Convective Bursts Episode of the Rapidly Intensified Typhoon Mujigae (2015)

The rapid intensification (RI) of tropical cyclones (TCs), defined as a 42 hPa drop in minimum sea level pressure (MSLP) in one day for western Pacific TCs (Holliday and Thompson, 1979) or a 15 m s^-1 increase in maximum sustained 10 m wind speed (MSW) in 24 h for Atlantic TCs (Kaplan and DeMaria, 2003), is challenging to accurately forecast because of its sudden occurrence. Unexpected RI episodes can cause serious economic losses and even casualties in coastal regions. As an example of an unexpected RI episode based on the above two criteria (Holliday and Thompson, 1979; Kaplan and DeMaria, 2003; Tang et al., 2018), Typhoon Mujigae (2015) made landfall in the Philippines, southern China, and northern Vietnam during early October 2015, and was the strongest storm of the year. In the island province of Hainan and the coastal province of Guangdong in China, around 60 000 fishing boats were recalled to harbor to shelter from the storm. Mujigae (2015) resulted in the death of 27 people and caused a total economic loss of US$4.25 billion. This highlights the necessity to improve our understanding of the RI process for typhoons like Mujigae (2015).

Over the past several decades (Hanley, 2002; Kaplan and DeMaria, 2003; Menelaou et al., 2013), many favorable environmental conditions for RI have been identified based on the Statistical Hurricane Intensity Prediction Scheme database, such as high sea surface temperature and ocean heat content, high relative humidity in the lower troposphere, weak vertical wind shear, and strong upper-tropospheric outflow. However, these factors do not effectively distinguish RI from non-RI TCs (Chen and Zhang, 2013; Tang et al., 2018).

Based on observations, (Rodgers et al., 2000), (Guimond et al., 2010), and (Fierro and Reisner, 2011) suggested that convective bursts (CBs) often develop before or synchronously with the onset of RI in TCs. Thus, as an important favorable factor that facilitates RI occurrence, CBs provide some predictive ability for RI identification and analysis. Previously, CBs were called "circular exhaust clouds" or "extreme convection" by (Gentry et al., 1970) and (Gray, 1998). The more common term, CBs (Steranka et al., 1986; Heymsfield et al., 2001; Menelaou et al., 2013; Guimond et al., 2016), is used in this study. The definition of a CB involves a wide range of criteria because of the different intensities of TCs (Chen and Zhang, 2013; Rogers et al., 2013; Wang and Wang, 2014; Hazelton et al., 2017; Tang et al., 2018; Wadler et al., 2018). Herein, deep convection that occurs in the upper troposphere (typically above 11 km) and consisting of one or more updrafts (resolvable for the model grid size) with vertical velocity larger than 7.5 m s^-1, is used to define a CB [refer to (Wang and Wang, 2014) and (Tang et al., 2018)]. By utilizing upper-level lightning data or numerical simulations, CB characteristics and their roles in RI can be resolved (Kelley et al., 2004; Hazelton et al., 2017). CBs contribute to the RI of TCs by moistening the mid-tropospheric atmosphere within the eyewall and inducing fast contraction of the radius of maximum wind (RMW), or by hydrostatically inducing a surface pressure decrease owing to a warm core from sinking and warming flanking intense updrafts (Rogers et al., 2002; Montgomery et al., 2006; Nolan, 2007).

In our previous study (Tang et al., 2018), the RI of Mujigae (2015) was reasonably reproduced by a 72 h simulation. Furthermore, the relationship between CBs and the potential vorticity anomaly before and during RI were explored by diagnostic analyses and sensitivity experiments. For CB episodes, anomalous active convection accompanies local energy supply/consumption. Also, in another of our articles (Yang et al., 2017), a new index indicating the convection activity degree (CAD) was presented from the viewpoint of the local total energy (TE) anomaly during a heavy rainfall event. The formula is neat and simple in form. It has been confirmed to be sufficiently robust to calculate and analyze real strong weather system cases (Yang et al., 2017). The advantages of this method include clear physical meaning, clean expression, and no need to calculate the interaction among various energy components. However, whether the CAD is correlated with CBs needs to be corroborated. If there is a correlation, then how to identify a CB episode and RI process using CAD from the viewpoint of the local TE anomaly should be explored. This will be helpful for routine application of the CAD index to rapidly intensified TC forecasting.

Therefore, several questions are focused on in this study: (2) For the rapidly intensified Typhoon Mujigae (2015), what are the spatiotemporal characteristics during the distinct stage of the CB episode? (3) What role do CBs play in the RI process? (3) To be convenient for routine application, how do we effectively identify a CB episode and RI process using the CAD index (derived from the viewpoint of the local TE anomaly)? To answer these questions, the RI process of Mujigae (2015) is reviewed on the basis of the 72 h simulation in (Tang et al., 2018) in section 2. Then, the CB features for the pre-RI, RI, and post-RI stages of Mujigae (2015) are analyzed in more detail than in our previous study (Tang et al., 2018), and the role of CBs in the RI of TCs is discussed in section 3. In addition, using the CAD index, the threshold of intense CAD for estimating the occurrence of a CB episode is derived and validated. A summary is given in the final section.

