side than simulation and estimation were increasing, and it was on the south side of the center. The asymmetric distri- also approaching the domain 3 boundary, so we do not bution of radar reﬂectivity was similar to the observation discuss the CE structure after that time. (Fig. 5). A strong echo simulated between radii 40 and

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FIG. 8. Time series of the azimuthal average of precipitation 2 intensity (color scale; mm h 1) simulated by the CReSS model from Ts 5 0 to 50 h. The outer eyewall moved inward during PS1 (below the horizontal dashed line at Ts 5 40 h) and was stationary during PS2 (above the dashed line). The approximate position of the outer precipitation peak during each period is shown by the oblique dashed lines.

60 km was the active convection associated with the inner eyewall, and another strong echo region between radii of 100 and 160 km corresponded to the outer eyewall. The simulated echo-top height, defined as the maximum height at which radar reflectivity of 20 dBZ was simulated, in the inner eyewall exceeded about 15 km, whereas, that associated with the outer eyewall was about 12 km. Thus, the echo-top heights of simulated Bolaven were higher than the observed echo-top heights. In the simulation, the echo-top height of the inner eyewall was higher than that of the outer eyewall; thus, the inner eyewall of simulated Bolaven was characterized by more active convection and stronger updrafts compared with the outer eyewall. This result is consistent with the radar observation on the Okinawa Main Island (Fig. 5). To determine whether the dynamical fields of the simulated CEs were consistent with the findings of previous numerical studies, we examined the azimuthally averaged fields of the three-dimensional wind in the

simulated Bolaven at Ts 5 30 h (Fig. 10). A strong inflow 2 in excess of 5 m s 1 was simulated below 1 km (Fig. 10c). FIG. 7. Distribution of precipitation intensity (color scale; The inflow had two peaks, at radii of 50 and 140 km, which 2 mm h 1) and sea level pressure (contour; hPa) simulated by the corresponded to the inner and outer eyewalls, and the 5 CReSS model at Ts (a) 15, (b) 24, and (c) 48 h. Black stars denote radial wind speed of the outer peak was higher than that the center of Bolaven. of the inner peak. The inflow boundary layer, defined by the height at which radial velocity vanishes, was thicker in the outer eyewall than in the inner eyewall. A weak

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FIG. 9. Vertical cross section of relative humidity (contours; %) and simulated radar re- ﬂectivity (color scale; dBZ) from south to north through the center of simulated Bolaven at Ts 5 30 h. The vertical black line denotes the storm center.

2 outflow of 3 m s 1 simulated at a radius of 120 km in the entropy flow in the inner eyewall. At least, these studies lower troposphere, from z 5 2 to 3 km did not appear in suggest that a decrease of moist entropy in the inner the inner eyewall region. Two tangential wind peaks were eyewall is important for the dissipation of the inner simulated at 1 km height: one at a radius of 40 km and the eyewall. If such a decrease is essential for the dissipation other at a radius of 140 km, corresponding to the two of the inner eyewall, in the case of the long-lived CEs the eyewalls (Fig. 10a). The height of maximum wind entropy supply to the inner eyewall will be sufficient (HMW) associated with each eyewall was at the top of after SEF. Although different dissipation mechanisms the inflow boundary layer, and the HMW of the inner have been proposed by other studies (e.g., Kossin et al. eyewall was slightly lower than that of the outer eyewall. 2000; Rozoff et al. 2008; Kepert 2013), we examine only The outer peak was broad, extending from a radius of the mechanism of decreasing moist entropy in the inner 100 km to a radius of 180 km. Similarly, two vertical wind eyewall. To investigate the maintenance mechanism of peaks were simulated at radii of 40 and 120 km. This wind the inner eyewall in simulated Bolaven after the SEF, we field structure is consistent with the results of previous performed an equivalent potential temperature budget numerical simulations of CE (e.g., Zhou and Wang 2011; analysis of the inner eyewall. Then, to investigate the Wu et al. 2012). In our simulation, the inner updraft peak path of the moist air mass carrying sufficient entropy to was stronger than the outer peak, and this distribution of maintain the inner eyewall of the long-lived CEs, we updraft strength corresponded to the distributions of carried out a backward trajectory analysis. simulated radar reflectivity and echo-top height (Fig. 9). a. Equivalent potential temperature budget analysis Moreover, the outer updraft peak tilted outward; this tilting induced the broader distribution of precipitation The volume integral of equivalent potential temper- associated with the outer eyewall. These characteristics of ature ue is defined as the broad outer eyewall are consistent with those of outer ððð eyewalls of CEM-type typhoons (Yang et al. 2013). Q [ ru e edV , V0 (2) Lq u [ u 1 y , 5. Maintenance of the simulated inner eyewall e P Cp Some studies have proposed a possible mechanism by which the moist entropy supply to the inner eyewall is where r is air density horizontally averaged; and V0 is intercepted by the outer eyewall leading to the dissipa- the integration domain of the equivalent potential tion of the inner eyewall after the SEF (e.g., Houze et al. temperature budget, which is a cylinder with a height of 2007; Rozoff et al. 2008). In a numerical experiment about 17 km and a radius of 60 km. The radius of performed with the Weather Research and Forecasting 60 km corresponds to the outside of the simulated inner Model, Zhou and Wang (2011) found that dissipation of eyewall after SEF (Fig. 8). The terms L, Cp, and P are the inner eyewall during an ERC was caused by a low- latent heat, constant pressure specific heat, and the

