Introduction

In an analysis of cloud to ground lightning observations using a global VHF antenna network (GLD360) it was determined that the geometric mean peak current (Ip) of negative polarity Cloud-to-Ground lightning strikes (CGs) for the first return stroke was ~ 10–30 kA over the continents1. In contrast, the geometric mean of Ip of CGs measured over the oceans in Said et al.1 varied in the range of ~ 25–45 kA. These energy categories of lightning strikes represent 95% of all CGs measured over the land and oceans globally during a one-year period (Op. Cit.). The spatial-temporal global distribution of total lightning (CGs + intra cloud lightning) in general has been previously determined based on satellite observations, where lightning occur most frequently over the land, during summertime in the northern temperate zone2, while over the oceans, lightning occurs much less frequently, by a factor of ~ 10 (Op. Cit.).

Previous studies, most notably Holzworth et al.3 showed based on the World-Wide Lightning Location Network (WWLLN) that high energy CGs (> 1 MJ) detected by a Very Low Frequency Time Of Arrival (VLF-TOA) antenna network, also known as Super Bolts (SBs), which represent substantially less than 1% of the total CGs included in their dataset, occurred predominantly over the oceans (> 90%). This is consistent with Hutchins et al.4, who showed that the ratio of lightning strokes observed by WWLLN, over the oceans and continents increases with increasing lightning stroke energy above 3000 J, where this ratio reaches a plateau value of ~ 2 for lightning strokes with energies in the range of 104–106 J. It is interesting to note that the analysis of Hutchins et al.4 excluded lightning flashes with energies above 1 MJ, which were the focus of the Holzworth et al.3 analysis.

Holzworth et al.3 defined two energy classes for SBs collected between 2010 and 2018, where the lower energy class included all SBs with energy > 1 MJ and the higher energy class included all SBs with energy > 2 MJ. Based on this classification Holzworth et al.3, identified a total of 8171 SBs throughout the study period with energies greater than 1 MJ, out of which 1719 events had energies greater than 2 MJ. These observations comprised 0.001% of all CGs recorded by WWLLN throughout the measuring period and have energies three orders of magnitude greater than the mean (1000 J). According to the conversion equation of Hutchins et al.4, the mean radiated stroke energy in the Holzworth et al.3 dataset is equivalent to a peak current of 35 kA assuming a triggering window of 1.33 µs. This mean value is substantially higher than the detection threshold (2 kA) of VLF-TOA lightning detection systems proposed by Krider et al.5. The cutoff energy for SBs used in Holzworth et al.3 is 1 MJ, which is equivalent to ~ 3000 kA according to the conversion equation of Hutchins et al.4 and assuming a triggering window of 1.33 µs. This Ip is extremely high, however, it is well known from basic electrodynamic principles that the lightning duration increases with the power of the lightning bolt and therefore the calculated Ip will decrease according to the Hutchins et al.4 equation and therefore assuming a two order of magnitude increase in the triggering window duration (133 µs), the cutoff Ip decreases to ~ 180 kA, which seems to be a much more reasonable value.

Nonetheless, according to the classification and global distribution of Holzworth et al.3, most of the SBs occurred in the northern hemisphere (72%) during the wintertime (Fig. 1a). Furthermore, it is also possible to identify global hotspots for SBs (Fig. 5 in Holzworth et al.3, including the Mediterranean Sea region (~ 24% of all SBs), the North Sea region (~ 16%), the Chilean high plateau (~ 10%), and off the coast of South Africa (~ 4%). Holzworth et al.3, also noted that most (86%) of the SBs occurred during the solar maximum (2013-15) and suggested that this correlation may be potentially causal. Finally, while lower energy CGs in general are most prevalent during the late afternoon to early evening hours6,7, according to the Holzworth et al.3 dataset, SBs exhibit a daily cycle with a maximum occurrence after midnight until 0600 and a minimum occurrence at midday (Fig. 1b). This daily variation is in opposite phase to the fair-weather atmospheric electric field strength variation, also known as the Carnegie Curve.

Fig. 1
Fig. 1
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Monthly (a) and daily (b) distributions of Lightning Superbolts (SBs) with energies greater than 1 MJ, based on the Holzworth et al.3 WWLLN dataset for the period 2010–2018. In panel (a), the orange and blue bars indicate the monthly distribution of SBs in the northern and southern hemispheres (NH and SH), respectively. The time axis in panel (b) is in UT.

