Reeh (1999) reviews what is known about the mass balance of the Greenland and Antarctic ice sheets, as well as prospects for resolving remaining uncertainties with modern observation methods, noting that the future contribution of the Greenland and Antarctic ice sheets to global sea level depends upon the past climate and dynamic histories of the ice sheets as much as it does upon future climate.

With respect to the potential impact of global warming, Reeh reports there is a broad consensus that a 1°C increase in temperature would create little net change in mean global sea level; for Greenland's contribution would be a sea level rise on the order of 0.30 to 0.77 millimeters per year, while Antarctica's contribution would be a fall on the order of 0.20 to 0.70 millimeters per year.  In addition, with respect to past climate change and the ice sheets' subsequent dynamic histories, "we do not know," says Reeh, "whether the ice sheets are currently in balance; neither do we know if their volume or mass has increased or decreased during the last 100 years."

Reeh also states that the most up-to-date techniques "are not capable of directly yielding the long-term background trend of ice sheet mass balance, unless applied over a period of many decades."  Hence, we truly do not know what is normal or abnormal in this regard, nor, therefore, do we know what to expect in the way of sea level change in either the near- or long-term.

In a radically different approach to the subject, Shankar and Shetye (1999) used long-term records of sea level and precipitation to explore the hypothesis that an increase in rainfall over India leads to a decrease in ocean water salinity along its coast that is ultimately expressed as an increase in sea level.  In support of this concept, they report that sea level measured at Mumbai (Bombay) - which is believed to be representative of the entire Indian Ocean - was generally low from 1880 to 1920, whereupon it rose for several decades, peaking in the late 1950s and falling thereafter, and that a roughly similar pattern was observed in annual all-India rainfall.

The two scientists note that their hypothesis "differs from those usually invoked in constructing scenarios of long-term changes in sea level," one of which they explicitly mention is the global warming hypothesis that "invoke[s] the rise in temperature in the upper ocean and the melting of polar ice caps" to explain the rise in sea level.  As they remark at the end of their paper, however, the data "do not allow separation of natural, very low-frequency variability of monsoon rainfall and sea level from that caused by other effects, including the warming of the globe due to anthropogenic effects," which leaves the task of attribution pretty much in limbo.

Yet another radically different take on the issue, especially as it pertains to the long-term future, is provided by Bratton (1999), who calculated the sea level change that would likely accompany a melting of the global ocean's inventory of submerged and sequestered methane hydrate, which upon dissociation looses 21% of its volume.  This approach suggests that the combined effects of methane hydrate melting and subhydrate gas release would lead to a global sea level decline conservatively estimated to range from 0.1 to 1.5 meter, but which may in the past have produced sea level drops of as much as 25 meters.

Bratton remarks that "such a mechanism may offset some future sea level rise associated with thermal expansion of the oceans," such as could occur in response to continued global warming.  Indeed, he states that the estimated sea level change is "of the same order of magnitude [but of opposite sign] as those associated with thermal expansion of the oceans, melting of nonpolar ice, and melting of the West Antarctic ice sheet."  Hence, it is not at all clear what impact these several simultaneously occurring phenomena might have on mean global sea level.  Maybe the Maldives might even grow in size!

A study that raises even more basic questions about changes in sea level and their relationship to postulated CO2-induced global warming is that of Yokoyama et al. (2000), who analyzed four distinct sediment facies in the tectonically stable Bonaparte Gulf of Australia to determine the maximum volume of land-based ice during the last ice age and the timing of the initial melting phase.  Among a number of other things they discovered, Clark and Mix (2000) point out in a companion article that the rapid rise in sea level caused by the melting of land-based ice that began approximately 19,000 years ago preceded the post-glacial rise in atmospheric CO2 concentration by about three thousand years.  Then, when the CO2 finally began to rise, it had to race to make up the time differential; but it still took it a couple more thousand years to catch up with the sea level rise, suggesting it was warming that drove the change in atmospheric CO2 concentration and not vice versa.

