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

4194 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

SACHIE KANADA Hydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Aichi, Japan

AKIYOSHI WADA Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Ibaraki, Japan

(Manuscript received 25 August 2014, in ﬁnal form 7 June 2015)

ABSTRACT

Extremely rapid intensification (ERI) of Typhoon Ida (1958) was examined with a 2-km-mesh nonhydrostatic model initiated at three different times. Ida was an extremely intense tropical cyclone with a minimum central pressure of 877 hPa. The maximum central pressure drop in 24 h exceeded 90 hPa. ERI was successfully simulated in two of the three experiments. A factor crucial to simulating ERI was a combination of shallow-to- moderate convection and tall, upright convective bursts (CBs). Under a strong environmental vertical wind 2 shear (.10 m s 1), shallow-to-moderate convection on the downshear side that occurred around the intense near-surface inflow moistened the inner-core area. Meanwhile, dry subsiding flows on the upshear side helped intensification of midlevel (8 km) inertial stability. First, a midlevel warm core appeared below 10 km in the shallow-to-moderate convection areas, being followed by the development of the upper-level warm core associated with tall convection. When tall, upright, rotating CBs formed from the leading edge of the intense near- surface inflow, ERI was triggered at the area in which the air became warm and humid. CBs penetrated into the upper troposphere, aligning the areas with high vertical vorticity at low to midlevels. The upper-level warm core developed rapidly in combination with the midlevel warm core. Under the preconditioned environment, the formation of the upright CBs inside the radius of maximum wind speeds led to an upright axis of the secondary circulation within high inertial stability, resulting in a very rapid central pressure deepening.

1. Introduction processes (e.g., Kepert 2012), TC vortex dynamics and associated convection (e.g., Montgomery and Enagonio Although there have been steady improvements in 1998; Montgomery et al. 2006), and air–sea interactions forecasting the tracks of tropical cyclones (TCs), fore- beneath the TC (e.g., Ito et al. 2011; Wada et al. 2014). casting their intensities remains a challenging issue (e.g., More accurate prediction of the rate of TC in- Wang and Wu 2004), because TC intensity and its changes tensification is a key factor for improving intensity involve a wide variety of processes over multiple temporal forecasts. According to TC best-track data, most in- and spatial scales. These processes include atmospheric tense TCs, specifically category 4 and 5 (Kaplan and and oceanic environmental phenomena (e.g., Gray 1968; DeMaria 2003) TCs on the Saffir–Simpson hurricane Hendricks et al. 2010; Riemer et al. 2010; Wada et al. scale (http://www.nhc.noaa.gov/aboutsshws.php), un- 2012), cloud microphysics (e.g., Sawada and Iwasaki 2007; dergo rapid intensification (RI). One of the definitions Zhou and Wang 2011), planetary boundary layer (PBL) 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 con- Denotes Open Access content. cern because of the serious damage caused by these storms, particularly in coastal regions. TC intensification is theoretically explained by sym- Corresponding author address: Sachie Kanada, Hydrospheric Atmospheric Research Center, Nagoya University, Furo-cho, metric and asymmetric mechanisms. The former involves a Chikusa-ku, Nagoya 464-8601, Japan. symmetric, overturning, balanced circulation above E-mail: [email protected] the PBL (Charney and Eliassen 1964; Ooyama 1969).

DOI: 10.1175/JAS-D-14-0247.1

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Recently, Vigh and Schubert (2009) used a balanced more important for triggering RI above the boundary vortex model to show that diabatic heating within a layer or inside the boundary layer and for determining region of high inertial stability inside the radius of the rate of intensification? maximum azimuthal mean wind (RMW) results in a First, the structural changes of the TC inner-core re- rapid increase of positive warm-core temperature gion just before and during RI need to be clarified. To anomalies. By applying the Sawyer–Eliassen equation provide this clarification, we performed numerical ex- to a balanced vortex, Pendergrass and Willoughby periments that allowed us to investigate the temporal (2009) also found that diabatic heating inside the evolution of atmospheric environmental conditions and RMW results in a rapid increase of tangential winds inner-core structures of an extremely intense TC ac- and, thus, a contraction of the RMW. companied by extremely rapid intensification (ERI). In contrast, the asymmetric mechanism highlights a We paid special attention to the structural changes of rotating, deep convection (i.e., vortical hot towers), the inner-core region before the onset of ERI to thor- generally in relation to the spinup mechanism of maxi- oughly understand the mechanisms associated with ERI mum tangential winds in the TC boundary layer, where processes in the inner-core region and to identify the the winds are affected by surface friction (Bui et al. 2009; inner-core structures and environmental conditions for Montgomery et al. 2014; Montgomery and Smith 2014; the onset of ERI. Smith et al. 2009). Many previous studies have linked deep convection around the storm center to TC intensification. In the late 2. Model and methodology 1980s, Steranka et al. (1986) found that maximum winds 2 a. Case description of TCs in most cases increased by 5 m s 1 or more within 24 h, during which time intense convection with high This study chose an extremely intense TC [minimum cloud tops lasted more than 9 h. Based on a composite central pressure (MCP) , 900 hPa] case that had un- analyses of airborne Doppler observations, Rogers et al. dergone the greatest rapid deepening, according to best- (2013) reported that intensifying TCs had a relatively track data, since 1952. A tropical depression formed from large amount of tall and vigorous convection [i.e., con- an easterly wave around the Marshall Islands on 20 Sep- vective bursts (CBs)] inside the RMW compared with tember 1958 and was named Ida at 1800 UTC 20 September steady-state TCs. Sanger et al. (2014) examined the (Fig. 1). The storm moved to the west while maintaining a spinup mechanism of rapidly intensifying Super Typhoon central pressure of 985 hPa. At 0000 UTC 22 September, Jangmi (2008) and reported the observation of multiple the TC changed direction to the northwest and initiated RI. rotating updrafts and a huge upright updraft with strong, The TC underwent an extremely rapid drop in central 2 low-level convergence and intense relative vorticity in- pressure (CP) at rates that exceeded 20 hPa (6 h) 1 from side the RMW. The contribution of CBs to an upper-level 0600 to 1200 UTC 23 September and reached an MCP of warm core have also been suggested in observational and 877 hPa at 0600 UTC 24 September. The maximum drop numerical studies (Chen and Zhang 2013; Guimond et al. rate of CP per 6 h (dCP6h) was 39 hPa. The TC then moved 2010; Heymsfield et al. 2001). northward and made landfall in Japan around 34.48N, Recently, Kieper and Jiang (2012) found that a ring- 139.08E at 1500 UTC 26 September. The TC caused tor- like axisymmetric pattern of precipitation detected from rential flooding in southeastern Japan that resulted in 1269 satellite observations was related to RI. Furthermore, fatalities. based on an 11-yr Tropical Rainfall Measuring Mission b. Model description database (http://pmm.nasa.gov/trmm), a statistical relationship existed between inner-core convection inten- The nonhydrostatic atmosphere model is based on the sity and TC intensification (Jiang 2012). However, that Japan Meteorological Agency (JMA) operational non- study also indicated that the increase of RI probability hydrostatic mesoscale model (JMANHM; Saito et al. above the climatological mean predicted by the existence 2007). The 2-km-mesh version (NHM2) includes bulk- of hot towers was not very large. In addition, the RI type cloud microphysics with an ice phase (Murakami probability without hot towers was still 4.9% (Jiang 2012). 1990), a clear-sky radiation scheme (Yabu et al. 2005), Moderate-to-deep convection and associated latent heat and a cloud radiation scheme (Kitagawa 2000). No cu- release significantly increased only after RI had been un- mulus parameterization scheme is adopted in NHM2. derway for at least 12 h (Zagrodnik and Jiang 2014). The model applies the Deardorff–Blackadar scheme There is debate about the importance of the axisym- (Deardorff 1980; Blackadar 1962) and the Louis scheme metric and asymmetric processes of TC intensification (Louis et al. 1982) with a surface-roughness-length for- (e.g., Nolan et al. 2007). Which of the mechanisms is mulation based on Kondo (1975) as the PBL scheme and

