In an earlier post I proposed an asymmetrical S-shape called the Gompertz curve as a simplified, nonphysical model describing satellite-era trends in minimum sea ice extent (Figure 4). If future ice extent follows the same trend, this model predicts a September 2011 mean extent of 4.4 million km2 (confidence interval 3.5–5.3), and extent falling below 1 million km2, “virtually ice-free,” by 2024. I emphasize that extrapolating curves is a what-if exercise, not based upon physical understanding. Sometimes a statistical approach yields predictions fairly close to those obtained from more sophisticated physical models, but how well any prediction anticipates the real Arctic will be tested in the months and years ahead.
The observational data in Figure 4 show a gradual early decline in extent, recently steepening. Linear models do not capture this pattern. Quadratic models capture the recent steepening but do less well with the gradual earlier decline, and they imply an accelerating descent toward zero ice. Both quadratic and Gompertz are equally simple (3 parameters), but the Gompertz behaves differently at start and finish — a gradual early decline from some asymptotic initial level, and a more abrupt but also asymptotic approach toward zero at the end. This end behavior corresponds to the idea that late-summer remnants of sea ice, perhaps along coasts and fjords of the Canadian Archipelago and Greenland, could persist through some years after most central Arctic Ocean ice is gone.
Sea ice extent is defined as the area of northern seas covered by ice above a certain concentration — in the case of NSIDC data, concentration above 15%. Sea ice area calculations adjust this by subtracting out estimates of the open water within that extent, arriving at a smaller (but less reliably measured) number representing the area actually covered by ice. Figure 5 graphs two well-known time series of northern sea ice area, published by Cryosphere Today (CT; data here) and the National Snow and Ice Data Center (NSIDC; data here). Data points are September means for 1979–2010. I adjusted the NSIDC data to assume 100% coverage in a central area unobserved by satellites, but made no similar adjustment for CT. The two series generally move together.
The curve in Figure 5 describes only the NSIDC area data (but would look fairly similar if drawn for CT instead). It suggests a September 2011 prediction of 3.1 million km2 area (confidence interval 2.4–3.8). The curve falls below 1 million by about 2022, showing what might happen if the area trend continued along this path. That prediction about area matches well with what Figure 4 predicts for extent.
Both area and extent are two-dimensional indexes. We have many indications that sea ice thickness, age and volume are decreasing as well, perhaps faster than area or extent. Ice volume should be a key index, but we lack time series of direct observations. The best available time series, based on modeling constrained by observations, reflects the efforts of an ice volume team (Schweiger, Zhang, Lindsay, Steele) at the Polar Science Center of the University of Washington. This group publishes a graph tracking sea ice volume anomalies estimated from their PIOMAS model (reference Zhang & Rothrock 2003).
Figure 6 applies a Gompertz model to PIOMAS mean September ice volume estimates for 1978–2010 (data courtesy of Jinlun Zhang). The Gompertz provides a good fit to volume estimates so far, which have indeed declined faster than area or extent. According to this model the year of steepest descent (2010) just passed. We cannot yet see whether deceleration has really started to occur. Figure 6 suggests that volume could drop below 2,000 km3, just over 10% of its 1978 value, by 2017 — or given the error bands, as early as 2013.
So these Gompertz models predict sea ice area and extent reduced to remnant levels in the 2020s, and volume reaching low levels half a decade or more before that. How do our results fit with each other, or with those from physical models? The Gompertz predictions fall toward the near end of the range of current scientific opinion, but seem qualitatively consistent with other studies — particularly in view of the varied thresholds used to define “seasonally ice-free conditions.” Moreover, the graphed curves in Figures 4–6 look misleadingly smooth. Actual behavior, even if the Gompertz models prove prescient, should fluctuate above and below the curves as past years have.
In a recent paper, Zhang et al. (2010) note that “summer ice volume may be more sensitive to warming while summer ice extent [is] more sensitive to climate variability.” Consequently, they expect that summer extent might continue to fluctuate around higher values even as volume continues to fall. That suggests a physical explanation for the offset in timing we see comparing Figures 4 and 5 (extent and area) with Figure 6 (volume). Under a warming scenario (4 degrees C surface air temperature increase over the Arctic by 2050), Zhang and colleagues project that summer ice volume could fall to low levels by 2025, while ice extent fluctuates above zero into the 2040s.
The most immediate forecasts of ice-free conditions have been proposed by Wieslaw Maslowski. In 2007 he offered a prediction that ice might be gone by 2013, based on a linear extrapolation of 1997–2004 volume trends. This extrapolation-based prediction met with some skepticism. Recently at the European Geosciences Union, however, Maslowski offered an almost equally early prediction based on more sophisticated work with a coupled ice/atmosphere/ocean/rivers model of the Arctic system. His model projects that Arctic seas could lose most of their late-summer ice by 2016, plus or minus three years (Maslowski quoted by Richard Black, BBC News 4/7/2011). These numbers are close to what we see in Figure 6.
Where various predictions most differ is in the details of late-stage behavior, which observations do not yet constrain.