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\title{A~multi-scale risk assessment for tephra fallout and airborne concentration from multiple Icelandic volcanoes -- Part 2: Vulnerability and impact}

\Author[1]{C.}{Scaini}
\Author[2]{S.}{Biass}
\Author[3]{A.}{Galderisi}
\Author[2]{C.}{Bonadonna}
\Author[1]{A.}{Folch}
\Author[4]{K.}{Smith}
\Author[5]{A.}{Hoskuldsson}

\affil[1]{CASE Department, Barcelona Supercomputing Center (BSC-CNS), Barcelona, Spain}
\affil[2]{Section of Earth and Environmental Sciences, University of Geneva, Geneva, Switzerland}
\affil[3]{Department of Civil, Architectural and Environmental Engineering (DICEA) -- University Federico II of Naples, Naples, Italy}
\affil[4]{Geography, College of Life and Environmental Science, University of Exeter, Cornwall~Campus, Penryn, UK}
\affil[5]{Nordic Volcanological Center, University of Iceland,  Reykjav\'{\i}k, Iceland}

\correspondence{C.~Scaini (saetachiara@gmail.com) and S.~Biass~(sebastien.biasse@unige.ch)}

\runningtitle{Impact assessment for tephra dispersal from multiple Icelandic volcanoes}
\runningauthor{C.~Scaini et~al.}

\received{2~March~2014}
\accepted{12~March~2014}
\published{}

\firstpage{1}

\maketitle

\begin{abstract}
We perform a multi-scale impact assessment of tephra fallout and dispersal from explosive volcanic activity in Iceland. A companion paper (Biass et al., 2014; A multi-scale risk assessment of tephra fallout and airborne concentration from multiple Icelandic volcanoes – Part I: hazard assessment) introduces a multi-scale probabilistic assessment of tephra hazard based on selected eruptive scenarios at 4 Icelandic volcanoes (Hekla, Askja, Eyjafjallajökull and Katla) and presents probabilistic hazard maps for tephra accumulation in Iceland and tephra dispersal across Europe. Here, we present the associated vulnerability and impact assessment that describe the importance of single features at national and European levels and considers several vulnerability indicators for tephra dispersal and deposition. At national scale, we focus on physical, systemic and economic vulnerability of Iceland to tephra fallout, whereas at European scale we focus on the systemic vulnerability of the air traffic system to tephra dispersal. This is the first vulnerability and impact assessment analysis of this type and, although it does not include all the aspects of physical and systemic vulnerability, allows identifying areas on which further specific analysis can be performed. Results include vulnerability maps for Iceland and European airspace and allow for the qualitative identification of the impacts at both scales in case of occurrence an eruption. Maps produced at national scale show that tephra accumulation associated with all eruptive scenarios considered can disrupt main electricity network, in particular in relation to an eruption of Askja volcano. Results also show that, if an eruption occurred at Hekla, Askja or Katla volcanoes, several power plants would be affected, causing a substantial systemic impact due to their importance for the Icelandic economy. Moreover, the Askja and Katla eruptive scenarios considered could produce substantial impact on agricultural activities (crops and pastures). At European scale, eruptive scenarios at Askja and Katla volcanoes are likely to affect European airspace producing substantial impacts, in particular, at Keflavík and London Flight Information Regions (FIRs), but also at FIRs above France, Germany and Scandinavia. Impacts would be particularly intense in case of long-lasting activity at Katla volcano. The occurrence of eruptive scenarios at Hekla volcano is likely to produce high impacts at Keflavík FIR and London FIRS, and in case of higher magnitude, can impact also France's FIRs. Results could support land use and emergency planning at national level and risk management strategies of the European air traffic system. Although we focus on Iceland, the proposed methodology could be applied to other active volcanic areas, enhancing the long-term tephra risk management. Moreover, the outcomes of this work pose the basis for quantitative analyses of expected impacts and their integration in a multi-risk framework.
\end{abstract}

\introduction 

Tephra dispersal and deposition during explosive volcanic eruptions can produce impacts at different scales, from local to continental. Compared to other volcanic hazards, tephra fallout is unlikely to cause casualties but, nonetheless, it often produces high systemic and socio-economic impacts (e.g. Wardman et al., 2012; Biass et al., 2012). On the other hand, the presence of volcanic ash in the atmosphere disrupts aerial navigation and may cause additional socio-economic impacts at larger scales, from regional to continental, depending on the eruption intensity and duration, ash properties and atmospheric circulation. For these reasons a comprehensive risk assessment of active explosive volcanoes that are located in areas with high population and flight density should always include the hazard associated with both tephra dispersal and accumulation.  
Iceland is amongst the most active volcanic areas in the word, hosting more than 30 volcanic systems displaying different eruptive styles and a wide range of volcanic products (Thordarson and Larsen, 2007). In a companion paper, Biass et al. (2014) present a probabilistic tephra hazard assessment from 4 Icelandic volcanoes (Hekla, Askja, Katla and Eyjafjallajökull), selected for showing recent activity, different levels of historical record, and a variety of eruptive styles and activities. In this manuscript we present the associated vulnerability and impact assessment in order to support more effective mitigation strategies in Iceland and Europe. 
Volcanic risk evaluation builds upon three factors: hazard, exposure and vulnerability (e.g., De la Cruz Reyna and Tilling, 2008). Exposure is a key element in risk assessment, since it “encompasses all elements, processes, and subjects that might be affected by a hazardous event. Consequently, exposure is the presence of social, economic, environmental or cultural assets in areas that may be impacted by a hazard” (Birkmann, 2013, p. 305). Thus, the identification of exposed targets largely depends on their location with respect to the impacted area for the considered hazard and to the type of hazard at stake. Finally, the exposure, although crucial for an effective risk assessment, does not account for the variability of response of people, infrastructure, goods or ecosystems to the hazardous event: such response depends on their susceptibility to be harmed or, in other terms, on their vulnerability. 
Vulnerability can be defined as the potential of exposed targets to be directly or indirectly damaged by a given hazard. Definitions, conceptual frameworks and methodologies for analyzing and assessing vulnerability are very heterogeneous, although “there is a clear recognition of the importance of place-based studies in examining vulnerability” (Cutter, 2013, p. 1089). In the last decade, vulnerability has been largely recognized as a multi-dimensional concept, comprising different aspects (physical, systemic, social, economic, environmental, institutional, etc.), constantly interacting in time and space (Birkmann, 2006; Galderisi et al., 2008; UNISDR, 2009; Menoni et al. 2011). In particular, the concept of systemic vulnerability is spreading in the scientific literature and refers to the fragilities arising as a consequence of interdependencies among elements and systems within a given territory, which can reduce its overall functioning in face of a hazardous event (Rashed and Weeks 2003; Menoni 2005; Galderisi et al. 2008; Pascale et al. 2010, Ensure, 2011). Territorial systems are characterized by a dense network of physical and functional interdependencies (Paton and Johnston, 2006, Hellstrom, 2007) and the potential impact of a hazard on a given element may reverberate on others, physically or functionally connected to the former. The concept of systemic vulnerability has been applied in several areas of natural hazards such as floods, earthquakes, tsunamis, etc. (e.g. Minciardi et al., 2005, Pascale et al., 2010) but, in volcanology, this concept has been introduced only recently (e.g. Galderisi et al. 2013). Systemic vulnerability has a particular relevance in the case of tephra fallout, which may produce much higher secondary than primary impacts, that is, the physical failure of an element may also impact other connected activities and infrastructures (Biass et al., 2012). For example, the failure of the electrical network can cause cascading effects on several productive activities, such as manufacturing, power generation, agriculture, or tourism. On the other hand, tephra dispersal and deposition largely affect transportation networks, which are crucial for accessibility to urban areas and emergency facilities. Finally, social and economic aspects of vulnerability have been deepened in scientific literature since the Nineties, but an unequivocal definition of both social and economic vulnerabilities and of their mutual relationships is still missing (Parker et al., 2009; Tapsell et al., 2010). 
The aim of this analysis is performing a vulnerability and impact assessment analysis at National and European level. Due to the large scale of the analysis and the lack of specific data, physical vulnerability is not considered in our assessment, with the exception of few specific elements of particular relevance (i.e., electric power plants and distribution network). A comprehensive assessment of physical vulnerability is beyond the scope of this paper. Moreover, we consider only one aspect of the systemic vulnerability, that is, the a priori identification of elements and systems that are particularly relevant from a systemic point of view. We do not account the cascading effects and spatial interdependences that may take place during the emergency. Through this simplified approach, the vulnerability and impact assessment presented here aims at identifying the areas that are likely to suffer the higher impacts, where more specific research should be performed. This approach is commonly adopted in risk management for hazardous phenomena whose physical impact on elements are not yet quantified, and in particular for those who not produce strong life losses and socio-economic impacts (Douglas, 2007). 
Iceland is considered a well-prepared and highly resilient country, but the traditional risk management strategies of the Icelandic civil protection have traditionally focused on the short-term reaction rather than on the long-term land use planning (Jóhannesdóttir and Gísladóttir, 2010). As a consequence, there is a lack of specific studies on vulnerability of the Icelandic territory to tephra deposition, although tephra fallout is a relatively frequent phenomenon in Iceland. Here we perform a vulnerability assessment taking into account that, according to the analysis of past events (Biass et al., 2014), agriculture, transportation and energy sectors are the most vulnerable to tephra accumulation. We focus on systemic and economic dimensions of vulnerability. To this aim, we define exposed targets, estimate vulnerability for each considered target and evaluate the expected impacts for all the eruptive scenarios defined in the previous hazard assessment.  Physical vulnerability of buildings is not considered because, according to the hazard analysis of Biass et al. (2014), expected tephra accumulations are unlikely to cause significant damage to buildings for the volcanoes and activity scenarios considered (proximal areas around the selected volcanoes are mostly unhabited). Moreover, our analysis is performed at a national scale (the whole Island), while physical vulnerability assessments require detailed on-site surveys, for example on building stock, which are usually performed at local scale. However, we consider physical vulnerability of the electricity network because its failure can trigger relevant impacts on the whole society. We also focus on the potential for temporary or permanent loss of economic activities, relevant to the maintenance of the level of welfare of population. 
The disruption of flights caused by the 2010 Eyjafjallajökull event was economically significant for both Europe and Iceland (Sammonds et al., 2010; Oxford Economics, 2010; Alexander, 2013). Using the last 10 years of the ERA-Interim reanalysis dataset, Biass et al. (2014) conclude that the probability of having upper troposphere winds blowing towards central and northern Europe is 6-8{{\%}, a value consistent with the 6{{\%} found by Sammonds et al. (2010). Given the 2010 experience, these probabilities suggest that assessing the vulnerability of the European air traffic system to Icelandic ash dispersal is relevant for the management of volcanic risk in civil aviation, particularly since no vulnerability assessment of any air traffic system specifically focused on volcanic ash hazard exists. Wegner and Marsh (2007) and Wilkinson et al. (2011) underlined some relevant aspects of the European air traffic network and showed that it is a scale-free network highly vulnerable to the disruption of the main hubs. Based on this finding, we develop the first assessment of vulnerability of the European airspace to tephra dispersal. The analysis is based on the systemic approach and aims to identify the critical features for the system, that is, the elements that can produce the highest systemic impacts on the whole European air traffic system in case of failure. As we did at National scale, we identify the distribution and the features of the exposed targets and define vulnerability indicators in order to evaluate the expected impact for the different eruptive scenarios considered in the hazard assessment. 