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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. surface boundary layer scheme, respectively. Basic con- the NHM5 experiment were provided every 6 h from the figurations are the same as in our previous studies JMA 55-year Reanalysis dataset (JRA-55; Ebita et al. (Kanada et al. 2012, 2013). The computational domain 2011) with a horizontal resolution of 1.258 for atmo- of NHM2 is 3980 km 3 2380 km (Fig. 1), and the number spheric ingredients and that of 0.568 for SST. of vertical levels is set to 55 (the lowermost layer is 20 m The numerical experiments were conducted as follows: and the top height is approximately 27 km). first, a numerical experiment with NHM5 nested in JRA-55 Initial and lateral boundary conditions for the NHM2 was performed starting at 0000 UTC 21 September. Next, experiments were provided every 6 h from the numerical the numerical experiments were conducted by using experiments with JMANHM with a horizontal resolu- NHM2 with the results of NHM5 for each initial time: tion of 5 km (NHM5). NHM5 used the spectral nudging 1200 UTC 21 September (2112), 1800 UTC 21 September method (Nakano et al. 2012), the Kain–Fritsch cumulus (2118), and 0000 UTC 22 September (2200) 1958. parameterization scheme (Kain and Fritsch 1993) and c. Analytical methods the level 3 Mellor–Yamada–Nakanishi–Niino closure PBL scheme (Nakanishi and Niino 2004). The compu- The approximate geometric center (centroid) of the tational domain of NHM5 is 5400 km 3 4600 km (Fig. 1). storm was determined for each numerical result of the Other configurations of NHM5 were as in NHM2. NHM based on the horizontal distribution of sea level Initial and lateral atmospheric boundary conditions pressure (Braun 2002). Because the pressure field ap- and sea surface temperature (SST) initial conditions for peared noisy around vigorous convection in the eyewall,

Unauthenticated | Downloaded 10/09/21 07:43 PM UTC NOVEMBER 2015 K A N A D A A N D W A D A 4197 the centroid was calculated at radial intervals of 2 km asymmetric at 1200 UTC 21 September. Simulated 2 and summed within radius R 5 100 km for every grid precipitation was intense (.30 mm h 1)tothewestand