Turman8, first characterized SBs based on optical measurements from the Vela satellites and land based worldwide VLF monitoring network measurements9. Turman8 considered the upper 2% of the optical spectrum from the Vela measurements of optical power and showed that the corresponding energy of VLF RF sferics measurements9, were significantly and positively correlated8. Thus, it was determined that the peak optical power of SBs is greater than 10 GW or 100 MJ in energy units of RF sferics that were output by the VLF system. In a later study, Kirkland10 determined the optical power threshold for SBs to be > 100 GW, an order of magnitude higher than the Turman threshold. Finally, in a recent study, a comparison was conducted between satellite optical power of lightning flashes and corresponding energy levels of CGs measured by WWLLN11. It was shown that lightning bolts with an optical intensity of > 100 GW, qualifying them as optical SBs10, had energies 2–3 orders of magnitude lower than the 106 J threshold defined by Holzworth et al.3. Together with the discrepancies between the classification of SBs by Turman3,8,10 in terms of occurrence (2%, 0.46% and 0.001%, respectively) and their energy (10 GW (100 MJ), 100 GW (1GJ) and 1 MJ, respectively) it is somewhat difficult to determine a cutoff energy or Ip for SBs based on state-of-the-art lightning detection networks Ip measurements, such as the Earth Networks Total Lightning Network (ENTLN). For example, in order to discuss the land-ocean differences, frequencies, spatial distributions and conditions under which SBs occur, it is imperative to provide a more robust SB Ip threshold for these state-of-the-art systems.

According to Cooray and Rakov12, assuming a maximum background electric field below thunderclouds of 150 kV·m−1, the theoretical upper limit for CGs peak current is 450–500 kA in the tropics and 300 kA in the temperate zones. Nonetheless, CGs with Ip > 500 kA and even > 1000 kA over the land have been measured and reported with VLF-TOA systems (e.g., Lyu et al.13,. In this study, we examined the ENTLN CG data from the period 2018–2021 to determine the cutoff Ip for SBs over the land and the oceans, which includes the upper 3% of all CGs included in the dataset. Where, according to Asfur et al.14, it is understood that the conductivity of the ground influences to a great extent the intensity of the lightning discharge. In addition, we will determine the annual, daily and global distributions of these SBs and their ocean-land ratios.

Methods and analysis protocols

The Earth Networks Total Lightning Network (ENTLN) is comprised of over 1800 wide band (1 Hz to 12 MHz range) TOA electric field lightning sensors deployed globally15. The reported median location accuracy of this system is ~ 100 m and the CG classification accuracy of 94%16,17. The ENTLN is capable of observing lightning return strokes or multiple strokes16. In this study, CG data were obtained and analyzed for the period January 2018 until December 2021 without differentiating between the first and following return strokes (https://www.earthnetworks.com/product/lightning-data/). The entire dataset (Ip = 2–1000 kA) included 1.72·109 CG events with positive and negative polarities. Out of this dataset, CGs with Ip ≥ 30 kA, which is equivalent to 550 J, according to the Hutchins et al.4 conversion equation, were extracted for further analysis. Altogether, the ENTLN subset (Ip > 30 kA) constitutes ~ 3.25% of all CGs with Ip = 2–1000 kA during 2018-21. The subset (Ip = 30–1000 kA) was binned into 2 kA bins for positive and negative polarities separately as well as separated for land and sea. Based on the distribution with Ip of percent of the total we tried to determine an Ip threshold for SBs over the continents and the oceans. Finally, the subsets of CGs with Ips > 30,50,100 and 200 kA over the continents and oceans were sorted by hour to determine their diel distributions and compare them to the Carnegie Curve.