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Exner function, respectively. The terms u and qy are potential temperature and water vapor mixing ratio, and these variables are calculated using the model output. Then the Qe budget equation is expressed as

dQ e 5 ADV 1 LHSH, (3) dt

where LHSH is the latent and sensible heat from the ocean, and advection of Qe (ADV) is deﬁned as ðð [ ru 1 ADV ev n dS VA, (4) Sl

and the first and second terms denote the lateral and vertical advections of Qe, respectively. The term Sl is the lateral surface area of the cylinder, and v and dS are the horizontal wind vector and an area element, respectively. The vector n is a normal unit vector, which is oriented inward. VA denotes vertical advection at the upper boundary of the cylinder (i.e., at 17-km height), but the amount of VA is much smaller than the amount of the lateral advection (not shown). Note that the sign of ADV is determined by net moist entropy flux associated with low-level inflow and upper-level outflow. This means that ADV is not always related to the negative contribution to Qe tendency even if the low-level Qe associated with the simulated Bolaven decreases with increasing radius. Thus, when the amount of Qe flux associated with low- level inflow is larger than that of upper-level outflow, ADV can be a positive contribution to the Qe tendency. In particular, a realistic decrease in the value of ue in the boundary layer does not have much effect on the budget as formulated, given a constant inflow mass flux. LHSH is calculated from the model output of latent and sensible heat as the area integral of a circle with a 60-km radius. The accuracy of the diagnosed budget is shown by comparing the diagnosed total budget (solid black line in Fig. 11) with the actual tendency (dashed black line in

Fig. 11). Before the SEF (from Ts 5 0 to 20 h), the ﬂuctu- ation of the diagnosed total budget is substantially different from that of the actual tendency. It might be because of catching-up processes in domain 3, which is initialized from

domain 2. However, from Ts 5 20 to 50 h, the fluctuation of the diagnosis is in parallel with the actual tendency, and the amount of the diagnosis is qualitatively acceptable compared to the amount of the actual tendency. Thus, we can discuss each term in Eq. (3) after the SEF. The ADV FIG. 10. Azimuthal-mean wind field structure at Ts 5 30 h: 21 5 21 term varied from 0 to 0.2 K h (red line in Fig. 11), and the (a) tangential wind Vt (contour interval 6.0 m s ), (b) vertical 21 21 LHSH term varied below 0.02 K h (blue line in Fig. 11) wind W (contour interval 5 0.1 m s ), and (c) radial wind Vr 2 (contour interval 5 3.0 m s 1). Negative radial wind speeds and was minor in comparison with the ADV term. indicate inflow. The Qe tendency in the inner eyewall can thus be mostly explained by the major source of ADV. The ADV term

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FIG. 12. Result of the backward trajectory analysis. Bold vectors denote four paths in total parcels (350) at each time (Ts 5 36 and 46 h). Black (red) numbers denote the numbers of parcels, which were traced back at Ts 5 36 (46) h along each path. At Ts 5 36 and 46 h, the numbers of parcels along paths 1–3 were 224 and 188, respectively.

directly. In other words, we cannot conclude that, for the FIG. 11. Time series of each term on the right-hand side of Eq. (3) and short-lived CEs, Q tendency becomes negative or close to their sum (TOTAL): ADV; LHSH; and dPTdt, the net tendency of Qe. e Note that all terms are normalized by volume integral of r. PS1 and PS2 zero after the SEF according to our result. It should be are as in Fig. 8. The 4-h moving average of the 1-min model output is investigated in a future study for the short-lived CEs. shown to ﬁlter out some high-frequency components. b. Trajectory analysis

