APPLICATION OF PROBABILISTIC TOOLS AND EXPERT ELICITATION FOR HAZARD ASSESSMENT AT

VOLCÁN DE COLIMA, MEXICO

By

Ingrid D. Fedde

A THESIS

Submitted in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE IN GEOLOGY

MICHIGAN TECHNOLOGICAL UNIVERSITY

2009

Copyright © Ingrid D. Fedde 2009

This thesis “APPLICATION OF PROBABILISTIC TOOLS AND EXPERT ELICITATION FOR HAZARD ASSESSMENT AT VOLCÁN DE COLIMA, MEXICO,” is hereby approved in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE IN GEOLOGY. DEPARTMENT:

Geological and Mining Engineering and Sciences Signatures: Thesis Advisor _____________________________________ Dr. José Luis Palma Thesis Advisor _____________________________________ Dr. William I. Rose Department Chair _____________________________________ Dr. Wayne P. Pennington Date _____________________________________

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TABLE OF CONTENTS ACKNOWLEDGEMENTS..................................................................................... v LIST OF FIGURES ...............................................................................................vi LIST OF TABLES ................................................................................................vii ABSTRACT ........................................................................................................ viii 1 INTRODUCTION ............................................................................................ 1

1.1 Background Volcán de Colima ............................................................. 3 1.2 Activity of Volcán de Colima ................................................................. 7 1.3 Research Objectives .......................................................................... 10 1.4 Review of the Literature...................................................................... 12

1.4.1 Probability of Eruptions at Volcán de Colima.......................... 12 1.4.2 Expert Elicitation at Montserrat............................................... 15 1.4.3 Bayesian Event Tree for Eruption Forecasting at Vesuvius................................................................................. 17

2 METHODS.................................................................................................... 18

2.1 Defining Unrest and Magmatic Unrest for an Active Volcano ............. 18 2.2 Event Trees ........................................................................................ 19 2.3 Bayes’ Theorem ................................................................................. 22 2.4 Prior Probability of Eruptions .............................................................. 25 2.5 Expert Elicitation Survey..................................................................... 27

2.5.1 Defining Aleatory and Epistemic Uncertainty.......................... 31 2.5.2 Weighting of Experts .............................................................. 32 2.5.2 Combining of Expert Opinions................................................ 36 2.5.3 Expert Feedback .................................................................... 38

2.6 Bayesian Event Tree Software ........................................................... 39 3 RESULTS AND DISCUSSION ..................................................................... 42

3.1 Expert Elicitation Results.................................................................... 42 3.1.1 Aleatory and Epistemic Uncertainty........................................ 42 3.1.2 Calibration of Experts Scores, Certainty and Weights............ 43 3.1.3 Data Thresholds Examined .................................................... 45 3.1.4 Eruption Probability Estimates................................................ 48

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3.1.5 Hazard Probability Estimates ................................................. 52 3.2 BET_EF Preliminary Results .............................................................. 53 3.3 BET_EF Results using Expert Elicitation............................................ 58 3.4 Vulnerability Analysis for Maximum Expected Event .......................... 60 3.4.1 Pyroclastic Flow Hazard ......................................................... 61 3.4.2 Tephra Fall Hazard.................................................................. 63

4 CONCLUSION.............................................................................................. 66

4.1 Recommendations for Future Work.................................................... 68 5 REFERENCES CITED................................................................................. 70 APPENDIX 1 – Expert Elicitation (Blank Form) ................................................ 77

APPENDIX 2 – Energy Cone Calculation ......................................................... 90

APPENDIX 3 – Expert Feedback...................................................................... 91

APPENDIX 4 – Bayesian Event Tree Inputs and Outputs ................................ 92

APPENDIX 5 – Event trees for Volcán de Colima ............................................ 95

APPENDIX 6 – Probability Density Functions for Volcán de Colima ................ 98

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ACKNOWLEDGEMENTS

Assistantship support for coursework was provided by the National Science Foundation, through EAR-0451447 and OISE-0530109. Field funding came from the Earth Hazards Exchange Program (EHaz) of the US Department of Education and support during the writing of the thesis came from EHaz and the Michigan Technological University’s Department of Geological & Mining Engineering and Sciences. I would like to thank Dr. Nick Varley, who heads the Centre of Exchange and Research in Volcanology (CIIV), for academic and research support and for the unforgettable volunteering program in Colima. I would also like to acknowledge the volunteers at the CIIV for their time and energy collecting and processing data and for furthering research in volcanology and monitoring at Volcán de Colima. I would like to thank the participants from the CIIV, the Colima Volcano Observatory, UNAM, Germany, Switzerland, the U.K., and the U.S that contributed to my research by completing the expert elicitation survey and giving very valuable comments. I am grateful to my advisor Dr. José Luis Palma for the steady support and guidance during the entire thesis process. Thanks to my cognate committee member Dr. Iosef Pinelis for probability and statistics support. A special thank you to my advisor Dr. William I. Rose for all the academic support and for remaining a source of encouragement through all the peaks and valleys, your authenticity is inspiring. Many thanks to my unofficial academic advisor Rüdiger Escobar-Wolf, for assistance in mapping, data processing/interpretation, results and analysis and my gratitude to my personal advisors Miriam Rios-Sanchez and Brian Anthony Ott for support and advice in all areas! This thesis is for my parents, my sisters, my niece, and friends who inspire me daily.

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LIST OF FIGURES Figure 1: Trans-Mexican Volcanic Belt ............................................................. 3

Figure 2: Volcán de Colima............................................................................... 4

Figure 3: Population Distribution....................................................................... 6

Figure 4: Magnitude-Frequency...................................................................... 13

Figure 5: Volcanic Event Tree......................................................................... 21

Figure 6: Recorded Eruptions ......................................................................... 25

Figure 7: Uncertainty ...................................................................................... 43

Figure 8: Expert Calibration ............................................................................ 44

Figure 9: Average Certainty ............................................................................ 45

Figure 10: Expert Response to Q3 ................................................................... 46

Figure 11: Expert Responses to Q13................................................................ 48

Figure 12: Combined Weighted Probability Estimates....................................... 50

Figure 13: Probability vs. Time .......................................................................... 51

Figure 14: Expert Response to Question 14...................................................... 53

Figure 15: Expert Hazard Probability Estimates ................................................ 55

Figure 16: Size Distribution ............................................................................... 57

Figure 17: BET Absolute Probability Output ...................................................... 58

Figure 18: Size Distribution ............................................................................... 60

Figure A5.1: Event Tree VEI 1........................................................................... 95

Figure A5.2: Event Tree VEI 2........................................................................... 95

Figure A5.3: Event Tree VEI 3........................................................................... 96

Figure A5.4: Event Tree VEI 4........................................................................... 96

Figure A5.5: Event Tree VEI 5........................................................................... 97

Figure A6.1: PDF for 1 month............................................................................ 98

Figure A6.2: PDF for 6 months .......................................................................... 98

Figure A6.3: PDF for 1 year............................................................................... 99

Figure A6.4: PDF for 10 years ........................................................................... 99

Figure A6.5: PDF for 50 years ......................................................................... 100

Figure A6.6: PDF for 100 years ....................................................................... 100

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LIST OF TABLES Table 1: Historical Eruptions............................................................................ 8

Table 2: Eruption Frequency ......................................................................... 13

Table 3: Mendoza-Rosas and De la Cruz (2008) Eruption Probability .......... 14

Table 4: Conditional Nodal Probability........................................................... 24

Table 5: Calculated relative frequency .......................................................... 26

Table 6: Example of the performance-based weight calculation.................... 34

Table 7: Example of item-based weight calculations ..................................... 35

Table 8: BET_EF software inputs and outputs .............................................. 40

Table 9: Data Thresholds .............................................................................. 47

Table 10: Expert Weighted Probability of eruptions ........................................ 49

Table 11: Combined Eruption Probability Estimates........................................ 50

Table 12 Comparasion of Estimates............................................................... 51

Table 13: Expert Weighted Probability of volcanic hazards............................. 53

Table 14: Combined Hazard Probability Estimates ........................................ 54

Table 15: Expert elicitation results and resulting BET outputs......................... 58

Table 16: Maximum population affected by pyroclastic flows .......................... 61

Table 17: Pyroclastic flow runout exceedence probability ............................... 61

Table 18: Pyroclastic flow risk analysis ........................................................... 62

Table 19: Tephra fall for significant eruptions .................................................. 63

Table 20: Maximum population affected by Tephra fall .................................. 63

Table 21: Tephra fall thickness exceedence.................................................... 64

Table 22: Tephra fall risk analysis ................................................................... 64

Table A4.1: Bayesian inputs .............................................................................. 91

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Abstract

APPLICATION OF PROBABILISTIC TOOLS AND EXPERT ELICITATION FOR

HAZARD ASSESSMENT AT VOLCÁN DE COLIMA, MEXICO

Located at the western end of the Trans-Mexican Volcanic Belt, Volcán de Colima (19°30’46’’, 103°37’02’’; 3860m) is an andesitic volcano having nearly continuous activity throughout the past 400 years. Historically, the activity of Colima has shown a cyclical eruptive behavior, with periods of repose, low level activity most of the time, and followed by large cycle-ending eruptions occurring approximately every 100 years. Typically, the cycle-ending eruptions are plinian. These have been recorded in 1622, 1818 and 1913. Although the volcano has maintained a low level of activity for the last 10 years, the possibility of a larger eruption in the near future is anticipated by some and highly relevant for hazard management. How likely is it that the current cycle of activity will end with a large explosive eruption? When could this happen and how large could such an eruption be? To address these questions, a probabilistic volcanic hazard assessment was developed for Volcán de Colima, which involved the application of probabilistic tools and an expert elicitation survey. Forty-two percent of the experts surveyed estimate that an eruption similar to the 1913 plinian event will occur within the next 10 years and combined expert opinion estimates a 52.7% likelihood of such an outcome. Seventeen percent of the experts surveyed estimate that a plinian event will occur within the next 5 years and combined expert opinion estimates a 42% likelihood of this occurrence. The eruption probability estimates from the expert elicitation as well as all known prior probability models, and past data were used as inputs into a probabilistic code (Bayesian Event Tree for eruption forecasting, BET_EF (Marzocchi et al. 2004), which calculates a likelihood of 14% for a plinian eruption in 10 years with respect to all other outcomes. During the 1913 eruption, pyroclastic flows and tephra falls affected the surrounding populated areas. Combined expert opinion for volcanic hazard probabilities estimates a 50% likelihood for these hazards affecting the runout distances considered, which could ultimately affect thousands of people living around the volcano. The application of expert elicitation and BET_EF to develop an in-depth probabilistic volcanic hazard assessment for Volcán de Colima is advanced now, and can be reapplied and reassessed as activity changes. The assessment could be used as a tool for monitoring the volcanoes activity as it progresses and potentially forecast future eruptions.

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1 INTRODUCTION

Eruption forecasting has long been a topic of interest among scientists and

authorities due to the uncertain behavior of volcanoes and the complexity in

predicting the exact moment that a volcano will erupt. The use of monitoring

techniques such as seismic networks, ground deformation, changes in gas

composition and flux have allowed scientists to more accurately determine the

timing of eruptions (Jimenez et al. 1995, Taran et al. 2001, De la Cruz-Reyna

and Reyes-Dávila, 2001, Murray and Ramirez, 2002, Galindo and Domínguez,

2002, Reyes-Dávila and De la Cruz-Reyna, 2002, Taran et al. 2002, Varley and

Taran, 2003, Stevenson and Varley, 2008, Varley et al. 2008). However,

determining the magnitude of impending eruptions can be challenging and

predicting the exact population and areas that will be impacted is even more

problematic before the actual event occurs. In most cases, forecasting an

eruption requires extended observations of the volcano’s behavior before it can

be certain that an eruption is imminent. Once an eruption occurs, adequate time

is needed for necessary actions to be taken, such as warning the public or

evacuating an area (Aspinall and Cooke, 1998, Sandri et al. 2003, Aspinall et al.

2003, Marzocchi and Woo, 2007, Baxter et al. 2008, De la Cruz-Reyna and

Tilling, 2008, Woo, 2008). When ground monitoring is not available as is

common at many remote volcanoes, volcanic activity is monitored with remote

sensing tools which can sense temperature anomalies, gas and ash emissions,

vegetation changes related to activity and ground deformation (Rees, 2001).

Probabilistic studies for eruption forecasting and hazard mitigation are now used

at volcanoes where there is great risk involved (Jones et al. 1999, Newhall and

Hoblitt, 2002, Aspinall et al. 2003, Marzocchi et al. 2004, 2007b, 2008, Lindsay et

al. 2008, Mendoza-Rosas and De la Cruz-Reyna, 2008, Neri et al. 2008). These

probabilistic studies supplement existing monitoring networks and add value to

forecasting efforts because they require scientists to take a broad look at the

entire volcanic system (both present and past data) in order to quantify the

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hazard in terms of probability of events, the magnitude of a possible eruptions,

the areas that have the greatest risk and the populations that will be affected.

Studies such as these are used for short-term forecasting to predict behavior of

an active volcano and help in decision making during an emergency, and for

long-term forecasting to assist in land use planning and long-term hazard

assessments (Marzocchi et al, 2008). Once the hazard is quantified and made

generally available to all, scientists and authorities can actively reduce the risk by

being prepared and having open channels of communication between each other

and the surrounding communities.

A detailed probabilistic volcanic hazard assessment (PVHA) is useful before,

during and after an emergency (Marzocchi et al, 2008). These assessments

involve detailed evaluation of two important aspects: (1) quantifying eruption

probabilities and (2) quantifying volcanic hazards. After quantifying the eruption

and volcanic hazards, the vulnerability can be examined, which helps scientists

determine areas that are at highest risk and generate ideas about how to mitigate

that risk. The collective use of social and scientific tools such as expert elicitation

and Bayesian Event Tree for Eruption Forecasting (BET_EF) are now being

implemented to create a more precise and detailed probabilistic volcanic hazard

assessment that encompasses a multitude of data from many different sources

(Marzocchi et al, 2008). The application of these tools for the purpose of

eruption forecasting provides useful information to scientists and the community

around the volcano, which may be adjusted repeatedly as expert opinions may

be expected to change with the activity of the volcano (Aspinall and Cooke

1998). This study will present the scientific and civil community with a

probabilistic hazard assessment at Volcán de Colima, Mexico. With the

changing and unpredictable nature of volcanic processes it is important to update

all available volcanic data as it becomes available and as experts opinions

change.

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1.1. Background Volcán de Colima

Volcán de Colima (19°30’46’’, 103°37’02’’; 3860m) is an andesitic stratovolcano

located at the western end of the Trans-Mexican Volcanic Belt (Figure 1) (Luhr

and Carmicheal, 1980, Bretón et al., 2002)

Figure 1: Trans-Mexican Volcanic Belt. Topography map of Mexico shows Volcán de Colima and other major volcanoes of Mexico located within the Trans-Mexican Volcanic Belt (TMVB). Michoacán-Guanajuato volcanic field (MGVF). Modified after Ferrari, 2004.

Colima is a complex system composed of the extinct andesitic stratovolcano,

Nevado de Colima, which is located 5.83 km north of the presently active Volcán

de Colima or Fuego de Colima (Figure 2).

Figure 2: Volcán de Colima. Topography map of Volcán de Colima showing major cities: Colima (approx. 32km from the vent) and Ciudad Guzman (approx. 27km), and the location of the Nevado Volcano Observatory.

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Because the volcano is located on the border between the states of Colima and

Jalisco, it is closely observed by the Protección Civil de Jalisco (PCJ) and closely

monitored by both the Observatorio Vulcanológico (www.ucol.mx/volcan) and the

Centro de Intercambio e Investigación en Vulcanología (CIIV) (www.ucol.mx/ciiv)

both within the University of Colima. The Comité Científico Asesor del Volcán de

Colima (www.volcandecolima.com) is the all-encompassing group that works

together to monitor the volcano and make decisions in times of crisis. The PCJ

and the Protección Civil de Colima (PCC) respond to evacuate towns

surrounding the volcano when there is a high hazard level given by the Comité

Científico Asesor del Volcán de Colima. For example, on February 5, 2002, the

growing dome of Volcán de Colima began to collapse and produce landslides

and lava flows down the south-southwest flank of the volcano (GVP, 2008). PCC

evacuated the town of La Yerbabuena (Figure 2), a town 6 km from the volcano.

After this evacuation, an 8 km danger zone was established by the two states

making it necessary to permanently move the town of La Yerbabuena just

outside the 8km zone (Stevenson and Varley, 2008). The town was relocated

except for a few families who refused to leave their homes and land. The

population within a 40 km radius of Volcán de Colima is 487,900 (based on the

LandScan 2007TM Global Population Database) (Figure 3), although the

population that could be affected by severe hazards is much less (Bretón et al.

2002).

Figure 3: Population Distribution. Map showing population distribution within a 40 km radius around the Volcán de Colima vent.

