Numerical Study on the Extremely Rapid Intensification of an Intense Tropical Cyclone: Typhoon Ida (1958) (original) (raw)

1. Introduction

Although there have been steady improvements in forecasting the tracks of tropical cyclones (TCs), forecasting their intensities remains a challenging issue (e.g., Wang and Wu 2004), because TC intensity and its changes involve a wide variety of processes over multiple temporal and spatial scales. These processes include atmospheric and oceanic environmental phenomena (e.g., Gray 1968; Hendricks et al. 2010; Riemer et al. 2010; Wada et al. 2012), cloud microphysics (e.g., Sawada and Iwasaki 2007; Zhou and Wang 2011), planetary boundary layer (PBL) processes (e.g., Kepert 2012), TC vortex dynamics and associated convection (e.g., Montgomery and Enagonio 1998; Montgomery et al. 2006), and air–sea interactions beneath the TC (e.g., Ito et al. 2011; Wada et al. 2014).

More accurate prediction of the rate of TC intensification is a key factor for improving intensity forecasts. According to TC best-track data, most intense TCs, specifically category 4 and 5 (Kaplan and DeMaria 2003) TCs on the Saffir–Simpson hurricane scale (http://www.nhc.noaa.gov/aboutsshws.php), undergo rapid intensification (RI). One of the definitions of RI is a central pressure drop greater than 42 hPa within 24 h (Holliday and Thompson 1979). The RI associated with extremely intense TCs is of great concern because of the serious damage caused by these storms, particularly in coastal regions.

TC intensification is theoretically explained by symmetric and asymmetric mechanisms. The former involves a symmetric, overturning, balanced circulation above the PBL (Charney and Eliassen 1964; Ooyama 1969). Recently, Vigh and Schubert (2009) used a balanced vortex model to show that diabatic heating within a region of high inertial stability inside the radius of maximum azimuthal mean wind (RMW) results in a rapid increase of positive warm-core temperature anomalies. By applying the Sawyer–Eliassen equation to a balanced vortex, Pendergrass and Willoughby (2009) also found that diabatic heating inside the RMW results in a rapid increase of tangential winds and, thus, a contraction of the RMW.

In contrast, the asymmetric mechanism highlights a rotating, deep convection (i.e., vortical hot towers), generally in relation to the spinup mechanism of maximum tangential winds in the TC boundary layer, where the winds are affected by surface friction (Bui et al. 2009; Montgomery et al. 2014; Montgomery and Smith 2014; Smith et al. 2009).

Many previous studies have linked deep convection around the storm center to TC intensification. In the late 1980s, Steranka et al. (1986) found that maximum winds of TCs in most cases increased by 5 m s−1 or more within 24 h, during which time intense convection with high cloud tops lasted more than 9 h. Based on a composite analyses of airborne Doppler observations, Rogers et al. (2013) reported that intensifying TCs had a relatively large amount of tall and vigorous convection [i.e., convective bursts (CBs)] inside the RMW compared with steady-state TCs. Sanger et al. (2014) examined the spinup mechanism of rapidly intensifying Super Typhoon Jangmi (2008) and reported the observation of multiple rotating updrafts and a huge upright updraft with strong, low-level convergence and intense relative vorticity inside the RMW. The contribution of CBs to an upper-level warm core have also been suggested in observational and numerical studies (Chen and Zhang 2013; Guimond et al. 2010; Heymsfield et al. 2001).

Recently, Kieper and Jiang (2012) found that a ringlike axisymmetric pattern of precipitation detected from satellite observations was related to RI. Furthermore, based on an 11-yr Tropical Rainfall Measuring Mission database (http://pmm.nasa.gov/trmm), a statistical relationship existed between inner-core convection intensity and TC intensification (Jiang 2012). However, that study also indicated that the increase of RI probability above the climatological mean predicted by the existence of hot towers was not very large. In addition, the RI probability without hot towers was still 4.9% (Jiang 2012). Moderate-to-deep convection and associated latent heat release significantly increased only after RI had been underway for at least 12 h (Zagrodnik and Jiang 2014).

There is debate about the importance of the axisymmetric and asymmetric processes of TC intensification (e.g., Nolan et al. 2007). Which of the mechanisms is more important for triggering RI above the boundary layer or inside the boundary layer and for determining the rate of intensification?

First, the structural changes of the TC inner-core region just before and during RI need to be clarified. To provide this clarification, we performed numerical experiments that allowed us to investigate the temporal evolution of atmospheric environmental conditions and inner-core structures of an extremely intense TC accompanied by extremely rapid intensification (ERI). We paid special attention to the structural changes of the inner-core region before the onset of ERI to thoroughly understand the mechanisms associated with ERI processes in the inner-core region and to identify the inner-core structures and environmental conditions for the onset of ERI.

2. Model and methodology

a. Case description

This study chose an extremely intense TC [minimum central pressure (MCP) < 900 hPa] case that had undergone the greatest rapid deepening, according to best-track data, since 1952. A tropical depression formed from an easterly wave around the Marshall Islands on 20 September 1958 and was named Ida at 1800 UTC 20 September (Fig. 1). The storm moved to the west while maintaining a central pressure of 985 hPa. At 0000 UTC 22 September, the TC changed direction to the northwest and initiated RI. The TC underwent an extremely rapid drop in central pressure (CP) at rates that exceeded 20 hPa (6 h)−1 from 0600 to 1200 UTC 23 September and reached an MCP of 877 hPa at 0600 UTC 24 September. The maximum drop rate of CP per 6 h () was 39 hPa. The TC then moved northward and made landfall in Japan around 34.4°N, 139.0°E at 1500 UTC 26 September. The TC caused torrential flooding in southeastern Japan that resulted in 1269 fatalities.

Fig. 1.

Fig. 1.

Fig. 1.

Domain of the NHM5 experiment and track of Typhoon Ida (1958) every 6 h indicated by closed black symbols. Closed square symbols indicate the location of the minimum central pressure. The rectangle outlined by the red line shows the domain of the NHM2 experiments. Black numbers indicate the day in September 1958. (top-right inset) Tracks of the TC simulated with NHM5 (blue), 2112 (green), 2118 (orange), and 2200 (red), as well as the best track (black). Corresponding colored numbers indicate integration times (h) for each simulation.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

b. Model description

The nonhydrostatic atmosphere model is based on the Japan Meteorological Agency (JMA) operational nonhydrostatic mesoscale model (JMANHM; Saito et al. 2007). The 2-km-mesh version (NHM2) includes bulk-type cloud microphysics with an ice phase (Murakami 1990), a clear-sky radiation scheme (Yabu et al. 2005), and a cloud radiation scheme (Kitagawa 2000). No cumulus parameterization scheme is adopted in NHM2. The model applies the Deardorff–Blackadar scheme (Deardorff 1980; Blackadar 1962) and the Louis scheme (Louis et al. 1982) with a surface-roughness-length formulation based on Kondo (1975) as the PBL scheme and surface boundary layer scheme, respectively. Basic configurations are the same as in our previous studies (Kanada et al. 2012, 2013). The computational domain of NHM2 is 3980 km × 2380 km (Fig. 1), and the number of vertical levels is set to 55 (the lowermost layer is 20 m and the top height is approximately 27 km).

