After my last post, a reader asked:
What’s most noticeable about this is the massive change in variability since 2007. Could you do some analysis of that?
I’ve done this before, but it bears repeating because it is a common point of confusion (as in, “What’s going on?”). The graph he refers to is of sea ice extent anomaly
and the dramatic increase in fluctuation since about 2007 is rather obvious.
But we need to keep in mind what anomaly is, and how it’s calculated. Anomaly is the difference between what a given day’s (or month’s) value, and what has historically been typical for that same time of year. Essentially, we subtract away the average annual cycle, so if a given year shows an annual cycle which is different from average, that difference — despite being part of the annual cycle during that year — will remain.
To define that “average” annual cycle, we first choose a baseline period; the time span we select to define what average means. For the above graph, the baseline period is from 1979 to 2000. What if we made a different choice? What if we used the data from 2007 up to now to define our baseline? With a different baseline period we’ll get different anomaly values, namely these:
That’s different! Suddenly it look like there was much more variation before 2007. Why? Because the annual cycle itself changed significantly in 2007. What we’ve really observed “since 2007” isn’t an increase in variability, it’s a change in the average annual cycle.
There are ways to estimate the annual cycle all by itself. One way to estimate its size is something called “windowed Fourier analysis,” and it gives something like this:
It shows “semi-amplitude,” which is just half the amplitude. Clearly it changed about 2007, and has remained higher than before since that time.
There are ways to estimate anomaly by subtracting an annual cycle which itself is allowed to change over time. This is done, for instance, with the CO2 data from Mauna Loa. Over the years, the size of the annual cycle in CO2 concentration has also increased, so the good folks at Mauna Loa base their “average annual cycle” on its average for the immediately past several years. Another way, which I’ve used many times, is to allow frequency/amplitude modulation of the annual cycle using Fourier analysis, and it gives me this:
When I subtract that from the original data, I get what I like to call “adaptive anomaly”:
With anomaly adapted to account for a changing annual cycle, it no longer looks like a dramatic increase in variability at 2007. Statistical tests bear this out; the variability has fluctuated (as it always does) but hasn’t shown any significant change.
What we do have, of course, is a genuine, and sizeable, change in the annual cycle; it got bigger. A close look reveals that this is because the annual minimum declined dramatically at that time, while the annual maximum simply continued declining at its existing rate. You can see this plainly in graphs of each year’s maximum and minimum values.
What brought about the sudden change? I don’t know, but I suspect it’s related to the fact that the extent of sea ice also depends on how much land area is available at given latitudes — land areas can’t hold sea ice! When sea ice retreats above the latitude where there’s no more land, a small change in the latitude of the sea ice corresponds to a bigger change in extent. You can read more about that here.
At this point, I’d like to congratulate all the readers who have read the last two posts. You now know a helluva lot more about Arctic sea ice and how it has changed, than most people. You know:
I’d guess that you are now prepared to discuss the issue intelligently. I’ll opine that you are far better prepared to discuss it intelligently than any of those who have recently been claiming it isn’t still declining.
And if you’re a regular reader here, you already know better than to trust any claims about “trend” based on ridiculously short time spans.
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