NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-18-2057-2018Development and assessment of uni- and multivariable flood loss models for Emilia-Romagna (Italy)Uni- and multivariable models for flood loss estimation in Emilia-Romagna, ItalyCarisiFrancescafrancesca.carisi@unibo.ithttps://orcid.org/0000-0003-3745-2513SchröterKaihttps://orcid.org/0000-0002-3173-7019DomeneghettiAlessiohttps://orcid.org/0000-0003-4726-5316KreibichHeidihttps://orcid.org/0000-0001-6274-3625CastellarinAttiliohttps://orcid.org/0000-0002-6111-0612University of Bologna, DICAM, Water Resources, Bologna, ItalyGFZ German Research Centre for Geosciences, Section 5.4 Hydrology, Potsdam, GermanyFrancesca Carisi (francesca.carisi@unibo.it)27July20181872057207927September201710October201725June20184July2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://nhess.copernicus.org/articles/18/2057/2018/nhess-18-2057-2018.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/18/2057/2018/nhess-18-2057-2018.pdf
Flood loss models are one important source of uncertainty in flood risk
assessments. Many countries experience sparseness or absence of comprehensive
high-quality flood loss data, which is often rooted in a lack of protocols and
reference procedures for compiling loss datasets after flood events. Such
data are an important reference for developing and validating flood loss
models. We consider the Secchia River flood event of January 2014, when a
sudden levee breach caused the inundation of nearly 52 km2 in northern
Italy. After this event local authorities collected a comprehensive flood
loss dataset of affected private households including building footprints and
structures and damages to buildings and contents. The dataset was enriched with
further information compiled by us, including economic building values,
maximum water depths, velocities and flood durations for each building. By
analyzing this dataset we tackle the problem of flood damage estimation in
Emilia-Romagna (Italy) by identifying empirical uni- and multivariable loss
models for residential buildings and contents. The accuracy of the proposed
models is compared with that of several flood damage models reported in the
literature, providing additional insights into the transferability of the
models among different contexts. Our results show that (1) even simple
univariable damage models based on local data are significantly more
accurate than literature models derived for different contexts;
(2) multivariable models that consider several explanatory variables
outperform univariable models, which use only water depth. However,
multivariable models can only be effectively developed and applied if
sufficient and detailed information is available.
Introduction
According to analyses of the Centre for Research on the Epidemiology of
Disasters (CRED), hydrological disasters (i.e., natural disasters caused by
river and coastal floods, flash floods, rainstorms) are the most
frequently recorded natural calamities occurring worldwide in the last 2
decades see, e.g.,. Also, the number of disasters
caused by hydrological events in 2016 exceeded by far that of any other type
of natural hazards .
Flooding was the third major cause of economic loss worldwide among all
natural disasters between 2006 and 2015 (the firsts were earthquakes and
storms), resulting in total damages larger then USD 300 billion. In Europe,
the proportion of flood impacts was even larger during the same decade, with
inundations ranked first in terms of total damage (i.e., USD ∼51 billion;
CRED). The CRED findings about the increasing amount of economic
loss starting from the second half of 20th century agree with the
analyses carried out by the Intergovernmental Panel on Climate Change (IPCC),
which highlighted that flood damages in the past 10 years were 10 times
higher than in the period 1960–1970 .
Future scenarios provided by and suggest
that extreme flood events at a global scale are expected to increase in terms
of frequency and magnitude. drew a hypothetical scenario
without any change in the meteorological forcing and found that loss would
increase anyway in the future due to exposure and socioeconomic changes
(e.g., higher demographic pressure, improved per capita wealth and living standards).
The implementation of the European Union Floods Directive (2007/60/EC) led flood
risk assessment and management to gain even greater interest and
references therein, forcing member states and
authorities to dedicate additional resources and efforts to the assessment,
mitigation and management of flood risk in the broader contexts of possible
climate change, population growth and economic changes
. However, despite these efforts, there
are still several open problems and limits that need to be discussed and
addressed in order to better assess flood risk and its evolution in time and space.
Among the three components that define flood risk (hazard,
exposure and susceptibility), this paper focuses in
particular on the last two, namely the qualification and quantification of
the exposed elements and the attribution of a loss value to them, as a
function of one or more flood intensity parameters and resistance
characteristics (damage models). The scientific literature of the last decade
shows a large number of innovative damage models that are capable of
estimating flood loss starting from one or more predictive variables.
Nevertheless, several authors indicate that damage models still provide an
important source of uncertainty in flood damage estimates, leading to
uncertainties which are comparable to or larger than those associated with
any other component .
One important source of uncertainty is the simplified representation of
complex damaging processes in terms of a stage-damage function
. Since linked the water level to
relative (i.e., the loss ratio) or monetary damages, most of the models used
today stick to this concept, using only water depth to estimate relative loss
see, e.g.,. Other
important influencing factors, such as flood duration and flow velocity, are
often not considered . Recently, some authors
see
developed multiparameter damage models including more than one predictive
variable, chosen among other hydraulic parameters (e.g., streamflow velocity,
duration of the inundation), resistance performance, precautionary
measures, and people's awareness of and experience with floods .
These models were shown to outperform univariable loss models, under the
condition that sufficiently large and detailed damage datasets are provided
. , ,
, and , among others, indicate the need
for a better understanding of the damage processes as a means to further
improve multivariable models.
A further aspect that contributes to the overall uncertainty in flood
risk assessment and modeling is the lack of sufficient, comparable and
reliable high-quality flood loss data . In the
absence of empirical damage data, loss models are either selected from the
literature or subjectively and schematically derived by experts using a
synthetic approach see, e.g.,.
In fact, data collected in the events' aftermath are crucial to construct new
models and validate existing ones ,
to adjust them for peculiar conditions of the study area, to improve the
consistency of the models themselves
and to provide information about their transferability in different analyses
and contexts . Many damage models
developed up to now are in fact internationally accepted as standard
methodologies for estimating flood damages , without being either tested or
calibrated for the specific study area . Indeed, using
damage models for geographical areas, socioeconomic conditions and flood
events that differ from those for which the models themselves have been
originally derived leads to the incorporation of large errors into the
assessment of flood risk . According to
, validation analyses were performed only for about 45 % of
literature models included in their review by means of comparisons with
observed data, while for the remaining models either the evaluation status is
unknown or the validation process is not explicitly described.
Concerning Italy, the scientific literature reports, on the one hand, several
examples in which models developed elsewhere are applied without calibration
or validation see, e.g.,, and on the other hand it
clearly states the limited exportability of empirical damage models
see, e.g.,on the transferability of the model developed on the basis
of specific flood event data by and
. associate the
generalized poor performance of loss models with a variety of reasons, among
which two are worth recalling. First, the Italian peninsula is characterized
by an extreme variability in geographical and geomorphological contexts as
well as in urban textures and building typologies. Second, Italian flood loss
datasets are generally of low quality and very often characteristic of small
areas, if compared to other European case studies see.
Study area, Secchia and Panaro rivers, location of the breach (yellow
dot), municipalities of interest (i.e., Bastiglia, Bomporto and Modena) and a
schematic of the inundation dynamics.
The analysis described herein assesses the performance of uni- and
multivariate empirical models developed on the basis of a recently compiled
Italian dataset. Our study highlights the problem of lacking consistent data
and the consequent difficulty in the development of robust and reliable
damage models for estimating flood loss to buildings and contents in local
applications. Furthermore, our study contributes to the understanding of
potential and limitations of flood damage modeling in northern Italy, aiming
at investigating the open problem of transferability of empirical damage
models to different areas and socioeconomic contexts.
