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edited Jun 4, 2020 at 16:03

This looks like it's a quantity that we don't have a particularly good grip on. Quoting from Rakov & Uman's Lightning: Physics and Effects (Cambridge University Press, 2003),

An approximate range for the electrostatic energy available for a lightning flash lowering a charge Q to ground can be evaluated by multiplying Q by the upper and lower limits for V, the magnitude of the potential difference between the lower boundary of the cloud charge source and ground. Assuming that Q = 20 C, thought to be typical for a cloud-to-ground flash, and using the range of V from 50 to 500 MV estimated earlier in this section, we find that each flash dissipates an energy of roughly 1 to 10 GJ (gigajoules). Note that a flash is typically composed of three to five strokes, and that the first stroke is usually a factor 2 to 3 larger (in terms of peak current and peak field) than a subsequent stroke, that is, any stroke other than the first. The above energy range inferred from electrostatic considerations is for all processes involved in a lightning discharge. Specifically, this energy estimate may well be dominated by the energy dissipated in the formation of numerous filamentary channels in the cloud that serve, in effect, to funnel cloud charges into the narrow channel to ground. Marshall and Stolzenburg (2001), from their balloon soundings of the electric field through thunderstorms and assumed minimum and maximum values of charge transfer, estimated the energy available for lightning to be in the range from 10 MJ to 10 GJ, the energy available for intracloud flashes (Chapter 9) being usually larger than that available for ground flashes. There is no consensus regarding the proportion in which the total return stroke energy is converted to thunder, hot air, light, and radio waves. According to Paxton et al. (1986), who used a gas dynamic model of the lightning return stroke (subsection 12.2.2), almost 70 percent of the total energy input to the channel is optically radiated from the channel. However, Few (1995), in his theory of thunder (subsection 11.3.2), assumes that essentially all the input energy is delivered to a shock wave 116 4. Downward negative lightning discharges to ground that subsequently is heard as thunder. As discussed in the first part of subsection 12.2.6, the total lightning energy input estimates of Paxton et al. (1986) and others, who employed gas dynamic models, differ from that of Few (1995) by two orders of magnitude or so.

Krider and Guo (1983) and Krider (1992) estimated that the radio-frequency power radiated by a subsequent return stroke at the time of the field peak, 3 to 5 GW, is about two orders of magnitude greater than the optical power radiated in the 0.4 to 1.1 µm range at the time of the field peak. The average zero-to-peak risetime of the subsequent stroke field waveforms was 2.8 µs. The total optical power, however, was found to dominate at later times, the peak optical power occurring about 60 µs after the electric field peak (because the risetime of the optical signal was determined by the geometrical growth of the return-stroke channel)

(emphasis added).

That said, it does look like the estimates of about 100 MJ to 10 GJ radiated as optical power capture the rough ballpark; assuming a photon energy of 2.5 eV gives a rough total of some $10^{25}$ to $10^{28}$ photons per lightning strike as a starting ballpark estimate.

This looks like it's a quantity that we don't have a particularly good grip on. Quoting from Rakov & Uman's Lightning: Physics and Effects (Cambridge University Press, 2003),

An approximate range for the electrostatic energy available for a lightning flash lowering a charge Q to ground can be evaluated by multiplying Q by the upper and lower limits for V, the magnitude of the potential difference between the lower boundary of the cloud charge source and ground. Assuming that Q = 20 C, thought to be typical for a cloud-to-ground flash, and using the range of V from 50 to 500 MV estimated earlier in this section, we find that each flash dissipates an energy of roughly 1 to 10 GJ (gigajoules). Note that a flash is typically composed of three to five strokes, and that the first stroke is usually a factor 2 to 3 larger (in terms of peak current and peak field) than a subsequent stroke, that is, any stroke other than the first. The above energy range inferred from electrostatic considerations is for all processes involved in a lightning discharge. Specifically, this energy estimate may well be dominated by the energy dissipated in the formation of numerous filamentary channels in the cloud that serve, in effect, to funnel cloud charges into the narrow channel to ground. Marshall and Stolzenburg (2001), from their balloon soundings of the electric field through thunderstorms and assumed minimum and maximum values of charge transfer, estimated the energy available for lightning to be in the range from 10 MJ to 10 GJ, the energy available for intracloud flashes (Chapter 9) being usually larger than that available for ground flashes. There is no consensus regarding the proportion in which the total return stroke energy is converted to thunder, hot air, light, and radio waves. According to Paxton et al. (1986), who used a gas dynamic model of the lightning return stroke (subsection 12.2.2), almost 70 percent of the total energy input to the channel is optically radiated from the channel. However, Few (1995), in his theory of thunder (subsection 11.3.2), assumes that essentially all the input energy is delivered to a shock wave 116 4. Downward negative lightning discharges to ground that subsequently is heard as thunder. As discussed in the first part of subsection 12.2.6, the total lightning energy input estimates of Paxton et al. (1986) and others, who employed gas dynamic models, differ from that of Few (1995) by two orders of magnitude or so.

Krider and Guo (1983) and Krider (1992) estimated that the radio-frequency power radiated by a subsequent return stroke at the time of the field peak, 3 to 5 GW, is about two orders of magnitude greater than the optical power radiated in the 0.4 to 1.1 µm range at the time of the field peak. The average zero-to-peak risetime of the subsequent stroke field waveforms was 2.8 µs. The total optical power, however, was found to dominate at later times, the peak optical power occurring about 60 µs after the electric field peak (because the risetime of the optical signal was determined by the geometrical growth of the return-stroke channel)

(emphasis added).

