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  • View in gallery

    Model domains and Typhoon Bolaven’s track. Domains 1, 2, and 3 are the areas enclosed by the solid line, the short-dashed line, and the long-dashed line, respectively. The simulated track in domain 3 is shown by dots, and the observed track is shown by cross marks. Open circles and squares show the location of Bolaven along each track at the initial time of 1200 UTC 24 Aug and the end time of 0600 UTC 27 Aug 2012 in domain 3.

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    (left) Color-enhanced microwave (89-GHz band) CE imageries of Typhoon Bolaven provided by the NRL website. (right) The averaged brightness temperature 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).

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    Distribution of precipitation intensity (color scale; mm h−1) estimated from radar reflectivity, observed by the JMA radar network in the Okinawa region at (a) 1800 UTC 25 Aug, (b) 0600 UTC 26 Aug, and (c) 1800 UTC 26 Aug 2012. The Okinawa Main Island is located in the center of each panel.

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    Time–radius cross section of the azimuthal mean of precipitation intensity (color scale; mm h−1) observed by the JMA radars from 30 to 54 h. The outer eyewalls move inward during PO1 (period below the dashed line) and were mostly stationary during PO2 (above the dashed line). The dashed line is at 46 h.

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    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 42 h. The black contour indicates a radar reflectivity of 20 dBZ. The vertical black line denotes the storm center.

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    Time series of (a) central pressure and (b) maximum wind speed of Bolaven in the best-track data of the JMA (red dots) and in the simulation by the CReSS model (black lines). The simulation time is shown on the horizontal axis; at 1200 UTC 24 Aug 2012. The best-track data are not only every 6 h but also include an additional estimation every 3 h, which is done for typhoons approaching Japan. The simulated intensity is plotted every 1 h. The maximum wind in the simulation is the maximum of azimuthally averaged surface wind speed within a radius of 100 km from the storm center.

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    Distribution of precipitation intensity (color scale; mm h−1) and sea level pressure (contour; hPa) simulated by the CReSS model at Ts = (a) 15, (b) 24, and (c) 48 h. Black stars denote the center of Bolaven.

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    Time series of the azimuthal average of precipitation intensity (color scale; mm h−1) simulated by the CReSS model from to 50 h. The outer eyewall moved inward during PS1 (below the horizontal dashed line at 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.

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    Vertical cross section of relative humidity (contours; %) and simulated radar reflectivity (color scale; dBZ) from south to north through the center of simulated Bolaven at h. The vertical black line denotes the storm center.

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    Azimuthal-mean wind field structure at 30 h: (a) tangential wind Vt (contour interval = 6.0 m s−1), (b) vertical wind W (contour interval = 0.1 m s−1), and (c) radial wind Vr (contour interval = 3.0 m s−1). Negative radial wind speeds indicate inflow.

  • View in gallery

    Time series of each term on the right-hand side of Eq. (3) and their sum (TOTAL): ADV; LHSH; and dPTdt, the net tendency of . Note that all terms are normalized by volume integral of ρ. PS1 and PS2 are as in Fig. 8. The 4-h moving average of the 1-min model output is shown to filter out some high-frequency components.

  • View in gallery

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

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    Results of backward trajectory analysis from Ts = (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 intensity (mm h−1). Times are Ts = (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.

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    Horizontal distribution of precipitation intensity (mm h−1). (a),(c),(e) The simulation, and (b),(d),(f) the radar observations. Stars denote the center of the simulated typhoon.

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    Radius–height cross sections of the major terms of the PV budget [Eq. (6)] at h. In each panel, contours indicate [PVU (1 PVU = 10−6 K kg−1 m2 s−1) based on 6-h averages]. The color scale shows (a) , (b) total tendency, (c) MADVR, (d) MADVZ, (e) MDIAR, (f) MDIAZ, (g) ASYMM, and (h) FRIC (PVU h−1). The dashed lines show the approximate position of the outer PV peak at each height.

  • View in gallery

    As in Fig. 15, but at h.

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    Radius–height cross sections of the sum of axisymmetric terms in Eq. (6) at h (PS1) and h (PS2) (PVU h−1). Contour and dashed lines are as in Figs. 15 and 16.

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    Radius–height cross section of (a) radial wind (m s−1) and (b) vertical wind (m s−1) diagnosed by the Sawyer–Eliassen equation at 30 h.

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    A conceptual model of the maintenance mechanism of the long-lived CEs of simulated Bolaven. (a) Height z and radius r cross section, and (b) horizontal (plan) view. In (a) solid vectors show the axisymmetric flows. The shaded regions show the axisymmetric terms of Eq. (6) during PS1 and PS2, and the region enclosed by the red line shows the contribution to contraction of the outer PV peak associated with ASYMM during PS2. Solid and dashed lines, which bound these regions, denote positive and negative contributions to contraction of the outer PV peak, respectively. The solid straight line shows the axis of the outer PV peak. In (b), regions of precipitation are shaded. Solid and dashed arrows indicate the movement of moist air masses associated with the nonaxisymmetric and axisymmetric boundary layer inflows, respectively. In regions bounded by dashed lines, interception of the nonaxisymmetric flows was insufficient.

  • View in gallery

    (a),(b) Distributions of analytical diabatic heating (color; K h−1) and tangential wind (contour; m s−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 case of a double eyewall, and (right) the case of a triple eyewall.

  • View in gallery

    Difference of radial velocity between double and triple eyewalls. Color and contour denote the relative (%) and absolute differences (m s−1). The relative difference is normalized by the mean radial wind speed (20 m s−1) below the height of 1 km in the outermost eyewall.

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

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  • 1 Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japan
  • | 2 Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, and Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan
  • | 3 Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan
Open access

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.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Satoki Tsujino, satoki@gfd-dennou.org

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.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Satoki Tsujino, satoki@gfd-dennou.org

1. Introduction

Tropical cyclones (TCs) often have several distinct concentric eyewalls (CEs). Some TCs with CEs undergo an eyewall replacement cycle (ERC), a phenomenon whereby the outer eyewall contracts after secondary eyewall formation (SEF) and the inner eyewall gradually dissipates. TCs undergoing an ERC exhibit rapid intensity changes. On the basis of aircraft observations, Black and Willoughby (1992), reported that Hurricane Gilbert (1988) had two clear CEs with peaks in the tangential wind field in both eyewalls, and then the maximum wind peak shifted from the inner eyewall to the outer eyewall, and the radius of maximum wind increased during the ERC. During an ERC, the rapid changes that occur in a TC intensity and wind field influence the accuracy of TC prediction. However, an ERC does not always occur after SEF. Yang et al. (2013, 2014), who used satellite data to study the characteristics of typhoons with CEs in the western North Pacific from 1997 to 2011, indicated that 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 important for more accurate prediction of TC intensity changes to understand not only the mechanisms of SEF and ERCs but also the mechanism by which long-lived CEs are maintained by some TCs.

