The Role of WISHE in the Rapid Intensification of Tropical Cyclones

Chieh-Jen Cheng Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan

Search for other papers by Chieh-Jen Cheng in
Current site
Google Scholar
PubMed
Close
and
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
Free access

Abstract

This study examines the role of surface heat fluxes, particularly in relation to the wind-induced surface heat exchange (WISHE) mechanism, in the rapid intensification (RI) of tropical cyclones (TCs). Sensitivity experiments with capped surface fluxes and thus reduced WISHE exhibit delayed RI and weaker peak intensity, while WISHE could affect the evolutions of TCs both before and after the onset of RI. Before RI, more WISHE leads to faster increase of equivalent potential temperature in the lower levels, resulting in more active and stronger convection. In addition, TCs in experiments with more WISHE reach a certain strength earlier, before the onset of RI. During the RI period, more surface heat fluxes could provide convective instability in the lower levels, and cause a consequent development in the convective activity. More efficient intensification in a TC is found with higher surface heat fluxes and larger inertial stability, leading to a stronger peak intensity, more significant and deeper warm core in TC center, and the axisymmetrization of convection in the higher levels. In both stages, different levels of WISHE alter the thermodynamic environment and convective-scale processes. In all, this study supports the crucial role of WISHE in affecting TC intensification rate for TCs with RI.

Corresponding author: Chun-Chieh Wu, cwu@as.ntu.edu.tw

Abstract

This study examines the role of surface heat fluxes, particularly in relation to the wind-induced surface heat exchange (WISHE) mechanism, in the rapid intensification (RI) of tropical cyclones (TCs). Sensitivity experiments with capped surface fluxes and thus reduced WISHE exhibit delayed RI and weaker peak intensity, while WISHE could affect the evolutions of TCs both before and after the onset of RI. Before RI, more WISHE leads to faster increase of equivalent potential temperature in the lower levels, resulting in more active and stronger convection. In addition, TCs in experiments with more WISHE reach a certain strength earlier, before the onset of RI. During the RI period, more surface heat fluxes could provide convective instability in the lower levels, and cause a consequent development in the convective activity. More efficient intensification in a TC is found with higher surface heat fluxes and larger inertial stability, leading to a stronger peak intensity, more significant and deeper warm core in TC center, and the axisymmetrization of convection in the higher levels. In both stages, different levels of WISHE alter the thermodynamic environment and convective-scale processes. In all, this study supports the crucial role of WISHE in affecting TC intensification rate for TCs with RI.

Corresponding author: Chun-Chieh Wu, cwu@as.ntu.edu.tw

1. Introduction

Although tropical cyclone (TC) track forecasts have been significantly improved in the past 30 years, accurate prediction of TC intensity remains a big challenge (Cangialosi and Franklin 2012; Falvey 2012; DeMaria et al. 2014). Rapid intensification (RI), commonly defined as either intensification by more than 30 kt (15.4 m s−1) (Kaplan and DeMaria 2003) or a reduction of the minimum sea level pressure (MSLP) of more than 42 hPa in a 24-h period (Holliday and Thompson 1979), is an important process impacting TC intensity evolution (Lee et al. 2016). Analyses (Kowch and Emanuel 2015) on the frequency of TC intensification indicated that there may not be special factors governing the high intensification rate, in part due to the statistically random environmental and internal variability. It is noteworthy that different processes related to RI had been suggested in the literature, while no single process on RI is considered dominant.

From the perspective of axisymmetric dynamics, the secondary circulation, induced by the diabatic heating or other external forcings, spins up the vortex (e.g., Eliassen 1951; Shapiro and Willoughby 1982). This intensification process is more efficient when the latent heating occurs in the area with large inertial stability (Schubert and Hack 1982; Shapiro and Willoughby 1982). The above process usually occurs within the radius of the maximum wind (RMW) of intensifying TCs. The strengthening secondary circulation may contribute both to the spinup of the tangential circulation, and to the subsidence within the eye.

It has been demonstrated that the establishment of an upper-level warm core, attributable to the subsidence, coincides with the onset of RI (e.g., Zhang and Chen 2012). The interaction between the vigorous convection and the formation of a warm core has been extensively documented (Zhang and Chen 2012; Chen and Zhang 2013; Wang and Wang 2014; Chang and Wu 2017). More recently, Chang and Wu (2017) found that a midlevel warm core (around 6–8-km height) is a common feature prior to and during RI.

Strong asymmetric convection in the TC inner-core region is known to play an important role in RI (Heymsfield et al. 2001; Reasor et al. 2009; Guimond et al. 2010; Zhang and Chen 2012; Chen and Zhang 2013; Rogers et al. 2013; Wang and Wang 2014; Chen and Gopalakrishnan 2015; Chang and Wu 2017). Convective bursts (CBs) inside the RMW can contribute to the large diabatic heating in the inner-core region with large inertial stability, thus spinning up the TC, the formation of the upper-level warm core, the deepening of the sea level pressure in TC center, and also the onset of RI (e.g., Chen and Zhang 2013; Wang and Wang 2014; Chang and Wu 2017). Moreover, the increase of equivalent potential temperature (θe) around the TC center or inside the RMW (Dolling and Barnes 2012; Miyamoto and Nolan 2018) in the low levels of the troposphere (Miyamoto and Takemi 2013), or the increase of radial θe gradient (e.g., Emanuel 1986; Smith 2003; Molinari et al. 2004), are important for TC intensification or RI, which provides a favorable condition for convection to occur. When there remains a negative radial gradient of θe (i.e., a higher value in a smaller radius), it could create a negative radial surface heat flux gradient. Therefore, the core region would be relatively warmer than the outer radii regions. A warm-core structure of a TC with thermal wind balance could further develop.

Energy transfer from the ocean strongly influences the evolution of TCs. Early studies (e.g., Riehl 1950; Kleinschmidt 1951; Ooyama 1969) pointed out the important role of surface enthalpy fluxes in TC intensification. Later, the wind-induced surface heat exchange (WISHE) mechanism was proposed by Emanuel (1986) and Rotunno and Emanuel (1987), and further discussed by Emanuel (1989, 1997). The WISHE process highlights the positive feedback between the sea surface heat fluxes and the surface wind during TC intensification. For WISHE to occur and persist, the presence of an incipient finite-amplitude vortex is essential. The accompanying surface heat fluxes (which are proportional to surface wind speed) of the sufficiently strong vortex effectively strengthen the vortex, further increasing the surface wind. Following reinforcement of the surface wind speed, the surface heat fluxes increase, which is a positive feedback that helps further amplify the vortex. Montgomery et al. (2009, 2015) examined the WISHE mechanism by artificially suppressing the feedback between the surface heat fluxes and the surface wind speed in their idealized experiments. In these studies, the surface wind is capped at a specified wind speed (e.g., 5, 10 m s−1) in the calculation of the surface heat fluxes. These experiments revealed that a storm with suppressed heat fluxes that continues intensifying, and yet with a reduced intensification rate, would eventually reach a weaker steady-state intensity. Recently, in a study of Hurricane Edouard (2014), Zhang and Emanuel (2016) demonstrated that the vortex did not intensify when the wind speed was capped at 5 m s−1, in contrast to the category-3 hurricane in their control experiment. They pointed out that real-world tropical cyclones are influenced by various negative factors such as the vertical wind shear (VWS) and the induced sea surface temperature cold wake, which are unfavorable for TC intensification, and thus the WISHE feedback could help the vortex to overcome those unfavorable factors and further develop. The WISHE mechanism therefore should play a quantitatively important role. These studies are mostly based on idealized frameworks (Montgomery et al. 2009, 2015; Zhang and Emanuel 2016), while Zhang and Emanuel (2016) also examined the critical role of WISHE under a real-case (Hurricane Edouard in 2014) environment. Nevertheless, these works did not fully explore influences from the environmental VWS (e.g., the asymmetry of the storm) when evaluating the role of WISHE. While the VWS could lead to a wavenumber-1 asymmetry of the storm, with a dominant upward motion in the downshear half of the storm and a downward motion in the upshear half (e.g., Corbosiero and Molinari 2002), it would also affect the intensification of TCs. The downdraft, especially in the upshear quadrant, can bring air with low θe downward into the boundary layer (e.g., Powell 1990; Molinari et al. 2004). Relative to the direction of VWS, the area of a storm can be divided into four quadrants as upshear left (UL), upshear right (UR), downshear left (DL), and downshear right (DR). Generation of strong updrafts or precipitation in the upshear (e.g., Zagrodnik and Jiang 2014; Rios-Berrios and Torn 2017; Rios-Berrios et al. 2018) or UL quadrants (e.g., Stevenson et al. 2014; Chen and Gopalakrishnan 2015) are important features before the axisymmetrization of the storm, or before the onset of RI. During the developing stage of TCs with moderate environmental VWS, convection develops mainly in the downshear quadrant and can further extends to the upshear quadrant (e.g., Stevenson et al. 2014; Finocchio et al. 2016; Rios-Berrios et al. 2016, 2018). Low θe caused by the downdraft could be compensated by sufficiently strong surface entropy fluxes and the vertical mass fluxes with high θe (Rios-Berrios et al. 2018). Furthermore, axisymmetrization of the storm (or a ring structure of the inner-core convection) could also be a key process before RI, which is evidenced by both the observational (e.g., Kieper and Jiang 2012) and numerical studies (e.g., Miyamoto and Takemi 2013). After forming an axisymmetric structure, the storm would begin to intensify more efficiently (Nolan et al. 2007). In this work, further emphasis is put on the role of WISHE in the scenario with environmental VWS.

