We propose the use of variable resolution boundaries based on central Voronoi tessellations (CVTs) to spatially aggregate building exposure models for risk assessment to various natural hazards. Such a framework is especially beneficial when the spatial distribution of the considered hazards presents intensity measures with contrasting footprints and spatial correlations, such as in coastal environments. This work avoids the incorrect assumption that a single intensity value from hazards with low spatial correlation (e.g. tsunami) can be considered to be representative within large-sized geo-cells for physical vulnerability assessment, without, at the same time, increasing the complexity of the overall model. We present decoupled earthquake and tsunami scenario-based risk estimates for the residential building stock of Lima (Peru). We observe that earthquake loss models for far-field subduction sources are practically insensitive to the exposure resolution. Conversely, tsunami loss models and associated uncertainties depend on the spatial correlations of the hazard intensities as well as on the resolution of the exposure models. We note that for the portfolio located in the coastal area exposed to both perils in Lima, the ground shaking dominates the losses for lower-magnitude earthquakes, whilst tsunamis cause the most damage for larger-magnitude events. For the latter, two sets of existing empirical flow depth fragility models are used, resulting in large differences in the calculated losses. This study, therefore, raises awareness about the uncertainties associated with the selection of fragility models and spatial aggregation entities for exposure modelling and loss mapping.
The spatial distribution of damage and/or losses expected to be incurred by an extensive building portfolio from a natural hazard event can be quantified and mapped once a physical vulnerability analysis is performed. For such a purpose, a set of fragility functions per building class is conventionally used. Fragility functions describe the probability of exceeding a certain damage limit state for a given intensity measure (IM) associated with a natural hazard, such as spectral acceleration at the yield period (e.g. Fäh et al., 2001) for earthquakes or tsunami inundation height for tsunamis (Koshimura et al., 2009). These vulnerability calculations are performed at the centroid of every aggregation unit of a building exposure model with some level of uncertainty associated with them (Bazzurro and Luco, 2005), or over weighted locations (e.g. Weatherill et al., 2015; Kappos et al., 2008). These aggregation entities can be very diverse, ranging from administrative units such as district/communes (e.g. Dunand and Gueguen, 2012) to urban blocks (e.g. Papathoma and Dominey-Howes, 2003; Kappos et al., 2008; Figueiredo et al., 2018; Kohrangi et al., 2021), regular grids (e.g. Erdik and Fahjan, 2008; Figueiredo and Martina, 2016), or variable-resolution CVT (central Voronoi tessellation) geo-cells (Pittore et al., 2020). Throughout the physical vulnerability assessment, it is implicitly assumed that the intensity observed or estimated at that location (i.e. centroid or weighted points) is representative for the entire aggregation area. Depending on the considered hazard footprint and IM attenuation, this assumption might not be valid if the aggregation area is too coarse compared to the correlation length of a highly varying IM. In addition to the aggregation of the building exposure itself, the importance of these geographical aggregation entities in natural hazard risk assessment is that they are ultimately used to calculate and map the expected damage and loss metrics (e.g. building replacement/repair costs, human casualties). The diverse types of visualisation and interpretations of this kind of geospatial data define the so-called thematic uncertainties (Smith Mason et al., 2017) that can heavily impact the decision-making processes (Viard et al., 2011). It is, therefore, important to find a compromise between the intrinsic resolution of the hazard IM, on the one hand, and the cartographic representation of the exposure models and risk metrics on the other.
When a geographically distributed hazard IM presents no significant spatial variability within distances of the order of tens of kilometres, they are said to be highly spatially correlated (e.g. Gill and Malamud, 2014; Merz et al., 2020). This is the case of hazards with relatively low attenuation and widespread footprints, such as ash-falls and earthquakes (de Ruiter et al., 2021). For the latter case, when seismic site conditions (e.g. soil amplification) and path effects (e.g. seismic directivity) are insignificant, seismic ground motion correlation lengths between 10 and 25 km are typical (e.g. Esposito and Iervolino, 2012; Schiappapietra and Douglas, 2020). On the other hand, hazards are described as being low spatially correlated if their IMs are highly prone to being modified by specific features of the propagation medium. For instance, the modelling of inland IMs from a tsunami (i.e. inundation depth, flow velocity, momentum flux) is highly dependent on the nature and resolution of the bathymetry and digital elevation models (e.g. Tang et al., 2009), coastal topography (e.g. Goda et al., 2015), coastal morphology (e.g. Song and Goda, 2019), and even the nature of the built-up areas that have the potential to interact with and modify the inundation footprint and flow velocities (e.g. Kaiser et al., 2011; Lynett, 2016). Moreover, in the case of earthquake-triggered tsunamis, the maximum tsunami IMs also depend on the properties of the triggering mechanism, for example, the earthquake's magnitude (e.g. Goda et al., 2014), slip distribution (Miyashita et al., 2020), and directivity of the radiated energy (e.g. Kajiura, 1972). Thus, the spatial correlation of inland IMs from tsunamis is very low and remarkably non-linear compared to the much more uniform and highly spatially correlated seismic ground motion. Efforts to visualise uncertainties in the tsunami hazard and risk mapping that address some of the aforementioned modifiers have been reported in a few studies (e.g. Goda and Song, 2016; Goda et al., 2020).