Typhoon Mujigae was the strongest typhoon in 2015, with a long lifetime from 2 to 5 October and northwestward movement from the western Pacific Ocean to Guangdong Province (Fig. 1a). Typhoon Mujigae (2015) originated from a weak tropical storm near (15.9^°N, 120.5^°E) on 2 October. The system subsequently developed into a strong tropical storm at 2000 UTC 2 October, a typhoon at 1400 UTC 3 October, and a strong typhoon at 2200 UTC 3 October (Fig. 1a). Starting from 0600 UTC 3 October, it evolved from a strong tropical storm into a strong typhoon, experiencing an RI episode, with an MSLP drop from 982 to 940 hPa and an MSW increase from 35 to 51 m s^-1 in 21 h [Fig. 1b in this study and Fig. 1c in (Tang et al., 2018)], satisfying the definition of RI (Tang et al., 2018). Thus, the lifetime of the TC can be classified into three stages: pre-RI (before 0600 UTC 3 October), the onset of RI (blue rectangular frame in Fig. 1b), and post-RI (after 0300 UTC 4 October).

The large-scale environment from GFS analysis data shows a strong upper-tropospheric outflow and low-level convergence, which is helpful for the development of deep convection. In addition, other meteorological conditions, such as convective available potential energy more than 2000 J kg^-1, sea surface temperature above 29^°C, and high ocean heat content, were also favorable for the RI of Typhoon Mujigae (Tang et al., 2018, Fig. 2).

Figure 1.  (a) Observed (green) and simulated (red) tracks of Typhoon Mujigae. (b) Time series of MSLP (red line; units: hPa) and MSW (blue line; units: m s^-1). (c) Evolution of vertical motion intensity at different height levels. The time series spans the whole simulation period from 0000 UTC 2 October to 0000 UTC 5 October 2015, except for the spin-up time (before 1200 UTC 2 October) not shown in (c). Blue frames in (b) and (c) indicate the RI stage from 0600 UTC 3 October to 0300 UTC 4 October 2015.

Figure 2.  Horizontal charts of radar reflectivity (shaded; units dBZ) and storm-relative flow vectors (units: m s^-1) at the z=1 km height level, CBs (black cross symbols), and sea level pressure (isolines; units: hPa). (a-h) Time series from 1200 UTC 2 October to 0600 UTC 4 October 2015 in 6 h intervals. The red line in (c) and (f) are utilized to make vertical cross sections in Fig. 4.

Figure 2.  (Continued)

Figure 3.  Time series of CBs. (a) CBs_100km (red curve) and CBs_200km (green curve), showing CB numbers within r=100 km and r=100-200 km, representing CBs within the inner-core and outer-ring regions. CBs_all (blue curve) denotes the sum of both. The smoothed thick and thin black lines are the 3 h moving averages of CBs_all and CBs_100km, respectively. (b) CBs within the eyewall region (light blue curve), showing CB numbers between r=0.75 RMW and r=1.25 RMW. (c) Time series of the RMW (km) at the 1 km and 11 km height levels at 10 min resolution. (d) Schematic diagram showing how eyewall CBs are computed in (b). The inner and outer rings (dotted circle) denote 0.75 RMW and 1.25 RMW, defined as the eyewall boundaries. The solid-line circle represents the RMW. The rectangle illustrates the radial spanning area of eyewall CBs counted.

To resolve more details of the CB episode and RI process for Typhoon Mujigae (2015), a high-resolution numerical simulation is performed by utilizing the Weather Research and Forecasting (WRF) model. GFS 0.5^° reanalysis data are used for the initial and boundary conditions. The model grids consist of a fixed outer nest with 18 km (253× 202) grid spacing and two inner nests that move with, and are centered on, the TC (Michalakes et al., 2005), with a horizontal resolution of 6 km (415× 415) and 2 km (253× 253), respectively. This modulating simulation is expected to produce finer and more realistic eye and eyewall structures than the slightly lower-resolution grids (10-3.3 km) in (Tang et al., 2018). The run uses the RRTM longwave radiation and Dudhia shortwave schemes, and the GCE microphysics scheme. For the outermost nest, the Kain-Fritsch cumulus parameterization scheme is used (Kain and Fritsch, 1990; Kain, 2004). However, the inner nests do not use cumulus parameterization. The simulation is integrated from 0000 UTC 2 October 2015 and lasts for 72 h. No bogus vortex is injected into the simulation. Therefore, the first 12 h is used as the spin-up time and is not included in subsequent analyses. The model outputs with 10 min intervals from the inner D03 domain are utilized for analysis.

