1. Introduction
The prediction of tropical cyclone (TC) intensity and intensity change has been one of the greatest challenges for the global operational forecast community and is the top priority for research by the National Hurricane Center, the Joint Typhoon Warning Center, and Australian Bureau of Meteorology (Rappaport et al. 2009; Marks and Ferek 2011; Leroux et al. 2018). The challenge lies in the ability to forecast rapid intensification (RI), which is defined as more than 15.4 m s−1 (30 kt) increase in the 10-m wind over a 24-h period (Elsberry et al. 2007; Kaplan et al. 2010; DeMaria et al. 2012).
Many previous studies indicate that RI occurs typically in an environment with warm SSTs, high ocean heat content (Chan et al. 2001; Shay and Brewster 2010), weak vertical wind shear (Gray 1968; Frank and Ritchie 2001), high tropospheric relative humidity, and away from land (Hanley et al. 2001). When the environment is favorable, TCs can extract energy from the underlying warm ocean surface, efficiently convert the thermodynamic energy to symmetric kinetic energy via different internal mechanisms (e.g., Ooyama 1964; Charney and Eliassen 1964; Rotunno and Emanuel 1987; Montgomery and Kallenbach 1997; Peng et al. 2008).
A favorable external large-scale environment is a necessary, but not sufficient condition for RI. Many slowly intensifying or steady maintenance TCs are embedded in large-scale environments with warm SST and weak vertical wind shear. It is suggested that internal processes, such as the variability in the eyewall structure, may play an essential role in determining the TC intensity change (Hendricks et al. 2010; Wu et al. 2016). Many numerical modeling and analyses have demonstrated that deep convective activity, both symmetric and asymmetric, near the eyewall serves to transport moist entropy from the surface to mid–upper layers of TC or create a lower tropospheric potential vorticity (PV) anomaly that decays and transfers energy back to the parent vortex, which is fundamentally important to the intensification process (e.g., Montgomery and Enagonio 1998; Kossin and Schubert 2001). More recently, researchers have found that the tendency of the tangential wind and MSLP is dependent on the location of convective heating and eddy momentum relative to the radius of maximum wind (RMW) (Musgrave et al. 2012; Peng et al. 2008). A heating source located near or inside the RMW can produce the highest heating efficiency and is more likely to lead to a higher TC intensity through the axisymmetrization of asymmetries (Nguyen and Molinari 2012) and by advecting relatively large angular momentum surfaces inward (Smith and Montgomery 2015, 2016). In addition to the heat and momentum forcing by symmetric and asymmetric convection, some observations have shown that the eyewalls in mature TCs are not always symmetric and the interface between the eye and eyewall can consist of several straight-line segments and mesovortices that give the eye a polygonal appearance (e.g., Kossin and Schubert 2004; Lee and Wu 2018). Theoretical research by Kossin and Schubert (2001) and Rozoff et al. (2009) further confirmed the existence of mesovortices rolling up from the eyewall vorticity ring and revealed an internal mechanism that influences the intensification process through eye–eyewall vorticity mixing in their 2D barotropic numerical models. In an unforced nondivergent barotropic model, the highly unstable vorticity annuli rapidly break down into several mesovortices, which undergo merger processes with their neighbors and relax into a more stable monopole (Kossin and Schubert 2001). In contrast to the unforced experiment, the forced experiment allows the generation of vorticity in the eyewall, which causes the vorticity to rebuild into an annular eyewall ring and dissipate in the core via Rayleigh friction. Eventually, an elevated annulus of vorticity is continually regenerated via episodic vorticity mixing by the generation of mesovortices and axisymmetrization (Rozoff et al. 2009). These mesovortices can mix high equivalent potential temperature (θe) air from the eye into the eyewall (Eastin et al. 2005a,b) and redistribute vorticity in the inner core (Kossin and Eastin 2001). As a result, the pressure field adjusts to the evolving flow, and the final state central pressure can sometimes be lower than the original vortex.
Despite multiple observational and theoretical studies showing a clear relationship between TC inner-core fine-scale structure and intensity variation, numerical studies, which can be used to investigate the fine detail processes using fully integrated atmospheric variables, have been limited (Hardy et al. 2021). Lee and Wu (2018) simulated polygonal eyewalls in Typhoon Megi and demonstrated that high surface heat fluxes, PV, and convective bursts with associated latent heat release are frequently observed at each vertex of the polygonal eyewalls, and these are essential for RI. Nguyen et al. (2011) reported a vacillation between symmetric and asymmetric transition within the eyewall accompanied by the migration of vortical hot towers (VHTs) within the polygonal eyewall in a simulation of Hurricane Katrina (2005). Additionally, based on a tangential wind budget, Hardy et al. (2021) indicated the importance of the combined eddy terms in deepening the cyclonic mean circulation for Typhoon Nepartak (2016) and suggested finer spatial and temporal numerical simulations are required to resolve the three-dimensional evolution of eyewall eddies. These recent case studies highlight the importance of the eddies within the eyewall toward lower-level TC spinup above the boundary layer. However, they either focus on the net azimuthal eddy terms in the tangential wind budget or the effect of VHTs on the eyewall-to-eye mixing during an eyewall vacillation RI cycle. In fact, the eddies within TCs are not limited to small-scale VHTs, but also genesis and axisymmetrization of mesovortices, which are frequently observed to form within mature TC polygonal eyewalls. The goal of this paper is to use high-temporal- and high-spatial-resolution numerical modeling of a real TC case to investigate how periodic variations in the eyewall structure and TC intensity are related to the evolution of eyewall mesovortices and associated eye-and-eyewall mixing processes.
