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  <front>
    <journal-meta><journal-id journal-id-type="publisher">NHESS</journal-id><journal-title-group>
    <journal-title>Natural Hazards and Earth System Sciences</journal-title>
    <abbrev-journal-title abbrev-type="publisher">NHESS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Nat. Hazards Earth Syst. Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1684-9981</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/nhess-21-1847-2021</article-id><title-group><article-title>Landslide risk management analysis on expansive residential areas – case
study of La Marina (Alicante, Spain)</article-title><alt-title>Landslide risk management analysis on expansive residential
areas</alt-title>
      </title-group><?xmltex \runningtitle{Landslide risk management analysis on expansive residential
areas}?><?xmltex \runningauthor{I.~Cantarino et~al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Cantarino</surname><given-names>Isidro</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Carrion</surname><given-names>Miguel Angel</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Palencia-Jimenez</surname><given-names>Jose Sergio</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-9587-7379</ext-link></contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Martínez-Ibáñez</surname><given-names>Víctor</given-names></name>
          <email>vicmarib@trr.upv.es</email>
        <ext-link>https://orcid.org/0000-0003-4445-2896</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Department of Geological and Geotechnical Engineering,
Universitat Politècnica de València, <?xmltex \hack{\break}?>Camino de Vera, s/n, 46071,
Valencia, Spain</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Department of Urban Planning, Universitat Politècnica de
València, Camino de Vera, s/n, 46071, Valencia, Spain</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Víctor Martínez-Ibáñez
(vicmarib@trr.upv.es)</corresp></author-notes><pub-date><day>15</day><month>June</month><year>2021</year></pub-date>
      
      <volume>21</volume>
      <issue>6</issue>
      <fpage>1847</fpage><lpage>1866</lpage>
      <history>
        <date date-type="received"><day>26</day><month>June</month><year>2020</year></date>
           <date date-type="accepted"><day>28</day><month>April</month><year>2021</year></date>
           <date date-type="rev-recd"><day>16</day><month>April</month><year>2021</year></date>
           <date date-type="rev-request"><day>5</day><month>August</month><year>2020</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2021 Isidro Cantarino et al.</copyright-statement>
        <copyright-year>2021</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021.html">This article is available from https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021.html</self-uri><self-uri xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021.pdf">The full text article is available as a PDF file from https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e116">Urban expansion is a phenomenon that has been observed since the mid-20th
century in more developed regions. One aspect of it is the urban development
of holiday resorts with second homes that generally appeared following world
political stabilisation. This residential expansion has often happened with
scarce control, especially in its early stages, allowing areas to be occupied
that are not so suitable in terms of the environment, culture and landscape,
not to mention the very geological risks of flooding, earthquakes and
landslides. Indeed, the risk of landslides for buildings occupying land in
zones at such risk is not a matter solely attributable to the geomorphological
characteristics of the land itself, nor is it simply a question of chance; it
is also due to its management of such land, generally because of a lack of
specific regulations. This study aims to lay down objective criteria to find
how suitable a specific local entity's risk management is by looking at the
evolution of its urban development procedures. It also aims to determine what
causes the incidence of landslide risk (geomorphology, chance, land
management, etc.) and finally to suggest control tools for the public bodies
tasked with monitoring such matters.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e128">Landslide risk evaluation, management and mitigation are aspects that have been dealt with profusely in recent decades in the literature specialising in
such matters. There is a multitude of studies on these matters, notably the
summary put forward by Dai et al. (2002) with a critical review of landslide
research and the strategies for reducing damages and losses, as well as the
relevant publications by Lee and Jones (2004) and Glade et al. (2005) with a
multidisciplinary perspective on landslide management. The recent review of
quantitative methods for analysing landslide risk by Corominas et al. (2014)
is also very noteworthy.</p>
      <p id="d1e131">It is important to consider that the risk associated with landslides is
changing as a consequence of environmental change and social developments.
Climate change, the increased susceptibility of surface soil to instability,
anthropogenic activities, growing (and uncontrolled) urban development and
changes in land use with increased vulnerability for the population and
infrastructure as a result all contribute to the change – and in most cases
the increase – in the risk of landslides (Gallina et al., 2016).</p>
      <p id="d1e134">Urban expansion is a phenomenon associated with an increase in living
standards and improvement in transport, communication and services outside the
traditional population hubs. Among the many aspects of this phenomenon being
studied, there is one that stands out as absolutely essential: the
organisation and regulation of this urban growth. Indeed, in the classic work
by De Terán (1982), the desired approach to urban planning is described as
the need to establish order in developing it, in view of the damage and
inconveniences caused by spontaneous urban development.</p>
      <?pagebreak page1848?><p id="d1e137">It is clear that urban expansion using unsuitable planning aggravates the
incidence of geological risks. Specifically, landslides are one of the most
dangerous natural disasters in terms of their frequency and the seriousness of
the damage they do, leading to loss of human life and social infrastructure in
practically the whole world, which has been increasing in recent decades (Lee
et al., 2017; Sandić et al., 2017; Cascini et al., 2005).</p>
      <p id="d1e141">One of the main causes that explain the rise in geological risks in
residential areas is expansive urban development processes, with a growing
trend observed in these risks on a global scale, especially as regards
landslides (Zhou and Zhao, 2013). These expansionary activities have
significantly increased the pressure on the land and consequently its effect
on the population due to the occupation of land unsuitable for residential
buildings (Fernández et al., 2016). This situation indicates improper
management of the land, caused by a lack of suitable zoning of risks that
hinders good planning for the use of the land (Cascini et al., 2005; and
Cascini, 2008).</p>
      <p id="d1e144">In other words, residential land usage may be exposed to greater natural risks
precisely because such phenomena are not included in urban planning.  When
such planning is properly applied, it may help reduce exposure to the risk
within urban areas. Indeed, it is considered to be a powerful tool in helping
efficient, equitable adaptation between land occupation and natural risks
(Hamma and Petrişor, 2018; Macintosh, 2013). There is a plethora of
references that agree on the link between landslides and urban development. In
some cases, there are rules on uses in said circumstances, but they have not
been taken into account, thereby allowing for illegal and irregular
occupation, as happened in the region of Campagna, Italy (Di Martire et al.,
2012). In other cases, the course of rivers has been changed as a result of an
increase in urban land, leading to negative effects on landslides as seen on
the coast of Genoa (Faccini et al., 2015) and the city of Doboj in Bosnia and
Herzegovina (Sandić et al., 2017).</p>
      <p id="d1e147">The great demand for residential land to develop tourism in particular has
caused similar situations. One example is the case cited by Katsigianni and
Pavlos-Marinos (2017) on the Greek island of Santorini. A similar situation is
seen in Mengshan, China (Peng and Wang, 2015), where engineering measures have
been introduced a posteriori in a mountain tourist resort with a high risk
of landslides. So, when drawing up and implementing urban planning, these
types of factors must be taken into account amongst many others in order to
suitably regulate the territory and prevent disorganised urban sprawl.</p>
      <p id="d1e150">Faced with this situation, which has been widely recognised around the world,
there is a need for risk governance to be duly included in urban planning
(Renn and Klinke, 2013), improving the resilience of urban developments
implemented and their possible growth (Zhai et al., 2015). It is also
necessary to carry out suitable zoning of the risks to help reduce disasters
(Wang et al., 2008). The great challenge is faced precisely in applying urban
governance, attempting to define effective systems and tools adapted to the
new context of natural risks (Birkmann et al., 2014). Some experiences have
shown the need to include the population's participation in tackling this
problem, encouraging the adoption of solutions and management of them, as
mentioned by Gough (2000) in New Zealand.</p>
      <p id="d1e153">For all these reasons, it is surprising that the effectiveness and results of
management of zones exposed to landslide risk have received less attention. In
the end, it is not only necessary to know how to quantify and locate the
risks, as well as to put forward steps to avoid or mitigate them, but also to
lay down procedures that can determine whether the management by technicians
and politicians is effective and if the risk has truly been mitigated.</p>
      <p id="d1e156">Thus, the main goal of this work is to determine whether the pace at which
zones at risk are being occupied has a point of inflection where it begins to
steadily decrease. This point of inflection should be the result of a
comprehensive application of specific regulations for the land that hinder or
restrict residential construction in that type of area. It is along these
lines that this paper suggests control tools for the public bodies tasked with
monitoring such matters.</p>
      <p id="d1e160">Another significant aim of this work should also be noted: this involves
differentiating correct management of the terrain (specifically addressing its
occupation by residential housing) from management that can clearly be
improved. In particular, considering the risk of landslides for residential
housing, the possibility of said risk becoming stabilised is studied over the
time series. In this case, the management can be deemed adequate.</p>
      <p id="d1e163">Nevertheless, if the risk increases over time, then it can be attributed to
improper management, which should be corrected. The aims of this work also
include analysing this situation, as well as determining what causes an
increase in landslide risk, for example by considering geomorphological
dynamics, inadequate land management and even bad luck.</p>
      <p id="d1e166">To ascertain the importance of these control tools, a case on the
Mediterranean coast has been studied in this work. Significant construction of
new buildings has sprawled along said coastline, flouting planning regulations
and thus proving the complete inefficiency of such regulations in containing
this phenomenon (Malvárez et al., 2003). That is why it is essential
to enforce the government regulations developed, as well as to activate
pertinent control mechanisms to ensure compliance.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>General methodology</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Objectives</title>
      <p id="d1e184">Given the background described above, it is necessary to determine the extent
to which residential areas are at risk of landslides, to understand the causes
of these risks and to improve the planning for them.
The basis for this should be a study of the behaviour of the risk taken upon building them and the
factors determining it. To do so, it is necessary to begin with a map of the
risk distribution and the annual residential construction data in a long time
series. By knowing this risk and construction data, one can estimate its
progress over time and whether a greater or lesser relative risk is<?pagebreak page1849?> being
taken. Specifically, it is understood that this evolution in risk must not be
exclusively a matter of the land's orographic characteristics, or even of
chance, but it should also be greatly influenced by the pertinent territorial
management.</p>
      <p id="d1e187">The first task to be carried out is to gather residential building data as an
annual summary for each local entity into which the zone of study is
divided. Studying temporal series can then provide a lot of dynamic
information about the evolution of a set of data. The series do not have to
follow constant growth patterns since, as will be seen, they may undergo
seasonal and other changes. This happens especially in the main data series to
be analysed, which is the evolution of residential construction over time. Of
course, it is also affected by the vagaries of big economic cycles, but such
supra-annual seasonality is not going to be studied in depth.</p>
      <p id="d1e190">The second dataset must arise from the geolocalised map of risk
distribution. Normally, this is based on a landslide susceptibility map (LSM)
that has been deemed stable during the period analysed. Indeed, the risk map
is calculated based on the temporal nature of construction and must be
approximately in sync with this process. Moreover, the occurrence of a
landslide is generally linked to trigger mechanisms that respond to events
subject to a specific return period. The probability calculation also uses
feedback from the appearance of these events, whose frequency is being
modified as a result of climate change. However, according to Gariano and
Guzzetti (2016), the effects of climate change on the type, extent, magnitude and direction of the changes in the slopes' stability conditions, as well as on the
location, abundance and frequency of the landslides, are not completely clear. In the end, climate change is not going to be taken into account
specifically in this work.</p>
      <p id="d1e193">The main goal of this research is to seek risk modification patterns
throughout a time series in local entities (hereinafter referred to as urban
administrative divisions, UADs). Three main, non-exclusive hypotheses are
proposed that enable the causes of the evolution in risk to be explained via a
specific line of reasoning:
<list list-type="order"><list-item>
      <p id="d1e198">random reason, with no clear reason explaining the phenomenon;</p></list-item><list-item>
      <p id="d1e202">geomorphological land characteristics: slope, lithology, land cover, etc.; and</p></list-item><list-item>
      <p id="d1e206">management by local or regional public bodies responsible for land planning.</p></list-item></list>
Simple observation of the annual evolution of risk in a specific zone is not
by itself very conclusive in determining whether it is due to one of the
causes described above. The trend has to be connected to the evolution of
construction, verifying the temporal correlation between the two series within
a local entity and among neighbouring local entities. This aspect will be
analysed in the section dealing with the evolution of risk.</p>
      <p id="d1e211">In keeping with the objectives described, it is necessary to have two
fundamental types of georeferenced data: the data on residential construction
evolving over time and the data concerning the risk as a result of occupying
the land, with the risk's distribution over time being variable depending on
the pace of construction.</p>
      <p id="d1e214">Logically, it is necessary to have data on the residential plots or parcels,
specifically the data on the built-up area of each residential parcel (as
“gross floor area”, hereinafter GFA), year of construction and geographic
location. These types of data are beginning to be easily obtainable in some
countries thanks to the development of public access digital cadastres (USA,
Australia, France, Germany and others), which also appear to be near
completion in many others. Currently, such data in Spain can be downloaded
sequentially by municipalities via the Spanish Cadastral Agency (DGC).</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Risk evaluation</title>
      <p id="d1e225">The quantitative risk evaluation is to be carried out by applying the known
general equation of risk (Eq. <xref ref-type="disp-formula" rid="Ch1.E1"/>), which includes the terms
<italic>hazard</italic> or probability, elements affected and their value
(<italic>exposure</italic>), and the seriousness of the damage
(<italic>vulnerability</italic>), based on the classic definitions from the Office of
the United Nations Disaster Relief Organization (UNDRO, 1979).

