There are (at least) two derived variables we can construct from extent and area. One, which I’ve called “spread,” is their ratio, i.e., extent divided by area. The other, which I’ve dubbed “split” (although I don’t think that’s such a good term) is their difference, i.e., extent minus area. These are related to how much the ice pack is broken up. If the ice pack were a single, unbroken solid piece then extent would equal area, so that the spread would be 1 and the split would be zero.
First let’s look at their time series. Here’s the spread:
Clearly the spread has increased over time, but only its annual maximum. The annual minimum has stayed surprisingly constant. The large increase in annual-maximum spread is simply due to the fact that sea ice cover has decreased so much, so that the same excess of extent over area (the same “split”) corresponds to a larger ratio of extent over area (a larger “spread”).
The split hasn’t shown the extreme time change which spread has undergone (although, as we’ll see, it does show some changes):
Although split actually does show some trends over time, there are different trends at different times of year:
There has been notable increase during May and June, with notable decrease during September through November (and to a lesser degree in December through March). Essentially, the ice pack has become more fragmented during May and June, less so during September through November.
The trends in spread show increase from April through October, peaking in August, but no significant change for November through March:
The lack of spread trend for November through March reveals that the decline in split has been in the same ratio as the decline in sea ice overall, to keep the extent/area ratio constant. The interesting cases are September and October, for which split has declined, but overall sea ice has declined even faster so that spread is on the increase. Also interesting are July and August, for which split has shown no trend but overall ice has reduced sharply, so the proportion of extent to area (the spread) has increased quite a lot.
Changes in the annual cycles are also revealed by windowed Fourier analysis. For split, the amplitude of the fundamental Fourier component shows changes but the long-term trend is far from linear:
The timing (as indicated by phase of maximum) of the fundamental Fourier component has changed dramatically:
Over the entire time span, the phase has changed by about 0.2 cycles (about 70 days). The most recent years (since 2010) show continuing decrease, the migration of the timing of maximum continuing until the very present. If we compute the average annual cycle for the 1980s, 1990s, and 2000s, we can see some of the migration toward earlier maxima even though this averages out the changes in the 1980s and omits the data since 2010 which continues this trend:
The relative phases (relative to the fundamental) of the higher harmonics of the Fourier series also show decline in the 1980s and continued decline since 2010:
Spread shows the continual amplitude increase which would be expected from its continual increase at maximum with stable minima:
Again we can average the cycle for the decades of the 1980s, 1990s, and 2000s, to illustrate the cycle change:
These two derived variables add to the overall picture of dramatic change in Arctic sea ice. The changes in split (the excess of extent over area) also show continued change after 2010, which further identifies 2010 as a banner year for sea ice change and again argues against the idea that Arctic sea ice has recently been “stabilizing.”
All told, every variable we’ve studied shows significant, in fact remarkable, change in Arctic sea ice. The northern ice pack is truly the “canary in a coal mine” which is warning us of the extremity of changes to come — soon — to the rest of the planet as a result of our throwing a monkey wrench into the machinery of the climate system. The question “Has mankind dramatically altered earth’s climate?” has been answered in the affirmative. The question before us now is, “Will mankind heed the warning signs which are in plain sight?”