Initial and lateral boundary conditions for the NHM2 experiments were provided every 6 h from the numerical experiments with JMANHM with a horizontal resolution of 5 km (NHM5). NHM5 used the spectral nudging method (Nakano et al. 2012), the Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1993) and the level 3 Mellor–Yamada–Nakanishi–Niino closure PBL scheme (Nakanishi and Niino 2004). The computational domain of NHM5 is 5400 km × 4600 km (Fig. 1). Other configurations of NHM5 were as in NHM2.

Initial and lateral atmospheric boundary conditions and sea surface temperature (SST) initial conditions for the NHM5 experiment were provided every 6 h from the JMA 55-year Reanalysis dataset (JRA-55; Ebita et al. 2011) with a horizontal resolution of 1.25° for atmospheric ingredients and that of 0.56° for SST.

The numerical experiments were conducted as follows: first, a numerical experiment with NHM5 nested in JRA-55 was performed starting at 0000 UTC 21 September. Next, the numerical experiments were conducted by using NHM2 with the results of NHM5 for each initial time: 1200 UTC 21 September (2112), 1800 UTC 21 September (2118), and 0000 UTC 22 September (2200) 1958.

c. Analytical methods

The approximate geometric center (centroid) of the storm was determined for each numerical result of the NHM based on the horizontal distribution of sea level pressure (Braun 2002). Because the pressure field appeared noisy around vigorous convection in the eyewall, the centroid was calculated at radial intervals of 2 km and summed within radius R = 100 km for every grid (, ) around the location of the CP (, ). The grid (X, Y) at which the summation was the smallest was selected as the storm center. The location of the pressure center was calculated in the same way as the storm center for every 500 m of altitude by using the pressure field at each altitude. The distance between the storm and pressure centers was defined as the tilt of the storm axis for each altitude. Radial (V r) and tangential (V t) winds determined relative to the storm center were calculated for each Cartesian grid. We also calculated the circulation center based on the method of Reasor and Eastin (2012). The rationale that underlies their method is similar to that for the above-mentioned method, but their method seeks a location that maximizes the azimuthal-mean V t on the storm-vortex scale. The initial guess position was moved within 20 km from the pressure center with a search radius interval of 5 km. However, the circulation center was difficult to determine in the upper troposphere, where V t was weak. Therefore, we mainly used the pressure center.

The radius of azimuthal mean maximum tangential wind for every 500 m of altitude (RMWaltitude) was calculated relative to the storm center. Following Rogers et al. (2013), the normalized radius r* was defined with respect to RMW2km. In this study r* ≡ _r/_RMW2km.

Vertical wind shear (VWS) was defined as the difference in the mean horizontal wind speed between altitudes of 1.5 km (~850 hPa) and 12.5 km (~200 hPa). Mean horizontal winds were calculated over a circular area with a radius of 500 km for the NHM2 experiments. The average of the horizontal winds over a 1000 km × 1000 km square based on JRA-55 data was used for the environmental VWS in the NHM5 experiment.

3. Results

a. Initial conditions for numerical experiments by NHM2

We used the results of the NHM5 experiment to specify atmospheric conditions at the initial time for each numerical experiment with the NHM2. The NHM5 simulated storm centers of Ida that were reasonable when compared to the Regional Specialized Meteorological Center Tokyo best-track data (Fig. 1). The error against the best-track storm center was less than 1° in the longitude–latitude coordinate system.

Figures 2a and 2b show the horizontal patterns of hourly precipitation and vertical vorticity at an altitude of 20 m by the NHM5 collocated at the storm center. The simulated inner-core horizontal patterns were asymmetric at 1200 UTC 21 September. Simulated precipitation was intense (>30 mm h−1) to the west and southwest of the storm center (Fig. 2a). Positive vertical vorticity was intense (>8 × 10−4 s−1) to the south of the storm center (Fig. 2b). The relation of the horizontal pattern of intense precipitation and vertical vorticity to the VWS (Fig. 2c) was consistent with the observational results reported by Reasor and Eastin (2012) and Reasor et al. (2013).

Fig. 2.

Fig. 2.

Fig. 2.

Storm-centered horizontal distributions of (a) hourly precipitation (mm h−1), (b) vertical vorticity (10−4 s−1) at an altitude of 20 m, and (c) specific humidity (g kg−1) at altitudes of 12 km, 3 km, and 20 m at (left) 1200 UTC 21 Sep, (middle) 1800 UTC 21 Sep, and (right) 0000 UTC 22 Sep 1958 simulated by the NHM5. Black arrows indicate horizontal winds at each altitude. Magenta contours indicate horizontal wind speeds of 15 m s−1. Black dots and squares in (c) indicate the pressure and circulation centers at each altitude. (c) (bottom) White arrows indicate the VWS derived from the JRA-55 dataset. (c) (top) The insets indicate locations of the pressure centers for altitudes of 0, 3, 6, 9, and 12 km.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

Figure 2c shows the simulated horizontal patterns of inner-core specific humidity at altitudes of 12 km, 3 km, and 20 m collocated at the storm center. The horizontal patterns were asymmetric at 1200 UTC 21 September. Relatively strong VWS was responsible for the tilt defined by the pressure centers to the downshear of the VWS. The pressure center was not specified at an altitude of 12 km within a 200-km radius of the storm center. The specific humidity was still less than 0.2 g kg−1 at an altitude of 12 km.

As the storm intensified, the horizontal patterns of the horizontal winds and hourly precipitation gradually became less asymmetric (Figs. 2a,b). At 1800 UTC 21 September, relatively dry air with a relatively low specific humidity of less than 8.0 g kg−1 at an altitude of 3 km (19 g kg−1 at an altitude of 20 m) appeared at distances of 100–400 km to the south and east of the pressure center (middle panels of Fig. 2c). Meanwhile, water vapor was gradually transported upward.