(Xcp630grid, Ycp630grid) around the location of the CP (Xcp, southwest of the storm center (Fig. 2a). Positive verti- 24 21 Ycp). The grid (X, Y) at which the summation was the cal vorticity was intense (.8 3 10 s )tothesouthof smallest was selected as the storm center. The location the storm center (Fig. 2b). The relation of the hori- of the pressure center was calculated in the same way as zontal pattern of intense precipitation and vertical the storm center for every 500 m of altitude by using the vorticity to the VWS (Fig. 2c) was consistent with the pressure field at each altitude. The distance between the observational results reported by Reasor and Eastin storm and pressure centers was defined as the tilt of (2012) and Reasor et al. (2013). the storm axis for each altitude. Radial (Vr) and tan- Figure 2c shows the simulated horizontal patterns of gential (Vt) winds determined relative to the storm center inner-core specific humidity at altitudes of 12 km, 3 km, were calculated for each Cartesian grid. We also calcu- and 20 m collocated at the storm center. The horizontal lated the circulation center based on the method of patterns were asymmetric at 1200 UTC 21 September. Reasor and Eastin (2012). The rationale that underlies Relatively strong VWS was responsible for the tilt de- their method is similar to that for the above-mentioned fined by the pressure centers to the downshear of the method, but their method seeks a location that maximizes VWS. The pressure center was not specified at an alti- the azimuthal-mean Vt on the storm-vortex scale. The tude of 12 km within a 200-km radius of the storm center. 2 initial guess position was moved within 20 km from the The specific humidity was still less than 0.2 g kg 1 at an pressure center with a search radius interval of 5 km. altitude of 12 km. However, the circulation center was difficult to determine As the storm intensified, the horizontal patterns of in the upper troposphere, where Vt was weak. Therefore, the horizontal winds and hourly precipitation gradu- we mainly used the pressure center. ally became less asymmetric (Figs. 2a,b). At 1800 UTC The radius of azimuthal mean maximum tangential 21 September, relatively dry air with a relatively low 21 wind for every 500 m of altitude (RMWaltitude) was cal- specific humidity of less than 8.0 g kg at an altitude of 2 culated relative to the storm center. Following Rogers 3km(19gkg 1 at an altitude of 20 m) appeared at dis- et al. (2013), the normalized radius r* was defined with tances of 100–400 km to the south and east of the pressure respect to RMW2km. In this study r* [ r/RMW2km. center (middle panels of Fig. 2c). Meanwhile, water vapor Vertical wind shear (VWS) was defined as the differ- was gradually transported upward. ence in the mean horizontal wind speed between altitudes At 0000 UTC 22 September, the specific humidity 2 of 1.5 km (;850 hPa) and 12.5 km (;200 hPa). Mean exceeded 0.2 g kg 1 around the storm center at an al- horizontal winds were calculated over a circular area titude of 12 km. The pressure and circulation centers with a radius of 500 km for the NHM2 experiments. The were specified within a radius of 15 km from the storm average of the horizontal winds over a 1000 km 3 1000 km center at all three altitudes. These NHM5 results square based on JRA-55 data was used for the environ- served as the initial conditions for the following three mental VWS in the NHM5 experiment. NHM2 experiments. b. Temporal evolution of the TC simulated by the NHM2 3. Results This subsection addresses the evolution of the simu- a. Initial conditions for numerical experiments by lated storm for each of the three NHM2 experiments. NHM2 Because a spectral nudging method (Nakano et al. 2012) We used the results of the NHM5 experiment to was not used, the simulated storm centers of Ida in the specify atmospheric conditions at the initial time for three NHM2 experiments were a few degrees different each numerical experiment with the NHM2. The NHM5 from the best-track storm center in the longitude–latitude simulated storm centers of Ida that were reasonable coordinate system (Fig. 1). However, the location of the when compared to the Regional Specialized Meteoro- simulated MCP at around 208N, 1358E was almost the logical Center Tokyo best-track data (Fig. 1). The error same as that of the best-track MCP. The exception was against the best-track storm center was less than 18 in the the 2112 simulation, when the simulated storm reached its longitude–latitude coordinate system. MCP 1 day later and 38 farther north from the best-track

Figures 2a and 2b show the horizontal patterns of storm center. Herein, the magnitude of dCP6h (see section hourly precipitation and vertical vorticity at an altitude 2a) is used as a metric to specify RI. of 20m by the NHM5 collocated at the storm center. Figure 3 indicates that the best-track dCP6h was greater The simulated inner-core horizontal patterns were than 20 hPa between 0600 and 1200 UTC 23 September.

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21 FIG. 2. Storm-centered horizontal distributions of (a) hourly precipitation (mm h ), (b) vertical vorticity 2 2 2 (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 2 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.

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Here, an experiment in which the extraordinary dCP6h 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 re- garded as an RI experiment. The onset of ERI and RI

was deﬁned as the time when the dCP6h 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. 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

FIG. 3. Temporal evolutions in 1958 of (a) CP and (b) rate of words, what factors control the onset of ERI? changes in CP in 6 h for the best track (closed black circle), JRA-55 To answer this question, we compared simulated (open circle), and NHM5 (blue) and for the 2112 (green), 2118 horizontal patterns of hourly precipitation in the three (orange), and 2200 (red) simulations. Dotted lines indicate the simulations from 1200 UTC 22 September to 0000 UTC onset times of ERI for the 2118 (orange) and 2200 (red) simulations 23 September collocated at the storm center (Fig. 4). and RI for the 2112 (green) simulation. During this period, dCP6h waslessthan10hPainthe three NHM2 simulations. All the simulations indicated

The extraordinary dCP6h values were simulated well in that strong VWS resulted in a shift of the circulation the 2118 and 2200 simulations, for which the MCPs were center at an altitude of 10 km toward the downshear 887 and 877 hPa, respectively. However, the simulated side. The amount of hourly precipitation was high on dCP6h never exceeded 20 hPa in the 2112 simulation. the downshear-left (DSL) side of the VWS, whereas

FIG. 4. Storm-centered composite horizontal distributions of hourly precipitation for the (top) 2112, (middle) 21 2118, and (bottom) 2200 simulations every 3 h. Magenta contours indicate the wind speed of 33.5 m s . 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.

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21 FIG. 5. (a) Radius–time cross sections of azimuthal-mean hourly precipitation (color; mm h ) 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 21 and RI in the 2118 (orange), 2200 (red), and 2112 (green) simulations. Sky-blue lines in (a) indicate Vr 5 2ms . Positive values of Vr always indicate inﬂow in this study. the hourly precipitation was relatively low on the right tended to be smaller in the ERI experiments than in the side of the VWS, in good agreement with Reasor 2112 simulation. et al. (2013). It should be noted that RMW10km, which was much At 1800 UTC 22 September, the horizontal pattern of larger than RMW0.5km and RMW2km, decreased rapidly 2 relatively weak precipitation (,20 mm h 1) developed a after the onset of ERI and RI in all the simulations. ringlike shape in the ERI experiments. The RMW2km These results indicate that each axis for MWS rapidly and radius of maximum wind speed (MWS) for the became upright as the central pressure rapidly deep- circulation center at an altitude of 10 km were almost ened. During the analysis period, the MWS always ex- the same among the three NHM2 simulations. How- isted in the IBL. Temporal evolutions of the MWS at an ever, in the ERI experiments, the RMW2km became altitude of 0.5 km revealed that the MWS started to in- smaller after 1800 UTC 22 September, whereas the crease 3–9 h before the onsets of both ERI and RI, at

