Since Jaxa resumed posting daily results of Arctic Sea Ice extent, I've been processing the data and posting plots here. I'm thinking of doing an interactive plotter for the various ice measures, similar to the climate plotter.You could choose which years to show.
So I started looking at means and anomalies, and thinking about trend calculations. The general method for anomalies seems to be to take a day-by-day average over some years and calculate discrepancies from that. The number of years is not huge, and there is a spike of variability near the maximum melt, so the daily mean is not free of the fluctuations from which an anomaly is sought. So I tried a multiple regression using trig functions and a secular trend.
An anomaly plot is useful for plotting in that it removes the seasonal oscillation, making the key information more visible. With the trig functions I can use a sidereal year, which gets rid of a minor but awkward leap year issue. I found four harmonics was sufficient as the magnitudes taper quite fast; using five made negligible difference.
I looked at the Jaxa data, and also the Arctic and Antarctic sea extent data from UIUC (Cryosphere Today).
There are two anomalies calculated - without and with trend adjustment. All curves have been very slightly smoothed, with a 5-point binomial filter.
JAXA IJISHere's the familiar Jaxa plot with the fitted periodic annual curve.
2012 is marked in black.
Here is the anomaly plot with trend, shown over the years from 2002:
The downtrend is about 65000 sq/m/year. Last years minimum was about 4500000sq km; at that rate of attrition it will be nearly 70 years before it disappears. However, there's no reason to expect that trend to apply over the period, and indeed the minima seem more variable than the general trend.
Now here is the same data plotted over a one year interval. Again 2012 is black. It shows that the anomaly so far this year is mid-range for the decade.
However, plotting the anomaly after allowing for trend shows that so far, 2012 is rather higher than expected.
UIUC Cryosphere Today Arctic
UIUC published data over a much longer period. They do their own anomaly calculations, which are in the data set and published on their website. But these are from the trig function regression. Here is the anomaly plot over years:
The trend is somewhat less than Jaxa, since the period is three times longer. Now the same plot superimposed.
There are now a lot of curves, so I've shown the last ten years with greater thickness.
Finally the trend-removed anomaly plot. Again 2012 is currently fairly high relative to recent years.
UIUC Cryosphere Today AntarcticFinally, for completeness, the Antarctic data. They are of course six months out of phase, and the trend is up rather than down, though the magnitude is less than Arctic. Here are the anomalies:
The same over years:
and with trend removed: