A Possible Cause for Preference of Super Bolt Lightning Over the Mediterranean Sea and the Altiplano

Exceptionally high‐energy lightning strokes >106 J (X1000 stronger than average) in the very low‐frequency band between 5 and 18 kHz, also known as superbolts (SB), occur mostly during winter over the North‐East Atlantic, the Mediterranean Sea, and over the Altiplano in South America. Here we compare the World‐Wide Lightning Location Network database with meteorological and aerosol data to examine the causes of lightning stroke high energies. Our results show that the energy per stroke increases sharply as the distance between the cloud's charging zone (where the cloud electrification occurs) and the surface decreases. Since the charging zone occurs above the 0°C isotherm, this distance is shorter when the 0°C isotherm is closer to the surface. This occurs either due to cold air mass over the ocean during winter or high surface altitude in the Altiplano during summer thunderstorms. Stroke energy decreases with the warm phase of the cloud, as proxied by the cloud base temperature, and increases with a more developed cloud, as proxied by the cloud top temperature, but to a much lesser extent than the distance between the surface and 0°C isotherm. Aerosols play no significant role. It is hypothesized that a shorter distance between the charging zone and the ground represents less electrical resistance that allows stronger discharge currents.


10.1029/2022JD038254
2 of 11 can reasonably use either peak current data or WWLLN stroke energy data to be equivalent markers for lightning strength.In this paper, we used the WWLLN as it was more available and accessible.Superbolts (SB) are exceptionally high-energy lightning strokes, with detected energy of above 10 6 J, which is three orders of magnitude higher than the mean energy per stroke of 10 3 J (Holzworth et al., 2019;Turman, 1977).Holzworth et al. (2019) used WWLLN to map the SB for 2010-2018 (Figure 1).According to the map, the SB occur globally and mostly over extra-tropical water.That is contrary to the global distribution of all lightning which shows about 10 times more strokes mainly over tropical continents than over oceans (Christian et al., 2003;Lay et al., 2007).Although SB can occur anywhere in the world, there are three main regions with the most detected and strongest SB (Figure 1): (a) the North-East Atlantic Ocean (NEAO) from ∼20°W to the European coastlines, and from the latitude of Spain to mid-Norway; (b) The Mediterranean Sea (MS); and (c) the Altiplano in South America.The majority of the SB (∼76%) occur during the northern hemisphere winter (November until February) (Holzworth et al., 2019), and constitute only ∼0.00045% of the total lightning strokes (Kirkland, 1999;Turman, 1977;Yair et al., 2021).The causes for the spatial and temporal distribution of SB remain unknown.
Nonetheless, there have been some speculations as to what might determine the energy per stroke.One theory, suggested by Asfur et al. (2020), says that lightning above saltier water are more intense.Asfur et al. (2020) described a lab experiment of discharges into saline water.The intensity of the discharges increased exponentially with the salinity of the water.Thus, they hypothesized that the higher conductivity of saline water, compared to moist soil, results in a more efficient discharge to the surface, a larger peak current, a brighter optical flash, and higher energy per stroke.However, it does not explain the similar frequency of SB over the Mediterranean and North Seas despite the differences in their salinity (Figure S1 in Supporting Information S1), nor can it explain the SB over the Altiplano.The soil salinity over rainy equatorial regions that includes the Altiplano is much smaller than the oceans (Ivushkin et al., 2019).Another theory was suggested by Yair et al. (2021) who presented the climatology of the east-Mediterranean SB.They suggest that such SB are more abundant in the presence of large amounts of desert dust aerosols, coming from the Sahara Desert.The dust is ingested into the marine clouds and contributes to convective invigoration, enhanced freezing, and efficient charge separation.However, much like the Asfur et al. ( 2020  A third theory was suggested by Pizzuti et al. (2022) who examined the SB over Northern and Western Europe during 2010-2020.They claim that the advection of sea spray aerosols and busy shipping lane emissions contribute to the convective invigoration that leads to enhanced cloud electrification over the English Channel compared to surrounding areas.Like the previously suggested theories, this one also discusses only a specific region and cannot explain the dearth of SB in other rainy regions with similar shipping density.In addition, the effects of fine ship emission aerosols and coarse sea spray (CSS) aerosols on invigoration are of opposite signs (Pan et al., 2022).
Eventually, the three above-mentioned studies (Asfur et al., 2020;Pizzuti et al., 2022;Yair et al., 2021) focus on specific regions and only above bodies of water (the MS and NEAO).Therefore, they might explain at best only part of the spatial distribution of the SB, but not all three main regions of SB occurrence, especially not the conspicuous SB region of the Altiplano.
As for the SB temporal distribution, Brook et al. (1982) showed that during winter thunderstorms the positive polarity lightning peak currents are stronger.They related it to the wind shear, as a more intense wind shear in winter thunderstorms results in a lateral separation between the charges.This separation ensures the initiating positive streamer toward the ground, instead of toward the negatively charged region that typically lies right beneath it.On the other hand, Orville et al. (1987) showed that the peak currents of lightning with both polarities were higher in the winter than in the summer.In addition, Brook (1992) showed that radiation associated with electric field breakdown is greater in winter than in summer in thunderstorms over Albany, New York.A higher electric field results in a higher accumulation of charge before the breakdown, where the electrostatic energy density goes up as the square of the electric field (Griffiths, 2018).The higher electric field can be found in clouds with smaller drops, because the presence of large drops (free water surface), lowers the breakdown voltage (Brook, 1992).According to Brook (1992), such was the case in the examined winter storms over Albanysaturation vapor pressure close to that over ice, which leads to the formation of ice at the expense of liquid water (Wegener-Bergeron-Findeisen process) and eventually little deformable liquid water for discharge initiation.
In addition, high precipitation rates in clouds with large drops increase the electrical conductivity (Kamra, 1979), which leads to earlier and weaker breakdown voltage.Another suggested factor that might affect the breakdown is the air density, where denser air leads to higher dielectric strength and a higher needed breakdown voltage, thus stronger lightning (Hirsh & Oskam, 1978).
Here we suggest a new hypothesis for the occurrence of SB, based on the robust results presented in this study.The hypothesis, which is suitable for both over land and ocean, as opposed to the theories of Asfur et al. (2020), Yair et al. (2021), and Pizzuti et al. (2022); and relates to the observations of both Orville et al. (1987), Brook (1992) and Holzworth et al. (2019), states that the main factor that sets the energy per stroke is the vertical distance between the charging zone and the surface, where shorter distance results in higher energy.The charging zone is the ice and supercooled water mixed phase zone of the cloud, in which the charge separation occurs (Williams et al., 1991).The altitude of charge separation within the charging zone depends on the updraft, collision rate, temperature, and cloud water content (Li et al., 2020;Pereyra et al., 2008;Reynolds et al., 1957;Takahashi, 1978).Thus, the strict lowest boundary of this zone is marked by the height of the 0°C isotherm.Unfortunately, WWLLN does not distinguish the polarity of each stroke, so this aspect could not be addressed in this study.
Further description and discussion of the new theory are presented in Section 3, preceded by the methodology in Section 2.

Methodology
In this study, the energy per lightning stroke was examined as a function of different variables of the thunderstorm in various regions of interest (ROI).
Lightning discharge of electromagnetic waves occurs over a wide spectrum.The long-wave radio frequencies propagate with low attenuation between the conducting Earth and the lower boundary of the ionosphere (Rodger et al., 2006) thus enabling the detection of VLF signals thousands of kilometers from the source.The calculation of the energy per stroke for each WWLLN detected lightning is done by using the root mean square (RMS) of the electric field during each sferic interval (Hutchins, Holzworth, Rodger, & Brundell, 2012).This value is obtained in the 6-18 kHz band over the triggering window of 1.33 ms.Then, the U.S. Navy Long Wave Propagation Capability algorithm (Ferguson, 1998;Thomson, 2010) models the VLF propagation from each detected stroke and determines the necessary energy to produce the measured RMS electric field (in the VLF band) at each WWLLN station (Hutchins, Holzworth, Rodger, & Brundell, 2012).The WWLLN has a relatively high daily and global detection efficiency (Holzworth et al., 2019;Hutchins, Holzworth, Brundell, & Rodger, 2012).However, to ensure the data are not biased or contaminated, only lightning with standard error in the fit for energy of less than 30%, and that were detected by at least seven WWLLN stations were considered (Holzworth et al., 2019).Each stroke's time and location were used to extract certain properties of the thunderstorm and the environment.The energy per stroke from WWLLN was then analyzed as a function of these properties.The said variables and their source are described as follows and illustrated in Figure 2: 1. Surface Height (H SFC )-the altitude at the closest pixel below the detected stroke coordinates.These data were obtained from the GEBCO (General Bathymetric Chart of the Oceans) database.The GEBCO is a high-resolution raster of heights that maps both the ocean's bathymetry and the land surface height.Its spatial resolution is 15 arc-seconds which corresponds to ∼450 m at the equator and less in higher latitudes.In this study, only the land surface height data were considered, and the oceans' surface height was set to 0 m.
2. 0°C isotherm height (H 0 )-the bottom height of the charging zone.Since the electrical charge separation occurs at subfreezing temperatures somewhere in the charging zone, the bottom boundary of this microphysical zone was taken.This is under the assumption that temperature decreases with height during atmospheric unstable conditions that are conducive to thunderstorms.The data were acquired from the National Centers for Environmental Prediction (NCEP) Final Operational Global Analysis data.The spatial resolution of NCEP is 2.5° latitude × 2.5° longitude and its temporal resolution is 4 × daily (every 6 hr) (Kanamitsu et al., 2002).
3. Cloud base temperature (CBT)-this variable was calculated by the 2-m temperature and the lifting condensation level, using the dry adiabatic lapse rate.These data were obtained from the Modern-Era Retrospective Analysis for Research and Application Version 2 (MERRA-2) reanalysis data.The MERRA-2 is a NASA meteorological reanalysis data set that uses the Goddard Earth Observing System Data Assimilation System version 5.This data set contains atmospheric components, meteorology characteristics as well as aerosols and atmospheric chemical constituents at a spatial resolution of 0.5° latitude × 0.625° longitude × 72 pressure levels and a temporal resolution of 24 X daily (every 1 hr) for the meteorological data and 8 × daily (every 3 hr) for the aerosol data (Gelaro et al., 2017).The CBT is used to determine the thickness of the warm phase at a constant H 0 to H SFC difference, which controls the potential of precipitation and the presence of graupel in the charging zone.  5. FA-Boundary layer fine aerosol concentration (dry radius < 1 μm (Pan et al., 2022)).These data are from the MERRA-2 data set as well.MERRA-2 aerosol data have five aerosol classes: dust, sea salt, sulfates, organic carbon, and black carbon (Buchard et al., 2015).According to the aerosol radius bin classification on the MERRA-2 website, the following aerosol types were considered as FA: hydrophilic and hydrophobic black carbon, hydrophilic and hydrophobic organic carbon, sulfate aerosols, and fine sea salt.
The lightning analyses in this study were done in three ROI (Figure 1): (a) the MS, (b) the Altiplano in South America (AP), and (c) the NEAO.We note here that the SB global distribution map (Figure 1) also has a relatively larger density of the strongest SB (over 2 × 10 6 J (red dots)) along the equator in the Atlantic and Indian Oceans, south of South Africa, and between ∼40°N and 40°S in the Pacific Ocean.However, to test our hypothesis, we focused on cases either where the H 0 is lower, that is, during the northern hemisphere winter or the H SFC is higher.According to Holzworth et al. (2019), the vast majority of the strongest SB occur during the northern hemisphere winter in these ROI and not elsewhere in the extratropics.Along the tropical oceans, H 0 remains fairly constant during the year; therefore, the hypothesis is not relevant to such cases.
Although SB constitute a small percentage of the total detected strokes per year, this study examines the conditions that may cause the highest energy of all the detected strokes and not just the defined SB.The analysis was done for data during 2013-2015, which are characterized by a high occurrence of SB (Holzworth et al., 2019).The total numbers of detected strokes over the different ROI are ∼3.9 × 10 6 over the MS, ∼7.46 × 10 5 over the NEAO, and ∼14 × 10 6 strokes over the AP.Detailed maps of the ROI are shown in Figure S2 in Supporting Information S1.