We consider one of the most comprehensive Italian flood damage datasets, which
consists of 1330 post-event data on flooded private properties in the
province of Modena (northern Italy), collected in the aftermath of the
Secchia River inundation (January 2014). The database contains information
about the affected properties, such as their location and structural
characteristics and the amount of loss suffered, concerning both structural
and nonstructural parts and installations (termed “buildings” from here on)
and furniture and household appliances (“contents”) of each building (see
Sect. and ). The raw data collected by local
authorities have been homogenized, geocoded and integrated with other useful
information including the outcomes of a detailed hydrodynamic numerical
simulation of the inundation event (see Sect. ).
Our study is structured into three main components.
First, concerning direct tangible economic damages to buildings, we use the
above dataset to derive uni- and multivariable damage models for the study
area and compare the accuracy in estimating damages with a selection of
established literature models.
Second, we calibrate empirical uni- and multivariable models to subsections
of the study area and validate them using the data observed in different
subsections (split-sample validation).
Third, we investigate the relationship between damages to buildings and
damages to contents, also developing an empirical damage model for the latter.
Study area and inundation event
Our study focuses on a real inundation event that occurred in Italy in 2014
and was
caused by a breach in the right embankment of the Secchia River during an
intense, yet not extreme, flood event. The collapse of the right levee
occurred on 19 January near the town of San Matteo, in the northern
part of the Modena municipality (see yellow dot in
Fig. ) and caused the inundation of the neighboring
municipalities of Bastiglia, Bomporto and Modena (violet, orange and green
polygons in Fig. , respectively) in less than 30 h.
The overflowing volume was estimated at between 36.3×106 and
38.7×106 m3, flooding an area of about 52 km2see, e.g.,. Towns and the surrounding countryside
remained flooded for more than 48 h, until a water volume in excess of
20×106 m3 was finally pumped out of the inundated area.
According to , the total estimated flood loss was about
EUR 500 million (about EUR 16 million considering only residential properties).
The study area includes the municipalities of Bomporto and Bastiglia and the
northern part of the municipality of Modena. It is located on the Secchia
downriver on the right side and it extends for approximately 112 km2. The area
is mainly flat and the main relieves consist of roads or railway embankments and
minor river levees. The aspect of the area is oriented in a northeastern
direction, along which ground elevations decrease from ca. 30 m a.s.l. in the
southwestern territories to ca. 18 m a.s.l. about 20 km northeastwards.
The delineation of the study area relies on different topographic boundaries.
The western boundary in Fig. is the right levee of the
Secchia River, while the eastern boundary consists of the left levee of the
Panaro River, which also flows towards the northeast, almost parallel to the
Secchia River. Roads, embankments and drainage channels which form the
southern and northern boundaries are an important control for flooding
dynamics and, in the northern part, they prevented urban
areas from being flooded.
The breach was first detected at 06:30 LT. Most likely it was triggered
either by direct river inflow into the riverside entrance of an animal burrow
system or by the collapse of an existing animal burrow, which was separated
by a 1 m earthen wall from the levee riverside and saturated during the flood
event . A trapezoidal part of the embankment, with a
base width of about 10 m, was removed and the embankment's top elevation
became immediately 1 m lower than the river water surface. The breach reached
a maximum bottom width of about 80 m and the embankment's top elevation
became equal to the ground level within 9 h (15:00 LT of
19 January 2014). Given the advanced state of the development of the breach when
it was first discovered, no repair of the breached levee was even attempted
as an immediate measure.
Thanks to several eyewitness accounts, video footage and studies conducted
by an ad hoc scientific committee , it was
possible to identify the flood event propagation dynamics, shown by the blue
arrows in Fig. . These data were used, together with local
accounts, pictures and videos of the flooded municipalities, to reconstruct
the event by means of a fully 2-D hydrodynamic model (see Sect. ).
Flood loss and hydrodynamic data
In the immediate post-event period, for the purpose of compensation,
authorities of the Emilia-Romagna region, Modena Province and affected
municipalities started a data collection campaign to obtain as much information
as possible on the damages caused by the flood event. According to regional
decree no. 8 of 24 January 2014, the aim of the survey was to quantify
the financial needs for the restoration of damaged public buildings,
infrastructure network, hydraulic and hydrogeological works, and
private properties for residential use, household contents, private
registered goods and goods related to the productive sector. Accordingly,
citizens and property owners were asked to fill out forms about public
property
damages, private properties, furniture and registered goods damages, and damages to the economic and productive activities and agriculture and
agro-industrial sectors. In the present analysis, damage assessment focuses
exclusively on private properties.
Number of forms filled by private owners per municipality.
MunicipalityAffectedAffected privateprivateproperties (availablepropertiesaddress and reportingat least damagesto buildings)Bastiglia1728887Bomporto624392Modena7651Total24481330
Authorities collected a total of 448 forms, divided as per the
affected municipalities. In order to geocode the position of every damaged
property, the complete database was filtered, considering only records for
which the complete address was provided. The database regards private
properties affected by different kinds of potential damages: damages to
buildings (structural and nonstructural parts and installations), content
damages (furniture and household appliances), and structural damages to common
parts and registered goods damages (cars, motorcycles, etc.). Our analyses
focus only on properties affected at least by damages to buildings. The
total number of considered forms is therefore 1330 (see
Table , second column).
The 1330 records were geocoded in a GIS environment, using the Google Maps
base map, this being one of the most complete freely available maps for the study
area; geocoding was followed by a careful manual control activity using
publicly available internet pictures, Google Street View and Google Earth.
This step enabled the correction of several wrong or inaccurate geocodings,
mainly in the rural areas, where distances between street numbers are higher.
Refundable assets in accordance with ordinance no. 2 of 5 June 2014 and
law no. 93 of 26 June 2014.
TypologyDescription Damages to– Structural parts:roofs, foundations, supporting structures, interior or exterior stairs,buildingsretaining walls for the stability of the building– Nonstructural parts:walls or delimitation fence, interior flooring, plastering, interiorand exterior painting, interior and exterior fixtures– Installations:electrical, heating, water, TV antenna, lifts, stair lifts for disabledor elderly peopleDamages to– Furniture and household appliances: refrigerator, dishwasher, oven, sink, stove, washer, contentsdryer, TV and personal computers.
Considered variables and their sources and ranges, for building and
content damage analysis.
VariableObservedSimulatedExternalRangesourcesMaximum water depth (m)√0.12–2.10 mMaximum water velocity (m s-1)√0–1.95 m s-1Flood duration (h)√2 – more than 30 hBuilding area (m2)√12–1100 m2Building value (EUR m-2)√902–1183 EUR m-2Structural typology (–)√masonry;reinforced concrete;combination of the twoMonetary damages to buildings (EUR)√EUR 40–160 000Relative damages to buildings (–)√0.05–0.97Monetary damages to contents (EUR)√EUR 0–100 000
The refund requests by citizens, collected from municipal authorities, were
divided into different asset typologies: building damages, content damages,
and
structural damages to common parts and registered goods. We neglected
structural loss to common parts and registered goods in our analyses because
of the limited number of data collected on these categories.