Both observational (e.g., Fig. 5 of Rogers et al. 2015; Fig. 3 of Sitkowski and Barnes 2009) and numerical (e.g., Fig. 7a of Rogers 2010; Fig. 3 of Stern and Zhang 2013; Fig. 8a of Wang and Wang 2014; Fig. 5a of Chang and Wu 2017) studies have revealed that the swirling wind field usually expands and intensifies during the RI period. As shown by Miyamoto and Takemi (2013), the surface wind speed and the heat fluxes simultaneously increase during the RI phase, suggesting that the WISHE mechanism may play a role in RI.

In this study, we investigate the role of surface heat fluxes, specifically the WISHE mechanism, in RI. Different from previous studies, experiments in this study are simulated with environmental VWS and real-time sea surface temperature, while analyses are more focused on TC evolution caused by the VWS. In addition, we would especially explore the role of WISHE in TCs with RI, which is a common stage in strong TCs (e.g., Lee et al. 2016).

A series of sensitivity experiments for Typhoon Megi (2010) are conducted with the surface wind speed used to calculate the heat fluxes being capped at different values. The model framework and experimental setup are described in section 2. In section 3, results from both the control experiment and sensitivity experiments are shown. Discussion and conclusions are presented in section 4.

2. Model and experiment designs

a. Control experiment (CTL)

The Advanced Weather Research and Forecasting (WRF, version 3.6.1, Skamarock et al. 2008) Model is used to simulate Typhoon Megi (2010). The initial fields and boundary conditions are derived from National Centers for Environmental Prediction Final reanalysis field at 1° × 1° resolution. There are three nested domains (334 × 250, 181 × 181, and 301 × 301), of which the two innermost domains follow the vortex center. The horizontal resolutions of the three domains are 12, 4, and 1.33 km, respectively. There are 35 vertical levels extending from the surface to 50 hPa, with enhanced resolution below 1-km height. The domain settings with 12- and 4-km resolution are the same as in Chang and Wu (2017), while the finest domain is broader (i.e., with more grid points), which can cover broader range of the TC vortex with the resolution of 1.33 km. The WRF single-moment 6-class microphysics scheme (Hong and Lim 2006), the Rapid Radiative Transfer Model (RRTM) scheme for longwave radiation (Mlawer et al. 1997), the Dudhia scheme (Dudhia 1989) for shortwave radiation, and the Yonsei University (YSU) planetary boundary layer scheme (Hong et al. 2006) are adopted. The Kain–Fritsch scheme (Kain and Fritsch 1993) is used in the coarsest domain. The selected physical parameterization schemes used are identical to those in Chang and Wu (2017).

All simulations begin at 0000 UTC 15 October 2010 (0 h), and are integrated for 4 days until 0000 UTC 19 October 2010 (96 h). The topography of the Philippines is removed from all simulations to avoid uncertainty in the results due to vortex interactions with the terrain at landfall.

b. Sensitivity experiments

To evaluate the role of WISHE, the surface heat fluxes from the ocean are artificially adjusted. To suppress the WISHE feedback, the values of surface wind speed for calculating surface heat fluxes are capped, while the simulated wind fields remain unchanged.

The surface heat fluxes are suppressed over the finest domain for the total duration of each sensitivity experiment. The three sensitivity experiments with the surface winds capped at 10, 15, and 20 m s−1 are referred to as CAP-10, CAP-15, and CAP-20, respectively. This method of suppressing the surface heat fluxes is the same as in the previous works of Montgomery et al. (2009, 2015), Zhang and Emanuel (2016), and Cheng and Wu (2018).

c. Definition of RI

In this study, RI onset is defined as when the maximum 10-m speed of the TC intensifies by more than 15.4 m s−1 in the following 24 h (Kaplan and DeMaria 2003). Since TC intensity may fluctuate (remains steady or even decreases for only few hours) during a 24-h period, a significantly intensifying period is identified during RI. The significantly intensifying period is defined as a 6-h period in which intensity increases by more than 3.8 m s−1 [this definition is also adopted in Judt and Chen (2016) and Rios-Berrios et al. (2018) to define the RI period], with the starting time being recognized as when the criteria is met continuously for 3 h. In addition, the RI period defined by reduction of the MSLP is also adopted in this study.

3. Results

a. Overview of experiments

As shown in Fig. 1, capping the surface heat fluxes in sensitivity experiments leads to different evolutions of intensity and RMW. In Fig. 1a, RI is defined by using the criteria of maximum 10-m wind speed, while in Fig. 1b, it is based on the MSLP. In the first few hours, the storms develop significantly, which is caused by adjustment of the vortex structure during the initial spinup. The following analyses would focus on the evolutions of TC after 6 h. Storms in CAP-20 and CAP-15 reach the intensification threshold for RI based on the criteria of increase in maximum surface wind speed, but not according to decrease of the MSLP. Compared to CTL, the sensitivity experiments show delayed RI (the RI onset time is 21 h in CTL, 27 h in CAP-20, and 34 h in CAP-15) with weaker peak intensity. TC intensity is found to fluctuate during the early hours of RI period in each experiment. Therefore, identifying the significantly intensifying period could further highlight the period with continuous intensification. The significantly intensifying period of each experiment (which is shown by the dashed arrows from 26 to 51 h in CTL, from 38 to 57 h in CAP-20, and from 43 to 61 h in CAP-15) well corresponds to the period in which the 10-m wind speed continuously increases by the largest extent. In CAP-20, although the increase of the maximum 10-m wind speed reaches the criteria of the significantly intensifying period from 27 to 35 h, the maximum 10-m wind speed decreases for a few hours immediately after that period (Fig. 1a). Therefore, the rapidly intensifying period defined in CAP-20 starts at later time (38 h). The significantly intensifying period is also delayed when the surface heat flux is suppressed. The intensity of CTL, CAP-20, and CAP-15 drops after 66 h due to the secondary eyewall formation (SEF) and eyewall replacement cycle (ERC), which occur after the RI period. In addition, the maximum reduction of the MSLP in 24 h is 49 hPa in CTL (from 23 to 47 h), 41 hPa in CAP-20 (from 30 to 54 h), and 41 hPa in CAP-15 (from 39 to 63 h).

Fig. 1.
Fig. 1.

