AbstractCoastal zones are experiencing rapid urbanization at unprecedented rates. At the same time, coastal cities are the most prone to climate-related vulnerability, including impacts of sea-level rise and climate-related coastal hazards under the present and projected future climate. Decision making about coastal urban climate adaptation can be informed by coastal climate services based on modeling tools. We develop a two-period coastal urban adaptation model in which two periods—the present and the future—are distinguished. In the model, a city agent anticipates sea-level rise and related coastal flood hazards with adverse impacts in the future period that, through damages, will reduce the urban income. However, the magnitude of future sea-level rise and induced damages are characterized by uncertainty. The urban planning agent has to make an investment decision under uncertainty: whether to invest in climate adaptation (in the form of construction of coastal protection) or not, and if so, how much. The decision making of the urban agent is derived from intertemporal maximization of expected time-discounted consumption. An exact solution in the closed form is derived for an analytically tractable particular case, for which it is shown that investment decisions depend discontinuously on the value of a single non-dimensional model indicator. When this indicator exceeds a certain threshold value, the urban agent discontinuously switches from the ‘business-as-usual’ (BaU) strategy when no adaptation investment is taken to a proactive adaptation. The role of coastal climate services in informing the decision making on adaptation strategies is discussed.