Hi Tim,
Thanks for the reply
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Saturn emits 1.78 times as much thermal energy as it gets from the sun, so it has a strong internal energy source that drives vertical convection.
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That would mean the internal heat source produces 0.78 of the Sun's input, which doesn't impress me as something that would lead to a million times stronger lightning.
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On Earth, all weather happens in the troposphere, which is at most 5 or 6 kilometers deep, so that's the limit on any vertical convection path length.
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Don't forget to include the sprites, blue jets and stuff like that, those effects are seen much higher in the atmosphere.
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The length of the convective path is directly related to the ability to separate charge and generate much stronger lightning.
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There's also a relation between buildup of charge and the ability of the atmosphere to discharge. At a certain level discharge occurs, irrespective of the potential to build to higher charges based on "convective path length", in other words there are limits to charge buildup.
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So it's easy to see why lightning should be more powerful on all of the giant planets than on Earth.
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I guess we don't know enough of Saturn's atmospheric activity to conclude this, I'm not surprised it is more powerful (after all size matters), but the factor of a million is certainly "astonishing" for Mr Gurnett, and I'm not going to argue his assessment.
Cheers.