At 0000 UTC 22 September, the specific humidity exceeded 0.2 g kg−1 around the storm center at an altitude of 12 km. The pressure and circulation centers were specified within a radius of 15 km from the storm center at all three altitudes. These NHM5 results served as the initial conditions for the following three NHM2 experiments.

b. Temporal evolution of the TC simulated by the NHM2

This subsection addresses the evolution of the simulated storm for each of the three NHM2 experiments. Because a spectral nudging method (Nakano et al. 2012) was not used, the simulated storm centers of Ida in the three NHM2 experiments were a few degrees different from the best-track storm center in the longitude–latitude coordinate system (Fig. 1). However, the location of the simulated MCP at around 20°N, 135°E was almost the same as that of the best-track MCP. The exception was the 2112 simulation, when the simulated storm reached its MCP 1 day later and 3° farther north from the best-track storm center. Herein, the magnitude of (see section 2a) is used as a metric to specify RI.

Figure 3 indicates that the best-track was greater than 20 hPa between 0600 and 1200 UTC 23 September. The extraordinary values were simulated well in the 2118 and 2200 simulations, for which the MCPs were 887 and 877 hPa, respectively. However, the simulated never exceeded 20 hPa in the 2112 simulation. Here, an experiment in which the extraordinary was (not) well simulated is called an ERI (RI) experiment. The 2118 and 2200 simulations were categorized as ERI experiments, whereas the 2112 simulation was regarded as an RI experiment. The onset of ERI and RI was defined as the time when the exceeded 10 hPa after 1200 UTC 22 September (Fig. 3b). The onset occurred at 1200 UTC 23 September for the 2112 simulation, at 0000 UTC 23 September for the 2118 simulation, and at 0300 UTC 23 September for the 2200 simulation.

Fig. 3.

Fig. 3.

Fig. 3.

Temporal evolutions in 1958 of (a) CP and (b) rate of changes in CP in 6 h for the best track (closed black circle), JRA-55 (open circle), and NHM5 (blue) and for the 2112 (green), 2118 (orange), and 2200 (red) simulations. Dotted lines indicate the onset times of ERI for the 2118 (orange) and 2200 (red) simulations and RI for the 2112 (green) simulation.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

The following question is raised from the results of the three NHM2 simulations: why did two of the three simulations successfully reproduce the ERI? In other words, what factors control the onset of ERI?

To answer this question, we compared simulated horizontal patterns of hourly precipitation in the three simulations from 1200 UTC 22 September to 0000 UTC 23 September collocated at the storm center (Fig. 4). During this period, was less than 10 hPa in the three NHM2 simulations. All the simulations indicated that strong VWS resulted in a shift of the circulation center at an altitude of 10 km toward the downshear side. The amount of hourly precipitation was high on the downshear-left (DSL) side of the VWS, whereas the hourly precipitation was relatively low on the right side of the VWS, in good agreement with Reasor et al. (2013).

Fig. 4.

Fig. 4.

Fig. 4.

Storm-centered composite horizontal distributions of hourly precipitation for the (top) 2112, (middle) 2118, and (bottom) 2200 simulations every 3 h. Magenta contours indicate the wind speed of 33.5 m s−1. RMW2km for each panel is depicted by a black circle. The circulation centers and corresponding RMWs at an altitude of 10 km for each panel are depicted by a black square and a white circle, respectively. Black arrows indicate the VWS for each simulation. The relative time of the onset for each ERI or RI is indicated in each panel.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

At 1800 UTC 22 September, the horizontal pattern of relatively weak precipitation (<20 mm h−1) developed a ringlike shape in the ERI experiments. The RMW2km and radius of maximum wind speed (MWS) for the circulation center at an altitude of 10 km were almost the same among the three NHM2 simulations. However, in the ERI experiments, the RMW2km became smaller after 1800 UTC 22 September, whereas the RMW2km varied without any trends in the 2112 simulation. At 0000 UTC 23 September, the distance between the storm and circulation centers decreased (<20 km), and the storm axis was almost upright for the ERI experiments.

Intensification is often accompanied by eyewall contraction. The evolutions of the eyewall precipitation are shown in Fig. 5 within the RMW at three altitudes: RMW0.5km, RMW2km, and RMW10km. RMW0.5km is assumed to be inside the TC inflow boundary layer (IBL). After the onset of ERI, precipitation rapidly intensified at the eyewall, and then the eyewall contracted. Areas with moderate precipitation (>20 mm h−1) roughly corresponded to RMW0.5km and RMW2km. Herein, RMW2km was applied as the reference, because most of the previous studies used RMW2km. RMW2km tended to be smaller in the ERI experiments than in the 2112 simulation.

Fig. 5.

Fig. 5.

Fig. 5.

(a) Radius–time cross sections of azimuthal-mean hourly precipitation (color; mm h−1) at an altitude of 20 m in the (left) 2112, (middle) 2118, and (right) 2200 simulations. Dotted line, black circles, and crosses indicate RMW0.5km, RMW2km, and RMW10km, respectively. (b) Temporal evolutions of MWS at an altitude of 0.5 km in the 2112 (green), 2118 (orange), and 2200 (red) simulations. Horizontal dotted lines indicate the onset times of the ERI and RI in the 2118 (orange), 2200 (red), and 2112 (green) simulations. Sky-blue lines in (a) indicate V r = 2 m s−1. Positive values of V r always indicate inflow in this study.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

It should be noted that RMW10km, which was much larger than RMW0.5km and RMW2km, decreased rapidly after the onset of ERI and RI in all the simulations. These results indicate that each axis for MWS rapidly became upright as the central pressure rapidly deepened. During the analysis period, the MWS always existed in the IBL. Temporal evolutions of the MWS at an altitude of 0.5 km revealed that the MWS started to increase 3–9 h before the onsets of both ERI and RI, at 0900 UTC 23 September and at 2100 and 1800 UTC 22 September 1958 for the 2112, 2118, and 2200 simulations, respectively (Fig. 5b).

Many previous studies have pointed out the relationship between the slope of eyewall updraft, TC intensification, and VWS (Hazelton et al. 2015; Reasor et al. 2013; Riemer et al. 2010). Most of these studies have indicated that weak VWS is favorable for TC intensification. However, the simulated Ida experienced strong VWS before and during the onset of ERI (Fig. 6). Figure 6 also indicates that the inner core was gradually moistening 3–6 h before the onset of ERI in the ERI experiments around 0000 UTC 22 September, while it was less moistened in the 2112 simulation at that time. How did simulated TCs evolve to initialize ERI in the strong VWS condition?

Fig. 6.

Fig. 6.

Fig. 6.