Results and Discussion
Our main hypothesis is that lightning strokes are more energetic when the vertical distance between the charging zone and the surface is shorter.To test this hypothesis, Figure 3 presents the mean stroke energy in 10 percentile intervals (J) as a function of the vertical distance between H 0 and H SFC (ΔH 0-S [m]) for the MS and NEAO (Figure 3a), and for the AP (Figure 3b).Within the AP lies Lake Titicaca which is a large body of water.Therefore, it was added to the analysis with the other bodies of water in Figure 3a.
Over the MS and NEAO, H SFC is 0 m and the H 0 ranges between ∼700 and ∼4,000 m (Figure 3a).It is clearly shown that for these regions the energy decreases sharply as ΔH 0-S increases.Over the NEAO the lightning reaches higher energy and in both regions, there is a stabilization when the distance exceeds ∼3,000 m.
The H 0 over the whole AP (Figure 3b) has a much lower variability compared to the other two regions (mean: ∼4,700 ± 200 m year-round) because the rainfall there occurs from tropical convection which always has a nearly constant H 0 (Garreaud et al., 2003;Harris et al., 2000;Schauwecker et al., 2017).However, the H SFC ranges between sea level and ∼5,000 m.Overall, the ΔH 0-S trend is similar to the trend over the bodies of water but the variability in the energy is much lower.Two possible explanations for that are (a) the peak points over land with very high local voltage gradient that might trigger lightning with lower breakdown voltage compared to the flat surface of the oceans; (b) and the lower air density in these altitudes that might lead to lower dielectric strength and weaker strokes.This might also explain the case of Lake Titicaca.It behaves similarly to the slope of the plots of the other bodies of water but with lower energy lightning like the AP that surrounds it.
Based on these results, it seems that for both land and ocean, our hypothesis is supported and the factor that determines the energy per stroke is the vertical distance between the surface and the charging zone.However, other factors were examined as well.
The first one is the thickness of the warm phase of the cloud, which can be used as a proxy for the warm precipitation depth and rate.As mentioned above, clouds with fewer large drops and lower precipitation rates, have higher breakdown voltage and stronger strokes.So, a thicker warm phase means a higher rain rate.Therefore, the breakdown voltage and the lightning energy are expected to be lower.The warm phase thickness is reflected in the change of CBT for a constant ΔH 0-S , where a warmer CBT means a thicker warm phase.Figure 4 shows the mean stroke energy (J) as a function of ΔH 0-S (m) binned by CBT intervals.
The red line is the warmest CBT (>20°C), and the green line is the coldest one (<0°C) which corresponds to higher and lower ΔH 0-S , respectively (Figure S3 in Supporting Information S1).
Since both lower ΔH 0-S and colder CBT correlate with higher energy values, the CBT does not add significant information to the overall trend.Although, there are some overlapping cases with the same low ΔH 0-S over the MS and AP, where the warmer CBT result in slightly higher energy.These small deviations might indicate other possible CBT-related factors.
Another factor that might affect the energy is the level of cloud development or the thickness of the charging zone.Several observational studies have shown that for the same cloud base height, higher cloud tops promote cloud electrification and increase the lightning rate due to enhanced charge separation (Atchley, 1983;Lhermitte & Williams, 1984;Williams, 1985Williams, , 2001;;Williams et al., 2005).
Figure S4 in Supporting Information S1 presents the energy per stroke as a function of the flash rate for the different ROI.The lightning strokes were related to the same storm by taking strokes within 5 km of each other and within a time frame of 20 min.Then, adjacent lightning (spatially and temporally) were examined, and the time between them was calculated.This results in the lightning frequency (or flash rate) in units of s −1 .Figure The data are binned by the same percentiles as in Figure 3 and the total number of data points for each region is the same as shown in Figure 3.
S4 in Supporting Information S1 as well as the work of Chronis et al. (2015) and Chronis and Koshak (2017), present evidence for higher energy at low flash rates, which is typical to the winter and cool-base storms.The thickness of the charging zone can be inferred from the CTT, where a more developed cloud reaches higher altitudes and colder temperatures for the same H 0 .Figure 5 shows the energy as a function of the ΔH 0-S binned by the CTT.Considering the effect of the flash rate, we would expect that colder CTT (toward the green line) would result in lower energy.However, Figure 5 shows a different behavior than the expected one: for the same ΔH 0-S values, colder CTT (more developed cloud), results in slightly higher energy.Over the MS and NEAO it is most noticeable in the lower ΔH 0-S