                <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M1" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>Risk</mml:mtext><mml:mo>=</mml:mo><mml:mtext>hazard</mml:mtext><mml:mo>×</mml:mo><mml:mtext>exposure</mml:mtext><mml:mo>×</mml:mo><mml:mtext>vulnerability</mml:mtext></mml:mrow></mml:math></disp-formula>

          The value of risk is generally calculated in monetary units (EUR), though
other types of unit may also be used (built-up <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, casualties,
etc.). In this work, the type of risk analysed is economic loss due to
landslide damage to residential buildings.</p>
<sec id="Ch1.S2.SS2.SSSx1" specific-use="unnumbered">
  <title>Hazard</title>
      <p id="d1e278">This is the probability of occurrence of a potentially damaging
natural phenomenon such as a landslide within a specific period of time in a
specific area. Calculation of this is normally based on a susceptibility
map. Specifically, for each level of susceptibility the hazard must be
calculated in units of probability, for which it is necessary to turn to
inventory data of landslides. These two types of probability – temporal and
spatial – are in keeping with Eq. (<xref ref-type="disp-formula" rid="Ch1.E2"/>):

                  <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M3" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>Hazard</mml:mtext><mml:mo>=</mml:mo><mml:mtext>Spatial probability</mml:mtext><mml:mo>×</mml:mo><mml:mtext>Temporal probability</mml:mtext><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="Ch1.S2.SS2.SSSx2" specific-use="unnumbered">
  <title>Exposure</title>
      <p id="d1e308">This includes people, property, systems or other elements present in hazard zones that are thereby subject to potential losses. Therefore, exposure indicates
the extent to which the elements at risk are actually located in the path of a
particular landslide (Corominas et al., 2014).</p>
</sec>
<?pagebreak page1850?><sec id="Ch1.S2.SS2.SSSx3" specific-use="unnumbered">
  <title>Vulnerability</title>
      <p id="d1e317">This is the degree of loss to a given element or set of elements within
the area affected by the landslide hazard. It is expressed on a scale of 0 (no
loss) to 1 (total loss). Vulnerability is probably the most difficult aspect
to assess, due to the complexity and the wide-ranging variety of landslide
processes (Glade, 2003). Following a technical/engineering approach, the
seriousness of the damage done is a function of the magnitude or intensity of
the landslide and the studied building's capacity for resistance.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Temporal evolution of risk</title>
      <p id="d1e329">The essential purpose of this work is to define a reliable, simple method that
will enable the risk's dynamics to be described. One strategy would be to
recognise if the risk taken increases or decreases at the same pace as the
construction of residential buildings. It would seem logical that this
variation of risk should be estimated not as an absolute value but in
relation to the volume of construction at a given time, ascertaining whether
there is a temporal correlation between these two variables or not.</p>
      <p id="d1e332">An ideal situation pattern can be put forward of working with a long series of
at least 40–50 years, since the beginning of the urban development boom in a
specific zone. Three main sections can be found in this series with two
different risk management types.</p>
      <p id="d1e335">Firstly, let us consider a suitable management type. In the early years of
this example situation pattern, there is disorganised construction occupying
the most profitable spaces but at the same time in not very suitable areas
from the point of view of geological risk and the impact on the environment
and the landscape. During the intermediate section, the occupation of zones at
risk begins to change pace as urban development legislation begins to appear,
along with land planning, environmental awareness, etc. The last section sees
a very clear drop in the pace of the risk's growth, as the land regulation
restrictions contemplated are directly applied. This theoretical behaviour is
shown in Fig. 1.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e341">Theoretical evolution of risk accumulated over time for a 1-year
series pattern.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021-f01.png"/>

        </fig>

      <p id="d1e350">However, a varying panorama of unsuitable or improvable risk can also be found
(Fig. 1). This type of growth in risk can arise when the pressure to build
residential housing is so great that spaces that do not have
the optimal conditions in terms of location and which until then had
maintained their natural characteristics become occupied. Building on such spaces may entail
taking greater risks because safer terrains have already been used up. Hence,
the great increase in risk in Sect. 3 (Fig. 1, “Improvable management”
line) should not be admissible in proper territorial management, and it is
thus essential to provide tools to demonstrate such anomalies as shown in this
work.</p>
      <p id="d1e353">For dynamic analysis of the data shown in Fig. 1, the two main annual data
series must be used: one based on the evolution of the residential built-up
area and the other on the risk affecting part of that built-up area. The
former is the gross floor area (GFA, in <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>), calculated every year
<inline-formula><mml:math id="M5" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> based on cadastral parcel data (CP<inline-formula><mml:math id="M6" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>) by means of Eq. (<xref ref-type="disp-formula" rid="Ch1.E3"/>):

                <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M7" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>GFA</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msub><mml:mtext>GFA</mml:mtext><mml:mrow><mml:mtext>(CP)</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          Once the value of <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:mtext>GFA</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> has been obtained, the simple moving average of order
3 for each year <inline-formula><mml:math id="M9" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula>, [<inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:mtext>MAvGFA</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>], is applied according to Eq. (<xref ref-type="disp-formula" rid="Ch1.E4"/>):

                <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M11" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtext>MAvGFA</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mtext>mean</mml:mtext><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mtext>GFA</mml:mtext><mml:mfenced close=")" open="("><mml:mrow><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          Applying the general equation of the risk (see Eq. 1) gives the risk value
(RV) in EUR for each cadastral parcel CP affected, in accordance with the
susceptibility map (Eq. <xref ref-type="disp-formula" rid="Ch1.E5"/>):

                <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M12" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mtext>RV</mml:mtext><mml:mtext>CP</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>H</mml:mi><mml:mtext>CP</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mtext>CP</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>CP</mml:mtext></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          Similarly, the simple moving average is calculated for the risk value MAvRV<inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
via Eqs. (<xref ref-type="disp-formula" rid="Ch1.E6"/>) and (<xref ref-type="disp-formula" rid="Ch1.E7"/>):

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M14" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E6"><mml:mtd><mml:mtext>6</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtext>RV</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msub><mml:mtext>RV</mml:mtext><mml:mrow><mml:mtext>(CP)</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E7"><mml:mtd><mml:mtext>7</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>MAvRV</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mtext>mean </mml:mtext><mml:mtext>RV</mml:mtext><mml:mfenced close=")" open="("><mml:mrow><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            A relationship is sought between the two series to explain the trend towards a
model of residential construction with increasing, stable or decreasing risk
with relation to the built-up area. It is proposed that the relationship
between risk and the built-up area should be used as an indicator of the
evolution of risk and the construction associated with it.</p>
      <?pagebreak page1851?><p id="d1e653">Within a specific period of time, in the two moving average series a
monotonically increasing interval can be selected that is limited by the years
[<inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>], where <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Two functions are defined for the
risk values and for the built-up area: <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mtext>RV</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mtext>GFA</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e744">It has been confirmed that the way growth in risk with time directly relates
to the pace of construction is determined by the behaviour of the quotient
between functions <inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Thus, for example, proposing two growth
ratios rRV and rGFA during the chosen period, which are approximately constant
and where rRV <inline-formula><mml:math id="M22" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> rGFA, it is easily shown that the quotient function is
growing. In the opposite case, rRV <inline-formula><mml:math id="M23" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> rGFA, the quotient function is
falling.</p>
      <p id="d1e789">The adimensional (relative) risk ratio (RR) between years <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
is defined in the following Eq. (<xref ref-type="disp-formula" rid="Ch1.E8"/>):

                <disp-formula id="Ch1.E8" content-type="numbered"><label>8</label><mml:math id="M26" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>RR</mml:mtext><mml:mo>(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mtext>RV</mml:mtext><mml:mo>(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mtext>RV</mml:mtext><mml:mo>(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mtext>GFA</mml:mtext><mml:mo>(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mtext>GFA</mml:mtext><mml:mo>(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mtext>rRV</mml:mtext><mml:mtext>rGFA</mml:mtext></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          To sum up, it is concluded that <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is a function whose growth slope is
defined by the risk ratio value (RR) for the chosen interval [<inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>]. The different options are summed up in Table 1.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e960">Characteristics of the risk ratio (RR).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="50mm"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="50mm"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">RR value</oasis:entry>
         <oasis:entry colname="col2">Type of curve</oasis:entry>
         <oasis:entry colname="col3">Characteristic</oasis:entry>
         <oasis:entry colname="col4">Discussion</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Monotonically increasing</oasis:entry>
         <oasis:entry colname="col3">Growth rate of the risk value greater than that of the built-up area.</oasis:entry>
         <oasis:entry colname="col4">Disproportionate risk growth, without restrictions or planning. <?xmltex \hack{\hfill\break}?>Unfavourable situation. <?xmltex \hack{\hfill\break}?>This must occur in Sect. 1 of Fig. 1.</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Monotonically constant</oasis:entry>
         <oasis:entry colname="col3">Growth rate of the risk value similar to that of the built-up area.</oasis:entry>
         <oasis:entry colname="col4">No well-defined evolution. <?xmltex \hack{\hfill\break}?>Situation not clearly favourable.</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Monotonically decreasing</oasis:entry>
         <oasis:entry colname="col3">Growth rate of the risk value less than that of the built-up area</oasis:entry>
         <oasis:entry colname="col4">Growth of risk restricted, which must be due to some type of criterion. <?xmltex \hack{\hfill\break}?>Favourable situation. <?xmltex \hack{\hfill\break}?>This must occur in Sect. 3 of Fig. 1.</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e1077">It is preferable to use the absolute values from the relationship between RV
and GFA in order to be able to compare their magnitudes between the different
municipalities. In addition, working with functions of accumulated values
RV<inline-formula><mml:math id="M33" display="inline"><mml:msub><mml:mi/><mml:mtext>acc</mml:mtext></mml:msub></mml:math></inline-formula> and GFA<inline-formula><mml:math id="M34" display="inline"><mml:msub><mml:mi/><mml:mtext>acc</mml:mtext></mml:msub></mml:math></inline-formula>, it is ensured that the two base
curves are monotonically increasing for the entire period being studied. It is
easily demonstrated that the quotient function of the accumulated series
RV<inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>acc</mml:mtext></mml:msub><mml:mo>/</mml:mo></mml:mrow></mml:math></inline-formula>GFAa<inline-formula><mml:math id="M36" display="inline"><mml:msub><mml:mi/><mml:mtext>acc</mml:mtext></mml:msub></mml:math></inline-formula> also meets the characteristics
determined for the RR value in Table 1.</p>
      <p id="d1e1119">These annual values can be transferred to a graph showing the resulting curve
in order to analyse its ascending or descending trend (Fig. 2).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e1124">Curve trend of different types of risk ratio.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021-f02.png"/>

        </fig>

      <p id="d1e1133">Equation (9) shows the calculation of the accumulated RR values for each year:

                <disp-formula id="Ch1.E9" content-type="numbered"><label>9</label><mml:math id="M37" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>RR</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mtext>RV</mml:mtext><mml:mtext>acc</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mtext>GFA</mml:mtext><mml:mtext>acc</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:mi>y</mml:mi></mml:msubsup><mml:mtext>RV</mml:mtext><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:mi>y</mml:mi></mml:msubsup><mml:mtext>GFA</mml:mtext><mml:mi>i</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          This equation is applied for the entire time series available, always starting
from an original year <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e1226">In these quotient functions, a simple deterministic trend is going to be
assumed. Two specific indicators can be extracted from these functions. The
first of these would be to calculate the trend of the curve <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:mtext>RR</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> simply by
means of Eq. (<xref ref-type="disp-formula" rid="Ch1.E10"/>), which gives the slope of the straight line <inline-formula><mml:math id="M40" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> that
joins the two points of the curve <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:mtext>RR</mml:mtext><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> between moments <inline-formula><mml:math id="M42" display="inline"><mml:mi>s</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M43" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula> with
periods of <inline-formula><mml:math id="M44" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> years.