(a) The maximum 10-m wind speed (m s−1) of each experiment (black: CTL; blue: CAP-10; magenta: CAP-15; red: CAP-20). The dotted lines (black: CTL; red: CAP-20; magenta: CAP-15) indicate the RI onset time defined by the increase of maximum 10-m wind speed. The dashed arrows indicate the significantly intensifying period (black: CTL; red: CAP-20; magenta: CAP-15). (b) The minimum sea level pressure (hPa) of each experiment. The dotted line (black: CTL) indicates the RI onset time defined by the change of minimum sea level pressure. (c) The radius of the maximum wind at 1-km height. The dotted lines (black: CTL; red: CAP-20; magenta: CAP-15) indicate the RI onset time defined by the increase of maximum 10-m wind speed. (d) Magnitude of the environmental vertical wind shear (between 850 and 200 hPa), calculated over the radius range within the inner 500 km. In (c) and (d), the dotted lines (black: CTL; red: CAP-20; magenta: CAP-15) indicate the RI onset time defined by the increase of maximum 10-m wind speed.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

b. Axisymmetric viewpoints and vortex evolution prior to and during RI

From Fig. 2, both tangential wind and vertical velocity clearly demonstrate the reinforcement of the inner eyewall convection just before and during RI in all experiments. Note that the strength of the eyewall (both tangential wind and convection) is weaker in all sensitivity experiments. In addition, RMW (Fig. 1c) fluctuates during the first 12 h and contracts before and during the RI period of CTL, CAP-20, and CAP-15. Before 48 h, the RMW of CTL is slightly smaller than CAP-20 and CAP-15 during most of the time, and this could be linked to the faster storm development in CTL. From 48 to 72 h, the RMW gradually reaches a relatively steady value in the experiments with RI, while the minimum value of the RMW in CAP-20 and CAP-15 is slightly smaller than CTL. Note that Stern et al. (2015) pointed out that the RMW would contract as the TC intensifies, but the contraction would cease before the peak intensity is reached. Moreover, Stern et al. (2015) also suggested that contraction of the RMW would slow down or stop when the sharpness of the tangential wind profile increases. Results (figures not shown) show that the sharpness of the radius–height profile of the azimuthally averaged tangential wind is more evident around 60 to 72 h (during this period the RMW fluctuates only slightly) in CTL than CAP-20 and CAP-15, which could explain the smaller value of RMW in CAP-15 and CAP-20. In addition, the results of the budget calculation in Li et al. (2019) suggested that both the increase of the radial gradient of horizontal and the vertical mixing (including the surface mixing) near the eyewall could prohibit the RMW contraction. With stronger intensity in CTL, larger magnitude of both the horizontal and vertical mixing could be expected and might result in larger RMW. At a later time, SEF and ERC are also observed subsequent to RI in CTL, CAP-20, and CAP-15 (figures not shown). These issues are beyond the scope of this study, while the relationship between SEF events and WISHE had been investigated in Cheng and Wu (2018). The inner core in this study is defined as from 0 to 80 km of the radius, which can cover most convection area identified by Fig. 2 before and during the RI period. The area of the inner core is same as the area marked out by using the definition in Chang and Wu (2017).

Fig. 2.
Fig. 2.

Time–radius Hovmöller diagrams of the azimuthal-mean vertical velocity (shaded, m s−1) and tangential wind (contours, m s−1) at 1-km height. In each panel, the dotted line indicates the RI onset time, and the solid red arrow indicates the significantly intensifying period. The light blue line is the RMW of each storm.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Strong diabatic heating in the inner-core region is important for amplification of the vortex, and the accompanying subsidence can initiate establishment of the warm core. In Fig. 3, strong diabatic heating and an increase in inertial stability are observed in the inner-core region, especially in CTL. After the onset of RI, both the diabatic heating and inertial stability continue to increase in CTL. The inertial stability also persistently increases in both CAP-20 and CAP-15. When the diabatic heating in the inner core occurs in the region with higher inertial stability, the associated higher heating efficiency (e.g., Schubert and Hack 1982) would be favorable for the TC spinup, although capping the surface heat fluxes leads to weaker diabatic heating and smaller inertial instability. Figure 3 also shows that the magnitude of the inertial stability sufficiently increases to 12 s−1 around 3- to 4-km height in CTL, CAP-20, and CAP-15, as well as in higher and lower altitudes just before or during RI onset. Increasing inertial stability with the diabatic heating attributable to the convection in the inner-core region could enhance the heating efficiency and lead to TC spinup, as compared to the earlier period. This feature is identified in CTL, CAP-20, and CAP-15, but the time is delayed in the sensitivity experiments.

Fig. 3.
Fig. 3.

Evolutions of the area-averaged (from 0- to 80-km radius) diabatic heating rate (shaded, K h−1) and inertial stability (contours, s−1) in the inner-core region using (a) CTL, (b) CAP-20, (c) CAP-15, and (d) CAP-10. In each panel, the light blue dashed line indicates the onset time of RI period, and the green arrow indicates the significantly intensifying period.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

In addition, establishment of the warm core in the mid- to upper troposphere and the lower stratosphere at the center of the vortex coincides with the RI period in each experiment (Fig. 4), which is shown by the increase of potential temperature (θ) around the storm center (averaged from 0- to 20-km radius). In CTL, CAP-20, and CAP-15, an increase in θ is first observed between 6- and 10-km height. Later, the phenomenon extends upward to a higher altitude (approximately 16-km height), as well as into the lower troposphere. In contrast, the intensity of the warm core in sensitivity experiments is relatively weak, especially in CAP-10. The weak warm core can also explain why the MSLP is higher in the sensitivity experiments (Fig. 1b).

Fig. 4.
Fig. 4.

Evolutions of the area-averaged (from 0- to 20-km radius) potential temperature change (shaded, K) from the initial time for (a) CTL, (b) CAP-20, (c) CAP-15, and (d) CAP-10. In each panel, the light blue line indicates the onset time of RI period, and the green arrow indicates the significantly intensifying period.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

The θe in the lower troposphere, especially in the boundary layer, can be affected by both upward heat fluxes from the sea surface (resulting in the increase of θe) and the downdraft from the upper layer (which reduces the value of θe). Figure 5 shows that with more WISHE, the increase of θe is more significant in CTL than that in the sensitivity experiments below 1-km height. Moreover, during the early time (before 30 h), the relatively low value of θe is distinct above 0.5-km height. With more surface heat fluxes in CTL and CAP-20, decrease of θe is prevented in the lowest few hundred meters. The area with low θe is also eliminated earlier, compared with those in CAP-15 and CAP-10. After RI onset, the maximum value of θe becomes higher with more surface heat flux due to more WISHE. Moreover, previous studies have suggested that the radial gradient of high θe at smaller radius is also an important feature. Figure 6 shows the time evolution of the azimuthally and vertically averaged θe in the upper part of the boundary layer. Although the value of θe outside the radius around 40 km remains similar among all experiments, after 18 h (i.e., the time just before the RI onset of CTL), θe in the inner-most 20-km radius increases faster and reaches higher maximum values in the experiments with stronger WISHE, resulting in earlier establishment of the gradient of θe in the inner-core region.

Fig. 5.
Fig. 5.

Evolutions of the area-averaged (from 0- to 80-km radius) equivalent potential temperature for (a) CTL, (b) CAP-20, (c) CAP-15, and (d) CAP-10. In each panel, the magenta line indicates the onset time of RI period, and the green arrow indicates the significantly intensifying period.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Fig. 6.
Fig. 6.

Time–radius Hovmöller diagrams of the vertically averaged (from 500-m to 1-km height) azimuthal-mean equivalent potential temperature (shaded and contours, K). In each panel, the light blue line indicates the RI onset time, and the green arrow indicates the significantly intensifying period.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Figure 7 shows the vertical mass flux (ρw, with ρ being density of air and w representing vertical velocity) in the inner-core region. Large and positive values represent vigorous convections, while positive but small or negative values can be caused by the downdrafts which bring cold and dry air downward to the lower levels. The downward transport of the dry air accompanied with low θe could be induced by the environmental VWS (e.g., Powell 1990), while the low θe can be compensated by surface heat fluxes. Furthermore, the surface heat fluxes could also enhance the convective instability (i.e., negative vertical gradient of θe), which is favorable for initiating convection and the accompanied upward mass flux. Before RI, the vertical mass flux and the vertical distribution of θe fluctuate in all experiments. During RI, the θe generally increases with time (despite fluctuations during the first few hours of RI period in CTL), especially during the significantly intensifying period. In CTL, CAP-20, and CAP-15, the vertical mass flux gradually increases and with fewer small or negative values over time during the significantly intensifying period, as compared to the period before RI. With more WISHE, the vertical mass flux increases relatively steadily at earlier times (i.e., the stronger WISHE shortens the fluctuation period), before turning stronger at later times. In contrast, in the experiment with less WISHE (i.e., CAP-10), the vertical mass flux is relatively small during the whole simulation time, which may be due to less surface heat fluxes from the sea surface. In CAP-10, the downdrafts with low θe cannot be compensated by the surface heat fluxes as effectively as in CTL or CAP-20.

