Control simulation
To validate the newly developed lightning model, we first checked the temporal evolution of maximum wind velocity, the vertical distribution of hydrometeors, and the charge density over the height (z)–radius (R) plane.
Figure 3 shows the time series of the maximum wind velocity at the height of 1 km for the simulation without the lightning model (up to 192 h). The maximum wind velocity remained at about 25 m s−1 until 60 h from the initial time of the simulation. It began to increase after 70 h, then rapidly increased from time of 70 to 100 h (called rapid intensification; RI). After the RI, the maximum velocity gradually increased and reached steady state (after time of 160 h). This temporal evolution was similar to that simulated by previous studies (Miyamoto and Takemi 2013), except that the maximum velocity at steady state was about 10 m s−1 weaker than that of the previous study. This weak velocity originated from the coarser grid spacing of this study (5 km) compared with that of the previous studies (2 km). Even though the maximum wind was weak, the basic characteristics of the TC lifecycle were reasonably reproduced.
The vertical structure of hydrometeors over the z–R plane, averaged during the last 12 h of the simulation, is shown in Fig. 4a. Eyewall clouds, which are mainly composed of graupel, snow, ice, and liquid water (i.e., cloud droplets and raindrops), are clearly seen within R smaller than 60 km and lower than 14 km. Above the height of 14 km, ice particles and snowflakes extend to the outer region (R > 60 km) as anvil cloud. These characteristics are typically seen in the simulation of TCs (e.g., Franklin et al. 2005). The large mixing ratio of hydrometeors (qhyd: sum of the mixing ratio of the five categories, i.e., cloud, rain, ice, snow, and graupel) below 6 km, where the temperature was warmer than 0 °C, indicates that warm rain processes, which do not include frozen hydrometeors, are dominant in eyewall clouds, as reported by a previous study of a TC (Fierro and Mansell 2017). These results demonstrate that SCALE successfully reproduced the TC simulated by previous studies.
The vertical distribution of the charge density is shown in Fig. 4b. Near the center of the TC (R < 50 km), the charge density varied from positive to negative to positive from the model bottom to top, which is quantitatively consistent with the reports of observational studies (e.g., Jacobson and Krider 1976; Krehbiel et al. 1979; Brook et al. 1982) and modeling studies targeting isolated convective clouds (MacGorman et al. 2001), squall line systems (Mansell et al. 2005; Mansell and Ziegler 2013), and TC (Fierro et al. 2007; Fierro et al. 2013). Thus, the structure of the charge density in TCs was reasonably reproduced by the lightning model implemented in SCALE.
The negative charge density between the height of 7 and 12 km is mainly composed of negatively charged graupel and snow/ice (dash-dotted green and orange lines, respectively, in Fig. 4b). The positive charge density within the height above12 km originates from positively charged ice and snow particles (solid orange line in Fig. 4b). The positive charge density within the height below 7 km is composed of positively charged graupel and raindrops obtained from melting graupel (solid green and black lines in Fig. 4b).
To examine the reason for the polarity of graupel, snow, and ice at each height, the charge separation for each time step simulated in the model and temporal evolution of charge density over z–R plane (Fig. 5) are useful. Around the height of 7 km, the temperature is warmer than − 10 °C. Under this condition, graupel is positively charged (Fig. 5a), and ice and snow are therefore negatively charged (Fig. 5b) based on the LUT shown in Fig. 1. Due to the positively charge separation for graupels, graupels are positively charged at this height during whole time of the simulation (Fig. 5d). The positively charged graupel falls down due to its greater density compared to ice and snow. The graupel and raindrops generated by melting graupel make up the positive charge density within the height below 7 km in the inner core region (solid black contour line in Figs. 4b and 5e). By contrast, the negatively charged snow and ice are carried upward by the upward velocity of the eyewall region and are distributed between the height of 6 and 11 km (Fig. 5c).
Around the height of 11 km, in contrast to the height of 7 km, graupel is negatively charged (Fig. 5a), and ice and snow are positively charged (Fig. 5b) because the temperature at this layer is included in the blue shaded area of the LUT (Fig. 1). The positively charged snow and ice are carried upward and create positively charged anvil clouds above the height of 10 km (Figs. 4b and 5c). Some of the negatively charged graupel falls down, while the rest is elevated by the upward velocity and distributed between the height of 9 and 16 km (Fig. 5d).
The relationships between charge density and hydrometeor type described above support the report of Fierro et al. (2007), which simulated a TC using a meteorological model coupled with a lightning model.