For CB episodes, anomalous active convection accompanies local energy supply/consumption. Updrafts lead to kinetic and potential energy changes. A warm core also increases the local internal energy. These combined effects result in a local TE anomaly, which can be calculated based on the local TE equation (Vallis, 2006; Yang et al., 2017): \begin{equation} \label{eq1} \frac{\partial E}{\partial t}+\nabla\cdot[{v}(E+p)]=0 , \ \ (1)\end{equation} where $E=\rho(v^{2}/2+I+\varPhi)$ is the TE (or total energy density, i.e., the TE per unit volume of the fluid), including the kinetic energy density (ρ v²/2), internal energy (I=c_vT, in which c_v and T denote the specific heat of dry air at constant volume and temperature, respectively) and potential energy $(\varPhi)$; the variables ρ and p denote density and pressure, respectively; and v represents the three-dimensional velocity vector.

A new index indicating the CAD is put forward from the viewpoint of the local TE anomaly [Eq. (2)] during a heavy rainfall event (Yang et al., 2017). It is expressed as Eq. (3), below, i.e., the absolute value of the flux form in Eq. (2): \begin{equation} \label{eq2} {\rm CAD}=|\nabla\cdot[\textbf{v}(E+p)]|. \ \ (2)\end{equation} Note that the material derivative of E in Eq. (2) is expanded into local tendency and advection, with the latter integrated into the flux form [Eqs. (2) and (3)]. One important point is that the flux form in Eqs. (2) and (3) includes not only the TE density flux (vE) but also an additional term (vp). That is, as the work is done by the fluid against the pressure force, an energy transfer occurs. It can be seen that the local change of TE in Eq. (2) is balanced by the flux divergence of E+p. Thus, a general conservation equation [Eq. (2)] is given, producing a regular and neat form. From Eq. (2), both the local TE evolution and its source and sink terms responsible for the TE tendency can be easily derived.

The CAD formula [Eq. (3)] is neat and simple in form for application in the calculation and analysis of real strong weather system cases. However, its effectiveness for the CB episode closely related to the RI of Mujigae (2015) should be validated. Therefore, by utilizing Eqs. (2) and (3), and based on Typhoon Mujigae (2015) and the close relationship between CBs and CAD derived from the energy viewpoint, we expect to obtain a CB threshold to provide a further indicator for RI forecasting.

In (Tang et al., 2018), we successfully obtained a 72 h two-way nested simulation with a 3.3 km resolution. The simulation is updated in this study. Except for a finer resolution (2 km) and renewed moving-nested configuration, the same model configuration and parameterization schemes are used. Therefore, a similar evolution of track and intensity are reproduced by the two simulations. In Fig. 1a, it can be seen that the typhoon track is well represented in the model (red), compared with that from the best-track data of the China Meteorological Administration (green), with only slight deviation toward the end of the period. For the TC intensity, the simulated MSLP and MSW shown in Fig. 1b also show a similar evolution to the observations (Tang et al., 2018, Fig. 1c), especially for the RI stage (within the blue frame in Fig. 1b). The domain-averaged vertical motion intensity at different height levels experiences several peaks during the whole simulation period, with the largest one located in the RI stage (Fig. 1c). Other physical factors, such as the structure of radar reflectivity and vertical wind shear, can also be used for mechanism analysis (Tang et al., 2018, Figs. A1 and 1d). However, the CB intensity and CB number will have small differences between two sets simulations, which become more resolvable and larger in total owing to the increased model grid spacing in this study (see subsection 3.2, below) relative to the 3.3 km model output [cf. Figs. 2 and 3 in (Tang et al., 2018)]. For more information about the simulation, please refer to (Tang et al., 2018).

First, the CB characteristics during the RI episode of the TC are examined, in particular before and at the onset time of RI. Figure 2 shows the horizontal distributions of radar reflectivity and storm-relative flow vectors at the 1 km height level and sea level pressure encircled by 1000 hPa isolines for the three different stages of TC development. The CB elements (cross symbols), based on the definition of (Wang and Wang, 2014) and (Tang et al., 2018) for this typhoon case (Tang et al., 2018), are also included. As well as the CB elements within a 100 km radius [mentioned in (Tang et al., 2018)], CBs within a distance of 100-200 km from the TC center are also included in this study, representing the number of convection elements in the inner-core and outer regions, respectively. They are denoted as CBs_100km and CBs_200km, respectively. The sum of both is denoted as CBs_all.