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Notice: This product was made utilizing the LandScan 2007TM High Resolution Global Population Data Set copyrighted by UT-Battelle, LLC, operator of Oak Ridge National Laboratory under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government has certain rights in this Data Set. NEITHER UT-BATTELLE, LLC NOR THE US DEPARTMENT OF ENERY, NOR ANY OF THEIR EMPLOYEES, MAKES ANY WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY LEGAL LIABILITY OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR USEFULNESS OF THE DATA SET.

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1.2 Activity of Volcán de Colima

Volcán de Colima is Mexico’s most active volcano with approximately 50

eruptions expressed in terms of Volcanic Explosivity Index (VEI 2, 3 and 4) since

1560 (Simkin and Siebert, 1994). The volcano has been active for approximately

2,500 years (Bretón et al. 2002). There have been at least two giant debris

avalanches at the Colima Complex (Stoopes and Sheridan, 1992). Accounts of

activity at Volcán de Colima have been recorded since 1523 AD and the first

formal monitoring stations were established in 1893 in the towns of Colima and

Zapotlán (Ciudad Guzman) (Bretón et al, 2002).

Volcán de Colima is considered to have a cyclical eruptive history with each

cycle lasting approximately 100 years (Luhr and Carmichael, 1980). The cycle

generally begins with a period of dormancy lasting approximately 50 years,

followed by a period of unrest of the volcano producing small and sometimes

larger magnitude eruptions which are relatively consistent and slow ascent of a

dome or several dome growths within the cycle period (Luhr and Carmichael,

1980). The cycle generally ends with a major Plinian eruption (VEI 4) clearing

the vent and producing pyroclastic flows traveling as far as 10 km from the

summit (Luhr and Carmichael, 1980). Therefore, the most vulnerable population

has been estimated to be around 209 residents in a 10 km radius of the summit

(based on the LandScan 2007TM Global Population Database). Major cyclical

ending eruptions (VEI 4) at Volcán de Colima have been recorded in 1622, 1818,

and 1913 (Bretón et al. 2002, Mendoza-Rosas and De la Cruz-Reyna, 2008)

(Table 1).

Table 1: The historically significant eruptions of Volcán de Colima (with magnitudes VEI 3 and VEI 4). The cycles of activity are highlighted. (Adapted from Bretón et al, 2002, Global Volcanism Program, Simkin and Siebert, 1994, Mendoza-Rosas and De la Cruz-Reyna, 2008).

Cycle Year VEI Hazard Produced 1523 3 Pyroclastic Flows 1576 3 Vulcanian type activity 1585 4 Ash blocked the sun and was distributed 220 km, covering fields,

death of cattle, pyroclastic flows to the SW 1590 3 Ash resulting in plague 1606 4 Ash blocked the sun and reached approx. 200 km 1611 3 Ash, sand and scoria 1622 4 Ash as far as 400 km NNE in Zacatecas 1690 3 Peléan type with ash and strong seismic 1711 3 Ash reaching Guadalajara as far as 200km 1770 3 Pyroclastic Flows down the South La Joya Barranca burying

cattle. Ash reached 550 km

1818 4

Ash obscured the moon. Yellow powder left deposits of 20 cm. Ash reported 425 km to the NE and Mexico City 470 km to the E, ballistics, lava to the SE in Barranco del Muerto, pyroclastic flows

1869 3 Ballistics noted, eruption cloud with tephra and lava flows 0.17 cubic km

1872 3 Incandesance and ash fall 1886 3 Large Vulcanian eruption producing ash in Colima 32 km away 1889 4 Abundant ash, accompanied by pyroclastic flows to the SE and

SW

1889 3 Abundant ash, accompanied by pyroclastic flows to the SE and SW

1890 4 Abundant ash emission as far as 300 km to the NE 1903 3 Ash fall up to 200km in the N and E directions 1908 3 Ash 1913 4 Ash reached 725km NNE PF lasted 4 days, removal of upper

100 m of crater widening the crater. 1997 3 Eruption out of 1994 crater produces ash and pyroclastic flows 2005 3 Eruption produces ash and pyroclastic flows

1st

2nd

3rd

4th

Saucedo et al (2005) describe the climactic events which occurred in 1913. First

a partial collapse of the external dome produced Merapi-type block-and-ash

flows and surges traveling 4 km from the summit. The second phase was a

Vulcanian explosion destroying most of the dome, producing lithic-rich fallout to

the NE and basal surges. Collapse of this column produced Soufrière-type block

and ash flows traveling 10kms confined within the barrancas. The third and last

phase of activity produced a Plinian eruption with a 21km high column which was

sustained for 8 hours. The eruption produced pumice fallout to the NE as far as

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725km. Partial collapses of the plinian eruption column led to ash flows extending

as far as 15 km.

Luhr and Carmichael (1980) first recognized the current (fourth in the historic era)

cycle of activity, which began in 1960 after a dormancy period of 47 years. Luhr

and Carmichael predict that the cycle will end sometime in the early part of this

century. Colima has been erupting lava from its summit, accompanied by vertical

explosions and occasional larger eruptions of VEI of 1 or 2 and two VEI 3 events

(Table 1) have been reported (GVP, 2008). Activity ceased from July 1994 to

November 1997, but eruptive activity resumed from Nov 1997 until the time of

this writing (May 2009). Thus Colima has been in a state of continuous unrest for

the last 10 years, with both explosive and effusive activity associated with the

growth of a dome in the summit crater (www.ucol.mx/volcan). The current dome

was first observed in February 2007 and has since been monitored for signs of

increased activity and for possible volcanic hazards relating to the dome growth

(www.ucol.mx/volcan).

The human consequences of explosive volcanism which produces events (VEI 4

or 5) are often forgotten by populations in one or two generations. Moreover, the

lessons learned from routine monitoring signs for a VEI 1-3 events at Volcán de

Colima in the last few decades may not provide clear warnings for larger

magnitude events. With Colima’s eruptive past and its cyclical pattern of events

ultimately leading to a major eruption, it seems desirable to apply expert opinion

and other probabilistic tools in developing a hazard assessment for the volcano

prior to the next significant eruption.

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1.3 Research Objectives

The aim of this study is to create a probabilistic volcanic hazard assessment

(PVHA) for Volcán de Colima by applying probabilistic tools and an expert

elicitation survey. A hazard assessment will consider the volcano’s historical

eruptions and present unrest state to quantify the probability of eruptions for long

term hazard assessment. With this information, the volcanic hazards produced,

and areas affected, i.e. run out distances and the vulnerability of the populations

will be estimated. Because smaller eruptions may go unreported, the frequency

of VEI 1 and 2 events are underestimated from records (Neri et al. 2008). Thus

this study will focus on the probability of a cycle ending eruption with larger

magnitude similar to the 1913 eruption at Volcán de Colima.

In order to quantify the hazard at Volcán de Colima as a result of eruptions, this

work will build upon the following aspects:

• A standard event tree modeled after Newhall and Hoblitt, 2002 and

Marzocchi et. al, 2008 will be created and used to illustrate the steps

taken in calculating an absolute probability of eruptions and hazards at

Volcán de Colima.

• An initial prior probability based only on historical data will be determined

by calculating the relative frequency of eruptions and the annual

probability for different eruption magnitudes (VEI) to be used as initial

estimates in the BET_EF software computation.

• An expert elicitation survey will be used to determine probability estimates

of eruptions based on different eruption magnitudes (VEI) and with varying

time periods (1 month, 6 months, 1 year, 10 years, 50 years, and 100

years).

• An expert elicitation survey will be used to determine probability estimates

of volcanic hazards based on different eruption magnitudes (VEI) and run-

out distances.

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• Time dependent eruption magnitude probability distributions will be

determined using the prior probability models, estimates from the expert

elicitation survey, historical reports of the eruptions at Volcán de Colima,

and the Bayesian Event Tree for Eruption Forecasting (BET_EF) software.

Once the eruption hazard is quantified, the vulnerability of the area around

Volcán de Colima will be estimated using Newhall and Hoblitt, 2002 exceedence

probability estimates, and Landscan population to determine two vulnerability

issues:

1. The probability that a volcanic hazard (pyroclastic flow, lahar and tephra

falls) will extend to a distance (d), given an eruption magnitude (VEI).

2. The population that will be affected given a certain hazard produced,

focusing on VEI 4 eruptions similar to the 1913 eruption.

The ultimate goal of this thesis is to demonstrate that studies such as these are

useful for any volcano where there is risk involved and if updated repeatedly

could be used to forecast future eruptions. In this case we apply these

methodologies to an andesitic volcano with activity patterns that are marked by

an open vent and continuous small magnitude eruptions and degassing, with

periods of elevated hazards. Similar BET_EF methodology has been used at

Vesuvius, a volcano with distinct reposes and brief highly explosive periods

(Marzocchi et al., 2004) and expert elicitation methodology was applied at

Montserrat, a volcano with similar eruptive styles to Volcán de Colima (Aspinall

and Cooke, 1998). Unlike the past BET studies, Colima is in a constant “unrest”

state and is highly likely to enter into a Plinian phase sometime within the next

ten years (Luhr and Carmicheal, 1980) based on the volcano’s past cyclical

activity. Therefore a study such as will clarify the likelihood of this occurrence.

1. 4 Review of the Literature

1.4.1 Probability of Eruptions at Volcán de Colima

Using a frequency method gives us a prior probability of eruptions, P(e), based

on the relationship between the number of past eruptions with respect to VEI and

the total number of eruptions in a specified sample period. This gives an

estimate of the relative frequency of eruptions with respect to VEI.

P(e)Events#Total

Events# vei≈ (1)

However, because there is a lack of completeness in the records for eruptions of

smaller magnitudes, it is difficult to make an accurate estimate of eruption

frequencies at Volcán de Colima using only this method (Table 2). Eruption

frequency of worldwide volcanoes may be determined using the frequency-

magnitude distribution based on the Gutenberg-Richter Law (1954) (Mendoza-

Rosas and De la Cruz-Reyna, 2008). The Gutenberg-Richter Law, which

calculates frequencies of earthquakes based on their magnitudes, can also be

applied to volcanoes with eruption magnitudes (VEI) (Mendoza-Rosas and De la

Cruz-Reyna, 2008). The equation relates eruption magnitude (MVEI) with the

eruption frequency (λVEI):

veivei bMalog −=λ (2)

Where a and b are constants of the global activity based on the historical

eruption data for VEI 2 – 6 and for various time intervals 20, 200, 1000, 2000

years, which is defined by Simkin and Siebert (1994), as a = 5.8 and b = 0.785

(Mendoza-Rosas and De la Cruz-Reyna, 2008). Frequency of eruptions (λvei) at

Volcán de Colima are compared in Table 2. Similar to earthquakes, frequency of

eruptions decreases as magnitude (VEI) increases (Mendoza-Rosas and De la

Cruz-Reyna, 2008) (Figure 4).

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Figure 4: Magnitude-Frequency. The global frequency of Holocene eruptions using the Gutenberg-Richter law (1954) and the total number of recorded events for Volcán de Colima.

Table 2: Eruption frequency values at Volcán de Colima calculated using a relative frequency method and compared to the the Gutenberg-Richter Law (1954) for Holocene

volcanoes. The frequency values are significantly different and show how the incompleteness of historical records (VEI 1 & 2) affect frequency calculations.

VEI # Reported Eruptions

Relative Frequency

# Eruptions Gutenberg-Richter

Relative Frequency

1 57 0.37500 103514 0.83604 2 51 0.33553 16982 0.13716 3 35 0.23026 2786 0.02250 4 9 0.05921 457 0.00369 5 0 0 75 0.00061

The frequency of events calculated using the relative frequency vs. the

Gutenberg-Richter Law (1948) brings forth the discrepancies within the reporting

of historical records. Historical records underestimate all events and small

magnitude eruptions are more frequently underestimated (Neri, 2008). This

relative frequency method assumes a complete record where all events,

specifically magnitudes, are equally likely over time. In summary we judge that

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incompleteness of the historical eruption record makes frequency of occurrence

for Volcán de Colima inaccurate.

Mendoza-Rosas and De la Cruz-Reyna (2008) calculate eruption probability at

Volcán de Colima using the Non-homogeneous Generalized Pareto-Poisson

Process (NHGPP) distribution. This distribution considers eruptions as a series

of independent, non-overlapping, physical events occurring in space A with and

intensity density λ(xi), where xi are the A-domain variables in which the process

develops (Mendoza-Rosas and De la Cruz-Reyna, 2008). The coordinates of xi

are time and magnitude (VEI) of a two-dimensional space, where the domain is

limited by the available historical eruption data. The eruption rate was calculated

for TMVB volcanoes and El Chichón where there are limits on the data such as a

short sample period, possible absence of large magnitude eruptions and an

incomplete record of the small magnitude eruptions, also uncertainties in the age

and magnitudes of historically significant eruptions (Mendoza-Rosas and De la

Cruz-Reyna, 2008). Once the eruption rate is calculated the eruption probability

is estimated with the NHGPP based on the extreme values (Table 3). These

estimates will be used as a measure to see how they compare to the estimates

that the expert elicitation survey and the BET_EF output provide.

Table 3: Volcán de Colima eruption hazard probability calculated by Mendoza-Rosas and De la Cruz (2008) using a NHGPP distribution.

VEI Years Probability VEI >2 20 0.63290

50 0.90840 100 0.96840 500 0.87936

VEI >3 20 0.35806 50 0.66361 100 0.86989 500 0.87935

VEI >4 20 0.17236 50 0.37367 100 0.59816 500 0.87180

15

1.4.2 Expert Elicitation and Montserrat

Eruption forecasting is a delicate subject. Communities surrounding volcanoes

as well as the general public depend on scientists “predictions”. When it comes

to any sort of natural disaster be it Hurricane Katrina or an eruption of Mount St.

Helens, the public wants to know exactly what nature will do and how it will affect

them. If the scientist is not able to make a strong case for the event, then the

scientist will loose credibility with the public. However if the scientist ends up

making a false prediction, then the public looses trust in any future forecasts.

Authorities also depend on the scientists to make accurate predictions. These

predictions aid authorities in the decision making process (evacuate, do not

evacuate) during a natural disaster.

An expert elicitation survey removes some of the apprehension that might go

along with making false predictions or in worst case scenario not informing

authorities to evacuate when the need for evacuation is necessary (Aspinall and

Cooke, 1998). With expert elicitation surveys the responsibility for tragic events

involving loss of life is not placed solely on the shoulders of one scientist who

made a false prediction. Expert elicitation is used in many risk analysis and

decision making processes including risk assessments for nuclear waste storage

at Yucca Mountain (Ho and Smith, 1997), impacts of global climate change

(Alberini et al, 2006), and assessing risk in the chemical and gas industry,

environmental, health, aerospace, occupational and banking sectors, etc. (Cooke

and Goossens, 2008). As well as being important during times of crisis, expert

elicitation is used as an objective way to form a consensus about a volcanoes

activity and what is needed to mitigate the hazards associated with the volcanic

activity for the present and in the future (Marzocchi et al., 2008).

The use of expert elicitation in volcanic hazard assessments is becoming an

exceedingly practical method for obtaining probability estimates and other

information which was before uncertain based on opinions of experts (Cooke

1991, Aspinall and Cooke 1998, Goossens and Cooke 2008, Marzocchi et al,

16

2008, Neri et al. 2008,). It develops a network between the scientists monitoring

the volcano and the community around the volcano as was seen at Montserrat in

1998 to present (Aspinall and Cooke, 1998). In 1995, the Soufrière Hills volcano

became active after 400 years of dormancy and was showing signs of an

impending eruption. The southern area of the island was evacuated prior to the

eruption in 1997, however when pyroclastic flows swept down the flanks of the

volcano there were 19 causalities, mostly farmers that went back into the area to

tend to their fields or home-owners looking after their residence (Aspinall and

Cooke, 1998). After the tragedy it was evident that the scientists needed to work

together within their network and with the community to open up a better wave of

communication. The scientists studying the volcano’s activity devised a method

of expert elicitation that allowed them to collectively monitor the volcano’s

behavior and hence change the hazard alert level when needed and when

agreed upon by the experts (Aspinall and Cooke, 1998). Expert elicitation has

been used at Montserrat since 1997, with a panel of scientists meeting every six

months to assess the level of hazard. First the panel updates the current

volcanic activity based on monitoring and current research at Soufrière Hills.

When there are qualitative assumptions, the panel uses a form of expert

elicitation to estimate critical parameters and their uncertainties (Aspinall, et al.

2009). They then include these estimations into an event tree that expresses

probabilities of occurrence and resultant hazards for particular volcanic events

over different time periods (Aspinall, et al. 2009).

