Last year I proposed Gompertz curves as naive, black-box models for predicting mean September Arctic sea ice extent, area or volume. Here's how that worked out:
Sep 2011 Sep 2011
NSIDC extent 4.4 4.6 million km2
Uni Bremen extent 4.6 4.6 million km2
NSIDC area 3.1 3.2 million km2
PIOMAS volume 4.9 4.2 thousand km3
These 2011 results were close enough for encouragement, so this year I thought I'd try again. I sent off a June 2012 SEARCH Sea Ice Outlook prediction of 4.3 million km2, with a 95% confidence interval from 3.4 to 5.1.
Equation for the curve in Figure 1 is approximately:
predicted extent = 7.58*exp(-exp(.0996*(year-2017.5)))
Among the class of simple black-box models, Gompertz curves have several appealing properties. They fit past data well, including the longer 1972-2011 Uni Bremen time series. One equally simple and naive alternative, the quadratic, tends to impose an unrealistic early rise before it bends to fit the steep later decline. When extrapolated, quadratics crash to zero (and then negative extent), unlike physical models which mostly approach zero more slowly, or even asymptotically -- like the Gompertz.
In any event, these Gompertz models are proposed not on physical grounds but as a kind of black-box null hypothesis to which more sophisticated physical models might be compared. Can other models from October the year before outperform this approach? One might hope so, but it seems a good challenge.
Continuing in this vein, the same approach yields a September 2012 mean NSIDC area prediction of 3 million km2, with confidence interval from 2.2 to 3.7 (Figure 2).
The PIOMAS volume prediction is 4 thousand km3, with confidence interval from 2 to 5.9 (Figure 3).
But all these are monthly means. What about daily values? The dailies have higher entertainment value on this blog and elsewhere, although they are often disdained (by me among others) as being too random to reasonably predict. In a sporting mood I tried it out anyway, coming up with a minimum 1-day Cryosphere Today prediction of 2.7 million km2, with confidence interval from 2.1 to 3.3 (Figure 4).
I was going to follow Figure 4 with a remark about daily values being harder to predict, but then hesitated and wondered, are they really? The surprising answer is no, at least with respect to Cryosphere Today area. The Gompertz model for minimum daily area graphed above leaves a residual standard deviation of just .29 million km2. A very similar model for CT September mean has a slightly higher residual sd (.34). That wasn't what I expected, so I'll explore the idea more systematically in the future.
And for better or worse, I'll revisit these estimates in October and fill out a table:
Sep 2012 Sep 2012
NSIDC extent 4.3 ___
NSIDC area 3.0 ___
PIOMAS volume 4.0 ___
CT area 1-day 2.7 ___