Figure 2 shows the spatial pattern of the CB elements. For the pre-RI, RI, and post-RI periods (Fig. 2 and Table 1), the distribution of intense updrafts shows large spatial and temporal variability for both eyewall convection, indicated by strong reflectivity signals, and CB elements. In the early stage (Fig. 2a), Mujigae remains as a tropical storm, with an MSLP of 991 hPa at 1200 UTC 2 October 2015 (Table 1). The convection of the spiral eyewall presents remarkable axis-asymmetric semicircle structures, with a long tail from the outer region (with a radius of more than 100 km) into the inner core (within a radius of 100 km). Most CB elements are distributed along the spiral rainband in the southeast and northwest quadrants. Until 1800 UTC 2 October (Fig. 2b), the extreme updrafts are weakened, manifesting as an appreciable reduction in CB number (Table 1). Correspondingly, the intensity of the TC has no obvious fluctuations at 1800 UTC 2 October. Even by 0000 UTC 3 October (Fig. 2c), the TC is only slightly intensified, with a 5 hPa drop in MSLP within 12 h. Before the onset of RI (i.e., 6 h earlier than RI), the number of CB elements within the inner core develops suddenly up to more than 100, concentrated in the eastern quadrants and accompanied by cyclonically rotating airflows in the TC system. The CBs within the outer region of >100 km radius distance from the TC center, are also displaced to the southwest quadrant. This sudden increase in CB elements might be an indicator of the RI of Typhoon Mujigae (2015). Until this moment, the eyewall is still an open semicircular structure. From 0600 UTC 3 October (Fig. 2d), it experiences RI and a closed-eyewall mode gradually forms. Almost all CBs occur within a 100-km-radius circle from the TC center. However, the distribution of intense updrafts becomes more symmetric and scattered. Then, the closed eyewall contracts (Fig. 2e) and merges (Fig. 2f) in the following 6 h. From 1800 UTC 3 October to 0300 UTC 4 October (Figs. 2d-g and 1b), the eyewall convection becomes more organized. The areal coverage of the CB elements shrinks and concentrates toward the inner-core region. In addition, the typhoon evolves from a tropical storm to a strong typhoon during this RI stage, with increasingly larger pressure gradients embracing the inner core of the TC. By 0300 UTC 4 October, the typhoon reaches its peak intensity (Fig. 1b), with a pattern of densely distributed isobaric lines. After that time (Fig. 2h), the CB number falls to nearly zero and the typhoon is weakened to a tropical storm. In addition, the post-RI stage for Typhoon begins.

In summary, there are three TC development stages: (2) the eyewall goes through an open pattern in the pre-RI stage; (3) closed spiral rainbands and eyewall shrinking, together with strengthening processes, occur in the RI stage; (3) weakening in the post-RI stage. The eyewall convection evolves from being increasingly organized to weakened. The CB elements are always located within the strong convective eyewall and displaced cyclonically following the air of the TC system. A sudden increase in CBs occurs just before the onset of RI (Fig. 2c and Table 1), which is consistent with previous studies reporting that CBs generally occur before or during RI (Rodgers et al., 2000; Guimond et al., 2010; Fierro and Reisner, 2011).

To quantify the relationship between CBs and RI, the time series of both are investigated (red curve in Fig. 3 and Fig. 1, and Table 1). Furthermore, the CBs in the outer-ring region with a radius of 100-200 km (CBs_200km) are also analyzed (green curve in Fig. 3). These additional analyses are helpful for us to estimate the relative importance of CBs within different radius scopes in RI. Also, it is useful to test whether the correlation between CBs and RI is sensitive to a distinct radius range (cf. different curves in Fig. 3). By comparing CBs_100km, CBs_200km, and their sum (CBs_all), it is found that the CB number within the 100 km range accounts for a large proportion of all the CBs in magnitude. In addition, their moving-average trend lines (per 3 h) evolve nearly synchronously throughout the entire process. Both CBs_ 100km and CBs_all have three peaks in CB numbers. The largest one occurs just before the onset of RI during 2100 UTC 2 October to 0300 UTC 3 October (Fig. 3 and Table 1), providing a significant predictive signal for RI. The second occurs between 1200 and 1800 UTC 3 October, and is related to the eyewall shrinking toward the inner core (Figs. 2e and f). However, the CBs_200km elements swing more frequently than the CBs_100km elements, with several equivalent waves but no prominent peak indicative of RI. In short, CBs within a 100 km radius suddenly develop before the onset of RI and end abruptly at the start (at about 0600 UTC 4 October) of the post-RI stage. Of interest is that, relative to the large jump and decrease in CBs_100km, CBs_200km waves are slower and maintain until 1200 UTC 4 October, retaining a buffer zone and serving as a transition between the environment and inner core of the TC system. Therefore, RI is more relevant to CBs_100km, compared with CBs_200km, in terms of both evolution trend and magnitude. Thus, CBs_100km during the RI of the TC is focused upon, referred to simply as CBs for brevity, in the context below. Note that the time series of CBs within the eyewall region (between 0.75 and 1.25 RMW) are also investigated (Figs. 3b-d), since CBs in the eyewall region inside the RMW might preferentially contribute to TC intensification (Rogers et al., 2013; Wadler et al., 2018). The eyewall is nearly upright from z=1 km to z=11 km during the pre-RI stage (Fig. 3c). From the onset of RI, a large outward tilt up to about 40 km happens, and eyewall shrinking is obvious with consistently decreasing RMW at 1 km and 11 km. For the CBs within the eyewall, they evolve in the same manner as the inner-core CBs (Fig. 3b), except for a lower CB number in magnitude, which indicates that the inner core's intense convection is mainly located in the surrounding region of the eyewall. Therefore, in the context of this study, the inner-core CBs are investigated, which not only reduces the statistical error in counting CBs brought from varied RMW calculations, but also collects enough statistical samples with predictive sense for RI.