Temporal variations in mean relative humidity between 0.75 < r* < 1.25 in the (a) 2112, (b) 2118, and (c) 2200 simulations. Black lines with open circles and arrows indicate VWS magnitude and direction, respectively. Each dotted line indicates the onset time for each ERI or RI.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

c. Temporal evolution of inner-core structure before the onset of ERI

The temporal evolution of the inner-core structure of the simulated TC in the 2200 simulation was examined 12 h before the onset of ERI. The horizontal distributions of vertical velocity and relative humidity at an altitude of 6 km indicated the subsiding strong flows in an area within which relative humidity was less than 50% to the north of the storm center at 1500 UTC 22 September (A in Fig. 7a). The horizontal scale of the dry area was much larger than that of convective downdrafts. Based on mean potential temperature (PT) anomalies, calculated from the mean PT within a radius of 400 km, a warm core appeared at an altitude of 6 km. In contrast, shallow-to-moderate updrafts were produced inside the RMW2km in the DSL quadrant at an altitude of 2 km (B in Fig. 7b). A cluster of updraft areas corresponded to the areas of relative humidity greater than 95% at an altitude of 2 km.

Fig. 7.

Fig. 7.

Fig. 7.

At altitudes of (a) 6 and (b) 2 km every 3 h in the 2200 simulation, horizontal distributions of (top) vertical velocity and (middle) relative humidity (RH). (a) (bottom) PT anomalies from the mean value within a radius of 400 km. The RMW for each relevant altitude is depicted by a white circle. Green contours and magenta arrows at an altitude of 6 km indicate horizontal wind speeds of 40 and 50 m s−1 and the VWS, respectively. Black arrows indicate horizontal winds for each altitude. Black dots indicate the pressure center for each altitude. The relative time of the onset of ERI is included in parentheses with the time for each panel.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

During 1800 and 2100 UTC 22 September, relatively strong and dry (relative humidity < 60%) subsiding winds flowed around the RMW6km in the upshear-left quadrant (C and D in Fig. 7a). Meanwhile, the updrafts were relatively strong on the left side of the VWS. At 0000 UTC 23 September, almost whole areas around the RMW were covered by airs of high relative humidity greater than 90% at both altitudes.

Reasor et al. (2013) investigated the relationships between mean shear and inner-core structures for cases with weak shear (<4 m s−1) and strong shear (>7 m s−1). In our study, the mean VWS 12 h before the onset of ERI in the 2200 simulation exceeded 13 m s−1, which is an extremely strong shear case. Figure 8 shows mean vertical cross sections of the inner-core area for each quadrant relative to VWS in the 2200 simulation from 1500 UTC 22 September to 0000 UTC 23 September. According to Reasor et al. (2013), the most intense near-surface inflow was in the downshear quadrants of the storm, and the most intense and tallest updrafts were formed from the leading edge of the near-surface inflow. In our study, tall, intense updrafts were also seen on the DSL side of the storm center outside the RMW2km at 1500 UTC 22 September (A in Fig. 8). Around the leading edge of the intense near-surface inflow, shallow-to-moderate updrafts formed, with top heights below 6 km (S in Fig. 8). The updraft areas closely corresponded to the areas with high relative humidity: water vapor near the surface was transported to the upper troposphere because of the updrafts. A warm core had appeared inside the area of shallow-to-moderate convection at altitudes below 8 km (WC1 in Fig. 8).

Fig. 8.

Fig. 8.

Fig. 8.

(a) Radius–height cross section of (left) USL and (right) DSL of relative humidity in the 2200 simulation. (b) As in (a), but for (left) USR and (right) DSR. Lines indicate V r (5, 20, and 40 m s−1; magenta), vertical velocity (1 m s−1; blue), and potential temperature anomalies (7 K; black). RMW2km is depicted by dotted lines in each vertical panel. Arrows indicate radial–vertical winds in each panel. The relative time of the onset for the ERI is included in parentheses with the time in each panel.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

At 1800 UTC 22 September, a tall, vigorous updraft formed around the RMW2km in the DSL (C0 in Fig. 8). The midlevel inflow (V r > 5 m s−1) appeared in the upshear-left (USL) and upshear-right (USR) quadrants of the storm (B in Fig. 8). At 2100 UTC 22 September, the inner-core area to the right side of the VWS became dry, although the warm core remained at altitudes below 10 km (WC1 in Fig. 8). In addition, the upper-level warm core appeared above an altitude of 10 km (WC2 in Fig. 8). At 0000 UTC 23 September, tall, vigorous updrafts developed at a radius of 45 km in the DSL (CB in Fig. 8). The onset of ERI occurred 3 h after the outbreak of CB.

The results indicate that inner-core moistening due to updrafts with a variety of heights would provide local environmental conditions conducive to tall vigorous updrafts before the onset of ERI. Numerous CBs have been observed inside the RMW2km of intensifying TCs (Rogers et al. 2013). Abundant diabatic heating caused by CBs inside the RMW leads to rapid intensification (Pendergrass and Willoughby 2009; Vigh and Schubert 2009). Moreover, the inner core with shallow-to-moderate convection led to the development of a warm core at altitudes below 10 km, although the simulated storm was affected by strong VWS (>13 m s−1). Thus, the central pressure gradually deepened (Fig. 3), and the storm circulation intensified from the lower troposphere (Fig. 5b). How are CBs associated with convection around the eyewall?

d. Features of the convection within the inner-core area

This subsection investigates statistical characteristics of convection around the eyewall. Following Rogers et al. (2013), we defined the location of the eyewall based on the criterion that 0.75 < r* < 1.25.

Four percentiles (1st, 50th, 99th, and 99.9th) were selected to examine the vertical profile of the cumulative distribution function that represented the eyewall vertical velocity (Fig. 9a). The strongest updraft (the 99th percentile) among the three periods shown in Fig. 9a occurred during the last 12 h before the onset of ERI and RI. During that period, it appeared at the highest altitude (A in Fig. 9a). The strongest updraft 12 h before the onset was stronger in the ERI experiments than that in the 2112 simulation.

Fig. 9.

Fig. 9.

Fig. 9.

