The Role of Near-Core Convective and Stratiform Heating/Cooling in Tropical Cyclone Structure and Intensity

Guanghua Chen Institute of Atmospheric Physics, Chinese Academy of Science, Beijing, and Key Laboratory of Meteorological Disaster of Ministry of Education, Nanjing University of Information Science and Technology, Nanjing, China

Search for other papers by Guanghua Chen in
Current site
Google Scholar
PubMed
Close
,
Chun-Chieh Wu Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan

Search for other papers by Chun-Chieh Wu in
Current site
Google Scholar
PubMed
Close
, and
Yi-Hsuan Huang Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan

Search for other papers by Yi-Hsuan Huang in
Current site
Google Scholar
PubMed
Close
Full access

Abstract

The effects of convective and stratiform diabatic processes in the near-core region on tropical cyclone (TC) structure and intensity change are examined by artificially modifying the convective and stratiform heating/cooling between 40- and 80-km radii. Sensitivity experiments show that the absence of convective heating in the annulus can weaken TC intensity and decrease the inner-core size. The increased convective heating generates a thick and polygonal eyewall, while the storm intensifies more gently than that in the control run. The removal of stratiform heating can slow down TC intensification with a moderate intensity, whereas the doubling of stratiform heating has little effect on the TC evolution compared to the control run. The halved stratiform cooling facilitates TC rapid intensification and a compact inner-core structure with the spiral rainbands largely suppressed. With the stratiform cooling doubled, the storm terminates intensification and eventually develops a double-eyewall-like structure accompanied by the significantly outward expansion of the inner-core size. The removal of both stratiform heating and cooling generates the strongest storm with the structure and intensity similar to those in the experiment with stratiform cooling halved. When both stratiform heating and cooling are doubled, the storm first decays rapidly, followed by the vertical connection of the updrafts at mid- to upper levels in the near-core region and at lower levels in the collapsed eyewall, which reinvigorates the eyewall convection but with a large outward slope.

© 2018 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: Dr. Guanghua Chen, cgh@mail.iap.ac.cn

Abstract

The effects of convective and stratiform diabatic processes in the near-core region on tropical cyclone (TC) structure and intensity change are examined by artificially modifying the convective and stratiform heating/cooling between 40- and 80-km radii. Sensitivity experiments show that the absence of convective heating in the annulus can weaken TC intensity and decrease the inner-core size. The increased convective heating generates a thick and polygonal eyewall, while the storm intensifies more gently than that in the control run. The removal of stratiform heating can slow down TC intensification with a moderate intensity, whereas the doubling of stratiform heating has little effect on the TC evolution compared to the control run. The halved stratiform cooling facilitates TC rapid intensification and a compact inner-core structure with the spiral rainbands largely suppressed. With the stratiform cooling doubled, the storm terminates intensification and eventually develops a double-eyewall-like structure accompanied by the significantly outward expansion of the inner-core size. The removal of both stratiform heating and cooling generates the strongest storm with the structure and intensity similar to those in the experiment with stratiform cooling halved. When both stratiform heating and cooling are doubled, the storm first decays rapidly, followed by the vertical connection of the updrafts at mid- to upper levels in the near-core region and at lower levels in the collapsed eyewall, which reinvigorates the eyewall convection but with a large outward slope.

© 2018 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: Dr. Guanghua Chen, cgh@mail.iap.ac.cn

1. Introduction

It has been long recognized that, in a tropical cyclone (TC), diabatic heating due to condensation and fusion of water vapor and freezing of cloud or rain droplets can produce positive buoyancy and ascent, while the diabatic cooling due to evaporation of cloud droplets or rainwater, melting of snow or graupel, and sublimation of snow and cloud ice can generate negative buoyancy and reduced ascent or descent (e.g., Yanai 1961; Shapiro and Willoughby 1982; Hack and Schubert 1986; Zhu and Zhang 2006). The complicated cloud microphysical processes play an essential role in the development and maintenance of a TC. Especially, the changes of TC structure and intensity are largely determined by the mutual competition between diabatic heating and cooling due to conversions among different microphysical categories. A great deal of research has documented the influence of diabatic processes associated with the hydrometeor phase change on TC structure and intensity. However, since accurate and direct measurement of diabatic processes in a TC is rather arduous, a variety of numerical simulations have been conducted to examine the roles of diabatic heating in TC structure and intensity.

The effect of diabatic processes within spiral rainbands on TC structure and intensity has drawn more attention. Generally speaking, the spiral rainbands in a TC can be categorized into outer and inner spiral rainbands. The outer spiral rainbands are radially far enough from the storm center such that the vertical structure of the convection within them is relatively unconstrained by the dynamics of the inner-core vortex of a TC (e.g., Wang 2009; Houze 2010). The inner spiral rainbands are generally within radii of about 2–3 times the radius of maximum wind (RMW), where dynamical control of the cyclonic vortex circulation could be dominant. By comparison with loosely organized outer spiral rainbands with embedded active convective cells, the inner spiral rainbands take on smooth lateral boundaries in the rapid filamentation zone (RFZ) immediately outside the eyewall where strain dominates vorticity and the filamentation time is less than the typical overturning time scale of individual convective clouds (e.g., Rozoff et al. 2006; Wang 2008a). It is commonly accepted that active outer-core spiral rainbands and the associated strong downdrafts due to evaporative and melting cooling of raindrops and snow/graupel can be regarded as a hostile factor to TC intensity (e.g., Bender 1997; Powell 1990). Thermodynamically, strong downdrafts beneath the melting level in outer raindbands can bring dry and cool air with low equivalent potential temperature (θe) from the midtroposphere into the inflow boundary layer. The lower-entropy air is advected to the core region by the boundary layer inflow and entrained into the eyewall, thus suppressing eyewall convection and reducing TC intensity. Dynamically, downdrafts may act as a barrier effect on the boundary layer inflow, which is detrimental to both mass and moisture convergence into the eyewall. On the other hand, perturbations to the eyewall by outer spiral rainbands can lead to a breakdown of the eyewall, weakening the eyewall convection and updrafts and thus inhibiting TC intensity (Willoughby et al. 1982; Shapiro and Willoughby 1982; Wang 2002). Based on the perspective of hydrostatic adjustment, Wang (2009) pointed out that the reduction in the surface pressure on the inward side of the diabatic heating in the outer spiral rainbands would decrease the horizontal pressure gradient across the RMW and thus the storm intensity in terms of the maximum wind in the lower troposphere, which, on the other hand, would increase the inner-core size of the storm. On the contrary, the increase in diabatic cooling in outer spiral rainbands tends to maintain both the intensity and inner-core compactness of a storm.

The diabatic heating at different radial locations can exert distinct influences on TC structure and intensity. The balanced response of the secondary circulation indicates that diabatic heating in the eyewall or just inside the RMW, where high inertial stability prevails, is more efficient to enhance the secondary circulation in the inner core. Thus, the TC intensifies faster. When located outside the eyewall or RMW where inertial stability is lower, heating mainly contributes to the enhancement of the outer-core primary circulation and thus increases TC size (e.g., Vigh and Schubert 2009; Pendergrass and Willoughby 2009). Of interest is the role of diabatic processes in inner spiral rainbands in TC structure and intensity change. Recently, based on idealized numerical experiments, Li et al. (2014) investigated how overall TC structure and intensity respond to diabatic processes in the inner-core rainband region by removing the diabatic heating and cooling within the RFZ. They found that the removal of heating (cooling) in the RFZ would reduce (increase) TC intensity, which is opposite to the effects of the diabatic process in outer spiral rainbands where heating (cooling) is generally negative (positive) to TC intensity as documented by Wang (2009). In addition, diabatic heating in the RFZ plays a key role in broadening the inner-core size, whereas diabatic cooling tends to limit the inner-core size.

On the other hand, previous studies have pointed out that precipitation in the eyewall and rainband regions primarily consists of two distinct regimes: convective and stratiform (e.g., Jorgensen 1984; Marks and Houze 1987; Houze 1997). Latent heating profiles in the stratiform region are quite different from those of the convective region. Houze (1997) showed that condensation heating was dominant through the whole depth of the troposphere in convective regions, whereas condensation heating in stratiform regions occurred aloft, and cooling associated with the evaporation and melting occurred below the cloud base that is close to the melting level. Based on the airborne dual-Doppler radar data collected during the Hurricane Rainband and Intensity Change Experiment, Hence and Houze (2008) proposed a conceptual model in which the rainband is convective upwind and through the middle portion of the rainband before becoming stratiform downwind. As the rainband becomes more stratiform, it also becomes wider. A number of studies have been devoted to exploring the evolution of convective and stratiform precipitation during tropical cyclogenesis (e.g., Tory et al. 2006; Raymond and Sessions 2007; Houze et al. 2009; Wang et al. 2010; Xu et al. 2014). For example, Tory et al. (2006) suggested that TC formation may be involved with the transition from a mean stratiform heating profile to a mean convective heating profile, as the low-level divergence associated with stratiform processes tends to spin down the low-level circulation. In a numerical model simulation of pre–Hurricane Felix (2007), Wang et al. (2010) documented that both convective and stratiform precipitation rates increase with time and that the mean convergence profile becomes dominantly convective near the wave pouch center because of the relatively large increase in convective precipitation. Using a three-dimensional, nonhydrostatic, linear model, Moon and Nolan (2010) imposed idealized convective- or stratiform-like rainband heating profile to examine the response of winds to spiral heat source. They discovered the common kinematic features, such as the overturning secondary circulation, descending midlevel radial inflow, and cyclonically accelerated tangential flow on the radially outward side of spiral rainbands. Besides, the stratiform rainbands can perform an essential role in the development of convective ring. In Fang and Zhang (2012), a wavenumber-1 pattern of stratiform rainband precipitation resulting from β shear can generate the evaporative cooling and thus sharpen the low-level equivalent potential temperature (θe) gradient outside the primary eyewall. This frontlike zone outside the eyewall region initiates the burst of convection outside the primary eyewall, triggering the subsequent secondary eyewall formation.

