[Geysers] About Grotto, Giant, and water levels

[Gordon Bower]

I got a few days behind on emails, and didn't see this interesting discussion until after it had petered out. As long as I don't say the word "webcam," presumably noone will be too offended... 

Several comments, no particular order. 

1) Grotto's discharge.

Using one number to describe Grotto's discharge rate, and just multiplying by the length of the eruption, is not going to work.   The discharge rate in the late stages of a marathon is a tiny fraction of what it is in the first hour of the eruption. (Eyeballing it, I'd say maybe 1/4.) This, in my view, explains several of the interesting features of the interval-vs-preceding-duration curve for Grotto.

Marathons can go on (not quite, but compared to the range of durations most geysers show) indefinitely.  Each additional hour of marathon adds only 10 or 20 minutes to the length of the following quiet period: a 10-11 hour marathon might be followed by 10-11 hours of quiet, while a 14-hour marathon might be followed by 12.  Every so often one of the freak 18 or 20 or 24 hour ones would happen, without much noticeable change on things by the next day. (Note for the newer gazers: in the early and mid 90s most marathons were say 8 to 12 hours, the long ones we are hearing about all the time now were rare and newsworthy.)  

I interpret this to mean that the discharge seen in the late stages of a long marathon represents (a very tiny bit more than) the rate at which water enters the system whether Grotto is erupting or not.  The first Grotto start after a marathon is the only time the system is full to the brim with non-boiling water. That first eruption *pours* out water. The second short Grotto after a marathon almost always starts an hour or two "late" (compared to the prediction formula.) Subsequent short-mode eruptions tend to involve a steady progression toward less spectacular starts, and to starting on or a little "early" from the predicted time.

David Schwarz made some speculations about heat and water that are very similar to my own thoughts on the matter. To briefly restate: each short-mode eruption seems to throw out more water than is regained during a short-mode interval, and short-mode eruptions seem to end from lack of energy with the system not empty. Marathons happen once the system is sufficiently drained of water and has nothing to do with the heat except boil boil boil and throw a few droplets of water out the top. Maybe this winter I'll finish that unfinished article I was working on, some years ago, about a mathematical model for Grotto and for geysers where heat and water availability weren't exactly proportional.

As far as I am aware, noone has ever found a reliable method to identify whether a particular eruption will end or become a marathon, except to wait and see. That is, marathons don't seem to look any different at the start from a typical weak late-in-a-series short eruption, except for the fact they don't end.

2) Estimating the volume involved.

Marler's Inventory describes using a weir to measure 470 (not 670) gallons per minute in September 1959. Working backwards this same 470 figure is obviously how the "225,000 gallons in 8 hours" figure in the first edition of Scott's book was calculated. I don't recall whether Allen and Day ever put a weir in at Grotto or not... I do remember thinking, when I first read Allen and Day and they described their weir installations in general, that Grotto was an obvious candidate for measuring discharge, since the runoff channels are conveniently out of public sight as they approach the river.

Without really knowing what the 1959 eruptions looked like, I don't know whether this means our assumption should be "470 gpm, but 2000 gpm in the first hour", or "an average of 470, meaning 1000 at the start and maybe 250 by the end."

Marler's estimate of 750,000 to 1,000,000 gallons per eruption of Giant was, obviously, not done with weirs. (A quick back of the envelope estimate you can do: a long eruption of Old Faithful is 8,000 gallons; figure the duration is an hour instead of 5 minutes, and the vent is 6 feet across instead of 2; 8000x3x3x12=864,000, pretending the heights are somewhat similar and drop off similarly as the eruption progresses.) I am bothered a little bit by how high this figure is, considering that Steamboat's discharge past the USGS stream gaging station at Norris was reported to only be something around 250,000, since the same back-of-envelope calculation would lead me to estimate about a million for Steamboat too.

One thing that's not possible now because Giant is semi-continuously active, but WAS possible in the 80s and 90s, is to see how much Grotto eruption time was "missing." After the 10 July 1997 Giant, its first eruption in a month, for instance, a 10-hour marathon was followed by a 15-hour interval, and the next few Grottos were barely 1 hour along but still 6 hours apart. I had the feeling looking at Lew and Jan Johns's 1997 data that it took  something like 4 days for Grotto to return to 'full speed'. I didnt' try to calculate the volume of  the missing eruptions at the time.... I may have to go back and do that.

3) Room for all that water.

A million gallons of water takes up a lot of space. Does the ground around Giant 'breathe'? My suspicion is that it does.  I actually wrote a grant proposal in 2002 to buy three portable tiltmeters, to be deployed north, south, and west of Giant. I had a theoretical argument that a 4000-cubic-meter "pluton" under Giant ought to cause at least 10 microradians of tilt, and argued that I'd be able to tell from the tiltmeters whether the water was being 'stolen' from Grotto or 'lived' under Giant,  and whether the water-storage area was elongated NNW-SSE like the alignment of thermal features or was the classic 'blob' shape. It didn't get funded --- mostly because the University of Alaska Geophysical Institute where I worked would have preferred to see the field equipment deployed in Alaska year round rather than in Yellowstone. Would be fun to try again. 

4) Anything else that we could check?

My fuzzy memory says that there have been a number of occasions when a Grotto eruption that started during or shortly before Giant turned out to be a marathon, even though it was a day or two "too early" for a marathon to occur. If, in fact, the necessary condition to trigger a marathon IS a running-on-empty system, then, yes, it'd make sense that Giant might induce a premature marathon.

Someone mentioned the timing of the recovery hot periods vs. Grotto durations and time since ends of marathons.  I don't know if that'd turn up anything interesting or not. Wouldn't hurt to try. One thing that does come to mind is in the days of shorter marathons, first hot periods often occurred almost the same time as first Grotto starts, while it seems from reading the listserv that these days, with longer marathons followed by longer intervals, the recovery hot period is often some hours before the first Grotto.