Proposed mechanisms of SEF include purely barotropic vorticity dynamics (Kuo et al. 2004, 2008), β-skirt axisymmetrization (Terwey and Montgomery 2008), a supergradient wind effect in the planetary boundary layer (PBL) (Huang et al. 2012; Abarca and Montgomery 2013), persistent rainband convection (e.g., Wang 2009; Judt and Chen 2010; Moon and Nolan 2010; Rozoff et al. 2012), and an unbalanced eddy process as a spinup mechanism of the outer eyewall within the PBL in particular (Wang et al. 2016). Studies of the ERC mechanisms have focused mainly on the dissipation of the inner eyewall. Rozoff et al. (2008) studied the analytical profiles of diabatic heating and tangential winds using a balanced vortex model and indicated that diabatic heating in the outer eyewall region statically stabilizes the inner eyewall region, allowing updrafts associated with the inner eyewall to gradually weaken. This result suggests that the inner eyewall does not decay as a direct result of subsidence associated with the outer eyewall; instead, the mechanism is indirect warming due to diabatic heating in the outer eyewall. On the basis of radar observations of Hurricane Rita (2005), which had clear CEs, Houze et al. (2007) reported that, after the outer eyewall forms, it chokes the inner eyewall by blocking the entropy supply to the inner eyewall. Zhou and Wang (2011) used a three-dimensional, nonhydrostatic, full-physics model and showed that the high entropy supply to the inner eyewall is cut off in the PBL below the outer eyewall. They also reported that more time is required for the ERC when the radius at which the outer eyewall forms is larger. This finding suggests that the time required for the ERC is determined by the radius of the outer eyewall and that the contraction of the outer eyewall controls the dissipation of the inner eyewall. Kepert (2013) showed by using boundary layer models and an imposed gradient wind field that a small perturbation in vorticity outside of the primary radius of maximum wind results in a relatively strong updraft, which, through feedbacks between the updraft, convection, and vorticity, can lead to formation and intensification of a secondary eyewall. Kepert and Nolan (2014) found by using boundary layer models and the gradient wind field based on a numerical simulation that the vertical velocity field can largely be reproduced as the frictional response to the gradient wind field.

The maintenance mechanism of long-lived CEs, however, is not well studied. Yang et al. (2013) classified typhoons with CEs into three types: 1) an ERC type, in which the inner eyewall dissipates less than 20 h after SEF; 2) a no replacement cycle (NRC) type, in which the outer eyewall dissipates less than 20 h after SEF; and 3) a CE maintenance (CEM) type, in which CEs are maintained for more than 20 h. They reported that the ERC, NRC, and CEM types comprise 53%, 24%, and 23%, respectively, of all typhoons with CEs. Although the CEM type is least common among typhoons with CEs, the intensity of CEM typhoons is higher than that of ERC and NRC typhoons (see Yang et al. 2013, their Fig. 4). Thus, the type should be taken into account for more accurate predictions of TC intensity changes. Yang et al. (2013) proposed that barotropic stability of core and ring vortices (Kossin et al. 2000) is a possible mechanism of CE maintenance. Kossin et al. (2000) performed a stability analysis with a nondivergent barotropic model and proposed that outer eyewall contraction and inner eyewall dissipation occur as a result of barotropic instability caused by the interaction of a core vortex (i.e., inner eyewall) with a ring vortex (i.e., outer eyewall). Indeed, Zhou and Wang (2011) indicated that barotropic instability between the inner and outer eyewalls acted during the ERC. Yang et al. (2013) proposed that CEs of CEM typhoons can be maintained for a long time if barotropic instability does not arise between the CEs (i.e., the core and ring vortices) after SEF. However, the model proposed by Kossin et al. (2000) does not include any diabatic heating or variations with height of the dynamic and thermodynamic fields. In real TCs, temporal variations of the storm are dominated by processes, such as acceleration of tangential winds due to diabatic heating (e.g., Shapiro and Willoughby 1982) and strong inflow in the PBL (e.g., Huang et al. 2012). It is difficult, however, to obtain information about such processes from satellite and radar observations. To investigate the maintenance mechanism of long-lived CEs, therefore, it is necessary to use a three-dimensional full-physics atmospheric model to perform numerical simulations of real TCs with long-lived CE.

Typhoon Bolaven (2012) is one example of a typhoon with long-lived CEs. Because the CEs were maintained for more than one day, Bolaven was a CEM-type typhoon (Yang et al. 2013). The operational radars of the Japan Meteorological Agency (JMA 2002) observed Bolaven and its CEs as the typhoon passed over the Okinawa islands. The purpose of the present study is to propose a possible maintenance mechanism of long-lived CEs through diagnostic analyses of a numerical simulation of Typhoon Bolaven (2012) with a three-dimensional nonhydrostatic full-physics model. To examine the maintenance mechanism, we focus on 1) maintenance of the inner eyewall and 2) contraction of the outer eyewall. We investigate the first by an entropy budget and backward trajectory analysis of the inner eyewall and the second by diagnosis of the potential vorticity (PV) budget. In section 2, the configuration of our numerical experiment is documented. Section 3 is an overview of Bolaven based on JMA’s operational observations. Section 4 is an overview of the simulated Bolaven and its CEs. We discuss the maintenance of the inner eyewall in section 5 and contraction of the outer eyewall in section 6. Finally, we present our conclusions regarding the maintenance mechanism of the long-lived CEs associated with the simulated Bolaven in section 7.

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 Cartesian 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; Tsuboki et al. 2015).

The cloud physics scheme was an explicit bulk cold rain scheme, which is a double moment for ice, snow, and graupel, based on Murakami (1990), Ikawa and Saito (1991), and Murakami et al. (1994). Cumulus parameterization was not utilized in this model. Subgrid-scale turbulent mixing was parameterized using 1.5-order closure with TKE prediction (Deardorff 1980). Momentum and energy fluxes at the surface were formulated according to Kondo (1975) for ocean and Louis et al. (1981) for land. No atmospheric radiation scheme was included because the sensitivity of the atmospheric and cloud radiation processes on the intensity and track was not significant when a simulation with radiation for only domain 2 was performed as a sensitivity test.

