By considering the unique sea-level "fingerprint" created by a melting ice sheet, a team of geophysicists in North America has developed a new method for pinpointing the sources of global sea-level rise. Their approach could provide a way to measure the impact of the Greenland and West Antarctic ice sheets – the greatest sources of uncertainty in projections of future sea-level changes.

Long-term variations in sea level are caused by processes including thermal expansion of the water, changes in ocean circulation, and changes in the size of glaciers and ice sheets. Measurements from tide gauges indicate a global average sea-level rise of 1–2 mm/yr during the 20th century. However, this estimate ignores geographical variations in sea level, and provides no information about the contribution of different processes.

One possible way to pick apart the total sea-level change is to look for the distinct pattern, or fingerprint, of a melting ice sheet. Close to the ice sheet, for example, the sea level tends to fall. This is a result of both the local uplift of the Earth's crust after being relieved of the great weight of the ice and a reduction in the ice sheet's gravitational pull on the ocean. Moving further away from the ice sheet, however, the sea level rises progressively.

Looking for fingerprints

Carling Hay at the University of Toronto and colleagues at Harvard University, along with Rutgers University geophysicists in Canada and the US, have developed a new statistical method for identifying these ice-sheet fingerprints. Their approach uses an algorithm known as the Kalman filter, which processes noisy measurements and provides an optimal estimate of a system's state. The Kalman filter is well suited for analysing sea-level change because it can use known information about the system to fill data gaps – a common occurrence with tide-gauge records.

In order to test this framework, the team created a sea-level record from scratch, containing known contributions from different processes. The researchers first removed the long-term trends from almost 600 tide-gauge records going as far back as 1807, isolating the short-term sea-level variability – the observational "noise". Then, at each tide-gauge site, a long-term, warming-forced sea-level trend was added, obtained from a climate-model simulation. Changes in land height caused by changes in glacial mass were supplied by an Earth model, and a globally uniform trend of 0.8 mm/yr was added to account for any unmodelled sources of sea-level rise, such as the melting of mountain glaciers.

Melt rates of 0.3 and 0.5 mm/yr were assumed for the Greenland (GIS) and West Antarctic (WAIS) ice sheets, respectively, along with their predicted fingerprints. The researchers then applied the Kalman filter to this synthetic dataset, initializing the algorithm with melt rates of zero.

Matching melt rates

The algorithm was found to estimate the melt rates most accurately when applied to the maximum number of tide gauges, providing enough information for the ice-sheet fingerprints to be separated from the globally uniform trend. The final estimated melt rates for the GIS and WAIS were 0.21 and 0.38 mm/yr, respectively, close to the values used in the synthetic dataset. The 1σ uncertainties associated with these values indicate the magnitude of ice-sheet melting that could potentially be detected in real sea-level records.

"It should be possible to use historical tide-gauge records to robustly infer positive Greenland and West Antarctic ice-sheet melt rates above 0.3 and 0.4 mm/yr, respectively," explains Hay. "We are now in the process of applying our methodology to historical sea-level records to provide a new estimate of total sea-level rise and ice-sheet melt rates over the 20th century," she adds.

Eric Leuliette, an oceanographer at NOAA's Satellite Oceanography and Climatology Division, comments that this approach is, however, unlikely to provide a complete picture of past sea-level changes. "Because of the lack of long tide-gauge records near some regions with glaciers, it may be impossible to use fingerprints to reconstruct all of the individual sources of 20th century sea-level rise," says Leuliette, who was not involved in this latest research. "But this study demonstrates that it may be possible to use tide gauges to at least constrain the contributions from Antarctica and Greenland."

Hay and colleagues eventually hope to apply their algorithm to satellite measurements of sea-surface height. Although these data are only available for the past 20 years, they offer near-global coverage.

The research is described in Proceedings of the National Academy of Sciences.