This looks like it's a quantity that we don't have a particularly good grip on. Quoting from Rakov & Uman's Lightning: Physics and Effects (Cambridge University Press, 2003),

An approximate range for the electrostatic energy available for a lightning flash lowering a charge Q to ground can be evaluated by multiplying Q by the upper and lower limits for V, the magnitude of the potential difference between the lower boundary of the cloud charge source and ground. Assuming that Q = 20 C, thought to be typical for a cloud-to-ground flash, and using the range of V from 50 to 500 MV estimated earlier in this section, we find that each flash dissipates an energy of roughly 1 to 10 GJ (gigajoules). Note that a flash is typically composed of three to five strokes, and that the first stroke is usually a factor 2 to 3 larger (in terms of peak current and peak field) than a subsequent stroke, that is, any stroke other than the first. The above energy range inferred from electrostatic considerations is for all processes involved in a lightning discharge. Specifically, this energy estimate may well be dominated by the energy dissipated in the formation of numerous filamentary channels in the cloud that serve, in effect, to funnel cloud charges into the narrow channel to ground. Marshall and Stolzenburg (2001), from their balloon soundings of the electric field through thunderstorms and assumed minimum and maximum values of charge transfer, estimated the energy available for lightning to be in the range from 10 MJ to 10 GJ, the energy available for intracloud flashes (Chapter 9) being usually larger than that available for ground flashes. There is no consensus regarding the proportion in which the total return stroke energy is converted to thunder, hot air, light, and radio waves. According to Paxton et al. (1986), who used a gas dynamic model of the lightning return stroke (subsection 12.2.2), almost 70 percent of the total energy input to the channel is optically radiated from the channel. However, Few (1995), in his theory of thunder (subsection 11.3.2), assumes that essentially all the input energy is delivered to a shock wave 116 4. Downward negative lightning discharges to ground that subsequently is heard as thunder. As discussed in the first part of subsection 12.2.6, the total lightning energy input estimates of Paxton et al. (1986) and others, who employed gas dynamic models, differ from that of Few (1995) by two orders of magnitude or so.

Krider and Guo (1983) and Krider (1992) estimated that the radio-frequency power radiated by a subsequent return stroke at the time of the field peak, 3 to 5 GW, is about two orders of magnitude greater than the optical power radiated in the 0.4 to 1.1 µm range at the time of the field peak. The average zero-to-peak risetime of the subsequent stroke field waveforms was 2.8 µs. The total optical power, however, was found to dominate at later times, the peak optical power occurring about 60 µs after the electric field peak (because the risetime of the optical signal was determined by the geometrical growth of the return-stroke channel)

(emphasis added).

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created Jun 26, 2019 at 9:28

Emilio Pisanty

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This looks like it's a quantity that we don't have a particularly good grip on. Quoting from Rakov & Uman's Lightning: Physics and Effects (Cambridge University Press, 2003),

An approximate range for the electrostatic energy available for a lightning flash lowering a charge Q to ground can be evaluated by multiplying Q by the upper and lower limits for V, the magnitude of the potential difference between the lower boundary of the cloud charge source and ground. Assuming that Q = 20 C, thought to be typical for a cloud-to-ground flash, and using the range of V from 50 to 500 MV estimated earlier in this section, we find that each flash dissipates an energy of roughly 1 to 10 GJ (gigajoules). Note that a flash is typically composed of three to five strokes, and that the first stroke is usually a factor 2 to 3 larger (in terms of peak current and peak field) than a subsequent stroke, that is, any stroke other than the first. The above energy range inferred from electrostatic considerations is for all processes involved in a lightning discharge. Specifically, this energy estimate may well be dominated by the energy dissipated in the formation of numerous filamentary channels in the cloud that serve, in effect, to funnel cloud charges into the narrow channel to ground. Marshall and Stolzenburg (2001), from their balloon soundings of the electric field through thunderstorms and assumed minimum and maximum values of charge transfer, estimated the energy available for lightning to be in the range from 10 MJ to 10 GJ, the energy available for intracloud flashes (Chapter 9) being usually larger than that available for ground flashes. There is no consensus regarding the proportion in which the total return stroke energy is converted to thunder, hot air, light, and radio waves. According to Paxton et al. (1986), who used a gas dynamic model of the lightning return stroke (subsection 12.2.2), almost 70 percent of the total energy input to the channel is optically radiated from the channel. However, Few (1995), in his theory of thunder (subsection 11.3.2), assumes that essentially all the input energy is delivered to a shock wave 116 4. Downward negative lightning discharges to ground that subsequently is heard as thunder. As discussed in the first part of subsection 12.2.6, the total lightning energy input estimates of Paxton et al. (1986) and others, who employed gas dynamic models, differ from that of Few (1995) by two orders of magnitude or so.

Krider and Guo (1983) and Krider (1992) estimated that the radio-frequency power radiated by a subsequent return stroke at the time of the field peak, 3 to 5 GW, is about two orders of magnitude greater than the optical power radiated in the 0.4 to 1.1 µm range at the time of the field peak. The average zero-to-peak risetime of the subsequent stroke field waveforms was 2.8 µs. The total optical power, however, was found to dominate at later times, the peak optical power occurring about 60 µs after the electric field peak (because the risetime of the optical signal was determined by the geometrical growth of the return-stroke channel)

(emphasis added).