(a) Vertical profiles of selected percentiles (1st, 50th, 99th, and 99.9th percentiles) of the cumulative distributions of eyewall vertical velocity in the 2112 (green), 2118 (orange), and 2200 (red) simulations (left) 12 h before the onset of ERI (RI), (middle) during ERI (RI), and (right) 12–24 h after the onset of ERI (RI). Black lines indicate mean mixing ratios of graupel and snow [(QG) + (QS); g kg−1] in a radius of 100 km for the 2112 (dotted lines), 2118 (dashed lines), and 2200 (solid lines) simulations during each relevant period. (b) Profiles of the number of grids with top altitude of updraft greater than 1 m s−1 within a radius of 100 km for each 0.5-km bin for upshear (cyan) and downshear (orange) quadrants in the 2200 simulations.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

After the onset of ERI, the updraft was strongest between altitudes of 5 and 10 km. The magnitude of the vertical velocity represented by the cumulative distribution function decreased considerably in the upper troposphere (B in Fig. 9a). The results were coincident with the rapid increase of graupel and snow mixing ratios (QG and QS, respectively), as McFarquhar et al. (2012) suggested. The updraft became progressively weak in the upper troposphere 12 h after the end of ERI. The magnitudes of the vertical velocities at the 99th and 99.9th percentiles were maximal around an altitude of 6 km. Rogers et al. (2013) defined CBs as the top 1% of the vertical velocity distribution at an altitude of 8 km. Based on the definition, we determined the CB threshold to be a vertical velocity of 11.1 m s−1.

The most intense and tallest convection and shallow-to-moderate convection coexisted in the inner-core area 12 h before the onset of ERI. Profiles of the numbers of updraft tops greater than 1 m s−1 indicated that shallow-to-moderate convection was dominant in the downshear quadrants of the inner core, whereas tall convection was dominant in the upshear quadrants at 1500 UTC 22 September 1958 (Fig. 9b). As the time progressed, the amount of moderate and tall convection increased in the downshear quadrants. The axisymmetric profiles in the upshear and downshear quadrants at 0000 UTC 23 September indicated the axisymmetrization of inner-core convection as the storm intensified.

The observational study of Sanger et al. (2014) suggested the importance to RI of multiple rotating updrafts near the eye before and during RI. The temporal evolution of vertical vorticity indicates that vertical vorticity became high (>30 × 10−4 s−1) around the leading edge of the intense near-surface inflows in the DSL (A in Fig. 10c) and around the inner edge of midlevel, dry, subsiding flows (A in Fig. 7a) at altitudes around 6–10 km in the USR at 1500 UTC 22 September 1958 (B in Fig. 10c). At that time, convection was shallow inside the RMW2km in the downshear quadrants, and there was a shallow midlevel warm core below 8 km. At 1800 UTC 22 September 1958, tall updrafts developed in the downshear quadrants (C0 in Fig. 10c), though the corresponding vertical vorticity was not intense.

Fig. 10.

Fig. 10.

Fig. 10.

Horizontal distributions of vertical vorticity at an altitude of (a) 8 km and (b) 20 m and (c) radius–height cross sections of vertical vorticity every 3 h in the 2200 simulation. Lines in (a) indicate V r (5 m s−1; magenta), vertical velocity (1 m s−1; cyan), and CB grids defined by updraft greater than 11.1 m s−1 (green). Lines in (c) indicate V r (5, 20, and 40 m s−1; magenta), vertical velocity (1 m s−1; cyan), and potential temperature anomalies (7 K; black). RMW2km is depicted by dashed lines in (c). Black circles in (a) and (b) indicate RMW8km and RMW0.5km, respectively. Arrows indicate horizontal and radial–vertical winds for each panel. Magenta arrows in (b) indicate the VWS. The relative time of the onset of ERI is included in parentheses with the time for each panel.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

The vertical vorticity continued to be intense around the leading edge of the near-surface inflow in the left quadrants and around the inner edge of the midlevel dry flows in the right quadrants. A CB formed just inside of the RMW2km at 0000 UTC 23 September in the 2200 simulation. The area of formation of the CB was coincident with an area of high vertical vorticity at all altitudes within the storm (CB in Fig. 10). The horizontal distribution of vertical vorticity at an altitude of 8 km indicates that the areas with high vertical vorticity (>30 × 10−4 s−1) in the downshear quadrants around the RMW2km were accompanied by areas with updrafts (Fig. 10).

Previous numerical studies (e.g., McFarquhar et al. 2012; Wang and Wang 2014) have indicated that updrafts in the middle-to-upper troposphere are most active before and during the onset of RI, and then the frequency of the updrafts in the upper troposphere decreases as the RI progresses (Fig. 9a). In views of the maximum vertical vorticity and warm-core development, we examined the temporal evolution of the mean updraft in the inner-core area (Fig. 11). The output of the wind components with a horizontal grid scale of 2 km was smoothed with a scale of 8 km before calculating the vertical vorticity, because our purpose was to examine the behavior of mesoscale vortices within the inner-core area.

Fig. 11.

Fig. 11.

Fig. 11.

Time–height cross section of mean vertical velocity within a radius of 100 km of the storm center in (a) 2112, (b) 2118, and (c) 2200 simulations. Black contours indicate the maximum vertical vorticity (10−3 s−1) within a radius of 100 km. (d)–(f) As in (a)–(c), but for the potential temperature anomaly averaged within a radius of 10 km from the mean value within a radius of 400 km. Black contours indicate mean QG + QS (g kg−1) within a radius of 100 km. Thick dashed lines indicate the onset times for each ERI or RI.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

Before the onset of ERI, mean updrafts were strong above an altitude of 10 km in all simulations. The marked difference of TC structure between ERI and RI simulations appeared below an altitude of 8 km. In the ERI simulations, mean updrafts greater than 1 m s−1 formed from an altitude of 1 km, whereas mean updrafts were small in the 2112 simulation.

In the ERI experiments, areas of vertical vorticity greater than 5 × 10−4 s−1 appeared in the low level. Figures 10b and 10c indicated that the areas were located around the leading edge of the near-surface inflow. In the ERI experiments, the areas of vertical vorticity greater than 5 × 10−4 s−1 appeared around an altitude of 9 km just before the onset of ERI (A in Fig. 11). After the onset, the areas of vertical vorticity greater than 5 × 10−4 s−1 extended to an altitude of 10 km, and mean updrafts increased in the lower troposphere.

