Microphysical Properties of Rainwater in Typhoon Usagi (2013): A Numerical Modeling Study

Cloud microphysical processes and the associated latent heat release are vital in determining the evolution of a tropical cyclone (TC) (Gamache et al., 1993; Zhang et al., 2002; Houze, 2010). The spatial distribution and quantity of hydrometeors can considerably affect the location and intensity of TC precipitation and even extreme rainfall in landfalling TCs (Wang et al., 2016; Xu et al., 2017). However, the devastating wind conditions often hinder observation of either the basic meteorological fields or cloud microphysical variables in the inner-core region, particularly when a TC is over the open ocean. As a result, studies on TC-related cloud microphysics are still limited and depend more on numerical modeling results.

In recent decades, instruments onboard advanced aircraft have become capable of measuring vertical velocity, directly capturing either solid/liquid particle images or cloud/rain characteristics at various developing stages of a TC. Using advanced airborne Doppler radar systems, the reflectivity in the eyewall and outer stratiform region have been detected along flight tracks during several TCs (Black et al., 1996; Rogers et al., 2007; Reinhart et al., 2014). (Rogers et al., 2007) quantitatively analyzed the distributions of vertical motion and radar echoes in the vertical direction in Hurricane Bonnie (1998) and Hurricane Floyd (1999) when they reached their mature stages. The authors found distinct differences in the distribution pattern between the eyewall and outer rainband region. They demonstrated that the mean reflectivity within the eyewall was around 35 dBZ in the lower troposphere and turned to be over 40 dBZ near the melting level. The reflectivity dropped remarkably above the freezing level with the existence of a secondary peak. This enhanced echo was proposed to be attributable to the mixture of frozen water and graupel that is lofted above the melting layer by vigorous updrafts. Such a mixed-phase region within the eyewall has also been captured by cloud droplet probes and other observations onboard aircraft (Heymsfield et al., 2006; Reinhart et al., 2014). A large concentration of frozen, homogeneously nucleated ice particles was measured at the flight level with temperatures from -32^°C to -45^°C in the inner core of Hurricane Karl (2010) during its rapid intensification (Reinhart et al., 2014), which partially explained the lower-than-expected reflectivity observed at the upper levels during its intensification. Throughout most of the troposphere, reflectivity values in the outer region were often lower than those in the eyewall, except for higher values representing the bright band of stratiform clouds in the outer region. The intermittent echo perturbations in both the eyewall and outer rainband region imply the existence of embedded convective cells (Rogers et al., 2007).

In addition, Tropical Rainfall Measuring Mission (TRMM) satellite data are widely used in obtaining long-term monitoring of TCs over tropical oceans. The active Precipitation Radar (PR) and passive Microwave Imager (TMI) onboard TRMM offer high spatiotemporal resolution products, including three-dimensional radar echoes, hydrometeor vertical distribution retrievals, and surface rainfall rate. Likewise, the composite radar reflectivity based on TRMM PR data generated in the Atlantic basin from 1998 to 2007 showed similar aforementioned features in other ocean TC basins (Hence2011,Hence2012). Based on 11 years of TRMM data, (Jiang and Ramirez, 2013) compared the radar reflectivity profile and surface precipitation in the inner-core region of TCs under four separated intensity change categories, i.e., rapidly intensifying, slowly intensifying, neutral, and weakening. They pointed out that the distribution of radar echoes was mostly concentrated around a median profile during the onset of rapid intensification, as compared to a wider pattern in other intensity change categories. They also proposed a minimum criterion involving raining area, total rain content, and the associated maximum near-surface radar echoes in the inner-core region that had to be reached before a TC underwent vigorous development. These observational studies have offered an opportunity to understand either the fundamental internal characteristics of cloud and precipitation structure in the eyewall and rainband region from a case-study perspective (Black and Hallett, 1986; Black et al., 1996; Rogers et al., 2007; Reinhart et al., 2014), or the statistical relationship between microphysics and TC-induced precipitation from a climatic perspective (Hence and Houze, 2011; Jiang et al., 2013; Jiang and Ramirez, 2013; Tao and Jiang, 2013; Bowman and Fowler, 2015; Yu et al., 2015, Yu et al., 2017; Leppert II and Cecil, 2016). However, because of flight and scanning restrictions (e.g., the scanning width of the PR onboard TRMM is less than 300 km; and observations are available only twice per day), the temporal evolution of cloud microphysical processes is rarely observed during a TC's lifetime.

Regional numerical models have advantages in exploring evolution processes for a specific TC once the simulated features reasonably match the observations. In fact, many sensitivity and comparison experiments have been carried out to examine the effects of a specific microphysical process on the formation, intensification and structure change of TCs (e.g., Wang, 2002, Wang, 2009; Zhu and Zhang, 2006; Li et al., 2015; Miller et al., 2015), and to evaluate the applicability of the current microphysical schemes in different models for TC simulations/forecasts (McFarquhar et al., 2006; Fovell and Su, 2007; Rogers et al., 2007; Pattnaik et al., 2011; Tao et al., 2011; Jin et al., 2014; Sun et al., 2015).

