We propose and investigate the reliability of simplified graphical tools, which we term Hypsometric Vulnerability Curves, HVCs, for assessing flood vulnerability and risk over large geographical areas and for defining sustainable flood-risk mitigation strategies. These curves rely on the use of inundation scenarios simulated by means of quasi-two-dimensional (quasi-2-D) hydrodynamic models that reproduce the hydraulic behaviour of the floodable area outside the main embankment system of the study river reach. We present an application of HVCs constructed on the basis of land use and census data collected during the last 50 years for assessing the recent dynamics of the flood vulnerability and risk over a large floodable area along a 350 km stretch of the River Po (Northern Italy). We also compared the proposed simplified approach with a traditional approach based on simulations performed with the fully-2-D hydrodynamic model TELEMAC-2-D, a widely employed and well-known 2-D finite-element scheme. By means of this comparison, we characterize the accuracy of the proposed simplified approach (i.e. quasi-2-D model and HVCs) for flood-risk assessment over large geographical areas and different historical land-use scenarios.

According to the Emergency Events Database (EM-DAT dataset;

Under this premise, the definition of a robust large-scale flood-risk
mitigation strategy requires us to take into account the interaction between
social and hydrological factors that characterize a specific area and to
adopt holistic approaches for assessing flood risk and its evolution in
time. To this aim, we propose an approach based on simplified hydrodynamic
models (i.e. quasi-two-dimensional, quasi-2-D) for assessing flood-risk over
large geographical areas. We present an application of the proposed approach
for quantifying flood-risk evolution during the last five decades (from 1954
to 2008) in a large flood-prone area (

As inundation processes on floodplains have a markedly two-dimensional (2-D) nature, the traditional approach to flood risk assessment resorts to the application of 2-D models for a quantification of hydraulic hazards. Based on topographic information, boundary and initial conditions and different mathematical and numerical schemes, 2-D models reproduce the inundation processes, simulating various flood intensity indicators such as water depth, flow velocity and dynamics of the flooding front.

The output of such models for reference inundation scenarios or sequences of hydraulic loads that are stochastically generated within a Monte Carlo framework (see e.g. Vorogushyn et al., 2010) are then used to assess the expected amount of economic damages in the study area. The scientific literature reports a wide set of depth-damage curves, in which the percentage of damage of a specific asset is related to the water depth. They are constructed on empirical damage data (i.e. historical inundations) or using expert judgment and synthetic analysis and refer to different applications contexts, diverse categories of buildings (i.e. residential, commercial, industrial, etc.; see e.g. Thieken et al., 2008) and the effect of factors which may influence the expected damages (e.g. contamination, levels of private precaution, etc.; see e.g. Kreibich et al., 2010).

Considering the traditional approach briefly recalled above, despite the high reliability of state-of-the-art fully-2-D hydraulic models, and although these models are not necessarily slower in terms of computation time than simpler models, their implementation requires difficult numerical solutions and time consuming pre-processing steps (Falter et al., 2012, and references therein). This complexity is not compensated in terms of accuracy, when compared to less complex schemes in terms of inundation extent and risk estimates (see e.g., Castellarin et al., 2011b and references therein).

Due to the limitations of the traditional procedure over a large-scale analysis, outlined in Sect. 2.1, we propose a simplified hydraulic approach in order to define a concise yet reliable methodology for flood risk assessments over large spatial areas. This approach consists of the development of an inundation scenario computed through a simplified quasi-2-D hydraulic model, that is a model combining 1-D river networks, for simulating the channels and the unprotected lateral floodplains, with hydraulically interconnected storage areas that reproduce the dyke-protected floodplains and the flood-prone areas outside the main embankment system (these latter named compartments hereinafter; see e.g. Castellarin et al., 2011a). The output of the model is then combined with graphical flood-vulnerability indexes described below, which are particularly suitable for large spatial scale assessments, and allows us to study the evolution in time of flood exposure, flood risk and economic damages.

The graphical tools we propose describe the flood-vulnerability within each
floodable compartment located outside the embankment by combining land-use
information (i.e. urban settlements, industrial or rural areas) with a
digital description of the compartment topography. In particular, for each
compartment and the land-use class of interest (e.g. urban and residential
areas) the graphical tool reports on the

An example of potential damage computation is reported in Fig. 1. Let us
focus for instance on urban areas, the maximum water level associated with a
given inundation scenario may be reported on the urban-area HVC as a
horizontal line (blue dashed line in Fig. 1b), which provides an indication
of the extent of the flooded urban area (A

Schematic representation of the combination of

The study area consists in the alluvial plain of the longest Italian river,
the Po river (about 650 km from west to east in the North of Italy). It
flows in the Northern part of Italy for about 650 km. Its river basin is
also the wider Italian catchment (about 71 000 km

Figure 2 shows the current river configuration. The main embankment system
extends for more than 2900 km and outside of it is located the “C-Buffer”
area (blue polygons, with an overall extent of about 6100 km

The analysis refers to a set of various data collected from different sources:

Study area: Po river basin and Regions of interests (Emilia-Romagna and Lombardy); the blue compartments (blue polygons) represent the area outside the levee system exposed to a residual flood risk (i.e. C-Buffer zone; AdB-Po, 1999).