A midlevel warm core was detected before the onset of ERI in the ERI experiments (Figs. 11d–f), despite the fact that the VWS exceeded 10 m s−1. In addition, an upper-level warm core gradually intensified at 1800 UTC 22 September. Chen et al. (2011) and Guimond et al. (2010) suggested that the subsidence of stratospheric air associated with the detrainment of CBs is attributable to the formation of upper-level warm cores. In our study, nonrotating CBs appeared around the RMW2km at 1800 UTC 22 September (C0 in Fig. 10). In combination with the midlevel warm core, the upper-level warm core rapidly developed, the result being a rapid deepening of sea level central pressure.

e. Temporal evolutions of the radial–altitude structures of simulated storms

To understand how the ERI occurred, the evolution of azimuthal-mean radius–altitude cross sections before the onset of ERI in the 2200 simulation was investigated for the quadrants relative to VWS (Fig. 12). We selected the DSL and USR quadrants, because the areas with intense vertical vorticity appeared around the leading edge of the DSL quadrant and around the inner edge of the midlevel intense flow in the USR quadrant. In general, areas with intense inertial stability appeared around the leading edge of deep and intense near-surface inflows, and the slope of the azimuthal-mean absolute angular momentum (AAM) surface tilted in the DSL quadrant. At 1500 UTC 22 September, the axis of azimuthal-mean updraft, defined by the radial locations of the maximum azimuthal-mean updraft for each altitude (the w axis) was located near radii of 70–90 km above an altitude of 5 km (Fig. 12a). On the other hand, areas with high inertial stability formed around the inner edge of the dry, subsiding, strong flows (A in Fig. 7a) with an upright AAM surface of 20 × 105 m s−1 around a radius of 40 km in the USR quadrant (Fig. 12e).

Fig. 12.

Fig. 12.

Fig. 12.

The evolution of radius–altitude cross sections of the azimuthal-mean AAM (shading; 105 m2 s−1), updraft (cyan contours; 0.5 m s−1), V r (red contours; 5 m s−1), and squared inertial stability (thick black contours; 3 and 5 × 10−6 s−1) from 1500 UTC 22 Sep to 0000 UTC 23 Sep for (a)–(d) DSL and (e)–(h) USR quadrants in the 2200 simulation. Magenta dotted lines indicate the axes of updraft defined by the radial locations of the maximum azimuthal updraft for each altitude (w axes). The relative time of the onset for each ERI or RI is included in parentheses with the time for each panel. (i) Mean AAM surface (20 × 105 m2 s−1) between 1500 UTC 22 Sep and 0000 UTC 23 Sep for each quadrant.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

At 1800 UTC 22 September, the w axis approached the storm center in the DSL quadrant (Fig. 12b). In the USR quadrant, the iso-AAM surface was more upright, with an area of intense inertial stability between altitudes of 2 and 7 km. At 2100 UTC 22 September, intense updrafts appeared between radii of 50 and 90 km in the DSL quadrant. In the USR quadrant, the shallow w axis moved back to around a radius of 70 km. However, the iso-AAM surface continued to move inward as the inertial stability increased within a radius of 30 km (Fig. 12g).

A rotating CB occurred in the DSL quadrant around a radius of 45 km at 0000 UTC 23 September (Fig. 10). The w axes in both the upper troposphere and near the surface were almost aligned in the area with high inertial stability (Fig. 12d). It is noteworthy that an intense inflow greater than 5 m s−1 increased the convergence around the CB below 5 km.

The mean AAM surface for each quadrant was compared in Fig. 12i. Large AAM appeared below 1 km in the shear-left quadrants in the IBL. Meanwhile, the mean AAM surface was the most upright in the USR quadrant, where inertial stability was relatively high. Before the onset of ERI, the intense VWS tilted the storm vortex (Fig. 4), resulting in intense midlevel shear-induced flows in the USR quadrant, as Reasor et al. (2013) and Rogers et al. (2015) reported. The vertical vorticity and thereby the inertial stability increased along the inner edge of the midlevel flows in the USR quadrant (Figs. 10a,c). However, the storm vortex in the ERI experiments became almost upright (Fig. 4) when the tall, vigorous, and upright updrafts with relatively high vertical vorticity formed where the inertial stability was relatively high at 0000 UTC 23 September (Fig. 12d). Thus, the w axis and AAM surface in the DSL quadrant attained a similar relationship for the intensifying storm: an upright w axis with a sloped AAM surface (Hazelton et al. 2015; Rogers et al. 2015). It was not clear whether the CB anchored the upper-level circulation center above the low-level center (Rogers et al. 2015) or weakened VWS was caused by the upright storm vortex at 0000 UTC 23 September. In either case, the outbreak of the CB was essential for the ERI through the latent heat release inside the RMW. The formation process of the CBs will be described in the discussion in section 4.

f. Rate of intensification and inner-core structure

The previous subsections described the structural changes of the inner core before the onset of ERI. This final subsection focuses on the mean structures of the inner-core area during the rapid intensification (Fig. 13) to elucidate the factors that are important for ERI. We compared the mean radius–altitude cross section in the 2112 simulation during the periods of most rapid intensification, from 1200 UTC 23 September to 0000 UTC 24 September, with those in the 2200 simulation from 0300 to 1500 UTC 23 September (Fig. 3). During that period, the VWSs for the 2112 and 2200 simulations weakened to 0.9 and 4.3 m s−1, respectively.

Fig. 13.

Fig. 13.

Fig. 13.

Mean radius–altitude cross sections of AAM (shading; 105 m2 s−1), vertical velocity (cyan contours; −1.0, −0.5, 0.5, 1.5, and 2.5 m s−1), potential temperature anomaly (green contours; −1, 5, and 10 K), QG + QS (magenta contours; 1, 2, and 4 g kg−1), and squared inertial stability (thick black contours; 3 and 5 × 106 s−1) in (a) the 2112 simulation (1200 UTC 23 Sep–0000 UTC 24 Sep), (b) the 2200 simulation (0300 UTC 23 Sep–1500 UTC 24 Sep), and (c) the difference between (b) and (a) (i.e., 2200 minus 2112). Arrows indicate AAM fluxes. Circles and dotted lines in (a) and (b) indicate w axes and radial locations of the maximum Vt, respectively. Circles in (c) indicate w axes in the 2200 (white) and 2112 (black) simulations. (d)–(f) As in (a)–(c), but for equivalent potential temperature in the low level. Contours indicate mean updraft (0.5 m s−1; cyan), V r (2, 10, 20, and 30 m s−1; green), squared inertial stability (10 and 20 × 106 s−1; black), and acceleration of mean V r (3 m s−1 h−1; white). In (f), contours indicate differences for mean updraft (0.5 m s−1; cyan), V r (5 and 10 m s−1; green), squared inertial stability (−0.5, 0, and 0.5 × 106 s−1; black), and acceleration of mean V r (3 and 5 m s−1 h−1; white).