Usually, the resolution of exposure models is constrained independently of
the hazard, and to a certain extent, also independently of the exposure
distribution. That might lead to poor exposure resolutions where it really
matters, i.e. in areas where buildings are densely distributed and/or
hazard intensities vary over short distances. Or, by contrast, it might lead to the
unnecessary computation demands for loss assessment in areas with few
exposed assets. If aggregation areas of the exposure model are coarser in
resolution than the typical correlation lengths of low spatially correlated
hazard intensities, then local variations in these intensities would remain
hidden in the vulnerability analysis, propagating the associated
uncertainties up to the loss estimates. This dependency between exposure
resolution and spatial correlation of hazard intensities has usually been
disregarded, although some examples can be found in soil liquefaction risk
assessment. Despite the fact that the hazard component can be spatially downscaled
(e.g. Bozzoni et al., 2021a),
thematic uncertainties related to visualisation and the interpretation of
risk metrics can arise if they are mapped over larger regional
administrative units (e.g. Yilmaz et al., 2021)
instead of being represented at more hazard-compliant resolutions (e.g.
Bozzoni et al., 2021b). Similarly, despite
building exposure models for flood and earthquake vulnerabilities being able
to be aggregated at moderate resolutions (e.g.
To the best of the authors' knowledge, different hazard footprints and the spatial correlation of their intensity measures for the construction of aggregation entities for exposure modelling have been seldom discussed in the literature. For instance, Chen et al. (2004) described the importance of ensuring a consistent delimitation of the resolution of exposure models along with the spatial variation in their two considered hazards, earthquakes and hailstorms, which impose damage footprints of very different extents. Meanwhile, Douglas (2007) and Ordaz et al., (2019) highlighted the importance of the geographical scale to represent the building exposure models that are affected differently, depending on variable hazard footprints. The study reported in Zuccaro et al. (2018) is perhaps the most advanced framework in the state of the art for the construction of a common aggregation entity for multi-hazard risk assessment, referred to as the minimum reference unit (MRU). This geographical unit coincides with the minimum resolution of analysis of input (i.e. hazard intensities and exposure model) and output elements (i.e. damage and loss estimates) and remarks that despite high-resolution hazard models, one would achieve neither an accurate risk assessment nor meaningful loss mapping if there is no compatibility between the cartographic representation of the building exposure model, the hazard footprints, and their IM correlation.
A denser set of geo-cells in the same area occupied by a coarser regular-sized cell or administrative units provides a denser arrangement of hazard intensity values (when there are local IM variations) to the set of fragility functions per considered hazard. When local IM variations are not sufficiently represented as finer aggregation entities during the vulnerability analysis, thematic uncertainties might appear in the mapping, visualisation, and interpretation of the loss estimates. Therefore, besides the conventional epistemic and aleatory uncertainties linked to the hazard, exposure, and vulnerability components, thematic uncertainties are also present in the risk chain when the loss metrics are mapped. Awareness of the thematic uncertainties as well as clear and meaningful vulnerability and loss mappings towards the most relevant hazards a community is exposed to is necessary to improve urban planning, mitigation strategies, and emergency response actions (e.g. Pang, 2008; Aguirre-Ayerbe et al., 2018).
We can distinguish two types of approaches formerly proposed in the
literature to investigate the exposure aggregation for natural hazard risk
applications.
Researchers can independently represent the building portfolio over a series of
aggregation entities such as administrative units, or equidimensional
regular grids, and explore their individual contribution to the uncertainty
in the losses imposed by certain hazard(s) to ultimately select a
representative aggregation model. This option has been explored in
Bal et al. (2010),
Frolova et al. (2017),
Senouci et al. (2018), and
Kalakonas et al. (2020) for seismic
vulnerability applications and in Figueiredo and Martina (2016)
for flood vulnerability. These studies discuss the weakness of physical
vulnerability mapping at the individual building scale and over coarse
aggregation areas and highlight the importance of finding an optimal
resolution for building exposure modelling while minimising the
uncertainties in the loss estimates. However, these attempts did not
explicitly address the spatial correlation or attenuation of the hazard
intensity onto the predefined aggregation areas and focused on the
vulnerability towards individual hazards rather than on multi-hazard risk
applications. Researchers can aggregate the exposure models over variably resolved entities that are not
necessarily administrative boundaries. This has been done in fewer studies.
For instance, Muis et al. (2016) assessed the
global population exposure to coastal flooding (from storm surges and
extreme sea levels) through the application of a hydrodynamical model based
on unstructured grids to ensure sufficient resolution in shallow coastal
areas. Scheingraber and Käser (2019) explored the
uncertainty in regional building portfolio locations for seismic risk
through the use of weighted irregular grids. This weighting was carried out
as a function of the population density and did not use any hazard IM or
footprints. Scheingraber and Käser (2020) described the
advantages of the former procedure in terms of computational efficiency and
the treatment and communication of uncertainties in probabilistic seismic
risk assessment on a regional scale. Alternatively, aggregating the building
portfolio into anisotropic CVT-based geo-cells (central Voronoi
tessellations) is suggested by Pittore et al. (2020).
In this study, we employ anisotropic CVTs to aggregate the residential
building exposure models. Voronoi regions have proved to be useful in
geographical partitioning (e.g. political districting;
Ricca et al., 2013), as well in other hazard-related
applications, such as climatological modelling (e.g.
