Analysis and Classification of

Volcanic Eruptions

Prof. S. C. Wirasinghe , PEng (APEGA)

Ms. H. Jithamala Caldera

I3R2 May 2014

Purdue University

Department of Civil Engineering, Schulich School of Engineering

University of Calgary

Canada

Outline

Primary and Secondary Disasters

Different Scales

Problem Statement

Objectives

Parameters Reflect the Severity

Severity Level Boundaries

Advantages and Limitations

Conclusion

What is a Volcano?

Crater of the

earth’s crust

Grow by adding layers and height with the accumulation of lava or ash

Primary Disasters

Ash flows

◦ 1902 - Mt. Pelee, Martinique

Ash falls

◦ Respiratory problems

◦ Coverage of houses, buildings, roads, and crops with ash

◦ 1991 - Chile's Cerro Hudson

Ash clouds

◦ Threat to air traffic

◦ Great circle routes to Japan over Alaska

Pyroclastic flows

◦ Mixtures of hot gas and ash flow high speeds

◦ Extreme heat and oxygen loss

Lava flows

◦ Destroy houses, roads, and other structures

Mudflows

◦ 1985 - Ruiz, Colombia

Secondary Disasters

Volcano collapses

◦ 1792 - Unzen in Japan

Pollution

◦ Emission of strong poisonous gasses

◦ Sulfur dioxide, hydrogen chloride, hydrogen fluoride, etc.

Disease

◦ 1991 - Pinatubo in Philippines

Tsunamis

◦ 1883 - Krakatau in Indonesia

Famines

◦ 1815 - Tambora in Indonesia

Climate anomalies

◦ 1815 - Indonesia's Tambora causing June snow falls and crop failures in New England, U.S.A.

Different Scales Distinguishing

Destructive Capacity of a Disaster

Volcanic Explosivity Index : VEI (Newhall, et al., 1982)

Different Scales Contd.

Disaster scope (Gad-ElHak, 2008)

Scope DisasterCasualties

(persons)

Area

Affected

(Km2)

I Small C < 10 or A < 1

II Medium 10 ≤ C < 100 or 1≤ A < 10

III Large 100 ≤ C < 1,000 or 10≤ A < 100

IV Enormous 1,000 ≤ C < 10,000 or 100 ≤ A < 1,000

V Gargantuan 10,000 ≤ C or 1,000 ≤ A

Different Scales Contd.

Fatality based disaster scale ( Wirasinghe, et. al.,

2013)

Type Fatality Range Example

Emergency 1 ≤ F < 10 A small landslide that kills one person

Disaster Type 1 10 ≤ F < 100Edmonton tornado, Canada -1987 that

killed 27 people

Disaster Type 2 100 ≤ F < 1,000Thailand flood-2011 that resulted in a

total of 815 deaths

Catastrophe Type 1 1,000 ≤ F < 10,000Hurricane Katrina-2005, U.S.A that killed

1833 people

Catastrophe Type 2 10,000 ≤ F < 100,000Tohuku earthquake and tsunami-2011,

Japan that killed 15882 people

Calamity Type 1 100,000 ≤ F < 1,000,000Haiti earthquake 2010 killed 316,000

people

Calamity Type 2 1,000,000 ≤ F < 10M China floods-1931 death toll 2,500,000

Cataclysm Type 1 10M ≤ F < 100M -

Cataclysm Type 2 100M ≤ F < 1B -

Partial or Full

Extinction1B ≤ F < 10B

•Meteor strike (diameter > 1.5 Km) -

estimated deaths :<1.5*109

•Pandemic (Avian influenza) – estimated

deaths : <2.8B

Problem Statement

History reveals some characteristics of

volcanism

◦ Necessary to document its full breadth.

◦ Essential data required for prediction may be

lost

Number of reported eruptions is increasing

◦ Incomplete records

◦ A few historical reports contain some, but not

all of the necessary data; most contain only a

brief and often ambiguous description of the

eruptions (Newhall, et. al, 1982)

Problem Statement Contd.

Several terms for the same event

◦ Volcanology, unfortunately, has no

instrumentally determined magnitude scale, like

that used by seismologists for earthquakes, and

it is easy to understand why one observer’s

“major” eruption might be another’s

“moderate,” or even “small” event (Siebert,

et.al., 2011)

Consistent interpretation, proper scale,

good understanding of volcanoes and an

expanded recording system are required

Severity Levels of a Volcano

Parameters reflects the severity

Severity level boundaries

Objectives

Parameters Reflect the Severity

Factors Relationship

• Intensity

• Fatalities

• Affected population

• Impacted Region

• Cost of damage

• Duration

• GDP per capita

Readiness

Response due to increase in wealth

• Population increase

• Economic expansion

Ordinal Logistic Regression

◦ Logit function : assume the residuals are logistically distributed

◦ Goodness of fit tests

◦ Overall model fits

Lack of data reduces the extent of the analysis

◦ Fatalities

◦ Injuries

◦ Houses damaged

◦ Missing people

◦ Damage (in million dollars)

Multicollinearity

◦ Spearman's rank correlation coefficient (ρ)

◦ Interval variable (ordered categories)

