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L. Hamilton

I just posted this on the other thread, but since the conversation is moving to this room ....

The graph linked below models September mimimum from the PIOMAS volume data (h/t to FrankD & Gas Glo). As with extent, I fit a Gompertz assymetrical S-curve, with 95% confidence intervals. Strictly a black-box exercise, but that seems like a fair way to start the new season.


L. Hamilton

Lodger was sharper-eyed than I was and noticed a typo. Neven, could you replace the NSIDC extent graph with this cleaner version (same URL)? Thanks!



Larry, it still says NSICD on top of the graph. :-)

Edit: My bad, didn't refresh. Replacing image as we speak.

Artful Dodger

Great work here... To be clear, Larry is predicting NSIDC Sep Average Sea Ice Extent (SIE), not the minimum Daily SIE published by IJIS.

This conforms with standards for the "Arctic Sea Ice Outlook", an international effort to provide a community-wide summary of the expected September arctic sea ice minimum. They are already running a March Contest: Win an Umbrella! (is that some obtuse reference to a Geo-engineering sunshade? :^)

Neven, not sure if we can call our friend Larry an 'amateur' Statistician, what with his PhD in Stats, Tenure, published Stats Textbooks and such... :^)

Question to Larry: can you deduce the inflection points for your two Gompertz curves (NSIDC SIE, PIOMAS Volume)? Notionally, the inflection should occur in the Year of maximum reduction in Sea Ice...


Neven, not sure if we can call our friend Larry an 'amateur' Statistician, what with his PhD in Stats, Tenure, published Stats Textbooks and such... :^)

Hehe. I wasn't sure what Larry's statistician status (now that's a great alliteration) was, which is why I - at least - put 'amateur' between single quotation marks. Sorry, professor Larry!

Artful Dodger

Participate in the Sea Ice Outlook User Survey!
Win an Arctic Umbrella

Access the survey here: http://www.surveymonkey.com/s/8H5XCBB

The survey is open until Friday, 25 March 2011.

Gas Glo

But I wanted to win an Arctic umbrella, so participate, but do it anonymously ;o)


There goes my Arctic umbrella. Thanks, Lodger.

L. Hamilton

Statistical semi-pro status maybe, since that's not my degree. I've worked on many different projects, not all Arctic related, while regression with graphics has been a common theme.

And speaking of the Sea Ice Outlook, I should send in that graphic when their doors open for business. Last year's guesses weren't too bad (guessed 4.8 and it was 4.9), probably due to luck.


I thought about the SIO as well. Maybe do a group thing, although I don't know how that could work. But it'd be kind of cool.


Maybe I'm confusing myself here, but ...

A logistic or Gompertz curve will project a smooth, well-behaved transition between two equilibirum states. But the physical mechanism here is about the presence of additional heat in the Arctic, and not directly about the absence of ice. So I don't see anything wrong with a curve that forecasts negative (implied) ice - it just means that the heat will really result in something other than melting.

How different might the Gompertz fit look if the final state were effectively, say, minus 2 million km^2?

L. Hamilton

Lodger asked about points of inflection for the NSIDC and PIOMAS Gompertz curves. Mind you, these are theoretical. But the inflection points (steepest slopes), in the notation I've used, should be
t = 2036-b3, y = b1/e
which gives approximately
year = 2017, extent = 2.8 (NSIDC)
year = 2008, volume = 6.3 (PIOMAS)

According to these estimates the PIOMAS volume curve is already past its inflection point, though rate of change still remains almost as steep.


That was my Arctic umbrella. Mine, mine, mine, stamps dainty foot.

(Do you reckon they'll be selling them as a fund raiser once the comp is over? They look fantastic.)

michael sweet

For a group SIO you could do a survey (like the one you already have up) but give more choices. Send in the area with the most votes (or calculate an average vote some way).


I would call that a prediction or a projection as it is based solely on past results. A forecast would also consider the current state of the sea ice as the melt begins.


Now, now, adelady, you've had an ozone hole for yonks.

Better leave the umbrella for the Scandies, and incidentally if you do see any Scandies about, they want to start phoning home the Ozzy "Slip, Slap, Slop" songs, only in Danish, Swedish, etc...

Gas Glo

>"For a group SIO you could do a survey (like the one you already have up) but give more choices. Send in the area with the most votes (or calculate an average vote some way)."

Lab lemmings pdf from a survey didn't seem very good:


I think you need to take account of strength of belief which you are only going to get from a betting market. I suggest we tell everyone here to join www.ideosphere.com and make some claims for minimum area and slope of linear trend for 2010 to 2013 minimums inclusive. I might contribute some money for a prize for the person who wins most play money on the arctic ice claims.