RMW2km varied without any trends in the 2112 simu- 0900 UTC 23 September and at 2100 and 1800 UTC lation. At 0000 UTC 23 September, the distance be- 22 September 1958 for the 2112, 2118, and 2200 simu- tween the storm and circulation centers decreased lations, respectively (Fig. 5b). (,20 km), and the storm axis was almost upright for the Many previous studies have pointed out the re- ERI experiments. lationship between the slope of eyewall updraft, TC in- Intensiﬁcation is often accompanied by eyewall con- tensiﬁcation, and VWS (Hazelton et al. 2015; Reasor traction. The evolutions of the eyewall precipitation are et al. 2013; Riemer et al. 2010). Most of these studies shown in Fig. 5 within the RMW at three altitudes: have indicated that weak VWS is favorable for TC in-

RMW0.5km, RMW2km, and RMW10km. RMW0.5km is tensification. However, the simulated Ida experienced assumed to be inside the TC inflow boundary layer strong VWS before and during the onset of ERI (Fig. 6). (IBL). After the onset of ERI, precipitation rapidly in- Figure 6 also indicates that the inner core was gradually tensified at the eyewall, and then the eyewall con- moistening 3–6 h before the onset of ERI in the ERI 2 tracted. Areas with moderate precipitation (.20 mm h 1) experiments around 0000 UTC 22 September, while it roughly corresponded to RMW0.5km and RMW2km. was less moistened in the 2112 simulation at that time. Herein, RMW2km was applied as the reference, because How did simulated TCs evolve to initialize ERI in the most of the previous studies used RMW2km.RMW2km strong VWS condition?

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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. c. Temporal evolution of inner-core structure before RMW were covered by airs of high relative humidity the onset of ERI greater than 90% at both altitudes. Reasor et al. (2013) investigated the relationships The temporal evolution of the inner-core structure of between mean shear and inner-core structures for cases 2 2 the simulated TC in the 2200 simulation was examined with weak shear (,4ms 1) and strong shear (.7ms 1). 12 h before the onset of ERI. The horizontal distribu- In our study, the mean VWS 12 h before the onset of 2 tions of vertical velocity and relative humidity at an al- ERI in the 2200 simulation exceeded 13 m s 1, which is titude of 6 km indicated the subsiding strong flows in an an extremely strong shear case. Figure 8 shows mean area within which relative humidity was less than 50% to vertical cross sections of the inner-core area for each the north of the storm center at 1500 UTC 22 September quadrant relative to VWS in the 2200 simulation from (A in Fig. 7a). The horizontal scale of the dry area was 1500 UTC 22 September to 0000 UTC 23 September. much larger than that of convective downdrafts. Based According to Reasor et al. (2013), the most intense near- on mean potential temperature (PT) anomalies, calcu- surface inflow was in the downshear quadrants of the lated from the mean PT within a radius of 400 km, a storm, and the most intense and tallest updrafts were warm core appeared at an altitude of 6 km. In contrast, formed from the leading edge of the near-surface inflow. shallow-to-moderate updrafts were produced inside the In our study, tall, intense updrafts were also seen on the

RMW2km in the DSL quadrant at an altitude of 2 km (B DSL side of the storm center outside the RMW2km at in Fig. 7b). A cluster of updraft areas corresponded to 1500 UTC 22 September (A in Fig. 8). Around the the areas of relative humidity greater than 95% at an leading edge of the intense near-surface inﬂow, shallow- altitude of 2 km. to-moderate updrafts formed, with top heights below During 1800 and 2100 UTC 22 September, relatively 6km (S in Fig. 8). The updraft areas closely corre- strong and dry (relative humidity , 60%) subsiding sponded to the areas with high relative humidity: water winds ﬂowed around the RMW6km in the upshear-left vapor near the surface was transported to the upper quadrant (C and D in Fig. 7a). Meanwhile, the updrafts troposphere because of the updrafts. A warm core had were relatively strong on the left side of the VWS. At appeared inside the area of shallow-to-moderate con- 0000 UTC 23 September, almost whole areas around the vection at altitudes below 8 km (WC1 in Fig. 8).

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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 2 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.

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FIG. 8. (a) Radius–height cross section of (left) USL and (right) DSL of relative humidity in the 2200 simulation. 21 (b) As in (a), but for (left) USR and (right) DSR. Lines indicate Vr (5, 20, and 40 m s ; magenta), vertical velocity 21 (1 m s ; 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.

At 1800 UTC 22 September, a tall, vigorous updraft altitudes below 10 km, although the simulated storm was 21 formed around the RMW2km in the DSL (C0 in Fig. 8). affected by strong VWS (.13 m s ). Thus, the central 21 The midlevel inflow (Vr . 5ms ) appeared in the pressure gradually deepened (Fig. 3), and the storm upshear-left (USL) and upshear-right (USR) quadrants circulation intensified from the lower troposphere of the storm (B in Fig. 8). At 2100 UTC 22 September, (Fig. 5b). How are CBs associated with convection the inner-core area to the right side of the VWS became around the eyewall? dry, although the warm core remained at altitudes be- d. Features of the convection within the inner-core low 10 km (WC1 in Fig. 8). In addition, the upper-level area warm core appeared above an altitude of 10 km (WC2 in Fig. 8). At 0000 UTC 23 September, tall, vigorous This subsection investigates statistical characteristics updrafts developed at a radius of 45 km in the DSL (CB of convection around the eyewall. Following Rogers in Fig. 8). The onset of ERI occurred 3 h after the et al. (2013), we defined the location of the eyewall outbreak of CB. based on the criterion that 0.75 , r* , 1.25. The results indicate that inner-core moistening due Four percentiles (1st, 50th, 99th, and 99.9th) were to updrafts with a variety of heights would provide local selected to examine the vertical profile of the cumulative environmental conditions conducive to tall vigorous distribution function that represented the eyewall ver- updrafts before the onset of ERI. Numerous CBs have tical velocity (Fig. 9a). The strongest updraft (the 99th been observed inside the RMW2km of intensifying TCs percentile) among the three periods shown in Fig. 9a (Rogers et al. 2013). Abundant diabatic heating caused occurred during the last 12 h before the onset of ERI and by CBs inside the RMW leads to rapid intensification RI. During that period, it appeared at the highest alti- (Pendergrass and Willoughby 2009; Vigh and Schubert tude (A in Fig. 9a). The strongest updraft 12 h before the 2009). Moreover, the inner core with shallow-to-moderate onset was stronger in the ERI experiments than that in convection led to the development of a warm core at the 2112 simulation.