Table shows in detail the different assets which
could be refunded for building and content damages. Table
summarizes all data collected and used in our study for each damaged
property, providing information about the original sources and grouping the
data into three different categories: observed (i.e., declared by owners in
the official forms), simulated by the hydrodynamic model and retrieved from an
external source. The rightmost column of the same table reports the ranges of
these variables within the study area. The following subsections detail the
information collected and summarized in Table .
Damages to buildings
As mentioned before, all 1330 considered records report at least
damages to buildings (structural and nonstructural parts and installations).
Authorities defined the final compensation granted to owners in accordance to
ordinance no. 2 of 5 June 2014 and law no. 93 of 26 June 2014,
which specifies refund criteria. For instance, considering the total amount
of money that authorities had available for the restoration of all kinds of
properties, the maximum coverage for each property was set to
EUR 85 000 for damages to buildings and EUR 15 000 for damages to
contents, setting a fixed amount of money for each room. In
addition, owners declarations about the amount of the restoration work of the
damaged parts, if higher than EUR 15 000, were verified by
authorities by means of expert technical reports. These controls probably
reduced the amount of damage claimed by owners, who commonly tend to
overestimate their loss and have less competency for estimating damages than
professionals have.
Nevertheless, the limited availability of money and the need for a
homogeneous criterion for all the affected properties led in many cases to a
much higher reduction of the amount of damage refundable to the owners. In
fact, refundable assets are only a cut percentage of assets that can be found
in a property and, in addition, experienced damages could be higher than the
maximum coverage established by authorities. The difference between overall
monetary refunded and claimed damages to buildings is equal to about
EUR 1.7 million (EUR 15.2 million of declared loss vs. EUR 13.5 million
of refunded loss). Given this significant difference, in order to preserve
the representativeness and consistency in loss data, we chose to consider observed damages in
our study as claimed by citizens in the forms they filled
(estimation of the financial need for restoration, without knowing the refund
criteria). We are aware that this choice can introduce overestimation of the
damages (particularly considering damages below EUR 15 000) for the
reason explained before, but we considered this possible error having less
influence on loss estimation, both quantitatively and methodologically,
relative to the distortions that would be systematically introduced by
adopting the result of the compensation phase.
Together with the amount of money requested for compensation, we also extracted
from the filled forms the available information on building footprints
and structural typology (masonry, reinforced concrete, etc.) because of their
potential impact on the damage process and therefore on damage modeling
see also previous studies, e.g.,.
In order to evaluate loss in relative terms (as the percentage of suffered
damage relative to the total value of the building), we retrieved the
economic value of each property from the Italian Revenue Agency reports
(Agenzia delle Entrate, AE, 2018). Every 6 months the AE issues the open-market
values (EUR m-2) for different assets (e.g., civil houses, offices,
stores) in each Italian administrative district (spatial scale of
municipality), taking into account different classes of residential and
industrial buildings and the overall economic well-being of the region. These
values are different for each homogeneous geographical area (OMI zone)
and set a minimum and a maximum market value per unit area. Focusing
on residential buildings, and in particular on their structural part without
including the cost of the land, we defined the buildings' economic
value (EUR m-2)
as the average of the values provided for each building in
the same OMI zone. Only the first floor of each building was
considered since the maximum water depth is always lower than or equal to 2.1 m (see
Table ). It is important to notice that these economic
values do not consider a possible fall in price due to catastrophic events.
Also, we are aware that reconstruction costs seem to be more suitable for
this kind of analyses, but they are not freely available in Italy or
homogeneous at a national level, different from OMI values.
Moreover, the use of these economic values at an aggregation level is still
informative for future ex ante damage estimation for planning activities and
it is in line with previous loss analyses at different scales see, e.g.,.
Damages to contents
We also analyze the monetary loss to household un-registered contents
(e.g., furniture and household appliances: refrigerator, dishwasher, oven, sink,
stove, washer, dryer, TV and personal computers).
Focusing on these data and looking at the refunded loss, because of the
stricter criteria for content damage compensation of ordinance no. 2 of
5 June 2014 and law no. 93 of 26 June 2014, the difference
between the requested and refunded amount is even more evident. It is equal to
about EUR 5.7 million (EUR 10.4 million of overall declared loss to
contents vs. EUR 4.7 million of refunded loss) and confirms the choice to
consider observed damages as claimed by owners.
Concerning this dataset, it is worth noting that we do not have any specific
information for each building on the items recorded under the generic
expression “contents”. Therefore, we cannot express these damages in terms
of relative loss over the overall movable property value. Also, the damage
models to household contents proposed by the scientific literature are fairly
rare and isolated some examples are represented by studies performed
by. Thus, we investigate the usefulness
of an indirect modeling approach, which is based on
regressing loss to contents against loss to buildings (see Sect. ), for this type of damage.
Hydrodynamic characterization of the inundation event
Forms collected from authorities for the purpose of compensation do not
include data on hydraulic variables, such as water depth, water velocity,
etc. Since these data are necessary for our analysis, the reconstruction of the
flood event is performed by means of TELEMAC-2D, a fully 2-D hydrodynamic
model which solves the 2-D shallow water Saint-Venant equations using the
finite-element method within a computational mesh of triangular elements
seefor details. This computational model
complies with the validation protocol by the International Association for
Hydro-Environment Engineering and Research (IAHR)
and has been successfully applied to case studies around the globe .
Concerning the inundation event, the dynamics of the wetting front were
strongly influenced by the presence of topographic discontinuities
e.g., road embankments, artificial as well as natural channels
belonging to the minor stream network; see. In order to
correctly reproduce ground elevation and discontinuities in the model, a
detailed lidar DEM with a spatial resolution of 1 m is used and an unstructured
triangular finite-element mesh of the study area is generated. The mesh
consists of 34 082 nodes connecting 66 596 elements with variable
length side from 1 to 200 m in flatter zones, covering a total of
112 km2. This accurate mesh ensures the correct representation of all major
linear discontinuities existing in the study area.
The outflowing hydrograph of the levee breach, as reconstructed by the
scientific committee that studied the event , is used as a
boundary condition, in particular as inflow to the boundary elements
representing the levee breach.
Maximum water depths simulated by the 2-D model; geolocated
building damages (colors reflect municipalities).
The calibration of the 2-D model is performed by varying floodplain roughness
coefficients in order to reproduce the real extent of the inundation, at
different time steps, as documented by maps and aerial images made available immediately post event by competent authorities and rescuers
, and as also confirmed by later studies see, e.g.,.
In particular, Manning's coefficient values were
differentiated between agricultural areas and urban areas, and resulting
coefficients (0.033 and 0.1 m-1/3 s, respectively) are in
line with values reported in the scientific literature see, e.g.,.
After the event, local authorities collected information about water depths
reached at different points of the inundated area. This information is used
for the validation of the model, together with pictures, videos and reports
made available on the Internet, as well as through in situ interviews. At about
50 points, uniformly distributed in the study area, simulation outcomes are
compared in terms of water depth with the information available. Results show
a good agreement between simulated and observed flooding dynamics, with the
residuals between observed and simulated water levels always smaller than
±20 cm. In order to avoid errors due to the model uncertainty, we
consider the area with simulated water depth greater than 10 cm to be “flooded”
see, e.g.,.
The calibrated and validated model is then used to reconstruct the detailed
spatiotemporal dynamics of the inundation event and to identify the spatial
distribution of the hydraulic variables of interest. In fact, combining 2-D
model outcomes and geocoded locations shown in
Fig. , it is possible to extract maximum
water depth, maximum flow velocity and duration of the inundation at each
site (see Table ). Maximum water depth and the maximum flow
velocity commonly refer to different time steps of the flood event.
