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  • 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 621629.https://doi.org/10.1016/j.epsl.2017.11.015

    Funders: Leverhulme Trust, NERC, EPSRC

    https://doi.org/10.1016/j.epsl.2017.11.015
  • Gratuitous pictures of volcanoes

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

    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 worldsuper-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 worldsuper-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 worldsuper-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

    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

    i = mi+1

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

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

    P(mi ) = 1 exp(

    midF (m)

    )= 1 exp

    (

    kj=i

    j

    ) 1 expi i as 1 i i+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

    i = mi+1

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

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

    P(mi ) = 1 exp(

    midF (m)

    )= 1 exp

    (

    kj=i

    j

    ) 1 expi i as 1 i i+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

    i = mi+1

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

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

    P(mi ) = 1 exp(

    midF (m)

    )= 1 exp

    (

    kj=i

    j

    ) 1 expi i as 1 i i+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 12 ka 370 420 1200 680, 21008 45714 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 worlds 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

    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 worlds 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):735748.

    Pyle, D. (1995). Mass and energy budgets of explosive volcanic eruptions.Geophysical Research Letters, 22(5):563566.

    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, 482:621629.

    Sheldrake, T. and Caricchi, L. (2017). Regional variability in the frequency andmagnitude of large explosive volcanic eruptions. Geology, 45(2):111114.

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