Fig. 7.
Fig. 7.

Evolutions of the area-averaged (from 0- to 80-km radius) equivalent potential temperature (contours, K) and vertical mass flux (shaded, kg m−2 s−1) for (a) CTL, (b) CAP-20, (c) CAP-15, and (d) CAP-10. In each panel, the straight dashed line indicates the onset time of RI period, and the green arrow indicates the significantly intensifying period.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Figure 8 shows the time- and azimuthally averaged analyses from the secondary circulation of all the experiments at different stages. In Fig. 8, the variables are calculated at different time periods after RI onset of each experiment. During the first 12-h period after RI onset, the diabatic heating rate is already lager than 18 K h−1 in the eyewall area, while in CAP-20 and CAP-15, the diabatic heating rate increases to this strength in the second 12-h period of RI. With larger diabatic heating rate, CTL can intensify relatively efficiently during the whole RI period than others. Since the strength of the inflows is related to the diabatic heating rate, Fig. 8 also shows that inflows in CTL are larger and deeper than those in other experiments. Larger inflows can bring in more absolute angular momentum inward from the outer radii, leading to more spinup. Strong convection, which brings diabatic heating, plays a key role in the distribution of diabatic heating and the secondary circulation. Comparisons of the evolution of strong convections among all experiments are discussed in the next section.

Fig. 8.
Fig. 8.

Radius–height plots of diabatic heating rate (shaded, K h−1), radial winds (black contours, m s−1), and absolute angular momentum (blue contours, m2 s−1), averaged for (a),(c),(e) the first and (b),(d),(f) the second 12-h periods after RI onset of (top) CTL, (middle) CAP-20, and (bottom) CAP-15.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

c. Strong convection before and during RI

Figure 9 shows the incidence of CBs (the grid point where reflectivity field at 2-km height is larger than 30 dBZ, and the vertically averaged vertical velocity between 700 and 300 hPa is more than 5 m s−1) and weak-to-moderate convection (the grid point where reflectivity field at 2-km height is larger than 30 dBZ, and the vertically averaged vertical velocity between 700 and 300 hPa is less than 5 m s−1) in the inner-core region by using definitions similar to those in Reasor et al. (2009) and Chang and Wu (2017, their section 2d). The suppression of the surface heat fluxes reduces the number of CBs and reduces weak-to-moderate convection during most of the integration time. Moreover, the increase of the grid points with CBs becomes apparent during the significantly intensifying period (shown by dashed arrows), and is accompanied by larger diabatic heating (Fig. 3) and development of the warm core (Fig. 4). The percentage of grid points of weak-to-moderate convection and CBs in the inner-core region are also considered before and around the onset of the RI. The percentage of grid points of weak-to-moderate convection inside the radius of 80 km constantly exceeds by around 20% in the first few hours of the RI period. Before 18 h, although the percentage of weak-to-moderate convection in all experiments reaches around 15%–20%, grid points of CAP-20, CAP-15, and CAP-10 decrease gradually. The grid points of weak-to-moderate convection increase again around each RI onset time in CAP-20 and CAP-15. The important role of weak-to-moderate convection, as identified here, is consistent with the findings in Chang and Wu (2017). In addition, the grid points of CBs are not closely correlated with the onset time of RI, which is in agreement with Rogers (2010).

Fig. 9.
Fig. 9.

Grid points with (a) convective bursts (CBs) and (b) weak-to-moderate convection in the inner-core region (from 0- to 80-km radius; black: CTL; blue: CAP-10; magenta: CAP-15; red: CAP-20) of each experiment. The dotted lines (black: CTL; red: CAP-20; magenta: CAP-15) indicate the onset time of RI period. The dashed arrows (black: CTL; red: CAP-20; magenta: CAP-15) indicate the significantly intensifying period. The horizontal dashed lines indicate the percentage of grid points in the inner-core region.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Figure 10 shows the differences of convection distribution between CTL, CAP-20, and CAP-15, which are identified by using the contoured frequency by altitude diagram (CFAD). Generally, both during the early stage (Figs. 10a,b) or after the onset of RI (Figs. 10c,d), more active convections are found at all altitudes in CTL than in the sensitivity experiments of both upward and downward vertical velocity, indicating that capping the surface heat fluxes decreases both the frequency and the strength of the convective activity within the inner core. In addition, differences of the vertical velocity distribution between the sensitivity experiments and CTL are larger in CAP-15 than in CAP-20. Figures 10e and 10f show differences of convection distribution in the TC center (within the radius of 20 km). Stronger sinking motion is shown in CTL, which is favorable for more deepening of the MSLP.

Fig. 10.
Fig. 10.

Differences (shaded, %) of contoured frequency by altitude diagram (CFAD) of vertical velocity between each sensitivity experiment and CTL: (a) CTL − CAP-20 and (b) CTL − CAP-15, averaged from 6 to 18 h and inside the radius of 80 km. (c),(d) As in (a) and (b), but for averages from the RI onset time to 24 h after the RI onset time of each experiment. (e),(f) As in (a) and (b), but for inside the radius of 20 km and averages during the 24-h period in which the vortex experiences the maximum decrease of minimum sea level pressure of each experiment.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Figure 11 shows the simulated reflectivity field and the direction of the environmental VWS (calculated between 200 and 850 hPa). Note that in all experiments, the convection is asymmetric in the early hours, while that in the eyewall becomes axisymmetric in CTL, CAP-20, and CAP-15 at different hours. At 15 h, convection around TC center is found in the DL and DR quadrants in all experiments (wavenumber-1 asymmetry), as a result of the effect of VWS, and is consistent with past studies (e.g., Corbosiero and Molinari 2002). In CTL and CAP-20, the nearly axisymmetric convection around the TC center is observed at around 30 h, while the axisymmetrization of the eyewall is delayed until 60 h in CAP-15 (figures not shown). Convection is found to be generated counterclockwise from the downshear quadrant to the whole upshear quadrant (CTL and CAP-20) or UL quadrant (CAP-15), which is also consistent with the previous studies (e.g., Stevenson et al. 2014; Finocchio et al. 2016; Rios-Berrios et al. 2016, 2018). In CAP-10, the convection appears markedly asymmetric in the inner-core region where strong convection is mainly found in the DL quadrant and part of the UL quadrant. These sensitivity experiments point out the role of axisymmetrization convection in RI, which along with how the VWS plays the role would be discussed in the next section.

Fig. 11.
Fig. 11.

The simulated reflectivity (shaded, dBZ) at 3-km height of all experiments at (left) 15, (center) 30, and (right) 45 h. The red dashed arrows indicate the directions of the VWS, which are calculated inside the radius of 500 km and in the coarsest domain.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

d. The axisymmetrization process

The axisymmetricity of convection can be viewed as evidence for establishment of the eyewall and maturity of the inner-core development. The definition of axisymmetricity in this study is determined by following the calculation in Miyamoto and Takemi (2013, their section 3b). Figure 12 shows the axisymmetricity in both the lower troposphere (averaged at 2–3-km height) and mid- to upper troposphere (averaged over 6–14-km height) in two different radial ranges (i.e., averaged over 20–40 and 20–80 km). Before 18 h, since convection in each experiment spreads out more widely to larger radii than at later periods, the calculations in Figs. 12a and 12c are based on a wider radial range. During the early hours, differences among the experiments are not substantial in the lower levels (Figs. 12a,b), but beginning 18 h the convection becomes more axisymmetric slightly earlier (Fig. 12b) in CTL and CAP-20 than in other experiments.

Fig. 12.
Fig. 12.

