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Most forest fires don't create strong enough firestorms (if they do at all) to funnel material high enough to have an effect -- most of the ash falls back down in a matter of weeks (even sooner if it gets rained out of the atmosphere). I'd compare nuclear blast firestorms with volcanic eruptions -- we do have a record of eruptions funneling material high enough into the troposphere and stratosphere to have a noticeable, longer-term effect on the climate (over the subsequent months and years).