Mar 22, 2013 - diverging connection, and (c) converging connection (based on Jensen ...... Tse S.D., Fernandez-Pello A.C. (1998) On the flight paths of metal ...
Project number: Project name: Project acronym: Theme:
Start date:
265138 New methodologies for multi-hazard and multi-risk assessment methods for Europe MATRIX ENV.2010.6.1.3.4 Multi-risk evaluation and mitigation strategies
01.10.2010
End date: 30.09.2013 (36 months)
Document: D5.2 Framework for multi-risk assessment Version: Final Responsible partner: NGI Month due: M24 Month delivered: M28 Primary authors(a): Farrokh Nadim and Zhongqiang Liu
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22.03.2013
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((a) see the Acknowledgements section for a full list of people contributing to this document) Reviewer: Gordon Woo
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Authorised: Jochen Zschau
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Public Restricted to other programme participants (including the Commission Services) Restricted to a group specified by the consortium (including the Commission Services) Confidential, only for members of the consortium (including the Commission Services)
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Abstract Many regions of the world are exposed to and affected by several natural hazards. The implementation of effective risk management strategies in these areas therefore requires that all relevant threats are assessed and considered. Compared to single-risk analysis, the examination of multiple risks poses a range of additional challenges due to the differing characteristics of hazards. The purpose of this deliverable is to develop a theoretical framework for consistent multirisk assessment. The work presented in this report is coordinated within MATRIX Task 5.2 “Development of a theoretical framework for consistent multi-risk assessment”. Where Task 2.1, Task 3.3 and Task 4.2 are developing models for the consistent assessment of single hazards, multi-hazards and time-dependent vulnerability, respectively, the work presented herein focuses on approaches and steps that are unique for consistent multi-risk assessment. The deliverable summarizes previous research on multi-risk assessment and proposes a new three-level framework for multi-risk assessment that could account for the possible interactions among the threats. Within this framework, the first level is a qualitative flow chart that guides the user to whether a multi-hazard, multi-risk approach is required for the problem at hand. The second level is a simplified, semi-quantitative approach to explore further the need for a detailed assessment. The third level is a detailed quantitative multi-risk analysis based on Bayesian networks. The key components of this framework, such as cascade hazards assessment, time-dependent vulnerability estimation, and the choice of the required level of sophistication, are addressed. The multi-risk assessment procedure outlined in the report integrates the results of the assessment of the risk posed by each threat, cascade effect, and the appropriate consideration of uncertainties, to provide a more rational estimate of multiple risks. Two detailed case studies, one dealing with the scenario of debris flow triggered by both earthquakes and precipitation that demonstrates the application of the model, and one dealing with the assessment of hazards and risks from volcanic eruption or tectonic seismic activity in the island of Santorini model, are presented in the report. Keywords: multi-risk, framework, three-level, qualitative, semi-quantitative, quantitative
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Acknowledgments The research leading to these results has received funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under grant agreement n° 265138. Different partners from the MATRIX project have collaborated in the preparation of this report. Here we include the entire list of people who participated (alphabetical order of institutions):
- AMRA: Alexander Garcia-Aristizabal; - ASPINALL: Gordon Woo, Willy Aspinall; - GFZ: Kevin Fleming; - NGI: Farrokh Nadim, Zhongqiang Liu, Bjørn Vidar Vangelsten; - TU-Delft: Pieter van Gelder
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Table of contents Abstract ................................................................................................................................. 3 Acknowledgments ................................................................................................................. 4 Table of contents ................................................................................................................... 5 List of Figures........................................................................................................................ 7 List of Tables ........................................................................................................................10 1
Introduction and objectives ............................................................................................11
2
Review of existing frameworks for multi-risk assessment ..............................................13
3
Principles of multi-risk assessment ................................................................................18
4
Description of the recommended framework for multi-risk assessment .........................20 4.1
The three-level multi-risk assessment framework ...................................................21
4.2
Event trees .............................................................................................................27
4.3
Bayesian networks for multi-risk assessment .........................................................30
4.3.1
Multi-hazard analyses .....................................................................................34
4.3.2
Time-dependent vulnerability assessment.......................................................36
4.3.3
Multi-risk assessment considering mitigation measures ..................................40
5
Time stepping Monte Carlo simulation...........................................................................44
6
Case studies .................................................................................................................46 6.1
Constructing causal networks for multi-risk assessment .........................................47
6.2
Quantifying the networks ........................................................................................48
6.2.1
Seismic hazard sub-network ...........................................................................48
6.2.2
Cascade effect sub-network ............................................................................51
6.2.3
Debris flow hazard sub-network ......................................................................52
6.2.4
Building damage sub-network .........................................................................53
6.3
Results ...................................................................................................................55
7
Summary and conclusions ............................................................................................56
8
References ....................................................................................................................57
Appendix A: Case study of Santorini unrest – Assessing hazards and risks from volcanic eruption or tectonic seismic activity ...............................................................................60 A.1
Introduction ............................................................................................................60
A.2 Inferring incipient eruption probabilities by application of Bayesian Belief Networks to volcanic unrest observations - case illustration: Santorini 2011- 2012 ...........................60 A.2.1
A basic BBN for Santorini ................................................................................61
A.2.2
Time-stepping BBN .........................................................................................64 5
A.2.3
Extending the BBN for additional datastreams ................................................66
A.2.4
Linking eruption scenario probabilities to ash and gas hazards .......................67
A.3
Santorini unrest multi-hazards: Kameni earthquake fault activation ........................68
A.3.1
Summary.........................................................................................................68
A.3.2
Seismic hazard assessment ............................................................................69
A.4
Discussion..............................................................................................................78
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List of Figures Figure 2.1 Global distribution of flood risk: (a) mortality, (b) total economic loss, and (c) economic loss as a proportion of GDP density (source: Dilley et al., 2005). .........................14 Figure 2.2 (a) Aggregated hazard map (based on 15 hazard indicators); (b) Integrated vulnerability map; (c) Aggregated risk. ..................................................................................15 Figure 2.3 Final output of the multi-risk analysis done for the city of Cologne, Germany (Grünthal et al., 2006): Risk curves of the hazards due to windstorms, floods and earthquakes for losses concerning buildings and contents in the sectors of private housing, commerce and industry (reference year: 2000). ...................................................................16 Figure 4.1 Schematic view of the steps followed in the MATRIX multi-risk assessment framework. ...........................................................................................................................20 Figure 4.2 Stages of risk assessment for single hazards. ....................................................21 Figure 4.3 The steps involved in the Level 1 multi-risk analysis (* Potential interactions of independent hazards could be introduced by mitigation measures, which affect total expected loss. For instance, house height increasing could reduce loss due to flooding, but increase loss due to earthquake). .........................................................................................21 Figure 4.4 The steps involved in the Level 2 multi-risk analysis. ...........................................23 Figure 4.5 Matrix approach for the identification of the interactions between hazards in Level 2 analysis (Modified after de Simeoni et al. 1999 and Kappes et al. 2010) ...........................24 Figure 4.6 The multi-risk assessment framework recommended by Marzocchi et al. (2012).27 Figure 4.7 Event tree with different scenarios, resulting damage levels and probability density function of the resulting damage. .............................................................................28 Figure 4.8 Example of a dynamic event tree for the case of evacuation decisions related to flooding. When it is decided to delay the evacuation decision at ti, another evacuation decision can be made at a next period. ................................................................................29 Figure 4.9 Simple Bayesian network to include different failures in time (early and late failure) (left) and the equivalent event tree (right). Note that the arrow between early and late failure is included to model that late failure will not be possible given that early failure has occurred). ............................................................................................................29 Figure 4.10 The three typical connections of Bayesian network: (a) serial connection, (b) diverging connection, and (c) converging connection (based on Jensen and Nielsen, 2007). .............................................................................................................................................31 Figure 4.11 A simple Bayesian network. ..............................................................................33 Figure 4.12 Bayesian network for multi-risk assessment. ....................................................34 Figure 4.13 Possible scenarios of multi-hazard interaction as considered in the MATRIX project. .................................................................................................................................34 Figure 4.14 Spatially explicit modelling and a likely propagation pattern of a cascade effect using a Bayesian network. ..........................................................................................35 Figure 4.15 Peak Ground acceleration map for a M=7 event over the area defined within the MATRIX Virtual-City. ............................................................................................................36 7
Figure 4.16 Seismic fragility curves for a low rise, low code RC building for the yield (green curve) and collapse (red curve). ...........................................................................................38 Figure 4.17 Debris flow fragility curve (Source: Fuchs et al. 2007). ......................................39 Figure 4.18 Fragility surface for a scenario involving a seismic event and debris flow for a low rise, low code RC building. .............................................................................................39 Figure 4.19 Seismic fragility curves considering various debris flow deposition heights.......40 Figure 4.20 Bayesian network applied to bi-risk assessment (earthquake and landslide) with possible decisions (modified after Einstein et al. 2010).........................................................40 Figure 4.21 Comparison of results for No action, Active countermeasure, Passive countermeasure and Warning system between this study and Einstein et al. (2010). ...........42 Figure 4.22 Sensitivity analysis of the resulting risk (utility) arising from varying the probability of a rockslide while employing different mitigation strategies. The horizontal marker arrows indicate where each measure is the best mitigating action. ...........................43 Figure 6.1 Principal sketch of the MATRIX Virtual-City region (Mignan, pers. com.). ...........46 Figure 6.2 Example locations of the 50 000 buildings and earthquake source in the MATRIX Virtual-City region (Mignan, pers. com.). ..............................................................................46 Figure 6.3 The Bayesian network for multi-risk assessment. ...............................................47 Figure 6.4 Specification of the discrete probabilities of distance. .........................................48 Figure 6.5 Specification of the discrete probabilities of magnitude. ......................................49 Figure 6.6 Conditional probabilities of PGA from 1000 Monte Carlo simulations (Partial). ...50 Figure 6.7 Specification of the discrete probabilities of PGA. ...............................................50 Figure 6.8 Specification of the discrete probabilities of PGA. ...............................................50 Figure 6.9 Conditional probabilities of reduction factor from 1000 Monte Carlo simulations (Partial) ................................................................................................................................52 Figure 6.10 Specification of the discrete probabilities of the RF for sandy soil after an earthquake using the values listed in Table 6.2. ...................................................................52 Figure 6.11 Specification of the discrete probabilities of deposition height...........................53 Figure 6.12 Fragility curves for different RC buildings..........................................................54 Figure 6.13 Risk curves for the selected site. ......................................................................55 Figure A.1 Basic four-parameter volcanic Bayesian Belief Network for Santorini unrest. .....61 Figure A.2 Conditional Probability Table (CPT) for one BBN node. .....................................62 Figure A.3 Santorini BBN with all observation nodes instantiated to null or negative states. .63 Figure A.4 Santorini BBN with all observation nodes instantiated to positive states. .............64 Figure A.5 Suggested time-stepping BBN for Santorini unrest, with four evidence streams .65 Figure A.6 Time-stepping BBN for Santorini unrest, with two steps hypothetically instantiated in sequence (rows 2-5, first two column sets); note changes to probabilities on target nodes (upper row) ...........................................................................................................................65 Figure A.7 Hypothetical Santorini BBN, instantiated over three time steps – note changes to eruption scenario probabilities ..............................................................................................66 8
Figure A.8 Extending the Santorini BBN to incorporate additional streams of observational evidence and data ................................................................................................................66 Figure A.9 ISC seismicity of Santorini region, 1900 – 2012, and area source zones for hazard model based on ‘complete’ data. ..............................................................................70 Figure A.10 Peak ground acceleration hazard curves for a site near Fira, Santorini, due to background tectonic seismicity and an activated Kameni fault, respectively. ........................71 Figure A.11
Framework of Santorini earthquake risk model...............................................77
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List of Tables Table 4.1 Coding of each hazard in the system. ..................................................................24 Table 4.2 Prior probabilities of the basic nodes for the case outlined in Figure 4.20. ...........41 Table 4.3 Conditional probabilities of Rockslide...................................................................41 Table 4.4 Conditional probabilities of Alarm.........................................................................41 Table 4.5 Conditional probabilities of Measure ....................................................................41 Table 4.6 Eight combinations of conditional probabilities of damage ...................................41 Table 4.7 Six combinations of conditional probabilities of Utility ..........................................41 Table 4.8 Conditional probabilities of Cost...........................................................................41 Table 4.9 Conditional probabilities of Cost_measure ...........................................................42 Table 6.1 Coefficients for the Ambraseys et al. (2005) PGA attenuation relationship ..........49 Table 6.2 Sandy soil properties at a given time following an earthquake .............................51 Table 6.3 Detailed information of the debris flow’s initiation area. ........................................52 Table 6.4 Precipitation intensity properties. .........................................................................53 Table A.1 BBN node state selections and evaluated probabilities (shown rounded on Figure A.3). .....................................................................................................................................63 Table A.2 Peak ground acceleration pga hazard levels and equivalent Intensities at given annual exceedance probabilities for background tectonic seismicity and for Kameni fault scenario ...............................................................................................................................72 Table A.3 Santorini earthquake risk model - results summary .............................................77
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1 Introduction and objectives Many regions of Europe are exposed to and affected by several types of natural hazard. The successful implementation of effective risk management strategies in these areas therefore requires all relevant threats to be assessed and considered. The core objective of the MATRIX project is to develop methods and tools to tackle multiple natural hazards within a common framework. This will allow risk analysts and decision-makers to optimise the risk assessment process, rationalise the data management for hazard and vulnerability reduction, and support cost-effective decisions on structural and non-structural mitigation/adaptation measures from a multi-hazard perspective. The assessment and mitigation of the risk posed by several natural and man-made threats at a given location requires a multi-risk analysis approach that could account for the possible interactions among the threats, including possible cascade events. Performing quantitative multi-risk analysis using the methodologies available today presents many challenges (e.g., Kappes et al., 2012, Marzocchi et al., 2012). The disaster scenarios are often qualitative, related to one reference event and rarely account for the associated uncertainties. Furthermore, the risks associated with different types of natural hazards such as volcanic eruptions, landslides, floods, and earthquakes are often estimated using different procedures and the produced results are not comparable, for example, velocity for debris flows, inundation depth for floods and peak ground acceleration for earthquakes. The events themselves could be highly correlated (e.g., floods and debris flows could be triggered by an extreme storm event), or one type of threat could be the result of another (e.g., a massive landslide that is triggered by an earthquake, a so-called cascade effect). In many situations, amplified risk resulting from hazard interactions has to be considered, while key characteristics of the elements at risk, represented by their “vulnerability” to specific threats, are not constant and change over time. In particular, an element’s exposure to one type of hazard might significantly increase its vulnerability to other types of hazards, e.g., ash falling and weighing upon buildings will increase their vulnerability to ground shaking. Methods for describing and quantifying vulnerability also vary significantly for different hazards. There is also the issue of the spatial and temporal scales under consideration (which also vary from hazard to hazard), as well as the actual metric used to express risk. Risk assessment is essentially an exercise in estimating the expected losses caused by an adverse event (single risk) or combination of several adverse events (multi-risk). The losses could be tangible (e.g., loss of life, loss of property, destruction of infrastructure, etc.) or intangible (e.g., deterioration of the “quality of life” in a community following a disaster event, loss of the reputation of the owner of an industrial complex affected by an adverse event, etc.). The main purpose of a risk assessment exercise is therefore to assist a decision-maker in identifying the optimum solution to the problem at hand. Models for the consistent assessment of risk associated with single- and multi-type hazards and time-dependent vulnerability are being developed in other MATRIX work packages. This deliverable provides the framework and methodology for using the multi-hazard, multivulnerability models to assess the expected tangible and intangible losses when there are significant interactions among the hazards. The characteristics of natural threats vary over several orders of magnitude over the temporal (e.g., duration of the event and typical return period of events) and spatial scales. This makes it difficult to make balanced, rational decisions if one faces a combination of risks from different threats. Societies and decision makers tend to focus their attention and resources on events that happen frequently, while the risk associated with a rare, extreme 11
event might be much greater. Even when the risks are comparable, in the eye of the public, a single event killing 1000 people is much worse than a thousand traffic accidents killing one person each. It is therefore not straightforward to compare and combine the risks from highfrequency, low impact events with those from low-probability, catastrophic-consequence ones. A further complicating factor is that, because of the nature of the problem, any estimation of risk involves uncertainty. The degree of uncertainty, both in the assessment of hazard and in the estimation of consequences, is normally much higher for the low-probability, high-impact events than for high-probability, low-impact ones. Improved decision-making under conditions of uncertainty is the raison d’être of all types of risk assessment, and multi-risk assessment is no exception. However, as commented above, uncertainties are rarely considered. In fact, within a recent comprehensive review of the challenges involved in multi-hazard risk assessment, this issue is not even mentioned (Kappes et al., 2012). It is obvious that a mathematically rigorous approach to multi-risk assessment that addresses all the challenges named above, as well as the uncertainties in all steps of the analysis, will be complicated and require resources and expertise, which may not be readily available. On the other hand, in many situations the decision-maker in charge of risk management can identify the optimum alternative among those options available without doing a detailed, rigorous multi-risk analysis. One may also encounter situations where the gain in the accuracy of the risk estimate through a rigorous multi-risk analysis approach, where the interactions among the different hazards are explicitly accounted for, is insignificant compared to the uncertainty in the risk estimate. Therefore, the framework recommended in this deliverable is based on a multi-level approach where the decision-maker and/or the risk analyst will not need to use a more sophisticated model than what is required for the problem at hand, or what would be reasonable to use given the available information.