The warm-rain processes are the dominant microphysical processes in the generation of rainwater in tropical convective systems where the observed raindrops form by vapor condensation, grow sufficiently by coalescence, and produce rainwater without a chance to glaciate (Heymsfield et al., 2006; Khain, 2009). A few numerical simulations combined with observations have also shown that warm-rain processes play a critical role in raindrop formation in TCs (Rosenfeld et al., 2012; Huang et al., 2014; Xu et al., 2017). (Huang et al., 2014) reported their simulation of Typhoon Morakot (2009) and concluded that liquid-phase microphysical processes, such as vapor condensation and raindrop evaporation, were responsible for the heavy rainfall in southwestern Taiwan. (Xu et al., 2017) showed that the high precipitation efficiency during the landfall of Typhoon Fitow (2013) was associated with moisture convergence, condensation, accretion of cloud water by rain, and raindrop loss/convergence, based on their particle trajectory analysis. In this study, we focus on a TC case that developed and maintained over the ocean with successive overpasses of TRMM. Specifically, we conducted a simulation to study the evolution of the cloud microphysical properties——especially the warm-rain processes.

The raindrop size distribution (RSD) is a key variable for the microphysical characteristics of cloud and precipitation, which largely affects quantitative precipitation estimation from remote sensing. The description of RSD shows significant variations under different types of rainfall conditions and areas, such as stratiform versus convective clouds or maritime versus continental systems. In fact, (Tokay et al., 2008) reported that the RSD in TCs was similar to that in tropical maritime convective precipitation (Bringi et al., 2003), based on the impact-type disdrometer observations in seven TCs that formed in the Atlantic basin. Higher concentrations of small and mid-size drops were observed without the presence of large drops in TCs, which was also detected in Hurricane Irene (2011) based on polarimetric radar observation (Ryzhkov et al., 2014). Also, there exists a difference in the RSD of Atlantic TCs and those in the central tropical Pacific basin, with slightly smaller-size raindrops having been observed in the latter basin (Tokay et al., 2008). On the contrary, (Chang et al., 2009) showed that lower-concentration but larger-size raindrops can be detected in landfalling typhoons near northern Taiwan, as compared to those in maritime convective systems, via ground-based disdrometer and C-band polarimetric radar data. This controversy may be related to the discrepancy in collecting raindrop samples, because only TCs at near-landfall stage were counted in (Chang et al., 2009); plus, a large amount of variation in RSD might be closely related to the effect of complex terrain. However, owing to a lack of successive observations, no attention has been paid to the RSD change in the inner-core and outer region during all stages of a TC.

In addition, water vapor is the basic source for hydrometeor particles, and plays a key role in warm-rain formation. Some water vapor budget analyses have been carried out to distinguish the effects of horizontal moisture transport, surface moisture flux, and local cloud condensation and evaporation on the total moisture balance and precipitation (Marks, 1985; Gamache et al., 1993; Braun, 2006; Yang et al., 2011; Fritz and Wang, 2014). (Marks, 1985) estimated that the moisture convergence into the eyewall region of Hurricane Allen (1980) was twofold larger than the amount of volumetric rainfall it produced. (Gamache et al., 1993) pointed out that ∼40% of the water vapor converging into the inner-core region (radius from the vortex center R<37.5 km) of Hurricane Nobert (1984) was actually contributed by sea surface evaporation, based on aircraft Doppler radar observations. Owing to the limitations of radar-retrieved wind fields and the related assumptions, their estimates were noticeably larger than those of many other studies (Braun, 2006; Yang et al., 2011). Based on a numerical simulation, (Yang et al., 2011) investigated the contribution of horizontal vapor convergence to the net condensation before and after the landfall of Typhoon Nari (2001), and demonstrated the critical effect of Taiwan's steep terrain. Although numerous studies have been carried out, research on the relationship between water vapor supply and the evolution properties of raindrop microphysics——especially during the various stages of a TC——is still rare.

In this study, Typhoon Usagi (2013), which formed in the Northwest Pacific on 16 September 2013 and made landfall in the Pearl River Delta of China, was simulated. It was captured four times over the ocean by the TRMM satellite, which gives a unique opportunity to investigate the microphysical structure and precipitation evolution during its intensification, mature, and weakening stages. The objective of this study is to investigate the successive evolution of cloud microphysical properties——especially those associated with rainwater processes——in Usagi (2013) during its different stages, based on TRMM satellite observations and high-resolution cloud-resolving simulations. In particular, to determine the key microphysical processes affecting the raindrop concentration in the inner-core and outer region during its different stages, we analyzed the evolution of RSD and source and sink terms of raindrop number concentration. By calculating the water vapor budget, we further indicate the corresponding dominant contributions of physical processes to the precipitation evolution. These results can advance our understanding of rainwater processes in a TC——especially the quantitative evolution of raindrops——and shed light on the physical relationships and interaction among raindrops, surface rainfall, and water vapor within a TC.

The rest of the paper is organized as follows: In section 2, we describe the observational data, the Morrison double-moment microphysical scheme, and the numerical experimental design. Verifications of the simulated track, intensity, and microphysics fields, such as brightness temperature and radar reflectivity, are presented in section 3. The RSD and associated rainwater features, including the source and sink terms of the raindrop concentration and water vapor budget, are discussed in section 4. Conclusions are given in section 5.

The observed typhoon track and intensity data were obtained from the China Meteorological Administration (CMA) TC best-track dataset over the western North Pacific (http://tcdata.typhoon.gov.cn/zjljsjj_zlhq.html). Two kinds of remote sensing data from the TRMM satellite were used to evaluate the model simulation. The polarization difference of brightness temperatures (PDT; Petty, 1994) at 19.35 GHz from TMI can reflect the horizontal distribution of liquid water content. The radar reflectivity at 13.8 GHz from PR (Kummerow et al., 2000) can provide a three-dimensional reflectivity structure and partly represent the integral behavior of hydrometeor size and number.