Direct Volcanic Effects vs. Total

Effects

Excellent linear relationship (ρ> 0.9 )

Volcanic effects alone can explain the

relationship

Total effects Categorised

Deaths Missing InjuriesDamage

Million $Houses

Volc

ano e

ffect

s

Cat

ego

rise

d

Deaths .984

Missing 1.000

Injuries .984

Damage

Million $.925

Houses .963

Relationship among Volcanic Effects

VEI Deaths Missing InjuriesDamage

Million$Houses

VEIρ 0.33 0.45 0.39 0.09 0.33

N 390 8 72 142 72

Deathsρ 0.90 0.71 0.54 0.50

N 9 77 69 63

Missingρ 0.92 0.50 1.00

N 5 3 2

Injuriesρ 0.64 0.54

N 22 28

Damage

Million$

ρ 0.90

N 53

Damage in million $ has a very good linear relationship with houses damaged

Lack of data with presence of missing number of people

Different approaches

Different link function (logit, probit, etc.)

Log transformation of death, house, injuries

Different periods

◦ Last 32 years (after 1982), after the VEI scale is introduced

◦ Last 114 years: after 1900

◦ Last 514 years: after 1500

Include interaction terms to the model (to address the multicollinearity effect)

◦ Death * Houses

◦ Death * Injuries

◦ Houses * Injuries

VEI grouping (lack of data in lower and higher levels of VEI)

◦ VEI (6,7,8->5)

◦ VEI(0,1->1) (5,6,7,8->5)

Best Fitted Models for Volcanic

Effects

Death Injuries Houses

Estimate P-value Estimate P-value Estimate P-value

Th

resh

old

(α

) VEI 1 -1.312 .000 -1.353 .021 -1.440 .037

VEI 2 .869 .000 1.024 .029 .991 .090

VEI 3 2.559 .000 2.948 .000 2.515 .000

VEI 4 4.211 .000 4.918 .000 4.130 .000

Location (β) .706 .000 .906 .001 .706 .004

Link function : logit and VEI is grouped (VEI 0,1 as VEI 1 and VEI 5,6,7,8 as VEI 5)

Individual variables are better than the combinations in explaining the relationship with VEI

Multicollinearity effect

Extreme Value Distribution (EVD)

Limiting distributions for the largest or the smallest of a very large collection of random observations from the same arbitrary distribution

Generalized Extreme Value Distribution

◦ Gumbel (GEV Type 1) distribution

◦ Frechet (GEV Type 2) distribution

◦ Weibull (GEV Type 3) distribution

Generalized Pareto distribution

◦ Exponential (GP0) distribution

◦ Pareto (GP1) distribution

◦ Beta (GP2) distribution

Identifying Extremes in Real Data

Block maximao X2, X6,X15,X16,X23

Largest (rth) order

statistics within blocks

o 2nd order statistics

o X2,X3,X6,X8,X12,X15,X16,X18,X23,X25

Extremes exceed a high

thresholdo (X2,X3,X6,X7,X8,X15,X23,X24,X25)

Extreme Fatalities of Volcanic

Effects in Different Volcanoes

Weibull (α = 0.33925, µ = 1, σ = 109.04) : dash line

Severity level Boundaries

Type Fatality Range Probability

Emergency 1 ≤ F < 10 0.348852

Disaster Type 1 10 ≤ F < 100 0.271215

Disaster Type 2 100 ≤ F < 1,000 0.259911

Catastrophe Type 1 1,000 ≤ F < 10,000 0.110283

Catastrophe Type 2 10,000 ≤ F < 100,000 0.009699

Calamity Type 1 100,000 ≤ F < 1M 0.000040

Calamity Type 2 1M ≤ F < 10M 0

Cataclysm Type 1 10M ≤ F < 100M 0

Cataclysm Type 2 100M ≤ F < 1B 0

Partial or Full Extinction 1B ≤ F < 10B 0

Example : Fatality Based Disaster

Scale for Volcanic Effects

Type

Example

Year Volcano Country Fatalities

Emergency 2011 Nabro Eritrea 7

Disaster Type 1 1975 Marapi Indonesia 80

Disaster Type 2 1991 Pinatubo Philippines 450

Catastrophe Type 1 1951 LamingtonPapua New

Guinea2942

Catastrophe Type 2 1985 Ruiz Colombia 23080

Volcanic eruptions : Emergency to the Calamity Type 1 level

No recorded historical record for Calamity Type 1

Unusual large (super volcanic) eruption has the potential to exceed the above mentioned levels

Calamity or even a partial or full extinction.

Advantages and Limitations

Overall place of a Volcanic disaster

Easy to recognize an event occurrence and enter it into a database

Good foundation to develop an advanced scale to classify disaster

Lack of Data ◦ Limited to five variables

Number of fatalities

Number of missing people

Number of injuries

Number of houses damaged,

Damage in million dollars

◦ Accuracy of the assigned VEI scale for volcanic eruptions before VEI scale was introduced, could have been tested through this approach

Conclusion

Initial step of scale development process

Multidimensional scale to understand the

volcanic eruptions

◦ Intensity

◦ Affected population

◦ Impacted Region

◦ Duration

◦ GDP per capita