Proxy evidence suggests that the recent declines in Arctic sea ice extent and volume are unprecedented over at least the last few thousand years (Polyak et al. 2010). Historical records indicate that the seasonal ice zone, an area of northern seas that is ice covered in winter but not in late summer, has been expanding gradually since 1870, and more rapidly in the past three decades (Kinnard et al. 2008). Reinforcing that conclusion, combined submarine and satellite measurements show that ice has been thinning over much of the Arctic Ocean since the 1950s, so the remaining cover increasingly consists of thinner seasonal ice (Kwok & Rothrock 2009).
These longer-term studies place recent satellite-era change in perspective. Sea ice extent, in particular, has been relatively straightforward to define and measure by satellite. As a result, we have daily time series of extent and area going back into the 1970s, which confirm a recently accelerating decline. Decline has been most noticeable in late summer, but is visible across all times of the year. A cycle plot (Cox 2006) in Figure 1 illustrates changes in average extent and area (NSIDC data) broken down for each month, from November 1978 through March 2011.
Each squiggly line in Figure 1 tracks the mean sea ice extent (blue) or area (orange) for a particular month over roughly the years 1978 to 2011. The vertical axis shows the absolute ice cover in millions of km2. Extent, for example, ranges from values near 16 million km2 in winters of the earlier years, to 5 million km2 or less in summers of recent years.
The declines visible in Figure 1 all are statistically significant. Figure 2 graphs the linear trends separately for each month.
Linear trends provide simple summaries of change, but they sometimes prove too simple. For example, in recent years September ice extent has been dropping at faster-than-linear rates. Five of the past six years fall below the regression line, as seen in Figure 3.
Trend lines fit to past data, such as those in Figures 2 or 3, provide convenient summaries (like two-dimensional averages) that describe how things have been changing. Projecting such trends into the future is purely a what-if exercise, interesting as conjecture but not grounded in physical understanding. With that caution firmly in mind, the linear trend in Figure 3 predicts a mean September 2011 ice extent of 5.2 million km2. If September ice extent continued to decline at the same rate, it would drop below 1 million km2 (an arbitrary level viewed as “virtually ice free” by many observers) in 2063.
Even 2063 is several decades earlier than projected in the conservative 2007 IPCC report. Given recent signs of accelerating decline, however, Arctic scientists now believe that virtually ice-free late summer conditions will probably arrive much sooner. To more realistically describe the emerging pattern of faster-than-linear decline, several kinds of curves have been suggested. Such curves are only slightly more complicated than a straight line, and no more physical, but they better fit recent data.
Figure 4 shows a Gompertz curve model for September ice extent. The Gompertz is an asymmetrical S-curve. Up-to-right versions are often used to describe biological growth. This down-to-right version begins with a slow decline from late-70s levels around 7.5 million km2, then falls more steeply — as does the actual extent. If September ice extent continued along this curve, it would drop below 1 million km2 by 2024. Unlike a linear model, which falls to zero at a steady rate and then keeps on going to make impossible predictions of negative extent, an S-curve like Figure 4 shows a rate of decline that slows and approaches zero asymptotically. This geometrical property corresponds to the intuitively appealing notion that late-summer remnants of sea ice might still be found in parts of the Arctic well after most of it is gone. In the equation at the top of Figure 4 the first parameter (7.551) gives the asymptotic starting level for this model, and the third parameter (2017) corresponds to the year of steepest descent.
The Gompertz prediction for September 2011 is 4.4 million km2, well below the linear prediction of 5.2. Whether either of these naive, trend-based predictions comes close to the reality will be known in just a few months. Gray bands in Figure 4 indicate statistical uncertainty estimated from the scatter of actual values around the curve (plus or minus two standard deviations). Thus, a more complete statement of the prediction in Figure 4 is that our point estimate is 4.4, but with a 95% confidence interval ranging from 3.5 to 5.3 million km2. Again, I emphasize that these are statistical predictions, not based on physical understanding.
Extent is a well measured but potentially misleading index for Arctic sea ice. Beneath the surface, it could be getting thinner, or a given extent could increasingly consist of first-year ice which is more saline than multi-year ice and hence easier to melt. Thinner, younger ice is more apt to fragment and melt rapidly in unfavorable conditions. The critical dimensions of ice thickness, age and volume might be declining faster than extent, in which case virtually ice-free summers could arrive sooner than Figure 4 suggests. How much sooner? In a following post I will apply the Gompertz model to trends in volume, with some surprising results.