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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Spatially-Distributed Multi-Hazard Risk Analysis</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Maryna Zharikova</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Gonzalo Barbeito</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Marian Sorin Nistor</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Stefan Wolfgang Pickl</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Universität der Bundeswehr</institution>
          ,
          <addr-line>Werner-Heisenberg-Weg 393GEB, München, Neubiberg, 85579</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>The paper dwells on the problem of multi-hazard risk analysis and management. The authors identify some gaps in existing disaster risk reduction research projects. To overcome these gaps a comprehensive approach to multi-hazard risk analysis is needed that considers all components of multi-hazard risk in dynamics with a spatial reference. The development of such an approach is the purpose of the article. The risk is presented in the form of the following components: hazard characteristics (danger, intensity, area affected by hazard), vulnerable object characteristics (location, vulnerability, speed of recovery), as well as spatio-temporal threat measured in time it takes for the hazard to reach the object. It's proposed to present hazard risk in dynamics as passing through the following three stages: potential risk, risk of threat, and risk of destruction. Individual risk is presented as a trajectory in ndimensional space of its parameters, multi-risk is assessed using operation of taking maximum. The proposed approach to risk analysis allows diagnosing the situation and making decisions throughout the entire disaster risk management cycle. Potential risk assessment can serve as a basis for long-term adaptation, active risk assessment can serve as a basis for early warning and response actions.</p>
      </abstract>
      <kwd-group>
        <kwd>1 Multi-hazard risk analysis</kwd>
        <kwd>threat</kwd>
        <kwd>danger</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction &amp; Related Works</title>
      <p>Infrastructure owners and operators are increasingly faced with the challenge of delivering
resilient infrastructure and mitigating the effects of multiple hazards and climate change effects.
Therefore, multi-hazard risk analysis methodologies are critical for infrastructure protection.</p>
      <p>The risk from a hazard, especially from multiple hazards, is a broad concept that depends on
many components characterizing both the source of risk, namely hazard (or hazards), and risk
receiver, namely assets or community affected by hazards.</p>
      <p>Currently, there is no single definition for the notion of risk itself and its components such as
vulnerability, resilience, et cetera.</p>
      <p>
        In the simplest case, hazard risk describes the combination of the probability of hazard
occurrence and potential impact on an asset or community (object of risk) [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. So, variables that
determine risk can be related to hazard or object.
      </p>
      <p>When it comes to hazard, risk analysis can include one hazard or multiple hazards, either
dependent or correlated. However, analyzing the risk from several interacting hazards in the
same area is one of the most challenging issues.</p>
      <p>
        There are also different understandings of risk components related to the objects at risk, such
as vulnerability, resilience, adaptation, and the correlation between them [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>
        The term “resilience” is critical to understand hazard impact on the object. Resilience
describes the emergent properties that the objects have, which allows them to withstand, respond
and/or adapt to a vast range of hazards by maintaining and/or enhancing their functionality [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>
        The concept of resilience has gone through a series of transformations. For example, in [
        <xref ref-type="bibr" rid="ref4 ref5">4,5</xref>
        ],
resilience and vulnerability are considered two opposing conceptions. Namely, vulnerability is
considered the flip side of resilience. When a social or ecological system loses resilience, it
becomes vulnerable to change that previously could be absorbed [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>
        According to the most comprehensive current approach [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], resilience originates from the
interaction of some adverse event (such as hazard) and some object to which the property of
resiliency is ascribed (it can be a single asset, infrastructure, people, communities, et cetera).
Thus, resilience has a form of a process of transformation and adaptation of the object exposed
to hazards.
      </p>
      <p>Resilience is a wide-ranging dynamic concept described by two groups of parameters relating to
vulnerability and recovery of the object affected by hazards. In practice, the dependence of these
parameters on hazard intensity is described by functions, e.g., functions of dependence of
fragility or vulnerability on intensity.</p>
      <p>Currently, hazard risk is being considered on different levels (Table 1). There are such levels
as a single asset, infrastructure, or community-country when it comes to the object of risk.
