Is The Forecasting Of The Eruption Of The Yellowstone Supervolcano
Possible?
Robert B. Trombley,
Ph.D.
Southwest Volcano Research Centre, 3405 S. Tomahawk Rd.,
Suite # 31, Apache Junction, Arizona USA 85219-9169
(swvrc@usa.net)
Abstract
The term “supervolcano” has no specifically defined scientific meaning. It was used by the producers of a British TV programme in 2000 to refer to volcanoes that have generated Earth's largest volcanic eruptions. As such, a supervolcano would be one that has produced an exceedingly large, catastrophic explosive eruption and a giant caldera. Because Yellowstone has produced three such very large caldera-forming explosive eruptions in the past 2.1 million years, the producers considered it to be a supervolcano.
Because there is no well-defined minimum size for a
"supervolcano," there is no exact number of such volcanoes. Examples of volcanoes that produced
exceedingly voluminous pyroclastic eruptions and formed large calderas in the
past 2 million years would include Yellowstone, Long Valley in eastern
California, Toba in Indonesia, and Taupo in New Zealand. The forecasting of eruptions of this
type of volcano presents extremely difficult and interesting new problems for
the volcanologist to solve.
Introduction:
Some 640,000 years ago the rumblings of an impending volcanic eruption sounded ominously across the Yellowstone country. Suddenly, in a mighty crescendo of deafening explosions, tremendous quantities of hot volcanic ash and pumice spewed from giant cracks at the earth's surface. Towering dust clouds blackened the sky, and vast sheets of volcanic debris spread out rapidly across the countryside in all directions, covering thousands of square miles in a matter of minutes with a blanket of utter devastation. Abruptly, a great smoldering caldera 30 miles across, 45 miles long, and several thousand feet deep - appeared in the central Yellowstone region, the ground having fallen into the huge underground cavern that was left by the earth shaking eruptions. Lava then began oozing from the cracks to fill the still smoking caldera. The third known supervolcano eruption of Yellowstone had occurred. The first two occurred 2 million and 1.2 million years ago. This frequency suggests a recurrence rate of one eruption approximately every 600,000 years. When Yellowstone erupts again, if it does, poses not only a general problem with forecasting but also a possible global threatening crisis. This paper will explore some of the problems with the long range forecasting of such a catastrophic eruption.
The Scenario:
Yellowstone is America's first and most famous National Park. Every year over 3 million tourists visit this stunning wilderness, but beneath its hot springs and lush forests lies a monster of which most of the public is completely unaware [Smith, 1980].
Most people's idea of a volcano is a symmetrical cone and this involves magma coming up, reaching the surface, being extruded either as lava or as explosive eruptions with ash, and these layers of ash and lava gradually accumulate until you're left with a classic cone shape. We volcanologists know this smooth flowing magma contains huge quantities of volcanic gases, like carbon dioxide and sulfur dioxide. Because this magma is so liquid these gases bubble to the surface, easily escaping. There are thousands of these normal volcanoes throughout the world. Around 50 erupt every year, but supervolcanoes are very different in almost every way.
First, they look different.
Rather than being volcanic mountains, supervolcanoes form depressions in the
ground. Despite never having seen a supervolcano erupt, by studying the
surrounding rock scientists have been able to piece together how supervolcanoes
are formed. Like normal volcanoes they begin when a column of magma rises from
deep within the Earth. Under certain conditions, rather than breaking through
the surface, the magma pools and melts the Earth's crust turning the rock
itself into more thick magma.
Although it is not clearly
understood why, but in the case of supervolcanoes a vast reservoir of molten
rock eventually forms. The magma here is so thick and viscous that it traps the
volcanic gases building up colossal pressures over thousands of years. When the
magma chamber eventually does erupt its blast is hundreds of times more
powerful than normal draining the underground reservoir. This causes the roof
of this chamber to collapse forming an enormous crater. All supervolcano
eruptions form these subsided craters. They are called calderas.
Such is the case with
Yellowstone – it is the largest single active system yet discovered. Figure 1
below shows the Yellowstone-Teton
Geologic System.
Figure 1. Yellowstone-Teton Geologic System
There are currently 23 permanent seismographs that are spread across the Park. They detect the sound waves which come from earthquakes deep underground. These waves travel at different speeds depending on the texture of what they pass through. Sound waves passing through solid rock go faster than those travelling through molten rock or magma. By measuring the time they take to reach the seismographs one can tell what they've passed through. Eventually this builds up a picture of what lies beneath Yellowstone. Figure 2, below, illustrates the location of the current seismometers around the Yellowstone system.
Figure 2. The current seismometers around Yellowstone.
The magma chamber that was found extends basically beneath the entire caldera. It is approximately 40-50 kilometres long, approximately 20 kilometres wide and it has a thickness of about 10 kilometres. So it's a giant in volume and essentially encompasses a half or a third of the area beneath Yellowstone National Park.