To simulate a realistic CE structure, the horizontal grid spacing of a numerical model must be less than 2 km (e.g., Wang et al. 2013). In general, to save numerical resources, two-way nesting methods are used in a typhoon simulation with high resolution. Use of the two-way nesting can change an environmental field in which the storm is embedded because of interactive communication of the two-way nesting between the fine-resolution and coarse-resolution domains. Two-way nesting is not supported in our model, and a one-way nesting method was used in our simulation with three computational domains (Fig. 1). Note that the influence of the storm-induced circulation on the environmental field cannot be estimated in our numerical simulation. The area of the outermost domain was 2140 km × 2390 km with a horizontal grid spacing of 5 km (domain 1), the middle domain was 1700 km × 1800 km with a 2.5-km resolution (domain 2), and the finest domain was 1200 km × 1500 km with a 1-km resolution (domain 3). The detailed configuration of the numerical model in each domain is summarized in Table 1. There were 45 vertical levels, the lowest grid interval was 200 m, and the upper boundary condition was a rigid lid. To prevent reflection of vertically propagating waves, a sponge layer was applied from a height of 17 km to the top of each calculation domain. The model tops of domains 1, 2, and 3 were at 25, 22.5, and 20 km, respectively. The initialization times of domains 1, 2, and 3 were 0000 UTC 22 August, 0600 UTC 23 August, and 1200 UTC 24 August 2012, respectively. The ending time of integration of all experiments was 0600 UTC 27 August 2012. The sea surface temperature (SST) was calculated by using a one-dimensional, vertical heat diffusion equation (Segami et al. 1989). The SST calculation did not take account of cooling due to vertical mixing or Ekman upwelling processes (e.g., Yablonsky and Ginis 2009), although in strong typhoons, SST cooling due to these processes can be large (Lin et al. 2008). Typhoon Bolaven was a category 3 typhoon, and the magnitude of SST cooling during its passage was about 1 K, based on the JMA’s Merged Satellite and In Situ Data Global Daily SST (MGDSST) dataset (JMA 1996). Thus, we considered SST cooling due to mixing and upwelling to be small in this case. For the initial SSTs, the MGDSST dataset, which has a 0.25° resolution, was used. The lateral boundary conditions were wave radiating with constant phase velocity (e.g., Klemp and Wilhelmson 1978). In the experiment, 6-hourly Global Spectral Model (GSM; JMA 2007) output data (horizontal resolution, 0.5° × 0.5°) provided by JMA (2002) were used for the initial atmospheric and boundary conditions of domain 1 (Davies 1983). Shuttle Radar Topography Mission data with a horizontal resolution of 30 s from the U.S. National Aeronautics and Space Administration were used for the terrain (U.S. Geological Survey 2005). No data assimilation was performed in our experiment. The best-track data were used for comparing the simulated and observed tracks of Bolaven.

Fig. 1.
Fig. 1.

Model domains and Typhoon Bolaven’s track. Domains 1, 2, and 3 are the areas enclosed by the solid line, the short-dashed line, and the long-dashed line, respectively. The simulated track in domain 3 is shown by dots, and the observed track is shown by cross marks. Open circles and squares show the location of Bolaven along each track at the initial time of 1200 UTC 24 Aug and the end time of 0600 UTC 27 Aug 2012 in domain 3.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

Table 1.

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

Table 1.

A backward trajectory analysis of air parcels carrying entropy supply to the inner eyewall was used to investigate paths of the air parcels. An equation to calculate the backward trajectory is expressed as follows:
e1
Here, indicates the location of the parcel at time t, and indicates wind velocities at . The parameter was calculated with wind velocities output in domain 3. The time interval of model output in domain 3 was 1 min for more accurate estimation of the trajectory analysis (described below). Then, linear interpolation in space and time was used to obtain . The time interval for the integration was 1 s. A fourth-order Runge–Kutta scheme was used for the time integration scheme. Trajectory parcels were located at heights of 200, 300, 400, 500, 600, 700, and 800 m. At each level, 50 parcels were arranged at equal intervals around a circle with a radius of 60 km from the center of the TC. This radius corresponded to the lateral boundary of the cylinder used in the equivalent potential temperature budget analysis. The levels at which the parcels were located are included in the azimuthal-mean inflow layer at the radius of 60 km at the start times of the backward trajectory calculation.

3. Overview of Typhoon Bolaven

Typhoon Bolaven formed in the western North Pacific (14.1°N, 142.1°E) on 19 August 2012. It slowly moved northwestward and passed over Okinawa Island on 26 August 2012 (Fig. 1). Bolaven made landfall on the coast of North Korea on 28 August 2012 and changed to an extratropical cyclone on 29 August 2012. The lifetime maximum wind speed and minimum central pressure of Bolaven of 100 kt (1 kt = 0.51 m s−1) and 910 hPa, respectively (i.e., category 3), were estimated at 1200 UTC 25 August 2012, before the TC passed over the Okinawa Islands. The estimation is based on the JMA best-track data (i.e., the maximum wind speed is the 10-min average value). On the other hand, estimation of the maximum wind speed and minimum central pressure based on the JTWC best-track data is 125 kt (1-min average) and 929 hPa at 1800 UTC 24 August 2012, respectively.

To check the eyewall structure observed in Bolaven, microwave imagery provided by the Naval Research Laboratory (NRL; https://www.nrlmry.navy.mil/TC.html) Marine Meteorology Division in Monterey, California (Hawkins et al. 2001), is shown in Fig. 2. As shown in Fig. 2b, Typhoon Bolaven qualitatively had triple eyewalls (McNoldy 2004; Zhao et al. 2016), although the innermost eyewall was very small and enclosed a pinhole eye (e.g., McNoldy 2004). Yang et al. (2013) developed an objective method to detect CEs of typhoons using microwave imagery, and Abarca et al. (2014) modified the method so that it could be used for the detection of triple eyewalls. These methods were used to examine the maintenance period of Bolaven’s triple eyewalls. In a typhoon with triple eyewalls, formation of the secondary eyewall is defined by Abarca et al. (2014) as the secondary minimum (≤230 K) of the brightness temperature, but its dissipation is not defined, unlike in the case of a typhoon with double eyewall. Thus, in the present study, the dissipation of the secondary eyewall was defined as the dissipation of the secondary minimum of the brightness temperature, similar to Yang et al. (2013). As shown in the right 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 classification 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).

Fig. 2.
Fig. 2.

(left) Color-enhanced microwave (89-GHz band) CE imageries of Typhoon Bolaven provided by the NRL website. (right) The averaged brightness temperature 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).

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

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). Consistent 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.

Fig. 3.
Fig. 3.

Distribution of precipitation intensity (color scale; mm h−1) estimated from radar reflectivity, observed by the JMA radar network in the Okinawa region at (a) 1800 UTC 25 Aug, (b) 0600 UTC 26 Aug, and (c) 1800 UTC 26 Aug 2012. The Okinawa Main Island is located in the center of each panel.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

Precipitation intensity was azimuthally averaged at each time from 30 h (1800 UTC 25 August) to 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, is used as a relative time in comparing simulation with observation, and 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 30 to 46 h, a period defined as period of observation 1 (PO1), and they maintained their position from 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 estimated by the radar observation, were at radii of about 20, 60, and 120 km at h (Fig. 4), respectively, and they were approximately 10, 20, and 60 km wide, respectively. The inner moat (i.e., the area of weak or no precipitation between the innermost and middle eyewalls) was 20–30 km wide, whereas the outer moat was 40–60 km wide at h. At h, the widths of the inner and outer moats decreased to 10 and 20 km with contraction of each eyewall, respectively.

Fig. 4.
Fig. 4.

