Lost Weekend…

Photograph from Wikipemedia Commons. Menengai Caldera in Kenya, one of the largest calderas on the planet.

How to kill a weekend.

As some of you have observed, last week I asked for anyone running across a caldera size and eruption volume to give me a quick shout here on the forums. Ostensibly, I was going to compile a spreadsheet in order to look at Hagstrum’s hotspot list compared to large caldera locations. Despite Carl’s disdain for the Antipode Impact idea, I think Hagstrum’s hotspot list is still pretty good, and it collates several other lists and weeds out some of the less than accepted ones.

While trudging through the calderas that were readily supplied, grabbing what info I could and trying to stay focused on DRE, the question of DRE again came up again in discussions. It wasn’t an actual argument or disagreement, but it did give me enough doubt in my data to seek other sources. Along the way, I found “Sulfur dioxide initiates global climate change in four ways” by Peter L. Ward. Well, to be truthful, I didn’t find that first, I found his table that supports his paper. I had to dig around to find the paper. I HIGHLY recommend the table. It is awesome. While the focus is on SO2 and climate change, they include the names of the tephra deposits that go with specific eruptions. Not all, but quite a few.

From his table, and with the re-worked VolcanoCafe user provided data, I came up with this (distraction#1) :

The first thing I would like to point out, is that it’s a log-log plot. The formula is a bit cantankerous to work with in Excel or on a calculator. (uses 10 raised to a power from a function that then has a logarithm in it.) The log-log plot was the only way to make it come out halfway usable. This formula was derived with DPlot, and in order to minimize the sigma fight (which I lost, quite readily) I left the individual points in place so that you can see just how far the estimate can be off. In one incarnation, I came up with the estimated value being within 0.77 of the actual value, 75% of the time. At this point I needed a beer and would continue later.

Moving back to the plot, and poking around in the text of the paper, I found that Professor Yukio Hayakawa of Gunma University (Japan) had compiled a list of large eruptions covering the last 2000 years. I had to go find that. Unfortunately, the list cuts off at 1999 with the eruption of Hudson in Chile. Distraction #2 involved updating the list with everything that happened since. While using his calculation of eruption magnitude, I decided to look back at how some of the calculations compared to fresher data from GVP. The paper uses M=log(m) -7, where m is the erupted mass in kg.

That’s actually a pretty handy formula. It sort of tracks with the VEI range, (but it’s not VEI, that’s different) Eyjafjallajökull comes in at 4.62, Merapi at 4.55, and Sarychev Peak at 5.04 when using GVP combined lava and tephra (DRE) volumes.

Photograph from Wikimedia Commons. The Somma caldera of Mt Aso in Japan.

I did find a problem with the data though… it wasn’t lining up with GVP info very well. In general, it was running 1.13 times the Hayakawa data when redone with GVP info. Then I ran into the problem of GVP not having anything more than a guesstimate for the VEI of some of the volcanoes with no tephra or magma volumes listed. (and these were pretty recent eruptions) Since Hayakawa used a lower cutoff of M=3.8, anything less than a VEI-4 would not get that high. (VEI=3 yeilds an M of 3.43). Ehh… give up and go find something to gnaw on. I did find out that my stepson had retribution against the Pelicans. I had skipped the King Mackerel fishing since I was “in the groove” with the data. The bait fish they were using had a tendency to attract the Pelicans attention but was so swift that it would be gone by the time the bird got to it.

Referring to Carl’s “Did you notice the erupting Supervolcano?” post, you will note that in the reference, it doesn’t state what the size of the Tondano Caldera eruption was. Being focused primarily on the geothermal energy capability of the system, that is understandable. Using the outline from Figure 5 of the paper, and applying our handy formula, we can get a ballpark estimate of how much “stuff” was involved. At roughly 30km by 9km, it comes in at 197km³… give or take. Solid VEI-7, but the calculation has a sigma of 351km³ so it could quite easily have been large enough to be withing spitting distance of VEI-8. (900km³ is within 2 sigma, and VEI-8 is 1000km³) 

[Editors remark (Carl): I actually was a bit more devious than that. For this caldera I have a bit more data. Through drill core samples I know how much of the caldera is infilled with original ash and later ash. That gave me the actual depth of the original caldera bottom. One should recognize the difference between a subsided caldera and a blow out large caldera event. The first one gently drops with lost material, the other ejects more material due to explosion, in this case when the ocean hit the magma inside the magma chamber. I then calculated the amount of DRE by size. To get a low enough number I did not assume that there was anything ontop, ie. that the volcano was flat with the surrounding landscape. I then got a 918 km^3 of ejected DRE. Size is not everything as I discovered, depth is equally important. Add a couple of the known active volcanoes before the large caldera event and you are comfortably at the 1000 cubic range for a comparatively small caldera. I then did a sanity check against known ash depths for the layer across distance, and fount it to be within the ballpark.]

