### Flood hazard

#### Hydrological Modelling and flood quantile estimations

The hydrological model proposed is the Continuum model. It is a continuous, distributed and physically based hydrological model able to reproduce the spatial-temporal evolution of soil moisture, energy fluxes, surface soil temperature, evapotranspiration and discharge.

#### Hydraulic modelling and hazard map derivation

The hydraulic model here applied to compute flood hazard maps is based on a simplified approach fit to determine flood maps on large areas, based on the manning’s equation. The Manning equation is an empirical equation that describes the relationship between water velocity in a river channel and the channel geometry, slope, and a roughness coefficient that characterizes the friction in the channel.

#### Flood scenarios generation

The next step is the generation of all possible flood events that can affect the areas of interest: the hazard maps provide water levels in flood prone areas for different return periods, but they do not represent flood events. A flood event or flood scenario usually affects only a portion of the country. The distinction between flood map and flood scenario is fundamental: flood risk estimates only based on flood maps are reliable if the area of interest is relatively small but, if the area is wide (e.g., country or regional level), it is necessary to generate all possible flood scenarios that can affect the area of interest with their probability of occurrence.

More detailed information:

The GIRI global flood hazard model (2023b)

*Alfieri, L., Campo, L., Gabellani, S., Ghizzoni, T., Herold, C., Libertino, A., Trasforini, E., & Rudari, R.*

### Inputs

- Topography (DEM)
- Catchment and soil characteristics
- Stream characteristics (cross-sections, bathymetry, n of Manning)

### Outputs

- Flood intensity maps

### 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 (Water velocity and depth)
- 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