We refer to an inundation scenario obtained by Castellarin et al. (2011a) using the UNET code, available as part of the software package HEC-RAS, that numerically solves the Saint–Venant equations through an algorithm that uses a classical implicit four-point finite difference scheme (Castellarin et al., 2011a, and references therein). Referring to a 500-year return period event, the authors develop a quasi-two-dimensional (quasi-2-D) hydraulic model relative to the middle-lower reach of Po river, which describes the main channel by means of cross-sections retrieved from a detailed digital elevation model (LiDAR, with a spatial resolution of 2 m). Storage areas connected to each other and/or to the main channel by means of weirs represent the dike-protected floodplains, mirroring an existing system of minor levees (see Castellarin et al., 2011b). The quasi-2-D model was calibrated referring to the historical flood event occurred in October 2000 (see Castellarin et al., 2011b for details). All the C-Buffer compartments are represented as storage areas connected to the main river, or to the dike-protected floodplains, by means of lateral structures that represent the main embankment crests. The behavior of the storage areas is controlled by volume-level curves by means of which the water level in case of inundation is computed as a function of the water volume exchanged with the main channel and/or adjacent storage areas. When the overtopping of the main embankments occurs, the model simulates the formation of breaches, whose width, depth and time of full development are retrieved from literature related to the Po river (see e.g. Govi and Turitto, 2000 and Castellarin et al., 2011a).

Reference inundation scenario: flooded C-Buffer compartments according to the quasi-2-D model (see Castellarin et al., 2011a and Fig. 2).

Comparison between the quasi-2-D and fully-2-D models for the flooded compartments of interest.

Compartment 10: DEM and comparison between the quasi-2-D and the fully-2-D model in terms of flooded areas (top panels) and flooded urban areas in 1954 and 2008 (bottom panels).

Starting from the results of the reference inundation scenario, we examine the flood-risk evolution in the C-Buffer during the last 50 years. Even though we refer to land-use scenarios of different historical periods, 1954 and 2008, we consider the current geometry of the main embankment system. Our choice is justified because the aim of the study is to assess the role of the urbanization in the flood-risk evolution, independently of all other factors. By combining the HVCs computed for 1954 and 2008 with the maximum water inundation levels provided by the quasi-2-D model, we quantify the direct flood losses in urban areas for each flooded compartment according to the methodology outlined in Sect. 2.2. Among the available depth-damage curves, we refer to the damage-curve implemented in the Multi-Colored Manual (MCM; Penning-Roswell et al., 2005) that estimates at best the expected losses for residential buildings as a function of the local water depth.

Table 1 reports the maximum water depth and the total overflow volume simulated through the quasi-2-D model for each flooded compartment, together with the estimate of the extent of urban areas flooded in 1954 and 2008 and of the economic damages associated to the reference inundation scenario.

The choice of the compartments to be considered, among all the compartments flooded in the quasi-2-D model, has been done considering the five most representative compartments, from a morphologically and residential point of view.

In particular, because of urban expansion, the overall urban extent affected
by the inundation scenario is equal to 420 ha in 1954 and 945 ha in 2008.
Consequently, we calculate an overall damage associated with urban buildings
equal to

We validate the proposed simplified approach against a series of simulations
of the reference inundation scenario through the fully-2-D hydrodynamic model
TELEMAC-2-D, which solves the 2-D shallow water Saint-Venant equations using
the finite-element method within a computational mesh of triangular elements
(see Galland et al., 1991 for details). In particular, TELEMAC-2-D is used to
simulate the inundation dynamics in the flooded compartments of interest by
using the overflowing flow-rates simulated with the quasi-2-D model as
boundary conditions; we then compare the inundation extents simulated by
TELEMAC-2-D with the corresponding extents retrieved from the quasi-2-D
schematization. First, we quantify the agreement between flooded urban areas
in 1954 and 2008 by means of the flood area index (FAI, see Falter et al.,
2012) defined as

Table 2 reports the FAI for flooded urban areas in 1954 and 2008 and for
each compartment of interest, showing also the difference in terms of damage
calculation for both years. The FAI index for flooded urban areas in 1954
and 2008 results very close to 1 (i.e. perfect agreement between simplified
and traditional flood-risk assessment) for three out of 5 compartments,
whereas the agreement is poorer for the remaining two compartments. The
differences in damage calculations mirror the results in terms of FAI, with
a minimum percentage difference of

We propose a simplified procedure (based on a quasi-2-D model and Hypsometric Vulnerability Curves, HVCs) for flood-risk assessment over large geographical areas and we compare its performances in estimating expected flood losses associated with two historical land-use scenarios with a traditional approach based on simulations from a fully-2-D hydrodynamic model. The analysis shows that the simplified approach is able of simulating the flooded areas in the compartments of interest with a reasonable accuracy. However, in two out of five study compartments we observe a significant difference in terms of simulated flood extent and flood-related damages. Looking at Fig. 3, one can observe that this inaccuracy results from an inappropriate compartment delineation. In the specific case of compartment 10, the simplified quasi-2-D model cannot correctly reproduce the flooding dynamics, since the inundation develops form the lowland portion of the compartment, regardless the position of the levee breach. On the contrary, the fully-2-D model ensures a correct reproduction of the flood dynamics given the topography of the study compartment. We expect that a more precise delineation of the compartments would lead to a higher accuracy of our procedure, which can thus be considered to be a valid simplified approach to assess the flood risk and its evolution in time over large geographical areas.

The study is part of the research activities carried out by the working group: Anthropogenic and Climatic Controls on WateR AvailabilitY (ACCuRAcY) of Panta Rhei – Everything Flows Change in Hydrology and Society (IAHS Scientific Decade 2013-2022).