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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) 1 (QS); 2 gkg 1] in a radius of 100 km for the 2112 (dotted lines), 2118 (dashed lines), and 2200 (solid lines) simulations during each relevant period. 2 (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.

After the onset of ERI, the updraft was strongest The most intense and tallest convection and shallow- between altitudes of 5 and 10 km. The magnitude of the to-moderate convection coexisted in the inner-core vertical velocity represented by the cumulative distri- area 12 h before the onset of ERI. Profiles of the 2 bution function decreased considerably in the upper numbers of updraft tops greater than 1 m s 1 indicated troposphere (B in Fig. 9a). The results were coincident that shallow-to-moderate convection was dominant in with the rapid increase of graupel and snow mixing ra- the downshear quadrants of the inner core, whereas tall tios (QG and QS, respectively), as McFarquhar et al. convection was dominant in the upshear quadrants at (2012) suggested. The updraft became progressively 1500 UTC 22 September 1958 (Fig. 9b). As the time weak in the upper troposphere 12 h after the end of ERI. progressed, the amount of moderate and tall convection The magnitudes of the vertical velocities at the 99th and increased in the downshear quadrants. The axisymmetric 99.9th percentiles were maximal around an altitude of profiles in the upshear and downshear quadrants at 6 km. Rogers et al. (2013) defined CBs as the top 1% of 0000 UTC 23 September indicated the axisymmetrization the vertical velocity distribution at an altitude of 8 km. of inner-core convection as the storm intensified. Based on the definition, we determined the CB thresh- The observational study of Sanger et al. (2014) sug- 2 old to be a vertical velocity of 11.1 m s 1. gested the importance to RI of multiple rotating

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2 2 updrafts near the eye before and during RI. The tem- vorticity greater than 5 3 10 4 s 1 appeared around an poral evolution of vertical vorticity indicates that verti- altitude of 9 km just before the onset of ERI (A in 2 2 cal vorticity became high (.30 3 10 4 s 1) around the Fig. 11). After the onset, the areas of vertical vorticity 2 2 leading edge of the intense near-surface inflows in the greater than 5 3 10 4 s 1 extended to an altitude of DSL (A in Fig. 10c) and around the inner edge of mid- 10 km, and mean updrafts increased in the lower level, dry, subsiding flows (A in Fig. 7a) at altitudes troposphere. around 6–10 km in the USR at 1500 UTC 22 September A midlevel warm core was detected before the onset 1958 (B in Fig. 10c). At that time, convection was shal- of ERI in the ERI experiments (Figs. 11d–f), despite 21 low inside the RMW2km in the downshear quadrants, the fact that the VWS exceeded 10 m s .Inaddition, and there was a shallow midlevel warm core below 8 km. an upper-level warm core gradually intensified at At 1800 UTC 22 September 1958, tall updrafts de- 1800 UTC 22 September. Chen et al. (2011) and veloped in the downshear quadrants (C0 in Fig. 10c), Guimond et al. (2010) suggested that the subsidence of though the corresponding vertical vorticity was not stratospheric air associated with the detrainment of intense. CBs is attributable to the formation of upper-level The vertical vorticity continued to be intense around warm cores. In our study, nonrotating CBs appeared the leading edge of the near-surface inflow in the left around the RMW2km at 1800 UTC 22 September (C0 quadrants and around the inner edge of the midlevel in Fig. 10). In combination with the midlevel warm dry flows in the right quadrants. A CB formed just in- core, the upper-level warm core rapidly developed, side of the RMW2km at 0000 UTC 23 September in the the result being a rapid deepening of sea level central 2200 simulation. The area of formation of the CB was pressure. coincident with an area of high vertical vorticity at all e. Temporal evolutions of the radial–altitude structures altitudes within the storm (CB in Fig. 10). The hori- of simulated storms zontal distribution of vertical vorticity at an altitude of 8 km indicates that the areas with high vertical vorticity To understand how the ERI occurred, the evolution 2 2 (.30 3 10 4 s 1) in the downshear quadrants around of azimuthal-mean radius–altitude cross sections be- the RMW2km were accompanied by areas with updrafts fore the onset of ERI in the 2200 simulation was in- (Fig. 10). vestigated for the quadrants relative to VWS (Fig. 12). Previous numerical studies (e.g., McFarquhar et al. We selected the DSL and USR quadrants, because the 2012; Wang and Wang 2014) have indicated that up- areas with intense vertical vorticity appeared around drafts in the middle-to-upper troposphere are most ac- the leading edge of the DSL quadrant and around the tive before and during the onset of RI, and then the inner edge of the midlevel intense flow in the USR frequency of the updrafts in the upper troposphere de- quadrant. In general, areas with intense inertial sta- creases as the RI progresses (Fig. 9a). In views of the bility appeared around the leading edge of deep and maximum vertical vorticity and warm-core develop- intense near-surface inflows, and the slope of the ment, we examined the temporal evolution of the mean azimuthal-mean absolute angular momentum (AAM) updraft in the inner-core area (Fig. 11). The output of surface tilted in the DSL quadrant. At 1500 UTC the wind components with a horizontal grid scale of 2 km 22 September, the axis of azimuthal-mean updraft, was smoothed with a scale of 8 km before calculating the defined by the radial locations of the maximum vertical vorticity, because our purpose was to examine azimuthal-mean updraft for each altitude (the w axis) the behavior of mesoscale vortices within the inner- was located near radii of 70–90 km above an altitude core area. of 5 km (Fig. 12a). On the other hand, areas with high Before the onset of ERI, mean updrafts were strong inertial stability formed around the inner edge of the above an altitude of 10 km in all simulations. The dry, subsiding, strong flows (A in Fig. 7a)withan 2 marked difference of TC structure between ERI and RI upright AAM surface of 20 3 105 ms 1 around a ra- simulations appeared below an altitude of 8 km. In the dius of 40 km in the USR quadrant (Fig. 12e). 2 ERI simulations, mean updrafts greater than 1 m s 1 At 1800 UTC 22 September, the w axis approached formed from an altitude of 1 km, whereas mean updrafts the storm center in the DSL quadrant (Fig. 12b). In the were small in the 2112 simulation. USR quadrant, the iso-AAM surface was more upright, In the ERI experiments, areas of vertical vorticity with an area of intense inertial stability between alti- 2 2 greater than 5 3 10 4 s 1 appeared in the low level. tudes of 2 and 7 km. At 2100 UTC 22 September, intense Figures 10b and 10c indicated that the areas were lo- updrafts appeared between radii of 50 and 90 km in the cated around the leading edge of the near-surface in- DSL quadrant. In the USR quadrant, the shallow w axis flow. In the ERI experiments, the areas of vertical moved back to around a radius of 70 km. However, the

