The answer is complicated, but in a sentence, Yellowstone sits on top of a volcanic hot spot that enjoys blowing up in a "supereruption" every few hundreds of thousands of years, but in the meantime, keeps itself fit by spewing geysers, unleashing thousands of earthquakes, and triggering hydrothermal explosions.
Those supereruptions occurred 2.1 million, 1.3 million, and 640,000 years ago. Do some simple math, and you realize that we are approaching time for another one of these eruptions if the pattern of previous eruptions holds. So let's look at three things: (1) What warning systems do we have? (2) How likely is it that Yellowstone will explode, and will the warning systems catch it? and (3) What will happen if it does?
So. Warning Systems. In this respect, Yellowstone has the best in the world. It is classified by the US Geologic Survey (USGS) as a high-risk area, and is being studied by numerous universities and research organizations. It is watched by thousands of seismometers, sensor arrays, GPS devices, and satellites for any slight change. If you are the paranoid type, just go to any of dozens of Yellowstone monitoring sites, and you will get your fill of self-perpetuated fear.
Second. Likeliness. Looking at earthquake activities, Yellowstone hasn't changed much in recorded history. Every so often, there is an "earthquake swarm," in which hundreds of small earthquakes happen in a matter of days or weeks. This happens every dozen or two years, but the one in late 2008 caught national attention, as it was one of the most powerful swarms ever recorded. This swarm was also combined with a relatively meteoric rise of the Yellowstone Caldera over the past three years--three inches per year, more than three times the maximally recorded rate of growth since measurements began in the 20s. However, all these events are normal, and can be explained away by any of a number of reasons--hydrothermal pressure from underground lakes affected by earthquakes, geothermal effects, etc.
So what if it explodes. Well, we are all doomed. The last eruption covered most of North America in up to a foot of ash, and dramatically changed global temperatures. There were mass local continental extinctions, and the direct effects of the explosion leveled most of what today is Wyoming, Montana, and Utah. Earthquakes of extreme magnitudes would be felt all across the world, and would destroy most buildings in North America. It's not likely that such a quake will strike, but if it does, let's just say we're in a great place to help rebuild the community afterwards.
Finally, rather than worry about the Yellowstone Caldera, perhaps a greater threat is the Long Valley Caldera, right here in California. In its last eruption, it spewed 600 cubic kilometers of rubble across the US, and very recently, there were some 6+ magnitude earthquakes coming from around there. Mounts St. Helens, Rainier, Hood, and Shasta are all close to home, and they happen to be 2, 3, 4, and 5 on the USGS's list of the most dangerous volcanic centers in the United States. Yellowstone, on the other hand, is number 21.
Maybe I should think twice now before scaling Rainer or Shasta, and tempt fate in Yellowstone instead.
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