# Yet more sea ice

A while ago, crowing over the extent of Arctic sea ice this winter and the possibility this would mean loadsa ice this summer, I noted that “it is clear from that, that the winter anomaly doesn’t correlate too closely with the summer minimum”. That was based on the IJIS plot, and on little more than that the 2008 winter ice is clearly on the high side while the summer ice was on the low side. C challenged my assertion, and drew some plots, and decided in the end that maybe I was right. He was also kind enough to send me his spread sheet, but I didn’t get along with it, so have faked up my own google spreadsheet: here if you’re interested.

And the pic below, if all the googly magic works out, is a plot of the winter (March) anomaly and the summer (September) anomaly. We see what we already know: ice is declining, and 2007/8 are anomalously low. If you scatter plot the anomalies, then there is a strong relationship, because of the linear trend.

So it is more interesting to know if one year’s winter anomaly is followed by a summer anomaly. Below is a scatter plot of the winter (March) anomaly-from-linear-trend against the summer (September) anomaly-f-l-t (making the possibly unwarranted assumption that I’ve got my excel script right).

I think it is a blob. There is little sign of a relation.

All this seems vaguely interesting, and you would have thought someone must have published on it. Anyone got a ref?

1. #1 crandles
2009/04/23

The scatter plot looked different and the numbers were different. March straight line differences were because I had used all the March figures 1979 to 2009 whereas you used 1978 to 2008 for consistency with availability of Sept data.

For Sept straight line, I got slope of -0.07806 and intercept of 162.2854. I do not know where your figures of -0.0697197 and 139.04053 come from but when I calculate the sum of errors squared for my straight line it comes to 8.08 whereas for your straight line it come to 9.83. It looks to me like your unwarrented assumption was indeed unwarrented. (Unless I have misunderstood f-l-t or erred in some other way.)

[Hmm. Dunno. Just checked, and nothing is obviously wrong. I’m using extent not area, were you? Using the slope to fit a line produces about the right answer. Your slope applied to my data produces clearly the wrong answer -W]

2. #2 crandles
2009/04/23

Thought I would plot this in case there might be some lagged correlation. I don’t see anything interesting though.

3. #3 Nick Barnes
2009/04/24

No relation. Is this plotting winter against the following summer, or summer against the following winter?

[It is march and september of the same year. It is easy enough to do march of one year against sept of the previous… if I got it right, it is:

Which looks like a somewhat better correlation -W]

Allow me to strongly recommend Google Charts for this kind of thing.

4. #4 Steve L
2009/04/24

I hope what you’ve done is plot the residuals of the March trend on the x and the residuals of the Sept trend on the y (paired by March and subsequent Sept). Of course, given the latest info that I’ve seen, April will be more interesting (assuming that as we get closer to Sept the relationship will improve).

5. #5 crandles
2009/04/24

>”Of course, given the latest info that I’ve seen, April will be more interesting (assuming that as we get closer to Sept the relationship will improve).”

I agree that at some point as the time difference decreases it is going to get better. However the correlation coefficient between April and August anomalies at 0.051 is barely greater than .0475 for Mar and Sep anomalies and a random system is likely to end up with a figure further from 0.

6. #6 crandles
2009/04/24

On to May and Jul anomalies ….

… and I get a correlation coefficient of -0.218

so if the ice stays high through May then we can expect a low Jul, or this is still a spurious correlation.

7. #7 Crandles
2009/04/24

>”[Hmm. Dunno. Just checked, and nothing is obviously wrong. I’m using extent not area, were you? Using the slope to fit a line produces about the right answer. Your slope applied to my data produces clearly the wrong answer -W]”

I suggest looking at 2005 based on this:

[-0.07806 * 1979 = -154; + 162.2854 = 7.8. This is not the right answer -W]

8. #8 Steve L
2009/04/24

Hi crandles. Doing always trumps supposing, so bully for you and [the opposite] for me. I still think there’s something to be said for ice thickness, so I’m on the side expecting a poor association (in 2009, anyway) between spring and late summer residuals. It’s an interesting relationship for a couple of reasons: (1) I figured more open ocean near the solstice would mean more solar radiation absorbed and therefore more summer melt; (2) if this isn’t correct then is there something about the warming effect of sea ice cover that needs more discussion (or at least more awareness on my part)?