In 2017, Tropical Cyclone Debbie made landfall on the east coast of Australia, causing 14 fatalities with an estimated $2.67 billion (U.S. dollars) in damage, making it the deadliest cyclone to hit Australia since TC Tracy in 1974. After reaching category 21 intensity, Debbie slowly intensified for approximately 15 h followed by an 18-h rapid intensification episode just offshore, reaching category 4 intensity before making landfall near Airlie Beach. The extremely weak steering flow, evolving environmental vertical wind shear, and rapidly changing inner structure of the TC contributed to the Australian Bureau of Meteorology (BoM) operational model forecast errors in Debbie’s intensity (∼40 hPa weaker than the observed central minimum pressure) and track (∼200–300 km away from the observed inland recurving point). After landfall, Debbie recurved to the south, rapidly weakened into a tropical low, and finally merged with a cold front, causing significant flooding to Queensland and New South Wales. In this study, a Weather Research and Forecasting (WRF) Model simulation using 1-km horizontal resolution and 10-min temporal output is used to better understand the detailed physical inner-core processes during the offshore intensification of TC Debbie. The paper is organized as follows: Section 2 describes the data and methodology; section 3 introduces the large-scale environment and the process of Debbie’s intensification; section 4 shows the kinetic energy evolution and tangential wind budget during the offshore intensification; section 5 presents the evolution of the inner-core structure during the offshore intensification, including both the slow intensification (SI) and RI stages. Discussion and conclusions are presented in section 6.
2. Data and method
a. Data
The observed gridded daily rainfall data and TC Debbie best track are obtained from the BoM archive. The global 6-hourly, 1° × 1° horizontal grid spacing final analysis gridded datasets (FNL) provided by the National Centers for Environmental Prediction are used as initial and boundary conditions for the numerical model. Infrared (IR) images from the Himawari satellite and radar observation data at Bowen station are obtained from the Australian National Computational Infrastructure (NCI).
b. Experiment design and model validation
The WRF (version 3.7.1) (Skamarock et al. 2008) is used to simulate the case of TC Debbie (2017). The model is configured with three nested domains, D01 (255 × 255 grid points), D02 (481 × 583 grid points), and D03 (985 × 985 grid points) centered at 20°S, 150°E with horizontal resolutions of 9, 3, and 1 km, respectively (Fig. 1a), and 61 vertical levels. Domains D01 and D02 are initialized at 0000 UTC 24 March and terminated at 0000 UTC 30 March 2017 with output every 3 h to cover the entire lifespan of TC Debbie before dissipating in the midlatitude trough. The 1-km domain D03 is initialized at 1200 UTC 26 March and terminated at 0000 UTC 28 March 2017 with output every 10 min to resolve the TC inner-core structure and to better capture the offshore intensification period. The physics parameterizations used for the simulation are as follows: the Kain–Fritsch cumulus parameterization only for D01 (Kain 2004), the new Thompson microphysics scheme (Thompson et al. 2008), the Rapid Radiative Transfer Model for GCMs (RRTMG) longwave and shortwave radiation schemes (Mlawer et al. 1997), and the University of Washington (UW) planetary boundary layer scheme (Bretherton and Park 2009). Three-dimensional spectral nudging is used for the first 72 h on D01 and D02 to prevent the synoptic environment from drifting too far from the FNL analyses while allowing convection and storm-scale disturbances to evolve freely (Deng and Ritchie 2020). In addition, the translating pressure fit technique developed by Kepert (2005) is used to determine the TC center from the high-resolution WRF simulation by fitting a translating pressure field representative of a tropical cyclone to the observations and minimizing the sum of the cost functions.
(a) The BoM best track (black line; dates are marked alongside the 0000 UTC position) and the WRF simulated tracks (red line) and (b) time series of the best track TC intensity (black) and simulated intensity (green), including central minimum pressure (solid line) and the maximum wind (dash–dotted line) for TC Debbie (2017). The topography (unit: m) and SST (unit: °C) are overlaid in (a). The red triangles in (a) and (b) correspond to the landfall of Debbie and the blue dot in (a) denotes the Bowen radar site. The gray shading in (b) highlights the studied offshore intensification period.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
Figure 1a shows the best track (black line) for TC Debbie from the BoM and the WRF simulation track (CTL, red line) from 24 to 30 March 2017. The simulated track is in good agreement with the observed track, including the initial northwest–southwest bend on 25 March, the landfall point at Airlie Beach on 28 March and the subsequent recurve to the southeast after making landfall. Figure 1b shows the observed and simulated tropical cyclone intensity evolution. Debbie intensified at a steady rate over the warm SSTs (>29°C, Fig. 1a) from 24 to 26 March. This was followed by offshore intensification from 0600 UTC 26 March to 0000 UTC 28 March prior to making landfall. After landfall, Debbie weakened quickly. The evolution of Debbie at different stages is well captured by the WRF Model. It is worth noticing that due to the offshore intensification, Debbie was upgraded to category 4 with 10-min maximum wind speeds over 47 m s−1 just offshore and the TC subsequently made landfall as a category 4 TC at 0000 UTC 28 March, causing widespread impact to coastal areas.