This manuscript is arranged as follows. Section 2 overviews the eruptive scenarios for the selected volcanoes and the findings from the hazard assessment of Biass et al. 2014). Section 3 presents the vulnerability and impact assessment to tephra fallout at National scale and section 4 the vulnerability and impact assessment to tephra dispersal at European scale. Section 5 discusses the advantages and disadvantages of the proposed methodology and the future research developments required to improve it. Finally, section 6 concludes with a summary.

\section{Eruptive scenarios and results from the hazard assessment}

A companion paper (Biass et al., 2014) presents a multi-scale probabilistic tephra hazard assessment for different eruptive scenarios of four highly active Icelandic volcanoes (Hekla, Askja, Katla and Eyjafjallajökull; Figure 1). These four volcanoes were selected either for their high probabilities of eruption and/or their high potential impacts and the associated hazard was assessed both at the national scale and the European scale dispersal for different scenarios based on the eruptive record (Table 1). Scenarios are associated to a Volcanic Explosivity Index (VEI) as described by Biass et al. (2014). Each scenario was modeled assuming a statistical set of inputs using TEPHRA (Bonadonna et al., 2005) and FALL3D (Costa et al., 2006; Folch et al., 2009) models for tephra fallout and dispersal respectively. 
Results of the hazard assessment at the national scale are probabilistic hazard maps for ground tephra accumulation. Given the rich historical record and high knowledge of Icelandic volcanic activity, it is possible for some volcanoes (e.g. Hekla) to associate scenarios with a “repose time”, while other volcanoes have a short documented eruptive history or do not seem to follow evolution patterns. Scenarios used in this work are not associated to a probability of occurrence, due to the high uncertainties of such approach. Thus, probabilistic hazard maps represent the expected situation conditioned to the occurrence of the scenario, that is, what is the probability of having critical tephra load at a given point, if the considered scenario occurs. 
Probabilistic hazard maps were computed for tephra load thresholds of 1, 10, and 100 kg/m², which correspond, approximately, to 0.1, 1, and 10 cm of accumulation at ground. At a European scale, results are probabilistic hazard maps (giving the probability of “disruption”) for ash mass concentration thresholds of 2 and 2x10-3 mg/m³. The second value (corresponding to a negligible mass concentration) was considered in order to estimate the impact in case of a zero-ash tolerance criterion. Moreover, Biass et al. (2014) provide maps of disruption mean persistence (according to Sulpizio et al., 2012) and arrival times for the 2 mg/m³ concentration threshold. The main findings from the hazard assessment are (scenarios and their acronyms are described in Table 1):

\begin{itemize}
\item A~10\,year recurrence rate eruption of Hekla (i.e., Hekla ERS
2000-type) only produces significant tephra accumulation close to the vent
and in the southern part of Iceland. Ash concentration has a~low probability
($< 1$\,{{\%}}) to exceed the threshold of 2\,\unit{mg\,m^{-3}} at any FL in
the UK airspace.

\item A~100\,year recurrence rate eruption of Hekla (i.e., Hekla ERS
1947-type) produces substantial tephra accumulation in the Southeastern part
of Iceland. However, far-range ash concentrations still have low
probabilities ($< 5$\,{{\%}}) of affecting the UK airspace with
concentrations above the 2\,\unit{mg\,m^{-3}} threshold at any FL.

\item A~moderate long-lasting basaltic eruption of Katla (i.e., Katla
LLERS with tephra production during 1--4\,days) is likely to produce
substantial tephra deposition in Southern Iceland. Ash dispersal has
a~substantial probability of reaching northern Europe, UK (5--20\,{{\%}}) and
central Europe ($\sim 5$\,{{\%}}) with concentrations exceeding
2\,\unit{mg\,m^{-3}} at any FL.

\item An eruption of Askja similar to that of 1875 (i.e., Askja OES
1875-type) is likely to produce massive tephra deposition in eastern Iceland.
Ash dispersal has a~substantial probability of reaching northern Europe, UK
(5--20\,{{\%}}) and central Europe ($\sim 5$\,{{\%}}) with concentrations
exceeding 2\,\unit{mg\,m^{-3}} at any FL.

\item An eruption of Eyjafjallaj\"{o}kull similar to 2010 (i.e.,
Eyjafjallaj\"{o}kull LLOES 2010-type) is likely to produce moderate tephra
accumulation south of the volcanic edifice around the town of V\`{\i}k. For
computational reason, probabilistic approaches to assess the airborne
concentration resulting from such a~long eruption were not applied.
\end{itemize}
Finally, in order to compare the relative impact of the different scenarios, one historical eruption was selected for each volcano for which ash dispersal and atmospheric concentrations were assessed using the same wind conditions of Eyjafjallajökull 2010 eruption. The selected eruptions include Hekla 1947, Katla 1918, Eyjafjallajökull 2010 and Askja 1875. The conclusion is that all eruptive events, if happened, would likely disrupt the European air traffic, with the most important perturbations caused by Katla 1918 and Hekla 1947. 
\section{National-scale vulnerability and impacts}

\subsection{Exposed targets}

In order to assess vulnerability and estimate potential impacts of tephra
fallout in Iceland, one needs first to identify the ``social, economic,
environmental or cultural assets in areas that may be impacted by a~hazard''
(Birkmann, 2013, p. 305). The main exposed targets have been identified based
on the scientific literature on tephra fallout impacts. In detail, the
exposed targets that we consider are:
\begin{enumerate}
\item \textit{Population}: Iceland has 320\,000 inhabitants of which
120\,000 live in Reykjav\`{\i}k, the capital. About 60\,{{\%}} of the total
population lives in the so-called Greater Reykjav\`{\i}k (Supplement Table~S1).
Recent trends (Byggdastofnun, 2012) show that population is growing around
the capital and in the eastern part of the country, were tephra fallout has
high probabilities of occurrence for some of the eruption scenarios
considered (Biass et~al., 2014). The central part of the island is mostly
uninhabited. Approximately one quarter of the population has reduced mobility:
in fact, a 15\,{{\%}} of inhabitants are under 10\,\unit{years} old and
a~9\,{{\%}} are over 70 (Statice, 2012). This segment of population is
potentially more exposed to suffer respiratory difficulties due to the
presence of suspended \chem{PM_{10}} (Baxter et~al., 1983; Horwell and
Baxter, 2006). In addition, all population is exposed to indirect impacts due
to failure of services (water and electricity supply, transportation, access
to health care. Data on population for each municipality and percentage of
exposed people are available in the Supplement Table~S2.

\item \textit{Emergency facilities, (e.g. hospitals, emergency
    shelters, police and fire stations):} the two main Icelandic
  hospitals are located in Reykjav\`{\i}k but other hospitals and local
  health centers, also considered in our analysis, exist in relevant
  towns such as Akureyri, Isafjordur, Nordfjordur and Selfoss. Police
  and fire stations are quite well distributed amongst the main
  towns. Finally, shelters are usually public buildings located in
  correspondence of areas of interest (monuments, touristic
  attractions) and towns but, for simplicity, we only consider schools
  as possible shelters.

\item \textit{Mobility network (e.g. road network and mobility nodes
    such as ports and airports):} the road network is directly exposed
  to tephra fallout, which may disrupt traffic reducing the capacity
  of the population to reach critical facilities and, indirectly,
  affecting services and productive activities. In absence of railway
  in Iceland, the road network is extremely important for internal
  mobility. A~main primary road circumvents Iceland along the
  coast. Disruption to mobility network, even if temporary can trigger
  relevant cascade effects. Ports are extremely important for the
  import-export activities in Iceland. In 2006, a~total of 6 Mtons of
  freight passed through Icelandic ports, which mainly export marine
products (25\,{{\%}}) and import/export ``other goods'' (49 and 51\,{{\%}}
respectively) including textile and manufacturing
  goods (Statice, 2012). Finally, airports are also important mobility
  nodes. The main airport in Iceland is Keflav\`{\i}k, which accounts for
  more than 97\,{{\%}} and 99\,{{\%}} of international passengers and
  freight traffic (Isavia, 2012). Important airports for domestic
routes are Reykjav\`{\i}k and Akureyri, accounting for approximately 25 and
50\,{{\%}} of domestic passengers and 47 and
  20\,{{\%}} of freight (goods and mail), respectively (Isavia,
  2012). Other smaller airports, including Egilsstadir, account for
  a~12.5\,{{\%}} of domestic traffic of passengers. The volume of the
  domestic air traffic is modest (around 800\,000 passengers per year;
  Isavia, 2012) but, nonetheless, important for the national economy,
  given the absence of a railway.

\item \textit{Electricity network:} the electricity network is
  a~critical infrastructure for economic activities and society in
  general. Electricity networks are very vulnerable to volcanic
  fallout (Wilson et~al., 2009a,~2012), and consequences of
  a~disruption of power generation and distribution are potentially
  dramatic. In Iceland, more than 80\,{{\%}} of the primary energy
  comes from renewable sources, hydroelectric (73\,{{\%}}) and
  geothermal plants (27\,{{\%}}) (Orkustofnun, 2012). More than 30
  hydroelectric plants are spread across the country, except in the
  southern area of the Vatnaj\"{o}kull ice cap (Icelandic national
  energy authority, 2012a), and up to 7 geothermal plants are located
  around the capital and in the northeast (Icelandic national energy
  authority, 2012b). Some of them are combined heat and power plants,
  which utilize geothermal water and steam.

\item \textit{Economic activities}: main economic activities in
  Iceland are services and industry, which in 2011 employed
  a~75.7  and a~18.4\,{{\%}} of the working population
  respectively (Landshagir, 2012). The comparison between greater Reykjav\`{\i}k and other regions shows that in the capital region services
  share a~higher percentage of employees while elsewhere industry
  dominates (Landshagir, 2012). In particular, aluminum smelters are
  strategic components of the Icelandic economy, constituting
  37.6\,{{\%}} of the total Icelandic exports and placing the country
  in the top-20 aluminum-producing nations worldwide. In 2011,
  aluminum smelter accounted for approximately 73\,{{\%}} of the gross
  electricity consumption (Lanshagir, 2012).

\item \textit{Agriculture}: the main agriculture activities are related to the
production of wool and milk, which only account for a~small percentage of the
national GDP (Joh\'{a}nnesson, 2010). The distribution of the main
agricultural areas (extracted from the Corine Land Cover raster map, see the
Supplement Fig. S1) shows that a~substantial part of the island is covered by
snow and ice, and the few agricultural areas are barely visible and located
in the proximities of main villages and coastal areas. Nevertheless,
agriculture is important for local development, being the main economic
resource for people living in small, isolated villages. Crops can suffer from
short to long-term impacts due to tephra accumulation (Wilson et~al., 2009b).
Fluoride absorption can impact cattle due to its toxicity and, unless direct
inhalation is not a~big concern, its ingestion through plants and water can
produce diseases (Dawson et~al., 2010).