Zarzycki and Jablonowski,
2014). We present for the first time how CVT can be constructed using
underlying combinations of geospatial distributions to achieve a larger
resolution of spatially aggregated building portfolios where it matters for
risk assessment. We adapt and customise their derivation to explicitly
account for the combination of a low-correlated hazard intensity (tsunami
inundation) and one exposure proxy (population density) to generate the
Voronoi regions.
The aggregated building portfolios are used for earthquake and tsunami scenario-based risk applications. We have systematically investigated six megathrust subduction earthquakes and their respective tsunamis with moment magnitudes ranging between 8.5 and 9.0. We consider the residential building stock of metropolitan Lima (Peru) classified in terms of one set of earthquake vulnerability classes and two sets of tsunami vulnerability classes. These building portfolios have been aggregated within six customised CVT models and administrative units at the highest resolution available (i.e. the block level). By using the respective set of fragility functions, we have independently calculated the direct losses from scenario-based physical vulnerability analyses (seismic ground shaking and tsunami inundation). We show that the implementation of this approach is beneficial not only in finding a balance between accuracy and computational demand, but also in the efficient representation of the loss estimates while reducing bias generated in the loss mapping. The role of the spatial correlation of both hazard intensities in the efficiency and accuracy of the CVT-based exposure models is also discussed. Since the main scope of this work is to investigate an efficient manner to aggregate the building exposure for risk applications considering multiple hazards, we have not investigated the conditional probabilities related to cascading events (e.g. Goda et al., 2018). Instead, we have assumed that every seismic rupture produces a tsunami. Hence, we are not accounting for cumulative damage on buildings due to consecutive ground shaking and tsunami (e.g. Park et al., 2019; Negulescu et al., 2020; Goda et al., 2021) or the risk due to other seismically induced hazards (i.e. earthquake-triggered landslides, liquefaction, ground failure; see Daniell et al., 2017).
The proposed methodology is composed of the following steps.
Simulate scenario-based hazards (i.e. earthquakes and tsunamis) with
the same spatially distributed intensities required by each fragility
assessment. Construct one (or a set of) representative underlying spatial
distribution (i.e. focus map(s); see Sect. 2.2).
This implies the selection and ranking (with numerical weights) of the
hazard intensities or exposure proxies. Generate CVT-based aggregation entities employing the focus map as an
underlying distribution and with different numbers of seeding points. Classify the exposed building stock of interest into vulnerability
classes per considered hazard and their aggregation into the CVT-based
geographical entities. Assess risk independently based on scenario per hazard type and discussion
of their associated thematic uncertainties in the loss mapping and
visualisation.
The uncertainties arising from steps 3 and 5 are explored through the
formulation of a condition tree.
We employ numerical earthquake and tsunami scenarios to replicate historical or hypothetical future events to simulate spatially distributed hazard intensities. For earthquakes, we simulate ground motions from suitable GMPEs (ground motion prediction equations). Cross-correlated ground motions are generated for the spectral periods that serve the fragility functions as intensity measures (IMs). For tsunamis, we employ the physical generation and propagation model TsunAWI (Harig et al., 2008) and simulate coastal inundation as the IM for tsunamis. The spatially distributed tsunami intensity values (inundation flow depth) are compatible with the IM of the selected set of fragility functions required in the vulnerability analysis.
The focus map drives the construction of a variable-resolution exposure
model for aggregating building portfolios. Focus maps were first introduced
by Pittore (2015) based on the work of Dilley (2005),
who proposed the spatial representation of composite indicators in
hot-spots. Equation (1) recalls the definition of a focus map,
Selectively increasing the spatial resolution of aggregated areas is beneficial for capturing low spatially correlated hazard intensity values such as tsunami inundation heights. This is achieved by the construction of geo-cells with variable resolution in the form of CVT. During this construction, the focus maps are used as underlying spatial intensities and are sampled using a Poisson point process (Cox and Isham, 1980) to generate a number of seeding points. These points are used as centroids of the Voronoi geo-cells and through an iterative relaxation process will converge to the final CVT geo-cells. The number of seeding points therefore defines the number of geo-cells of the resulting tessellation. CVTs are computed in various iteration steps using the simple relaxation method originally proposed by Lloyd (1982) until the distance between the geometrical centroid of the geo-cell and the weighted mass centroid generated by the raster distribution falls below a defined threshold, or after a given maximum number of iterations. Since the relaxation process is based on the underlying focus maps as generating distribution, CVT cell sizes are inversely proportional to the intensity of the focus map. Each CVT geo-cell in fact becomes a minimum resolution unit, as proposed in Zuccaro et al. (2018), and the resulting tessellation sets the basis for a variable-resolution exposure model. Voronoi regions inherently fulfil spatial properties such as compactness and contiguity (without holes or isolated parts) (Ricca et al., 2008).
Epistemic uncertainties underlying the two steps discussed above are
explored by a condition tree with these hierarchical levels:
selection of a suitable scheme (sets of building classes and their
associated fragility functions) to describe the building inventory in the
study area for risk assessment; weight arrangement values ( determination of the number of seeding points sampling the Poisson point
process driven by a focus map that drives the generation of CVT-based
geo-cells.
The condition tree presents a summary of assumptions for uncertainty
treatment (Beven et al., 2018). Through the
construction of alternative multi-resolution exposure models, the impact of
every level of the condition tree is systematically investigated once the
vulnerability assessment is performed.