17

1.4.3 Bayesian Event Tree for Eruption Forecasting at Vesuvius

The implementation of all possible data into a statistical code such as the

Bayesian Event Tree for Eruption Forecasting (BET_EF) was designed by

Marzocchi et. al in 2004 and a version 2.0 was released in 2008. The BET_EF

software was developed as a tool for estimating the probability of an eruptive

event given all relevant knowledge. This approach implements all available

information such as theoretical models, a priori beliefs, monitoring data and all

available past data (Marzocchi, 2008). The software enhances eruption

forecasting efforts by the use of monitoring data. Therefore it broadens the use

of monitoring data and may affect the way that the volcano is monitored in the

future. Marzocchi et al. 2004 defines the uses of the Bayesian Event Tree

software for:

• Long-term eruption forecasting with respect to land use management and

long-term volcanic hazard assessment.

• Short-term eruption forecasting for decision making during emergencies.

• Use of monitoring data and an eruptive history along with expert elicitation

for determining probabilities of occurrence and hence improve eruption

forecasting capabilities for future eruptions.

The software has been applied during hypothetical tests at Mount Vesuvius

(MESIMEX) (Marzocchi et al. 2006) and at the Auckland Volcanic Field (AVF)

(Ruaumoko) (Lindsay et al 2008) and applications are underway at Campi

Flegrei, Etna, Marapi, and Cotopaxi (Lindsay et al 2008). MESIMEX (Major

Emergency SIMulation Exercise for volcano risk) was tested by the Italian Civil

Protection Department in October 2006 for a hypothetical high hazard eruption of

Vesuvius, and Ruaumoko was tested by the Auckland Civil Defense in March

2008. In both cases the software was used as a supplemental scientific tool to

help in the decision process within the emergency exercises (Marzocchi, 2007b,

Lindsey, 2008).

18

2 METHODS A probabilistic volcanic hazard assessment (PVHA) is a quantitative way of

presenting data that has been merely subjective before (Marzocchi et. al, 2008).

Based on its history, Volcán de Colima may be headed toward a plinian eruption

in the next decade or two (Luhr and Carmichael, 1980), but without a quantitative

judgement, what does that really mean? The question is how likely is that to

happen? when will it happen? what magnitude of eruption is most likely? where

will it affect and how many will be at risk? These are all questions that the PVHA

can attempt to answer objectively and thus can be tested because it is a

quantitative study and not simply a subjective view. These types of studies are

beneficial because you can also measure the uncertainty in them and keep

updating them as more information is gathered and accessed. It is an evolving,

developing, quantitative model for hazard assessment and arguably every

hazardous volcano should have and maintain one.

2.1 Defining Unrest and Magmatic Unrest for an Active Volcano

With the previous work done at other volcanoes (Vesuvius, Auckland Volcanic

Field) (Marzocchi 2004, 2007, 2008, Lindsay 2008), the beginning of unrest was

marked by a clear onset of activity from a previous dormant state. At Volcán de

Colima it is harder to define unrest by just a clear onset of activity that leads to an

event, because the volcano is in a continuous state of unrest. Within the cycles,

there are marked times of dormancy and marked times of activity. Colima began

the fourth cycle of activity after a period of 47 years of being inactive and has

been relatively active since when looking at the system as a whole. Within the

cycles there have been years where the volcano has experienced no activity and

years of activity displaying different levels of explosivity. Activity ceased during a

four year period from July 1994 to November 1997. For the last ten years (1998

– present) the volcano has been erupting consistently. This pattern of unrest is

at a low level of activity and does not necessarily mean a dangerous level of

unrest, as is assumed at Vesuvius when the volcano awakes after years of being

19

dormant. The volcano had a gentle onset of activity following with intermittent

eruptions lasting 35-70 years (Luhr and Carmicheal, 1980). The volcano then

completes the cycle with a large explosion after approximately 30-65 years of this

low level activity.

Magmatic unrest can be clearly defined by the presence of an active dome or no

dome. There have been four dome growths within the crater in the last ten years

with each one ending in a dome destructive event which involves filling of the

crater and lava flows (Varley et al., 2008). The presently active dome at Colima

began growing in February 2007 and has visibly grown within the last 2 years,

however relative to the previous dome effusion rates (approximately 2 m3/s) the

current dome is an example of slow effusion (approximately <0.02 m3/s) (Varley

et al., 2008). If dome effusion trends at Volcán de Colima continue, the effusion

rate should increase, filling the crater, and producing lava flows (Varley et al.,

2008). This assessment is not attempting to evaluate extreme cases (edifice

collapse) or changes in low level activity; therefore the hazard assessment will

focus mainly on anticipating of larger explosive eruptions. Scientists at

volcanoes like Vesuvius and AVF are pressured to make quick and sound

decisions as they may have very little time to respond to a crisis. The continuous

activity at Volcán de Colima makes eruption forecasting ambiguous and requires

a constant monitoring of activity for any increase in seismicity, gas flux, and

fumarole temperatures. The PVHA is a useful way of tracking the activity

through time and when updated often, proves as a practical eruption forecasting

tool (Marzocchi et al., 2008).

2.2 Event Trees

One method to present these probabilistic studies is through the use of event

trees, which illustrate the essential constituents considered in developing a

PVHA. The event trees are representative of all potential and considered

outcomes for a volcanic system. The volcanic event tree examines the onset of

unrest, the subsequent volcanic activity and the final outcomes. Specifically, the

20

probability of an eruption, possible hazards, sectors affected, runout distances

reached and vulnerability of population and infrastructure (Newhall and Hoblitt,

2002, Aspinall et al. 2003, Marzocchi et al. 2004, 2008, Lindsay et al. 2008).

Newhall and Hoblitt (2002) define an event tree as “a graphical, tree-like

representation of events in which branches are logical steps from a general prior

event through increasingly specific subsequent events (intermediate outcomes)

to final outcomes.” Essentially it is a complex flow chart in which the branches

are dependent on the course of activity that the volcano exhibits and probabilities

are estimated for each event at “nodes” given that the previous event occurs. If

the event occurs, the branch continues, if the event prior does not occur the

branch terminates. At each node a conditional probability is calculated based on

the previous event and at the end of the event tree the “final” outcome is

calculated with an absolute probability. Event tree paths are different for each

volcano depending on activity patterns, composition, volcano structure,

vulnerable populations, etc. The nodes on the event tree represent the results of

the previous activity and the branches formed from node to node represent the

resultant path of the activity. At each node, a conditional probability, such as the

probability that an explosive eruption will occur given a magmatic intrusion

(P(3|2)), is calculated and the branch continues (Figure 5). Each node is

dependent on the previous node and a relationship between the nodes for a

particular branch (Magnitude) is dependent. Thus, if the probability increases for

a VEI 2 eruption then the probability of the other VEIs will increase or decrease

to keep the system in equilibrium. Newhall and Hoblitt (2002), Aspinall et al.

(2003), Marzocchi (2008), have designed volcanic event trees for Montserrat and

Vesuvius volcanoes. This event tree illustrates the path for volcanic activity and

is the main structural design for the BET_EF software, which contains the same

nodal structure of the event tree.

A volcano event tree was designed for Volcán de Colima (Figure 5) to illustrate

the possible outcomes of eruptions and hazards at Colima and to illustrate the

BET_EF and expert elicitation survey framework. With that said, an event tree

should be a representation of all likely possibilities within a system.

It should be observed that this event tree for Volcán de Colima focuses on VEI

events that are within a plausible range (VEI 1-5) for Colima’s current state of

unrest and considering the possibility of a cycle ending eruption. Therefore

extreme levels of activity (high and low) were not considered. It should also be

noted that the hazards focused on were pyroclastic flows, lahars and tephra fall

for this study. Hazards associated with dome collapse, lava flows, ballistics, and

debris avalanches were not included in this study. Although these hazards could

be significant to Volcán de Colima, these hazards are considered to be extreme

levels of hazards (high and low) and were not considered for this study.

Figure 5: Volcanic Event Tree. A volcanic event tree illustrates the path of a restless volcano to activity (intrusion or no intrusion) to eruption with specified magnitude and the subsequent hazards produced, distances reached and the vulnerability of population and infrastructure. This event tree is specific to possible eruptive phenomenon at Volcán de Colima Notation: U (Unrest); I (Magmatic Intrusion); Ei (Eruption) Explosive Eruption, Effusive Eruption, No Eruption, Sector Collapse; Mi (Magnitude) VEI 1, 2, 3, 4, 5; Hi (Hazard) Pyroclastic Flows, Tephra Fall, Lahars; Di (Runout Distance) Distance 1, Distance 2, Distance 3; V (Vulnerability) Population and Infrastructure. (Adapted from Newhall and Hoblitt 2002, Aspinall et al. 2003, and Marzocchi et al. 2008).

21

The advantages of using event trees and expert elicitation during episodes of

volcanic activity have been outlined in the Review of the U.S. Geological

Survey's Volcano Hazards Program, 2008 as the following:

• The progress of volcanic activity and possible outcomes are clear to

everyone involved.

• Discussion among scientists can focus on tractable questions.

• Differences in scientific opinion are identified, and therefore are more

easily discussed.

• Widely varying interpretations can be weighted.

• A simple record of decision making is produced.

2.3 Bayes’ Theorem

The fundamental statistical approach used to estimate eruption and hazard

probability in this study is the Bayes’ Theorem of probability for the estimation of

eruption probability using the methodologies described by Newhall and Hoblitt

(2002) and Marzocchi et al (2004, 2008). This theorem is the basis for the

BET_EF software that was implemented in this study.

The Bayes’ theorem is defined as (Winkler, 2003):

))P(A'A'BP(A)P(A)BP(

A)P(A)BP(B)AP(

+= (3)

where:

B)AP( is the conditional probability of event A given event B occurs.

A)BP( is the conditional probability of event B given event A occurs.

P(A) is the prior probability of event A without knowledge of event B.

)A'BP( is the conditional probability of event B given a complementary to

event A or called not A.

)P(A' is the prior probability of event A not happening.

22

Bayes’ theorem is used to calculate the conditional probability at each node of an

event tree (Figure 5) and within each node of the BET_EF software given the

outcomes at the previous nodes and eventually an absolute probability for the

final outcome, which is calculated by taking the product of all conditional

probabilities (Table 4). For example, the conditional probability of a magmatic

intrusion P(I|U) is calculated by taking the conditional probability of a volcanic

unrest given a magmatic intrusion P(U|I) multiplying by the prior probability of a

magmatic intrusion P(I) and dividing by P(U|I) P(I) plus the conditional probability

of unrest given that a magmatic intrusion does not occur P(U|I’) and the prior

probability of the magmatic intrusion not happening P(I’).

))P(I'I'UP(I)P(I)UP(

I)P(I)UP(U)IP(

+= (4)

The branches of an event tree then continue with the calculation of the

conditional probability of the following node and then so on and so forth. To

compute the final probability or an absolute probability of all previous conditional

nodes, the product of all the previous nodes is calculated (Marzocchi et al.,

2008).

)DVP()HDP()MHP()EMP(I)EP(U)IP(P(U))P( jjijijii ••••••=π (5)

23

Table 4: Conditional Probability calculation for each node of an event tree (Figure 5) specific to a volcanic system for Volcán de Colima. At each node of an event tree, the corresponding Bayes’ theorem considers the previous activity(j) and determines a probability for the resultant outcomes (i) that were considered for Volcán de Colima. Notation: U (Unrest); I (Magmatic Intrusion); Ei (Eruption) Explosive Eruption, Effusive Eruption, No Eruption, Sector Collapse; Mi (Magnitude) VEI 1, 2, 3, 4, 5; Hi (Hazard) Pyroclastic Flows, Tephra Fall, Lahars; Di (Runout Distance) Distance 1, Distance 2, Distance 3; V (Vulnerability) Population and Infrastructure. Adapted from Newhall and Hoblitt, 2002, Marzocchi et al. 2008.

Conditional Probability Unknown Response

)P(U'P(U)P(U)P(U)

+= Unrest?

Volcán de Colima is currently in a state of unrest. Therefore the P(1) ≈1.

))P(I'I'UP(I)P(I)UP(I)P(I)UP(

U)IP(+

= Magmatic Intrusion?

There is currently a magmatic intrusion present at the volcano in the form of a dome structure. Therefore (P2|1) ≈1.

)')P(E'EIP())P(EEIP( iiii +))P(EEIP(

I)EP(ii

i = Eruption?

Based on calculations made using the responses from the expert elicitation survey, the probability for eruptions is estimated using a relative frequency model and expert elicitation

)')P(M'MP(E))P(MMEP())P(MMEP(

)EMP(iijiij

iijji

+=

Magnitude?

Based on calculations made using the responses from the expert elicitation survey, the probability for eruptions were calculated for a series of VEI magnitudes and time scales.

)')P(H'HP(M))P(HHMP())P(HHMP(

)MHP(iijiij

iijji

+=

Hazards?

Based on calculations made using responses from the expert elicitation survey, the probability of hazards were calculated for a series of VEI.

)')P(D'DP(H))P(DDHP( iijiij +))P(DDHP(

)HDP(iij

ji =

Distance?

Based on calculations made using the responses from the expert elicitation survey, the probability for hazards were calculated for VEI and different distances (see Appendix1).

))P(V'V'P(DV)P(V)DP(V)P(V)DP(

)DVP(jj

jj

+= Vulnerability?

The probability that a population will be affected by the hazards and distances reached above. The population that will be affected is taken into account.

24

The Bayesian Event Tree uses this framework of volcanic event trees to combine

a volcano’s eruptive history with present monitoring data and expert elicitation to

provide valuable probability information before, during, and after an eruption

(Marzocchi et al. 2008, Lindsay et al 2008). Before the eruption, a probability of

occurrence may lead to estimates of when and how large an eruption is likely.

During the eruption the estimates are played out and accuracy is determined.

After the eruption the new information can then be added into the equation to

determine an updated estimate (Marzocchi et al., 2008).

2.4 Prior Probability of Eruptions using Historical Data

Prior Probability of the eruptions for the initial estimates using the BET_EF is

based on past frequency of eruptions. Historical eruption accounts and eruption

magnitudes were compiled from 5 sources, Simkin and Siebert (1994), Global

Volcanism Program (http://www.volcano.si.edu/), Bretón et al. (2002), Mendoza-

Rosas and De la Cruz-Reyna (2008), and current activity reports by the Colima

Volcano Observatory (Figure 6).

25

Figure 6: Recorded Eruptions. Historical eruptions with Volcanic Explosivity Index of 2, 3, and 4 at Volcán de Colima. This figure shows the four historic cycles of activity with each cycle ending in a VEI 4 eruption (Table 1). The current fourth “cycle” phase has not yet been completed. VEI 2 eruptions are shown on this graph, but are historically underreported and

therefore incomplete. (Adapted from Simkin and Siebert, 1994, Bretón et al, 2002, Global Volcanism Program GVP, 2008, Mendoza-Rosas and De la Cruz-Reyna, 2008, Colima Volcano Observatory, 2008).

Prior eruption probabilities can be calculated in many ways. The easiest and

quickest method is using a classical frequency method. In volcanic hazard

analysis a frequency of occurrence for eruptions of different magnitudes is

calculated to determine a prior probability or initial likelihood estimate of future

eruptions. This method gives us an annual probability based on number of

eruptions per year with respect to VEI.

Years

Events# veivei ≈λ (6)

Eruption probability for Volcán de Colima based on historical data is estimated in

Table 5. The time frame used for each VEI was chosen where the data was

assumed to be the most complete. Therefore for VEI 1 and 2 the time frame is

less than for VEI 3, 4, and 5.

Table 5: Calculated probability of occurrence using a relative frequency method for annual probability of eruptions with a specified time frame in years. Time frame was chose based on completeness of record.

VEI Number of Eruptions

Time (years)

Annual Probability λvei

1 57 189 0.3015873 2 51 264 0.1931820 3 35 485 0.0721649 4 9 485 0.0185567 5 0 485 -

A volcano’s eruptive history tells us a great deal about the possibility of future

eruptions and activity. The relative frequency method assumes that all events

are equally likely and non-discriminate. It does not consider the cyclic patterns of

lower probability for times of inactivity versus a higher probability when the

volcano is in a state of unrest. It assumes a complete record where all events

specifically magnitudes are equally likely over time. Due to the volcano’s

unpredictable nature and variability, this relative frequency method is not the best

for determining a volcanoes prior eruption probability and therefore when

26

27

creating a PVHA it is important to determine prior probability using the most

useful and relevant methods possible.

2.5 Expert Elicitation Survey

In accordance with the Michigan Technological University Institutional Review

Board’s procedures for the use of human subjects for research (Project: Remote

Sensing for Hazard Mitigation and Resource Protection in Pacific Latin America,

Protocol #M0177) a consent to participate form and an expert elicitation survey

were created specifically for the Volcán de Colima (see Appendix 1). The survey

was designed with principles from Aspinall and Cooke (1998) and Aspinall et al.