Therefore, different diabatic heating/cooling processes, resulting from multiscale three-dimensional interaction, usually exhibit varied vertical profiles, which can play distinct roles in TC evolution. So far, no distinction has been made to evaluate the respective effect of convective and stratiform heating/cooling in the near-core rainband region on overall TC structure and intensity in a full-physics three-dimensional modeling framework. To insightfully address this issue, we will first partition the near-core rainbands into two regimes and then examine the response of TC structure and intensity to the artificially modified convective and stratiform heating/cooling in the near-core region. The rest of the paper is organized as follows: Section 2 introduces the model configuration and partitioning technique. The verification and sensitivity experimental design is described in section 3. Section 4 discusses the results from the control run and a variety of sensitivity experiments in which the diabatic processes associated with the convective and stratiform precipitation are artificially modified in the near-core region. The conclusions and discussion are summarized in the last section.

2. Model setting and partitioning technique

The model used in this study is the Advanced Research Weather Research and Forecasting (WRF) Model, version 3.6. In the control experiment, the model is initialized with an axisymmetric cyclonic vortex on an f plane centered at 18°N in a quiescent environment over the ocean with a constant sea surface temperature of 29°C. The model contains four domains, all with 274 × 274 grid points and with horizontal grid spacing of 54, 18, 6, and 2 km, respectively. The innermost domain has a fine-enough resolution to capture the major TC inner-core features. The model has 30 vertical levels in the terrain-following sigma coordinate with the model top at 50 hPa. The innermost domain is designed to move with the model TC center such that the model TC is always located in the center of the finest domain. The major model physics parameterizations include the WRF single-moment 6-class microphysics scheme (WSM6) with graupel (Hong et al. 2004), the Yonsei University (YSU) planetary boundary layer scheme (Noh et al. 2003), the Rapid Radiative Transfer Model radiation scheme (Mlawer et al. 1997), and the Dudhia scheme (Dudhia 1989) for longwave and shortwave radiation, respectively. Since the experiment contains no large-scale environmental flows, the outer spiral rainbands are nearly confined within the finest domain. As such, no cumulus parameterization is employed in the domains.

An axisymmetric baroclinic vortex similar to that used by Rotunno and Emanuel (1987), which is in gradient wind balance with the maximum azimuthal surface wind speed of 12 m s−1 at a radius of 108 km, is initialized in the model. The tangential wind decreases gradually with height and becomes zero at about 16 km. Solving the hydrostatic and thermal wind balance equations yields the initial mass and thermodynamic fields associated with the vortex. The environmental thermodynamic profiles are specified as the climatology in the TC peak region (5°–20°N, 130°–170°E) during July–September from 1979 to 2012 based on the Japanese 55-year Reanalysis (Ebita et al. 2011).

To evaluate the role of near-core convective and stratiform heating/cooling in the TC structure and intensity, the partitioning algorithm of Rogers (2010) was incorporated in the WRF source code to identify the convective and stratiform grid points. The partitioning algorithm depends on the horizontal distribution of simulated reflectivity and vertical velocity, using three criteria (Steiner et al. 1995): intensity of reflectivity, peakedness (excess of reflectivity over a background value), and area within an intensity-dependent radius around a convective grid. At each time step of integration, the modified WRF code can automatically identify whether each grid point is categorized into convective, stratiform, or other precipitation type.

3. Verification and sensitivity experimental design

After a spinup period of 62 h in the control run (CTL), the simulated storm achieves a structure similar to real TCs with the sea level pressure of 956 hPa and maximum surface tangential wind of 49 m s−1. Figure 1a shows the plan view of simulated radar reflectivity at the height of 0.5 km at 62 h of integration, which features an echo-free elliptic eye that is surrounded by a nearly closed eyewall with high reflectivity. Connecting to the outer edge of the eyewall, the well-organized inner rainbands spiral outward within radii of 40 and 80 km. For the convenience of terminology, the annular region between radii of 40 and 80 km is referred to as the near-core region in this study. Farther radially outward, the outer spiral rainbands are more loosely organized, characterized by the numerous embedded convective cells. As displayed in Fig. 1b, it is clear that the eyewall region between 20 and 40 km is dominated by convective precipitation. In the near-core region, the radially narrow and azimuthally elongated convective precipitation related to the inner spiral rainbands is embedded within the stratiform precipitation regions. In contrast, more isolated and scattered convective precipitation is observed in the upwind and middle sectors of the outer spiral rainband outside 80 km, while the stratiform precipitation is predominant in the northeastern downwind region of it, in good agreement with the findings in previous studies (e.g., Hence and Houze 2008; Moon and Nolan 2010). In terms of the azimuthal-mean structure (Figs. 1c,d), the near-surface maximum diabatic heating is located at about the radius of 20 km slightly inside the maximum azimuthal-mean tangential wind, implying that the simulated storm would intensify further because of the effective conversion of diabatic heating to kinetic energy for a TC with convective bursts located inside the RMW (e.g., Vigh and Schubert 2009; Rogers et al. 2013). The vertical velocity is collocated with the diabatic heating with a radially outward slope with height, extending from the surface to the upper troposphere. A salient feature is that the secondary maximum diabatic heating and upward motion can be seen outside the radius of 80 km in the mid- to upper troposphere, indicative of the active outer rainbands. Corresponding to the condensation heating release in the eyewall and adiabatic descent in the eye at the mid- to upper levels, the azimuthal-mean θe displays the localized maxima. Outside the eyewall, the low-entropy air pools in the mid- to lower troposphere because of the evaporative cooling of rain and cloud droplets associated with the downdrafts from the spiral rainbands.

Fig. 1.
Fig. 1.

(a) Plan view of radar reflectivity at 0.5 km (dBZ), (b) the distribution of other (blue), stratiform (green), and convective (red) precipitation, (c) the radius–height cross section of azimuthal-mean diabatic heating (color shaded; K s−1) and tangential wind (contours; m s−1), and (d) the radius–height cross section of azimuthal-mean vertical velocity (color shaded; m s−1) and equivalent potential temperature (contours; K) at 62 h of integration in CTL. The range circles in (a),(b) are at every 40-km radius from the TC center.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

The partitioning algorithm is validated to effectively categorize the different precipitation regimes in the simulation (see appendix A). To examine the effect of distinct heating/cooling regimes in the near-core region on TC structure and intensity change, the partitioning algorithm was applied in the annulus between radii of 40 and 80 km, within which most of the inner rainbands are embedded at 62 h of CTL. However, the caveat should be noted that because the TC structure and intensity both evolve with time in the following sensitivity experiments, the so-called near-core region fixed between 40 and 80 km does not necessarily represent the region of inner rainband or RFZ. Nevertheless, the results cannot qualitatively, but may quantitatively, alter the effect of near-core convective and stratiform diabatic process on TC structure and intensity change. Taking into consideration the distinct vertical heating profiles as displayed in Fig. A1b, the four sets of sensitivity experiments, each set comprising two comparative runs, were initialized at 62 h of CTL as listed in Table 1. In the first set, the near-core convective heating in the microphysics scheme was removed and increased by 50%, which are referred to as CH0 and CH150, respectively. In the second set, a similar procedure was performed to remove and double the stratiform heating in SH0 and SH200. In the third set, the stratiform cooling in the near-core region was reduced by 50% and doubled in SC50 and SC200. To assess the competing effects of stratiform heating and cooling, both the stratiform heating and cooling were removed and doubled simultaneously in SHC0 and SHC200 in the fourth set. To diminish the edge effect due to the abrupt change near the lateral boundary of the modification region, the linear transition zones between radii of 40–50 and 70–80 km were set when modifying the diabatic heating/cooling. Considering the response of inner-core size and surface pressure to the convective heating and stratiform cooling is significant in the preliminary experiments, the convective heating was only increased by 50% in CH150 and the stratiform cooling reduced by 50% in SC50. Besides, other supplementary experiments with the increase and decrease by 25% in the convective and stratiform heating/cooling were also carried out, in which the results are qualitatively similar to the conclusions in this study except that the TC structure and intensity vary to a relatively lesser extent as opposed to the counterparts in the present sensitivity experiments.

Table 1.

Summary of the experimental design.

Table 1.

4. Results

a. Intensity comparison and structural evolution in CTL

Figure 2a displays the intensity evolution of the simulated TCs in terms of the minimum sea level pressure (MSLP). Overall, the storms can be grouped into three categories according to their ultimate intensity and distinct intensity change. In the first category, the original continuous intensification of the storm halts shortly, even followed by a slow weakening in CH0, SC200, and SHC200. Specifically, the simulated TC in CH0 terminates rapid intensification and experiences a persistent weakening from 93 to 111 h with an MSLP of 954 hPa at the end of the simulation, which is weakest in the final intensity among all the experiments. The storm in SC200 sustains a moderate intensification before 78 h, followed by a slow weakening with a final intensity of 949 hPa. The TC in SHC200 exhibits the strongest sea surface pressure filling before 90 h, and afterward, it reintensifies at a slow rate. In the second category, the TC in SH0 has a rapid intensification before 75 h, and then the intensification quickly slows down with a moderate final MSLP of 921 hPa. In the third category, all the TCs in CTL, CH150, SH200, SC50, and SHC0 achieve relatively strong final intensity. The TC in CTL has an averaged deepening rate of 1.6 Pa h−1 until 93 h followed by an oscillatory intensification with an ultimate intensity of 900 hPa. The storm in CH150 first exhibits relatively slow intensification, followed by a rapid intensification between 99 and 108 h with a final MSLP of 894 hPa. The TC in SH200 has also a slow intensification before 75 h, and afterward, its intensity evolves similar to that in CTL. By comparison, the TCs in SC50 and SHC0 have a similar intensity change, both experiencing the drastic intensification and achieving the ultimate MSLP of 885 and 881 hPa, respectively.

Fig. 2.
Fig. 2.