The Weather Research and Forecasting (WRF) model, version 3.8.1 (Skamarock et al., 2008), was used for the simulation. Three domains with respective horizontal resolutions of 18, 6 and 2 km were configured in the simulation, each with 50 vertical levels from the surface to 10 hPa. The intermediate and innermost grids (D02 and D03) were automatic vortex-following moving nests (Fig. 1). Two-way feedbacks were allowed between the neighboring domains. Grid nudging, including wind and temperature above the lowest five model levels, was applied in the outermost domain (D01) to ensure the large-scale features were close to the driving fields. The experiment was initialized at 0000 UTC 18 September 2013 and integrated for 108 hours. The initial and boundary conditions were obtained from the 1^°× 1^° NCEP-FNL analysis. The physical schemes used in the simulation included the Yonsei University planetary boundary layer parameterization (Hong et al., 2006), the Dudhia shortwave radiation scheme (Dudhia, 1989), the rapid radiative transfer model longwave radiation scheme (Mlawer et al., 1997), the Morrison double-moment cloud microphysical scheme (Morrison and Gettelman, 2008; Morrison et al., 2009), and the Kain-Fritsch cumulus parameterization (Kain, 2004) for the outermost domain (D01) only.

Figure 1.  The triple-nested WRF model domains with horizontal resolutions of 18, 6 and 2 km for D01, D02 and D03, respectively. D02 and D03 are automatic vortex-following moving nest grids.

In the Morrison microphysical scheme, the hydrometeor spectra, except cloud droplets, are prescribed by the inverse exponential distribution. Both the mixing ratio and number concentration of rain, ice, snow and graupel are prognostic variables that partially determine the formation and interaction of these hydrometeors, which in turn alter cloud dynamics and thermodynamics. The main source and sink terms for the number concentration of raindrops in the Morrison scheme are snow and graupel melting (NSMLTR, NGMLTR), autoconversion of cloud water to rain (NPRC1), self-collection of rain (NRAGG<0), breakup of rain (NRAGG>0), and loss of rain due to evaporation (NSUBR) (Morrison et al., 2009). The microphysical variables were all obtained from the innermost domain (D03) and saved at 1-h intervals for analysis.

The simulated track and intensity of Usagi (2013) and the evolution of its basic structure and microphysical fields, including the distributions of liquid water content and vertical radar reflectivity profiles, were compared to best-track data and TRMM satellite observations. Typhoon Usagi (2013) reached its maximum intensity of 915 hPa with a maximum wind speed of 60 m s^-1 and showed three intensity change episodes, defined as rapid intensification (before 1200 UTC 19 September), mature (from 1200 UTC 19 to 0600 UTC 21 September), and slow weakening (after 0600 UTC 21 September) stages over the ocean according to the 24-h intensity change.

Figure 2 compares the simulated track and intensity in Domain 03 with the CMA best-track data. In general, the model captured the main features of TC movement and intensity change, especially the intensification during the first 36 h (∼25 m s^-1 d^-1 in observation and ∼20 m s^-1 d^-1 in the simulation) and the mature stage in the following 30 h (<5 m s^-1 d^-1 in both observation and the simulation). When Usagi (2013) passed through the Bashi Channel (from 1800 UTC 20 to 0600 UTC 21 September), a visible increase in maximum wind speed occurred in the model, which is taken as the mature stage in our discussion (this re-intensification was also shown in the Joint Typhoon Warning Center dataset). After the system entered the South China Sea (from 0600 UTC 21 to 1200 UTC 22 September) and finally made landfall on the coast of South China, it decayed slowly. In addition, the landfall location differed by about 100 km between the simulation and observation after long-term simulation, and the model TC moved a little bit faster than that in the best-track data, partly due to the stronger storm in the simulation.

Figure 2.  (a) Comparison of the best track (every 6 h; black) and the simulated track (every 1 h; red) of Typhoon Usagi (2013), with blue triangles denoting the overpass locations of the TRMM satellite. (b) Time series of minimum sea level pressure (units: hPa, solid lines) and surface maximum wind speed (units: m s^-1, dash lines) of the best track (every 6 h; black) and the simulated storm (every 1 h; red). The blue curve in (b) represents the time series of the simulated radius of maximum wind (RMW; units: km) and dark-blue vertical solid lines show the TRMM overpass times. According to the 24-h intensity change, three stages are marked as the intensification, mature and weakening stages.

In previous studies, simulation results have been commonly compared with retrieved satellite products, but the hydrometeor particle size distributions (PSDs) from retrieval algorithms are usually inconsistent with those in microphysical schemes. In our study, the Satellite Data Simulator Unit (SDSU; Masunaga et al., 2010) was used to illustrate how the simulated TC would be observed if the TRMM satellite flew over the site. The surface and atmospheric parameters used in the SDSU were the same as those from our model outputs, and the assumed PSDs in the SDSU were in agreement with those in the Morrison scheme. Figure 3 shows the observed polarization difference of brightness temperatures at four scanning times (two of which were in the intensification stage, while the other two were in the mature stage). The PDTs imply thermal emission by integrated liquid water mostly below the melting layer. The lower the PDT is, the more liquid water content (both cloud water and rain) the system contains, according to the physical characteristics of low-frequency microwave imager measurements (Wiedner et al., 2004). During the intensification stage, the outer spiral rainband rapidly developed with much more cloud cover in the low PDT (e.g., <5 K), while the eyewall gradually diminished (Figs. 3a and b, 3e and f). In the late mature stage, Usagi (2013) exhibited a remarkable axisymmetric pattern when it passed through the Bashi Channel, with the outer convective rainband completely merged into the original eyewall (Figs. 3d and h). Note that the simulated eye and eyewall were somewhat larger than observed. Additional tests indicated that this was not due to the cloud microphysical scheme used, and might have been caused by other model physics, such as the horizontal diffusion and PBL scheme (Otkin et al., 2017). The simulation generally reproduced the basic horizontal structure of the observed storm.