Results

The global density distribution of CGs per 0.25° × 0.25° cell, which was normalized to the area of each cell in km2 for all events with Ip > 30 kA (negative and positive polarities) that occurred during the study period, indicate significantly higher densities over the land than over the oceans (Fig. 2), with the highest densities over the continents in the southern hemisphere. The 30 kA threshold was chosen based on several studies that showed the average Ip of typical negative CG strokes detected by VLF-TOA antennae networks have an Ip of 30–40 kA1,18,19,20,21,22). The “hotspots” of high continental lightning densities are apparent over the Andes region, Northern Columbia and Venezuela (Lake Maracaibo) in south America, in South Africa, the Maritime Continent in Southeast Asia and Northern Australia. This “hotspot” distribution is similar to the one described by Albrecht et al.23 that was based on optical intensity records. Over the oceans, CGs with Ip > 30 kA is relatively equally distributed (mostly lower than 1000 strikes per 0.25° × 0.25° per year) between the latitude of 60°S and 60°N, with empty patches in the southern Atlantic and Pacific oceans extending out from Western Africa and South America, respectively. There is also a sporadically bare patch of ocean extending from North America out into the Pacific Ocean and a bare meridional band along the equator in the Pacific Ocean. It should be noted that the regions bare of CGs with Ips > 30 kA in the southern hemisphere in the Atlantic and Pacific oceans as well as along the equatorial pacific correspond to upwelling regions along the continents and along the equator. Despite the relatively low densities in the oceans, it is possible to identify oceanic regions with relatively higher densities (1000–3000 strikes per 0.25°X0.25° per year) in the Mediterranean Sea, Gulf of Mexico, Arabian Sea, the regions across from Liberia and Cameroon in the Atlantic Ocean, in the region off the coasts of Mexico and California in the Pacific Ocean and others. It is interesting to note that in the region of the North Sea and English Channel the density of CGs with Ip > 30 kA is very low and in large areas even bare. This finding is contradictory to the distributions of SBs in the North Sea and English Channel during the period 2010–2018, presented in Holzworth et al.3.

Fig. 2
Fig. 2
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The global average CGs density (# km−2·yr−1) distribution for all CG events with Ip > 30 kA that occurred over the period 2018–2021.

As stated above, the relative proportion of CGs with Ip > 30 kA from the total analyzed dataset is ~ 3.25%, while continental CGs comprises 2.8% and oceanic CGs 4.1% of the total number of CGs with Ip > 2 kA over land and oceans, respectively. This result is consistent with the findings of Silverman et al.24 for CGs over the eastern Mediterranean Sea. In Fig. 3, the proportion of lightning events out of the total CGs is presented as a function of an increasing Ip threshold in a log-linear plot. According to Fig. 3b, it is evident that the proportion of all CGs with Ip > 50 kA is strongly influenced by the proportion of the total occurring over the oceans and the peak sea to land ratio actually has two distinct peaks with values of 15 and 13 at Ip > 120 and 150 kA, respectively. In Fig. 3c, the proportion of CGs decreases with increasing Ip along a sigmoidal curve, dropping very quickly to 0.01% at ~ 500 kA and continues to decrease slowly to 0.0006% at 900 kA and drops quickly beyond to 0.00001% at 1000 kA. It should be noted that there is a high degree of skepticism regarding peak currents greater than the upper theoretical limits of Cooray and Rakov12 (300–500 kA). Nonetheless, it is interesting to note that the percentage at 500 kA threshold, which is the highest theoretical limit for lightning bolts in the tropics according to Cooray & Rakov12 is 0.001%, i.e., 1 out 105 CGs are have an Ip > 500 kA.

Fig. 3
Fig. 3
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The proportions of CGs with Ip > 30 kA out of the total number of CGs recorded over the period 2018–2021 globally (blue line) with Ip > 2 kA, over the continents (green line) and over the oceans (orange line). The black dashed curve represents the ratio of CGs with Ip > 30 kA over the oceans (sea) and continents (land). The black and red dashed lines indicate the proposed proportions of SBs out of the total number of CGs with Ip > 2 kA.

The diel distribution of CGs with Ip > 30, 50, 100 and 200 kA, yields different distributions for the land and the sea (Fig. 4). The graph illustrates how the occurrence of lightning strikes varies throughout the diel cycle over land and sea for different Ip thresholds, compared to the fair-weather electric field (Carnegie Curve), which was calculated according to Harrison25. Generally, the normalized occurrence of high Ip lightning strikes over land exhibit a notable increase during the afternoon and evening hours, with a marked decrease in the early morning and late night. In contrast, the normalized occurrence of high Ip CGs over the sea exhibits peak values during the late afternoon and early evening hours and decreases to minimum values during the early morning hours. Overall, the sea distributions correspond well with the normalized fair-weather Carnegie Curve, while the land distribution are out of phase.