Time evolution of the simulated (a) MSLP and (b) radius of the azimuthal-mean hurricane-force surface wind (33 m s−1) in all experiments.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

For convenience to compare the results in the sensitivity experiments with that in CTL, the structural evolution in CTL is first presented. As shown in Fig. 3a, the lower-level θe inside the RMW maintains a large value through the whole integration, while being low outside 40 km between 66 and 72 h because of the evaporative cooling related to the downdrafts from the active spiral rainbands outside the eyewall (Fig. 4). Correspondingly, the stratiform grids between radii of 40 and 80 km display a relatively larger areal fraction compared to the convective grids around 70 h (Fig. 5a), indicating that this region is dominated by stratiform precipitation. As the storm intensifies continuously, the stratiform spiral rainbands outside the eyewall begin to fade, and the convective ring in the eyewall becomes vigorous (Fig. 4), accompanied by the dominance of the areal percentage of convective grids over that of stratiform grids within the near-core region after 75 h (Fig. 5a). In addition, accompanied by the enhanced eyewall convective updrafts, the midlevel inflows immediately outside the eyewall split into two branches: one ascends to the upper levels along with the eyewall updrafts, and the other descends to the top of the inflow boundary layer, resulting in the azimuthal-mean 3-km descending motion emerging just outside the eyewall after 92 h (Fig. 3b). To further substantiate the thermodynamic structural evolution, Fig. 6 depicts the θe anomaly in the near-core region. Consistent with the θe evolution shown in Fig. 3a, the negative θe anomaly exists beneath 5-km height around 70 h. However, the θe anomaly in the inflow boundary layer transits to the positive value as the spiral rainbands weaken after 75 h. Although the negative θe anomaly between the heights of 1.5 and 6 km gradually increases and intermittently penetrates downward, the air with positive θe anomaly occupies in the inflow boundary layer, accounting for the storm oscillatory intensification in CTL after 87 h (Fig. 2a).

Fig. 3.
Fig. 3.

Radius–time Hovmöller diagram of azimuthal-mean (a) θe (shaded; K) and tangential wind (contour; m s−1) at 0.5 km and (b) vertical velocity at 3 km (shaded; m s−1) and radial wind at 0.5 km (contour; m s−1) in CTL.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

Fig. 4.
Fig. 4.

Plan view of the simulated composite reflectivity (dBZ) at 3-h intervals from 64 to 109 h in CTL. The composite reflectivity includes all vertical levels from the surface up to 10 km. The black range circles are placed at every 40-km radius from the storm center.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

Fig. 5.
Fig. 5.

Time evolution of the areal fraction of convective (solid black; %) and stratiform precipitation (dashed black; %) within radii of 40 and 80 km in (a) CTL, (b) CH0, (c) CH150, (d) SH0, (e) SH200, (f) SC50, (g) SC200, (h) SHC0, and (i) SHC200. For convenience to compare with TC intensity and structure, the time evolution of the MSLP (solid red; hPa) and the radius of the azimuthal-mean hurricane-force surface wind (solid blue; km), as displayed in Fig. 2, are also displayed, respectively, using the right y axis.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

Fig. 6.
Fig. 6.

Time–height cross section of θe anomaly (colored shading; K) with respect to that at 62 h of simulation time averaged within radii of 40 and 80 km in (a) CTL, (b) CH0, (c) CH150, (d) SH0, (e) SH200, (f) SC50, (g) SC200, (h) SHC0, and (i) SHC200.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

An important parameter to measure structural evolution is TC inner-core size, which is closely related to various factors such as environmental humidity, synoptic flow patterns, inner-core diabatic process, and initial vortex size (e.g., Hill and Lackmann 2009; Li et al. 2015; Liu and Chan 2002; Li et al. 2015; Xu and Wang 2010). In this study, the size of a TC is examined in terms of near-surface hurricane-force wind (33 m s−1). As shown in Fig. 2b, the storm inner-core size in CTL increases by approximately 20 km from 62 to 81 h, followed by a slow expansion until 100 h and then a steady radius of near-surface hurricane-force wind at 74 km. Both the azimuthal-mean near-surface tangential and radial winds also display a similar evolution (Figs. 3a,b). By the argument of azimuthal-mean tangential momentum budget, the inward advection of absolute vertical vorticity by the radial inflow would facilitate the outward expansion of positive azimuthal-mean tangential wind tendency, responsible for the increase in the storm inner-core size in CTL.

b. Results in CH0 and CH150

In CH0 with the removal of convective heating, the storm immediately halts intensification and weakens steadily after 93 h (Fig. 2a). The composite simulated radar reflectivity as shown in Figs. 7a–h displays a small-size eye surrounded by the eyewall convective ring that attenuates with time. Radially outward exists a nearly cloud-free region within radii of 40 and 80 km. Farther outside 80 km, there are several outer spiral rainbands. Correspondingly, the near-core negative θe anomaly extends from the surface through 6 km (Fig. 6b), and the θe in the inflow boundary layer outside the eyewall is remarkably lowered (Fig. 8a), which efficiently cuts off the inward supply of high-entropy air and thus weakens the eyewall convection and the storm intensity. Besides, the areal fraction of convective grids between radii of 40 and 80 km only sustains around 30% (Fig. 5b). Moreover, of interest is that the percentage of stratiform grids has an apparent decreasing tendency with less than 10% at the end of integration, implying that the maintenance of the stratiform component largely depends on the well-organized parent convective component, in good agreement with previous studies that revealed that less-organized scattered convection limits stratiform precipitation coverage, while the mature mesoscale convective system is accompanied by extensive stratiform precipitation area (e.g., Rickenbach and Rutledge 1998; Houze 2004). The suppression of both convective and stratiform heating leaves a moat-like region within 40 and 80 km in terms of vertical velocity (Fig. 9a) and diabatic heating (Figs. 10a,b), flanked by the inner and outer convective rings and forming a structure like concentric eyewalls.

Fig. 7.
Fig. 7.

Plan view of the simulated composite (a)–(h) reflectivity (dBZ) and (i)–(p) PV at 8-h intervals from 64 to 120 h in CH0. The composite reflectivity and PV include all vertical levels from the surface up to 10 km. The black range circles are placed at every 40-km radius from the storm center.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

Fig. 8.
Fig. 8.

As in Fig. 3a, but in (a) CH0, (b) CH150, (c) SH0, (d) SH200, (e) SC50, (f) SC200, (g) SHC0, and (h) SHC200.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

Fig. 9.
Fig. 9.

As in Fig. 3b, but in (a) CH0, (b) CH150, (c) SH0, (d) SH200, (e) SC50, (f) SC200, (g) SHC0, and (h) SHC200.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

Fig. 10.
Fig. 10.

Radius–height cross sections of the azimuthal-mean diabatic heating (shaded; K s−1), tangential wind (contours; m s−1), and secondary circulation (arrows; m s−1) with the vertical velocity multiplied by a factor of 6 in (a),(b) CH0 and (c),(d) CH150 averaged over (a),(c) 66–78 and (b),(d) 96–108 h. The contours of 35 m s−1 in the azimuthal-mean tangential wind are bold.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

As the storm weakens and the eyewall convection fades, the TC inner-core size shrinks drastically with the smallest radius of hurricane-force surface wind speed among all the experiments (Fig. 2b). In addition, the potential vorticity (PV) evolution in Figs. 7i–p features an elliptic-shape PV structure rotating cyclonically around the storm center before 72 h. Thereafter, the PV structure becomes more symmetric, with an annular maximum PV inside the RMW and a low-PV core in the eye. As the storm intensity weakens, the radial gradient of PV begins to lessen, which is attributed to the suppressed convective heating ring and the PV mixing between the eye and the eyewall as described in the observational study by Kossin and Eastin (2001) and the numerical study by Wu et al. (2016).

In contrast to CH0, with the convective heating increased by 50% within the near-core region in the CH150, the striking feature is that the storm has a relatively slow intensification rate during the early stage, and even the intensity levels off during 66–78 h (Fig. 2a). On one hand, the relatively low entropy in the boundary layer during this period is contributive to the leveling off of intensity (Fig. 8a). On the other hand, the enhanced convective heating imposed in the near-core region would reduce the surface pressure between 40 and 80 km and thus flatten the horizontal pressure gradient across the RMW (not shown), which causes a smaller increase of the maximum tangential wind in contrast to that in CTL (cf. Fig. 3a and Fig. 8b). As discussed by Wang (2009), this hydrostatic adjustment is responsible for the TC slow intensification before 78 h. Afterward, in response to the increased convective heating outside the eyewall, the TC inner-core size in terms of the azimuthal-mean tangential wind quickly expands outward (Fig. 2b). As a result, accompanied by the high inertial stability building up outside the original eyewall region where the maximum convective heating is located, the conversion ratio of diabatic heating to kinetic energy can be effectively increased, thus warming the atmospheric column and lowering the surface pressure (Schubert and Hack 1982; Hack and Schubert 1986), leading to the rapid intensification during the late stage of simulation.

In addition, the radial extent of upward motion and diabatic heating is broadened with time, forming a thick eyewall (Figs. 9b, 10c,d, and 11a–h). Owing to the outward-tilted eyewall, the convective heating at the mid- to upper level within radii of 40 and 80 km is more pronounced, which induces the strengthening of midlevel inflow around the height of 8 km (Figs. 10c,d). During the period of rapid intensification, one of the branches associated with the midlevel inflow descends outside the eyewall (Figs. 9b and 10d). Although the descent-induced low-entropy air can penetrate intermittently downward into the inflow boundary layer outside the eyewall (Figs. 6c and 8b), the surface heat flux related to the increased wind speed in response to the enhanced convective heating can facilitate the recovery of entropy by extracting the energy from the underlying ocean. Moreover, the maximum θe anomaly with larger than 8°C extends downward from approximate 12-km height through 8 km starting from 84 h (Fig. 6c), positively contributing to the rapid intensification during the late stage of simulation. After 111 h, the low-entropy air at the lower level induced by the descending motion associated with the midtropospheric inflow achieves the peak so as to offset the intensification, which nearly levels off the storm intensity (Fig. 2a). Accompanied by the broadening and outward expansion of the eyewall, the coverage percentage of convective grids has a significant increase, accounting for about 90% at the end of simulation, while that of stratiform grids has a gradual decrease (Fig. 5c).

