Background
The author writes that "if the removal of groundwater from storage in the continental subsurface is sufficiently large and persistent, it can represent a substantial transfer of water mass from the land to the oceans, and thereby represent a measureable contributor to long-term sea level rise," citing the studies of Sahagian et al. (1994), Gornitz et al. (1997), Konikow and Kendy (2005), Huntington (2008) and Milly et al. (2010).

What was done
For the world as a whole between 1900 and 2008, as Konikow describes it, he assessed "the magnitude of long-term groundwater depletion by developing the first comprehensive aquifer-based estimate of changes in groundwater storage using direct volumetric accounting," after which he compared the groundwater depletion results he obtained with the results of concomitant sea level rise observations.

What was learned
The U.S. Geological Survey researcher reports that groundwater depletion over the period 1900-2008 was about 4,500 km³, which is equivalent to a global sea-level rise of 12.6 mm, or just over 6% of the total observed rise. In addition, he notes that the rate of groundwater depletion has increased markedly since about 1950, with maximum rates occurring during the most recent period (2000-2008), when it averaged ~145 km³/year.

As for sea level rise, Konikow notes that the average rate of rise over the 20th century was 1.7 ± 0.5 mm/year; but he adds that the rate may have accelerated in recent years, citing the work of Church and White (2006), Bindoff et al. (2007) and Lettenmaier and Milly (2009). Over the period 1961-2003, for example, he reports that the average rate of sea level rise was 1.8 ± 0.5 mm/year, as does Church et al. (2011). Over the period 1993-2003, however, Konikow notes that Bindoff et al. (2007) have mean global sea level rising by an estimated rate of 3.1 ± 0.7 mm/year; but Church et al. (2011) indicate that the latter researchers likely overestimated the upper-ocean thermosteric component of the global sea level rise in obtaining such a large result.

What it means
All things considered, Konikow states that a "better understanding and quantification of the contribution of groundwater depletion to sea-level rise should facilitate an improved understanding of 20th century sea-level rise." And when one looks at the two phenomena side-by-side, one is driven to conclude that the late 20th-/early 21st-century increase in groundwater depletion has likely been responsible for a good deal of the simultaneous increase in the rate of mean global sea level rise over that period, which conclusion should not be all that surprising, in light of the fact that global temperatures have not experienced much of an increase -- if any -- over the past decade or so, as has also been noted by Church et al. (2011).

References
Bindoff, N.L., Willebrand, J., Artale, V., Cazenave, A., Gregory, J., Gulev, S., Hanawa, K., Le Quéré, C., Levitus, S., Nojiri, Y., Shum, C.K., Talley, L.D. and Unnikrishnan, A. 2007: Observations: Oceanic Climate Change and Sea Level. In: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M. and Miller, H.L. (Eds.) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, United Kingdom.

Church, J.A. and White, N.J. 2006. A 20th century acceleration in global sea-level rise. Geophysical Research Letters 33: 10.1029/2005GL024826.

Church, J.A., White, N.J., Konikow, L.F., Domingues, C.M., Cogley, J.G., Rignot, E., Gregory, J.M., van den Broeke, M.R., Monaghan, A.J. and Velicogna, I. 2011. Revisiting the earth's sea-level and energy budgets from 1961 to 2008. Geophysical Research Letters 38: 10.1029/2011GL048794.

Gornitz, V., Rosenzweig, C. and Hillel, D. 1997. Effects of anthropogenic intervention in the land hydrologic cycle on global sea level rise. Global and Planetary Change 14: 147-161.

Huntington, T.G. 2008. Can we dismiss the effect of changes in land-based water storage on sea-level rise? Hydrological Processes 22: 717-723.

Konikow, L.F. and Kendy, E. 2005. Groundwater depletion: A global problem. Hydrogeology Journal 13: 317-320.

Lettenmaier, D. and Milly, P.C.D. 2009. Land waters and sea level. Nature Geoscience 2: 452-454.

Milly, P.C.D., Cazenave, A., Famiglietti, J.S., Gornitz, V., Laval, K., Lettenmaier, D.P., Sahagian, D.L., Wahr, J.M. and Wilson, C.R. 2010. Terrestrial water-shortage contributions to sea-level rise and variability. In: Church, J.A., Woodworth, P.L., Aarup, T. and Wilson, W.S. (Eds.) Understanding Sea-Level Rise and Variability. Wiley-Blackwell, Oxford, United Kingdom, pp. 226-255.

Sahagian, D.L., Schwartz, F.W. and Jacobs, D.K. 1994. Direct anthropogenic contributions to sea level rise in the twentieth century. Nature 367: 54-57.