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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 21 21 vertical vorticity every 3 h in the 2200 simulation. Lines in (a) indicate Vr (5 m s ; magenta), vertical velocity (1 m s ; cyan), and CB grids 21 21 21 deﬁned by updraft greater than 11.1 m s (green). Lines in (c) indicate Vr (5, 20, and 40 m s ; magenta), vertical velocity (1 m s ; 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.

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FIG. 11. Time–height cross section of mean vertical velocity within a radius of 100 km of the storm center in 2 2 (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 2 of 10 km from the mean value within a radius of 400 km. Black contours indicate mean QG 1 QS (g kg 1) within a radius of 100 km. Thick dashed lines indicate the onset times for each ERI or RI. iso-AAM surface continued to move inward as the The w axes in both the upper troposphere and near the inertial stability increased within a radius of 30 km surface were almost aligned in the area with high inertial (Fig. 12g). stability (Fig. 12d). It is noteworthy that an intense in- 2 A rotating CB occurred in the DSL quadrant around a ﬂow greater than 5 m s 1 increased the convergence radius of 45 km at 0000 UTC 23 September (Fig. 10). around the CB below 5 km.

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5 2 21 FIG. 12. The evolution of radius–altitude cross sections of the azimuthal-mean AAM (shading; 10 m s ), updraft (cyan contours; 21 21 26 21 0.5 m s ), Vr (red contours; 5 m s ), and squared inertial stability (thick black contours; 3 and 5 3 10 s ) 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 2 or RI is included in parentheses with the time for each panel. (i) Mean AAM surface (20 3 105 m2 s 1) between 1500 UTC 22 Sep and 0000 UTC 23 Sep for each quadrant.