(2002) in mind. The questions considered the above event tree nodes and the

inputs into the BET_EF software. For the sake of simplicity, a discrete testing

method was used as opposed to the quantile method of testing. Roger M Cooke,

(Experts in Uncertainty, 1991) defines the discrete testing method (page

73)……”In discrete testing the expert is presented with a number of events. For

each event, he is asked to state his probability that the event will occur….. His

probabilities are discredited, either by himself or by the experimenter, such that

only a limited number of probability values are used……..This is closely related

to the Delphi Method (Helmer, 1966), which asks experts to state a probability

estimate for an uncertain event. The median and the interquantile range typically

the upper and lower 25th percentiles of the experts values are then computed

(Cooke, 1991). The results are sent back to the experts and the experts are

asked if they would like to revise their previous estimation based on the median

value and spread of the data. The process is completed several times until the

uncertainty, or spread of data is minimized (Cooke, 1991). The smaller spread in

the data represents the experts having reached a degree of consensus (Cooke,

1991).

The elicitation applied at Colima did not ask participants for their probability

distribution, but asked for a single average probability estimate similar to the

Delphi Method. Instead of repeating the process, the experts were asked to

28

state their certainty for each answer and thus their answers were weighted

according to their level of confidence. The information obtained from the survey

provided useful information for data thresholds, previous beliefs about hazards

and probability estimates based on weighted expert judgments.

The expert elicitation will accomplish four objectives:

1. Identify the aleatory and epistemic uncertainty within the survey (See

Section 2.5.1).

2. Determine expert weights using a performance based method and an

item weighting method (See Section 2.5.2).

3. Obtain threshold information for monitoring parameters at Volcán de

Colima that indicate anomalous levels of activity (See Section 3.1.2).

4. Combine expert’s weighted probability estimates for eruptions and

hazards that will be used as prior probability P(vei, t) models within the

BET software (See Section 2.5.3).

The design of the Volcán de Colima expert elicitation survey included three sets

of questions (Appendix 1). The questions were to be answered to the best of the

expert’s personal knowledge and without the use of any outside sources. With

each question, the expert was asked to state their certainty (level of confidence)

for the answer that they provided. The first set of questions (Appendix 1; Q1,

Q4, Q5, Q7, Q9, Q10, Q11, Q12, Q14, and Q15) are called the control questions

or within the literature the seed variables (Cooke, 1991). The ten control

questions [j=1…..10] were used to determine the knowledge and thus determine

a weight for each expert (ei). The experts were asked to answer the set of

multiple-choice and short-answer questions and to state their certainty (Cij) for

each answer given a scale of [0-not certain1, 2, 3……. 10-certain], (which is later

reformed to a [0, 1] scale). Questions varied in difficulty and content with most

concerning historic eruptions at Volcán de Colima and a number of questions

about other volcanoes and disasters in history. Two questions (Q7 and Q14)

within the seed variables were considered arbitrary. Nonetheless, they provide

29

information for comparison of the experts. These questions were considered as

part of the control questions regardless of the answer given and thus were a

measure of the expert’s level of confidence more than anything. Within the first

set of questions were five data threshold questions (Appendix 1; Q2, Q3, Q6, Q8,

and Q13). These questions were asked to determine normal and anomalous

levels for monitoring data (volcanic tremors, fumarole temperatures, and SO2

flux). Question 13 was asked in an attempt to gather information on when the

experts think the next big eruptive event comparable to the 1913 eruption will

occur.

The second set of questions (Appendix1; Q16) is a probability set to estimate the

likelihood of an eruption at Volcán de Colima of different magnitudes (VEI 1, 2, 3,

4 and 5) and for different time periods (1 month, 6 months, 1 year, 10 years, 50

years, 100 years). The third set of questions (Appendix 1; Q17) is a probability

set to estimate the likelihood of different hazards that may occur at Colima given

an eruption of specified magnitudes (VEI 1, 2, 3, 4 and 5) and run-out distances

corresponding to the specified hazards(pyroclastic flows, lahars, and tephra fall).

The experts were asked to answer these two sets of probability questions and to

state their certainty (Cik) for each answer [k=1….30] provided on the equivalent

scale of [0-not certain1, 2, 3……. 10-certain], which is later reformed to a [0, 1]

scale. Hazard maps were constructed for the third set of questions to allow the

experts to estimate which areas and distances the hazards would reach

(Appendix 1). Run-out distances for the pyroclastic flow map were calculated

using an energy cone calculation, Appendix 2 (Sheridan et.al, 1995, Newhall and

Hoblitt, 2002) and the existing hazard map “Mapa de Peligros Volcán de Fuego

Colima” constructed by the Universidad de Colima, Observatorio Vulcanológico

(Navarro et al., 2003). Distance and area for the lahar map were determined

using the Volcán de Colima hazard map referencing the lahar hazards within

channels (Navarro et al., 2003) and creating buffer zones for local watersheds of

250 and 750 meters. The tephra maps were constructed based on the

vulnerable populations surrounding the volcano that could potentially be affected

30

by smaller magnitude eruptions (distances ~10 km from the summit),

intermediate magnitude eruptions (distances ~20 km from the summit) and large

magnitude eruptions (distances >40km from the summit). It was observed and

later suggested by an expert that the ash hazard is most likely to affect the west,

northwest, north and northeast populations. Nonetheless a radial distribution

was chosen based on the unpredictability of this particular hazard due to wind

direction and speed. Thus, for simplicity, it was desirable to include all directions

and populations. It is also observed that ash at Colima has traveled as far as

725 km during the 1913 eruption (GVP, 2008). The populations immediately

surrounding the volcano, including the cities of Colima (32 km) and Ciudad

Guzman (27 km) were the main focus for this particular hazard.

The survey was tested on a group of students at Michigan Technological

University that had experience working at Volcán de Colima or had experience

working with expert elicitation surveys. The comments that were received from

the test group and advisors were used to reformat the survey and correct any

unclear elements to the survey. The survey was then distributed electronically to

over 60 likely participants. In total 12 participants answered the electronic

survey. The survey included members of both the CIIV and the Colima Volcano

Observatory and other prominent scientists that have been working with the

Volcano presently and within the distant past, including scientists from the

Universidad Nacional Autónoma de México (UNAM) and experts from the United

Kingdom, Germany, Switzerland, and the United States. The participant’s names

and individual responses remain anonymous. This is to insure that answers are

given without any bias to how they may be perceived, scored, or held

accountable for their answers in any way whatsoever. An expert ID number is

assigned to each expert in a random way and has no correspondence to the

performance of the expert. The results are available to the involved participants,

but identities of the other survey participants are not revealed.

31

2.5.1 Defining Aleatory and Epistemic Uncertainty

When constructing an expert elicitation it is important to define the uncertainty

associated within the survey and as a result of the expert’s responses. Aleatory

and epistemic uncertainties have been identified within expert elicitation surveys

(Hora, 1996, Apeland, 2001, Daneshkhah, 2004, Neri, 2008). Aleatory

uncertainty is defined as the uncertainty due to natural unpredictability of a

system and consequently is irreducible (Daneshkhah, 2004). The system, in the

case of aleatory uncertainty, relates to both the unpredictability of the Volcán de

Colima volcanic system and the unpredictability of the answers to the survey

itself. Epistemic uncertainty is defined as the uncertainty due to the lack of

expert’s knowledge about the behavior of the system and thus can be reduced

with further research (Daneshkhah, 2004). The system, in the case of epistemic

uncertainty, is due to both the lack of knowledge about volcanic processes at

Volcán de Colima, or lack of knowledge about historical eruptions or disasters,

and possible lack of knowledge on how to complete an expert elicitation survey.

The seed variables within the survey attempt to identify and quantify the aleatory

and epistemic uncertainty, however, the uncertainty based on how the

participants will answer the survey or how they perceived and answered the

questions or the bias that exist with each expert is beyond the scope of this

paper. Thus, only the uncertainty associated with the experts responses given to

these particular seed questions are established, without regard of who has

experience taking surveys or if the survey is predictable. The first set of

questions contained information that could be considered to measure the

aleatory uncertainty (Appendix 1- Q2, Q3, Q5, Q6, Q8, and Q11) and epistemic

uncertainty (Appendix 1-Q1, Q4, Q9, Q10, Q12, and Q15). The questions

considered to have aleatory uncertainty are those that would have to be

answered as a best guess such as the data threshold or any question associated

with the unpredictability of the system. The questions considered to have

epistemic uncertainty are those with a known true value, which if the expert

answered incorrectly there would be uncertainty associated with the expert’s lack

32

of knowledge. To reduce the uncertainty associated with the each individual’s

varying degree of aleatory and epistemic uncertainty, weights are assigned to

each expert.

2.5.3 Weighting Experts

Once the surveys were collected, the challenging task was to determine the

combination of expert opinions using an unbiased and logical system. Because

experts had varying experience working with Volcán de Colima, it was evident

that an equal weighting scheme would not be adequate for this study. The

expert’s individual weight is important to such a study because the weight allows

each expert’s probability estimates to be incorporated into the final estimation.

The extent to which it is included depends on the knowledge that the expert

exhibits based on a set of control questions and their individual item weights. To

combine the expert opinions, a two part weighting scheme would have to be

used. The weights were determined based on methods from Cooke (1991),

Cooke (1999), Bedford and Cooke (2001), Ayyub (2001), Cooke and Goossens

(1999, 2008). It should be noted that Cooke (1991) uses a structured expert

judgment method proven to be very useful in volcanic hazard assessments. The

method has been tested for a total of 29,079 volcano and dam structured

elicitations (Cooke and Goossens, 2008). Although these proper scoring

methods and equations are derived to be used on structured expert elicitation

with quantile distributions, the basic principles and methods can be applied to the

discrete testing method used at Volcán de Colima (Cooke, 1991). The weighting

(wi……wn) of each expert (i) was determined using two different methods (Bedford

and Cooke, 2001).

(1) Performance-based weights (wi’): Cooke (1991) uses a performance-based

method involving proper scoring rules which defines the weight of an expert by

the product of a calibration and an information score. Cooke and Goossens

(1999) define the calibration score as a measure of statistical likelihood, very

loosely characterized as "correspondence with reality". Thus, the calibration

33

score will be the score (Sij) corresponding to the correct and incorrect answers of

the control questions. Which loosely means that if the experts are corresponding

with reality, the score is high and the farther they are out of touch with the reality,

the less they are scored. The information score is defined by Cooke and

Goossens (1999) as a measure of how much information is contained within the

quantile distributions by determining the degree to which the distribution is

concentrated. Information within a distribution cannot be measured absolutely

when working with quantile measurements. However, the use of discrete

certainty values is in essence a measure of the information of an expert’s

certainty with each answer. Thus the information score of each question is the

expert’s self-stated certainty for that answer (Cij), such that if the certainty is low

then it will contain less information and a certainty that is high will contain more

information. Much like a distribution that is spread out within the quantile

measurements of fractile-structured elicitations contains less information than a

distribution that is concentrated over a value. Because the survey was not

designed as a structured expert judgment with quantile probability distributions,

but instead asking for an average probability estimates and self-stated certainty,

the equations for the proper scoring rules proposed by Cooke (1991) could not

be implemented. Rather than give each expert equal weights, the following

method was chosen for allowance of each expert’s performance to be used in

estimating the probability of eruptions and hazards at Volcán de Colima.

The control questions are then scored (Sij) on a scale of {-1} for an incorrect

answer and {1} for a correct answer for each question (see example below). This

scoring method takes into account the expert’s self-stated certainty as well as the

accuracy of their answers, such that if they answer incorrectly and with a high

level of certainty they are marked down more than if they answer incorrectly but

state a low level of certainty. The experts total score was determined by the

summation of the product of score received for each answer, Sij = {-1, 1} and

their relative certainty Cij = [0, 0.1, 0.2, 0.3…..1] for the particular answer given.

(7) ( ) ij

10

1j iji CSeScoreTotal ∑

=

•=

The relationship between the each expert’s exam score (Si) and their stated

certainty (Ci) values for the 10 control questions gave a total weighting

factor(wi’)for each expert depending on their exam score and their level of

confidence. The scores are then normalized so that the sum is equaled to one

(Cooke, 1991) (Table 6).

∑

=

=12

1ii

ii

)Score(eTotal

)Score(eTotal'w , where Σwi’=1 (8)

Table 6: Example of the performance-based weight calculation. The self-stated certainty and grading score is used in determining a performance-based weight for Expert #X. The answer score is multiplied by the self-stated certainty and then summed for a total score. The total score is then normalized relative to the combined expert’s scores to determine a performance-based weight for Expert #X. This was completed for all experts to obtain an individualized weight for each expert dependent on their exam performance.

EXPERT #X Q1 Q4 Q5 Q7 Q9 Q10 Q11 Q12 Q14 Q15 Stated Answer d d c SO2 d b e d 513264 a

Certainty (Cij) 0.8 0.8 1 0.8 0.9 0.6 1 0.9 1 1 Correct

Incorrect √ √ √ √ √ X √ √ √ √

Score (Sij) 1 1 1 1 1 -1 1 1 1 1 Total

Sij·Cij 0.8 0.8 1 0.8 0.9 -0.6 1 0.9 1 1 7.80

wx’= 7.80 56.35

wx’= 0.134871

The primary concern with this weighting method is in the situation of an expert

performing badly on the control questions and thus receiving a weight less than

zero. This is an issue that was not encountered in the survey, however had the

issue arose where an expert receives a wx’ <0, the expert would have been given

a weight of zero and subsequently their probability estimate for the performance

based weights would have been omitted from the probability calculations.

34

(2) Item weights: An item weight method was defined within the second and third

set of questions of the expert elicitation survey. Cooke and Goossens (1999)

state that item weights are potentially more attractive than global weights as they

allow an expert to up- or down-weight their response for individual items

according to how much they feel they know about that item in particular.

Essentially it is giving experts the opportunity to weight themselves for items of

interest. The second weight (wi’’) was computed using each experts self-stated

certainty for eruption probability estimates in question 16, given a magnitude and

time domain (VEI, time) and for hazard probability estimates in question 17,

given a magnitude and distance reached (VEI, distance) for potential eruptions

and hazards at Volcán de Colima. Thus expert’s certainties (C(vei, t)ik) for each

question [k=1…… 30] were summed and normalized relative to one another

(Table 7).

∑

=

=12

1iik

ikki

t) (VEI,

t) (VEI,

C

C''w , where Σwik”=1 (9)

Table 7: Example of item-based weight calculations for an eruption of VEI 1 and time period of 1 month. The self-stated certainty for each expert for each probability estimate (VEI, t) and (VEI, d) is used in determining a weight for the experts. The self-stated certainty for each question is summed and then normalized for the 12 experts. This was completed for all experts to obtain an individualized weight dependent on their self-stated certainty for each answer. ORIGINAL SELF-STATED CERTAINTY FOR EACH EXPERT Expert

ID VEI 1 month 6 months 1 year 10 years 50 years 100 years

1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 1 0.7 0.6 4 1 0.1 0.4 0.6 1 1 1 5 1 6 1 0.4 0.4 0.4 0.5 0.8 0.9 7 1 1 1 1 1 1 1 8 1 9 1 0.4 0.5 0.6 0.9 0.9 0.9 10 1 0.1 0.2 0.3 0.4 1 1 11 1 0.8 0.9 0.9 0.9 0.9 0.9 12 1 1 1 1 1 1 1

sum 6.5 7 6.8 7.7 8.6 8.7

Norm-factor 0.15385 0.142857 0.1471 0.12987 0.11628 0.114943

35

36

able 7 (continued)

ALCULATED NORMALIZED WEIGHTS FOR EACH EXPERT 50 years 100 years

T CExpert VEI 1 month 6 months 1 year 10 years ID

1 1 0.15385 0.14286 0.1471 0.12987 0.11628 0.11494 2 1 0.15385 0.14286 0.1471 0.12987 0.11628 0.11494 3 1 0.10769 0.08571 0 0 0 0 4 1 0.01538 0.05714 0.0882 0.12987 0.11628 0.11494 5 1 0 0 0 0 0 0 6 1 0.06154 0.05714 0.0588 0.06494 0.09302 0.10345 7 1 0.15385 0.14286 0.1471 0.12987 0.11628 0.11494 8 1 0 0 0 0 0 0 9 1 0.06154 0.07143 0.0882 0.11688 0.10465 0.10345 10 1 0.01538 0.02857 0.0441 0.05195 0.11628 0.11494 11 1 0.12308 0.12857 0.1324 0.11688 0.10465 0.10345 12 1 0.15385 0.14286 0.1471 0.12987 0.11628 0.11494

expert receives a weight of a zero.

nions is discussed in Cooke (1991),

It should be noted that in some cases the

This does not necessarily mean that their estimate did not count for some reason

pertaining to their performance, but rather they opted out of answering that

particular question and thus there was no probability estimate to weight.

2.5.3 Combining Expert Opinions

The weighted combination of expert opi

Cooke and Goossens (1999), Ayyub (2001), and Bedford and Cooke (2001).

These two weighting factors are applied to each expert’s probability estimates for

Q16 and Q17 to obtain a combined expert opinion, which will then be used as

probability inputs into the BET_EF software. The method used is a weighted

arithmetic mean (Bedford and Cooke, 2001) of all probability estimates given

magnitude, time, and distance for hazard probabilities. The weighted arithmetic

mean is the sum of the product of each expert’s weight and individual probability

estimate.