In addition to the tripole structure in the inner core region, we note the negative charge density originating from negatively charged raindrops (dash-dotted black line in Fig. 4b) seen between the radius range of 50 and 80 km. The negatively charged raindrops are generated from the melting of negatively charged graupels, and the polarity exhibits a dipole structure from bottom to upper layer. The graupels originally obtain negative charge density above the height of 10 km. The graupels are transported outside of the TC by the centrifugal force with falling to lower layer. As a result of the transport by the centrifugal force, the graupels are outside of eyewall region (i.e., between the radius range of 50 and 80 km), when they fall to the height of 0 °C (Fig. 5f).
The tripole pattern near the center and dipole pattern outside the center are similar to the schematic illustration of the vertical structure of charge density and hydrometeors of a squall line system derived from the videosonde observation in Figure 7 of Takahashi and Keenan (2004).
Effect of aerosols on hydrometeors and charge density structure in a TC
The successful simulation of the vertical structures of qhyd and charge density of the TC encouraged us to investigate the impact of aerosols on these structures. Figure 6 shows maximum wind velocity at the height level of 1 km with N0 of 10 cm−3, 100 cm−3 (control simulation), and 1000 cm−3 without the lightning model. The impact of aerosols on the strength of the TC is weak. This result is contrary to the reports of previous studies (e.g., Rosenfeld et al. 2012; Khain et al. 2008a), which suggested that a TC is weakened with increasing aerosol number concentrations. This inconsistency is explained by the difference in the structure of the TC in the previous studies compared to that in the present study. Based on the previous reports, an increase in aerosols suppresses precipitation in the outer rain band region and reduces the pressure gradient between the outer rain band region and center of the TC through the cold-pool dynamics and feedback. The change in pressure gradient weakens the TC. For the TC simulated in this study, the outer rain band was not clear, and the cold-pool dynamics and feedback missed.
Figures 4a, 7a, and 8a show the vertical distributions of the cloud water mixing ratio and cloud number concentration with N0 of 10 cm−3, 100 cm−3, and 1000 cm−3. In the inner core region, the qhyd below the melting level (z = 6 km), mainly composed of liquid water particles, became large at N0 of 10 cm−3. The qhyd decreased as the aerosol number concentration increased. By contrast, the qhyd above the melting level, which corresponds to mixed-phase clouds, became large as the aerosol concentration increased. The results can be interpreted using the cloud invigoration hypothesis, suggested by Rosenfeld et al. (2008) as follows.
In the pristine condition (when N0 is 10 cm−3), size of hydrometeors around the cloud base tend to be larger than the control case, as demonstrated by the smaller number concentration of cloud droplets compared to the control case (solid black contour line, Fig. 7a). The large cloud droplets easily coalesce into large raindrops and rain out before reaching the melting level. As a result, the warm rain process dominates. The dominant warm rain process reduces the qhyd above the melting level in the pristine condition.
By contrast, in the polluted condition (when N0 is 1000 cm−3), the size of cloud droplets is smaller due to ACI, as demonstrated by the large number concentration of cloud droplets compared to the control case (solid black contour line, Fig. 8a). In this case, the coalescence is suppressed around the height of 7 km, and rain generation is prohibited. As a result of the prohibition on raindrop formation, cloud droplets remain small and are easily carried above the melting level by the updraft in the eyewall region. In this case, ice-phase cloud particles become larger, as demonstrated by the large qhyd around the height of 11 km (Fig. 8a).
These impacts of aerosols on cloud structure largely affect the structure of charge density, as shown in Figs. 4b, 7b, and 8b. Under the pristine condition (when N0 is 10 cm−3; Fig. 7b), the positively charged anvil, which is simulated within the height above 12 km in the control case (Fig. 4b), is more obscure than in the control simulation (Fig. 7b). Additionally, the positive charge density composed of positively charged graupel and raindrops below the height of 8 km is clearer than in the control case (Fig. 7b, d). In contrast to the pristine condition, the negative charge density is distributed from the surface up to about the height of 10 km, and the tripole structure is not seen under the polluted condition (when N0 is 1000 cm−3; Fig. 8b).
The reason for the dependence of the charge density on aerosols can be examined from the distribution of the charge separation rate of graupel, as shown in Fig. 8c. The ice and snow particles are given the same charge density, as shown in Figs. 5b, 7c, and 8c, but opposite polarities.
