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Precipitation minus evaporation over continents is the freshwater flux which can be sustainably exploited by mankind. Over a catchment and longer time periods, this flux is also the amount of water which flows into the ocean. An essential question for semi-arid areas of the world is how well this freshwater flux can be estimated and predicted to evolve under climate change and human water use. Knowing this flux is thus an essential element in regional water resources management. Here we examine this question over the catchment of the Mediterranean Sea. Using a novel data assimilation methodology that incorporates observed discharges of rivers in a land surface model, new estimates of the freshwater flux to the Mediterranean Sea for the period 1980-2013 are proposed. We find that more freshwater (40-60%) flows into the sea than previously estimated. The hypothesis we advance is that previous estimates have underestimated the discharges of the large number of unmonitored coastal basins and neglected submarine ground water flows. The proposed error bars on the estimate indicate that the degrading river gauging station network limits our ability to monitor this branch of the water cycle reliably. Nevertheless, the uncertainty is small enough to allow the identification of regions in which non-climatic decreases in the freshwater flows exist over the period.