Again, I'll put our estimates in context of some other estimation methods.

- Climatology 1979-2000: 7.03 million km^2
- Climatology 1979-2008: 6.67 million km^2
- Linear Trend Climatology 1979-2008: 5.31 million km^2
- Wang, Wu, Grumbine model: 5.0 million km^2
- Wu, Grumbine, Wang model: 4.8 million km^2
- Grumbine, Wu, Wang statistical ensemble: 4.4 million km^2

The two climatology means (22 and 30 years) are relatively close to each other, and are far away from anything we've seen in years. Taking the 30 year trend, from the first 30 years of the satellite record, gives 5.31 million km^2, which is close to a figure seen in recent years (5.36 in 2009), but well above any of our estimates or the 4.9 seen last year.

Below the fold for a few more words about our 3 estimates:

The new model method is Wanqiu Wang's. For this, he took the sea ice output from the CFS 2.0 model (Coupled Forecast System) and compared the model's extent for September to the observed. For all Septembers. Then derive a relationship between what the model thought would happen and what did. The model is biased towards too much ice cover, something we've known for a long time, so his correction is to reduce the model's estimate. Take a look at the link, as you can see more detail on the sea ice -- monthly to 9 months lead -- estimated from the model. The estimate's variability is 0.5 million km^2 vs. observation ('1 sigma'). And the estimate is 5.0 million km^2.

Last fall, I mentioned that Xingren Wu and I were thinking of some

new experiments on the CFS to see if we could improve the model's raw sea ice estimates. Well, so far it looks good, in that we were able to use a 30 cm cutoff thickness, instead of the 60 cm we used last year. Not as good as we'd hoped -- 10 cm -- but a big improvement. Or at least it's a big improvement if this year's estimate turns out as good or better than last year's! Again we used an ensemble of estimates from the model. The '1 sigma' spread is 0.22 million km^2.

The statistical estimate's method is the same one as last year. Just that we now have another year of data to use in making the regressions. The '1 sigma' spread is still 0.5 million km^2. The estimate is 4.41 million km^2 -- well below last year's 4.78. The reason for the large change is not that last year was such a low ice cover year; the statistical estimator was actually too low last year. The reason for the decline is that the curve I used is now entering the period where year by year the changes will be relatively large. If this approach is reasonably correct, then this year should indeed see a large drop. If we don't see it, I'll have to go back to think of a different pretty simple statistical method.

'1 sigma':

This may look strange to some. What I mean is that if you drew a normal, 'bell', curve, the central 2/3rds of the area would be this close (whether higher or lower) to the mean. 1/6th of the time, the observation would be higher than the mean plus '1 sigma', and 1/6th of the time it would be lower than mean minus '1 sigma'. A few percent of the time you'd see something more than 2 times as far away from the mean. And, if you collected enough observations, you'd see some that are more than 3 times as far.

I mentioned last fall and described in a bit of detail how you can combine different estimates of the same quantity. It relies not only on the estimate, but the variability (the 1 sigma again) of the estimates. Applied here, the joint estimate is 4.77 million km^2. Not terribly surprising to see it come in close to the Wu model estimate since it is close to the middle of the other two and has the lowest variability.

update:

See also Larry Hamilton's estimates at:

http://neven1.typepad.com/blog/2011/04/trends-in-arctic-sea-ice-extent.html

http://neven1.typepad.com/blog/2011/04/trends-in-arctic-sea-ice-volume.html

(more to come on Wednesday)

## 6 comments:

In a “what if” spirit earlier this year, I proposed the Gompertz curve as a plausible alternative to the linear, quadratic or logistic curves others were using as simple summaries for trends in Arctic ice extent, area and volume. While claiming no scientific insights, I think it’s interesting to note that this naive statistical approach yields roughly the same prediction (4.4m km^2) as more sophisticated physical modeling for this year’s minimum.

Graph here:

http://neven1.typepad.com/.a/6a0133f03a1e37970b014e8747f65a970d-pi

Rationale & discussion (originally two posts on extent, area and volume at Neven’s Sea Ice Blog) here:

http://neven1.typepad.com/blog/2011/04/trends-in-arctic-sea-ice-extent.html

http://neven1.typepad.com/blog/2011/04/trends-in-arctic-sea-ice-volume.html

Also sent to SEARCH Sea Ice Outlook for the June and July 2011 reports:

http://www.arcus.org/search/seaiceoutlook/2011/july

I might add that the trend for PIOMAS September volume estimates appears more ominous, and also (so far) looks like it could be following a Gompertz curve:

http://neven1.typepad.com/.a/6a0133f03a1e37970b014e87616da4970d-pi

As a visual reference, both graphs include a horizontal line at some arbitrary low level we might call "virtually ice free" (1m km^2 extent, 2k km^3 volume).

Thanks larry. I had looked for your write up, having read it before, but couldn't find it (or Chris Randles') at Neven's. I'll update the post itself

Well my guess is 3.9 km^2. What odds do you give me for that +/- 0.1km^2?

If I recall correctly, this is a lot higher than you've been suggesting in previous years. Why the change?

The midpoint between our guesses is 4.15 million km^2.

For you, this is 2.5 sigma above your estimate, given your sigma, so you figure there's less than a 1% chance of reality turning out to be higher than that.

For me, it's 0.25 million below my guess, but my confidence (my 1 sigma) is only 0.5 million km^2. So it's only 0.5 sigma below my guess. So I figure there's a 30% chance that September will below 4.15 million km^2.

Given our respective degrees of confidence and estimates, you should offer me 30:1 odds (you pay 30 quatloos to my 1) on an over/under bet compared to 4.15 million km^2.

So, you up for that? No bet if it's exactly 4.15 reported from NSIDC, but otherwise we go ahead? I'll put up the 50 I won from you last time :-)

3.9 km^2 is much higher than I predicted for 2009, but my method then was obviously wrong so I am not going to repeat the same mistake. It was based on the idea that there is a biennial oscillation and that we had passed a tipping point.

The idea of a biennial oscillation is obviously wrong, which an inspection of the September ice extents would have made clear. Also clear, is that we have not yet reached the tipping point, but that does not mean that I no longer believe that it exists. Once the September ice extent gets too low for the ice to completely recover by March, then it is bye-bye Arctic sea ice, both summer and winter.

My estimate of 3.9 +/-0.1 is not based on what I think will happen. My idea is to place a bet which produce the best return for the least risk. In other words, I expected odds of 10:1 for an estimate so out of line with that of everyone else. I regard as a 50% possibility that this year's minimum will be a record. So even if I did not win this year on average I would make a profit.

As you may have gathered, I am not at all confident that my estimate is correct so I have to decline your offer of a 30:1 odds on bet.

However, you are an honest man and I am sure you would not like to make an unfair profit, so I'll take your odds and bet 50 quatloos that the ice extent will NOT lie between 4.0 and 3.8 km^2 at 30:1. No new record this year and I win Q1500 :-)

Cheers, Alastair.

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