Calculating Catastrophe

Gordon Woo

• Publisher: ICP
• Year: 2011
• ISBN:
  9781848168930
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Watch a video interview with Gordon Woo

Book Launch of Calculating Catastrophe

Calculating Catastrophe has been written to explain, to a general readership, the underlying philosophical ideas and scientific principles that govern catastrophic events, both natural and man-made. Knowledge of the broad range of catastrophes deepens understanding of individual modes of disaster. This book will be of interest to anyone aspiring to understand catastrophes better, but will be of particular value to those engaged in public and corporate policy, and the financial markets.

The author, Dr. Gordon Woo, was trained in mathematical physics at Cambridge, MIT and Harvard, and has made his career as a calculator of catastrophes. His diverse experience includes consulting for IAEA on the seismic safety of nuclear plants and for BP on offshore oil well drilling. As a catastrophist at Risk Management Solutions, he has advanced the insurance modelling of catastrophes, including designing a model for terrorism risk.

Contents:

• Natural Hazards:
  • Causation and Association
  • Extra-Terrestrial Hazards
  • Meteorological Hazards
  • Geological Hazards
  • Geomorphic Hazards
  • Hydrological Hazards
• Societal Hazards:
  • Political Violence
  • Infectious Disease Pandemics
  • Industrial and Transportation Accidents
  • Fraud Catastrophe
• A Sense of Scale:
  • Size Scales of Natural Hazards
  • Hazard Spatial Scales
  • The Human Disaster Toll
  • Models of a Fractal World
• A Measure of Uncertainty:
  • The Concept of Probability
  • The Meaning of Uncertainty
  • Aleatory and Epistemic Uncertainty
  • Probability Ambiguity
  • The Weighing of Evidence
• A Matter of Time:
  • Temporal Models of Hazards
  • Long-Term Data Records
  • Statistics of Extremes
• Catastrophe Complexity:
  • Emergent Catastrophes
  • Financial Crashes
  • Ancillary Hazards
• Terrorism:
  • A Thinking Man's Game
  • Defeating Terrorist Networks
  • Counter-Radicalization
• Forecasting:
  • Earthquake Forecasting
  • Verification
  • River Flows and Sea Waves
  • Accelerating Approach to Criticality
  • Evidence-Based Diagnosis
• Disaster Warning:
  • Decision in the Balance
  • Evacuation
  • The Wisdom of Experts
• Disaster Scenarios:
  • Scenario Simulation
  • Footprints and Vulnerability
  • Fermi Problems
• Catastrophe Cover:
  • Probable Maximum Loss
  • Coherent Risk Measures
  • The Samaritan's Dilemma
• Catastrophe Risk Securitization:
  • Catastrophe Bonds
  • The Price of Innovation
• Risk Horizons:
  • Ecological Catastrophe
  • Climate Change
  • War and Conflict Resolution

Readership: Applied mathematicians, earth and atmospheric scientists, civil engineers, geographers, economists and general public.

Chapter 1

Natural Hazards

I would find it easier to believe that
two Yankee professors would lie than
that stones should fall from the sky.
President Thomas Jefferson

‘There is no crash at the moment, only a slight premonitory movement of the ground under our feet.’ The context of this warning was a mid-19th century crisis in England; not a seismic one, although tremors are felt from time to time, but one involving the Bank of England, soon after it assumed the responsibilities and liabilities of a central bank. Metaphors from the landscape of natural hazards, such as seismic shock, storm, tsunami, and tidal wave, are commonly used to describe man-made catastrophes such as financial crashes and political violence. This is not mere linguistic hyperbole; there are common roots in their calculational framework which make a knowledge of natural hazards relevant for those aspiring to deepen their understanding of man-made hazards, and to lessen the degree of surprise they may cause.

One of the most insidious aspects of natural hazards is the protracted timescale of hundreds of thousands of years over which they occur. Collective memory of a natural disaster, such as an earthquake, tends to fade into amnesia after several generations of seismic quiescence. No wonder that a fatality from an earthquake on a fault that last ruptured during the Ice Age should seem as incredible as a victim of a woolly mammoth. There are many arcane geological hazard phenomena which would meet with similar incredulity and awe were they to recur in our own time, save for evidence of their occurrence preserved for posterity in the geological record.