The radar echo detected by TRMM/PR is a total equivalent reflectivity factor that represents the joint characteristics of hydrometeor effective size and amount. Because of the narrow swath width of PR, only three reference observations are available (one of which detected only part of the outer rainband). The individual contoured frequency by altitude diagram (CFAD; Yuter and Houze, 1995) is plotted with a 2.5-dBZ frequency interval and 250-m vertical spacing to describe the characteristics of the vertical distribution of radar echoes. To reduce the time mismatch with the observations, the model outputs at ±1 h were used (Fig. 4). Overall, the slope of reflectivity changed drastically like a nose-tailed profile at all stages. An obvious bright band existed at the height of 5.5 km in the observation, while it was ∼ 0.5 km higher in the simulation, indicating the coexistence of convective and stratiform clouds and stronger warm-rain processes in the simulation. In general, the model successfully captured the main distribution pattern of radar echoes in the warm-rain part, but overestimated ice-phase hydrometeors above the 0^°C level. During the intensification stage, the occurrence of infrequent echoes (e.g., <2.0%) extended to high levels or exhibited large values of >40 dBZ, indicating that more large-size solid and liquid hydrometeors may have grown in the embedded convective cells in Usagi (2013) at this stage. Meanwhile, the highest occurrence probability increased from 25-30 to 30-35 dBZ, which generally resulted from either the formation of large-size precipitation particles or the increase in the number concentration of small-size particles during storm intensification (Figs. 4a and b, 4d and e). Note that the occurrence frequency of radar reflectivity below 15 dBZ in the simulation was a little higher than that in the observation, which was likely due to more small-size raindrops existing in the simulation. By the end of the mature stage, more observed radar echoes between 30 and 35 dBZ were apparent below the melting level all the way to the surface (Fig. 4c). This may imply the equilibrium size distribution of raindrops resulting from collision-coalescence and breakup processes vertically and more homogeneous sizes of raindrops at a given height horizontally, corresponding to the uniform horizontal distribution of the PDT shown in Fig. 3d. However, a forward tilt could be seen in the simulation, owing to the occurrence of more ice particles aloft as well as the slight decrease in rainwater content toward the surface, jointly caused by the accretion of cloud water by rain and evaporation of rain (Wang et al., 2013). Moreover, the uncertainty of radar echoes, especially in the lower troposphere because of the inevitable attenuation, should also be another effect.

Figure 3.  Horizontal distributions of polarization difference of brightness temperature (units: K) at (a, e) 0100 UTC 19 September, (b, f) 0900 UTC 19 September, (c, g) 0800 UTC 20 September, and (d, h) 0200 UTC 21 September 2013, from (top) TRMM/TMI observations and (bottom) model simulation. The black lines in the top panels indicate the scanning areas of TRMM/PR. The black circles in the simulation represent two-times the radius of maximum wind and are used to separate the inner-core region and the outer region.

Figure 4.  CFAD of radar reflectivity at (a, d) 0100 UTC 19 September, (b, e) 0900 UTC 19 September, and (c, f) 0200 UTC 21 September 2013, from (top) TRMM/PR observations and (bottom) model simulation. The model outputs at 1 h are used to reduce the time mismatch with the observations. The shading represents the frequency percentage of radar echoes at each height.

Although some discrepancies existed in the simulation and there was a lack of sufficient cloud microphysical observations for a more detailed verification of the simulation, we can state with reasonable confidence that the model captured the overall structure and intensity changes, as well as the cloud structures, as discussed in the above section. Therefore, the model outputs provided useful high temporal and spatial resolution data to investigate the evolution of microphysical processes within the TC system. Since the variability of microphysical processes may differ in different parts of a TC, we analyzed the data from the inner-core and outer region separately, which correspond to the areas within and outside two times the radius of maximum wind (the black circles in Figs. 3e-h). Note that the outer region ends at the boundary of the innermost domain, which is large enough to cover the outer spiral rainband of this large typhoon case. The evolutions of liquid and ice water paths were firstly compared (Fig. 5). In the inner-core region, the liquid water processes started a bit earlier than the ice processes, but the quantity of ice water soon reached about twice as large as the liquid water, and this ratio remained constant throughout the intensification stage. However, from the early mature stage and thereafter, the liquid water was quantitatively comparable with the ice water, confirming the importance of warm-rain processes in the TC. Moreover, in the outer region, the liquid and solid hydrometeors formed simultaneously and the former was relatively weak in the entire stage. The evolution of warm-rain processes, especially the change in raindrops and the associated source and sink terms of rain number concentration are thus discussed in the following sections.

Figure 5.  Time series of liquid water path and ice water path (units: g m^-2) for (a) the inner-core region and (b) the outer region of the simulated Usagi (2013).