The Problem:
Conventional eruption
forecasting of “normal” volcanoes is difficult enough. The forecasting of supervolcanoes
presents even more difficult problems.
Eruption forecasting has made some progress with the advent of the
software package, Eruption Pro 10.3, [Trombley, 2002] and its ability to
correctly forecast conventional volcanoes eruptions. The current goal of forecasting volcanic eruptions is to
provide the best forecasts possible based on the geologic history of the
volcano under study as well as on the day-to-day vitals signs of the volcano in
terms of earthquakes, surface deformation, temperature, gas emissions, and
other measurements. While all of
these characteristic vital signs would also apply to supervolcanoes, there are
other problems that arise.
The eruption of a
conventional volcano is not considered a rare
event albeit that some volcanoes erupt rarely. In terms of supervolcanoes, eruptions are extremely rare events. With respect to rare event statistics,
if we consider a rare event, E ,
with a probability of 1/n where n is a “large” number, we do not expect
the event (eruption) to occur in a single trial (year), i.e., we are surprised
if it does [Meyers, 1990].
However, in a sequence of trials, the chance of an eruption occurring
becomes more likely.
The question at hand
becomes, What is the probability of E
occurring at lease once in n trials
? (1 – 1/n)n is the
probability that E does not occur at
all.
\ Pr(E
once or more) = 1
- [ 1 -
1/n]n (1)
But if n is large,
1 - (1/n)n ~ e-1 (2)
\
Pr(E once or
more) @ 1 -
e-1 = 0.63
If one considers one version
of Chauvenet’s criterion, which is to throw away and event whose probability of
occurrence is < ˝ n.
The probability of a legitimate occurrence in n trials of an event whose probability is 1/2n is
1
- [ 1 – (1/2n)]n
= 1 - { [1 – (1/2n)]2n }1/2
(3)
@ 1 -
e-1/2 for
n large
= 1
- 0.606 =
0.39
The reader should judge for himself or herself if the straight forward application of the criterion is wise. Probably not ! Therefore, we can conclude that conventional rare event statistics will not work with supervolcanoes.
Other Techniques:
Conventional techniques such as those currently used by SWVRC’s Eruption Pro 10.3, are also inadequate to properly forecast the eruption of the Yellowstone caldera. The primary reason is that we do not have a history of the volcanoes previous eruptions. Only the current seismicity and deformation parameters can be input to the software programme. This provides an inadequate set of input parameters in order for the programme to properly forecast.
Another probability
distribution that may be considered is the negative binomial distribution
function. The negative binomial
distribution is used when the number of successes is fixed (in this case 3
since there have been two known eruptions to date) and we’re interested in the
number of failures before reaching the fixed number of successes.
In this case, we now suppose
that the trials are continued until the event has occurred exactly r times. We want to determine the probability, Pr(N = n), that this
will require exactly n trials where N is the number of trials.
Pr(N-n) =
Pr{[(r – 1) events in the first trial (n – 1) trials] and one event on the nth trial)}
=
Pr{(r – 1) events in (n – 1) trails}Pr{1 on nth}
= (n-1)C(r-1)
p(r-1) q(n-r)
= bneg(n)
(4)
\ bneg(n) = (n-1)C(r-1)
p(r-1) q(n-r),
n = r, r+1, …….. (5)
where,
p =
probability of success &
q = 1 – p = probability of failure
This
distribution is called the negative binomial since the probabilities may be
obtained from successive terms of the expansion of a negative binomial, for
example,
∞
S (n-1)C(r-1)
pr qn-r
= pr (1 – q)-r
n=r
Which may be written = (Q – P)-r
where Q = 1/p , P = q/p, and Q – P = (1/p)(1-q) = 1
We may rewrite bneg(n)
by substituting s
= n – r whence
Pr(s) = (r+s-1)C(r-1) pr qs (6)
In the case of Yellowstone, with r = 3, p = 1.67E-06, and x = 640,000 then this calculates
out to a .99999967 probability of failure from year to year at this time.
The Consequences:
Supervolcanoes are eruptions and explosions of catastrophic
proportions. These types of
eruptions are absolutely apocalyptic in scale. It is difficult to imagine an eruption this tremendous. The main factor governing the size of
this type of eruption of the amount of magma available. If an enormous amount of magma has
accumulated in the crust, then you have the potential for a very , very large
eruption.
The exact
geological conditions needed to create a vast magma chamber exist in only a
very few places on earth, so there are only a few known supervolcanoes in the
world. The last one to erupt was
Toba 74,000 years ago [Rampino, Self, 2000). No modern human has ever witnessed a supervolcano eruption. Volcanologists are not even sure where
all the supervolcanoes are but one that is known is Yellowstone National
Park.