After analyzing the CB characteristics, a new question is addressed: How do CBs result in TC RI? The question will be answered by exploring the dynamical field, e.g., the lower-level inflow and upper-level outflow above the top of convection columns, and by probing the thermodynamic variables, such as perturbation temperature. The question will also be addressed by investigating the relationship between CBs and warm-core formation.

3.3.1 CBs and lower/upper-level inflow/outflow

Figure 4 shows the vertical distribution of CBs within the eyewall convective region for the pre-RI and RI stages. At 0000 UTC 3 October, deep convection extends upwards to the 16 km height level with a radial scale of about 10 km (from r=65 km to r=75 km), where the eyewall convection develops with a maximum reflectivity larger than 55 dBZ. The eyewall convective zone is divided into three obvious layers characterized by distinct inflow-outflow modes. Below the 3 km height level, homodromous inflows ascend slantwise at the inner side of the eyewall owing to convergence induced by wind speed shear. Between the 3 and 11 km levels, wind direction shear causes more intense airflow convergence and updraft than in the lower layer. For the upper layer above the height of 13 km, narrow and strong divergent outflows dominate and reflectivity anvils take shape. The upper-lower coupled configuration of inflow and outflow is constricted into the narrow eyewall zone, which is favorable for the occurrence of extremely deep convection. Until 1800 UTC 3 October, although the eyewall shrinks from r=70 km to r=40 km and the outer eyewall redevelops at z>60 km, the cloud top with strong reflectivity (>50 dBZ) drops to the height of 9 km. The eyewall becomes more solidified because of well-organized eyewall convection (Fig. 2f). It is difficult for the outside environmental atmosphere to penetrate the inner-core TC region through the eyewall. The lower-level inflow air heaps up at the inner-flank eyewall. This mass accumulation leads to convergent ascent. The strengthened lower-level inflows intensify updrafts therein (cf. Fig. 4a and b), while the weakened and widely stretched upper-level outflows do not create a more favorable situation for deep convection development, compared with the case shown in Fig. 4a. It can be inferred that lower-level convergent inflow is more related to the lower-layer upward motion. However, upper-level divergent outflow is advantageous for the updraft element to be pulled upwards to a higher level, the pumping action of which prompts the growth of extremely deep convection. Certainly, besides dynamical variables, the higher θ_e and temperature perturbation within the eyewall also provide advantageous thermodynamic conditions to accelerate updraft (Figs. 4a and b). Therefore, as a favorable environmental factor, the coupled lower-level inflow and upper-level outflow accompanying CBs, both interact and the CBs have positive feedback effects on development of inflow/outflow. The CBs shown in Fig. 4a are closely related to strong divergent outflow confined in a narrow space above the cloud top. The development of lower-level convection, though not reaching the criteria of a CB, is more associated with the low-level convergent inflow.

Figure 4.  Vertical cross sections of radar reflectivity (shaded; units: dBZ), equivalent potential temperature (black isolines; units: K), perturbation temperature (blue isolines; units: K), and in-plane storm-relative flow vectors (units: m s^-1) along the red lines in Figs. 2c and f, at (a) 0000 UTC and (b) 1800 UTC 3 October 2015.

3.3.2. CBs and double warm-core structures

CBs are closely related to the upper-level warm-core structure, which has been shown in several examples of TC intensification (Zhang and Chen, 2012; Chen and Zhang, 2013; Tang et al., 2018). For Typhoon Mujigae (2015) in this study, a clear warm layer with several warm cores is also detected above 16 km (blue isolines in Fig. 4a). These warm cores have perturbation temperature values higher than 4 K. They are located above the cloud top and extend from the eyewall (r=70 km) to the TC center, induced by sinking and warming of the divergent outflow. Comparatively, at 1800 UTC 3 October (Fig. 4b), the strongest reflectivity falls to the 8 km height level, located at r=40 km, and the divergent outflow subsidence from the top of this updraft column coalesces with the centripetal airflow between the 6 and 10 km height levels. Meanwhile, upper-level warming continues at the height of 16 km, notwithstanding weakening reflectivity and eyewall convection therein. Therefore, the decline of the tops of intense updraft elements from Fig. 4a to Fig. 4b facilitates the propagation of the upper-level warm core toward the middle troposphere from above the 16 km height level to the level below 10 km. Thus, the double upper-lower coupled warm-core mode occurs. The shrinking of the eyewall from r=70 km to r=40 km facilitates centripetal development of a positive temperature anomaly owing to a shortened transport path, speeding up the growth of the warm-core pattern. By simple use of the hydrostatic equation, the double warm cores of stratospheric and tropospheric origin can explain the cause of Mujigae's RI and the continuous deepening of the TC.