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M45" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtext>mRR</mml:mtext><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:mrow><mml:mtext>mean</mml:mtext><mml:mo>(</mml:mo><mml:mtext>RRt</mml:mtext><mml:mi mathvariant="normal">…</mml:mi><mml:mtext>RRt</mml:mtext><mml:mo>+</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mtext>mean</mml:mtext><mml:mo>(</mml:mo><mml:mtext>RRs</mml:mtext><mml:mi mathvariant="normal">…</mml:mi><mml:mtext>RRs</mml:mtext><mml:mo>+</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>-</mml:mo><mml:mi>s</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E10"><mml:mtd><mml:mtext>10</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mo>∀</mml:mo><mml:mi>t</mml:mi><mml:mo>&gt;</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            These reference points should be located in the temporal series at the moments
prior to and after decisive changes in land management policy. It can also be
used at the start of the series in order to learn the behaviour of risk in the
early years of residential expansion.</p>
      <p id="d1e1392">Within the analysis of the temporal series of risk, it is worth noting that it
may also be important to study the synchronisation of their peaks to explain
certain types of behaviour. Firstly, this may be done among the different
geographically neighbouring local entities. For example, a specific type of
municipal management would stand out if big differences are found with the
neighbouring entity, especially if their geomorphological characteristics are
very similar. To do so, three causes can be put forward to explain an external
temporal correlation among neighbours, which fit with the hypotheses put
forward in Sect. 2.1:
<list list-type="order"><list-item>
      <p id="d1e1397">With a total lack of synchronisation and without demonstrating behavioural
patterns, the cause must occur randomly as a result of not very notable
effects that cannot be analysed globally.</p></list-item><list-item>
      <p id="d1e1401">With synchronisation among neighbouring entities, the cause must be due to
geomorphological characteristics of the terrain, since they are
autocorrelated by geographic proximity.</p></list-item><list-item>
      <p id="d1e1405">With differing synchronisation in nearby areas but with certain patterns of
behaviour in wider areas, the cause must be sought in the different ways of
managing the land.</p></list-item></list>
Secondly, the internal synchronisation of construction peaks with the risk
peaks for the same local entity should coincide in time under theoretical
conditions. However, another two situations may also occur, which show that
the construction and risk assumed are not necessarily governed by logic.
Their possible reasons could be the
<list list-type="order"><list-item>
      <p id="d1e1411">risk peak brought forward – buildings with a greater level of risk may be of
greater commercial interest (e.g. due to dominant locations with the best
views) and are thus built sooner;</p></list-item><list-item>
      <p id="d1e1415">risk peak delayed – suitable parcels begin to become scarce after a period of
intense building activity, so that the last buildings are in a worse
location and thus a greater risk is assumed.</p></list-item></list>
A global view of the process is necessary, together with a complete study of
the temporal series. It is usually preferable to summarise it in specific
indicators that directly reflect the situation of the comprehensive temporal
series for each of the urban administrative divisions (UADs, municipality
equivalent) into which the study area is divided.</p>
      <p id="d1e1419">These indicators enable direct comparisons to be made and analogies and
differences to be seen more easily between different UADs. To do so, variables that are not affected by the area of the UADs analysed should be used. One
solution is to calculate specific variables distributed homogeneously over the
land's area.</p>
      <p id="d1e1422">The most relevant factor is without a doubt the RR, derived from the quotient
function RR(y), calculated as a summary of the complete series in
Eq. (<xref ref-type="disp-formula" rid="Ch1.E11"/>):

                <disp-formula id="Ch1.E11" content-type="numbered"><label>11</label><mml:math id="M46" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>RRt</mml:mtext><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>∑</mml:mo><mml:mtext>RV</mml:mtext><mml:mo>(</mml:mo><mml:mtext>EUR</mml:mtext><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>∑</mml:mo><mml:mtext>GFA</mml:mtext><mml:mo>(</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>×</mml:mo><mml:mn mathvariant="normal">1000</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi><mml:mtext>GFA</mml:mtext></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi><mml:mtext>RV</mml:mtext></mml:mrow></mml:math></inline-formula> are total values for the complete period
per UAD.</p>
      <p id="d1e1493">The risk ratio defined in Eq. (<xref ref-type="disp-formula" rid="Ch1.E11"/>) allows us to know how much risk has
been assumed throughout the period under study and to be able to relate it to
the other territorial units by specifying if it is greater or lesser than the
average for the zone of work. It is thus possible to highlight the units that
are assuming an excessive risk.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e1502">Global indicators per UAD.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="70mm"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="40mm"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="50mm"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Name</oasis:entry>
         <oasis:entry colname="col2">Formula</oasis:entry>
         <oasis:entry colname="col3">Notes</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Total risk ratio, RRt (EUR per 1000 <inline-formula><mml:math id="M52" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of GFA)</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:mtext>RRt</mml:mtext><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Σ</mml:mi><mml:mtext>RV</mml:mtext><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Σ</mml:mi><mml:mtext>GFA</mml:mtext><mml:mo>×</mml:mo><mml:mn mathvariant="normal">1000</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">Already described in the text (Eq. 11).</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mean RR, RRm (EUR per 1000 <inline-formula><mml:math id="M54" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of GFA)</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:mtext>RRm</mml:mtext><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Σ</mml:mi><mml:mtext>RR</mml:mtext><mml:mo>/</mml:mo><mml:mtext>ny</mml:mtext></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">Less useful as it is an average of averages.</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mean no. of floors per CP, NFm</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:mtext>NFm</mml:mtext><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>(</mml:mo><mml:mtext>GFA</mml:mtext><mml:mo>/</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>CP</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>ny</mml:mtext></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">Interesting to know the type of buildings in the UAD.</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mean no. of floors in CP affected by risk, NFmr</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:mtext>NFmr</mml:mtext><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>(</mml:mo><mml:mtext>GFAr</mml:mtext><mml:mo>/</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>CP</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>ny</mml:mtext></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">Interesting to know the type of buildings affected in the UAD.</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mean distance from the CP to the UAD's historical centre in a straight line, Dhc (m)</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:mtext>Dhc</mml:mtext><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Σ</mml:mi><mml:mtext>Dhc</mml:mtext><mml:mo>(</mml:mo><mml:mtext>CP</mml:mtext><mml:mi>i</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>nCP</mml:mtext></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">Quantifies the importance of the residential expansion.</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mean distance from CP to the coast in a straight line, Dc (m)</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:mtext>Dc</mml:mtext><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Σ</mml:mi><mml:mtext>Dc</mml:mtext><mml:mo>(</mml:mo><mml:mtext>CP</mml:mtext><mml:mi>i</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>nCP</mml:mtext></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">Establishes the proximity of the UAD to the sea.</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Average slope of the UAD, SLm (<inline-formula><mml:math id="M60" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:mtext>SLm</mml:mtext><mml:mo>=</mml:mo><mml:mtext>mean Slope cells</mml:mtext></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M63" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>)  (GIS calculated)</oasis:entry>
         <oasis:entry colname="col3">Indicates the type of profile (mountainous, flat, etc.).</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Built-up area per unit of surface area, SpGFA (<inline-formula><mml:math id="M64" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of GFA per <inline-formula><mml:math id="M65" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of UAD)</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:mtext>SpGFA</mml:mtext><mml:mo>=</mml:mo><mml:mtext>GFA</mml:mtext><mml:mo>/</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>UAD</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">Rate or intensity of residential construction for the total of the UAD.</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Risk per unit of surface area, SpRV (<inline-formula><mml:math id="M67" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">EUR</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> of UAD)</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:mtext>SpRV</mml:mtext><mml:mo>=</mml:mo><mml:mtext>RV</mml:mtext><mml:mo>/</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>UAD</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">Rate or intensity of risk (specific risk) for the total of the UAD.</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Slope of the straight trend line, mRR (<inline-formula><mml:math id="M69" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">See Eq. (<xref ref-type="disp-formula" rid="Ch1.E10"/>)</oasis:entry>
         <oasis:entry colname="col3">Determines the trend of the RR value in a specific period.</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e1505">CP: cadastral parcel; <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>CP</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>: surface area of the CP (GIS calculated);
nCP: number of CPs; ny: number of years in the series; <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>UAD</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> urban
administrative division surface area (<inline-formula><mml:math id="M51" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>).</p></table-wrap-foot></table-wrap>

      <p id="d1e1999">A summary of other indicators that can be calculated for each UAD is shown in
Table 2.</p>
</sec>
</sec>
<?pagebreak page1852?><sec id="Ch1.S3">
  <label>3</label><title>Case study: La Marina</title>
      <p id="d1e2011">The work by Cantarino et al. (2014) emphasises that Alicante was the province
most affected by landslide risk value on<?pagebreak page1853?> residential buildings in the Valencia
Community region (Spain), with more than EUR 1 million in 2005 and 2009
each. This is chiefly due to the coastal zones in the north-west of the
province (La Marina administrative division) with a high demand for housing,
which is an area susceptible to higher landslide risks.</p>
      <p id="d1e2014">Thus, the area selected for this study is located in this area of Alicante
(south-eastern Spain) bordering the Mediterranean Sea (Fig. 3). The area
includes 50 municipalities, covers 1335 <inline-formula><mml:math id="M70" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> and has a population of
201 442 inhabitants according to the 2011 census (Spanish National Institute
of Statistics, INE). This population has seen a notable increase since the
1990s (over 50 <inline-formula><mml:math id="M71" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>) basically due to tourist activity, though today
it has fallen to 171 826 inhabitants in the last census (INE, 2018) as a
result of the economic crisis. It is a populated mountainous environment
rising from sea level to around 1500 <inline-formula><mml:math id="M72" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>. Its profile is shaped by its
proximity to the sea, with a river system that deeply dissects the territory.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e2046">La Marina area. Location of some municipalities mentioned in the
text.</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021-f03.png"/>