During the offshore intensification period (gray shading in Fig. 1b), the best track maximum wind (black line) was initially steady at 30 m s−1 and pressure increased from 0600 to 2100 UTC 26 March. Subsequently, the maximum surface winds rapidly increased from 30 to 49 m s−1 and the central pressure decreased 31 hPa to 949 hPa in the 24 h until making landfall at 0000 UTC 28 March, satisfying the threshold for rapid intensification defined by Elsberry et al. (2007) and Kaplan et al. (2010). Therefore, the observed offshore intensification period can be divided into an SI stage followed by an RI stage. The simulated offshore process is also characterized by these two stages, with SI through 0300 UTC 27 March followed by RI (Fig. 1b). Specifically, the simulated SI occurred from 1200 UTC 26 March to 0300 UTC 27 March, when the maximum wind increased just 6 m s−1 and the minimum pressure slowly decreased 9 hPa in 15 h. The simulated RI occurred from 0300 to 1600 UTC 27 March, during which the TC intensification rate almost doubled with the maximum wind increasing more than 12 m s−1 in 13 h and peaking at 52 m s−1, and the central pressure decreasing 20hPa to 950 hPa. Although the TC intensification rate is slightly underestimated and both the simulated SI and RI periods differ somewhat from the best track records, overall, the characteristics of the SI and RI are well captured by the WRF high-resolution simulation, and this will be used to explore the physical mechanisms during the offshore period.
3. Synoptic background and Debbie’s dynamic and thermodynamic evolution
Prior to landfall, Debbie’s circulation was at least 10° north of any midlatitude troughs and located between two mid- to upper-level high pressure systems, one to the southwest over the continent and the other to the northeast over the Coral Sea (Figs. 2a,c). As a result, the environmental vertical wind shear (VWS) and steering flow over Debbie were generally weak (black line in Fig. 3c) and Debbie moved relatively slowly toward the east coast of Australia (red line in Fig. 3c). At lower levels (Figs. 2b,d), there were large amounts of moisture around Debbie and the midlatitude cold air to the south was remote from the TC inner circulation. Under the favorable environment, Debbie’s cyclonic tangential wind, low-level shallow radial inflow, and upper-level radial outflow along with the upper-level warm anomaly increased throughout the troposphere from 24 March and became more significant from 1200 UTC 26 March (Figs. 3a,b). During the offshore intensification prior to landfall on 28 March, Debbie had developed vertically into a deep cyclonic system with a maximum warm anomaly near 200 hPa.
(a),(c) The 200 hPa horizontal wind speed (shaded: ≥20 m s−1), “H” denoting high pressures, and 500-hPa horizontal wind vectors and geopotential height (black contours; interval: 20 dam); (b),(d) 850 hPa horizontal wind vectors, geopotential height (black contours; interval: 20 dam), specific humidity (red shading; unit: g kg−1), and temperature (blue shading; <8°C) at (a),(b) 1200 UTC 26 Mar and (c),(d) 0000 UTC 28 Mar 2017.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
Time–height cross sections of (a) mean tangential wind (black contours; unit: −1 × m s−1) and radial wind (shading) within a 500 km radius and (b) temperature anomaly between within 100 km radius and a 500–600 km annulus. (c) Time series of (a) 200–850 hPa environmental vertical wind shear averaged in a 200–800 km annulus of Debbie’s center (black line vector indicates shear direction; unit: m s−1) and TC motion speed (red line). The black triangle denotes the landfalling time.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
After landfall, the TC circulation rapidly eroded as Debbie was captured by a midlatitude trough, which is reflected in the increasing environmental VWS and steering flow over Debbie (Fig. 3c). Correspondingly, the tangential wind weakened, a negative temperature anomaly rapidly developed in the boundary layer below 800 hPa, and the upper-level temperature anomaly decayed slowly.
4. Kinetic energy evolution and tangential wind budget during offshore intensification
After examining the external large-scale environment, this section will look at the internal eyewall processes to better understand why Debbie underwent offshore intensification. Because many studies have emphasized the importance of the eyewall asymmetry in TC spinup above the boundary layer (e.g., Nolan et al. 2007), we will first investigate the role of symmetric kinetic energy and eddy kinetic energy.
