Dr. Gordon Woo

16 September, 2014

SMARTER THINKING ABOUT

CATASTROPHES

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The district of Ronchi,

located at an altitude

of 318 m,

has about 140

inhabitants and is

located in the south

of Termeno village,

Northern Italy. ICRM S

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Landslide in Ronchi di Termeno 21 January 2014

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Disaster: an unfavourable aspect of a star

What actually happened historically was NOT pre-determined;

it is just one specific realization of what might have happened

in a stochastic process.

Where event data are abundant, and events are frequent,

most of what can happen has already happened

a number of times.

However, for rare extreme events,

the actual historical dataset is sparse.

Consideration of counterfactual ‘near-miss’

scenarios augments a meagre dataset. Antikythera

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‘Lateral thinking is concerned with

the generation of new ideas,

and breaking out of the concept

prisons of old ideas.’

Lateral thinking avoidance

of systemic risk

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Stochastic modelling of the past

2014

Whereas stochastic analysis of future scenarios

is commonly undertaken, this is hardly ever done

for past events. ICRM S

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Earthquake recurrence on faults

STRESS STRESS

TIME TIME

Idealized Periodic Model Actual Behaviour

Variable

strength Variable stress drop

Identical

strength

Constant stress build-up

Constant stress drop

Non-uniform stress build-up

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Aperiodic recurrence intervals

EAST NANKAI TROUGH SAN ANDREAS FAULT (S. Cal.) 1944 1857 dt = 90 years dt = 45 years

1854 1812 147 years 332 years

1707 1480 209 years 130 years

1498 1350 138 years 250 years 1360 1100

264 years 100 years

1096 1000 ICRM S

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Stochastic modelling the past:

The Parkfield sequence 1857

1881

1901

1922

1934

1966

24

20

21

12

32

Average interval of about 22 years

1966 + 22 = 1988! ICRM S

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The Parkfield puzzle

Stress loading increase over time:

includes a Brownian motion term. A better sense of the

next occurrence is obtained by randomizing the accidental

historical dates.

( )t W t

Yes - in 2004

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Recognizing the bounds of knowledge

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A great M8.6 strike-slip earthquake occurred off Sumatra on 11 April 2012.

This may be the largest strike-slip earthquake ever recorded in the world.

The large Sumatran earthquakes in 2004, 2005, and 2007 triggered one another and

may have triggered this event. Future earthquakes near Sumatra may be more likely

to happen sometime in the coming decades.

Why are

seismologists

surprised

so often?

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San Andreas Fault ruptures

The Big One The Bad One ICRM S

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Counterfactual history Catastrophes are extreme events.

In all branches of catastrophe science, history is a vital data

resource because catastrophes are rare.

But much can be gleaned from a detailed study of near-misses

- catastrophes that might have been.

‘The terror of the unforeseen

is what the science of history hides.’

Philip Roth IC

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16 January 2013: terrorist attack

on gas plant at InAmenas, Algeria

A stray terrorist bullet

accidentally caused a

power outage

that automatically

shut down the plant.

This prevented the

terrorists from

setting off a large

explosion. ICRM S

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Interactions between the natural, man-made and virtual environments.

Multi-hazard events coupling geological and meteorological actions.

Unusual and bizarre combination of natural and technological (Na-Tech) disasters.

Risks unknown to science

Emergent phenomena can arise from complex nonlinear

systems, which may constitute novel modes of risk, e.g...

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Counterfactual disasters:

resampling history

The risk state of a system can be represented in terms of n

underlying risk variables, some of which may be hidden and

not directly observable:

{ (1), (2),... ( )}S X X X n

Perturbing these state variables leads to a resampled

virtual disaster history.

These variables include measures of both physical hazard

proximity parameters, and organizational parameters,

e.g. system defences and controls.

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{ X(1), X(2),….X(n)}

Danger

Physical

Space

(distance

to hazard

threshold)

Organizational space

(adequacy of system defences and controls)

Proximity to danger in both physical

and organizational space

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East Bay Hills wildfire

October 1991

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The Oakland Hills fire, killed

25 people, injured 150, and

destroyed more than 3,800

homes.

