3.3.2. Analysis

It is assumed in this study that buildings cannot collapse. Variables such as the erosion of the terrain over which the building is located could be responsible for a possible structural collapse, rather than the water level itself. In addition, this type of failure is very unusual, thus its consideration could undermine the curve profile for the frequent cases (i.e., no collapse). Therefore, the maximum relative damage established is limited to the percentage that represents the building components over the construction costs (i.e., floors, carpentry, electrical installation, air conditioning, plastering, cladding, painting, etc.). In order to set this maximum loss, construction price records [54] have been consulted, and for each construction stage we considered the relative damage that flooding can cause. As an example, the maximum loss resulted in 34% for dwellings, 30% for industries, 15% for car parks, and 36% for offices. On the other hand, furniture and household furnishings, such as crockery, metal

shelves, or pallet trucks, are not generally ruined by flooding. Thus, a maximum relative damage value has been set for this type of asset, between 90% and 97% depending on the type of property.

Fourteen types of properties have been proposed, and the available records have been classified accordingly. For each type of property and asset (i.e., building, furniture and household furnishings, and inventory) the correlation between economic damage and water depth inside the property has been analyzed. It should be noted that economic damage refers to the actual damage assessed by the flood surveyor rather than the compensation paid by the CCS (usually a lower amount).


**Table 3.** Summary of available records per type of property.

To standardize the diversity of geographical locations, economic level of construction, and type of property, the first action was to develop relative depth-damage curves by determining the ratio between economic damage and total property value. To do this, we set the value of each asset according to the availability of either the assessment of the flood surveyor or the insured amount, when a prior evaluation of the assets was not done. The asset value set divided by the total square meters of the entire building (i.e., whether flooded or not) results in the cost per square meter (€/m2). In turn, the value set by the flood surveyor divided by the flooded floor area results in the damage per square meter (€/m2). It has to be noted that buildings may have different numbers of upper floors, which usually results in a single flooded floor, and thus the total floor area is not flooded. The ratio between cost and damage per square meter provides the relative damage value, which has been averaged among all records from the same type of property, as indicated in Table 4 for a commercial property. Thus, the 67 records classified as general trade and corresponding to building assets are grouped into 23 different water depths inside the property.

We analyzed the correlation between relative damage and water depth for each type of property and asset. A great variety of coefficients of determination have been obtained, offering a good fit in some cases but a poor one in others. For industrial use and building assets, an accurate correlation was observed (*R<sup>2</sup>* = 0.81); however, in the case of general trade, a very poor value was obtained (*R<sup>2</sup>* = 0.0022) (Figure 5).


**Table 4.** Records from commercial use (building), grouped by water depth inside the property.

For the scatter plot of some types of properties and assets, some outliers were identified for which low water depths caused unexpectedly high damage values. Some explanations in this regard may be given: 1) the heterogeneity of construction elements, 2) different furniture quality and costs, 3) stowage conditions, and 4) the existence of cold stores. As an example, the red dot in Figure 5 (general trade and inventory) indicates that very high relative damage occurred to the inventory (i.e., 70%) of a general trade when the property was only flooded by 1 cm.

Overall, some other inconsistencies may be discussed:


Particularly in terms of building assets, the linear correlations present an accurate fit in some cases but not in others, highlighting that, overall, the phenomenon is not well explained for low depths. It has been observed that for buildings from the majority of property types, the maximum relative damage is reached at 180 cm of water depth. This is the depth fixed for all buildings to reach maximum damage.

**Figure 5.** Relationship of water depth inside the property and relative damage to building, furniture and household furnishings, and inventory, for industrial and general trade property uses.

