## 1. Introduction

[2] In the debate about climate change induced sea level rise, land loss is a commonly mentioned consequence [*Nicholls et al*., 2010; *Devoy*, 2008]. On a closer look, however, it turns out that land loss itself is often a result of extreme events, such as storm surges, which either erode the coastline [*Stive et al*., 2002] or inundate the considered area so frequently that a repeated restoration might be inefficient and the land is abandoned.

[3] Considering sea levels, one can observe that the mean sea level is superposed by fluctuations, whose magnitudes significantly surpass the expected mean sea level rise. Accordingly, if one wants to investigate consequences of sea level rise, these fluctuations need to be taken into account. Tides and winds are the main influencing factors of these fluctuations [*Woodworth et al*., 2011] and together with the mean sea level they determine the magnitude of an extreme event. Thus, extreme floods are influenced by climate change in two ways: via sea level rise and via meteorological changes. We study the consequences of these two effects as well as the impact of potential flood protection measures on the expected flood damages, where damages describe the monetary losses in a specific area. Furthermore, the variability of the damages is examined.

[4] We employ extreme value theory for the characterization of flood events [*Katz*, 2010], and damage functions [*Merz et al*., 2010], in order to obtain the associated damages. Accordingly, the distribution of extreme sea levels is translated via the damage function into the distribution of damages, i.e., the probability that a damage higher than a certain value occurs is related to the probability that the annual maximum flood exceeds a certain level. In particular, sea level rise, which is the main driver for changing extreme value behavior [*Menéndez and Woodworth*, 2010], leads to modified damages. Additionally, climate change could alter meteorological patterns, which induces a change of variability of extreme events [*McInnes et al*., 2013; *Woth et al*., 2006] and in turn affects the damage distribution.

[5] We elaborate this setting in a general sense and analytically derive relations for the expectation value of the damages and the standard deviation as a function of the mean sea level and as a function of the variability of annual maximum sea levels. The resulting expressions describe the asymptotic behavior and highlight the importance of the damage function. We complement the results with an analysis of the effect of a protection measure in the form of a dike or a sea wall protecting the area from floods up to a specific maximum sea level. Again, we derive analytical expressions and find that in this case the expressions depend sensitively on the extreme value behavior of sea levels.

[6] All general results are supported by numerical calculations for the city of Copenhagen and a case study area in Kalundborg (Denmark).

[7] The manuscript is organized as follows. In section 2, our approach connecting extreme sea levels and damage functions is introduced. Information on the two case studies is provided in section 3. Changes in the extremes are presented in section 4 and the influence of protection in section 5. In section 6, we draw conclusions and discuss limitations of our findings. Detailed derivations are provided in the Appendix A.