The ongoing question on Metaculus about Antarctic sea ice has had its community median prediction move quite distinctly the past few days, where it’s now at 85 % after having spent some time above 95 %.

I analysed this question before it opened, and came in with a fairly strong prediction. Did I make a mistake? Let’s re-run the analysis and see how much of the conclusion has changed.

The reason for the community median movement in the past few days is this:

Whereas the ice coverage usually starts to stall and begin to recede by this time of year, this year the ice seems to keep expanding, and it’s getting closer to the previous all-time low.

It is instructive to also look at the relative distance between these curves.

On this plot, we see more clearly that the 2023 curve still is about a third down to the largest distance it had this year, so in terms of distance it’s really not worth all that much ado yet. However, there’s a very fast upward-aiming trend. Straight-line interpolation would have it break over the current minimum in only a few days. (!)

Over the year so far, these past few days have seen a long string of steps upward, including some of the largest upward steps this year.

Here are five replications from this step distribution.1¹ Again, drawing blocks of 20 to get autocorrelation, heteroskedasticity, etc. for free.

Drawing many more, we see that there are actually a some that go above the zero line, which indicates the current minimum – but not that many.

Running 50,000 simulations, about 1.2 % of them go over the current minimum any day of September. I believe the community has over-corrected for what looks like a scary trend on an absolute plot but does not account for the variability of random walks.

But while I believe this, I also I fully expect to be wrong2² Because polar ice coverage is not a random walk!, and if I am, we’ll probably know in the next few days.

---

There’s one methodological problem with the approach to this analysis. Imagine a series of 250 coin tosses, where we just happened, by incredibly bad luck, to get about 65 % tails and 35 % heads. As a random walk, that would result in a low-ish value today. However, if we draw blockwise from this distribution of coin tosses to predict future coin tosses, we would not be getting a fair representation of what future steps look like, because we’re drawing from an unlucky streak.

The same would be true for ice extent changes – if we’re drawing from an unlucky streak we will underestimate the opportunity for the ice extent to keep growing. If this is the case, it might seem more appropriate to draw blockwise steps from previous years’ movements, rather than from this year to date.

There are two reasons I don’t believe this is as big of a problem as it may seem:

1. We are clearly looking at an outlier in terms of ice coverage – this has been confirmed by multiple observers using multiple methodologies. Things in the polar environment have changed in a way that alters the ice extent. We need to use changes from the current year to get an up-to-date picture of what happens.
2. We are actually not looking at an unlucky string of coin tosses. If we think of the ice coverage steps this year as coin tosses, we have seen 50.3 % tails – fully within what we might expect after 250 days.3³ Corresponds to a z score that just about fails a significance test at the 5 % level. The main reason the coverage is so low this year is that it started out low. Seriously! Look at the relative plot! the difference today is about where it started for the year. It took nothing special for the random walk to achieve this.