\item \textit{Water supplies}: Tephra fallout can disrupt water supply
  networks and water treatment plants (Stewart et~al., 2006). In
  Iceland, the areas close to active volcanoes are not densely
  populated and the disruption of water supply in urban areas seems
  not a~big issue. However, tephra fallout can contaminate ground and
  surface waters, which are in some cases used for
  domestic/agricultural use (about a~95\,{{\%}} of the national water
  consumption relies on high-quality groundwater and only a~5\,{{\%}}
  on surface water; Gunnarsd\'{o}ttir, 2012). This is usually the case
  of isolated farms, where no official quality controls are performed
  and, consequently, are more exposed to this hazardous
  phenomenon. Moreover, farms can suffer the indirect impact of tephra
  fallout on livestock, as it can contaminate water used for beverage
  (Wilson et~al., 2009a; Dawson et~al., 2010).
\end{enumerate}
This list of exposed targets is not exhaustive but accounts for the
main aspects generally considered in the literature. Amongst all these
exposed targets, we selected the most significant for the national
context based on practical considerations and data
availability. Figure~2 shows maps of the considered features, based on
several data sources: the national GIS dataset (Landm{\ae}lingar
Islands, 2012), the European statistics database (Eurostat, 2012) and
the Iceland National Statistics (Statice, 2012). In detail, Fig.~2a
shows the location of the critical features considered (hospitals and
schools that could be potentially be used as shelters), and the
national road network. Our systemic vulnerability analysis is based on
the ease for population to reach critical facilities using the road
network. Figure~2b shows the location of hydroelectric power plants
and the electricity distribution network. The most densely populated
areas and the main productive activities (aluminum smelters), also
displayed in the map. Figure~2c shows the location of mobility nodes,
relevant for the Icelandic socio-economic system. Airports can be
directly disrupted by tephra fallout but also by tephra dispersal in
the atmosphere, which may cause airspace closure. Import/export activities
at ports and airports can suffer indirect damage due to the disruption
of the road network, power plants and productive activities.

\subsection{Vulnerability assessment}

As mentioned, our vulnerability assessment focuses on the systemic and
economic dimensions of vulnerability. This choice results from
numerous factors, related partly to scientific and methodological
aspects including: (i) the low probability of exposed population to
suffer relevant structural failure of buildings and human casualties
resulting from tephra accumulations suggested by the hazard analysis;
(ii) the scale of the vulnerability and impact assessment (i.e. the
whole country); (iii) the priorities for improving effective
mitigation strategies in Iceland, defined through close cooperation
between local stakeholders and the Icelandic Civil Protection and;
(iv) the availability of accurate and up-to-date data. As a~result,
based on the different categories of exposed targets, we defined
vulnerability themes and indicators (Table~2) focused on the following
aspects:
\begin{itemize}
\item physical vulnerability, limiting the analysis to electric power
  plants and distribution networks;

\item systemic vulnerability, which refers to the interdependencies
  among exposed targets capable of reducing the overall functioning of
  the system itself and, namely, its capacity to react in the
  emergency phase following an event;

\item economic vulnerability, which refers to the potential for
  temporary or permanent loss of economic activities and assets which
  are crucial for the Iceland economy and, consequently, for the
  maintenance of the level of welfare of population. It is worth
  noting that economic activities (such as agricultural activities) or
  economic assets (industries, energy production sites etc.) can be
  indirectly affected by, for example, the interruption of
  transportation services.
\end{itemize}
Physical vulnerability has been quantified considering the
hydroelectric power plants and the electricity distribution network
due to their high vulnerability to tephra fallout (Wardman et~al.,
2012). Geothermal and combined-power plants are not considered
because, a~priori, are much less vulnerable to tephra fallout given
their thick reinforced concrete structure with few or no openings. We
assign a~vulnerability value of 1 to all exposed hydroelectric plants
and aerial sections of the distribution network because detailed data
to rank the vulnerability of each particular plant was not publicly
available. The electricity distribution network has significant
interdependencies with information infrastructures, other utilities
and services and economic activities (Pederson et~al.,~2006; Laprie
et~al.,~2007; Beccuti et~al.,~2012). As a~result, a~disruption of
hydroelectric plants and/or distribution network may result in severe
failures of dependent sectors, as demonstrated by the blackouts in
Italy (2003) and Germany (2006), which impacted large areas of Western
Europe (Menoni and Margottini, 2011).

The systemic vulnerability assessment has been performed considering
accessibility, which is a~key issue during emergency situations. According to
Bertolini et~al.~(2005), accessibility can be defined as ``the amount and
diversity of places that can be reached within a~given travel time and/or
cost''. During a~crisis, bi-directional accessibility is crucial for both
evacuating population to safe areas and dispatching rescue teams (Galderisi
and Ceudech, 2010). Although the disruption of the mobility networks due to
tephra accumulation is generally temporary, it can result in significant cascade
effects reducing accessibility to and from inhabited areas, emergency
facilities, mobility nodes, power plants or industrial sites, with relevant
consequences in terms of increasing losses and slowing recovery. Here we
consider the accessibility to emergency facilities (hospitals and shelters)
for using the road network. The driving time is assessed using the
\textit{Spatial Analyst} toolbox in \textit{ESRI ArcMap 10.2} (Esri, 2012).
The hierarchy of the road network is accounted using the official speed
limits. Figure~3 shows the analysis of accessibility from inhabited areas to
shelters, hospitals and fire stations. Based on this accessibility analysis
we obtain the map of the most vulnerable areas.

Finally, and given its complexity, quantity and diversity of data, the
economic vulnerability assessment has been performed considering the
agricultural sector only, assessing its relevance at a~municipality level
(Fig.~4). In order to estimate the importance of agricultural activities, we
combine three different types of data: percentage of agricultural area,
production of milk and production of wool. The percentage of agricultural
area for each municipality was estimated by extracting pastures and crops
from the CORINE Land Cover map
(\url{http://ec.europa.eu/agriculture/publi/landscape/about.htm}), containing
an inventory of soil use information at high resolution (100\,\unit{m}). The
production of milk (\unit{L\,year^{-1}}) and wool for each municipality
during 2012 was provided by the Icelandic Regional Development Institute
(Byggdastofnun, 2012). Wool production is expressed in terms of ``support
entitlements'', i.e. the National entitlements that municipalities receive
from central government for their wool production and according to their
percentage on the total production of the municipality (\'{A}.~Ragnarsson,
personal communication, October~2012). Values of these three agricultural
indicators have been classified in a~5-classes vulnerability ranking (very
low, low, medium, high and very high vulnerability) using the natural breaks
method (Jenks, 1967), commonly used in most GIS software and especially
suitable for visualizing differences between classes (maps for each indicator
are given in the Supplement Fig.~S1).

\subsection{Impact assessment}

Before performing an impact analysis, it is necessary to determine the link between a quantitative hazard value (threshold) and each vulnerability indicator. 
Regarding the electricity network, there are two main impacts of tephra fallout: collapse/failure of network elements and flash-over of components. Wilson et al. (2012) define critical values of ash deposition for infrastructures based on well-documented impacts of past eruptions, and propose the value of 10 cm as threshold for producing medium to high damages on network elements (towers, poles and lines). Moreover, Wilson et al. (2011) show that collapse of lines happened for tephra fallout of similar magnitude, while impacts to transformers can happen for lower fallout values. There are few evidences of impacts on electricity power plants, but it is known that tephra fall is likely to produce its disruption or shut-down (Wardman et al., 2012). In particular, coarse ash is more likely to produce tephra-induced abrasion on turbines whereas a deposition of fine ash as thick as 50-100 mm may not cause strong abrasion. Moreover, in hydroelectric plants, tephra can engulf water channels and affect the turbines limiting power plant functionality. Finally, Wardman et al. (2012) show that lower values of tephra fallout (5-10 mm) can cause tephra-induced insulation flash-over of components and provide a fragility curve for such phenomenon. Thus, in order to include all effects, and according to the fragility curve, we assume that 1 cm tephra fallout has a 60{\%} probability of causing disruptions of components. It is worth noticing that we used a fragility curve for wet tephra, adopting a conservative approach, while dry tephra is not likely to produce flash-over.   

Regarding the road network, tephra depositions\,$> 1$\,\unit{mm} ($\sim
1$\,\unit{kg\,m^{-2}}) can produce lack of visibility and disorient drivers,
cause significant damage to vehicle's components and eventual engine failure
(Wilson et~al., 2012). However, this value does not take into account
differences in road design, typology of vehicles and other aspects such as
population preparedness and coping capacity, which are becoming an important
element of risk analysis (Frischknecht et~al., 2010). In the case of Iceland,
critical deposition thresholds for road disruption could be considerably
higher due to the characteristics of the fleet of vehicles and the resilience
of population, used to coping with road traffic disruptions during winter
snowfalls. We assume that a~moderate disruption of the road network may
happen with $\sim 10$\,\unit{kg\,m^{-2}} tephra accumulation, while
100\,\unit{kg\,m^{-2}} would provoke the total blockage of road
transportation (Biass et~al., 2012). Finally, we consider that an
accumulation of 1\,\unit{cm} ($\sim 10$\,\unit{kg\,m^{-2}}) can produce
damages to agriculture and impact livestock (Wilson et~al., 2009a; Biass
et~al., 2012), as occurred during past eruptions in Iceland (Thorarinsson and
Sigvaldason, 1972; Gudmundsson et~al., 1992; Hoskuldsson et~al., 2007).

Overlapping probabilistic hazard maps with vulnerable features allows for the identification of potential impacts, which is conditioned to the occurrence of the considered eruptions (Biass et al., 2014). We estimated the number of power plants and the total length of the electricity network having respectively 5, 10 and 20{\%} probability of being impacted (i.e. covered by a critical tephra load \,$> 10$\,\unit{kg\,m^{-2}}) in case of occurrence of each scenario. Impacted features are identified by performing a GIS-based overlap of a probabilistic hazard map and an exposed target map (Fig. 2b). We assume that vulnerable parts of the network (section 3.2)  covered by tephra load greater than 10 \unit{kg\,m^{-2}} (i.e. approximately 1 cm thickness)  are expected to be disrupted, and contribute to the systemic damage. Impacts of lower tephra fallout values is not considered here, also accounting for the fact that not all components are necessarily directly exposed to tephra fallout. Expected impacts are calculated in  Table 3. We partially account for the uncertainties related to the critical threshold choice by varying the probability of overpassing it between 5 and 20{\%} (Table 3 and 4). Note that Katla has a high impact on power plants at any value of probability considered, due to its close proximity to 5 power plants. Moreover, tephra fallout from a Hekla-1947-type eruption can impact important electricity lines that connect power plants to the rest of the network, while the occurrence of Hekla-2000 scenario has a low probability ($< 5$\,{{\%}}) of impacting power plants and electrical infrastructure. Both Hekla-1947 and Katla scenarios have a high probability (up to 20{\%}) of impacting important power lines that bring electricity to the southeastern region. An eruption at Eyjafjallaj\"{o}kull similar to that of 2010 could also impact these power lines (with a 10{\%} probability). Finally, in case of an eruption at Askja of 1875-type, electricity power lines may also suffer strong impacts. The occurrence of such scenario may in fact disrupt an important line that connects the Eastern part of the country with geothermal and hydroelectric power plants located in the North, and provides electricity to an important aluminum smelter (Fig. 2b). Note that, although an eruption at Hekla of 2000-type does not seem to affect any power plant, Biass et al. (2014) show that low tephra accumulations  ($\sim 1$\,\unit{kg\,m^{-2}}) can be produced in the area surrounding the volcano, so that the possibility of having impacts due to Hekla-2000-type scenario should not be discarded.

