**2. Literature Review and Analysis**

Even though there is currently no universally trusted system for assessing flood damage in urban areas, most damage models rely on depth-damage curves (also known as stage-damage functions) for simplicity [11]. In order to apply damage models to assess the economic impact of flooding over urban areas, the required floodwater depths across the inundated area are usually obtained from 2D simulations [12]. In this section, some of the most relevant damage models worldwide are presented together with a variety of depth-damage curves developed for regions across the world and those specifically developed for Spanish regions.

#### *2.1. Flood Damage Models*

Different approaches have been adopted worldwide in order to develop models to assess damage due to flooding. However, all share a common purpose: evaluating the cost-effectiveness of projects designed to alleviate flood impacts.

In the USA, two well-known models are currently being used to assess the damage caused by floods and other natural hazards. The first is HAZUS-MH [13], which is a multihazard estimation model developed by the U.S. Federal Emergency Management Agency (FEMA) that assesses the impacts of earthquakes, wind, and floods. It was mainly developed by the U.S. National Flood Insurance Program (NFIP), because the insurance industry plays a key role when it comes to natural hazards. The outputs of the damage module are area-weighted estimates of damage as a percentage of replacement cost, at the Census Block or for a given building. Since the U.S. NFIP pays claims based on depreciated value, the model considers depreciation as opposed to cost of repair as the general measure of economic loss. The damage assessment model includes a library of more than 900 damage curves estimating damage to various types of buildings and infrastructure. Some drawbacks of this model are the complexity of the data input process and the U.S. regional-based stage-damage curves. The second well-known model is HEC-FDA [14], developed by the U.S. Army Corps of Engineers (USACE), which is a freely downloadable software provided together with the rest of the Hydrologic Engineering Center (HEC) resources, and includes extensive documentation. Among its several features, it stores hydrologic and economic data necessary for analysis, provides tools to visualize data and results, and computes expected annual damage. Generic depth-damage relationships are provided to be utilized for a flood damage study conducted in the USA, in the absence of regionally developed relationships.

A comprehensive study conducted by Jongman et al. [15] compares seven different damage models developed for a variety of regions across Europe and the United States: FLEMO (Germany), Damage Scanner (Netherlands), the Rhine Atlas (Rhine Basin), the Flemish Model (Belgium), Multi-Coloured Manual (MCM) (United Kingdom), HAZUS-MH (United States), and the JRC (Germany, European Commission/HKV). The fact that five out of the seven models are based on aggregated land use data (e.g. CORINE) rather than individual objects (HAZUS-HM and MCM) indicates that the scale of work is an essential matter when either selecting or developing a damage model. Moreover, it should be noted that only two out of the seven models are based on individual objects, which indicates the complexity of developing such detailed damage models. While the object-based models can control for varying building density in areas with same CORINE land use, the area-based models can be applied for rapid calculations over larger areas. However, object-based models such as HAZUS-MH and MCM use a large number of object types and corresponding flood damage characteristics [16]. FLEMO, HAZUS-MH, and the Rhine Atlas models are empirically based and could be more accurate when applied to similar case studies. The others are mainly synthetic with the intrinsic issue of their unreliable application to another region or country. An essential improvement in these recent damage models is their GIS-based characteristic; however, the complexity of the data input process, together with the inherent regional (USA) dependency of depth-damage curves, may be considered as important drawbacks.

As Jongman et al. [15] noted, the use of depth-damage curves involves great uncertainty, which makes the models very sensitive. The need to adjust asset values to the regional economic situation and property characteristics when using aggregated land use data was also highlighted by Jongman et al. [15]. In addition, the actual damage to a property is not only due to floodwater depth, but also to factors such as the time of the year the flood occurs, flood duration, water velocity, suspended debris, or warning time. Therefore, there is an intrinsic uncertainty to depth-damage approaches and a known influence of these other factors on the extent and severity of flood damage to buildings and their contents. However, it is a general practice to accept the water level as a fundamental criterion for estimating the damage caused by these events. Lately, other factors beyond the water level have been incorporated into so-called multiparameter damage models; nonetheless, such models require more complex and extensive datasets [17].

Next, we will present descriptions of a variety of depth-damage curves developed for different parts of the world, and a more in-depth analysis of those performed for Spanish regions.
