Reliable long-term flood forecasts are needed because floods, among environmental disasters worldwide, do most damage to lives and property, a problem that is likely to increase as climate changes. The objective of this paper is to critically examine scientific approaches to flood forecasting under deep uncertainty and ambiguity as input to flood policy, and to explore alternative approaches to the development of better forecasts along with the necessary organizational support. This therefore a paper on science policy Aleatory (i.e. frequentist) probability estimates have dominated the science, attached to which are irreducible uncertainties. The lower priority given to finding a physical theory of floods means that ambiguity is high, particularly in relation to choosing a probability density function for forecasting. The historical development of flood forecasting is analyzed within the UncertaintyAmbiguity Matrix of Schrader, S. Riggs, W.M., and Smith, R.P. (1993). Choice over uncertainty and ambiguity in technical problem solving. Journal of Engineering and Technology Management, 10, 13-99 showing that considerable uncertainty and ambiguity exist and are likely to continue. The way forward appears to be a mix of: broadening the information input to forecasts by engaging many disciplines, Bayesian analyses of probabilities, scenario analyses of catastrophic floods based on all available evidence, and adaptive forecasting in the face of climate change.