On the Processes Leading to the Rapid Intensification of Typhoon Megi (2010) (original) (raw)
1. Introduction
While tropical cyclone (TC) track forecasts have improved significantly during the past 20 yr, the progress in intensity forecasts has been relatively slow, about 33%–50% of those track model improvements at 24–72-h forecast periods (Cangialosi and Franklin 2012; Falvey 2012; DeMaria et al. 2014). TC intensity forecasting remains as a challenging task since TC intensity change is affected by multiscale processes (Wang and Wu 2004), ranging from synoptic (environmental conditions), to vortex, to convective, to turbulent, to microscales (Marks and Shay 1998). In addition, the operational prediction of rapid intensification (RI) has been shown to be particularly difficult (Elsberry et al. 2007). Unexpected RI episodes could cause serious loss of life and property to the coastal regions, indicating the importance in improving our understanding of the mechanisms leading to RI.
Kaplan and DeMaria (2003, hereafter KD03) used the Statistical Hurricane Intensity Prediction Scheme to investigate the environmental difference between RI and non-RI TCs. Synoptic conditions conducive to RI were identified, including weaker vertical wind shear (VWS), higher relative humidity in the lower troposphere, warmer sea surface temperatures (SSTs), stronger upper-level easterly wind, and fewer external forcings like trough systems. Based on the same dataset, it was also found that rapidly intensifying TCs intensify more rapidly during the 12-h period prior to RI. In KD03, RI was defined when a TC intensifies by more than 30 knots (kt; 15.4 m s−1) during a 24-h period. Although the aforementioned environmental conditions were found statistically different between the RI and non-RI cases, some exceptions were also documented. For instance, rapidly intensifying TCs had been observed and simulated in high-VWS environments (Molinari and Vollaro 2010; Nguyen and Molinari 2012; Kanada and Wada 2015), pointing out that these favorable environments are neither necessary nor sufficient conditions for RI. Besides, there are other important forecast and scientific problems related to RI that remain to be fully studied, such as 1) the difference of intensification rate between the slowly and rapidly intensifying TCs (Hendricks et al. 2010) and 2) the precise time of RI onset. It is thus important to further investigate the inner-core dynamics and their interaction with the surroundings prior to and during RI.
Earlier theoretical works have emphasized the synergetic interactions between the convective heating and the axisymmetric, overturning circulation related to TC intensification. Secondary circulation triggered by external forcing (latent heat or friction) drives an inward advection of greater angular momentum, resulting in acceleration of swirling winds (e.g., Eliassen 1951; Ooyama 1969; Ooyama 1982; Shapiro and Willoughby 1982). Using a balanced vortex model, Schubert and Hack (1982) and Vigh and Schubert (2009) showed that latent heat located inside the radius of maximum azimuthal-mean wind (RMW), where inertial stability {defined as 
, where 
is the azimuthal-mean tangential wind and f is the Coriolis parameter} is large, acts to intensify the vortex most efficiently.
Ranging from meso- to convective scale, both observational and numerical studies have suggested that vortical hot towers or convective bursts (CBs) with cold cloud tops and intense vertical motions near the storm center may play an important role in rapidly intensifying processes (Heymsfield et al. 2001; Reasor et al. 2009; Guimond et al. 2010; Zhang and Chen 2012; Chen and Zhang 2013; Rogers et al. 2013; Wang and Wang 2014; Chen and Gopalakrishnan 2015). Using satellite, Doppler radar, and in situ data, Heymsfield et al. (2001) found that the vigorous vortical hot tower, which extends to an altitude of nearly 18 km, can induce mesoscale subsidence in the eye. This subsidence occupied a substantial vertical depth in the eye and was identified to result in about 3°C warming. Guimond et al. (2010) discovered that intense eyewall updrafts (upward motion greater than 20 m s−1), which are flanked by downdrafts of 10–12 m s−1, are transported toward the eye by 15–20 m s−1 inflow over a deep layer (0.5–10 km), followed by the succeeding axisymmetrization of the warm-core structure and a 11-hPa pressure drop in 1 h 35 min. The aforementioned studies indicated that CBs were observed during RI. In addition, CBs had also been detected prior to RI in other observational studies (Stevenson et al. 2014; Rogers et al. 2015; Susca-Lopata et al. 2015). By comparing the inner-core characteristics between intensifying and steady-state hurricanes, Rogers et al. (2013) showed that CBs and latent heat located inside the RMW are important features of intensifying hurricanes, consistent with the theoretical study of Schubert and Hack (1982) and Vigh and Schubert (2009). Recently, numerical studies (Zhang and Chen 2012; Chen and Zhang 2013; Wang and Wang 2014) showed that upper-level warming due to the subsidence of stratospheric air associated with the detrainment of CBs straddling the RMW initiates RI in the simulated Hurricane Wilma (2005) and Typhoon Megi (2010). These numerical and observational studies (e.g., Heymsfield et al. 2001; Guimond et al. 2010; Chen and Zhang 2013; Wang and Wang 2014) suggested a possible mechanism leading to RI. Namely, CBs occurring inside the RMW may create extra latent heat at the place, where there is high inertial stability, and are also accompanied by intense subsidence with high–potential temperature (θ) air from stratosphere, which is favorable for the warming aloft in the eye. The minimum sea level pressure (MSLP) drop associated with the upper-level warm-core structure is thus conducive to initiate RI.
Some studies indicated that the low-level air in the eye has high values of equivalent potential temperature 
and can provide the fuel for intense convection in the eyewall (Montgomery et al. 2006; Barnes and Fuentes 2010; Miyamoto and Takemi 2013; Wang and Wang 2014). Based on the GPS dropwindsonde dataset, Barnes and Fuentes (2010) showed that the difference in 
between the eye and eyewall decreases remarkably during the RI period of Hurricane Lili (2002). They hypothesized that the warm-
air in the eye is transported into the eyewall through the eye–eyewall mixing process (e.g., Persing and Montgomery 2003; Cram et al. 2007), stimulating vigorous convection, and thus likely initiates the RI. However, they pointed out that the volume of the eye is small compared with the eyewall, thus the high-
air in the eye could not sustain the whole RI episode. Similarly, Wang and Wang (2014) examined the slantwise convective available potential energy (SCAPE) and found that SCAPE decreases significantly with increased CB activity in the eyewall after the RI onset. They considered the CBs to be triggered/supported by the SCAPE in the eye region. Employing an idealized full-physics model, Miyamoto and Takemi (2013) found that the inner-core air parcel would acquire more enthalpy as a result of the increased axisymmetricity, which actuates the intense convection within the eyewall and strengthens the secondary circulation. Consequently, the reinforced secondary circulation gives rise to the RI onset. Note that there may be an alternative process not directly related to CBs which initiates RI. In the numerical study of Rogers (2010), it was suggested that the onset of RI is linked to an increase of convective precipitation and low-level upward mass flux, but neither the intensity nor the number of CBs seem to be a key for RI. However, Rogers (2010) indicated that CBs located inside the RMW about 6 h prior to RI may play some roles in enhancing the vortex-scale secondary circulation. The enhanced secondary circulation is accompanied by increased PV and inertial stability, which are conducive to the RI onset. Using satellite data, Kieper and Jiang (2012) demonstrated that a ringlike axisymmetric precipitation pattern could be a useful predictor for RI. In addition, Zagrodnik and Jiang (2014) indicated that compared with slowly intensifying TCs, rapidly intensifying TCs contain broader precipitation area, especially at the upshear quadrants, and more symmetric rainfall distribution in the inner-core region. The above-mentioned broader precipitation is composed of shallow convection and stratiform precipitation. Meanwhile, the moderate-to-deep convective area increases significantly 12 h after the RI onset. Recently, Tao and Jiang (2015) indicated that moderate-to-deep precipitation contributes less total volumetric rain and latent heat to the inner-core region of rapidly intensifying storms at the onset of RI, as compared to the slowly intensifying TCs. They further argued that RI is more likely triggered by widespread shallow-to-moderate precipitation, and that the appearance of more moderate-to-deep precipitation in the middle of RI is more like a response to the strengthening of the vortex.
Given the distinct possible processes to initiate RI presented in aforementioned studies, we are motivated to study the mechanisms leading to RI via a numerical study of Typhoon Megi (2010) and to compare our findings with previous studies (e.g., Wang and Wang 2014). To understand the mechanisms leading to RI, we try to answer the following questions:
- What are the key features at various scales prior to the RI of Megi?
- What are the possible causes and/or effects of these precursors to RI?
- What is the uncertainty of RI with respect to different microphysical processes (e.g., Li and Pu 2008) in the numerical model?
