Old Faithful, the iconic American geyser, is also a statistician's delight. Its eruption can be predicted only based on the length of the previous eruption, and Old Faithful's eruption durations are bimodal. That means that there are two distinct eruption durations. The range can be from about 70 minutes to about 100 minutes, plus or minus 10 minutes on either side. The longer the previous eruption, the longer the interval, possibly because it takes longer for the underground chambers to refill after a longer eruption.
Park rangers at the Old Faithful visitor center time the duration of the eruptions, and Ranger Rita Garcia explained the process to me. There are numerous pre-eruptions, all timed, but the eruption itself doesn't begin until the height of the spray is sustained at 15-20 feet. The ranger notes the start time, height, and duration of the eruption. There are detailed records going back 40 years, and archival but less detailed records before that. Old Faithful's eruptions are "unusually regular." Though we don't know for sure (it's too hot!) the belief is that Old Faithful has its own water reservoir, one that is low in silica for a geyser. But no one knows for sure. (That's OK - we may yet figure it out. You can see my review of Samuel Arbesman's book "The Half-Life of Facts, which explains why technical and scientific progress occur at fixed rates, here.)
You might be wondering how the rangers measure the height of the eruption. The visitor center, which you can see in the background of the picture above, is below the grade of Old Faithful. And it's not as if there's a helpful measuring stick next to the geyser. But look at the picture below.
You can see what's happening now using the National Park Service's Old Faithful webcam here. And there's a good explanation of why geysers erupt here. And here is a link to the Geyser Observation and Study Association if you want to learn more.
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