When Yellowstone
goes off again, and it will, it will be a disaster for the United States and
eventually, for the whole world.
We volcanologists believe it would all begin with the magma chamber
becoming unstable. Observations
would begin by seeing bigger earthquakes, greater uplifting as magma intrudes
and gets nearer and nearer the surface.
An earthquake may send a rupture through a brittle layer similar to
breaking the lid off a pressure cooker.
This would generate sheets of magma, which will perhaps rise up to 30,
40 or 50 kilometers sending gigantic amounts of debris into the
atmosphere. Pyroclastic flows
would cover the whole region, killing tens of thousands of people in the
surrounding area.
The ash carried
in the atmosphere and deposited over vast areas of the United States would have
devastating effects. A plume of
material that goes up into the atmosphere, globally, from the eruption would
produce the climatic effects. This
would spread worldwide and have a cooling effect that would most likely destroy
the growing season on a global scale.
As Dr. Ted Nield, of the Geological
Society of London, stated once, “When a
supervolcano goes off, it is an order of magnitude greater than a normal
eruption. It produces energy
equivalent to an impact with a comet or an asteroid.” “You can try diverting an asteroid, but there is nothing at
all you can do about a supervolcano.”
The eruption will throw out cubic kilometers of rock, ash,
dust, sulfur dioxide and so on into the upper atmosphere, where it will reflect
incoming solar radiation, forcing down temperatures on the earth’s
surface. It would be the
equivalent of a nuclear winter.
The effects would last for four or five years with crops failing and the
whole ecosystem breaking down.
Current Monitoring:
There are currently 23 seismic monitoring stations about Yellowstone and the site has been examined on a number of occasions for deformation progress/decline.
Yellowstone Park had last
been surveyed in the 1920s when the elevation, the height above sea-level, was
measured at various points across Yellowstone. 50 years later, Dr. R. B. Smith surveyed the same
points. Smith stated “ The idea was to survey their elevations and
to compare the elevations in the mid-70s to what they were in 1923 and the type
of thing that we did is to make recordings at a precision level of a few
millimetres.” The two
sets of figures should have been similar, but as the survey team moved across
the Park, they noticed something unexpected: the ground seemed to be heaving
upwards. The results of the
survey indicated that this caldera has uplifted at that time 740 millimetres in
the middle of the caldera. As the
measuring continued, it became apparent that the ground beneath the north of
Yellowstone was bulging up, tilting the rest of the Yellowstone Park downwards
(see Figure 3 below.) As we venture into the 21st
century, once again the Yellowstone caldera appears to be on the uplift swing
of the cycle.
Figure 3. Caldera
uplifting/subsidence and associated earthquake phenomenae.
Things To Look For In Monitoring:
We volcanologists believe that the eruption of the Yellowstone caldera would all start with the magma chamber becoming unstable. As previously mentioned, one would probably start seeing bigger earthquakes, also you may see parts of Yellowstone uplifting as magma intrudes and gets nearer and nearer the surface. And maybe an earthquake sends a rupture through the brittle layer, as if you've broken the lid of the pressure cooker. This would generate sheets of magma which, will be probably rising up to 30, 40, 50 kilometres sending gigantic amounts of debris into the atmosphere.
Conclusions:
The only reasonable
conclusion that one can come to in studying the current Yellowstone caldera
environment is that there is no current way to reasonably and accurately forecast
the eruption of the Yellowstone caldera. There has been no eruption of a supervolcano
in recent times and although scientists have never witnessed a supervolcano
eruption, they can calculate how large they are. There is no recorded data available on
the last eruption of Yellowstone, or any other supervolcanoes (e.g., Toba)
for that matter. This writer
agrees with the observation of colleague Dr. Michael Rampino, “It’s
really not a question of if it’ll go off, it’s a question of when because
sooner or later one of these large super eruptions will happen.”
REFERENCES
1 Smith, R.B., and Christiansen, R.L.,
1980, “Yellowstone Park as a window on
the Earth's interior”: Scientific American, volume 242, pages 104-117.
2 Trombley, R. B., & Toutain, J. P., 2002, “Eruption Pro 10.3 – The New & Improved
Long-Range Eruption Forecasting Software "
“, paper
to be presented
at the 16th Caribbean
Geological Conference, 16 June - 21 June 2002, Bridgetown, Barbados.
3 Meyer, S.L., 1975, “Data Analysis For Scientists And Engineers”, John Wiley & Sons, Inc., Pg. 189
& Pg. 283
4
Smith, R.B., and
Braile, L.W., 1994, “The Yellowstone hotspot”:
Journal of Volcanology and Geothermal Research, v. 61, pages 121-187.
5
Rampino, M. R.,
and Self, S., 2000, “Encyclopedia of Volcanoes, Volcanism And Biotic Extinctions”,
Pgs. 1090-1091
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