Okay, back to the data. In 2009, Deligne, Coles, and Sparks put out a paper entitled “Recurrence rates of large explosive volcanic eruptions”. Yet another kick arse piece of work. In it, they use Extreme Value Theory to attack the problem of recurrence rates of large eruptions. Now that is something that I can appreciate. Extreme Value Theory deals with the failings of the Gaussian curve… out there in the tail, the realm of the infamous Black Swan that I am always yammering about exists. I have to go back and read that paper. Anyway, they mentioned Hayakawa’s list, and then using those methods, took the list back to the last 10000 years. Hmm… what can we do with that? I have the Greenland Temperature from the ice core data available, so I plotted it. It didn’t look that interesting until I ran an integral of the M value, then detrended it. That brings out the relative change in the sum that is going on without the actual data trend obscuring it. Plotted against the temperature, it look… “interesting”

There are a couple of peaks that seem coincidental, but for the most part, not a flipping thing there. I found it interesting that there was a peak in activity about 3527 BC and over all, volcanic activity has been declining ever since. I don’t know why that is. That’s just what it looks like. Being a glutton for punishment, and since it was “just sitting there,” I ran a couple of correlation routines on it to see if anything was present, but not obvious. Pearon’s correlation coefficient of 0.0111. Okay, I didn’t really expect a linear correlation. Spearman’s rho is supposed to be able to detect non-linear relationships, and I expected a higher score. I got 0.0017. What? It’s worse? “Wow.”

I have, on this computer, a program called “Formulize” by Eureqa. It’s free, unless you want to use a server farm. You can set it up and run it on your on PC and it will churn through whatever data you feed it and try to find a formula that relates the data sets. It’s the ultimate “beat the data with a stick” program. It can yield garbage… (generally if you feed it garbage) but it’s pretty good at coming up with something. So, I turned it loose. It turns out, that if you have a delay of 1405 days, it can roughly predict the temperature in Greenland from the running detrended integral of the Volcanic activity with a correlation coefficient of 0.7177. (Actually pretty good considering where we started out from) I calculated a sigma for the function based on what the formula predicted and what the actual data was.

That… was distraction 3.

What’s it all mean? Beats me. Greenland is just one point on the globe. There seems to be a 1405 and 1422 day delay relationship in the data, or about 3.8 years. Formulize also ground on a 4.13 and 4.44 year offset for a while. It was quite fun watching it dance back and forth with the delay. Make of it what you will.

And now the all important caveat: I am not a Geologist or trained in any of the fields that have been touched on in this post. My specialty is electronics and cross correlating threats… if you must know. (such as the 230 knot Shvall torpedo tested by Iran having been designed for 533mm torpedo tubes postulated as a design criteria… and the the Kilo class sub launched from Bandar Abass last week or so, having six 533 mm tubes. And that’s all from published data in various sources on the web.) But.. I don’t do that anymore. Volcanoes will have to do.

What to take away from this post, something that can be used by my fellow volcanophiles, is the first plot. You can find a hole in the ground in Google Earth and do a ballpark estimate of how much material may have come out of it when it initially formed. Remember that it may not have all happened at once.

Several thousand years of activity can produce the same effect.

Enjoy!

GEOLURKING

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Sulfur dioxide initiates global climate change in four ways – Ward (2009)
http://tetontectonics.org/Climate/SO2InitiatesClimateChange.pdf
And the table:
http://www.tetontectonics.org/Climate/Ward2009TableS1.pdf

Hayakawa Paleovolcanology Laboratory
http://www.edu.gunma-u.ac.jp/~hayakawa/English.html

Recurrence rates of large explosive volcanic eruptions – Deligne, Coles, and Sparks (2010)
http://www.globalvolcanomodel.org/documents/Deligne%20et%20al%20(2010).pdf
Data Set
ftp://ftp.agu.org/apend/jb/2009jb006554/2009jb006554-ds01.pdf