values (Figures 5a and 5b), and over the AP (Figure 5c) it seems to be more significant over the higher ΔH 0-S values.This could be explained by Han et al. (2021) who recently showed the non-linearity of the flash rate as a function of the ice fraction, where more developed clouds are expected to have more ice.When the ice fraction is rather small, the clouds are governed by liquid droplets with no efficient charge separation, thus lower flash rate and higher energy.As the ice fraction increases to an optimum point, the clouds tend to have sufficient ice hydrometeors and supercooled droplets to produce the most lightning activities efficiently.Beyond that optimum point, the ice phase becomes dominant, and the cloud experience less efficient charge separation again, which lowers the lightning rate and increases the energy.In any case, the thickness of the charging zone impacts the energy per stoke on a much smaller scale than the ΔH 0-S .
A third speculated factor is the aerosols effect.Pan et al. (2022) showed that adding fine aerosols (FA) increases the lightning density significantly while adding coarse sea spray (CSS) weakens it.Figure 5 shows the mean stroke energy (J) as a function of ΔH 0-S (m) binned by boundary layer FA (Figures 5a-5c) and CSS (Figures 5d  and 5e) concentration intervals.The CSS concentration over the AP is not shown since it is negligible over land.
As shown in the figure, the contribution of the different classes of aerosols does not have a significant effect on the detected energy as it does on the lightning density.
Our results (Figures 3-6) support the following possible physical explanation: when the vertical distance between the charging zone and the surface is shorter, the charging zone is less isolated from the ground.The column of isolating air is shorter and there is less electrical resistance in the lightning channel.Therefore, the electrical current is enhanced, and the indicated energy is larger.This hypothesis might hint at the mechanism of a capacitor.The electric field strength in a capacitor is directly proportional to the voltage applied and inversely proportional to the distance between the plates, that is,   =   .By reducing the length of the discharge channel (d), the resistive-capacitive (RC) time constant of discharge is also shortened, resulting in an increase in peak current for the same amount of charge transfer.On the other hand, a shorter channel length (or antenna) may lead to a decrease in the radiated energy for the same channel current.This discrepancy can be solved by the fact that lightning have not only vertical channels but also horizontal ones (Mazur et al., 1998).Therefore, smaller ΔH 0-S do not necessarily decrease the radiated energy.3 and the total number of data points for each region is the same as shown in Figure 3.
The lowered charging zone can also imply a larger breakdown voltage (V), due to the higher density of the surrounding air.In addition, colder CBT which means a thinner warm phase lowers the rain rate and causes an increase in the breakdown voltage.
Overall, the increase of V and decrease of d increase the electric field (E), which allows for more accumulation of charge before the breakdown, and higher lightning energy.
In contrast to the previous theories presented above (Asfur et al., 2020;Pizzuti et al., 2022;Yair et al., 2021), which explain only part of the global distribution of SB and only above bodies of water, this theory applies both over land and ocean.
Alongside our proposed physical explanation, we acknowledge the possibility that there may be other factors and phenomena that contribute to the global SB distribution.One such factor is the magnitude of charge (Q) present in the charging zone.It is possible that a combination of a large Q with a large ΔH 0-S or a smaller Q with a shorter ΔH 0-S could produce the same effect on the lightning energy.However, since we do not have data on Q, we can  d, e) concentration intervals.The particle mixing ratio intervals in each panel are determined by the percentiles: 0%-30%, 30%-60%, and 60%-100%.The CSS concentration is negligible over land and thus is not shown over the Altiplano.The data are binned by the same percentiles as in Figure 3 and the total number of data points for each region is the same as shown in Figure 3.only speculate on this connection without definitive proof.In addition, as discussed above regarding Figure 5, the discrepancy between the expected and the observed behavior could be explained by the non-linearity of the ice fraction to flash rate ratio.However this a speculation that might require validation, since the development level of the cloud is merely a proxy for the ice content.
We emphasize that this paper suggests a possible physical explanation based on the robust observations in the three main regions with the most SB over the globe.Analyses of different ROI, other than the three mentioned here, and with a broader set of data to test and suggest other possible explanations and phenomena for the SB were left for future studies.

