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# Damage functions and damage factors

Damage functions are defined as the mathematical models that translate the magnitude of a physical hazard event into the damage caused to specific items or a group of items, considering also the levels of an item’s exposure and vulnerability (Prahl et al., 2016). Damage functions are typically developed from empirical research to assess the cost of the damage caused to a particular asset type by a hazard event in a specific locality. Accordingly, developing damage functions requires highly localised case studies, including geographical, physical, and socioeconomic conditions (Prahl, 2016). However, the requirement for localised data is also a major limiting factor and reason for the lack of available damage functions (Merz et al., 2010). This is coupled with inconsistent data across regions, especially in developing countries that do not have the resources to capture post-disaster data points (Prahl et al., 2016). Despite these limitations, damage functions are still the best available methodology to quantify physical risks on the most granular level to specify between different hazard types, asset classes, and locations.

There are two types of damage estimated by damage functions – absolute and relative damage. The absolute damage approach considers the value of assets and outputs the estimated monetary damage of an item or a group of items. The relative damage approach quantifies damage as a fraction or percentage of damage against the total damage and, hence, outputs a ratio expressed in percentage instead of a monetary value (Kaveckis et al., 2011; MRC, 2019). Our work focuses on the relative damage approach and its respective damage functions. This allows us to quantify the proportion of damage to each asset first, which can subsequently be transformed into absolute damage.

The output of the relative damage functions is referred to as a damage factor, which is commonly defined as the ratio of repair costs to replacement costs (Prahl, 2016). The calculated damage factor will be within the range of 0 and 1, where 0 represents no damage as there are neither repair nor replacement costs. Consequently, when the value is 1, the cost of repair is the same as that of replacement, meaning an asset is 100 per cent damaged and needs to be replaced. As such, damage factors are interchangeably interpreted as the percentage of the asset value that needs to be repaired or replaced.

In our approach, we apply 33 damage functions for flood and storm hazards to calculate each asset’s damage factor across various infrastructure classes in different regions. In the case of a missing available damage function for a specific asset in a particular region, we adopt a hierarchical approximation approach to select the next available comparable damage function. For example, if there is no damage function for Liquid Storage (TICCS subclass IC403020) in the United Kingdom, we would choose a comparable damage function for Energy and Water Resources (TICCS superclass IC40) in the United Kingdom. Additionally, we would widen the scope of the geographical region and select a damage function for Energy and Water Resources within the European continent. The third-order priority would be to adopt a global damage function for that sector. Appendix I and Appendix II provide an overview of all damage functions used in our models for flood and wind, respectively.

It is important to note that there are no damage functions available for thermal stress, as most assets are built to withstand extreme temperatures. Hence, such hazard events cause assets to suffer more from operational than physical damage. As a result, we differentiate in our models between flood- and storm-related hazards and damage from thermal stress.

Kaveckis, G., Paulus, G., & Mickey, K. (2011). Potential contribution of Hazus-MH to flood risk assessment in the context of the European Flood Directive. In A. Car, G. Griesebner, & J. Strobl (Eds.), Geospatial Crossroads @ GI_Forum 2011 Proceedings of the Geoinformatics Forum Salzburg. Germany: Herbert Wichmann Verlag. ISBN 978-3-87907-509-6.

Merz, B., Kreibich, H., Schwarze, R., & Thieken, A. (2010). Review article "Assessment of economic flood damage", Natural Hazards and Earth System Science, 10, 1697–1724, https://doi.org/10.5194/nhess-10-1697-2010

MRC (2019). Best practice guidelines for flood risk assessment. Vientiane: MRC Secretariat. https://doi.org/10.52107/mrc.ajg54c

Prahl, B.F. (2016). On damage functions for the estimation of storm loss and their generalization for climate-related hazards. (Dissertation). Retrieved June 18, 2023, from https://d-nb.info/1124841245/34

Prahl, B.F., Rybski, D., Boettle, M., & Kropp, J.P. (2016). Damage functions for climate-related hazards: Unification and uncertainty analysis. Natural Hazards and Earth System Sciences, 16, 1189–1203. https://doi.org/10.5194/nhess-16-1189-2016

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