Analysis and Classification of Volcanic Eruptions Prof. S. C. Wirasinghe, PEng (APEGA) Ms. H. Jithamala Caldera I 3 R 2 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 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 Ash flows 1902 - Mt. Pelee, Martinique Ash falls Respiratory problems Coverage of houses, buildings, roads, and crops with ash 1991 - Chile's Cerro Hudson
Secondary Disasters 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. Volcano collapses 1792 - Unzen in Japan Pollution Emission of strong poisonous gasses Sulfur dioxide, hydrogen chloride, hydrogen fluoride, etc. Disease 1991 - Pinatubo in Philippines
Different Scales Distinguishing Destructive Capacity of a Disaster Volcanic Explosivity Index : VEI (Newhall, et al., 1982)
Different Scales Contd. Scope Disaster Casualties (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 Disaster scope (Gad-ElHak, 2008)
Different Scales Contd. Type Fatality Range Example Emergency 1 F < 10 A small landslide that kills one person Disaster Type 1 10 F < 100 Edmonton tornado, Canada -1987 that killed 27 people Disaster Type 2 100 F < 1,000 Thailand flood-2011 that resulted in a total of 815 deaths Catastrophe Type 1 1,000 F < 10,000 Hurricane Katrina-2005, U.S.A that killed 1833 people Catastrophe Type 2 10,000 F < 100,000 Tohuku earthquake and tsunami-2011, Japan that killed 15882 people Calamity Type 1 100,000 F < 1,000,000 Haiti 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 Extinction 1B F < 10B Meteor strike (diameter > 1.5 Km) - estimated deaths :<1.5*10 9 Pandemic (Avian influenza) estimated deaths : <2.8B Fatality based disaster scale ( Wirasinghe, et. al., 2013)
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 Objectives Parameters reflects the severity Severity level boundaries
Parameters Reflect the Severity Factors Intensity Fatalities Affected population Impacted Region Cost of damage Duration GDP per capita Readiness Response due to increase in wealth Population increase Economic expansion Relationship 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)
Volcano effects Categorised Direct Volcanic Effects vs. Total Effects Total effects Categorised Deaths Missing Injuries Damage Million $ Houses Deaths.984 Missing 1.000 Injuries.984 Damage.925 Million $ Houses.963 Excellent linear relationship (ρ> 0.9 ) Volcanic effects alone can explain the relationship
Relationship among Volcanic Effects VEI Deaths Missing Injuries Damage Million$ Houses VEI Deaths Missing Injuries Damage Million$ ρ 0.33 0.45 0.39 0.09 0.33 N 390 8 72 142 72 ρ 0.90 0.71 0.54 0.50 N 9 77 69 63 ρ 0.92 0.50 1.00 N 5 3 2 ρ 0.64 0.54 N 22 28 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)
Threshold (α) Best Fitted Models for Volcanic Effects Death Injuries Houses Estimate P-value Estimate P-value Estimate P-value 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 maxima o X 2, X 6,X 15,X 16,X 23 Largest (rth) order statistics within blocks o 2 nd order statistics o X 2,X 3,X 6,X 8,X 12,X 15,X 16,X 18,X 23,X 25 Extremes exceed a high threshold o (X 2,X 3,X 6,X 7,X 8,X 15,X 23,X 24,X 25 )
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 Lamington Papua New Guinea 2942 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