On the theoretical side of the issue, Wild and Ohmura (2000) studied the mass balances of the Greenland and Antarctic ice sheets using two general circulation models (GCMs) developed at the Max Plank Institute for Meteorology of Hamburg, Germany: the older ECHAM3 GCM and its new-and-improved replacement, the ECHAM4 GCM.  Mass balance calculations were made by each model for both current and doubled atmospheric CO2 concentrations.  Under the doubled atmospheric CO2 scenario, the mass balance of the Greenland ice sheet was projected to be negative in both models, indicative of a net reduction in its size.  However, the newer ECHAM4 mass balance results for Greenland were "significantly smaller" than the older ECHAM3 results (-63 vs. -229 mm per year).

The two models were in close agreement in their projections for the Antarctic ice sheet, however, where the ECHAM4 and ECHAM3 models projected net increases in ice sheet growth of +22 and +23 mm per year, respectively.  Furthermore, at the time of doubled CO2, Wild and Ohmura state that the ECHAM3 model projected a sea level rise "close to zero" (0.2 mm per year), while the ECHAM4 model projected a sea level fall of 0.6 mm per year.  Consequently, the new-and-improved GCM suggested global warming would actually cause sea level to decline, indicating once again just how tenuous are climate model predictions of warming-induced sea level rise.

In a review of several concepts related to real-world assessments of changes in sea level, Diez (2000) says that early analyses of rising sea level trends "created panic that led to risky conclusions and reckless efforts to remedy the surmised problems," an opinion that he says is shared by other analysts who question the statistical meaning and geographical representation of the available data, as well as their quality.

To begin, mean sea level is affected by a host of eustatic and isostatic factors, "all of which," in the opinion of Diez, "have a great local and/or regional variability, suggesting modifications are required in current gauges to accurately determine the actual value of global sea level change."  In addition, the review points out that no corrections or allowances are made in the data for short-term natural processes such as ENSO, storm surges, tides and tsunamis, or for anthropogenic-induced land subsidence caused by the removal of oil and natural gas, or for the irregular placement of gauges and the influence of dikes and other maritime structures that can all influence local sea level readings.  As a result, Diez states that "the consideration of all these sources of possible inaccuracies in the gauge data system firmly undermines the principal support for the present quantitative prediction of current and future sea level rise trends."

Diez also criticizes current sea level models for their inadequacies, asserting (1) that the "simplicity of their structure leads to conclusions with only a relative accuracy," (2) that most such models "have completely refused to consider the possibility that the world's oceans may be capable of completely eradicating carbon dioxide from the atmospheric-lithospheric system," and (3) that "some have even completely ignored or underestimated the oceanic solubility of CO2."  Hence, there is much work to be done, including the collecting of large amounts of additional accurate data, before reliable quantitative assessments of sea level trends can be made, while reliable estimates of how sea level might be affected by future increases in the air's CO2 concentration are even further down the road.

In another paper that discusses the many complexities associated with the assessment of global sea level change, Douglas and Peltier (2002) review what we know about this important subject and give their prognosis for the future.  Mean global sea level (GSL), according to them, was relatively stable for the past few millennia, but it "abruptly began to rise near the mid-19th century."  In this regard, however, they note that no studies "have detected any significant acceleration of GSL rise during the 20th century."

With respect to these observations, we know that the air's CO2 content began to rise at about the same time, i.e., 1850.  However, its rate of rise has been anything but constant.  Over the first half of this period (1850 to 1925), for example, the atmosphere gained about 20 ppm of CO2, whereas over the second half (1925-2000) it gained about 65 ppm.  Hence, it would appear to be a good bet that the historical rise in mean global sea level has not been driven by the concomitant rise in the air's CO2 content.

