How Much Energy Goes Up? Sprite and Transient Luminous Event Energetics Against the Lightning Budget

The energy accounting for upward atmospheric discharges is derived from published brightness, size and occurrence-rate scales. A sprite's optical energy is derived from first principles from the Rayleigh brightness unit: a spatially averaged brightness of 1.50 MR over a projected area of 1.60e9 m2 gives an optical power of 6.81 MW and an optical energy of 34.1 kJ over a 5 ms effective duration. Dividing by an adopted optical fraction of 1e-3 gives a total deposited energy of 34.1 MJ per central sprite (scenario bracket 1.15 MJ to 341 MJ; full cross bracket 0.11 MJ to 3.41 GJ), a factor of 1.55 above the independent satellite-based estimate of 22 MJ per sprite. Summing sprites, halos, elves, blue jets and gigantic jets at their global occurrence rates gives a combined transient luminous event power of 12.13 MW centrally (bracket 1.14 MW to 43.8 MW), dominated by elves at 11.083 MW. Against the 44 GW global lightning budget (44 flashes per second at 1e9 J per flash) the ratio is 2.76e-4, or 0.028 per cent, and under the worst pairing of inputs it reaches 0.99 per cent without crossing one per cent: transient luminous events are a rounding error in the global energy budget, while remaining the only electrical deposition at 40-95 km altitude. All numbers are produced by the deposited compute.py. AI use is disclosed: drafting and computation assistance was provided by Dave, an AI system built and operated under the author's direction. The author, William Alexander Aldred, directed the work and is sole author of record.