During the offshore intensification period, vortex characteristics can be quantitatively measured by comparing the evolution of the azimuthally averaged symmetric kinetic energy (SKE) and eddy kinetic energy (EKE). The SKE and EKE in Fig. 4 are averaged vertically from the surface to 12 km in the troposphere, where the most significant cyclonic vortex variation occurred. The kinetic energy activity is different prior to, and after 0300 UTC 27 March. This divides the whole period into two different stages: the SI stage occurring prior to 0300 UTC 27 March and the followed RI stage occurring after 0300 UTC 27 March 2017. During SI, SKE was relatively weaker, less than 900 m2 s−2, and the maximum SKE propagated radially inward with time. The EKE was active inside the RMW, maximized about 30 km inside the RMW and even extending into the center at times. During RI, the SKE increased rapidly over 900 m2 s−2 and the EKE strengthened and the maximum shifted to approximately 15 km just inside the RMW on the periphery of the eyewall. The evolution in kinetic energy with time in Fig. 4 suggests that the symmetric circulation and asymmetric eddy activity behaves quite differently during the SI and RI stages.
(a) SKE (unit: m2 s−2) and (b) EKE (unit: m2 s−2) averaged between 0 and 12 km. The white line represents the RMW averaged in the 0–12 km layer.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
The budget analysis shows that the SUM generally matches the TED, both indicating that the cyclonic tendency of tangential wind is mostly confined near and inside the RMW and extends vertically from the surface up to 10 km with the largest tendency in the mid- to upper layers (figure not shown). Cyclonic spinup of the TC through the entire tropopause clearly occurs inside and at the RMW rather than outside the RMW. Time-averaged terms in Eq. (1) relative to the position of the RMW are plotted for the 5 km vertical level to represent the characteristics of wind budget of troposphere (Fig. 5). During the SI stage, the negative SUM (or TED) is larger inside the RMW than at the RMW with a minimum value at −30 km, indicating that the greatest cyclonic tendency of mean tangential winds occurred 30 km inside the RMW at this stage (Fig. 5a). Moreover, the negative SUM is mostly contributed by the EDDY_H from −30 km inward and by EDDY_V and ADV_V from −30 km outward near the RMW. ADV_H is positive from −50 to 50 km relative to the RMW and only contributes to an anticyclonic (spindown) tendency. In other words, the TC intensification during SI is due to the radial cyclonic eddy activity close to the center of the TC and the vertical transport of eddies and mean circulation near the RMW. Furthermore, the budget also demonstrates that the EKE activity maximized at 30 km inside of the RMW in Fig. 4 is mostly due to the radial flux of eddies (EDDY_H) during SI. After 0300 UTC 27 March for the RI stage (Fig. 5b), the minimum SUM (or TED) occurs at −10 to 0 km, much closer to the RMW. While the overall magnitude of the SUM (TED) is similar to that during the SI period, the contributions for increasing cyclonic tangential winds are EDDY_V and ADV_V near the RMW. Similar characteristics of mean tangential wind budget can be found for other vertical layers in mid–upper troposphere but with greater cyclonic tendency close to the RMW (figure not shown). Moreover, the EKE activity maximized at 15 km inside of the RMW in Fig. 4 is mainly due to the eddy vertical transport during this stage as the radial cyclonic eddy activity is much smaller inside the RMW.
Mean tangential wind budget (m s−1 day−1) at a height of 5 km averaged during (a) SI and (b) RI.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
In summary, the cyclonic tendency of the mean tangential wind occurs over a broader region inside the RMW during SI but occurs closer to the RMW during RI. As discussed by Shapiro and Willoughby (1982), this can lead to a faster spinup of tangential winds well inside the RMW than at the RMW itself and possibly a rapid contraction in RMW (or eyewall) during SI. This result is consistent with the dynamical study of a balanced vortex in response to diabatic heating (e.g., Wu and Ruan 2021). When the eddy and associated adiabatic heating are shifted closer to the TC center, it can lead to the inward propagation of the maximum tangential wind toward the TC center through the heat-induced overturning circulation, so that the TC RMW contracts rapidly. When the forcing is sufficiently strong, then the increased tangential wind inside the RMW greatly exceeds the initial maximum tangential wind and a rapid contraction in RMW and rapid intensification can happen simultaneously; otherwise, the intensity of the TC only slightly changes. That is why a rapid contraction of the RMW is observed in many TCs with larger RMW prior to rapid change in TC intensity (Chen et al. 2011). When the RMW contracts to a small size, the vertical eddy vorticity mixing and advection close to the RMW can result in the rapid TC intensification. This can further be explained by a statistical study by Wu and Ruan (2021), suggesting that the same imposed forcing closer to the RMW is able to produce a much higher TC intensification rate for smaller RMW.
5. The inner-core structure during offshore intensification
In addition to favorable large-scale environmental conditions (e.g., weak VWS, warm SST), the above budget analysis indicates that eddy activity near and inside the RMW appears to be an important internal factor during the offshore intensification period when Debbie intensified from category 2 to category 4. In this section, more detailed inner-core processes will be explored during both the SI and RI stages.