Fig. 4
Fig. 4
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Diel distributions of land (empty markers) and sea (full markers) normalized frequencies of high Ip cloud-to-ground strokes above different peak current thresholds (Ip > 30,50,100 and 200 kA, left Y axis) compared the normalized fair-weather atmospheric electric field Carnegie Curve (Blue dashed line, right Y axis), that was calculated according to Harrison25. The time axis in UT.

Discussion and conclusions

Previous studies, based on optical and VLF observations, determined that lightning superbolts (SBs) occur predominantly over the oceans. Turman8 based his conclusion on 3 years of Vela optical observations (1972-75), which consisted of thousands of flashes (as reported). Where, 1% of the flashes were categorized as SBs that occurred predominantly over the north west Pacific near the coast of Japan. Holzworth et al.3 based his conclusion on 10 years of WWLLN data, which recorded millions of flashes by ~ 70 antennas distributed globally. Where, 0.001% of the CGs were categorized as SBs, out of which > 90% occurred over the oceans, specifically in regions including, the Mediterranean Sea, the Northern Sea, the Indian and Atlantic oceans along the equator, and along the 45°N and 45°S parallels across the Pacific and Atlantic oceans. In this study, which is based on the ENTLN data consisting of ~ 109 CGs, collected by ~ 1800 antennas distributed globally, during the period 2018–2021, the proportion of high peak current CGs over the oceans compared to land was greater than 1 starting at Ip > 50 kA and no more than ~ 15 for Ip > 120 kA (Fig. 3). For Ip > 200 kA, the peak sea to land ratio of 2.4 occurs at Ip > 380 kA and decreases to a relatively constant ratio of 1.2 from Ip > 550 kA. These findings are inconsistent with the findings of Turman3,8, with respect to the sea-land cloud-to-ground stroke ratios. However, it should be noted that within the threshold range of 90–180 kA, the average sea to land ratio is ~ 9, i.e., 90% of the CGs in this threshold range occur over the oceans, similar to the result of Holzworth et al.3 as displayed in Fig. 5. According to Fig. 5, there are a number of occurrence “hotspots” of CGs with Ip > 100 kA, most notably in maritime SE Asia, the China Sea, the northern Indian Ocean, in the Indian Ocean off of South Africa, on the Atlantic Ocean side of southern Africa in the Cuvelai-Etosha Basin region, the tropical east Atlantic and east Pacific, northern Gulf of Mexico, the Atlantic region of the NE USA and finally the central region of South America along the Andes Plateau. However, unlike Holzworth et al.3, the bulk of CGs with Ip > 100 kA did not occur in the Mediterranean Sea and North Sea regions. In fact, according to the ENTLN dataset, there were barely any CGs with Ip > 100 kA in the North Sea.

Fig. 5
Fig. 5
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The global multi annual mean density distribution (km−2·yr−1) of all CG events with Ip > 100 kA that occurred over the period 2018–2021.

The theoretical upper thresholds for peak current values in cloud-to-ground strokes in the tropics and temperate zones according to Cooray and Rakov12 are 500 and 300 kA, respectively. Thus, the proportions of strong strokes with peak currents in the above ranges of the total based on the ENTLN data in the present study varies in the range 0.0003–0.003%, where the sea-land ratio varies in the range ~ 1.5–2.4 (Fig. 3). It appears that the occurrence of CGs with peak currents in the range 50–190 kA is substantially more frequent over sea than land, suggesting that these high peak current discharges over the oceans are more the rule than the exception. Thus, if SBs are characterized as extremely rare events (0.0001%) according to Holzworth et al.3, then according to this dataset, the threshold for SBs, should be set higher than 700 kA, where the sea-land ratio is relatively constant with increasing Ip at ~ 1.5. However, despite the fact that Ip > 500 kA has been previously measured by VLF-TOA systems and reported in the scientific literature26, it is generally accepted that these extreme values are not real and most likely measurement artifacts. Nonetheless, it should be noted that the theoretical upper limits of Ip for CGs determined by Cooray & Rakov12 were calculated under the assumptions that Ip is limited by the maximum measured atmospheric breakdown potential of 150 kV·m− 1 and the mean lightning discharge duration of 100 µs following the reanalysis of measurement from Cooray et al.27. These values appear to be relatively arbitrary considering the large variation of observed discharge durations (e.g., Smorgonskii et al.26–30 µs – 1928 ms) and observed values of the ambient electric field strength measured in the vicinity of the lightning discharge, which do not even attain the experimental breakdown potential for air of 3 MV·m− 128.