Damage models
As already discussed in Sect. , damage models return
the amount of loss potentially suffered by certain elements (population,
buildings, economic activities, ecosystem, etc.) as a result of a specific
flood event, thus providing an estimate of the objects' susceptibility. These
models associate relative (or monetary) loss with different input variables.
The most frequently used loss models in Europe are univariable damage
models, i.e., they estimate the amount of damage as a function of a single
input variable, most commonly water depth
, distinguishing among different
building uses, types, etc. . Although each model is developed
with different approaches and uses different economic values for assets, the
damage values can be relativized based on each different context in order to
make the models comparable to each other.
This section briefly recalls well-known and largely employed literature
depth–damage models (also called stage-damage models, shown in
Fig. ). Furthermore, it describes empirical depth–damage
models and a multivariable loss model that we derived for the Secchia loss
dataset. All uni- and multivariable models illustrated here are applied for
predicting loss to buildings and household contents resulting from the
January 2014 Secchia flood event.
Literature stage-damage models and observed data: grey points in the
background represent the observed relative loss (buildings only); literature
models are limited to the maximum water depth reconstructed for the
inundation event through the 2-D hydrodynamic model (i.e., 2.5 m).
Literature damage modelsMulti-Coloured Manual (MCM) model
The depth–damage curve implemented in the Multi-Coloured Manual
MCM; is considered to be one of the most
comprehensive and detailed models for flood damage estimation in Europe and
it is used as a support for water management policy and quantitative
assessment of the effect of investment decisions
. This model estimates loss based
almost exclusively on synthetic analysis and expert judgment from the
insurance industry or engineers .
Different from the majority of other damage models, MCM estimates building
damages using a monetary depth–damage curve, i.e., it defines monetary
potential loss relative to water depth, rather than providing damage ratios
. Similar to previous
studies see, e.g., and aiming at performing a fair
comparison among all considered models, we make use of the relative
depth–damage curve as obtained by , who rescaled the
original MCM monetary curve by referring the total building damage (100 %)
to an average pre-flood depreciated building value in 2005 pound sterlings (GBP) see Table 2 in.
Flood Loss Estimation MOdel for the private sector (FLEMOps)
The Flood Loss Estimation MOdel for the private sector (FLEMOps)
is an empirical model based on an extensive dataset from
2158 private households that were significantly affected by flood
events in 2002, 2005 and 2006 in Germany. According to ,
the database used for identifying FLEMOps was compiled through computer-aided
telephone interviews with a sample of people affected by these serious
events. FLEMOps assesses relative flood damages to private households by
referring to several factors: inundation depth, building type, building
quality, water contamination and private precaution. Although the original
FLEMOps was developed as a multivariable model, in this study we
implemented it as a univariable one, by referring to the water depth as the
only parameter available in our data collection. The curve taken into account
in this study (see Fig. ) is the one that considers a
uniform distribution of building types in the study area
see, while no information about building quality, water
contamination and private precaution was available (concerning these last
three factors, the first classes of the original model are considered).
Rhine Atlas damage model
The Rhine Atlas damage model was designed by the International Commission
for the Protection of the Rhine (ICPR) for hydraulic risk assessment
within the watershed of the Rhine River after two
severe floods caused a large amount of economic damage in Germany and the
evacuation of 250 000 people in the Netherlands in 1993 and in 1995 . For
developing the model, damage intensity and maximum damage values were set on
the basis of collected empirical data in the two mentioned floods and expert
judgments, combined with a synthetic approach . This model
includes five different stage-damage functions, each of which is associated
with a different land-use class derived from the CORINE Land Cover project
. The Rhine Atlas model used in this
analysis (see Fig. ) is the stage-damage curve
associated with the residential sector.
Joint Research Centre (JRC) damage models
These curves were developed by the European Commission's Joint Research
Centre – Institute for Environment and Sustainability (JRC-IES)
as part of a project to estimate trends in European
flood risk under climate change . They consist of
different depth–damage functions and maximum damage values which can be used
by all EU countries (see Fig. ). On the basis of
land-use data retrieved from the CORINE project
, stage-damage functions were identified
for 10 countries from existing studies for example, depth–damage
models based on , and , were
used to develop a stage-damage model for the UK and, regarding
Germany, depth–damage functions were chosen using a combination of many
existing models; see and applied to the corresponding damage
classes. In addition, an average of all available land-use-specific curves
was used to develop a model for countries where stage-damage curves were not
available (“JRC other countries”), and Italy is among these
. We selected seven out of
the 11 JRC available curves for our analysis: we neglected the curves that provide the
highest and the lowest damage estimation for water depths between 0 and
2.5 m, which is the range that includes our observed data. In fact, these curves
would be located, respectively, above and below the observed grey data points
in Fig. and would provide unrealistic over- and
underestimations for our case study. Therefore, the curves that we
considered for our analysis are JRC Belgium, JRC Czech Republic,
JRC Germany, JRC Netherlands, JRC Switzerland, JRC UK and JRC other countries.
Models developed on Secchia datasetSecchia Empirical damage model (SEMP)
The Secchia empirical damage model (SEMP) is an empirical stage-damage
curve that we derive from the observed relative loss for the inundation event
of 2014. It is obtained by binning water depth values into 25 cm wide classes
(i.e., 0–25, 25–50 cm) and by calculating the median damage for each
bin. Then, for each bin the median damage value is associated with the mean
water depth of the bin itself (e.g., 12.5, 37.5 cm), and the
empirical damage curve is then obtained by linearly interpolating the binned
values. This curve is obviously limited to the maximum water depth resulting
from the 2-D simulation. Further, the intercept is equal to zero in order to
reproduce a realistic and representative situation of the buildings in the
study area where only a few affected buildings have a basement: a water depth
equal to zero means no damages. Different class subdivisions have been
tested (from 10 cm to 1 m water depth) and the one chosen (25 cm) results in the
one with the best performance in terms of root-mean-square error (RMSE – see
Sect. for details) in reproducing observed
loss data. Table in the Appendix displays the curve's formulation.
We obtain the Secchia square root regression damage models (SREGx)
by regressing observed relative loss against maximum
water depth (SREGd), maximum water velocity (SREGv) and building footprint or area
(SREGa) recorded for every building. It is
worth pointing out that SREGa refers only to footprints of
buildings that are flooded during the considered event (i.e., a real
inundation or a flooding scenario). Regression curves based on water depth
and building area have an intercept equal to zero: for the reason explained
in Sect. , no damages are produced if the
water depth or the footprint of the building are null. Conversely, the
intercept of the regression model based on water velocity is different from
zero because it is possible to also have damages if the water is stagnant.
We tested linear, logarithmic and square root regression of observed data,
obtaining the best prediction performance in terms of RMSE with the latter.
The identified regression relationships read
DSREGd=0.113h,DSREGv=0.007v+0.104,DSREGa=0.009a,
where DSREGd (–), DSREGv (–) and
DSREGa (–) represent relative economic damages to buildings
estimated by referring to the maximum water depth h (m), maximum
water velocity v (m s-1) and building area a (m2), respectively.
For the sake of completeness, we point out that an additional curve has been
developed based on the maximum intensity (i.e., water depth times velocity),
but it is not reported here and in the following paragraphs because it does
not improve the results.