Anyone interested?


I think I'm going to do this, not right now, but when the time comes, in 2 months or so:

Concur with all the guest authors of the blog, write up something, send it around for feedback, change everything, send it to ARCUS.

But first I want to have an idea of how the ice did this winter, look at the satellite images, look at statistics, read NSIDC reports and other stuff, listen to what others have to say, etc. Two months is a long time in the Arctic.


I have an issue with using a fit on Sept extent to project an ice free Arctic date as that measure includes about 1 million sq km of open water. It's fine for projecting this year's minimum though. That's why the volume fit (PIOMAS) reaches zero sooner I think, I'd expect similar results if a Gompertz fit was done to the CT area data.




Thanks very much for doing that volume fit. Very interesting results.

I'm planning to try to smash these results with thickness trends I've been working on to see if the resulting area/extent projections gels with predictions purely with area or extent numbers.

The issue that I think is missing from pure 2d projections is the (suspected) increase in the amount of ice that is simply melting through from the bottom up, and hope that this exercise might highlight that. (Of course it may just turn out to be an elaborate way of proving to myself that a * b / b = a. I do that sort of thing...)

L. Hamilton

Phil. mentions the Cryosphere Today area data, which was on my do-list too. When you're holding a hammer, there sure are lots of nails!


L. Hamilton

I should add that I completely agree with Phil. and everyone else who thinks that curve-fitting (whether extent, area or volume) is at best a very iffy way to predict when the Arctic will be ice-free in late summer.

Still it's interesting to see what you get.


idunno, those songs now need more words. We don't just slip, slop, slap any more. We also seek and slide - shade and sunnies.

(Everyone does know that 'sunnies' is the correct abbreviation for sunglasses, don't they?)


I think the reason that lab lemming's survey didn't do very well is his "winner take all" methodology. It encouraged people to bet "unclaimed" areas, rather than areas they actually believed would be correct.

If, instead, he held a weighted raffle based on the height of each person's curve at the eventual answer, the results would (at least in theory) have been more meaningful. I'm going to suggest it at the other site.

Kevin McKinney

"(Of course it may just turn out to be an elaborate way of proving to myself that a * b / b = a. I do that sort of thing...)"

I do so enjoy a mathematical joke that I actually get!

L. Hamilton

Some folks might have noticed that I used a trick to make time run backwards in my Gompertz models upthread. (Reminds me of the story about the mathematician who solved the problem of Saturn's rings, with only two simplifying assumptions: that the rings are square, and they are an infinite distance from Saturn.)

In my case the trick solved a convergence problem I initially encountered, but later I was too lazy to clean this up. Now in the spirit of making things better, here are versions of the graphs without backwards time. They look exactly the same except the equation at top of each graph is a little simpler, and its last parameter equals the year of inflection.

They use the same URLs as the old, so no links are broken, but your browser might or might not let you see the new versions.

NSIDC extent:

PIOMAS volume:

CT area:

L. Hamilton

Regarding a contribution to the SIO from blog citizens, my first thought is that unweighted voting is a fine way to go. But the votes should be numerical and given in an individual post to a thread created for this purpose, with whatever you want to add for explanation. Averaging the votes could be done after the "deadline" by hand, that shouldn't be hard and would avoid other problems.

The SIO focuses on NSIDC September mean, but there's no reason Neven could not also organize a variety of local consensus-meters for IJIS or other stats of interest.

We'd be testing the hypothesis that our consensus can guess well.

L. Hamilton

Back to real ice ... the NE coast of Greenland was interesting to watch last year, as shorefast ice broke off in large chunks.

MODIS got a clear view of this area today. It's striking how much more broken up the ice looks now:

compared with this time last year:


Forecasting the Arctic bathtub is not what I would like to see realized. But given the strong Atlantic heat content I expect the usual icebridge in the direction of Severnaya Zemlya to be broken this year. You can see now, march 2011, how broken up the pack looks right north of the Franz Josef Islands. And how easy the strong westerlies create large ‘polynia’s’ around Novaya and Severnaya Zemlya. Kara Strait is open, Vilkitsky Strait is breaking up. I think the La Nina-cooling nor Wayne Davidson’s projection of a 2011 atmosphere set not to be the warmest in history (temps in the Archipelago were quite low last two months) will have much effect. That accounts IMO for a pack from Banks Island to Fade Isblink on Greenland. But it will not be as broad as we were used to. It won’t reach Svalbard, the North Pole will be a ‘flip-coin’ and I expect just a ‘tail‘ in the northern Beaufort Sea and some isolated remnants in the north East Siberian Sea.
Which leads to a projection of 3.8 MK. That is not unrealistic, because the high concentration ice last year was 3.5 MK. And a lot of the low concentration is headed for melt. The stuff formed in feb and march so far doesn’t look as if it is going to last.

