Basic principles of multi-risk assessment: a case study in Italy

Abstract

The assessment of the impact of different catastrophic events in a given area requires innovative approaches that allow risks comparison and that account for all the possible risk interactions. In the common practice, the risk evaluation related to different sources is generally done through independent analyses, adopting disparate procedures and time--space resolutions. Such a strategy of risks evaluation has some evident major drawbacks as, for example, it is difficult (if not impossible) to compare the risk of different origins, and the implicit assumption of independence of the risk sources leads to neglect possible interactions among threats and/or cascade effects. The latter may amplify the overall risk, and potentially the multi-risk index could be higher than the simple aggregation of single-risk indexes calculated considering each source as independent from the others. In this paper, we put forward some basic principles for multi-risk assessment, and we consider a real application to Casalnuovo municipality (Southern Italy), in which we face the problem to make different hazards comparable, and we highlight when and how possible interactions among different threats may become important.

Appendix: Analysis of risks induced by a single source

The procedures for probabilistic hazard and risk assessment from different sources are hereafter described. The discussion is focused on the preliminary single-risk assessments made for the case study of Casalnuovo. For more details on specific methodologies applied, see Marzocchi et al. (2009).

1.1 Seismic risk in Casalnuovo

The most recent evaluation of the probabilistic seismic hazard in the Casalnuovo area, as provided by the National Seismic Hazard Map (http://www.INGV-zonesismiche.mi.ingv.it), is represented in Fig. 4. The 90th percentile of the peak ground acceleration in the next 50 years is in the range 0.15–0.175 g. The same map has been also expressed in terms of seismic intensity (Gomez Caprera et al. 2007), where Casalnuovo shows a 10% of probability to overcome an intensity VIII in the next 50 years. Since the process is time-independent, the annual probability is p _VIII  = 0.002.

Fig. 4

Probabilistic seismic hazard in the Casalnuovo area taken from the National Seismic hazard map (a_max are in units of g)

In order to estimate the expected damage for such a kind of event, we have to assume the vulnerability of the buildings, the level of damages, and how these parameters reflect on the probability of having casualties. The relationship between intensity (I) and degree of damage has been defined for some municipalities close to Casalnuovo by Zuccaro et al. (2008) for the 2007 version of the Italian Civil Protection Emergency Plan of Mount Vesuvius. Buildings have been gathered in four categories (from A to D) according to their structural characteristics, and five levels of increasing damage have been defined. The probability of damage (y-axis) of an earthquake of intensity VIII as a function of possible damage level (x-axis) for four different building typologies is reported in Fig. 5. Casalnuovo has prevalent D type buildings, as the surrounding areas [see, for example, Fig. 15 in Zuccaro et al. (2008)].

Fig. 5

Probability of damage as a function of damage level for an earthquake of I = VIII. The curves are relative to four typologies of buildings Zuccaro et al. (2008)

Using the plot in Fig. 5, the expected damage corresponding to I = VIII will be:

$$ \begin{aligned} \hbox{Damage}\,4 &= 0.1\% \\ \hbox{Damage} \leq 3 &= 99.9\% \\ \end{aligned} $$

(7)

while earthquakes of I = VII will produce Damage level less than 4 in the Casalnuovo area.

It can be assumed that only Damage level 4 (partial collapses) or more can lead to casualties of people living inside the buildings. Therefore, no risk for people can be assumed for I=VII. Specifically, a person living in a building suffering Damage 4 has 5% of probability to be killed (Zuccaro et al. 2008). The risk for human life can be estimated assuming that the number of people staying on average inside one building is given by the total number of citizens (47,940) divided by the number of edifices (3,615), i.e., 13.26. This is a very rough assumption, since we assume that all citizens will be inside a building at the time of the earthquake. Actually, this number will be lower, but in this way, we accommodate partially the possible death of people on the street caused by a building collapse. The risk for human life $\mathbf{R}_{\hbox{Seis}}$ is composed by three factors: (1) the probability of occurrence of a I = VIII earthquake, (2) the average number of edifices with expected damage level 4, and (3) the average number of people killed inside a building with expected damage level 4. Such a probability is:

$$ {\mathbf{R}}_{\hbox{Seis}} = 0.002 (0.001 \times 3,615) (0.05 \times 13.26) = {\mathbf{0.005}} $$

(8)

1.2 Volcanic risk assessment: the ash fall hazard

Historical data indicate that ash fall is the main adverse event due to eruptions of Mt. Vesuvius in the Casalnuovo area. Due to volcano morphology and the distance from the volcano, other possible adverse events, such as pyroclastic flows, lava flow, and lahars, have been very rare in this area. Actually, Casalnuovo is out of the red zone of danger defined by the Mt. Vesuvius Civil Protection Emergency Plan, but it is well within the zone under threat of ash fall. However, we remark that the inclusion of such events does not pose further conceptual problems. The probabilistic ash fall hazard assessment is obtained through the use of Bayesian Event Tree (BET) (e.g., see Fig. 6). The full description of the method is described in Sect. 2.2 of Marzocchi et al. (2009). The set up of the conditional probabilities at each node were taken from Marzocchi et al. (2004).