      </fig>

      <p id="d1e2056">La Marina is located in the province of Alicante, which is the Valencia
Community region's province with the highest landslide rate per unit of
surface area (Hervás, 2017). Its extensive mountainous orography reaches
the coastal strip itself, which is not free from risk. This situation is
aggravated by being highly attractive for tourism and its residential
occupation.</p>
      <p id="d1e2059">This territory is typical of urban expansion around the Mediterranean basin,
which is becoming increasingly intensive and no longer necessarily fostered or
supported by the main coastal cities (EEA, 2006). It is an example of the
so-called “rural sprawl” generated by second homes for the local population
(in some cases first homes too) and of “residential tourism” for people
from northern Europe, who spend long periods on the Mediterranean
coast. Although initially there was a move towards recovery and restoration of
traditional rural constructions, strong demand has led to a proliferation of
new-build housing units (Pardo-García and Mérida-Rodríguez,
2018).</p>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Data used</title>
<sec id="Ch1.S3.SS1.SSSx1" specific-use="unnumbered">
  <title>Basic mapping</title>
      <p id="d1e2074">The official maps from the Spanish National Geographic Institute (IGN) provided the
borders and areas for the municipal territories to calculate the UADs. They
also gave the <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M74" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> DEM (digital elevation model) to calculate
the mean slope of each municipality.</p>
</sec>
<sec id="Ch1.S3.SS1.SSSx2" specific-use="unnumbered">
  <title>Landslide database</title>
      <p id="d1e2103">The national Spanish database for landslides BD-MOVES from the Geological and Mining Institute of Spain (IGME) was used, which follows the INSPIRE
regulations (Infrastructure for Spatial Information in the European
Community). BD-MOVES, created in 2014, is made up of two blocks or sets of
georeferenced spatial information: one referring to the description of the
intrinsic, relatively invariable characteristics of landslides, and another
referring to different<?pagebreak page1854?> activity events that led to said landslides, including
morphometrics, triggering factors, damage and other data.</p>
      <p id="d1e2106">The other source of data is the landslide map to <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">50</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">000</mml:mn></mml:mrow></mml:math></inline-formula>-scale in vector
format drawn up by the Valencia government's Regional Department of Public
Works in the project entitled “Lithology, exploitation of industrial rocks
and landslide risk in the Valencia Community” (COPUT, 1998). This map uses
geological and geotechnical data from the IGME, <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">50</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mn mathvariant="normal">000</mml:mn></mml:mrow></mml:math></inline-formula>-scale topographical
maps and aerial photographs available at that time.</p>
</sec>
<sec id="Ch1.S3.SS1.SSSx3" specific-use="unnumbered">
  <title>Cadastral parcels</title>
      <p id="d1e2145">The information referring to cadastral plots or parcels was obtained from the
cadastral mapping available from the DGC according to European INSPIRE
guidelines. This cadastral information is provided by interoperable services
(WMS and WFS) and can be downloaded in three datasets: cadastral parcels,
buildings and addresses. For this study, the former has been chosen because it
contains the main item defining the building. Within this item, we can find
the data necessary for each parcel: built-up area (GFA), year of construction
and type of usage. Only functional and residential parcels have been used for
the series 1960–2017.</p><?xmltex \hack{\newpage}?>
</sec>
<sec id="Ch1.S3.SS1.SSSx4" specific-use="unnumbered">
  <title>Classes of susceptibility to landslides</title>
      <p id="d1e2155">To calculate the level of hazard, the starting point was the landslide
susceptibility map (LSM) drawn up in a previous study (Cantarino et al.,
2019). Its characteristics are pixels of <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:mn mathvariant="normal">25</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M78" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> as the unit
of surface area and the spatial-multicriteria method (SCME) to weight the
factors for obtaining the susceptibility values. The three significant factors
used were slope gradient, lithology and land cover.</p>
      <p id="d1e2178">Specifically, the thresholds of susceptibility classes defined by Cantarino et
al. were used. These thresholds were obtained by means of objective,
meticulous classification based on a ROC (receiver operating
characteristic) analysis, which uses the intrinsic variability of the data and is one
of the first applications of this type of map. For this study, the spatial
probability for each class has been determined by comparing these susceptible
areas with the ones indicated in the inventory. This information, together
with the temporal probability, has enabled the hazard and finally the risk to
be calculated.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e2184">Land susceptibility index (LSI) values for the classes under
consideration</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Class</oasis:entry>
         <oasis:entry colname="col2">Level</oasis:entry>
         <oasis:entry colname="col3">LSI interval</oasis:entry>
         <oasis:entry colname="col4">No. of pixels</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1</oasis:entry>
         <oasis:entry colname="col2">Very low</oasis:entry>
         <oasis:entry colname="col3">10–35</oasis:entry>
         <oasis:entry colname="col4">526 777</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2</oasis:entry>
         <oasis:entry colname="col2">Low</oasis:entry>
         <oasis:entry colname="col3">35–60</oasis:entry>
         <oasis:entry colname="col4">359 376</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3</oasis:entry>
         <oasis:entry colname="col2">Medium</oasis:entry>
         <oasis:entry colname="col3">60–95</oasis:entry>
         <oasis:entry colname="col4">692 863</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4</oasis:entry>
         <oasis:entry colname="col2">High</oasis:entry>
         <oasis:entry colname="col3">95–149</oasis:entry>
         <oasis:entry colname="col4">350 051</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">5</oasis:entry>
         <oasis:entry colname="col2">Very high</oasis:entry>
         <oasis:entry colname="col3">149–340</oasis:entry>
         <oasis:entry colname="col4">201 170</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TOTAL</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">2 130 237</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e2187">Source: Cantarino et al. (2019)</p></table-wrap-foot></table-wrap>

      <p id="d1e2314">Table 3 shows the susceptibility levels established via the susceptibility
indices (LSIs) that define them, together with the number of pixels affected.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e2320">La Marina area. Susceptibility, landslides location and areas with
instabilities.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021-f04.png"/>

          </fig>

      <p id="d1e2329">Figure 4 with some data used is attached, indicating the three highest
levels of susceptibility, together with the location of landslides according
to the Spanish Geological Survey (BD-MOVES) and the areas with instabilities
according to the Valencia regional government (COPUT).</p><?xmltex \hack{\newpage}?>
</sec>
</sec>
<?pagebreak page1855?><sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Implementation of the method</title>
      <p id="d1e2342">Figure 5 shows the flow chart indicating the method followed, which is
explained in the above sections. It involves analysing the evolution over
time of the residential parcel areas and landslide risks assumed in the
urban expansion period in the La Marina area of Alicante province, from 1960
to 2017. Within this interval, a period of intense construction activity can
be seen between 2000 and 2008, followed by a period of slowdown caused by
the general economic crisis that occurred at the end of the decade of 2000
and which has not yet clearly ended.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e2347">Flow chart of the work procedure.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021-f05.png"/>

        </fig>

      <p id="d1e2356">Following the method described, firstly the cadastral parcels with their
built-up gross floor area (GFA) were analysed, and then it was seen how the
latter evolved over time together with the surface area affected by
landslide risk. The final calculation used 1-year periods to summarise the
values dealt with individually for each parcel and as a moving average, MAv
of order 3, according to Eqs. (<xref ref-type="disp-formula" rid="Ch1.E4"/>) and (<xref ref-type="disp-formula" rid="Ch1.E7"/>).</p>
      <p id="d1e2364">The process followed for risk evaluation was based on locating the peak
value of the three high susceptibility levels (between class 3 and class 5; see
Table 3) for each cadastral parcel, affected by a buffer of 20 <inline-formula><mml:math id="M79" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> around it.
All cadastral parcels of an area of less than 10 <inline-formula><mml:math id="M80" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> were eliminated
beforehand. The risk per parcel was then calculated, based on its maximum
LSI value.</p>
      <p id="d1e2386">As previously mentioned, possible changes in some of the factors involved in calculating
the risk (such as those due to climate change) are not taken into account. The
variation in real risk that may arise due to these changes is considered to be
of little significance and therefore does not affect the final results.</p>
      <p id="d1e2389">By applying the equation to calculate the risk value (RV) shown in
Eq. (<xref ref-type="disp-formula" rid="Ch1.E5"/>) for each cadastral parcel, it is possible to calculate the
risk in monetary units (EUR) at the 2018 value. The year of construction is
not considered, since in general the value is for the cost of reconstruction
at the current value if affected by a landslide.</p>
<sec id="Ch1.S3.SS2.SSSx1" specific-use="unnumbered">
  <title>Hazard</title>
      <p id="d1e2399">For the temporal probability in Eq. (<xref ref-type="disp-formula" rid="Ch1.E2"/>) (see Fell et al., 2008), one
has to turn to databases such as BD-MOVES from the IGME, which indicates the
landslides and the date. For the spatial probability, work has been done with
the COPUT's risk mapping for the zone under study.</p>
      <p id="d1e2404">In BD-MOVES, 13 landslides over the last 20 years are listed, though 5 of them
are small slips. Summarising, it is<?pagebreak page1856?> possible to estimate 8 landslides for this
period, with an annual probability <inline-formula><mml:math id="M81" display="inline"><mml:mrow class="unit"><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Pa</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula>. This annual
probability should be adjusted downwards by an adjustment factor of
<inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mtext>aj</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, but this value has been maintained since the inventory is not
complete and the landslides that have not been included should be accounted
for (Lee, 2009).  Said probability was calculated in Eq. (<xref ref-type="disp-formula" rid="Ch1.E12"/>).

                  <disp-formula id="Ch1.E12" content-type="numbered"><label>12</label><mml:math id="M84" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtext>Pa</mml:mtext><mml:mo>=</mml:mo><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mtext>number of recorded events</mml:mtext><mml:mtext>number
of years in the record</mml:mtext></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>×</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mtext>aj</mml:mtext></mml:msub></mml:mrow></mml:math></disp-formula>

            To calculate the spatial probability Ps, landslides that appear
in COPUT's aforementioned map (1998) were selected, describing their limits and
cross-referencing this information with susceptibility levels 3, 4 and 5 of
the map listed in Table 3. The results are shown in Table 4.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T4" specific-use="star"><?xmltex \currentcnt{4}?><label>Table 4</label><caption><p id="d1e2473">Probability of occurrence and associated hazard by susceptibility
level.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Class</oasis:entry>
         <oasis:entry colname="col2">Level</oasis:entry>
         <oasis:entry colname="col3">Level surface</oasis:entry>
         <oasis:entry colname="col4">Risk surface</oasis:entry>
         <oasis:entry colname="col5">Spatial probability</oasis:entry>
         <oasis:entry colname="col6">Temporal probability</oasis:entry>
         <oasis:entry colname="col7">Hazard</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(L)</oasis:entry>
         <oasis:entry colname="col3">area (<inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, ha)</oasis:entry>
         <oasis:entry colname="col4">area (<inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>RL</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, ha)</oasis:entry>
         <oasis:entry colname="col5">(Ps)</oasis:entry>
         <oasis:entry colname="col6">(Pa)</oasis:entry>
         <oasis:entry colname="col7">(<inline-formula><mml:math id="M87" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1</oasis:entry>
         <oasis:entry colname="col2">Very low</oasis:entry>
         <oasis:entry colname="col3">32 923.6</oasis:entry>
         <oasis:entry colname="col4">0</oasis:entry>
         <oasis:entry colname="col5">0</oasis:entry>
         <oasis:entry colname="col6">–</oasis:entry>
         <oasis:entry colname="col7">0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2</oasis:entry>
         <oasis:entry colname="col2">Low</oasis:entry>
         <oasis:entry colname="col3">22 461.0</oasis:entry>
         <oasis:entry colname="col4">0</oasis:entry>
         <oasis:entry colname="col5">0</oasis:entry>
         <oasis:entry colname="col6">–</oasis:entry>
         <oasis:entry colname="col7">0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3</oasis:entry>
         <oasis:entry colname="col2">Medium</oasis:entry>
         <oasis:entry colname="col3">43 303.9</oasis:entry>
         <oasis:entry colname="col4">25 529</oasis:entry>
         <oasis:entry colname="col5">0.0005895</oasis:entry>
         <oasis:entry colname="col6">0.4</oasis:entry>
         <oasis:entry colname="col7">0.00024</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4</oasis:entry>
         <oasis:entry colname="col2">High</oasis:entry>
         <oasis:entry colname="col3">21 878.2</oasis:entry>
         <oasis:entry colname="col4">233 675</oasis:entry>
         <oasis:entry colname="col5">0.0106807</oasis:entry>
         <oasis:entry colname="col6">0.4</oasis:entry>
         <oasis:entry colname="col7">0.00427</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">5</oasis:entry>
         <oasis:entry colname="col2">Very high</oasis:entry>
         <oasis:entry colname="col3">12 573.1</oasis:entry>
         <oasis:entry colname="col4">406 913</oasis:entry>
         <oasis:entry colname="col5">0.0323637</oasis:entry>
         <oasis:entry colname="col6">0.4</oasis:entry>
         <oasis:entry colname="col7">0.01295</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Total</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">133 139.8</oasis:entry>
         <oasis:entry colname="col4">666 120</oasis:entry>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e2727">Classes 1 and 2 of the susceptibility map (LSM) are not taken into account
because they do not show a probability of being affected by risk of
landslide. Thus, for each level L of the LSM shown in Table 4, the value of
hazard level is obtained using Eq. (<xref ref-type="disp-formula" rid="Ch1.E13"/>).

                  <disp-formula id="Ch1.E13" content-type="numbered"><label>13</label><mml:math id="M88" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>H</mml:mi><mml:mtext>CP</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mtext>LSImax</mml:mtext><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>RL</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>×</mml:mo><mml:mtext>Pa</mml:mtext><mml:mo>=</mml:mo><mml:mtext>Ps</mml:mtext><mml:mo>×</mml:mo><mml:mtext>Pa</mml:mtext><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

            where <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the total surface area of level L, and
<inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>RL</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the surface area of level L affected by risk of landslides.</p>
</sec>
<sec id="Ch1.S3.SS2.SSSx2" specific-use="unnumbered">
  <title>Exposure</title>
      <p id="d1e2814">Only residential housing, which is generally terraced or detached, is to be
considered as affected elements. Buildings or high-rise residential blocks are
not built in the areas dealt with (with the notable exception of the
municipality of Benidorm) but in areas that are generally flat and/or near
the coast. The mean number of floors confirms this matter (see NFm in
Table 2).</p>
      <p id="d1e2817">The value of these elements only takes into account the gross floor (built-up)
area and not the value of land that is not affected by landslides.  Taking into
account only the cost of constructing the building to calculate the building
execution unit cost, the tables of the Institut Valencià de
l'Edificació are used (IVE; see <uri>https://www.five.es/productos/herramientas-on-line/modulo-de-edificacion/</uri>, last access: 20 May 2021). To do so, the definition of basic
building module (BBM; EUR/built-up <inline-formula><mml:math id="M91" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) is used, which represents the
material cost of implementation per built-up square metre of the reference
building, implemented under conventional worksite conditions and
circumstances.</p>
      <p id="d1e2834">The BBM for December 2018 for single-family detached houses of fewer than three
floors with an inhabitable surface area of over 70 <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> and with high-quality finishings and fittings is EUR 829 <inline-formula><mml:math id="M93" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. This value remained practically constant
throughout 2018, and even as of 2008 it has been above
EUR 800 <inline-formula><mml:math id="M94" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Open-plan buildings of three floors or more, up to 80
homes, and an inhabitable surface area of between 45 and 70 <inline-formula><mml:math id="M95" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> are
valued at EUR 780 <inline-formula><mml:math id="M96" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. To a large extent, the homes affected are
of the single-family type, so the value of reconstruction has been taken to be
constant at EUR 800 <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</p>
      <?pagebreak page1857?><p id="d1e2916">The value for reconstructing each cadastral parcel is calculated according to
Eq. (<xref ref-type="disp-formula" rid="Ch1.E14"/>), without taking into account the value of the land.