21 Q rapidly decreased (from 0.16 to 0.04 K h )afterTs 5 24 h The e budget analysis (section 5a) indicated that the (the time of SEF), and gradually increased (from 0.04 to entropy supply to the inner eyewall was mainly via moist air 21 0.1 K h )fromTs 5 28 to 40 h. Then, it gradually decreased inflow in the PBL. Thus, by determining the paths by which from Ts 5 44 h again. However, the moist entropy supply the moist air masses arrived at the inner eyewall in the PBL, (i.e., ›Qe/›t) to the inner eyewall was maintained during PS1 we can explain the continuous entropy supply to the inner and PS2. Moreover, the vertical distribution of azimuthally eyewall after the SEF. Therefore, we calculate backward 5 averaged lateral advection of Qe at each level shows that trajectories at Ts 36 (i.e., during PS1) and 46 h (i.e., dur- the positive contribution to ADV was concentrated mainly ing PS2) of air parcels from locations at the radius of 60 km in the PBL (not shown). This concentration is consistent at various levels within the PBL, as described in section 2. with the radial wind field shown in Fig. 10c because the The trajectory parcels were traced back to 12 h before 5 5 azimuthally averaged lateral advection was mainly brought (corresponding to Ts 24hinthecaseofTs 36 h and 5 5 by axisymmetric inflow. The long duration of PS1 implies Ts 34hinthecaseofTs 46 h). We found that the that the positive entropy supply to the inner eyewall was parcels followed four paths. The first path (path 1 in Fig. 12) ineffective in causing the inner eyewall to decay. More- passed a radius of 120 km at a height below 1 km (i.e., the over, during PS2 the positive entropy supply to the inner parcels passed the outer eyewall within the PBL); the sec- eyewall could be mostly maintained. The positive entropy ondpath(path2inFig. 12) traced the area of subsidence supply was mainly supported by the constant-inflow mass outside of the inner eyewall; the third path (path 3 in flux during PS1 and PS2. Thus, in simulated Bolaven, the Fig. 12) was traced back to a height of 100 m above the 1 inner eyewall was maintained for more than one day be- ground level within a radius of 120 km; and parcels cause of an insufficient interception of positive entropy associated with the fourth path (path 4 in Fig. 12)re- supply to the inner eyewall during PS1 and PS2. Why did mained within the PBL around the radius of 60km. the positive entropy supply that was sufficient to maintain The parcels of the fourth path wandered in and out the the inner eyewall continue after the SEF? To answer this question, we next conduct a backward trajectory analysis. We caution that the budget analysis is diagnosed for only 1 In the CReSS model, the lowest level of the vertical grid is at the long-lived CEs in the simulation, and the result cannot 100-m height. Thus, we cannot trace back to where the parcels were be applied to short-lived CEs (e.g., Zhou and Wang 2011) before they appear at the lowest level.

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FIG. 13. Results of backward trajectory analysis from Ts 5 (a)–(d) 36 and (e)–(h) 46 h. The black dots denote air parcels passing through the radius of 120 km (black bold circles) below the height of 1 km: that is, within the PBL in the outer eyewall. The color scale shows precipitation 21 intensity (mm h ). Times are Ts 5 (a) 36 h, (b) 34 h 20 min, (c) 30 h 40 min, (d) 24 h, (e) 46 h, (f) 44 h, (g) 42 h 30 min, and (h) 34 h. boundary of the cylinder used in the Qe budget analysis. result in the effective interception of the entropy supply to These parcels corresponded to high-frequency compo- the inner eyewall. nents in the Qe budget analysis, which were removed in In contrast, parcels arriving at a radius of 60 km at Fig. 11 by the use of the 4-h moving average. Thus, parcels Ts 5 46 h mainly appeared to pass through two regions along paths 1, 2, and 3 contribute to the Qe budget in (Figs. 13e–h): 1) a region of weak precipitation on the Fig. 11.AtTs 5 36 h, 159 parcels, corresponding to 71% of northwest side of the outer eyewall, indicated by the group the number of the parcels (224) along paths 1–3, passed of parcels on the northwest side around a radius of 120 km in along the first path, and at Ts 5 46 h, 150 parcels (80%) Fig. 13f, and 2) a region of strong precipitation on the east passed along that path (Fig. 12). Therefore, we discuss here and northeast parts of the outer eyewall, shown by the group only those parcels that followed the first path, which made of parcels distributed around a radius of 120 km from east to the major contribution to the Qe budget. northeast of the center (Figs. 13f,g). These asymmetric Parcels arriving at a radius of 60 km at Ts 5 36 h along the structures appeared in radar observations. Figure 14 shows first path did not preferentially originate from certain azi- horizontal distributions of simulated and observed pre- muthal locations outside the outer eyewall (Figs. 13a–d). cipitation around PS2 and PO2. The asymmetries of the This relatively homogeneous distribution implies that the precipitation (i.e., strong precipitation east and southeast of parcels were carried by an axisymmetric radial flow during the storm and weak precipitation northwest of the storm) in PS1. Thus, the axisymmetric inflow in the PBL into the in- the outer region qualitatively continue in both the simula- ner and outer eyewalls and moat (Fig. 10c) brought a suf- tion and observations. ficient entropy supply to maintain the inner eyewall. In the first region (i.e., the weak precipitation region), the net buoyancy2 in the PBL was weaker than that in the Therefore, during PS1, the Qe budget in the inner eyewall was controlled mainly by axisymmetric dynamic fields of the other regions of the outer eyewall (not shown), and the air mass (parcel group) experienced weak buoyancy outer eyewall. This result is consistent with the findings of Zhou and Wang (2011), who reported that the interception of the entropy supply by the axisymmetric structure of the outer eyewall leads to the decay of the inner eyewall. In our 2 In this context, net buoyancy is the sum of thermal buoyancy, case, the axisymmetric structure of the outer eyewall did not water loading, and dynamic pressure gradient force.