Time–radius cross section of the azimuthal mean of precipitation intensity (color scale; mm h−1) observed by the JMA radars from 30 to 54 h. The outer eyewalls move inward during PO1 (period below the dashed line) and were mostly stationary during PO2 (above the dashed line). The dashed line is at 46 h.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

The three-dimensional structure of Bolaven’s observed CEs was revealed by Constant Altitude Plan Position Indicator radar reflectivity data obtained by the JMA radar on Okinawa Main Island. At 42 h (Figs. 3b and 5), the echo-top height, defined here by the 20-dBZ contour, on the south side of both the innermost 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. 5.
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 42 h. The black contour indicates a radar reflectivity of 20 dBZ. The vertical black line denotes the storm center.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

4. Results

a. Track and intensity of simulated Typhoon Bolaven

In this paper, only the results of the domain 3 simulation are presented. The time length of integration is 66 h. The simulated track (Fig. 1) is estimated by the method of Braun (2002), which calculates the azimuthal variance of sea level pressure for 50 radii between 1 and 50 km at each grid point within a radius of 65 km from the minimum sea level pressure grid and searches for the point of minimum variance. This method is often used to determine TC centers in simulations performed with a high-resolution nonhydrostatic model (e.g., Mashiko 2005). The root-mean-square error of the simulated track to the observed track was 168 km. In Fig. 1, the western bias of simulated Bolaven (i.e., the error in the initial location on domain 3) was mainly influenced by the error of the track arising from the simulations of domain 1 and domain 2 (not shown). In the domain 1 simulation, another typhoon, Tembin, was present over the sea to the east of Taiwan, and the track of simulated Bolaven in domain 1 was influenced by the wind field of typhoon Tembin through vortex–vortex interaction (e.g., Fujiwhara effect). However, the simulated track of Bolaven was nearly parallel to the observed track (Fig. 1). The time series of central pressure of the JMA best track and simulated Bolaven (Fig. 6a) showed that the simulated central pressure was 926 hPa when the minimum central pressure of 910 hPa was estimated on the basis of satellite observations. For the time series of wind speed, the simulated wind speed was about 40 m s−1 during the maximum wind speed of 47.5 m s−1 estimated by satellites. The intensification rates of the simulated central pressure and wind speed are different from the estimated pressure and wind speed in the best track during 10–24 h. On the other hand, the simulated pressure and wind speed are nearly flat, similar to the estimation in the best track during 27–45 h at least. However, after h (i.e., when Bolaven was in the East China Sea), the differences of central pressure and wind speed between the simulation and estimation were increasing, and it was also approaching the domain 3 boundary, so we do not discuss the CE structure after that time.

Fig. 6.
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 in the simulation by the CReSS model (black lines). The simulation time is shown on the horizontal axis; at 1200 UTC 24 Aug 2012. The best-track data are not only every 6 h but also include an additional estimation every 3 h, which is done for typhoons approaching Japan. The simulated intensity is plotted every 1 h. The maximum wind in the simulation is the maximum of azimuthally averaged surface wind speed within a radius of 100 km from the storm center.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

b. Distribution and lifetime of precipitation

At 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 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 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 radar observations (Fig. 3).

Fig. 7.
Fig. 7.

Distribution of precipitation intensity (color scale; mm h−1) and sea level pressure (contour; hPa) simulated by the CReSS model at Ts = (a) 15, (b) 24, and (c) 48 h. Black stars denote the center of Bolaven.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

The axisymmetric distribution of the simulated CEs and its time variation can be shown by a radius–time cross section of the azimuthally averaged precipitation intensity (Fig. 8). Two peaks of intense precipitation were simulated: one between radii of 40 and 60 km and the other between 100 and 160 km. The width of the simulated moat was about 40 km. The simulated inner eyewall was located at mostly the same position as the observed middle eyewall, and the simulated outer eyewall was at the same position as the observed outermost eyewall. In the numerical experiment, the precipitation peak associated with the innermost eyewall of observed Bolaven was not simulated. However, the two simulated precipitation peaks were maintained from to 50 h.

Fig. 8.
Fig. 8.

Time series of the azimuthal average of precipitation intensity (color scale; mm h−1) simulated by the CReSS model from to 50 h. The outer eyewall moved inward during PS1 (below the horizontal dashed line at 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.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

The radius of the simulated outer eyewall gradually decreased from to 40 h [period of simulation 1 (PS1) in Fig. 8] and was approximately steady from to 50 h (PS2 in Fig. 8). The observed CEs of Bolaven exhibited the same characteristics. Thus, on the basis of the simulated precipitation distribution and lifetime, simulated Bolaven is classified as a CEM-type typhoon according to the criteria of Yang et al. (2013).

c. Vertical structure of the CEs

To compare the structure of radar reflectivity between observed and simulated Bolaven, we estimate the simulated radar reflectivity by the method of Murakami (1990) from the simulated mixing ratios of liquid and ice hydrometeors. At h, a region with low relative humidity (RH) and no echo within the radius of 30 km corresponded to the eye of simulated Bolaven (Fig. 9). Another low-RH region between radii of 80 and 110 km was the moat of simulated Bolaven. The RH distribution showed that the moat was deeper on the north side than on the south side of the center. The asymmetric distribution of radar reflectivity was similar to the observation (Fig. 5). A strong echo simulated between radii 40 and 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).

Fig. 9.
Fig. 9.

Vertical cross section of relative humidity (contours; %) and simulated radar reflectivity (color scale; dBZ) from south to north through the center of simulated Bolaven at h. The vertical black line denotes the storm center.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

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 h (Fig. 10). A strong inflow in excess of 5 m s−1 was simulated below 1 km (Fig. 10c). The inflow had two peaks, at radii of 50 and 140 km, which corresponded to the inner and outer eyewalls, and the radial wind speed of the outer peak was higher than that 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 outflow of 3 m s−1 simulated at a radius of 120 km in the lower troposphere, from 2 to 3 km did not appear in the inner eyewall region. Two tangential wind peaks were simulated at 1 km height: one at a radius of 40 km and the other at a radius of 140 km, corresponding to the two eyewalls (Fig. 10a). The height of maximum wind (HMW) associated with each eyewall was at the top of the inflow boundary layer, and the HMW of the inner eyewall was slightly lower than that of the outer eyewall. The outer peak was broad, extending from a radius of 100 km to a radius of 180 km. Similarly, two vertical wind peaks were simulated at radii of 40 and 120 km. This wind field structure is consistent with the results of previous numerical simulations of CE (e.g., Zhou and Wang 2011; Wu et al. 2012). In our simulation, the inner updraft peak was stronger than the outer peak, and this distribution of updraft strength corresponded to the distributions of simulated radar reflectivity and echo-top height (Fig. 9). Moreover, the outer updraft peak tilted outward; this tilting induced the broader distribution of precipitation associated with the outer eyewall. These characteristics of the broad outer eyewall are consistent with those of outer eyewalls of CEM-type typhoons (Yang et al. 2013).

Fig. 10.
Fig. 10.