Different risk measurement metrics are qualitative (descriptive) or quantitative, static, or
timedependent. Risk analysis can take into account one hazard or multiple hazards, either
independent or correlated. If we consider hazards of different nature, restoring the damage due to
one hazard is not expected to improve the performance against another hazard.
The problem of multi-hazard risk analysis and management is tackled in several disaster risk
reduction research projects. Table 2 shows some of the limitations found in these projects and
how they could be overcome.</p>
      <p>How to overcome the gap
Risk should be related to
multihazards, their interactions with
climate drivers, and their
cascade/simultaneous effects on
the object.</p>
      <p>
        Static risk assessment. Hyogo Framework for Action The methods for dynamic
2005-2015 [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. assessment of risk and its
components should be developed.
      </p>
      <p>
        Qualitative approach. Hyogo Framework for Action The quantitative approaches to
2005-2015 [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]; the assessment of risk and its
Sendai Framework for components should be developed.
      </p>
      <p>
        Disaster Risk reduction
20152030 [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ].
      </p>
      <p>
        Local level (focusing on emBRACE Resilience The methods for quantification of
specific asset or infrastructure Framework – community risk at a regional, country, and
level). resilience [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]; international scale should be
TRANSRISK [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] – transport developed.
      </p>
      <p>infrastructure.</p>
      <p>According to Table 2, the existing risk-related projects most commonly consider independent
hazards or only certain kinds of hazards. Usually, risk and its components are assessed statically
and qualitatively and on a local level (focusing on specific areas, specific assets, or specific
infrastructure level). In addition, much of the work on multi-hazard risk consider vulnerability
instead of resilience.</p>
      <p>Although several multi-hazard risk issues are analyzed, much remains to be done in the field
of multi-hazard risk analysis. To overcome the limitations mentioned above, a comprehensive
approach is needed that considers all components of multi-hazard risk in dynamics.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Multi-Hazard Risk Analysis</title>
      <p>Risk originates from the interaction of hazard and some objects (infrastructures, communities, et
cetera) affected by the hazard.</p>
      <p>
        In this sense, risk dimensions comprise characteristics of hazard such as danger and intensity,
characteristics of an object such as vulnerability and speed of recovery, as well as the proximity
of object and hazard (Fig.1). Therefore, their relative position matters. For example, the risk for
some objects arises when the object is situated close to disaster. Therefore, the spatial reference
is of great importance here [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ].
We need to distinguish potential hazard that has not yet occurred and active hazard that is
already identified and spreading [13].
      </p>
      <p>A potential hazard is characterized by danger, which is a characteristic of a certain area of
territory and is assessed by a probability of hazard occurrence. Active hazard is characterized by
threat, which is a spatial-temporal characteristic reflecting the proximity of hazard and
vulnerable object. In simple words, a threat is measured in the time it takes for the hazard to
reach the object.</p>
      <p>Considering this, we can distinguish potential risk related to potential hazards and real-time
active risk related to active hazards.</p>
      <p>Risk in the context of this work is an assessment of the relationship between hazard scenarios
– sources of risk, and vulnerable objects at risk – risk receivers.</p>
      <p>It is proposed to consider three stages of risk (Fig.2).</p>
      <p>The 1st stage is a potential risk; it is characterized by danger and exists until hazard
occurrence when danger is materialized.</p>
      <p>The 2nd stage is the risk of threat, which exists from the moment of hazard occurrence to the
moment when hazard reaches the object and is characterized by threat. During this stage, the
hazard poses a threat to the object. The threat is a spatial-temporal characteristic of proximity
between hazard and vulnerable object. In simple words, a threat is measured in the time it takes
for the hazard to reach the object.</p>
      <p>The 3rd stage is the risk of destruction, which exists from the time when the hazard reaches
the object when a threat is materialized. This stage is characterized by the change in the value of
the object. The purpose of decision-making is to prevent this stage. This stage requires recovery
actions and recovery costs [14].