Summary
This study presents a new theory that might explain what causes exceptionally energetic lightning strokes also known as superbolts (SB).The SB are globally spread with three main hotspots of high concentration in the NEAO, the MS, and the Altiplano in South America.The electrification in deep convective clouds occurs within the mixed phase microphysical zone of supercooled droplets, ice crystals, and graupel particles.This microphysical zone is referred to as the charging zone where the level of the 0°C isotherm is its lower boundary.Analyzing the energy per stroke as a function of the distance between the charging zone and the surface, the cloud base and top temperature, and the boundary layer fine and coarse aerosol concentrations resulted in clear insights.The most conspicuous result shows that the energy per stroke decreases sharply as the distance between the charging zone and the surface increases.We hypothesize that when the distance between the charging zone and the surface is shorter, the charging zone is less isolated from the ground and there is less electrical resistance, which leads to more electrical current and larger indicated energy.Colder cloud base temperature, which is a proxy for a thinner warm phase, also correlates with high energy values, due to a lower rain rate.The lower rain rate decreases the air conductivity and allows for higher breakdown voltage.It was also found that a cloud with a colder top temperature, which is a proxy for the vertical development of the cloud, results in slightly higher energy for the same charging zone to surface distance.This opposes the considerations of a higher flash rate in developed clouds that should reduce the energy but agrees with the higher ice faction consideration expected in more developed clouds.The added FA or CSS do not seem to have a significant impact on the detected energy.
These findings and possible physical explanations are valid for lightning over both land and ocean, as opposed to previously suggested theories that explained only part of the picture and are based on our robust results.However, further research is required to cover other regions and to further substantiate the hypothesis and additional explanations.
) theory, the Yair et al. (2021) theory cannot explain the similarly intense SB over the NEAO.