The building stock of interest is classified in terms of several sets of mutually exclusive, collectively exhaustive vulnerability classes, whose aggrupation describes a set of classes (scheme) specific to the considered hazard (i.e. earthquake and tsunami). A top-down approach is used to make use of aggregated census data and ancillary data for the seismically oriented building classes. Subsequently, the proportions assigned to each seismically oriented building class are reassigned to tsunami-oriented classes through the use of inter-scheme compatibility matrices as presented in Gomez-Zapata et al. (2021c). This method is partly based on the taxonomic disaggregation of every building type within a source and a target scheme as proposed by Pittore et al. (2018) for seismic vulnerability applications and by Charvet et al. (2017) for the definition of tsunami-oriented building classes. Then, the classified building stocks are aggregated into every CVT model obtained in the former step.
The fragility of the building portfolio to the considered earthquakes and tsunami scenarios is calculated separately over every aggregation exposure model (see Sect. 2.1). This decision is based on the recent findings of Petrone et al. (2020), who found fundamentally different structural responses to both perils. Consequently, the authors argued that the intensity of the seismic ground motion does not play a significant role in the building's structural tsunami response unless it induces structural yield. The latter is assumed for the vulnerability analysis, considering the objective of this study of evaluating an optimal exposure model for risk assessment from the considered hazards. The scenario-based risk assessment makes use of a set fragility function associated with each building class and whose IMs are compatible with the hazard intensities modelled in Sect. 2.1. Each of their damage states has a loss ratio assigned to total replacement cost per hazard-dependent building class.
According to Petersen et al. (2018), Peru,
among all the South American countries, has the largest number of
inhabitants and, considering a 10 % probability of exceedance in 50 years,
may experience a ground shaking greater than VIII (modified Mercalli
intensity scale, MMIS). This makes Peru the country in which the largest
average annual fatalities from earthquakes are expected in South America. In
the same study, Lima, with nearly 10 million inhabitants, has been
identified as the capital city exposed to the highest seismic hazard in the
region, in line with Salgado-Gálvez et al. (2018),
who also ranked the city's seismic hazard at the same level. Earthquakes are
mostly attributed to the oceanic Nazca Plate subducting beneath the South
American plate (Villegas-Lanza et al.,
2016). In 1746, a giant megathrust earthquake with an estimated magnitude of
Local authorities have conducted studies for emergency management and recovery planning considering tsunami and earthquake scenarios (e.g. PREDES, 2009), including qualitative risk estimations. Among others, the Japanese SATREPS project contributed to the improvement of the exposure model of Lima using satellite imagery and census data (Matsuoka et al., 2013). On the seismic vulnerability side, the project SARA, led by the Global Earthquake Model (GEM), made a significant contribution to classifying the residential building stock of Peru (Yepes-Estrada et al., 2017) and to assign appropriate fragility functions for similar classes (Villar-Vega et al., 2017), while more specific models for confined masonry have been reported in Lovon et al. (2018). On the tsunami vulnerability side, Adriano et al. (2014) estimated tsunami damage probabilities for two tsunami scenarios over the residential building portfolio classified into four building classes and employed the empirical tsunami fragility functions developed by Suppasri et al. (2013) after the 2011 Japan tsunami. Furthermore, Ordaz et al. (2019) analysed the probabilistic physical risk to both hazards in Callao, remarking upon the importance of addressing simultaneous losses.
We have simulated six earthquakes and tsunami scenarios offshore of Peru
with moment magnitudes between
Median seismic ground motion for a single realisation using the
Montalva et al. (2017) GMPE for peak ground acceleration (PGA)
and spectral acceleration (SA) for periods of 0.3 and 1.0 s and for three
scenarios (
Although a sensitivity analysis on the GMPE(s) selection is outside the
scope of this study, such a choice may influence the resulting
cross-correlated ground motion fields. This comes from the manner in which
the residuals and soil nonlinearity are accounted for in the functional form
of the selected attenuation model
(Weatherill et al., 2015). Although the
Montalva et al. (2017) GMPE uses Vs
Tsunami simulations are based on the source parameters suggested by Jimenez
et al. (2013). We fixed all earthquake parameters except for the slip value
specifying the magnitude over a range from
Summary of TsunAWI model parameters used in the tsunami simulations.
Section of the triangular mesh used for the TsunAWI simulations in the La Punta sector (Callao district). The mean resolution in the pilot area is approximately 20 m, whereas the shortest edge length measures about 7 m. The basemap and data are from © OpenStreetMap contributors 2021. Distributed under the Open Data Commons Open Database License (ODbL) v1.0.
Section of the triangular mesh together with the inundation data product (10 m raster) for the tsunami scenario involving a magnitude 8.8 event in the Callao harbour area. The basemap is from © OpenStreetMap contributors 2021. Distributed under the Open Data Commons Open Database License (ODbL) v1.0).
Expected tsunami inundation height (m) for two local areas within Lima for six tsunami scenarios (with locations in Fig. 1). Map data: © Google Earth 2021.
Figure 2 displays a small section of the model
domain and shows the resolution of the triangular mesh which is directly
connected to the water depth and bathymetry gradient in the ocean, whereas
the edge lengths are shortest in the coastal part of the study area, where
tsunami inundation is expected. The model bathymetry and topography were
built from several datasets. The ocean part is based on the GEBCO
bathymetry (General Bathymetric Chart of the Oceans, GEBCO_08
Grid, version 20090202, see
Example of the construction of focus map and CVT models
for Lima.