Eleven died in traffic jams

while evacuating. Eight others

died on narrow streets in the

same area.

The economic loss has been

estimated at $1.5 billion. X(1): wind strength

X(2): ignition number

X(3): fire-fighting capacity

“It’s hard to get organized and run for

your life at the same time!”

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FEMA: US Fire administration commentary The most significant factor that should be recognized from this incident is that the

fire was beyond the capability of fire suppression forces to control.

The stage was set by a number of contributing factors that created the

opportunity for disaster. When the Santa Ana wind condition was added to

those risk factors, the combination was more than any fire department could

handle.

One fire official said that if the same fire risk factors had been present in a park or

forest, the area would have been closed to all activities.

As long as the wind was present, the fire was going to continue to spread,

no matter what strategy and tactics were used and no matter how much

equipment and how many firefighters were there to try to stop it.

‘The fire was contained only when the wind changed.’ IC

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Deterministic view of history

Historical hazard experience is regarded as binary –

an event either happened or it did not.

If it didn’t, …then it didn’t.

But what if the environmental

circumstances had been somewhat

different? What was the chance of a

disaster? ICRM S

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Long Wharf, Boston: the blizzard of February 2013

A four-foot storm surge hit Boston at low tide, not high tide.

With the high tide already a foot higher than average because of the

new moon, coincidence of the storm surge with this high tide would

have given rise to the 100-year flood. ICRM S

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Hurricane Irene: August 2011

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As of August 25th, 2011,

a counterfactual analysis can be

undertaken to assess the likelihood

that the insured loss from Hurricane

Irene might have been in excess of

$50 billion.

This is estimated from an RMS study

of the possible track evolution of the

hurricane as it funnelled through the

track selection gates marked in green.

This likelihood is estimated to be in

excess of 1%. ICRM S

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Random aspects of event history

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0 1 2 3 4 5 6 7 8 Years

Suppose that over a period of 8 years, there are four crisis events

when a dice is thrown, with an event arising if the outcome is a

six. The expected number of events is 4/6, yielding an annual

frequency of (4/6)/8 = 1/12.

But there is about an even chance (0.48) of no event occurring.

IC

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Probability distribution function

for key dynamic hazard parameter

Threshold T for

hazard event

to occur

( )f z

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Time series of danger periods

0 1 2 3 4 5 6 7 8 years

The expected number of events over the 8 year time interval

is the sum of the tail probabilities:

4

1

( )k

k T

f z dz

T T T T

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Counterfactual

volcano hazard analysis

In the 1994 edition of ‘Volcanoes of the

World’, published by the Smithsonian

Institution, the known volcanic eruptions

are catalogued.

However, unrest periods are not given

so much attention.

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Site hazard: American University of the

Caribbean School of Medicine

The government of Montserrat granted AUC a 25-

acre parcel of land near Plymouth, where a new

campus of 17 buildings was built. AUC began

conducting classes at its new campus in Montserrat

in January 1980.

On September 17, 1989, Hurricane Hugo hit the

island, severely damaging the campus.

The Montserrat campus was rebuilt and AUC reopened it

for classes in September 1990. ICRM S

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Montserrat volcano hazard in the 1980’s

Montserrat provides a practical

application for counterfactual

analysis.

Volcano-seismic activity

damaged buildings in the 1890s,

1930s and 1960s.

For previous episodes of unrest, a counterfactual analysis

allowing for the aleatory uncertainty in volcano dynamics would

inform assignments of the probability that the unrest is magmatic,

potentially leading to an eruption. IC

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Maximizing the use of historical unrest data

The crisis in the mid-1930s raised fears of a potential major eruption.