To avoid near-surface, instantaneous wind perturbations, the maximum azimuthally averaged tangential wind and the radius of maximum wind are both shown in Fig. 6 for the low levels (averaged between 1 and 2 km height, the same below) and middle levels (averaged between 5 and 6 km height, the same below) of the troposphere. Generally, the trends in the tangential wind are consistent between the two levels whereas the RMW shows more obvious contraction with time in the middle levels compared with the low levels. During SI, the circulation intensifies approximately 5 m s−1 in 15 h (solid lines), whereas the RMW decreases rapidly from 110 to 80 km in the middle levels (blue dotted line) but is relatively constant at approximately 75 km in the low levels (red dotted line). During RI, the tangential wind increases 15 m s−1 in 13 h and the RMW decreases steadily in both layers. The RI stage is separated into three subperiods (RI-1, RI-2, and RI-3) based on the time series of tangential wind. During each of the subperiods, the wind speed decreases or remains constant briefly (low levels and midlevels, highlighted by blue arrows) followed by a rapid increase (pink arrows), accompanied by a small decrease in RMW. Debbie’s intensity remains relatively constant after 1800 UTC 27 March until landfall at 0000 UTC 28 March.
Time series of the maximum azimuthally averaged tangential wind (solid line) and the radius of maximum wind (dotted line) for the low levels (averaged from 1 to 2 km; red) and the middle levels (averaged from 5 to 6 km; blue). The dashed and solid vertical lines separate the SI and three subperiods of RI. The blue arrows and pink arrows highlight the brief decreases and following increases in wind speed during each subperiod of RI.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
From the previous section, the midlevel RMW contraction during SI is largely attributed to the greater cyclonic spinup inside the RMW than near the RMW due to the radial cyclonic eddy transport. Moreover, the slow contraction in RMW but faster TC intensification during RI is due to the greater cyclonic vertical transport of both the eddies and the mean circulation being much closer to the RMW, thus enhancing the efficiency of spinup of tangential winds at the RMW rather than inside the RMW. Two questions are raised. What are the specific characteristics of the eddies in the vicinity of the RMW at each stage? How is the eddy evolution associated with TC intensity change? These will be addressed in the following section.
a. SI stage
During SI, the radial eddy activity inside the RMW is most active at midlevels, so the hourly evolution of simulated reflectivity and vorticity are presented for middle layers in Figs. 7 and 8. Generally, the TC eyewall evolves from an asymmetric, large open ring to a small, closed ring. Initially, the northern portion of the eyewall band weakens and the western sector spirals cyclonically inward, eventually taking the place of the eastern sector of the eyewall (Fig. 7). Similar asymmetric eyewall evolution was also found by Reasor et al. (2009) in Hurricane Guillermo using Doppler radar observations. Typically, eyewall contraction is closely related to the contraction of the RMW (Shimada and Horinouchi 2018; Li et al. 2019). This can help to explain why the midlevel RMW decreases from 110 km to about 80 km during this period (black circle in Fig. 7). At the same time, the eastern sector of the original eyewall spirals outward and forms a strong outer rainband (Figs. 7a–d). The vorticity evolution in Figs. 8a–d shows similar characteristics. The northern portion of the vorticity ring deforms and opens a gap. Wavelike perturbations can be seen closer to the eye as the broken vorticity branch propagates inward and are finally organized into an enclosed vorticity ring, resulting in vorticity mixing toward the eye.
Plan view of simulated hourly reflectivity (unit: dBZ) averaged in the 5–6 km layer in a 300 km × 300 km box centered on Debbie’s center at hourly intervals from 1600 to 2300 UTC 26 Mar 2017 during SI. The cross indicates the TC center and the black circle indicates the RMW at that level.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
As in Fig. 7, but for relative vorticity (unit: −10−4 s−1) in a 200 km × 200 km box.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
In summary, SI is characterized by an asymmetric eyewall contraction and radial mixing of vorticity between the eyewall and eye in middle layers. Because of this inward eddy (potential) vorticity migration and mixing, the wind within the eyewall increases most rapidly inside of the RMW rather than at the RMW itself as discussed in the tangential wind budget in Fig. 5. Therefore, the RMW shifts inward toward the TC center and the notable contraction in the eyewall occurs. In addition, cross sections of angular momentum (AM; Fig. 9), which are closely related to the slope of the RMW or eyewall show that during the asymmetric eyewall contraction, AM increases most significantly at 5–10 km of the atmosphere within 100 km and the slope of the AM surfaces becomes steeper largely due to the midlevel radial vorticity mixing and vertical advection inside of the RMW. This results in the formation of a more complete and tighter eyewall, which prepares for the following RI stage. Recent observation studies also suggest that a storm is more likely to experience RI after the RMW contracts to a smaller size as the convective heating close to the RMW produces more efficient TC intensification (Wu and Ruan 2021).
As in Fig. 7, but for the radial–height cross section of angular momentum (AM; unit: −105 m2 s−1). The black contours denote the AM values of −15 and −30 × 105 m2 s−1, respectively, and the dashed lines in (e)–(h) show the change in AM relative to 4 h ago.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
b. RI stage
From 0300 UTC March 2017, Debbie began RI, which consists of three subperiods, RI-1, RI-2, and RI-3, respectively. Compared to SI, the eddy vertical flux increased considerably near the RMW on the periphery of the eyewall (brown line in Fig. 5b). Because the behavior of simulated vorticity associated with the TC eyewall in the middle levels (figure not shown) are similar to those at lower levels, but the characteristics of mesovortices appear to be much clearer in the low levels, the horizontal distributions of reflectivity and vorticity averaged over the 1–2 km layer are presented (Figs. 10 and 11).
