**3. Limitations in the approach to risk and vulnerability assessment**

Risk matrices approaches are widely used by public administration as a basis for risk management decisions, with applications [5] from terrorism risk analysis, to highway construction project management, to dam and levee safety and climate change risk management. Risk matrices are widely used for risk reporting, risk prioritization, and risk monitoring [6].

On one hand, they are easy to use and intuitive, and they are often defended as a practical way to flood-risk management, especially when quantitative information is scarce or nonexistent [7]. On the other hand, their theoretical basis is superficial and their employ in decision making is hard, especially when different technical solutions for flood-risk management have to be compared to each other.

At present state, it is sustained that "*the flood directive asks for vulnerability parameters only. The risk as such is not explicitly requested, but implicitly the notion of risk is an integrated part*" (*Handbook on good practices for flood mapping in Europ*e [8]). In other terms, the EFD does not require a quantitative estimation of risk. The cited handbook addresses the map of assets at risk (i.e., the distribution of population, vulnerable groups, and buildings at risk) more than to "*risk maps.*"

The same *Floods Directive Reporting Schemas* [9], which should be followed by countries in reporting to European Commission, allow different methods for reporting, and quantitative estimation is optional. Actually, according to the reporting schema, damage can be indicated (i) as a range, (ii) as a percentage of the total GDP for the flood event, (iii) by classes (Insignificant, Low, Medium, High, Very high), or (iv) by means of other numerical measure indicative of the degree of (potentially) adverse consequences, leaving a wide choice for implementation.

Therefore, the report of quantitative damage is not compulsory, qualitative estimations are widespread, even if the risk formula, which implies the quantification of risk, is often reported in official documents (see [9], p.23).

There are several practical problems with matrix approach, either with respect to the guidelines of the EFD or theoretical.

As far as the Po basin District Authority ([4], p. 17) is concerned, the risk is assessed by the combination of the damage and hazard classes, through a matrix approach. The rows show the damage classes and the columns the hazard levels, that is, the probability of flood occurrence. The implementation of this matrix allowed associating a risk class to each exposed

**Figure 1.** The matrices adopted in PGRA, by Po basin District Authority. Hazard classes P1, P2, and P3 refer to the return

To distinguish the different impacts in terms of human life and anthropic activities risk, three different matrices were used, each for a different flooding process: (i) first matrix (a) in **Figure 1** refers to flooding in main rivers, (ii) second matrix (b) to lake flooding and Apennines rivers,

On the basis of hazard and flood-risk maps, the District Authorities prearrange the flood-risk

Risk matrices approaches are widely used by public administration as a basis for risk management decisions, with applications [5] from terrorism risk analysis, to highway construction project management, to dam and levee safety and climate change risk management. Risk matrices are widely used for risk reporting, risk prioritization, and risk monitoring [6].

On one hand, they are easy to use and intuitive, and they are often defended as a practical way to flood-risk management, especially when quantitative information is scarce or nonexistent [7]. On the other hand, their theoretical basis is superficial and their employ in decision making is hard, especially when different technical solutions for flood-risk management have

At present state, it is sustained that "*the flood directive asks for vulnerability parameters only. The risk as such is not explicitly requested, but implicitly the notion of risk is an integrated part*" (*Handbook on good practices for flood mapping in Europ*e [8]). In other terms, the EFD does not

management plans (PGRA), coordinated at the level of river basin district.

**3. Limitations in the approach to risk and vulnerability assessment**

and (iii) third matrix (c) refers to plane secondary rivers.

period indicated in EFD (P1 for T = 20–50; P2 for T = 100–200; P3 for T = 500).

20 Natural Hazards - Risk Assessment and Vulnerability Reduction

element (receptor).

to be compared to each other.

First, the scales shown in the matrix are ordinal (i.e., rank-ordered); consequently, mathematical operations with ordinal scales are meaningless.

Second, the risk matrix generally shows only probability and consequence, and rank risks by that pair of measures; vulnerability is implicitly considered in the matrix or set equal to a constant value.

Third, communication to people may reveal to be captious; for example, the damage in D4 class in **Table 1** is not necessarily twice the damage of D2 class, in spite of the damage class indication.

Fourth, it is questionable if risk matrices actually improve decision making. Cox has been particularly critical of risk matrix and hazard ranking systems, concluding that "*Applying portfolio optimization methods instead of risk prioritization ranking, rating, or scoring methods can achieve greater risk-reduction value for resources spent"* [10].

The present limitations of risk mapping approach adopted in the implementation of EFD can be reviewed and in the next step of "*…reconsideration and updating…*" in the flood directive.

Actually, the *management plans for flood risk (PGRA)* should be periodically reviewed, and if necessary updated, taking into account "*…the likely impacts of climate change on the occurrence of floods*" (EFD, art.14). Italian legislation provides the time limits to review the preliminary flood-risk assessment (before 09/22/2018 and at a later stage, every 6 years), the hazard maps and flood risk (before 22.9.2019 and thereafter every 6 years) as well as the Management Plans (before 22.09.2021 and thereafter every 6 years).

To this aim, ISPRA edited "*Methodological proposal for updating hazard and risk maps for risk mapping*" [11]. The document aims at proposing some approaches, taken from scientific literature, to be implemented in the revision and updating of the flood-risk maps.

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 the following paragraph.