Artful Dodger

Larry PLU-LEESE! Do NOT use the term "trick" when discussing Climate :^)


Regarding Surveys & "Gues-timates" as mentioned in above comments.

PIPS (U.S. Naval Research Lab)is running an onLine Survey - Feedback - ,,, etc... about use of their prediction - projection products.


In view of some austerity programs in government the more feedback they receive there is a possibility a lot activity could keep projects open and onLine to folks like us. Tell them something.


Hi all,

This just in from Ricky Gervais on BBC Radio 1.

"If you have to cut a hole in the water, don't go swimming there."

L. Hamilton

"Larry PLU-LEESE! Do NOT use the term "trick" when discussing Climate :^)"

Sometimes I'm ironic.

Say, does someone know where I could find the numerical data for Kinnard's, or Kwok & Rothrock's (or other) pre-70s reconstructions of ice extent? It might be interesting to see how well we can model the trends in longer series.

Artful Dodger

Sorry, Adalady. But I promise to post a picture of mine when it arrives ;^)


It looks like we are headed towards a double peak maximum according to NSIDC daily SIE numbers:

March 26: 14,706,416
March 27: 14,830,941(+124,525)
March 28: 14,989,485 (+158,554)

We are only about 120k below the "maximum" of 15,110,022 reached on the 7th March.
Similar story from CT, where SIA has been increasing steadily in the last few days reaching 12,926 k on Mar 26, only a whisker away from the "maximum" 13,102 k.

According to NSIDC, the main areas of growth are Bering and Okhotz and to a lesser extent Barents and Greenland. Winter is not over yet folks, and we could still have a later maximum in 2011 than in 2010,although likely to be much lower.


Phil, I'd agree with you if it weren't for the PIPS arrows growing bigger again:

IJIS extent numbers have been going down for a few days, and usually CT area numbers lag a few days so they are bound to go down again today or tomorrow. NSIDC numbers also take a while, because they run a 5-day mean, I believe.


On the other hand, after a second look I think there's a chance you might be right, Phil. There seems to be some ice forming in that huge polynya off Novaya Zemlya, which is showing up I believe in the CT sea ice area graph for Barents.

And arrows have grown a bit smaller on PIPS:

But maybe we should take this to the latest SIE update post?


The NZ polynya seems to be booked against Kara, nor Barents (check the map down the page on the CT link).

Kara area has grown very slightly in the last few days - the only real change I can see is a small amount of ice being advected eastwards through Kara Strait from the Barents into Kara.

Barents has grown more - but that is because of loose pack being advected southwards down the east side of Svalbard, from Central Basin into Barents.

Both movements are largely driven by a Low pressure system centred on 80N 90E, which is producing westerly winds around Novaya Zemlya and notherlies past Svalbard.

L. Hamilton

Gas Glo or FrankD, how should I cite the PIOMAS volume data you linked upthread?

I'm working on a guest post that will pull together the 3 Gompertz graphs, and also an updated cycle plot, to get them all in one place.

BTW, I ran a Gompertz model for March extent, just to see what it predicts based on the trend from past March's. The March-to-March trend (unlike September) is roughly linear, leading to a predicted mean for March 2011 of 14.9. But we're below that already. My guess for actual NSIDC March mean is 14.4.

Jon Torrance


Your numbers don't seem quite to match what I see at the NSIDC and CT web sites. Some clarification and/or correction might be in order.


The NZ polynya seems to be booked against Kara, nor Barents (check the map down the page on the CT link).

You're right, Frank. Thanks.

Gas Glo

PIOMAS data should be attributed

We'd appreciate your reference to the following paper for using the data:

Zhang, Jinlun and D.A. Rothrock: Modeling global sea ice with a thickness and enthalpy distribution model in generalized curvilinear coordinates, Mon. Wea. Rev. 131(5), 681-697, 2003.

Perhaps add some thanks for unofficial numbers pixel counted from graph by the relevant person Wipneus or FrankD see open thread 3.
search for snipt may help find comments.

L. Hamilton

Thanks, will do.



Unfortunately, I am unable to access the NSIDC data as their servicea are down until 4 April (Pretty sure I got it right though!). However, I can confirm the CT data here , with a slight downtick (-13 k) recorded for March 28.