Plan view of simulated reflectivity (unit: dBZ) in the low levels (averaged in the 1–2 km layer) in a 300 km × 300 km box centered at Debbie’s center (a)–(c) at the beginning and (d)–(f) at the end of (a),(d) RI-1, (b),(e) RI-2, and (c),(f) RI-3. The cross indicates the TC center. The exact times are (a) 0320, (b) 0820, (c) 1420, (d) 0700, (e) 1100, and (f) 1700 UTC 27 Mar 2017.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
As in Fig. 10, but for relative vorticity (unit: −10−4 s−1) in a 200 km × 200 km box.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
Generally, the plan view in Fig. 10 presents a strong and tight eyewall ring. During each of the subperiods, the ring of enhanced reflectivity evolves from a more irregular pattern with distinct straight-line segments along the inner edge (Figs. 10a–c) to a more symmetric regular circle by the end (Figs. 10d–f). The corresponding vorticity in Fig. 11 clearly shows the breakdown of the eyewall into a variety of mesovortices at the beginning of RI-1, RI-2, and RI-3, resulting in eyewall shapes of a triangle, pentagon, and rhombus, respectively (Figs. 11a–c), and corresponding to the short pause in TC intensification in Fig. 6 (indicated by blue arrows). Martinez et al. (2022) also confirmed that the eyewall asymmetry hinders TC intensification in their idealized simulations. The eyewall then evolves to a relatively axisymmetric smooth pattern by the end of each subperiod due to the axisymmetrization of these mesovortices (Figs. 11d–f). The vorticity of the eyewall appears to be enhanced by the end of each subperiod and this corresponds to the rapid increase of the maximum azimuthally averaged tangential wind in Fig. 6. The eyewall evolution during RI resembles the study of Kossin and Schubert (2001) and Rozoff et al. (2009) in their highly idealized two-dimensional nondivergent barotropic model with a forced condition. In their results, the highly unstable annulus of vorticity rapidly breaks down into several mesovortices initially. This is followed by mesovortex merger and axisymmetrization within the annulus of vorticity.
Observations also support the likely activity of mesovortices within the eyewall of Debbie. Despite the attenuation of the radar reflectivity in the east quadrant of Debbie, its eyewall structure can still be seen in the radar observations from the Bowen radar station (Figs. 12a,b). Within the eyewall convective ring, reflectivity evolves from several maxima (Fig. 12a) to a relatively uniform ring (Fig. 12b). The corresponding cloud-top temperatures from the Himawari satellite IR images (Figs. 12c,d) also shows the change in cloud-top temperature within the eyewall from the asymmetric strong convection to relative axisymmetry. The transition between the two phases can be observed successively during the RI of Debbie. Many studies also confirm that even in the mature stage of severe tropical cyclones, the eyewall is not always axisymmetric and may experience shape evolution (Kossin and Schubert 2001; Otto and Soderholm 2012; Cha et al. 2020). After the three cycles, the RI period ends with a more axisymmetric, broadened vorticity ring (Fig. 11f) compared to its initial time and Debbie reaches its lifetime maximum intensity just prior to making landfall. The periodic evolution of the eyewall is reflected in the cross sections of equivalent potential temperature (θe, Fig. 13). At the beginning of each subperiod, there is much lower θe in the region of the eyewall (Figs. 13a–c). By the end of each subperiod, higher θe extends upward from the surface in the vicinity of the eyewall and even links up with the region with high θe at the upper levels, resulting in an overall increase in θe within the eyewall (Figs. 13d–f).
(a),(b) Observed radar reflectivity (unit: dBZ) at Bowen station and (c),(d) IR cloud-top temperature images (unit: °C) from the Himawari satellite at (a),(c) 1250 and (b),(d) 1630 UTC 27 Mar 2017.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
As in Fig. 10, but for the radial–height cross section of θe (unit: K).