Time evolutions of axisymmetricity of vertical velocity in different vertical and radial ranges: (a) 2–3-km altitude, averaged from 20- to 80-km radius; (b) 2–3-km altitude, averaged from 20- to 40-km radius; (c) 6–14-km altitude, averaged from 20- to 80-km radius; and (d) 6–14-km radius, averaged from 20- to 40-km radius. The dotted lines (black: CTL; blue: CAP-10; magenta: CAP-15; red: CAP-20) indicate the onset time of the RI period. The dashed arrows (black: CTL; blue: CAP-10; magenta: CAP-15; red: CAP-20) indicate the significantly intensifying period.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

In the higher levels, axisymmetricity of the convection in CTL is larger than those in other experiments after 24 h in Fig. 12c and 36 h in Fig. 12d. The increase of axisymmetricity in the radial region between 20 and 40 km of radius is not evident until 36 h, but then becomes significant close to the significantly intensifying period, with the increase in CTL being the most prominent. During the later hours, the decrease of axisymmetrization in CTL, CAP-20, and CAP-15 is associated with the establishment of the outer eyewall, and results in the weakening of the inner eyewall (figures not shown). In addition, the axisymmetricity of CAP-10 in both vertical ranges remains small during the simulation time (this feature is also shown in Fig. 2d). In all, the convection, especially the deep convection (6–14-km height), in experiments with more surface heat fluxes becomes relatively axisymmetric earlier than in the other experiments.

e. Spinup of the vortices during the period prior to and just after the RI onset time of CTL (21 h)

Figure 13 shows the 10-m wind field (averaged from 15 to 18 h) and the vertical velocity (18 h) at 3-km height. During this period, the convection is stronger and the wind field is broader and stronger in CTL than those of CAP-10, CAP-15, and CAP-20, while all experiments show asymmetric convection distribution. From the asymmetric standpoint, Figs. 10a and 10b also show that more active and stronger convection could be found in CTL than those in other experiments, and the convective available potential energy (CAPE) could be one of the factors triggering these convections. Figure 14 shows the azimuthally and vertically averaged CAPE, calculated with the air parcel released between 500-m and 1-km height. The distribution and the magnitude of CAPE are similar among all the experiments at the first few hours of simulations (i.e., before 3 h), while the differences in CAPE between CTL and other experiments gradually increase, especially during the period from 15 to 24 h (near the RI onset time of CTL). This is because after environmental CAPE is consumed, the convective instability in the lower levels could be further enhanced by the surface heat fluxes. Therefore, the convection in the experiments with more surface heat fluxes (which can be induced by larger wind field) is more active, releasing more diabatic heating in the inner-core region (results not shown) with larger inertial stability (Fig. 3). Moreover, in this period, the magnitude of the environmental VWS between 850 and 200 hPa, as calculated over the radial range within inner 500 km, is relatively large (around 8 to 10 m s−1, Fig. 1d). More WISHE could provide more surface heat fluxes to reduce the effect from the environmental VWS (as discussed in the subsection related to Fig. 5, and in the following subsection). Therefore, faster vortex spinup could also be found in CTL than others during this period.

Fig. 13.
Fig. 13.

The 10-m wind field (averaged from 15 to 18 h) and the vertical velocity at 3-km height at 18 h for (a) CTL, (b) CAP-20, (c) CAP-15, and (d) CAP-20. The purple contours in (a)–(c) correspond to the wind speed of 30 m s−1, and the blue contours in (a)–(d) correspond to the wind speed of 20 m s−1.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Fig. 14.
Fig. 14.

Time–radius Hovmöller diagrams of the convective available potential energy (CAPE) (shaded, J kg−1), calculated and averaged from 500-m to 1-km altitude (calculated with the air parcel released between 500-m and 1-km height). Contours are the tangential wind at 1-km height (m s−1).

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

f. Influences from the VWS

The asymmetry of the vortices can be affected by the presence of environmental VWS. The VWS is about 12 m s−1 in an earlier period (around 12 h), then gradually decreases to around 4 m s−1 at a later time in all experiments (Fig. 1d). In Figs. 1517, analyses of the TC structure are conducted by targeting different quadrants. Previous studies have pointed out that development of the convection in the UL quadrant is a crucial factor when TC is undergoing spinup or just before significant intensification. In all experiments, convection and tangential wind speed are strongest in the DL quadrant before the RI onset of each experiment, as compared to other quadrants. After the onset of RI, convection and tangential wind in all quadrants start to intensify, while the convection becomes more organized earlier in both UL and DL quadrants than in other quadrants. During the significantly intensifying period, strength of the vertical velocity and the tangential wind in DL and UL quadrants continues to increase. Although the tangential wind in both DR and UR quadrants also intensifies, development of the convection is suppressed and delayed. In particular, the convection in DR and UR quadrants begins to develop after the significantly intensifying period in CAP-20 and CAP-15. Moreover, the downdrafts in the upshear quadrant may induce relatively cold air downward, reducing θe in the lower levels and prohibiting the convection, while enough strong surface heat fluxes can partially offset this effect. Figure 18 shows the mass fluxes and the azimuthally averaged θe in the inner-core region in the UL quadrant. During the early hours, mass fluxes are small or even negative in all experiments, with fluctuating θe. In CTL, θe gradually increases below 1-km height at an earlier time than those of other experiments, and contributing to the increase of convective instability. After the RI onset time, the more WISHE in an experiment (among CTL, CAP-20, and CAP-15), the earlier is the eruption of the strong and positive upward mass fluxes, which can also be depicted by the different development times of the tangential wind field and convection among the experiments in the UL quadrant (Figs. 1517).

Fig. 15.
Fig. 15.

Time–radius Hovmöller diagrams of the azimuthal-mean vertical velocity (shaded, m s−1) and tangential wind (contours, m s−1) at different quadrants relative to the direction of vertical wind shear in CTL. Panels show the (a) Downshear left (DL), (b) downshear right (DR), (c) upshear left (UL), and (d) upshear right (UR) quadrants. The dotted line indicates the RI onset time, and the green arrow indicates the significantly intensifying period.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Fig. 16.
Fig. 16.

As in Fig. 15, but for CAP-20.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Fig. 17.
Fig. 17.

As in Fig. 15, but for CAP-15.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

Fig. 18.
Fig. 18.

As in Fig. 7, but for the UL quadrant of each experiment.

Citation: Journal of the Atmospheric Sciences 77, 9; 10.1175/JAS-D-20-0006.1

4. Summary and discussion

RI is one of the important processes in TC intensity evolution. This study investigates how the feedback between the surface wind and surface heat fluxes affects RI. The WRF Model is used to conduct a series of simulations on Typhoon Megi (2010), consisting of a control experiment and several sensitivity experiments. The sensitivity experiments with capped WISHE feedback show delayed storm development and weaker peak intensity, which are indicated by the maximum 10-m wind speed and the MSLP. This is consistent with the results from previous studies (Montgomery et al. 2009, 2015; Zhang and Emanuel 2016) which have demonstrated that suppressing WISHE causes delayed intensification of TCs and weaker peak intensity. Strong suppression of the WISHE mechanism leads to a weak TC without undergoing RI, which is consistent with the simulation of Hurricane Edouard in Zhang and Emanuel (2016).

Analyses of the sensitivity experiments demonstrate that both the thermodynamic environment and the convective-scale processes are clearly affected by the suppression of surface heat fluxes. The experiments with stronger WISHE can produce more active and stronger convection in both before RI onset and during the RI (Fig. 10). In the inner-core region, reduced inertial stability, weaker diabatic heating, weaker and shallower warm-core structure, and less active CBs and weak-to-moderate convection can all be found in the sensitivity experiments. These features result from a weaker TC in the experiments with highly suppressed surface heat fluxes. Since suppressing the WISHE would affect the development of TC both before and during RI, possible explanations are summarized below by focusing the discussion on two separate time frames.