                  <disp-formula id="Ch1.E14" content-type="numbered"><label>14</label><mml:math id="M98" display="block"><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi>E</mml:mi><mml:mtext>CP</mml:mtext></mml:msub><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mo>(</mml:mo><mml:mtext>EUR</mml:mtext><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mtext>GFA</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>(</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mtext>BBM</mml:mtext><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>(</mml:mo><mml:mrow class="unit"><mml:mi mathvariant="normal">EUR</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="Ch1.S3.SS2.SSSx3" specific-use="unnumbered">
  <title>Vulnerability</title>
      <p id="d1e2983">In order to determine landslide magnitude (LM) in a geographical area, it is
crucial to create a landslide inventory to know the main landslide types,
landslide morphometric parameters, landslide velocity and observed damage.
These data are not provided by the available landslide databases such as BD-MOVES
and COPUT.</p>
      <p id="d1e2986">In the La Marina area, the predominant failure mechanism for shallow slides is
along the existing dip planes of the Cretaceous limestone geological
formations. According to Fell (1994), these landslides are defined as small
landslides. The shallow slides occurring in the study area are rapid
landslides, according to the velocity scale proposed by Cruden and Varnes
(1996), with a typical velocity ranging from
1.8 <inline-formula><mml:math id="M99" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">h</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> to
3 <inline-formula><mml:math id="M100" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">min</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. In La Marina, damage or loss caused by past landslides
is poorly documented and this is a major constraint in drawing up
vulnerability curves. However, field observations have shown that shallow
slides that have occurred in the study area did not have enough energy to
completely destroy a building. Typical damage produced by shallow slides in
the study area is shown by cracks opening up in the buildings' walls. This
type of damage caused by landslides in buildings is classified by Leone (1996)
at level III (from I to V), which corresponds to a structural damage of
0.4–0.6 on a scale ranging from 0 to 1. Taking into account the previous
example and the fact that shallow slide characteristics in the study zone do
not vary too much in terms of affected area, depth of the slip surface,
velocity, volume and typical damage, we assumed a single fixed value for LM (in
accordance with the level of susceptibility). Therefore, the LM was assumed to
be 0.6 for the area of study on a heuristic scale ranging from 0 to 1 (Silva
and Pereira, 2014) (see Table 5).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T5"><?xmltex \currentcnt{5}?><label>Table 5</label><caption><p id="d1e3026">Vulnerability related to the number of floors.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Number of</oasis:entry>
         <oasis:entry colname="col2">Landslide</oasis:entry>
         <oasis:entry colname="col3">Building</oasis:entry>
         <oasis:entry colname="col4">Final</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">floors</oasis:entry>
         <oasis:entry colname="col2">magnitude</oasis:entry>
         <oasis:entry colname="col3">resistance</oasis:entry>
         <oasis:entry colname="col4">vulnerability</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">(NF)</oasis:entry>
         <oasis:entry colname="col2">(LM)</oasis:entry>
         <oasis:entry colname="col3">(BR)</oasis:entry>
         <oasis:entry colname="col4">(FV)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.6</oasis:entry>
         <oasis:entry colname="col3">30 <inline-formula><mml:math id="M102" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.42</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">8–4</oasis:entry>
         <oasis:entry colname="col2">0.6</oasis:entry>
         <oasis:entry colname="col3">20 <inline-formula><mml:math id="M103" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.48</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4–2</oasis:entry>
         <oasis:entry colname="col2">0.6</oasis:entry>
         <oasis:entry colname="col3">10 <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.54</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.6</oasis:entry>
         <oasis:entry colname="col3">0 <inline-formula><mml:math id="M106" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">0.6</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e3198">The other factor to evaluate the final vulnerability, FV, is to estimate the
considered residential buildings' resistance (BR) taking into account the
type, materials, age and height of the building (Kappes et al., 2012). Within
the zone under study, the construction techniques, materials used (mainly
concrete), and structure are quite similar and are considered to be
sufficiently resistant with a generally good state of conservation seen in the
buildings. The biggest difference one can find is in the mean number of floors
for each building, though the type of home affected has a low number on
average (see NFm in Table 2) with not very significant variations.</p>
      <p id="d1e3202">Papathoma-Köhle et al. (2017) identify a list of indicators for one
particular kind of landslide (debris flow) physical vulnerability assessment
of buildings. One of them, the height of the building, directly influences the
degree of loss. In accordance with Papathoma-Köhle et al., the higher the
building, the fewer the expected losses, so a greater BR is considered in
these cases (Table 5).</p>
      <p id="d1e3205">Equation (<xref ref-type="disp-formula" rid="Ch1.E15"/>) enables the final vulnerability FV to be calculated, in
which the BR depends solely on the number of floors NF, and Table 5 gives the
values obtained by applying it.

                  <disp-formula id="Ch1.E15" content-type="numbered"><label>15</label><mml:math id="M107" display="block"><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext>FV</mml:mtext><mml:mo>=</mml:mo><mml:mtext>LM</mml:mtext><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mtext>BR</mml:mtext><mml:mtext>NF</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="Ch1.S3.SS2.SSSx4" specific-use="unnumbered">
  <title>Risk</title>
      <p id="d1e3245">The final calculation of risk for each cadastral parcel is the result of
applying Eq. (<xref ref-type="disp-formula" rid="Ch1.E3"/>). Thus, in accordance with the equations shown above,
the final expression for the calculation of the risk value for each CP is

                  <disp-formula specific-use="align" content-type="numbered"><mml:math id="M108" display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mtext>RV</mml:mtext><mml:mtext>CP</mml:mtext></mml:msub><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mo>(</mml:mo><mml:mtext>EUR</mml:mtext><mml:mo>)</mml:mo><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mfenced close=")" open="("><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>RL</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>×</mml:mo><mml:mtext>Pa</mml:mtext></mml:mrow></mml:mfenced><mml:mo>×</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mtext>GFA</mml:mtext><mml:mo>×</mml:mo><mml:mtext>BBM</mml:mtext></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E16"><mml:mtd><mml:mtext>16</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mo>×</mml:mo><mml:mfenced close="]" open="["><mml:mrow><mml:mtext>LM</mml:mtext><mml:mo>×</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mtext>BR</mml:mtext><mml:mtext>NF</mml:mtext></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

             <?pagebreak page1858?> As a final reflection on the application of this or any other method for
calculating risk, it should be noted that there is some difficulty in
obtaining precise results due to the lack of official data and specific,
up-to-date studies in the sphere being studied. Some of these procedures are
based on data that are not very exact and even on subjective evaluations,
which means some error must be assumed in the results obtained, though this
does not invalidate the objectives or the validity of the index originally
proposed in our study. For this reason, the global calculation of
Eq. (<xref ref-type="disp-formula" rid="Ch1.E16"/>) has been carried out using the main factors without including
ones considered to be less relevant.</p>
</sec>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Risk curve and trend</title>
      <p id="d1e3350">The year the temporal series begin is determined in Spain and in the Valencia
Community region as 1960, which marked the start of tourism expansion on the
Mediterranean coast. The year approximately coincides with when the Act on Centres and Zones of National Tourist Interest (Ley 197/1963 sobre Centros y Zonas de Interés Turístico Nacional) was passed (year 1963),
which notably fostered residential construction in coastal areas without
taking into account geological risks.</p>
      <p id="d1e3353">As has been mentioned, to study the evolution of risk, the proposal is to use
a complete analysis of the temporal series of the risk ratio value (RR) as the
basis. Indeed, the shape of the RR<inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> curve, as well as the behaviour of the
two annual series of GFA<inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and RV<inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, enables the characteristics of the
evolution of risk to be established for the entire period.</p>
      <p id="d1e3392">When the RR(<inline-formula><mml:math id="M112" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula>) has been calculated, its three singular points are extracted to
define the straight lines and calculate their slope via Eq. (<xref ref-type="disp-formula" rid="Ch1.E10"/>).
Specifically, the mean points of the curve were used for the two different
periods that include the decades 1960–1969, 1980–1989 and 2000–2009 for a
time interval of 20 years. The slopes calculated have been called <italic>mRR Lo</italic> for the lower (earlier) period (1960s and 1980s) and <italic>mRR Hi</italic> for the
higher (later) period (1980s and 2000s).</p>
      <p id="d1e3410">The first period analysed explains the historical evolution, marking the
beginning of the trend, which is why the mean points have been selected from
the 1960s and 1980s. For the second period, the decades of the 1980s and 2000s
were used. This period acts as a reference for the substantial change in land
policy, which should have brought about a clear change in trend.  Indeed, it
was in the 1990s that the first official study on the risk of landslides
appeared (COPUT, 1998). Such work continued with legislative activity that
fostered the prevention of natural or induced risk.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Results</title>
      <p id="d1e3422">The values of these indicators calculated for the 50 municipalities that make
up La Marina are shown in Table 6, accompanied by their interval of
variation. A series of annual values were calculated for the 50 municipalities
of La Marina area as a whole. The total values for the built-up area (GFA) and
risk (RV) are shown in Table 6. The mean values are listed in the same table,
as well as their interval of variation of the global indicators in the
previous Table 2.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T6" specific-use="star"><?xmltex \currentcnt{6}?><label>Table 6</label><caption><p id="d1e3428">Total values and global indicators per municipality. For
indicators, means and variation intervals.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Name</oasis:entry>
         <oasis:entry colname="col2">Value</oasis:entry>
         <oasis:entry colname="col3">Name</oasis:entry>
         <oasis:entry colname="col4">Value</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Total GFA (<inline-formula><mml:math id="M113" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">41 642 352</oasis:entry>
         <oasis:entry colname="col3">Total risk value, RV (EUR)</oasis:entry>
         <oasis:entry colname="col4">5 013 178</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Total risk ratio, RRt</oasis:entry>
         <oasis:entry colname="col2">192.5 [0.21–869.3]</oasis:entry>
         <oasis:entry colname="col3">Dhc (m)</oasis:entry>
         <oasis:entry colname="col4">1490.1 [95–3954]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mean RR, RRm</oasis:entry>
         <oasis:entry colname="col2">208.5 [0.3–988]</oasis:entry>
         <oasis:entry colname="col3">Dc (m)</oasis:entry>
         <oasis:entry colname="col4">8728.1 [1047–19 466]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mean risk, RVm (EUR)</oasis:entry>
         <oasis:entry colname="col2">2154.7 [31–23 252]</oasis:entry>
         <oasis:entry colname="col3">SLm (<inline-formula><mml:math id="M114" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col4">16.23 [9.8–24.6]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">NFm</oasis:entry>
         <oasis:entry colname="col2">2.09 [1.41–5.85]</oasis:entry>
         <oasis:entry colname="col3">SpGFA (<inline-formula><mml:math id="M115" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> of UAD)</oasis:entry>
         <oasis:entry colname="col4">26 643 [470–170 659]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">NFmr</oasis:entry>
         <oasis:entry colname="col2">1.87 [1.07–5.95]</oasis:entry>
         <oasis:entry colname="col3">SpRV (<inline-formula><mml:math id="M116" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">EUR</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> of UAD)</oasis:entry>
         <oasis:entry colname="col4">3388  [11–37 412]</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">mRR Lo (<inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">41.5 [<inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:mn mathvariant="normal">83.7</mml:mn><mml:mo>∼</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">89.2</mml:mn></mml:mrow></mml:math></inline-formula>]</oasis:entry>
         <oasis:entry colname="col3">mRR Hi (<inline-formula><mml:math id="M119" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col4">16.9 [<inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:mn mathvariant="normal">86.5</mml:mn><mml:mo>∼</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">87.8</mml:mn></mml:mrow></mml:math></inline-formula>]</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e3675">The values of these indicators can be explained logically and are subsequently
used to classify the municipalities via a cluster analysis. On drawing up the
graphs, the ratios between the total values of GFA and RV from Table 6 were
used, which is approximately <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> (GFA : RV).</p>
      <p id="d1e3691">As a result of the analysis of the RR, GFA and RV graphs (see the available
research data), some interesting behaviour can be found. The comparative
graphs of GFA and RV are particularly useful. In general, a marked stability
can be seen in the final stretch of the last 10 years, possibly caused by the
slowdown in construction after the 2008 crisis. This enables us to affirm that
acquisition of residential land with low risk has not been exhausted.</p>
      <p id="d1e3694">The annual risk peak values are also seen to appear usually after the
construction peaks, or at least they are seen very clearly in municipalities
with the greatest construction activity. Recalling the possible causes for
this situation (listed in Sect. 2.3), this may be due to the fact that after
an intense construction period the last parcels to be allotted are usually in
zones of greater risk, since those of lesser risk have been allotted
first. However, in municipalities with less construction, the construction
peaks are more synchronised and even appear before the risk peaks.</p>
      <p id="d1e3697">Lastly, there is no synchronisation found between the different curves in
neighbouring municipalities.  Nevertheless, a few behavioural patterns have
been obtained in the geographic area under study. Hence, as explained in Sect. 2.3
for the so-called internal synchronisation, the most probable cause should be
sought in the differing land management and not in geomorphological or random
causes.</p>
      <p id="d1e3700">Figure 6 shows the evolution of two neighbouring coastal municipalities that
represent those with greatest residential construction with a slope close to
the average, but which have very different characteristics in assuming risk.
They are Calpe (also known as Calp) and Altea (see locations in Figs. 3 and 4) – the former with
<inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:mtext>RR</mml:mtext><mml:mo>=</mml:mo><mml:mn mathvariant="normal">79.8</mml:mn></mml:mrow></mml:math></inline-formula> and the latter with <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:mtext>RR</mml:mtext><mml:mo>=</mml:mo><mml:mn mathvariant="normal">463.3</mml:mn></mml:mrow></mml:math></inline-formula>.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e3729">Evolution of the annual series of GFA, RV and RR in the
municipalities of Calpe <bold>(a–c)</bold> and Altea <bold>(d–f)</bold>.</p></caption>
        <?xmltex \igopts{width=475.161024pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021-f06.png"/>