Biass et al.~(2014) show that in case of occurrence of considered eruptive scenarios defined for Katla and Askja, the probability of having tephra deposition of 10 and 1  \unit{kg\,m^{-2}} in southern Iceland is substantial (ranging between 20 and 50{\%}) and eastern Iceland (5 to 20{\%}). Thus, agricultural activity in these areas can be impacted and livestock can suffer from fluorine intoxication due to water and soil contamination. We estimated the area devoted to agricultural activities that has 5, 10 and 20{\%} probability of being impacted (i.e. covered by a critical tephra load >10 \unit{kg\,m^{-2}}) in case of occurrence of each eruptive scenario. Results are summarized in Table 4 and 5 and can be compared with the corresponding tephra accumulation hazard maps and vulnerability maps (Fig. 4 and SM, fig. S1). The highest impacts on crops are caused by the occurrence of the considered LLERS at Katla, followed by  a 2010-type LLOES at Eyjafjallaj\"{o}kull, while pastures are expected to be particularly impacted in case of a 1875-type OES at Askja and the considered LLERS at Katla. A 2000-type ERS eruption at Hekla volcano is not likely to impact agricultural activities. 

Impacts are also estimated on the basis of the accessibility analysis using
least-cost-distance models (Wood and Schmidtlein, 2012). Using the census
contained in the official GIS database (i.e. polygons of habited areas;
Landm{\ae}lingar Islands, 2012), we calculated the size of population located
in areas classified in terms of travel time (Fig.~5) to critical facilities:
schools (Fig.~3a), hospitals (Fig.~3b) and police/fire stations (Fig.~3c).
The \textit{Spatial
  Analyst} toolbox of the \textit{ESRI ArcMap 10.2} software was used to
calculate the shortest travel time from any pixel on the map to reach
a~critical facility using the road network. The hierarchy of the
official road network (Landm{\ae}lingar Islands, 2012) as well as the
speed limit for each road class were respected and implemented in
a~cost raster for accessibility analysis.

\section{European-scale vulnerability and impacts}

As clearly demonstrated during the Eyjafjallaj\"{o}kull eruption in
2010, the European air traffic system is largely vulnerable to loss of
functionality of its elements when exposed to volcanic ash. The
magnitude of systemic impacts depends on the relevance of the
disrupted elements, and impacts of ash clouds can occur very far from
the source (Ceudech et~al., 2011). Here, we analyze the systemic
vulnerability of European air traffic system and the
socio-economic vulnerability of the areas hosting its main airports.

\subsection{Exposed targets}

We define vulnerability indicators based on the analysis of
European air traffic system, including main exposed airports and
aviation routes. The analysis is performed at the European scale but
we focus on those regions where our hazard assessment indicates that
impacts from ash dispersal can be significant.

The European air traffic network has more than 2000 international airports
handling approximately 170\,000 overall daily flights on average (Wegner and
Marsh, 2007). However, over 50\,{{\%}} of the European air traffic
concentrates in the top 35 airports (Wegner and Marsh, 2007). The European
air traffic network is scale-free (Wilkinson et~al., 2011), meaning that
these main hubs are the most relevant to the system, and therefore highly
vulnerable to its failure. The main European hub is London Heathrow, with 61
million terminal passengers on international flights in 2010 (Heathrow
Airports, 2013), followed by Paris Charles de Gaulle. The 5 London airports
(Heathrow, Gatwick, Stansted, Luton and City) account together for more than
60\,{{\%}} of the total number of UK passengers according to the UK
Department of Transport. In 2011, London's airports handled more than 120
million passengers and 1.7 million tons of freight (CAA, 2012). Moreover, the
most intense freight traffic in Europe during 2009 was between UK and 4
European states: Germany, Netherlands, France, and Belgium
(PricewaterhouseCoopers, 2011). The London area is therefore one of the most
critical and strategic points within the European air traffic network and the
airspace between London, Paris, Frankfurt and Amsterdam constitutes the
densest part of the European civil aviation network. It therefore follows
that the European air traffic network is particularly vulnerable to the
failure of some of these strategic hubs.

At a~national level, Keflav\'{\i}k airport is also strategic for the
Icelandic economy. In 2011, Keflav\'{\i}k handled 97.5\,{{\%}} of all
international passengers (1.75 million; Keflav\'{\i}k international airport,
2012), 49.2\,{{\%}} of domestic passengers (0.75 million), and more than
99\,{{\%}} of all cargo operations. Air-based commercial relationships with
Europe are very important for the Icelandic socio-economic system. In fact,
the EEA market (i.e. the 27 EU countries plus Iceland, Norway and
Liechtenstein) accounts respectively for 82.7 and 61.9\,{{\%}} of total
Icelandic exports and imports. The main commercial partners are Netherlands,
Germany, UK, and Norway. Iceland's imports come mainly from Norway, USA,
Germany, Netherlands and the UK (Statice, 2012). According to the 2011
statistics, Keflav\'{\i}k's most important passenger destinations were
Copenhagen, London and Oslo. During 2010--2011 the Icelandic airspace
experienced a~9\,{{\%}} growth of traffic (counting over-flights) (Isavia,
2012) and, although peripheral in the European network, it is strategic for
intercontinental flights from and to the USA and Canada. Disruption of air
traffic connections can therefore impact substantially on both local and
regional economies.

Based on these considerations, the exposed targets for our systemic
vulnerability analysis are the main airports and routes to North and
central Europe and the most relevant socio-economic features of the
areas where the main airports are located. In order to have
a~vulnerability assessment meaningful to civil aviation stakeholders,
we consider European airspace sectors, following the current
classification (EUROCONTROL, 2005). Flight Information Regions (FIRs)
are sub-divided according to their specific role into CTA (Control
Area), OCA (Oceanic Control Area), ACC (Area Control Center) and UAC
(Upper Area Control), which are airspace sectors not hosting airports
(EUROCONTROL, 2005). Aerial sectors represent a~key component of the
air traffic network because each sector has an associated capacity,
which is the main parameter for air traffic management (Leal de Matos
and Ormerod, 2000; Leal de Matos and Powell, 2002; Dell' Olmo and
Lulli, 2003).

Finally, we note that the territorial context of an airport is also
relevant for the estimation of socio-economic vulnerability and impact
because the vulnerability of a~region is proportional to its
dependence on air traffic.

\subsection{Vulnerability indicators}

Table~5 summarizes the systemic and socio-economic vulnerability
indicators defined for the European air traffic system. Figures~6--10
show vulnerability maps produced for the considered features
(airports, routes, airspace sectors and European
regions). Visualization is performed through the open source GIS Qgis
(\url{http://www.qgis.org/en/site/}), using the European GIS database
(GISCO, 2013) and European air traffic database (courtesy of
EUROCONTROL). Unless specified otherwise, all indicators are
reclassified in a~qualitative 5-class ranking, ranging from very low
to very high, using the natural breaks method (Jenks,
1967). Vulnerability indicators include:
\begin{enumerate}
\item Strategic airports. We assume that the higher the traffic of an
  airport, the higher its relevance and, consequently, the higher the
  vulnerability of the system to its potential disruption. We
  classified all European airports according to traffic of passengers
  and freight during 2012 (Eurostat, 2013) and this identified
  Frankfurt, London Heathrow, Amsterdam and Paris Charles de Gaulle as
  the strategic elements for the European air traffic system in terms
  of passengers and goods. Given that the probability of ash dispersal
  affecting southeastern Europe is low (Biass et~al., 2014) and that
  we aim to assess the vulnerability within a~more constrained domain,
  we performed the same analysis for central and northwestern
Europe. Having selected the most relevant airports in central and northern
Europe in terms of air traffic values (Supplement Table~S3), we ranked
  them according to passengers and freight values (Fig.~6). The most
  relevant airports are London Heathrow, Paris Charles de Gaulle,
  Frankfurt, Amsterdam, and Munich, which were already identified as
  main hubs at the European level. Copenhagen airport also has a~high
  relevance for traffic to northern-Europe (including Iceland).

\item Strategic routes, classified in two ways. The first
  classification builds upon the average number of connections between
  each pair of European airports in 2012 (courtesy of Eurocontrol). We
  assume that the higher the number of connections the higher the
  importance of the route and the higher the systemic vulnerability of
  the system to its failure. This classification reveals that the top
  5 connections are: Madrid--Barcelona (Spain), Istanbul--Izmir
  (Turkey), Paris--Toulouse (France), Oslo--Bergen (Norway) and
  Barcelona--Palma de Mallorca (Spain). Constraining the analysis to
  central and northwestern Europe, the most relevant connections are
  London--Paris, Paris--Frankfurt, London--Edinburgh, London--Dublin,
  Munich--Frankfurt, Copenhagen--Aalborg, Oslo--Trondheim,
  Oslo--Bergen and Oslo--Stavanger. This analysis underlines that the
  main city pairs are often composed of national connections between
  first and second largest cities, as described by Wegner and Marsh
  (2007). The second classification is based on air traffic
  (passengers and freight) for each city pair, that is, for the main
  routes between a~considered airport and its partners (Eurostat,
  2013). This kind of classification considers the relevance of
  European routes for a~selected sub-system constituted by the
  considered airport and its main European partners. For example, we
  show two relevant cases: the London hub, strategic for European air
  traffic, and Keflav\'{\i}k airport, the most important in
  Iceland. The relative importance of routes is a~measure of the
  vulnerability of the sub-system to the disruption of that particular
  route. In our analysis, the London hub includes the city's 4 main
  airports: Heathrow, Gatwick, Stansted and Luton. Figure~7 shows
  strategic routes of London airports for passengers (left) and
  freight (right), for Heathrow airport (top) and for the other three
  airports, displayed together (bottom). The top London destinations
  ($> 1.2$ million passengers\,year$^{-1}$) are Dublin, Edinburgh, Paris and
  Frankfurt. London Heathrow--Dublin is the most important connection
  with more than 1.5 million passengers per year. In terms of cargo,
  Stansted is also an important hub with main destinations to
  Frankfurt, Brussels, Stockholm and Paris. Figure~8 shows the most
  important partners for Keflav\'{\i}k airport in terms of passengers
  (a) and goods (b). Copenhagen, London and Oslo are strategic
destinations for passengers, whereas Amsterdam, London, Paris, and Koln--Bonn
are main nodes for freight transportation. It is worth
  noting that the main passenger routes from Keflav\'{\i}k airport
  have the same order of magnitude as the less relevant route for the
  London hub ($\sim 300$\,000 passengers per year). Keflav\'{\i}k
  routes, if classified using the same range used for the London
  airports, would fall into the low vulnerability class and their
  relevance would be diminished in the subsequent impact
  analysis. Using a~scale-dependent classification criterion allows
  identification of routes that can be secondary at a~broader European
  scale but are strategic for the national scale.

\item Number of daily European flights in each airspace sector, which
gives a~measure of the airspace congestion. For simplicity, our
analysis uses data of one of the peak days during 2012 (29 June) and
assumes that this particular day is representative of high-traffic
situations in Europe. For each airspace sector, we counted how many
times per day the sector is crossed by flights at any FL and assign
a~vulnerability value accordingly. Figure~9 shows that the most
congested airspace sectors are located in France (Brest, Paris,
Marseille FIRs), southern UK (London FIR), Germany (Langen, Bremen,
Hannover FIRs), Netherlands (Amsterdam FIR) and Italy and Spain
(Milan, Rome, Madrid FIRs). Some FIRs show lower traffic rate compared
to the surrounding areas, for example Ireland (Shannon FIRs) and other
regions of France (Bordeaux and Reims FIRs).