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2 Review of existing frameworks for multi-risk assessment Effective risk reduction in areas that are prone to several natural hazards is only possible if all relevant threats are considered and analysed. However, in contrast to single-hazard analyses, the examination of multiple hazards poses a range of additional challenges due to the differing physical characteristics of the processes of concern. This refers to the assessment of the hazard level, as well as to the various elements’ vulnerability toward distinct processes, and to the resulting risk level. The multi-risk concept therefore refers to a complex variety of combinations of risk (i.e., various combinations of hazards and of the resulting vulnerabilities) and for this reason it requires a review of existing concepts of risk, hazard, exposure and vulnerability, within a multi-risk perspective (Carpignano et al., 2009). A multi-risk approach entails a multi-hazard and a multi-vulnerability perspective (Carpignano et al., 2009). The multi-hazard concept may refer to (e.g., MATRIX deliverable D3.1 “Review of existing procedures”, Garcia-Aristizabal et al., 2012a): (1) the fact that different sources of hazard might threaten the same exposed elements (with or without temporal coincidence), or (2) one hazardous event can trigger other hazardous events (cascade effects). On the other hand, the multi-vulnerability perspective may refer to (1) a variety of exposed sensitive targets (e.g., population, infrastructure, cultural heritage, etc.) with possibly different degrees of vulnerability towards the various hazards, or (2) time-dependent vulnerabilities, in which the vulnerability of a specific class of exposed elements may change with time as consequence of different factors (for example, wear and tear upon a structure, the occurrence of other hazardous events, etc.). The MATRIX Deliverable D5.1 (“State-of-the-art in multi-risk assessment”, Garcia-Aristizabal et al., 2012b) reviewed the main applications and research initiatives in the field of multi-risk, considering reports from European-funded projects (and the derived papers) as well as other international initiatives (reports and papers). From the bibliographic review performed, it emerged that most – if not all – of the initiatives on multi-risk assessment have developed methodological approaches that consider the multi-risk problem in only a partial way, since their analyses concentrated upon risk assessments for different hazards threatening the same exposed elements. Within this context, the main emphasis has been towards the definition of procedures for the homogenization of spatial and temporal resolution for the assessment of different hazards. On the other hand, for vulnerability, being a wider concept, there is a stronger divergence in its definition and assessment methods. Considering physical vulnerability, a more-or-less generalized agreement on the use of vulnerability functions (fragility curves) has been reached, which facilitates the application of this type of multi-risk analysis. However, for other kinds of vulnerability assessment (e.g., social, environmental, etc.) it is less clear as to how to integrate them into a multi-risk framework. In general, within the reviewed frameworks, the final multi-risk index is generally estimated as a simple aggregation of the single indices estimated for different hazards; other approaches consider a single hazard at a time and multiple exposed elements (e.g., buildings, people, etc.) for the vulnerability, which are combined and weighted according to expert opinion and subjective assignment of weights, while others combine the two, i.e., consider multiple hazards and multiple exposed elements, with associated weights (e.g., Carpignano et al., 2009). The choice of the methodology strongly depends on both the scale of the study and the availability of information (for both hazard and vulnerability assessments). It is noteworthy that many of the approaches found define theoretical frameworks for the multi-risk assessment that, when applied to real cases, are generally simplified. This is mainly due to the difficulty in obtaining the detailed information needed. It is also interesting to point out 13
that many of the reports discuss the importance of the interaction among hazards and cascading of events for a fully multi-hazard perspective. However, few efforts have been done in order to define a rigorous methodology (e.g., Carpignano et al., 2009). The different approaches may be categorised, arbitrarily, as a function of the considered scale: 1. Large-scale approaches. 2. Medium-scale approaches. 3. Regional- to local-scale approaches. The large-scale multi-risk procedures generally emphasize the areas with the (relatively speaking) highest risks, highlighting wide (country- or continent-size) areas affected by different hazards (e.g., UNDP, MUNICH RE maps, the World Bank Global Hotspots approach, etc.). These large-scale maps are generally based on a simple hazard aggregation, and usually represent a simple risk indicator. An example of the kind of results produced by a large-scale approach is shown in Figure 2.1, where results for the global distribution of flood risk following the World Bank approach are presented (Dilley et al., 2005). This kind of result represents a synoptic methodology principally addressed to global policies where the objective is to identify hotspots where natural hazard impacts may be largest, although this leads to a very low level of reliability at the local scale.
Figure 2.1 Global distribution of flood risk: (a) mortality, (b) total economic loss, and (c) economic loss as a proportion of GDP density (source: Dilley et al., 2005).
As we go to finer scales of analysis, multi-risk assessment is generally based on more detailed assessments. For these kinds of procedures, risk from different hazards is quantified 14
either using common metrics (in general, expected mortality or economic losses over a given timeframe – normally 1 year), or based on normalized indices resulting from the grouping of hazard intensities and vulnerability degrees in generic classes (low to high). The results are generally expressed using risk curves or risk indices that, as a result of the homogenized analysis, may be ranked and allow direct risk comparisons for different typologies of natural and man-made adverse events. Many of the European initiatives on multi-risk assessment, for example EC-TIGRA, TEMRAP (The European multi-hazard risk assessment project), ESPON (2007)1, and ARMONIA (Applied multi Risk Mapping of Natural Hazards for Impact Assessment), can be categorized as medium-scale approaches. For example, some results obtained by the ESPON project are shown in Figure 2.2 (Schmidt-Thomé, P. Ed., 2005).
(a)
(b)
(c)
Figure 2.2 (a) Aggregated hazard map (based on 15 hazard indicators); (b) Integrated vulnerability map; (c) Aggregated risk.
At the level of regional- to local-scale approaches, different specific initiatives can be found, for example, the projects NARAS (Natural Risks Assessment, Marzocchi et al., 2009), RISKNAT; MEDIGRID, and CAPRA (Central American Probabilistic Risk Assessment)2, as well a comparative multi-risk assessment in Cologne, Germany (Grünthal et al., 2006), a regional multi-risk project in the Piedmont region, Italy (Carpignano et al., 2009), and so forth. As an example of this category, the results obtained by Grünthal et al. (2006) from their comparative multi-risk assessment in Cologne are shown in Figure 2.3. In this case, three different types of natural hazards (wind storms, river floods and earthquakes) are quantitatively compared in terms of direct economic losses, resulting in risk curves plotting the direct economic losses against the annual probability (Figure 2.3).
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http://www.espon.eu/main/ http://web.worldbank.org/WBSITE/EXTERNAL/COUNTRIES/LACEXT/EXTLACREGTOPURBDEV/0,, contentMDK:22277760~pagePK:34004173~piPK:34003707~theSitePK:841043,00.html 15 2
Figure 2.3 Final output of the multi-risk analysis done for the city of Cologne, Germany (Grünthal et al., 2006): Risk curves of the hazards due to windstorms, floods and earthquakes for losses concerning buildings and contents in the sectors of private housing, commerce and industry (reference year: 2000).
The state-of-the-art review on multi-risk assessment methods described in MATRIX D5.1 (Garcia-Aristizabal et al., 2012b) highlighted the different features and gaps to be considered in the development of a MATRIX framework for multi-risk. The main points discussed were: -
-
-
Different methodologies have been identified, ranging from simplified approaches to innovative and advanced methods. Nevertheless, practically all the reported studies present important problems when transformed into practical applications. For instance, any methodological approach for multi-risk assessment is strongly constrained by both data availability (for hazard and vulnerability assessment) and the scale of the problem; Multi-risk approaches may imply multiple hazards affecting the same exposed elements, and/or one or more hazard affecting different categories of exposed elements. In the first case, quantitative risk assessment is generally more viable since a common metric for loss assessment is easier to be defined (i.e., risk harmonization based on the harmonization of effects). In the second case, considering different categories of exposed elements (e.g., buildings, population, green areas, environmental, etc.) implies difficulties in both the definition of a common metric for loss assessment, and how to weight the different categories of exposed elements. This kind of analysis involves strong subjective decisions that are not always easy to justify, and the risk quantification is generally performed using normalized indices that may allow, for example, individual hotspots of high risk to be identified. The most basic requisite for a quantitative multi-risk assessment is the definition of a target area, common time frame, a quantitative assessment of hazards (generally in probabilistic terms), a coherent vulnerability assessment (i.e., linked to the intensity measure parameterizations adopted for the hazard assessment), and a defined metric to quantify losses (e.g., Marzocchi et al., 2012). 16
-
-
-
A strong limitation found up to now is that none of the analysed studies produce a rigorous methodology for multi-hazard assessment. Most of the multi-risk methodologies consider the effects of different hazards as being independent, neglecting the possibility of hazard interaction or cascade effects. Conversely, multirisk assessment requires also a careful evaluation of the interaction between vulnerabilities to different hazards. For example, the seismic vulnerability of an edifice changes significantly if the roof is loaded by volcanic ash. Only very little effort appears to have been devoted to tackle this issue. One of the main gaps found for the practical application of the more important quantitative multi-risk methodologies found in the literature is the lack of fragility curves derived by intensity (of the hazardous event) vs. typology of exposed elements. This topic can be considered as one of the most significant matters to be addressed for future developments in multi-risk analysis, especially in high-resolution analysis (i.e., at the local scale). Another knowledge gap found is in the treatment of uncertainties. None of the methodologies consider uncertainty quantification at any step of the process (except for some specific hazard assessment approaches), nor propagate (epistemic) uncertainties up to the final risk values.
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3 Principles of multi-risk assessment Methodologies for multi-risk assessment are becoming a new research field in risk assessment and management because they allow the taking into account of dependencies among different risks. From the scientific viewpoint, these methodologies focus on comparability between different types of risks, cascading hazards, and time-dependent vulnerability within the framework of conjoint or successive hazards. Currently, the evaluation of risks resulting from difference sources is generally done through independent analyses, adopting different procedures and time-space resolutions. The multi-risk analysis is then considered to be the sum of the single risk assessments. This may lead to the severe underestimation or overestimation of the real risk because of two reasons. First, the single type risk assessments are not always suitable for inter-comparison because they deal with different spatial and temporal resolutions and use different approaches to measure vulnerability. Second, the single risks sources are rarely strictly independent and often causal, since spatial and temporal relationships often exist among the hazards. Single risk approaches make it difficult to compare risks because of the implicit assumption of independence of the risk sources. These problems can be overcome through the development of new approaches which can provide reliable quantitative estimations of individual and coupled events and account for “cascade effects” that are usually neglected in single risk analyses. However, multi-risk analysis is a widely interdisciplinary field and specialists for various natural hazards need to work together in order to understand the longterm evolution of the governing physical system and the various triggering mechanisms. Multi-risk assessment poses a greater challenge than classical single risk assessment and has several features and implications to be considered – both in the technical modelling procedures and in aggregating and comparing the results. Some basic principles that have to be taken into account are listed below:
Different hazard models (e.g., a seismic hazard model and a landslide runout model) and their outputs (e.g., maps of peak ground acceleration and deposit depth) should be integrated within a common framework, in which different hazards and scientific methodologies could be integrated into a unified model. Hazard scenarios covering all possible intensities and relevant hazard interactions should be selected carefully and accurately. The consideration of triggering effects and/or cascade of adverse events may be extremely important in the assessment of a reliable multi-risk index. Key characteristics of the elements at risk, represented by their “vulnerability” to specific threats, are not constant and change over time. In particular, complex interactions are present among cascading hazards in multi-risk analysis. The vulnerabilities of the elements at risk are sometimes also correlated to each other. On the other hand, exposure to one type of hazard might increase the vulnerability significantly to other types of hazard. This point should be kept in mind during multirisk analysis. Risks from different hazards and return intervals for an asset could be compared. On one hand, it is important for economical and mitigation planning; on the other hand, the most dangerous hazard that threatens an area should be identified. It is necessary to define a common time frame and common reference damage for all the single risks, for example, the risk of a monetary value loss or having a number of casualties. The final consideration is on the meaning of multi-risk for making mitigation actions. The results of multi-risk analyses may show that mitigation actions should not necessarily be focused on reducing the highest ranked risk. A rational mitigation 18
policy has to focus on the risks that could be effectively reduced. In other words, it is not rational to spend all the available resources to reduce 0.01% of the highest risk, when with the same amount of money one could reduce a significant percentage of all other risks. The decisions regarding the optimal mitigation actions have to consider the results of multi-risk assessment together with a sound cost-benefit analysis.
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4 Description of the recommended framework for multi-risk assessment The MATRIX multi-risk assessment framework is a multi-level process which assumes that the end user (decision-maker or risk analyst) has identified the relevant threats and has carried out an assessment of the risk(s) (at the level of sophistication required for the problem at hand) associated with each single hazard(s). Figure 4.1 shows the general steps of the multi-risk assessment framework as considered in MATRIX. The overall multi-risk assessment process composes the following stages: (1) risk assessment for single hazards, (2) level 1: qualitative multi-risk analysis, (3) level 2: semi-quantitative multi-risk analysis, and (4) level 3: quantitative multi-risk analysis. The details are described in the following paragraphs.
Risk assessment for single hazards
Level 2 analysis (Semi-quantitative)
Monitor and review
Communicate and Consult
Level 1 analysis (Qualitative)
Level 3 analysis (Quantitative)
End
Figure 4.1 Schematic view of the steps followed in the MATRIX multi-risk assessment framework.
In the first step, it is assumed that the risk assessment for the single hazard(s) roughly follows the classical approach that is comprised of the following stages (Figure 4.2):
Definition of space/time assessment window (target area, time window) and the risk metric quantifying the expected losses (e.g., economic loss, fatalities, etc.). Threat(s) identification (e.g., earthquake, volcano, landslide, meteorological events, etc.). Single hazard assessment (e.g., rate of occurrence, pathway, intensity measure, etc.). Assessment of the vulnerability of the elements at risk (receptors) (e.g., people, buildings, environment, etc.). Assessment of the consequences in terms of the chosen metric (e.g., loss of life, economic losses, environmental degradation, etc.).
Once the results of the single-hazard risk assessment(s) are available, the user embarks on a three-level process, which becomes more detailed and rigorous as the user moves from one level to the next. The user moves to a higher level analysis only if the problem at hand 20
requires a more accurate risk estimate and, equally important, if the data needed for doing the more detailed analysis are available.
Definition of target area and time window
Hazard identification Hazard assessment Quantified by probability and intensity measure
Risk assessment Vulnerability assessment
Figure 4.2 Stages of risk assessment for single hazards.
4.1
The three-level multi-risk assessment framework
The key features of the three-level multi-risk assessment framework are highlighted in this section. The selection of which of these three levels is to be used depends on the outcome of the preliminary risk assessment for single hazard(s). Level 1 analysis The Level 1 analysis comprises a flow chart type list of questions that guides the end user as to whether or not a multi-type assessment approach, which explicitly accounts for cascading hazards and dynamic vulnerability within the context of conjoint or successive hazards, is required. Each question will be supplied with an exhaustive list of answers that the user should choose from. This process is shown schematically in Figure 4.3.
Level 1 analysis (Qualitative) More than one hazard?
No
More than once during time window?
No
Yes Yes Hazard interactions?
No
Time-dependent vulnerability?
Yes
Cascade events
Level 3 analysis
Affects triggering with some time lag
Potential interactions introduced by mitigation measures*
Timedependent vulnerability
No
Yes
Level 2 analysis
End
Figure 4.3 The steps involved in the Level 1 multi-risk analysis (* Potential interactions of independent hazards could be introduced by mitigation measures, which affect total expected loss. For instance, house height increasing could reduce loss due to flooding, but increase loss due to earthquake).
21
The flow chart will include, for example, these questions:
What is the purpose of the risk assessment exercise? (answers: identifying the most critical risk scenarios and choosing the optimal risk mitigation measures, assessing the adequacy of resources and level of preparedness for post-event response, setting the disaster insurance premium, cost-benefit analysis for a specific risk reduction measure, other reasons, …). Which natural threats are relevant for your area of interest? (answers: earthquake, landslide, volcanic eruption, tsunamis, wildfire, winter storm, storm surge and coastal flood, fluvial flood, snow avalanche, other perils, ..) (If the user has chosen only one natural hazard from the list) How likely is it that the dominant natural threat could happen more than once during the time window of concern with an intensity that will cause significant loss? (answers: very likely, likely, unlikely, very unlikely, virtually impossible).
Note: At this stage, if the user has chosen only one natural hazard from the list and chooses very unlikely or virtually impossible as the answer to the above question, then there is no need to go any further and a more detailed multi-risk assessment is irrelevant.
Cascading events: Could a hazard trigger another hazard in your list (example: an earthquake triggering a landslide, landslide debris blocking a river and causing flooding when the landslide dam breaks, earthquake causing collapse of flood defence structures and leading to flood, etc.)? (answers: yes or no). Conjoint events: Could several hazards in your list occur simultaneously because they are caused by the same external factors (example: earthquakes and volcanic eruptions are both caused by tectonic processes, winter storms and storm surges, fluvial floods and debris flows caused by extreme precipitation events, ..)? (answers: yes or no).
Note: The user will be provided with some guidance and examples for questions such as the previous two, which may not be straightforward.