Figure 5a shows the time-height distribution of the warming core (shaded) superposed with the time series of potential temperature (isoline) at the eye center. Rather than a single upper-level warm core (Zhang and Fritsch, 1988; Hirschberg and Fritsch, 1993; Holland, 1997; Zhang and Chen, 2012) or a middle-level warm core (e.g., Liu et al., 1997; Halverson et al., 2006), a double warm core is present in Fig. 5. In terms of the evolution of Typhoon (MSLP in Fig. 1b), only a slight variation of the temperature perturbation before RI is seen. After 0000 UTC 3 October, an upper-level warm core of >2 K develops near z=15 km first, 6 h earlier than the onset of RI. From 0600 UTC 3 October, the lower-level warming with a temperature perturbation >2 K also begins below the 4 km level. Then, sharp warming occurs with a large horizontal gradient of temperature perturbation and vertical gradient of potential temperature (Fig. 5), accompanied by the RI of Mujigae (2015). At about 0300 UTC 4 October, a deep warming column forms with an upper-level warm core of >7 K centered at z=15 km and another mid-troposphere warm core of >6 K at z=7 km, representing a maximum temperature change with respect to the initial time. At this moment, the TC intensity reaches its peak, and then moves into the post-RI stage.

Figure 5.  Time-height cross section of perturbation temperature (shaded; units: K) superposed with the time series of potential temperature (isolines; units: K) at the eye center of Typhoon Mujigae from 0000 UTC 2 October to 0000 UTC 5 October 2015.

Figure 6 shows the horizontal distributions of potential temperature, vertical motion, and storm-relative flow vectors at the 14 km height level at 10 min intervals during RI. It shows the cyclonic advection of warm anomalies (red shaded) associated with nearby CBs (white contours) within the RMW (black circle), and eventually these warm anomalies are trapped in the eye of TC. The warm anomalies are collocated well with the CBs near the RMW, implying that warm air with high potential temperature accelerates the upward motion because of large buoyancy. The compensating subsidence (black isolines) accompanying the CBs near the RMW could produce a warm anomaly of about 10 K, which is cyclonically advected downstream by weak rotational flows. The symmetric upper-level divergent outflows effectively protect the warm core from ventilation by environmental flows, which facilitate warm-core formation by securing the warm anomalies within the RMW and by being trapped in the central calm-flow region. As an obvious contrast, the warm core does not develop vigorously before RI despite the presence of CBs (Fig. 5 and Fig. 7). To give some explanation, the horizontal distributions of potential temperature and vertical motion are also analyzed before RI (Fig. 7). As an obvious contrast to the warming scenario related to the organized cyclonic flow (Fig. 6), eyewall convection is not organized well in the pre-RI period. Asymmetric outflow aloft——especially the western semicircle of strong divergence outflow——emanates most of the subsidence warming produced by the CBs away into the outer region of the RMW with less inertial stability.

Figure 6.  Horizontal distributions of potential temperature (units: K), storm-relative flow vectors (units: m s^-1), and vertical motion (white/black isolines represent upward/downward motion) at the 14 km height level. The RMW at an altitude of 1 km is plotted as a black circle. The times are from (a) 1700 UTC to (g) 1800 UTC 3 October, at 10 min intervals.

Figure 7.  As in Fig. 6, except for times from (a) 0300 UTC to (d) 0340 UTC 3 October, at 10 min intervals.

Combined with the CB onset time (i.e., at 0000 UTC 3 October), several features that are indicative of a CB episode, such as the formation of the upper-level warm core and the presence of a large warming gradient (in terms of both the horizontal gradient of temperature perturbation or vertical gradient of potential temperature), occur just after 0000 UTC 3 October. Afterwards, the warm core continues to increase during the whole RI process and develops synchronously with the MSLP, with the warmest core, lightest air mass column, lowest SLP, and strongest TC occurring at the same time. This warming trend stops at the end time of the CB episode, i.e., at 0300 UTC 4 October. After that time, the warm core becomes increasingly weaker and the reverse process begins. Surface pressure increases after a period of decline, and Typhoon Mujigae (2015) evolves from a strong typhoon to a tropical storm again.

It can be seen that the double warm core is closely related to updrafts and CBs, but the upper-level warm core is more correlated with CBs. The double warm core speeds up the TC intensification. The large temperature gradient, i.e., the sudden warming of the TC center, is the key to RI. During this cycle, CBs accelerate the RI by promoting warm-core formation.

For CB episodes, anomalous active convection accompanies local energy supply/consumption. Updrafts lead to kinetic and potential energy changes. The warm core also increases the local internal energy. These combined effects result in a local TE anomaly. From the local TE equation [Eq. (2)] and the CAD index [Eq. (3)], indicating the active degree of convection, the CAD can characterize the local TE evolution. Furthermore, the attribution of CAD is deduced from local TE source and sink terms. Thus, these aspects are explored during the CB episode of the rapidly intensified Typhoon Mujigae (2015).