For the unrest in 1966-1967, instrumental monitoring data exist to support

the estimation of a high eruption likelihood. e.g. Shepherd J.B. et al. (1971)

Volcano-Seismic crisis in Montserrat, West Indies, Bulletin Volcanologique:

‘Sharp increases in seismic and solfataric activity occurred in 1966 and these events

indicated the abnormally high risk of an eruption in the near future. A network of four

short period seismographs was established in the island in May 1966 and between

this date and the end of 1967, 723 local earthquakes were recorded, of which 32

were reported felt in the island. Hypocentres were determined for 189 of these

earthquakes, and most of these lay in a WNW to ESE belt beneath the Soufriere

Hills, at depths of less than 15 km.’ ICRM S

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Time series of volcanic unrest periods

1890 1930 1960

For each unrest period, the time-dependent eruption probability

can be estimated from the available data.

The expected number of eruptions over the century time interval

is the sum of the tail unrest probabilities:

3

1

( )k

k T

f z dz

T T T

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‘Near-miss’ data in volcano risk analysis

Stochastic models for unrest periods, rather than just actual eruptions, need to be developed.

For Montserrat, the expected number of eruptive events in the century from 1890 – 1990 is about 1.

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Plymouth was destroyed

in August 1997 A baseline frequency would thus have

been about 1%, which is higher than

using the time to the last eruption in

1630, and would have yielded a more

pessimistic and realistic assessment of

volcanic hazard at Plymouth. IC

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An unusual day

‘The really unusual day would be one

where nothing unusual happens.’

Persi Diaconis,

mathematician and magician

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The Improbability Principle

‘As someone who happened to meet his future

wife on a plane, on an airline he rarely flew,

I wholeheartedly endorse David J. Hand’s

fascinating guide to improbability,

a subject that affects the lives of all,

yet until now has lacked a coherent

exposition of its underlying principles.’

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‘Traces of the tsunami damage were found from

Miyagi Prefecture (4) to Fukushima Prefecture. (7)

However, in the most recent study, the researchers

found evidence of damage in Iwate Prefecture (3),

leading them to believe the earthquake that caused

the tsunami might have measured around a

magnitude of 9.’ Japan Society of Engineering Geology meeting,

Osaka, 12 October 2007

Sanriku

earthquake

869

‘When you have eliminated the

impossible, whatever remains,

however improbable,

must be the truth.’

Sherlock Holmes,

The Sign of the Four

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The law of inevitability

The law of truly large numbers

The law of selection

The law of the probability lever

The law of near enough

Hand’s five laws of improbability

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The Law of Inevitability

From a complete list of outcomes,

one of them must occur.

‘It’s a little difficult to ascertain

where the NASA satellite will

come down because there are

so many variables involved.

But it will definitely come down

in some part of the world.’ ICRM S

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On 15 February 2013, the Russian district of Chelyabinsk, with a population of more

than 1 million, suffered the impact and atmospheric explosion of a 20-meter-wide

asteroid, the largest impact on Earth by an asteroid since Tunguska, 1908.

Popova et al., Science, November 2013 IC

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Virginia State Lottery

In the 1990s, the Virginia State Lottery was based on choosing

6 numbers from 1 to 44, giving a probability of 1 in 7,059,052

That any one ticket would be a jackpot winner.

On 15 February 1992, the jackpot had rolled over to $27 million.

A consortium of 2500 small investors, mostly Australian, formed

an international Lotto Fund to buy every combination of numbers.

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If two targets are equally

attractive, terrorists will tend

to attack that which has worse

security.

Terrorist target substitution

Once a terrorist moves to a target, alternative targets of

opportunity will be chosen if the designated target is too secure.

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On October 17, 2012, Quazi Nafis, a 21-year-old Bangladeshi, attempted to set

off a 1,000 bomb outside the Federal Reserve Bank, after originally intending to

strike Wall Street.

Target substitution in New York

Liberty Street, NY Wall Street, NY ICRM S

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The Law of Truly Large Numbers

With a large enough number of opportunities,

any outrageous thing is likely to happen.

On 14 June 1999, in Arizona, a 14 year old girl, Shannon Smith,

was killed by a bullet that landed on top of her head.

[It has since become illegal to fire guns into the air.]