Dynamic vulnerability: Could the occurrence of one of the hazards in your list significantly influence the vulnerability of some of the elements at risk to another event of the same type or to other hazards (example: a building partially damaged by an earthquake has a higher vulnerability to the next earthquake or to floods and landslides, ash fall from a volcanic eruption on roof tops will increase the mass and hence may increase the seismic vulnerability of the building, a storm surge may weaken the foundation of buildings in coastal areas and increase their vulnerability to earthquakes, etc.) ? (answers: yes or no). Dynamic hazard: Could the occurrence of one of the hazards in your list significantly influence the occurrence probability of other hazards (example: a strong earthquake could weaken the soil in a slope and increase the probability of landslide during extreme precipitation events, etc.)? (answers: yes or no).
Additional questions may, of course, be added, depending upon the situation at hand. If the Level 1 results strongly suggest that a multi-type assessment is required, then the end user moves on to Level 2 to make a first-pass assessment of the effects of dynamic hazard and time-dependent vulnerability. If cascading events are potentially a concern, the user goes directly to the Level 3 analysis.
22
Before a risk analyst is satisfied with a Level 1 analysis alone, diligence and lateral thinking are required to ensure, as far as possible, that rare ‘black swan’ combinations of hazard events, perceived as being very unlikely or hitherto unknown, have not been overlooked or ignored. Flooding, for example, may be caused directly by some styles of surface fault rupture (Quigley et al., 2010). Furthermore, some multi-hazard scenarios may be mediated by modes of engineering or technological failure, which may not necessarily be easy to anticipate. For example, a windstorm can topple electricity line poles and cause a power blackout that could disable water pumping equipment, and hence precipitate flooding. Likewise, the resulting damaged electrical cables could spark wild fires (e.g., Tse and Fernandez-Pello, 1998). Level 2 analysis In the Level 2 analysis, the interactions among hazards and dynamic vulnerability are assessed approximately using semi-quantitative methods. The steps involved in the Level 2 analysis are shown in Figure 4.4.
Level 2 analysis (Semi-Quantitative)
Yes
Greater than hazard interaction threshold? No
Yes
Greater than timedependent vulnerability threshold?
Resources & relevant data available for Level 3 analysis
No
No
Yes Level 3 analysis
End
Figure 4.4 The steps involved in the Level 2 multi-risk analysis.
To consider hazard interactions and time-dependent vulnerability, the suggested method in MATRIX multi-risk level 2 analyses is a matrix approach based on system theory. This kind of matrix has been used in various fields, including environmental issues (Simeoni et al. 1999; de Pippo et al. 2008), rock engineering (Hudson, 1992) and natural hazard assessment (Kappes et al. 2010). The assumption of this approach consists of the comprehension and description of the relationships among agents and processes in the evolution of system. Figure 4.5 shows an example to explain this approach. Firstly, a matrix is developed by means of the choice of a couple of hazards, considered as the basic components of the system (Figure 4.5a). It will be followed by a clockwise scheme of interaction (Figure 4.5b), with the description of the mutual influence between different hazards (Figure 4.5c). More specifically, each element of the row, which crosses one of the hazards in the mean diagonal, shows the influence of this hazard on the system, thus indicating the cause of the phenomena; whereas each element of the column, which crosses the same hazard analysed, shows the influence of the system on this hazard, thus focusing on the effect of the 23
phenomena. After the descriptions contained in the matrix, they are assigned numerical codes varying between 0 (No interaction) and 3 (Strong interaction) with intervals of 1, as a function of their degree of the interaction intensity (Figure 4.5d, 4.5e). Once all the hazards in the matrix are filled, it is possible to verify the degree of the impact of each hazard on the others and the effect from other hazards. In order to avoid the excessive weighting of a single hazard, the sum of the codes for the row and the column is considered. Table 4.1 shows the coding result for each hazard.
a
H1 H2
b
Hi
Influence of Hi on Hj
Influence of Hj on Hi
Hj
H3 H4 H5 H6 e TARGET
Slides (H4)
2
0
Debris flows (H5)
2
1
1
River floods (H6)
2
d Semi-quantitative matrix coding method 0 – No interaction 1 – Weak interaction 2 – Medium interaction 3 – Strong interaction
c
Slides (H4)
Deposits supply
Cut off a flow in a water course
No interaction
Debris flows (H5)
Change of river bed morphology
Erosion/ saturation of deposits
Remobilisation of deposits
River floods (H6)
Figure 4.5 Matrix approach for the identification of the interactions between hazards in Level 2 analysis (Modified after de Simeoni et al. 1999 and Kappes et al. 2010)
Table 4.1 Coding of each hazard in the system.
Number 1 2 3 Total
Hazard Slides Debris flows River floods
Causes (Rows) 4 2 2 8
Effects (Columns) 1 3 4 8
Causes + Effects 5 5 6 16
It can be seen that slides are the dominant hazard caused by other hazards because they have the maximum number of causes. On the other hand, river floods are the hazards most sensitive to the influence of other hazards, with the maximum number of effects. In the scoring system above, the maximum possible value of each off-diagonal cell in Figure 4.5a is 3. Therefore the maximum possible value for the total sum of each row is 3(n – 1), where n is the number of hazards. Likewise, the maximum possible value for the total sum of each column is 3(n – 1). This means that the maximum possible value for the total sum of causes and effects is:
24
HI, max = 23n(n – 1) = 6n(n – 1)
Eq.(1)
where n is the number of hazards and HI is the hazard interaction index. Therefore, the maximum possible value for the hazard interaction index is HI, max = 632 = 36 for the example considered in Table 4.1. Given the uncertainties and possible excessive or moderate weighting of single hazards, a threshold hazard interaction index HI equal to 50% of HI, max is recommended for considering a more detailed Level 3 analysis. If the hazard interaction index is less than this threshold, Level 3 analysis is not recommended because the additional accuracy gained by the detailed analyses is most likely within the uncertainty bounds of the simplified multi-risk estimates. Otherwise, Level 3 analysis is recommended. In the example above, the threshold hazard interaction index derived from Eq.(1) is HI, threshold = 18 (50% of 36), while the total value of causes and effects is 16, hence we do not need to do Level 3 analysis. An illustration of the suitability and adequacy of a Level 2 analysis would be an urban assessment of earthquake loss for a specific event magnitude and epicentre. Apart from the direct shaking loss, there may be indirect losses from urban landslides. Provided that the proportion of the urban region threatened by landslides is comparatively small, then a Level 2 analysis with a conservative estimate of landslide loss might typically be adequate. However, an example of a region where this is manifestly not the case is Monaco. Due to its steep topography and small geographical extent, a very high proportion of the property in Monte Carlo is exposed to landslide risk from an occasional Magnitude 6 earthquake. Another conjoint hazard example of a European locality where Level 2 methods are inadequate for real-time risk assessment is the Aegean island of Santorini, which is one of the most notorious disaster landmarks of European history. Recent geodetic unrest at the Santorini Caldera, which started in January 2011 after almost sixty years of quiescence (Newman et al., 2012), indicated an elevation of both earthquake and volcanic risk. Furthermore, these tectonic hazards are closely coupled dynamically: a large earthquake might trigger a volcanic eruption and vice versa. The impact of volcanic ash fall and earthquake activity could damage houses, force the closure of hotels and disrupt the island’s fragile tourism economy. Furthermore, additional hazards may be generated: landslides may be induced along the steep caldera cliffs, and local tsunamis might be created that would endanger shipping vessels within the caldera. For this economically significant and topical European multi-peril risk assessment, geoscientific inferences about the opaque caldera interior have to be made on the limited basis of the sparse monitoring data available. Combining disparate geodetic, seismological and geochemical observations in a systematic evidence-based manner requires the adoption of Bayesian methods within the context of a Level 3 analysis (Aspinall et al., 2006). Level 3 analysis In Level 3 analysis, the interactions among hazards and dynamic vulnerability are assessed quantitatively with as high accuracy as the available data allows. Basically, the user/analyst should follow the process suggested by Marzocchi et al. (2012), and depicted schematically in Figure 4.6. The procedure for multi-risk analysis (MRA) as illustrated in Marzocchi et al. (2012), starts from the identification of the main steps to be followed, in a similar way as described in the level 1 analysis for single risk assessment, except for the definition of possible hazard interactions (at both the hazard and vulnerability levels). This is as follows: 25
Definition of the space-time window for the risk assessment and the metric for evaluating the risks; Identification of the risks impending on the selected area; Identification of the selected hazard scenarios covering all possible intensities and relevant hazard interactions; Probabilistic assessment of each scenario; Vulnerability and exposure assessment for each scenario, taking into account the vulnerability arising from the combined hazards; loss estimation and multi-risk assessment; Loss estimation and multi-risk assessment.
Of particular interest in multi-risk analysis is the description of the interactions (again at both the hazard and vulnerability levels). Specifically for this point, Marzocchi et al. (2012) introduce some concepts of the interaction between hazards, arguing that similar ideas may be straightforwardly extrapolated for vulnerability assessment. Considering for example two different threatening events, whose occurrence is E1 and E2, then the probability of E1 occurrence (H1) can be written as (Eqn. 3 in Marzocchi et al., 2012):
H1 p E1 p E1 E2 p E2 p E1 E2 p E2
Eq.(2)
where p represents a probability or a distribution of probability, p(E1|E2) is the probability of E1 occurring given E2 occurs, and E2 means that the event E2 does not occur, leading to p(E1|Ē2) being the probability of E1 occurring given E2 does not occur. The generalization of this expression to more than two events does not pose any particular conceptual problem, even though it may require a more cumbersome formulation. This general expression may represent different particular cases that can be of interest, some of which are described in Marzocchi et al. (2012). Of particular interest are, for example, interactions that may play a role in short-term probabilistic hazard/risk assessment (e.g., of the order of days). For example, the occurrence of heavy rain (E2) changes significantly the landslide occurrence (E1) probability within a time horizon of days. Weather forecasts may track the time evolution of p(E2) that leads to a time evolution of p(E1) through Eq.(2). In this case, the most challenging scientific problem is the reliable estimation of p(E1|E2), which may be obtained by theoretical models, empirical laws, or expert opinion (e.g., see the cascading hazard assessment section in Fig. 4.4, where it is defined as
H 3' f ' S3 S2 ; in this case, S2 and S3 are two interacting hazard sources in which S2 can
be a triggering mechanism for S3). It is worth remarking upon the differences this scheme has with long-term assessments; in the long-term perspective, a local landslides database already accounts for the fact that most of the landslides are due to heavy rain or storms. In other words, it is expected that the database will provide a reliable estimation of p(E1) directly. On the other hand, Figure 4.6 also highlights the possible interactions at the vulnerability level. In this case, interactions at the hazard level may or may not occur: if an interaction at the hazard level occurs, this is the same case as described in the previous paragraph, whereas in the case of no interaction at the hazard level, it refers to the independence of the sources, i.e., H (1,2) f1 f 2 . The central point here refers to the interactions at the vulnerability level. In this case, the occurrence of a given hazard event implies an effect on the vulnerability of the exposed element to another hazard, regardless of whether this event is related to another. Following the notation shown in Figure 4.6 from Marzocchi et al. 26
(2012), let us consider the case where hazard sources S1 and S2 may present an interaction at the vulnerability level for a given class of exposed elements (e.g., that the occurrence of an event from S2 may modify the vulnerability function g() to events from S1). Then, if the vulnerability function of the exposed elements to a hazard from source 1 is V1 g1 H1 ,
after the occurrence of an event from S2, the vulnerability can be expressed as
V1' g1' H 1
2
.
Figure 4.6 The multi-risk assessment framework recommended by Marzocchi et al. (2012).
Specific tools that could be used for carrying out such analysis include: -
4.2
Event trees (described below in Sec. 4.2) Bayesian networks (described below in Sec. 4.3) Time stepping Monte Carlo simulation (Chapter 5)
Event trees
Following the general definition of risk, an event tree is a suitable approach for analysing a set of scenarios. It can be used to analyse and display different discrete scenarios, their 27
corresponding probability of occurrence and the resulting consequences. An event tree can show the likelihood of a sequence of failures, e.g., the conditional probability that system B will fail given the failure of system A. By combining the estimates of the Pf (failure probability) and Cf (consequences of failure) of the scenarios, the probability density function (PDF) of consequences can be derived. This PDF is the basis for the estimation of different risk metrics, such as the expected damage or the risk-curve. The event tree is a logical and visual representation (see Figure 4.7) of the set of scenarios that can occur. In more detailed and advanced calculations, full probabilistic analyses can be made using continuous distributions as input to generate the probability density functions of failures or consequences. Fig. 4.7 shows the representation of an initiating event, which can result in 3 possible scenarios in step 1 (system A), and, depending upon the realised scenario in step 1, leads to 1 or 2 possible scenario’s in step 2 (system B).
damage
scenarios
Pdf of damage
System B System A
No
Small
Continuous pdf
large
Figure 4.7 Event tree with different scenarios, resulting damage levels and probability density function of the resulting damage.
The probability of failure and the consequences can be dependent upon the timing of human interventions. The effect of human intervention and its timing can in turn be modelled by means of dynamic event trees. These are techniques that are used to characterize the effects of emergency response decisions for nuclear hazards and floods (see Acosta and Siu (1993) and Westberg (2010)). An example of a dynamic event tree is given in Figure 4.8 for the example of a flood evacuation plan. These trees can be used to capture both the likelihood of successful human intervention3 and the effect of the timing of the intervention on the consequences4. Within a broader context, these techniques can be used to evaluate various options for the timing of human intervention in a risk-based framework based on characteristics such as:
The benefits and costs associated with early intervention. Costs and risks of unnecessary and / or too late intervention. Costs and benefits of decisions to delay interventions to gather more (certain) information to be able to make better-informed and more certain decisions.
3
The earlier the intervention, the greater the chance of success as there will be sufficient time for implementation of the necessary measures. 4 The later an intervention, such as evacuation, is implemented, the smaller will its effect on the consequences, such as in this case the loss of life, will be. 28
Figure 4.8 Example of a dynamic event tree for the case of evacuation decisions related to flooding. When it is decided to delay the evacuation decision at t i, another evacuation decision can be made at a next period.
Similar to the event tree shown above, one or multiple events can be added to include the different possible failures over time. In this case, Bayesian networks (Sec. 4.2) are more suitable. In the figure below (Figure 4.9), it is shown how in the case of a storm event, a levee can either fail early during the storm (large damage) or later during the storm (less damage, as there will be more time for evacuation and mitigation actions). Conditional probabilities can be used to describe the likelihood of early or late failure during the storm5. Naturally, this situation implies there is sufficient information to make a decision or to be at least aware that a decision may need to be made.
Event tree Early failure storm
Late failure
Damage
No early failure No late failure No storm
No damage
Figure 4.9 Simple Bayesian network to include different failures in time (early and late failure) (left) and the equivalent event tree (right). Note that the arrow between early and late failure is included to model that late failure will not be possible given that early failure has occurred).
5
Note that the two factors concern irreversible changes between states (i.e., an evacuation cannot be changed to a non-evacuation; a late failure cannot change to an early failure) and these are represented by unidirectional relationships in the influence diagram. The situation becomes more complex when representing bidirectional relationships (i.e., system that can change from state A to B, and change back from B to A during a future time step) and multiple states. 29
The tendency of natural hazard events to seek out weaknesses and degrade the performance of human interventions can be very strong. This engenders a degree of nonlinear coupling between the disaster and effective responses, which may be significant. A classic example is of an earthquake damaging the exterior of a fire station sufficiently to prevent fire trucks from exiting to put out fires and rescue victims. Within a flood context, as discussed above in the report, emergency workers may themselves be stranded at home by floodwaters and be unable to join rescue missions. A more extreme scenario is one where key safety managers are absent from duty, for a variety of reasons, e.g., on vacation, sick, searching for, or looking after family members etc.. Holiday periods, such as August in Europe, Christmas or Easter, are particularly awkward times for hazardous events to occur. One of the consequences of a natural disaster may be a breakdown of civil order, and opportunist looting. The UK looting riots of August 2010 were allowed to spread because of under-staffing: many police were away on vacation, including the police chief in the London district where street violence first erupted.
4.3
Bayesian networks for multi-risk assessment
A new quantitative multi-risk assessment model based on Bayesian networks (BaNMuR) is introduced to both estimate the probability of a triggering/cascade effect and to model the time-dependent vulnerability of a system exposed to multi-hazard. The flexible structure and the unique modelling techniques offered by Bayesian networks make it possible to analyse cascade effects through a probabilistic framework. Furthermore, the interactions between hazards and the uncertainties involved may be captured using a Bayesian network. In particular, this methodology is well suited for treating uncertainties associated with hidden geodynamic variables, which are not directly observable from the Earth’s surface (e.g., model uncertainty in causal relationships between unobservable volcanic processes and surface manifestations or monitoring data). The probabilities of hazardous events are updated on the basis of any new information gathered. This framework shows how the updating of probabilities due to the interaction of hazards helps to update the vulnerability and total risk quantitatively and how mitigation measures influence the multi-risk consequences. A Bayesian network (BN), (also called a belief network, Bayes nets or causal network), is an increasingly popular method for reasoning under conditions of uncertainty and modelling uncertain domains. It has been applied to a wide variety of problems, ranging from terrorist threats (Hudson et al., 2002), the nuclear industry (Kim and Seong, 2006), dam risk analysis (Smith, 2006), environmental modelling and management (Aguilera et al. 2011), earthquake risk management (Bayraktarli et al. 2005; Bensi et al. 2011) and landslide risk management (Stassopoulou et al. 1998; Straub, 2005). A BN is a probabilistic model based on directed acyclic graph and may be expressed as
BS G Z , E where BS is the network's structure,
Eq.(3)
Z is the set of random variables z1 , z2 ...zn , and
E Z Z is the set of directed edges, representing the probabilistically conditional dependency relationship between random variables. Each variable Z i can be defined in a discrete and finite outcome space (discrete random variable) or as a continuous outcome 30
space (continuous random variable). For discrete random variables, the probability measure
z Pr Z z p z is the joint probability mass function (PMF). For continuous random
variables,
z N Pr Z z z f ( z ) is the joint PDF.