37

eighted arithmetic mean calculated using performance-based weights

(10)

where:

is the calculated probability of an eruption of given magnitude (VEI)

i’ sed weight for each expert

eighted arithmetic mean calculated using item weights

(11)

here:

IW is the calculated probability using item weights given a specified

ik’’

ated probability for Q16 given a specified

he probabili erformance-based weights and

ty

W

∑12

ˆ'P w =

•=1i

ikiPW t)(vei,t)(vei, p

(vei,t)PWP

and within a given time period t, or the probability of a hazard for given magnitude (VEI) and within a given distance, d, using performance based weights.

is the calculated performance-baw

is the expert (i) estimated probability for Q16 given a specifiedp̂ ikt)(vei, magnitude and time (vei, t) and for Q17 given a specified

magnitude and distance (vei, d) W

ik

12

ikIW t)(vei,t)(vei, p̂''P w∑ •= 1i=

w

(vei,t)P magnitude and time, P(vei, t) or specified magnitude and distance P(vei, d) for each expert [i=1…12] and for each question [k=1…30].

is the calculated item weight for each expert i and each question w item j

ikt)(vei, is the expert estimp̂magnitude and time (vei, t) and for Q17 given a specified

magnitude and distance (vei, d)

ties are calculated based on the pT

the individual item weights and then they are averaged to compute an average

weighted probability based on the both weighting methods for eruption probabili

estimates and hazard probability estimates. The probability was also calculated

using an equal expert weighting (w = 1/12) for reference.

38

.5.4 Expert Feedback

to give suggestions at the end of the survey (Appendix

the case of this survey, the use of remote (electronic) elicitation was used.

cess may have deterred survey participation.

hout a survey

licitation may be easily misplaced or put behind other more

iven a chance to answer questions at the same relative

he

emote expert elicitation include:

c or formally.

ble.

at

to be used as “data”.

lthough the electronic survey may contribute to a lower number of experts

y

2

The experts were asked

1; Q18). The suggestions gave incite to which survey questions were confusing

and what the survey was lacking (Appendix 3).

In

This was the main limiting factor in the survey. A total of sixty experts were

asked to participate with twelve experts responding. The disadvantages for

remote expert elicitation include:

• A non-formal elicitation pro

• Experts are not formally trained on how to take the survey.

• Questions about the survey cannot be quickly answered wit

mediator.

• Electronic e

urgent priorities.

• Experts are not g

time (i.e. the survey began in November and ended in January) with a

formal setting the survey is released at the same time and gathered at t

same time.

The Advantages for r

• The survey is completed regardless of electroni

• Participation from experts in different parts of the world is possi

• There is no time constraint therefore experts may fill out the elicitation

their leisure and as their availability allows.

• Low cost and ability to gather quality opinions

A

willing to participate, it is more convenient for both the experts and the surve

owner. The expert elicitation was useful for this study and significantly

contributed to the quality of data available.

39

.6 Bayesian Event Tree for Eruption Forecasting

nce the PVHA with probability

t

be

t al

reation of a generic Bayesian Event Tree (Figure 5) for explanation of

ility for an absolute and/or conditional

he use of this software for this study will take the existing knowledge of past

s,

F

e

2

The BET_EF software is used in this study to enha

calculations of different Volcanic Explosivity Indexes (VEI), with focus on the

long-term eruption forecasting as hypothetical applications such that no curren

monitoring data was used in this study. The software is used to determine

probability of eruptions for different time scales at Volcán de Colima and can

easily updated when new monitoring data, expert opinions, and updated past

records becomes available because it is based on a Bayesian probability

approach. Use of the BET_EF software involves three steps (Marzocchi e

2008).

1. C

the steps taken within the software.

2. Estimation of the conditional probability at each node (Table 4) of the

event tree using all relevant data.

3. Combination of each nodal probab

probability distribution for any event.

T

data, such as number of unrest episodes, number of magmatic unrest episode

number of known eruptions since 1523 (Figure 6), the prior probability model is

estimated by using the relative frequency method, and also the probability

estimates obtained from the expert elicitation survey. Inputs into the BET_E

software include probability estimates for VEI eruptions and time frames from th

expert elicitation as well as the use of inputs into the software (Table 8, Appendix

4) are as follows:

40

able 8: BET_EF software inputs and outputs.

DEL: r probability of unrest in the next month (<1) __________

ence: Equivalent number of data __________

idence: Length of catalog __________

NO

f magmatic unrest in the next month (<1) __________ ence: Equivalent number of data __________

___

NO

robability of eruption given a magmatic unrest in the next month (<1)___

s __________

onitored magmatic unrest episodes __________

atic intrusions VE

___

__________ idence: Number of eruptions __________

nitored parameters __________ SIZ

of groups to be defined: size1, size 2 etc. N)

this size idence: Equivalent number of data

l to 1

TINPUTS

Unrest NODE 1 – • MO

o Prioo Confid

• PAST DATA: o Number of known unrest episodes __________ o Conf

• MONTIORING DATA: o Number of monitored parameters __________ o Name of monitored parameters __________

DE 2 – Magmatic Intrusion • MODEL:

o Prior probability oo Confid

• PAST DATA: o Number of known magmatic unrest episodes _______o Confidence: Length of catalog __________

• MONTIORING DATA: o Number of monitored parameters __________ o Name of monitored parameters __________

DE 3 – Eruption • MODEL:

o Prior po Confidence: Equivalent number of data __________

• PAST DATA: o Number of known eruptions __________ o Confidence: Number of magmatic unrest episode

• MONTIORING DATA: o Number of monitored parameters __________ o Number of mo Name of monitored parameters __________

weight, threshold interval, measures during past magmNT LOCATION – Volcán de Colima • Input latitud n• MODEL:

e/lo gitude, map, and central volcano dimensions

o Prior probability of eruption at each Vent Location _______o Confidence: Number of eruptions __________

• PAST DATA: o Number of known eruptions at each vent locationo Conf

• MONTIORING DATA: o Number of monitored parameters __________ o Name of mo

E GROUPS – VEI 1, 2, 3, 4, 5 • SIZE

o Insert the number GROUPS

o Do you want that the size distribution depends on vent location (Y/• MODEL:

o Size 1 - prior probability of eruption with this size given eruption o Confidence: Equivalent number of data

• PAST DATA: o Size 1 - number of known eruptions witho Conf

• Model/Past for each of the 4 locations which must be equa

41

Table 8 (co

e (VEI) robability for Magnitude (VEI 1,2,3,4,5), Vent Location

or Magnitude (VEI 1)

n

he software takes all available data input and produces a conditional and

ich

ty

dy,

ntinued) OUTPUTS NODE 4 – Magnitud

• Conditional P• Absolute Probability f

o Cumulative Distribution Function (CDF) 10th percentile of distributio Median of distribution 90th percentile of distribution Average of distribution

o Probability Density Function (PDF)

T

absolute probability at each node (Node 1 -probability of unrest, Node 2 –

probability of magmatic intrusion, and Node 3 – probability of eruptions) wh

are considered to be the intermediate outcomes (Sandri et al., 2003). The final

outcome or probability of eruption of different magnitudes and time frames are

calculated as an absolute and conditional probability. The software produces a

cumulative distribution function and a probability density function at for each

size/type group (VEI 1-5). The absolute probability estimates with a probabili

distribution and cumulative distribution function and with the average, 10th,

median, and 90th percentile probability values.

eruption forecasting with input of The software can be used for short term

monitoring data to improve the probability estimates. In the case of this stu

data input was from the prior probability model, expert judgment and past data

which allowed only for long-term hazard assessment.

42

RESULTS AND DISCUSSION essment for Volcán de Colima provides

rd

a

of

.1 Expert Elicitation Results

ncertainty using Seed Variables

stem

y that

erts

3The probabilistic volcanic hazard ass

results for three different components of the assessment. (1) Processing of

expert judgment results in prior estimations of eruption probabilities and haza

likelihoods. (2) Bayesian Event Tree for Eruption Forecasting computes a

likelihood of eruptions by using all applicable knowledge; expert judgments,

priori beliefs, theoretical models, and historical data. (3) Vulnerability analysis

the population surrounding Volcán de Colima is determined based on results of

the probability analysis and past occurrences at the volcano.

3

3.1.1 Aleatory and Epistemic U

Within the 15 seed and threshold questions, the aleatory and epi ic

uncertainty was identified and quantified. The measure of the uncertaint

the experts exhibited when answering the questions was derived by taking the

opposite of the experts self stated certainty (uncertainty = 1-Cij) to arrive at their

uncertainty value. The aleatory uncertainty was quantified by taking the experts

uncertainty value dealing with questions that quantify the aleatory uncertainty

(Section 2.5.1). The epistemic uncertainty was quantified by taking the experts

uncertainty value dealing with questions that quantify the epistemic uncertainty

(Section 2.5.1). The uncertainty for each expert was then averaged. Overall, the

aleatory uncertainty is greater than their epistemic uncertainty, suggesting that

the experts felt less confident answering questions with regard to unknown

aspects about Colima’s eruptions, hazards, and data thresholds and the exp

felt more confident answering questions with known answers such as questions

about accounts, dates, and disasters in history. On average about half of the

experts showed lower aleatory and epistemic uncertainty and half showed a

higher level of uncertainty (Figure 7).

Figure 7: Aleatory and Epistemic Uncertainty. The aleatory and epistemic uncertainty for expert responses was identified within the seed and data threshold questions.

3.1.2 Calibration of Experts Scores, Certainty and Weights

The expert’s total scores and total overall certainty where used as a calibration of

the experts. If an expert is perfectly calibrated the correct answer score will be

equal or nearly equal to the certainty for that answer such that if they answered

all answers correctly they received a score of 1 for that question and if they are

well calibrated their certainty stated will be 1 or nearly 1 depending on how

confident they answered. The method used for the calibration and information

scores determines the level of knowledge the expert has based on their answers

and level of confidence in their answer based on their stated certainty. If an

expert scored high on the exam but had an overall low certainty, then that expert

is considered to be under confident in their answers. If the expert scored low on

the exam, but had an overall high certainty, then that expert is overconfident in

their answers and will be relatively unreliable. Results of expert scores shows

that they were reasonably consistent with each other, however there was an

43

average overestimation in their confidence with their resulting exam scores

(Figure 8).

Figure 8: Expert Calibration. Scoring of the expert’s control questions shows the overestimation (above the Perfect Calibration line) or underestimation (below the Perfect Calibration line) of confidence in survey participants. Most of the participants are overestimating their confidence.

The expert’s self-stated certainty values are used as a measure of reliability. If

the expert has a high confidence in answers that they answer incorrectly, they

could be viewed as unreliable. The expert is considered reliable if they answer

correctly with high certainty or incorrectly with low certainty. The experts that

have low certainties for both correct and incorrect answers suggest that they are

underestimating their level of confidence. Overall, experts showed a lower

certainty for answers that were incorrect and a higher certainty for answers that

were correct which makes them reliable. Some experts stated low certainty for

both incorrect and correct answers suggesting they are underestimating their

ability (Figure 9).

44

Figure 9: Average Certainty. The relationship between experts average self-stated certainty for correct and incorrect answers. The expert is reliable if they have a higher certainty for correct answers and a low certainty for incorrect answers. The seed variables pointed out an interesting discrepancy between expert’s

beliefs and the literature for the last cyclical eruption (1913). Eight of the 12

experts stated that the 1913 eruption was a VEI 3 where in most of the literature

and historically it is referred to as a VEI 4. The total volume of the 1913 eruption

was estimated at 0.31km3 (Saucedo et al. 2005), indicating a VEI 4 (Simkin and

Seibert, 1994).

3.1.3 Data Thresholds Examined

The five data threshold questions (Appendix 1-Q2, Q3, Q6, Q8, Q13) determined

threshold information for monitoring data at Volcán de Colima - seismic, thermal

infrared and SO2 flux. The thresholds were chosen based on the average and

standard deviation from the mean of expert responses. The answers and the

self-stated certainties given by the experts were also a determining factor in

45

choosing the thresholds (Example- Figure 10). If an expert had a low certainty

for their answer and their answer did not fall within the standard deviation of the

other data responses it was omitted from the threshold range. The range of

threshold values were quite variable but gave a low threshold and high threshold

for the questions asked (Table 9). This threshold information could potentially

be used within the BET_EF software for the monitoring data threshold

information considered when inputting data i.e. for short term eruption

forecasting.

Figure 10: Expert Response to Q3. The expert’s response vs. certainty for each answer shows the grouping and a difference between the higher certainty and lower certainty stated. The thresholds where chosen based on the standard deviation from the mean and the certainty was considered. Therefore the threshold chosen for how many continuous days of volcanic tremor allowable is 10 – 28 days.

46

47

Table 9: Estimated data threshold information based on expert elicitation results. What is the highest

number of Volcanic Tremors/day at

Volcán de Colima before the threat of

an impending eruption with a VEI ≥

3 becomes significant?

How many days of continuous volcanic tremor are allowable at Volcán de Colima before the threat of

an impending eruption with a VEI ≥

3 becomes significant?

What is the highest fumarole

temperature (°C) at Volcán de Colima before threat of an impending eruption

with a VEI ≥ 3 becomes

significant?

What is the highest

acceptable level of SO2 flux

(tonnes/day) at Volcán de Colima before threat of an impending eruption

with a VEI ≥3? Average 287.50 19.20 579.55 4943.00 Standard Deviation 396.84 24.62 392.93 6552.53

Deviation from Mean 119.65 8.99 129.78 2675.05

Thresholds 168 – 400 tremors/day 10 – 28 days 450 – 710°C 2270 – 7620

tonnes/day Background ~10 tremors/day ~250°C ~274 tonnes/day

Although threshold information varied widely, with respect to question 13 which

stated “When do you think the next big eruptive episode (comparable to the 1913

eruption of Volcán de Colima will occur?” 17% of experts agreed that the next

big eruptive episode comparable to the 1913 eruption at Volcán de Colima will

occur in the next 5 years, 42% of experts agreed within the next 10 years (see

results below – Figure 11). This is comparable to and quantifies Carmicheal and

Luhr’s (1980) statement that the next cyclical ending eruption will be sometime in

the early part of this century.

When do you think the next big eruptive episode (comparable to the 1913

eruption at Volcán de Colima) will occur?

5 years 17% experts

10 years 42% experts

50 years 33% experts

100 years 8% experts

Figure 11: Expert Responses to Q13. Response and matching certainty bars for each expert’s answer shows that 43% of experts agreed that the next big eruptive episode at Volcán de Colima will occur in 5-10 years. The expert’s certainty bars for their given response increases from left (most certain) to right (less certain).

Despite being overconfident in their seed variables, overall the experts were

consistent in how they answered questions, such that if they were unsure about

an answer they stated a lower level of confidence in that answer and therefore

their probability estimate results and resulting certainty can be validated or

trusted. Once the experts were identified, scored, and weighted, their initial

probability estimates were combined to produce a weighted and combined

probability for eruptions of magnitude, (VEI) and time, t.

3.1.4 Eruption Probability Estimates

The comparison of the two weighting schemes with the equal weighting (w=1/12)

are shown in Table 10 for each VEI and time period questioned. The

performance-based weighted probabilities are significantly less than the

individual item weights. This suggests that the higher probability using the item

48

49

weights were a result of some expert’s overconfidence shown in Figure 8 and the

performance-based weighted probability estimates were possibly too strict, when

compared to the equal weighted probabilities. Ayyub (2001) states that the

primary disadvantages to the item weight method are the bias and

overconfidence that result in inaccurate self assessments.

Table 10: Weighted Expert Elicitation Probability Estimates for Eruptions given VEI and time period.

Eruption Probability Estimates using Equal Weighting VEI 1 month 6 months 1 year 10 years 50 years 100 years 1 0.69091 0.76364 0.81000 0.96000 0.99000 0.99000 2 0.41909 0.53727 0.58100 0.79000 0.90000 0.96500 3 0.28191 0.34555 0.41010 0.59100 0.79091 0.88818 4 0.09092 0.13637 0.19092 0.43645 0.53364 0.68818 5 0.08000 0.10000 0.10000 0.17001 0.30637 0.47500

Eruption Probability Estimates using Performance-Based Weighting VEI 1 month 6 months 1 year 10 years 50 years 100 years 1 0.63673 0.70541 0.64046 0.70861 0.72919 0.72919 2 0.46806 0.58208 0.53345 0.66699 0.70000 0.71029 3 0.31198 0.38447 0.37799 0.55129 0.77418 0.79768 4 0.07116 0.13159 0.20657 0.51393 0.57732 0.70078 5 0.05040 0.07098 0.07098 0.13478 0.27833 0.53200

Eruption Probability Estimates using Item Weighting VEI 1 month 6 months 1 year 10 years 50 years 100 years 1 0.84615 0.84857 0.87353 0.96883 0.99070 0.98966 2 0.58726 0.68508 0.71927 0.87486 0.87811 0.88753 3 0.36471 0.42745 0.51875 0.73167 0.86957 0.91413 4 0.09437 0.14375 0.21887 0.54035 0.65633 0.80529 5 0.08060 0.10909 0.10794 0.17115 0.33444 0.53424

To neutralize the effect of the overconfidence and the strict scoring weights the

average of the performance based probability and the item weighted probability

is calculated and shown with resulting uncertainty (Table 11, Figure 12). The

averaging of these two weighted probabilities ensures that both methods are

included into the estimate and therefore there is lessened weighting bias.

