Seasonal Sea Ice Variation

An Eccentric Anomaly: Ed Davies's Blog

There's a certain sick fascination to be had watching the Arctic sea ice disappear over the years. The minimum extent (area of ocean covered by at least 15% ice) happens each year in September at the end of the melt season and it's preceded by a period of speculation as to what the cover will be this year. As well as the overall downward trends in the sea-ice extents there's also, of course, year-to-year variation.

What I wondered was, how early in the year do you get a reasonable idea of what the September extent could be, so I decided to plot a few graphs to have a look. For example, 2012 was a record low year which was preceded by a sudden drop in extent in early June. 2013 has been bouncing around in the same general ball-park as 2012 until the last few weeks where it hasn't followed last year's curve. (See the NSIDC daily graph for whatever's happening now.)

The data used here comes from the US National Snow & Ice Data Center. In particular, the numbers are found from their Sea Ice Index page, formally: Fetterer, F., K. Knowles, W. Meier, and M. Savoie. 2002, updated 2009. Sea Ice Index. Sea ice extents 1978 to 2013. Boulder, Colorado USA: National Snow and Ice Data Center. http://dx.doi.org/10.7265/N5QJ7F7W.

The graphs are generated by a Python script, extent.py, supported by linreg.py.

Here's a plot of the data for May and September each year. They're averages for each month so September's values aren't quite the minimums reached but fairly indicative.

Note how September's figures are declining much more precipitously. As I understand it, the near-maximum areas in the spring are largely limited by the landmasses bounding the Arctic Ocean and so are, at least for now, less affected by warming. Looking at the September curve it seems that a quadratic fit might work better. This is definitely true for sea-ice volume (which takes into account the reducing thickness as well as area of the ice) and so is probably a better measure.

Anyway, the question is: how well do earlier months predict the ice extent in September. A scatter plot of extent in May (across the bottom) vs extent in September (up the side):

Hmmm, looks like there's a degree of prediction going on. When the extent in May is high the extent in September is high too and vice-versa.

Not so fast! As we saw in the first graph the extents for both months are decreasing so this doesn't tell us how well current variations for May predict current variations for September. We can see this by splitting the points for the 20th and 21st centuries (red horizontal crosses for the 20th and green diagonal ones for the 21st):

Within each century the correlations between May and September extents no-longer look so good.

What we're interested in, though, is the variation so let's work directly with that by taking the residuals, the differences between the actual extents and the linear regression lines fitted to them.

Notice the much smaller vertical scale on this chart; year-to-year variation is, of course, much smaller than the absolute amounts of ice. Still, while it sometimes looks like there's a bit of connection between the two months' residuals it's not at all obvious what's going on. Here's a scatter plot of the residuals which might help:

Firstly, it's nice to see that the areas of the plot covered by the data from the two centuries now overlap much better. Though there's been some change in the extents there's not been so much change in the variations.

Less happily from the point of view of second guessing the ice there's very little correlation between the May and September residuals, looking at all of the data or each of the centuries' data individually. May's variation from the straight line fit doesn't tell us much about what the following September's is likely to be.

OK, maybe June's residuals will tell us more:

Hmm, that's a bit better; there aren't points in the bottom-right or top-left corners of the graph meaning that particularly high or low extents in June do not lead to the opposite corresponding variation in September.

By the time we know July's average we're definitely getting somewhere.

And by the end of August we've got a pretty good idea of what will happen in mid-September.

In general, we can conclude that it's the weather from June onwards which determines the short-term variation in the sea-ice extent minimum which happens in the following September.

Of course, that doesn't say anything to contradict the overall trend.