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

During the periods of greatest intensification, the secondary circulation became strong for both the 2112 and 2200 simulations. In this paper, the term “secondary circulation” is used in the context of the azimuthal-mean structure. The outflow from the secondary circulation was notably intense above an altitude of 12 km. In the 2200 simulation, the w axis followed the upright iso-AAM surface below an altitude of 12 km (Fig. 13b). The mean radius–altitude cross section of AAM fluxes indicated that a large amount of AAM was transported inward, both at the top of the near-surface inflow and at altitudes around 8–10 km in the 2200 simulation. The w axis was upright within the areas with high inertial stability. The upright axis with high inertial instability indicates that the response to the sources of convective heating has become relatively large (Shapiro and Willoughby 1982; Pendergrass and Willoughby 2009; Vigh and Schubert 2009).

In the 2112 simulation, the w axis was upright between 4 and 10 km (Fig. 13a), though the iso-AAM surface sloped outward more than in the 2200 simulation. Hazelton et al. (2015) have indicated that intensifying TCs tend to have iso-radar-reflectivity surfaces (which can be considered as a proxy for updrafts), which are more upright than iso-AAM surfaces. Indeed, the VWS for the 2112 simulation was almost neutral (0.9 m s−1) during the period, and the simulated TC in the 2112 simulation underwent RI. However, the rate of intensification was much smaller in the 2112 simulation than in the 2200 simulation, because the upright updraft was outside the high–inertial stability region.

Figure 13c shows the differences of mean radius–altitude cross sections of the AAM, updraft, PT anomalies, and inertial stability between the 2112 and 2200 simulations. In the 2200 simulation, intense, near-surface inflow helped transport relatively large AAM inward. Otherwise, AAM was transported inward at altitudes between 7 and 10 km outside a radius of 50 km. Areas of negative PT anomalies were almost coincident with the areas with inward AAM fluxes at altitudes between 7 and 10 km. Intense updrafts provided a large amount of QG and QS in the middle-to-upper troposphere. The loading effect and evaporative cooling of water substances contributed to the inward transportation of the AAM flux. In the 2200 simulation, a warm core was extremely intense from the lower to the upper troposphere. The rapid development of an extremely intense warm core contributed to the rapid deepening of the sea level central pressure.

The ERI storms possessed more-intense near-surface inflow than the RI storm (Figs. 13d–f). Outside the RMW, the inertial stability was higher in the 2112 simulation than in the 2200 simulation, which might be related to the weaker inflow in the 2112 simulation, as Rogers et al. (2015) suggested. The near-surface inflow was able to penetrate farther into the storm center compared to the inflow in the 2112 simulation. From the leading edge of the near-surface inflow, the azimuthal-mean updraft became more intense and upright. In addition, the area with an intense and upright updraft corresponded to the area with higher equivalent potential temperature (EPT) in the 2200 simulation (375 K) than in the 2112 simulation (370 K). The higher the EPT became around the leading edge near the storm center, the stronger became the azimuthal-mean updraft and therefore convective heating. The previous study claimed that the contributions of high heat fluxes in the eye region seemed to be too small to explain cyclone intensity changes (Bryan and Rotunno 2009). However, the sensitivity experiments of Xu and Wang (2010) indicated that heat fluxes within the eye played a role in reducing the RMW and that heat fluxes underneath the eyewall contributed to the storm intensity. Thus, high EPT resulted in low CP. The great acceleration of mean V r appeared just around the updraft, indicating that the intense updraft was introducing large amounts of moist air near the surface.

4. Discussion

a. The roles of CBs

Previous studies have indicated that the key factor for the onset of ERI is the outbreak of rotating CBs inside the RMW (e.g., Guimond et al. 2010). In our study, the rotating CBs were produced at 0000 UTC 23 September, though other CBs without high vorticity (e.g., C0) appeared around the RMW2km prior to that time. To understand how the rotating CB formed, three-dimensional structures of three CBs before the onset were compared (Fig. 14). At 1800 UTC 22 September, a tall, vigorous CB formed near a radius of 60 km. However, it formed near the surface far from the area with high vorticity, and the updraft was weak below 4 km. Meanwhile, the CB at 2100 UTC 22 September formed from an area with high vorticity near the surface. In areas with intense updraft, a large amount of QG was generated. The areas with high vorticity around an altitude of 10 km were associated with downdrafts just inside the area with intense updrafts. At 0000 UTC 23 September, tall, vigorous, rotating updrafts formed from the leading edge of near-surface inflow in high–vertical vorticity areas. The areas with intense downdraft below the area with abundant QG corresponded to the area with intense V r (>15 m s−1) (Fig. 14b). The features indicate that the downdraft supported the upright updrafts inside the RMW and intensified the vertical vorticity of the CB below 4 km.

Fig. 14.

Fig. 14.

Fig. 14.

Horizontal distributions of updraft (shading; m s−1) at altitudes of (a) 10, (b) 4, and (c) 0.5 km for (left) 1800 and (middle) 2100 UTC 22 Sep 1958 and (right) 0000 UTC 23 Sep in the 2200 simulation. Lines indicate vertical vorticity (4 and 10 × 103 s−1; black), V r (15 m s−1; magenta), and QG (1 g kg−1; cyan). (d) As in (a)–(c), but for the vertical cross sections shown in (a)–(c). Green lines indicate relative humidity (90%). A location of the cross section for each time is shown by the diagonal lines in (a)–(c). The maximum values within 2° from the section were selected.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

Before the onset of ERI, the azimuthal-mean EPT increased rapidly near the surface around the storm center (Fig. 15). It is noteworthy that ERI began when the location of the inner edge of the updraft at an altitude of 1 km was able to intrude into the area with EPT > 375 K around 0000 UTC 23 September. The differences of mean specific humidity below 1 km at the radius of maximum azimuthal updraft were approximately 1 g kg−1 between the ERI and RI simulations (not shown).

Fig. 15.

Fig. 15.

Fig. 15.

Radius–time cross sections of azimuthal-mean equivalent potential temperature at an altitude of 100 m (color; K), with vertical velocity at an altitude of 1 km (short-dashed contours: 0.3 m s−1; thick black contours: 0.5, 1.0, 1.5, and 2.0 m s−1). Dotted lines indicate the RMW0.5km (magenta) and the onset time (black) for each simulation.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

Rogers et al. (2015) discussed the processes that caused the CB inside the RMW. In our case, the rotating CBs formed inside the RMW2km, in which the air became warm and humid, with the aid of downdrafts associated with a large amount of QG. The updraft transported abundant water vapor around the storm center to the upper troposphere. Also, the CBs were a large source of storm-scale vertical vorticity and helped increase the tangential wind, the result being an increase of inertial stability inside the RMW2km. An increase of inertial stability prevents air parcels from being displaced in the radial direction and allows for a more efficient dynamic response to imposed sources of convective heating (Hack and Schubert 1986; Pendergrass and Willoughby 2009; Vigh and Schubert 2009).

b. The role of shallow-to-moderate convection

One of the notable characteristics of the temporal evolution of the inner-core structure in the ERI simulations was shallow-to-moderate convection with a midlevel warm core before the onset of ERI (Figs. 8, 10, and 11). Shallow-to-moderate convection played a crucial role in gradual inner-core moistening in the ERI experiments. In contrast, the northerly dry flow was too intense to maintain shallow-to-moderate convection and a midlevel warm core in the 2112 simulation. Both the dry layer above an altitude of 10 km and the tilt of the storm axis played a crucial role in inhibiting the formation of shallow-to-moderate convection.