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21 FIG. 14. Horizontal distribution of precipitation intensity (mm h ). (a),(c),(e) The simulation, and (b),(d),(f) the radar observations. Stars denote the center of the simulated typhoon. when passing through this region. Therefore, it was the first region (not shown). If the inflow is sufficiently difficult for the outer eyewall to intercept the moist air strong in the PBL below the outer eyewall, the upward mass in the first region. In the second region (i.e., the forcing that the parcels experience during passing in the strong precipitation region), the air mass experienced PBL is insufficient to lift the parcels from the PBL to the stronger net buoyancy by comparison, but inflow in the free atmosphere. As a result, the parcels can sub- PBL below that region was also much stronger than in sequently pass through the second region and arrive at

Unauthenticated | Downloaded 10/06/21 08:39 AM UTC NOVEMBER 2017 T S U J I N O E T A L . 3623 ð the inner eyewall. During PS2, the entropy supply to the 2p u [ 1 u l inner eyewall was therefore controlled mainly by the p d and 2 0 nonaxisymmetric dynamic ﬁelds of the outer eyewall. 0 u [ u 2 u,

6. Contraction of the simulated outer eyewall where u is an arbitrary variable. Therefore, ›P/›t rep- CEs associated with a TC can be regarded as rings of resents the tendency of the PV associated with the high vorticity (e.g., Kossin et al. 2000) or of PV (e.g., eyewall. The derivation of Eq. (6) is shown in the Zhou and Wang 2011). Thus, the change in the azi- Appendix A, including the expression of the FRIC muthally averaged PV represents the change in the CEs term. Note that the asymmetric fields are associated with time. To examine the tendency of the PV change, with convection and rainbands in the CEs. 5 5 we carried out a PV budget analysis of the outer eyewall. Figure 15 (Ts 36 h, PS1) and Fig. 16 (Ts 43 h, PS2) Here, PV is defined as show the radius–height cross sections of the budget analysis, which is averaged over 6 h. First, except in the inner eyewall v =u region, the total budget tendency (Figs. 15b, 16b), which is [ a the sum of all terms on the right-hand side of Eq. (6),is P r , 0 qualitatively similar to the simulated net tendency (Figs. 15a, 16a), which is the time variation of P. In addition, where v is absolute vorticity, u is potential tempera- a FRIC is very small in both periods. In radius–height cross ture, and r is basic air density, which is horizontally 0 sections at T 5 36 h, MDIAR and MADVZ were positive averaged. The PV (P) budget equation is (e.g., Wang s along the inside of the outer PV peak, and MDIAZ and 2002) as follows: MADVR were negative, whereas these terms had the MADVR 1 MADVZ opposite sign along the outside of the outer PV peak ›P 5 1MDIAR 1 MDIAZ (5) (Figs. 15c–f). The distributions of these major terms were ›t 1ASYMM 1 FRIC, similartothoseinthecaseofasingleeyewall(Wang 2002; Wu et al. 2016). For contraction of the PV peak to occur, the 1 › [2 radial gradient of ›P/›t should be negative at the outer PV MADVR › (rP u), r r peak; that is, ›P/›t inside the outer PV peak should be 1 › larger than that outside the outer PV peak for contraction to MADVZ [2 (r P w), r › 0 occur. Thus, if MDIAR and MADVZ are larger than 0 z MDIAZ and MADVR, the outer PV peak is expected to 1 › contract. The magnitudes of MDIAR and MDIAZ depend MDIAR [ (rQv ), r ›r ar mainly on the radial and vertical gradients of axisymmetric diabatic heating in the outer eyewall, and the magnitudes of 1 › MDIAZ [ (r Qv ), and MADVR and MADVZ depend mainly on axisymmetric r ›z 0 az 0 radial and vertical flows in the outer eyewall. Therefore, the 1 › 1 › values of these major terms in Eq. (6) depend on axisym- ASYMM [2 (rP0u0) 2 (r P0w0) › r › 0 metric flows and diabatic heating in the outer eyewall. r r 0 z In radius–height cross sections at Ts 5 43 h (Fig. 16), the 1 › 1 › distribution patterns of the axisymmetric terms in Eq. (6) 1 (rQ0v0 ) 1 (r Q0v0 ). 5 r ›r ar r ›z 0 az (6) were similar to those at Ts 36 h (Fig. 15), but the contri- 0 bution of ASYMM (Fig. 16g) to the PV budget in the outer 5 Here, u and w are radial and vertical velocity components, eyewall was larger than it was at Ts 36 h (Figs. 15g). The var and vaz are radial and vertical absolute vorticity, and Q ASYMM term represents the contribution of individual is diabatic heating. MADVR and MADVZ are radial and convection and rainbands. Moreover, ASYMM was nega- vertical advections of P due to mean flow. MDIAR and tive in the low and middle troposphere around the outer PV MDIAZ are generation of P due to radial and vertical peak and positive within the PBL outside of the outer PV gradients of mean diabatic heating. ASYMM is advection peak (Fig. 16g). In association with the decrease in and generation of P associated with asymmetric structure. ASYMM above 3 km, the total PV tendency inside the FRIC, which denotes the effects of surface friction and outer eyewall was decreased by a mainly negative region at turbulent viscosity, is much smaller than the other terms. radii of around 80–100 km during PS2 (Fig. 16b). Within the Overbars and primes denote azimuthal averages and de- PBL, the total PV tendency outside the outer eyewall was viations from the average, respectively, computed as follows: increased by the positive region around radii of 70–90 km

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FIG. 15. Radius–height cross sections of the major terms of the PV budget [Eq. (6)] 26 21 2 21 at Ts 5 36 h. In each panel, contours indicate P [PVU (1 PVU 5 10 Kkg m s ) based on 6-h averages]. The color scale shows (a) ›P/›t, (b) total tendency, (c) MADVR, (d) MADVZ, (e) MDIAR, (f) MDIAZ, (g) ASYMM, and 2 (h) FRIC (PVU h 1). The dashed lines show the approximate position of the outer PV peak at each height.

