With NASA plans for stopping a potential cataclysm I found the following statement repeated by several news sources (like BBC):

But Yellowstone explodes roughly every 600,000 years, and it is about 600,000 years since it last exploded, which should cause us to sit up and take notice.

I had a hard time finding any information regarding how forgetful distribution of eruptions is and what other free parameters are (like μ or σ if it is normally distributed) - other than this question. Is the distribution of Yellowstone supervolcano as regular as journalist seems to imply?

I hope that narrowing it to single supervolcano make it distinct enough to be non-duplicate and narrow enough to make it answerable.

  • @DavePhD I see - this is one of those "two points are a trend, three points are a confirmed trend". Assuming it will erupt "tomorrow" it gives μ = 0.70 million and unbiased σ = 0.89 (biased = 0.73). σ ≥ μ is rarely a good sign for trend. I'm going back to worrying about toddlers shooting me as this seems a more likely cause of my demise. – Maciej Piechotka Aug 23 '17 at 2:33
  • I'm deleting my comment, because the answer says more accurately what I was trying to say. – DavePhD Aug 23 '17 at 11:43
  • Isn't it also the case that we'd know well before (read: decades before) it happens when it actually will happen thanks to measuring the lava lake underneath and seismic events- – Magisch Aug 24 '17 at 8:19
  • Looks like it's Europe's turn. – Count Iblis Aug 25 '17 at 0:46
up vote 19 down vote accepted

To restate your question, How can we statistically describe the intervals between mega-volcano eruptions? Do they follow a particular probability distribution with known parameters? Can we use this to make any conclusions at all about Yellowstone?


We know of three eruptions 2.1 million years ago (mya), 1.2 mya, and 0.64 mya. This is an interval of 900,000 years and 600,000 years. The eruption 2.1 mya was violent enough to erase all evidence of previous eruptions, along with destroying half a continent. As summarized in the comments, two intervals cannot be used to describe a statistical distribution with any kind of confidence.


This page, written by the United States Geological Service, makes a claim about the improbability of an imminent eruption and then says that their numbers are basically made up.

QUESTION: What is the chance of another catastrophic volcanic eruption at Yellowstone? ANSWER: Although it is possible, scientists are not convinced that there will ever be another catastrophic eruption at Yellowstone. Given Yellowstone's past history, the yearly probability of another caldera-forming eruption can be approximated as 1 in 730,000 or 0.00014%. However, this number is based simply on averaging the two intervals between the three major past eruptions at Yellowstone — this is hardly enough to make a critical judgment.


This article looks at the frequency and recurrence rate of smaller volcanoes. It concludes that mega volcanoes do not follow the same pattern as smaller volcanoes, and we don't really have enough data to make real conclusions about giant volcanoes. Their focus is on the global occurrence of volcanism, not the reoccurrence patterns of individual volcanoes. They also limit their data to more recent volcanoes, for which we have more reliable data.


This article models super eruptions. "Super-eruptions are extremely rare events. Indeed, the global frequency of explosive volcanic eruptions is inversely proportional to the volume of magma released in a single event." If we can't learn much about mega volcanoes from small volcanoes, and we have little historical data about mega-volcanoes, it seems likely that the data to answer your question just does not exist.


This paper attempts to collect all of the mega-volcanoes from the last 36 million years. He found 47 massive eruptions. When I look at his collection, there are only a few calderas that show evidence of multiple mega-volcanoes. This work focuses on global recurrance times. He also discusses the limitations of his data, particularly how volcanoes from millions of years ago might be completely missed. Some of the volcanoes he described may have reerupted multiple times, but the evidence was never found.


Summary: I don't think the data to statistically describe how long it takes for an individual volcano to re-erupt exists. Distinguishing what type of distribution is used and properly statistically describing that takes a fair amount of data.

  • 13
    This is somewhat comforting re: the unlikelihood of an eruption, but then that "violent enough to destroy all evidence of prior eruptions along with half a continent" took that comfort right away again... – Shadur Aug 23 '17 at 7:12
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    @Shadur in all honesty, if ANY volcano on Earth erupts with the force of Yellowstone from 2.1 mya, it won't matter where it is. It's going to drastically change the way we live on this planet. – DenisS Aug 23 '17 at 14:08
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    @dennisstallings Oh, that's so much more reassuring, yes... – Shadur Aug 23 '17 at 14:10
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    @jwenting If Yellowstone goes up there's not going to be anyone left to sue. – Shadur Aug 24 '17 at 13:35
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    @Jwenting I don't see the statement of probability by the USGS as hedging bets, I see it as an honest description of how uncertain their statistics are. When I sit in presentations of scientific research, the most common criticism I hear is that the presenter is making conclusions that go beyond what their data say. Many scientists develop a reflex to hedge their statements to what is well supported by data. – BobTheAverage Aug 24 '17 at 16:00

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