Section 2 describes the experimental design used to perform the control experiment, the sensitivity experiments with different cloud microphysical schemes, the definitions used to distinguish different types of precipitation and identify the storm center, and the synopsis of Megi. The key features, especially at the vortex to convective scales prior to RI are presented in section 3. In section 4, the PV budget is conducted, and the Sawyer–Eliassen (SE) model diagnostics (e.g., Eliassen 1951; Shapiro and Willoughby 1982; Hack and Schubert 1986) are adapted to examine the physical links between these precursors. Section 5 compares inner-core evolutions between the control experiment and a sensitivity experiment with different intensification rate. A possible path triggering RI is discussed in section 6.
2. Experimental design
a. Synopsis of Megi
Typhoon Megi (15W) was the strongest and most persistent TC in the western North Pacific during 2010, developing from the tropical equatorial waves in early October 2010 (Fang and Zhang 2016). A tropical depression was declared by the Joint Typhoon Warning Center (JTWC) and Japan Meteorological Agency (JMA) on 12 October 2010, and it further intensified into a tropical storm, named Megi by JMA at 1200 UTC 12 October. Megi became a category-1 typhoon at 0000 UTC 14 October, and it continued intensifying until 0000 UTC 15 October. However, the intensification stagnated between 0000 UTC 15 October and 0000 UTC 16 October. It started intensifying again after 0000 UTC 16 October, and the intensification rate increased to a higher level than that prior to 0000 UTC 15 October. In the meantime, MSLP dropped from 956 to 903 hPa and the peak 10-m winds increased from 90 kt (46 m s−1) to 160 kt (82 m s−1). The second intensification phase started from 0000 UTC 16 October and can be categorized as a case with RI, according to the definition given by KD03.
b. Experimental design and analytical methods
The Weather Research and Forecasting (WRF) Model (version 3.4.0; Skamarock et al. 2008) is employed to conduct the 4-day simulations initiated at 0000 UTC 15 October, which is about 24 h before the observational onset of RI associated with Megi. Experiments are set up in triple-nested domains while the inner two nests are vortex following (Fig. 2). Each domain has 334 × 250, 181 × 181, and 181 × 181 grid points, with grid spacing of 12, 4, and 1.33 km, respectively. The innermost domain contains a horizontal areal coverage of 240 km × 40 km, enough to resolve the inner-core region of Megi. Vertical grid meshes include 35 levels in the terrain-following σ coordinates from the surface to 50 hPa,1 with enhanced vertical resolution below 1-km height and at the outflow layer (z = 14–16 km). The initial fields and boundary conditions are derived from National Centers for Environmental Prediction final reanalysis field at 1° × 1° resolution (Rogers et al. 2001). In the coarse grid spacing (12 km), Kain–Fritsch cumulus parameterization (Kain and Fritsch 1993; Kain 2004) is adopted. In all three domains the following parameterization schemes are used: 1) the WRF single-moment 6-class microphysics scheme (WSM6; Hong and Lim 2006) with hydrometeor of water vapor, cloud water, rain, snow, graupel, and cloud ice, 2) Rapid Radiative Transfer Model (RRTM; Mlawer et al. 1997) for longwave and (Dudhia 1989) shortwave radiation schemes, and 3) Yonsei University (YSU) PBL parameterization with the Monin–Obukhov surface-layer scheme (Hong et al. 2006). Note that the results associated with θ budget and the convective-scale analyses are based on 2-min output, the vortex-scale analyses are based on 10-min output, while the synoptic analyses are based on 1-h output. The highest temporal-resolution (1 min) results are applied in the PV budget.
The approximate geometric center (centroid) of the storm is determined for each analysis based on the horizontal distribution of pressure, similar to Kanada and Wada (2015). The geometric center is calculated at horizontal distances of 1.33 km and summed within the radius of 90 km from the simulated vortex-tracking center for every grid 
around the location of the CP 
. The grid (X, Y) at which the summation is the smallest is selected as the storm center. The tilting distance between the low-level pressure geometric center and upper-level pressure geometric center is very small (about 10–15 km, figures not shown), which indicates that errors resulting from the vertical tilting are limited. For the analyses of the budgets, which calculate the vertical advection terms, the fixed surface center is used for the whole column. On top of that, the center varying with height is applied for the other analyses.
c. Sensitivity to cloud microphysical schemes
Li and Pu (2008) demonstrated that the intensification rates of the simulated Hurricane Emily (2005) during its early RI stage were sensitive to the different cloud microphysical schemes. Therefore, it is feasible to evaluate the uncertainty of RI by conducting experiments with various cloud microphysical schemes (listed in Table 1). The complexity of the hydrometeor species in these cloud microphysical schemes is different. The impact of the WRF single-moment 3-class (WSM3; Hong et al. 2004) scheme is examined in this study, and is also compared with the control simulation using WSM6 for the microphysical scheme (CTRL). In WSM3, three classes of hydrometeors—water vapor, cloud water–cloud ice, and rain–snow—are considered. The ice processes (cloud ice and snow) exist below or equal to 0°C, and the number of ice particles is a function of ice content. When the temperature is above 0°C, cloud water and rain are exhibited.
Table 1.
List of the cloud microphysics sensitivity experiments and their physics options.
d. Definitions of RI and different types of precipitation
We modify the convective–stratiform partitioning algorithm based on Rogers (2010), which made certain modifications on the method originally developed by Steiner et al. (1995). CBs, defined by an averaged vertical velocity higher than 5 m s−1 between 700 and 300 hPa, are not included in the convective precipitation. This definition of CB is more similar to that in Reasor et al. (2009). The modified convective region is categorized as “weak to moderate convection” in this study. Except for the weak-to-moderate convection, definitions for other types of precipitation are as in Rogers (2010). Although Rogers (2010) provided a detailed description for the definitions related to the different types of precipitation, the partitioning algorithm given by Rogers (2010) might potentially underestimate the contributions from CBs owing to their inherent vertical slope (e.g., Fig. 3 of Harnos and Nesbitt 2016). The shortcomings of the definitions and their possible impacts on the results will be further discussed in section 6.
The definition of RI adopted in this study is that when the maximum surface wind speed increases by more than 30 kt (15.4 m s−1) during a 24-h period (from KD03), which has been widely employed in other studies (e.g., Wang and Wang 2014).
3. Results—Features at different scales prior to RI
a. Comparisons with observations
As shown in Fig. 1, the RI of Megi is generally well reproduced by the WRF Model.
Fig. 1.
(a) The time series of WRF-forecasted maximum surface wind (m s−1, red and black solid lines) and minimum central pressure (hPa, red line) from 0000 UTC 15 Oct to 0000 UTC 18 Oct 2010 based on the 6-h JTWC best-track data (black dashed lines). (b) The time series of WRF-forecasted RMW (km, red and black solid lines) at z = 0.02 km and observed RMW (black dashed line) from the 6-h JTWC best-track data for the same period as (a). The vertical black lines indicate the RI onset. The red lines are derived from the 10-min simulated results, and black solid lines are averaged within 1 h.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Although the simulated onset of RI commences about 6 h earlier and the simulated peak intensity is 5–7 m s−1 weaker than observation, the simulated intensification rate is close to the JTWC best-track data (Fig. 1a). Note that the simulated maximum surface wind speed starts intensifying after 1800 UTC 15 October, while the MSLP commences deepening after 2000 UTC 15 October (Fig. 1a), implying that there is an uncertainty associated with the onset time of RI. This uncertainty was also addressed in McFarquhar et al. (2012). The onset time of RI is defined as 1800 UTC 15 October, and all the analyses prior to RI are relative to this time throughout the whole study. It should also be noted that no special initialization scheme or data assimilation is applied here. Therefore, the initial vortex is weaker than the real TC. Nevertheless, the simulated Megi spins up very quickly with sharp reduction in the RMW (Fig. 1b) during the first few hours, and the simulated RMW resembles the observation when RI begins. However, it is worth noting that the central SLP deepens dramatically (~20 hPa) with the substantial increase of surface maximum wind (~20 m s−1) during the first 1–2 h of the simulation, implying that the first 1–2 h of simulation is the spinup period. Therefore, most analyses associated with the first 3 h of simulation are omitted in the following study. The comparison between the model-predicted track of Megi and the best-track analysis is shown in Fig. 2. Although there is a southward bias associated with the simulated storm, the model generally well captures the movement of Megi during the 4-day simulation (Fig. 2).
Fig. 2.