3.3.3. Depth-Damage Curves' Development for Barcelona

Based on the analysis of the available data and applying corrections according to the expert opinion, nationwide relative depth-damage curves are initially developed. As stated by Van Vloten [55], in situations where there are no previous damage data or when the elements at risk are not comparable, consulting expert opinions on the matter is a good choice. This involves asking their opinion on the percentage of damage they expect for each structural type and for each hazard intensity. Expert opinions are also sought in the U.S. HAZUS methodology for the assessment of the impacts of flooding, for which depth-damage functions were derived from expert opinion and historical data [56], as has been done in the present study. The report of the Gulf Engineers & Consultants (GEC) [51], developed for the USACE, explicitly highlighted the importance of insurance experts as a primary source for obtaining depth-damage relationships. Also, in the work done by Bedford et al. [57], a variety of depth-damage curves were proposed based on expert opinions and damage claims in 1993 and 1995.

To make the depth-damage curves applicable to a specific municipality (i.e., Barcelona), these must be monetized by converting relative damage into economic damage per square meter (€/m2). In order to do this, the economic level of the target city is included. We must stress the importance of monetizing the curves of each type of asset separately and aggregating them afterwards into a single curve per type of property. In doing so, the disparity of prices for each type of asset in different municipalities may be taken into account. For instance, the cost of a building could be the same between two different municipalities, while the furniture, household furnishings, and inventory prices could be significantly different.

#### 3.3.4. Regional Transferability to Other Spanish Urban Areas

Departing from the semi-empirical depth-damage curves developed for Barcelona in the project RESCCUE, the present research goes further, proposing a methodology to transfer them to other Spanish municipalities. This allows for the use of depth-damage curves for flood damage assessments at a national level through curves obtained under a standard methodology.

The regional transfer of Barcelona's curves to a large number of the 8131 Spanish municipalities considers demographic, economic, and geographical factors, as they substantially influence the prices of goods and services across the country [16]. Regional adjustment indices have been obtained, taking as a reference Barcelona, based on indicators that are used as proxies of the expected regional price variability for the different assets' curves (Figure 10). The original 14 types of property uses were grouped into three general sectors: commercial, industrial, and residential and others. These have been classified by type of asset in order to obtain three indicators (i.e., building, furniture and household furnishings, and inventory) (Table 5). For instance, the prices of buildings used as warehouses are assumed to vary, as commercial buildings do, but warehouses' furniture, household furnishings, and inventory are more closely related to the price variability of the industrial sector. Relevant economic or market data at the municipal level are scarce, which was a limiting factor when developing the curves. Thus, when necessary, assumptions were made regarding the price or value variability of similar structures within a municipality.


**Table 5.** Relationship between property uses and general sectors for assets.

Buildings, for the residential and others sector, represent the physical structure of the living space and the indicator selected to define their relative value per municipality is the average tax value per square meter for all properties' transactions during the reference year 2020. These were obtained from an online real estate agent (www.idealista.com). For municipalities with no data available, the lowest value of their corresponding autonomous region has been considered as a proxy of the value, as those not represented are small, low-income towns. The baseline assumption is that the differences at a municipal level of the costs of damage reconstruction are comparable to the differences in property value. Continuing with the residential and others sector, the cost of damage to furniture and household furnishings is assumed to be aligned with the average disposable income per municipality. Hence, the indicator to compute the variation in content damage curves for the residential sector among municipalities is obtained through the statistics published by three sources: 1) the National Tax Agency (www.agenciatributaria.es), 2) the regional tax agency of the Basque Country (www.eustat.eus), and 3) the statistics agency of Navarra (www.navarra.es). Data were limited by the information provided by tax agencies that display small municipalities' results in groups; thus, it was not possible to include municipalities with under 3000 inhabitants.

The residential and others sector does not consider inventory. Not all types of property uses include all three asset types. For instance, while car parks only consider building assets, offices contain the three types of assets.