It is worth mentioning here that we do not aim to validate the inundation results for a specific event, which would require the optimisation of the elevation and source model. Rather, we investigate the tsunami impact for a range of magnitudes with simplified sources. Tsunami inundation heights from the six scenarios over the two most tsunami-prone areas in the study area (La Punta sector (Callao) and the Chorrillos district (southern Lima)) as seen in the white squares in the tsunami maps of Fig. 1 are shown in Fig. 4. Conversely, significant tsunami inundation is not expected in the central Lima area due to the presence of sizable cliffs.
The resultant CVT geo-cells. The area commonly exposed to a
Spatial distribution of Vs
Focus maps have been constructed as inputs to generate CVT-based aggregation
boundaries for the building exposure model for seismic and tsunami risk
assessment. The spatial population density (PD) in Lima at the block level
(INEI, 2017) has been combined with a “worst-case” scenario of
tsunami inundation height (TI) obtained from a
Three seeding sets have been generated by sampling the heterogeneous Poisson
point processes defined by the two focus maps including 5000, 10 000, and
50 000 initial points. We obtained six CVT aggregation entities for
residential building exposure modelling by applying the Lloyd relaxation
method as described in Pittore et
al. (2020) and recalled in Sect. 2.3. As an
example, the resultant CVT-based model obtained from the focus map from set
(1) and the 5000 seeding points (model PD30_TI70_5000) is depicted in Fig. 6.
The area jointly exposed to the earthquakes' ground motion and the largest
tsunami footprint (
The residential building stock of metropolitan Lima (Peru) has been classified in terms of one scheme oriented towards seismic vulnerability and two tsunami-related schemes with related building classes. They have been constructed following Sect. 2.4. The logical steps are depicted in the flowchart shown in Fig. 8. The initial input is the official census dataset for Lima compiled by the Peruvian statistics institution (INEI, 2017) at the block level. It provides the number of buildings for each block and a few exposure attributes regarding the type of predominant dwelling, floor, and façade materials at the dwelling level. The mapping scheme proposed through expert elicitation in the SARA project (GEM, 2014; Yepes-Estrada et al., 2017) for Peru has been used to relate the census attributes with the proportions expected for 21 building classes. Subsequently, the dwelling fractions (per building unit) proposed in the same study have been used to obtain the building counts for every urban block. The building portfolio is therefore spatially distributed into every CVT-based model through a simple disaggregation procedure addressing their mutual intersections with the block-based model.
Two tsunami reference schemes are selected to classify the building stock of metropolitan Lima, namely Suppasri et al. (2013) and De Risi et al. (2017), to explore the epistemic uncertainty in their classification. While the first one addresses 10 building classes in terms of predominant material and number of stories, the second only accounts for four classes based solely in terms of building material. Steel classes are not included since they have not been deemed representative in Lima (Yepes-Estrada et al., 2017). Thus, we retain seven and three classes, respectively. Considering SARA as the source scheme, the approach presented in Gomez-Zapata et al. (2021c) was used to obtain the SARA – Suppasri et al. (2013) and SARA – De Risi et al. (2017) inter-scheme compatibility matrices shown in Fig. 9. Through their use, the building stock is represented in terms of the building classes of the target tsunami schemes. An example of how to calculate these matrices can be consulted in Gomez-Zapata et al. (2021d).
Flowchart outlining the process for constructing the building exposure model for metropolitan Lima, including the condition tree used for the construction of CVT-based exposure models for the aggregation of earthquake and tsunami vulnerability building classes. (*District-based aggregation entities are only used for seismic risk to compare absolute loss values.)
Inter-scheme compatibility matrices for Lima showing the
compatibility level between the seismically oriented reference scheme SARA and
the tsunami-oriented target schemes:
Example of the building class frequency distribution in
“La Punta” (Callao) mapped using the seismically oriented SARA scheme
(Yepes-Estrada et al., 2017).
Variability of area (km
Every building portfolio for the two considered hazards is aggregated upon the block-based aggregation entities: the six CVT-based models and, for the seismic risk (using SARA), over the third Peruvian administrative level division (districts). The building class frequency distribution in the “La Punta” sector (Callao) is depicted in Fig. 10a and b in terms of the seismically oriented SARA scheme and in Fig. 10c and d in terms of the two selected tsunami schemes. These models are available in Gomez-Zapata et al. (2021e).
As suggested by Petrone et al. (2020), due to
the fundamentally different structural responses to both perils, the direct
economic losses of the aggregated building portfolios for the six scenario
earthquakes and the corresponding tsunamis have been separately estimated.
The variability of the aggregation areas that form every residential
building exposure model of the entire Callao–Lima area is depicted in
Fig. 11a and listed in
Table 2a. Conversely, if we narrow down the
exposed area to the largest tsunami footprint (
Variability in the area (in square metres) of the geo-cells that
compose every aggregation area for exposure modelling, for
Tsunami and seismic risk assessments on classified residential building portfolios are carried out using the publicly available software DEUS (Brinckmann et al., 2021).