      </fig>

      <?pagebreak page1860?><p id="d1e3745">Calpe is a mountainous coastal municipality with a high construction rate but
a clearly low risk, with a lower risk than the average according to
Fig. 6a. In terms of cumulative value, Fig. 6b also shows the construction as
being more significant than risk, with a sharper slope for the
former. Figure 6c shows there is an early stage in the 1970s with a risk peak,
which then gradually falls. The RR indicator is very low and everything seems
to indicate suitable management over the last 20 years, taking on a
comparatively low risk. This pattern is similar to “Suitable management”
line of Fig. 1.</p>
      <p id="d1e3748">In Altea, on the other hand, a greater risk is seen to be assumed in the
second half of the series, which is above average (Fig. 6d). Moreover, Fig. 6e
shows risk more significantly than construction. Figure 6f indicates an
appropriate beginning for the RR value, but later the relative risk grows. As
the indicator value is very high, it can be concluded that this municipality's
management should clearly be revised, with a change in trend sought. In both
cases we can see risk peaks that come after their corresponding construction
peaks. This pattern is similar to “Improvable management” line of Fig. 1.</p>
      <p id="d1e3751">The possible explanation could be that the plots at greatest risk of landslide
begin to be used at a greater pace once the best plots have been occupied
following a period of intensive building activity. In other words, it is
possible that when suitable plots become scarce, the next buildings are
constructed in a worse location and thus a greater risk is taken on.</p>
      <p id="d1e3754">For the other municipalities, a similar criterion has been followed. High RR
values and a straight line with an increasing trend in the second half of the
period point to a necessary revision of the protocols in granting construction
licences, in view of the growing risk assumed. On the other hand, RR values
lower than the average coupled with a decreasing trend indicate a lowering
risk and improved land management.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e3759">Evolution of the annual series of GFA, RV and RR for the La Marina
area.</p></caption>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021-f07.png"/>