There are three typical connections in a Bayesian network: serial connections, diverging connections, and converging connections (Jensen and Nielsen, 2007), as shown in Figure 4.10.
z1 z1
z2
z2
z3 z2
(a)
z1
z3 (b)
z3 (c)
Figure 4.10 The three typical connections of Bayesian network: (a) serial connection, (b) diverging connection, and (c) converging connection (based on Jensen and Nielsen, 2007).
Serial connection In the serial connection shown in Figure 4.10(a), z1 has an influence on z2, which in turn influences z3. Obviously, evidence about z1 will influence the certainty of z3 through z2 and vice versa. On the other hand, if the state of z2 is exactly known, then the channel is blocked, and z1 and z3 become independent, which can be described as z1 and z3 being d-separated given z2. A similar situation in multi-hazard risk assessment is that an earthquake (z1) affects the potential for landslides (z2), and in turn a landslide dam (z3). If we know the state of the landslide, then no matter how big the earthquake is, the landslide dam would not be influenced. The joint probability function of the three variables is thus calculated as
P( z1 , z2 , z3 ) P z3 z1 , z2 P( z1 , z2 ) P z3 z1 , z2 P z2 z1 P ( z1 )
Eq.(4)
P z3 z2 P z2 z1 P ( z1 ) Diverging connection In the diverging connection in Figure 4.10(b), the influence can pass between the child nodes (z2, z3) unless the state of the parent node (z1) is known. It is thus said that z2 and z3 are dseparated given z1. A similar situation in multi-risk assessment is that one hazard (e.g., volcanic eruptions) could trigger other hazards, e.g., volcanic earthquakes and pyroclastic flows. The volcanic earthquake and pyroclastic flow are dependent if the volcanic eruption is unknown, as a large probability of volcanic earthquake often means a large probability of pyroclastic flow and vice versa. However, if the volcanic eruption condition is known, the volcanic earthquake and pyroclastic flow would be independent. The joint probability function of these three variables is calculated as
31
P( z1 , z2 , z3 ) P z3 z1 , z2 P( z1 , z2 ) P z3 z1 , z2 P z2 z1 P ( z1 )
Eq.(5)
P z3 z1 P z2 z1 P ( z1 ) Converging connection In the converging connection shown in Figure 4.10(c), the parent nodes (z1, z2) are independent if nothing is known about the child node (z3). In other words, the parent nodes (z1, z2) are dependent on the condition that there is knowledge about the child node (z3). A similar situation in analysing multi-risk is that both earthquake (z1) and intense precipitation (z2) affect the occurrence of landslides (z3). If the occurrence of a landslide is known, then the earthquake and intense precipitation are dependent. For example, if there is no landslide event, we may believe that the probability of earthquake and intense precipitation must be very small. But if the occurrence of landslide is unknown, the other two parameters would be independent. The joint probability function of the three variables is given by
P( z1 , z2 , z3 ) P z3 z1 , z2 P( z1 , z2 )
Eq.(6)
P z3 z1 , z2 P z2 P ( z1 )
In practice, a Bayesian network often consists of all the above three types of connections. The joint probability function of random variables in a Bayesian network can be expressed in the compact and general form as
n
P( z1 , z2 ,..., zn ) P zi pa zi i 1
Eq.(7)
where pa zi is the parent set of zi . It should be noted that if a child node zi has no parents, then the equation reduces to the unconditional probability of p zi . A simple BN with five variables is illustrated in Figure 4.11. These nodes are: two basic nodes [Magnitude (M) and Distance (D)], two medium nodes [Seismic severity (S) and Landslide severity (L)], and one end node [Building damage (B)]. The prior probability of B can be calculated by
P B B1 P B B1 , M M i , D D j , S Sk , L Lm 2
2
2
2
Eq.(8)
i 1 j 1 k 1 m 1
In this case, as both M and D are the parents of S, S is the parent of L, and both S and L are the parents of B, the following equation can be derived according to Eq.(8):
P B B1 , M M i , D D j , S S k , L Lm
P M M i P D D j P S Sk M M i , D D j
Eq.(9)
P L Lm S S k P B B1 S S k i , L Lm where the (conditional) probabilities on the right hand side of the equation are quantified with available information (e.g., statistical data, judgment, and physical and empirical methods).
32
M1=Small magnitude M2=Large magnitude
Magnitude
S1=Low severity S2=High severity
D1=Small distance D2=Large distance
Distance
Seismic severity
L1=Low severity L2=High severity
Landslide severity
Building damage B1=No damage B2=Some damage B3=Collapse Figure 4.11 A simple Bayesian network.
The BN allows one to enter evidence as input, meaning that probabilities in the network are updated when new information is made available, for instance, a case with a small magnitude and large distance. This information will propagate through the network and the posterior probabilities of B, P( B B1 ) can be calculated as:
P B B1 M M 1 , D D2
P M M 1 , D D2
P B B , S S , L L , M M , D D 2
P B B1 M M 1 , D D2
2
j 1 i 1 3 2 2
1
j
i
1
2
Eq.(10)
P B B , S S , L L , M M , D D k 1 j 1 i 1
k
j
i
1
2
where the joint probabilities in the above equation are calculated with Eq.(8) based on the theorem of Bayesian networks. This simple example shows the procedure of risk analysis using Bayesian networks, namely:
Building the structure of a Bayesian network; Quantifying the nodes (basic probability tables) and arcs (conditional probability tables); Calculating the prior probabilities of target variable; Obtaining the posterior probabilities for a specific case by updating the prior probabilities with evidences from the specific case.
A conceptual Bayesian network multi-risk model may be built as shown in Figure 4.12. To determine the whole risk from several threats, the network takes into account possible hazards and vulnerability interactions. This would include the events:
independent but threatening the same elements at risk with or without chronological coincidence (the column marked in deep orange color in Figure 4.12); dependent on one another or caused by the same triggering event or hazard; this is mainly the case of “cascading events” (the column marked in green color in Figure 4.12). 33
This network consists of three main sub-networks for (1) multi-hazard, (2) time dependent vulnerability and (3) risk assessment and management, as detailed in the following sections.
Source 1 (S1)
Threatening the same elements at risk (independent)
Triggering or cascade effect
Source 2 (S2)
Hazard 2 H2=f2(S2)
Hazard 1 H1=f1(S1)
Vulnerability 2 V2=g2(H2) V1'=g1'(H1,2) V2'=g2'(H1,2)
Risk assessment (for Source 1)
…..
Source n (Sn)
Hazard 3 H3=f3(S3)
…..
Hazard n Hn=fn(Sn)
Vulnerability 3 V3=g3(H3)
…..
Vulnerability n Vn=gn(Hn)
Risk assessment (for Source 3)
…..
Risk assessment (for Source n)
Cascade hazard H3'=f(S3 S2)
H1,2=f1*f2 Vulnerability 1 V1=g1(H1)
Source 3 (S3)
V3'=g3'(H3')
Risk assessment (for Source 2)
Multi-risk (Ranking or integration in a single risk index)
Actions, multi-risk management
Figure 4.12 Bayesian network for multi-risk assessment.
4.3.1 Multi-hazard analyses A number of possible scenarios of single hazards and cascade events have been identified for the MATRIX case studies (MATRIX deliverable D3.1, Garcia-Aristizabal et al., 2012a). A Bayesian network may therefore be built as shown in Figure 4.13 to describe the interactions between hazards.
Figure 4.13 Possible scenarios of multi-hazard interaction as considered in the MATRIX project.
34
It is obvious that one hazardous event could trigger other hazardous events (cascade effects) and how to measure these cascade effects quantitatively becomes an urgent issue. The approach outlined here is used to identify the likely propagation path of cascade effects, and to conduct cascade effect probability based on GIS, spatial analysis, and BN. Multi-risk modelling is based on the grid dataset (Figure 4.14a), where each cell corresponds to an independent sample that has the predictive indicators and the target variable. The gridbased format enables us to collect a variety of data from different sources and to integrate them within a consistent modelling system of BN using geospatial techniques. To model the cascade effect probability, the following steps are taken: Step 1: Using the relevant threats identified and the assessment of the relevant risk(s) which have been done, the primary hazard cells (e.g., earthquake) where the cascade effect is likely to start is determined (e.g., X1 Figure 4.14b). The probabilistic hazard assessment of X1 is usually estimated through the analysis of existing databases. Step 2: According to the type of possible hazard scenarios, the maximum influence distance from the primary hazard cells to nearby cells is specified on the basis of existing theoretical models. Those nearby cells are defined as potential secondary hazard cells (e.g., X2, X3, X4 in Figure 4.14b, assuming they are landslides). Step 3: Using theoretical models or empirical laws, an estimation of P(X2|X1), P(X3|X1), and P(X4|X1) may be obtained. Step 4: Substituting the secondary hazard cell for the primary unit, steps 2 and 3 are repeated to determine potential tertiary cells (e.g., X5, X6 in Figure 4.14b, assuming they are dams). An estimation of P(X5|X2), P(X5|X3) , P(X5|X4), P(X6|X2), P(X6|X3) and P(X6|X4) may be obtained. After the likely propagation pattern of the cascade effect is developed as a BN, the probability of the primary hazard event and the conditional probabilities of other secondary and tertiary hazard events (or higher-order hazard events) are calculated. X1
X1 X2
X2
X3 X4
X3
X4
X5
X6
X5 X6
a. Grid dataset Figure 4.14
b. bayesian network modeling
Spatially explicit modelling and a likely propagation pattern of a cascade effect using a Bayesian network.
Once knowing the propagation pattern of the cascade effect, the occurrence probability of the cascade effect can therefore be estimated. Generally, the probability of the cascade 35
effect (Pcascade) is calculated as the multiplication of the probability of the primary event (Pprimary) and the conditional probability of the impacted cells (Pconditional):
Pcascade Pprimary Pconditional
Eq.(11)
For a cascade effect to be in the primary level, it is necessary that the hazard in the primary cells propagates into the nearby cells. For example, in Figure 4.14, considering X2, X3, X4 as the secondary cells, the probability of the first level cascade effect is calculated as:
Pfirst level P X 1 P X 2 X 1 P X 3 X 1 P X 4 X 1
Eq.(12)
Similarly, the cascade effect could proceed to the second level and the probability of the second level of the cascade effect is calculated as:
Psec ond level P X 1 P X 2 X 1 P X 3 X 1 P X 4 X 1 P X 5 X 6 X 2, X 3, X 4
Eq.(13)
Taking an earthquake triggered landslide scenario for example, once an earthquake has happened, the occurrence probability of the cascade effect for slope stability affected can be estimated with respect to seismic hazard intensity measures (e.g., peak ground acceleration, Figure 4.15).
Figure 4.15 Peak Ground acceleration map for a M=7 event over the area defined within the MATRIX Virtual-City.
4.3.2 Time-dependent vulnerability assessment Predicting building damage is critical for the evaluation of economic losses and should be estimated with an acceptable degree of credibility in order to determine the potential losses that are dependent upon the performance of buildings subjected to various hazard 36
excitations. Fragility curves represent the cumulative distribution of damage, which specify the continuous probability that the indicated damage-state has been reached or exceeded, and could provide graphical information on the distribution of damage. Fragility curves can either be empirical or analytical, based on the source of the data and the type of analysis employed to obtain them. The limit state (LS) probability for a building exposed to a single hazard can be expressed in terms of discrete random variables as follows:
i 0
x 0
Pf P LS I i P I i P D C I i P I i
Eq.(14)
where I is the intensity measure of the hazard and LS (limit state) is the condition in which the load demand D due to the hazard is greater than the capacity C. The conditional probability P LS I i is the probability of reaching LS at a given hazard intensity level,
I i . The term P I i is the marginal hazard probability. For continuous random
variables, Eq.(14) can be expressed as
Pf
i
i 0
Fr (i) g I i di
Eq.(15)
where Fr i is the fragility function in the form of a cumulative distribution function (CDF) and g I i the hazard function in the form of a probability density function (PDF) . In the case of a structure subjected to a multi-hazard situation involving additive load effects (e.g., earthquake + landslide + landslide dam), the convolution concept must be expanded. This multi-hazard form is calculated as
Pf ... P LS I1 i1 i1 0 i2 0 i3 0
in 0
P I1 i1
where the conditional probability P LS I1 i1
I 2 i2 I 2 i2
I 3 i3 ... I n in I 3 i3
... I n in
Eq.(16)
I 3 i3 ... I n in is the probability that the limit state is reached at given intensity levels of i1 , i2 , i3 … in acting simultaneously. I 2 i2
Eq.(16) can also be expressed in terms of continuous random variables as
Pf
i1
i1 0
i2
i3
i2 0
i3 0
...
in
in 0
Fr (i1 , i2 , i3 ..., in ) g I1 i1 g I2 i2 g I3 i3 ...g I n in di1di2di3...din Eq.(17)
When the problem is reduced to a two-hazard case, considering for instance, earthquakes and landslides, the limit state probability for a building storey can be written in the following form:
Pf P LS I1 i1 i1 0 i2 0
I 2 i2 P I1 i1
I 2 i2
Eq.(18)
For continuous random variables, the LS probability is
Pf
i1
i1 0
i2
i2 0
Fr (i1 , i2 ) g I1 i1 g I 2 i2 di1di2
Eq.(19)
37
where Fr i1 , i2 is a fragility surface expressed as a joint distribution function in terms of hazard intensities I1 and I 2 . It should be noted that it is conservative to assume that g I1 i1
and g I2 i2 correspond to the maximum intensities, since the two maximum events (earthquake and landslide) sometimes do not occur simultaneously. We will now expand upon the cascade event example of a debris flow triggered by earthquake. Currently, we adopt the seismic fragility curves for RC building developed by the Syner-G project (Tsionis et al. 2011). The LS probability for a building exposed to an earthquake can be expressed as:
1 PGA P dsk PGA pgaLS , k ln pga k LS , k
Eq.(20)
where PGA and pgaLS , k are mean values of the performance point and of the damage limit state threshold, k is the standard deviation of the natural logarithm of the peak ground acceleration normalized to the acceleration for the k-th limit state. An example of seismic fragility curves for a low rise, low code RC building at the yield and collapse limit states is shown in Figure 4.16 (Tsionis et al. 2011). 1 0.9
Probability of exceedance
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PGA (g)
Figure 4.16 Seismic fragility curves for a low rise, low code RC building for the yield (green curve) and collapse (red curve).
For the debris flow fragility curve (Figure 4.17), we adopt the example provided by Fuchs et al. (2007), expressed as:
V 0.11h2 0.22h
Eq.(21)
where V is the debris flow vulnerability and h is deposition height.
38
1 0.9 0.8
Vulnerability
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.5
1
1.5
2
2.5
3
Deposition Height (m)
Figure 4.17 Debris flow fragility curve (Source: Fuchs et al. 2007).
In the case of a system subjected to two hazards (as is the case with earthquakes and debris flow load considered in this study), an alternative formulation must be sought such that the fragility is expressed in terms of the two demands (hazards). When the vulnerabilities to the hazards are completely independent, the multi-hazard vulnerability factor will be one minus the probability that the building has not collapsed after having been exposed to the two hazards one after the other,
1 Pf 1 Pf 1 1 Pf 2
Eq.(22)
where Pf is the limit state probability for the building exposed to two hazards, and Pf 1 and
Pf 2 are the limit state probabilities for the building at given hazard intensity measures due to hazards H1 and H 2 , respectively. The seismic fragilities, including the combination of probabilistic debris flow load (additional seismic weight), are presented over three-dimensions, where the x-axis is the peak ground acceleration, the y-axis the deposition height, and the z-axis the fragility (see Figure 4.18). Seismic fragility curves that consider different deterministic debris flow deposition height effects have also been developed (see Figure 4.19).
Figure 4.18 Fragility surface for a scenario involving a seismic event and debris flow for a low rise, low code RC building.
39
1 0.9
Probability of exceedance
0.8 0.7 0.6 0.5 0.4 0.3 0.2 Seismic Seismic + 1m deposition height Seismic + 1.5m deposition height
0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PGA (g)
Figure 4.19 Seismic fragility curves considering various debris flow deposition heights.
