For several years, I’ve forecast the Arctic sea ice extent to be observed during September (when it reaches its minimum). For the most part my forecasts have been successful, although I was farther off this year than previously because sea ice extent dipped well below the existing trend line — and that’s how I make my predictions, by extending the existing trend line for September sea ice extent, 1 year into the future.
Here’s the base data for this method, September average sea ice extent from NSIDC, together with the model used to make the forecast:
The model is simple: a quadratic function of time. Fitting this to the observed data and extrapolating a year forward gives the prediction: 4.03 +/- 0.9 million km^2.
That’s one way — and it has worked well in the past. But there are others. For instance if I smooth the observed data with my modified lowess smooth and extend that a year forward, I get this:
This method gives a lower prediction, only 3.91 million km^2. That’s because, even though the model has less “curvature” in the later years, it has a steeper slope compared to the previous model:
I prefer model 2 to model 1, not just because it gives smaller overall residuals, but also because it fits the endpoints of the data (especially at the beginning) better. But their predictions are not really that different
But wait — there’s more! Some of you may recall that when you transform ice extent to the latitude of the ice edge, the data reveal more consistent behavior over time. For one thing, the trend rates (by linear regression) don’t vary so much throughout the year, being more consistent from one month to another and one season to another. For another thing, if you look at sea ice anomaly (the difference between a given month’s extent and the average for that same month), there’s a clear pattern which emerges in 2007:
What happened is that the annual cycle got bigger — greater difference between winter and summer extent. This is also clear if we us a time-frequency method (in this case, windowed Fourier analysis) to study the size (i.e., amplitude) of the annual cycle directly:
The graph shows the semi-amplitude, which is just half the amplitude of the fundamental Fourier component. Since 2007 it has been much greater, indicating a considerably larger annual difference between minimum and maximum extent.
Some people have even made a big deal about this. For instance, Roger Pielke Sr. interpreted it as a sign that “since 2006, the reduction has stopped and even reversed..” This is grossly mistaken, but he simply didn’t do the math. Judith Curry interprets it as a sign of a change point, an idea which falls to pieces when you consider latitude rather than extent, but Judith tends to consider anything that looks funny as a “regime shift” so she can blame sea ice loss on anything and everything at the same time. As for doing the math, I can’t recall ever having seen that from her.
If we plot latitude anomaly rather than extent anomaly, there’s no sign of “change point” or “regime shift” in 2007:
Note that the trend is upward because the ice is retreating northward. There are visual signs of, perhaps, an annual-cycle change from 2004 to 2008, but they’re easily within the boundaries of natural variation, not evidence of the kind of changes Curry wishes she could blame sea ice change on. She really needs to learn to “do the math.” I’m not holding my breath.
We can take the values of September sea ice latitude and fit a quadratic trend to make a prediction for next year, just as we did with extent:
The prediction is for the ice edge to reach latitude 79.09N, which corresponds to an extent of 4.10 million km^2 — a wee bit higher than the forecast from using extent alone.
And yet again, we can extrapolate the smoothed curve rather than just a quadratic model, using the latitude rather than extent data:
This model predicts the ice edge will reach latitude 79.29N, with extent equal to 3.97 million km^2.
So there you have it, four models, all statistical, with four different — but only slightly so — predictions. For the record, the “old method” predicts 4.03, but (for not entirely scientific reasons) I think I prefer the final model at 3.97. And you can attach a “+/- 0.9″ to both of them.
The fact that all these models give nearly the same forecast is simply a reflection of the fact that they’re all short-range statistical forecasts based on the same central idea: that the trend will continue. There will be fluctuation of course, and at +/- 0.9 it can be considerable. But I don’t expect 2013 to break the 2012 record, in fact I don’t expect the 2012 record to be broken until 2015 or 2016, and possibly even a few years later. That’s the nature of fluctuation, even when the trend continues. And I do expect that the trend will continue, for a very simple reason: global warming.