Azimuthal-mean wind field structure at 30 h: (a) tangential wind Vt (contour interval = 6.0 m s−1), (b) vertical wind W (contour interval = 0.1 m s−1), and (c) radial wind Vr (contour interval = 3.0 m s−1). Negative radial wind speeds indicate inflow.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

5. Maintenance of the simulated inner eyewall

Some studies have proposed a possible mechanism by which the moist entropy supply to the inner eyewall is intercepted by the outer eyewall leading to the dissipation of the inner eyewall after the SEF (e.g., Houze et al. 2007; Rozoff et al. 2008). In a numerical experiment performed with the Weather Research and Forecasting Model, Zhou and Wang (2011) found that dissipation of the inner eyewall during an ERC was caused by a low-entropy flow in the inner eyewall. At least, these studies suggest that a decrease of moist entropy in the inner eyewall is important for the dissipation of the inner eyewall. If such a decrease is essential for the dissipation of the inner eyewall, in the case of the long-lived CEs the entropy supply to the inner eyewall will be sufficient after SEF. Although different dissipation mechanisms have been proposed by other studies (e.g., Kossin et al. 2000; Rozoff et al. 2008; Kepert 2013), we examine only the mechanism of decreasing moist entropy in the inner eyewall. To investigate the maintenance mechanism of the inner eyewall in simulated Bolaven after the SEF, we performed an equivalent potential temperature budget analysis of the inner eyewall. Then, to investigate the path of the moist air mass carrying sufficient entropy to maintain the inner eyewall of the long-lived CEs, we carried out a backward trajectory analysis.

a. Equivalent potential temperature budget analysis

The volume integral of equivalent potential temperature is defined as
e2
where ρ is air density horizontally averaged; and is the integration domain of the equivalent potential temperature budget, which is a cylinder with a height of about 17 km and a radius of 60 km. The radius of 60 km corresponds to the outside of the simulated inner eyewall after SEF (Fig. 8). The terms are latent heat, constant pressure specific heat, and the Exner function, respectively. The terms θ and are potential temperature and water vapor mixing ratio, and these variables are calculated using the model output. Then the budget equation is expressed as
e3
where LHSH is the latent and sensible heat from the ocean, and advection of (ADV) is defined as
e4
and the first and second terms denote the lateral and vertical advections of , respectively. The term is the lateral surface area of the cylinder, and and are the horizontal wind vector and an area element, respectively. The vector 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 tendency even if the low-level associated with the simulated Bolaven decreases with increasing radius. Thus, when the amount of flux associated with low-level inflow is larger than that of upper-level outflow, ADV can be a positive contribution to the tendency. In particular, a realistic decrease in the value of 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 to 20 h), the fluctuation 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 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 term varied from 0 to 0.2 K h−1 (red line in Fig. 11), and the LHSH term varied below 0.02 K h−1 (blue line in Fig. 11) and was minor in comparison with the ADV term.

Fig. 11.
Fig. 11.

Time series of each term on the right-hand side of Eq. (3) and their sum (TOTAL): ADV; LHSH; and dPTdt, the net tendency of . Note that all terms are normalized by volume integral of ρ. PS1 and PS2 are as in Fig. 8. The 4-h moving average of the 1-min model output is shown to filter out some high-frequency components.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

The tendency in the inner eyewall can thus be mostly explained by the major source of ADV. The ADV term rapidly decreased (from 0.16 to 0.04 K h−1) after h (the time of SEF), and gradually increased (from 0.04 to 0.1 K h−1) from 28 to 40 h. Then, it gradually decreased from 44 h again. However, the moist entropy supply (i.e., ) to the inner eyewall was maintained during PS1 and PS2. Moreover, the vertical distribution of azimuthally averaged lateral advection of at each level shows that the positive contribution to ADV was concentrated mainly in the PBL (not shown). This concentration is consistent with the radial wind field shown in Fig. 10c because the azimuthally averaged lateral advection was mainly brought by axisymmetric inflow. The long duration of PS1 implies that the positive entropy supply to the inner eyewall was ineffective in causing the inner eyewall to decay. Moreover, during PS2 the positive entropy supply to the inner eyewall could be mostly maintained. The positive entropy supply was mainly supported by the constant-inflow mass flux during PS1 and PS2. Thus, in simulated Bolaven, the inner eyewall was maintained for more than one day because of an insufficient interception of positive entropy supply to the inner eyewall during PS1 and PS2. Why did the positive entropy supply that was sufficient to maintain 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 the long-lived CEs in the simulation, and the result cannot be applied to short-lived CEs (e.g., Zhou and Wang 2011) directly. In other words, we cannot conclude that, for the short-lived CEs, tendency becomes negative or close to zero after the SEF according to our result. It should be investigated in a future study for the short-lived CEs.

b. Trajectory analysis

The budget analysis (section 5a) indicated that the entropy supply to the inner eyewall was mainly via moist air inflow in the PBL. Thus, by determining the paths by which the moist air masses arrived at the inner eyewall in the PBL, we can explain the continuous entropy supply to the inner eyewall after the SEF. Therefore, we calculate backward trajectories at (i.e., during PS1) and 46 h (i.e., during PS2) of air parcels from locations at the radius of 60 km at various levels within the PBL, as described in section 2. The trajectory parcels were traced back to 12 h before (corresponding to h in the case of h and h in the case of h). We found that the parcels followed four paths. The first path (path 1 in Fig. 12) passed a radius of 120 km at a height below 1 km (i.e., the parcels passed the outer eyewall within the PBL); the second path (path 2 in Fig. 12) traced the area of subsidence outside of the inner eyewall; the third path (path 3 in Fig. 12) was traced back to a height of 100 m above the ground level within a radius of 120 km;1 and parcels associated with the fourth path (path 4 in Fig. 12) remained within the PBL around the radius of 60 km. The parcels of the fourth path wandered in and out the boundary of the cylinder used in the budget analysis. These parcels corresponded to high-frequency components in the budget analysis, which were removed in Fig. 11 by the use of the 4-h moving average. Thus, parcels along paths 1, 2, and 3 contribute to the budget in Fig. 11. At h, 159 parcels, corresponding to 71% of the number of the parcels (224) along paths 1–3, passed along the first path, and at h, 150 parcels (80%) passed along that path (Fig. 12). Therefore, we discuss here only those parcels that followed the first path, which made the major contribution to the budget.

Fig. 12.
Fig. 12.

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

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

Parcels arriving at a radius of 60 km at h along the first path did not preferentially originate from certain azimuthal locations outside the outer eyewall (Figs. 13a–d). This relatively homogeneous distribution implies that the parcels were carried by an axisymmetric radial flow during PS1. Thus, the axisymmetric inflow in the PBL into the inner and outer eyewalls and moat (Fig. 10c) brought a sufficient entropy supply to maintain the inner eyewall. Therefore, during PS1, the budget in the inner eyewall was controlled mainly by axisymmetric dynamic fields of the 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 case, the axisymmetric structure of the outer eyewall did not result in the effective interception of the entropy supply to the inner eyewall.

Fig. 13.
Fig. 13.