4.3.3 Multi-risk assessment considering mitigation measures Mitigation measures influence the outcome of multi-risk analyses and represent the most important practical aspect since it is here where something can be done about multi-risk. The multi-risk assessment framework outlined in this deliverable should be useful for risk managers by helping them to understand what type of management/mitigation measures can reduce risk to an optimum level within a multi-risk perspective. A Bayesian network for rockslides triggered by earthquakes, modified after Einstein et al. (2010), is outlined in Figure 4.20. The earthquake occurrence probability is assumed to be 0.2. Possible management measures include no action, active and passive countermeasures, and warning systems, where the latter could be considered a type of passive countermeasure. Specifically, active countermeasures, such as retaining walls or drainage systems, reduce the effects of certain types of hazard, i.e., produce a lower probability of failure and a reduced risk. With passive countermeasures, for instance, rockfall nets or protective sheds, the vulnerability would be reduced. The corresponding prior probabilities are shown in Table 4.2. The conditional probabilities of states for the other nodes are shown in Table 4.3-Table 4.9.
Alarm
Measure
Cost_measure
Earthquake
Rockslide Decision Damage
Utilities
Cost
Figure 4.20 Bayesian network applied to bi-risk assessment (earthquake and landslide) with possible decisions (modified after Einstein et al. 2010).
40
Table 4.2 Prior probabilities of the basic nodes for the case outlined in Figure 4.20.
Nodes
States Happens Does not Passive Active No action Warning system
Earthquake (EQ)
Decision
Probabilities 0.2 0.8 0.25 0.25 0.25 0.25
Table 4.3 Conditional probabilities of Rockslide.
EQ
Parent nodes
Decision
Passive
Rockslide (RS)
Happens Does not
0.307 0.693
Happens No Active action 0.077 0.307 0.923 0.693
Warning system 0.307 0.693
Passive 0.207 0.793
Does not No Active action 0.052 0.207 0.948 0.793
Warning system 0.207 0.793
Does not No Active action 0.5 0.5 0.5 0.5
Warning system 0.1 0.9
Table 4.4 Conditional probabilities of Alarm
Parent nodes Alarm
RC Decision
Passive
Yes No
0.5 0.5
Happens No Active action 0.5 0.5 0.5 0.5
Warning system 0.9 0.1
Passive 0.5 0.5
Table 4.5 Conditional probabilities of Measure
Parent nodes
Alarm
Yes
Decision
Passive
Active
Yes No
0 1
0 1
Measure
No
No action 0 1
Warning system 1 0
Passive
Active
0 1
0 1
No action 0 1
Warning system 0 1
Table 4.6 Eight combinations of conditional probabilities of damage
Parent nodes
EQ Measure Decision RS
Damage
Happens Yes Passive Does Happens not
No damage Level 1 Level 2
Active Happens
Does not
No action Does Happens not
Warning system Does Happens not
0.3
0.8
0.05
0.8
0.05
0.8
0.44
0.8
0.4 0.3
0.1 0.1
0.52 0.43
0.1 0.1
0.52 0.43
0.1 0.1
0.3 0.26
0.1 0.1
Table 4.7 Six combinations of conditional probabilities of Utility
Decision
Parent nodes
Damage Utility
No action No damage 0
Active
Level 1
Level 2
No damage
Level 1
Level 2
-10000
-20000
0
-10000
-20000
Table 4.8 Conditional probabilities of Cost
Parent nodes Utility
Decision
Passive
Active
No action
Warning system
-1250
-2000
0
-500 41
Table 4.9 Conditional probabilities of Cost_measure
Parent nodes
Measure
Cost_measure
Yes
No
-1000
0
The results obtained using the described Bayesian network of the entire risk assessment and decision are shown in Figure 4.21. In contrast to Einstein et al. (2010), we assume there is a cascade probability for rockslides equal to 0.1 and some changes in the damage node. The utilities, i.e., the risk, will change due to the cascade probability and conjoint vulnerability. On the other hand, different mitigation measures result in different utilities. The warning system, showing the lowest (negative) utility, is found to be the best mitigation measure.
0 -500
Expected loss
-1000 -1500 -2000 -2500 -3000 -3500 -4000
This study Einstein et al. 2010 Passive
Active
No action
Warning system
Mitigation measures
Figure 4.21
Comparison of results for No action, Active countermeasure, Passive countermeasure and Warning system between this study and Einstein et al. (2010).
Compared to Einstein et al. (2010), expected losses for these four mitigation measures increase due to the cascade probability triggered by earthquake. Thus, neglecting the cascade effect could underestimate the risks. Furthermore, it should be noted that this result is based on many parameters that can vary, for instance, the costs; the probability of slope failure or the reliability of the warning system. Therefore, sensitivity analyses were conducted to assess the effects of these variations on the results. Figure 4.22 investigates the effect of changing the probability of rockslide occurrence against different measures. As expected, for very low failure probabilities, no action is preferred; otherwise a warning system is the best choice, except for very high probabilities where active countermeasures are preferred. It is worth noting that this is only one example, and the sensitivity of the decision to other factors needs to be similarly investigated.
42
Active
Warning system No action
Figure 4.22 Sensitivity analysis of the resulting risk (utility) arising from varying the probability of a rockslide while employing different mitigation strategies. The horizontal marker arrows indicate where each measure is the best mitigating action.
43
5 Time stepping Monte Carlo simulation The Monte Carlo simulation (MCS) technique is widely applied to study the importance of uncertainty for the performance of complex systems. MOVE (2010) presented the most commonly used methods for the propagation of uncertainty, including MCS. The term “Monte Carlo simulation” embraces a wide class of computational algorithms which are effectively capable of simulating complex physical and mathematical systems. The simulations are performed by the repeated deterministic computation of user-defined transformation models using random values as input (i.e., random values drawn from usergenerated sampling distributions). MCS is often used when the model is complex, nonlinear, or involves several uncertain parameters. The number of evaluations/repetitions necessary to establish the probability distributions of the output parameters will depend on the number of input parameters, their probability distributions, the complexity of the propagation model and the accuracy requirements of the output. A simulation can easily involve over 10,000 evaluations of the model. MCS allows for the consistent processing of uncertainties in input parameters and models, regardless of the degree of linearity and the complexity of the transformation models, and of the magnitude of uncertainties in parameters and models. Other notable advantages of MCS over other techniques include: (a) the possibility of appreciating (to the degree of precision desired by the user and imposed by the quality of input data) the shape of the output variable; (b) the possibility of including complex mathematics (e.g., logical statements) with no extra difficulty; and (c) the possibility to model transformation uncertainties directly and to assess its effect on model outputs. MCS requires the generation of artificial samples of random input variables from purposely selected distributions. Such a process requires sequentially: (a) the assignment of a probability distribution type; (b) the assignment of characteristic distribution parameters; and (c) sampling from the distributions. In addition, computation power needs may be fairly large for more complex models. In the MATRIX-CITY platform, the MCS technique is combined with a forward time stepping algorithm. Each MSC simulation produces a possible hazard scenario for the considered time period, with each scenario having a probability associated with it. Each scenario gives as output a loss estimate based on the chosen risk metric. In this way, the final output is a probabilistic distribution curve for the risk metric. The key aspects of this platform are given below. The purpose of the MATRIX-CITY multi-risk platform is to assess the role of interdependencies between hazards and risks, at the scale of the test sites, be it Naples, the French West Indies, Cologne or the Virtual City. Any given test site can be considered as a complex system with many degrees of freedom and interdependencies, which cannot be described analytically (deterministic solution), but may be through Monte Carlo methods (probabilistic solution). A Monte Carlo simulation environment thus forms the core processing of the multi-risk platform. All time-dependent engines (or TD engines for short) are “branched” into it with the time-dependent processes computed using a time-stepped approach (see below). The primary variables are the event occurrence time, drawn from a probability distribution, and the time itself, since hazard and risk are conditional on previous events (instantaneous triggering process) as well as on time-dependent processes, e.g., diffusion of aftershocks, structural ageing. Thus, a sequential Monte Carlo method is used for recursively estimating 44
posterior probabilities. The principle of the proposed sequential Monte Carlo simulation algorithm is defined as follows: Definition of the event time series: 1. Sample a set of n events drawn from one or more (up to n) probability distributions within the time window [t0, tmax]. If it applies, identify the role of each event on subsequent events: 2. Go to ti, the occurrence time of the first event in the time window chronology. Record event i. 3. Apply the TD rate engine to update all probabilities of occurrence or their distributions, conditional on event i and ti. 4. Repeat steps 1, 2 and 3 with t0 = ti while ti < tmax. Compute the expected damages and losses for the time series defined in step 4: 5. Apply the TD vulnerability engine to update vulnerability functions, conditional on ti (aging) and/or on event i - 1 if i > 1, with i the event increment from the time window chronology. 6. Apply the damage engine to compute mean damage ratio i from vulnerability functions provided by step 5 and from intensity Ii of event i. 7. Apply the risk metrics engine to compute loss Li. 8. Apply the TD exposure engine to subtract Li from assets A. 9. Repeat steps 5, 6, 7 and 8 for i=i+1 until i = n. The stochastic process is repeated N times, with N large enough to obtain stable results. It follows that N paths are defined, with some more probable that other ones. This approach, based on a process described by probability distributions, is more robust than the use of deterministic scenarios, which requires some expert judgment. Moreover, the complexity of the modelled system is such that some unexpected, but potentially significant cascade scenarios (black swans), may emerge naturally for a given test site. Additional details may be found in Mignan (2012). The implementation of the theoretical framework (TD engines) as part of the Virtual City concept (D7.2) will offer the opportunity of answering questions concerning under which conditions the new multi-risk approach provides significantly different and better results in comparison to the application of single-type risk assessment methods, and under which conditions this will not be the case. These answers are essential for estimating the impact the MATRIX project results may have, especially on disaster management in Europe.
45
6 Case studies The case described here is based on the Virtual-City software tool being developed within the MATRIX project as part of the more general MATRIX-Common IT system or MATRIXCITY platform (Figure 6.1, Mignan, 2012). Another detailed case study about assessing the hazards and risks from volcanic eruption or tectonic seismic activity in Santorini is provided in Appendix A. The MATRIX-CITY considers a 100 km by 100 km region threatened by various natural hazard types. The elements at risk consist of 50 000 identical low rise concrete buildings distributed within a 20 km by 20 km area inside the Virtual Region (Figure 6.2). The earthquake source zone is a 45-km-long linear source (Black line in Figure 6.2), where the start point and end point are (0.3, 38.8) and (35, 65), respectively.
Figure 6.1 Principal sketch of the MATRIX Virtual-City region (Mignan, pers. com.).
Figure 6.2 Example locations of the 50 000 buildings and earthquake source in the MATRIX Virtual-City region (Mignan, pers. com.).
46
This case is used to explain how to perform multi-risk assessments within a complicated system based on the BaNMuR model described above. Therefore, it is not a validation of the performance of the model. The case partly makes use of artificial data (including the earthquake source) and partly typical engineering values (as for the soil parameters and rainfall intensity). The scenarios consider debris flows triggered by both earthquake and precipitation. We take one cell for example, the central coordinate of which is (40.005, 40.005).
6.1
Constructing causal networks for multi-risk assessment
A Bayesian network is built with the program Bayes Net Toolbox (BNT) on the basis of the MATrix LABoratory (MATLAB) suite, as shown in Figure 6.3. There are 17 nodes and 19 arcs in the network. The network consists of five main sub-networks for seismic hazard, cascade effect, debris flow hazard, building damage and risk assessment referring to the network in Figure 6.3a-d.
(a) Sub network for Seismic hazard
(b) Sub network for Cascade effect Distance (D)
Peak ground acceleration (PGA)
Time (T)
Magnitude (M)
Reduction factor (RF)
(c) Sub network for Debris flow Precipitation intensity (PI) hazard Channel width (CW)
Maximum soil water capacity (MSWC)
Water depth (WD)
Watershed area (WA) Friction angle (FA)
Slope (S)
Deposition height (DH)
(e) Sub network for Risk assessment
Building damage (BD)
Story (S)
Structure code (SC)
(d) Sub network for Vulnerability assessment
Cost (C)
Figure 6.3 The Bayesian network for multi-risk assessment.
47
6.2
Quantifying the networks
6.2.1 Seismic hazard sub-network To do probabilistic seismic hazard analysis, the procedures described by Cornell (1968) are used here:
Identification of all earthquake sources capable of producing ground motions; Characterization of the temporal distribution of earthquake recurrence; Prediction of the resulting ground motion intensity as a function of location and magnitude, specifying the uncertainty in ground motion intensity.
To predict peak ground acceleration at a site, the distribution of distances from the earthquake epicentre to the site of interest is necessary. The seismic sources are defined by epicentres that are assumed to have equal probability. In the Virtual-city, these equal probability locations fall along the line that defines the fault. Using the geometric characteristics of the source, the distribution of distances can be calculated as shown in Figure 6.4.
Probability Mass Function
0,5
0,455
0,4
0,3
0,2
0,168 0,110
0,098
0,091
0,078
28-31 31-34 Distance/km
34-37
37-40
0,1
0,0 22-25
25-28
Figure 6.4 Specification of the discrete probabilities of distance.
The distribution of earthquake magnitudes in a region generally follows a distribution observed by Gutenberg and Richter (1944):
log m a bM
Eq.(23)
where m is the rate of earthquakes with magnitude greater than M , and a and b are constants which are generally estimated using statistical analysis of historical observations. a indicates the overall rate of earthquakes in a region, and b the relative ratio of small to large magnitudes. The above described Gutenberg-Richter recurrence law is sometimes applied with a lower and upper bound. The lower bound is represented by a minimum magnitude mmin below which earthquakes are ignored due to their lack of engineering importance (usually mmin = 4). 48
The upper bound is given by the maximum magnitude mmax that a given seismic source can produce, following the empirical relationship of Wells and Coppersmith (1994):
mmax 5.08 1.16log10 ( L)
Eq.(24)
where L is the length of line source. On the basis of the equation above, the line source can produce a maximum magnitude of 7.0 at any point along its length. Setting a range of magnitudes of interest, using the bounds mL and mU , Eq.(25) can be used to compute the probability that an earthquake magnitude falls within these bounds (Figure 6.5).
P mL M mU mmin M mmax
m m m m L
min
U
Eq.(25)
max
0,8
Probability Mass Function
0,684 0,6
0,4
0,216 0,2 0,068 0,022
0,007
0,002
6.0-6.5
6.5-7.0
0,0 4.0-4.5
4.5-5.0
5.0-5.5 5.5-6.0 Magnitude, Mw
Figure 6.5 Specification of the discrete probabilities of magnitude.
Figure 6.3a shows the constructed BN by conditioning peak ground acceleration (PGA) on magnitude and distance. The ground motion prediction equation proposed by Ambraseys et al. (2005) is used here:
log PGA a1 a2 M w a3 a4 M w log D2 a52 a6 SS a7 S A a8 FN a9 FT a10 FO Eq.(26) where S S =1 for soft soil sites and 0 otherwise, S A =1 for stiff soil sites and 0 otherwise, FN =1 for normal faulting earthquakes and 0 otherwise, FT =1 for thrust faulting earthquakes and 0 otherwise and FO =1 for odd faulting earthquakes and 0 otherwise. The coefficients are given in Table 6.1. Table 6.1 Coefficients for the Ambraseys et al. (2005) PGA attenuation relationship
PGA
a1 2.522 a6 0.137
a2 -0.142 a7 0.050
Component a3 -3.184 a8 -0.084
a4 0.314 a9 0.062
a5 7.6 a10 -0.044 49
The conditional probabilities of PGA given the magnitude and distance to the epicentre are calculated using a Monte Carlo simulation in Microsoft Excel (Figure 6.6), as shown in Figure 6.7. The resulting seismic hazard curve is shown in Figure 6.8.
Figure 6.6 Conditional probabilities of PGA from 1000 Monte Carlo simulations (Partial). 1,0
0,6 0,4 0,1413
0,2
0,0317
0,0023
0,0002
0,0001
0.32-0.4
0.4-0.48
0,0 0-0.08
0.08-0.16
0.16-0.24 0.24-0.32 PGA (g)
Figure 6.7 Specification of the discrete probabilities of PGA.
1 Annual probability of exceedance
Probability Mass Function
0,8244 0,8
0,1 0,01 0,001 0,0001 1E-05 0
1
2
3 PGA (g)
4
5
6
Figure 6.8 Specification of the discrete probabilities of PGA.
50
6.2.2 Cascade effect sub-network Soil properties can be influenced by earthquakes. Post-earthquake soil strengths may be lower than pre-earthquake (static) strengths for zones that are susceptible to strength loss. As time pass, the progression of soil self-healing will result in increased shear strength compared to that shortly after the earthquake. According to Luna et al. (2013), the reduction factor of soil shear strength f s can be calculated as
fs
(tan ' ) After (tan ) Before '
s db w db s db w db w d w
1 1 e
1.3 M 9.5
1070000 M
8.1
D
e 0.5T
Eq.(27)
where is the effective internal friction angle of the soil, d b is the depth of the failure surface, '
d w is water table depth, s is the soil unit weight, w is the specific weight of water, D is the distance to the epicenter, T is the time after the earthquake and M is the earthquake magnitude. The values of these properties for sandy soil following an earthquake are listed in Table 6.2.
Table 6.2 Sandy soil properties at a given time following an earthquake
Water unit weight Soil unit weight Failure depth
w (N/m3) s (N/m3) d b (m)
Ground water depth
9800
T
20000 2
d w (m)
1 1
(a)
Tangent of effective internal friction angle tan '
0.9
Using the values listed in Table 6.2, Eq.(27) can be simplified to become
fs
2 2 0.6
1 1 e
1.3 M 9.5
1070000 M
8.1
D
Eq.(28)
The conditional probabilities of the reduction factor (RF) given the magnitude and distance to epicenter are calculated using a Monte Carlo simulation in Microsoft Excel (Figure 6.9), as shown in Figure 6.10.