9. #9 Crandles
2009/04/24

>”[-0.07806 * 1979 = -154; + 162.2854 = 7.8. This is not the right answer -W]”

Huh? Do you mean that 7.8 is the right answer and -0.06972 * 1979 + 139.04 = 1.065 is the wrong answer. Anyway to get to your sl Sept I took figures from your spreadsheet of 7.2 + .5379 to get 7.738 which is close to the correct figure and the line gained by doing this is straight most of the time but not in 2005.

[Errrm, I mean that 7.8 is clearly not the right answer, if the question is “what is the September anomaly for 1979”. 1.065 is certainly plausible -W]

10. #10 Crandles
2009/04/25

The difference between 1.065 and 7.738 is 6.6727 which is the average of the Sept extent figure. Your intercept needs correcting by this 6.6727 and when you sort out 2005, I expect your figures will come into line with mine.

[I’m not fitting extent, I’m fitting anomaly -W]

11. #11 Crandles
2009/04/25

Given that we are talking about anomaly from linear trend, it seems rather bizarre to do you fit to anomaly from average rather than fit of Sep extent. Unnecessarily having two anomalies is only likely to add confusion which it appears to have done. Since you said I was wrong, I don’t see why I shouldn’t tell you that it is you that are wrong. However this isn’t important.

[It seemed natural to me. But as you say, this in’t the problem -W}

The figure in cell E28 of your spreadsheet appears to be wrong by 1.63; it should be:
5.57-6.6727=-1.1027 not +0.5273.

[OK, I agree. Thanks for finding that. It is a cut-n-paste formula error, mostly because my laptop screen is small. Now I agree with your slope. I don’t think this changes the text. I’ve given you edit permissions -W]

12. #12 Gareth
2009/04/25

I’m pretty certain that the ARCUS sea ice outlook exercise last year included a forecast based on the sorts of correlations you’re discussing — and I seem to remember that you didn’t get any predictive value until you reached May (for the following September). On the other hand, the ARCUS site seems to have moved all last year’s reports, and even though their own search lists the sequence of monthly reports, all the links are broken. So I could be completely wrong…

[Isn’t it irritating when folk are so cr*p they can’t even manage a functional web site? But if you start from this year http://www.arcus.org/search/seaiceoutlook/, the archive points your to may/june/july for 2008. That suggests they didn’t even try doing it based on March or April -W]

13. #13 Eli Rabett
2009/04/27

How about if you try the Dec-Jan-Feb median temperature anomaly from 80 degrees north vs. extent (or maybe the minimum anomaly).

[Sounds a bit like hard work with the tools I now have. Though temps should to some extent be reflected in the extent anyway -W]

14. #14 Gareth
2009/04/27

I found the June 2008 ARCUS predictions stashed on my computer: several teams mention that there is no correlation before June, and that late June is better… Now I’ll have to see if I can find the end of season summary to see how good the stats-based predictions were.

ARCUS will be running the same exercise for 2009.

15. #15 Eli Rabett
2009/04/28

Essentially the entire Arctic Ocean area always freezes during the winter. The differences in winter ice extent are in the areas south of the Bering Straits, the Siberian/Korean coast, the eastern coast of Greenland and the area north of iceland, pretty much all of which always melt during the summer, winter ice extent does not appear to Eli to be a particularly good thing to try and correlate against summer ice extent. Better, IEHO would be some sort of metric showing how long and deep the winter freeze inside the Arctic circle was.

[Yes, I think I agree with you. And so do the stats -W]