Figure 6 shows the simulated RSD below 5.5 km with a 24-h interval, using the prescribed RSD in the Morrison microphysical scheme. In general, the raindrop number concentrations (Nr) of various diameters in the inner-core region were obviously higher than those in the outer region, and the maximum raindrop diameter (Dr) was also greater in the inner-core region owing to stronger convective activities. Consistent with the fact that the CFAD of radar reflectivity showed an increase in the occurrence probability of larger reflectivity below the melting layer, a synchronous increase in the number concentration at all raindrop sizes can be seen in the inner-core region during the intensification stage (Fig. 6a), although small-size raindrops formed more rapidly than large-size ones in the outer region (Fig. 6b). The oscillation of RSD in the inner-core region as the large-size (small-size) raindrops decreased (increased) with the weakened updrafts (Figs. 7a and b) in the early mature stage, while the opposite change appeared after the re-intensification of the TC in the late mature stage, indicating that the intensity of upward motion directly affected the evolution of the raindrop spectrum. Yet, the concentrations of large-size raindrops remained nearly unchanged in the outer region through the mature stage. During the decaying stage, plenty of smaller raindrops occurred, and the larger ones further decreased in both regions, especially when Usagi (2013) approached the coast of South China. This will be further discussed in the next subsection.

Figure 6.  Volumetrically averaged (below 5.5 km height) RSD with 24-h intervals for (a) the inner-core region and (b) the outer region of the simulated Usagi (2013).

Figure 7.  Time-height cross sections of (a, b) vertical motion (units: m s^-1) and (c, d) condensation rate (units: g kg^-1 s^-1) in (left) the inner-core and (right) the outer region of the simulated Usagi (2013) from 1200 UTC 18 September to 1200 UTC 22 September 2013.

Since the variance of raindrop size was mainly controlled by rainwater content and number concentration, and the precipitation in the inner-core and outer regions was highly consistent with the rainwater content (Fig. 8g), the evolutions of these two variables and the source and sink terms of raindrop number concentration in cloud areas (hydrometeor mixing ratio >1.0^-5 kg kg^-1) were therefore analyzed. Clearly, the mixing ratio of rainwater in the inner core had a more uniform vertical distribution, while the number of raindrops was concentrated near the melting level (∼5.25 km) and the lower troposphere (∼ 1.25 km). The mixing ratio (number concentration) in the inner core was three times (twice) as large as that in the outer region, which resulted in relatively large raindrops (∼ 2 mm) at a height of about 3 km in the eyewall (Figs. 8e and f).

Figure 8.  Time-height cross sections of (a, b) mixing ratio (Qr, units: g kg^-1), (c, d) number concentration (Nr, units: kg^-1), and (e, f) mass-weighted diameter (Dm, units: mm) of raindrops, in (left) the inner-core and (right) the outer region of the simulated Usagi (2013). Time series of precipitation (units: mm h^-1) and volumetrically averaged rainwater content (units: g m^-3) from 1200 UTC 18 September to 1200 UTC 22 September 2013 are shown in (g).

The evolution of these variables illustrates how rainwater developed and exchanged between the inner-core and outer regions. The formation of raindrops near the melting level was attributed to the ice process through the melting of solid hydrometeors and warm-rain processes associated with cloud water/rain coalescence and autoconversion. It is noteworthy that the rainwater in the outer region initially formed at near the melting layer and gradually increased downward during the intensification stage (Fig. 8b), and the raindrop number in the outer region fell somewhat behind that in the inner-core region. That is, the rainwater in the outer region might be seeded by the melting of smaller ice particles that were advected radially outward from the eyewall and contributed to the generation of the outer spiral rainband. This feature was observed and documented in earlier studies as well (Black and Hallett, 1986; Marks et al., 1987). In the early mature stage, the enhancement of rainwater in the outer region was accompanied by a decrease in rainwater in the inner core, which was induced by the substantive growth of outer convective rainbands. Note that when Usagi (2013) became relatively more symmetric in the late mature stage, an evident increase in rainwater occurred in the inner-core region, which was related to the significantly enhanced upward motion and condensation (including deposition) rate of cloud droplets (ice particles) shown in Fig. 7. When the TC approached the south coast of mainland China, large amounts of raindrops formed again. The increase in raindrop number in the outer region was consistent with the enhanced upward motion likely induced by the coastal terrain. However, the updrafts and the water vapor condensation in the inner-core region continually decreased during this stage (Figs. 7a and c). The significantly increased raindrops were likely due to the enhanced horizontal convergence of cloud water (e.g., the averaged horizontal convergence beneath 850 hPa increased from -8.8× 10^-7 g m^-2 s^-1 at 1800 UTC 21 September to -9.6× 10^-7 g m^-2 s^-1 at 1200 UTC 22 September) and then the autoconversion of cloud droplets to raindrops at the low levels.

As mentioned in section 3, the simulated maximum wind speed also showed a re-intensification starting from 1800 UTC 20 September. The sudden increases in both horizontal wind and inner-core updrafts were probably attributable to the interaction between dynamic and thermodynamic processes (Houze, 2010). So, the evolutions of basic thermodynamic fields, such as convective available potential energy (CAPE) and low-level anomalous equivalent potential temperature θ _e (by subtracting the mean values at individual heights), were examined. High CAPE of about 1600-2400 J kg^-1 in the outer region (Fig. 9a) provided large convective instability to air parcels during the intensification of the storm and promoted the development of convective outer rainbands as well. The radial inflow dominated the low levels in this period, which transported lots of water vapor and energy into the inner-core region. While obvious change occurred when the outer rainband reached to a mature stage, the accompanying downdrafts reduced the inward transport of water vapor and exerted a successively negative thermodynamic effect on eyewall buoyancy, and inhibited further intensification of the TC (figure not shown) (Powell, 1990; Wang, 2009). In the observed TMI image (Figs. 3a and b), we can clearly see that when the vigorous outer rainband formed in the southwestern quadrant of Usagi (2013), the original eyewall with the enclosed annulus of heavy water content gradually vanished. During 1200 UTC 20 to 1200 UTC 21 September, the occurrence of higher θ _e with larger CAPE in the lowest 1.0 km indicated that moisture and heat flux were again transported inward (Figs. 9a and b) as the outer rainbands merged into the original eyewall, which re-intensified the TC.