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The mean AAM surface for each quadrant was com- 8–10 km in the 2200 simulation. The w axis was upright pared in Fig. 12i. Large AAM appeared below 1 km in within the areas with high inertial stability. The upright axis the shear-left quadrants in the IBL. Meanwhile, the with high inertial instability indicates that the response to mean AAM surface was the most upright in the USR the sources of convective heating has become relatively quadrant, where inertial stability was relatively high. large (Shapiro and Willoughby 1982; Pendergrass and Before the onset of ERI, the intense VWS tilted the Willoughby 2009; Vigh and Schubert 2009). storm vortex (Fig. 4), resulting in intense midlevel shear- In the 2112 simulation, the w axis was upright between 4 induced flows in the USR quadrant, as Reasor et al. and 10 km (Fig. 13a), though the iso-AAM surface sloped (2013) and Rogers et al. (2015) reported. The vertical outward more than in the 2200 simulation. Hazelton et al. vorticity and thereby the inertial stability increased (2015) have indicated that intensifying TCs tend to have along the inner edge of the midlevel flows in the USR iso-radar-reflectivity surfaces (which can be considered quadrant (Figs. 10a,c). However, the storm vortex in the as a proxy for updrafts), which are more upright than iso- ERI experiments became almost upright (Fig. 4) when AAM surfaces. Indeed, the VWS for the 2112 simulation 2 the tall, vigorous, and upright updrafts with relatively was almost neutral (0.9 m s 1) during the period, and the high vertical vorticity formed where the inertial sta- simulated TC in the 2112 simulation underwent RI. bility was relatively high at 0000 UTC 23 September However, the rate of intensification was much smaller in (Fig. 12d). Thus, the w axis and AAM surface in the DSL the 2112 simulation than in the 2200 simulation, because quadrant attained a similar relationship for the in- the upright updraft was outside the high–inertial tensifying storm: an upright w axis with a sloped AAM stability region. surface (Hazelton et al. 2015; Rogers et al. 2015). It was Figure 13c shows the differences of mean radius– not clear whether the CB anchored the upper-level cir- altitude cross sections of the AAM, updraft, PT anom- culation center above the low-level center (Rogers et al. alies, and inertial stability between the 2112 and 2200 2015) or weakened VWS was caused by the upright simulations. In the 2200 simulation, intense, near- storm vortex at 0000 UTC 23 September. In either case, surface inflow helped transport relatively large AAM the outbreak of the CB was essential for the ERI inward. Otherwise, AAM was transported inward at through the latent heat release inside the RMW. The altitudes between 7 and 10 km outside a radius of 50 km. formation process of the CBs will be described in the Areas of negative PT anomalies were almost coincident discussion in section 4. with the areas with inward AAM fluxes at altitudes between 7 and 10 km. Intense updrafts provided a large f. Rate of intensification and inner-core structure amount of QG and QS in the middle-to-upper tropo- The previous subsections described the structural sphere. The loading effect and evaporative cooling of changes of the inner core before the onset of ERI. This water substances contributed to the inward trans- final subsection focuses on the mean structures of the portation of the AAM flux. In the 2200 simulation, a inner-core area during the rapid intensification (Fig. 13) warm core was extremely intense from the lower to the to elucidate the factors that are important for ERI. We upper troposphere. The rapid development of an ex- compared the mean radius–altitude cross section in the tremely intense warm core contributed to the rapid 2112 simulation during the periods of most rapid inten- deepening of the sea level central pressure. sification, from 1200 UTC 23 September to 0000 UTC The ERI storms possessed more-intense near-surface 24 September, with those in the 2200 simulation from inflow than the RI storm (Figs. 13d–f). Outside the 0300 to 1500 UTC 23 September (Fig. 3). During that RMW, the inertial stability was higher in the 2112 sim- period, the VWSs for the 2112 and 2200 simulations ulation than in the 2200 simulation, which might be re- 2 weakened to 0.9 and 4.3 m s 1, respectively. lated to the weaker inflow in the 2112 simulation, as During the periods of greatest intensification, the sec- Rogers et al. (2015) suggested. The near-surface inflow ondary circulation became strong for both the 2112 and was able to penetrate farther into the storm center 2200 simulations. In this paper, the term ‘‘secondary cir- compared to the inflow in the 2112 simulation. From the culation’’ is used in the context of the azimuthal-mean leading edge of the near-surface inflow, the azimuthal- structure. The outflow from the secondary circulation was mean updraft became more intense and upright. In ad- notably intense above an altitude of 12 km. In the 2200 dition, the area with an intense and upright updraft simulation, the w axis followed the upright iso-AAM sur- corresponded to the area with higher equivalent po- face below an altitude of 12 km (Fig. 13b). The mean tential temperature (EPT) in the 2200 simulation radius–altitude cross section of AAM fluxes indicated (375 K) than in the 2112 simulation (370 K). The higher that a large amount of AAM was transported inward, both the EPT became around the leading edge near the storm at the top of the near-surface inflow and at altitudes around center, the stronger became the azimuthal-mean updraft

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5 2 21 FIG. 13. Mean radius–altitude cross sections of AAM (shading; 10 m s ), vertical velocity (cyan contours; 21.0, 2 20.5, 0.5, 1.5, and 2.5 m s 1), potential temperature anomaly (green contours; 21, 5, and 10 K), QG 1 QS (magenta 2 2 contours; 1, 2, and 4 g kg 1), and squared inertial stability (thick black contours; 3 and 5 3 106 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 21 21 the low level. Contours indicate mean updraft (0.5 m s ;cyan),Vr (2, 10, 20, and 30 m s ; green), squared inertial 6 21 21 21 stability (10 and 20 3 10 s ; black), and acceleration of mean Vr (3 m s h ; white). In (f), contours indicate 21 21 differences for mean updraft (0.5 m s ;cyan),Vr (5 and 10 m s ; green), squared inertial stability (20.5, 0, and 6 21 21 21 0.5 3 10 s ; black), and acceleration of mean Vr (3 and 5 m s h ;white).

Unauthenticated | Downloaded 10/09/21 07:43 PM UTC NOVEMBER 2015 K A N A D A A N D W A D A 4211 and therefore convective heating. The previous study became warm and humid, with the aid of downdrafts as- claimed that the contributions of high heat ﬂuxes in the eye sociated with a large amount of QG. The updraft trans- region seemed to be too small to explain cyclone intensity ported abundant water vapor around the storm center to changes (Bryan and Rotunno 2009). However, the sensi- the upper troposphere. Also, the CBs were a large source tivity experiments of Xu and Wang (2010) indicated that of storm-scale vertical vorticity and helped increase the heat ﬂuxes within the eye played a role in reducing the tangential wind, the result being an increase of inertial