Returning to polar ice sheets for a moment, van der Veen (2002) had as his objective "to evaluate the applicability of accumulation and ablation models on which predicted ice-sheet contributions to global sea level are based, and to assess the level of uncertainty in these predictions arising from uncertain model parameters."  His reason for doing so was his belief that with "greater societal relevance comes increased responsibility for geophysical modelers to demonstrate convincingly the veracity of their models to accurately predict future evolution of the earth's natural system or particular components thereof."  In stepping forward to perform this task, however, he was forced to conclude that "the validity of the parameterizations used by glaciological modeling studies to estimate changes in surface accumulation and ablation under changing climate conditions has not been convincingly demonstrated."

Some of the problems associated with model testing, of course, are observational, i.e., there must be a documented history capable of being simulated.  With respect to the mass balance of the Greenland Ice Sheet, however, van der Veen notes that "it is currently not well known whether or not the ice sheet is growing or shrinking, although most studies agree that the whole of Greenland is not far out of balance in either direction."  Hence, if what is "known" is really not all that certain, there is little opportunity to assess model performance.  Furthermore, even if a model prediction turns out to be consistent with present or past observations, van der Veen notes that "there is no guarantee that the model will perform equally well when used to predict the future," especially if one of the model parameters extends into a range that is beyond the range within which the model was tested.

Admittedly, these observations appear to suggest it is essentially impossible for a model to ever be "proven" to be a valid tool for assessing the likelihood of future events; and that perspective is correct.  At best, says van der Veen, models can only be confirmed "by matching observational data that were not used to calibrate model parameters."  But even then, considering the observations of the preceding paragraph, it really becomes a matter of faith as to how well one believes a model that has successfully replicated the past will predict the future.

Laying these considerations aside - but remembering they imply that whatever follows may be even less well defined than what is suggested by the numbers - van der Veen calculates that within the context of greenhouse-warming-induced sea level change, uncertainties in model parameters are sufficiently great to yield a 95% confidence range of projected contributions from Greenland and Antarctica that encompass global sea-level lowering as well as rising by 2100 A.D. for low, middle and high warming scenarios based on surface mass balance calculations.  Hence, even for the worst of the global warming projections - which could well be way off base itself, as we personally believe it is - there could be little to no change in mean global sea level due to the ongoing rise in the air's CO2 content.

In view of these findings, van der Veen concludes that the confidence level that can be placed in current ice sheet mass balance models "is quite low."  Paraphrasing an earlier assessment of the subject, in fact, he says that today's best models "currently reside on the lower rungs of the ladder of excellence."  Hence, it is not surprising that he states that "considerable improvements are needed before accurate assessments of future sea-level change can be made."

Braithwaite and Raper (2002) perform a similar analysis for mountain glaciers and ice caps, excluding the Greenland and Antarctic ice sheets.  They begin by noting that "the temperature sensitivity of sea level rise depends upon the global distribution of glacier areas, the temperature sensitivity of glacier mass balance in each region, the expected change of climate in each region, and changes in glacier geometry resulting from climate change."  They end by reporting that "none of these are particularly well known at present," concluding that "glacier areas, altitudes, shape characteristics and mass balance sensitivity are still not known for many glacierized regions and ways must be found to fill gaps."

Considering the problems standing in the way of acquiring this important knowledge, Braithwaite and Raper estimate that satisfactory solutions "will probably take a decade of work by many different groups in a number of disciplines."  As a result, reliable predictions of glacier behavior and its impact on sea level over the next hundred years would appear to be well beyond our grasp at the present time.

In another take on this issue, Munk (2003) notes that "surveys of glaciers, ice sheets, and other continental water storage can place only very broad limits of -1 to +1 mm/year on sea level rise from freshwater export," which essentially means that we haven't a clue as to what is really happening in the area of overall cryospheric response to putative global warming.  He also notes that "polar melting would result in movement of water mass toward the equator, causing a decrease in the rate of Earth's rotation," but he reports that "observations show a (nontidal) increase in Earth's rotation (attributed to a movement of mass toward the poles in response to the unloading of ice mass since the last glacial maximum)," which again leaves us guessing as to the net effect of the modest global warming of the past century on sea level trends.

