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The authors use the runaway air breakdown model of upward discharges to calculate optical, radio, and X-ray radiation generated by red sprites. Red sprites are high altitude (up to 90 km) lightning discharges. Aircraft based observations show that sprites are predominantly red in color at altitudes above {approximately}55 km with faint blue tendrils, which extend downward to an altitude of 40 km; the duration of a single sprite is less than 17 ms, their maximum brightness is about 600 kR, and estimated total optical energy is about 1--5 kJ per event. The ground based observations show similar results, and provide some additional information on spatial and temporal structure of sprites, and on sprite locations. One difference between aircraft and ground-based observations is that blue tendrils are rarely observed from the ground. Sprites usually occur above the anvils of large mesoscale convective systems and correlate with strong positive cloud to ground discharge. Upward discharges are the most probable source of X-ray emission observed above large thunderstorm complexes by the Compton Gamma-ray Observatory. To escape the atmosphere these {gamma}-rays must originate above 25 km altitude. Red sprites are usually observed at altitudes higher than 50 km, and are therefore a likely source of this x-ray emission

Optical, radio and x-ray radiation of red sprites produced by runaway air breakdown