Fig. 6

Event Tree scheme for probabilistic volcanic hazard assessment

The annual probability of Ash Fall in Casalnuovo can be estimated using the probabilities at the nodes at the Bayesian event tree, as indicated in Marzocchi et al. (2004, 2009):

$$ \left [\pi \right ] = 12 \sum_{\rm VEI} \left [\Uptheta_1\right ] \left [\Uptheta_2\right ] \left [\Uptheta_3\right ] \left [\Uptheta_5^{\rm (VEI)}\right ] \left [\Uptheta_{6, \rm{VEI}}^{\rm (TF)}\right ] \left [\Uptheta_{7,{\rm VEI}}^{\rm (Casalnuovo)}\right ] \left [\Uptheta_{8,{\rm VEI}}^{\rm (threshold)}\right ] $$

(9)

where the summation is for eruptions with Volcanic Explosion Index (VEI = III, IV, and V+), and the factor 12 transforms the month probability (node 1) into annual probability. We stress that this approximation holds when the probabilities are small as in the present case. The multiplication is performed through 1,000 values randomly selected for each node. At the end, we have four distributions, each one relative to a specific thickness. These distributions are reported in Figs. 7, 8, 9, and 10.

Fig. 7

Probabilistic tephra fall hazard map for Mount Vesuvius. The dialog box reports the 10, 50, and 90th percentiles of the annual probability of exceedance of a thickness of 10 cm

Fig. 8

The same as Fig. 7, but relative to a thickness of 20 cm

Fig. 9

The same as Fig. 7, but relative to a thickness of 40 cm

Fig. 10

The same as Fig. 7, but relative to a thickness of 60 cm

The Figs. 7, 8, 9, 10 represent the exceedance probabilities calculated in a time frame of 1 month. The annual probability for any specific thickness (in cm) can be approximated as:

$$ \begin{aligned} P_{10} &= P_{(10 < \hbox{thickness} \leq 20)} = 12 * (0.0003-0.0002) = 0.0012 \\ P_{20} &= P_{(20 < \hbox{thickness} \leq 40)} = 12 * (0.0002-0.0001) = 0.0012 \\ P_{40} &= P_{(40 < \hbox{thickness} \leq 60)} = 12 * (0.0001-0.00007) = 0.00036 \\ P_{60} &= P_{(60 > \hbox{thickness})} = 12 * (0.00007) = 0.00084\\ \end{aligned} $$

(10)

In order to retrieve the individual risk, we need to incorporate the vulnerability. Using a density of 900 Kg/m3 for dry ash deposits and the probability of collapse as a function of the load reported by Zuccaro et al. (2008), the probability of collapse P _c for different thickness of the ash deposits on the roofs of a building are:

$$ \begin{aligned} P_c(10\,\hbox{cm})&= 0.00\\ P_c(20\,\hbox{cm})&=0.01\\ P_c(40\,\hbox{cm})&= 0.15\\ P_c(60\,\hbox{cm})&= 0.60\\ \end{aligned} $$

(11)

The collapse from ash fall can be compared to a Damage 4 for seismic risk. If we assume that the probability for human beings living inside the building to be killed by a collapse is 0.05 (the same as in the case of earthquakes), the annual volcanic risk for human life is:

$$ \begin{aligned} {\mathbf{R}}_{\hbox{Volc}} &= 0.0012 (0.01\times 3615) (0.05 \times 13.26) \\ &= 0.00036 (0.15 \times 3615) (0.05 \times 13.26) \\ &= 0.00084 (0.60 \times 3615) (0.05 \times 13.26) \\ &= {\mathbf{1.37}} \\ \end{aligned} $$

(12)

1.3 Hydrogeological risk assessment

The geological nature, the topography, the climatic conditions and particularly the carefree use of land have made Campania one of the Italian regions with the highest hydrogeological risk. Exposure to hydrogeological risk is therefore a problem of great social relevance, both for the number of potential casualties and for the high exposed value, consisting of homes, industries, infrastructures, life-lines and cultural heritage. Possible change of scenarios in relation to climate change is of further concern for the near future.

