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.
I must protest at the repeated use of the word “unphysical” to describe quadratic and higher-order polynomial curve-fitting to the sea ice data. If the outcome is pleasing, then clearly the model is good.
I also challenge the notion that sea ice extent can’t fall below zero. Why, look at the figure you posted; the bottom of that graph is clearly below the zero mark. That proves that it *could* happen.
😉
Amac,
Well… at least I didn’t way it was “unphysical” on *twitter* or “behind someone’s back”!
Wait, William Connolley is not the alarmist here?
MikeN,
Nope. As snide as Connelley can be, he is not an alarmist. 🙂
Could you improve your fits by using data for all 12 months rather than just data for September? I know you would have to deal with seasonal effects, but I’d think the uncertainty introduced by that would be less than the reduction caused by having more information.
And of course, if you did a fit to all the data, you could still make predictions for individual points.
It is rather like watching your lawyer driving off a cliff in your new Ferrari or Kissinger’s view on the Iran-Iraq war when he wished both sides could lose.
I used a sixth order polynomial fit for the ENSO index minus the Missouri state temperature anomaly and it gave me a very pleasing fit. It looked like a hockey stick.
Lucia
This is somewhat off topic about betting but I believe is relevant to Arctic sea ice extent.
Back in August, on the Arctic Sea Ice extent, Nick Stokes linked to his circular representation of Arctic Sea Ice:
http://moyhu.blogspot.com/p/latest-ice-and-temperature-data.html#fig1
This representation has a magnifying glass, which shows a methodically growing sea ice until two days ago. Now there is an abrupt decline.
I believe this decline represents Tropical Cyclone Nuria which has entered the Bering Sea forcing sea ice to either pile up upon itself or be pushed out to the Atlantic side.
This picture of storms pushing the sea ice around may be validation of the idea that the lowest sea ice extent, I believe was 2007, may have been due to weather and storm issues as opposed to atmospheric Arctic temperatures or ocean currents.
As Emril would say — bam!
I wonder if Rob would be interested in buying “bet insurance” from anyone? It might be a good idea to look around for any takers. I’m heading north this week and it looks really cold!
Have a great and successful hunt! Stay warm!
My comment seems to have disappeared so here goes again.
Slightly off topic of betting but on the subject of Sea Ice. Nick Stokes has a representation of Arctic Sea Ice on the August thread of Arctic Sea Ice extent.
http://moyhu.blogspot.com/p/latest-ice-and-temperature-data.html#fig1
I have been following the accumulation of sea ice in the Arctic and there has been a steady increase until 2 days ago when there was a sudden down turn.
I speculate that the down turn is due to Tropical Typhoon Nuria which is blowing through the Bering Straits and either piling sea ice upon itself reducing the apparent sea ice extent, or the typhoon is blowing the ice out the other end; i.e., the Atlantic.
This mechanism would explain the 2007 low ice extent when it was speculated that the sea ice had been blown out into the Atlantic due to a weather related storm.
Betting on sea ice extent should include weather factors which can change the specially observed sea ice extent.
Lucia,
if you do a Gompertz fit how do you determine a, the asymptotic value?
Buck Smith,
The “R” package does it. 🙂
RiHo08
Depends what you mean by “should include”. “Random” or “unpredictable” factors are a feature not a bug in betting. Those betting can include any caveats they like. For Football, it could be a “provided quarterback is not injured” clause — or that could be left to “sh*t happens”. In climate bets, you can have a “no volcano” clause, or that can be left as “sh*t happens”. It’s up to those betting do decide on what “out” clauses they have.
It seems to me that connolley/dekker left a broad band of “no one wins” to deal with a large amount of “shit happens” factors. After that the “win” would seem to go with someone who was “more right than wrong”.
Currently, the most likely outcome is “no one wins”. But could a well timed hurricane kick up and make Dekker win? Yes. For now it looks like that’s what he’ll need to win. But it could happen.
Could a volcano have a well timed eruption, cover the skies, cause undue cooling and make Connelley win? Yes.
Could just “mildly cooler just slightly slower melting make Connelley win? Yep. We’ll see.
Doing a Gompertz fit on Arctic sea ice is a classic example of begging the question. The Gompertz fit assumes that the ice is going to zero. The Gompertz curves calculated after the minimum in 2012 have done rather badly in 2013 and 2014. Ice volume has recovered substantially as well.