We'll give this some more thought. But it's premise - comparing nuclear explosions with volcanoes - is, in part, erroneous. We're enclosing the link, above, which might prove interesting.
Volcanic ejecta can stay in the atmosphere for decades. Depending on the nature of the eruption, particulates can be, literally, "injected" far higher into the upper atmosphere than smoke simply "rising up" from fires. The upper part of the initial "plume" from a nuclear blast might reach into the stratosphere, but the bulk of it would stay lower and be more susceptible to meteorological cleansing processes. And, the sheer mass of volcanic dust from an eruption would be far greater than that of any imaginable smoke generated from even multiple nuclear weapons blasts or the surface fires they might engender. The smoke from debris fires would definitely not go as high, or stay as long. And, there just wouldn't be as "much" of it.
In other words, when it comes to volcanic pollution, compared to any other source excepting an asteroid impact, there's more of it, it goes higher and it stays longer.
Oddly, I (Joe) have some direct research knowledge on that topic which - perhaps even more oddly - I am not allowed to discuss in much detail, nor to reveal the sources. However, I can tell you that some study has been given to what might happen if very large nuclear weapons were intended and designed to explode after being driven deep beneath the surface - much like a "bunker buster" bomb on steroids.
Underground test explosions are usually smaller than true weapon-sized blasts, and the subsurface chambers for them are both built to contain them, and are far deeper than the scenario I helped study/conceptualize. But, even test bombs create surface craters.
In any case, when truly large nuclear explosions were modeled to occur at moderate depths, the amount of atmospheric ejecta - and subsequently predicted climatic effects - were greater, much greater, than equivalent atomic blasts on the surface.
Those conjectured subsurface nuclear explosions mimicked - on a smaller scale, mind you - volcanic eruptions. If there were enough of them, and we did look at that, they would rival volcanic effects.
I can't go into much more detail without violating oaths and such. I know that might sound a little far-fetched, but I might be able to track down a web-based trace of what I was involved in. If so, I'll send it along in another email, and let your imagination fill in the details.
And, an excerpt from the linked article:
"Peter Gleckler of the Lawrence Livermore National Laboratory in California and colleagues compared climate models that included volcanoes with those that did not. To their surprise they found that volcanoes seem to have a cooling effect on the oceans that lasts for up to a century after an eruption."
In other words, the climatic effects of a major volcanic eruption can be far greater and last far, far longer than any conceivable surface fires - even "mass" fires caused by nuclear weapons.
That help?

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