Fig. 11.
Fig. 11.

As in Fig. 7, but for sensitivity experiment CH150.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

In contrast to the compact and axisymmetric and compact PV annulus in CH0, the PV ring in CH150 forms an irregular and large-sized eyewall structure (Figs. 11i–p), indicative of the barotropic instability. When the barotropic instability grows to finite amplitude, the vorticity in the eyewall region pools into discrete areas, creating the appearance of a polygonal eyewall as displayed in Fig. 11 (Schubert et al. 1999). On the other hand, the resultant asymmetric mixing in the eye and the eyewall may have a negative impact on the storm intensity, leading to a decrease of maximum wind speed (e.g., Nolan and Montgomery 2002; Yang et al. 2007), which may be also responsible for the slow intensification during the early stage in CH150. However, as a major PV source, the enhanced convective heating in the near-core region can sustain a large high-PV annulus, compensating the redistribution of PV due to the advection or mixing away from the eyewall, which is in agreement with previous studies (e.g., Wu et al. 2016).

c. Results in SH0 and SH200

When removing the stratiform heating in the near-core region in SH0, the falling of the storm MSLP is still pronounced in the first 12 h and afterward slows down with a moderate final intensity. Meanwhile, the radius of hurricane-force wind changes little between 72 and 90 h, followed by a slow increase (Fig. 2b). The comparison of results in CH0 and SH0 implies that the convective heating in the near-core region plays a more important role in TC intensification and expansion of inner-core size as opposed to the stratiform heating. In terms of the coverage fraction as shown in Fig. 5d, the time-mean areal percentage of convective grids between 40 and 80 km exceeds 30% that still support a certain percentage of stratiform precipitation. Correspondingly, there is still discernible lower-tropospheric upward motion outside the eyewall, especially after 90 h (Fig. 9c), which accounts for the slow outward expansion of inner-core size during the late stage, quite different from the absence of near-core ascent in CH0 (cf. Figs. 9a,c). Although the negative θe anomaly in SH0 dominates at the mid- to lower level outside the eyewall, its magnitude and areal extent are much smaller by comparison with those in CH0 (cf. Figs. 6b,d and Figs. 8a,c). The radius–height cross sections in SH0 show the similar vertical structures during the early and late stages with a compact convective eyewall and noticeable diabatic cooling at the mid- to upper level outside it (Figs. 12a,b), suggesting that the azimuthal-mean structure in SH0 evolves comparatively steadily. The storm only experiences a slow intensification after 72 h, as shown in Fig. 2a.

Fig. 12.
Fig. 12.

As in Fig. 10, but in (a),(b) SH0 and (c),(d) SH200.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

The intensity evolution in the simulated storm in SH200 bears a resemblance to that in CTL but with a relatively slow intensification at the early stage. Similar to that in CH150 in the above subsection, the inner-core size in SH200 also expands outwards because of the stratiform heating, though to a lesser degree (Fig. 2b). However, unlike the enhanced deep-tropospheric convective heating as in CH150, the diabatic heating in SH200 concentrates at the mid- to upper level because of the vertical dipole structure. As a result, there exists a secondary heating at the height of 10 km near the radius of 60 km, which is more effective in inducing the midtropospheric inflow (Fig. 12c), consistent with the results in Fudeyasu and Wang (2011). With the outward expansion of the inner-core size, the eyewall is radially broadened, though its width and strength are apparently smaller than those in CH150 because of the different magnitudes and vertical depths of diabatic heating (cf. Figs. 10d and 12d).

Especially after 90 h, the structural evolution of the simulated TC in SH200 shares similarity with that in CTL in terms of intensity (Fig. 2a), inner-core size (Fig. 2b), azimuthal-mean structure (cf. Fig. 3a and Fig. 8d; Fig. 3b and Fig. 9d), areal coverage of convective and stratiform grids (Figs. 5a,e), and θe anomaly in the near-core region (Figs. 6a,e). Because of the intensification of the storm and the increase of the inner-core size, the convective region associated with the eyewall expands outward beyond 40 km. Meanwhile, the spiral rainbands outside the eyewall fade away gradually, analogous to those in CTL as shown in Fig. 4. Consequently, the areal coverage of convective precipitation is largely dominant over that of stratiform precipitation in the near-core region after 82 h, such that the doubled near-core stratiform heating has little effect on the storm evolution, producing the structural feature and intensity change similar to those in CTL after the early adjustment.

d. Results in SC50 and SC200

The diabatic cooling from evaporation of cloud droplets and rainwater as well as melting of snow and graupel mainly occurs in the mid- to lower troposphere in the stratiform precipitation region. Naturally, the reduced stratiform cooling in SC50 can elevate the θe in the mid- to lower troposphere. Owing to the reduction of low-entropy air penetrating into the inflow boundary layer and the strong air–sea entropy exchange associated with the storm intensification, the inflow boundary layer in the near-core region is nearly occupied by the high θe through the integration (Figs. 6f and 8e), forming a relatively thick layer with positive θe anomaly from the surface to about 2 km after 75 h. As the high-entropy air spirals inward in the eyewall region, the eyewall buoyancy and convection is enhanced, and thus the TC intensifies rapidly, which is consistent with previous studies (e.g., Zhu and Zhang 2006; Sawada and Iwasaki 2010; Li et al. 2014). The radius of hurricane-force surface wind in SC50 broadens quickly during the first 12 h as the MSLP drops drastically, followed by a slow outward expansion from 76 to 120 h (Fig. 2b). Although the radius of hurricane-force surface wind in SC50 evolves similar to that in SH200, the simulated storm develops a more compact inner-core structure with the spiral rainbands outside the eyewall suppressed largely at the late stage of simulation (Fig. 13). The azimuthal-mean radius–height cross section shows that the simulated storm during the early stage is characterized by positive diabatic heating outside the eyewall because of the vigorous rainband convection and decreased stratiform cooling (Fig. 14a). After 96 h, the diabatic heating gradually transits to the diabatic cooling outside the eyewall above the inflow boundary layer, which likely results from the enhanced melting of ice parcels and subsequent evaporation of raindrops because of the strengthened eyewall convection (Figs. 9e and 14b). This deep-tropospheric compensating subsidence can suppress the convection activity outside the eyewall, leading to a decreasing tendency in the areal coverage of convective and stratiform precipitation at the late stage, as compared to those in CH150 and SH200 (cf. Figs. 5c,e,f). Meanwhile, the negative θe anomaly at the lower level above the inflow boundary layer becomes enhanced during the late stage (Fig. 6f). These halt the storm rapid intensification after 100 h (Fig. 2a).

Fig. 13.
Fig. 13.

As in Fig. 4, but for the sensitivity experiment SC50.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

Fig. 14.
Fig. 14.

As in Fig. 10, but for the sensitivity experiments (a),(b) SC50 and (c),(d) SC200 averaged over (a),(c) 66–78 and (b),(d) 108–120 h.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

The simulated storm in SC200 can shortly cease the rapid intensification, subsequently experiences a weakening, and then sustains a nearly stable intensity after 84 h (Fig. 2a). As expected, the doubled stratiform cooling generates the low θe in the lower troposphere in the near-core region (Figs. 6g and 8f), thus prohibiting the convection in the eyewall region because of the inward transport of low-entropy air and weakening the storm intensity. In terms of the azimuthal-mean fields, Fig. 9f shows that the radial extent of eyewall updraft becomes narrow with time. One intriguing feature is that a pronounced updraft region is observed to emerge just outside 80 km and then contract inward starting from about 96 h, which bears some resemblance to the eyewall replacement cycle as documented in a number of previous studies (e.g., Willoughby et al. 1982; Terwey and Montgomery 2008; Huang et al. 2012; Zhu and Zhu 2014). However, careful comparison with typical concentric eyewalls discovers that no evident moat with downdrafts occurs between the inner and outer convective updrafts in this case (Fig. 9f), and moreover, the outer convective annulus does not form one closed convective ring, which may be attributed to the lack of sufficient filamentation process due to relatively weak shear deformation. The detailed dynamics of the formation of the outer convective band and subsequent eyewall replacement cycle is beyond the scope of the current study; it has been discussed in detail in a follow-up work of Chen (2017, manuscript submitted to J. Atmos. Sci.), who examined the effect of increased low-level near-core diabatic cooling on the secondary eyewall formation and replacement. In response to the outer convective heating, the radius of hurricane-force surface wind rapidly expands outward after 102 h, prompting the increase of the inner-core size (Figs. 2b and 8f).

The azimuthal-mean cross sections in Figs. 14c,d show that, during the early stage averaged between 66 and 78 h, the maximum eyewall diabatic heating and tangential wind are centered at the radius of 20 km, and the low-tropospheric diabatic cooling occurs between radii of 40 and 80 km. In contrast, during the late stage averaged from 108 to 120 h, the eyewall convection is significantly reduced, together with the decreased radial width of eyewall updrafts and the lowered height of large tangential winds in the eyewall region (Figs. 14c,d). Besides, the original lower-tropospheric diabatic cooling between 40- and 80-km radii is replaced by the diabatic heating, concurrent with a secondary diabatic heating maximum just outside the radius of 60 km. In addition, the lower-tropospheric tangential wind (as denoted by bold lines in Figs. 14c,d) has a notable outward penetration in response to the outer secondary heating. A number of previous studies have confirmed that the secondary eyewall formation is accompanied by an outward expansion of outer wind fields and the inertial stability changes. The wind field expansion usually contains a distinct secondary local maximum, which leads to a secondary frictional updraft maximum through the boundary layer dynamics. The coupling of upward motion at the lower and middle to upper levels outside the primary eyewall is potentially favorable for the secondary eyewall formation (e.g., Huang et al. 2012; Rozoff et al. 2012; Zhang et al. 2017).