\item Relevance of air traffic for European regions, based on
a~combination of four regional indicators: population (Eurostat, 2013, data
from 2012), total number of passengers and tons of freight transported by air
(Eurostat, 2013, data from 2011) and multi-modal accessibility, which takes
into account the presence/absence of alternative transport modes and their
cost (ESPON, 2004; TRACC, 2010, p.~17). We use multi-modal accessibility
produced by the ESPON project (ESPON{\copyright}, 2013) as an indicator of
vulnerability: areas having low multi-modal accessibility are therefore more
vulnerable to the failure of one transportation mode due to the limited
variety of alternative transportation modes available. According to F\"{u}rst
et~al.~(2000) multi-modal indicators have much more explanatory power with
respect to regional economic performance than any accessibility indicator
based only on a~single mode. We propose a~first-level assessment of
socio-economic vulnerability by combining these four indicators under the
assumption that vulnerability increases when the dependency on air traffic is
higher and the multi-modal accessibility lower. All indicators are referred
to the 2003 NUTS-2 regions (Nomenclature of Territorial Units for
Statistics), a~hierarchical system for dividing the economic territory of the
EU for the application of regional policies. We combine the 4 indicators by
summing the values for each NUTS2 region, and reclassifying the resulting map
into 5 vulnerability classes. Population, air traffic and multi-modal
accessibility are classified in 5 equal interval classes, while the
multi-modal accessibility database produced by the ESPON project is already
ranked in to 5 qualitative classes, ranging from 1 (highly below average) to
5 (highly above average). Air traffic data show that the areas which most
rely on air traffic correspond to the regions hosting the main European
cities of London, Paris, Frankfurt and Amsterdam. But socio-economic
vulnerability is not only related to the volume of air traffic: for example
Ireland has a~low multi-modal accessibility (Supplement Fig.~S2), but
a~considerable population (Supplement Fig.~S2). The resulting vulnerability
map (Fig.~10) facilitates recognition of the areas most dependent on air
traffic, where a~relatively high population and/or air traffic values are
associated with low multi-modal accessibility. The most vulnerable NUTS-2
areas are therefore the ones hosting the cities of London, Paris, Frankfurt
and Amsterdam. Also, Ireland, Norway and northern France show a~medium-high
vulnerability. Due to the intrinsic nature of being an island, air traffic
cannot easily be substituted with alternative transportation means. For
this reason, Ireland has medium vulnerability to air traffic disruptions.
\end{enumerate}
Given the differences in the indicators of vulnerability we evaluate
the expected impacts for each single vulnerability feature, i.e. for
the national-scale assessment, we do not merge the different thematic
vulnerability maps (Figs.~6--10) into a~single map. However, once
the strategic elements and their relevance are identified, it is
possible to assess the expected impacts of each eruptive scenario
through a~GIS-based overlap of hazard and vulnerability maps.

\subsection{Impact assessment}

We propose three different methods for assessing the impacts of tephra
dispersal on European air traffic. Each method focuses on producing
specific results, and could be used to support risk management
strategies at different levels. It is worth reminding that impact assessment results are conditioned to the occurrence of the eruptive scenario (Biass et al., 2014).

The first method consists of a~qualitative GIS-based visual overlap of
hazard and vulnerability maps. The graphical overlap allows for an
immediate identification of the routes that have the highest
probability of being disrupted for each scenario. For example, the
overlap of the Askja hazard map for all FLs and
the main passenger routes between London Heathrow and Europe (Fig.~7a)
reveals which routes would have the highest probability of being
disrupted in this scenario. The overlap of hazard and vulnerability
can also be performed using hazard maps for specific FLs and averaged arrival time and persistence maps, which
allow for the potential duration of a~disruption to be inferred.

The second method estimates the impact (movements disrupted,
passengers and freight stranded) at given airports by multiplying the
average atmospheric persistence time of a~given hazardous ash
concentration for a~given eruptive scenario by
the hourly-averaged traffic. Here, we assume that, if the critical ash
concentration is reached at any FL over an airport, all flight
operations are disrupted. For example, Tables~6 and 7 show the
expected impacts at London Heathrow and Keflav\'{\i}k airports for the
different eruptive scenarios considered, respectively. Air traffic
values for London Heathrow are estimated dividing yearly averages
(CAA, 2012; Heathrow airport, 2013) by 365. Keflav\'{\i}k air traffic
values are inferred from Keflav\'{\i}k airport 2011 facts and figures
(Keflav\'{\i}k International Airport, 2011). According to Biass
et~al.~(2014) the probability of having more than 24\,h of disruption
at London airports from Askja-1875 and Katla-1918 scenarios is about 5
and 1\,{{\%}} respectively. The probability of having more than 24\,h
of disruption due to Hekla activity are lower than 1\,{{\%}}. Thus,
there is a~substantial probability of having strong disruptions in the
London area due to high-magnitude explosive volcanic eruptions at
Askja and Katla, and a~low probability of having impacts at London due
to lower magnitude events at Hekla volcano.

Finally, the third method consists of overlapping hazard and
vulnerability data and combining the values on a~cell-by-cell basis,
i.e. multiplying hazard and vulnerability values within each cell. To
do that, hazard and vulnerability maps are converted to raster format
(geotiff) using GRASS GIS (Neteler et~al., 2012). We use probabilistic
hazard maps for each scenario that account for the probability of
disruption at any FL (Biass et~al., 2014) and vulnerability maps of
the airspace sectors (Fig.~9). Such maps are then overlapped on
a~cell-by-cell basis and the resulting impact map is reconverted to
vector format, aggregating the maximum impact value over FIRs
areas. The final results are impact maps containing impact values for
each FIR, reclassified in 5 qualitatively impact classes (very low to
very high impact) using the method of natural breaks. These results
are shown in Fig.~11. It has to be stressed that the resulting impact
represents relative comparison between FIRs rather than a~quantitative
impact. The Hekla ERS 2000-type scenario (Fig.~11a) produces very high
impacts in the Reykjav\'{\i}k FIR, high impacts in the London FIR and
low impacts in the Shanwick Oceanic Control Area (OCA) and the Norway FIRs, but is not expected to
affect central Europe. The Hekla ERS 1947-type scenario (Fig.~11b)
produces very high impacts in the Reykjav\'{\i}k FIR, and Paris, Brest
and Marseille FIR, high impacts in the London FIR and low impacts in
the Shanwick Norway and Sweden FIRs. Such a~scenario is also likely to
result in low impacts in the northern Germany and Poland FIRs. Both
the Katla LLERS (c) and the Askja OES 1875-type (d) scenarios are
likely to produce high impacts in the Keflav\'{\i}k FIR as well as the
southern UK and France FIRs, mostly due to their high traffic rates
(and therefore, high vulnerability). These scenarios can also produce
high impacts in the Norway, Sweden, Austria and Germany FIRs. Low
impacts are expected in the rest of Europe.

\section{Discussion}

Outcomes of our impact assessment are derived from probabilistic analysis, which are conditioned to the occurrence of specific eruptions at specific volcanoes described in the hazard scenarios of Biass et al. (2014). Volcanoes were selected based on the probability of eruption and significance of associated impact, while the hazard scenarios were derived from field observations to be statistically representative. However, an eruption at a different volcano or a different type of activity at the selected volcanoes cannot be excluded, and, therefore, the impact in zone other than those identified in our assessment cannot be discarded. The main value of our work is the new multi-source multi-scale strategy introduced to assess both hazard and impact at different scales that can be easily applied to other volcanoes and other hazard scenarios. Nonetheless, considering the wide range of hazard scenarios investigated and the statistically representative meteorological conditions analyzed at the European scale, our hazard and impact assessments can be considered as a first level evaluation for the whole Icelandic region. 

\subsection{National-level vulnerability and impact assessment}

The methodology presented here to assess vulnerability to tephra
fallout at a~national scale was developed for the particular case of
Iceland in cooperation with local stakeholders and the Icelandic Civil
Protection Department, and uses only publicly available data. However,
the method could potentially be applied in different geographic and
socio-economic contexts where similar public censuses are
available. The list of exposed features identified in Sect.~3.1 is
valid elsewhere and Table~8 lists the type of data that, ideally,
should be included in any comprehensive vulnerability assessment. For
example, from a~socio-economic point of view, the role of productive
activities and the number of employees for activity or sector should
be taken into account. Industrial and tertiary activities, for
example, often constitute the backbone of the socio-economic system,
driving local development and distribution of resources. In terms of
transportation, one inconvenience is that national statistics are
rarely given by transport mode, making it difficult to identify the
precise contribution of air traffic to the socio-economic
system. Also, water supply has been recognized as an exposure target
in a~few isolated cases (Sect.~3.1) but not taken into account for the
estimation of impacts, because it needs to be treated at a~more local
scale. Census of water supply systems (for example, water quality
control and monitoring) may support response strategies, in particular
for areas with strong agricultural sectors (Fig.~4) that can suffer
substantial impacts from tephra fallout (Sect.~3.3). Finally, only
a~few datasets were available at a~municipality level or in the form
of disaggregated data (that is, data available at the same
administrative level used for collection). For example, most economic
and labor market indicators were produced at the national level. This
lack of disaggregated data is a~common problem in most risk
assessments, and the availability of disaggregated datasets, or data
sources defined at lower administrative levels, would improve the
vulnerability assessment presented here.

Figures 3 and 4 allow identifying the spatial distribution of the most vulnerable areas and targets according to the considered vulnerability themes. It is important to stress that the vulnerability scores, expressed either as numerical scores or qualitative judgments, normally represent comparative (i.e. relative) values. This makes the merging of different vulnerability maps into a single final map a complex process. On one hand, the perspective of single indicators can be lost when combined with others. On the other hand, single merged maps are more synthetic and workable if they involve no loss of information. In this work, and given the very different nature of the indicators considered, we prefer not to overlap maps of different vulnerability categories. Nonetheless, the comparison of information related to each vulnerability indicator can provide a significant support both to land use and emergency planning. 

Results from national vulnerability and impact assessments allow definition of priority areas for risk mitigation strategies. Comparison of population values with other vulnerability indicators can support the prioritization of interventions for long-term vulnerability mitigation plans. For example, northeastern Iceland has a substantial probability of being affected by deposition of tephra in case of occurrence of OES at Askja, and this hazardous phenomenon should be considered in long-term territorial plans. Recent population statistics (Bygg{\dh}astofnun, 2012) show a positive trend in this area due to the construction of a dam and the consequent generation of employment. The increase of population and the arrival of non-local workers, less familiar with an active volcanic environment, should be taken into account, e.g. through educational programs. The results of the impact assessment can also support Icelandic policies in the main strategic sectors such as transportation, economic activities, or location of critical facilities. Table 3 shows that the largest impacts are expected from the occurrence of selected eruptive scenarios (Table 1) at Askja, Katla and Hekla volcanoes, due to the presence of power plants and a main power line in their surroundings. Results suggest that moderate tephra fallout from a 1947-type ERS at Hekla volcano can produce major impacts on the surrounding power plants. Occurrence of low-magnitude activity of 2000-type ERS at Hekla does not seem to produce such major impacts but, given its very high frequency (10-years repose time, Höskuldsson et al. 2007), should also be taken into account. In fact, repeated tephra fallout could have long-term impacts on power plant equipment and external components. Expected impacts on agricultural activities are in general limited to the few crops located in the southeast of the island. Table 4 shows that the major impacts on crops are expected in case of a LLERS at Katla and a 2010-type LLOES at Eyjafjallaj\"{o}kull. Moreover, ash fallout from the occurrence of eruptive scenarios at Askja  and Katla is expected to cover several square km of pasture in the South and East of Iceland (Table 4). Due to the importance of agricultural activities (wool in particular) for the Icelandic economy, these results should be taken into account in order to improve preparedness and reduce impacts on the national socio-economic system. Finally, results of the accessibility analysis (Fig 3, Fig. 5) help the identification of zones with limited access to critical infrastructure by classifying the population in terms of travel time to strategic features (hospitals, police/fire stations and potential shelters). This analysis accounts for the travel speed of the road network, where pixels outside the road network are only allowed an average walking speed. Note that unlike agent-based strategies, the resulting model is time-independent and does not attempt to account for dynamic travel time costs due to route capacity or road congestion (Wood and Schmidtlein, 2012). However, least-cost-distance models still provide key information for preparedness and planning by identifying heterogeneities in the accessibility over the entire territory rather than modeling the behavior of individuals. A combined look at figures 1 and 3 highlights how most of the critical infrastructures are clustered around the main towns, with the main zone of low accessibility being the Vatnaj\"{o}kull area. Figure 5 is a combination of the analysis performed in figure 3 and the population census, and helps visualize the number of people as a function of the travel time to critical infrastructures. Figure 3c also shows that although unhabited, Vestfj\"{o}r{\dh}ur, the northwesternmost peninsula, has a low accessibility to police/fire stations. This is clearly reflected in figure 5, where a travel time greater than 3h is associated to thousands of people. As a result, such a method is valuable to plan the implementation of additional critical infrastructures for future crises.