The WRF-forecasted track (blue line) and observed track (red line) from the JTWC best-track data at 6-h intervals indicated by solid circles from 0000 UTC 15 Oct to 1800 UTC 18 Oct 2010. The model domains with triply nested, movable meshes (D02 and D03) used for the simulation are represented by the black rectangles.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
The simulated total graupel mass within the column could serve as a proxy of deep convection for comparison with low brightness temperature observed by satellite (Spencer et al. 1994; McFarquhar et al. 2012). Figure 3a indicates that the model reproduces the convective asymmetry prior to RI, but there is some radial difference of the simulated location associated with the deep convection. When the simulated Megi reaches its peak intensity, the robust and compact eyewall with RMW of about 20 km is generally captured by the model (Fig. 3c). Meanwhile, the deep convection relatively concentrating in the southern eyewall can be identified both in the observation and simulation (Figs. 3c and 3d). In addition, the simulation is examined by comparing with the intensive observation data acquired during the Impact of Typhoons on the Ocean in the Pacific 2010 (ITOP) field program. The radial profiles of flight-level and surface winds between the simulation and the observation are compared. It is shown that the simulated peak winds are slightly weaker than the observed winds at around 2200 UTC 17 October (Figs. 4b and 4c). On the other hand, the simulated wind fields are closer to the observations at 1200 UTC than the simulated results around 2200 UTC 17 October (Figs. 4a and 4c). The weaker simulated wind profiles presented around 2200 UTC 17 October may be attributed to an unrealistic eyewall replacement process in the simulation (figure not shown), which occurs after the simulated Megi reaches its peak intensity. This unrealistic eyewall replacement process probably hinders further intensification of the simulated Megi. Nevertheless, previous comparisons between the simulation and the observation demonstrate that the model-predicted results reasonably reproduce the intensification process of Megi. Therefore, these results could provide a prospective basis for further exploration that is helpful to understand the factors responsible for the RI of Megi.
Fig. 3.
(a) Column-integrated graupel mass content (g m−2) derived from simulated fields with 1.33-km resolution at 2000 UTC 15 Oct. (b) The 85-Ghz brightness temperature measured by Multifunctional Transport Satellite (MTSAT) at 1959 UTC 15 Oct. (c) As in (a), but for 0840 UTC 17 Oct. (d) As in (b), but for 0836 UTC 17 Oct. Note that the x and y axes for (a) and (c) indicate the distance (km) from the TC center.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Fig. 4.
Flight-level winds (kt, red line) and surface winds (kt, black line) for radial distance through (a) simulated Megi at 1200 UTC 17 Oct, (b) simulated Megi at 2200 UTC 17 Oct, and (c) Typhoon Megi observation from ITOP field program [0630 UTC, pass l; from D’Asaro et al. (2014)]. In (c) solid blue dots represent the lowest 150-m dropsonde winds and the green line indicates the surface rain rate (mm h−1). The x coordinates for (a) and (b) indicate distance (km) from the simulated TC center. The azimuthal angles of the radial profiles relative to the storm centers for (a) and (b) are similar to (c).
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
b. Synoptic environment
Prior to the onset of RI, the thermodynamic environmental conditions, including the high SSTs and the moist lower troposphere (Table 2), are beneficial to RI, as suggested by the previous statistical studies (KD03; Kaplan et al. 2010, hereafter K10). However, the large-scale dynamic patterns are more complicated than those thermodynamic conditions. Namely, the larger upper-level divergence and smaller relative eddy flux convergence (REFC) are favorable environmental conditions for RI as identified by KD03 (Table 2). In contrast to these conditions, the simulated mean VWS exceeds 8 m s−1 (Table 2), which is detrimental for TC intensification, and the VWS further increases 6 h prior to RI. Although the VWS decreases slightly by 1600 UTC 15 October, the magnitude of decrease (~0.5 m s−1) is pretty small, as compared with the amplitude of increase 6 h prior to RI (~5 m s−1). This suggests that the decreasing shear could not be the factor leading to the RI. In all, the environmental conditions prior to RI is somewhat mixed for TC intensification. Hence, the inner-core processes likely play a crucial role in initiating RI.
Table 2.
The mean magnitudes of the different synoptic variables identified in the 15-h simulation prior to RI in this study for the CTRL experiment and the statistical studies conducted by KD03 and K10. REFC is the 200-hPa relative eddy flux convergence averaged from r = 100 to 600 km, SST at the TC center, while RHLO is the 850–700-hPa mean relative humidity averaged from r = 200 to 800 km, D200 the 200-hpa divergence averaged from r = 200 to 800 km, SHR the 850–200-hPa vertical shear averaged from r = 200 to 800 km, and U200 the 200-hPa u component of wind averaged from r = 200 to 800 km.
c. Vortex-scale evolution
During 0000 and 0500 UTC 15 October, the surface RMW of the simulated Megi decreases considerably from about 100 km to less than 50 km (Fig. 1b). This considerable reduction of RMW may be linked to the spinup stage of the simulation, which is ascribed to the unrealistic initial storm structure in the final analysis data. The RMW undergoes large fluctuations from 0600 to 1200 UTC 15 October, which may be related to the transient development of the mesoscale convective system near the TC center (Figs. 1b, 5a, and 8a). The contraction of vortex from 0500 to 0700 UTC 15 October is rather asymmetric (figure not shown), implying that the relatively weak background vortex is affected by the temporally active convection. During the succeeding 6 h prior to RI, the fluctuation of surface RMW gradually diminishes (Fig. 1b). Consistent with the result of Wang and Wang (2014), but different from other numerical studies (e.g., Fig. 1b of Chen and Gopalakrishnan 2015), the contraction of simulated RMW during RI is relatively insignificant (Fig. 1b). Furthermore, both the tangential wind and the radial wind strengthen before the RI commences (Fig. 5a), supporting the statement made by Rogers (2010) that the enhanced primary circulation and secondary circulation could be the precursors responsible for RI. It is worth noting that the sudden development of convective system near the TC center precedes the intensification of the primary circulation (Fig. 5a), suggesting that the development of temporary convective system may be conducive to the spinup of the initial weak TC vortex via strengthening of the storm-scale secondary circulation.
Fig. 5.
(a) The radius–time cross section of the azimuthal mean for tangential wind (shaded according to top color bar m s−1) and radial wind (dashed contours at −3 m s−1 intervals) at 0.02-km height. The azimuthal mean for vertical velocity at 2-km height is presented by thick black contours at 0.5 m s−1 intervals. (b) The time–height cross section of total PV (contours, PVU) and mean inertial stability (shaded according to middle color bar, 10−4 s−1) within a radius of 80 km from the simulated TC center. (c) The time–height cross section of the axisymmetricity associated with tangential wind within a radius from 20 to 80 km from the simulated TC center (shaded according to bottom color bar, %). The black solid lines denote the onset of RI at 1800 UTC 15 Oct.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
In this study, the radius of 80 km serves as an estimate of the inner-core size since it covers most of the grid points inside the RMW and its azimuthal-mean tangential wind approximates to the damaging-force wind (25.7 m s−1) that is used to define the inner-core size in Knaff et al. (2007) and Xu and Wang (2010). Therefore, most of the analyses are conducted inside the radius of 80 km.
In addition to the azimuthal-mean tangential wind, PV, inertial stability and axisymmetricity (e.g., Miyamoto and Takemi 2013; Wang and Wang 2014) can also serve as important dynamical parameters for describing vortex-structure evolutions. Here, as in Miyamoto and Takemi (2013), the axisymmetricity is defined as
where A is a physical variable (e.g., tangential wind, vorticity, and PV); r and λ are the radial and tangential direction, respectively; and the prime stands for the deviation from the azimuthal average. In this study, tangential wind is used as A in Eq. (1). Figures 5b and 5c show increases in midlevel PV, inertial stability above 4-km height, and axisymmetricity throughout the troposphere about 4–6 h prior to RI, consistent with Rogers (2010) and Miyamoto and Takemi (2013), which suggested that the increased PV and the axisymmetric vortex structure would be a good indicator of whether a TC is undergoing RI. Unlike the axisymmetric dynamical structure shown in Fig. 5b, the convective pattern prior to the RI is asymmetric and becomes more symmetric 3 h after the RI commences (Fig. 6), suggesting that the axisymmetric convective ring may be the result instead of the cause for RI in this case. The asymmetric convective pattern prior to RI is rather inconsistent with the observational findings (e.g., Kieper and Jiang 2012).
Fig. 6.
The time–azimuthal angle (°) cross section of averaged simulated reflectivity (shaded, dB_Z_) within the radius of 20 and 80 km from the simulated TC center at 1-km height. The black line denotes the onset of RI.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
d. Evolution of the warm-core structure
A warm core with magnitude of 6–6.5 K located at z = 6–8 km is identified in Fig. 7a. The hydrostatic equation is used to assess the impact of this warm core on the reduction of MSLP. Figure 7b indicates that the diagnostic pressure is about 3–4 hPa higher than the modeled pressure. It is speculated that this error may be ascribed to the rather insufficient vertical resolution, which cannot resolve the comprehensive vertical virtual temperature distribution at the TC center. Nevertheless, the error would not affect the relative importance of this warm core. The warming above 5 km contributes more to the MSLP reduction (Fig. 7b). It is thus hypothesized that the warm core located at midlevels may be one of the important precursors prior to RI. Furthermore, the midlevel warm core is stronger at the onset of RI than that 6–12 h prior to RI, suggesting that the warm core at z = 6–8 km with certain strength (about 6.5 K) is important for the onset of RI. The possible mechanisms contributing to the formation of the midlevel warm core are discussed in section 5.
