We’re witnessing a remarkable decline in Arctic sea ice. The annual minimum is taking a nosedive:
Bear in mind that we haven’t yet reached the minimum this year, so the 2012 value will end up being even lower than the value plotted.
But that’s not the only change taking place. We can investigate in greater detail by studying how the cycles have changed over time. One way to do this is with windowed Fourier analysis. I took each 2-year time span (nearby spans overlapping by 1 year) and fit a 2nd-order Fourier series in order to quantify the size and shape of the annual cycle.
Here’s how the amplitude (actually semi-amplitude, which is just half the full amplitude) of the fundamental Fourier component changed:
The dramatic low extent in 2007 ushered in a new era of greater amplitude. But it’s not just the main Fourier component whose amplitude increased, so did the 2nd harmonic:
In fact the 2nd harmonic amplitude increased more — proportionally — than the 1st harmonic (the fundamental), so the relative amplitude (the ratio of their amplitudes) also increased:
That’s not all. We can use windowed Fourier analysis to measure the phase of each component of the Fourier series. We can then compute the relative phase for higher harmonics, which is their phase when the fundamental is at phase zero. Here’s the relative phase (in cycles) of the 2nd harmonic:
Note that it’s always near 0.5. This means that when the fundamental is at maximum (during late winter) the 2nd harmonic is at minimum so they partly cancel, but when the fundamental is at minimum (during late summer) the 2nd harmonic is too so they reinforce each other. That makes the minimum more “pointy” while the maximum is more flat.
Note also that the relative phase has gotten closer to 0.5 lately. That’s because the annual cycle has become more symmetrical, with the rise to maximum and the fall to minimum occurring at more nearly the same rate.
The summer minimum has consistently occurred around mid-September, but the change in relative phase is because the winter maximum has migrated to later in the year. It’s now just about 6 months after the summer minimum, whereas before it occured a little bit earlier.
We can see this plainly if we compute the average annual cycle for the data before 2007, and compare that to the average annual cycle after 2007. Here they are, with pre-2007 data in blue and post-2007 in red:
The most obvious feature is that the minimum has declined much more than the maximum. But it’s also evident that the winter max is now around mid-March, when it used to happen in early March or even late February.
Part of the reason for the greater decline at minimum is simple geometry, due to the placement of land masses in the northern hemisphere. But there may be other contributing factors as well. As for the phase change, with maximum occurring slightly later in the year, I don’t know why.