Jon Torrance


Abandoning hints, the CT data you just linked to shows the maximum extent for March as 13,144 k not 13,102 k (the value for the next day) and, while some NSIDC services may be down, their last news post dated March 23rd, in which they say the likely maximum extent for the year reached on March 7 was 14.64 million square kilometer not 15,110,022, is still accessible online. Obviously, it doesn't take a genius to imagine how you made the mistake with the CT area data, though you would do well to actually look at the data carefully the next time someone tells you they think you've made a mistake, but I really have no idea what the "NSIDC daily SIE numbers" you're presenting are. They certainly aren't the numbers underlying the chart at http://nsidc.org/data/seaice_index/images/daily_images/N_stddev_timeseries.png so please do clarify where you got them and what they're supposed to represent, after the NSIDC finishes their data center work if you can't do it before then. Thanks.



The NSIDC data I referred to can be found in the Excel spreadsheet(masie_extent_sqkm.csv) which is linked at the top of the Sea Ice Graphs sheet that was prepared by Neven. This link is not currently working for the reasons which I mentioned before. This spreadsheet gives a breakdown of SIE by basins, however it seems to have a wider scope than CT. I do not know why the total differs from the total reported in the NSIDC. I agree with you that these numbers do not seem to match the chart either. But there they are!

As a non-specialist, my intention in posting this comment was to raise questions about inconsistencies and get answers. Sometimes, there is a simple explanation which I may have overlooked. However, I resent being patronized simply because my comment "doesn't fit". I had the impression that the spirit of this forum was that it was a platform shared by people from different backgrounds, those who know a lot and those who want to learn. But in my view ( a Teacher's view), I believe it is OK for those who want to learn to be critical ( in a constructive way) and to ask questions. I think we had an exchange about this same issue back in August/ September.



The "masie_extent_sqkm.csv" is saved at
which is a Microsoft Works SpreadSheet because I don't have EXCEL on my home computer, but EXCEL should open.
Day 087 I think is March 28.

This late in freeze season "double or max peak" or "double dip" deserves a a separate topic/thread.

In the meantime, have a look at an "extract" from it at
which I'm using to minimize any big deal about a double (or triple) peak max extent.

Do you think Hudson Bay area has lost 11630 km^2 or is it because of NSIDC marking Region (10) on meridian of longitude 65-W instead of 70-W placing Ungava Bay in Hudson region instead of Baffin.

And perhaps Foxe Basin in Hudson also instead of traditional to Canadian_Archipelago giving a Hudson maxed out extent well beyond
Hudson Bay, 822324 km^2
Encyclopædia Britannica - Online
819,000 km^2

Does CT use the same degrees of longitude to mark regions as NSIDC?



Thanks for providing a link to this copy of the spreadsheet. It did open in Excel. Your summary is very useful.
It looks indeed like the definition of the various basins is different from CT. NSIDC also includes the Baltic sea (115k) which doesn't seem to form part of CT. I guess Cook Inlet would be counted as part of the Bering Sea. I am not sure about Hudson Bay!

Artful Dodger

Certainly, MASIE data includes more Basins than other data sets. MASIE basins are:

  • Beaufort_Sea
  • Chukchi_Sea
  • East_Siberian_Sea
  • Laptev_Sea
  • Kara_Sea
  • Barents_Sea
  • Greenland_Sea
  • Baffin_Bay_Gulf_of_St._Lawrence
  • Canadian_Archipelago
  • Hudson_Bay
  • Central_Arctic
  • Bering_Sea
  • Baltic_Sea
  • Sea_of_Okhotsk
  • Yellow_Sea
  • Cook_Inlet

Jack, the Metadata that defines the Basin boundaries is also on the MASIE FTP server. Have a look when it's back up. I don't have Excel either... OpenOffice.org is a free download and it easily saves any type of MS Office file.

Phil, it's a simple matter to compare Apples to Apples within the MASIE data (just remember the daily NSIDC SIE graph uses Oranges :^) Also, it might actually be possible to deduce NSIDC numbers from MASIE just by dropping a couple of the Basins above. I encourage you to give it a try with March 8th, since we know NSIDC SIE to within +/- 50K km^2

Jon, you have one of the highest 'Signal-to-Noise' ratios of any Commenter here on Neven's blog. Lord knows you've helped me with your comments. You might consider cutting Phil a break. His heart is in the right place, and he can help us in ways you do not imagine (but Nevin and I know ;^)

Cheers everybody! Enjoy your Time!


Well, someone is in a good mood ever since he won an Arctic umbrella! :-p

Gas Glo

Congratulations on your umbrella win Neven. A good home for it.


