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In some coastal cities there is an urgent need to decide on adaptation investments given the long periods needed to complete the relevant infrastructures. However such decisions are usually made under significant uncertainty due to local climate change and socio-economic impacts. The Intergovernmental Panel on Climate Change (IPCC) has developed four global scenarios according to different representative concentration pathways (RCPs); however, using these scenarios directly is equivalent to using incomplete information in the decision-making process because they do not provide information on what sea level rise behavior is most probable. In this study, I propose a model which assigns probabilities to IPCC scenarios with Local Sea Level Rise (LSLR) information. I obtain expected damage and risk measures for the world's 120 major coastal mega-cities at specific moments in time. That is, I consider uncertainty in both scenario selection and within each scenario. With this information it is possible to make adaptation investment decisions under uncertainty with a criterion of not exceeding certain risk levels in the future. The paper shows that in the year 2100 for the equal probability mixed scenario (25% RCP 2.6, 50% RCP 4.5 and 25 RCP 8.5) the expected damage is US$ 1,251,732 millions for New Orleans and US$ 1,196,517 millions for Guangzhou. The risk measurements show that in that year the damage in the 5% of worse cases will be US$ 2,800,756 millions for Guangzhou and US$ 1,832,466 millions for New Orleans. However, not all countries have sufficient resources to make the necessary adaptation investments, so we analyze expected damage and risk according to World Bank country income groups. The paper shows that the USA and China will need to make major adaptation investments in the future. The coastal LSLR risk in lower-income cities is also calculated. [ABSTRACT FROM AUTHOR]