Regarding the commercial and industrial sectors, the price variability among municipalities of the furniture (there are no household furnishings related to these sectors) and inventory has been explained through two indicators (*n* = 2): a) average revenues of each of the two sectors at the autonomous region scale, and b) the number of businesses per sector at a municipality level. The Sauerbeck index [58] (Equation (1)) was applied, defined as the arithmetic average of two or more reference prices to the rest of the municipalities' relative values, on the basis of Barcelona prices. This was found to be the most appropriate way to introduce two related datasets that were at different geographical scales.

$$\text{Index}\_{\text{s,mi}} = \frac{1}{n} \times \frac{AV\_{\text{s,mi}}}{AV\_{\text{s,m0}}} + \frac{NC\_{\text{s,mi}}}{NC\_{\text{s,m0}}},\tag{1}$$

where *n* is the number of indicators (*n* = 2), s is the sector represented (i.e., commercial or industrial), mi denotes municipality i, and m0 is the reference municipality (i.e., Barcelona); *AVs,mi* represents the average economic value for the sectors of the autonomous region municipality i belongs to; *NCs,mi* stands for the number of companies of sector s registered in municipality i; and *AVs,m0* and *NCs,m0* represent the same values for the reference city of Barcelona.

In the furniture and household furnishings asset category, the variable AV takes the average investments in tangible assets per autonomous region for all companies registered under commercial and services sectors on the one hand, and the industrial sector on the other hand. For the inventory, the variable AV considers the average business revenue per autonomous region and sector. The number of commercial (commercial and services registered companies) and industrial companies per municipality (NC) comes from the national statistics office (www.ine.es). The lack of economic data at a local scale was an obstacle to including more precise values, and the two datasets alone do not provide any relevant measure. However, when combined they provide the local average revenue of the businesses belonging to each of the sectors displayed.

In summary, the spatial variability of the damage costs for the furniture and household furnishings can be explained by the differences in the average investment in tangible assets per municipality. In this sense, a city where the average investment to improve their assets is higher than the reference city (i.e., Barcelona), the damage caused to its business would be higher. The average local revenues are proposed to explain the inventory costs' variability. This follows the rationale that, the higher the revenue in a municipality, the higher the inventory would be stocked in local businesses. Hence, the damage would be higher in the case of a flooding event. The spatial costs variability for buildings was established based on the property values for commercial, industrial, and residential sectors. The lack of data at a municipal level of commercial and industrial property values limited the range of action. However, the official property values (€/m2) of the three sectors from the Spanish Registrar Chartered Institute (www.registradores.org) were used to obtain the value variation at the autonomous regional level, which was then applied to the municipal property values. The final regional adjustment indices (RI) are obtained as decimal fractions referring to Barcelona (i.e., the unit).

### 3.3.5. Temporal Transferability

Regarding the price variability over time, a method to transfer damage curves to the future has been applied to the original depth-damage curves developed for the year 2020 in Barcelona. The time horizon has been set to 2060, defined by the availability of the economic forecast. Long-term economic forecasting is a projection based on an assessment of the economic climate in individual countries and the world economy using both econometric models outputs and expert judgement [59]. Therefore, they can be characterized by uncertainty and complexity [60]. Considering this, and the scarcity of

long-term projections, a temporal indicator has been developed using the OECD real GDP long-term forecast for Spain [61]. This is the most reliable source of information of its kind. Using the year 2020 as a reference, an indicator of the potential economic growth has been included up to 2060 in order to transfer present damage costs to future estimates. The final temporal adjustment indices (TI) are obtained as decimal fractions referring to 2020. Consequently, in order to obtain the depth-damage curve of a certain municipality for a specific year, the total adjustment index (TAI) (Equation (2)) will be applied to each monetized asset curve of Barcelona (Table 7 and Figure 12):

$$TAI \,\,=\,\text{RI} \,\,\text{\*}\,\,\text{T}\,\,\,\,\}\tag{2}$$

where TAI is the total adjustment index, RI is the regional index, and TI is the temporal index.

Figure 6 presents the expected economic trend until 2060, thus the current depth-damage curves can be updated accordingly by multiplying the monetized aggregated curves (i.e., including building and contents) by the temporal index for a specific year obtained through this function.

**Figure 6.** Temporal adjustment indices to transfer present damage costs to future estimates for buildings and contents until the year 2060. Values based on the OECD real GDP long-term forecast for Spain [61].