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FIG. 16. As in Fig. 15, but at Ts 5 43 h.

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FIG. 17. Radius–height cross sections of the sum of axisymmetric terms in Eq. (6) at Ts 5 36 h (PS1) and Ts 5 43 h 2 (PS2) (PVU h 1). Contour and dashed lines are as in Figs. 15 and 16. in ASYMM. Figure 17 shows the sum of all axisymmetric and Wang (2011) also indicated that the duration of the terms in Eq. (6) at Ts 5 36 h and Ts 5 43 h. Distribution ERC depends on the radius of SEF. However, they im- of the axisymmetric contributions was positive (nega- plicitly assumed that the outer eyewall had an approxi- tive) inside (outisde) of the outer PV peak during PS1 mately axisymmetric structure. If the nonaxisymmetric and PS2. It indicates that the axisymmetric components structure of the outer eyewall is considered, the duration help the contraction of the outer eyewall during PS1 of the ERC does not depend only on the radius of SEF, and PS2. These results indicate that the slow contrac- because the entropy supply to the inner eyewall due to tion of the outer eyewall during PS2 was caused mainly the nonaxisymmetric structure of the outer eyewall pre- by ASYMM, compared with the other axisymmetric vents the decay of the inner eyewall. Moreover, non- contributions (Figs. 15, 16). Associated with the de- axisymmetry was also observed by the JMA radar: crease in the total PV tendency inside the outer eyewall although highly axisymmetric precipitation rings were in the low and middle troposphere and the increase observed during PO1 (Figs. 3a,b, 4), during PO2 (Fig. 4) outside the outer eyewall within the PBL, the con- the horizontal distribution of the precipitation rings tracting speed of the outer eyewall during PS2 became showed clear nonaxisymmetry and a strong rainband on slower than it was during PS1. Thus, 1) the difference in the east side of Bolaven (Fig. 3c). This distribution is the contracting speed of the outer eyewall between PS1 similar to that of the simulation during PS2 (Fig. 7c). and PS2 may have been caused by the weakening PV Abarca and Montgomery (2015), however, indicated inside the outer eyewall associated with convection and that strong inflow associated with the eyewall in the PBL rainbands (i.e., ASYMM), and 2) the nonaxisymmetric plays an important role in the contraction of the eyewall. structure of the outer eyewall, as well as the axisymmetric The strong inflow is not estimated in a diagnosis ob- structure, may control its contraction. In addition, the tained with the Sawyer–Eliassen equation, which is nonaxisymmetric structure played an important role in based on a gradient wind balance vortex. According to section 5 because the maintenance of the entropy supply Abarca and Montgomery (2015), the maximum speed of to the inner eyewall (Fig. 11) was caused by the non- the strong inflow associated with the eyewall within the 2 axisymmetric structure in the outer eyewall during PS2 PBL exceeds about 28 m s 1 in their numerical simula- (Figs. 13e–h). Zhou and Wang (2011) focused on the tion. Based on the Sawyer–Eliassen equation, the max- axisymmetric aspects of CEs, and the role of the non- imum speed of the PBL inflow diagnosed from their 2 axisymmetric structure of the outer eyewall remained to model output is only 16 m s 1. In their simulation, the be answered. The results of the present study suggest that unbalanced inflow associated with the eyewall is very the contraction of the outer eyewall is also controlled by strong. However, in our simulation the unbalanced in- the nonaxisymmetric structure of the outer eyewall. Zhou flow is very small. Figure 18 shows transverse circulation

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of Wang et al. (2016). However, qualitatively, the diagnosed distribution patterns resemble the simulated circulation patterns (see Figs. 10b,c) around each eyewall. In particular, the maximum speed of the axisymmetric inflow associated with the outer eyewall within 21 the PBL was about 15 m s at Ts 5 30 h (Fig. 10c), which is quantitatively similar to the maximum speed 2 (about 15 m s 1) of the PBL inflow diagnosed by the Sawyer–Eliassen equation (Fig. 18a). This result implies that the role of unbalanced dynamics is not significant in our simulation. In fact, agradient wind, which corresponds to the degree of unbalanced flow, was not strong around the lower levels of the outer eyewall during either PS1 or PS2 in our simulation (not shown). The lack of the unbalanced dynamics role proposed by Abarca and Montgomery (2015) may be essential for the maintenance of long-lived CEs. Note that we cannot quantitatively estimate the contracting speed from an unbalanced flow in our simulation. Therefore, we cannot definitively state that the maintenance of long-lived CEs is directly caused by the lack of the unbalanced flow. However, the role of a lack of unbalanced dynamics in the maintenance of long-lived CEs should be investigated in a future study.