Seismic losses for the entire study area are initially presented for a
The seismic vulnerability analysis is performed at every geo-cell centroid,
where the buildings are aggregated. We consider each IM value resulting from
1000 realisations of spatially cross-correlated and uncorrelated ground
motion fields. The resultant distributions for the
Computed loss distributions from a
The financial loss results that we have obtained in Fig. 12 are similar to the loss
distribution estimated by Markhvida et al. (2017),
who investigated the possible losses of the residential building stock of
Callao (aggregated into a regular grid (
Spatially distributed losses in the “La Punta” sector
(Callao) induced by seismic ground shaking of a
Despite the remarkable differences between the area distributions of the
models (Fig. 11,
Table 2), we do not observe significant
differences in the absolute seismically induced losses, which might be explained
by the high spatial correlation of seismic ground motion and the resolution
of the Vs
To constrain the economical consequence model used in the tsunami risk
assessment, the inter-scheme conversion matrices depicted in
Fig. 9 are used to obtain the replacement cost
values per building class from the corresponding maximum scoring class in
SARA. We have assumed loss ratios 5 %, 15 %, 45 %, 65 %, 85 %, and
100 % for each of the six damage states proposed by
Suppasri et al. (2013) and similarly, but
starting with 15 %, for the five ones proposed in
De Risi et al. (2017). A similar approach has been
recently adopted by Antoncecchi et al. (2020). The impact
of using more exhaustive approaches (e.g. Suppasri et
al., 2019) is worth exploring, but out of the scope of this paper. Both
tsunami vulnerability schemes have been associated with a set of empirical
fragility functions with tsunami inundation height in metres as the IM. They
were derived from the same building damage dataset collected after the great
2011
Losses induced by six tsunamis for the six CVT models normalised
with respect to the ones at the block level. Tsunami vulnerability has been
computed using the set of building classes proposed in
Absolute losses (USD) for six tsunami scenarios for the residential building portfolio of Lima classified in terms of two reference schemes and aggregated at the block-based model.
Discrepancy between the tsunami-induced losses between each CVT-based model and the block model for the six scenarios. The values obtained from the Suppasri et al. (2013) and De Risi et al. (2017) schemes are denoted by stars and circles respectively.
The absolute loss values expected after the six tsunami scenarios are reported in Fig. 15 at the block level for the two vulnerability reference schemes. The fragility models of Suppasri et al. (2013) predict larger values with respect to the model proposed by De Risi et al. (2017), whose functional values were found within the range as if flow velocity was accounted for. These findings are in line with the observations of Park et al. (2017) and Song et al. (2017). These studies concluded that flow depth models predict higher probabilities of complete damage for buildings than models that employed tsunami velocity in their derivation. Nevertheless, the aggregation of various building classes into less diversified schemes (e.g. only in terms of construction material in De Risi et al., 2017) might also have influenced the results due to the simplifications involved in the assigning of the financial consequence models. Crowley et al. (2005) described a similar effect for seismic risk applications.
Spatial distribution of tsunami-induced normalised losses (
We have computed the discrepancy in the tsunami loss estimations obtained for each CVT model with respect to the block-based model (Fig. 16). This is minimised for the larger magnitudes and higher-resolution models (50 000 geo-cells). This analysis shows that the Suppasri et al. (2013) fragility model leads to slightly larger differences (with respect to the block-based model) for the three lower magnitudes, whereas De Risi et al. (2017) show larger differences for the three larger ones. These differences are minimised for the highest-resolution model.
Estimates at the block level are around 3 times less efficient (i.e. much larger file sizes; see Table 2) compared to the CVT models with 50 000 geo-cells for which almost identical results are obtained (Fig. 14) and around 23 times greater than CVT models with 5000 geo-cells for which overestimations by less than around 20 % are expected for the three largest magnitudes (Fig. 16). Aggregation entities with lower resolutions lead to overestimations in the tsunami-induced losses. Similar findings were reported in Figueiredo and Martina (2016) in a flood risk analysis.
Spatial distribution of tsunami-induced normalised
losses (
Tsunami loss outcomes for the
Comparison of the independent earthquake-induced losses (EQ) for two ground motion field conditions (using the 1000 GMF for each case: with a spatial cross-correlation model (Corr.) and spatially uncorrelated model (No Corr.) and the tsunami-induced losses (TS) under two tsunami reference schemes for six magnitude scenarios over every common area exposed to both perils.
Considering Fig. 18, it can be noted that the overall mapped area is increasingly reduced as the resolution of the CVT models increases. This is due to the lack of residential buildings within the three large parcels, namely “Country Club de Villa”, “Reserva Laguna de Villa”, and “Refugio de Vida Salvaje Pantanos de Villa” that occupy most of the exposed area in the block-based model. These zones represent the largest area values in Fig. 11b. This model assigns the largest loss values in the Chorrillos district to these three large blocks due to the assumption of using a single tsunami intensity as being representative of the entire enclosed area. Therefore, if the block polygons are too coarse compared to the hazard footprint and IM spatial correlation, biases in the loss assessment are expected. This highlights the importance of hazard-driven entities for exposure spatial aggregation.
In Fig. 19 we compare the absolute losses induced
by each hazard scenario onto the building portfolio exposed to both perils
(e.g.
We observe that in our estimations for the commonly exposed area to both
perils in Lima, the earthquake event dominates the median losses at lower
magnitudes (
The derivation of CVT-based aggregation entities for building exposure modelling is subject to epistemic uncertainties, namely the selection of weights for the pooling of geospatial layers into the focus map and the selection of seeding points that provide the initial seeding set and control the overall number of geo-cells. Through the application of a condition tree, we have selected different sets of these two components to investigate the impact of customised CVT-based geographical entities to aggregate building portfolios as well as through the reconnaissance of thematic uncertainties in the loss mapping and visualisation. Voronoi regions inherently fulfil spatial properties such as compactness and contiguity which are useful to identify areas with comparatively homogeneous physical vulnerabilities.