The path to comprehending natural hazards has been arduous, not least because such events are not well suited to laboratory study. All natural hazards are macroscopic phenomena, governed fundamentally by the laws of classical physics which were known in the 19th century. Although the laws of physics are sufficiently concise and elegant as to fill a large tablature of mathematics, the emergence of complex spatial structures cannot be explained so succinctly, if indeed sufficient observations exist to permit quantitative explanation. Writing down large sets of nonlinear equations is one matter, solving them is another.

Yet hard problems do have solutions. Among these are physical situations where microscopic fluctuations do not average out over larger scales, but persist out to macroscopic wavelengths. A breakthrough in the understanding of such phenomena was made by the theoretical physicist Ken Wilson, whose Nobel prize-winning ideas of the renormalization group centred on modelling the dynamical effects of scale changes,¹ and whose early and opportunist use of computers allowed him to overcome major technical obstacles in replicating calculations at different scales. Experimental evidence suggests a strong analogy between the equilibrium phase transitions studied by Wilson and the statistical behaviour of types of turbulent flow.²

A fundamental understanding of fluid turbulence is not only needed for windstorm research, but corresponding ideas from statistical physics hold promise in furthering the understanding of earthquakes and volcanic eruptions. Strands of seismological evidence support the view that, prior to a major earthquake, a critical state may be approached where one part of the system can affect many others, with the consequence that minor perturbations may lead to cascade-type events of all sizes. Even though the fundamental tectonic mechanisms for earthquake generation are now quite well understood, the role of small external perturbations in triggering earthquakes is still scientifically contentious. Indeed, even though there was an accumulation of anecdotal evidence for one earthquake triggering another at a large distance, it took the Landers, California earthquake of 1992 to provide an unequivocal seismological demonstration. Whether it is one seismic event triggering another, or a volcanic eruption triggering an earthquake, the causal dynamical associations between hazard events need to be unravelled.

1.1 Causation and Association

On 10 April 1815, the 13,000 foot Indonesian volcano Tambora exploded in the most spectacular eruption recorded in history. One hundred and fifty km³ of material was ejected, and the eruption column soared as high as 43 km, which left a vast cloud of very fine ash in the upper atmosphere. This cloud reduced significantly the amount of solar radiation reaching the Earth’s surface, and caused a dramatic change in the climate of the northern hemisphere in the following year. To this day, the year 1816 is recollected as the year without a summer.

According to Mary Shelley, staying in Geneva, ‘It proved a wet, ungenial summer, and incessant rain often confined us for days to the house.’ Her poet husband Percy Bysshe Shelley rued the cold and rainy season. Upon the suggestion of their literary neighbour, Lord Byron, they all spent their confinement indoors writing ghost stories. Byron sketched a tale of vampires – she wrote Frankenstein.³ A tenuous chain of causation thus links the world’s greatest gothic novel with its greatest documented eruption. Tambora was neither a necessary nor sufficient condition for Frankenstein to be written. But the following counterfactual statement can be made: without the eruption of Tambora, Frankenstein most likely would never have been created. Akin to the writing of Frankenstein, the occurrence of a hazard event may be tenuously, yet causally connected with a prior event, which might have taken place at a significant separation of time and distance.

In deteriorating weather, on the evening of 27 March 1977, two Boeing 747 jets collided on the ground at Los Rodeos airport in Tenerife, killing 583 people.⁴ Neither plane was even scheduled to be there. Both had been diverted from Las Palmas airport on the island of Gran Canaria, where separatist terrorists had earlier exploded a bomb in the passenger terminal. The following counterfactual statement might be made: if it had not been for this terrorist attack, the accident would not have happened. The long delayed KLM pilot would not have been in the predicament where he was very anxious to take off, even without proper clearance. But it cannot be said that the world’s worst aviation disaster prior to 9/11 was also caused by a terrorist attack.

A formal discussion of the causation issue is worthwhile, because causal claims may have a subjunctive complexity. If a woman says her hair is brown because she dyes it, we infer that if she had not dyed her hair it would have been some other colour. This kind of counterfactual conditional is not necessarily correct: a brunette can dye her hair brown.⁵

After a succession of two hazard events, the public may enquire whether the first event caused the second. The reply is often unsatisfactory. The formal scientific response is to decline to admit a causal connection unless a direct physical link can be established and its effects demonstrated. Where a massive mountain rockslide dams a river and forms a lake, the cause of a subsequent outburst flood is clear: both the rockslide and the lake are visible, and the situation can be monitored remotely by satellite.