3.4.1. Spatial distributions of local TE anomaly and CAD index

Figure 8 shows the vertical distributions of convective eyewalls (see the reflectivity, shaded), updrafts (gray contours), and CAD index (blue contours). From 1800 UTC 2 October to 0000 UTC 3 October (Figs. 8a and b), a strong reflectivity column (>50 dBZ) stretches from the center at z=6 km upwards to z=16 km. Updrafts evolve from shallow to deep convection within the strong reflectivity zone. The CAD index also suddenly develops, with denser CAD isolines confined within a higher and narrower column from z=4-17 km relative to the case of 6 h earlier shown in Fig. 8a, which is coincident with the CB episode. At 0600 UTC (Fig. 8c), RI begins. Closed eyewalls form, then shrinks toward the center of the TC, from r=50 km to r=40 km (Fig. 8d). Meanwhile, synchronous progress of CBs and CAD occurs following the merging and shrinkage of eyewalls. From pre-RI to RI, a sharp strengthened CAD signal is present at the start time of the CB episode (cf. Figs. 8a and b). Furthermore, CAD values, together with CBs, confined to eyewalls, change from asymmetric (Figs. 8a and b) to axis-symmetric (Figs. 8c and d). In general, the CAD index derived from the local TE anomaly signifies the spatial evolution of the updraft column, with the strong CAD signals corresponding to the CB episode.

The spatial features show that almost all intense CAD develops in the convective eyewall, in the same manner as CBs. The number of intense CAD values presents a sharp increase about 6 h before the onset of RI, providing some indicative signal for the RI of the typhoon. Accompanying the continuous growth of CAD, the development of CBs maintains, and the compensating subsidence accompanying CBs near the RMW could produce a warm anomaly. The symmetric upper-level divergent outflows effectively protect the warm core from ventilation by environmental flows, contributing to RI by a fall in hydrostatic pressure. Thus, the CAD is effective for estimating the occurrence of a CB episode and predicting the RI of a typhoon in the pre-RI period. Even during RI, CAD keeps contributing to RI by associated CBs (and the compensating subsidence warming of CBs). Therefore, this CAD index might be a valuable tool for identifying CB episodes and forecasting rapidly intensified typhoons.

Figure 8.  Vertical cross sections of radar reflectivity (shaded; units: dBZ), vertical motion (gray contours), and CAD index (blue contours) along zonal TC centers at (a) 1800 UTC 2 October, (b) 0000 UTC 3 October, (c) 0600 UTC 3 October, and (d) 1800 UTC 3 October 2015.

3.4.2. Attribution of CAD

To explain the attribution of CAD, the components contributing to CAD are investigated. That is, the sources and sinks responsible for energy variations in Eq. (2) are explored. Reverting back to Eq. (2), if the divergence flux term is moved to the right-hand side of the formula, a minus sign is attached and it becomes $-\nabla\cdot[v(E+p)]$. This new form is composed of four terms ($-v\cdot \nabla E, -v\cdot \nabla p , -E\nabla \cdot v , -p\nabla \cdot v$), denoting E and p advection effects for the former two terms and three-dimensional divergence of E and p for the latter two. It is the coaction among them that produces the local TE anomaly. Figure 9 shows the vertical distributions of vertical motion (shaded) and components contributing to CAD (isolines).

Figure 9.  Vertical distributions of vertical motion (shaded; units: m s^-1) and components contributing to CAD (isolines; units: kg m^-1 s^-2): $(a, e), -v\cdot \nabla E; (b, f)-v\cdot \nabla p; (c, g) -E\nabla \cdot v; (d, h) -p \nabla \cdot v$. The left-hand panels are at 0000 UTC and the right-hand panels are at 1800 UTC 3 October 2015.

Figure 9.  (Continued)

At 0000 UTC 3 October (Figs. 9a-d, 2c, and 8b), positive advection of E and p(contours in Figs. 9a and b, with solid lines representing positive advection) and divergence of E and p (contours in Figs. 9c and d; with dashed lines denoting divergence) overlay the strong updraft (shaded). Thus, advection and divergence effects have clear roles: one supplies the energy for the local convection growth and the other expends local energy. These effects offset each other as positive advection and divergence of E and p owing to their opposite signs, and the remaining parts (their net effect) account for the graphical distribution of the local TE anomaly (with its absolute value shown in Fig. 8b). At 1800 UTC 3 October (Figs. 9e-h, 2f, and 8d), the left convective eyewall develops. There are nearly axis-symmetric double signal-bands of advection and divergence components of CAD, maintaining active convection within the symmetric eyewall. Therefore, advection effects provide sources for local TE accumulation, which further supplies active convective growth.

3.4.3. Relationship between CAD evolution and CBs

To further explore the correlation between CAD and CBs, the temporal evolution of CAD, which characterizes the local TE anomaly, is shown in Fig. 10. At various height levels, the CAD values have similar evolution tendencies from the trend lines (bright yellow curves), with peaks during the RI period. Combined with the time series of vertical motion intensity (Fig. 1c), the variation of the CAD intensity is basically consistent with the variation of vertical velocity intensity from 0000 UTC 2 October to 0000 UTC 5 October, demonstrating their close correlation. For example, the CAD values are larger than 20 and 10 kg m^-1 s^-2 at the 11.60 km and 6.57 km levels (Fig. 10), accompanied by convection intensities up to 0.7 and 0.5 m s^-1 (Fig. 1c), respectively. Thus, the occurrence and development of CAD may be key to identifying a CB episode for a rapidly intensified typhoon.