To further depict the unique structural evolution in SC200, Fig. 15 demonstrates the azimuthal-mean cross sections of vertical motion, tangential wind, and secondary circulation at 3-h intervals. It is evident that the descending motion related to the doubled stratiform cooling dominates the mid- to lower troposphere in the near-core region from 73 to 79 h (Figs. 15a–c). Immediately outside 80 km, the upward motion is robust as well, which is centered in the upper troposphere and extends downward through the lower level. The near-surface divergence in the near-core region is associated with the lower-level descending motion resulting from the lower-entropy air, which can decelerate the boundary inflows on its radially outward side, favorable for the lower-tropospheric convergence and the ascending motion just outside 80 km and thus facilitating the downward development of outer rainbands. As the outer convective rainband spirals inward intermittently, the area of descending motion in the near-core region begins to shrink (Figs. 15d–k). Especially after 106 h, the outer convective updrafts reinvigorate and contract inward, forming a double-eyewall-like structure (Figs. 15l–p). Similarly, as depicted in Fig. 16, the simulated radar reflectivity shows that the inner rainband is suppressed because of the enhanced stratiform cooling around 73 h, and the outer convective ring resides at a large radius. Afterward, the near-core region is perturbed by scattered deep convective vortices emanating from the outer convective ring. Starting from 109 h, the deep convective cells become compact and are organized into an inward-contracting secondary convective band, accompanied by the weakening and even breakdown of the inner primary eyewall, analogous to the secondary eyewall replacement.

Fig. 15.
Fig. 15.

Radius–height cross sections of the azimuthal-mean vertical velocity (color shaded; m s−1), tangential wind (contours; m s−1), and secondary circulation (arrows; m s−1) with the vertical velocity multiplied by a factor of 6 at 3-h intervals from 73 to 118 h.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

Fig. 16.
Fig. 16.

As in Fig. 4, but for the sensitivity experiment SC200 from 73 to 118 h.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

e. Results in SHC0 and SHC200

To assess the competing effect of stratiform heating and cooling on TC intensity and structure, the experiments with both the stratiform heating and cooling doubled and removed were conducted in SHC0 and SHC200, respectively. Comparison of the results between SHC0 and SC50 shows that the intensity and structure almost share similar characteristics (e.g., Figs. 2, 6f,h, 8e,g, and 9e,g). One noticeable discrepancy is that, during the early stage of simulation, the storm in SHC0 has a more rapid intensification and a smaller radius of hurricane-force surface wind in contrast to that in SC50 (Figs. 2a,b). For example, at 75 h of simulation, the MSLP and the radius of hurricane-force surface wind are 918 hPa and 59 km in SHC0, respectively, and 928 hPa and 67 km in SC50. The comparison in Fig. 14a and Fig. 17a shows that there exists an enhanced mid- to upper heating immediately outside 40 km in SC50, which is responsible for the relatively larger inner-core size and slower intensification in SC50 than in SHC0 during the early stage of simulation, as interpreted in CH150 and SH200 in the previous subsections. As the storms intensify, the intensity and inner-core size in both experiments almost keep the same pace (Fig. 2), as well as the areal fractions of convective and stratiform grids in the near-core region after 87 h (cf. Figs. 5f,h). During the late stage of simulation, the resemblance in intensity between SC50 and SHC0 implies that the absence of stratiform heating in SHC0 is negative to the rapid intensification resulting from the complete removal of stratiform cooling.

Fig. 17.
Fig. 17.

As in Fig. 10, but for the sensitivity experiments (a),(b) SHC0 and (c),(d) SHC200.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

With both the stratiform heating and cooling doubled in SHC200, the storm achieves on a whole the weakest intensity among all the experiments. The simulated storm in SHC200 has an evident weakening before 90 h, but afterward, it reintensifies slightly until the end of the simulation (Fig. 2a). Correspondingly, the low-entropy air occupies at the height below 6 km between 40- and 80-km radii in SHC200 (Figs. 6i and 8h). One intriguing feature is that the inner-core size in SHC200 experiences a drastic increase especially after 90 h, with the radius of hurricane-force surface wind expanding from 55 km at 90 h to 83 km at 120 h (Fig. 2b). In the meanwhile, the simulated TC generates a large-sized eye surrounded by a noticeably outward-tilted and wide eyewall (Fig. 17d). As shown in Fig. 9h, the radius of maximum 3-km vertical velocity is nearly doubled from 62 to 120 h. Similarly, the simulated radar reflectivity demonstrates that the diameter of cloud-free eye has a pronounced increase with time (Fig. 18).

Fig. 18.
Fig. 18.

As in Fig. 4, but for the sensitivity experiment SHC200 from 67 to 112 h.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

The following questions naturally arise as to how and why the simulated storm can form a large-sized eye with large eyewall slope. As shown in Figs. 17c,d, the azimuthal-mean structures between the early and late stages of simulation exhibit quite distinct features. Over 66–78 h of simulation, the eyewall updrafts are weakened greatly. Because of the doubled stratiform heating and cooling in the near-core region, the upper-level diabatic heating stretches outward from the top of the eyewall to about the radius of 80 km, and the diabatic cooling appears beneath. Meanwhile, the contours of azimuthal-mean tangential wind with less than 35 m s−1 outside the radius of 40 km slope outward with height in response to the enhanced upper-level stratiform heating and lower-level stratiform cooling in the near-core region (Fig. 17c). During the late stage of simulation, the eyewall updrafts are observed to be reinvigorated, and the azimuthal-mean tangential wind apparently expands and tilts outward with height (Fig. 17d), forming a large-sized eye and wide eyewall. Accordingly, the convective precipitation is predominant between 40- and 80-km radii, leading to the dominance of convective areal coverage over the stratiform one (Fig. 5i). The evolution described above can be clarified from the radius–height cross section of the azimuthal-mean tangential wind and vertical motion at 1-h intervals from 84 to 99 h (Fig. 19), which covers the period of rapid expansion of inner-core size as displayed in Fig. 2b. Because of the doubled lower-level stratiform cooling and upper-level stratiform heating in the near-core region, the striking feature is that the large expansion of inner-core size occurs at the mid- to upper level from 84 to 88 h (Figs. 19a–e), namely, forming a twofold structure in terms of the azimuthal-mean tangential wind. Especially at 84 and 85 h, there are two maxima of azimuthal-mean tangential wind, one being located within the inflow boundary layer at a radius of 25 km, the other near 6-km height at a radius of 60 km. Meanwhile, the eyewall convective updrafts are largely decreased, and thus, the storm intensity is weakened before 90 h owing to the radially inward intrusion of low-entropy air. After 90 h, the upper-level updrafts in the near-core region begin to strengthen and penetrate downward and inward and start to be connected to the lower-level updrafts in the collapsed eyewall, reinvigorating the eyewall convection (Figs. 19g–p). Meanwhile, the original lower-level downdrafts related to the doubled stratiform cooling in the near-core region are lessened and expelled outward. Eventually, the updrafts in the lower-level eyewall region are robustly connected to those in the mid- to upper-level near-core region, rebuilding a well-organized eyewall with a largely outward slope with height, especially at 99 h. With the reinvigoration of the collapsed eyewall, the simulated storm has a discernible intensification after 90 h, as exhibited in Fig. 2a. On the other hand, it is the large outward slope in the eyewall convection that induces the rapid expansion of inner-core size, forming a large-sized eye in SHC200, because the response of the low-level tangential wind to heating in the largely outward-tilted eyewall is an increase outside the RMW and a decrease near and inside the RMW, which can inhibit an inward contraction and favor an expansion of the RMW. This result is also consistent with that documented by Wang (2008b), who studied the structure and formation of an annular hurricane that has a quasi-axisymmetric structure with large eye and wide eyewall.

Fig. 19.
Fig. 19.

As in Fig. 15, but for the sensitivity experiment SHC200 at 1-h intervals from 84 to 99 h.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

5. Conclusions and discussion

The mixture of convective and stratiform precipitation features the near-core region immediately outside the eyewall. This study makes an attempt to evaluate the relative contribution of convective heating and stratiform heating/cooling between radii of 40 and 80 km to the structure and intensity change of a TC in a quiescent environment. Given that convective precipitation is dominated by deep-tropospheric heating, while stratiform precipitation is characterized by mid- to upper-level heating and lower-level cooling, the four sets of sensitivity experiments initialized at 62 h of CTL, each consisting of two runs, were conducted to assess the effects of increased and decreased convective heating, stratiform heating, stratiform cooling, and both stratiform heating and cooling, respectively.

The results show that the removal of convective heating within the near-core region in CH0 can effectively eliminate the inner rainband activity. Together with the decrease in the areal coverage of stratiform precipitation, a moat-like zone forms outside the eyewall where the low-entropy air occupies the lower troposphere that is hostile to the inward transport of high-entropy air. As a result, the eyewall updrafts are significantly suppressed, the inner-core size is contracted, and the simulated TC decays and transits to a PV monopolar structure. In contrast, in CH150 with the convective heating in the near-core region increased by 50%, the storm first intensifies at a relatively slow rate because of the decreased tangential wind in contrast to that in CTL, which results from the relatively flattened horizontal pressure gradient across the RMW in light of the hydrostatic adjustment. Later, in response to the increased convective heating outside the eyewall, the TC inner-core size quickly expands outward in such a way that the high inertial stability is built close to the maximum convective heating. Hence, the conversion ratio of the diabatic heating to the kinetic energy can be effectively increased, responsible for the rapid intensification during the late stage of simulation. Meanwhile, the dynamically unstable PV ring promotes the PV mixing between the eyewall and the eye and the formation of the polygonal eyewall structure in CH150.

In SH0 with the removal of stratiform heating in the near-core region, the simulated storm maintains a slow intensification with a moderate final intensity. Unlike the moat-like structure outside the eyewall in CH0, there still exists a certain number of lower-level updrafts associated with convective precipitation between 40 and 80 km, accounting for the slow outward expansion of inner-core size. Moreover, the magnitude and areal coverage of the negative θe anomaly at the mid- to lower level outside the eyewall in SH0 are quite smaller than those in CH0, indicating that the stratiform heating in the near-core region plays a secondary role in TC structure and intensity change. In SH200 with the stratiform heating doubled, the TC structure and intensity change share similar evolution to those in CTL, except a relatively slow intensification during the early stage due to the comparatively quick expansion of inner-core size associated with the increased stratiform heating. The resemblance between SH200 and CTL during the late stage suggests that the doubled stratiform heating in the near-core region plays a minor role in the storm evolution after the initial adjustment.