7. Summary and conclusions To investigate a possible maintenance mechanism of long-lived CEs associated with a typhoon, a high- resolution numerical experiment for Typhoon Bolaven (2012) was performed with the CReSS model, which is a three-dimensional, nonhydrostatic, full-physics model. The validation of the numerical experiment using observed data showed that the typhoon track, intensity, and maintenance of CEs were reasonably simulated, except for the observed innermost eyewall. The main-

21 tenance period could be split into two phases: one of FIG. 18. Radius–height cross section of (a) radial wind (m s ) 2 and (b) vertical wind (m s 1) diagnosed by the Sawyer–Eliassen gradual contraction (PS1; about 16 h after SEF) and one equation at Ts 5 30 h. of mostly steady maintenance (PS2; about 8 h after PS1). The CE maintenance mechanism is explained by two diagnosed by the model output of tangential wind, dia- features: 1) the lack of dissipation of the inner eyewall batic heating, and frictional forcing at Ts 5 30 h, based and 2) the constancy of the large radius of the outer on the Sawyer–Eliassen equation (e.g., Fudeyasu and eyewall. We have summarized our results in a schematic Wang 2011). We caution that the diagnosed circulation diagram (Fig. 19). With regard to feature 1, to examine is not completely identical to the simulated circulation. the entropy supply to the inner eyewall, we carried out a The difference between simulation and diagnosis Qe budget analysis of the inner eyewall and investigated suggests that the simulated axisymmetric circulation the path of the moist air mass to the inner eyewall by a cannot be interpreted completely based on a balanced backward trajectory analysis. We found the entropy vortex. In particular, there is a difference in the midlevel supply to the inner eyewall during PS1 and PS2 sufﬁ- outﬂow between the simulation and reproduction in ciently maintained after the SEF. The backward tra- the outer eyewall. It could be induced by the difference jectory analysis revealed that the moist air mass that between linear and nonlinear boundary layer models brought entropy to the inner eyewall passed through the (Kepert 2013), and it is also indicated in Fig. 12 PBL of the outer eyewall during both PS1 and PS2. This

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the maintenance mechanism of the inner eyewall differed between PS1 and PS2. During PS1, the maintenance of the inner eyewall was governed mainly by the axisymmetric structure of the outer eyewall, whereas, during PS2, it was governed by the nonaxisymmetric structure of the outer eyewall. With regard to feature 2, we investigated the axisymmetric PV budget around the outer eyewall. Positive contributions to the contraction of the outer eyewall are made mainly by the generation of PV as a result of the radial gradient of axisymmetric diabatic heating and PV advection due to axisymmetric updrafts in the outer eyewall. These terms lead to a negative radial gradient of the PV tendency on the outer PV peak and the following contraction of the outer eyewall. In contrast, the generation of PV as a result of the vertical gradient of diabatic heating and PV advection due to the axisymmetric midlevel outflow inside of the outer eyewall prevented the outer eyewall from contracting. Thus, the radial gradient ›P/›t at the outer PV peak is negative when the outer eyewall contracts. In Fig. 19a, the negative gradient corresponds to the pattern where MDIAR 1 MADVZ is positive in the shaded region bounded by the solid line, and MDIAZ 1 MADVR is also positive in the shaded region bounded by the dashed line. However, the radial gradient of MDIAZ 1 MADVR is positive around the PV peak, and it is negative contribution to contraction of the outer eyewall. The nonaxisymmetric contributions to the PV tendency around the outer eyewall during PS2, however, FIG. 19. A conceptual model of the maintenance mechanism of the long-lived CEs of simulated Bolaven. (a) Height z and radius r caused ASYMM to be negative inside the outer eyewall cross section, and (b) horizontal (plan) view. In (a) solid vectors in the low and middle troposphere (the region enclosed show the axisymmetric flows. The shaded regions show the axi- by the red dashed line in Fig. 19a) and positive outside symmetric terms of Eq. (6) during PS1 and PS2, and the region the outer eyewall within the PBL (the region enclosed enclosed by the red line shows the contribution to contraction of by the red dashed line in Fig. 19a). The diagnosis reveals the outer PV peak associated with ASYMM during PS2. Solid and dashed lines, which bound these regions, denote positive and that contraction of the outer eyewall during PS1 (i.e., negative contributions to contraction of the outer PV peak, re- period of slow contraction) was governed mainly by the spectively. The solid straight line shows the axis of the outer PV axisymmetric structure of the outer eyewall, but during peak. In (b), regions of precipitation are shaded. Solid and dashed PS2, (i.e., steady period) contraction was governed by arrows indicate the movement of moist air masses associated with not only the axisymmetric but also the nonaxisymmetric the nonaxisymmetric and axisymmetric boundary layer inflows, respectively. In regions bounded by dashed lines, interception of structure of the outer eyewall. the nonaxisymmetric flows was insufficient. The results of the present study reveal that the maintenance of long-lived CEs is controlled by both finding indicates that there was insufficient interception the axisymmetric and nonaxisymmetric structure of the of entropy in the PBL of the outer eyewall after the SEF outer eyewall. This finding suggests that the dissipation (solid arrow in Fig. 19a). The path of the moist air mass, of the inner eyewall associated with an ERC depends however, differed between PS1 and PS2. During PS1, not only on the radius of the SEF (Zhou and Wang 2011) the moist air mass passed through the PBL below the but also on the structure of the outer eyewall. Moreover, outer eyewall at all azimuthal angles (dashed arrows in long-lived CEs are maintained by the distribution of Fig. 19b). In contrast, during PS2, it passed through two diabatic heating (i.e., PV source) in the outer eyewall. regions below the outer eyewall: one of weak convection Here, we focused on only one TC with long-lived and the other where the boundary layer inflow was CEs, and the proposed maintenance mechanism is a strong (solid arrows in Fig. 19b). This result suggests that prototype for long-lived CEs. Without more numerical