The analysis of impacts performed here is essentially qualitative. The underlying vulnerability assessment does not include a physical vulnerability analysis  of the elements at stake, due to the limited availability of data at the scale of the analysis. The definition of critical ash load thresholds does not rely on fragility curves, instrument commonly recognized amongst the risk management community but having a very limited application to volcanology (ENSURE, WP 1 – Del. 1.1.1). In particular, fragility curves to tephra fallout are available for building typologies (associated to a given physical vulnerability), but are still not well characterized in case of ash fallout on main infrastructures, for which there are many factors (composition, humidity) that play an important role (Wilson et al. 2011). In addition, ash load thresholds can vary with weather conditions. For example, wet tephra has a higher impact on electric components (Wardman et al. 2012) and enhances the effects of ash coverage on road traffic (Wilson et al., 2011). Wilson et al. (2009) pointed out the seasonal character of vulnerability, an important factor for certain activities such as agriculture and farming that have a seasonal character (Joh\'{a}nnesson, 2010). For example, the same hazardous phenomenon could produce higher impacts to crops during the sowing, growth and flowering phases, while less impacts are expected to unplowed fields. Adapting thresholds to seasonal and weather variation would support the definition of specific seasonal strategies. Finally, we adopted the same threshold for all eruptive scenarios ignoring that impacts can depend on many factors such as ash grain-size and composition (Wilson et al., 2009). Even though we adopted different grain-size distributions for each eruptive scenario (Biass et al., 2014), no study exists on ash load threshold dependency on granulometry and composition. Identifying critical ash load thresholds with single values introduces limitations to the usage of results. But given that the main aim of this work is identifying the areas and features that are expected to be impacted, results can support detailed impact assessment analysis at specific areas, necessary in order to produce more reliable results. Nowadays there is a growing need for specific studies to be performed in order to define quantitative thresholds that produce physical damages of elements and, eventually, systemic impacts. In future, fragility curves would allow accounting for hazard intensity and probability of damage, and our impact assessment methodology would be developed accordingly. 

\subsection{Vulnerability and impact assessment of European air traffic}

We have proposed a~vulnerability assessment that identifies the
elements (airports, routes and airspace sectors) likely to cause major
impacts to the European air traffic system in the case of tephra
dispersal from eruption of an Icelandic volcano. London is recognized
to be the core of the European aviation system, followed by Paris,
Amsterdam and Frankfurt according to the number of connections handled
(Fig.~6). Our analysis has also identified the routes that have the
highest socio-economic relevance, constrained to central and
northwestern Europe based on the outcome of the hazard assessment
(Biass et~al., 2014). The analysis emphasizes the role of minor
connections that, despite being secondary at European level, are
strategic for national economies. For example, the analysis of air
traffic at London and Keflav\'{\i}k airports showed that
London--Dublin and Reykjav\'{\i}k--Copenhagen are very important
routes (Figs.~7 and~8) and their disruption could affect national
economies and those of their commercial partners. We also estimated
vulnerability of FIRs (Fig.~9) based on traffic data from a~peak
day. This first-order estimation could be enhanced using air traffic
data during a~larger time interval to account for weekly/seasonal
traffic variability. Moreover, other indicators for FIRs, for example
accounting for the different types of flights (charter, commercial,
business, cargo) could also be considered. Despite these
methodological limitations, the identification of strategic airspace
sectors is an important result itself given that current air traffic
management procedures are based on airspace capacity (Cook, 2007).

The methodology proposed in this work is flexible enough to include new
administrative boundaries and new procedures in the vulnerability assessment.
This is important if, as expected, regulation changes occur. At a~European
level, new trends in air traffic management are driven by the Single European
Sky Commission Project (SESAR,
\url{http://ec.europa.eu/transport/modes/air/sesar/}), aimed at ensuring
capacity and safety needs to European aviation. The SESAR program includes
the constitution of Functional Airspace Blocks (FABs), expected to be
operative in the next few years, which would reduce airspace fragmentation
and support integrated airspace management (Arroyo, 2008). In case of
ash-contaminated airspace, the new SESAR regulation framework could be
included in the analysis to support the development of new centralized
strategies. It has also been suggested that the short-term capacity of
sectors may be negotiated in order to allow rerouting of flights to opened
FIRs, thus improving the performance of the network. However, procedures to
be adopted in the case of ash-contaminated airspace (e.g. the possibility of
overflying ash clouds) are still under discussion. The idea that the airlines
will be able to decide whether to fly or not in ash-contaminated airspace has
been proposed by EUROCONTROL and implemented during the 2011 VOLCEX exercise,
as described in the final report (ICAO, 2011). This new paradigm could be
implemented in the EUR/NAT region by several stakeholders that, after the
approval of a~Safety Risk Assessment (SRA; Boli\'{c} and Siv\v{c}ev, 2011;
EASA, 2012), would be able to decide whether to fly or not through
ash-contaminated airspace sectors. The introduction of SRA underlines the
importance of having a~long-term perspective in risk-management procedures
and plans. Long-term risk management plans could also avoid secondary
impacts, e.g. the lack of fleet at non-contaminated areas during the closure
of main airports. For example, Icelandair managed to move aircraft from
Keflav\'{\i}k to a~secondary hub in the UK (Ulfarsson and Unger, 2011) to
maintain operations in non-contaminated areas (and in particular,
Intercontinental routes). Long-term hazard assessment
and vulnerability and impact analysis can therefore support SRAs and
mitigation measures and enhance the response in the case of volcanic ash
contaminated airspace. It is worth noticing that there is still no agreement on critical ash concentration thresholds or any other method (retrievals, measurements, ingestion rate) that may be used to characterize critical conditions for aircraft. This poses a high limitation to the application of impact assessment methodologies such as the one presented here. Further work should support the definition of thresholds and fragility functions in order to increase reliability of results.

In this work, we have proposed several ways of estimating impacts on the air
traffic system and our results give a~wide perspective of the spatial and
temporal magnitude of impacts. According to Fig.~11, all eruptive scenarios
produce impacts in the London area, but the Askja OES 1875-type and Katla
LLERS scenarios can result in major impacts for the whole European air
traffic system. Low-magnitude, short-duration activity such as Hekla ERS
2000-type does not result in high impacts to central European air traffic,
but can disrupt relevant connections for the national economies involved
(i.e. Reykjav\'{\i}k--Copenhagen, London--Dublin). The probability of having
hazardous mass concentrations for more than 12\,h (Biass et~al., 2014) show
that high-magnitude scenarios such as the Askja OES 1875-type event can
produce major disruptions ($> 1$\,{{\%}} probability) to London air traffic.
Also, lower-magnitude but long-lasting activity such as a~Katla LLERS
scenario has a~$> 1$ and $> 5$\,{{\%}} probability of producing 12\,h lasting
disruption respectively to London and Scotland, where the important airports
of Glasgow and Edinburgh could be affected. Tables~6 and 7 show expected
disruptions to Keflav\'{\i}k and London airports, based on averaged data.
Note that this first-level impact assessment does not take into account the
hour of the day and/or the day of the year in which a~disruption occurs,
which neglects differences between peak and off-peak (night and early
morning) times. Average persistence times give information on the expected
duration of disruptions, but given that the standard deviation for
persistence time is in the order of 5--10\,h (Biass et~al., 2014), a~high
uncertainty is associated with these values. Nevertheless, this analysis
allows estimation of the order of magnitude of expected impacts and may
support the definition of an ``acceptable risk'' based on averaged long-term
values, which could eventually support a~practical framework for risk
management. Finally, average arrival time maps identify
which airports and areas may need response plans and gives an idea of how
much time is available for operations such as moving aircraft into hangars or
part of the fleet to other airports. In fact, Guffanti et~al.~(2010) have
shown how most damaging incidents during the last 60\,\unit{years} occurred
within the first 1000\,\unit{km} from source volcanoes and within the first
24\,h after eruption onset. The results of this impact assessment may
therefore support the definition of strategies for many stakeholders involved
in air traffic management during volcanic eruptions.

We also estimated impacts on FIRs (Fig.~11), accounting for the presence of
ash at all FLs. The same impact analysis has been performed at specific FLs
(Supplement Fig.~S3) leading to significantly different results. In fact,
impacts at a~given FL strongly depend on the range of column heights of each
eruption scenario, which in turn influences the probability of having ash at
different FLs. For example, the Hekla ERS 2000-type scenario does not produce
impacts at FL300 but only at lower levels. Consequently, a~long-term impact
assessment based on FL300 underestimates the expected impacts of
low-magnitude eruptions such as the Hekla ERS 2000- and 1947-types.
Analogously, impact assessment at airports (Tables~6 and~7) could be done
considering all FLs or restricted at FL050, where most takeoff and landing
operations take place. Given that air traffic management is based on the
capacity of airspace sectors and these include several FLs (Cook, 2007), the
second option seems more useful for decision-making. For these reasons, we
encourage the use of expected impact maps at FIRs, that are comprehensive of
all FLs and provide a~synthetic, conservative and meaningful support for the
development of a~Safety Risk Assessment (SRA) and other risk management
plans.

Finally, this work has estimated the socio-economic vulnerability of Europe
to air traffic disruptions. The 2010 eruption of Eyjafjallaj\"{o}kull
demonstrated that impacts at strategic airports such as London produce major
systemic impacts to the rest of the European air traffic network and indirect
socio-economic impacts at a~global scale (Oxford Economics, 2010). One
example is the interruption of Kenya exports to the UK (BBC News, 2010),
which caused an economic impact to Kenyan agricultural sectors (Alexander,
2013). Here we did not describe such interactions, but proposed a~methodology
to compare different sources of information that quantifies the dependency of
European areas on air traffic. The combination of demographic, trade and
accessibility information (Supplement Fig.~S3) identifies NUTS-2 regions with
higher dependency on air traffic (Fig.~10), that is, more vulnerable to air
traffic network disruptions. Moreover, the comparison of vulnerability maps
for NUTS-2 regions and impact assessment results (Fig.~11 and Tables~6 and~7)
identifies the most impacted areas from explosive eruptions in Iceland. For
example, Ireland has a~high vulnerability because it is an island (which
inherently has a~low multi-modal accessibility) and has strong social and
commercial relationships with the UK, resulting in high socio-economic impacts in
case of air traffic disruption. Also Nordic countries such as Denmark and
Norway are likely to be affected, in particular those regions with lower
multi-modal accessibility. Flexibility of the transportation system and
multi-modal accessibility are in fact critical factors that strongly
influence the societal response to air traffic disruptions (Alexander, 2013).  Moreover, a strategy that allows taking advantage of all different transportation means can strongly reduce losses during emergencies, as showed bu Jones and Bolivar (2011) for the case-study of Malta during the 2010 aviation disruption.
Finally, civil aviation disruption is not only a~problem for private
stakeholders, but affects all of society, requiring procedures to mitigate
the socio-economic risk (Vainikka, 2010). Results of the vulnerability and
impact assessment performed at European level can support a~socio-economic
impact analysis and the development of risk management plans. Data from
European projects such as Eurostat, ESPON and TRACC are extremely relevant to
support this analysis.

