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Damage cost curves -- relating the typical damage of a natural hazard to itsphysical magnitude -- represent an indispensable ingredient necessary forclimate change impact assessments. Combining such curves with the occurrenceprobability of the considered natural hazard, expected damage and related riskcan be estimated. Here we study recently published city scale damage costcurves for coastal flooding and demonstrate which insights can be gained fromthe functions only. Therefore, we include protection cost curves -- relatingthe typical investment costs necessary to protect a city against a naturalhazard of certain magnitude -- which are analogous to and consistent with theabove mentioned damage cost curves. Specifically, we motivate log-logisticfunctions, which exhibit a power-law increase at the lower end, and fit them tothe cost curves. As expected, cities with large maximum potential loss(typically large cities) are also more costly to protect. Moreover, we studythe idealized case of continuous adaptation, i.e.\ increasing protection levelsin the same pace as sea-level rise, and compare the associated costs withresidual damage from extreme events exceeding the protection. Based on thefitted exponents we find that in almost all cities the residual damage risesfaster than the protection costs. Raising coastal protection can lead to lulloneself in a deceptive safety.

Sea-level rise and continuous adaptation: residual damage rises faster than the protection costs