Unauthenticated | Downloaded 10/06/21 08:39 AM UTC NOVEMBER 2017 T S U J I N O E T A L . 3629 simulations and observations of CEM-type typhoons, it is APPENDIX A impossible to say whether the proposed mechanism of long-lived CEs is applicable to all TCs with long-lived Derivation of the PV Budget Equation CEs. For example, Yang et al. (2013) noted that the l characteristic structure of the moat between CEs is im- In the cylindrical coordinate system (r, , z)ofthe A1 portant for their maintenance, on the basis of the baro- CReSS model, the governing anelastic equations tropic framework. Moreover, the lack of the unbalanced are as follows: dynamics proposed by Abarca and Montgomery (2015) ›v 1 may be important for the maintenance of the outer eye- 52v =v 2 =p 2 f k 3 v 1 (g 1 B)k 1 F, (A1) ›t r wall. To understand the essential mechanism of the 0 maintenance of long-lived CEs, idealized numerical ex- ›u 52v =u 1 Q, and (A2) periments and advanced observations of long-lived CEs ›t = r 5 are needed in addition to more numerical simulations of ( 0v) 0, (A3) real TCs having CEs. We caution that in our experiment the observed in- where v is a three-dimensional wind vector, v 5 nermost eyewall was not simulated, but the lack of this ui 1 yj 1 wk,and= is a three-dimensional gradient eyewall has small influence in our hypothesis (see operator, = 5 i ›/›r 1 j ›/(r›l) 1 k ›/›z. The variables p, r u appendix B). Thus, our mechanism is limited on the B, g, 0, , Q,andF are pressure, buoyancy, gravitational explanation of the maintenance between the secondary acceleration, hydrostatic density, potential temperature, and tertiary eyewalls in the observed Bolaven. The diabatic heating, and a three-dimensional external forcing maintenance mechanism of the observed innermost such as friction, respectively. Note that hydrostatic density r eyewall should be addressed by a future study of Ty- 0 depends on height z. Taking the rotation of momentum phoon Bolaven (2012). In addition, our numerical sim- [Eq. (A1)], we obtain the vorticity equation, ulation was performed using the one-way nesting ›v method. Note that the influence of the storm-induced a 52v =v 1 v =v 2 v (= v) › a a a circulation on the environmental field in which the t 1 storm is embedded is not represented in our numerical 2 = 3 = 1 3 = 1 = 3 (A4) r ( p) k B F, simulation. Therefore, our hypothesis cannot explain 0 the influences of the environmental condition on long- v [ = 3 1 lived CEs as reported by Yang et al. (2013). It should be where a v f k is absolute vorticity. Dividing r investigated by another future study. Eq. (A4) by 0 leads to › v 1 1 1 Acknowledgments. The authors thank Dr. S. Kanada a 52 v =v 1 v =v 2 v (= v) ›t r r a r a r a and Mr. M. Kato of Nagoya University, Dr. J. D. 0 0 0 0 Keppert of the Centre for Australian Weather and 2 1 = 1 3 = 1 1 3 = 1 1 = 3 Climate Research, and Dr. K. Ito of the University of r r ( p) r k B r F. 0 0 0 0 the Ryukyus, for their excellent suggestions and com- (A5) ments. The authors thank the editor, Dr. Chun-Chieh Wu, and three anonymous reviewers for their helpful By using the continuity equation [Eq. (A3)], the first and and thoughtful comments and suggestions in the man- third terms on the right-hand side of Eq. (A5) can be uscript. Some of the results were obtained by using written as the K computer at the RIKEN Advanced Institute for Computational Science (Proposal hp120282). The › v v 1 1 1 a 52v = a 1 v =v 2 = 3 (=p) satellite microwave images were made available by ›t r r r a r r the Naval Research Laboratory Marine Meteorology 0 0 0 0 0 1 1 Division in Monterey, California. This study was sup- 1 3 = 1 = 3 r k B r F. (A6) ported by the ‘‘formation of a virtual laboratory for di- 0 0 agnosing the Earth’s climate system (VL)’’ project, However, by taking the gradient of Eq. (A2), supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT). We used the drawing library of Dennou Common Library (DCL) A1 Originally the CReSS model used the Cartesian coordinate, developed and maintained by GFD Dennou Club (http:// but we applied a cylindrical coordinate system for our diagnosis. www.gfd-dennou.org/library/dcl/) for this study. Thus, the PV budget equation is derived in cylindrical coordinates.