51
Figure 6.9 Conditional probabilities of reduction factor from 1000 Monte Carlo simulations (Partial)
Probability Mass Function
1,0
0,9773
0,8 0,6 0,4 0,2 0,0119
0,0047
0,0024
0,0015
0,0022
0.95-0.9
0.9-0.85 0.85-0.8 Reduction factor
0.8-0.75
0.75-0.7
0,0 1-0.95
Figure 6.10 Specification of the discrete probabilities of the RF for sandy soil after an earthquake using the values listed in Table 6.2.
6.2.3 Debris flow hazard sub-network Takahashi (1991) proposed a comprehensive theory behind the mechanism of debris flow dynamics. The debris flow deposition height DH can be quantified as
tan FA DH WD, FA, S WD k1 1 1 tan S
1
Eq.(29)
where k1 Cb db 1 with db 2.65 the relative density of the grains and Cb 0.7 the volumetric concentration of the sediments. Other letters are corresponding variables in Figure 6.3. The theoretical equation regarding the water depth is
WD CW , PI , S , MSWC ,WA k2 WA 5 3 k3 CW tan S 0
2
MSWC PI MSWC 20 if PI MSWC 20 PI MSWC 20 otherwise
Eq.(30)
3 where k2 0.278 is a constant and k3 25 m s is the coefficient of bed roughness. The
other parameters are defined in Figure 6.3. The watershed area, channel width, slope angle and maximum soil water capacity used herein are shown in Table 6.3, while the precipitation intensity properties are listed in Table 6.4.
Table 6.3 Detailed information of the debris flow’s initiation area. 2
Watershed area WA (m ) Channel width CW (m)
2000000 2
Maximum soil water capacity MSWC (m/s) Tangent of slope angle tan S
5*10 0.2
-9
52
Table 6.4 Precipitation intensity properties.
Return period 1.35 5 20 100 1000 10000
Annual frequency 0.7389 0.2 0.05 0.01 0.001 0.0001
Precipitation intensity (m/s) 0.000002 0.000005 0.00001 0.000015 0.00002 0.000025
The debris flow hazard curve can therefore be calculated, as shown in Figure 6.11.
Annual probability of exceedance
1 0,1 0,01 0,001 0,0001 0,00001 0
0,5
1
1,5
2
Deposition height (m) Figure 6.11 Specification of the discrete probabilities of deposition height.
6.2.4 Building damage sub-network As introduced in Section 4.3.2., the fragility curves for the RC building can be obtained on the basis of Eq.(22). The classes of building examined in terms of their storeys include low rise, medium rise and high rise, while the states of structure code are low code, medium code and high code. The fragility curves are shown in Figure 6.12a-i. The limit state of probabilities can be easily calculated from these curves. In the following, only results for a low rise, low code building located in the grid specified above is considered.
(a) Low rise, Low code
(b) Low rise, Medium code
53
(c) Low rise, High code
(e) Medium rise, Medium code
(g) High rise, Low code
(d) Medium rise, Low code
(f) Medium rise, High code
(h) High rise, Medium code
(i) High rise, High code Figure 6.12 Fragility curves for different RC buildings.
54
6.3
Results
For the type of building assessed in the selected site, the average rebuilding cost for the "collapse" damage state is estimated as 200,000 Euro, and the average repair costs for the "yielding" damage state as 50% of the unit rebuilding cost. The final risk curves are calculated as shown in Figure 6.13. It is worth noting that the mean expected loss will increase with respect to the same return period, taking into account cascade effects (i.e., sub-network for cascade effect in Figure 6.3b). Cascade effect
No cascade effect
Probability of exceedance (1/a)
1
0,1
0,01
0,001
0,0001 0
40000
80000 120000 160000 Mean expected loss (Euro)
200000
Figure 6.13 Risk curves for the selected site.
55
7
Summary and conclusions
Quantification of all the natural and anthropogenic risks that can affect an area of interest is a basic factor for the development of a sustainable environment, land-use planning, and risk mitigation strategies. To date, risk assessment is generally achieved through independent analyses, adopting non-uniform procedures and different time-space resolutions. In fact, the assumption of independence leads to the neglect of possible interactions among threats and/or cascade effects, which may underestimate the total risk. In general, it may be argued that interactions between natural hazards play a major role in changing the risks in most of the cases. On the other hand, in most of the cases, only qualitative estimates of the risk level are available. In this study, we have put forward some basic principles for multi-risk assessment (MRA) that are often overlooked and a consistent framework for MRA. The developed procedure consists of three levels: (1) Level 1 qualitative analysis, (2) Level 2 semi-quantitative analysis, and (3) Level 3 quantitative analysis. In this way, MRA is performed step by step. An application of the quantitative Bayesian network model via the Virtual-city tool illustrates its use. In this specific case, the scenario of debris flow triggered by both earthquakes and precipitation is considered. The calculated mean expected loss increases with respect to the same return period, taking into account cascade effects. The present quantitative model using a Bayesian network has several features: (1) It is a probabilistic model instead of a deterministic model. The uncertainties in the parameters and their inter-relationships are represented by probabilities. (2) A large number of parameters and their inter-relationships can be considered in a systematic structure in the model. The probabilities of one parameter can be updated via available information. The change in one parameter will influence the others in the network through their inter-relationships. (3) Physical mechanisms, previous studies, and statistical data can be incorporated within the Bayesian network.
.
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8
References
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Garcia-Aristizabal, Marzocchi A., W. (with: Woo G., Reveillere A., Douglas J., Le Cozannet G., Rego F., Colaco C., Fleming K., Vorogushyn S., Nadim F., Vangelsten B. V., and ter Horst W.), (2012b). State-of-the-art in multi-risk assessment, Deliverable D5.1. New methodologies for multi-hazard and multi-risk assessment methods for Europe (MATRIX), contract No. 265138. Gutenberg B., Richter C. F. (1944) Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34:185-188. Grünthal G., Thieken A., Schwarz J., Radtke K., Smolka A. and Merz B. (2006) Comparative risk assessment for the city of cologne – storms, floods, earthquakes, Natural Hazards, 38(12), 21-44. Hudson J. A. (1992) Rock engineering system. Ellis Horwood Ltd., Chichester. 185pp. Hudson L., Ware B., Laskey K., and Mahoney S. (2002) An application of Bayesian networks to antiterrorism risk management for military planners. Technical Report, Digital Sandbox, Inc.. Jensen F.V., Nielsen T.D. (2007) Bayesian networks and decision graphs (second edition). Springer Verlag. Kappes M.S., Keiler M., Glade T. (2010) From single- to multi-hazard risk analyses: a concept addressing emerging challenges. In Malet, J.-P., Glade, T. & Casagli, N. (Eds.), Mountain Risks: Bringing Science to Society. Proceedings of the International Conference, Florence. CERG Editions, Strasbourg, 351-356. Kappes M.S., Keiler M., von Elverfeld K. and Glade T. (2012) Challenges of analysing multihazard risk: a review, Natural Hazards,64(2), 1925-1938, DOI 10.1007/s11069-012-0294-2. Kim M.C., Seong P.H. (2006). A computational method for probabilistic safety assessment of I&C systems and human operators in nuclear power plants. Reliability Engineering and System Safety. 91(5), 580-593. Marzocchi, W., Mastellone, M. and Di Ruocco, A. (2009) Principles of multi-risk assessment: interactions amongst natural and man-induced risks. Tech. report. European Commission, http://www.scribd.com/doc/16902233/Principles-of-MultiRisk-Assessment, access 19 July 2009 Marzocchi W., Garcia-Aristizabal A., Gasparini P., Mastellone M. L., and Di Ruocco A. (2012). Basic principles of multi-risk assessment: a case study in Italy. Nat. Hazards, 62(2):551-573. DOI 10.1007/s11069-012-0092-x Mignan A. (with Euchner, F. and Kästli, P.), (2012) Report on the MATRIX common IT platform Deliverable D7.1. New methodologies for multi-hazard and multi-risk assessment methods for Europe (MATRIX), contract No. 265138. Newman A.V. et al. (2012) Recent geodetic unrest at Santorini caldera, Greece. Geophysical Research Letters, 39, L06309, doi:10.1029/2012GL051286. Quigley M., Van Dissen R., Villamor P., Litchfield N., et al. (2010) Surface rupture of the greendale fault during the Darfield (Canterbury) earthquake, New Zealand: initial findings. Bulletin of the New Zealand society for earthquake engineering, 43(4), 236-242. 58
Schmidt-Tomé P., (Editor), Kallio H., Jarva J., Tarvainen T., Greiving S., Fleischhauer M., Peltonen L., Kumpulainen S., Olfert A., Schanze J., Bärring L., Persson G., Relvão A. M., Simeoni U., Calderoni G., Tessari U., Mazzini E., (1999) A new application of system theory to foredunes intervention strategies. Journal of Coastal Research 15 (2), 457–470. Smith M. (2006) Dam risk analysis using Bayesian Networks. Proceedings of 2006 ECI Conference of Geohazards, Lillehammer, Norway. Stassopoulou A., Petrou M. and Kittler J. (1998) Application of a Bayesian network in a GIS based decision making system. International Journal of Geographical information science, 12(1), 23-45. Straub D. (2005) Natural hazards risk assessment using Bayesian networks. 9th International Conference on Structural Safety and Reliability (ICOSSAR 05), Rome, Italy, June 19-23. Takahashi T. (1991) Debris flow. Rotterdam: A.A. Balkama. IAHR Monograph. Tse S.D., Fernandez-Pello A.C. (1998) On the flight paths of metal particles and embers generated by power lines in high winds – a potential source of wildland fires, Fire Safety Journal, 30(4), 333-356. Tsionis G., Papailia A., Fardis M., N. (2011) Analytical fragility functions for reinforced concrete buildings and buildings aggregates of Euro-Mediterranean Regions-UPAT methodology. Syner-G project 2009-2012. Luna B. Q., Vangelsten B. V., Liu Z. Q., Eidsvig U. and Nadim F. (2013) Landslides induced by the interaction of an earthquake and subsequent rainfall-A spatial and temporal model. Proccedings of 18th International Conference on Soil Mechanics and Geotechnical Engineering, Paris, France, September 2-6. Wells D. L., Coppersmith K. J. (1994) New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement. Bull. Seismol. Soc. Am., 84, 974-1002.
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Appendix A: Case study of Santorini unrest – Assessing hazards and risks from volcanic eruption or tectonic seismic activity
A.1 Introduction The provision of advice in the face of unpredictable and potentially dangerous geophysical hazards is becoming increasingly fraught for frontline scientists, and better and more formalized ways of handling uncertain data and information are needed. While the most common presumption was that unrest centred in the Thera caldera from late 2011 through early 2012 was the result of magmatic intrusion at shallow depth, it is also plausible that it was due to wider tectonic stresses, and not simply or necessarily solely volcanic in origin. If this possibility is ignored or discounted – something that can easily happen, say, with volcanologists focusing on their specialisms in a crisis - the corollary is that volcanic hazard levels may be over-stated. On the other hand, ignoring the possibility that tectonic seismic hazard levels are elevated under the volcanic interpretation may be even more disastrous: whereas volcanic activity could cause disruption and a few casualties at worst, a significant local earthquake might result in hundreds of deaths and casualties on the island. Thus the 2011-2012 unrest situation was one where multi-hazards could have developed (and may still do so). This report assesses quantitatively the hazard probabilities associated with both forms of geophysical activity, and outlines ways in which the evidence can be treated and corresponding risk estimates enumerated. As a rational evidence-based formalism, the Bayesian Belief Network formulation offers an appropriate tool for weighing different strands of evidence in the light of their differential diagnostic powers, and for documenting the way in which all related uncertainties are characterized, assessed and treated jointly. This formalism is illustrated for assessing volcanic hazards at Santorini, given a state of unrest, before moving on to a counterpart appraisal of earthquake hazards and risks.
A.2 Inferring incipient eruption probabilities by application of Bayesian Belief Networks to volcanic unrest observations - case illustration: Santorini 2011- 2012 This part of the report illustrates some of the ways a Bayesian Belief Network (BBN) formulation can be used in situations of suspected volcanic unrest in order to evaluate multiple strands of observational evidence and data with the purpose of inferring relative probabilities of different potential eruptive outcomes. The principles of the BBN concept are not outlined here, but can be found in the literature (e.g. Jensen and Nielsen, 2007; Darwiche, 2009)6, as can an earlier application to volcanic risk assessment (Aspinall et al 2003)7. The BBN is a helpful graphical construct that can be used for other natural hazards situations where evidence pertaining to the likelihood of an incipient event is indirect, uncertain or very complex in a multi-parameter sense. One important attribute of the BBN is the possibility to include expert judgements in the evidential mix, together with observational data, empirical relationships or model outcomes; others are the capability to incorporate negative evidence 6
Jensen, F.V., Nielsen, T. D. (2007) Bayesian networks and decision graphs (second edition). Springer, 447pp; Darwiche, A. (2009) Modeling and reasoning with Bayesian networks. CUP, 548pp. 7 Aspinall, W.P., Woo, G., Voight, B. and Baxter, P.J. (2003). Evidence-based volcanology; application to eruption crises. Journal of Volcanology and Geothermal Research: Putting volcano seismology in a physical context; in memory of Bruno Martinelli 128, 273-285.
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in the BBN (e.g. a cessation of gas flux) and to cope with situations where information is only partially complete (e.g. when an instrumental data stream drops out). In this illustration, the case of recent unrest at Santorini is used as a basis for demonstrating a formalized procedure for weighing and combining strands of evidence; values and probabilities reproduced in what follows are tentative and indicative - in a real crisis all would be subject to detailed expert appraisal. In brief, there was an increase in local seismicity within the Thera caldera in early 2011, accompanied by inflationary deformation centred in the caldera, with seismicity escalating and inflation increasing over subsequent months. Other signs of unrest, such as unusual bubbling in the water and a temperature rise, were also reported. By the end of 2011 into early 2012, levels of activity were sufficiently strong to cause scientific concern about the possibility of an ensuing volcanic eruption in the near future. Here we present three alternative BBN models for illustrating the Santorini situation: (1) a basic net for evaluating eruption probabilities at one moment in time, utilising four traditional key indicators for unrest due to volcanic activity; (2) the same basic net, extended to illustrate how eruption probabilities can be updated through time as these indicators change; and (3) a more complex single instant net, in which multiple lines of other data are added to reflect the diversity and differential evidential worth of modern monitoring techniques. A key conclusion for hazard management is that, even with three or four basic indicators, it is not feasible or defensible to attempt to mentally weigh implications of unrest signs probabilistically – a structured procedure is essential for enumerating Bayes Rule rationally and reliably.
A.2.1 A basic BBN for Santorini Figure A.1 shows a basic four-parameter BBN8 for Santorini, compiled originally in March 2012 when eruption concern was high. The target node “Santorini_eruption_probs” comprises four alternative impending scenarios: “Non-magmatic”, “Failed intrusion”, “Lava flow or dome 1st” and “Explosion 1st”.
Figure A.1 Basic four-parameter volcanic Bayesian Belief Network for Santorini unrest.
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Netica v4.14 (2010) www.norsys.com 61
Implicit in this probabilistic formulation is some time window for occurrence of one of the scenarios as the first/next event: again, just for illustration, one year ahead is assumed on the basis that historical data for Santorini allow us to estimate base-rate annual probabilities of occurrence for each scenario (n.b. the state labelled “non-magmatic” extends to include nothing eruptive happens in the chosen interval). These base-rates are adopted as prior probabilities in the BBN top target node:
Node: Santorini_eruption_probs Failed_Intrusion
0.005
LavaFlow_or_Dome_1st 0.014 Explosion_1st Non_magmatic
0.001 0.98
In other words, in any random year – without additional monitoring information – there is a 2% chance of eruptive activity, with a lava flow or dome-forming eruption three times more likely than a failed intrusion episode, and the latter five times more likely than an explosion being the first new eruptive action. This leaves a prior balance probability of 98% that no eruptive activity ensues in the following 12 months. Although often overlooked when unrest near a volcano is being informally assessed, it is essential to include a state such as “Nothing happens” (here titled “Non-magmatic”) because the possibility will always exist that the signs of unrest are generated by some cause other than incipient eruptive/intrusive magmatic movement or pressurization at depth (see Discussion, below). Posterior probabilities on the target node are calculated by “instantiation” of some or all the observation nodes (i.e. the target priors are updated through observation or detection of evidential information). Four basic observational monitoring nodes are included in the BBN: DC_seismicity; LP_Hybrid_Tremor; Inflation, and Gas9.
Figure A.2 Conditional Probability Table (CPT) for one BBN node.
9
The node DC_seismicity stands for double-couple (i.e. rock stress failure) earthquakes, which may be either pure tectonic type or volcano-tectonic, depending upon the causal process. Where both tectonic and volcanic processes are possible, the nature of DC quakes can be ambiguous. The node labelled LP_Hybrid_Tremor encapsulates (non-double-couple) Long Period, Hybrid seismic events and volcanic tremor, all conventionally interpreted – if observed close to or under a volcano as indicators of magmatic fluid or gas movement. Inflation captures the notion of ground deformation uplift due either to magma movement or pressurization, or possibly due to tectonic fault processes – another potentially ambiguous sign. The node Gas represents the detection, or non-detection, of gas flux or gases with a magmatic imprint.