CVT-based aggregation entities for building exposure modelling can be further customised. For instance, the underlying focus map can be modified in order to integrate other components such as seismic microzonations with higher resolutions than the one we have employed in this work, the spatial presence of certain taxonomic building attributes that may drive the physical vulnerability towards a given hazard (e.g. soft-storey in seismic vulnerability and openings/building foundation in tsunami vulnerability; Alam et al., 2018), and a high-resolution DEM (digital elevation model). However, caution should be taken not to double count their contribution if the hazard simulations have already been performed using these input data (e.g. DEM in landslide susceptibility and tsunami inundation) as well as a wise selection of their respective weights in the focus map construction. Furthermore, CVT model generation would benefit from further improvements such as outlining an iterative approach that can seek a minimum geo-cell size from a convergence criterion imposed by spatially correlated hazard IM lengths.
Several of the limitations in this study could be addressed in the future. For instance, it is worth conducting sensitivity analyses that address the differential impact of the selection of other GMPEs, as well as their combination in logic trees (Scherbaum et al., 2005). In addition, it is relevant to include the calculation of an exhaustive set of stochastic tsunami flood scenarios (with respect to the considered magnitudes) for the evaluation of losses. Likewise, having a higher-resolution digital surface model with spatially distributed roughness values is likely to allow the generation of more accurate results. Physics-based tsunami fragility functions based on intensities more relevant to the building failure mechanisms such as momentum flux (e.g. Macabuag et al., 2016; Attary et al., 2017) would benefit future risk simulations. However, this is subject to their actual availability for typical Peruvian building classes. More comprehensive approaches to adapt such as “foreign” empirical fragility models (e.g. Suppasri et al., 2019; Paez-Ramirez et al., 2020), as well as the need for future development of analytical functions for the South American context (e.g. Medina et al., 2019), would benefit future risk assessment studies for Lima. Another area that would benefit from future research is the differential selection of loss ratios with dependencies on the building classes, as for instance recently investigated by Kalakonas et al. (2020) for seismic risk applications. This might be also relevant for tsunami-induced losses that are strongly influenced by the presence and cost of non-structural building elements. Accordingly, more refined financial tsunami consequence models such as the one proposed by Suppasri et al. (2019) and/or Triantafyllou et al. (2019) are worth exploring when detailed information about prices and built-up areas at the individual building level are available for the study area. In the presented example case, we make use of the concept of inter-scheme conversion matrices (e.g. Fig. 9) to further prove their usefulness to derive exposure models (i.e. spatial distribution of building classes and replacement costs). This is novel because, if we can know these characteristics for a single exposure scheme (e.g. seismic vulnerability oriented), we could get the same descriptors for another vulnerability scheme (e.g. tsunami). This procedure ensures the comparability across the different schemes, and this compatibility had not been considered so far in the related scientific literature for multi-hazard exposure modelling. This aspect also outlines that various exposure models existing in the literature can actually be complemented and compared in a probabilistic manner. On the one hand, the latter ensures that the exposed residential assets classified under various schemes have approximate replacement costs, and thus, the hazard-dependent risk estimates can be comparable with each other. On the other hand, caution should be taken when interpreting the presented results. Neither the damages induced by debris impacts nor scour, relevant for a clearer tsunami vulnerability assessment (Charvet et al., 2015), is included in our modelling. Moreover, it is worth mentioning that larger indirect losses can be expected from buildings with other occupancies (e.g. Chen et al., 2018) that we have not considered herein.
CVT-based models can be beneficial to define efficient, multi-hazard aggregation entities for earthquake and tsunami risk assessment, not only in Lima, but also in other coastal cities exposed to similar hazards. Furthermore, it is worth investigating the usefulness of mapping cumulative damage and losses in hazard sequences, i.e. when a first hazardous event modifies the fragility of buildings that are then affected by a successive event, e.g. an earthquake affecting an area that is then struck by a tsunami.
This work has introduced a novel contribution to derive spatial aggregation entities with variable resolution for large-scale building portfolios for physical risk assessment applications. To this aim, we have presented a workflow to find an adequate resolution of the exposure model where it really matters, i.e. in areas where buildings are densely distributed and/or hazard intensities vary over short distances. This contrasts with the current state of the art related to building exposure modelling (aggregation) that uses regular grids or purely administrative boundaries for exposure aggregation.
In the context of earthquake and tsunami risk, we take advantage of the focus map concept to integrate spatially correlated hazard intensity measures (IMs) with exposure proxies (i.e. population density) in order to spatially identify hot-spot areas where higher values from both spatial distributions are expected. These resultant focus maps can then be sampled by a heterogeneous Poisson point process, as proposed by Pittore et al. (2020) in order to generate variable-resolution aggregation entities in the form of central Voronoi tessellations (CVTs). Each CVT geo-cell becomes a minimum resolution of risk computational analysis, handling the inputs (i.e. hazard intensities and exposure model) and output elements (i.e. damage and loss estimates).
Variable-resolution CVT-based exposure models proposed in this work have
proved their efficiency in integrating large-area building portfolios for
combined earthquake and tsunami loss estimations. Several advantages over
conventional models based on administrative aggregation entities are as follows.