Before RI, the vortices in all experiments are relatively weak and the convection distribution is asymmetric. A wavenumber-1 structure of the convection could result from the environmental VWS. Strong convection is found in the DL quadrant (Figs. 15a17a), while downward mass fluxes with low θe are shown in UL quadrant (Fig. 18). During this period, the initial environmental CAPE could support development of the convection in the first few hours. Then WISHE starts to play important roles, such as providing the convective instability and reducing the negative influence from the environmental VWS. Stronger and more active updrafts (Fig. 10) and broader wind field (Fig. 13) are found in the experiments with more surface heat fluxes, in particular large differences of the storm structure between CTL and CAP-10. With stronger WISHE, TCs could intensify to a certain strength (which can be shown by the inertial stability in Fig. 3) earlier, followed by further intensification.

After the early period (i.e., before the RI onset time of CTL), the initial environmental CAPE is gradually consumed (Fig. 14), and the convective instability (i.e., increase of the θe in the lower levels) could be further enhanced by the surface heat fluxes. More surface heat fluxes could compensate the low θe induced by the downdrafts both in the lower levels (Fig. 5) and in the UL quadrant (Fig. 18), leading to continuous increase of the θe during the RI period (Fig. 6). Earlier increase of θe is found in the experiments with more WISHE, which could earlier trigger the convection in the upshear quadrant, followed by earlier axisymmetrization of the storm vortices (Figs. 11 and 12). These processes point out that the WISHE could overcome the negative effect from the downdrafts and the environmental VWS, resulting in the spinup of the vortices. With less WISHE (CAP-10), the vortex may not develop to the same strength as the vortex originally could. In the RI stage, gradual increase of the low-level θe (Fig. 5) is found, along with higher θe in the inner-core region (Fig. 6). In addition, after the onset time of RI in each experiment, the convection in the higher levels (Fig. 12d) then becomes axisymmetric, especially during the significantly intensifying period. An axisymmetric structure could lead to effective vortex spinup, while differences among the experiments are found. More WISHE could lead to more diabatic heating, which is associated with strong convection in the inner-core region (Fig. 10) and resulting in relatively strong inflows and efficient spinup (due to more diabatic heating and higher inertial stability). Stronger peak intensity is consequently found in the experiments with more WISHE. The downward motion in the vortex center is also more active with more WISHE (Fig. 10), leading to stronger warm core and lower MSLP. To sum up, WISHE could affect the TC evolution both in the pre-RI stage (in a stage where the TC starts to gradually intensify) and during the RI stage.

In all, following previous studies exploring the role of WISHE in TC development (e.g., Montgomery et al. 2009, 2015; Zhang and Emanuel 2016), this study demonstrates the key role WISHE plays in affecting TC intensification rate. Furthermore, this work specifically focuses on the intensifying TC both before and after RI, and includes further analyses of the RI case considering the effect from the VWS. Note that the interactions between TCs and environmental VWS with suppression on WISHE could be complicated and case dependent, and thus are worthy of further exploration.

Further in-depth examinations remain to be carried out. For instance, detailed analyses of evolutions of θe or other parameters affecting the thermodynamic structure of TC in the lower levels are needed. Furthermore, idealized experiments can be conducted to investigate the importance of WISHE in RI in an idealized-designed environment. Additional ensemble experiments will also be useful for evaluation of the characteristics and uncertainty under different vortex structures and environmental conditions.

Acknowledgments

This work is supported by the Ministry of Science and Technology of Taiwan under Grants MOST 107-2111-M-002-016-MY3, and by the Office of Naval Research through Grants N62909-16-1-2169 and N00014-20-1-2467. We thank the three anonymous reviewers for their helpful and in-depth comments.

REFERENCES

  • Cangialosi, J. P., and J. L. Franklin, 2012: Atlantic and eastern North Pacific forecast verification. Proc. 66th Interdepartmental Hurricane Conf., Charleston, SC, Office of the Federal Coordinator for Meteorology, http://www.ofcm.gov/meetings/TCORF/ihc12/Presentations/01b-Session/03-IHC_2012_Verification_(2012)_v2.pdf.

  • Chang, C., and C. Wu, 2017: On the processes leading to the rapid intensification of Typhoon Megi (2010). J. Atmos. Sci., 74, 11691200, https://doi.org/10.1175/JAS-D-16-0075.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, H., and D.-L. Zhang, 2013: On the rapid intensification of Hurricane Wilma (2005). Part II: Convective bursts and the upper-level warm core. J. Atmos. Sci., 70, 146162, https://doi.org/10.1175/JAS-D-12-062.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, H., and S. G. Gopalakrishnan, 2015: A study on the asymmetric rapid intensification of Hurricane Earl (2010) using the HWRF system. J. Atmos. Sci., 72, 531550, https://doi.org/10.1175/JAS-D-14-0097.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, C., and C. Wu, 2018: The role of WISHE in secondary eyewall formation. J. Atmos. Sci., 75, 38233841, https://doi.org/10.1175/JAS-D-17-0236.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Corbosiero, K. L., and J. Molinari, 2002: The effects of vertical wind shear on the distribution of convection in tropical cyclones. Mon. Wea. Rev., 130, 21102123, https://doi.org/10.1175/1520-0493(2002)130<2110:TEOVWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • DeMaria, M., C. R. Sampson, J. A. Knaff, and K. D. Musgrave, 2014: Is tropical cyclone intensity guidance improving? Bull. Amer. Meteor. Soc., 95, 387398, https://doi.org/10.1175/BAMS-D-12-00240.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dolling, K. P., and G. M. Barnes, 2012: The creation of a high equivalent potential temperature reservoir in Tropical Storm Humberto (2001) and its possible role in storm deepening. Mon. Wea. Rev., 140, 492505, https://doi.org/10.1175/MWR-D-11-00068.1.

    • 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
  • Eliassen, A., 1951: Slow thermally or frictionally controlled meridional circulation in a circular vortex. Astrophys. Norv., 5, 1960.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585605, https://doi.org/10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1989: The finite-amplitude nature of tropical cyclogenesis. J. Atmos. Sci., 46, 34313456, https://doi.org/10.1175/1520-0469(1989)046<3431:TFANOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1997: Some aspects of hurricane inner-core dynamics and energetics. J. Atmos. Sci., 54, 10141026, https://doi.org/10.1175/1520-0469(1997)054<1014:SAOHIC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Falvey, R., 2012: Summary of the 2011 western Pacific/Indian Ocean tropical cyclone season. Proc. 66th Interdepartmental Hurricane Conf., Charleston, SC, Office of the Federal Coordinator for Meteorology, http://www.ofcm.gov/meetings/TCORF/ihc12/Presentations/01b-Session/05-JTWC_2012_IHC_Final.pdf.

  • Finocchio, P. M., S. J. Majumdar, D. S. Nolan, and M. Iskandarani, 2016: Idealized tropical cyclone responses to the height and depth of environmental vertical wind shear. Mon. Wea. Rev., 144, 21552175, https://doi.org/10.1175/MWR-D-15-0320.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Guimond, S. R., G. M. Heymsfield, and F. J. Turk, 2010: Multiscale observations of Hurricane Dennis (2005): The effects of hot towers on rapid intensification. J. Atmos. Sci., 67, 633654, https://doi.org/10.1175/2009JAS3119.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, G. M., J. B. Halverson, J. Simpson, L. Tian, and T. P. Bui, 2001: ER-2 Doppler radar investigations of the eyewall of Hurricane Bonnie during the Convection and Moisture Experiment-3. J. Appl. Meteor., 40, 13101330, https://doi.org/10.1175/1520-0450(2001)040<1310:EDRIOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holliday, C. R., and A. H. Thompson, 1979: Climatological characteristics of rapidly intensifying typhoons. Mon. Wea. Rev., 107, 10221034, https://doi.org/10.1175/1520-0493(1979)107<1022:CCORIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., and J.-O. J. Lim, 2006: The WRF single-moment 6-class microphysics scheme (WSM6). J. Korean Meteor. Soc., 42, 129151.

  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, https://doi.org/10.1175/MWR3199.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Judt, F., and S. S. Chen, 2016: Predictability and dynamics of tropical cyclone rapid intensification deduced from high-resolution stochastic ensembles. Mon. Wea. Rev., 144, 43954420, https://doi.org/10.1175/MWR-D-15-0413.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kain, J. S., and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: The Kain–Fritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 24, Amer. Meteor. Soc., 165–170, https://doi.org/10.1007/978-1-935704-13-3_16.

