In the Mediterranean Sea, we obtain the best agreement using a steric correction from the regional oceanographic model MFSTEP and a continental hydrological leakage correction derived from the global continental hydrological model WaterGAP2. The inter-annual time series show a correlation of 0.85 and a root mean square (RMS) difference of 15 mm. The two estimates have similar accuracy and their annual amplitude and phase agree within 3 mm and 23 days respectively. The GRACE-derived mass-induced sea level variability yields an annual amplitude of 27 ¡À 5 mm peaking in December and a trend of 5.3 ¡À 1.9 mm/yr, which deviates within 3 mm/yr from the altimetry-derived estimate.
In the Black Sea, the series are less consistent, with lower accuracy of the GRACE-derived estimate, but still show a promising agreement considering the smaller size of the basin. The best agreement is realized choosing the corrections from WaterGAP2 and from the regional oceanographic model NEMO. The inter-annual time series have a correlation and RMS differences of 0.68 and 55 mm, their annual amplitude and phase agree within 4 mm and 6 days respectively. The GRACE-derived seawater mass signal has an annual amplitude of 32 ¡À 4 mm peaking in April. On inter-annual time scales, the mass-induced sea level variability is stronger than in the Mediterranean Sea, with an increase from 2003 to 2005 followed by a decrease from 2006 to 2008.
Based on mass conservation, the mass-induced sea level variations, river runoff and precipitation minus evaporation are combined to derive the strait flows between the basins and with the Atlantic Ocean. At the Gibraltar strait, the net inflow varies annually with an amplitude of 52 ¡À 10 ¡Á 10?3 Sv peaking end of September (1 Sv = 106 m3 s?1). The inflow through the Bosphorus strait displays an annual amplitude of 13 ¡À 3 ¡Á10?3 Sv peaking in the middle of March. Additionally, an increase of the Gibraltar net inflow (3.4 ¡À 0.8 ¡Á 10?3 Sv/yr) is detected.