In Italy, the identification, delimitation and outlining of the boundaries of the areas that present flood and landslide probabilistic hazards and risks are under the competence of the River Basin Authorities, established by the Law 183/89 and identified as the responsible authority for the basin planning. Each River Basin Authority used different criteria for the definition of the areas at landslide or flooding risk. Figure 11 represents the flood hazard map for the area and is the result of the harmonization for the Campania territory of the information of hydrogeological asset plans given by each local River Basin Authority of Campania region (e.g. Autorità di Bacino Nord-Occidentale della Campania 2002).

Fig. 11

Map of the flood hazard in Campania

The Casalnuovo territory does not have significant landslide probabilistic hazard. Flooding risk is moderate (R1 o R2) in some localized areas of the municipality due to a hazard of level P1 (see Figs. 11, 12). The annual probability of inhabitants in the Casalnuovo municipality to be killed by a hydrogeological event has been evaluated using the AVI catalog and average number of inhabitants. The AVI catalog reports the number of casualties in Campania Region for each event and the historical sequence of event. The result has been downscaled to the Casalnuovo number of residents. The results are:

$$ \begin{aligned} P_{\rm flooding} &= 1.4 \times 10^{-7} \\ P_{\rm landslide} &= 2.0 \times 10^{-8}\\ \end{aligned} $$

(13)

From these numbers, the annual risk for flooding $(\mathbf{R}_{\rm flooding})$ and for landslide $(\mathbf{R}_{\rm landslide})$ can be calculated. Looking at similar past events in Campania Region, we can assume that a landslide impacts few tens of inhabitants, while a flood can impact one order of magnitude larger. Therefore, we can estimate:

$$ \begin{aligned} {\mathbf{R}}_{\rm flooding} &= 1.4 \times 10^{-7} \times 300 = {\mathbf{4.2 \times 10^{-5}}}\\ {\mathbf{R}}_{\rm landslide} &= 2.0 \times 10^{-8} \times 30 = {\mathbf{6.0 \times 10^{-7}}}\\ \end{aligned} $$

(14)

Fig. 12

Map of the flood hazard in Casalnuovo

1.4 Industrial risk

The map of the Casalnuovo municipality, reported in Fig. 3, shows the localization of the industrial risk sources (A: industrial site for LPG storage) that can generate adverse events in the area. The most likely risk source is the pipe-bridge collapse. In the classical risk assessment, the pipe-bridge can undergo a catastrophic collapse due to the macroscopic growth of microscopic material defects. Partial collapses and the subsequent breakage of the whole pipe-bridge have been taken into account in Sect. 2.4 in Marzocchi et al. (2009). This information will be used to evaluate the conditioned probability to have casualties death due to the exposure to the heat flux generated by the fire of the LPG released by the pipelines after its collapse.

In the following, the probability of each section of the event tree is reported [for details, see Marzocchi et al. (2009)]:

$$ \begin{aligned} P(\Uptheta_B) &= 2.09 \times 10^{-4}\\ P(\Uptheta_E) &= 6.50 \times 10^{-2}\\ P(\Uptheta_F) &= 1.25 \times 10^{-1}\\ P(\Uptheta_G) &= 5.00 \times 10^{-1}\\ P(\Uptheta_H) &= 2.16 \times 10^{-1}\\ P(\Uptheta_I) &= [1: 0.01]\\ \end{aligned} $$

(15)

where $P(\Uptheta_B)$ is the probability of release of a specific substance due to a pipe-bridge collapse; $P(\Uptheta_E)$ is the probability that the event occurs under the form of a specific phenomenon (e.g. toxic release, explosion fire, etc.); $P(\Uptheta_F)$ is the probability that a specific phenomenon goes toward a specific direction; $P(\Uptheta_G)$ is the probability that the phenomenon has a certain intensity distribution in an area where the consequences are to be investigated; $P(\Uptheta_H)$ is the probability of the presence of people where the phenomenon occurs, and $P(\Uptheta_I)$ is the probability of death of people in the area, due to the exposure to the phenomena generated by the event. The individual risk is then:

$$ r_i = \prod_{J=A}^{I} \Uptheta_{J,i} $$

(16)

By applying the product of the probability values for each event, the following individual risk index range is obtained for the death of population in the risk area (117 m from the risk source localization):

$$ 1.83 \times 10^{-9} < IR < 1.83 \times 10^{-7} $$

(17)

Assuming that 10 people will be in that area of influence (117 m from the explosion), we can estimate the direct annual industrial risk as

$$ {\mathbf{1.83 \times 10^{-8}}} < {\mathbf{R}}_{Ind} < {\mathbf{1.83 \times 10^{-6}}} $$

(18)

In our calculation, and for the sake of example, we consider the average of this distribution, i.e., $\mathbf{R}_{Ind} ={1.83 \times 10^{-7}}$