PerspectiveOcean Science

Ocean Freshening, Sea Level Rising

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Science  27 Jun 2003:
Vol. 300, Issue 5628, pp. 2041-2043
DOI: 10.1126/science.1085534

The rate of the global sea level rise and its causes has been debated for a century, but no definitive conclusion has been reached. Traditional tide gage estimates are attributed to two causes: thermal expansion of warming oceans, and freshwater exports from continents. 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. A recent survey of global ocean freshening provides an alternative estimate but raises a host of new issues.

Sea level rise played an important role in recent assessments by the Intergovernmental Panel on Climate Change (IPCC) (1, 2). In their reports, the IPCC generally assumed a sea level rise in the 20th century of 1.5 to 2.0 mm/year, largely on the basis of tide gage records (3). The main causes of this rise are the thermal expansion and hence lower density of a warming ocean (steric rise) and the import of fresh water from continents (eustatic rise). In 1995, the IPCC concluded that “the rise in sea level has been due largely to the concurrent increase in global temperature over the last hundred years” but went on to refer to additional contributions from “melting of glaciers, ice caps and ice sheets” [(1), p. 363]. Thus, the 1995 IPCC report considered the rise to be primarily steric.

The situation changed radically when Levitus and co-workers (4, 5) reported an increase in global ocean heat storage by 2 × 1023 J (equivalent to 0.44 W/m2) in the past 50 years. This ocean warming is consistent with a steric rise of just 0.5 mm/year. The record (red curve in the first figure) is dominated by oscillations on decadal time scales, introducing large errors into estimates of century-scale trends. Nonetheless, the thermal expansion of 0.5 mm/year falls far short of the traditional estimates of 1.5 to 2.0 mm/year. The data thus suggest a dominant (rather than secondary) role for the eustatic contributions.

A large eustatic rise?

Red and blue curves are the temperature-induced (δhT) and salinity-induced (δhS) components of the steric anomaly, δhsteric = δhT + δhS. The time series are spatially averaged (50°S to 65°N), 5-year running means computed for the upper 3000 m of the ocean. Shaded bands give standard errors; dashed lines are least-squares trends. The green curve gives the eustatic rise, calculated as 36.7 δhS (see text). The total sea level rise from the temperature and salinity surveys (after correction for melting sea ice) is the sum of the thermosteric and the eustatic rise, δhT + 36.7 δhS = 0.5 + 1.4 = 1.9 (mm/year). [Adapted from (7)]

Yet the IPCC's “central” estimate (2) for the eustatic contribution is only 0.2 mm/year (although the error bars are so generous as not to preclude a substantial eustatic contribution). Further, polar melting would result in movement of water mass toward the equator, causing a decrease in the rate of Earth's rotation. In contrast, 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). Hence, the combined steric and eustatic contributions fall well short of 1.5 to 2.0 mm/year. Therein lies the enigma (6).

A recent survey by Antonov et al. (7) may provide some possible clues to solving the enigma. The authors showed that the mean salinity of the global ocean has decreased slightly between 1954 and 1997. Combining the increased temperature and decreased salinity, one obtains a steric sea level rise (8) of

δhsteric = δhT + δhS

= 0.50 + 0.05 = 0.55 (mm/year)

The salinity-related steric expansion, δhS, of 0.05 (±0.02) mm/year (blue curve in the first figure) is widely interpreted as a minor addition to thermal expansion, δhT. But interpretation of the salinity-induced component depends on the source of the expansion. If the decrease in salinity is associated with melting of ice sheets and other changes in continental water storage, then it provides independent evidence for a dominant eustatic contribution. In any case, it must not be counted twice, once steric and once eustatic.

Here, I consider three modes of ocean freshening. First, there are regions of large freshening in which the salinity-induced and temperature-induced steric rises nearly cancel [for example, such a situation occurred in the Labrador Sea between 1960 and 1980 (7)]. Such events are associated with intrusions of cold, fresh waters into warm, salty waters of equal density and leave the global average salinity unchanged. Second, melting of floating ice fields may freshen the ocean without raising sea level. Third, fresh water may be imported from continents. Only this third mode leads to a global eustatic rise in sea level: δheustatic = (ρ/Δρ)δhS where ρ = 1028 kg/m3 is the density of seawater and Δρ = 28 kg/m3 is the incremental density of seawater relative to fresh water of the same temperature.

The multiplier, ρ/Δρ = 36.7, is a consequence of conservation of mass (see the second figure). Its large value is perhaps surprising, but can be made plausible by the following consideration. Adding a layer δh of fresh water to fresh water (Δρ = 0) raises the level without decreasing salinity. Clearly, the density perturbation δρ must be proportional to the salinity (Δρ), δρ = -Δρ(δh/h), which is consistent with δheustatic = (ρ/Δρ)δhS.