Results of backward trajectory analysis from Ts = (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 intensity (mm h−1). Times are Ts = (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.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

In contrast, parcels arriving at a radius of 60 km at h mainly appeared to pass through two regions (Figs. 13e–h): 1) a region of weak precipitation on the northwest side of the outer eyewall, indicated by the group of parcels on the northwest side around a radius of 120 km in Fig. 13f, and 2) a region of strong precipitation on the east and northeast parts of the outer eyewall, shown by the group of parcels distributed around a radius of 120 km from east to northeast of the center (Figs. 13f,g). These asymmetric structures appeared in radar observations. Figure 14 shows horizontal distributions of simulated and observed precipitation around PS2 and PO2. The asymmetries of the precipitation (i.e., strong precipitation east and southeast of the storm and weak precipitation northwest of the storm) in the outer region qualitatively continue in both the simulation and observations.

Fig. 14.
Fig. 14.

Horizontal distribution of precipitation intensity (mm h−1). (a),(c),(e) The simulation, and (b),(d),(f) the radar observations. Stars denote the center of the simulated typhoon.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

In the first region (i.e., the weak precipitation region), the net buoyancy2 in the PBL was weaker than that in the other regions of the outer eyewall (not shown), and the air mass (parcel group) experienced weak buoyancy when passing through this region. Therefore, it was difficult for the outer eyewall to intercept the moist air mass in the first region. In the second region (i.e., the strong precipitation region), the air mass experienced stronger net buoyancy by comparison, but inflow in the PBL below that region was also much stronger than in the first region (not shown). If the inflow is sufficiently strong in the PBL below the outer eyewall, the upward forcing that the parcels experience during passing in the PBL is insufficient to lift the parcels from the PBL to the free atmosphere. As a result, the parcels can subsequently pass through the second region and arrive at the inner eyewall. During PS2, the entropy supply to the inner eyewall was therefore controlled mainly by the nonaxisymmetric dynamic fields of the outer eyewall.

6. Contraction of the simulated outer eyewall

CEs associated with a TC can be regarded as rings of high vorticity (e.g., Kossin et al. 2000) or of PV (e.g., Zhou and Wang 2011). Thus, the change in the azimuthally averaged PV represents the change in the CEs with time. To examine the tendency of the PV change, we carried out a PV budget analysis of the outer eyewall. Here, PV is defined as
eq1
where is absolute vorticity, θ is potential temperature, and is basic air density, which is horizontally averaged. The PV (P) budget equation is (e.g., Wang 2002) as follows:
e5
e6
Here, u and w are radial and vertical velocity components, and are radial and vertical absolute vorticity, and Q is diabatic heating. MADVR and MADVZ are radial and vertical advections of due to mean flow. MDIAR and MDIAZ are generation of due to radial and vertical gradients of mean diabatic heating. ASYMM is advection and generation of associated with asymmetric structure. FRIC, which denotes the effects of surface friction and turbulent viscosity, is much smaller than the other terms. Overbars and primes denote azimuthal averages and deviations from the average, respectively, computed as follows:
eq2
eq3
where φ is an arbitrary variable. Therefore, represents the tendency of the PV associated with the eyewall. The derivation of Eq. (6) is shown in the Appendix A, including the expression of the FRIC term. Note that the asymmetric fields are associated with convection and rainbands in the CEs.

Figure 15 ( h, PS1) and Fig. 16 ( h, PS2) show the radius–height cross sections of the budget analysis, which is averaged over 6 h. First, except in the inner eyewall region, the total budget tendency (Figs. 15b, 16b), which is the sum of all terms on the right-hand side of Eq. (6), is qualitatively similar to the simulated net tendency (Figs. 15a, 16a), which is the time variation of . In addition, FRIC is very small in both periods. In radius–height cross sections at h, MDIAR and MADVZ were positive along the inside of the outer PV peak, and MDIAZ and MADVR were negative, whereas these terms had the opposite sign along the outside of the outer PV peak (Figs. 15c–f). The distributions of these major terms were similar to those in the case of a single eyewall (Wang 2002; Wu et al. 2016). For contraction of the PV peak to occur, the radial gradient of should be negative at the outer PV peak; that is, inside the outer PV peak should be larger than that outside the outer PV peak for contraction to occur. Thus, if MDIAR and MADVZ are larger than MDIAZ and MADVR, the outer PV peak is expected to contract. The magnitudes of MDIAR and MDIAZ depend mainly on the radial and vertical gradients of axisymmetric diabatic heating in the outer eyewall, and the magnitudes of MADVR and MADVZ depend mainly on axisymmetric radial and vertical flows in the outer eyewall. Therefore, the values of these major terms in Eq. (6) depend on axisymmetric flows and diabatic heating in the outer eyewall.

Fig. 15.
Fig. 15.

Radius–height cross sections of the major terms of the PV budget [Eq. (6)] at h. In each panel, contours indicate [PVU (1 PVU = 10−6 K kg−1 m2 s−1) based on 6-h averages]. The color scale shows (a) , (b) total tendency, (c) MADVR, (d) MADVZ, (e) MDIAR, (f) MDIAZ, (g) ASYMM, and (h) FRIC (PVU h−1). The dashed lines show the approximate position of the outer PV peak at each height.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

Fig. 16.
Fig. 16.

As in Fig. 15, but at h.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

In radius–height cross sections at h (Fig. 16), the distribution patterns of the axisymmetric terms in Eq. (6) were similar to those at h (Fig. 15), but the contribution of ASYMM (Fig. 16g) to the PV budget in the outer eyewall was larger than it was at h (Figs. 15g). The ASYMM term represents the contribution of individual convection and rainbands. Moreover, ASYMM was negative in the low and middle troposphere around the outer PV peak and positive within the PBL outside of the outer PV peak (Fig. 16g). In association with the decrease in ASYMM above 3 km, the total PV tendency inside the outer eyewall was decreased by a mainly negative region at radii of around 80–100 km during PS2 (Fig. 16b). Within the PBL, the total PV tendency outside the outer eyewall was increased by the positive region around radii of 70–90 km in ASYMM. Figure 17 shows the sum of all axisymmetric terms in Eq. (6) at h and h. Distribution of the axisymmetric contributions was positive (negative) inside (outisde) of the outer PV peak during PS1 and PS2. It indicates that the axisymmetric components help the contraction of the outer eyewall during PS1 and PS2. These results indicate that the slow contraction of the outer eyewall during PS2 was caused mainly by ASYMM, compared with the other axisymmetric contributions (Figs. 15, 16). Associated with the decrease in the total PV tendency inside the outer eyewall in the low and middle troposphere and the increase outside the outer eyewall within the PBL, the contracting speed of the outer eyewall during PS2 became slower than it was during PS1. Thus, 1) the difference in the contracting speed of the outer eyewall between PS1 and PS2 may have been caused by the weakening PV inside the outer eyewall associated with convection and rainbands (i.e., ASYMM), and 2) the nonaxisymmetric structure of the outer eyewall, as well as the axisymmetric structure, may control its contraction. In addition, the nonaxisymmetric structure played an important role in section 5 because the maintenance of the entropy supply to the inner eyewall (Fig. 11) was caused by the nonaxisymmetric structure in the outer eyewall during PS2 (Figs. 13e–h). Zhou and Wang (2011) focused on the axisymmetric aspects of CEs, and the role of the nonaxisymmetric structure of the outer eyewall remained to be answered. The results of the present study suggest that the contraction of the outer eyewall is also controlled by the nonaxisymmetric structure of the outer eyewall. Zhou and Wang (2011) also indicated that the duration of the ERC depends on the radius of SEF. However, they implicitly assumed that the outer eyewall had an approximately axisymmetric structure. If the nonaxisymmetric structure of the outer eyewall is considered, the duration of the ERC does not depend only on the radius of SEF, because the entropy supply to the inner eyewall due to the nonaxisymmetric structure of the outer eyewall prevents the decay of the inner eyewall. Moreover, nonaxisymmetry was also observed by the JMA radar: although highly axisymmetric precipitation rings were observed during PO1 (Figs. 3a,b, 4), during PO2 (Fig. 4) the horizontal distribution of the precipitation rings showed clear nonaxisymmetry and a strong rainband on the east side of Bolaven (Fig. 3c). This distribution is similar to that of the simulation during PS2 (Fig. 7c).

