Figure 2 shows the monthly variation of AOD and lightning over the study regions. For region R1 (South Africa), aerosol concentration decreased from February (AOD: 0.59) till May (AOD: 0.33), with January being almost equal to February (AOD: ~0.56). AOD started increasing in June (AOD: 0.67), followed by a decrease till October (AOD: ~ 0.26), and an increase till December (AOD: 0.51). For this polluted region, R1, LA increased from January (~ 0.71×10− 5 lightning/km2/day) till March (~ 1.82×10− 4 lightning/km2/day), followed by a decrease for July and August (~ 0.42×10− 5 lightning/km2/day). The LA, however, increased in November (~ 1.27×10− 4 lightning/km2/day) and then marginally decreased in December (~ 0.74×10− 5 lightning/km2/day) over the region.
In region R2, (NW South America), AOD increased from January (~ 0.44) to May (~ 0.55) and then decreased to about ~ 0.29 in October, followed by an increase till December (~ 0.37). For this region, LA decreased from January (~ 0.09×10− 6 lightning/km2/day) to May (~ 0.028×10− 4 lightning/km2/day) and follows the reverse trend of aerosol. The LA increased to ~ 0.3×10− 5 lightning/km2/day in September, and then decreased till December (~ 0.1×10− 5 lightning/km2/day). For this region, generally opposite trend was noticed between AOD and lightning.
In the humid region of Indonesia (R3), AOD increased from January (~ 0.30) to March (~ 0.59), followed by a decrease in June-July (~ 0.30), an increase in October (~ 0.40), and a decrease in November-December (~ 0.24). Lightning over Indonesia increased from January (~ 0.01×10− 7 lightning/km2/day) to May (~ 1.12×10− 4 lightning/km2/day) and decreased during December (~ 0.03×10− 6 lightning/km2/day) with a slightly increase in August and September (~ 0.6×10− 5 lightning/km2/day). Like region R2, an opposite relationship is also noticed between AOD and lightning over this region (R3).
In the low aerosol loading region, R4 (South America), AOD decreased from January (~ 0.14) to July (~ 0.11), with marginal augmentation in June (~ 0.13), followed by an increase in September (~ 0.34) and a decrease in December (~ 0.15). For this region, the LA decreased from January (9.52×10− 5 lightning/km2/day) to June-July (5.21×10− 5 lightning/km2/day) and followed the decreasing trend of AOD. The LA increased in October (1.45×10− 4 lightning/km2/day) and decreased in December (1.22×10− 4 lightning/km2/day).
For region R5 (North America), AOD increased from January (~ 0.10) till August (~ 0.32) and then steeply decreased till October (0.12) and mildly decreased till December (~ 0.10). The LA increased from January (0.27×10− 5 lightning/km2/day) to July (2.48×10− 4 lightning/km2/day), and then it decreased in December (0.21×10− 5 lightning/km2/day). A positive correlation was revealed between AOD and LA in this region.
Figure 3 depicts the annual variation in AOD and LA over the region. Figure shows that aerosol continued to increase from 2005 to 2014 (r = 0.62, at a significant level of more than 95%) in region R1, however, it decreased in region R2, R4, and R5 (r = -0.64, r = -0.39, and r = -0.74, respectively, at a significant level more than 95%), and for region R3, aerosol remained uniform (r = − 0.12, at a significant level of more than 95%) during 2005 to 2014. Annual LA over the region is almost consistent for all the regions, R1 to R5 (r = − 0.03, r = 0.13, r = 0.03, r = 0.06, and r = 0.17, respectively, at a significant level of more than 95%).
The LA versus AOD and relative humidity are shown in Fig. 4. For R1, LA was about 3.75×10− 4 lightning/km2/day when AOD was around 0.16, and it increased to nearly 4.51×10− 4 lightning/km2/day for AOD about 0.25. The LA decreased (4.00×10− 4 lightning/km2/day) for 0.35 AOD, increased (4.64×10− 4 lightning/km2/day) for 0.45 AOD, and decreased again to 3.95×10− 4 lightning/km2/day for 0.55 AOD. The LA continued to decrease from 4.84×10− 4 to 3.84×10− 4 lightning/km2/day when AOD increased from 0.63 to 1.04 and augmented slightly at AOD 1.34 (4.13×10− 4 lightning/km2/day). A positive correlation (r = 0.19, at a significant level of more than 95%) has been seen between relative humidity and LA (Fig. 4R1c).
In region R2, LA decreased from 6.32×10− 5 lightning/km2/day to 5.91×10− 5 lightning/km2/day when AOD increased from 0.15 to 0.33 (Fig. 4R2a). The LA increased (7.17×10− 5 lightning/km2/day), decreased (6.64×10− 5 lightning/km2/day) and then again increased to 1.20×10− 4 lightning/km2/day at AOD 0.44, 0.55, and 0.63, respectively. The LA dropped to 2.87×10− 5 lightning/km2/day at AOD 0.75 and augmented to 1.82×10− 4 lightning/km2/day at AOD 1.02. It further decreased to 3.48×10− 4 lightning/km2/day (at AOD 1.26) and to 3.37×10− 5 lightning/km2/day (at AOD 2.21). For this region R2, a highly negative correlation (r= -0.86, at a significant level of more than 95%) has been observed between relative humidity and LA (Fig. 4R2c).
In region R3, LA was about 1.54×10− 4 lightning/km2/day at AOD 0.15 and increased marginally to 1.87×10− 4 lightning/km2/day at AOD 0.34. It decreased to 1.19×10− 4 lightning/km2/day at AOD 0.83 and to 8.06×10− 5 lightning/km2/day at AOD 2.47, followed by increased lightning to 2.01×10− 4 lightning/km2/day and 1.68 ×10− 4 lightning/km2/day at AOD 0.75 and 0.95, respectively. The correlation between relative humidity and LA was almost non-existent (r = 0.03, at a significant level of more than 95%).
In region R4, LA increased from 3.15×10− 4 lightning/km2/day at AOD 0.12 to 4.36×10− 4 lightning/km2/day at AOD 0.53. It decreased to 1.92×10− 4 lightning/km2/day at AOD 1.02 and then increased to 7.05×10− 4 lightning/km2/day at AOD 1.27. The LA retained almost the same density at higher AOD. A negative correlation between LA and relative humidity (r= -0.56, at a significant level of more than 95%) has been observed for R4 (Fig. 4R4a-c).
For region R5, LA was 1.16×10− 4 lightning/km2/day at AOD 0.13 and increased to 2.93×10− 4 lightning/km2/day at AOD 0.53. The LA decreased to 1.92×10− 5 lightning/km2/day at AOD 0.70 and augmented to 5.54×10− 4 lightning/km2/day at AOD 0.82. An opposite relationship between relative humidity and LA has been seen over the region R5. A negative correlation between relative humidity and lightning (r= -0.57, at a significant level of more than 95%) has also been observed.