RMW and that heat fluxes underneath the eyewall con- stabilityinsidetheRMW2km. An increase of inertial sta- tributed to the storm intensity. Thus, high EPT resulted in bility prevents air parcels from being displaced in the ra- low CP. The great acceleration of mean Vr appeared just dial direction and allows for a more efficient dynamic around the updraft, indicating that the intense updraft was response to imposed sources of convective heating (Hack introducing large amounts of moist air near the surface. and Schubert 1986; Pendergrass and Willoughby 2009; Vigh and Schubert 2009). b. The role of shallow-to-moderate convection 4. Discussion One of the notable characteristics of the temporal evo- a. The roles of CBs lution of the inner-core structure in the ERI simulations was Previous studies have indicated that the key factor for shallow-to-moderate convection with a midlevel warm core the onset of ERI is the outbreak of rotating CBs inside the before the onset of ERI (Figs. 8, 10,and11). Shallow-to- RMW (e.g., Guimond et al. 2010). In our study, the ro- moderate convection played a crucial role in gradual inner- tating CBs were produced at 0000 UTC 23 September, core moistening in the ERI experiments. In contrast, the though other CBs without high vorticity (e.g., C0) ap- northerly dry flow was too intense to maintain shallow-to- peared around the RMW2km prior to that time. To un- moderate convection and a midlevel warm core in the 2112 derstand how the rotating CB formed, three-dimensional simulation. Both the dry layer above an altitude of 10 km structures of three CBs before the onset were compared and the tilt of the storm axis played a crucial role in in- (Fig. 14). At 1800 UTC 22 September, a tall, vigorous CB hibiting the formation of shallow-to-moderate convection. formed near a radius of 60 km. However, it formed near Whereas deep convection is assumed to play an essential the surface far from the area with high vorticity, and the role in TC intensification via latent heat release, Kieper updraft was weak below 4 km. Meanwhile, the CB at and Jiang (2012) found a satellite-detected precipitative 2100 UTC 22 September formed from an area with high ‘‘cyan’’ ring pattern around the TC center, indicating that vorticity near the surface. In areas with intense updraft, a there were low-level water clouds and warm rain, a good large amount of QG was generated. The areas with high predictor of RI. In addition, Zagrodnik and Jiang (2014) vorticity around an altitude of 10 km were associated with revealed that there is little difference in the frequency of downdrafts just inside the area with intense updrafts. At moderate-to-deep convection between stable TCs, slowly 0000 UTC 23 September, tall, vigorous, rotating updrafts intensifying TCs, and TCs that have just initiated RI. Jiang formed from the leading edge of near-surface inflow in (2012) then posed a question: are CBs neither a necessary high–vertical vorticity areas. The areas with intense down- nor a sufficient condition for RI? draft below the area with abundant QG corresponded to Shallow-to-moderate convection enables latent heat 21 theareawithintenseVr (.15 m s )(Fig. 14b). The fea- to be supplied to the inner-core area so that it contrib- tures indicate that the downdraft supported the upright utes to develop a midlevel warm core (Figs. 8 and 11). updrafts inside the RMW and intensified the vertical vor- On the other hand, the previous observational and nu- ticity of the CB below 4 km. merical studies also suggested that the subsidence by Before the onset of ERI, the azimuthal-mean EPT in- CBs induced a warm core (Chen and Zhang 2013; creased rapidly near the surface around the storm center Guimond et al. 2010; Heymsfield et al. 2001). If the (Fig. 15). It is noteworthy that ERI began when the loca- warm core formed through the latter processes, it should tion of the inner edge of the updraft at an altitude of 1 km develop after the CB penetrated the tropopause. In- was able to intrude into the area with EPT . 375 K around deed, an upper-level warm core (WC2 in Fig. 8) rapidly 0000 UTC 23 September. The differences of mean specific developed after the appearance of tall and intense up- humidity below 1 km at the radius of maximum azimuthal draft in DSL (e.g., C0) in the 2200 simulation, whereas 2 updraft were approximately 1 g kg 1 between the ERI and the midlevel warm core formed before 1800 UTC RI simulations (not shown). 22 September in the ERI experiments (Fig. 11). More- Rogers et al. (2015) discussed the processes that over, moderate convection also leads to an increase of the caused the CB inside the RMW. In our case, the ro- ambient vertical vorticity (Wissmeier and Smith 2011). tating CBs formed inside the RMW2km,inwhichtheair Indeed, the ERI started after a midlevel warm core was

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21 FIG. 14. Horizontal distributions of updraft (shading; m s ) at altitudes of (a) 10, (b) 4, and (c) 0.5 km for (left) 1800 and (middle) 3 21 2100 UTC 22 Sep 1958 and (right) 0000 UTC 23 Sep in the 2200 simulation. Lines indicate vertical vorticity (4 and 10 3 10 s ; black), Vr 2 2 (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 28 from the section were selected. coupled with an upper-level warm core. These results Typhoon Ida, in 1958. Ida had undergone the most rapid indicate that both deep and shallow-to-moderate con- deepening, greater than 20 hPa in 6 h, since 1952, ac- vection are necessary for producing ERI. cording to the Regional Specialized Meteorological Center Tokyo best-track data. The three simulations were conducted by using a 2-km-mesh nonhydrostatic 5. Summary and conclusions model initiated at three different starting times: 1200 UTC The goal of this study was to elucidate the inner-core 21 September (2112), 1800 UTC 21 September (2118), structure and environmental conditions associated with and 0000 UTC 22 September (2200) 1958 based on the the onset of extreme rapid intensiﬁcation (ERI). Nu- results of a numerical simulation using a 5-km-mesh merical experiments were performed for an intense TC, nonhydrostatic model.

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FIG. 15. Radius–time cross sections of azimuthal-mean equivalent potential temperature at an altitude of 100 m (color; K), with vertical 2 2 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.

2 Under a strong environmental VWS (.10 m s 1), two dry, subsiding, and strong flow increased the inertial of the three experiments (2118 and 2200) were able to stability. As the storm axis was upright, the storm vortex simulate an ERI comparable to the best-track ERI, intensified, and the upper-level warm core gradually de- whereas one of the three experiments (2112) simulated veloped. When the leading edge of the near-surface in- moderate intensification (RI) and, thus, a relatively flow had reached the vicinity of the storm center, deep, weak maximum intensity. vigorous and upright updrafts resulted in the upright axis The evolution of the inner core of simulated Ida in of the secondary circulation within the areas of high in- the ERI experiments is summarized in Fig. 16.Both ertial stability and helped transport warm humid air in- shallow-to-moderate and tall convection were active ward along with high vertical vorticity. The warm cores at in the inner-core area before the onset of ERI. Because of different altitudes merged and then developed rapidly, the formation of shallow-to-moderate convection around the result being rapid deepening of the sea level central the leading edge of intense near-surface inflow on the pressure. Meanwhile, the vortex for the 2112 simulation downshear side of the storm center, the inner-core area greatly tilted to the northwest at 0000 UTC 22 September 2 was gradually moistened, and the midlevel warm core 1958 (Fig. 17). Dry air (specific humidity , 0.1gkg 1) developed through the latent heat release even with a covered the eastern and northern sides of the inner strong VWS. On the upshear side of the inner-core area, core at an altitude of 12 km. The delay of the vortex

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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* 5 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.

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study was supported by the Ministry of Education, Cul- ture, 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.

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