What was done
The authors, in their words, "attempt an independent estimate of eustatic sea level rise based on the measured freshening of the global ocean, and with attention to the contribution from melting of sea ice (which affects freshening but not sea level)."

What was learned
Wadhams and Munk report that their analysis produces "a eustatic rise of only 0.6 mm/year" and, when a steric contribution of 0.5 mm/year is added to the eustatic component, "a total of 1.1 mm/year, somewhat less than IPCC estimates."

What it means
Perhaps the most interesting finding of Wadhams and Munk's analysis is that "the continental run-off which is 'allowed' after subtracting the effect of sea ice melt is considerably lower than current estimates of sub-polar glacial retreat, suggesting a negative contribution from polar ice sheets (Antarctica plus Greenland) or from other non-glacial processes."  In this regard, they assert that "we do not have good estimates of the mass balance of the Antarctic ice sheet, which could make a much larger positive or negative contribution."  It is also possible that current estimates of sub-polar glacial retreat may be too large.  In any event, it is clear that we do not know either of these terms as well as is needed to arrive at an accurate value of global sea level rise (or fall), nor can we measure it directly with great accuracy, due to tide gauge records that Wadhams and Munk describe as "poorly distributed and subject to a large and uncertain correction for post-glacial uplift."  The bottom line of their analysis thus suggests there is considerable uncertainty associated with a number of basic parameters that are related to the water balance of the world's oceans; and until these uncertainties are satisfactorily resolved, we cannot be confident that we know precisely what is happening in terms of the vertical displacement of this important watery realm that covers the vast majority of the planet's surface.