*2.2. Depth-Damage Curves in the World*

Within damage models, depth-damage curves, also known as vulnerability curves, are used to represent the vulnerability of elements at risk. These can be found in either a relative or an absolute form, by considering percentages of the total property value or damage expressed in monetary terms, respectively. While relative curves are more transferable in space and time, since they do not depend on the market value of assets, absolute curves need a periodic recalibration to incorporate depreciation and inflation. In addition, depth-damage curves can be classified by their development process, namely analytical, empirical, and synthetic, and a combination of these could also be possible. The first group (analytical) are laboratory-based curves, where the effect of flood variables, such as depth, velocity, or duration, is assessed through monitoring. Empirical curves are developed through the collection of properties' damage data by means of survey campaigns. Synthetic functions are derived from the study of a theoretical standard property, assuming that all properties within the studied area are similar. This last type of curve is proposed when no actual data are available. Within the literature, other approaches have been found in terms of classification of the curves, such as by land use, building structure type, building contents or inventory, social status (income level), duration of flood, and warning time. Moreover, curves for buildings (i.e., structures) and contents are usually provided separately.

An important collection of damage curves is provided by the HAZUS-MH model, which offers to users the Federal Insurance Administration's (FIA) "credibility weighted" depth-damage curves and selected curves developed by various districts of the U.S. Army Corps of Engineers (USACE). The latter group is included in the HEC-FDA model and described in the Economic Guidance Memorandum (EGM) 04-01 developed by the USACE [18], with the purpose of providing guidance for the use of generic depth-damage curves in their flood damage reduction studies. These are developed based on actual flood losses in various parts of the United States (from 1996 to 2001) in the framework of the Flood Damage Data Collection Program, aiming at providing Corps districts' offices with standardized relationships for estimating flood damage. These cover one-story homes, two- or more story homes, and split-level homes, all of them with or without basements.

More recently, Huizinga et al. [19], as one of the JRC technical reports, carried out work to provide a methodology and a database of depth-damage functions for a variety of assets and land use classes (i.e., residential, commercial, industrial, transport, infrastructure, and agriculture). This work is based on an extensive literature survey to normalize damage curves for each continent at a national scale. The purpose of this work was trying to bridge the gap on the inability to compare flood damage assessments from different countries. The variety of depth-damage curves developments across countries is displayed in Table 1, at a national level, and Table 2 at a regional level. These tables summarize the main characteristics and sources of depth-damage curves found in the literature.


#### **Table 1.** Relative depth-damage curves at a national level.

**Table 2.** Relative depth-damage curves at a regional level.


For comparison purposes, a variety of European residential relative depth-damage curves [19] have been represented together in the graph in Figure 1.

**Figure 1.** Residential depth-damage curves for European countries proposed by Huizinga et al. [19].

As can be observed, there is no correlation between the economic development and the estimated damage percentage of the countries. For instance, the curves developed for the Netherlands present the lowest estimated damage percentage, while it ranks third on GDP per capita of the countries listed [41]. This could be attributed to the level of investment in adaptation measures against flood events of in Netherlands [42], causing lower potential flood event damage compared to other countries. Such dispersion of damage among curves in different European regions was also highlighted by Velasco et al. [5], where seven different types of curves for residential and commercial uses were compared.

#### *2.3. Depth-Damage Curves in Spain*

Only a few recent depth-damage curves' developments have been found for Spain, almost all of them addressing specific regions and only one providing national coverage. In 2013, in the framework of a Flood Defense Master Plan for the Spanish region of Marina Baja (Alicante), relative depth-damage curves for the different CORINE land uses in the region studied [43] were developed. The curves were validated based on actual damage data (i.e., claims paid) provided by the Spanish Insurance Compensation Company, CCS hereafter, and the City Councils of the region studied. Only one month later, in July 2013, the Ministry of Agriculture, Fisheries and Food published the report "Propuesta de mínimos para la metodología de realización de los mapas de riesgo de inundación" [44] (proposal for a common methodology of flood risk maps development). The purpose of this document was to offer a common framework to implement the Directive 2007/60/EC on the assessment and management of flood risks in Spain, and a nationwide relative depth-damage curve was proposed. It was based on the flood damage caused in the Spanish Ebro basin. Only four water levels were considered, assuming total damage (i.e., 100%) when the water depth exceeds 2 m, and 20% for depths lower than 30 cm. The single curve did not distinguish among land uses, although a table to monetize (€/m2) it according to different land uses was provided.

In 2015, an updated version of the former Flood Risk Prevention Territorial Action Plan for the Spanish Autonomous Community of Valencia (PATRICOVA) [45] was published. Again, a single relative depth-damage curve was provided, not distinguishing by type of land uses either. It stated that, regardless of the type of land use flooded, below 80 cm of water depth low damage were expected; however, once the water level exceeds this value, the damage increases rapidly up to a depth of 1.2 m, when the increase levels off. Finally, the River Basin Management Plan produced by the Eastern Cantabrian Spanish River Basin District [46], part of the requirements of the Directive 2007/60/EC, has been reviewed. A single relative depth-damage curve is found in this Plan, which is the result of averaging others developed for other countries, such as the USA (FEMA) and the United Kingdom (Flood Hazard Research Centre). The monetization of these curves is conducted by providing the maximum estimated value per land use. Unlike previous developments, in this case building and contents are differentiated. It considers a percentage from the building damage to constructing the contents' depth-damage curve. All reviewed depth-damage curves for Spanish regions have been jointly graphed and are presented in Figure 2.

Ritter et al. [47] conducted a flood damage assessment for the Spanish municipality of Agramunt, in which the depth-damage curves for Spain were selected from the database provided by Huizinga et al. [19]. It was concluded that the total computed damage for an actual riverine flood event was clearly overestimated after being compared with the claims paid by the Spanish Insurance Compensation Consortium (CCS). This may indicate that the depth-damage curves employed for the study could overestimate individual assets.

Although there might be other curves developed regionally in Spain, the review conducted has been considered enough to identify the great variety of approaches taken. As observed in Figure 2, where residential and general depth-damage curves are represented together, the damage for the same water depth varies significantly. For instance, a water depth of 2 m would suggest total damage if the nationwide curve is applied, and only 52% of total damage for the ones developed for the region of Marina Baja. Low water depths would also provide a very different level of damage depending on the curve selection. While the nationwide curve starts from 20% damage, the Marina Baja region curve does not rise above zero until a 10 cm water depth. This is assumed to be the average height of pavement curbs. Moreover, some of them aggregate building and contents (i.e., furniture and household furnishings) damage, while others consider them separately.

**Figure 2.** Depth-damage curves for Spanish regions.