Fig. 7.
(a) The time–height cross section of averaged T υ (K, contours) and T υ perturbation (K, shaded) within a radius of 20 km from the simulated TC center. (b) The time series of averaged surface pressure (hPa) within a radius of 20 km from the simulated TC center of the model-output result (black line). The red line denotes the diagnostic pressure. The blue line denotes the diagnostic pressure from the T υ profile not considering the warming below 5.5-km height [
below z = 5.5 km equals to zero]. The purple line denotes the diagnostic pressure from the temperature profile not considering the warming between 5.5- and 11-km height [
between z = 5.5 and 11 km equals to zero]. The black lines denote the onset of RI.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
It should be mentioned that the reference temperature profile used to calculate the warm-core anomaly is defined as the averaged virtual temperature within the 558–648-km annulus moving with the storm at the same time, which is same as the reference state used in Stern and Nolan (2012). In addition, the details regarding the calculation of hydrostatic pressure are shown in appendix D.
e. Convective-scale evolution
Several periods with active convection composed of weak-to-moderate convection and CBs can be identified (Fig. 8a) prior to RI. Simultaneously, the latent heat increases significantly inside the RMW (Fig. 9c), where the heating could strengthen the warm core effectually (Vigh and Schubert 2009). Note that the active convection is located outside or around the low-level RMW (Figs. 8a and 1b), while it lies inside the mid- to upper-level RMW (Figs. 8a), consistent with the findings in Susca-Lopata et al. (2015). Therefore, the latent heat mainly increases substantially within the mid- to upper troposphere inside the RMW (Fig. 9c). The increased latent heat is mostly caused by the weak-to-moderate convection, while the CBs confined to tiny areas also play some nonnegligible role (Figs. 9a and 9b). From another viewpoint, during the periods with active convection, both the increased weak-to-moderate convection and CBs are located at inner radius with higher inertial stability (Figs. 8b and 8c), which is the only factor determining the heating efficiency in this study. Other parameters affecting Rossby deformation radius, such as static stability and scale height, almost do not change with time (figures not shown). It is believed that the active convection generating large amount of latent heat is indispensable to the strengthening of the vortex-scale secondary circulation. This hypothesis will be validated using a SE model in section 4. Meanwhile, comparing Figs. 8 and 9 with Fig. 5, we note that during the periods with active convection, the total PV and mean inertial stability increase significantly, implying that the prosperous inner-core convection can facilitate the enhancement of TC dynamical structure. In addition, the dynamical axisymmetricity decreases strikingly before gradually increasing when vigorous convection begins to develop. It is speculated that the seesaw between the asymmetric and symmetric TC structures prior to 1300 UTC 15 October, congruent with the numerical results conducted by Nguyen et al. (2011) during the intensification of the simulated Hurricane Katrina (2005), appears to play an important role in transferring the kinetic energy from the eddies to the mean flows. The increased kinetic energy in the mean flow, indicating enough vortex-scale inertial stability, is essential to the onset of RI (e.g., Rogers 2010).
Fig. 8.
(a) The time–radius cross section of areal percentage accounted as weak-to-moderate convection (shaded according to the top color bar, %) and CBs (red contours, at 5% intervals) at different radius, overlaid with the RMW (black dots) at the 7.5-km height. (b) The time–height cross section of averaged inertial stability (shaded according to the bottom color bar, 10−4 s−1) for grid points identified as CBs within a radius of 80 km from the simulated TC center. (c) As in (b), but for weak-to-moderate convection.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Fig. 9.
(a) The time–height cross section of the total latent heat (104 K h−1) contributed by CBs within the RMW. (b) As in (a), but for weak-to-moderate convection. (c) The time–height cross section of the total latent heat within the RMW.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
An interesting characteristic is that both the CBs and weak-to-moderate convection are relatively inactive during 1400–1800 UTC 15 October (Fig. 8a). This period with silent convection may impede the onset of RI, thus delayed until 1800 UTC 15 October. Furthermore, it can be noted that the convection becomes more active with the moderate increase of the latent heat between 1800 and 2100 UTC 15 October (Figs. 8a and 9c), which could play a favorable role in the triggering/maintenance of RI.
4. More insights from the PV budget and Sawyer–Eliassen model
In the previous section, the temporary inner-core active convection, gradually strengthened primary circulation, and a warm core with certain strength at midlevel (6–8-km height) are identified prior to RI. It is of scientific interest to examine the physical relation between the active convection and the gradually improved storm structure. Namely, the aim is to find out how the active convection contributes to the increased PV, especially within the mid- to upper troposphere (about 5–9-km altitude). Whether the convection in the inner-core region is active or inactive is defined by the criteria of 0.53% of the CB’s areal percentage inside the radius of 80 km. Periods in which CB’s areal ratio is greater than (less than) 0.53% are defined as “active CB phase” (“nonactive CB phase”). The durations of these two phases are equally both 7.5 h prior to the onset of RI. Figure 10 shows the distributions of active CB phase and nonactive CB phase. Note that the weak-to-moderate convection is also relatively more vigorous during the active CB phase (Fig. 8a), suggesting that the areal ratio of CBs is an ideal index for determining whether the inner-core convection is active or not. The first 3-h integration during the early spinup period is excluded in our calculation. Figure 11a quantitatively demonstrates that the PV tendency above 5-km height during the active CB phase is substantially larger than that during the nonactive CB phase. It is also worth pointing out that the PV tendency above 5-km height during the nonactive CB phase is negative, suggesting that active convection provides necessary conditions for the mid- to upper-level PV to increase. The PV budget is conducted to clarify the processes contributing to the different PV tendencies (Figs. 11b,c,d) between the active and the nonactive CB phases. The approximate PV tendency equation neglecting the frictional effect and the vorticity associated with the vertical velocity (e.g., Wu et al. 2016) in a height coordinate can be written as
Equation (2) is integrated over area of a circle with the radius of 80 km:
where P is PV, V is horizontal wind,
the horizontal gradient operator, w the vertical velocity,
the density,
the diabatic heating rate, q the absolute vorticity vector,
the relative vorticity, and
the three-dimensional gradient operator. The net PV tendency is determined by three terms on the right-hand side of Eq. (2): the horizontal advection, the vertical advection, and the diabatic heating (DH) terms that depend on gradients of
and q. It is acceptable that the frictional effect is ignored in Eq. (3) (e.g., Harnos and Nesbitt 2016; Wu et al. 2016), since the increase of PV mainly concentrates above the boundary layer (Fig. 5b).
Fig. 10.
Time series from 0000 to 1800 UTC 15 Oct of the areal percentage (%) of CBs inside the radius of 80 km from the simulated center. The red line denotes 1% of CB’s areal ratio, and the black line denotes the onset of RI. The moments in red shadow are defined as “active CB phase,” and the moments in green shadow are defined as “nonactive CB phase.”
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Fig. 11.
(a) The height–potential vorticity tendency cross sections of total PV tendency (PVU h−1) within a radius of 80 km from the simulated TC center. (b) As in (a), but for horizontal PV advection (103 PVU h−1). (c) As in (a), but for vertical PV advection (103 PVU h−1). (d) As in (a), but for heating-induced PV (103 PVU h−1). Black lines denote the active CB phase. Blue lines denote the nonactive CB phase.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
It should be known that the calculation of PV budget and the following SE model diagnoses are based on another experiment (CTRL_1min) with the same settings as CTRL, except that the temporal resolution of the output is increased to 1 min. In addition, the output vertical grid meshes are interpolated to 45 levels but the number of vertical levels for numerical integration is still 35 layers. On top of that, the 1–2–1 smoother has been applied to x, y, and z directions for the PV tendency and three diagnostic terms on the right-hand side of Eq. (3).
For the levels above 5-km height, the increased PV tendency during active CB phase is mainly provided by the horizontal advection and vertical advection terms (Figs. 11b,c). Although the DH term offsets most of the positive PV tendency contributed by the advective terms (Fig. 11d), the sum of the three terms on the right-hand side of (2) is still positive above 5-km height. The horizontal advection term seem to contribute more PV tendency in the mid- to upper levels (z = 4–8 km), and the vertical advection term provides more PV tendency in the upper levels (z > 8 km), while the DH term offsets a great amount of the increased PV caused by the vertical advection term in the upper levels. In general, the vertical advective effect redistributes the PV, namely transporting the PV from the lower troposphere to the mid- to upper troposphere. The amplitudes of the advective PV tendencies including the horizontal and vertical PV advections are greater during the active CB phase, and it is speculated that this may be related to the different vortex structure and strength of secondary circulation between the active CB phase and the nonactive CB phase. The mean properties of these fields are shown in Fig. 12.