Probability estimates for eruptions of specified magnitude and for time periods

were combined from the expert elicitation survey using the above two weighting

schemes (Eqs. 8 and 9).

Table 11: Combined Eruption Probability Estimates showing resulting

uncertainty in the experts estimates. Combined Expert Eruption Probability Estimates

(Performance Based and Item weights) VEI 1 month 6 months 1 year 10 years 50 years 100 years 1 0.74144 0.77699 0.75700 0.83872 0.85995 0.85942 ±0.11398 ±0.08450 ±0.08089 ±0.02211 ±0.01 ±0.01 2 0.52676 0.63055 0.62546 0.78975 0.83117 0.84327 ±0.09946 ±0.09605 ±0.09687 ±0.09597 ±0.05374 ±0.02114 3 0.33834 0.40596 0.44837 0.64148 0.82187 0.85590 ±0.07108 ±0.07900 ±0.08486 ±0.10095 ±0.060984 ±0.04083 4 0.08276 0.13767 0.21272 0.52714 0.61683 0.75304 ±0.02112 ±0.02786 ±0.04145 ±0.08658 ±0.08108 ±0.09231 5 0.06550 0.09004 0.08946 0.15297 0.30639 0.53312 ±0.02 ±0.02981 ±0.02981 ±0.04955 ±0.06497 ±0.08396

Figure 12: Combined Weighted Probability Estimates. The expert estimates of probability show the relationship between probability and Volcanic Explosivity Index (VEI) with respect to time. Trends show that probability increases with time and decreases with large

magnitude eruptions (Figure 12). The trend also shows a leveling off of smaller

magnitude eruptions with larger time periods and a leveling off of larger

magnitude eruptions with a shorter time period. This is a result of uncertainty.

50

The longer the time period the less uncertainty associated with the smaller

magnitude events and the larger the eruption the less uncertainty for shorter time

periods (Figure 13).

Figure 13: Probability vs. Time. Expert combined probability estimates for eruptions of given magnitude and with respect to time. Probability estimates calculated using the NGHPP by Mendoza-Rosas and De la

Cruz, 2008; show approximately a magnitude higher or lower than those

estimates given by the experts and in some estimates, significantly higher (Table

12). The prior probability estimates calculated from expert opinion will be

combined with historical data for further probability estimation within the BET_EF

software.

51

52

Table 12: Comparasion of the estimates of Mendoza and De la Cruz, 2008 with estimates interpolate from the expert elicitation survey

Mendoza-Rosas and De la Cruz, 2008

Expert Judgment

VEI Years Probability Probability >2 20 0.63290 0.71867

50 0.90840 0.82187 100 0.96840 0.85590 500 0.87936 0.96974

>3 20 0.35806 0.55558 50 0.66361 0.54531 100 0.86989 0.69410 500 0.87935 0.87103

>4 20 0.17236 0.24829 50 0.37367 0.30639 100 0.59816 0.53312 500 0.87180 0.61347

3.1.5 Hazard Probability Estimates

The experts were asked to rank the hazards from most hazardous to least

hazardous on a scale [1….6] affecting the populations surrounding the Volcán de

Colima (Figure 14). Results from this indicate that the highest risk hazards are

pyroclastic flows and debris avalanches in terms of populations affected.

Populations could also be affected by lahars and tephra fall which most experts

ranked in the middle range (3, 4). The least likely to affect populations were

ballistics, and lava flows.

Figure 14: Expert Response to Question 14. The experts were asked to rank the hazards based on the population that could be injured surrounding Volcán de Colima from 1 most hazardous to 6 least hazardous to the populations. The results show that debris avalanches, pyroclastic flows, tephra falls, and lahars are the most hazardous and lava flows and ballistics are the least hazardous to surrounding populations.

Probability estimates for volcanic hazards of specified magnitude and for

distance were combined from the expert elicitation survey using the above two

weighting schemes (Eqs. 8 and 9). The comparison of the two weighting

schemes with the equal weighting (w=1/12) are shown in Table 13 for each VEI

and distance questioned.

53

54

Table 13: Expert Elicitation Probability for volcanic hazards given eruption of VEI and distance the hazard travels from the summit.

Hazard Probability Estimates using Equal Weighting VEI PFD1 PFD2 LD1 LD2 TD1 TD2 TD3 1 0.33636 0.02727 0.44545 0.10000 0.39091 0.23636 0.13636 2 0.56667 0.13333 0.65000 0.20833 0.59167 0.35833 0.20833 3 0.71667 0.35833 0.82500 0.51667 0.76667 0.60833 0.47500 4 0.89167 0.62500 0.89167 0.72500 0.95833 0.86667 0.75000 5 0.93333 0.82500 0.92500 0.80833 1.00000 0.94167 0.89167

Hazard Probability Estimates using Performance-Based Weighting VEI PFD1 PFD2 LD1 LD2 TD1 TD2 TD3 1 0.29059 0.02076 0.39947 0.05555 0.38376 0.24827 0.14481 2 0.58030 0.14774 0.65963 0.18057 0.60657 0.37196 0.24277 3 0.73177 0.31890 0.83869 0.49494 0.78030 0.62724 0.52209 4 0.91837 0.59707 0.92671 0.72591 0.96406 0.88083 0.79299 5 0.96122 0.84827 0.96903 0.80941 1.00000 0.94366 0.89743

Hazard Probability Estimates using Item Weighting VEI PFD1 PFD2 LD1 LD2 TD1 TD2 TD3 1 0.2575 0.022989 0.450667 0.086747 0.392593 0.22 0.133333 2 0.523377 0.131601 0.661918 0.195709 0.569225 0.339479 0.231666 3 0.698765 0.317333 0.82963 0.509091 0.765909 0.634483 0.496429 4 0.894444 0.58625 0.903409 0.735 0.958696 0.863736 0.786207 5 0.934737 0.816484 0.938462 0.806897 1 0.94 0.896703

The performance-based weighted and the item weighted probability estimates

are not significantly varied from each other, as was seen with the eruption

probability estimates. This suggests that the experts are stating less

overconfidence in these answers. Conceivably, there is less certainty when

answering these questions and the higher uncertainty could be a result of the

hazards associated with larger magnitude eruptions having not been first-hand

experienced by this generation of experts giving rise to a higher uncertainty

about the possibilities of hazards. The uncertainty could have been a result of

the hazard maps and runout distances being too long compared to the current

hazard maps (Navarro et al. 2003). As was identified by experts, the pyroclastic

flow distance 2 was exceedingly long (20km) and according to Saucedo (2005),

pyroclastic flows from the 1913 eruption have been said to reach a maximum

distance of 15km. Nonetheless the hazard probabilities were estimated using the

two distances chosen (Table 14, Figure 15).

Table 14: Combined Volcanic Hazard Probability Estimates showing resulting uncertainty in the experts estimates.

Combined Expert Hazard Probability Estimates (Performance Based and Item weights)

VEI PFD1 ~12km

PFD2 ~20km

LD1 ≤20km

LD2 ≤40 km

TD1(5cm) 10 km

TD2(5cm) 20km

TD3(5cm)>40 km

1 0.27405 0.02188 0.42507 0.07115 0.38818 0.23413 0.13907 ±0.09271 ±0.01949 ±0.07904 ±0.04671 ±0.10484 ±0.07660 ±0.06363 2 0.55184 0.13967 0.66077 0.18814 0.58790 0.35572 0.23722 ±0.06666 ±0.04975 ±0.05435 ±0.05702 ±0.10621 ±0.07925 ±0.07633 3 0.71527 0.31812 0.83416 0.50202 0.77311 0.63086 0.50926 ±0.05482 ±0.05567 ±0.04286 ±0.05482 ±0.07107 ±0.09330 ±0.09221 4 0.90641 0.59166 0.91506 0.73045 0.96138 0.87229 0.78960 ±0.03362 ±0.05240 ±0.03981 ±0.04626 ±0.0193 ±0.04323 ±0.05435 5 0.94798 0.83238 0.95375 0.80815 1.00000 0.94183 0.89707 ±0.02562 ±0.04105 ±0.04105 ±0.04515 ±0 ±0.02599 ±0.03579

Figure 15: Expert Hazard Probability Estimates. The combined estimtates using the performance-based and item weighting. The volcanic hazard increases with magnitude and decreases with distance. Thus shorter distance hazards are much more likely at Volcán de Colima.

55

Trends show that probability increases with magnitude and decreases with

runout distance (Figure 15). The uncertainty with estimates becomes less as the

magnitude increases, indicating that the occurrence of hazards at Volcán de

Colima are more likely with larger eruptions. The least likely hazard is a

pyroclastic flow at distance 2, which is due to the overestimation of runout

56

distance (PD2) calculated using the energy cone. Pyroclastic flows with respect

to distance 1 (PD1) have high probability of occurrence. Lahars (LD1) are the

most likely to occur with small magnitude eruptions and tephra fall (TD1) is the

most likely to occur with large magnitude eruptions. Based on the overall results of the expert elicitation for eruptions and hazard

assessment, the highest probability hazards at Colima are pyroclastic flows for

distance 1 (PFD1) and Tephra fall hazards at 10km and for larger events at 20km

and >40km. Another hazard present at Volcán de Colima is the resultant

pyroclastic flows with larger events of VEI 3, 4 and 5. Pyroclastic flows have

been modeled at Volcán de Colima (Saucedo et al. 2005). The tephra fall

depends on wind speed and direction and therefore is hard to estimate the

likelihood of sectors that will be affected. Lahar hazards are the most likely at

Volcán de Colima, however it is hard to quantify the actually hazard and flow

length because lahars are not always associated with eruptions, but sometimes a

secondary affect of eruptions and due to heavy rainfall which is more likely to

occur during the rainy season. Lahars are usually confined to surrounding

channels and thus it is hard to determine the vulnerability of populations or

number affected.

3.2 BET_EF Preliminary Results

The BET_EF software was used for this study to obtain long-term probability

distributions relative to magnitude and time periods assessed within the expert

elicitation survey and based on all available data. First the software was

implemented with the use of prior probability information from the annual

probability of eruptions, past eruptions, and prior models (Figure 16 and 17).

VEI Average 10th % 50th % 90th % Size 1 8.36E-01 8.33E-01 8.37E-01 8.40E-01 Size 2 1.37E-01 1.34E-01 1.37E-01 1.40E-01 Size 3 2.24E-02 2.09E-02 2.24E-02 2.37E-02 Size 4 3.68E-03 3.13E-03 3.66E-03 4.28E-03

Size 5+ 6.09E-04 3.74E-04 5.86E-04 8.55E-04 Figure 16: Size Distribution. Size distribution values illustrating average probability for eruptions within the next month for all Volcanic Explosivity Indices (VEI). Output generated in BET_EF software using only historical data and prior frequency of eruptions using the Gutenberg-Richter Law (1954) Global Frequency. The conditional probability results are computed into Cumulative Distribution

Functions (CDF) and Probability Density Functions (PDF) (Figure 17). The

results are computed for a long-term hazard assessment and give results for

unrest, magmatic unrest, eruptions, and eruptions of different magnitudes based

on the prior probabilities calculated above (Table 5). The Cumulative distribution

gives quantiles of 10th, 50th and 90th percentiles and shows a beta distribution.

The resulting uncertainty can be computed from these data outputs and also

shown as a result of the spread of data within the Probability Density Functions.

57

Figure 17: BET Absolute Probability Output. Output for volcanic eruption probability showing the Cumulative Distribution Functions (CDF) and Probability Density Functions (PDF) for an magmatic unrest at Volcán de Colima leading to an eruption out of vent location 1 and with VEI 1.

3.3 BET_EF Results using Expert Elicitation

The eruption probability estimates from the expert elicitation survey can then be

incorporated into the model and are used as inputs into the BET_EF software

(Appendix 4-Size/Type Groups). The software requires identification of the

number of sizes to be entered into the software. In the case of this study, five

size groups (VEI 1-5) were used. These sizes represent the event tree outcomes

and they are thus a 1-normalized sample for the weighted arithmetic mean

estimates. The calculation for this is the 1-normalized weighted arithmetic mean

(Bedford and Cooke, 2001). 58

∑

=

•= 12

1i

ikiBET

t)(vei,

t)(vei,t)(vei,

P

p̂P w (12)

Expert weighted and normalized probabilities, past data, and prior probability

models are input into the software (Appendix 4). The software was used to

calculate an absolute probability The software was used to calculate absolute

probabilities of eruptions at the Volcán de Colima using historical records of the

volcano and the relative frequency method (Figure 18).

Input into the BET_EF software was completed to investigate the long-term

hazard for time periods of 1 month, 6 months, 1 year, 10 years, 50 years and 100

years. These data outputs for the absolute probability were reintroduced into the

event tree for representation of the probabilities (Appendix 5). Outputs from the

BET_EF software were computed in MATLAB to determine a cumulative

distribution for the 10th, 50th and 90th percentile groups. The data was then fit to

a probability density function using a using Beta Distribution calculation

(Appendix 6). The eruption probability that was determined by the expert

elicitation was used as inputs into the software and compared to the outputs from

the software (Table 15). Monitoring data was not added to the calculations and

only the use of the expert probabilities and historical eruptions, unrest and

magmatic unrest was used to determine the probability of sizes of eruption for

the future (Figure 18). Table 15: BET Results. Expert elicitation results and resulting BET outputs.

VEI 1 month 6 months 1 year 10 years 50 years 100 years EXPERT ELICITATION RESULTS 1 0.42215 0.38075 0.35513 0.28635 0.25145 0.22457 2 0.29877 0.30817 0.29314 0.26868 0.24307 0.22048 3 0.19189 0.19783 0.21000 0.21680 0.23771 0.22216 4 0.04848 0.06799 0.09888 0.17587 0.17794 0.19485 5 0.03872 0.04527 0.04285 0.05229 0.08983 0.13794 BET_EF RESULTS using Expert Elicitation and Historical Data 1 0.478 0.467 0.459 0.4411 0.4242 0.4151 2 0.304 0.317 0.317 0.3372 0.3392 0.3377 3 0.1637 0.1737 0.1903 0.2276 0.2514 0.2634 4 0.0445 0.0563 0.0815 0.139 0.151 0.1789 5 0.00995 0.0117 0.0145 0.018 0.0304 0.0467

59

VEI Average 10th % 50th % 90 % Size 1 0.411 0.387 0.411 0.434 Size 2 0.308 0.287 0.308 0.33 Size 3 0.201 0.18 0.201 0.22 Size 4 0.0511 0.0402 0.051 0.0617

Size 5+ 0.0294 0.0218 0.0295 0.0394

Figure 18: Size Distribution. Output generated in BET_EF software using historical data and expert elicitation results. Size distribution values illustrating average probability of eruptions within the next month for all Volcanic Explosivity Indices (VEI). 3.4 Vulnerability Analysis for Maximum Expected Event

The final branch in the event tree (Node 7 - Figure 5) represents the final

outcome and determines the vulnerability of persons and infrastructure.

Vulnerability is described by De La Cruz-Reyna et al., (2008) as the expected

percentage loss of the exposed value should the hazardous manifestation occur

(i.e. probability of loss). Hazard and vulnerability go hand in hand when

determining risk and this relationship is notably defined by Fournier d’Albe (1979)

as:

Risk = hazard * vulnerability* value (13)

60

61

Where risk is calculated by taking the probability of a hazard multiplied by the

vulnerability (probability of loss) and multiplied by the value (number of people or

monitory value that will be lost). Studies such as these are very useful in

concluding a hazard assessment and indeed may be the single most important

part. However, there is a lack of knowledge and high uncertainty when

determining vulnerability because it must be assumed that the person will be

present when the hazard arrives (Newhall and Hoblitt 2002). Because the

vulnerability of the area was not determined using expert opinion, the percentage

loss is hard to estimate. Undoubtedly the population (209 residents) within a

10km radius is the most vulnerable to pyroclastic flows and tephra fall for a

maximum expected event.

The best that can be done to determine vulnerability with this study is to estimate

the value (# persons) within hazardous areas used for the expert elicitation and

calculate the maximum expected loss for a maximum expected event. To

determine an estimate of the value lost at Volcán de Colima, it is important to

look at the historical records on prominent hazards at the volcano. Historically

not many deaths have been reported at the volcano. There are reports for

earthquake related fatalities, including one earthquake that was resultant of a

high level of volcanic activity in 1911. During this earthquake, 1300 people lost

their lives in Zapotlán, Colima, and surrounding villages (New York Times, 1911).

But primary volcano related deaths are not a common occurrence at the volcano

or have gone unreported.