\subsection{Caveats}

First, the main aim of this work is identifying the areas that are expected to suffer impacts in case of occurrence of the selected scenarios, at both National and European scale. Given the difficulty of gathering specific data, our analysis does not account for physical vulnerability of most features. Thus, our simplified approach does not include an analysis of spatial inter- and intra-dependencies and cascading effects, as it relies on the characterization of physical vulnerability, beyond the scope of this work. The systemic aspects is covered only partially, by identifying specific elements and infrastructures that are important to the system performance on a priori basis and assessing their expected impacts. This limitation is particularly important with regards to road and electricity network disruptions, whose failure may cause the disruption of dependent services and infrastructures and eventually lower the capacity of response of areas. Studies on electricity infrastructure vulnerability suggest that this analysis should start identifying where, how often and for how long electricity supply will be interrupted. This analysis should be performed by splitting the network at specific delivery points, implying a detailed knowledge of its structure (Kjølle et al, 2011). In order to be realistic and produce usable results, this kind of analysis requires therefore a collaboration between involved stakeholders (infrastructure holders, service providers and end users). The same conclusion can be drawn at the European scale, where interdependencies between elements are tightly related to specific management plans of stakeholders involved (airlines, service providers). Thus, our work poses the basis for a specific analysis of these interdependencies by performing the first vulnerability and impact assessment for tephra fallout and dispersal in Iceland and Europe, and pointing out this issue to the stakeholders involved in territorial planning and long-term risk management.
Second, the methodology proposed here is focused on a specific hazard caused by explosive volcanic eruptions (i.e. volcanic ash fallout and dispersal). But, given that at both scales there are other hazards that potentially affect the exposed targets, outcomes of our vulnerability and impact assessment could support multi-risk initiatives and be interfaced with specific analyses. For these reasons, we base our methodology on an integrated framework for vulnerability assessment proposed within the European Project ENSURE (Menoni et al., 2012). At European scale, this work may contribute to a multi-risk assessment including other hazards for aviation, such as volcanogenic SO2 or mineral dust. At national scale, volcanic eruptions are the hazardous phenomenon that pose the higher threat to societies by means of many hazardous phenomena such as lava flow and Jökulhaups (glacial outburst floods). In particular, in 1996 and 2011, Jökulhaups in Southern Iceland destroyed parts of Route 1 (main Ring Road) and two bridges. It is worth noticing that these events usually happen at very local scale, while ash fallout and dispersal have a wider spatial range. For these events to be analyzed in a multi-risk framework, eruptive scenarios should be modified and/or complemented in order to include these events. Further work is therefore required in this field and may enhance the integration of our results in a multi-risk framework.

\conclusions

This work represents the first example of a strategy that can be applied to various volcanic settings for the multi-scale impact assessment for tephra dispersal and deposition.  The outcomes of such a strategy are designed to support decision-making at both the national and the European scale. In particular, impact maps could improve preparedness and help develop risk mitigation actions in Iceland and support long-term risk management plans of companies that operate in the European airspace (e.g. SRA).  Based on our analysis of the economic system at national level and of critical airports, FIRs and air traffic routes at the European scale, we can draw the following conclusions:

At the national scale:
\begin{itemize}
\item In case of occurrence occurrence of a 1875-type OES at Askja volcano, electricity network has a 10~\,{{\%}} probability of being impacted for 700 \unit{km}. The occurrence of LLERS at Katla and a 1947-type ERS at Hekla have a 10~\,{{\%}} probability of impacting more than 250 \unit{km} of the national electricity network. Finally, the occurrence of a 2010-type LLOES at Eyjafjallaj\"{o}kull has a  10~\,{{\%}} probability of disrupting 122 \unit{km} of the electricity network. 

\item In case of occurrence of  a 1947-type ERS at Hekla 5 power plants have a 10{\%} probability of being affected by ash fallout. If selected scenarios at Askja or Katla happened, 4 power plants would have a 10{\%} probability of being affected by ash fallout,  while other eruptive scenarios (2000-type at Hekla and 2010-type at Eyjafjallaj\"{o}kull have a low, but not null, probability of producing impacts on power plants.

\item In case of occurrence of any of the selected eruptive scenarios, 1-10 \unit{km2} of Icelandic croplands have a 10{\%} probability of being affected by ash fallout. Occurrence of eruptive scenarios at Askja and Katla have a 10{\%} probability of affecting 287 and 125 \unit{km2} of pasture lands, respectively.
\end{itemize}

At the European scale:
\begin{itemize}
\item The occurrence of a 2000-type ERS at Hekla is likely to cause very high impacts to the  Reykjav\'{\i}k FIR (~950 passengers stranded for at least 5\,\unit{h}) and high impacts for the London FIR  ($\sim 23$\,000 passengers stranded for at least 3\,\unit{h});

\item The occurrence of a 1947-type ERS at Hekla is likely to cause very high impacts to the Reykjavík FIR ($\sim 1$500 passengers stranded for at least 8 h) and high impacts for the London FIR ($\sim
  27$\,000 passengers stranded for at least 4\,\unit{h}). The FIR of
  Paris, Brest and Marseille would also be strongly impacted;

\item The occurrence of a 1875-type OES at Askja is likely to cause very high
  impacts to the Reykjav\'{\i}k FIR ($\sim 3$600 passengers stranded
  for at least 18\,\unit{h}) and high impacts for the London FIR
  ($\sim 60$\,000 passengers stranded for at least 8\,\unit{h}). FIRs
  above France, Germany and Scandinavia would also be impacted;

\item The occurrence of a LLERS scenario at Katla is likely to cause a~very high impact to
  the Reykjav\'{\i}k FIR ($\sim 4$300 passengers stranded for at
  least 21\,\unit{h}) and high impact for the London FIR ($\sim
  78$\,000 passengers stranded for at least 10\,\unit{h}). It is also
  likely that FIRs above France, Germany and Scandinavia would be
  strongly impacted.
\end{itemize}

\Supplementary{pdf}

\begin{acknowledgements}
  This work has been funded by the Spanish Research Project
  ``Atmospheric transport models and massive parallelism: applications
  to volcanic ash clouds and dispersion of pollutants at an urban
  micro-scale'' (ATMOST, CGL2009-10244) and the Fonds National Suisse
  project ``Volcanic-Ash Dispersal from Selected Icelandic Volcanoes:
  Risk Assessment for the European Region''
  (IZK0Z2{\_}142343). S. Biass is supported by SNF ({\#}200021-129997)
  and ESF/MemoVolc ({\#}5193) subsides. Simulations have been done at
  the Earth Sciences department of Geneva University and Barcelona
  Supercomputing Center (BSC-CNS), using the MareNostrum
  supercomputer. We thank the EUROCONTROL Network Management
  department for providing data and for their suggestions. Thanks to
  \'{A}rni Ragnarsson (Icelandic Regional Development Institute),
  Torfi J\'{o}hannesson (University of Iceland, Department of
  Agricultural Sciences) for data on agricultural production, and to
  Landm{\ae}lingar Islands for providing the local GIS database. We
  acknowledge the ESPON European Project for the accessibility
  data.
\end{acknowledgements}

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\begin{table}%T1
\caption{Synthesis of the eruptive scenarios considered in the tephra hazard
assessment (Biass et~al.,~2014). ERS: Eruption Range Scenario, OES: One
Eruption Scenario, LLERS: Long Lasting Eruption Range Scenario LLOES: Long
Lasting One Eruption Scenario. Tephra accumulation and dispersal was assessed
for Hekla, Askja and Katla, while for Eyjafjallaj\"{o}kull only tephra
accumulation was modeled (Biass et~al., 2014).}\scalebox{.9}[.9]{
\begin{tabular}{lllccc}
\tophline
Volcano&Modeling&Reference&Column&VEI&Eruption  \\
 & strategy & eruption & height (km a.s.l) & & duration \\
\middlehline
Eyjafjallaj\"{o}kull&LLOES&2010&2.5--7.8&2&40\,days \\
Hekla&ERS&2000&16.0--30.0&2&0.5--1\,\unit{h} \\
Hekla&ERS&1947 &6.0--16.0&3&0.5--1\,\unit{h} \\%%%
Katla&LLERS &Historical moderate/large$^{\mathrm{a}}$&10.0--25.0&--&1--4\,days \\
Askja&OES&1875 (C\,$+$\,D phases)&22.8--26.0&5&1\,\unit{h}\,$+$\,1.5\,\unit{h}  (C\,$+$\,D phases) \\
\bottomhline
\end{tabular}}
\label{tab1}
\end{table}



\begin{table}%T2
\caption{Indicators (and estimators) defined for the systemic vulnerability from tephra fallout.}
\begin{tabular}{lll}
\tophline
Category&Theme&Indicator (at municipality level) \\
\middlehline
Physical&Electric power plants and&Constant vulnerability\,$=$\,1 \\
 & distribution network  & \\[1.5mm]
Systemic&Accessibility&Travel time to critical facilities, energy \\
  & & production sites and mobility nodes \\[1.5mm]
Socio-economic&Agricultural areas&Combination of 3 factors: agricultural \\
  & & area, milk and wool production \\
\bottomhline
\end{tabular}
\label{tab2}
\end{table}


%t3
\begin{table}
\caption{Estimated impacts to electricity generation and distribution systems
for different eruptive scenarios. For each eruptive scenario, we calculated
the length of the electricity distribution system and the number of power
plants having 5, 10 and 20\,{{\%}} probability of being affected by
a~critical ash fallout of 10\,\unit{kg\,m^{-2}}. Note that the Hekla ERS
1947-type has the highest impact on power plants due to the location of the
volcano, close to 5 power plants.}
\begin{tabular}{lccccccc}
\tophline
Eruptive scenario&\multicolumn{3}{c}{Length impacted (km)}&&\multicolumn{3}{c}{Number of power plants} \\
Probability ({{\%}}) for 10\,\unit{kg\,m^{-2}}&5 & 10 & 20 &&5 & 10 & 20 \\
\middlehline
Hekla EES & 0 & 0 & 0 &&0 & 0 & 0   \\
Hekla ERS & 500 & 263 & 106 && 6 & 5  & 4  \\
Askja OES & 1400 & 655 & 109 &&5 & 4 & 1 \\
Katla LLERS&671 & 267 & 135 &&6 & 4 & 0 \\
Eyjafjallajokull LLOES&207 & 122 & 73 &&2 & 0 & 0 \\
\bottomhline
\end{tabular}
\label{tab3}
\end{table}



