‘Apocalyptic volcanic super eruption that couldDESTROY civilisation is much closer than we

thought, say experts’

Jonathan (Jonty) RougierSchool of Mathematics, University of Bristol

Southampton, Nov 2018

J.C. Rougier, R.S.J. Sparks, K.V. Cashman, and S.K. Brown, 2018, Theglobal magnitude-frequency relationship for large explosive volcaniceruptions, Earth and Planetary Science Letters, 482, pages 621–629.https://doi.org/10.1016/j.epsl.2017.11.015

Funders: Leverhulme Trust, NERC, EPSRC

Gratuitous pictures of volcanoes

Sakurajima, Japan. One of the world’s most active volcanoes.Source: https://www.hakaimagazine.com/sites/default/files/facebook-sakurajima.jpg

Gratuitous pictures of volcanoes

The Aira caldera. A magnitude 8.0 eruption about 28 ka ago.

A sense of scale

Magnitude is measured on the scale of Pyle (2000):

M = log10(ejected mass in kg)− 7.

So M = 4 is 100 Mt of mass, and M = 5 is 1 Gt, and so on.

M = 4 A problem for your region

M = 5 A problem for your country

M = 6 A problem for surrounding countries too

M = 7 A problem for your continent

M = 8 A problem for the whole world—super-eruption.

A sense of scale

Magnitude is measured on the scale of Pyle (2000):

M = log10(ejected mass in kg)− 7.

So M = 4 is 100 Mt of mass, and M = 5 is 1 Gt, and so on.

M = 4 A problem for your region

M = 5 A problem for your country

M = 6 A problem for surrounding countries too

M = 7 A problem for your continent

M = 8 A problem for the whole world—super-eruption.

A sense of scale

Magnitude is measured on the scale of Pyle (2000):

M = log10(ejected mass in kg)− 7.

So M = 4 is 100 Mt of mass, and M = 5 is 1 Gt, and so on.

M = 4 A problem for your region

M = 5 A problem for your country

M = 6 A problem for surrounding countries too

M = 7 A problem for your continent

M = 8 A problem for the whole world—super-eruption.

Problems with the recordTimes and magnitudes are inferred from geology: this is not easy!

Source: http://www.scielo.cl/fbpe/img/rgch/v31n2/img03-10.jpg

Problems with the record

Lots of ‘piling up’ at the integers (‘magnitude-rounding’)

(nb, log scale!)

Problems with the recordLots of under-recording

Problems with the recordRestrict attention to period where the recording probability is ≈ 1

Problems with the recordRestrict attention to period where the recording probability is ≈ 1

Estimating the magnitude/frequency curveSemi-empirical estimate of the global exceedance probability curvefor explosive volcanic eruptions. MLE and 95% confidence interval.

Estimating the magnitude/frequency curveFully parametric estimate of PEX, using Generalized Pareto distri-bution truncated at M = 9.3.

Estimating the magnitude/frequency curveFully parametric estimate of PEX, using Generalized Pareto distri-bution truncated at M = 9.3.

Mathematical interludeWhy can we overplot the probability of exceedance (PEX) curve withestimates of bin rates?

Let m1 < · · · < mk+1 =∞ be magnitude ‘fence-posts’. Under ourmarked Poisson process model, eruptions in bin [mi ,mi+1) have rate

µi = λ

∫ mi+1

mi

dF (m), i = 1, . . . , k,

per year. The probability of exceedance at M = mi is

P̄(mi ) = 1− exp(−λ∫ ∞

mi

dF (m))

= 1− exp(−

k∑j=i

µj

)≈ 1− exp−µi ≈ µi as 1� µi � µi+1.

So we can overplot the PEX curve with estimates of bin rates if we putthem at the lefthand end of the bin.

