**5. The IRP model**

On the basis of the proposal of the ISPRA document, a model (named IRP model) has been proposed by public administration in Piemonte region to quantify and evaluate risks, in view of the revision of the flood-risk maps. The model can also be a usable instrument to fulfill the requirements of the Re.N.Di.S. (National Repository for Soil defense) platform, described in

Flood damage quantification and assessment is not only a (optional) requirement for the implementation of EFD, but it has recently become a requirement for the evaluation of the

Actually, with the recent 2015 decree of the President of the Ministry Council (2015DPCM in the following), a new discipline to evaluate the priority of public financing for flood protection projects came into force in Italy. To set priorities is fundamental when financial resources are scarcer than necessities. Actually, at the moment, the total needs for protection (by considering all the kinds of natural hazards, which are floods, landslides, flash floods, debris flows) amount to about 30G€, by far higher than the resources available at the moment

The model for prioritization proposed by the 2015DPCM is based on a score approach.

According to the 2015DPCM, flood defense projects have to be collected into the so-called Re.N.Di.S. procedure, which is a national repository of projects for soil defense. For a given project, either the assessments by public administration, or the level reached by design, or the effectiveness of the designed countermeasures are scored. The Re.N.Di.S. procedure allows to associate a total score to each proposed project, included in the Re.N.Di.S. procedure. The

For the sake of simplicity, it can be said that, for a given project of flood protection measures included in the Re.N.Di.S procedure, the priority to financing is based on its total score: the higher is its score, the higher is its ranking and therefore the probability for public financing. As shown in **Table 3**, flood damage evaluation score is relevant with respect to other criteria:

> **Total financing requirements**

**Public financing requirements**

the following paragraph.

(**Table 2**).

criteria are listed in **Table 3**.

**4. The Re.N.Di.S. platform for planning**

22 Natural Hazards - Risk Assessment and Vulnerability Reduction

projects of countermeasures and for the eligibility of public financing.

if the damage evaluation is given, there is a 10-point score.

**Total number of interventions eligible for financing**

\*The total includes avalanches, soil-slips, coastal erosion, and other natural hazards.

Floods in Italy 3284 15,046.00 M€ 13,809.40 M€ Floods in Piemonte 417 1179.20 M€ (not available) Total\* 9397 29,110.00 M€ 26,407.90 M€

**Table 2.** Total amount of proposed interventions for risk reduction and financing necessities (taken from [12]).

In order to overcome the constraints of the present methodologies for risk mapping, Regione Piemonte public administration in collaboration with the Politecnico of Turin and the University developed a methodology for risk assessment and quantification, which is based on the quantification of the *Index of Proportional Risk* (IRP).

The model has been developed by referring to specific types of risk, according to **Table 4**.

The IRP is quantified by applying the following expression:

$$\text{IRP} = \frac{1}{T} \sum\_{l=1}^{N} \mathbf{e}\_{l} \mathbf{A}\_{l} \mathbf{v}(\mathbf{h}) \tag{2}$$

*different methodologies employed for various damage models in different countries*…*damage assessments cannot be directly compared with each other, obstructing also supra-national flood damage* 

Index of Proportional Risk (IRP) Flood-Risk Assessment Model and Comparison to Collected Data

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25

The discussion about the depth-damage curve to be adopted for risk mapping is in course among regions in Po watershed basin, the Po District authority, the Turin University, the

In the proposed model [14, 15], exposure is evaluated by referring to the OMI (*estate market observatory*, free available online, [17]) database. The exposure *E* of each receptor has been computed by the product of the area A of the receptor for its economic value "e"; this parameter is reported in the *OMI* dataset and, as applied in [14, 15], varies depending on the prevalent use of receptors (commercial, residential) and their location in the urbanized areas (*OMI*

zones), which are considered homogeneous from the economic market point of view.

h Water depth, computed at the centroid of the receptor. For receptors outside the flooding area, it is h = 0. The depth h is calculated at the barycenter of the i-th receptor, that is, by using a GIS terminology, at its *centroid*

A Receptors are contained in the Regione Piemonte BDTRE database, available to public (in *shape* format). The area of the receptors can be easily and automatically quantified by means of GIS software (e.g., QGIS©)

**Figure 2.** An example of the application of the procedure to the Chisola river. The map has been obtained by referring to the 2016 flood. Risk classes are on a log-scale (R1 class: 0–1000.00€; R2 class: 1000.00–10,000.00€; R3 class: 10000.00–

100,000.00€; R4 class: >100,000.00€; the blue line indicates the borders of the flooding areas).