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
As shown above in Fig. 11, the entire RI stage is accompanied by mesovortex activity. How is the eddy activity in the vicinity of the eyewall related to the change of TC strength? To explain the periodic intensification in RI-1, RI-2, and RI-3, the time–radius evolution of PV and θe is depicted in Fig. 14. The position of the TC eyewall is approximated by the 0.5 m s−1 black contours of upward velocity in Figs. 14a–c. At the start of each RI subperiod cycle, there is inward cyclonic PV mixing from the inner edge of the eyewall to the eye region (highlighted by black solid lines in Fig. 14a) and weakening of the eyewall PV. This process corresponds to the transition from an enhanced vortex ring to several mesovortices and inward mixing of these mesovortices (Figs. 10a–c and 11a–c). As a result, a more irregular pattern of eyewall is formed and a brief pause in the TC intensification is observed (blue arrows in Fig. 6). The vigorous inward-directed movement of small-scale cyclonic vortices (e.g., mesovortices or VHTs) was also found by Rozoff et al. (2009) in their barotropic model and discussed by Nguyen et al. (2011) in Hurricane Katrina. Moreover, the eye downdrafts, which are maximized along the inner edge of the eyewall, greatly suppress the vertical development of mesovortices as they travel into the eye by stabilizing the air in the eye (Fig. 15a). This could explain why, in comparison to the idealized 2D simulation by Rozoff et al. (2009), these mesovortices only exist below the middle levels of the atmosphere for a brief time and no clear monopole structure is detected in the eye. Subsequently, these mesovortices are deformed under the strong horizontal wind shear between the eye and eyewall and finally axisymmetrize and merge into the inner edge of the eyewall PV (Figs. 11 and 14a). Correspondingly, the eyewall PV annulus appears to recover from the outward cyclonic PV transport from the eye to the inner edge of the eyewall (highlighted by curly black dashed lines in Fig. 14a). Thermodynamically, the axisymmetrization of the mesovortices is followed by the vertical and radial transport of high-θe air masses from the warm ocean surface in the eye up (Fig. 15b) and radially from the eye region outward to the inner edge of the eyewall by asymmetric outflow (Fig. 15c and highlighted by curly black dashed lines in Fig. 14c). The horizontal distribution of asymmetric wind and pressure in Fig. 15d highlights that the strong eye-to-eyewall radial outflow is produced between an upstream high pressure and a downstream low pressure, which is associated with mesovortices with the horizontal size of ∼10 km and overlaid with the strong updraft and high reflectivity (indicated by a black star in Fig. 15). The transport of high-θe air from the eye to the eyewall explains the increase in the θe air within the eyewall in the middle to lower levels (Fig. 13) and the enhanced buoyant eyewall updrafts at the end of each RI subperiod (Fig. 14d). GPS dropwindsondes launched in the eye and eyewall of Hurricanes Guillermo and Georges consistently showed that the θe in the lower levels of the eye can exceed the eyewall by 5–10 K; and the outward advection of high-θe air in the eye into the eyewall is described as an apparent source of enhancing buoyant eyewall convection (Eastin et al. 2005b; Barnes and Fuentes 2010).
The radius–time section of azimuthally averaged (a) PV (units: −PVU; 1 PVU = 10−6 K kg−1 m2 s−1; shading), (b) radial gradient of PV, (c) θe (units: K; shading) at midlevels, and (d) vertical ascent (units: ×10−1 m s−1) averaged from the surface to midlevels. The black solid contours in (a)–(c) are the vertical velocity every 0.5 m s−1. The horizontal black lines indicate the end of the subperiods. The curly black dashed lines in (a) and (c) mark the transport of cyclonic PV and θe from the eye to the inner edge of eyewall, respectively; the black solid lines in (a) mark the transport of cyclonic PV from the inner edge of eyewall to the eye; and the curly red dashed lines in (a) and (d) mark the transport of cyclonic PV and upward motions toward the outer edge of the eyewall, respectively.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
Height cross section along A–B indicated in (c) of (a) reflectivity (shading) and downdrafts (blue contours) and (b) θe. Horizontal distribution of (c) θe (units: K; shading) and asymmetric winds (vectors) and (d) reflectivity (units: dBZ; shading) asymmetric winds (vectors) and asymmetric pressure (negative: blue contours; positive: red contours) at 1 km height. The green circle is drawn at a radius of 38 km from the center in (d). The black star indicates the approximate location associated with a mesovortex.
Citation: Journal of the Atmospheric Sciences 80, 2; 10.1175/JAS-D-22-0011.1
In summary, the eye-to-eyewall transport of cyclonic PV and high-θe air occur concurrently during the axisymmetrization of the mesovortices, contributing to the recovery and reinvigoration of eyewall convective activity. During this process, the maximum azimuthally averaged tangential wind increases in the later period of each of RI-1, RI-2, and RI-3 (pink arrows in Fig. 6). The intensification of the TC during the axisymmetrization is also discussed by Kossin and Schubert (2001) and Miller (2001), who attribute the intensification to the transfer of kinetic energy from the asymmetric mesovortices to the mean flow. At the same time, outward of the maximum PV region, another inward cyclonic PV transport (highlighted by curly red dashed lines in Fig. 14a) associated with upward motion (Fig. 14d) can be seen at and to the outer edge of the eyewall, which may be related to the inward propagation of outer rainbands (Nguyen et al. 2011). The eyewall PV ring broadens and strengthens as a result due to the cyclonic PV transport toward the eyewall.
6. Discussion and conclusions
Debbie intensified from category 2 to category 4 just offshore and made landfall on 28 March 2017 as a category 4 TC, causing widespread and disastrous damage. During the offshore period, it was embedded in a very favorable large-scale environment for intensification, including weak VWS and high SST, and it experienced two periods of intensification at varying rates defined for the purposes of this study as SI followed by RI. Distinct internal eyewall processes were identified as being important for the vortex evolution and intensification.