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Before the eruption scenario probabilities can be calculated, however, a conditional probability table (CPT, sometimes “contingency table”) needs to be enumerated for each observational node. This involves quantifying the full matrix of probabilities for the particular unrest signs being present or absent, conditional on each of the volcanic states being true (n.b. inference of the latter states is unavoidable because they cannot be observed or determined independently). The values inserted in the CPT can come from the statistics of historical precedents at the subject volcano – more commonly with additional guidance from other similar volcanoes – with derived conditional probabilities usually moderated by expert judgement. The example of the LP_Hybrid_Tremor node CPT is shown in Figure A.2. In Figure A.3, the four observation nodes are instantiated to background, absent, neutral and uncertain, respectively, with the eruption probabilities updated accordingly. The BBN shows rounded probabilities, and more precise values are tabulated below with the corresponding node state selections.
Figure A.3 Santorini BBN with all observation nodes instantiated to null or negative states. Table A.1 BBN node state selections and evaluated probabilities (shown rounded on Figure A.3). Non_magmatic Failed_Intrusion LavaFlow_or_Dome_1st Explosion_1st Santorini_eruption_probs
Gas
Inflation
DC_seismicity
LP_Hybrid_Tremor
0.99983
0.00011934
5.494e-005
Magmatic_imprint
Uncertain
Hydrothermal
0
1
0
Positive
Neutral
Negative
0
1
0
Elevated
Background
0
1
Present
Absent
0
1
3.6699e-007
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At the other extreme, Figure A.4 shown the same basic BBN instantiated this time with all observational node set to their positive states. This very strong, joint evidence for the existence of volcanic unrest engenders significant changes in the eruption scenario probabilities: on this evidence, if activity continues there is perhaps a 77% chance in the following twelve months of a lava flow or dome-forming event, and a much smaller but notinsignificant probability of an explosive eruption. A failed intrusion episode, similar to Guadeloupe 1976, is also a real possibility: from the CPT values deployed here, this is evaluated twice as likely as an explosion.
Figure A.4 Santorini BBN with all observation nodes instantiated to positive states.
It should be borne in mind that a BBN analysis such as this serves to inform judgements about eruptive potential - it should not be relied on, on its own, as an operational decision tool.
A.2.2 Time-stepping BBN Of course, unrest is never static and levels and trends in the different indicators can and will change with time. As a consequence, inferences about the eruptive potential of the system will shift. Coherent, and auditable, tracking of hazard level is desirable. This is a major challenge, even with the assistance of the BBN methodology. Following the previous section, Figure A.5 shows one way this might be set up for an unrest episode with four basic data streams, such as that at Santorini: following the initial assessment, two time-step updates are presented, identifying trends or trend changes in the unrest indicators. The time-step is not defined in this illustration, but typically could be on a timescale of days, weeks or months. Enumerating the conditional probabilities for the CPTs in such a BBN is a major undertaking, and developing a time-stepping BBN for operational application requires much preceding thought and work. Figure A.6 - 7 depict three hypothetical sets of update instantiations (nodes shaded green), showing illustrative evolving changes in calculated eruption probabilities. 64
Figure A.5 Suggested time-stepping BBN for Santorini unrest, with four evidence streams
Figure A.6 Time-stepping BBN for Santorini unrest, with two steps hypothetically instantiated in sequence (rows 2-5, first two column sets); note changes to probabilities on target nodes (upper row)
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Figure A.7 Hypothetical Santorini BBN, instantiated over three time steps – note changes to eruption scenario probabilities
A.2.3 Extending the BBN for additional datastreams The preceding examples illustrated BBN applications when there are just four unrest symptoms. Modern volcano monitoring can entail multi-parameter diagnostics, including different techniques for measuring the same fundamental variable (e.g. deformation gauged by GPS and InSAR). Nowadays, the number of such indicators easily exceeds any feasible chance of assimilating all the various hazard level implications without the assistance of a structured procedure. An example of what might be involved is shown in Figure A.8, with instantiated nodes shaded pink (n.b. not all such techniques were deployed at Santorini, and data were not necessarily available from others for entry to a BBN).
Figure A.8
Extending the Santorini BBN to incorporate additional streams of observational evidence and data
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With all these indicative nodes and compound CPT relationships, this is a substantial but still tractable BBN. Note that this model exemplifies an extension of the conversation to secondary indicators, such as “Sea_temp” and “Sea_state”, in relation to which an above ambient temperature or bubbling is presumed to be evidence of elevated (submarine) gas output. In this example it is also included a node “Felt_quakes”, with discrete enumerated states, quantified in terms of number of events in a given time in specified ranges. This contrasts with the other nodes, which simply express qualitative categorical states. The reason for including such a node here is to exemplify how one particular manifestation of volcanic unrest can be construed to make it is coherent with older, pre-instrumental historical information. The latter may provide valuable and robust benchmark rates of occurrence from previous eruptions and episodes of unrest, at this or other volcanoes. One particular strength of the BBN approach, not illustrated by Figure A.8, is what happens if data becomes not available or is incompletely reported. In this case, the Bayesian framework offers a powerful means for handling missing data, which can be regarded in a model in just the same way as unknown variables. For instance, if the “Felt_quakes” node is not instantiated, then the BBN calculates their expected mean rate, and an estimate of its uncertainty, given the state setting of all other nodes in the network and their conditional probability relationships. In this way a BBN can elegantly handle missing values from prior distributions and by inference from other parameter findings – an extensive literature expounds the principles (e.g. Daniels and Hogan, 2008 is a recent text)10.
A.2.4 Linking eruption scenario probabilities to ash and gas hazards The BBN approach provides a transparent framework for deriving eruption scenario probabilities which can then be used as elemental foundations for quantitative assessments of contingent hazards and risks. For instance, stochastic models of ash and gas hazard are available to describe the dispersal of ash and SO2 during future eruptions. For Santorini ashfall hazards, two alternative scenarios might be adopted as the most likely or expected eruptions, based on analysis of explosive activity during historic eruptions: these eruptions are characterized by slow lava extrusion over periods of 2 to 4 years with weak but persistent explosions and ash venting. A third, more extreme, scenario is a sub-Plinian explosive eruption, which has not happened historically but is commonplace in the geological record. This latter scenario might be regarded as a worst considered case. Taking decadal time series of regional wind reanalysis data (e.g. European Centre for Medium-range Weather Forecasts), it is possible to provide a statistical model for wind speed and direction variations across Thera, related to season and height. Preliminary analysis of these data shows that a consistent low altitude wind direction is rarely maintained for more than a few days across the island. Monthly data show that up to about 1 km wind directions are S while above 1 km altitude winds are predominantly E-SE and are weaker over the summer (June - August). With an ash model using empirical relations for source ash flux and plume height (e.g. TEPHRA2 code), ash transport for each scenario can be modelled as a time series of ash plumes in different height bins (typically 0.5, 1, 2 and 3 km) with event durations and frequencies consistent with historic eruptions. Where historic data are insufficient to develop a full statistical model, inter-event times for each plume size bin can be simply modelled as independent Poisson processes, each with a different rate parameter 10
Daniels, M.J. and Hogan, J.W. (2008) Missing data in longitudinal studies: strategies for Bayesian modelling and sensitivity analysis. Chapman & Hall.
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based on historical observations. Simulation output can be used then to estimate probability of exceedance for key ash loading thresholds, namely 100 kg m2 (roof collapse), 10 kg m2 (significant crop damage), 1 kg m2 (likely dangerous suspended ash levels for severe aeronautical engine damage) and 0.001 kg m2 (likely suspended ash concentration equivalent to commercial aviation safety limit). Outputs take the form of probabilistic maps and exceedance probability curves for key locations, each conditioned on initiating event probability as determined by the eruption BBN analysis approach (above). The hazard and risk analysis for proximal effects can be extended to an assessment of gas hazard and further assessment of ash hazard on Thera by using an air pollution model for tracers in the boundary layer (e.g. AERMOD) to estimate ground level concentrations. Typically, gas hazard assessment might be based on two nominal constant fluxes (say, 200 and 800 tons/day SO2) for the duration of the eruption, noting that there is very little evidence to constrain the SO2 flux from Santorini eruptions. Exceedance probabilities can be calculated based on daily exposure targets set by the World Health Organization. These might include two WHO (interim) targets of 125 and 50 pg/m3 and an Air quality Guideline (AQG) of 20 pg/m3. For estimating ash concentrations, a source flux of 2315 kg/s might be assumed as typical and, for this flux value, many localities on Santorini would experience mean levels of suspended ash concentration that approach or exceed the values that resulted in disruption of flights in Europe from Icelandic ash in 2010. Preliminary findings indicate that air transport will likely be problematic during explosive eruptions and will likely be a challenging management issue for maintaining reliable air routes even in low level ashing events. Ferry movements into the caldera bay may also be disrupted. Preliminary findings also indicate exceedance of the AQG across the island but it is in the E, SE and S sectors where higher concentrations are likely to be experienced and frequently exceeded. On the other hand, Therasia and Oia would have low ash and gas hazards impacts so would be suitable areas for emergency response centres and emergency critical infrastructure. The likelihood of such exceedances and impacts would be conditional on the probability of eruption style and duration, hence the relative probabilities of these various hazard and risk scenarios require stochastic ash and gas dispersal models to be closely coupled to the event scenario probabilities, as enumerated by the BBN analysis, described above.
A.3 Santorini unrest multi-hazards: Kameni earthquake fault activation Whilst the preceding discussion has addressed volcanic eruption hazards and risks specifically, and ways to quantify likelihoods of occurrence probabilistically – motivated by good evidence of active deformation and elevated seismicity in an active caldera setting – the possibility exists that the unrest may have a tectonic element which could also give rise to a short-term elevated level of earthquake hazard. According to the mapped seismicity, the tectonic feature that might be implicated in this episode of unrest would be the Kameni fault system, cutting through the caldera.
A.3.1 Summary Relying on conservative modelling assumptions throughout, if there is a 10% probability11 the Kameni fault system might be seismically activated by a magmatic intrusion to produce a magnitude 4Mw or greater earthquake, then ‘normal’ seismic acceleration hazard levels on Thera could be temporarily increased above background by a factor of 10x or more in terms 11
Derived from an assumed 50% chance of magmatic event, factored by 20% probability of significant associated quake from historical precedents.
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of acceleration/Intensity exceedance probabilities. Higher risks may obtain locally where adverse topography and ground conditions influence soil-structure interactions. Damaging Intensities from MMI VII up to MMI IX across Thera are conceivable in this scenario. Cursory inspection of the island building stock suggests that many structures are modern, with some intrinsic seismic resistance capacity, which should perform tolerably well in seismic shaking at ‘normal’ expected levels. However, there are also significant numbers of older, weak masonry properties with poor seismic collapse susceptibility. Capacity margins in both types could be eroded during extreme acceleration intensities, say from a very close, shallow earthquake of magnitude 6Mw, with the situation exacerbated by poor ground conditions and steep topography in places. To assess seismic performance of both types of structure on Thera, the magnitude 6.0M 1999 Athens earthquake represents a plausible analogue for the Kameni fault earthquake scenario. Given the assessed likelihood of the scenario event, a tourist spending two weeks on the island would have an estimated risk of death of about 8 x 10-6 (1-in-125,000) in that time. For the UK population aged 25 – 64 years, the chance of accidental death in a fortnight is about 4 x 10-5 (or, 1-in-26,000). Thus, a holiday on Santorini could add an additional 20% to a British tourist’s risk of losing his or her life by external accident. However, for a person indoors on Santorini when the scenario earthquake occurs, the probability of being a fatality is about 0.5%. For emergency planning it follows that the expected death toll could be upwards of 5 for every thousand persons on island. To this can be added another 15 or so people who would suffer significant injury – mostly broken limbs. The associated uncertainties on these estimates are substantial - an order of magnitude or more, either way. If the quake struck at a time when most tourists were out-of-doors, the toll would be much reduced.
A.3.2 Seismic hazard assessment Given the historical precedent of damaging earthquakes sometimes preceding eruptions in the Santorini caldera, a scoping exercise is undertaken to ascertain the approximate impact on local seismic hazard levels due to the potential for a significant earthquake on the Kameni fault system, activated by the magmatic intrusion episode12. The basis13 of the present analysis is comparison of peak ground acceleration (pga) hazard levels, with the Kameni fault activated, against the long-term pga hazard on Santorini due solely to background regional seismicity. In order to estimate seismic hazard, multiple moderately-conservative modelling assumptions are made (not recorded in this note). Background seismic hazard “Normal” tectonic seismicity14 in the area around Santorini from 1900 – 2012 is shown on Figure A.9, with filled circles denoting events that comprise data above defined magnitude reporting completeness thresholds over that period.
12
This is one possible earthquake occurrence scenario of a number that could be conjectured for Santorini in the light of elevated seismicity near and around the island; others are not considered here. 13 While this analysis has been done without detailed discussion or input from colleagues in Greece, a new paper by Chouliaris et al. (2012: Nat Haz Earth Syst Sci, 12, 859-866) contains very similar findings about seismicity in and around Santorini. 14 Data from: International Seismological Centre, On-line Bulletin, http://www.isc.ac.uk, Internatl. Seis. Cent., Thatcham, United Kingdom, 2010. 69
To calculate long-term tectonic seismic hazard exposure on Santorini, a single broad area source zone is delineated (Figure A.9 - dashed orange lines) with three separate depth bands (0-40km; 40-100km; 100-150km depths). Each sub-volume is presumed to contain a statistically-homogeneous rate of spatial earthquake activity (while inspection of Figure A.9 shows this clearly is a simplification, the impact on the hazard estimation is not substantial). An established code, PRISK 15 , is used to enumerate probabilistic seismic hazard with a logic-tree formulation to accommodate epistemic uncertainties; accepted procedures are also adopted for defining aleatoric uncertainty distributions for random variable parameters in the model.
Figure A.9
ISC seismicity of Santorini region, 1900 – 2012, and area source zones for hazard model based on ‘complete’ data.
This basic zonal area source model produces the lower (black) seismic hazard exceedance curve shown on Figure A.10 for a rock site location (black triangle on Figure A.9) close to the town of Fira. To give this curve context, the expected (mean) pga that corresponds to an event with a 10% chance of exceedance in 50 years (i.e. annual exceedance probability of 0.0021, or a “475-year return period” event), is about 0.3g. This is similar to hazard mapping results for the island vicinity presented by Weatherill & Burton (2010)16 and other studies, and gives confidence that the simplified seismotectonic model developed here is suitable for present comparison purposes. Local earthquake hazard model
15
Courtesy Dr Gordon Woo. Weatherill, G. and Burton, P.W. (2010) An alternative approach to probabilistic seismic hazard analysis in the Aegean region. Tectonophysics 492, 253-278. 70 16
The origin of the hazard model co-ordinate system is the volcano location given by GVP: i.e. 36.404°N 25.396°E. Positions are expressed in kmE kmN relative to this point, e.g. with Fira marked at [3.1, 2.7], Kamari at [6.3, -6.5]. Three area source zones are adopted, with parameters or weighted parameter distributions decided as suitable for this scoping exercise. Adding a Kameni fault source The potential impact of the Kameni fault system, if activated to produce magnitude 4Mw or greater by magmatic intrusion, is evaluated by adding to the seismotectonic model a SW-NE striking, 6km long, vertical fault (see short purple lineament in caldera, on Figure A.9). This fault is modelled with a weighted three-point distribution for plausible maximum magnitude: 5.2; 5.7; 6.0Mw (wts: 0.3; 0.5; 0.2). One of the key factors for assessing the consequent seismic hazard is the probability that the fault is activated at magnitude 4Mw or greater. There have been at least two historic eruptions in the caldera preceded by an earthquake in this magnitude range, out of about ten magmatic or eruptive episodes. Thus the assumption is made here that the probability of such an earthquake recurring in the near future, conditional on magmatic activity, is roughly 0.2. If we further assume, indicatively, that the probability present unrest escalates to become a significant intrusive or eruptive event is about 0.5, then the current likelihood of induced earthquake activation of the Kameni fault system is thus about 0.1. Peak acceleration hazard results Using this latter probability to define the current activation potential of the modelled fault (and adopting other weighted parameter distributions typical for fault modelling, but not expounded in detail here), the upper (red) expected hazard curve on Figure A.10 is obtained.
Figure A.10
Peak ground acceleration hazard curves for a site near Fira, Santorini, due to background tectonic seismicity and an activated Kameni fault, respectively.
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This curve shows two features: at relatively high probabilities of exceedance (i.e. 0.1 p.a. or greater), the addition of the fault to the model does not significantly elevate pga levels, compared to the background exposure; at low probabilities, however, the ground motion hazard increases rapidly, due to the inclusion of the fault. At an exceedance probability of 0.0021 p.a., for instance, peak acceleration could be close to 1g, three times higher than the corresponding background exposure level. And, the relative increase above background grows even more emphatic at very low probabilities of occurrence. Also shown on Figure A.10 are the 10% and 90% model confidence bounds about these hazard curves. These indicate very substantial uncertainty associated with the fault-based model case, such that the lower, 10% confidence line falls close to and, in places, encompasses the curve for the basic tectonic model. This said, the ‘expected’ (mean) curve for the fault scenario is located much more towards its own upper confidence region. Thus, the presence of an active, shallow seismogenic fault within the Santorini caldera which might be taken closer to failure due to stresses arising from magmatic intrusion - could engender the possibility of very strong ground shaking on the island if the whole fault ruptures. More detailed modelling of current tectonic stress conditions is justified. This analysis is solely for the case of ground motions at a rock site on flat terrain. There is no question the steep caldera wall topography can trap seismic energy and "amplify" it in places: Prof. K Papazachos, at a workshop on Thera in March 2012, indicated acceleration intensification at places on the caldera rim may be a factor of 2x, or greater, due to topography17.