    • Crossref
    • Export Citation
  • Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics of rapidly intensifying tropical cyclones in the North Atlantic basin. Wea. Forecasting, 18, 10931108, https://doi.org/10.1175/1520-0434(2003)018<1093:LCORIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kieper, M. E., and H. Jiang, 2012: Predicting tropical cyclone rapid intensification using the 37 GHz ring pattern identified from passive microwave measurements. Geophys. Res. Lett., 39, L13804, https://doi.org/10.1029/2012GL052115.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kleinschmidt, E., Jr., 1951: Grundlagen einer theorie der tropischen zyklonen. Arch. Meteor. Geophys. Bioklimatol., 4A, 5372, https://doi.org/10.1007/BF02246793.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kowch, R., and K. Emanuel, 2015: Are special processes at work in the rapid intensification of tropical cyclones? Mon. Wea. Rev., 143, 878882, https://doi.org/10.1175/MWR-D-14-00360.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., M. K. Tippett, A. H. Sobel, and S. J. Camargo, 2016: Rapid intensification and the bimodal distribution of tropical cyclone intensity. Nat. Commun., 7, 10625, https://doi.org/10.1038/ncomms10625.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Y., Y. Wang, and Y. Lin, 2019: Revisiting the dynamics of eyewall contraction of tropical cyclones. J. Atmos. Sci., 76, 32293245, https://doi.org/10.1175/JAS-D-19-0076.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miyamoto, Y., and T. Takemi, 2013: A transition mechanism for the spontaneous axisymmetric intensification of tropical cyclones. J. Atmos. Sci., 70, 112129, https://doi.org/10.1175/JAS-D-11-0285.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miyamoto, Y., and D. S. Nolan, 2018: Structural changes preceding rapid intensification in tropical cyclones as shown in a large ensemble of idealized simulations. J. Atmos. Sci., 75, 555569, https://doi.org/10.1175/JAS-D-17-0177.1.

    • 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 atmosphere: 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
  • Molinari, J., D. Vollaro, and K. L. Corbosiero, 2004: Tropical cyclone formation in a sheared environment: A case study. J. Atmos. Sci., 61, 24932509, https://doi.org/10.1175/JAS3291.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., N. V. Sang, R. K. Smith, and J. Persing, 2009: Do tropical cyclones intensify by WISHE? Quart. J. Roy. Meteor. Soc., 135, 16971714, https://doi.org/10.1002/qj.459.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., J. Persing, and R. K. Smith, 2015: Putting to rest WISHE-ful misconceptions for tropical cyclone intensification. J. Adv. Model. Earth Syst., 7, 92109, https://doi.org/10.1002/2014MS000362.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., Y. Moon, and D. P. Stern, 2007: Tropical cyclone intensification from asymmetric convection: Energetics and efficiency. J. Atmos. Sci., 64, 33773405, https://doi.org/10.1175/JAS3988.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ooyama, K., 1969: Numerical simulation of the life cycle of tropical cyclones. J. Atmos. Sci., 26, 340, https://doi.org/10.1175/1520-0469(1969)026<0003:NSOTLC>2.0.CO;2.

    • 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
  • Reasor, P. D., M. D. Eastin, and J. F. Gamache, 2009: Rapidly intensifying Hurricane Guillermo (1997). Part I: Low wavenumber structure and evolution. Mon. Wea. Rev., 137, 603631, https://doi.org/10.1175/2008MWR2487.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Riehl, H., 1950: A model for hurricane formation. J. Appl. Phys., 21, 917925, https://doi.org/10.1063/1.1699784.

  • Rios-Berrios, R., and R. D. Torn, 2017: Climatological analysis of tropical cyclone intensity changes under moderate vertical wind shear. Mon. Wea. Rev., 145, 17171738, https://doi.org/10.1175/MWR-D-16-0350.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rios-Berrios, R., R. D. Torn, and C. A. Davis, 2016: An ensemble approach to investigate tropical cyclone intensification in sheared environments. Part I: Katia (2011). J. Atmos. Sci., 73, 7193, https://doi.org/10.1175/JAS-D-15-0052.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rios-Berrios, R., C. A. Davis, and R. D. Torn, 2018: A hypothesis for the intensification of tropical cyclones under moderate vertical wind shear. J. Atmos. Sci., 75, 41494173, https://doi.org/10.1175/JAS-D-18-0070.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R. F., 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. F., P. D. 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
  • Rogers, R. F., P. D. Reasor, and J. A. Zhang, 2015: Multiscale structure and evolution of Hurricane Earl (2010) during rapid intensification. Mon. Wea. Rev., 143, 536562, https://doi.org/10.1175/MWR-D-14-00175.1.

    • 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
  • 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
  • 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
  • Sitkowski, M., and G. M. Barnes, 2009: Low-level thermodynamic, kinematic, and reflectivity fields of Hurricane Guillermo (1997) during rapid intensification. Mon. Wea. Rev., 137, 645663, https://doi.org/10.1175/2008MWR2531.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.

    • Crossref
    • Export Citation
  • Smith, R. K., 2003: A simple model of the hurricane boundary layer. Quart. J. Roy. Meteor. Soc., 129, 10071027, https://doi.org/10.1256/qj.01.197.

  • Stern, D. P., and F. Zhang, 2013: How does the eye warm? Part I: A potential temperature budget analysis of an idealized tropical cyclone. J. Atmos. Sci., 70, 7390, https://doi.org/10.1175/JAS-D-11-0329.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stern, D. P., J. L. Vigh, D. S. Nolan, and F. Zhang, 2015: Revisiting the relationship between eyewall contraction and intensification. J. Atmos. Sci., 72, 12831306, https://doi.org/10.1175/JAS-D-14-0261.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stevenson, S. N., K. L. Corbosiero, and J. Molinari, 2014: The convective evolution and rapid intensification of Hurricane Earl (2010). Mon. Wea. Rev., 142, 43644380, https://doi.org/10.1175/MWR-D-14-00078.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, H., and Y. Wang, 2014: A numerical study of Typhoon Megi (2010). Part I: Rapid intensification. Mon. Wea. Rev., 142, 2948, https://doi.org/10.1175/MWR-D-13-00070.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zagrodnik, J. P., and H. Jiang, 2014: Rainfall, convection, and latent heating distributions in rapidly intensifying tropical cyclones. J. Atmos. Sci., 71, 27892809, https://doi.org/10.1175/JAS-D-13-0314.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, D.-L., and H. Chen, 2012: Importance of the upper-level warm core in the rapid intensification of a tropical cyclone. Geophys. Res. Lett., 39, L02806, https://doi.org/10.1029/2011GL050578.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., and K. A. Emanuel, 2016: On the role of surface fluxes and WISHE in tropical cyclone intensification. J. Atmos. Sci., 73, 20112019, https://doi.org/10.1175/JAS-D-16-0011.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
Save
  • Cangialosi, J. P., and J. L. Franklin, 2012: Atlantic and eastern North Pacific forecast verification. Proc. 66th Interdepartmental Hurricane Conf., Charleston, SC, Office of the Federal Coordinator for Meteorology, http://www.ofcm.gov/meetings/TCORF/ihc12/Presentations/01b-Session/03-IHC_2012_Verification_(2012)_v2.pdf.

  • Chang, C., and C. Wu, 2017: On the processes leading to the rapid intensification of Typhoon Megi (2010). J. Atmos. Sci., 74, 11691200, https://doi.org/10.1175/JAS-D-16-0075.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, H., and D.-L. Zhang, 2013: On the rapid intensification of Hurricane Wilma (2005). Part II: Convective bursts and the upper-level warm core. J. Atmos. Sci., 70, 146162, https://doi.org/10.1175/JAS-D-12-062.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, H., and S. G. Gopalakrishnan, 2015: A study on the asymmetric rapid intensification of Hurricane Earl (2010) using the HWRF system. J. Atmos. Sci., 72, 531550, https://doi.org/10.1175/JAS-D-14-0097.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, C., and C. Wu, 2018: The role of WISHE in secondary eyewall formation. J. Atmos. Sci., 75, 38233841, https://doi.org/10.1175/JAS-D-17-0236.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Corbosiero, K. L., and J. Molinari, 2002: The effects of vertical wind shear on the distribution of convection in tropical cyclones. Mon. Wea. Rev., 130, 21102123, https://doi.org/10.1175/1520-0493(2002)130<2110:TEOVWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • DeMaria, M., C. R. Sampson, J. A. Knaff, and K. D. Musgrave, 2014: Is tropical cyclone intensity guidance improving? Bull. Amer. Meteor. Soc., 95, 387398, https://doi.org/10.1175/BAMS-D-12-00240.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dolling, K. P., and G. M. Barnes, 2012: The creation of a high equivalent potential temperature reservoir in Tropical Storm Humberto (2001) and its possible role in storm deepening. Mon. Wea. Rev., 140, 492505, https://doi.org/10.1175/MWR-D-11-00068.1.