Fig. 12.
(a) The height–radius cross sections of time-averaged azimuthal-mean radial wind (shaded according to the top color bar, m s−1) and vertical velocity (contours at 0.2 m s−1 intervals) during active CB phase. (b) As in (a), but for nonactive CB phase. (c) The height–radius cross sections of time-averaged azimuthal-mean latent heat (shaded according to the bottom color bar, K h−1) and tangential wind (contours at 3 m s−1 intervals) during active CB phase. (d) As in (c), but for nonactive CB phase.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
The axisymmetric upper-level outflow, upward motions, and diabatic heating are clearly greater during the active CB phase. In addition, the weak axisymmetric radial outflow within the radius of 30–40 km can be identified during the active CB phase, while it is far away (r > 80 km) from the TC center during the nonactive CB phase. It is assumed that the stronger secondary circulation above the boundary layer is evoked by the larger latent heat associated with more vigorous convection during the active CB phase. In addition, the more intense primary circulation throughout the troposphere during the nonactive CB phase appears to be a consequence of the stronger secondary circulation during the active CB phase, since the active CB phase precedes the nonactive CB phase (Fig. 10). In the following analyses, the balanced model based on the SE equation (Eliassen 1951; Shapiro and Willoughby 1982; Hack and Schubert 1986) is employed to elucidate the relative relationship between the latent heat and the secondary circulation as well as the possible impact of different patterns of secondary circulation on the evolution of vortex structure. The details of the balanced model are depicted in appendix C.
Figures 13a and 13b show axisymmetric tangential wind and diabatic heating at moments chosen from the active CB phase and the nonactive CB phase, respectively. It is clear that the latent heat during the active CB phase is much greater than that during the nonactive CB phase, and that the balanced transverse circulation during the active CB phase is much more intense. In other words, stronger radial inflow, outflow, and upward motions are identified during the active CB phase (figure not shown). Figures 13c and 13d indicate that the PV advection resulting from the balanced transverse circulation is significantly larger in the mid- to upper levels during the active CB phase. In addition, we break down the larger PV advection into the radial and vertical components, suggesting that the vertical advection occupies a more important part in increasing the mid- to upper-level PV at 1248 UTC 15 October (Figs. 13e and 13f). However, the positive horizontal PV advection identified above the 5-km height (Figs. 11b and 13f) is somewhat counterintuitive since there is no larger PV at outer radii transported toward the inner-core region. Instead, the mid- to upper-level outflow associated with the active convection (Fig. 12a) tends to transport the larger inner-core PV away from the TC center. A further investigation indicates that the increased PV mainly arises from the enhancement of vorticity (Fig. 14a). Upward transport of vorticity is an important source for the increased mid- to upper-level vorticity during the active CB phase (Fig. 14b). The CBs make a substantial contribution to the upward vorticity flux (>50%) between 5 and 8 km in the inner-core region (Fig. 14c), corresponding to the insightful finding in Wang (2014a). It is thus suggested that the CBs, releasing less diabatic heating than the weak-to-moderate convection (Fig. 9), likely have an important impact on the amplification of mid- to upper-level vortex.
Fig. 13.
(a) The height–radius cross section of azimuthal-mean latent heat (shaded, K h−1) and tangential wind (contours at 4 m s−1 intervals) at 1248 UTC 15 Oct, one moment of active CB phase. (b) As in (a), but for 1508 UTC 15 Oct, one moment of nonactive CB phase. (c) The height–radius cross section of PV advection (shaded, PVU h−1) due to the transverse circulation diagnosed by the SE model at 1248 UTC 15 Oct. (d) As in (c), but for 1508 UTC 15 Oct. (e) The height–radius cross section of PV advection (shaded, PVU h−1) due to the radial velocity diagnosed by the SE model at 1248 UTC 15 Oct. (f) As in (e), but due to vertical velocity.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Fig. 14.
The height–vorticity tendency cross sections of (a) total vorticity tendency (s−1 h−1) within a radius of 80 km. (b) As in (a), but for total vertical vorticity advection. (c) Total vertical vorticity advection (s−1 h−1) contributed by the CBs inside a radius of 80 km. Black lines denote the active CB phase. Blue lines denote the nonactive CB phase.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Overall, the results from the PV budget and SE model underscore the key role of strong secondary circulation associated with large latent heat generated by the active convection, which has a vital influence on the improvement of TC structure prior to RI. Furthermore, the increased CBs during the active CB phase play a key role in transporting the momentum upward and intensifying the TC circulation above the 5-km height.
5. Sensitivity experiment’s results
a. Convective-scale, vortex-scale, and warm-core comparisons
A series of experiments is carried out to evaluate the uncertainty of intensification rate under different cloud microphysical schemes. One should note that the onset timing of intensification for each simulation is different. The experiment employing WSM3 as the cloud microphysical scheme (WSM3) has the slowest intensification rate (Table 3) compared with other experiments including CTRL. Therefore, WSM3 is chosen for a comprehensive comparison with CTRL to verify the importance of the several precursors leading to RI identified in sections 3 and 4. Both WSM3 and CTRL experiments show similar intensities and tracks in the early stages of the simulations, but RI occurs only in CTRL, not in WSM3. In addition, the synoptic environmental conditions are similar between these two simulations, except that the stronger upper-level divergence is identified in CTRL (figure not shown). However, it is unclear whether RI is caused by the larger upper-level outflow or by other processes, such as more active inner-core convection. Therefore, it is necessary to further explore the inner-core processes in CTRL and WSM3.
Table 3.
List of the first-24-h intensification rates for different sensitivity experiments listed in Table 1. Note that the onset times of intensification for each experiment are different.
Figures 15b and 15d show that more latent heat inside the RMW prior to RI can be identified in CTRL, especially above the melting layer (~4-km height). The RMWs for both simulations are examined and it is found that the RMW is slightly larger in WSM3 in the mid- to upper levels (figures not shown). This indicates that heating within the RMW is more efficient in amplifying the CTRL vortex because of both the stronger primary circulation and smaller RMW relative to WSM3. Grid points of the CBs and weak-to-moderate convection inside the RMW are more numerous in CTRL than those in WSM3 (Figs. 15a and 15c). Examinations of the total latent heat inside the RMW contributed by different types of precipitation show that the increased latent heat inside the RMW in CTRL (Fig. 15b), especially within the 6–12-km height range, is mostly contributed by the more active weak-to-moderate convection (Fig. 16). The more active CBs play a minor role in providing the increased latent heat inside the RMW for CTRL (Fig. 16). Figure 16 suggests that the active weak-to-moderate convection inside the RMW seems to be more important than the CBs in triggering the RI of CTRL.
Fig. 15.
(a) Time series of the number of CB grid points (gray) within the RMW at 8-km height and the number of weak-to-moderate convection grid points (black) within the RMW at 3.35-km height for the CTRL experiment. (b) The time–height cross section of total latent heat (104 K h−1) within the RMW at different levels for the CTRL experiment. (c) As in (a), but for the WSM3 experiment. (d) As in (b), but for the WSM3 experiment. The thick black lines denote the onset of RI in the CTRL experiment.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Fig. 16.
The time-averaged total latent heat inside the RMW (104 K h−1) contributed by different types of precipitation separated by the partitioning algorithm from Rogers (2010) for (a) CTRL and (b) WSM3 from 0300 to 1800 UTC 15 Oct. The black lines denote the time-averaged total latent heat inside the RMW, the red lines the total latent heat contributed by CBs, the orange lines the total latent heat contributed by weak-to-moderate convection, the blue lines the total latent heat contributed by stratiform precipitation, the green lines the total latent heat contributed by other precipitation, and the purple lines the total latent heat contributed by the no-rain region.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
The convective activity is closely related to the strength of the storm-scale secondary circulation, as validated in section 4. Figure 17 shows the time-averaged radial winds and contour frequency distributions (CFDs) of vertical velocity in CTRL and WSM3. Figure 17e indicates that the updrafts in CTRL are stronger than those in WSM3 mainly at z = 1–8 and z = 14–18 km. For the downdraft distributions, the downward motions in CTRL are also stronger than those in WSM3 at z = 3 and z = 14–16 km. These characteristics are consistent with several previous studies (e.g., McFarquhar et al. 2012; Chen and Zhang 2013; Wang and Wang 2014), suggesting the presence of intense vertical velocity in the upper troposphere prior to the onset of RI. Figures 17c, 17d, and 17f show that the radial outflow at z = 16 km in CTRL is considerably greater than WSM3, corresponding to the stronger updrafts in the upper troposphere. In addition, the radial inflow outside the radius of 60 km in CTRL is slightly stronger than that in WSM3 in the boundary layer (Fig. 17f), and the enhanced convergence can be identified in CTRL between the radii of 50 and 70 km (figure not shown). Those features are also connected to the more intense updrafts in the lower troposphere documented in CTRL (Fig. 17e).