Intensities From the hazard estimation results of the present analysis and adopting, with the usual caveats about such conversions, two alternative acceleration-Intensity relations formulated for Greece by Tselentis and Danciu (T&D 2008: Equations 1 & 3)18, Table A.2 presents the peak accelerations and shaking Intensities that may be anticipated from an ‘ordinary’ regional tectonic event and from a fault-rupturing earthquake on the Kameni fault system. Table A.2 Peak ground acceleration pga hazard levels and equivalent Intensities at given annual exceedance probabilities for background tectonic seismicity and for Kameni fault scenario
Intensity (T&D 2008) Eq. Eq. 1 3
Annual exceedance probability
Background seismicity pga
0.5
0.01g
III
0.1
0.07g
0.05
0.1g
17
USGS Instr. Intensity
Activated Kameni fault pga
n/a
III
VI
-
VII
-
Intensity (T&D 2008)
USGS Instr. Intensity
USGS Potential damage
Eq. 1
Eq. 3
0.02g
IV – V
V
IV
None
V
0.16g
VIII
VII
VI
Light
VI
0.32g
IX
VII
VII
Moderate
Whilst this is significant, it is not exceptional: other places in the world have less extreme topography effects but much worse ground conditions, and evince even higher amplifications in earthquakes. 18 Tselentis, G-A. and Danciu, L. (2008) Empirical Relationships between Modified Mercalli Intensity and Engineering Ground-Motion Parameters in Greece. Bull. Seismol. Soc. Am., 98, 1863-1875. Equation 1 of Tselentis and Danciu provides a straight conversion from measured peak acceleration to Modified Mercalli Intensity MMI, albeit with major scatter on the relation such that the uncertainty on any individual conversion can be plus-or-minus one MMI scale unit, or greater. Their Equation 3 includes additional explanatory variables – magnitude, epicentral distance and soil type – and while it has slightly lower scatter than Equation 1, there is still about one MMI scale unit of variance present. 72
0.01
0.18g
VIII
-
VI – VII
0.63g
X
VII VIII
VIII
Moderate to Heavy
0.0021
0.30g
IX
-
VII
0.96g19
XXI
VIII
IX
Heavy
0.001
0.37g
IX
-
VIII
1.12g
XI
VIII
IX
Heavy
Additional Intensity attributions corresponding to peak ground acceleration ranges are cited on Table A.2 from a scheme of intensity classifications proposed by the USGS20. The Modified Mercalli and USGS Instrumental Intensities shown on Table A.2 should be regarded with great caution, not least because of the extensive uncertainty attending such conversions. This said, the predictions of T&D 2008 Eq.3 look more realistic than those produced by Eq. 1 (see footnote[13]). In particular, an expected MMI VII for pga 0.30g or 0.32g appears much more plausible than MMI IX, in terms of building damage effects. This view is borne out by the USGS counterpart conversion descriptors. In summary, Table A.2 suggests that the current annual exceedance probability for acceleration (0.3g) and for Intensities (VI – VII) which mark a rough threshold for damage is about 5% - 10% probability. This is significantly higher than the ordinary, long-term background exposure hazard level, gross uncertainties in Intensity conversions notwithstanding21. Building stock The 0.0021 p.a. exceedance probability hazard level (or 475-year return period) is often used in building codes as a design criterion for ordinary structures. In the case of Santorini, this hazard level is estimated to be of the order of 0.25g to 0.35g for ‘normal’ regional tectonic event activity. A superficial survey of the island building stock suggests that quite a lot of structures on Santorini are modern, post-1976 earthquake buildings that benefit from some seismic resistance capacity; most should perform tolerably well in shaking intensities expected at the background seismicity 475-year level. Although these structures may not have been built to the highest anti-seismic standards in worldwide terms, they usually seem to have lots of steel in them, many or most have ring beams, and most have quite small window openings, so infill walls should provide significant lateral shear resistance, as well. In addition, they are mainly quite squat structures compared to buildings seen in many seismic parts of the world, and do not have evidently over-heightened elevation-to-plan ratios. These buildings can be classified as Type D structures – ’shear wall or moderate code RC frame construction’ according to the scheme outlined by Spence and So (2009)22 in a recent report for the U.S. NEHRP Project.
19
At the 26-29 March 2012 Santorini Workshop, Prof. K Papazachos presented some seismic ground motion modelling results (details unconfirmed with the author, as yet), which suggested that the 50-year 10% prob. exceedance pga for points on the caldera rim is about 0.25g, for a magnitude 5.5Mw event modelled on the Kameni fault. Note, however, that this estimate does not include an abnormal elevated fault activation probability, as assumed here. 20 http://earthquake.usgs.gov/earthquakes/shakemap/background.php#intmaps 21 But see also last section of this note for remarks on difficulties in interpreting historical Intensities. 22 Spence R. & So E. (2009) Estimating Shaking-Induced Casualties and Building Damage for Global Earthquake Events. NEHRP Grant number 08HQGR0102 Final Technical Report. 106pp 73
However, Prof. Spence23 (pers. comm.) expresses the view that it is possible that quite a lot of the visitors to Santorini stay not in modern hotels but in independent small guesthouses, many of which may be of older poor-quality rubble masonry, some even with masonry vaulted roofs - the kind of island village architecture which makes the town of Thera a postcard attraction. Such properties therefore should be classified as Class A (‘weak masonry’, likely similar to many buildings in Athens), with greatly increased seismic collapse susceptibility, relative to Type D structures24. Moreover, poor ground conditions and steep topography could result in some buildings being compromised, especially the older masonry ones, if more extreme accelerations and intensities were experienced in a close-by earthquake on the Kameni fault system. A detailed survey of the Santorini building stock by earthquake engineering specialists would be beneficial for weighing up seismic risks posed by a near-by fault rupture. Death and injury risk assessment This section extends the seismic hazard discussion, above, to provide indicative death and injury risk estimates commensurate with the scenario of a strong earthquake on the Kameni fault line, under Santorini. These estimates are based on assumptions about building fragilities (a function of building typology and construction), collapse rates as a function of shaking Intensity, and consequent lethality rates given building damage or collapse. The starting point for putting numbers to risks is mainly guided by global findings on seismic shaking-induced casualties and building damage, presented in the recent report by Spence and So (2009). In addition, information is taken from the associated Cambridge Earthquake Impact Database CEQID 25 , in particular in relation to the damage impacts of the 1999 Athens earthquake. The latter was a magnitude 6M (USGS) earthquake that had a focal depth of 10km, producing epicentral Intensity 7.7 (USGS instrumental intensity scale) and peak ground acceleration pga ~ 0.36g. It is, therefore, a close seismo-physical analogue to the conjectured scenario event on the Kameni fault, discussed above. In the 1999 Athens earthquake, 143 people were killed and more than 2,000 injured (USGS PDE). About 3,800 buildings out of 74,400 surveyed suffered severe structural damage (CEQID), most needing to be demolished. In the immediate epicentral area, the survey of Fyli district, 7km from the quake centre, indicated135 properties out of 909 were severely damaged, with a further 374 suffering repairable structural damage. This particular damage experience data from Athens is only partially transferable to the Santorini situation because of possible differences in building stock age and anti-seismic structural capacities. Therefore, the Athens survey findings are considered jointly with the Spence and So global damage and lethality relations to provide judgement guidance on likely building impacts in a Santorini scenario quake. Leaving aside details of how numbers are arrived at here, the probabilities of exceedance of the various levels of damaging Intensities listed Table A.1 are compounded with collapse rates and lethality rates, duly modified for Santorini. This numerical exercise suggests that, given the current perceived likelihood of a significant earthquake under the island, the
23
Emeritus Professor of Architectural Engineering, Cambridge University. I am indebted to Prof Robin Spence for advice on this important aspect. 25 www.ceqid.org accessed 20 April 2012 24
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corresponding annualized mortality rate for a permanent resident of Santorini indoors at the time of the quake26, is about 1-in-5,000 per annum (IRPA, in health and safety speak). This is based on the assumption that building types A and D exist in roughly equal proportions amongst Santorini properties. However, where ground conditions enhance shaking, the risk exposure could be significantly higher than assumed, especially in poorer quality buildings. For a tourist spending two weeks on island the corresponding risk for the fortnight is, therefore, about 8 x 10-6 (1-in-125,000). For the UK population aged 25 – 64 years, the chance of accidental death in a fortnight is about 4 x 10-5 (or, 1-in-25,000). Thus, a holiday on Santorini could add an additional 20% to a tourist’s risk of losing his or her life by external accident. As another comparative reference, for the same age group the accidental drowning mortality rate (in the UK) per fortnight is approximately 8x lower than this – at about 1 x 10-6 or 1-in-1 million [27]. To give a context for emergency planning, these fatality risk estimates can be expressed another way: if a person is indoors on Santorini when the scenario earthquake occurs, then the probability he or she becomes a fatality is about 5 x 10-3, or a 0.5% chance. Thus, on the basis of these assumptions about building types, the estimated death toll might be of order 5 per thousand souls. Such an estimate does not appear incongruent with the death toll of 143 in the 1999 Athens earthquake. If the quake struck at a time when most tourists are on the beach or out-and-about, the toll would be reduced. To this estimate can be added another, perhaps, 15 per thousand who would suffer significant injury due to building elements falling on them – in earthquakes, about a third of such injuries are broken legs (Spence and So, 2009). Again, the time-of-day would be a critical factor determining overall casualty numbers. There are, however, substantial uncertainties associated with all these estimates, and fatality and casualty numbers in an actual earthquake easily could be less if the earthquake shaking is moderated by source effects or damage occurs at the ‘right’ time of day; on the other hand, it also might be an order of magnitude or more greater if exacerbating factors come into play, such as landslides, ground failure and topographic amplification effects. Refining these latter uncertainties would require detailed specialist surveying of building standards and ground conditions locally, and more in-depth understanding of the seismology of the area. Remarks on historic Intensities While historic Intensity reporting is prone to inflated level assignments, even today attempting to infer peak acceleration levels from reported Intensities is fraught, given the major uncertainties involved. Care is needed with old historic Intensity assignments because they can be elevated by a unit or more - not by observed physical effects on buildings, but by sensible effects on people: depending upon a lot of factors, there can be a mismatch between Intensities derived from numbers of sleepers wakened, persons scared and running into street, etc., and those defined by actual dynamic damage effects to structures in the same quake. 26 27
Fatality rates for persons out-of-doors in earthquakes are negligible. n.b. this is for UK residents; drowning rates for holiday-makers abroad may be higher. 75
In the case of assessing the situation for Santorini, a key issue is the possible circular reasoning that may have occurred in relation to the very damaging magnitude 7.6M 1956 Amorgos earthquake, 50km distant from the island. The argument goes thus: while that earthquake was unquestionably big, the damage on Santorini at the time - and hence Intensity assignments based on this damage - will have reflected the ancient, friable unreinforced faced-rubble vernacular buildings that existed then (and the same applied in the earlier 1707 quake). In subsequent analyses of this major event, those Intensities appear to have been converted to equivalent acceleration values28, and these pseudo-accelerations then used for anchoring retro-analysis using modern ground motion prediction modelling. It may well be that when these model output acceleration values were used to determine counterpart Intensities, in reverse, some model parameter adjustments were needed to accurately replicate the strong damage Intensities associated with the 1956 earthquake. This could, in effect, induce artificially high pga outcomes in subsequent runs when the model basis is transferred from the Amorgos case to the Kameni fault case. In addition, the contemporary modelling technique (stochastic fault rupture) is very difficult to constrain without some empirical measurements from small local quakes; until now such reference quakes have not occurred near Santorini, and so actual records for this purpose did not exist. It can be conjectured that a repeat now of the 1956 Amorgos earthquake (i.e. about magnitude 7.5Mw at a distance of 50km) would not result in extensive Intensity VIII structural damage levels in many modern buildings on Santorini, and might even struggle to produce assured Intensity VII damage in a lot of them. Casualty risk assessment A simplified quantitative risk assessment model (Figure A.11) is constructed to estimate potential fatality and injury numbers on Santorini in the event of a moderate magnitude earthquake on a fault in the Kameni line. This is formulated as a Monte Carlo simulation based on a probabilistic earthquake Intensity hazard model interfaced with Spence & So (2009) building classifications and performances. There are several random variables in this model, expressed as statistical distributions, to represent uncertainties in seismological factors, in building collapse vulnerability (damage level D5), and in consequent human impacts. The main elements of the model are random variables and statistical characterizations: 1. Probabilities of MM Intensity xx or greater at Fira, Kamari (range: MMI IV – XII due to Kameni fault quake magnitude 4 – 6Mw) 2. Percentage area of island suffering elevated Intensity effects due to topography etc. (Uniform [10% - 30%]) 3. Proportion Class A to Class D building types in mix: PB (Normal[0.4,0.1]) 4. D5 damage collapse lethalities (Lognormal[0.2,0.05]) 5. Injured-to-dead – ratio / quantiles (PertAlt[0.5, 3.0, 6.0 ; 0.1, mode, 0.9]) 6. Time-of-day, as day / night (Discrete[0.75, 0.25]) 7. Average daytime occupancy : percentages / quantiles (PertAlt[5%, 25%, 70%; 0.1, mode, 0.9])
28
Such conversion relationships are among the most unsatisfactory in the whole of seismology, and their use would be eschewed by many seismologists. 76
8. Night-time occupancy: percentages / quantiles (PertAlt[85%, 95%, 97.5%; 0.1, mode, 0.9])
Building stock model
[Class A,D; PB] Seismic Intensity exceedance model
D5 collapse vulnerability
[Class; Intensity]
Figure A.11
D5 collapse lethality rates
Occupancy rates
Fatality and injury numbers
[day/night]
[expected / worst] case]
Framework of Santorini earthquake risk model
Table A.3 Santorini earthquake risk model - results summary
Deaths per 1000 population
Overall risk estimates [event at any time of day or night]
‘Worst case’ [night-time event]
Expected [mean]
3
Minimum
0
Injured per 1000 population 12
35% CHANCE LESS THAN 1
0
90%ile high exceedance 99%ile high exceedance Expected [Mean]
9
30
30
130
6
24
Minimum
0
90%ile high exceedance 99%ile high exceedance
15% CHANCE LESS THAN 1
0
16
60
52
220
20% CHANCE LESS THAN 1
15% CHANCE LESS THAN 1
Table A.3 provides a summary of the results of applying the earthquake risk model outlined above to the Santorini situation, showing both the expected (mean) death rates and injury rates for an event at any time of day and for one occurring at night-time (‘worst case’), together with estimates of corresponding upper tail probability exceedance values.
77
It is considered helpful that these latter values are also communicated because they would probably represent important factors for informing decisions made by civil authorities; their omission from advice could be misleading.
A.4 Discussion The BBN example for the recent Santorini unrest outlined above, although not applied formally in the episode, serves to demonstrate that care is needed to properly consider not only positive pieces of (volcanic) evidence but also to include negative evidence, alternative propositions and hypotheses. For instance, it is not abundantly certain that the caldera earthquakes and uplift during 2011 – 2012 were due solely to magmatic changes or movements – there may have been a strong tectonic element involved. For instance, Papoutsis et al (2013)29 report that inflation ceased at the end of February 2012, just at the time when significant seismic activity switched to a location about 40km SW of Thera, and died back in the caldera. Furthermore, other contemporaneous seismicity during 2011 2012, elevated above background, had taken place off island to the NE, near the submarine Kolumbo volcano and along a known major regional tectonic feature that has hosted big earthquakes in the recent past. Thus while the unrest that was centred in the Thera caldera might have been the result of volcanic action it is also plausible that it was due to wider tectonic stresses, and was not simply or necessarily volcanic in origin. If this possibility is ignored or discounted – something that can easily happen with volcanologists focusing on their specialisms in a crisis - the corollary is that volcanic hazard levels may be over-stated. On the other hand, ignoring the possibility that tectonic seismic hazard levels are elevated may be even more disastrous: whereas volcanic activity could cause disruption and a few casualties at worst, a significant local earthquake. Although constructing a BBN for the different possibilities does not guarantee such pitfalls can be avoided, the danger of misstating hazards and risks is greatly reduced if a structured and comprehensive approach is taken to the assessment and enumeration of all forms of potential natural hazards. Given what has happened in the L’Aquila earthquake trial, a rational framework for assessing uncertain scientific evidence in unrest circumstances surely now must be a sine qua non for Earth scientists involved in such work.
29
Papoutsis, I. Papanikolaou, X., Floyd, M., Ji, K.H., Kontoes, C., Paradissis, D. and Zacharis V. (2013) Mapping inflation at Santorini volcano, Greece, using GPS and InSAR. Geophysical Research Letters, 40, 267-272.
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