The decreased stratiform cooling in SC50 can elevate the θe in the mid- to lower troposphere and favor the formation of a thick boundary layer with the high-entropy air. In such a way, the inward transport of high-entropy air in the inflow boundary layer fuels the eyewall updrafts and triggers the TC rapid intensification. As the simulated storm intensifies further, the compensating subsidence outside the eyewall tends to suppress the outer spiral rainbands, producing a compact inner-core structure. Afterward, the lower-level θe outside the eyewall related to the compensating subsidence begins to be lowered such that the simulated TC eventually terminates the rapid intensification and then maintains roughly a steady state. The doubled stratiform cooling in SC200 is effective to eliminate the TC rapid intensification because of the low-entropy air prevailing from the surface to the midtroposphere during the early stage. However, the outer spiral rainbands immediately outside 80 km still appear active because of the lower-level convergence caused by the decelerated inflows, which can emanate sporadically the convective cells radially inward. Later, as the outer rainbands contract inward, a double-eyewall-like structure arises during the late stage of simulation. Meanwhile, the inner eyewall starts to collapse, and the inner-core size expands rapidly in response to the secondary convective ring.

The vertical dipole profiles of diabatic heating/cooling associated with stratiform precipitation were removed and doubled in SHC0 and SHC200, respectively. In SHC0 with both the stratiform heating and cooling removed, the structure and intensity change bear close resemblance to those in SC50 with the stratiform cooling halved except that the simulated storm in SHC0 has a more rapid intensification and a smaller inner-core size during the early stage of simulation because of the absence of the stratiform heating. By comparison, the doubling of both the stratiform heating and cooling in SHC200 would generate the weakest storm among all the experiments. During the late stage of simulation, the mid- to upper-level updrafts related to the enhanced stratiform heating between 40 and 80 km are connected to the lower-level updrafts in the collapsed eyewall, producing a largely outward-tilted eyewall and a large inner-core size. Meanwhile, the eyewall convective updrafts are reinvigorated, and the simulated storm reintensifies discernibly.

Overall, the comparison of the areal coverage of convective and stratiform grids and the change of TC inner-core size and intensity, as exhibited in Fig. 5, indicates that the inner-core size of the simulated TCs has a good relationship with the near-core convective heating, especially in the experiments with the rapid expansion of the inner-core size, such as CH150, SC200, and SHC200. For the experiments with the moderate increase of the inner-core size, such as CTL, SH200, SC50, and SHC0, the averaged coverage percentages of convective grids in the near-core region all reach around 50%. In contrast, the intensity change of the simulated TCs does not display a uniform and robust relationship with the areal coverage of two precipitation regimes in the near-core region, which depends on the different TC development stage and individual case with distinct experimental setting. For example, the weakening storms may either correspond to a small fraction of convective and stratiform grids in CH0 or take on a large areal coverage of convective grids during the late stage in SC200 with the occurrence of concentric eyewall replacement and in SHC200 with a wide and largely outward-tilted eyewall.

In some previous studies, the β effect was examined in terms of TC structure and intensity change (e.g., Fang and Zhang 2012; Rozoff et al. 2012). It is found that the TC simulated on a β plane with variable Coriolis parameter f is weaker in intensity but larger in size and strength than the TC simulated on an f plane with constant f. The effect of β shear facilitates the asymmetric structure as the TC intensifies, leading to the formation of an extensive stratiform region outside the primary eyewall. Therefore, in order to compare the differences in TC intensity change and structural evolution on f and β planes, the extra experiments are supplemented in which the same storm structure as shown in Fig. 1 is used to restart the integration on a β plane (referring to appendix B). The results show that the intensity variation, TC inner-core size change, and azimuthal-mean structural evolution on a β plane are qualitatively similar to those on an f plane, suggesting that the role of the near-core convective and stratiform diabatic processes in the TC structure and intensity change is robust despite the different plane configuration.

Extending the arguments based on the artificially modified convective and stratiform heating/cooling in this study, these experiments also provide some implications on potential physical processes that lead to TC structure and intensity change. For example, the appropriate lower-level diabatic cooling in the near-core region may favor the formation of concentric eyewall and subsequent eyewall replacement cycle, as demonstrated in SC200. All the extra experiments initialized with the different restart time but the same experimental setting as in SC200 also ultimately display the similar structural evolution as in SC200. A detailed examination is under way to shed light on the underlying dynamic and thermodynamic processes. Besides, the enhancement of vertical heating contrast with upper-level heating and lower-level cooling in the near-core region is likely to develop a largely outward-tilted eyewall and thus form a large-sized eye, as exhibited in SHC200. On the other hand, since most of the numerical models cannot resolve accurately mesoscale cumulus convection, they have to employ cumulus and microphysics parameterization schemes that consist of various empirical parameters. The specification of these parameters may to a large extent determine the areal fraction of convective and stratiform precipitation and thus the vertical profile of diabatic heating in the near-core region. Therefore, the improvement in representation of thermodynamic structure in the near-core region would contribute to accurate prediction of TC structural evolution and intensity change. For real TCs on a spherical coordinate, future work should focus on how the large-scale environmental conditions, such as background flows and relative humidity, govern dynamic and thermodynamic characteristics in the TC near-core region that greatly affect TC structure and intensity change.

Acknowledgments

The authors highly acknowledge the helpful comments of three anonymous reviewers. This study was supported by the National Natural Science Foundation of China (Grants 41475074 and 41775063), the National Basic Research Program of China (Grant 2014CB953902), and the open project of Key Laboratory of Meteorological Disaster of Ministry of Education, NUIST (KLME1604). The second and third authors are supported by the Ministry of Science and Technology of Taiwan under Grants MOST 105-2628-M-002-001 and 106-2111-M-002-013 -MY5.

APPENDIX A

Validation of Partitioning Algorithm

This appendix shows that the portioning algorithm used in this study can effectively classify the different precipitation regimes including convective, stratiform, and other precipitation types. The composite vertical profiles of vertical velocity, diabatic heating, divergence, and relative vorticity for the convective, stratiform, and other precipitation grid points within 40- and 80-km radii averaged between 48 and 72 h of CTL are exhibited in Fig. A1. On average, among the total 3780 grid points, there are 1420, 1660, and 480 grid points for the convective, stratiform, and other precipitation, respectively. For the convective precipitation grids, the composite upward motion dominates throughout the whole troposphere with a maximum of 0.67 m s−1 near 11-km height. In contrast, the counterpart in the stratiform precipitation grids takes on a dipole structure, that is, upward motion above the height of 6 km with a maximum of 0.46 m s−1 at 12.5-km height and downward motion below with a minimum of −0.14 m s−1 at 2-km height (Fig. A1a). The diabatic heating associated with convective precipitation occupies throughout most of the troposphere with a maximum at 5 km, except the existence of shallow cooling below 0.3 km. The vertical profile of diabatic heating associated with the stratiform precipitation is similar to that of vertical motion with the upper-level heating and lower-level cooling bounded at 6-km height that, on average, corresponds to stratiform cloud base (Fig. A1b). Correspondingly, the convective precipitation grids feature apparently convergence below 3 km, divergence above 9 km, and weak net divergence in between. By comparison, the stratiform precipitation has a convergence layer between 2 and 10 km, flanked by the divergence layers above and below it (Fig. A1c). The large relative vorticity extends upward from 1 through 12 km for the convective regime, indicative of a deep layer with strong cyclonic vorticity. The stratiform regime exhibits a maximum vorticity at 7 km that coincides with the height of the maximum convergence (Fig. A1d). The characteristics of convective and stratiform regimes as shown in Fig. A1 are well consistent with the findings in previous studies (e.g., Houze 1997). In contrast to the stratiform regime, the maximum upward motion and heating in the other-type precipitation regime are located at the higher altitude and have smaller magnitudes, which seems to be analogous to the features of anvil cloud.

Fig. A1.
Fig. A1.

The vertical profile of (a) vertical velocity (m s−1), (b) diabatic heating rate (×10−3 K s−1), (c) divergence (×10−4 s−1), and (d) relative vorticity (×10−4 s−1) averaged for convective (solid), stratiform (dashed), and other (dotted) grids between 40- and 80-km radii.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

APPENDIX B

Intensity Change and Structural Evolution on a β Plane

To further substantiate the effect of near-core convective and stratiform diabatic heating/cooling on TC structure and intensity, the extra sensitivity experiments are performed, in which the same storm structure as shown in Fig. 1 is initialized to restart the integration on a β plane. On average, the storms on a β plane are drifted northwestward about 200 km at the end of simulation in contrast to the counterparts on an f plane because of the β effect. Figure B1 displays the time evolution of MSLP and radius of hurricane-force surface wind in the sensitivity experiments on a β plane. Overall, the storm intensity on a β plane has a similar variation but with a slightly larger magnitude in MSLP, by comparison with the counterpart on an f plane in each experiment (cf. Fig. 2a and Fig. B1a). Especially in SH200, the storm intensity on a β plane exhibits a quicker decay at the end of integration, because of the more robust outer spiral rainbands (not shown). Besides, the TC inner-core sizes (represented by the radius of hurricane-force surface wind) on a β plane experience the temporal variation similar to those studied on an f plane. However, note that the storms on a β plane generally have a larger inner-core size than those on an f plane (cf. Fig. 2b and Fig. B1b), which can be attributed to the more active and well-organized outer stratiform rainbands in the β-configured experiments as documented by previous studies (e.g., Fang and Zhang 2012; Rozoff et al. 2012).

Fig. B1.
Fig. B1.