Secchia Multi-Variable damage model (SMV)
The Secchia multivariable model (SMV) of this study takes advantage of the
Secchia 2014 dataset by applying data mining procedures used by
. While used Bagging decision trees from the
MATLAB toolbox implementation, the multivariable model derived in this study
uses the random forest (RF) algorithm implemented in the R package randomForest by .
Both RF and Bagging decision trees are tree-building
algorithms which can be used for predicting continuous dependent variables.
The procedure of growing each tree consists of the approximation of a
nonlinear regression structure, recursively repeating a subdivision of the
given dataset into smaller parts in order to maximize the predictive
accuracy of the model. The classification and regression tree (CART)
methodology is used to select and split variables and to
identify leaf nodes which give the prediction for the dependent variable.
CART uses an exhaustive search method on a randomly chosen set of variables
to identify the variable with the best split based on a measure of node
impurity (in our case the RMSE of the response values in the respective
parts). The splitting is stopped if either a threshold for the minimum number of
data points in leaf nodes is reached or if no further splitting is possible.
These steps create a tree structure with several nodes, whereby the beginning
node is called the root node and the last nodes are called leaf nodes. Each
resulting node of the tree represents the answer to the partition question
asked in the previous interior nodes and the prediction for an input x1,
x2, …, xk depends on the response variable of all the parts of
the original dataset that are needed to reach the terminal node
. A possible problem of regression trees is overfitting,
i.e., growing trees that are too large and with many leaves, some of which are
associated with small subsamples. As a consequence, the model may work well
with the training data but will show clearly worse performance for
independent validation data. In order to reduce this overfitting,
proposed the RF algorithm, which uses several bootstrap
replica of the learning data for which regression trees are learned.
RF considers a limited number of variables for each split to learn the trees. The
responses from all trees are aggregated in terms of the mean value of all
predictions. The procedure with a qualitative example for RF is shown in
Fig. , while an example of a built tree for the Secchia case
study is reported in Fig. in the Appendix.
The RF algorithm has the advantage of also providing estimates regarding the
importance of variables in the tree-building procedure and thus, in our
case, of evaluating the relative importance of the contribution of each
independent variable in representing the damage process: randomly permuting
the values of the predictor variables, the algorithm simulates the absence of
a particular variable and calculates the difference of the prediction error
with and without the permutation. The variables being randomly permuted,
leading to a strong decrease in predictive performance, is considered
important for the prediction, given the variables' influence on the prediction process
is very high.
Random forest method . An example of a regression
tree built for the Secchia case study is shown in the Appendix (see
Fig. ).
The RF algorithm is used in many different scientific fields, from flood
hazard assessment to computer-aided diagnosis
, passing through gene selection ,
earthquake-induced damage classification and many others.
The numerous applications show the many advantages of using the RF method,
including high prediction accuracy, acceptable tolerance of outliers and
noise, and easy avoidance of overfitting problems. In the last years, some
applications of this method to flood risk have been performed
see,
but literature in this field is still scarce if compared to the numerous
studies that use simpler univariable models. Nevertheless,
demonstrated that tree-based models are able to improve the performance of
existing models like stage-damage functions and to better identify the most
informative independent variables and their interactions (e.g., they can
identify different importance levels of the same variable, depending on the
value of another variable).
Another important advantage of this algorithm is that no assumptions about
independence, distribution or residual characteristics are needed. Further,
RF allows the inclusion of both continuous, e.g., water depth or velocity, and
categorical variables, e.g., building type. Conversely, multivariable
models need a sufficient number of data in order to correctly identify
complex relationships among variables. This is one of the reasons why this
kind of model is scarcely used in regions where comprehensive,
multidimensional databases are not available .
For RF learning, we consider all the variables that are available, collected
from authorities, simulated by means of the hydrodynamic model and retrieved
from external sources: maximum water depth, maximum water velocity, flood
duration, building area, economic building value per unit area and building
structural typology.
Spearman correlation between relative loss (buildings only) and
predictive variables: maximum water depth, maximum water velocity, flood
duration, structural type (masonry, masonry and reinforced concrete, or
reinforced concrete), building area and building value per unit area. Empty boxes
indicate statistically nonsignificant correlation coefficients at a 5 %
significance level.
Results and discussionComparison of literature and empirical damage models
Figure shows the results of the correlation
analysis between relative flood loss to buildings and the available six
predictive variables: maximum water depth, maximum water velocity, flood
duration, building value per unit area, building area and building structural
typology. Since the latter is a categorical variable, it is converted to dummy
variable encoding in order to calculate the correlation of continuous and
categorical data together. We refer to the Spearman correlation coefficient
in order to also take into account nonlinear relationships among
variables. Empty boxes represent correlations that are not statistically
significant at a 5 % significance level. The variables that are
significantly correlated with the relative loss to buildings are maximum
water depth, building value per unit area and building structural typology.
However, correlation coefficients are low, precisely lower than ±0.18 in
all the cases. Similar results were obtained in terms of Pearson's
correlation, but the values are not shown for the sake of brevity.
Figure shows the output of the RF evaluation of the
importance of the six predictive variables within the SMV model. This concept
is different from the correlation one: in fact, while the Spearman
coefficient indicates how well the relationship between two variables can be
described using a monotonic function, the RF algorithm evaluates the importance
of a variable by assessing the worsening in the performance of the model when
that specific variable is not included in the database. In contrast to other
studies see, e.g.,, the dataset does not reveal a distinct
importance for individual variables; not even water depth stands out. The
descriptive capability of water depth is only slightly stronger than water
velocity and building area, while the remaining predictors show very little importance.
Importance of predictive variables considered in SMV (building area,
building value per unit area, flood duration, maximum water velocity, maximum
water depth, structural type).
Relative damages to buildings estimated with (a) SEMP (blue dots) and
SREGd (dark red dots), (b) SREGv (dark red
dots), and (c) SREGa (dark red dots). Grey points in the background
represent observed relative loss to buildings.
Figure shows in the background the observed relative
damage to buildings, collected in the three affected municipalities
(i.e., Bastiglia, Bomporto and Modena) as a function of maximum water depth (Fig. a), water velocity (Fig. b)
and building area (Fig. c).
Despite the statistically significant correlation with water depth (see
Fig. ), a very large noise can be observed in all
diagrams, which implies that one variable alone explains only a very limited
part of the damage process. This is confirmed from the outcomes of both the
correlation assessment (see Fig. ) and the
importance analysis (see Fig. ).
Relative damages to buildings estimated with SMV.
Taking the maximum water depth as the only explanatory variable,
Fig. a represents the damages to buildings estimated by
means of the univariable models developed based on the Secchia dataset (SEMP, with
blue dots, and SREG_d, dark red dots). In a similar fashion, Fig. b, c show the relative loss to
buildings as a function of maximum water velocity and building area, estimated
by means of SREGv and SREGa, respectively (dark red dots in both diagrams).
Results of the application of the multivariable model (SMV), described in
Sect. , are shown in Fig. ,
which highlights the good performance of this model.
Table quantifies the discrepancy
between observed and predicted loss values for local empirical models in
terms of four different performance metrics, namely bias, mean absolute error (MAE),
RMSE and the difference between estimated and
observed overall monetary loss to buildings (ΔLOSS), which are defined
as follows:
bias=1n∑i=1nPi-Oi,MAE=1n∑i=1nPi-Oi,RMSE=1n∑i=1nPi-Oi2,ΔLOSS=∑i=1nPi⋅BAi⋅BVi-∑i=1nOi⋅BAi⋅BVi∑i=1nOi⋅BAi⋅BVi⋅100,
in which Oi and Pi are observed and predicted
relative damages at the ith site, respectively; n is the
number of sites in the study area; and BAi and BVi are building area and
building value per unit area at the ith site, respectively (see Table ).
