### Earthquake

A probabilistic seismic hazard assessment aims to evaluate ground shaking due to the occurrence of earthquakes. The probabilistic approach recognizes the limited information on catastrophic events that have occurred in the past, the uncertainty of the events that may occur in the future and the uncertainty of the vulnerability of exposed population and their assets.

This methodology is based on the use of instrumental seismicity to represent the hazard. The earthquake catalogue comprised of recorded earthquakes and the estimation of maximum magnitudes by general regions provide the input for the hazard calculations, while the smoothed seismicity approach is the tool used to perform the computations. The seismic hazard results are obtained for each computation site, in terms of probabilities of exceeding a given intensity value in different periods of time, while it is also possible to obtain the results in terms of non-exceedance probability and of equivalent annual exceedance rate.

### Inputs:

- Source model and seismicity
- Attenuation functions
- Geological, geophysical and geotechnical data
- Topography

### Outputs:

- Hazard intensity (peak ground acceleration, spectral acceleration, velocity or displacement)
- Design spectra

### Exposure

**exposed elements database**

- Georeferenced location
- Infrastructure component

characterization, material, height, length, construction system - Infrastructure indicators

Population served, national socioeconomic indicators

### Inputs:

- Georeferenced infrastructure elements data
- National indicators
- Population census

### Outputs:

- Infrastructure elements database

### Vulnerability

The vulnerability of infrastructure components is defined using mathematical functions that relate the intensity to the direct physical impact. Such functions are called *vulnerability functions* and they must be estimated and assigned for each one of the components identified, and for each hazard considered. Vulnerability functions provide the variation of the probability moments of the *relative loss* with increasing intensity (see Figure below).

Vulnerability functions allow the transformation from the occurrence of a hazard event and the local intensities caused by it, to quantification of direct losses on the exposed elements

### Inputs:

- Vulnerability functions for each class of exposed elements
- Hazard intensity measure

### Outputs:

- Relative damage [%]

### Risk

The proposed fully probabilistic risk assessment considers multiple events of multiple hazards, which implies the simulation of thousands of possibilities in which those hazards may manifest, under future changing climates. For each simulated event, the damage to the infrastructure system is quantified through the vulnerability functions. Repeating this process for different hazard events results in different damages simulated for the same infrastructure, each rendering some economic loss with a probability of occurrence. Typically, low damage events have a higher probability of occurrence, which means they are more frequent, and high damage events have lower probabilities or are less frequent (see Figure below). This collection of loss amounts and probabilities makes up a truly probabilistic and multi-hazard risk assessment of any infrastructure system. This process will be applied to all infrastructure sectors country-by-country

*Illustration of the calculation of loss in an event-based probabilistic risk assessment*

Although disaster risk is fully quantified by the set of losses, it is more practical to express it as condensed metrics that summarize the results into curves or point estimates. Two of the most widely used metrics are the **Probable Maximum Loss (PML)** curve and the **Average Annual Loss (AAL)**.

The **PML** curve describes the variation of losses to the return period. It fully integrates all the consequences, even of different hazards, to define the feasibility that large loss amounts occur sometime in the future.

On the other hand, the **AAL **is a multi-annual loss average, like an insurance premium, i.e., it quantifies an annual loss that, in the long term, accumulates to the total amount of losses that will be caused by disasters to the infrastructure. It is a multi-hazard metric as well.

### Inputs

- Hazard (peak ground acceleration, spectral acceleration, velocity or displacement)
- Exposed elements database (classified by portfolio)
- Vulnerability (by exposed element class)

### Outputs

Risk metrics:

- Loss Exceedance Curve (LEC)
- Average Annual Loss (AAL)
- Probable Maximum Loss (PML)
- Risk maps