Fig. 17.
Fig. 17.

Radius–height cross sections of the sum of axisymmetric terms in Eq. (6) at h (PS1) and h (PS2) (PVU h−1). Contour and dashed lines are as in Figs. 15 and 16.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

Abarca and Montgomery (2015), however, indicated that strong inflow associated with the eyewall in the PBL plays an important role in the contraction of the eyewall. The strong inflow is not estimated in a diagnosis obtained with the Sawyer–Eliassen equation, which is based on a gradient wind balance vortex. According to Abarca and Montgomery (2015), the maximum speed of the strong inflow associated with the eyewall within the PBL exceeds about 28 m s−1 in their numerical simulation. Based on the Sawyer–Eliassen equation, the maximum speed of the PBL inflow diagnosed from their model output is only 16 m s−1. In their simulation, the unbalanced inflow associated with the eyewall is very strong. However, in our simulation the unbalanced inflow is very small. Figure 18 shows transverse circulation diagnosed by the model output of tangential wind, diabatic heating, and frictional forcing at h, based on the Sawyer–Eliassen equation (e.g., Fudeyasu and Wang 2011). We caution that the diagnosed circulation is not completely identical to the simulated circulation. The difference between simulation and diagnosis suggests that the simulated axisymmetric circulation cannot be interpreted completely based on a balanced vortex. In particular, there is a difference in the midlevel outflow between the simulation and reproduction in the outer eyewall. It could be induced by the difference between linear and nonlinear boundary layer models (Kepert 2013), and it is also indicated in Fig. 12 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 the PBL was about 15 m s−1 at h (Fig. 10c), which is quantitatively similar to the maximum speed (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.

Fig. 18.
Fig. 18.

Radius–height cross section of (a) radial wind (m s−1) and (b) vertical wind (m s−1) diagnosed by the Sawyer–Eliassen equation at 30 h.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

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 maintenance period could be split into two phases: one of gradual contraction (PS1; about 16 h after SEF) and one of mostly steady maintenance (PS2; about 8 h after PS1).

The CE maintenance mechanism is explained by two features: 1) the lack of dissipation of the inner eyewall and 2) the constancy of the large radius of the outer eyewall. We have summarized our results in a schematic diagram (Fig. 19). With regard to feature 1, to examine the entropy supply to the inner eyewall, we carried out a budget analysis of the inner eyewall and investigated the path of the moist air mass to the inner eyewall by a backward trajectory analysis. We found the entropy supply to the inner eyewall during PS1 and PS2 sufficiently maintained after the SEF. The backward trajectory analysis revealed that the moist air mass that brought entropy to the inner eyewall passed through the PBL of the outer eyewall during both PS1 and PS2. This finding indicates that there was insufficient interception of entropy in the PBL of the outer eyewall after the SEF (solid arrow in Fig. 19a). The path of the moist air mass, however, differed between PS1 and PS2. During PS1, the moist air mass passed through the PBL below the outer eyewall at all azimuthal angles (dashed arrows in Fig. 19b). In contrast, during PS2, it passed through two regions below the outer eyewall: one of weak convection and the other where the boundary layer inflow was strong (solid arrows in Fig. 19b). This result suggests that 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.

Fig. 19.
Fig. 19.

A conceptual model of the maintenance mechanism of the long-lived CEs of simulated Bolaven. (a) Height z and radius r cross section, and (b) horizontal (plan) view. In (a) solid vectors show the axisymmetric flows. The shaded regions show the axisymmetric terms of Eq. (6) during PS1 and PS2, and the region enclosed by the red line shows the contribution to contraction of the outer PV peak associated with ASYMM during PS2. Solid and dashed lines, which bound these regions, denote positive and negative contributions to contraction of the outer PV peak, respectively. The solid straight line shows the axis of the outer PV peak. In (b), regions of precipitation are shaded. Solid and dashed arrows indicate the movement of moist air masses associated with the nonaxisymmetric and axisymmetric boundary layer inflows, respectively. In regions bounded by dashed lines, interception of the nonaxisymmetric flows was insufficient.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

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 at the outer PV peak is negative when the outer eyewall contracts. In Fig. 19a, the negative gradient corresponds to the pattern where MDIAR + MADVZ is positive in the shaded region bounded by the solid line, and MDIAZ + MADVR is also positive in the shaded region bounded by the dashed line. However, the radial gradient of MDIAZ + 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, caused ASYMM to be negative inside the outer eyewall in the low and middle troposphere (the region enclosed by the red dashed line in Fig. 19a) and positive outside the outer eyewall within the PBL (the region enclosed by the red dashed line in Fig. 19a). The diagnosis reveals that contraction of the outer eyewall during PS1 (i.e., period of slow contraction) was governed mainly by the axisymmetric structure of the outer eyewall, but during PS2, (i.e., steady period) contraction was governed by not only the axisymmetric but also the nonaxisymmetric structure of the outer eyewall.

The results of the present study reveal that the maintenance of long-lived CEs is controlled by both the axisymmetric and nonaxisymmetric structure of the outer eyewall. This finding suggests that the dissipation of the inner eyewall associated with an ERC depends not only on the radius of the SEF (Zhou and Wang 2011) but also on the structure of the outer eyewall. Moreover, long-lived CEs are maintained by the distribution of diabatic heating (i.e., PV source) in the outer eyewall.

Here, we focused on only one TC with long-lived CEs, and the proposed maintenance mechanism is a prototype for long-lived CEs. Without more numerical simulations and observations of CEM-type typhoons, it is impossible to say whether the proposed mechanism of long-lived CEs is applicable to all TCs with long-lived CEs. For example, Yang et al. (2013) noted that the characteristic structure of the moat between CEs is important for their maintenance, on the basis of the barotropic framework. Moreover, the lack of the unbalanced dynamics proposed by Abarca and Montgomery (2015) may be important for the maintenance of the outer eyewall. To understand the essential mechanism of the maintenance of long-lived CEs, idealized numerical experiments and advanced observations of long-lived CEs are needed in addition to more numerical simulations of real TCs having CEs.

