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I want to say thank you to Larry for helpful suggestions and allowing me to go ahead with submitting this.

Apologies also if you are not into geeky maths stuff.

You are forgiven. ;-)

Well, it's not that I'm not into it. I just don't get any of it!

Thanks a lot, Gas Glo, for sharing your submission to the SEARCH Sea Ice Outlook. We now have two ASI blog commenters submitting. Great stuff, guys. I take my hat off to you.

Patrice Pustavrh

Nice job, Gas Glo/crandles :).. And as for Apologies also if you are not into geeky maths stuff: I am so glad that you showed us how things can be done mathematically. Even if I am not capable doing this (I basically understand your method, maybe, if I won't be sure about some detail after reading it couple of times, I will ask you for some help), it is nice to see how you did it. Now, it is on me to do some googling about some terms.

Yvan Dutil

I have planned to do a meta-analysis of all prediction based on their previous performance. However, I have been too lazy.

L. Hamilton

I didn't revise my own prediction this month, but I understand that some of the other models sent in to the SEARCH SIO have gone noticeably lower. They must be seeing something....


The PIOMAS volume at end of June was 12.261 so using end of June data Gompertz fit of 4.44 is reduced by 0.8 to 4.36m km^2.

However both 4.44 and 4.36 get rounded to 4.4 to avoid suggesting too much precision.

All that effort for no adjustment :o( , oh well ;)

Thank you for the comments. If I lose half the readership for every equation used and probably a greater proportion for technical terms like confidence intervals, credible intervals, Root mean square errors(RMSE), standard errors..., it is suprising if I have any readers left.

Re Patrice's 'Even if I am not capable',
I doubt I am capable either... ;o)

L. Hamilton

As for losing readership, there are two levels -- an "executive summary" where you put place your bet on some number, then the justification where IMHO it really is best to lay out the steps and equations behind your number. Pictures are good too.

That's not just so others can figure out what you did. In my case, at least, it really helps *me* to figure out what I did when I come back to it weeks or months later.

dominik lenné

Actually I don't understand many of the details of the above analysis, but as it uses a purely statistical model with no physical elements in it, its worth might be limited. As I read, the Gompertz - function is used in population or usage statistics, where it describes some kind of saturation behaviour. In our case, the driving force, i.e. the heat transfer into the arctic, may well have significant variations, which may accelerate or slow down the process considerably and unexpectedly. Also, with steady driving force, the behaviour of the now-thickest areas of ice is of importance - it might well be, that it melts all away! There we have to enter some discussion about where those areas are (in the nearest vicinity of Greenland and the Canadian Islands north costs), why there of all places (influence of ice shields???) and wether some protecting function of the adjacent land masses will be sufficient to keep a rest of summer ice over a longer time "alive".


Certainly it is only a statistical model. I would suggest there are several contributions using multiple linear regression to which your comments would also apply.

I have tried to keep my predictors down to ones that have obvious physical cause and effect and I would suggest have other statistical contributors.

>"heat transfer into the arctic, may well have significant variations"

Are you thinking random weather variations which are hard to predict more than a week in advance or systematic changes as the ice gets thinner?

If random hard to predict variations, then I think multiple linear regression is regarded as a good technique to extract the systematic and average the remaining random residuals.

If systematic changes as the ice gets thinner are these going to change the trends from previous years? Why this year? But if so and you can reliably tell us how, then a better prediction can be made.

I certainly agree that if there is a lot of thick ice getting thinner and down to the thickess that can be melted in a season then we could get a non-linear response moving away from a gompertz curve. However, the area reaching such critical thickness could also increase fairly steadily over a number of years and effect might already be picked up by the gompertz curve.

Beauford Gyre and Transpolar Drift tend to pack the ice against Greenland and Canadian Archipelago. It has occured to me that the mass of ice is considerably less now so it is now being packed in there with a small hammer rather than an almighty sledge hammer so the ice may well not build up its thickness or density as quickly as in the past. Nevertheless, I still think there is more ice than can be melted this season. If the weather is good for melting and transport, next year could be a different story....

dominik lenné

With this heat transfer thing, I had in mind something like changing medium time scale weather patterns, like the north atlantic oscillation, which may change its sign and consequently break the trend. Actually this is a denialist way of arguing. You are of course right insofar as any trend already started some years ago is incorporated in the statistical model.

(An other interesting question is, whether the north atlantic oscillation isn't itself broken by sea ice levels so low - that is, whether there is a "weather pattern tipping point". This would then be the kind of nonlinearity you mentioned.)

Concerning the packing of ice against the Greenland and Canadian Islands north coast as cause for the higher ice thickness there i would be thankful for one or two links.


Hmm not sure about links/papers for that but maybe:

An animation shows it:


Quote: "This is as expected since the Beaufort Gyre and Transpolar Drift Stream tend to push the ice pack around the Arctic Ocean in a clockwise direction causing the ice to the north to pile up along the natural barriers to this flow (Fig"


The Gompertz fit of 9 July NSIDC areas is for 6.260 whereas the area is only 6.146 so are is now below the gompertz fit by 0.114.

The multiple regression factors have changed to give more weight to area and less to volume which is not surprising with the area information now more up to date. The factors are now 0.871 for area and 0.0557 for volume.

So the method now calculates
4.438-.114*.871-1.433*.0557 = 4.26 m km^2

This is slightly higher than the 4.22 calculated with 4 July data.

I should have added more graphics

The predictors appear to have some skill:

I wondered if the predictor anomalies might have non linear impact but that is not apparent from this scatter plot:

Patrice Pustavrh

@crandles/gas glo: I think you did a really decent model, but, what about running it on a couple of days average value (just for the smoothing purpose) ? Just for try, but you may find some of the fits better, I think (and don't know cause I didn't crunch any of the numbers). But, if you have things set up in your model and you can easily rerun them, I'd be pleased to see the outcome.



I didn't really expect it to make much difference but I tried averaging area over 7-9 instead of just using 9th. (I haven't bothered also trying this with volume.)

period used, r2, SE, est
9th July only, 0.5276, 0.3162, 4.2593
7-9 July average, 0.4668, 0.3360, 4.2396

.01 to the estimate seems little difference. The r2 and se seem to have got markedly worse. Perhaps on other dates an averaging would make them markedly better. If so and I attempted to use any improvements possible, such decisions would appear to me to be cherrypicking.

Were you expecting a different conclusion to that?


Time for another update with area to 17th July just released at 4.4555. Though this is 177k above 2007's 4.279, it is a little below the Gompertz fit for 17th July of 5.520. So area residual is 0.065

So the estimate is now for gompertz fit of 4.438-(0.860*0.065)-(0.063*1.433)=4.292

That is almost spot on the 2007 minimum suggesting a 50:50 chance of a record low. But there are 2 things to bear in mind:

If area has gone down more rapidly than suggested by gompertz fits then perhaps volume has also done the same since last volume update to 30th June.

Secondly weather could be turning against a record low.

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