In all the explanations of how global electric circuit on Earth works, I've always encountered statements like "thunderstorms generate ionospheric potential" (which is about 250 kV). E.g. here: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2009JA014758
But how is that possible? Thunderstorm (or, more specifically, a lightning strike) is inherently a discharge rather than a generator. It's the breakdown of an abstract capacitor rather than the charging of it. For all intents and purposes, thunderstorms should reduce any potential difference that exists around them rather than sustain it.
Can somebody explain, what actually drives the upward current that is observed above thunderstorms? Surely it cannot be lightning itself, so what then?
(I'm perfectly aware that there is also a downward current in fair weather; but the same question remains - where is the generator that causes it?)