| Summary: | Confidence in projections of global-mean sea level rise (GMSLR) depends on an ability to account for GMSLR during the twentieth century. There are contributions from ocean thermal expansion, mass loss from glaciers and ice sheets, groundwater extraction, and reservoir impoundment. Progress has been made toward solving the enigma of twentieth-century GMSLR, which is that the observed GMSLR has previously been found to exceed the sum of estimated contributions, especially for the earlier decades. The authors propose the following: thermal expansion simulated by climate models may previously have been underestimated because of their not including volcanic forcing in their control state; the rate of glacier mass loss was larger than previously estimated and was not smaller in the first half than in the second half of the century; the Greenland ice sheet could have made a positive contribution throughout the century; and groundwater depletion and reservoir impoundment, which are of opposite sign, may have been approximately equal in magnitude. It is possible to reconstruct the time series of GMSLR from the quantified contributions, apart from a constant residual term, which is small enough to be explained as a long-term contribution from the Antarctic ice sheet. The reconstructions account for the observation that the rate of GMSLR was not much larger during the last 50 years than during the twentieth century as a whole, despite the increasing anthropogenic forcing. Semiempirical methods for projecting GMSLR depend on the existence of a relationship between global climate change and the rate of GMSLR, but the implication of the authors' closure of the budget is that such a relationship is weak or absent during the twentieth century.
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