3.4.1 Pyroclastic Flow Hazard

Pyroclastic flows and basal surges at Volcán de Colima have been modeled and

the hazard assessed for this type of hazard by Saucedo et al. 2005, and

Sheridan and Macias, 1995. Saucedo et al. (2005) describes at-risk villages of

La Becerrera, San Antonio, El Naranjal, Atenguillo, El Fresnal, San Marcos and

Yerbabuena in terms of pyroclastic flows. Yerbabuena, which is at the highest

risk with a probability of approximately 91% for large pyroclastic flows including

62

pumice and block and ash flows (Sheridan and Macias, 1995). Ash clouds

associated with pyroclastic flows could potentially affect Tonila and Queseria

villages (Saucedo et al., 2005). Pyroclastic flows are usually confined by

barrancas and therefore it is difficult to estimate the vulnerable populations and

the likelihood that an area will be occupied at the time of a pyroclastic flow.

Using the energy cone distances (Appendix 4) and the LandScanTM 2007 Global

Population Database, the vulnerable population was estimated for each

pyroclastic flow distance (Table 16). Table 16: Maximum population affected by pyroclastic flows

for distances 12km and 20km. Hazard Distance Population Pyroclastic Flow 10km 209 Pyroclastic Flow (PD1) ~12km 6,854 Pyroclastic Flow (PD2) ~20km 25,612

Table 17: Pyroclastic flow runout exceedence probabilities from Newhall and Hoblitt, 2002. Runout distance arranged by VEI and Vertical Drop (H). The vertical drop used for Volcán de Colima is H ≥ 2km in the table. Distances outside Colima’s 8 km exclusion zone are highlighted.

Exceendence Probability VEI 0.95 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05

1-2 4.1 4.4 4.9 6.5 6.9 7.2 7.4 8.2 10.5 11.9 13.5 Km 3 4.6 4.8 5.2 5.8 6.5 7.6 9 10.9 12.8 14.5 15.2 Km

4-5 7.3 7.7 8.1 8.5 9.6 12.5 14.6 17.4 21.6 28.1 33 Km

Maximum risk for pyroclastic flows resulting from a VEI 4 (comparable to 1913)

within 10 km distance from the Volcán de Colima summit was calculated using

the BET output probabilities and Newhall and Hoblitt (2002) exceedence

probabilities (Table 17). Vulnerability is set at one, which is stating the highest

probability of loss. This is subject to debate because it assigns maximum

vulnerability of 1 to each of the 209 residents and is higher than the actual

vulnerability.

63

Table 18: Risk analysis for maximum expected event (VEI 4) and pyroclastic flow hazard at Volcán de Colima for populations within a 10km zone, probability that a VEI will occur in time periods assessed and the exceedence probability (Newhall and Hoblitt, 2002).

Time Distance (km) Probability Exceedence

Probability Population Vulnerability Risk

1 Month 10 0.0445 0.55 209 1 2.445% 6 Months 10 0.0563 0.55 209 1 3.096%

1 year 10 0.0815 0.55 209 1 4.482 % 10 years 10 0.139 0.55 209 1 7.645% 50 years 10 0.151 0.55 209 1 8.305% 100 years 10 0.1789 0.55 209 1 9.839%

The risk is shown in percent for each person residing within the 10 km zone and

for time periods specified (Table 18). The percent risk to each of the residents is

fairly high and resulting from using the energy cone area and maximum

vulnerability for residents. The vulnerability of populations surrounding Volcán de

Colima needs to be investigated further for a more in-depth risk assessment.

3.4.2 Tephra Fall Hazard

Tephra fall is a principle hazard at Volcán de Colima with the capacity to affect

the most people during large magnitude eruptions. However, tephra falls do not

generally injure people directly without the failure of infrastructure, usually the

hazard results from ashfall exceeding 10 cm of dry tephra or 5 cm of wet tephra

for most structures (Newhall and Hoblitt, 2002). Tephra falls have traveled as far

as 725 km from the summit as was observed after the 1913 eruption (Table 19).

It has been reported that tephra fall in Ciudad Guzman has caused roofs to

collapse under the load of the tephra during historical eruptions (Martin del

Pozzo, 1995).

64

Table 19: Principle direction and maximum distance of Tephra fall for significant eruptions at Volcán de Colima (Global Volcanism Program, VAAC).

Date VEI Distance Direction 10 Jan 1585 4 220km - 13 Dec1606 4 200km - 8 June 1622 4 400km NNE 1711 3 132km NE -Guadalajara 1744 2 32km SW-Colima 10 March 1770 3 550km - 15 Feb 1818 4 425; 470km NE; E 13 August 1872 3 30km NW 15 March 1873 3 32km SW-Colima 5 Nov 1889 2 75km NW 18 Dec 1889 3 110km NE 4 Jan 1890 2 100km - 16 Feb 1890 4 300km NE 18 Nov 1890 3 100km - 20 Feb. 1903 3 25.5km NE and SW-Colima 24 Feb. 1903 3 200km NNE 20 Jan. 1913 4 725km NNE 28 Aug. 2003 3 60km NW 30 May 2005 - 80km NE and SE

Tephra fall at Colima can disperse widely and affect higher number of population

at greater distances than any other hazard. Based on a radial dispersion and

using the LandScanTM 2007 Global Population Database, the vulnerable

population was estimated for each tephra fall distance (Table 20). The current

hazard map (Navarro et al. 2003) shows the direction of tephra dispersal

typically to the NW and NE based on wind speed and wind directions at Volcán

de Colima. This would therefore affect less people than a radial distribution. Table 20: Maximum population affected by Tephra fall for

radial distances 10, 20 and 40km Hazard Distance Population

Tephra Fall (TD1) 10km 209 Tephra Fall (TD2) 20km 31,218 Tephra Fall (TD3) >40km ± 487,904

65

Table 21: Tephra fall thickness exceedence probabilities from Newhall and Hoblitt, 2002. Fallout thickness arranged by VEI and distance from the summit. The vertical drop used for Volcán de Colima is H ≥ 2km in the table. Thickness greater than 10 cm (exceeding bearing strength of roofs) are highlighted (Newhall and Hoblitt, 2002).

Exceedence Probability

VEI Dist. 0.95 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05

10km 0.1 0.1 0.2 0.3 0.5 0.8 1.3 2 3 4.5 5.4 Cm 1-2 20km 0 0.1 0.1 0.2 0.3 0.4 0.5 0.8 1.2 2.3 - Cm

40km 0 0.1 0.1 0.1 0.1 0.2 0.2 0.3 0.4 0.7 - Cm 10km 0.2 0.7 1.8 3.1 4.8 7.1 10.4 15.3 23.6 40.8 58.6 Cm

3 20km 0.1 0.1 0.5 1 1.2 2.5 4 6.8 11.9 19.4 28.2 Cm

40km 0.1 0.1 0.3 0.4 0.6 0.9 1.3 2.2 5.3 10.1 - Cm 10km 6.2 12 28 35.7 41.6 55.3 99.1 159.7 235.1 416.7 619.7 Cm

4-5 20km 3 5.5 11 17.4 22.9 29.5 71.9 118.3 199.5 262.6 326.8 Cm 40km 1.6 2.4 5.4 11.6 15.4 26.7 58.7 95.8 114.1 231.4 440.3 Cm

Maximum risk for a tephra falls resulting from a VEI 4 (comparable to 1913)

within 10 km distance from the Volcán de Colima summit was calculated using

the BET probability output and the Newhall and Hoblitt (2002) exceedence

probabilities (Table 21). Vulnerability is estimated at 0.25 assuming that that the

probability of loss is much less than that of pyroclastic flows. The actually

vulnerability is unknown but estimated (Table 22). Table 22: Risk analysis for maximum expected event (VEI 4) and tephra fall hazard (12 cm) at Volcán de Colima for populations within a 10km zone, probability that a VEI will occur in time periods assessed and the exceedence probability (Newhall and Hoblitt, 2002).

Time Distance (km)

Probability VEI 4

Exceedence Probability

Population (Value) Vulnerability Risk

1 Month 10 0.0445 0.9 209 0.25 1.00% 6 Months 10 0.0563 0.9 209 0.25 1.267%

1 year 10 0.0815 0.9 209 0.25 1.833% 10 years 10 0.139 0.9 209 0.25 3.127% 50 years 10 0.151 0.9 209 0.25 3.397% 100 years 10 0.1789 0.9 209 0.25 4.025%

Tephra fall risk is much less than pyroclastic flows, however is still relatively high.

This indicates that the vulnerability estimates for the tephra fall are much higher

than the actual vulnerability and an in-depth tephra load and structure

assessment needs to be implemented for the correct vulnerability values.

66

4 CONCLUSIONS Although it is still impossible to predict exact timing of eruptions and the

outcomes that result from them, scientists are becoming more advanced in

determining the possibilities of outcomes and thus being more prepared for these

outcomes. Using the past, theoretical models, and the opinions of experts to

identify the possibilities leads to a probability model for possible eruption

magnitudes and how likely are these eruptions and within what time frames.

Historically, Volcán de Colima has displayed cyclical behavior and the last cycle-

ending eruption occurred in 1913 with a large magnitude eruption (VEI 4). In this

context, the volcano is highly likely to erupt with another large magnitude

eruption sometime in the near future. The 1913 eruption destroyed the dome

present, sending pyroclastic flows as far as 10km. Partial plinian column

collapses sent pyroclastic flows as far as 15 km from the summit. If the volcano

does erupt with a large magnitude eruption, the hazards produced by this

eruption will affect the vulnerable populations surrounding the volcano and

especially the population within a 10 km distance from the summit.

Combined expert opinion showed that there is a 52.7% chance that the volcano

will erupt with a VEI 4 eruption within 10 years and 42% of experts believe that

the eruption will occur within this time frame. Expert opinion also showed that

there is a 42% likelihood that the volcano will erupt within the next 5 years and

17% of the experts determined this time frame to be the most probable. Along

with eruption probability estimates, the combined expert opinion for eruptive

hazard probability estimates showed that if the volcano did erupt with a large

magnitude eruption then hazards could affect areas surrounding the volcano that

are populated. The likelihood of all the considered hazards affecting all the

runout distances for a VEI 4 eruption were above 50%, which is fairly high when

thinking about the hazards individually. The BET_EF output gave a 14%

likelihood of this happening with respect to all other outcomes and with minimal

associated uncertainty. The BET_EF software was used as a way to combine

67

these relevant data and illustrate the uncertainty associated with these estimates

when looking at the probability density functions. The use of probabilistic tools

and expert elicitations is helpful in creating probabilistic volcanic hazard

assessments for volcanoes where probability of destructive events resulting in

loss of life and infrastructure is high.

The expert elicitation study provided useful information to determine what is

unknown about the volcano and what is possible to occur in the future. As well

as establishing a preliminary study with the participants of the survey, the results

can now be seen as a collaborative effort between the many groups and

organizations working at Volcán de Colima. Elicitation allowed this group of

experts to combine their opinions and thus their opinions can be used as

quantifiable data. As well as probabilistic studies, expert elicitation can be used

to raise volcano hazard levels as is seen at Montserrat and Vesuvius, make

important decisions during volcanic crisis and come to a consensus on what has

been uncertain about the volcano prior to the elicitation such as the data

threshold information that was quantified in this study. Data thresholds were

determined using the experts mean and standard deviation of their data

threshold responses. The wide span within their estimates showed that there is

an inconsistency between the groups monitoring the volcano and the actual data

threshold estimates could thus not be accurately determined. However, the

questions could be reintroduced to the experts to show the inconsistencies and

perhaps allow them to come up with a consensus in these data thresholds

estimates in a more formal setting. This would only reinforce the collaboration

between the monitoring groups and thus advance the monitoring efforts at

Colima.

Updating the data as expert’s opinions change and adding new data and

information as it becomes available is a highlight to hazard assessments. They

are evolving assessments and can be used as another tool in the monitoring of a

high risk volcano. The probabilistic volcanic hazard assessment prepared for

68

Volcán de Colima is a preliminary assessment prepared in the wake of what may

be the next big explosive eruption comparable to the 1913 eruption.

Probabilistic hazard assessments can also be used during times of crisis by

addition of monitoring data and observing the evolving probabilities. This is

helpful in aiding scientists make important decisions during times of increased

hazards and in emergency situations. Hazard assessments are useful for long-

term hazard assessment as they help to identify areas at highest risk and

vulnerability of population and infrastructure. The probabilistic hazard studies

can aid in preparation of hazard maps by determining which areas are at highest

risk and adding the vulnerability of populations.

The vulnerability of populations within 10km of the volcano is most worrying

when considering the maximum expected event. The event could affect

approximately 209 residents within 10km of the summit and would put them at

risk of experiencing pyroclastic flows and tephra fall. The maximum risk of being

affected by a pyroclastic flow for a person within 10km of the volcano and when

considering the likelihood of a VEI 4 eruption within the next ten years is 7.465%.

This is considerably high for a risk assessment and thus cannot be used as a

final estimate. This estimate could be further refined with an in-depth risk

assessment and would greatly benefit hazard mitigation and risk reduction efforts

at Volcán de Colima.

4.1 Recommendations for Future Work

Based on the work that has been accomplished and the work that still is possible

at Volcán de Colima the following recommendations are made:

• Restructure the expert elicitation survey based on retrospection and

experts comments (Appendix 3) and based on more accurate modeling of

pyroclastic flows and tephra fall direction and distances within the

literature.

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• Restructure the expert elicitation to incorporate expert opinion of

probability distributions for the different events (VEI and time) such that

the quantile method and the proper scoring rules may be implemented

and the EXCALIBUR software (Cooke, 1991) may be used.

• Continual updating of hazard information with expert elicitation surveys in

a formal setting. Structure an organized method for delivering the expert

elicitation surveys and using expert elicitation at Colima would be

beneficial to the volcano monitoring groups within the Colima network.

This may help with communication problems between the groups

monitoring the volcano and may bring about fewer inconsistencies within

threshold information.

• In order for a study like this to be of use the continual updating of

information needs to be addressed in the BET_EF software. As new

information becomes available, the information should be input into the

software. As well as continual expert elicitation in the event of an

emergency.

• Monitoring data of the volcano can be used in the event of an emergency

for short-term forecasting and can dramatically change the probability

when implemented into the software. Therefore there is a need to study

this further.

• Update hazard maps as new data becomes available. Continuing with

detailed hazard modeling and evaluation of the exposure and vulnerability

at Volcán de Colima would be beneficial to the probabilistic hazard

assessment.

• Construct a detailed risk assessment involving vulnerability studies for

surrounding populations.

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APPENDIX 1 – Expert Elicitation Consent to Participate and Survey (Blank Forms)

CONSENT TO PARTICIPATE IN RESEARCH Compiled study of expert opinion for the probability of eruptions and volcanic hazards at Volcán de Colima, México.

You are asked to participate in a research study conducted by Ingrid Fedde and from the Geological Sciences Department at Michigan Technological University as part of a Master’s thesis project. Your participation in this study is entirely voluntary. The following information will be presented to you through a survey. Please ask questions about anything that you do not understand before consenting to participate in this survey. • PURPOSE OF THE STUDY This study is to determine the probability of eruptions and volcanic hazards at Volcán de Colima through the use of expert elicitation surveys and the Bayesian Event Tree for Eruption Forecasting (BET_EF) computer software. The results of both methods will be used in the study and compared for accuracy. • PROCEDURES If you volunteer to participate in this study, you will be asked to do the following things: 1. Complete the written survey, anticipated to take approximately thirty minutes, which will require you to give your expert opinion on the volcano’s state of unrest, likelihood of eruptions and volcanic hazards, and areas affected by volcanic hazards at Colima. The survey is to be completed without the use of any references. Following the survey, the researcher will compile the expert opinions and compute a single probability with the information gathered. The results will be made available to you upon request. 2. You are welcome to contact the investigator to make editorial changes or add additional comments. After final analysis of information, all surveys will be destroyed. • POTENTIAL RISKS AND DISCOMFORTS This study is not intended to provoke any physical or emotional discomfort. All efforts will be made to ensure confidentiality. The answers you provide will remain anonymous and completely confidential. The information provided will remain confidential to the extent of the law. In the event of physical and/or mental injury resulting from participation in this research project, Michigan Technological University does not provide any medical, hospitalization or other insurance for participants in this research study, nor will Michigan Technological University provide any medical treatment or compensation for any injury sustained as a result of participation in this research study, except as required by law.