Figure 9.  Radius-time Hovmöller diagram of (a) CAPE (units: J kg^-1) and (b) layer-averaged anomaly of θ _e (units: K) averaged between 0 and 1.0 km in the simulated Usagi (2013) from 1200 UTC 18 September to 1200 UTC 22 September 2013. The black lines represent two-times the radius of maximum wind.

The number concentration directly affects the size distribution of hydrometeors and also determines the microphysical processes in specific particle growth modes. What the dominant microphysical processes are at different stages of a TC and how specific hydrometeors interact with others is quite important but seldom analyzed in the literature. To address these issues, we plotted time-height cross sections of source and sink terms of raindrop number concentration (Fig. 10), such as melting of snow and graupel, autoconversion, evaporation, self-collection, and breakup processes. Similar to the vertical distribution of the number concentration, there were two concentrated layers for the microphysical processes at different heights. Near the melting level, raindrops grew vigorously in a mixed-phase state by melting of snow/graupel particles and autoconversion of cloud droplets to rain (Figs. 10a-d). The strength of ice microphysics in the formation of raindrops was a bit greater than the warm-rain processes at high levels. The newly generated small raindrops grew immediately by self-collection at the levels below the maximum autoconversion (Figs. 10e and f). When the diameter of raindrops exceeded a certain criterion (Morrison et al., 2012), breakup occurred (Figs. 10g and h) and evaporation efficiency sequentially enhanced in some unsaturated areas (Figs. 10i and j). The pure warm-rain processes are the dominant growth mechanisms in the lower troposphere below 3 km. Different from what happened near the melting level, the raindrops that formed by autoconversion of cloud droplets grew further by self-collection at about the same maximum level near the height of 1.25 km, while the breakup process that contributes to the balance with self-collection occurred just above the surface layer. The largest mass-weighted raindrop diameter exceeding 2.2 mm near the surface (in Figs. 8e and f) corresponded well with the maximum breakup rate there. The breakup rate of large raindrops had the same order of magnitude as the autoconversion and self-collection, especially in the inner-core region. These directly affect the rainfall intensity in a TC but remain a major challenge for models to reproduce these parameterized microphysical processes accurately.

Figure 10.  Time-height cross sections of source and sink terms (units: kg^-1 s^-1) of raindrop number concentration, including: (a, b) melting of snow and graupel to raindrops; (c, d) auto-conversion of cloud droplets to raindrops; (e, f) self-collection of raindrops; (g, h) breakup of raindrops; and (i, j) reduction of number concentration due to evaporation, in (left) the inner-core region and (right) the outer region of the simulated Usagi (2013) during 1200 UTC 18 September to 1200 UTC 22 September 2013.

Some differences existed in the source and sink terms of raindrop number concentration between the inner-core region and outer rainbands. This partly revealed the different evolution in the dynamical field during the different stages of the TC. The autoconversion of cloud droplets to raindrops and self-collection/breakup rates of raindrops in the inner-core region were evidently (2-4 times) greater than those in the outer region. The concentrated layers of microphysical processes were a little bit higher in the eyewall because of relatively strong updrafts (e.g., the layer of maximum breakup was at 4.5 km in the inner core but was at the height of 3.5 km in the outer region). Raindrops in the lower layer in the inner-core region grew by significant self-collection, and then underwent breakup until finally falling out to form precipitation along with evaporation through the unsaturated layer below the cloud. On the contrary, raindrops outside the eyewall were mainly autoconverted from cloud droplets and self-collection without evident breakup near the surface, but evaporation was comparable with that in the inner-core region owing to the fact that small raindrops evaporated first.

We further performed water vapor budgets for the inner-core and the outer regions because water vapor connects the synoptic-scale motion and local cloud microphysics, which is critical to the evolution of a storm and highly correlated to rainfall intensity (e.g., Xu et al., 2017). Following (Fritz and Wang, 2014), the governing equation for water vapor q _v in cylindrical coordinates in a TC-following framework can be written as: \begin{eqnarray} \dfrac{\partial q_{\rm v}}{\partial t}&=&-\dfrac{1}{r}\dfrac{\partial(rq_{\rm v}u)}{\partial r}-\dfrac{1}{r}\dfrac{\partial(q_{\rm v}v)}{\partial\lambda} -\dfrac{\partial(q_{\rm v}w)}{\partial z}+\nonumber\\ &&q_{\rm v}\left(\dfrac{1}{r}\dfrac{\partial(ru)}{\partial r}+\dfrac{1}{r}\dfrac{\partial v}{\partial\lambda} +\dfrac{\partial w}{\partial z}\right)-C+E+B_{\rm v}+R_{\rm esd} , \ \ (1) \end{eqnarray} where q _v is the water vapor mixing ratio; r is the radius from the storm center; Λ is the azimuth; z is height; u, v and w are the tangential, radial and vertical winds, respectively. The term on the left-hand side of the equation represents water vapor tendency; the first three terms on the right-hand side are the horizontal and vertical flux convergence terms. A flux convergence (divergence) yields a positive (negative) change. The fourth term is related to the three-dimensional airflow divergence. C represents condensation and deposition per unit mass; E is evaporation and sublimation; B _v is the planetary boundary contribution to the water vapor tendency; and R _esd is the residual term due to numerical errors. Using shorthand notation, the terms in Eq. (1) are referred to as Tend, HFC, VFC, Div, Cond, Evap, PBL, and R _esd, respectively.