As in Fig. 2, but on a β plane.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

The azimuthal-mean vertical velocity and tangential wind on a β plane also bear close resemblance to those on an f plane (cf. Fig. B2 and Figs. 8 and 9). By comparison, the ascending motion outside the primary eyewall on a β plane generally becomes stronger and more expansive. The relatively active outer spiral rainbands tend to be negative to the storm intensity but favor the expansion of TC inner-core size, which is in good agreement with the differences in TC intensity and inner-core size between the two planes as exhibited in Fig. B1. To sum up, although the inclusion of β effect alters to a certain degree the storm intensity and structure, the plane configuration in the simulations cannot qualitatively change the role of the near-core convective and stratiform diabatic processes in the TC intensity and structure.

Fig. B2.
Fig. B2.

Radius–time Hovmöller diagram of azimuthal-mean vertical velocity at 3 km (color shaded; m s−1) and tangential wind (contours; m s−1) in (a) CH0, (b) CH150, (c) SH0, (d) SH200, (e) SC50, (f) SC200, (g) SHC0, and (h) SHC200 on a β plane.

Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0122.1

REFERENCES

  • Bender, M. A., 1997: The effect of relative flow on the asymmetric structure in the interior of hurricanes. J. Atmos. Sci., 54, 703724, https://doi.org/10.1175/1520-0469(1997)054<0703:TEORFO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107, https://doi.org/10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ebita, A., and Coauthors, 2011: The Japanese 55-year Reanalysis “JRA-55”: An interim report. SOLA, 7, 149152, https://doi.org/10.2151/sola.2011-038.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fang, J., and F. Zhang, 2012: Effect of beta shear on simulated tropical cyclones. Mon. Wea. Rev., 140, 33273346, https://doi.org/10.1175/MWR-D-10-05021.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fudeyasu, H., and Y. Wang, 2011: Balanced contribution to the intensification of a tropical cyclone simulated in TCM4: Outer-core spinup process. J. Atmos. Sci., 68, 430449, https://doi.org/10.1175/2010JAS3523.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hack, J. J., and W. H. Schubert, 1986: Nonlinear response of atmospheric vortices to heating by organized cumulus convection. J. Atmos. Sci., 43, 15591573, https://doi.org/10.1175/1520-0469(1986)043<1559:NROAVT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hence, D. A., and R. A. Houze, 2008: Kinematic structure of convective‐scale elements in the rainbands of Hurricanes Katrina and Rita (2005). J. Geophys. Res., 113, D15108, https://doi.org/10.1029/2007JD009429.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hill, K. A., and G. M. Lackmann, 2009: Influence of environmental humidity on tropical cyclone size. Mon. Wea. Rev., 137, 32943315, https://doi.org/10.1175/2009MWR2679.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., J. Dudhia, and S.-H. Chen, 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103120, https://doi.org/10.1175/1520-0493(2004)132<0103:ARATIM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Houze, R. A., Jr., 1997: Stratiform precipitation in regions of convection: A meteorological paradox? Bull. Amer. Meteor. Soc., 78, 21792196, https://doi.org/10.1175/1520-0477(1997)078<2179:SPIROC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Houze, R. A., Jr., 2004: Mesoscale convective systems. Rev. Geophys., 42, RG4003, https://doi.org/10.1029/2004RG000150.

  • Houze, R. A., Jr., 2010: Clouds in tropical cyclones. Mon. Wea. Rev., 138, 293344, https://doi.org/10.1175/2009MWR2989.1.

  • Houze, R. A., Jr., W.-C. Lee, and M. M. Bell, 2009: Convective contribution to the genesis of Hurricane Ophelia (2005). Mon. Wea. Rev., 137, 27782800, https://doi.org/10.1175/2009MWR2727.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, Y.-H., M. T. Montgomery, and C.-C. Wu, 2012: Concentric eyewall formation in Typhoon Sinlaku (2008). Part II: Axisymmetric dynamical processes. J. Atmos. Sci., 69, 662674, https://doi.org/10.1175/JAS-D-11-0114.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jorgensen, D. P., 1984: Mesoscale and convective-scale characteristics of mature hurricanes. Part I: General observations by research aircraft. J. Atmos. Sci., 41, 12681286, https://doi.org/10.1175/1520-0469(1984)041<1268:MACSCO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kossin, J. P., and M. D. Eastin, 2001: Two distinct regimes in the kinematic and thermodynamic structure of the hurricane eye and eyewall. J. Atmos. Sci., 58, 10791090, https://doi.org/10.1175/1520-0469(2001)058<1079:TDRITK>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Q., Y. Wang, and Y. Duan, 2014: Effects of diabatic heating and cooling in the rapid filamentation zone on structure and intensity of a simulated tropical cyclone. J. Atmos. Sci., 71, 31443163, https://doi.org/10.1175/JAS-D-13-0312.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Q., Y. Wang, and Y. Duan, 2015: Impacts of evaporation of rainwater on tropical cyclone structure and intensity—A revisit. J. Atmos. Sci., 72, 13231345, https://doi.org/10.1175/JAS-D-14-0224.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, K., and J. C. Chan, 2002: Synoptic flow patterns associated with small and large tropical cyclones over the western North Pacific. Mon. Wea. Rev., 130, 21342142, https://doi.org/10.1175/1520-0493(2002)130<2134:SFPAWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marks, F. D., Jr., and R. A. Houze Jr., 1987: Inner core structure of Hurricane Alicia from airborne Doppler radar observations. J. Atmos. Sci., 44, 12961317, https://doi.org/10.1175/1520-0469(1987)044<1296:ICSOHA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16 66316 682, https://doi.org/10.1029/97JD00237.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moon, Y., and D. S. Nolan, 2010: The dynamic response of the hurricane wind field to spiral rainband heating. J. Atmos. Sci., 67, 17791805, https://doi.org/10.1175/2010JAS3171.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Noh, Y., W. Cheon, S. Hong, and S. Raasch, 2003: Improvement of the K-profile model for the planetary boundary layer based on large eddy simulation data. Bound.-Layer Meteor., 107, 401427, https://doi.org/10.1023/A:1022146015946.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., and M. T. Montgomery, 2002: Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices. Part I: Linearized formulation, stability, and evolution. J. Atmos. Sci., 59, 29893020, https://doi.org/10.1175/1520-0469(2002)059<2989:NTDPTB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pendergrass, A. G., and H. E. Willoughby, 2009: Diabatically induced secondary flows in tropical cyclones. Part I: Quasi-steady forcing. Mon. Wea. Rev., 137, 805821, https://doi.org/10.1175/2008MWR2657.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Powell, M. D., 1990: Boundary layer structure and dynamics in outer hurricane rainbands. Part II: Downdraft modification and mixed layer recovery. Mon. Wea. Rev., 118, 918938, https://doi.org/10.1175/1520-0493(1990)118<0918:BLSADI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., and S. L. Sessions, 2007: Evolution of convection during tropical cyclogenesis. Geophys. Res. Lett., 34, L06811, https://doi.org/10.1029/2006GL028607.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rickenbach, T. M., and S. A. Rutledge, 1998: Convection in TOGA COARE: Horizontal scale, morphology, and rainfall production. J. Atmos. Sci., 55, 27152729, https://doi.org/10.1175/1520-0469(1998)055<2715:CITCHS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R., 2010: Convective-scale structure and evolution during a high-resolution simulation of tropical cyclone rapid intensification. J. Atmos. Sci., 67, 4470, https://doi.org/10.1175/2009JAS3122.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R., P. Reasor, and S. Lorsolo, 2013: Airborne Doppler observations of the inner-core structural differences between intensifying and steady-state tropical cyclones. Mon. Wea. Rev., 141, 29702991, https://doi.org/10.1175/MWR-D-12-00357.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rotunno, R., and K. A. Emanuel, 1987: An air–sea interaction theory for tropical cyclones. Part II: Evolutionary study using a nonhydrostatic axisymmetric numerical model. J. Atmos. Sci., 44, 542561, https://doi.org/10.1175/1520-0469(1987)044<0542:AAITFT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rozoff, C. M., W. H. Schubert, B. D. McNoldy, and J. P. Kossin, 2006: Rapid filamentation zones in intense tropical cyclones. J. Atmos. Sci., 63, 325340, https://doi.org/10.1175/JAS3595.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rozoff, C. M., D. S. Nolan, J. P. Kossin, F. Zhang, and J. Fang, 2012: The roles of an expanding wind field and inertial stability in tropical cyclone secondary eyewall formation. J. Atmos. Sci., 69, 26212643, https://doi.org/10.1175/JAS-D-11-0326.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sawada, M., and T. Iwasaki, 2010: Impacts of evaporation from raindrops on tropical cyclones. Part I: Evolution and axisymmetric structure. J. Atmos. Sci., 67, 7183, https://doi.org/10.1175/2009JAS3040.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., and J. J. Hack, 1982: Inertial stability and tropical cyclone development. J. Atmos. Sci., 39, 16871697, https://doi.org/10.1175/1520-0469(1982)039<1687:ISATCD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schubert, W. H., M. T. Montgomery, R. K. Taft, T. A. Guinn, S. R. Fulton, J. P. Kossin, and J. P. Edwards, 1999: Polygonal eyewalls, asymmetric eye contraction, and potential vorticity mixing in hurricanes. J. Atmos. Sci., 56, 11971223, https://doi.org/10.1175/1520-0469(1999)056<1197:PEAECA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shapiro, L. J., and H. E. Willoughby, 1982: The response of balanced hurricanes to local sources of heat and momentum. J. Atmos. Sci., 39, 378394, https://doi.org/10.1175/1520-0469(1982)039<0378:TROBHT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., R. A. Houze Jr., and S. E. Yuter, 1995: Climatological characterization of three-dimensional storm structure from operational radar and rain gauge data. J. Appl. Meteor., 34, 19782007, https://doi.org/10.1175/1520-0450(1995)034<1978:CCOTDS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Terwey, W. D., and M. T. Montgomery, 2008: Secondary eyewall formation in two idealized, full-physics modeled hurricanes. J. Geophys. Res., 113, D12112, https://doi.org/10.1029/2007JD008897.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tory, K., M. Montgomery, N. Davidson, and J. Kepert, 2006: Prediction and diagnosis of tropical cyclone formation in an NWP system. Part II: A diagnosis of Tropical Cyclone Chris formation. J. Atmos. Sci., 63, 30913113, https://doi.org/10.1175/JAS3765.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vigh, J. L., and W. H. Schubert, 2009: Rapid development of the tropical cyclone warm core. J. Atmos. Sci., 66, 33353350, https://doi.org/10.1175/2009JAS3092.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, Y., 2002: Vortex Rossby waves in a numerically simulated tropical cyclone. Part II: The role in tropical cyclone structure and intensity changes. J. Atmos. Sci., 59, 12391262, https://doi.org/10.1175/1520-0469(2002)059<1239:VRWIAN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, Y., 2008a: Rapid filamentation zone in a numerically simulated tropical cyclone. J. Atmos. Sci., 65, 11581181, https://doi.org/10.1175/2007JAS2426.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, Y., 2008b: Structure and formation of an annular hurricane simulated in a fully compressible, nonhydrostatic model—TCM4. J. Atmos. Sci., 65, 15051527, https://doi.org/10.1175/2007JAS2528.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, Y., 2009: How do outer spiral rainbands affect tropical cyclone structure and intensity? J. Atmos. Sci., 66, 12501273, https://doi.org/10.1175/2008JAS2737.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, Z., M. Montgomery, and T. Dunkerton, 2010: Genesis of pre–Hurricane Felix (2007). Part II: Warm core formation, precipitation evolution, and predictability. J. Atmos. Sci., 67, 17301744, https://doi.org/10.1175/2010JAS3435.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Willoughby, H., J. Clos, and M. Shoreibah, 1982: Concentric eye walls, secondary wind maxima, and the evolution of the hurricane vortex. J. Atmos. Sci., 39, 395411, https://doi.org/10.1175/1520-0469(1982)039<0395:CEWSWM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wu, C.-C., S.-N. Wu, H.-H. Wei, and S. F. Abarca, 2016: The role of convective heating in tropical cyclone eyewall ring evolution. J. Atmos. Sci., 73, 319330, https://doi.org/10.1175/JAS-D-15-0085.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xu, J., and Y. Wang, 2010: Sensitivity of the simulated tropical cyclone inner-core size to the initial vortex size. Mon. Wea. Rev., 138, 41354157, https://doi.org/10.1175/2010MWR3335.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xu, Y., T. Li, and M. Peng, 2014: Roles of the synoptic-scale wave train, the intraseasonal oscillation, and high-frequency eddies in the genesis of Typhoon Manyi (2001). J. Atmos. Sci., 71, 37063722, https://doi.org/10.1175/JAS-D-13-0406.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yanai, M., 1961: A detailed analysis of typhoon formation. J. Meteor. Soc. Japan, 39, 187214, https://doi.org/10.2151/jmsj1923.39.4_187.