      </fig>

      <p id="d1e3769">To conclude, Fig. 7 shows the joint evolution of the whole La Marina area
(excluding Altea and Benitachell due to the bias they would introduce).
Figure 7a shows continual growth in construction and risk almost
simultaneously, indicating a clear similarity with the curve pattern shown in
Fig. 1 in the three intervals. These curves show a marked jump in the decade
of 2000, coinciding with a period of clear economic boom associated with
intense construction activity (known as the “Spanish property bubble” from
1998 to 2008). Finally, Fig. 7b shows fast growth in risk during the first part
of the period under consideration, levelling out and becoming comparable to
the growth in residential area in the second part of this period. To sum up,
no generalised drop is seen in the risk growth rate, so it is hoped that in
coming years the urban development regulations in force will end up serving
their purpose.</p>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Discussion</title>
      <p id="d1e3781">The analysis of the graphs for municipalities is very revealing in learning
the effectiveness of their management in lowering the risk of landslides.
However, it is important to observe how the municipalities studied are
organised and what type of association there may be among them. To do so, a
cluster analysis was applied in order to determine the types of groupings that
can be found in the area being studied. This type of analysis is a tool that
has widely shown its usefulness in grouping urban areas by means of indicators
(Huang et al., 2007; Stewart and Janssen, 2014; Goerlich et al., 2017).</p>
      <p id="d1e3784">The variables to be included in the cluster analysis as explanatory variables
were the indicators for each municipality in keeping with Table 6.  They are
variables for the period from 1960 until today. However, some of them were
discarded a priori. Firstly, this includes the mean number of floors NFm, as
there is little variability in this. The mean distance to the historical
centre, Dhc, is intended to be a measurement of residential expansion, but it
is excessively related to the size of municipality and the location of its
historical centre, so that it was also used little. Lastly, mRR Lo was not
considered as it is not a main variable and behaves as secondary in the
current evolution of risk.</p>
      <p id="d1e3787">Hence, the variables initially selected for the cluster analysis were mean
slope SLm, mRR Hi, SpGFA, Dc, SpRV, RRt and RRm, previously standardised.
Nevertheless, on carrying out an analysis of prior correlations to avoid
variables that do not explain variance as a whole so much, it was found that
SpGFA has a very strong linear relationship with the variables SLm, Dc, RRm
and SpRV. This means that the rate of construction increases in flat and
coastal areas, leading to less risk. Thus, it was decided to eliminate this
group of variables from the cluster analysis.</p>
      <?pagebreak page1861?><p id="d1e3790">Finally, the analysis was carried out only with the following indicators: the
rate of built-up area SpGFA (in <inline-formula><mml:math id="M124" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> of UAD), the total risk
ratio RRt (EUR per 1000 m<inline-formula><mml:math id="M125" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> of GFA) and the final section of slope of the
straight trend line mRR Hi (<inline-formula><mml:math id="M126" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>). These indicators have proven to be
sufficiently explanatory variables to be able to establish groups with
homogeneous characteristics. In this analysis, all hierarchical methods were
tested with different numbers of clusters. Ward's method and the Manhattan
distance gave the best results. Various attempts were made to find the optimum
cluster number of 10 and seeking to differentiate two municipalities with
clearly different behaviour: Calpe and Benidorm. Finally a solution was chosen
with the greatest number of clusters in order to isolate these unique cases,
with 14 in total.</p>
      <p id="d1e3832">The centroids of the 14 clusters have been organised into four sets – A, B, C
and D (from smallest to biggest in magnitude) – according to the percentile
values (90th, 60th, 30th and 0th) of the three variables chosen for the
analysis (see Table 7). These limits thus established are particularly
intended to restrict the upper values of the series
(<inline-formula><mml:math id="M127" display="inline"><mml:mo lspace="0mm">&gt;</mml:mo></mml:math></inline-formula> 60th percentile in A and B). It is thus possible to more
clearly highlight the cases that should be addressed in order to manage risks
properly. Four types of evaluation for risk building management have been
defined for the final curve section value (mRR Hi).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T7" specific-use="star"><?xmltex \currentcnt{7}?><label>Table 7</label><caption><p id="d1e3845">Centroid classification values.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry namest="col6" nameend="col7" align="center">Risk management </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Percentile</oasis:entry>
         <oasis:entry colname="col2">Level</oasis:entry>
         <oasis:entry colname="col3">Code</oasis:entry>
         <oasis:entry colname="col4">SpGFA <inline-formula><mml:math id="M128" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 1000</oasis:entry>
         <oasis:entry colname="col5">RRt</oasis:entry>
         <oasis:entry colname="col6">mRR high</oasis:entry>
         <oasis:entry colname="col7">Type</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">100th–90th</oasis:entry>
         <oasis:entry colname="col2">Very high</oasis:entry>
         <oasis:entry colname="col3">A</oasis:entry>
         <oasis:entry colname="col4">170.7–131.7</oasis:entry>
         <oasis:entry colname="col5">821–626</oasis:entry>
         <oasis:entry colname="col6">86–80</oasis:entry>
         <oasis:entry colname="col7">Very improvable</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">90th–60th</oasis:entry>
         <oasis:entry colname="col2">High</oasis:entry>
         <oasis:entry colname="col3">B</oasis:entry>
         <oasis:entry colname="col4">131.7–20.8</oasis:entry>
         <oasis:entry colname="col5">626–163</oasis:entry>
         <oasis:entry colname="col6">80–48</oasis:entry>
         <oasis:entry colname="col7">Improvable</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">60th–30th</oasis:entry>
         <oasis:entry colname="col2">Low</oasis:entry>
         <oasis:entry colname="col3">C</oasis:entry>
         <oasis:entry colname="col4">20.8–4.5</oasis:entry>
         <oasis:entry colname="col5">163–88</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">48</mml:mn></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">40</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">Reviewable</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">30th–0th</oasis:entry>
         <oasis:entry colname="col2">Very low</oasis:entry>
         <oasis:entry colname="col3">D</oasis:entry>
         <oasis:entry colname="col4">4.5–0.9</oasis:entry>
         <oasis:entry colname="col5">88–0</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">40</mml:mn></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">72</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">Suitable</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e4059">Each of these classes is defined as the result of a new grouping into four
clusters for each variable. Table 8 shows the cluster results organised by
levels and includes two indicators that provide information relevant to the
established clusters. Those two indicators are the mean slope (SLm in degrees)
and the specific risk rate (SpRV in <inline-formula><mml:math id="M133" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">EUR</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), previously defined
in Table 2. Table 9 explains each cluster's most relevant characteristics and
the municipalities within each of them; if the trend is different for the
first section, then the name of the municipality is marked at the end with an
asterisk (<inline-formula><mml:math id="M134" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>).</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T8" specific-use="star"><?xmltex \currentcnt{8}?><label>Table 8</label><caption><p id="d1e4091">Cluster centroids and their levels. Organised from A (max) to D
<inline-formula><mml:math id="M135" display="inline"><mml:mrow class="unit"><mml:mo>(</mml:mo><mml:mi mathvariant="normal">min</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> according to Table 7.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="10">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:colspec colnum="8" colname="col8" align="left" colsep="1"/>
     <oasis:colspec colnum="9" colname="col9" align="left"/>
     <oasis:colspec colnum="10" colname="col10" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col8" align="center" colsep="1">Cluster centroids </oasis:entry>
         <oasis:entry namest="col9" nameend="col10" align="center">Other indicators (mean) </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Cluster</oasis:entry>
         <oasis:entry colname="col2">SpGFA <inline-formula><mml:math id="M138" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 1000</oasis:entry>
         <oasis:entry colname="col3">Level 1</oasis:entry>
         <oasis:entry colname="col4">RRt</oasis:entry>
         <oasis:entry colname="col5">Level 2</oasis:entry>
         <oasis:entry colname="col6">mRR Hi</oasis:entry>
         <oasis:entry colname="col7">Level 3</oasis:entry>
         <oasis:entry colname="col8">Cluster</oasis:entry>
         <oasis:entry colname="col9">SLm</oasis:entry>
         <oasis:entry colname="col10">SpRV <inline-formula><mml:math id="M139" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 1000</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">number</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
         <oasis:entry colname="col8">CODE</oasis:entry>
         <oasis:entry colname="col9"/>
         <oasis:entry colname="col10"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1</oasis:entry>
         <oasis:entry colname="col2">170.7</oasis:entry>
         <oasis:entry colname="col3">A</oasis:entry>
         <oasis:entry colname="col4">86</oasis:entry>
         <oasis:entry colname="col5">D</oasis:entry>
         <oasis:entry colname="col6">38</oasis:entry>
         <oasis:entry colname="col7">C</oasis:entry>
         <oasis:entry colname="col8">ADC</oasis:entry>
         <oasis:entry colname="col9">11.3</oasis:entry>
         <oasis:entry colname="col10">14.62</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2</oasis:entry>
         <oasis:entry colname="col2">152.3</oasis:entry>
         <oasis:entry colname="col3">A</oasis:entry>
         <oasis:entry colname="col4">80</oasis:entry>
         <oasis:entry colname="col5">D</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M140" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>58</oasis:entry>
         <oasis:entry colname="col7">D</oasis:entry>
         <oasis:entry colname="col8">ADD</oasis:entry>
         <oasis:entry colname="col9">13.8</oasis:entry>
         <oasis:entry colname="col10">12.15</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3</oasis:entry>
         <oasis:entry colname="col2">69.5</oasis:entry>
         <oasis:entry colname="col3">B</oasis:entry>
         <oasis:entry colname="col4">500</oasis:entry>
         <oasis:entry colname="col5">B</oasis:entry>
         <oasis:entry colname="col6">86</oasis:entry>
         <oasis:entry colname="col7">A</oasis:entry>
         <oasis:entry colname="col8">BBA</oasis:entry>
         <oasis:entry colname="col9">14.5</oasis:entry>
         <oasis:entry colname="col10">34.34</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4</oasis:entry>
         <oasis:entry colname="col2">62.7</oasis:entry>
         <oasis:entry colname="col3">B</oasis:entry>
         <oasis:entry colname="col4">146</oasis:entry>
         <oasis:entry colname="col5">C</oasis:entry>
         <oasis:entry colname="col6">53</oasis:entry>
         <oasis:entry colname="col7">B</oasis:entry>
         <oasis:entry colname="col8">BCB</oasis:entry>
         <oasis:entry colname="col9">10.7</oasis:entry>
         <oasis:entry colname="col10">9.17</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">5</oasis:entry>
         <oasis:entry colname="col2">81.4</oasis:entry>
         <oasis:entry colname="col3">B</oasis:entry>
         <oasis:entry colname="col4">39</oasis:entry>
         <oasis:entry colname="col5">D</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M141" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>13</oasis:entry>
         <oasis:entry colname="col7">C</oasis:entry>
         <oasis:entry colname="col8">BDC</oasis:entry>
         <oasis:entry colname="col9">10.8</oasis:entry>
         <oasis:entry colname="col10">3.74</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">6</oasis:entry>
         <oasis:entry colname="col2">20.9</oasis:entry>
         <oasis:entry colname="col3">C</oasis:entry>
         <oasis:entry colname="col4">72</oasis:entry>
         <oasis:entry colname="col5">D</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M142" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1</oasis:entry>
         <oasis:entry colname="col7">C</oasis:entry>
         <oasis:entry colname="col8">CDC</oasis:entry>
         <oasis:entry colname="col9">  6.1</oasis:entry>
         <oasis:entry colname="col10">0.01</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">7</oasis:entry>
         <oasis:entry colname="col2">20.0</oasis:entry>
         <oasis:entry colname="col3">C</oasis:entry>
         <oasis:entry colname="col4">164</oasis:entry>
         <oasis:entry colname="col5">C</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M143" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>65</oasis:entry>
         <oasis:entry colname="col7">D</oasis:entry>
         <oasis:entry colname="col8">CCD</oasis:entry>
         <oasis:entry colname="col9">14.2</oasis:entry>
         <oasis:entry colname="col10">1.96</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">8</oasis:entry>
         <oasis:entry colname="col2">18.6</oasis:entry>
         <oasis:entry colname="col3">C</oasis:entry>
         <oasis:entry colname="col4">154</oasis:entry>
         <oasis:entry colname="col5">C</oasis:entry>
         <oasis:entry colname="col6">71</oasis:entry>
         <oasis:entry colname="col7">B</oasis:entry>
         <oasis:entry colname="col8">CCB</oasis:entry>
         <oasis:entry colname="col9">14.3</oasis:entry>
         <oasis:entry colname="col10">2.81</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">9</oasis:entry>
         <oasis:entry colname="col2">0.9</oasis:entry>
         <oasis:entry colname="col3">D</oasis:entry>
         <oasis:entry colname="col4">679</oasis:entry>
         <oasis:entry colname="col5">A</oasis:entry>
         <oasis:entry colname="col6">82</oasis:entry>
         <oasis:entry colname="col7">A</oasis:entry>
         <oasis:entry colname="col8">DAA</oasis:entry>
         <oasis:entry colname="col9">22.1<inline-formula><mml:math id="M144" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.94</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">10</oasis:entry>
         <oasis:entry colname="col2">3.5</oasis:entry>
         <oasis:entry colname="col3">D</oasis:entry>
         <oasis:entry colname="col4">296</oasis:entry>
         <oasis:entry colname="col5">B</oasis:entry>
         <oasis:entry colname="col6">77</oasis:entry>
         <oasis:entry colname="col7">B</oasis:entry>
         <oasis:entry colname="col8">DBB</oasis:entry>
         <oasis:entry colname="col9">19.6<inline-formula><mml:math id="M145" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.93</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">11</oasis:entry>
         <oasis:entry colname="col2">4.4</oasis:entry>
         <oasis:entry colname="col3">D</oasis:entry>
         <oasis:entry colname="col4">88</oasis:entry>
         <oasis:entry colname="col5">D</oasis:entry>
         <oasis:entry colname="col6">54</oasis:entry>
         <oasis:entry colname="col7">B</oasis:entry>
         <oasis:entry colname="col8">DDB</oasis:entry>
         <oasis:entry colname="col9">18.8<inline-formula><mml:math id="M146" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.41</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">12</oasis:entry>
         <oasis:entry colname="col2">1.6</oasis:entry>
         <oasis:entry colname="col3">D</oasis:entry>
         <oasis:entry colname="col4">821</oasis:entry>
         <oasis:entry colname="col5">A</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M147" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>72</oasis:entry>
         <oasis:entry colname="col7">D</oasis:entry>
         <oasis:entry colname="col8">DAD</oasis:entry>
         <oasis:entry colname="col9">23.2<inline-formula><mml:math id="M148" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">1.36</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">13</oasis:entry>
         <oasis:entry colname="col2">2.5</oasis:entry>
         <oasis:entry colname="col3">D</oasis:entry>
         <oasis:entry colname="col4">324</oasis:entry>
         <oasis:entry colname="col5">B</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M149" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>66</oasis:entry>
         <oasis:entry colname="col7">D</oasis:entry>
         <oasis:entry colname="col8">DBD</oasis:entry>
         <oasis:entry colname="col9">22.3<inline-formula><mml:math id="M150" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.79</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">14</oasis:entry>
         <oasis:entry colname="col2">4.5</oasis:entry>
         <oasis:entry colname="col3">D</oasis:entry>
         <oasis:entry colname="col4">105</oasis:entry>
         <oasis:entry colname="col5">C</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M151" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>39</oasis:entry>
         <oasis:entry colname="col7">D</oasis:entry>
         <oasis:entry colname="col8">DCD</oasis:entry>
         <oasis:entry colname="col9">16.7<inline-formula><mml:math id="M152" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">0.52</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e4106"><inline-formula><mml:math id="M136" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula> Inland hilly areas (<inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mtext>SLm</mml:mtext><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">17</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>).</p></table-wrap-foot></table-wrap>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T9" specific-use="star"><?xmltex \currentcnt{9}?><label>Table 9</label><caption><p id="d1e4821">List of clusters with their characteristics and municipalities
assigned. Grouped by intensity construction ratio (SpGFA) from high to low.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="1cm"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="50mm"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">SpGFA</oasis:entry>
         <oasis:entry colname="col2">Cluster</oasis:entry>
         <oasis:entry colname="col3">Other remarkable characteristics</oasis:entry>
         <oasis:entry colname="col4">Risk building</oasis:entry>
         <oasis:entry colname="col5">Municipalities</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">CODE</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">management</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Very</oasis:entry>
         <oasis:entry colname="col2">ADC</oasis:entry>
         <oasis:entry colname="col3">Very low RR</oasis:entry>
         <oasis:entry colname="col4">Reviewable</oasis:entry>
         <oasis:entry colname="col5">Benidorm<inline-formula><mml:math id="M154" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">high</oasis:entry>
         <oasis:entry colname="col2">ADD</oasis:entry>
         <oasis:entry colname="col3">Very low RR and trend</oasis:entry>
         <oasis:entry colname="col4">Suitable</oasis:entry>
         <oasis:entry colname="col5">Calpe<inline-formula><mml:math id="M155" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">BBA</oasis:entry>
         <oasis:entry colname="col3">High RR and very high growth trend</oasis:entry>
         <oasis:entry colname="col4">Very improvable</oasis:entry>
         <oasis:entry colname="col5">Altea, Benitachell</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">High</oasis:entry>
         <oasis:entry colname="col2">BCB</oasis:entry>
         <oasis:entry colname="col3">High trend</oasis:entry>
         <oasis:entry colname="col4">Improvable</oasis:entry>
         <oasis:entry colname="col5">Teulada</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">BDC</oasis:entry>
         <oasis:entry colname="col3">Very low RR</oasis:entry>
         <oasis:entry colname="col4">Reviewable</oasis:entry>
         <oasis:entry colname="col5">L'Alfàs del Pí, Xabia<inline-formula><mml:math id="M156" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, La Nucía<inline-formula><mml:math id="M157" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Denia<inline-formula><mml:math id="M158" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Villajoyosa, Ondara, El Verger</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">CDC</oasis:entry>
         <oasis:entry colname="col3">Very low RR</oasis:entry>
         <oasis:entry colname="col4">Reviewable</oasis:entry>
         <oasis:entry colname="col5">Beniarbeig, Benidoleig<inline-formula><mml:math id="M159" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Benissa<inline-formula><mml:math id="M160" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Finestrat<inline-formula><mml:math id="M161" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Gata de Gorgos<inline-formula><mml:math id="M162" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Orba<inline-formula><mml:math id="M163" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Low</oasis:entry>
         <oasis:entry colname="col2">CCD</oasis:entry>
         <oasis:entry colname="col3">Very low growth trend</oasis:entry>
         <oasis:entry colname="col4">Suitable</oasis:entry>
         <oasis:entry colname="col5">Benidoleig<inline-formula><mml:math id="M164" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Ràfol d'Almúnia</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">CCB</oasis:entry>
         <oasis:entry colname="col3">High growth trend</oasis:entry>
         <oasis:entry colname="col4">Improvable</oasis:entry>
         <oasis:entry colname="col5">Callosa, Polop, Pedreguer, Pego, Sanet y Negrals</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">DAA</oasis:entry>
         <oasis:entry colname="col3">Very high RR and growth trend</oasis:entry>
         <oasis:entry colname="col4">Very improvable</oasis:entry>
         <oasis:entry colname="col5">Confrides</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">DBB</oasis:entry>
         <oasis:entry colname="col3">High RR and growth trend</oasis:entry>
         <oasis:entry colname="col4">Improvable</oasis:entry>
         <oasis:entry colname="col5">Alcalalí, Benifato, Benigembla,  Benimantell,  Lliber, Orxeta, Relleu<inline-formula><mml:math id="M165" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Xaló</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Very<?xmltex \hack{\hfill\break}?>low</oasis:entry>
         <oasis:entry colname="col2">DDB</oasis:entry>
         <oasis:entry colname="col3">High growth trend</oasis:entry>
         <oasis:entry colname="col4">Improvable</oasis:entry>
         <oasis:entry colname="col5">Bolulla, Castell de Castells, Vall d'Ebo, Murla, Senija, Tormos, Vall de Laguar, Xaló</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">DAD</oasis:entry>
         <oasis:entry colname="col3">Very high RR; very low trend</oasis:entry>
         <oasis:entry colname="col4">Suitable</oasis:entry>
         <oasis:entry colname="col5">Castell de Guadalest,  Sella<inline-formula><mml:math id="M166" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">DBD</oasis:entry>
         <oasis:entry colname="col3">Very low trend</oasis:entry>
         <oasis:entry colname="col4">Suitable</oasis:entry>
         <oasis:entry colname="col5">Adsubia, Beniardá<inline-formula><mml:math id="M167" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Tárbena</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">DCD</oasis:entry>
         <oasis:entry colname="col3">Very low trend</oasis:entry>
         <oasis:entry colname="col4">Suitable</oasis:entry>
         <oasis:entry colname="col5">Benimeli<inline-formula><mml:math id="M168" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Vall d'Alcalà<inline-formula><mml:math id="M169" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Parcent<inline-formula><mml:math id="M170" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Sagra<inline-formula><mml:math id="M171" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>, Vall de Gallinera<inline-formula><mml:math id="M172" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e4824"><inline-formula><mml:math id="M153" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula> Municipalities with a change in trend from the first part of a series to
the second.</p></table-wrap-foot></table-wrap>