To compare each budget term during different stages, Fig. 11 shows the azimuthally and temporally averaged (for the three stages) HFC, VFC, Cond, and Evap. Owing to the incompressibility and continuity of the air mass, HFC is almost in an opposite phase to VFC in all stages (Figs. 11a-f), particularly in the lowest 2 km where most water vapor was present. Abundant warmer and moister air parcels from the surrounding ocean surface were transported inward to the eyewall region and entrained vertically into the mid-to-upper troposphere by strong eyewall updrafts (Zhang et al., 2002; Braun, 2006). It is noteworthy that the altitude where positive VFC (or negative HFC) started to appear was ∼ 0.5 km higher in the outer region than in the inner-core region, implying a deeper boundary layer in the outer region of the TC (Kepert, 2001; Kepert, 2001). Condensation and deposition were the major sinks of water vapor. They removed most of the water vapor transported by vertical motion in the eyewall and in the outer rainbands above the boundary layer (Figs. 11g-i). The HFC, VFC and Cond showed visible increases in the mature stage compared to the intensification stage, especially in the mid-troposphere in the outer region, due to active outer rainbands. Overall, the total vapor flux convergence (HFC plus VFC) and the net condensation (Cond plus Evap) were nearly balanced in the simulation.

Figure 11.  Azimuthally and temporally averaged water vapor budget terms (units: kg m^-3 h^-1) during the (left) intensification, (middle) mature, and (right) decaying stages: (a-c) horizontal moisture flux convergence (HFC); (d-f) vertical moisture flux convergence (VFC); (g-i) condensation and deposition (Cond); and (j-l) evaporation and sublimation (Evap); only shown up to 12 km height above the surface.

Figure 12 shows the temporal evolution of each vertically integrated area-averaged budget term (kg m^-2 h^-1) and the fractional contributions of the source and sink terms of water vapor. We can see that the budget terms in the inner-core region were almost twice as large as those in the outer region. The nearly synchronous HFC with Cond indicated that the water vapor supply was critical and closely related to the thermodynamic change of the TC. The nearly opposite trends of HFC (and Cond) between the inner-core and outer regions during the mature stage indicated the presence of strong interaction between the two regions. Nevertheless, during all stages, Cond was the most dominant sink term that consumed plenty of water vapor. Note that an evident difference in the contribution by local cloud evaporation in the separated regions existed. That is, Evap accounted for only half of HFC in the inner-core region, while it had similar magnitude to HFC in the outer region (Figs. 12a and b). This suggested that local cloud evaporation (including evaporation of cloud water and rain, and sublimation of cloud ice) and the inward moisture transport from the environment were equally important in the water vapor budget in the outer region. In addition, the contribution of VFC was not negligible in the inner-core region, because of the strong eyewall updrafts. The leading terms in the water vapor budget (e.g., Cond and HFC) significantly increased in the inner-core region, while they slowly increased in the outer region during the intensification stage of the storm, corresponding to the formation of outer spiral rainbands generated after the vortex underwent a short period of intensification. Both Cond and HFC in the outer region reached a peak in the mature stage, and then decreased without a maintenance period as they appeared in the inner-core region. These results confirmed that a competing relationship of the water vapor budget between the inner-core and the outer regions existed during the mature stage of the storm. A visible re-enhancement of moisture in the inner-core region occurring around 1800 UTC 20 September was attributed to the earlier inward transport of potential energy from the outer region. Cond in the outer region began to decrease after 1200 UTC 20 September along with the outer rainbands merging into the original eyewall, and the TC began to weaken as Cond decreased continuously in both the inner-core and outer regions.

Figure 12.  Time series of vertically integrated, area-averaged budget terms (units: kg m^-2 h^-1) of water vapor for the (a) inner-core region and (b) outer region from 1200 UTC 18 September to 1200 UTC 22 September 2013. The ratio of evaporation from the surface to horizontal flux convergence, as well as the ratios of horizontal flux convergence and vertical flux convergence to net condensation, are shown in (c).

Figure 12c shows the ratio of HFC (VFC) to the total net condensation and the ratio of PBL to HFC. The contribution of HFC in the inner-core region was a little bit smaller than that in the outer region, but both accounted for more than 75% of the regional net condensation. The evaporation from the ocean surface marked as PBL accounted for ∼ 10% of the horizontal vapor transport due to the nearly saturated condition in the inner-core boundary layer. However, in the outer region the PBL contribution was much larger and accounted for up to 40% of the horizontal vapor transport during the intensifying and decaying stages because the horizontal moisture convergence was relatively weak and the mean relative humidity near the surface layer in the outer area was generally less than 90%. The plentiful water vapor from sea surface evaporation in the outer region was somewhat different from that in previous studies (e.g., Yang et al., 2011). Note that the fractional contribution of VFC in the outer region became negative in the late mature stage owing to the formation of downdrafts and enhanced boundary-layer moisture transport. It is clear that the primary source term of water vapor in both the inner-core and outer region was horizontal moisture flux convergence, and the contribution of PBL was important especially in the outer region.