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• POTENTIAL BENEFITS TO SUBJECTS AND/OR TO SOCIETY This study will not give you any specific benefits besides the opportunity to share your expert opinion. However, your participation will provide an educational benefit because it will give the researcher the opportunity to exercise skills learned in coursework as well as the chance to learn about your opinions. There is also the possibility that this research will be published, which will benefit the scientific and civil community. The investigator does not promise tangible benefits as a result from participation in this project. • CONFIDENTIALITY Any information that is obtained in connection with this study and that can be identified with you will remain confidential and will be disclosed only with your permission. Confidentiality will be maintained by means of personal anonymity. The researcher will keep their surveys in a safe place. After analysis of the information, the surveys will be destroyed. • PARTICIPATION AND WITHDRAWAL You can choose whether or not to be in this study. If you volunteer to be in this study, you may withdraw at any time without consequences of any kind or loss of benefits to which you are otherwise entitled. You may also decline to answer any questions you do not want to answer. There is no penalty if you withdraw from the study and you will not lose any benefits to which you are otherwise entitled. However, your participation in this survey will be greatly appreciated because it will significantly improve the quality of the study. • RIGHTS OF RESEARCH SUBJECTS The MTU Institutional Review Board has reviewed my request to conduct this project. If you have any concerns about your rights in this study, please contact Joanne Polzien of the MTU-IRB at 906-487-2902 or email jpolzien@mtu.edu. • IDENTIFICATION OF INVESTIGATORS If you have any questions or concerns about this research, please contact the investigator: Ingrid Fedde: (719) 252 5547. idfedde@mtu.edu Jose L. Palma: jose@mtu.edu I understand the procedures described above. My questions have been answered to my satisfaction, and I agree to participate in this study. I have been given a copy of this form. ________________________________________ _________________________ Signature of Subject Date

THIS IS A SURVEY TO DETERMINE A COMPILED EXPERT OPINION OF THE PROBABILITY OF ERUPTIONS AND VOLCANIC HAZARDS AT VOLCAN DE COLIMA. THE SURVEY WILL BE ANALYZED AND USED IN PART FOR A PROBABILISITC MODEL. PLEASE USE YOUR EXPERT OPINION ONLY AND ENTIRELY WITHOUT THE USE OF REFERENCES OR ANY OTHER OUTSIDE SOURCES. YOUR IDENTITY WILL REMAIN ANONYMOUS. THANK YOU FOR YOUR PARTICIPATION. Instructions: Please answer to the best of your knowledge and experience, if you do not understand a question, please feel free to ask questions. Any questions or comments can be addressed to Ingrid Fedde (idfedde@mtu.edu) After answering each question please indicate how certain you are about your answer on a scale from 0(not certain) – 10 (certain).

Volcanic Explosivity Index (VEI)

Figure from USGS Volcanic Hazards Program Photo Glossary at: http://volcanoes.usgs.gov/Imgs/Jpg/Photoglossary/VEIfigure.jpg

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1. What is the estimated VEI of the May 18, 1980 eruption at Mount St. Helens? a. VEI 2 b. VEI 3 c. VEI 4 d. VEI 5 e. VEI 6 Answer _______________ Certainty ______________

2. In your opinion, what is the highest number of Volcanic Tremors/day at Volcán de Colima before the threat of an impending eruption with a VEI ≥ 3 becomes significant?

Answer _______________ Certainty ______________

3. In your opinion, how many days of continuous volcanic tremor are allowable at Volcán de Colima before the threat of an impending eruption with a VEI ≥ 3 becomes significant?

Answer _______________ Certainty ______________

4. What has been the largest historical eruption recorded at Volcán de Colima

since 1600? a. VEI 1 b. VEI 2 c. VEI 3 d. VEI 4 e. VEI 5

Answer _______________ Certainty ______________

5. Which hazard(s) could affect the city of Colima with eruption of VEI 4? Indicate

all that apply a. Lava flows/Dome Building b. Pyroclastic flows c. Tephra falls d. Lahars

Answer _______________ Certainty ______________

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6. In your opinion, what is the highest fumarole temperature (°C) at Volcán de Colima before threat of an impending eruption with a VEI ≥ 3 becomes significant?

Answer _______________ Certainty ______________

7. In your opinion, what monitoring parameter is the most important at Volcán de

Colima to predict an impending eruption ≥ VEI 3? a. Increase in seismicity b. Increase in SO2 output c. Fumarole Temperature increase d. Change in frequency of eruptions Answer _______________ Certainty ______________

8. In your expert opinion, what is the highest acceptable level of SO2 flux (tonnes/day)

at Volcán de Colima before threat of an impending eruption with a VEI ≥3?

Answer _______________ Certainty ______________

9. How many causalities occurred during the 1985 eruption of Nevado del Ruiz in

Colombia? a. 100-1,000 causalities b. 1,000-10,000 causalities c. 10,000-20,000 causalities d. 20,000-30,000 causalities e. 30,000-50,000 causalities f. 50,000-100,000 causalities g. 100,000-1,000,000 causalities

Answer _______________ Certainty ______________

10. What year did Montserrat’s Soufrière Hills volcano first show signs of unrest

after historically being dormant? a. 1987 b. 1991 c. 1995 d. 1997

Answer _______________ Certainty ______________

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11. What types of hazards are typical of a VEI 3 eruption at Volcán de Colima? a. Lava flows/Dome Building b. Tephra falls c. Pyroclastic flows d. Lahars e. All of the above

Answer _______________ Certainty ______________

12. What was the VEI of the 1913 eruption at Volcán de Colima? a. VEI 1 b. VEI 2 c. VEI 3 d. VEI 4 e. VEI 5

Answer _______________ Certainty ______________

13. In your opinion and based on the frequency of eruptions at Volcán de Colima,

when do you think the next big eruptive episode (comparable to the 1913 eruption at Volcán de Colima) will occur? Indique your best estimate.

Never 1 2 3 4 5 10 50 100 200 years

Answer _______________ Certainty ______________

14. Rank the hazards based on the population that could be injured surrounding

the Volcán de Colima? (1 most hazardous to 6 least hazardous) _____ Lava flows _____ Pyroclastic flows _____ Tephra falls _____ Lahars _____ Debris avalanche _____ Ballistics

Certainty ______________

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15. How many causalities where there in the capital city of Plymouth during the 1997 eruption of Montserrat?

a. 0-25 causalities b. 26-50 causalities c. 51-100 causalities d. 100-1,000 causalities e. 1,000-10,000 causalities Answer _______________ Certainty ______________

16. Given the past eruptions and the current state of activity at Volcán de Colima, in your opinion what is the likelihood that there will be an eruption of a magnitude, given in the table below, within each specific time window? Please use the table given below to indicate according to your opinion, what is the likelihood of an eruption happening during each of the time windows and of the specific VEI given in the table. Please also indicate your level of certainty about your answer.

Likelihood Not likely Somewhatlikely Highly likely

0 1 2 3 4 5 6 7 8 9 10

Certainty Not certain Somewhatcertain Certain

0 1 2 3 4 5 6 7 8 9 10

VEI 1 month 6 months 1 year 10 years 50 years 100 years

Likelihood 1 Certainty Likelihood 2 Certainty Likelihood 3 Certainty Likelihood 4 Certainty Likelihood 5 Certainty

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**********Use the Previous Maps to Complete the Following Questions*********

17. Given a volcanic eruption of VEI 1 – 5, what is the likelihood that a volcanic

hazard will extend to the distance given in the maps presented above (Distance 1, Distance 2, Distance 3)? Mark all that apply with appropriate rating of likelihood from 0(not likely) to 10(likely,) and an appropriate rating of uncertainty 0(not certain) to 10(certain). Follow the hypothetical example given below(inside the gray box) for lava flows (not considered in the real cases of this survey):

EXAMPLE – LAVA FLOWS (using map 1) If an expert believes that the likelihood of a lava flow reaching distances 1 and 2 for eruptions of VEI 1, 2, 3, 4 and 5 increases from unlikely to very likely, he MAY fill the table in the following way:

VEI Distance 1 Distance 2

Likelihood 7 0 1 Certainty 7 10 Likelihood 6 0 2 Certainty 6 10 Likelihood 3 0 3 Certainty 7 10 Likelihood 0 0 4 Certainty 10 10 Likelihood 0 0 5 Certainty 10 10

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PYROCLASTIC FLOW HAZARD – Use Map 1

VEI Distance 1 ≤12km

Distance 2 ≤20km

Likelihood 1 Certainty Likelihood 2 Certainty Likelihood 3 Certainty Likelihood 4 Certainty Likelihood 5 Certainty

LAHAR HAZARD – Use Map 2

VEI Distance 1 ≤20km

Distance 2 ≤40 km

Likelihood 1 Certainty Likelihood 2 Certainty Likelihood 3 Certainty Likelihood 4 Certainty Likelihood 5 Certainty

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TEPHRA FALL HAZARD (Thickness ≥ 5 cm) – Use Map 3

VEI Distance 1 10 km

Distance 220 km

Distance 3 >20 km

Likelihood 1 Certainty Likelihood 2 Certainty Likelihood 3 Certainty Likelihood 4 Certainty Likelihood 5 Certainty

18. Please use this space to make any comments or suggestions that you feel would improve this survey or study. Thank you.

APPENDIX 2 – Energy Cone using Heim Coefficients Elevation/Distance (H/L) for PF runout distance Eight distances (L) were determined using the previous pyroclastic flow hazards (Navarro et al., 2003) and elevations at those distances (H) were determined. The plume height was calculated for 100, 300, and 500m height over the summit. Points H Elev. L Dist H/L Points H Elev. L Dist H/L Points H Elev. L Dist H/L Points1 1071 14680 0.20 1 1071 14680 0.21 1 1071 14680 0.22 0.4 2 1223 14936 0.18 2 1223 14936 0.20 2 1223 14936 0.21 0.3 3 1237 13660 0.20 3 1237 13660 0.21 3 1237 13660 0.23 0.2 4 1469 10280 0.24 4 1469 10280 0.26 4 1469 10280 0.28 5 1256 11611 0.23 5 1256 11611 0.25 5 1256 11611 0.27 6 1111 14613 0.19 6 1111 14613 0.21 6 1111 14613 0.22 7 1092 14300 0.20 7 1092 14300 0.21 7 1092 14300 0.23 8 3218 2526 0.29 8 3218 2526 0.37 8 3218 2526 0.45 Summit 3860 Summit

Heig3860 Summit

Heig3860

Height of plume over the summit (m)

ht of plume over the summit (m) ht of plume over the summit (m) 100 300 500

Total elev. 3960 Total elev. 4160 Total elev. 4360

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APPENDIX 3 –Expert Responses to Question 18 (above): • “Ask for probability of 1-5 instead of 1-10”. • “For question 16, it would be better to show a clear example like question

17, to have better certainty in the scores”. • “The parameters considered in questions 2 and 3 are of little relevance.

More relevant is the seismic energy released and the changes in the rate of liberation”.

• “The probabilities must be expressed as fractions in Rank 0-1 or as percents in the rank of 0-100. Rank of 0-10 is inconsistent with the published literature”.

• “In the concept of the maps of pyroclastic flows and lahars, the distances for a VEI event =1 are very long, the Pyroclastic Flow distances are shorter to 6 km and lahars shorter to 10 km, in the last 20 years, therefore there must be 3 distances not only 2”.

• “In the map of tephra, the direction and wind speed are determining in the distance of fallout, the hazard map of the Volcán de Colima by the Volcano Observatory of the University of Colima, show the influence of these two factors (direction and wind speed) based on the statistics of 8 years of Vaisala radiosonde. This map is the official map of the authorities of Civil defense of Colima”.

• “Q2. Still think it is impossible to say. I answered thinking more in terms of Long Period events”.

• “Q6. Also this is not a good question. There is a max. temp. which is the magma temp. (about 900) but this was reached in 2001 with no fear of large eruption”.

• “Most of my info came from looking at the field-based hazard map of Navarro et al (2003). Others experts will get their data from previous models. It will be interesting to see if they agree and what it says about the models if they do not agree”.

• “Hard to use logarithmic VEI scale with integer only linear probability estimate”.

• “Much of the questions require more familiarity with the VEI system than with Colima itself. It would be worth sending the questions to people who deal with it a lot and know a VEI 4 when they see one”.

• “For many questions, I would have preferred to give a range of my estimate. (Q12, VEI 3-4, as I am uncertain which but am more confident that it is not 1,2, or 5)”.

• “For many of the questions, I have noted how I interpreted them if I felt that there could be misunderstanding. (e.g. lava flows wont injure many people ,but if it collapsed to a pyroclastic flow then it will, so even though the presence of a lava flow confuses things more dangerous my scores may not reflect that, it is the pyroclastic flow that does the damage).”

• “Volcanic Ash should replace Tephra Fall. The probability by the definition must be in the rank 0-1.”

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APPENDIX 4– Bayesian Event Tree Inputs and Outputs using expert opinion Table A4.1: Bayesian inputs

Bayesian Event Tree Eruption Forecasting 1 Month 6 Months 1 year 10

years 50 years 100 years

NODE 1 - Unrest Model Prior Probability of unrest in the next month (<1) 1 1 1 1 1 1 Confidence: Equivalent number of Data 10 10 10 10 10 10 Past Data Number of known unrest episodes 224 224 224 224 224 224 Confidence: Length of the catalog (number of inference intervals) 418 418 418 418 418 418

Monitoring Data Number of monitored parameters Name of Monitored Parameters and Threshold Interval Fumarole Temperatures Seismicity SO2 Flux NODE 2 - Magmatic Intrusion Model Prior Probability of magmatic unrest given an unrest in the next month 1 1 1 1 1 1

Confidence: Equivalent number of Data 10 10 10 10 10 10 Past Data Number of known magmatic unrest episodes 4 4 4 4 4 4 Confidence: Number of unrest episodes 10 10 10 10 10 10 Monitoring Data Number of monitored parameters Number of monitored unrest episodes

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Table A4.1 (continued): Bayesian inputs NODE 3 - Eruption Model Prior probability of eruption given a magmatic unrest in the next month

0.117098

0.117098

0.117098

0.11709

0.117098

0.117098

Confidence: Equivalent number of data 10 10 10 10 10 10 Past Data

Number of known eruptions 152 152 152 152 152 152 Confidence: Equivalent number of magmatic unrest episode (node 2)

Equivalent number of unrest episodes (node 1) 224 224 224 224 224 224 Monitoring Data Number of monitored parameters Number of monitored magmatic unrest episodes Name of Monitored Parameters and (its weight, threshold interval, measures during past magmatic intrusions)

Vent Locations Latitude: 19.512708 Central Volcano Dimensions Longitude: -103.617444 Inner Radius (km): 0.2875 Volcanic Area Map Sectors Strike (Degrees): 90 Min Latitude: 19.458289 Outer Radius (km): 1.2 Max Latitude: 19.567321 Min Longitude: -103.559022 Max Longitude: -103.674821 Map Dimensions (km x km):12.14 km

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Table A4.1 (continued): Bayesian inputs

Vent Location - 2 Vent 1 = .0994 (crater) Vent 2=0.006 (Volcancito)

Model/Past for each of the 4 locations which must be equal to 1 152 eruptions ~6 eruptions (Volcancito)

Size/type Groups Insert the number of groups to be defined size1, size 2 etc. 5

Do you want that the size distr. depends on vent location? no Model/Past Equivalent number of data: Size 1 - prior probability of eruption with this size given eruption: 0.42252 0.38065 0.35490 0.28431 0.25026 0.22353

Size 1 - number of known eruptions with this size: 57 Size 2 - prior probability of eruption with this size given eruption: 0.30018 0.30891 0.29323 0.26771 0.24189 0.21933

Size 2- number of known eruptions with this size: 51 Size 3- prior probability of eruption with this size given eruption: 0.19281 0.19888 0.21021 0.21745 0.23918 0.22262

Size 3- number of known eruptions with this size: 35 Size 4- prior probability of eruption with this size given eruption: 0.04716 0.06744 0.09973 0.17869 0.17951 0.19586

Size 4- number of known eruptions with this size: 9 Size 5- prior probability of eruption with this size given eruption: 0.03733 0.04411 0.04194 0.05185 0.08916 0.13866

Size 5- number of known eruptions with this size: 0

APPENDIX 5 – Event trees for Volcán de Colima The event trees were constructed using the BET_EF results (10th-50th-90th percentiles) and the expert elicitation hazard probability estimates. Figure A5.1: Event Tree VEI 1 – Eruption and resulting hazard probability for time period of 1 month

Figure A5.2: Event Tree VEI 2 – Eruption and resulting hazard probability for time period of 1 month

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Figure A5.3: Event Tree VEI 3 – Eruption and resulting hazard probability for time period of 1 month

Figure A5.4: Event Tree VEI 4 – Eruption and resulting hazard probability for time period of 1 month

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Figure A5.5: Event Tree VEI 5 – Eruption and resulting hazard probability for time period of 1 month

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APPENDIX 6 –Probability Density Functions for Volcán de Colima The Beta probability density functions were calculated using the 10th, 50th, and 90th percentiles of the BET_EF output for the 6 time periods assessed. Figure A6.1: Probability Density Function for BET_EF output for 1 month

Figure A6.2: Probability Density Function for BET_EF output for 6 months

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Figure A6.3: Probability Density Function for BET_EF output for 1 year

Figure A6.4: Probability Density Function for BET_EF output for 10 years

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Figure A6.5: Probability Density Function for BET_EF output for 50 years

Figure A6.6: Probability Density Function for BET_EF output for 100 years