Against this backdrop, Munk considers other ways of assessing contemporary sea level behavior, focusing on the observation of Antonov et al. (2002) that the mean salinity of the global ocean decreased slightly between 1954 and 1997.  Here too, however, there are knotty problems that stand in the way of a clear exposition of what may be happening.  In addition, Munk notes that "the jury is still out on the interpretation of the tide gauge records," and that "the large discrepancy between the sea ice thinning estimates from the sonar method and the wave method leaves the interpretation of freshening in limbo."

With respect to the future, Munk notes the great promise of "global coverage by satellite altimetry (which is replacing tidal estimates)," but he cautions that "it will take several decades [our italics] to obtain good estimates of the role of global warming in sea level rise."  In the meantime, as he puts it, "20th-century sea level remains an enigma - we do not know whether warming or melting was dominant, and the budget is far from closed."

In concluding this brief review of difficulties associated with predicting changes in sea level., we note the study of Bye (1998), who analyzed theory and data related to seafloor spreading in an effort to determine its potential contribution to changes in sea level, as well as its potential to influence climate.  The primary conclusion of this study was that seafloor spreading may be directly responsible for a mean sea level rise of approximately 1 mm per year.  This is a very significant finding, especially when it is remembered that the mean rate of sea level rise over the past century is believed to be of approximately the same magnitude.

Bye also identified a potential feedback mechanism arising from the calving of icebergs that is postulated to be driven by flotation forces generated by seafloor-spreading-induced sea level rise.  And he notes that this phenomenon could induce global warming, as "the reduction in ice cap volume would tend to produce interglacial conditions."  Hence, Bye's work provides yet another explanation for the historical sea level rise of the recent past, and it elucidates "a mechanism whereby plate tectonics can actually drive climate."  This is also a very significant finding, for Bye notes that "at present, we are experiencing just such a phase" of "enhanced plate tectonic activity."

When all is said and done, it is thus quite clear there is no compelling reason to believe that the type of global warming earth has experienced over the past century or so - CO2-induced or otherwise - will lead to catastrophic increases in sea level, even if it continues apace for quite some time to come.  It is also clear that much decades-long work will be required to better refine this assessment of the issue.

References
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Braithwaite, R.J. and Raper, S.C.B.  2002.  Glaciers and their contribution to sea level change.  Physics and Chemistry of the Earth 27: 1445-1454.

Bratton, J.F.  1999.  Clathrate eustasy: Methane hydrate melting as a mechanism for geologically rapid sea-level fall.  Geology 27: 915-918.

Bye, J.A.T.  1998.  Sea level change due to oscillations in seafloor spreading rate.  Physics of the Earth and Planetary Interiors 109: 151-159.

Clark, P.U. and Mix, A.C.  2000.  Ice sheets by volume.  Nature 406: 689-690.

Diez, J.J.  2000.  A review of some concepts involved in the sea-level rise problem.  Journal of Coastal Research 16: 1179-1184.

Douglas, B.C. and Peltier, W.R.  2002.  The puzzle of global sea-level rise.  Physics Today 55: 35-40.

Munk, W.  2003.  Ocean freshening, sea level rising.  Science 300: 2041-2043.

Reeh, N.  1999.  Mass balance of the Greenland ice sheet: Can modern observation methods reduce the uncertainty?  Geografiska Annaler 81A: 735-742.

Shankar, D. and Shetye, S.R.  1999.  Are interdecadal sea level changes along the Indian coast influenced by variability of monsoon rainfall?  Journal of Geophysical Research 104: 26,031-26,042.

van der Veen, C.J.  2002.  Polar ice sheets and global sea level: how well can we predict the future?  Global and Planetary Change 32: 165-194.

Wild, M. and Ohmura, A.  2000.  Change in mass balance of polar ice sheets and sea level from high-resolution GCM simulations of greenhouse warming.  Annals of Glaciology 30: 197-203.

Yokoyama, Y., Lambeck, K., Deckker, P.D., Johnston, P. and Fifield, L.K.  2000.  Timing of the Last Glacial Maximum from observed sea-level minima.  Nature 406: 713-716.