Performance of the uni- and multivariable models developed based on local
data in estimating relative damages and overall monetary loss to buildings
(see Eqs. , , and ;
the observed overall monetary loss is equal to EUR 15.2 million). Models are
ranked according to RMSE values, from the lowest to the largest. Corresponding
results for literature models are reported in Table .
Performance of different literature univariable models in estimating
relative damages and overall monetary loss to buildings (see Eqs. ,
, and ; the observed overall monetary
loss is equal to EUR 15.2 million). Models are ranked according to RMSE values,
from the lowest to the largest. Corresponding results for uni- and multivariable
models developed based on local data are reported in Table .
SMV is associated with the lowest RMSE value (i.e., 0.062), which is less than
half the RMSE value of the second-to-best models (i.e., SREGd
and SREGv, with an RMSE value of 0.125).
SREGa and SEMP provide slightly worse relative loss
estimations than the previous models (RMSE equal to 0.129 and 0.130,
respectively). Results are similar in terms of bias and MAE, although some
differences can be pointed out for SREGx models, which
present a bias value that is slightly lower than the one derived from SMV estimation.
Concerning literature models described in Sect.
and illustrated in Fig. ,
Table shows that FLEMOps and JRC
Czech Republic outperform the others in terms of RMSE (RMSE equal to 0.125
and 0.127, respectively) and are comparable with the models developed based on
Secchia's dataset. RMSE values derived from the relative loss estimation with
JRC Netherland, JRC Germany, JRC Belgium and Rhine Atlas are between 0.131
and 0.143, while the worst performance in terms of RMSE is associated with
JRC Switzerland, JRC other countries, MCM and JRC UK (RMSE values higher
than 0.2). These outcomes reflect the fact that all these latter damage curves are in the upper part of the diagram in Fig. and
significantly apart from the rest of the models, which are instead close to
each other. We obtained similar results in terms of bias and MAE.
Analogous results can be observed in terms of ΔLOSS, which is reported
in the rightmost column of both
Tables and . This indicator, different from
MAE and RMSE and similar to bias, highlights the tendency of models to
under- or overpredict damages to buildings; yet ΔLOSS focuses on the
overall monetary damage in a given area, whereas bias refers to relative
damages. Hence, ΔLOSS clearly shows if a model is biased in predicting
the overall monetary loss, that is, if the model systematically predicts
higher or lower (positive and negative bias, respectively) damages for the
entire study area than those observed. This is shown in
Fig. , in which most of the predictions provided by SMV,
especially for observed relative damages higher than 10 %, lie under the
1:1 line: this means that the model is negatively biased. Predictions obtained
with the other models are spread more evenly around the 1:1 line, denoting a
smaller bias. In terms of bias and ΔLOSS, SMV seems to have a slightly
worse performance than SREGd, SREGv and SREGa (and FLEMOps, regarding these specific outcomes).
The large overestimation of overall losses associated with JRC UK, MCM,
JRC other countries, JRC Switzerland and JRC Belgium reported in
Table is expected from the
comparison among these models and empirical data presented in
Fig. . The overestimation may result from morphologic
and socioeconomic contexts for which these models were constructed, as well
as criteria adopted for their development, which might differ considerably
from our case study and empirical models. For example, due to the diverse
study area topographies and land uses, floods can propagate with various
dynamics, differently influencing hazard indicators. Also, building
characteristics and the overall well-being of an area can differ considerably
among regions and countries, therefore compromising the transferability of
literature curves.
Another feature of the rightmost column of
Table worth noting is that four of the literature
models that perform the best in terms of RMSE (JRC Czech Republic,
JRC Netherlands, JRC Germany and Rhine Atlas) underestimate the overall monetary
loss. This fact can be explained by several reasons, among which an important
one is certainly comparing damages claimed by citizens with the four models
listed above, which were developed on the basis of expert-based judgment only,
or by considering expert knowledge together with empirical data.
Validation of the models: performance of the uni- and multivariable
models in estimating relative damages to buildings, developed based on two-thirds and
validated based on the remaining one-third of the local data. Models are listed as in
Table .
An additional important factor that influences the performance of literature
models applied to the Secchia case study is the different scale on which
these curves are calibrated and applied: some of them are developed to be
applied at the microscale (e.g., MCM, FLEMOps), while others are developed to be applied at the mesoscale
(e.g., Rhine Atlas, JRC curves). However, among mesoscale models there is a
large variability in terms of performance. In several practical applications,
identifying the best performing damage model a priori can be an extremely
difficult task. This is also complicated by difficulties in obtaining
detailed information about original datasets used for developing literature
models (including damage data and characteristics of the flood event and of
typology of affected buildings). Deeper investigation on model properties and
assumptions (e.g., hazard and vulnerability features based on the context for which they
have been derived,
values used for translating monetary damage into relative
damage, level of aggregation of original data) can guide the selection of
models; moreover, a variety of them should be used to additionally obtain
information on associated uncertainty .
Validation of locally derived damage models
The results reported in Table refer
to calibrations of empirical models based on our entire dataset. We also
validate all empirical models by using a split-sample validation procedure.
Specifically, two-thirds of the records are randomly selected from the
dataset for calibrating each model, which is then applied to the remaining
one-third of the data. Bias, MAE and RMSE calculated in this context and
reported in Table are very similar to
the ones reported in Table concerning
SREGx and SEMP. Results of the validation of SMV by means of
the same approach instead indicate lower performance of this model, when
calibrated on a smaller dataset (see
Table ). In fact, values of bias, MAE
and RMSE are twice as high as values reported in
Table . These outcomes highlight the
need for extensive datasets for identifying robust and reliable damage
models. From the comparison of the different considered models (uni- and
multivariable), it is clear that this aspect is more evident for the
multivariable model, whose performance is significantly worse when
calibrated on a smaller number of observed data. Conversely,
univariable models, though simpler than SMV, appear more robust in the case of a
smaller number of calibration data, providing better results in the validation.
Based on the output of Sect. , it is worth
noting that the application to the Secchia case study of JRC other countries,
in which Italy should be included, provides very poor results in terms of
building loss. This confirms how challenging the identification of a regional
or large-scale model with a general validity could be see also
Sect. and.
This section further assesses the transferability of damage models to very
similar socioeconomic contexts.
In order to test the transferability of the empirical locally derived models
to similar contexts, we identify analogous models (SREGx,
since it is the best model among the locally derived ones, and SMV)
on the basis of the building loss data collected in a single municipality
and then apply these models for predicting flood building loss in a
neighboring municipality. In particular, among the three municipalities
considered in the study (i.e., Bomporto, Bastiglia and Modena), we consider
Bastiglia (887 observed records) and Bomporto (392 observed
records) because of the larger number of data available. We calibrate the
models on Bomporto's subset (Bo_MV, Bo_REGd,
Bo_REGv and Bo_REGa) and we apply them
for predicting Bastiglia's flood damages to buildings. Then, we calibrate the
same models on the Bastiglia subset (Ba_MV, Ba_REGd,
Ba_REGv and Ba_REGa) and apply them to Bomporto.