    • 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
  • Eliassen, A., 1951: Slow thermally or frictionally controlled meridional circulation in a circular vortex. Astrophys. Norv., 5, 1960.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585605, https://doi.org/10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1989: The finite-amplitude nature of tropical cyclogenesis. J. Atmos. Sci., 46, 34313456, https://doi.org/10.1175/1520-0469(1989)046<3431:TFANOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., 1997: Some aspects of hurricane inner-core dynamics and energetics. J. Atmos. Sci., 54, 10141026, https://doi.org/10.1175/1520-0469(1997)054<1014:SAOHIC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Falvey, R., 2012: Summary of the 2011 western Pacific/Indian Ocean tropical cyclone season. Proc. 66th Interdepartmental Hurricane Conf., Charleston, SC, Office of the Federal Coordinator for Meteorology, http://www.ofcm.gov/meetings/TCORF/ihc12/Presentations/01b-Session/05-JTWC_2012_IHC_Final.pdf.

  • Finocchio, P. M., S. J. Majumdar, D. S. Nolan, and M. Iskandarani, 2016: Idealized tropical cyclone responses to the height and depth of environmental vertical wind shear. Mon. Wea. Rev., 144, 21552175, https://doi.org/10.1175/MWR-D-15-0320.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Guimond, S. R., G. M. Heymsfield, and F. J. Turk, 2010: Multiscale observations of Hurricane Dennis (2005): The effects of hot towers on rapid intensification. J. Atmos. Sci., 67, 633654, https://doi.org/10.1175/2009JAS3119.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, G. M., J. B. Halverson, J. Simpson, L. Tian, and T. P. Bui, 2001: ER-2 Doppler radar investigations of the eyewall of Hurricane Bonnie during the Convection and Moisture Experiment-3. J. Appl. Meteor., 40, 13101330, https://doi.org/10.1175/1520-0450(2001)040<1310:EDRIOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holliday, C. R., and A. H. Thompson, 1979: Climatological characteristics of rapidly intensifying typhoons. Mon. Wea. Rev., 107, 10221034, https://doi.org/10.1175/1520-0493(1979)107<1022:CCORIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., and J.-O. J. Lim, 2006: The WRF single-moment 6-class microphysics scheme (WSM6). J. Korean Meteor. Soc., 42, 129151.

  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, https://doi.org/10.1175/MWR3199.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Judt, F., and S. S. Chen, 2016: Predictability and dynamics of tropical cyclone rapid intensification deduced from high-resolution stochastic ensembles. Mon. Wea. Rev., 144, 43954420, https://doi.org/10.1175/MWR-D-15-0413.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kain, J. S., and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: The Kain–Fritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 24, Amer. Meteor. Soc., 165–170, https://doi.org/10.1007/978-1-935704-13-3_16.

    • Crossref
    • Export Citation
  • Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics of rapidly intensifying tropical cyclones in the North Atlantic basin. Wea. Forecasting, 18, 10931108, https://doi.org/10.1175/1520-0434(2003)018<1093:LCORIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kieper, M. E., and H. Jiang, 2012: Predicting tropical cyclone rapid intensification using the 37 GHz ring pattern identified from passive microwave measurements. Geophys. Res. Lett., 39, L13804, https://doi.org/10.1029/2012GL052115.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kleinschmidt, E., Jr., 1951: Grundlagen einer theorie der tropischen zyklonen. Arch. Meteor. Geophys. Bioklimatol., 4A, 5372, https://doi.org/10.1007/BF02246793.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kowch, R., and K. Emanuel, 2015: Are special processes at work in the rapid intensification of tropical cyclones? Mon. Wea. Rev., 143, 878882, https://doi.org/10.1175/MWR-D-14-00360.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., M. K. Tippett, A. H. Sobel, and S. J. Camargo, 2016: Rapid intensification and the bimodal distribution of tropical cyclone intensity. Nat. Commun., 7, 10625, https://doi.org/10.1038/ncomms10625.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Y., Y. Wang, and Y. Lin, 2019: Revisiting the dynamics of eyewall contraction of tropical cyclones. J. Atmos. Sci., 76, 32293245, https://doi.org/10.1175/JAS-D-19-0076.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miyamoto, Y., and T. Takemi, 2013: A transition mechanism for the spontaneous axisymmetric intensification of tropical cyclones. J. Atmos. Sci., 70, 112129, https://doi.org/10.1175/JAS-D-11-0285.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miyamoto, Y., and D. S. Nolan, 2018: Structural changes preceding rapid intensification in tropical cyclones as shown in a large ensemble of idealized simulations. J. Atmos. Sci., 75, 555569, https://doi.org/10.1175/JAS-D-17-0177.1.

    • 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 atmosphere: 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
  • Molinari, J., D. Vollaro, and K. L. Corbosiero, 2004: Tropical cyclone formation in a sheared environment: A case study. J. Atmos. Sci., 61, 24932509, https://doi.org/10.1175/JAS3291.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., N. V. Sang, R. K. Smith, and J. Persing, 2009: Do tropical cyclones intensify by WISHE? Quart. J. Roy. Meteor. Soc., 135, 16971714, https://doi.org/10.1002/qj.459.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., J. Persing, and R. K. Smith, 2015: Putting to rest WISHE-ful misconceptions for tropical cyclone intensification. J. Adv. Model. Earth Syst., 7, 92109, https://doi.org/10.1002/2014MS000362.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., Y. Moon, and D. P. Stern, 2007: Tropical cyclone intensification from asymmetric convection: Energetics and efficiency. J. Atmos. Sci., 64, 33773405, https://doi.org/10.1175/JAS3988.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ooyama, K., 1969: Numerical simulation of the life cycle of tropical cyclones. J. Atmos. Sci., 26, 340, https://doi.org/10.1175/1520-0469(1969)026<0003:NSOTLC>2.0.CO;2.

    • 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
  • Reasor, P. D., M. D. Eastin, and J. F. Gamache, 2009: Rapidly intensifying Hurricane Guillermo (1997). Part I: Low wavenumber structure and evolution. Mon. Wea. Rev., 137, 603631, https://doi.org/10.1175/2008MWR2487.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Riehl, H., 1950: A model for hurricane formation. J. Appl. Phys., 21, 917925, https://doi.org/10.1063/1.1699784.

  • Rios-Berrios, R., and R. D. Torn, 2017: Climatological analysis of tropical cyclone intensity changes under moderate vertical wind shear. Mon. Wea. Rev., 145, 17171738, https://doi.org/10.1175/MWR-D-16-0350.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rios-Berrios, R., R. D. Torn, and C. A. Davis, 2016: An ensemble approach to investigate tropical cyclone intensification in sheared environments. Part I: Katia (2011). J. Atmos. Sci., 73, 7193, https://doi.org/10.1175/JAS-D-15-0052.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rios-Berrios, R., C. A. Davis, and R. D. Torn, 2018: A hypothesis for the intensification of tropical cyclones under moderate vertical wind shear. J. Atmos. Sci., 75, 41494173, https://doi.org/10.1175/JAS-D-18-0070.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rogers, R. F., 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. F., P. D. 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
  • Rogers, R. F., P. D. Reasor, and J. A. Zhang, 2015: Multiscale structure and evolution of Hurricane Earl (2010) during rapid intensification. Mon. Wea. Rev., 143, 536562, https://doi.org/10.1175/MWR-D-14-00175.1.

    • Crossref