The non-inductive charge separation around the height of 7 km, by which graupel is positively charged, is clearly seen under the pristine condition (Fig. 7c). It gradually becomes unclear with increasing aerosol concentrations, and it is not seen under the polluted condition (when N0 is 1000 cm−3; Fig. 8c). In the pristine condition, the size of graupel generated around the height of 7 km is larger than in the control simulation due to ACI. In this case, the collision of graupel with ice and snow easily occurs. Therefore, the non-inductive charge separation rate is larger (Fig. 7c). The large charge separation results in the large positive charge density around the height of 7 km (Fig. 7b, d). In this case, the large-sized positively charged graupel easily falls down and melts into raindrops, resulting in the widely distributed positive charge density below about 8 km height (Fig. 7b, d). The negatively charged ice and snow generated by the collision with the graupel in this layer are not easily carried to the anvil layer due to the large size; therefore, the positively charged anvil is more obscure under the pristine condition (Fig. 7b) than in the control simulation (Fig. 4b), although the tripole structure is weakly seen.
By contrast, under the polluted condition, the non-inductive charge separation around the height of 7 km is not clear (Fig. 8c). The unclear charge separation also originates from ACI described as follows. The size of the graupel is smaller than in the control case due to ACI, and the collision of graupel with ice/snow at the height of 7 km is prohibited. This prohibition results in the small amount of non-inductive charge separation in the polluted case (Fig. 8c). Alternatively, the collision of graupel and ice/snow frequently occurs at the height around 11 km because the graupel gradually becomes large while rising up to the height of 11 km, and graupel is negatively charged in this layer (Fig. 8b, d). The frequent collisions induce the large non-inductive charge separation around the height of 11 km. The negatively charged graupel originating from the charge separation falls down and melts into negatively charged raindrops (Fig. 8d). This results in the negative charge density from the surface to about the height of 12 km. As a result of the processes shown above, the dipole structure of the charge density is seen in the polluted case.
In summary, the impact of aerosols is clear in the layer in which non-inductive charge separation mainly occurs. Due to the aerosol effect, the charge separation, which occurs about the height of 7 km, is not clear in the polluted condition. The tripole structure becomes obscure, and the dipole structure is seen in the polluted condition.
Effect of aerosols on the number of lightning flashes in a TC
The large impact of aerosols on the charge density resulted in a large dependence of the number of flashes on the aerosol concentration, as shown in Fig. 9. The flash number is defined as the number that the neutralization scheme is called, and it cannot be compared with the observed flash number. However, we can discuss the relative difference of the flash number. The flash number in pristine and control simulations was mostly the same regardless of the aerosol number concentration. Under the polluted condition (i.e., when N0 is larger than 500 cm−3), the flash number was much larger than under the pristine condition. The dependence of the flash number on the aerosol number concentration originates from the vertical structure of the charge density. As described in the previous section, the tripole structure is seen in the control simulation and the pristine condition. The tripole structure in pristine condition is not clear with tangentially and temporally averaged charge density (Fig. 7b), but tripole structure is clearly seen in snapshot. By contrast, the vertical structure of charge density is a dipole in the polluted condition. The dipole structure tends to create a large |E| magnitude because E is calculated as the gradient of the Laplacian of the charge density (Eqs. (5) and (6)). The large |E| in the polluted condition results in frequent occurrences of |E| larger than Eint. As a result of the large |E|, the flash number under the polluted condition is much larger than that under the pristine condition. The dipole structure is clear when N0 is larger than 500 cm−3; therefore, the flash number becomes large when N0 is larger than 500 cm−3.
These dependencies of the lightning frequency in TC inner core upon aerosols should be compared with the observation, but the dependency has not been observed due to the difficulty to isolate the aerosol effects from the observation. However, in view of the effect of the aerosol on the lightning, the contrast of lightning frequency over the ocean and the continent for convective clouds in tropical region gives some hints to imply the effect of aerosol on lightning with TCs. Over the continent, aerosol number concentration is larger than that over the ocean. Satellite observation using Tropical Rainfall Measuring Mission (TRMM) Lightning Imaging Sensor (LIS) data (Zipser et al. 2006) and using TRMM LIS and Optical Transient Detector (OTD) (Albrecht et al. 2016) reported the larger frequency of the flush over the continent than the ocean. In addition, an observational study reported the possibility of the positive correlation between the aerosol optical depth and flush number (Yuan et al. 2011). As well as these studies, the dependency of the aerosols on the lightning density simulated in this study is qualitatively similar to the results of the satellite observation using TRMM LIS data (Liu et al. 2012; Stolz et al. 2015). They conducted the statistical analyses using 9-year data of TRMM LIS measurement and reported that the total lightning density is larger with the larger aerosol number concentration. To understand the relationship between our results and the results of the satellite observation, we need to make a detailed comparison between modeling results and observation from satellite in the future.