CVT-based models provide alternative an approach to aggregate an extensive
building portfolio constructed from ancillary data (i.e. population) in the
case when existing administrative aggregation areas are not suitable (either
not publicly available or too coarse in resolution) for a certain area of
interest, as well as to perform scenario-based risk assessments for various
hazards. We have observed that CVT-based models correct some bias in the spatial
aggregation of buildings due to the smaller, more compact areas in
high-resolution CVT geo-cells with respect to a coarser block-based cell.
This correction is further propagated to the loss estimates due to the
higher density of IM values employed by the respective fragility functions
during the loss assessment. This is especially observed in areas of the
largest concentration of exposed assets located within the hazard footprint
area and where local spatial variations in the IM are expected, leading to
more accurate estimates. CVT-based exposure models are computationally more efficient than the block-based models in
earthquake and tsunami vulnerability assessments. This is advantageous when
thousands of stochastic realisations of hazard scenarios are calculated over
the aggregation boundaries that are used to model building portfolios. CVT-based exposure models have shown to be beneficial for mapping loss estimates in continuous
space with adjacent and compact geo-cells. These features allow the spatial
identification of zones with similar vulnerability to the hazards considered
and within the area of interest. They contribute to a more intuitive
visualisation and interpretation of the loss mapping and hence contribute to
raising awareness about epistemic and thematic uncertainties in the loss
mapping.
For the portfolio exposed to both perils in Lima, we have found that the
expected median loss values induced by seismic ground shaking are
insensitive to the representation of the exposure model over varying
resolutions. Thus, we confirm the findings of Bal et
al. (2010) and expand them to the case when cross-correlated ground motion
fields are considered. However, this contrasts with the tsunami loss
results, whose differences with respect to a high-resolution model (i.e.
block-based) decrease as the resolution of the CVT geo-cells increases.
Similarly, these differences are remarkably minimised for incrementally
correlated tsunami intensities from the large-magnitude tsunami scenarios
(i.e.
Bearing in mind the scope of this study, but also the limitations presented in the discussion section, we are not claiming that the economic losses we have obtained for the residential building stock of Lima are exhaustive. Instead, through the adoption of the condition tree, we have drawn a branched methodological workflow to explore the differential impact of the exposure aggregation models, and the selection of building schemes on the epistemic and thematic uncertainties that are embedded in scenario-based risk applications. As described by Beven et al. (2018), condition trees facilitate the communication of the meaning of the resulting uncertainties while providing a clear audit trail for their analysis that can be reviewed and evaluated by others (e.g. local experts and stakeholders) at a later date. This study also highlights the relevance of hazard-based aggregation entities for exposure modelling, risk computations, and loss mapping. Thus, the continuous understanding of those uncertainty sources will contribute to enhancing future risk communications, mitigation, and disaster management activities by local decision-makers.
The codes and data models used in this paper have been made
available in open repositories
(Brinckmann
et al., 2021,
JCGZ and MP worked on the conceptualization and methodology. JCGZ and NB worked on the exposure modeling and the software used in risk assessment. JCGZ and RZ obtained the focus maps and CVT models under the supervision of MP. JCGZ carried out the ground motion simulations under the supervision of FC. SH developed the tsunami flood data products. JCGZ wrote the original draft with contributions from all other authors. All authors have read and accepted the published version of the paper.
The authors declare that they have no conflict of interest.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article is part of the special issue “Future risk and adaptation in coastal cities”. It is not associated with a conference.
The authors want to express their gratitude to Glendy Linares, Waldor Arevalo, and Walter Tapia from the Peruvian Office of National Security and Defence (Ministry of Housing, Construction and Sanitation) for providing the INEI (2017) census geo-dataset. Thanks to Catalina Yepes (GEM) for providing the SARA exposure model and mapping schemes for Lima. Thanks to Kim Knauer (EOMAP) for a unified topography and bathymetry dataset for the study region. We thank Sandra Santa-Cruz and Nicola Tarque (PUCP); Miguel Estrada, Diana Calderón, and Fernando Lázarez (CISMID); Luis Ceferino and Mary Chris Suarez (YANAPAY); Alireza Mahdavi (AWI); and Omar Campos (DHN) for the fruitful discussions regarding the seismic and tsunami hazard and risk in Lima during some of the authors' visits to the city. Likewise, we thank Tiziana Rossetto, Dina D'Ayala, Ingrid Charvet, Carmine Galasso, Juan Palomino (UCL), and Pierre Gehl (BRGM) for the feedback during the 2019 Multi-hazard EPICentre encounter in London. Thanks also goes to Heidi Kreibich (GFZ) for the invitation to the 2020-AOGS-EGU NatHazards virtual seminar, during which we were inspired by Anawat Suppasri to continue this study. Special thanks to Cecilia Nievas, Graeme Weatherill, Henning Lilienkamp, Matthias Rüster, and Jörn Lauterjung (GFZ) for their advice during the elaboration of this study. We thank Mario Salgado-Gálvez and the three anonymous reviewers for their feedback. We would like to thank Kevin Fleming for careful proofreading of a previous version of the paper.
The authors disclose receipt of the financial support for the research and publication of this article from the RIESGOS project (Multi-risk analysis and information system components for the Andes region), funded by the German Federal Ministry of Education and Research (BMBF) grant no. 03G0876, as part of the funding programme CLIENT II – International Partnerships for Sustainable Innovations.
This paper was edited by Liang Emlyn Yang and reviewed by Mario A. Salgado-Gálvez and three anonymous referees.