Fig. 17.
(a) The time-averaged CFDs of simulated vertical velocity (m s−1) at each height between 0300 and 1800 UTC 15 Oct for the CTRL experiment; contours represent frequencies (shaded according to the top color bar, %) of the occurrence of vertical velocity within a radius of 80 km from the simulated TC center. (b) As in (a), but for the WSM3 experiment. (c) The radius–height cross section of time-averaged azimuthal-mean radial wind (shaded according to the second color bar, m s−1) between 0300 and 1800 UTC 15 Oct for the CTRL experiment. (d) As in (c), but for WSM3 experiment. (e) Difference of frequencies (shaded according to the third color bar, %) plotted as the CFDs of vertical velocity for the CTRL experiment minus that for the WSM3 experiment. (f) Difference of wind speed (shaded according to the bottom color bar, m s−1) plotted as the azimuthal-mean radial wind for the CTRL experiment minus that for the WSM3 experiment.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Enough strength of primary circulation and warming at mid- to upper altitudes may also be crucial for initiating RI, as suggested by the previous analyses. It is shown that the inner-core PV, inertial stability, and dynamical axisymmetricity are greater in CTRL than those in WSM3 (Figs. 5b, 5c, 18a, 18c, and 18d). Remarkable differences are identified 4–6 h prior to 1800 UTC 15 October, especially above the 5-km height. A comparison of warm-core structures reveals the presence of greater warming above z = 6 km in CTRL (Figs. 7a and 18b). It is also found that WSM3 has less mid- to upper-level PV, inertial stability, latent heat, warming, and weaker secondary circulation by comparing it with the other sensitivity experiments (Figs. B1–B4). These comparisons again confirm the relative importance of the indicators including the temporary active convection inside the RMW, the sufficient strength of the primary circulation, and a warm core with a certain magnitude at 6–8-km height prior to RI, as suggested by previous analyses.
Fig. 18.
(a) The time–height cross section of total PV (shaded according to the top color bar, 104 PVU) within a radius of 80 km from the simulated TC center for the WSM3 experiment. (b) The time–height cross section of averaged θ (K, contours) and θ perturbation (K, shaded according to the second color bar) within a radius of 20 km from the simulated TC center for the WSM3 experiment. The reference temperature profile is defined as the 960 km × 960 km area-averaged θ(z) centered at storm center at the initial time. (c) As in Fig. 17a, but for mean inertial stability (10−4 s−1, shaded according to the third color bar). (d) The time–height cross section of mean axisymmerticity (%, shaded according to the bottom color bar) within a radius between 20 and 80 km from the simulated TC center for the WSM3 experiment. The black lines denote the onset of RI in CTRL.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
b. Causes leading to different warm-core developments
As shown in Fig. 8b, the warming above the 5-km height could efficiently induce the MSLP drop. Therefore, it is of scientific interest to investigate what mechanisms contribute to the greater midlevel (z = 6–8 km) warming in CTRL. By comparing Figs. 15a and 15c with Figs. 7a and 18b, it can be noted that more vigorous convection precedes the formation of the warm core located at the midlevels in CTRL. It is possible that the stronger latent heat has an important impact on the warm-core development. Note that Ohno and Satoh (2015) employed an SE model to diagnose the balanced response to heating. Their results showed that heating-induced transverse circulation significantly contributed to the warm-core formation near the tropopause. Therefore, we also utilize the SE model to evaluate the impact of secondary circulation on the developments of warm cores. Figures 19a and 19b show the selected profiles at the same time (1248 UTC 15 October) of azimuthal-mean latent heat and tangential wind from CTRL and WSM3, individually. These moments, prior to the different developments of warm cores, will be diagnosed by the SE model to understand the 
tendency associated with the balanced transverse circulation. Figure 19c indicates that the secondary circulation triggered by the greater latent heat in CTRL is critical to the stronger 
tendency within the eye. Furthermore, the height of the maximum diagnosed 
tendency in CTRL is consistent with the simulated warm-core height. In addition, not surprisingly, the 
tendency is mostly contributed by vertical advection (figures not shown). Under the axisymmetric framework, vertical downward advection is the only term that can contribute to the warming in the eye, since horizontal inward advection brings the lower-
air outside the eye into the eye region, which tends to reduce 
within the eye.
Fig. 19.
(a) As in Fig. 13a. (b) As in Fig. 13b, but for the WSM3 experiment. (c) The total θ advection (contour, K h−1) due to the transverse circulation diagnosed by the SE model at 1248 UTC 15 Oct for the CTRL experiment (black line) and the WSM3 experiment (blue line) within a radius of 20 km from the simulated TC center.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
However, Stern and Zhang (2013) indicated that the eddy radial
advection accounted for the warming within the eye during the RI period in an idealized TC simulation. Hence, the contribution from eddies is examined through the
budget:
Equation (5) is integrated over a circle with the radius of 20 km; the areal average of Eq. (5) can be written as
where B equals to
, u is the radial wind, and the overbars denote the azimuthal mean. In addition,
is the azimuthal-mean
tendency,
is the diabatic heating term, including the model-output latent heat and
tendency due to effects of radiations and PBL parameterization,
is the
tendency due to azimuthal-mean radial
advection, and
is the
tendency due to eddy component of radial
advection (ERAD). On the vertical advection terms,
is the
tendency from azimuthal-mean vertical
advection (MVAD), and
represents the
tendency caused by eddy component of vertical
advection. These terms are calculated at 2-min intervals on the height coordinates. Figures 20c and 20d show each term of Eq. (6) averaged within the radius of 20 km at 1248 UTC 15 October, respectively. The contributions from azimuthal-mean radial
advection and eddy component of vertical
advection to the warming can be basically neglected. It should be noted that the effect of diabatic heating is comparable with the advective terms, and CTRL features more warming due to diabatic heating at z = 8–10 km. This may be related to more stratiform precipitation moving into the eye at this moment (figure not shown), since CTRL has more vigorous convection inside the RMW. In addition, these analyses indicate that the warming caused by ERAD is as critical as the warming from MVAD (Fig. 20a) and that the asymmetric horizontal advection contributes greater warming at low troposphere in CTRL, as compared with WSM3 (Fig. 20c). Furthermore, the
budgets at 0800 UTC 15 October, when the warm cores of CTRL and WSM3 newly formed, are also performed (Figs. 20a and 20b). Note that the incipient warm core at 7-km height in CTRL is stronger than that in WSM3 (Figs. 7a and 18b) at 0800 UTC 15 October. Figure 20a indicates that the azimuthal-mean subsidence plays an essential role in the greater warming above z = 6 km in CTRL, as compared with that in WSM3 (Fig. 20b). Despite that there are some residual errors in the lower troposphere in CTRL (Fig. 20a), this result demonstrates that the azimuthal-mean subsidence that may be related to the detrainment of active convection inside the RMW (Fig. 15a) is the critical mechanism leading to the formation of midlevel warm core in CTRL.
Fig. 20.
Each term in Eq. (6) for (a) CTRL experiment and (b) WSM3 experiment at 0800 UTC 15 Oct. The black lines indicate azimuthal-mean θ tendency, the red lines the DH term, yellow lines the θ tendency due to azimuthal-mean radial θ advection, light-blue lines the θ tendency due to the eddy component of radial θ advection (ERAD), orange lines the θ tendency from azimuthal-mean vertical θ advection (MVAD), and blue lines the θ tendency caused by the eddy component of vertical θ advection. These terms are calculated at 2-min intervals on the height coordinates. (c) As in (a), but for 1248 UTC 15 Oct. (d) As in (b), but for 1248 UTC 15 Oct.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
These results suggest that MVAD contributes to the formation of incipient midlevel warm core in CTRL, while ERAD also accounts for the low-level warming that cannot be ignored in the eye. In addition, these mechanisms seem to be more active in rapidly intensifying TCs.