Whereas deep convection is assumed to play an essential role in TC intensification via latent heat release, Kieper and Jiang (2012) found a satellite-detected precipitative “cyan” ring pattern around the TC center, indicating that there were low-level water clouds and warm rain, a good predictor of RI. In addition, Zagrodnik and Jiang (2014) revealed that there is little difference in the frequency of moderate-to-deep convection between stable TCs, slowly intensifying TCs, and TCs that have just initiated RI. Jiang (2012) then posed a question: are CBs neither a necessary nor a sufficient condition for RI?

Shallow-to-moderate convection enables latent heat to be supplied to the inner-core area so that it contributes to develop a midlevel warm core (Figs. 8 and 11). On the other hand, the previous observational and numerical studies also suggested that the subsidence by CBs induced a warm core (Chen and Zhang 2013; Guimond et al. 2010; Heymsfield et al. 2001). If the warm core formed through the latter processes, it should develop after the CB penetrated the tropopause. Indeed, an upper-level warm core (WC2 in Fig. 8) rapidly developed after the appearance of tall and intense updraft in DSL (e.g., C0) in the 2200 simulation, whereas the midlevel warm core formed before 1800 UTC 22 September in the ERI experiments (Fig. 11). Moreover, moderate convection also leads to an increase of the ambient vertical vorticity (Wissmeier and Smith 2011). Indeed, the ERI started after a midlevel warm core was coupled with an upper-level warm core. These results indicate that both deep and shallow-to-moderate convection are necessary for producing ERI.

5. Summary and conclusions

The goal of this study was to elucidate the inner-core structure and environmental conditions associated with the onset of extreme rapid intensification (ERI). Numerical experiments were performed for an intense TC, Typhoon Ida, in 1958. Ida had undergone the most rapid deepening, greater than 20 hPa in 6 h, since 1952, according to the Regional Specialized Meteorological Center Tokyo best-track data. The three simulations were conducted by using a 2-km-mesh nonhydrostatic model initiated at three different starting times: 1200 UTC 21 September (2112), 1800 UTC 21 September (2118), and 0000 UTC 22 September (2200) 1958 based on the results of a numerical simulation using a 5-km-mesh nonhydrostatic model.

Under a strong environmental VWS (>10 m s−1), two of the three experiments (2118 and 2200) were able to simulate an ERI comparable to the best-track ERI, whereas one of the three experiments (2112) simulated moderate intensification (RI) and, thus, a relatively weak maximum intensity.

The evolution of the inner core of simulated Ida in the ERI experiments is summarized in Fig. 16. Both shallow-to-moderate and tall convection were active in the inner-core area before the onset of ERI. Because of the formation of shallow-to-moderate convection around the leading edge of intense near-surface inflow on the downshear side of the storm center, the inner-core area was gradually moistened, and the midlevel warm core developed through the latent heat release even with a strong VWS. On the upshear side of the inner-core area, dry, subsiding, and strong flow increased the inertial stability. As the storm axis was upright, the storm vortex intensified, and the upper-level warm core gradually developed. When the leading edge of the near-surface inflow had reached the vicinity of the storm center, deep, vigorous and upright updrafts resulted in the upright axis of the secondary circulation within the areas of high inertial stability and helped transport warm humid air inward along with high vertical vorticity. The warm cores at different altitudes merged and then developed rapidly, the result being rapid deepening of the sea level central pressure. Meanwhile, the vortex for the 2112 simulation greatly tilted to the northwest at 0000 UTC 22 September 1958 (Fig. 17). Dry air (specific humidity < 0.1 g kg−1) covered the eastern and northern sides of the inner core at an altitude of 12 km. The delay of the vortex development resulted in a 0.7°C-cooler SST beneath the inner core for the 2112 simulation than those for the 2118 and 2200 simulations by the time that the TC in the 2112 simulation was ready for RI (Fig. 16f).

Fig. 16.

Fig. 16.

Fig. 16.

(top) Temporal evolutions of (a),(b) mean potential temperature anomalies (K) between altitudes of 10 and 15 km and 2 and 7 km, respectively; (c) squared mean inertial stability between altitudes of 2 and 10 km for r* = 0.75–1.25; (d) rates of change in CP in 6 h; (e) VWS; (f) SST; and (g),(h) RH between altitudes of 3 and 6 km, and below 2 km, respectively, for the 2112 (dotted lines), 2118 (dashed lines), and 2200 (solid lines) simulations. The onset time for each ERI or RI is shown by the vertical lines for 2112 (dotted), 2118 (dashed), and 2200 (solid). Text indicates the events related to the 2200 simulation (black), the 2112 simulation (green), and the environment (magenta). (bottom) Modeled after Figs. 14 and 15 of Hazelton et al. (2015), schematic diagrams of the evolutions of the inner core for the 2200 simulation in relation to slopes of w axis (black arrow), AAM surface (dashed line), and warm cores at the different altitudes. C0 and CB indicate tall updrafts (e.g., C0 in Fig. 8) and tall, vigorous, and rotating updrafts (e.g., C0 in Fig. 8), respectively.

Citation: Journal of the Atmospheric Sciences 72, 11; 10.1175/JAS-D-14-0247.1

Our results indicate that both the shallow-to-moderate and the deep convection in the inner core contributed to ERI when the VWS was strong. The combination of warm cores at different altitudes from near the surface to the upper troposphere enhanced the rate of intensification. Microphysical processes also helped the formation of the upright, rotating CBs that trigger ERI. Further studies are needed to clarify the factors and mechanisms that control the rate of intensification of intense TCs.

Acknowledgments

The authors are grateful to three anonymous reviewers for instructive comments. This study was supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan under the framework of the Sousei Program and JSPS-KAKENHI Grant 26400466 and MEXT-KAKENHI Grant 25106708. Numerical simulations were performed using the Earth Simulator.

REFERENCES