Figure shows the results of
these split-sampling experiments. Figure a refers to
Bastiglia's relative damages to buildings, estimated via Bo_MV and
Bo_REGd, while Fig. b indicates Bomporto's
damages estimated via Ba_MV and Ba_REGd; in each graph
grey dots represent the estimation of relative loss using the multivariable
models and red dots indicate relative damages to buildings estimated with
square root regression models.
(a) Bastiglia relative damages to buildings estimated with
Bo_REGd (red dots) and Bo_MV (grey dots); (b) Bomporto
relative damages to buildings estimated with Ba_REGd (red dots) and
Ba_MV (grey dots).
Square root regression models in
Fig. show rather poor
performances, capable of capturing only the average loss, while better
results seem to be associated with multivariable models in both graphs. Some
differences between the two panels are worth noting: grey dots in Fig. a (application of models calibrated in Bomporto with 392 data to
Bastiglia) seem to overestimate relative loss to buildings, while in Fig. b (application of models calibrated in Bastiglia with 887 records
to Bomporto) they lie closer to the 1:1 line. The studies performed in terms
of relative damages to buildings related to maximum water velocity and
building area present very similar results and are reported in the Appendix
(see Figs. and ).
These outcomes are also visible in Table ,
which presents the results of the split-sampling experiments in terms of the
usual bias, MAE and RMSE indexes. While uni- and multivariable models
calibrated on Bastiglia's data and applied to Bomporto's subset do not differ
much, with slightly better performances for Ba_MV, Bo_MV is associated
with much higher prediction errors when applied to Bastiglia. The worse
performance of Bo_MV can be explained by the smaller size of the Bomporto
subset of data used for its calibration (less than a half of Bastiglia's
sample). As already outlined in Sect. , in
order to have robust results from multivariable models, a large number of
empirical data are required. Furthermore, the inundated area in Bomporto is
larger than in Bastiglia (see Fig. ). This
explains rather clearly the difference in terms of accuracy of Ba_MV and
Bo_MV in Table : the higher the loss
data density the more robust the relationship between different predictor
variables and loss data and the higher the ability of the model to explain
local characteristics of the study area .
Transferability of the models: performance of different uni- and
multivariable models in estimating relative damages to buildings in different
contexts. In the upper tables, the models were calibrated on Bomporto's dataset
(392 records) and validated in Bastiglia, while in the bottom tables the models
were calibrated on Bastiglia's dataset (887 records) and used to estimate
damages in Bomporto. The left tables report performance of the models in the
calibration phase, while the right tables show performance of the validation study.
BiasMAERMSEBiasMAERMSE(–)(–)(–)(–)(–)(–)Calibration on Bomporto's dataset Validation on Bastiglia's dataset (392 records) (887 records) Bo_MV-0.0110.0310.0530.0940.1400.159Bo_REG_d-0.0020.0850.118-0.0230.0850.128Bo_REG_v0.0000.0850.1180.0000.0920.127Bo_REG_a-0.0120.0850.125-0.0210.0880.131Calibration on Bastiglia's dataset Validation on Bomporto's dataset (887 records) (392 records) Ba_MV-0.0120.0390.0680.0070.0840.115Ba_REG_d-0.0020.0900.1260.0230.0960.121Ba_REG_v0.0000.0910.1260.0120.0900.119Ba_REG_a-0.0080.0910.1300.0020.0910.126
Distribution of water depths (a) and observed relative
damages (b) in the three considered municipalities.
The transferability of the models is also hampered by the different
distribution of the water depths in the different municipalities:
Fig. shows that water depths in Bastiglia are
lower than in Bomporto, despite the quite similar distribution of observed
relative damages. This might be due to the fact that, other than being a hazard,
different buildings' vulnerability plays an important role in the damage
process too and it also explains prediction errors in the analysis.
This aspect has to be taken into consideration whenever the loss estimation
is performed by using a model calibrated for a different flood event.
Modeling flood loss to contents
Similar to the procedure for assessing damages to buildings, first of all
we analyze the Spearman correlation between the observed flood loss to
contents and all potential predictive variables, included monetary damages to
buildings. Figure shows the results of
this assessment, where full boxes represent a statistically significant
correlation coefficient at a 5 % significance level. On the one hand,
similar to the analysis for building loss, the maximum water depth and the
structural typology are significantly correlated with damages to
contents, although their correlation coefficients are low. On the other
hand, damages to contents turn out to be significantly correlated with the
building footprint (Spearman correlation coefficient equal to 0.27) instead
of the building value. A noteworthy feature of
Fig. is the very strong and statistically
significant positive correlation between damages to buildings and their
contents (Spearman correlation coefficient equal to 0.59).
Spearman correlation between monetary loss (contents only) and
predictive variables: maximum water depth, maximum water velocity, flood
duration, structural type (masonry, masonry and reinforced concrete, or
reinforced concrete), building area, building value per unit area and monetary
loss to buildings. Empty boxes indicate statistically nonsignificant
correlation coefficients at a 5 % significance
level.
We therefore explore the possibility of exploiting the relationship between
monetary loss to buildings and contents for predicting the latter. We test
different types of mathematical relationships (i.e., linear, square root,
logarithmic and bi-logarithmic regressions), and the square root regression
is the one with the best prediction performance in terms of RMSE, i.e.,
the one that best relates monetary building loss with damages to contents.
In fact, RMSE is equal to EUR 10 569, while it was
EUR 10 882, 10 971 and 15 531 for linear,
logarithmic and bi-logarithmic relationships, respectively. The identified
regression relationship reads
Dcontents=116Dbuildings-2311,
where Dcontents (EUR) represents economic damages to
contents, and Dbuildings (EUR) indicates loss to
buildings. Figure depicts empirical
vs. predicted monetary loss to contents with Eq. ().
Performance of different uni- and multivariable models in estimating
relative damages and overall monetary loss to contents (see Eqs. ,
, and ; the observed overall monetary
loss is equal to EUR 10.4 million). The first row shows the performance of
Eq. () applied to the observed monetary damages to buildings;
the first block represents the results of the application of Eq. ()
to monetary building damages estimated with locally derived models, while the
second represents those estimated with literature models. Models in each group are
ranked according to RMSE values, from the lowest to the largest.
Empirical vs. predicted monetary loss to contents for the
Secchia 2014 inundation event. Monetary loss to contents is predicted as a
function of monetary loss to buildings through
Eq. ().
In the last component of our analysis, we apply Eq. () for
estimating damages to contents as a function of the estimates of monetary
building loss resulting from the uni- and multivariable damage models that
we considered in our study.
Table lists the performance metrics bias,
MAE, RMSE and ΔLOSS obtained while predicting monetary loss to
contents as described. The first row in
Table reports, as a reference term, the same
performance indexes that can be obtained when Eq. () is
applied to observed damages to buildings. In the second row, the first block
of Table shows the performance in
estimating monetary content loss, applying Eq. () to monetary
damages to buildings, estimated with empirically derived models. The best
performance in terms of RMSE is always associated with SMV, followed by SEMP
and SREGx, all with comparable RMSE values. The
outcomes for literature models (last block of
Table ) also reflect the results that we
obtained when modeling building loss, presented in
Sect. . The ranking of the best-performing
literature models in terms of RMSE for an indirect assessment of content
loss is JRC Czech Republic, JRC Netherlands, JRC Germany, FLEMOps, Rhine
Atlas and JRC Belgium. Evidently, models associated with poor performances in
predicting monetary loss to buildings are also not reliable for indirectly
predicting loss to building contents by means of Eq. ()
(see JRC Switzerland, JRC other countries, MCM and JRC UK). The performance
of most considered models, with the exception of the last six in
Table , show a difference between overall
observed and predicted monetary loss to contents that does not exceed
EUR ±20 million. Different from the results obtained when predicting
damages to buildings, 11 damage models overestimate content loss, while
SEMP, JRC Netherlands, JRC Germany and Rhine Atlas underestimate them. Small
differences in the models' ranking, compared to
Tables and ,
are probably due to the fact that the regression curve for content damages is
applied to predicted building damages, which are themselves affected by uncertainty.