c. Understanding the factors affecting convective activities
The above results suggest that more vigorous convection generating greater latent heat inside the RMW is a key initial condition responsible for the onset of RI. Therefore, factors contributing to the active convection should be clarified. Rogers et al. (2013) proposed that the slope of eyewall convection, outer-core inertial stability in lower troposphere that would affect the strength of inflow and the radius of supergradient wind may determine the radial distribution of upward motions, thus creating the difference of latent heat relative to the RMW. These possible factors are examined during 1100–1300 UTC 15 October, when the convection in CTRL is significantly more vigorous than WSM3. However, the eyewall slope is more upright above z = 8 km in WSM3 than that in CTRL (Figs. 21a and 21b). Moreover, the difference of outer-core inertial stability is insignificant between CTRL and WSM3 and the radius of supergradient wind is closer to the TC center in WSM3 than that in CTRL (figures not shown). Therefore, the difference of latent heat inside the RMW is resulted from the strength of convection, not from the location of it (Figs. 21a and 21b). Increased inner-core surface enthalpy flux (SEFX) is conducive to the eyewall active convection and TC intensity (Xu and Wang 2010). The SEFX is larger for most of the time during and prior to the development of active convection in CTRL than that in WSM3 (Fig. 21c). The magnitude of SEFX is associated with near-surface wind speed, and the surface radial inflow in CTRL is slightly more intense than that in WSM3 outside the radius of 60 km (Fig. 17f). We therefore suggest that the larger SEFX in CTRL may be mainly contributed by the stronger inner-core surface tangential wind. The azimuthal-mean tangential wind in CTRL is roughly 3–6 m s−1 greater than that in WSM3, and this difference presents 2 h prior to the development of vigorous convection (figures not shown). The larger deficit of moisture near the surface may be another process contributing to the enhanced SEFX in CTRL. It is found that the moisture discrepancy between the oceanic surface and the lowest model level is larger in CTRL than that in WSM3 (figure not shown). The decreased moisture near the surface may be associated with the representation of graupel in WSM6 microphysics used in CTRL. The downdrafts caused by the fallout of graupel bring the cold and dry air to the surface layer; therefore, the surface moisture decreases. The stronger downdrafts can also initiate convective cells, as suggested by Penny et al. (2016).
Fig. 21.
(a) The height–radius cross section of time-averaged azimuthal-mean latent heat (shaded, K h−1) and vertical velocity (contours at 0.2 m s−1 intervals) during 1100 and 1300 UTC 15 Oct for the CTRL experiment. (b) As in (a), but for the WSM3 experiment. (c) Time series of mean enthalpy fluxes (J m2) within a radius of 80 km from the simulated TC center for the CTRL (blue line) and WSM3 (red line) experiments. (d) Time series of mean radial θ e fluxes (K h−1) from the eye to eyewall at the radius of 30 km below 1-km height for the CTRL (blue line) and WSM3 (red line) experiments.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Recently, some researches proposed that eyewall intense convection could be triggered by the high-
air transported from the eye (Barnes and Fuentes 2010; Miyamoto and Takemi 2013; Wang and Wang 2014), and this process may lead to RI. Figure 21d indicates that more high-
air is transported into the eyewall in CTRL during the period with active convection. In addition, evaluation of the excess energy in the eye, as defined by Barnes and Fuentes (2010), shows that CTRL is characterized by less excess energy (figure not shown). This could be attributed to more high-
air mixed into the eyewall in CTRL. However, from the energetic standpoint, this mechanism, compared with larger SEFX identified in CTRL, provides less fuel (J s−1) for the development of convection. The energy coming from SEFX outside the radius of 30 km is at least two orders of magnitude larger than that provided by the transportation of high-entropy air from the eye to eyewall, consistent with the statement made by Bryan and Rotunno (2009). Consequently, the larger SEFX should be the dominant process leading to the active convection in CTRL.
6. Concluding remarks and discussions
This study aims to clarify the mechanisms leading to the RI of Typhoon Megi (2010). By comparing the best-track, satellite, and aircraft observational data, it is demonstrated that the RI process is reasonably well reproduced using a high-resolution WRF simulation. Furthermore, the PV budget and SE model are utilized to gain more physical insights between the different possible predecessors prior to RI. Finally, a series of sensitivity experiments is carried out to evaluate the validity of these precursors.
The results of PV budget show that when the CBs are active, the simulated PV tendency is remarkably greater above the 5-km height. The increased CBs during the active CB phase, transporting a large amount of vorticity to the mid- to upper levels, probably have a critical impact on the enhancement of vortex above the 5-km height. In addition, the vertical advection makes an important contribution to the upper-level PV, and the intense updrafts may be triggered by the latent heat of active convection. The SE model is applied to diagnose the balanced response of latent heat and it is shown that when convection is vigorous, the enhanced latent heat strengthens the secondary circulation, which mainly enhances the vertical PV advection. The reinforced secondary circulation also contributes to the midlevel warming within the eye because it enhances the azimuthal-mean subsidence, which is also the possible mechanism giving rise to the formation of midlevel warm core. On top of that, the results of 
budget indicate that the radial advection linked to eddy process plays a nonnegligible role in the warming at lower-level eye.
Comparisons of sensitivity experiments with different cloud microphysical schemes suggest that more active convection, particularly the larger areal coverage of weak-to-moderate convection, inside the RMW with greater latent heat, stronger secondary circulation, more robust primary circulation at mid- to upper elevations, and a midlevel warm core are the key indicators for RI. The larger SEFX accounts a major part in enhancing the more active convection in CTRL, while the transportation of high-
air from the eye to eyewall is also helpful but to a much lesser amplitude than the former. In addition, the convective discrepancies between CTRL and WSM3 imply the potentially dominant role of the weak-to-moderate convection on the onset of RI, while the CBs play a supporting role yet to a lesser extent. Note that this relative importance is based on the modified partitioning algorithm given by Rogers (2010). The overall stronger convective strength (Figs. 17e and B4) is implicitly linked to the onset of RI since it is directly associated with the greater magnitude of vortex-scale secondary circulation above the boundary layer. Our study provides quantitative evidences (Fig. 17e and B4) in supporting the assumption by Rogers (2010) that the amplified secondary circulation has an essential role on the onset of RI and the critical role of weak-to-moderate convection, accordant with the observational findings documented by Tao and Jiang (2015). However, neither the gradually increased trend nor the extremely large number of CBs seems to be an absolute necessity for RI.
On the other hand, our results suggest that the warming above the 5-km height contributes to the MSLP drop efficiently, consistent with Chen and Zhang (2013). However, the simulated height of the warm core at the onset of RI is different from that in Chen and Zhang (2013), which showed that the upper-level warm core is located at z = 14 km. In our results, the warm core located at z = 6–8 km is more consistent with that in Stern and Nolan (2012) and Chen and Gopalakrishnan (2015), suggesting that the RI is not necessarily triggered by the upper-level warm core near the tropopause. Regarding the mechanisms contributing to the formation of the midlevel warm core, it is suggested that the azimuthal-mean subsidence associated with detrainment of active convection inside the RMW is the major process.
On the vortex-scale evolutions, our results highlight the importance of strengthened primary circulation and increased dynamic axisymmetricity prior to the RI, which was documented in several previous studies (e.g., Rogers 2010; Miyamoto and Takemi 2013). Unlike the symmetric dynamic structure prior to RI, the convective pattern is more asymmetric owing to the moderate-to-high VWS, similar to that in Chen and Gopalakrishnan (2015), which investigated the asymmetric RI of Hurricane Earl (2010). However, the convective evolution prior to the RI is somewhat inconsistent with the axisymmetric convective pattern observed by previous satellite-based studies (e.g., Kieper and Jiang 2012; Zagrodnik and Jiang 2014). These comparisons imply that the enhanced primary circulation and axisymmetric wind structure may be more important than the ringlike convective pattern in initiating RI.
Although many precursors responsible for RI found in this study (including the active convection inside the RMW, stronger secondary circulation, mightier primary circulation, and a warm core ascertained at midaltitude) are also identified by previous observational and numerical researches (e.g., Rogers et al. 2013; Brown and Hakim 2015), our study highlights the role of the synergistic interactions between these characteristics in creating a favorable pre-RI condition. Namely, this research provides the possible physical links to bridge the gaps between the precursors leading to the RI proposed in previous studies. Our work is more comparable with Rogers (2010), which suggested that the changes of vortex structure play a key factor explaining why RI happens. Rogers (2010) proposed that the enhanced inertial stability and primary circulation, resulted from the amplified secondary circulation associated with increased convective precipitation, would be the essential signature prior to the RI. However, our result is somewhat different as compared to Chen and Zhang (2013) and Wang and Wang (2014), which highlighted that the RI onset is directly triggered by the upper-level warm core induced by the subsidence of stratospheric air. They further suggested that the subsidence with high-θ air is associated with the detrainment of CBs.
The discrepancies between CTRL and WSM3 also underscore that the ice processes play an important role in triggering/maintaining the RI, consistent with several previous studies (McFarquhar et al. 2012; Miller et al. 2015; Harnos and Nesbitt 2016). The ice processes including graupel, supercooled water, and sublimation are neglected in the microphysical treatment of WSM3. Therefore, the latent heat associated with ice processes is reduced in WSM3, as compared with CTRL using WSM6 as the microphysical scheme.
