We are now in the interval between various factions reporting about the year end surface temperatures and people debating the eventually demise of NH Sea Ice. On the latter topic: Some people wanted to revisit the Connelly/Dekker ice bet, which I had discussed way back in 2011. I hunted down my “super-mega-curve fitting” script, and re-ran it. The discussion of all the fits can be found in Connelly Dekker Bet….
Those whose memories go back that far will recall that back in 2011, recall Connelly describe a bet with Dekker that went as follows
If both NSIDC and IARC-JAXA September 2016 monthly average sea ice extent report are above 4.80 million km^2, RD pays WMC US$ 10,000. If both are below 3.10 million km^2, WMC pays RD US$ 10,000. In all other cases the bet is null and void
I wrote a script that evaluates the NSIDC sea ice extent data, then does super-mega curvefitting (no physics!) to prognosticate the probability that either Connolley or Dekker will need to fork over (or win) any money.
I believe at the time Jeff Id reported the super-mega curve-fitting makes his head explode. Note: Jeff prefers physics to fitting data to mis-assorted algebraic functions. I do to.
However, here we are only trying to estimate how likely either gentleman is to win under the assumption that we can prognosticate using curve fitting. The hitch is: we have no idea what sort of curve fit we should use. Should we assume ice extent will follow a ‘straight line fit’? A quadratic? A cubic? None of these are physical as all can create projections permitting NH ice extent can to fall below zero or exceed the entire area of the earth. I added a “Gompertz” which at least has the attractive feature that the sea ice extent cannot fall below zero. (I should also add the fact that we are extrapolating only a few years forward partially mediates the nuttiness involved in these curve fits.)
Afterwards considering the possibility that any of these (utterly unphysical) curve fits might describe the data, I combine the uncertainty intervals in a way that expands the intervals relative to what they would be if we believed we knew what sort of algebraic model described the evolution of ice extent over time.
It’s worth noting: these are likely still not big enough. But they may be large enough to give us an idea of whether the bet is likely to turn out Dekker Win/Connelley Win /Draw. Many will recall that back in 2011, the sooper-dooper- head exploding model said
Under my “weighted” model (black below), the probability Rob would owe WC $10,000 was 8.5% while the probability WC would owe Rob was 36.4%. The most likely outcome was a draw with no-one paying anyone anything.
Since that time, the ice extent has bounced back a bit. Incorporating the new data into the curve fit, it looks like Rob had better set aside a fund to pay WC. The weighted model suggest Rob has a 30.7% chance of having to pay WC. Meanwhile WC has a 4% chance of having to pay Rob. So far, WC’s confidence in models appears to be holding out well– but we can’t be sure. In any case, “no one wins” is still the most likely outcome no matter which curve fit we try to use to “explain” the data.
The various fits are shown below. The probabilities cited are from the upper black line.
Those of you getting excited by the ‘prediction’ that the ice will begin recovering over time: I saw that and thought, Really? It turns out that projected uptick is due to the projection based on the fit to the 4th order polynomial which wiggles around and then turns up. We have very few points to fit and it turns out the AIC criterion likes that fit — or at least likes it enough to not discount the possibility that it describes the data.
That said: fourth order fit is unphysical: I wouldn’t advise anyone betting on that. Of course nearly all the fits are unphysical, so obviously, one isn’t going to eliminate the fourth relative to the quadratic fit on the basis that it is ‘unphysical’. What the analysis should highlight is the danger of using unphysical fits. You’ll notice that the quadratic fit– which AIC likes ‘better’ than fourth order predicts a decline in NH Ice. Meanwhile the fourth order fit cannot be be ruled out. This means that one should recognize that these projections are highly uncertain; we do not have enough data to decide whether a model that predicts imminent spiral-of-death is loss is much better or worse than one that predicts recovery.
(DeWitt: Thanks for the chart!)