Emissions control cannot address the consequences of global warming for weather disasters until decades later. We model regional-level mitigation or adaptation, which reduces disaster risks to capital in the interim. Mitigation depends on belief regarding the adverse consequences of global warming. Pessimism jumps with a disaster and slowly reverts in the absence of arrivals. Mitigation spending by firms is less than first-best because of externalities. We prove that capital taxes to fund public mitigation, which requires collective action, restores first-best. We apply our model to country-level mitigation of major tropical cyclones, using GDP growth damages, government flood-control budgets, and climate-model projections of increasing cyclone frequency. For a typical country exposed to cyclones, a disaster arrival not only damages its capital stock, but elevates perceived risks, and as a result has persistent effects on taxes, the mix of private and public mitigation, growth, and welfare.