Emissions abatement alone cannot address the consequences of global warming for weather disasters. We model how society adapts to manage disaster risks to capital stock. Optimal adaptation—a mix of firm‐level efforts and public spending—varies as society learns about the adverse consequences of global warming for disaster arrivals. Taxes on capital are needed alongside those on carbon to achieve the first best. We apply our model to country‐level control of flooding from tropical cyclones. Learning rationalizes empirical findings, including the responses of Tobin's q, equity risk premium, and risk‐free rate to disaster arrivals. Adaptation is more valuable under learning than a counterfactual no‐learning environment. Learning alters social‐cost‐of‐carbon projections due to the interaction of uncertainty resolution and endogenous adaptive response.