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Most climate change impacts manifest in the form of natural hazards. Damage assessment typically relies on damage functions that translate the magnitude of extreme events to a quantifiable damage. In practice, the availability of damage functions is limited due to a lack of data sources and a lack of understanding of damage processes. The study of the characteristics of damage functions for different hazards could strengthen the theoretical foundation of damage functions and support their development and validation. Accordingly, we investigate analogies of damage functions for coastal flooding and for wind storms and identify a unified approach. This approach has general applicability for granular portfolios and may also be applied, for example, to heat-related mortality. Moreover, the unification enables the transfer of methodology between hazards and a consistent treatment of uncertainty. This is demonstrated by a sensitivity analysis on the basis of two simple case studies (for coastal flood and storm damage). The analysis reveals the relevance of the various uncertainty sources at varying hazard magnitude and on both the microscale and the macroscale level. Main findings are the dominance of uncertainty from the hazard magnitude and the persistent behaviour of intrinsic uncertainties on both scale levels. Our results shed light on the general role of uncertainties and provide useful insight for the application of the unified approach.

In contrast to recent advances in projecting sea levels, estimations about the economic impact of sea level rise are vague. Nonetheless, they are of great importance for policy making with regard to adaptation and greenhouse-gas mitigation. Since the damage is mainly caused by extreme events, we propose a stochastic framework to estimate the monetary losses from coastal floods in a confined region. For this purpose, we follow a Peak-over-Threshold approach employing a Poisson point process and the Generalised Pareto Distribution. By considering the effect of sea level rise as well as potential adaptation scenarios on the involved parameters, we are able to study the development of the annual damage. An application to the city of Copenhagen shows that a doubling of losses can be expected from a mean sea level increase of only 11 cm. In general, we find that for varying parameters the expected losses can be well approximated by one of three analytical expressions depending on the extreme value parameters. These findings reveal the complex interplay of the involved parameters and allow conclusions of fundamental relevance. For instance, we show that the damage typically increases faster than the sea level rise itself. This in turn can be of great importance for the assessment of sea level rise impacts on the global scale. Our results are accompanied by an assessment of uncertainty, which reflects the stochastic nature of extreme events. While the absolute value of uncertainty about the flood damage increases with rising mean sea levels, we find that it decreases in relation to the expected damage.