3.4.4. CAD threshold for estimating CBs

From the relationship between CAD and convection development, a typical correlation between them is found from both the spatial distribution and temporal evolution perspective. A new question is now addressed: At what critical CAD value does a CB episode occur? To derive the threshold of CAD to estimate CB episodes, a scatter diagram is plotted in Fig. 11. The x and y axes denote convection intensity and CAD, respectively. The scatter diagram (Fig. 11) shows a typical linear dependence between the two variables, and fitting shows a linear relationship of y=13.435x-0.8337 and a coefficient of determination of R²=0.9317, indicating an acceptable goodness of fit. Based on this formula, for a convection intensity value (i.e., the control variable x) of 7.5 m s^-1, which is used as a threshold value to determine CBs, the CAD value (y) is 99.9. For convenience of application, an approximate value of 100 for CAD, i.e., intense CAD (ICAD), is obtained and utilized as the threshold to evaluate CB episodes for typhoons.

3.4.5. Consistent evolution of CB and ICAD

Based on the ICAD index for determining CB episodes, the ICAD number is analyzed and compared with the CB number (Fig. 12). Both have consistent evolution tendencies and three obvious peaks, with the largest CB and ICAD beginning at 0000 UTC 3 October, 6 h before RI. The sharp increase in ICAD might be indicative of the onset of the CB episode. In this sense, the ICAD threshold is effective for estimating the occurrence of CBs and predicting the RI of TCs, at least for Typhoon Mujigae (2015).

Figure 10.  Evolution of domain-averaged CAD(units:kg m^-1 s^-2) at various height levels. The bright yellow curves denote the trend lines.

Figure 11.  Scatter diagram of the relationship between CAD and convection intensity. The x and y axes denote convection intensity and CAD, respectively. The relationship formula is y=13.435x-0.8337, with a coefficient of determination of R²=0.9317.

Figure 12.  Time series of CB number and ICAD number.

3.4.6. Possible impact of different microphysical schemes

To enhance the robustness of the results in this section, the possible impacts of microphysical schemes in WRF is discussed (e.g., the WSM 6-class graupel scheme and Morrison 2-moment scheme). Distinct microphysical schemes produce different CB activities and CAD features. However, from the vertical cross sections of radar reflectivity, vertical motion, and CAD index (not shown but similar to Fig. 6), both CBs and CAD are collocated within the eyewall region, and both are matched well. For both the WSM 6-class graupel scheme and Morrison 2-moment scheme, the CBs and CAD values have consistent evolution. Furthermore, their CAD thresholds are 99.4862 and 99.1459, respectively. Relative to the CAD value (100) derived from above analyses, the error is kept within 1% range.

In addition, another rapidly intensified typhoon, Typhoon Hato, is simulated. The CAD threshold value for Hato is 99.0058. Relative to the CAD value (100) derived in the Typhoon Mujigae (2015), the error is also kept within 1%. With the CAD threshold, the derived ICAD number also has consistent evolution with CBs in another TC case, i.e., Hato. However, owing to length restrictions, the figures are not shown in the present paper.

Based on a 72 h simulation of the rapidly intensified Typhoon Mujigae (2015), the CB characteristics for the pre-RI, RI, and post-RI stages are investigated. The role of CBs in the RI of the TC is analyzed in terms of both thermodynamic and dynamic variables. From the viewpoint of the local TE anomaly, the CAD index is used to estimate the CAD. By data fitting the correlation between CAD intensity and convection intensity, an ICAD threshold to determine CB episodes is derived. The results can be summarized as follows:

(2) The development of Typhoon Mujigae (2015) can be classified into three stages: pre-RI, RI, and post-RI. By investigating the spatial pattern and temporal evolution of CB elements within the inner-core and outer regions of the typhoon eyewall, we show that CBs within a 100 km radius develop suddenly before the onset of RI and end abruptly at the start of the post-RI stage, providing us with some predictive clue for the RI of TCs.

(3) The role of CBs in the RI of Typhoon Mujigae (2015) is explored. The combination of the lower-level inflow and upper-level outflow pushes a relay-race-like transmission of convective activity, favorable for the development of deep convection. Thermodynamically, there is a decline in hydrostatic pressure, which results from a double warm-core structure (induced by compensating subsidence warming associated with CBs near the RMW of stratospheric and tropospheric origin), and leads to the RI process.

(3) For the CB episodes, anomalous active convection accompanies local energy supply/consumption. By utilizing the CAD index, which indicates the active degree of convection derived from the local energy anomaly, the spatial evolution of updraft columns can be determined, with strong CAD signals corresponding to CBs. The CAD attribution analyses show that advection effects provide sources for local TE accumulation, which further supplies active convection growth. After the relationship formula between CBs and CAD is deduced by data fitting, a threshold to evaluate CBs for typhoons, ICAD (with a value of 100), is derived for convenient application. It is verified that the ICAD threshold is effective for estimating the occurrence of CBs and predicting the RI of typhoons.