The risk from one hazard (potential or active) for a certain object is individual. In case there are
several sources of risk for a particular object, a multi-risk is created. Fig. 3 shows three stages of
individual risk.
Fig. 4 shows multi-risks for two objects o1 and o2 from three spreading hazards (in the locations
h1, h2, and h3) and two potential sources of hazards (in the locations h4 and h5).
Active risk is characterized by threat. The threat model consists of a set of zones around the
contour of the hazard having different degrees of threat to valuable objects. Some objects can be
affected by a multi-threat from several active hazards simultaneously (Fig.5).
Multi-threat for the object can be assessed using the operation of taking the maximum of threat
assessments from individual hazards:
,
where n is the number of hazards that simultaneously pose a threat to the  ℎ object.
Therefore, risk dimensions comprise hazard characteristics (danger, intensity), object
characteristics, and spatial-temporal characteristics reflecting the proximity of hazard and
vulnerable object (threat) (Fig. 6). Thus, we can present risk as a point in the n-dimensional
space of its parameters. However, when we combine various components into a single risk
assessment, we face one problem: different risk components have different units of
measurement. Therefore, to obtain risk assessment for the object O from the hazard H, we should
first normalize the values of risk components so that, e.g., bring them to the range from 0 to 1,
and multiply them.</p>
      <p>In the case of several sources of hazards that simultaneously affect the vulnerable object, we
obtain a multi-risk. For example, Figure 7 shows multi-risk for the object O from three hazards
H1, H2, and H3.
Each individual risk is dynamic and can be presented as a trajectory in the n-dimensional space
of its parameters. For example, the graphs in Figure 8 show three trajectories of three individual
risks for the object O and 3 points on their trajectories, presenting three individual risk
assessments at the time moment t.
Suppose that at time moment t some object is simultaneously affected by k individual risks
presented in the form of points in n-dimensional space of parameters pi :</p>
      <p>…</p>
      <p>Then multi-risk they create will also be presented as the point in the same space of
parameters, but each coordinate will be assessed as a maximum value among the corresponding
coordinates of individual risks:</p>
      <p>In general, dynamic risk assessment can be assigned to each object and each area of the
territory. Moreover, for each object, we can build a multi-risk trajectory on a time interval
[t1,…,tn] as a sequence of risk values at successive points in time [R(t1),…, R(tn)].</p>
    </sec>
    <sec id="sec-3">
      <title>3. Conclusions</title>
      <p>Spatially distributed integrated assessment of multi-hazard risk can serve as a basis for
diagnosing the situation and decision making throughout the entire disaster risk management
cycle. Active risk assessment can serve as a basis for early warning and response actions in
realtime systems. Potential risk assessment can be used for long-term adaptation strategies and
resilience building [15]. Spatial distribution of risk makes it possible to identify areas or objects
that require the primary attention of a decision-maker.
[13] M.Zharikova, V.Sherstjuk, Situation diagnosis based on the spatially-distributed dynamic
risk assessment, in: Proceedings of IEEE 14th Untern. Conf. CSIT, 2019, pp. 205-209
[14] M.Zharikova, Dynamic spatial-distributed fire risk analysis, Predicting, monitoring, and
assessing fire dangers and risks, IGI Global; responsible editor N. Baranovskiy, Hershey
PA, USA, 2019, pp. 191-120. doi:10.4018/978-1-7998-1867-0.ch005
[15] G.Barbeito, D.Budde, M.Moll, S.Pickl, B.Thiebes, A Hybrid AI and Simulation-Based
Optimization DSS for Post-Disaster Logistics, in: Proceedings of 2020 International
Conference on Security and Management (SAM'20), 2021, pp. 245-259</p>
    </sec>
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