I grew up hating math. Detesting it’s very existence with an unbridled passion that knew no bounds. I was like this all through school… until Junior and Senior years. Those years, our new Principal, Mr Pendergast, put together a couple of courses to prepare us for what we may run into if any of us ever got up the gumption to try college. In retrospect, I think what he was doing was a last ditch effort to help some of the more idiot minded, such as myself, get up to a point to where at least our eyes didn’t glaze over when we ran into it. What Mr. Pendergast taught us was “Analytic Geometry.” About halfway through that course, I came to the realization that there was actually a useful purpose in moving numbers around on paper. If you did it right, it could actually tell you things that you didn’t know, such as where the collective debris ball from a car collision would wind up at. (which direction it would go). I never did get very far in college, managing to drop out and join the military. At the time I dropped out, I had a horrendous GPA. The only two classes that I managed to get decent grades in were Psychology and Calculus. A pretty odd combination of skill sets. After doing 20 years in the Navy, I found interesting uses for math, such as component failure rates and managing to sort of predict what spares I would need to have on hand when we deployed. Getting tasked with attending quality control inspector classes for a shipyard period that we were on allowed me some exposure to statistical analysis and the world of Dr Deming. Deming is one of the reasons that Japanese automakers were able to overcome some manufacturing issues that they were having. I rank Dr Deming’s work up there with the likes of William Sealy Gosset. Where Dr Deming brought us Japanese autos that were not lemons, Gosset’s work gave us consistent tasting beer. Gosset worked for Arthur Guinness & Son. In order to prevent loss of trade secrets, Guinness would not allow Gosset to publish any of his work under his own name, but they did allow him to use the pseudonym of “Student” in his published material.
Now, why this article? Simple really. Following my Rumerian “The Crapshoot” article, and Albert’s “Once in a Blue Moon” article, it seemed appropriate to tie them in. Only this time, I’ll drag a volcano along for the ride.
As frequent readers know, I have a thing for “Black Swans.” Not the actual events, but just sitting in amazement and awe at the phenomena. Preferably before they play out, but while they happen is just as good. I’ve written about the 2011 Tohoku quake and tsunami and lamented how preparing for something that remote in probability is hard to sell to the investors. Recently, a perceived potential Black Swan made the news as millions of terrified New Yorkers huddled down and braced for a storm that delivered an epic four inches of snow. For the most part, this was caused by a media that literally ate up the warnings from the Mayor… who actually believed forecast that the weather guessers told him. If you look at the historical record of New York’s “massive” snow storms, and then look at what they were claiming was coming at them, it would have been a one in one point five million sort of event. Yeah, that would have been epic… only it wasn’t. Do note that the overall region did get a sizable snowfall… just not where they predicted that it was going to occur. I have a feeling that like volcanoes, snowstorms don’t really care about statistics either. They do what the prevailing conditions dictate, no matter how hard anybody wants it be how they think it should. This is a key thing that you really really need to remember whenever anyone starts spouting off terms like “overdue” for an eruption. Volcanoes just don’t give a rat’s patootie what so ever. There is always something there that wasn’t taken into consideration or evaluated.
Before I forget to mention it… according to Google’s calculator gizmo, one in a blue moon is 1.16699016 × 10-8 hertz. Taking the reciprocal you get 85,690,525… so by their calculations, a “one in 85,690,525” event is a once in a blue moon fit. This is based off of the “number of full moons in a season” definition. But, one in 85,690,525 roughly equates to a roughly 5.6 standard deviation event. That’s in the realm of Black Swans, so “nyah!”
Okay, time to pick on a volcano. Back before I realized just how little volcanoes cared about stats, I took a look at Hekla’s repose intervals. Using the Global Volcano Program’s listing of known eruptions, I get this.
Notice that as the years crawl by, the probability of having had an eruption start to climb. On the right hand side is the probability that hekla would have erupted by that year. Seems pretty straight forward, but it’s not. It only uses data back to the 1104 eruption, and Hekla is far older than that. There is a lot of Hekla’s history that is just not represented by the available data. Another insidious thing is that Hekla is not a generic run of the mill volcano. It doesn’t follow the same sheet of music that other more well known volcanoes do. Hekla is technically, an overgrown fissure cone row. Sure, it has the mass of a stratovolcano, but that is not how it was formed, and not how it operates. Tectonic stresses do just as much to govern Hekla’s action as does magma chamber pressure. That’s the reason IMO has strainmeters monitoring Hekla. Watching those and you may get an indication before it erupts… if you know what to look for. For Hekla 2000, the Burfell strainmeter took a serious dive and someone happened to notice. Seismically, absolutely nothing happened until about an hour before it went. The characteristic was due to the fissure line that makes up Hekla opening up. When the quakes did start to occur, they were only detectable by instruments. In fact, the quakes did not cross into the realm of human perception until about 15 minutes before the actual eruption. That would have been a really bad place to be standing.
One item that has come up in discussion on the forum, is that the size of Hekla’s eruptions are strongly dependant on the length of repose time. That’s not a bad statement, and it is supported by the records over at GVP.
The linear curve (it’s a line) has a correlation coefficient of about 0.56. Not a strong fit, but it does show some merit. I imagine that if we had access to actual volume data, it would be somewhat better. The “3.5” point is an artificial point. It was used to fill a gap in the data so that the repose interval data would not have a massive break halfway through the listing. “3.5” was an average data value. Little stunts like that are what some people do to get the formulas to work. Where it bites you is when you don’t consider how the data was massaged in order to get it to work. Media people tend to gloss over stuff like that, even though it is quite important to note it because that could throw the whole analysis approach completely off. I did it to make it work and to illustrate that point.
Will Hekla erupt? Well, yeah, eventually. When it’s good and ready. The tectonic stress changes that caused Bardabunga to erupt out at Holuhraun could become manifest around Hekla, and if she has the pressure, she might erupt. Several months ago, I tracked a wad of magma via GPS data that mysteriously took off to the Southeast and disappeared somewhere under the plains out there. I have no idea what that was about, but it was pretty wild seeing the GPS illustrate it so well.
This is”the lump” when it moved/slid out from under Hekla over a year ago. Dunno where it eventually went. Red is uplift, blue is down. GPS data is interpreted from IMO plots and represented by a poly sheet overlying a Google 3D image of the area.