A new reanalysis of the global ocean circulation is used to distinguish between the steric and eustatic components of sea level rise. Recent altimeter observations indicate an increase in the rate of sea level rise during the past decade to 3.2 mm/yr, well above the centennial estimate of 1.5--2 mm/yr. This apparent increase could have resulted from enhanced melting of continental ice or from decadal changes in thermosteric and halosteric effects. The contribution from steric effects is explored using the new eddy-permitting Simple Ocean Data Assimilation version 1.2 (SODA1.2) reanalysis of global temperature, salinity, and sea level spanning the period 1958--2001. The applicability of this ocean reanalysis for sea level studies is evaluated by comparing subseasonal variability with a collection of 20 tide gauge station sea level records, comprising a total of 740 years of data. A positive relationship is found at all gauge stations, with an average correlation of r = 0.7 after correction for the inverted barometer effect. Dynamic height calculated relative to 1000m from the SODA1.2 reanalysis, used as a proxy for the steric component of sea level, is compared with satellite-derived sea level for the years 1993--2001. During this 9-year period dynamic height increases at a global rate of 2.3 ¿ 0.8 mm yr-1, a substantial acceleration beyond the multidecadal steric rate of 0.5 mm yr-1. The similarity of the rate of increase in the thermosteric contribution to sea level rise as well as the similarity of its spatial structure in comparison with satellite-derived sea level rise suggests that the recent acceleration in sea level rise is explainable to within the error estimates by fluctuations in warming and thermal expansion of the oceans.