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Evelyn Marie Adams won the New Jersey Lottery twice in

just four months: first in 1985, then again the next year.

Her winnings were $5.4 million.

The chance of her winning twice in this time span was about

one in a trillion.

However, accounting for all the lotteries in the world; the

number of players; the number of tickets they buy; and the

number of weeks they play; all leads to a truly large number.

With enough events, the chance that one will happen can be

very large.

Double lottery wins

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Animal earthquake forecasting

A population of reproductively active

common toads was monitored over a

period of 29 days, before, during and

after the M6.3 earthquake at L'Aquila,

Italy, which occurred on 6 April 2009.

Toads at the study site, 74 km distant from L'Aquila, showed a dramatic

change in behaviour 5 days before the earthquake, abandoning spawning

and not resuming normal behaviour until some days after the event. ICRM S

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The zoologists remark that,

‘Whether toads would exhibit similar behaviour at other

locations and preceding other large seismic events

remains to be seen, but the results reported here suggest

that toads detect whatever phenomenon is giving rise to

the perturbations in the ionosphere and are thus able to

anticipate seismic events.

Testing this hypothesis would, however, be very difficult,

given the rarity and unpredictability of earthquakes.’ ICRM S

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The Law of Selection

You can make probabilities as high as you like,

if you choose after the event.

By looking back at what actually happened,

probabilities can be changed.

This is postdiction rather than prediction. ICRM S

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Postdiction of catastrophes

The postdiction of catastrophes with the advantage of

hindsight raises an important issue in catastrophe

modelling.

The original event probabilities may have been

underestimated.

How can probabilities be better updated?

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Strain

Finite

Failure

Time

t f

A B t t fm[ / ]1

A B

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Time variation of the cumulative strain

for the eastern part of the southern Aegean

Papazachos

et al.

BSSA

2002

Benioff

Strain

1.0E+8

8.0E+7

6.0E+7

4.0E+7

2.0E+7

0.0E+7

1960 1970 1980 1990 2000

The generation of the strong Cythera

earthquake on 8 January 2006 with M 6.9,

epicenter coordinates φ = 36.2° N

and λ = 23.4° E satisfies this

intermediate-term prediction.

(BSSA, 2007)

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The Law of the Probability Lever

A slight change in circumstances

can have a huge impact on probabilities.

A slight change in the shape of a distribution can alter probabilities from

being incredibly small to being part of the familiar course of events. ICRM S

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Very few people have ever experienced an electric shock

due to lightning. In UK, for example, the average number

per year from 1988 to 2012 is only 29.

However, this risk is far higher for those whose work or

recreation keeps them outdoors.

Major Walter Summerford was struck twice by lightning,

before a third strike left him completely paralysed.

Even his gravestone was struck by lightning.

Non-uniform casualty risk : Lightning

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The % Death Per Case (DpC) is modelled by a Weibull distribution: Pr (DpC > X ) = exp ( - [X/A]B )

Infectious disease lethality modelling

Long-tailed distribution for the % Death Per Case (DpC)

Likelihood of Lethality of Pandemic Virus

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.0 10.0 20.0 30.0

Death per Case (%)

Probability of Exceedance

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The Law of Near Enough

Events which are sufficiently similar

are regarded as identical.

By relaxing the criteria for a match, we can increase the

probability of an apparent coincidence. Events which

might seem extremely unlikely can turn out to be quite

probable on closer examination. ICRM S

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Near coincidences

The psychoanalyst Carl Jung, has recounted the following

coincidence:

‘A young woman I was treating had a dream in which she

was given a golden scarab. Suddenly I heard a noise

behind me, I turned round and saw a scarabeid beetle,

which is the nearest analogy to a golden scarab that one

finds In our latitudes.’ ICRM S

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Ensemble probability forecasting of weather

What about ‘coincident’

clusters of hazard events,

e.g. large earthquakes?

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‘Coincidence

is God’s way

of remaining

anonymous.’

Albert

Einstein

Unknown Unknown Centre

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MIT

Chinese

Students

Club

1944

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