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›(=u) The last term on the right-hand side of Eq. (A10) cor- 52=(v =u) 1 =Q, (A7) ›t responds to the FRIC term in Eq. (5). =u 1 v r and calculating ( ) Eq. (A6) ( a/ 0) Eq. (A7),we obtain, APPENDIX B › v v =u =u a 52 = =u a 2 ( ) = 1 3 = › ( ) r v ( ) r r r ( p) Limitations of the Simulation t 0 0 0 0 =u =u We show that our proposed mechanism can still be 1 ( ) 3= 1 ( ) = 3 r (k B) r ( F) applied to the simulated CEs in spite of the lack of an 0 0 v innermost eyewall, which was observed by the JMA 1 a = radar, in our simulation. As discussed in section 6, r Q. 0 qualitatively, the transverse circulation diagnosed by the (A8) Sawyer–Eliassen equation resembles the simulated circulation (see Figs. 10b,c and Figs. 18a,b) around each The second and third terms of the above equation vanish eyewall. This resemblance suggests that the simulated u 5 u r 5 u because (p, ) and B B( ). Thus, we obtain the circulation can be qualitatively explained by the di- PV budget equation, agnosis. Thus, in this section we discuss the limitations of ›P (=u) v our simulation based on the Sawyer–Eliassen equation. 52v =P 1 (= 3 F) 1 a =Q, ›t r r In particular, we examine whether the existence of an 0 0 v innermost eyewall, as observed by the JMA radar, can [ =u a P ( ) r . (A9) influence our proposed mechanism. Thus, we consider 0 an analytical vortex with double eyewalls based on Finally, we can rewrite advection to the flux form by using Pendergrass and Willoughby (2009) (Fig. B1a). This the continuity equation and expressing it in the cylindrical vortex exhibits diabatic heating and a wind peak corre- B1 coordinate system, except for friction term, as follows: sponding to each eyewall. Here, Pendergrass and Willoughby (2009) considered a single vortex repre- ›P › › › 52 (rPu) 2 (r Pw) 1 (rQv ) sented by Eqs. (12a), (12b), and (12c) in their paper. In ›t r ›r r ›z 0 r ›r ar 0 the present study, the equations that represent tangen- › (=u) tial wind y(r, z) on annular coordinates (r, z) are mod- 1 (r Qv ) 1 (= 3 F). r › 0 az r (A10) 0 z 0 ified as follows:

" # y 5 r # # (r, z) Vmax,m(z) ,0 r R1,1(z), Rmax,m(z) " # y 5 r 3 2 1 # # (r, z) Vmax,m(z) [1 A(xm)] Vo,mA(xm), R1,m(z) r R2,m(z), (B1) Rmax,m(z) " # ( # # , r 2 R (z) R2,m(z) r R1,m11(z), m M, y(r, z) 5 V 5 V (z) exp 2 max,m , o,m max,m 300 km # 5 R2,M(z) r, m M.

Then, r 2 R where m represents the mth eyewall in a vortex with M x 5 1,m , R (z) 5 R (z) 1 dr , m 2 2,m 1,m m eyewalls. The term R1,m(z) is determined by Eqs. (2) and R2,m R1,m (3) in Willoughby et al. (2006). In the double eyewalls R (z) 5 R (0) 1 zdR , (Fig. B1a), max,m max,m max,m (B2) z V (z) 5 V (0) 1 2 , max,m max,m 18 km B1 The maxima, widths, and slopes of the diabatic heating are 5 3 2 4 1 5 A(xm) 10xm 15xm 6xm estimated from the simulation result.

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21 FIG. B1. (a),(b) Distributions of analytical diabatic heating (color; K h ) and tangential wind (contour; 2 2 2 ms 1), and (c),(d) radius–height cross sections of radial (contour; m s 1) and vertical (color; m s 1)winds diagnosed from their distributions. (left) The caseofadoubleeyewall,and(right)thecaseofatriple eyewall.

5 5 21 5 5 5 21 Vmax,1(0) Vmax,2(0) 50 m s , Vmax,1(0) Vmax,2(0) Vmax,3(0) 50 m s , 5 R (0), R (0), R (0) 5 15, 50, 100 km, Rmax,1(0), Rmax,2(0) 50, 100 km, max,1 max,2 max,3 (B3) dR , dR , dR 5 16/18, 16/18, 128/18, and dR , dR 5 16/18, 128/18, and max,1 max,2 max,3 max,1 max,2 dr , dr , dr 5 20, 20, and 40 km. dr , dr 5 20, 40 km. 1 2 3 1 2 (B4)

Figures B1c and B1d show the diagnosed transverse Moreover, we consider another vortex with triple circulation for each vortex. Note that no frictional eyewalls (Fig. B1b), whose positions are determined by forcings are imposed on the analytical vortices (Fig. B1) the JMA radar observations (Figs. 4, 5). In the triple in the diagnosis of the transverse circulation, unlike in eyewalls (Fig. B1b), the case of the simulated typhoon (Fig. 18). Around the

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