The SI stage is characterized by radial eddy activity and asymmetric eyewall contraction, notably at midlevels. The original east vorticity ring associated with the TC eyewall propagates outward, eventually being replaced by cyclonically inward-moving convection from the north and west side of the TC. A smaller and vertically aligned eyewall forms at the end of this SI stage. Similar eyewall contraction processes were seen from both radar and rainfall data by Reasor et al. (2009) and Shimada and Horinouchi (2018).
The subsequent RI stage is characterized by three rounds of eyewall breakdown into eyewall mesovortices and subsequent redevelopment, which are closely related to the variation of TC intensity. The brief pause of TC intensification at the start of each sub-RI cycle is associated with the breakdown of the eyewall into mesovortices most likely due to barotropic instability. Once generated in the eyewall, these inward-directed mesovortices stir the cyclonic PV air between the eyewall and the eye region causing the annular eyewall structure to collapse temporarily. The subsequent TC recovery and intensification is completed by axisymmetrization of the eyewall mesovortices, which greatly enhances the eyewall θe and broadens the eyewall PV band during each sub-RI cycle. The thicker, more enhanced PV ring in the eyewall at the end of each subperiod of RI likely then develops the dynamical instability for eyewall breakdown for the next round. This is inferred from the radius–time section of radial gradient PV. A close examination of the radial PV gradient evolution in Fig. 14b shows that at the start of RI-2 and RI-3 at 0730 and 1200 UTC 27 March, respectively, the radial PV gradient is positive anywhere from the eye to 50 km radius, and then reverses in sign to negative from 50 km to about 80 km radius. The change in the sign of the mean PV gradient is a necessary condition for barotropic instability, which explains the breakdown of the unstable eyewall ring and the formation of mesovortices (Schubert et al. 1999). However, this mechanism cannot explain RI-1 because the radial gradient within the eye is still negative at the start of RI-1 period at 0300 UTC 27 March (black dashed lines). It is suggested that some other factors may also contribute to the initialization of the generation of mesovortices, such as the external rainband. The RI cycle ends when Debbie makes landfall. It is unclear whether the cycle would have continued had landfall not disrupted the cycle.
Two previous studies have investigated the roles of eddies in lower-level TC spinup and TC intensity variation by examining a tangential wind budget (Hardy et al. 2021) and the migration of VHTs during the eyewall phase transition between the ringlike structure and monopole structure (Nguyen et al. 2011). In contrast, this study uses a high-resolution simulation to resolve distinctly different eddy activity during the SI stage and the subsequent RI stage during an offshore intensification of TC Debbie. During the SI stage, inward-spiraling eyewall convection and associated radial eddy activity contributes to significant midlayer asymmetric eyewall contraction and replacement. This creates an inner-core structure that is ready for the subsequent RI stage. The subsequent RI stage is characterized by the periodic genesis and axisymmetrization of mesovortices, which directly results in the periodic breakdown and reestablishment of the eyewall and associated TC rapid intensification, which further supports the theoretical work by Rozoff et al. (2009). While this study has further elucidated the distinct mechanisms associated with periods of SI versus RI, there are still remaining questions. Future work includes simulating TC Debbie in a variety of idealized environments including removing the land to see if the RI cycles continue in order to understand whether there is an element of the environment or land surface that is contributing to eyewall breakdown during RI and extending the study to more cases to see how common the eddy evolution observed during Debbie’s RI period is. Furthermore, the BoM operational model forecasts will be examined to understand its limitations in being able to forecast future events similar to TC Debbie.
Based on the Australian tropical cyclone intensity scale: cat 1: 34–47 kt; cat 2: 48–63 kt; cat 3: 64–85 kt; cat 4: 86–107 kt; cat 5: > 107 kt (1 kt ≈ 0.51 m s−1). All measurements are using a 10-min mean wind.
Acknowledgments.
We thank Dr. Jeff Kepert from the Australian Bureau of Meteorology for providing the TC center-finding code and Joshua Soderholm from the Australian Bureau of Meteorology for providing the radar datasets in our study. Computing resources were provided by the Australian National Computational Infrastructure (NCI). The first author is supported by Australian Research Council (ARC) funded Discovery Early Career Researcher Award project (DE200101435).
Data availability statement.
The observed gridded daily rainfall data are downloaded from the BoM website at http://www.bom.gov.au/jsp/awap/rain/index.jsp. TC Debbie best track are obtained from the BoM archive at http://www.bom.gov.au/cyclone/history/index.shtml. The FNL datasets are openly available from https://rda.ucar.edu/datasets/ds083.2/. The numerical model simulations upon which this study is based are too large to archive or to transfer. Instead, we provide all the information needed to replicate the simulations in section 2. IR images from the Himawari satellite and radar observation data at Bowen station can be accessed via the NCI THREDDS service at https://dapds00.nci.org.au/thredds/catalog/rr5/satellite/obs/himawari8/FLDK/2017/03/27/catalog.html and https://dapds00.nci.org.au/thredds/catalog/rq0/24/2017/vol/catalog.html, respectively.
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