Conclusions
Our study focuses on the development and validation of flood loss models
based on a comprehensive database of observed loss data (1330 records),
collected after a recent inundation event in Italy. We derived empirical uni-
and multivariable damage models, whose performance has been compared with
that of stage-damage functions in the literature (MCM, FLEMOps,
Rhine Atlas and JRC models for different countries).
Consistent with the findings of , ,
and , locally identified empirical models provide better
estimation of relative and monetary damages to buildings. This result
underlines the criticality and uncertainty associated with the application of
literature damage models to different contexts from the ones in which they
were originally developed. Even though some literature models have
performance similar to locally identified empirical models, the difficulty to
retrieve detailed information about their development data and procedures
makes it difficult to identify a priori the best-performing literature models.
This hampers the practical utilization of literature models themselves for
predictive purposes. The results of this study strengthen the need, in case a
literature curve should be applied, for a more informed and rational
selection of damage models; e.g., the level of detail of each input variable
required should not be overlooked nor neglected.
Concerning the estimation of relative loss to buildings, the Secchia
Multi-Variable model (SMV), which was developed using the RF
approach, outperforms the other considered models. This outcome is
confirmed with regards to the content damages, estimated with a regression
function applied to the monetary damages to buildings estimated with
different models. Regression trees composing the multivariable forest also
provide the important advantage of avoiding the need for a parametric function
that works with all the data. Also, RF provides useful information about the
relationship among the variables and how to exploit the local relevance of
predictors. These can be very useful information for authorities and
stakeholders to define preventive measures and/or mitigation strategies.
The study on the transferability of empirical models, i.e., models calibrated
on the dataset of one given municipality and applied to a different one
located close by, shows that the best performance is controlled by the size
and consistency of the loss dataset. This consideration is valid for all
models, but especially for the multivariable one, which requires a large
number of data to ensure a reliable loss estimation
. To completely exploit the potential of such
models and sustain the possibility of exporting their use in different areas, it
is necessary to pursue a detailed and structured acquisition of explanatory
variables. According to ,
,
and , the most urgent need in Italy, concerning flood
loss estimation, is to identify guidelines, valid for the whole country, to
collect consistent and comparable data, even if they relate to different
contexts. According to , data-collection protocols are
urgently needed for harmonizing and standardizing the compilation of
flood loss datasets. These data should include further useful information, such as observed water depths,
flood duration, presence of sediments, contamination rate, early warning or
precautionary measures adopted, and other indications of the
building composition (numbers of floors, type of contents, presence of
basements, building condition, etc.), preferably collected immediately
post event see also, in
addition to that commonly collected.
As it emerges from our analysis, in the case of limited and uncertain
information, empirically univariable models still represent a good
compromise between model complexity and reliable damage estimations.
Different from other studies, which developed site-specific models but
rarely tested them in other regions, this analysis focuses on
transferability and demonstrates that models can be transferred to other
contexts with satisfying results, provided that they are similar in
terms of territorial structure and building characteristics. Since the
creation of a “one-size-fits-all” model is almost impossible due to large
variability in geographical and geomorphological contexts as well as urban
patterns and building typologies in Italy, the definition of various damage
models for different standardized Italian contexts is of paramount importance
to increase the reliability of future flood risk analyses. The adoption of
probabilistic modeling concepts could add another useful level of detail in
terms of quantitative information about the uncertainty.
Damage data used in this study, as well as building
characteristics, provided by the Emilia-Romagna Region Regional Agency for Civil
Protection and Po River Basin Authority, are not publicly accessible for
privacy reasons. Economic building values can be found at
https://wwwt.agenziaentrate.gov.it/servizi/Consultazione/ricerca.htm.
Secchia Empirical damage model (SEMP)
SEMP is the linear interpolation of points with specific coordinates,
calculated as explained in Sect. . These
coordinates are reported in Table .
SEMP model: empirical curve obtained from the binning procedure in
terms of water depth (h) and relative damage to buildings (see Sect.
for the procedure adopted to develop the curve).
h(m)Relativedamage(–)0.0000.0000.1250.0580.3750.0580.6250.0590.8750.0601.1250.0601.3750.0721.6250.0941.8750.1612.1000.226Secchia Multi-Variable damage model (SMV)
SMV is an ensemble of several regression trees, built from the bootstrap
replica of the learning data, as explained in
Sect. . Figure reports a
qualitative example of one of these regression trees for the Secchia case
study, cut off at an arbitrary level for the sake of clarity.
Example of a tree built with the RF algorithm on the basis of the
Secchia dataset. White boxes represent splitting nodes, together with the
indication of the splitting variable and its splitting value; grey boxes
represent final nodes and the estimation of the relative building damages of
that branch. The tree is cut off at an arbitrary level for the sake of
clarity.
Validation of the locally derived damage models
Figures and
show the results of the validation of the locally derived models, which estimate
relative damages to buildings as a function of maximum water velocity and
building area.
(a) Bastiglia relative damages to buildings estimated with
Bo_REGv (red dots) and Bo_MV (grey dots); (b) Bomporto
relative damages to buildings estimated with Ba_REGv (red dots) and
Ba_MV (grey dots).
(a) Bastiglia relative damages to buildings estimated with
Bo_REGa (red dots) and Bo_MV (grey dots); (b) Bomporto
relative damages to buildings estimated with Ba_REGa (red dots) and
Ba_MV (grey dots).
The original dataset was checked, homogenized and geocoded
by FC, who also performed the numerical analyses, within the activities of her
PhD thesis. KS and HK had an essential role in the development of the multivariable
model while AD and AC contributed to the development and testing of the
empirical univariable ones. All authors made a substantial contribution to the
critical interpretation of results and provided important ideas to further
improve the study. All authors actively took part in drafting, writing and revising the paper.
The authors declare that they have no conflict of interest.
Acknowledgements
The Emilia-Romagna region, Regional Agency for Civil Protection and Po River
Basin Authority are kindly acknowledged for providing the datasets used in
this study. In fact, part of the activity was performed with the support and
contribution of the Civil Protection Agency of Emilia-Romagna under a
5-year framework research agreement with the Department of Civil,
Chemical, Environmental and Materials Engineering (DICAM) of the University
of Bologna . The present work was also developed
within the framework of the Panta Rhei Research Initiative of the
International Association of Hydrological Sciences (IAHS). Funding was partly
provided by the University of Bologna, the SYSTEM-RISK
Marie Skłodowska-Curie European Training Network (EU grant 676027) and the
IMPREX project (EU grant 641811). Finally, the authors would like to
sincerely thank the two anonymous reviewers for their effort to improve the
paper with valuable comments and suggestions.
Edited by: Margreth Keiler
Reviewed by: two anonymous referees
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