In this study, version 3.8.1 of the WRF model was configured for vortex-following, nested meshes, with the finest resolution of 2 km to simulate the track, intensity and evolution of the microphysics fields of Typhoon Usagi (2013) over the ocean from 0000 UTC 18 September to 1200 UTC 22 September 2013. Compared to the CMA best track and the TMI/PR observations from the TRMM satellite, which included two snapshots during the intensification stage and two in the mature stage, our simulation reproduced the track and intensity of the TC, as well as the main features of the observed PDT and radar reflectivity, reasonably well. Further analyses of rainwater and the related source and sink terms of raindrop number concentration, as well as the water vapor budget, revealed the microphysical properties in the inner-core and outer regions during different stages of Usagi (2013). The main results can be summarized as follows:

(1) The raindrop number concentrations and the maximum raindrop size in the inner-core region were obviously greater than those in the outer region owing to the stronger convection in the former region. During the intensification stage, the number concentration at all raindrop sizes increased synchronously in the inner-core region, while the small-size raindrops formed more rapidly, with the number of large-size ones nearly unchanged, in the outer area. An oscillation of RSD was apparent in the inner core during the mature stage, corresponding directly to the change in updrafts. The large-size raindrops decreased and small-size ones increased along with the decrease in upward motion in the early mature stage, while the opposite change took place in the late mature stage. During the decaying period, the number of smaller raindrops further increased and the larger ones dramatically decreased in both regions, especially when Usagi (2013) approached the coast of South China, due to the increased convergence of cloud water and autoconversion of cloud droplets to raindrops.

(2) An overall schematic illustration of the rainwater distribution and associated microphysical processes is given in Fig. 13. Two layers of maximum number concentrations of raindrops existed (at ∼ 5.25 km and ∼ 1.25 km height). The dominant source terms in the upper levels were the melting of ice particles and autoconversion of cloud droplets to raindrops. The contributions of snow and graupel melting were greater than those of the warm-rain processes in the formation of raindrops. After the raindrops grew vigorously by coalescence below the maximum autoconversion layer, breakup occurred when raindrops reached a threshold diameter, and evaporation simultaneously reduced the number concentration of raindrops under unsaturated areas. Warm-rain processes were repeated in the low levels but showed different contributions among each process compared with high levels. Raindrops were formed by autoconversion of cloud droplets and grew by self-collection nearly in the same layer, and the breakup of large raindrops was the most important process near the surface. However, raindrops below the height of 1 km outside the eyewall showed no evident breakup, while evaporation was comparable to that in the inner-core region owing to the unsaturated environment and smaller raindrops there. In addition, the ice-related microphysics in the upper levels was stronger than the pure warm-rain processes in the low levels during the intensification stage of the storm. The rainwater content in the outer region gradually increased from the melting level downward to the surface, suggesting that small ice particles advected radially outward might have contributed considerably to the development of outer convective rainbands.

Figure 13.  Schematic illustration of the number concentration and mass-weighted diameter of raindrops, and the preferred layers for melting of snow and graupel to raindrops (NSMLTR, NGMLTR), autoconversion of cloud droplets to raindrops (NPRC), self-collection/breakup of raindrops [NRAGG(SC)/NRAGG(BU)], and reduction of concentration due to evaporation (NSUBR). The blue area represents the centered layer of the cloud droplet mixing ratio, the height of which is always higher than that of the raindrop number concentration (shaded with green slashes). The balance among the self-collection, breakup and evaporation processes leads to the formation of the largest raindrops at 2.0-3.5 km height and in the near-surface layer (shaded with gray vertical lines).

(3) The primary terms in the water vapor budget were the horizontal moisture transport and condensation in both the inner-core and outer region. The vertical flux convergence also contributed noticeably in the inner-core region, indicating the importance of convective updrafts in the eyewall during the intensification stage. The contribution of evaporation from the ocean surface (PBL) was relatively small (∼ 10%) in the inner-core region, but accounted for up to 40% of horizontal moisture flux convergence in the outer region during the intensification and decaying stages owing to the drier conditions in the near-surface layer in the outer region. This indicated that the role played by the PBL process varied with region and evolution stage of the storm. In the meantime, both HFC and Evap had similar magnitudes in the outer region. This meant that water vapor could have derived equally from local cloud evaporation in the storm and inward transport from the environment. However, Evap accounted for only half of the HFC in the inner-core region owing to the almost saturated low-level environment. Furthermore, the synchronous evolution of Cond and HFC implied that the water-vapor change was closely related to the thermodynamic change in the storm. Both Cond and HFC increased significantly in the inner-core region, while they increased slowly in the outer region, during the intensification stage of the storm, indicating that local cloud microphysical processes initiated earlier in the inner-core region than in the outer region. A competing relationship of the water vapor budget between the inner-core and outer region existed, especially during the late intensification and mature stages. The continuous decrease in condensation and deposition in these two regions might have foreshadowed the beginning of the storm's weakening in Usagi's case.

Note that the results of this study were obtained based on a single numerical simulation of Typhoon Usagi (2013), which showed an outer spiral rainband that merged into the eyewall. The finding of competing changes in the inner-core and outer region is an interesting topic worthy of further investigation. Features related to the warm-rain processes need to be studied with more TC cases and the use of other microphysical schemes. The results from this study strongly suggest that more attention needs to be given to the parameterizations of breakup and evaporation in numerical models, since they are the key microphysical processes that directly affect the low-level microphysics and surface precipitation of TCs.