V(h) The equation for vulnerability is contained in the JRC publication for "Europe" [13]

**Table 5.** Constitutive elements in the proposed model (H, E, V) and discussion (see [14, 15] for details).

, as indicated in the OMI database; OMI database is periodically

*assessments*" [13].

**Item Description**

Politecnico of Turin, and of Milan.

e The value of the receptor expressed in €/m2

updated and available to public

where *N*: total number of receptors in the flooding area; *T*: return period (years); *h*: flow depth (m); *A*: area of the receptor (m2 ); *e*: OMI value (€/m2 ); *v*(*h*): vulnerability (adim.); *IRP* dimension is €/year. The multiplication of the IRP and the return period is called *index of proportional damage* (IDP).

The model implicitly assumes the definition of risk contained in the EFD, as it refers either to the probability (the return period) or to the consequences of flood in terms of the flood damage.

According to Eq. (2), the model assumes that the total risk is proportional to the area of the receptor. A short description of the terms in Eq. (2) is given in **Table 5**.

The vulnerability V(h) is estimated by means of the JRC "European" curve in [13].

Flood depths maps can be easily obtained by following the procedure contained in [14, 15] and widely applied in the project of "Orco river flooding assessment," developed in collaboration with the former Po basin Authority [16].

The choice of the JRC curve has been guided by the necessity to adopt a "robust" formulation, which is based on a "*…globally consistent database…*" of depth-damage curve.

The proposal of a vulnerability curve usable for Po river floodplain is not simple, in particular due to the lack of detailed damage data, so that a vulnerability curve cannot be easily obtained for the receptors in Piemonte region and Padana plain.

As it is well known, many flood damage models using depth-damage curves have been proposed in scientific literature in different countries. They are generally based on analysis of past flood events and on regression of available data. However, such damage curves are not available for all regions, and their use can be questionable in some areas. Moreover, "*due to* 


**Table 4.** Natural hazards and types of processes to which the IRP model refers to.

*different methodologies employed for various damage models in different countries*…*damage assessments cannot be directly compared with each other, obstructing also supra-national flood damage assessments*" [13].

The model has been developed by referring to specific types of risk, according to **Table 4**.

<sup>T</sup> ∑ i=1 N

); *e*: OMI value (€/m2

The vulnerability V(h) is estimated by means of the JRC "European" curve in [13].

which is based on a "*…globally consistent database…*" of depth-damage curve.

obtained for the receptors in Piemonte region and Padana plain.

Type of risk Direct and tangible risks; the model

Type of processes Major river flood processes in plains.

**Table 4.** Natural hazards and types of processes to which the IRP model refers to.

Main field of application/

objective

receptor. A short description of the terms in Eq. (2) is given in **Table 5**.

where *N*: total number of receptors in the flooding area; *T*: return period (years); *h*: flow depth

sion is €/year. The multiplication of the IRP and the return period is called *index of proportional* 

The model implicitly assumes the definition of risk contained in the EFD, as it refers either to the probability (the return period) or to the consequences of flood in terms of the flood

According to Eq. (2), the model assumes that the total risk is proportional to the area of the

Flood depths maps can be easily obtained by following the procedure contained in [14, 15] and widely applied in the project of "Orco river flooding assessment," developed in collabo-

The choice of the JRC curve has been guided by the necessity to adopt a "robust" formulation,

The proposal of a vulnerability curve usable for Po river floodplain is not simple, in particular due to the lack of detailed damage data, so that a vulnerability curve cannot be easily

As it is well known, many flood damage models using depth-damage curves have been proposed in scientific literature in different countries. They are generally based on analysis of past flood events and on regression of available data. However, such damage curves are not available for all regions, and their use can be questionable in some areas. Moreover, "*due to* 

> has been developed by referring to structural (and content) damage

By taking into account sediment transport, the model can also be applicable to stream floods

**Applicability Possible extension**

ei Ai v(h) (2)

); *v*(*h*): vulnerability (adim.); *IRP* dimen-

The model allows to obtain a quantitative estimation of damages (and risks), to which other damages (and risks) can be correlated

The model can be extended to processes like debris flows/soil-slips, as far as E is concerned. The approach to H and V

(e.g., indirect damages)

should be revised

Spatial and land planning Possible extension to real-time risk (civil protection)

The IRP is quantified by applying the following expression:

IRP = \_\_<sup>1</sup>

24 Natural Hazards - Risk Assessment and Vulnerability Reduction

ration with the former Po basin Authority [16].