Figure 1 .
Figure 1.Global distribution of all superbolts between 2010 and 2018.The blue points are lightning strokes with 1-2e 6 J, and the red points are with >2e 6 J. Adapted from Holzworth et al., 2019.The polygons are the regions with the most detected and strongest SB: (1) The Mediterranean Sea (magenta); (2) the North-East Atlantic Ocean (green); and (3) the Altiplano (blue).

4.
Cloud top temperature (CTT)-the charging zone upper boundary.The CTT can be used as a proxy for the vertical development of the cloud, or the thickness of the charging zone, where colder CTT means a more developed cloud.The CTT data were also obtained from the MERRA-2 reanalysis data.

Figure 2 .
Figure 2. Illustration of deep convective cloud, with the thunderstorm and environmental properties as described in Section 2.

Figure 3 .
Figure 3.The mean energy per stroke as a function of the distance between the 0°C isotherm height and the surface height (ΔH 0-S ) for Lake Titicaca (red), the Mediterranean Sea (green), and the North-East Atlantic Ocean (purple) in panel (a), and for the Altiplano (cyan) in panel (b).The lightning cases are binned in intervals of 10 percentiles in all regions.The total number of data points for each region is shown on the plot.

Figure 4 .
Figure 4.The mean energy per stroke as a function of the ΔH 0-S for (a) the Mediterranean Sea, (b) North-East Atlantic Ocean, and (c) the Altiplano.The color of the lines indicates the cloud base temperature bins.The data are binned by the same percentiles as in Figure3and the total number of data points for each region is the same as shown in Figure3.

Figure 5 .
Figure 5.The mean energy per stroke as a function of the ΔH 0-S for (a) the Mediterranean Sea, (b) North-East Atlantic Ocean, and (c) the Altiplano.The color of the lines indicates the cloud top temperature bin.The data are binned by the same percentiles as in Figure3and the total number of data points for each region is the same as shown in Figure3.

Figure 6 .
Figure 6.The mean energy per stroke as a function of the ΔH 0-S for (a, d) the Mediterranean Sea, (b, e) North-East Atlantic Ocean, and (c) the Altiplano.The color of the lines indicates the boundary layer fine aerosol (a-c) and coarse sea spray (CSS) (d, e) concentration intervals.The particle mixing ratio intervals in each panel are determined by the percentiles: 0%-30%, 30%-60%, and 60%-100%.The CSS concentration is negligible over land and thus is not shown over the Altiplano.The data are binned by the same percentiles as in Figure3and the total number of data points for each region is the same as shown in Figure3.