It is a frustration of Earth science that the interior of the Earth can be so opaque to human observation. Thus a geophysicist might freely speculate on, but not elaborate in precise numerical detail, the connection between the 1902 Caribbean volcanic eruption of Mt. Pelée and that of St. Vincent on the previous day, just 165 km to the south.

Whenever there is some constancy with which events of one kind are followed by events of another, scientists may wish to claim an association between the two kinds of event. But from the positivist philosophical viewpoint, this statement of empirical correspondence does not warrant drawing any inference on causation.⁶ In his probabilistic theory of causation, the mathematical philosopher Suppes required that the cause should raise the probability of the effect.⁷ Thus, even if occasionally an Indian rain dance is actually followed by a downpour, we do not say that the rain dance caused the rain. Similarly, even if occasionally a tornado near Topeka, Kansas is followed by an earthquake in California, we do not say that the tornado caused the earthquake.⁸

But how is the transition to be made from mere association to causation? This is particularly hard to establish when the effect of a preventive cause is an event, such as catastrophe, that does not materialize. Unfortunately, counterfactual statements of the kind, ‘If this had not happened, then that would not either’, have their weaknesses.⁹

The dictum of the statistician Ronald Fisher was to make the theories more elaborate. There are two ways in which this can be achieved. The first way, which is standard in pharmaceutical drugs testing, is by performing experiments, with a statistical design carefully chosen to discern causal factors. If variation of one feature X causes variation in another Y, then Y can be changed by an intervention that alters X. This procedure unfortunately is not feasible for observational sciences, because experimental conditions are those imposed by Nature.

The alternative mode of elaboration is to relate the phenomenon to scientific knowledge. Thus, epidemiological results are best interpreted in terms of an underlying biochemical process. Recalling the studies demanded by Ronald Fisher to establish, beyond the doubt of a sceptical geneticist, a causal link between smoking and lung cancer, the gaps in knowledge of the causal links between natural hazards seem more excusable, if no less regrettable.

Recognizing the dynamical complexity of the systems involved, there is advantage in representing event associations in a way which allows their relationships to be scientifically explored. Alas, the associations between some pairs of hazard events are far from transparent, and the infrequency of the phenomena and sparsity of data make hard work of attempts at statistical correlation. One of the measures for coping with small event datasets is to aggregate the data, some of which relate to binary variables, taking values of 0 or 1 according to whether something did or did not happen. But an analyst must beware of statistical illusions such as Simpson’s paradox: there can be a positive association between two binary variables, even though, conditional on a third variable, the association may actually be negative.¹⁰

With a view to gauging the effect of even minor perturbations, the dynamical basis of each natural hazard is sketched here in an interdisciplinary way. This style of presentation is uncommon in the Earth and atmospheric sciences, despite the fact that some of the most senior seismological institutes have been accommodated with meteorological institutes; a vestige of an era when scientists thought there was such a phenomenon as ‘earthquake weather’. A period German barometer even marked earthquake at the end of the dial after severe storm. Had the maker lived in Nordlingen, within the Ries Basin of southern Germany, the site of a major meteorite crater, perhaps the very end of the dial might have signified meteorite impact.

1.2 Extra-Terrestrial Hazards

Galileo was the first scientific observer of lunar craters, but it was three and a half centuries after the publication of Sidereus Nuncius (The Starry Messenger) in 1610 that the impact of large meteorites was appreciated as their cause, rather than giant volcanoes. Even after the physicist Chladni had published, at the beginning of the 19th century, memoirs on stony and metallic meteors falling from space, professional astronomers were very reluctant to accept impact theories for seemingly patent geometrical reasons: most lunar craters are circular rather than elliptical. The fact that high velocity impacts are similar to explosions, and hence form circular craters, was not appreciated until a century later.

Four hundred years after Galileo, another Italian made an important meteorite impact observation – using not a telescope focused on the moon, but satellite images on Google Earth. Vicenzo De Michele, former curator of the Natural History Museum in Milan, spotted the 45 m wide Kamil crater in the southern Egypt desert in 2008. It is reckoned this was caused by an iron meteorite hurtling to Earth at more than 12,000 km/hr. This is a notable discovery, because weathering makes such well-preserved impact craters very exceptional.