Freshening the ocean.

The unperturbed ocean (A) has a depth h and a density ρsea = ρfresh + Δρ = 1000 + 28 = 1028 (kg/m3). Continental runoff adds a layer δh of density ρfresh (B). Thorough mixing of this layer with the underlying ocean (C) results in a perturbation δρ (a negative quantity) relative to the initial density. The additional change in depth, δ(δh), due to mixing is negligible. Equating the total water masses before and after mixing, mB = mC, yields a eustatic sea level rise δheustatic = -h(δρ/Δρ). The steric rise δhsteric = - ∫ dz δρ/ρ = -h(δρ/ρ), and accordingly δheustatic = (ρ/Δρ)δhsteric = 36.7 δhsteric.

The salinity-induced steric sea level rise δhS = 0.05 ± 0.02 mm/year then yields a eustatic rise of 36.7 δhS = 1.8 (±0.7) mm/year. A eustatic rise of 1.8 mm/year over an ocean area of 3.6 × 108 km2 would require a melt volume of 650 (±250) km3/year. Antonov et al. obtained a value of 471 km3/year following a somewhat different argument (7). These are, however, upper limits because of contributions to the freshening of the ocean from melting sea ice.

Sea ice covers an area of ∼107 km2 (with ±30% seasonal departures) at a thickness of ∼3 m (9, 10). The total sea ice volume is thus 30,000 km3. Shrinking of the ice-covered area reduces the volume by 0.3% or 90 km3 per year. There is, however, no consensus on the rate of sea ice thinning. Johannessen et al. (10) place their confidence in the measurements by Nagurnyi et al. (11) of the dispersion of elastic-gravity waves in the floating ice cover. These waves are generated by ocean swell and propagate hundreds to thousands of kilometers into the ice sheet; their dispersion is sensitive to ice thickness. From these data, Johannessen et al. deduce a thinning by only 4% over the past 20 years. This thinning is equivalent to a loss of 60 km3/year, yielding a total loss of sea ice from shrinking and thinning of 150 km3/year.

This annual loss is equivalent to about 135 km3 of fresh water, which must be subtracted from the above estimate of the eustatic sea level rise (650 km3/year). Hence, the eustatic rise corresponds to 515 km3/year, or 1.4 mm/year (green curve in the first figure). Adding this eustatic rise to the steric rise of 0.5 mm/year, we end up with an estimated 1.9 mm/year for the total sea level rise—near the upper limit of the traditional estimates of 1.5 to 2.0 mm/year.

I do not propose that this is the solution to the enigma. Cabanes et al. (12) have presented evidence for a bias in the location of the tide gages, favoring regions of abnormal thermal expansion. They argue for a 20th-century mean rate of 0.5 mm/year dominated by thermal expansion. Miller and Douglas (13) have reanalyzed the same basic data set in large ocean regions and come up with a traditional estimate of global sea level rise dominated by the eustatic contribution. The jury is still out on the interpretation of the tide gage records.

With regard to the thinning of sea ice, submarine transects with upward-looking sonars indicate a much higher rate of thinning by 1.5 m over the past 20 years (9). Some of this thinning may result from changes in ice distribution caused by changes in wind stress over the Arctic. The sonar data give 600 to 800 km3 of fresh water per year—more than enough to account for the entire freshening. This would leave no room for a eustatic contribution (consistent with Cabanes et al.) and would suggest a continental water import (14) that is in line with the lower limits of the IPCC assessment.

The large discrepancy between the sea ice thinning estimates from the sonar method and the wave method leaves the interpretation of freshening in limbo. As mentioned above, the global ocean heat storage has increased by 2 × 1023 J in the past 50 years, or 4 × 1021 J/year on average (4, 5). A proportional increase over the arctic sea ice area would melt 400 km3/year. But we must allow for the larger than average increase in radiation at high latitudes and the effective albedo of the floating ice sheet. The two effects might just cancel; in any event, these considerations suggest a substantial contribution to ocean freshening from melting sea ice.

The future is another story. Global coverage by satellite altimetry (which is replacing tidal estimates) shows a notably larger than average level rise in the last decade of the century (15). The detection of the relatively slow century-scale trend is plagued by the dominance of high (decadal) frequencies in the spectrum of the rate of sea level variability. It will take several decades to obtain good estimates of the role of global warming in sea level rise.

In the meantime, 20th-century sea level remains an enigma—we do not know whether warming or melting was dominant, and the budget is far from closed. Ocean freshening, despite large error bars, places some welcome independent constraints on sea level rise and will hopefully be the focus of further research.

References and Notes

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