*4.1. Relative Depth-Damage Curves Development*

The relative damage corresponding to intermediate water depths (between 10 cm and 180 cm), when the coefficient of determination is acceptable, has been set as the range for the linear regression. Nevertheless, relative damage for low depths (<10 cm) has been adapted according to the opinion of the flood expert surveyor. Regarding the damage related to high water depths (>180 cm), the maximum value has been set. Therefore, only in those situations where the correlation was not accurate enough has the curve been adjusted according to expert opinion. Figure 8a showcases an example of a relative depth-damage curve proposed for the building of an industrial property. Inventory for commercial uses, though, except for those elements that require cold stores, tends to be at the same height, and accordingly its damage is also evenly distributed, as shown in Figure 8b. For the inventory, a maximum 100% relative damage has been considered, assuming that those elements that can be saved after flooding (e.g., plastic, construction materials, etc.) are not representative.

**Figure 8.** Proposed relative depth-damage curves and actual damage recorded for type of asset and property: (**a**) industrial buildings and (**b**) inventory, general trade.

Overall, the best correlations (linear) (i.e., high *R2*) were found for furniture and household furnishings, with values of *R<sup>2</sup>* = 0.74 for restaurants and *R2* = 0.82 for workshops. In these cases, damage related to low depths was set according to the expert opinion, and the maximum damage was set between 90% and 97% according to the type of property. Figure 9 shows, as an example, the relative depth-damage curves proposed for furniture and household furnishings in restaurants and workshops.

**Figure 9.** Proposed relative depth-damage curves and actual damage recorded for furniture and household furnishings and type of property: (**a**) restaurants and (**b**) workshops.

Figure 10 shows the proposed relative depth-damage curves for each asset, building, furniture and household furnishings, and inventory, according to 14 different types of property uses. These semi-empirical curves are developed to be applied in any Spanish municipality. Therefore, the curves' shape are invariable in both space (in Spain) and time.

**Figure 10.** Relative depth-damage curves for Spanish cities: (**a**) buildings, (**b**) furniture and household furnishings, and (**c**) inventory.

#### *4.2. Monetization of Relative Damage for Barcelona*

To monetize the curves for Barcelona, initially the deciles (cost(€)/m2) from the distribution of the data sample for each type of property and asset have been determined. According to expert opinion, a specific decile has been established for each type of property based on the target city. In some cases, the expert suggested providing an average value or making a direct estimation when the deciles did not match with his criterion, as Table 6 presents.

**Table 6.** Proposed cost (€/m2) for assets (i.e., building, furniture and household furnishings, and inventory) for each type of property in Barcelona.


Once an adequate cost per square meter was associated with each property and asset according to the expert opinion for Barcelona, depth-damage curves were constructed for each asset. The following aggregation of the three types of assets provided the total depth-damage curves (Figure 11).

**Figure 11.** Semi-empirical depth-damage curves for Barcelona.

For those type of properties and assets with data scarcity or those that presented a low coefficient of determination, the expert used his criterion to adjust a curve from other property uses expected to be similar.