Supplemented by terrestrial research, such as the iridium analysis which gave Luis Alvarez an initial clue to a meteorite impact at the boundary between the Cretaceous and Tertiary periods,¹¹ planetary physicists have been able to quantify the mechanics of the cratering process, and to model the environmental consequences of large impacts.¹² Such studies show that, if sufficiently energetic, an impact by an asteroid or comet would be capable of causing a global catastrophe.

There are three main populations of potential extra-terrestrial impactors. First, there are asteroids which are in Earth-crossing orbits of moderate eccentricity. Such orbits overlap that of the Earth and undergo intersections due to orbital precession: a swivelling of orientation due to the gravitational attraction of the planets. These asteroids are composed largely of iron and rock, and are far less easy to spot than comets. Originating predominantly from the main asteroid belt, they may wander into orbits whose orbital period is harmonically related to that of Jupiter. The gravitational effects of Jupiter can force these asteroids into orbits taking them repeatedly through the inner solar system.

The second population of potential impactors consists of comets in orbits similar to those of the above asteroids, which stay within the inner solar system. None of the discovered comets could collide with the Earth, at least for the next few centuries, and those in the Jupiter family may be more likely to hit Jupiter instead or be ejected from the solar system. By contrast, it is much harder to detect so-called extinct comets, which no longer display cometary activity and thereby appear point-like.

The third population of potential impactors includes occasional comets with periods longer than twenty years. The latter typically have greater impact velocities of 50 km/s, compared with about 20 km/s for the asteroids and short period comets. The known long period comets include members of the Halley family. But the chance that any of these known comets would collide with the Earth is minuscule. For Halley’s Comet itself, it is as low as 0.5% in a million orbits. But the number of Earth-crossing active and extinct Halley-family comets is thought to be much larger than the number discovered, and these remain an unidentified and unquantified threat.

According to Steel et al., the major concern for humanity is not so much the large global impact which might occur once in a hundred thousand years, or more rarely still, but regionally devastating impact events, which occur in clusters every thousand years or so, during epochs of high influx.¹³ The Chinese historical record of meteorite observations, which dates back to the 5th century, attests to the danger posed by meteor clusters. In 1490, many were killed when stones, some the size of goose eggs, reportedly fell like rain.

Early in the 20th century, on 30 June 1908, it was Siberia that experienced a major impact event. Trees were flattened over an area of more than 2,000 km² in the region of the Tunguska River. A century later, in 2010, a Russian expedition deploying ground penetrating radar located a crater, carrying the icy signature of a comet, rather than a meteorite. Had it struck 4 hours and 47 minutes later, St. Petersburg would have been obliterated. Such a possible natural catastrophe is one of the most intriguing counterfactuals of 20th century politics, with untold consequences stemming from the end of the Romanov dynasty.

1.2.1 Solar storms

Galileo was the first to observe and appreciate the imperfections of the Sun, known as sunspots. Two and a half centuries later, on 1 September 1859, in the course of his daily sunspot observation, an English amateur astronomer, Richard Carrington, observed and reported for the first time a solar flare, which is a sudden, rapid, and intense variation in brightness of the Sun. This was so extremely bright that the associated 1859 space weather event remains one of the largest ever observed, as well as the first. A recurrence of this solar superstorm in the 21st century would severely affect satellite r...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Contents
• Cover photograph of Anak Krakatau
• Prologue: CHAOS, CRISIS AND CATASTROPHE
• 1 NATURAL HAZARDS
• 2 SOCIETAL HAZARDS
• 3 A SENSE OF SCALE
• 4 A MEASURE OF UNCERTAINTY
• 5 A MATTER OF TIME
• 6 CATASTROPHE COMPLEXITY
• 7 TERRORISM
• 8 FORECASTING
• 9 DISASTER WARNING
• 10 DISASTER SCENARIOS
• 11 CATASTROPHE COVER
• 12 CATASTROPHE RISK SECURITIZATION
• 13 RISK HORIZONS
• Epilogue: BLACK AND RED SWANS
• Bibliography
• Index