      <p id="d1e5303">As can be seen in Tables 8 and 9, the municipalities with high and very high
RR have been differentiated in italics. This situation only occurs with
municipalities with a high rate of construction in zones at risk, or in inland
too, with very mountainous municipalities where residential buildings are
positioned more easily in risk zones, leading to a higher RR. In
municipalities with improvable management (BBA, DAA and DBB cluster codes),
these high RR values seem to be due to the fact they have been taking on
higher risk rates over the last 20 years than in the rest of the historical
series. On the other hand, if there is suitable management (only DAD cluster
code), these are municipalities that took on greater risks in their first
30 years than they currently do.</p>
      <p id="d1e5306">Table 9 is shown in map form in Fig. 8. These maps show the municipal
distribution of the groups obtained by means of the cluster analysis, as well
as their specific risk values (SpRV).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e5311">Map of La Marina: <bold>(a)</bold> with cluster groups<inline-formula><mml:math id="M173" display="inline"><mml:msup><mml:mi/><mml:mo>∗</mml:mo></mml:msup></mml:math></inline-formula>; <bold>(b)</bold> with the
SpRV value.<?xmltex \hack{\\}?><inline-formula><mml:math id="M174" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula> D1 clusters: DAA, DBB and DDB; D2 clusters: DAD, DBD and DCD.</p></caption>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/21/1847/2021/nhess-21-1847-2021-f08.png"/>

      </fig>

      <p id="d1e5345">Based on the results obtained, it is seen that many of the municipalities with
suitable management today began with overexposure of residential construction
in risk zones (marked with “<inline-formula><mml:math id="M175" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula>”) in the early decades of the series. This is
also seen in the Fig. 1 (Suitable management line) or in the fact that the mRR
Lo value exceeds the mRR Hi value. This is logical because during the initial
period the protection policies were not so developed.  Taking advantage of
this lack of control, together with the urban development initiative proposed
by tourism legislation, it was possible to construct a greater number of
buildings in unsuitable areas.</p>
      <p id="d1e5358">In the maps in Fig. 8, the municipalities of cluster BBA (Altea and
Benitachell) clearly stand out (see location in Fig. 4), where a growing
occupation of risk zones can be seen. Indeed, according to Table 8, this
cluster has the highest RR value of all the municipalities in groups Axx, Bxx
and Cxx, as well as its SpRV and the clearest upward trend. These are
therefore the clearest examples of coastal municipalities that should review
their criteria for considering land as apt for urban development. Both
municipalities are in the process of reviewing their municipal approaches,
since in their<?pagebreak page1862?> previous plans established in the aforementioned first period
there were no limits established as regards use based on geological risks.</p>
      <p id="d1e5361">At the other extreme, there are the mountainous municipalities in groups Dxx
(see the maps in Fig. 8) with a high mean slope (<inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">17</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>). Their
location can be clearly seen in the inland strip with broad unstable areas
where it is more probable for construction to occur in them. This seems to be
the reason why this group has many municipalities with a high RR value,
sometimes burdened with this since the beginning of the series due to the
effect of homes in the urban hub itself.  Furthermore, since these are
municipalities with low populations (under 5000 inhabitants), they do not
usually have the means to draw up land regulation plans or the technical staff
to update them.</p>
      <p id="d1e5378">Perhaps cluster DDA (Confrides; see location in Fig. 4) is the paradigm among
these mountainous municipalities, since it has the second lowest construction
rate but a high RR and a growing trend towards risk. It is also the one with
the parcels furthest from the coast. It does not have land planning, and
according to COPUT (1998) it is one of the municipalities with the greatest
density of landslides per unit of area in La Marina. Although this does not
affect a significant number of homes in absolute values, in these conditions
an improvement in the trend values and risk indicators would seem to be far
off. Indeed, this is a singular case in which the municipality has not
expressed urban development intentions in any of the three previous periods
but will necessarily have to adapt to the land planning regulations in force.</p>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <label>6</label><title>Conclusions</title>
      <p id="d1e5389">As a final reflection, it would seem reasonable to think that studies on the
mechanics and distribution of landslides, the growth in information about
behaviour of the ground, the restrictions imposed on residential expansion,
etc., should progressively improve the effectiveness in tackling the risks.
However, it has been shown that not all municipalities are capable of reducing
the incidence of these risks over time and that, according to Fig. 8, this
incidence is still generally high. So why is this happening?</p>
      <?pagebreak page1864?><p id="d1e5392">In Sect. 2.1, three possible hypotheses have been put forward to explain this
situation. Firstly, the analysis cluster does not enable a direct relationship
to be seen between the land's geomorphological characteristics (mainly the
mean slope SLm) and the variation in risk. In other words, there are
contradictory cases. The same could be said about municipalities with a
greater or lesser volume of construction, proximity to the coast, etc.  Hence,
a greater or lesser risk value and a growing or falling trend cannot be
attributed to the intrinsic qualities of the municipalities studied. Nor can
they be attributed to strictly random factors, since there is coherent
behaviour within the clusters analysed.</p>
      <p id="d1e5395">The above conclusions are bolstered when one considers the lack of temporal
correlation found for the data in neighbouring series, together with the
existence of global behaviour patterns (see Sect. 2.3). As a result of all of
this, the assumption of greater or lesser risk and its temporal evolution
seems to be exclusively due to the third hypothesis initially put forward in
the aforementioned Sect. 2.1; i.e. land management. In this study, procedures
have been proposed that are based on analyses of graphs and risk indicators in
order to find trends and behaviours that may subsequently help to improve this
land management.</p>
      <p id="d1e5398">The risk ratio (RR) developed in this article stands out as a robust indicator
for directly finding the relationship between residential construction and its
associated risk. It is especially useful for coastal municipalities with a
high rate of construction, since it differentiates between those that take on
a higher risk than those that do not.  Nevertheless, in municipalities located
in the inland mountainous strip – with a low residential construction density,
with a high susceptibility and which do not usually have land planning – the values
are also high. In these cases it is not possible to strictly attribute these
values to unsuitable management.</p>
      <p id="d1e5402">In general, it is seen that coastal municipalities are more prone to assume
greater specific risk (see Fig. 8), although the pace of growth in risk is
lower than for construction. In mountainous municipalities in the inland
strip, precisely the opposite happens. Of course there are a fair number of
exceptions to this rule, but two coastal municipalities especially stand out,
where their great construction intensity is exceeded by the growing pace of
occupation of zones at risk. This is group BBA, which includes Altea and
Benitachell (the characteristics of Altea have already been specified in
Fig. 6). Although their land occupation has not reached the level of very high
intensity construction ratio (SpGFA), both municipalities are characteristic
for having high SpGFA and RR values, which shows a growing occupation of
locations at risk.</p>
      <p id="d1e5405">Benidorm (ADC cluster) is precisely an example worth highlighting (Fig. 4).
It is a coastal municipality that is internationally known as a holiday
destination with a notably mountainous profile. It has one of the biggest
construction rates in the area, but this has not led to occupation of
extensive risk areas, although there is a slight upward trend. It is not
surprising, then, that this is the only example of “vertical” construction,
where the mean number floors per building (5.85) is significantly greater than
in the other municipalities in the study (2.09).  Hence, it can be considered
a suitable policy if the objective is to provide a greater amount of built-up
area in relation to the risk taken (<inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:mtext>RR</mml:mtext><mml:mo>=</mml:mo><mml:mn mathvariant="normal">86</mml:mn></mml:mrow></mml:math></inline-formula>, found in the 30th percentile).</p>
      <p id="d1e5420">To sum up, none of the basic risk parameters in any municipality seems to be
determined by randomness, and only in the most mountainous ones is it
determined by the orographic conditions of the land. Monitoring and
restriction of building in risk zones must be applied mainly in the coastal
municipalities with a greater rate of construction. Residential construction's
avoidance of zones at risk of landslide will depend on the municipal
technicians having complete, up-to-date information in their urban development
regulation planning; in other words, they should have been reviewed in the
last decade. Only in this way will it be possible to have objective criteria
in order to enforce urban development regulations and their implicit
“precautionary principle” in order to guarantee the greatest possible level
of protection.</p>
      <p id="d1e5423">The risks of landslide are a result of human activity itself, and it is also
of great human concern to minimise them. The mechanisms for monitoring and
control that should be working to reduce them must not be solely the
responsibility of the municipality, but also of public bodies of greater
hierarchy that may ensure they are applied by using their best resources and
regulatory capacity. Tools have been developed in this work to take objective
decisions to suitably adapt land management, and this can be extended to other
residential areas. Applying them does not guarantee that the problem will be
eliminated, but at least it will help alleviate them and act as a guide to
solve them.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e5430">Borders and areas for the municipal territories
and the <inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> m DEM (digital elevation model) are
available on the Spanish Geographic Institute (IGN, 2021; <uri>https://centrodedescargas.cnig.es/CentroDescargas/index.jsphttps://www.ign.es/web/ign/portal</uri>). The database for landslides was processed from BD-MOVES, available on the Geological and Mining Institute of Spain (IGME, 2021; <uri>http://mapas.igme.es/gis/rest/services/BasesDatos/IGME_BDMoves_ES/MapServer</uri>) and also from the project entitled “Lithology, exploitation of industrial rocks and landslide risk in the Valencia Community”, available online on COPUT (Valencia regional government website, <uri>http://politicaterritorial.gva.es/documents/20551069/169376163/05.1+Litologia+aprovechamiento+de+rocas+industriales+y+riesgo+de+deslizamiento+en+la+Comunitat+Valenciana/e5113e77-3ad2-4f5e-89e3-df36337f206b</uri>, COPUT, 1998). The information referring to cadastral plots or parcels was obtained from the cadastral mapping available from the Spanish Cadastral Directorate (DGC, 2021; <uri>http://www.catastro.minhap.es/webinspire/index.html</uri>). The landslide susceptibility map (LSM) with a resolution of <inline-formula><mml:math id="M179" display="inline"><mml:mrow><mml:mn mathvariant="normal">25</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:math></inline-formula> m in La Marina can be found in Cantarino et al. (2019). Further information can be made available upon request to the corresponding author.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e5473">All authors contributed to conceptualisation, led by IC, who also
conducted the formal analysis and initial draft. JSPJ had a leading role on urban
planning perspective. MAC contributed to validation and data visualisation. VMI critically<?pagebreak page1865?> reviewed the paper and contributed to the preparation of the final version.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e5479">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e5485">Authors acknowledge funding from Department of Geological and Geotechnical
Engineering, Universitat Politècnica de València.</p></ack><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e5490">This paper was edited by Paola Reichenbach and reviewed by Eleftheria Poyiadji and two anonymous referees.</p>
  </notes><ref-list>
    <title>References</title>

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<abstract-html><p>Urban expansion is a phenomenon that has been observed since the mid-20th
century in more developed regions. One aspect of it is the urban development
of holiday resorts with second homes that generally appeared following world
political stabilisation. This residential expansion has often happened with
scarce control, especially in its early stages, allowing areas to be occupied
that are not so suitable in terms of the environment, culture and landscape,
not to mention the very geological risks of flooding, earthquakes and
landslides. Indeed, the risk of landslides for buildings occupying land in
zones at such risk is not a matter solely attributable to the geomorphological
characteristics of the land itself, nor is it simply a question of chance; it
is also due to its management of such land, generally because of a lack of
specific regulations. This study aims to lay down objective criteria to find
how suitable a specific local entity's risk management is by looking at the
evolution of its urban development procedures. It also aims to determine what
causes the incidence of landslide risk (geomorphology, chance, land
management, etc.) and finally to suggest control tools for the public bodies
tasked with monitoring such matters.</p></abstract-html>
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