Mathematical interludeWhy can we overplot the probability of exceedance (PEX) curve withestimates of bin rates?Let m1 < · · · < mk+1 =∞ be magnitude ‘fence-posts’. Under ourmarked Poisson process model, eruptions in bin [mi ,mi+1) have rate

µi = λ

∫ mi+1

mi

dF (m), i = 1, . . . , k,

per year. The probability of exceedance at M = mi is

P̄(mi ) = 1− exp(−λ∫ ∞

mi

dF (m))

= 1− exp(−

k∑j=i

µj

)≈ 1− exp−µi ≈ µi as 1� µi � µi+1.

So we can overplot the PEX curve with estimates of bin rates if we putthem at the lefthand end of the bin.

Mathematical interludeWhy can we overplot the probability of exceedance (PEX) curve withestimates of bin rates?Let m1 < · · · < mk+1 =∞ be magnitude ‘fence-posts’. Under ourmarked Poisson process model, eruptions in bin [mi ,mi+1) have rate

µi = λ

∫ mi+1

mi

dF (m), i = 1, . . . , k,

per year. The probability of exceedance at M = mi is

P̄(mi ) = 1− exp(−λ∫ ∞

mi

dF (m))

= 1− exp(−

k∑j=i

µj

)≈ 1− exp−µi ≈ µi as 1� µi � µi+1.

So we can overplot the PEX curve with estimates of bin rates if we putthem at the lefthand end of the bin.

Estimating the magnitude/frequency curve

Return periodsM

agni

tude

(orV

EI)

Pyle

(199

5)

Mas

onet

al.(

2004

)

Sieb

ert

etal

.(20

10)

Deli

gne

etal

.(20

10)

Sheld

rake

and

Caric

chi(

2017

)

Us 95% CI5 8 10 8 6 14 11, 176 59 200 35 51 110 80, 1707 420 1–2 ka 370 420 1200 680, 21008 45–714 ka 17 ka 5.2 ka, 48 ka

What happened next?

What happened next?

What happened next?

What happened next?

What happened next?

Actually, there ARE some practical consequences

Actually, there ARE some practical consequences

1. National scale risk management

(A caricature:) If a volcanic super-eruption is going to wipe outmost of the world’s population in about 17 thousand years, thenwhy are we managing the risk of 100 fatalities at a UK nuclearfacility down to once every 10 million years?

https://upload.wikimedia.org/wikipedia/commons/d/df/Hinkley_Point_Nuclear_Power_Station.jpg

Actually, there ARE some practical consequences

2. Local risk management

Using our insights from modelling the global catalogue, we are nowmodelling all of the world’s dangerous volcanoes individually butsimultaneously, in order to produce regional risk maps showing theinteraction of hazardous volcanoes and populations. The followingmap for Indonesia is still a work in progress:

References

Deligne, N., Coles, S., and Sparks, R. (2010). Recurrence rates of large explosivevolcanic eruptions. Journal of Geophysical Research, 115:B06203.

Mason, B., Pyle, D., and Oppenheimer, C. (2004). The size and frequency of thelargest explosive eruptions on earth. Bulletin of Volcanology, 66(8):735–748.

Pyle, D. (1995). Mass and energy budgets of explosive volcanic eruptions.Geophysical Research Letters, 22(5):563–566.

Pyle, D. (2000). Sizes of volcanic eruptions. In Sigurdsson, H., Houghton, B.,McNutt, S., Rymer, H., and Stix, J., editors, Encyclopedia of Volcanoes. AcademicPress, London, UK.

Rougier, J., Sparks, R., Cashman, K., and Brown, S. K. (2018). The globalmagnitude-frequency relationship for large explosive volcanic eruptions. Earth andPlanetary Science Letters, 482:621–629.

Sheldrake, T. and Caricchi, L. (2017). Regional variability in the frequency andmagnitude of large explosive volcanic eruptions. Geology, 45(2):111–114.

Siebert, L., Simkin, T., and Kimberly, P. (2010). Volcanoes of the World. Universityof California Press, Berkeley and Los Angeles CA, USA, 3rd edition.