  • Yang, B., Y. Wang, and B. Wang, 2007: The effect of internally generated inner-core asymmetries on tropical cyclone potential intensity. J. Atmos. Sci., 64, 11651188, https://doi.org/10.1175/JAS3971.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., D. Tao, Y. Q. Sun, and J. D. Kepert, 2017: Dynamics and predictability of secondary eyewall formation in sheared tropical cyclones. J. Adv. Model. Earth Syst., 9, 89112, https://doi.org/10.1002/2016MS000729.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhu, T., and D.-L. Zhang, 2006: Numerical simulation of Hurricane Bonnie (1998). Part II: Sensitivity to varying cloud microphysical processes. J. Atmos. Sci., 63, 109126, https://doi.org/10.1175/JAS3599.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhu, Z., and P. Zhu, 2014: The role of outer rainband convection in governing the eyewall replacement cycle in numerical simulations of tropical cyclones. J. Geophys. Res. Atmos., 119, 80498072, https://doi.org/10.1002/2014JD021899.

    • Crossref
    • Search Google Scholar
    • Export Citation
Save
  • Bender, M. A., 1997: The effect of relative flow on the asymmetric structure in the interior of hurricanes. J. Atmos. Sci., 54, 703724, https://doi.org/10.1175/1520-0469(1997)054<0703:TEORFO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107, https://doi.org/10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ebita, A., and Coauthors, 2011: The Japanese 55-year Reanalysis “JRA-55”: An interim report. SOLA, 7, 149152, https://doi.org/10.2151/sola.2011-038.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fang, J., and F. Zhang, 2012: Effect of beta shear on simulated tropical cyclones. Mon. Wea. Rev., 140, 33273346, https://doi.org/10.1175/MWR-D-10-05021.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fudeyasu, H., and Y. Wang, 2011: Balanced contribution to the intensification of a tropical cyclone simulated in TCM4: Outer-core spinup process. J. Atmos. Sci., 68, 430449, https://doi.org/10.1175/2010JAS3523.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hack, J. J., and W. H. Schubert, 1986: Nonlinear response of atmospheric vortices to heating by organized cumulus convection. J. Atmos. Sci., 43, 15591573, https://doi.org/10.1175/1520-0469(1986)043<1559:NROAVT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hence, D. A., and R. A. Houze, 2008: Kinematic structure of convective‐scale elements in the rainbands of Hurricanes Katrina and Rita (2005). J. Geophys. Res., 113, D15108, https://doi.org/10.1029/2007JD009429.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hill, K. A., and G. M. Lackmann, 2009: Influence of environmental humidity on tropical cyclone size. Mon. Wea. Rev., 137, 32943315, https://doi.org/10.1175/2009MWR2679.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., J. Dudhia, and S.-H. Chen, 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103120, https://doi.org/10.1175/1520-0493(2004)132<0103:ARATIM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Houze, R. A., Jr., 1997: Stratiform precipitation in regions of convection: A meteorological paradox? Bull. Amer. Meteor. Soc., 78, 21792196, https://doi.org/10.1175/1520-0477(1997)078<2179:SPIROC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Houze, R. A., Jr., 2004: Mesoscale convective systems. Rev. Geophys., 42, RG4003, https://doi.org/10.1029/2004RG000150.

  • Houze, R. A., Jr., 2010: Clouds in tropical cyclones. Mon. Wea. Rev., 138, 293344, https://doi.org/10.1175/2009MWR2989.1.

  • Houze, R. A., Jr., W.-C. Lee, and M. M. Bell, 2009: Convective contribution to the genesis of Hurricane Ophelia (2005). Mon. Wea. Rev., 137, 27782800, https://doi.org/10.1175/2009MWR2727.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, Y.-H., M. T. Montgomery, and C.-C. Wu, 2012: Concentric eyewall formation in Typhoon Sinlaku (2008). Part II: Axisymmetric dynamical processes. J. Atmos. Sci., 69, 662674, https://doi.org/10.1175/JAS-D-11-0114.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jorgensen, D. P., 1984: Mesoscale and convective-scale characteristics of mature hurricanes. Part I: General observations by research aircraft. J. Atmos. Sci., 41, 12681286, https://doi.org/10.1175/1520-0469(1984)041<1268:MACSCO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kossin, J. P., and M. D. Eastin, 2001: Two distinct regimes in the kinematic and thermodynamic structure of the hurricane eye and eyewall. J. Atmos. Sci., 58, 10791090, https://doi.org/10.1175/1520-0469(2001)058<1079:TDRITK>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Q., Y. Wang, and Y. Duan, 2014: Effects of diabatic heating and cooling in the rapid filamentation zone on structure and intensity of a simulated tropical cyclone. J. Atmos. Sci., 71, 31443163, https://doi.org/10.1175/JAS-D-13-0312.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Q., Y. Wang, and Y. Duan, 2015: Impacts of evaporation of rainwater on tropical cyclone structure and intensity—A revisit. J. Atmos. Sci., 72, 13231345, https://doi.org/10.1175/JAS-D-14-0224.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, K., and J. C. Chan, 2002: Synoptic flow patterns associated with small and large tropical cyclones over the western North Pacific. Mon. Wea. Rev., 130, 21342142, https://doi.org/10.1175/1520-0493(2002)130<2134:SFPAWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marks, F. D., Jr., and R. A. Houze Jr., 1987: Inner core structure of Hurricane Alicia from airborne Doppler radar observations. J. Atmos. Sci., 44, 12961317, https://doi.org/10.1175/1520-0469(1987)044<1296:ICSOHA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16 66316 682, https://doi.org/10.1029/97JD00237.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moon, Y., and D. S. Nolan, 2010: The dynamic response of the hurricane wind field to spiral rainband heating. J. Atmos. Sci., 67, 17791805, https://doi.org/10.1175/2010JAS3171.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Noh, Y., W. Cheon, S. Hong, and S. Raasch, 2003: Improvement of the K-profile model for the planetary boundary layer based on large eddy simulation data. Bound.-Layer Meteor., 107, 401427, https://doi.org/10.1023/A:1022146015946.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., and M. T. Montgomery, 2002: Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices. Part I: Linearized formulation, stability, and evolution. J. Atmos. Sci., 59, 29893020, https://doi.org/10.1175/1520-0469(2002)059<2989:NTDPTB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pendergrass, A. G., and H. E. Willoughby, 2009: Diabatically induced secondary flows in tropical cyclones. Part I: Quasi-steady forcing. Mon. Wea. Rev., 137, 805821, https://doi.org/10.1175/2008MWR2657.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Powell, M. D., 1990: Boundary layer structure and dynamics in outer hurricane rainbands. Part II: Downdraft modification and mixed layer recovery. Mon. Wea. Rev., 118, 918938, https://doi.org/10.1175/1520-0493(1990)118<0918:BLSADI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., and S. L. Sessions, 2007: Evolution of convection during tropical cyclogenesis. Geophys. Res. Lett., 34, L06811, https://doi.org/10.1029/2006GL028607.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rickenbach, T. M., and S. A. Rutledge, 1998: Convection in TOGA COARE: Horizontal scale, morphology, and rainfall production. J. Atmos. Sci., 55, 27152729, https://doi.org/10.1175/1520-0469(1998)055<2715:CITCHS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R., 2010: Convective-scale structure and evolution during a high-resolution simulation of tropical cyclone rapid intensification. J. Atmos. Sci., 67, 4470, https://doi.org/10.1175/2009JAS3122.1.

    • Crossref