Sea Ice Odds

I've been working out, finally, my thoughts on what the sea ice cover will be like for the Arctic, in September 2009. That for the average for the month, rather than minimum at any time.

But also a good time to return to some basics about sea ice. Two different questions we could ask about ice cover are: 1) what area of the earth (Arctic ocean, Hudson Bay, ...) has sea ice floating on it? 2) If I look at a grid of sea ice coverage, what is the area of the grid cells that has any noticeable ice in it? The former is sea ice area, and the latter is sea ice extent. See some of the web sites I link to on the right for samples.

In terms of measurement, extent is much easier to get than area. If there is sea ice in an area, it usually covers a large fraction of the surface around there. Extent doesn't worry about whether it was 70% covered or 95% covered. As long as, on the average, you can correctly distinguish between more than 15% and less than 15%, you're set. Sea ice area, on the other hand, is more challenging. Now you have to be confident that when the satellite says '10% water', all 10% are because of the ocean. Problem is, the water could also be ponds that are on the surface of the ice. (Melt ponds; we're not very creative in our vocabulary.) You can't have an ice floe entirely covered by melt ponds -- the water would run off. So extent is still safe, even if area could be off by 30% in a part of the pack with lots of melt ponds.

My prediction, then, regards the extent of ice, rather than the area. Predict numbers you can measure more reliably if you have a choice. For other reasons, it's for the average extent for the whole month. (As computed by the NSIDC, and, again, Arctic only).

The prediction is: 4.92 million km^2, with a standard deviation to it of 0.47 million km^2. 2008 showed 4.67 million km^2, and 2007 showed 4.30 million km^2 for the month's average. I'm not saying that the sea ice is 'recovering'. Actually, if my method (which, notice, I haven't told you what it is) is right, then I also expect the Arctic ice to be going to zero sometime after 2022, which is on the early end of estimates. How much after requires the next step of sophistication in the method. That'll come later. Recovery would mean 6.67 million km^2 (the mean of the last 30 years, arguably, it should mean more like 7.4 million). All that's involved is that 2007 and 2008 were extraordinary, which we already knew, and remain extraordinary even after going to a better :-) model for the progression.

I don't make cash bets, or recommend doing so. I will, however, bet honor points. (Quatloos, a group I was in named it.) One place I'll be making such a bet is Stoat, William Connolley's site. Then again, we'll have to see if he finds it attractive. Given my prediction, one obvious bet is even money that the September average will be less than (or more than) the number I gave, 4.92 million km^2. Someone who thinks the sea ice has recovered (which does not include William) should be leaping up with glee to take the 'more than' side of the bet. Actually, though, if they really believed that ice had recovered, they should go for even odds the the ice would be more than 6.67 million km^2.

This is where we get to the 'odds' mentioned. If someone believes that there's been no real change in the sea ice cover, just some bouncing around, or if they think it has recovered, this means they have a particular stastical model in mind. Namely, that sea ice in any given year should be about the mean. And there's a degree of spread (the standard deviation). This model says, given the last 30 years of observations, that we should see (every year) 6.67 million km^2, with a standard deviation of 0.87. The 0.87 is the measure of spread. One wouldn't be surprised to see ice cover be less than 5.8 million km^2, about 1 year in 6 should do so. On the other hand, only 1 year in 40 should be more than 2 standard deviations below normal, 4.9 million km^2. Someone who believes that the Arctic ice has recovered, then, should be offering me 20:1 odds that the Arctic ice extent will be more than 4.97 million km^2 (working this number out with full detail).

So I'll invite those who've been saying that Arctic sea ice has recovered the 20:1 bet -- they owe me 20 quatloos if the the Arctic ice extent averages less than 4.97 million km^2 for September, as computed by NSIDC. I give them 1 if it's more. I'll also invite you to refer people who say that the Arctic (or who just say 'sea ice') has recovered to this note. Or, if they prefer, I'll give 20 quatloos to their 1 that the figure will be less than 6.67 million km^2. By their thinking, it's even chance that it'll be more than 6.67. By mine, it's awfully unlikely.

Also open to other offers. Add them to the comments. I might be slow to respond, but offers will be considered through the end of June. If you think the trend is a simple straight line, your prediction is for 5.46 million km^2, with standard deviation 0.53 (again based on 30 years). You should offer your 5 quatloos to my 3 that the figure will be greater than my prediction of 4.92. I'll give 5 to your 3 that it will be less than 5.46. Notice that there's a symmetry to the odds.

Oh well. I hope I haven't just confused most everyone, and bored to tears the rest.

Currently having technical difficulties, but I'm adding a poll at the bottom about how it'll turn out. The numbers are centers of the ranges. 5 means 4.75 through 5.25, for instance.