As previously mentioned in section 2d, the convective–stratiform partitioning algorithm utilized in this study may underestimate the contributions from CBs. Several studies indicated CB’s inherent vertical slope due to the slantwise convection within the eyewall (Wang 2014b; Harnos and Nesbitt 2016). Therefore, the actual contribution of latent heat provided by CBs would be probably greater than that shown in Fig. 9a if the vertical slope of CBs is considered. In contrast, the contribution from weak-to-moderate convection might be less than that identified in Fig. 9b since part of the weak-to-moderate convection could be the slantwise CBs.
In summary, a plausible path leading to RI is described in Fig. 22: gradually increased vortex-scale enthalpy flux plays a major role in leading to the development of temporal active convection. The accompanied reinforced secondary circulation results in the strengthened primary circulation at mid- to upper levels, which can also facilitate the formation of midlevel warm core. Additionally, the robust primary circulation in the mid- to upper troposphere protects the warm core from being disrupted by the ventilation effect, and the heating efficiency of the vortex enhances as well. The development of the warm core above the 5-km height effectively lowers the MSLP. The strengthened inertial stability and the development of midlevel warm core provide a favorable environment for the onset of RI.
Fig. 22.
Schematics of radial distributions of inner-core convection, latent heat, primary circulation, secondary circulation, transportation of high-θ e air from the eye to eyewall, azimuthal-mean subsidence, surface enthalpy flux, and warm-core structure in (a) CTRL and (b) WSM3. CTRL has several distinct features prior to RI: more robust primary circulation and a warm core located at mid- to upper levels, resulting from the stronger secondary circulation. The more active convection with larger latent heat triggers the stronger secondary circulation. The larger surface enthalpy flux and barotropic instability–induced transport of high-θ e air from the eye to eyewall can be beneficial to the development of active inner-core convection.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
It is thus important to know the applicability of the possible pathway leading to RI described in Fig. 22. We found that the relative humidity within the eye above the 8-km height in CTRL is lower than that in WSM3 3–5 h prior to RI (figures not shown), suggesting that the onset of RI may be linked to the development of the TC eye (Fig. 22). This is consistent with the previous numerical studies (e.g., Fig. 5e of Rogers 2010 and Fig. 3a of Miller et al. 2015; Fig. 2a of Kanada and Wada 2015). However, the percentage of TCs having eyes prior to RI seems to be relatively low in reality. Observational studies indicated that the mean intensity of TC at the onset of RI is 58 kt (29.6 m s−1) in the North Atlantic (KD03), while the median intensity at which TC develops an eye is 56 kt (28.6 m s−1) (Vigh et al. 2012), implying that about half of TCs have eyes when the RI commences. Note that the simulated Megi’s intensity exceeding 40 m s−1 (~78 kt) at the onset of RI is stronger than the observational mean value (Fig. 1a). Furthermore, Shu et al. (2012) indicated that around 37% of RI cases reach typhoon intensity (>62 kt; 31.6 m s−1) at the onsets of RI over the northwestern Pacific. We therefore think the plausible route leading to RI may be applicable to around 30% of the rapidly intensifying TCs over the northwestern Pacific.
Further studies are needed to verify the path proposed above. The impact of different environmental flow on the predictability of RI also remains to be clarified. Studies with high-resolution ensemble simulations under different synoptic environment are worth being conducted to explore the impact of TC–environment interaction on storm intensity changes. In addition, more realistic partitioning algorithm considering the 3D updraft-scale convection as in Wang (2014b) or Harnos and Nesbitt (2016) should be applied to future numerical studies. In the end, some spinup signals may be mixed into the pre-RI characteristics in this study because of the poor representations of initial vortex structure. Although those signals do not affect the robustness of the major findings in this study, suitable initialization schemes should be utilized in future works.
Acknowledgments
This work is supported by the Ministry of Science and Technology of Taiwan under Grant MOST 104-2628-M-002-004, the Office of Naval Research through Grant ONR-N62909-13-1-NO73, and Microsoft Research Asia Grant FY14-RES-SPONSOR-024. Valuable comments from three anonymous reviewers that helped improve the quality of the manuscript are highly appreciated.
APPENDIX A
List of Symbols and Abbreviations
TABLE A1 provides a complete list of symbol and abbreviation definitions.
Table A1.
List of symbols and abbreviations. Note that WSM3 not only indicates a specific microphysics scheme but also represents the experiment employing WSM3 as the microphysics scheme.
APPENDIX B
Verification of the Precursors Leading to RI in the Other Sensitivity Experiments
We checked the inertial stability, PV, warm-core anomaly, radial inflow, and column-accumulated total latent heat at different inertial stabilities and vertical velocity within the inner-core region for all of the experiments (Figs. B1–B4).
Fig. B1.
(a) Time-averaged area-mean inertial stability (10−4 s−1) within a radius of 80 km averaged from 3 h prior to RI onset to RI onset for CTRL and other sensitivity experiments. (b) As in (a), but for total potential vorticity (104 PVU). The blue lines are CTRL, red lines Kessler, green lines Lin, purple lines WSM3, cyan lines WSM5, orange lines Ferr, gray lines WDM5, and aqua lines WDM6. Note that the onset times of intensification for each experiment are different, and WSM3 failed to undergo RI during the first 24 h of intensification.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Fig. B2.
(a) Time-averaged area-mean θ perturbation (K) within a radius of 20 km averaged from 3 h prior to RI onset to RI onset for CTRL and other sensitivity experiments. The blue lines are CTRL, red lines Kessler, green lines Lin, purple lines WSM3, cyan lines WSM5, orange lines Ferr, gray lines WDM5, and aqua lines WDM6. Note that the onset times of intensification for each experiment are different, and WSM3 failed to undergo RI during the first 24 h of intensification.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Fig. B3.
(a) Time-averaged column-integrated total latent heat (K h−1) at different inertial stability values (10−3 s−1) within a radius of 80 km averaged from 12 h prior to RI onset to RI onset for CTRL and other sensitivity experiments. The blue lines are CTRL, red lines Kessler, green lines Lin, purple lines WSM3, cyan lines WSM5, orange lines Ferr, gray lines WDM5, and aqua lines WDM6. Note that the onset times of intensification for each experiment are different, and WSM3 failed to undergo RI during the first 24 h of intensification.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Fig. B4.
(a) Time-averaged area-mean radial wind (m s−1) within the radius between 30 and 100 km averaged from 12 h prior to RI onset to RI onset for CTRL and other sensitivity experiments. (b) As in (a), but for vertical velocity averaged within a radius of 80 km. The blue lines are CTRL, red lines Kessler, green lines Lin, purple lines WSM3, cyan lines WSM5, orange lines Ferr, gray lines WDM5, and aqua lines WDM6. Note that the onset times of intensification for each experiment are different, and WSM3 failed to undergo RI during the first 24 h of intensification.
Citation: Journal of the Atmospheric Sciences 74, 4; 10.1175/JAS-D-16-0075.1
Basically, WSM3 has the weakest inertial stability at z = 4–7 km, the lowest PV at z = 6–11 km (Figs. B1), and the least warming within the eye above z = 6 km (Fig. B2). Furthermore, Fig. B3 indicates that WSM3 has the least latent heat within the grid points with inertial stability from 0.45 × 10−3 to 1 × 10−3 s−1, which implies that WSM3 has the least latent heat at the mid- to upper troposphere (z = 7–13 km). On top of that, the comparisons of radial wind and vertical velocity indicate that WSM3 has the weakest upper-level outflow and mid- to upper-level updrafts (Fig. B4). Overall, these analyses demonstrate that WSM3 has the weakest primary circulation, secondary circulation, warm-core intensity, and latent heat in the inner-core region prior to the onset of its intensification, as compared with other sensitivity experiments undergoing RI.
APPENDIX C
The Balanced Model
Here we use the SE equation based on Hack and Schubert (1986) in height coordinates as given in Wu et al. (2016). The diagnostic equation for streamfunction is written as
where R, Z,
, and Q represent the potential radius [i.e., the radius at which a parcel must be moved (conserving angular momentum) in order to change its tangential velocity to zero], height, potential temperature at the surface, and diabatic heating, respectively;
is the static stability;
is the inertial stability;
is the azimuthal-mean radial wind; and
is the azimuthal-mean vertical wind. In this study, the quantities used to define the vortex and its forcing in the SE model are directly derived from the WRF Model simulation at 2-min intervals, converted into the cylindrical coordinates, and then azimuthally averaged. The SE model is used to diagnose the axisymmetric secondary circulation and its accompanying PV advection with which the balanced vortex responds to the azimuthal-averaged diabatic heating. Note that the SE boundary conditions are characterized by streamfunction values equal to zero. The equation is solved by numerical inversion, using the successive over relaxation scheme. In addition, the SE equation is solved with a radial grid spacing of 2 km (slightly larger than the horizontal resolution used in the simulation), while the vertical resolution is uniform with a grid spacing of 0.194 km extending from the surface to the 19.4-km height.
APPENDIX D
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