Considering the continental subset of the Ip > 30 kA, the relative proportion of continental CGs out of the total continental CGs (0–1000 kA) is 2.8% (Fig. 3). Similarly, the relative proportion of ocean CGs with Ip > 30 kA out of the total oceanic CGs (0–1000 kA) is 4.1%. Where, it should be noted that most of the CGs with Ip > 30 kA occurred in the latitudinal range of 40°S to 40°N (Fig. 2). It is interesting to note that the Ip for 0.01% of CGs over the continents is 165 kA, while over the oceans it is 260 kA. Thus, assuming that 0.01% of all CGs can be characterized as SBs, it is apparent that the Ip threshold over the oceans is substantially greater than the threshold over the continents. This finding is consistent with the findings of Said et al.1 and the conclusions of Asfur et al.14, who suggested that the lightning intensity is strongly influenced by the conductivity of the receiving surface (solid ground − 0–10 mS·cm− 1 compared to seawater – 50–60 mS·cm−1). Finally, the sea to land ratio of CGs increases from a minimum value of ~ 0.8 at Ip > 30 kA to a maximum value of ~ 15 at Ip > 123 kA (Fig. 3). After the maxima, the ratio drops rapidly to ~ 1.9 at ~ 190 kA and remains relatively steady thereafter.

The relative contribution of oceanic and continental lightning activity to the diel variation in the fair-weather electric field, the Carnegie Curve, has been previously investigated by Liu et al.29. In their study, it was shown that the diel variations in the electrical activity of clouds over both land and oceans in the latitudinal range of 35°S to 35°N, determined from TRMM rainfall reflectance measurements, were in phase with the Carnegie Curve. In this study, the contribution of CGs over the oceans with 80 < Ip < 150 kA relative to CGs over the land in the same Ip range is apparently in phase with the Carnegie Curve during the afternoon, but out of phase throughout the night and early morning hours (Fig. 6). This result suggests that that the relative contribution of CGs with Ip > 30,50,100 and 200 kA over the ocean to the Carnegie Curve in the afternoon and early evening is significant, while the relative contributions during the nighttime is insignificant. However, it can be inferred from Fig. 4 that the combined diel distributions of land and ocean CG frequencies is in phase with the Carnegie Curve, where the highest correlation coefficient is observed for SBs with Ip > 50 kA (R2 = 0.84) (Figure S1).

Fig. 6
Fig. 6
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Hourly distributions of ratios of the cumulative frequencies above the Ip thresholds between 30 and 1000 kA (every 2 kA) for CGs over the oceans and the land measured globally by ENTLN during the period 2018-21. The dashed white line represents the fair-weather atmospheric electric field strength calculated according to Harrison25 and adjusted to the Ip threshold axis scale.

In conclusion, the analysis of this global dataset shows that high intensity CGs with Ip greater than 125–155 kA observed over the period 2018-21, occur 13–15 times more often over the oceans relative to the continents. Above this range the sea to land ratio decreases to an average value of 1.6 for Ip > 180 kA, which is somewhat lower than the theoretical upper limit for Ip of 300 kA, estimated for temperate latitudes12. Where, the recorded CGs with Ip > 500 kA, which is the upper theoretical limit of Ip estimated for the tropics, represents ca. 0.0003% of the total lightning. This percentage is an order of magnitude smaller than the proportion determined by Holzworth et al.3 for SBs that predominantly occur over the oceans. Finally, the diel distributions of high intensity CGs indicate that they occur predominantly over the oceans throughout the entire day and are in phase with the fair-weather atmospheric electric field strength throughout the afternoon and early evening hours, but are in opposite phase during the nighttime and early morning hours. However, the combined diel distributions of CGs with Ip > 50 kA (land and ocean) exhibit a strong positive correlation with diel variation of the Carnegie Curve.