%t4
\begin{table}
\caption{Estimated impacts to agricultural activities for different eruptive
scenarios. Area of crops and pasture having 5, 10 and 20\,{{\%}} probability
of being affected by a~critical ash fallout of 10\,\unit{kg\,m^{-2}}. Katla
LLERS and Eyjafjallaj\"{o}kull LLOES 2010-type scenarios cause the greatest
impacts to crops, while pastures are particularly affected by eruptions of
types Askja OES 1875 and Katla LLERS.}
\begin{tabular}{lccccccc}
\tophline
Eruptive scenario&\multicolumn{3}{c}{Crops impacted (\unit{km^2)}}&&\multicolumn{3}{c}{Pastures impacted (\unit{km^2)}} \\
Probability ({{\%}}) for 10\,\unit{kg\,m^{-2}}&5& 10& 20&&5& 10& 20 \\
\middlehline
Hekla EES&0& 0& 0&&0& 0& 0 \\
Hekla ERS&10& 0& 0&&281& 13& 0  \\
Askja OES &10& 1& 0& & 586 & 287 &   26   \\
Katla LLERS  &        14 &         7 &         1 &&        361 &         125 &         101  \\
Eyjafjallajokull LLOES &        12 &         9 &         7 &&12& 9& 7 \\
\bottomhline
\end{tabular}
\label{tab4}
\end{table}



\begin{table}%T5
\caption{Indicators (and estimators) defined for systemic vulnerability of the European air traffic system to tephra dispersal.}
\scalebox{.75}[.75]
{\begin{tabular}{llll}
\tophline
Vulnerability category&Vulnerability Theme&Vulnerability Indicator&Vulnerability Estimator  \\
\middlehline
\multicolumn{2}{l}{Systemic}              & Airports (all Europe and    & Passengers ($n$\unit{\,day^{-1}})  \\
\multicolumn{2}{l}{Relevance of features} & North-West Europe)          &   Good (\unit{t\,year^{-1}})\\[1mm]
\multicolumn{2}{l}{~} &Routes (all Europe)&Number of average daily  \\
                        & & & connections \\[1mm]
\multicolumn{2}{l}{~} &Main Routes (North-West Europe)&Passengers ($n$\unit{\,day^{-1}})  \\
 & & & Goods (\unit{t\,year^{-1}}) \\[1mm]
\multicolumn{2}{l}{~} &Airspace sectors (FIRS, All Europe)&Traffic rate per FIR \\[2mm]
Socio-economic&Air traffic and&Population  &Population/Nuts2  \\
 & development &   Air traffic &  goods/Nuts2  \\
 & & &  passengers/nuts2 \\[1mm]
&&Accessibility&Multi-modal accessibility/Nuts2 \\
\bottomhline
\end{tabular}}
\label{tab5}
\end{table}


\begin{table}%T6
  \caption{First-order estimation of expected impacts at London Heathrow airport for different eruption scenarios based on the averaged persistence. Air traffic values are based on yearly averages (CAA, 2012).}
\begin{tabular}{lllll}
\tophline
Eruptive Scenario&Mean persistence&Movements&Passengers&Freight \\
 & all FLs (h) & disrupted ($n$) & stranded ($n$) & stranded (t) \\
\middlehline
Hekla-2000 ERS&$\sim 3$&$\sim 160$&$\sim 23\,000$&$\sim 600$ \\
Hekla-1947 ERS&$\sim  4$&$\sim 180$&$\sim 27\,000$&$\sim 700$ \\
Katla LLERS&$\sim 10$&$\sim 530$&$\sim 78\,000$&$\sim 2000$ \\
Askja OES&$\sim 8$&$\sim 410$&$\sim 60\,000$&$\sim 1500$ \\
\bottomhline
\end{tabular}
\label{tab6}
\end{table}

\begin{table}%T7
  \caption{First-order estimation of expected impacts at Keflav\'{\i}k airport for different eruption scenarios based on the averaged persistence. Air traffic values are based on Keflav\'{\i}k airport 2011 facts and figures (Isavia, 2012).}
\begin{tabular}{lllll}
\tophline
Eruptive scenario&Mean persistence&Movements&Passengers&Freight \\
 & all FLs (h) & disrupted ($n$) & stranded ($n$) & stranded (t) \\
\middlehline
Hekla-2000 ERS&$\sim 5$&$\sim 20$&$\sim 950$&$\sim 20$ \\
Hekla-1947 ERS&$\sim 8$&$\sim 30$&$\sim 1500$&$\sim 40$ \\
Katla LLERS&$\sim 21$&$\sim 90$&$\sim  4300$&$\sim 110$ \\
Askja OES&$\sim 18$&$\sim 70$&$\sim  3600$&$\sim 90$ \\
\bottomhline
\end{tabular}
\label{tab7}
\end{table}



\begin{table}%T8
  \caption{Availability, sources and type of data used for the vulnerability assessment to tephra fallout at national scale.}
\scalebox{.75}[.75] {\begin{tabular}{lclll} \tophline
Data&Available&Source&Coverage&Type \\
\middlehline
Population&Yes&Statice&Municipalities&Number \\
Population trends&Yes&Bygg{\dh}astofnun&Municipalities&Percentage \\
Population age&Yes&Statice&Municipalities&Number \\
Power plants&Yes&Landm{\ae}lingar Islands&Disaggregated&Location \\
 & &\url{http://www.or.is/en/about} & & \\
Aluminum smelters&Yes&Landm{\ae}lingar Islands&Disaggregated&Location \\
Hospitals&Yes&Landm{\ae}lingar Islands&Disaggregated&Location \\
Shelters&Yes&Landm{\ae}lingar Islands&Disaggregated&Location \\
Police stations&Yes&Landm{\ae}lingar Islands&Disaggregated&Location \\
Fire stations&Yes&Landm{\ae}lingar Islands-&Disaggregated&Location \\
Road Network&Yes&Landm{\ae}lingar Islands&Disaggregated &Digital map \\
Electricity network&Yes&Landm{\ae}lingar Islands&Disaggregated &Digital map \\
Ports (import-export)&Yes&Statice&Disaggregated&Import/export values  \\
Airports (air traffic)&Yes&Isavia&Disaggregated&Passengers/freight values \\
Land use&Yes&Corine Land Cover&Homogeneous areas&Corine classification \\
Milk production&Yes&Bygg{\dh}astofnun&Municipalities&Liters/support entitlements \\
Wool production&Yes&Bygg{\dh}astofnun&Municipalities&Support entitlements \\
Civil protection units &No&--&--&-- \\
Productive activities&No&--&--&-- \\
Employees for productive &&&&\\
{activities/sectors}&&&&\\
Average income&No&--&--&-- \\
Water supply&No&--&--&-- \\
\bottomhline
\end{tabular}}
\label{tab8}
\end{table}




\begin{figure}
\includegraphics[width=80mm]{nhessd-2014-0078-f1n}
\caption{Map of Iceland showing the location of the 4 volcanoes
  considered in the hazard assessment and the main cities and towns. The
  administrative units (municipalities) used for the national
  vulnerability analysis are given in the Supplement.}
\label{nhessd-2014-0078-f01}
\end{figure}



\begin{figure}
\includegraphics[width=70mm]{nhessd-2014-0078-f2n}
\caption{Exposure maps for: \textbf{(a)} the road network and critical
  infrastructures (hospitals, local health care centers and schools,
  that can be used as ash shelters), \textbf{(b)} electricity
  distribution network, hydroelectric and geothermal power plants,
  production sites and main locations (urban areas), \textbf{(c)} main
  transport nodes: ports and airports.}
\label{nhessd-2014-0078-f02}
\end{figure}

\begin{figure}
\includegraphics[width=70mm]{nhessd-2014-0078-f3n}
\caption{Accessibility to critical facilities including, from top to
  bottom, hospitals, schools and fire stations. All maps display the
  time in minutes required to reach a~given facility by road.}
\label{nhessd-2014-0078-f03}
\end{figure}

\begin{figure}
\includegraphics[width=100mm]{nhessd-2014-0078-f4n}
\caption{Thematic vulnerability map for agriculture. The 5-class
  qualitative ranking is based on a~combination of three indicators:
  production of milk, production of wool and percentage of
  agricultural area, all available at a~municipality level. Maps for
  each indicator are given in the Supplement.}
\label{nhessd-2014-0078-f04}
\end{figure}

\begin{figure}
\includegraphics[width=100mm]{nhessd-2014-0078-f5n}
\caption{Number of people as a~function of driving time to reach the
  closest critical infrastructures (i.e. hospital, police/fire station
  and schools).}
\label{nhessd-2014-0078-f05}
\end{figure}

\begin{figure}
\includegraphics[width=120mm]{nhessd-2014-0078-f6}
\caption{Main airport hubs in central and northwestern Europe
  depending on the traffic of passengers \textbf{(a)} and goods \textbf{(b)}
  during 2010 (Eurostat, 2012). The values represent the relevance of
  these airports for passengers and freight air traffic. The most
  relevant airports are London Heathrow, Paris Charles de Gaulle,
  Frankfurt, Amsterdam, and Munich.}
\label{nhessd-2014-0078-f06}
\end{figure}

\begin{figure}
\includegraphics[width=120mm]{nhessd-2014-0078-f7}
\caption{Main European routes from/to London Heathrow (top) and the
  rest of the airports in Greater London (Gatwick, Luton and Stansted,
  displayed together, bottom). Routes are ranked according to their
  importance in terms of passengers (left) and freight (right)
  traffic. The vulnerability classification is based on the whole
  range of air traffic data between main London airports and the
  considered European airports in 2010 (Eurostat, 2012). The same
  classification criterion is used for all figures and the comparison
  underlines that Heathrow airport handles the most strategic routes
  (corresponding to more than 1.2 million passengers per year).}
\label{nhessd-2014-0078-f07}
\end{figure}

\begin{figure}
\includegraphics[width=120mm]{nhessd-2014-0078-f8}
\caption{Main European routes of passengers \textbf{(a)} and freights
  \textbf{(b)} from/to Keflav\'{\i}k airport. Analysis is performed
  for the routes connecting the main airports shown in Fig.~6. The
  vulnerability classification is based on 2010 data (Eurostat,
  2012).}
\label{nhessd-2014-0078-f08}
\end{figure}

\begin{figure}
\includegraphics[width=90mm]{nhessd-2014-0078-f9}
\caption{Vulnerability classification of the European airspace
  sectors, based on the air traffic rate in the sector during a~peak
  day of 2012 (source: EUROCONTROL). FIRs with very high vulnerability
  values (blue) are London, Paris and Munich.}
\label{nhessd-2014-0078-f09}
\end{figure}

\begin{figure}
\includegraphics[width=120mm]{nhessd-2014-0078-f10}
\caption{Vulnerability of the NUTS-2 regions, calculated as a~combination of
population, air traffic values and multi-modal accessibility value (see the
Supplement Fig.~S2 for individual maps). High vulnerability areas are those
having high population and low accessibility rates, for example Ireland and
Norway.} \label{nhessd-2014-0078-f10}
\end{figure}

\begin{figure}
\includegraphics[width=120mm]{nhessd-2014-0078-f11}
\caption{Expected impacts of tephra dispersal on European airspace
  sectors (FIRs) in case of occurrence of the different scenarios considered: \textbf{(a)} Hekla
  2000-type, \textbf{(b)} Hekla 1947-type, \textbf{(c)} Askja
  1875-type and \textbf{(d)} Katla scenarios.}
\label{nhessd-2014-0078-f11}
\end{figure}

\end{document}
