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

Abstract

Damage cost curves -- relating the typical damage of a natural hazard to its physical magnitude -- represent an indispensable ingredient necessary for climate change impact assessments. Combining such curves with the occurrence probability of the considered natural hazard, expected damage and related risk can be estimated. Here we study recently published city scale damage cost curves for coastal flooding and demonstrate which insights can be gained from the functions only. Therefore, we include protection cost curves -- relating the typical investment costs necessary to protect a city against a natural hazard of certain magnitude -- which are analogous to and consistent with the above mentioned damage cost curves. Specifically, we motivate log-logistic functions, which exhibit a power-law increase at the lower end, and fit them to the cost curves. As expected, cities with large maximum potential loss (typically large cities) are also more costly to protect. Moreover, we study the idealized case of continuous adaptation, i.e.\ increasing protection levels in the same pace as sea-level rise, and compare the associated costs with residual damage from extreme events exceeding the protection. Based on the fitted exponents we find that in almost all cities the residual damage rises faster than the protection costs. Raising coastal protection can lead to lull oneself in a deceptive safety.