We caution that in our experiment the observed innermost eyewall was not simulated, but the lack of this eyewall has small influence in our hypothesis (see appendix B). Thus, our mechanism is limited on the explanation of the maintenance between the secondary and tertiary eyewalls in the observed Bolaven. The maintenance mechanism of the observed innermost eyewall should be addressed by a future study of Typhoon Bolaven (2012). In addition, our numerical simulation was performed using the one-way nesting method. Note that the influence of the storm-induced circulation on the environmental field in which the storm is embedded is not represented in our numerical simulation. Therefore, our hypothesis cannot explain the influences of the environmental condition on long-lived CEs as reported by Yang et al. (2013). It should be investigated by another future study.

Acknowledgments

The authors thank Dr. S. Kanada and Mr. M. Kato of Nagoya University, Dr. J. D. Keppert of the Centre for Australian Weather and Climate Research, and Dr. K. Ito of the University of the Ryukyus, for their excellent suggestions and comments. The authors thank the editor, Dr. Chun-Chieh Wu, and three anonymous reviewers for their helpful and thoughtful comments and suggestions in the manuscript. Some of the results were obtained by using the K computer at the RIKEN Advanced Institute for Computational Science (Proposal hp120282). The satellite microwave images were made available by the Naval Research Laboratory Marine Meteorology Division in Monterey, California. This study was supported by the “formation of a virtual laboratory for diagnosing the Earth’s climate system (VL)” project, supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT). We used the drawing library of Dennou Common Library (DCL) developed and maintained by GFD Dennou Club (http://www.gfd-dennou.org/library/dcl/) for this study.

APPENDIX A

Derivation of the PV Budget Equation

In the cylindrical coordinate system () of the CReSS model,A1 the governing anelastic equations are as follows:
ea1
ea2
ea3
where is a three-dimensional wind vector, , and is a three-dimensional gradient operator, . The variables , and are pressure, buoyancy, gravitational acceleration, hydrostatic density, potential temperature, diabatic heating, and a three-dimensional external forcing such as friction, respectively. Note that hydrostatic density depends on height z. Taking the rotation of momentum [Eq. (A1)], we obtain the vorticity equation,
ea4
where is absolute vorticity. Dividing Eq. (A4) by leads to
ea5
By using the continuity equation [Eq. (A3)], the first and third terms on the right-hand side of Eq. (A5) can be written as
ea6
However, by taking the gradient of Eq. (A2),
ea7
and calculating · Eq. (A6) · Eq. (A7), we obtain,
ea8
The second and third terms of the above equation vanish because and . Thus, we obtain the PV budget equation,
ea9
Finally, we can rewrite advection to the flux form by using the continuity equation and expressing it in the cylindrical coordinate system, except for friction term, as follows:
ea10
The last term on the right-hand side of Eq. (A10) corresponds to the FRIC term in Eq. (5).

APPENDIX B

Limitations of the Simulation

We show that our proposed mechanism can still be applied to the simulated CEs in spite of the lack of an innermost eyewall, which was observed by the JMA radar, in our simulation. As discussed in section 6, qualitatively, the transverse circulation diagnosed by the Sawyer–Eliassen equation resembles the simulated circulation (see Figs. 10b,c and Figs. 18a,b) around each eyewall. This resemblance suggests that the simulated circulation can be qualitatively explained by the diagnosis. Thus, in this section we discuss the limitations of our simulation based on the Sawyer–Eliassen equation. In particular, we examine whether the existence of an innermost eyewall, as observed by the JMA radar, can influence our proposed mechanism. Thus, we consider an analytical vortex with double eyewalls based on Pendergrass and Willoughby (2009) (Fig. B1a). This vortex exhibits diabatic heating and a wind peak corresponding to each eyewall.B1 Here, Pendergrass and Willoughby (2009) considered a single vortex represented by Eqs. (12a), (12b), and (12c) in their paper. In the present study, the equations that represent tangential wind on annular coordinates () are modified as follows:
eb1
Then,
eb2
where m represents the mth eyewall in a vortex with M eyewalls. The term is determined by Eqs. (2) and (3) in Willoughby et al. (2006). In the double eyewalls (Fig. B1a),
eb3
Fig. B1.
Fig. B1.

(a),(b) Distributions of analytical diabatic heating (color; K h−1) and tangential wind (contour; m s−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 case of a double eyewall, and (right) the case of a triple eyewall.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

Moreover, we consider another vortex with triple eyewalls (Fig. B1b), whose positions are determined by the JMA radar observations (Figs. 4, 5). In the triple eyewalls (Fig. B1b),
eb4

Figures B1c and B1d show the diagnosed transverse circulation for each vortex. Note that no frictional forcings are imposed on the analytical vortices (Fig. B1) in the diagnosis of the transverse circulation, unlike in the case of the simulated typhoon (Fig. 18). Around the outer eyewall, the differences between the two vortices are within about 2 m s−1 (radial wind; Fig. B2) and 0.5 m s−1 (vertical wind) in the lower and middle troposphere. The relative differences in the maximum values of the radial and vertical flows around the outermost eyewall between the double- and triple-eyewall vortices are less than 10% (Fig. B2).

Fig. B2.
Fig. B2.

Difference of radial velocity between double and triple eyewalls. Color and contour denote the relative (%) and absolute differences (m s−1). The relative difference is normalized by the mean radial wind speed (20 m s−1) below the height of 1 km in the outermost eyewall.

Citation: Journal of the Atmospheric Sciences 74, 11; 10.1175/JAS-D-16-0236.1

For the PV budget analysis, the low-level inflow is related to MADVR, MADVZ, MDIAR, and MDIAZ, which are major terms in the PV budget, in the outer eyewall of the simulated Bolaven. Thus, the difference in low-level inflows between the double and triple eyewalls causes fluctuation of the major terms only within 10%. In the moist entropy budget analysis, the low-level inflow directly influences the lateral moisture supply. To check the influence of the innermost eyewall on the budget, at a radius of 60 km of each vortex, the lateral mass flux (; where is air density and is radial wind) was integrated from 0 to 17 km. The relative difference was about 12%. Thus, the difference in low-level inflows leads to a fluctuation of the major term (ADV) of only about 12%. This amplitude of the fluctuation is similar to that of LHSH.

On the basis of the qualitative discussion above, we conclude that the innermost eyewall has only a small effect on our hypothesized CE maintenance mechanism. Thus, we consider that the proposed mechanism is applicable to the outer eyewall, even though the innermost eyewall was not simulated.

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1

In the CReSS model, the lowest level of the vertical grid is at 100-m height. Thus, we cannot trace back to where the parcels were before they appear at the lowest level.

2

In this context, net buoyancy is the sum of thermal buoyancy, water loading, and dynamic pressure gradient force.

A1

Originally the CReSS model used the Cartesian coordinate, but we applied a cylindrical coordinate system for our diagnosis. Thus, the PV budget equation is derived in cylindrical coordinates.

B1

The maxima, widths, and slopes of the diabatic heating are estimated from the simulation result.

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