(m); *A*: area of the receptor (m2

*damage* (IDP).

damage.

The discussion about the depth-damage curve to be adopted for risk mapping is in course among regions in Po watershed basin, the Po District authority, the Turin University, the Politecnico of Turin, and of Milan.

In the proposed model [14, 15], exposure is evaluated by referring to the OMI (*estate market observatory*, free available online, [17]) database. The exposure *E* of each receptor has been computed by the product of the area A of the receptor for its economic value "e"; this parameter is reported in the *OMI* dataset and, as applied in [14, 15], varies depending on the prevalent use of receptors (commercial, residential) and their location in the urbanized areas (*OMI* zones), which are considered homogeneous from the economic market point of view.


**Table 5.** Constitutive elements in the proposed model (H, E, V) and discussion (see [14, 15] for details).

**Figure 2.** An example of the application of the procedure to the Chisola river. The map has been obtained by referring to the 2016 flood. Risk classes are on a log-scale (R1 class: 0–1000.00€; R2 class: 1000.00–10,000.00€; R3 class: 10000.00– 100,000.00€; R4 class: >100,000.00€; the blue line indicates the borders of the flooding areas).

The IRP model can be easily used to rank flood risk, according to quantitative criteria. At present, it can be used to calculate the risk (and the damage) on receptors (buildings), as well as for risk mapping (**Figure 2**).

by the Council of Ministry. Consequently, some companies, which were affected by the flood and suffered extensive property damages, asked for the *declaration* of the emergency *status* and also claimed the restoration of damages and the reinstallation of adequate defenses in order to continue to stipulate insurance with adequate contractual conditions. The Council of Minister declared the emergency *status* on December 16, 2016, only for Turin and Cuneo Provinces. Afterwards, Regione Piemonte public administration asked to extend the *declaration* to Asti and Alessandria. On February 23, the Council of Ministers approved the resolution, extending the emergency *status* to the provinces of Asti and Alessandria, providing the

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After the flood event, the Regional Departments started some activities, aiming to map and assess the flood effects, upon which the hazard evaluations of the IRP model have been based.

• systematic mapping of requested interventions by means of the EMETER (*Emergency and Territory Management Information System*) application; the EMETER is a web-GIS system useful for regional officials of the Public works Directorate, which operates both in ordi-

• field surveys along the main rivers, including Bormida river and Tanaro river; the technicians carried out systematic surveys in order to integrate and evaluate the information deriving from remote sensing; analysis of satellite data from the Cosmo platforms and

• acquisition and processing of aerial photographs; a flight was made in the week following the event; aerial photo interpretation allowed to integrate the satellite and ground surveys.

Flood maps were the basis upon which the hazard estimation procedure of IRP started from.

In this application, the exposure of receptors in the flooded area refers to the 2018 OMI database. The variability in time of the asset value (i.e., from the date when the flood occurred to present days) is negligible. The total number of flooded receptors and municipalities is

After the 2016 flood, data of damages have been collected by public administration according to the civil protection procedures [18]*"Procedure for the recognition of the needs for the restoration of damaged public and private structures and infrastructures, as well as for the damages to economic and productive activities, to cultural heritage, and to the housing assets."* The procedures are followed by Regione Piemonte administration [19, 20] and are available to public. According to them, the requests for residential and productive damage indemnification have to be collected in the so-called *B-sheet* (*Recognition of the needs for the restoration of private buildings* sheet, which contains all the requests regarding residential damages*)* and *C-sheet* (*Recognition of damages suffered by economic and productive activities* sheet, which contains all the requests regarding damages to economic/productive activities), respectively. These have to be filled by privates

from the platforms belonging to the European Copernicus system was performed;

The procedure to obtain the flood depth maps has been described elsewhere [14, 15].

allocation of financial resources.

These activities are the following:

summarized in **Table 6**.

and confirmed by technical assessments.

nary situations and in case of extraordinary events;