Ah, if only, Gas Glo. No, it is our very own Lodger who received it! He's everyone's envy now, especially when it rains. :-)

Artful Dodger

Well, I guess it's true... Winning an Umbrella has put me in a good mood ( if only I could get past that ominous Geo-engineering Sun-Shade thingy :^) Cheers!


Artful Dodger | March 31, 2011 at 08:44
"the Metadata that defines the Basin boundaries is also on the MASIE FTP server"

Thanks will look deeper. Haven't examined the FTP server directories contents. You got a quick link (lazy help) for later.

How about a picture of a new umbrella - very large resolution??

Gas Glo

In that case, congratulations lodger - still a good home for it.

Now where is that green with envy emoticon?
(and why are they lying about notifying winners in April?)


Phil263 | March 31, 2011 at 08:30
"looks indeed like the definition of the various basins is different from CT. NSIDC also includes the Baltic sea (115k) which doesn't seem to form part of CT. I guess Cook Inlet would be counted as part of the Bering Sea. I am not sure about Hudson Bay!"

Yes, some good reasons for saying "A Region" versus "THE Area."


Larry - what Gas Glo said, although PIOMAS results are not just from a single paper, but are the work of the Ice Volume Team at the Polar Science Centre - Zhang of course, but also Axel Schweiger, Ron Lindsay and Mike Steele, who have all co-authored with Zhang. Perhaps if you are going to do some serious analysis, the best thing would be to write to them and ask if they would be willing to share their data.

But I should just clarify one point: As Gas Glo mentions, I simply pixel counted, but Wipneus did not, and probably achieved more accurate results: he used a graphics package to derive his values (Inkscape, he mentions in Open Thread 3).

The thing to note here is that one pixel on the PIOMAS graph represents 9-10 days, over which time volume can vary quite a bit, so each data "point" is a vertical line. I simply took the midpoint of each line to establish an average value for that 9-10 day period. A vector graphics package extraction is going to be more accurate in finding an appropriate value for any given data "point".

I don't have a vector graphics package so I can't replicate Wipneus' data (our differing approaches did get similar results though). But I can go on pixel counting, so I've continued to update mine because I can. If Wipneus updates his version of the data, it will probably be more accurate than mine, methodologically speaking.

The differences go to intent - I went with a simple approach was because I wanted an answer to simple question: Given that a quadratic curve fits the data better than the linear trend included on the PIOMAS graph, how much sooner does that curve reach zero, compared to the linear fit ? To which the answer is about 15 years.


Artful Dodger

Hi Jack,

Canna take a new pic until it arrives in the mail, until then this will have to do:


Ref the FTP link to MASIE metadata, I don't bookmark that sort of stuff. Will be EZ 2 find when the Server comes back up... It'll be right, Mate!


And just to make everyone's day. I got an umbrella too.

Woo hooo!

(So the threatened outbreak of petulant footstamping has been averted.)

Jon Torrance


I'm not a specialist in this area either - few of us here are. If I were, maybe I would have thought of the possibility that that was the MASIE data you were presenting not the usual SIE data (which I don't think is available on a daily basis anywhere - you had me wondering whether you'd found a non-NSIDC data source and had simply typed NSIDC out of habit). In any case, I really had no idea where you were getting that data from nor what it was exactly and couldn't believe you were just making up numbers so I had to ask. My apologies if that, or more likely mostly my pique over your not actually double checking the CT area data when challenged on that but merely linking to it came off as patronizing.

That said, and against my possibly better judgement, I have a problem with your writing "However, I resent being patronized simply because my comment "doesn't fit"." when no one in this comment thread used the phrase "doesn't fit" until you did. If you want to paraphrase what someone said, say so. If you use quotation marks, use them to enclose an actual quotation.

Peter Ellis

Eh, not come across "scare quotes" before? Fairly standard English orthography, I'd have thought.

Peter Ellis

Top marks for nested punctuation though: I
always get lost half way through. What this language *really* needs is brackets...


Congratulations, adelady, you deserve that umbrella (although now I'm doubly jealous).

So, 2 out of 3 umbrellas went to ASI blog commenters. Not bad!



Thanks for your response. As Peter said, the qutotation marks were used as " scare quotes" and did not mean to refer to anything that had actually been written on this blog. It was my own interpretation of your response and this is why it was put between quotes. May be I should have used single quotes (') as the BBC does when they report something that hasn't been quite confirmed by facts.


FrankD: If Wipneus updates his version of the data

There is a slight problem with the PIOMAS graphics. The last updated anomaly graph seems now to be based on 1979-2010 means. Yet the averages plot has not been updated, showing 1979-2009 averages. It does not matter much, but the month-to-month differences are visible if you lay the graphs on top of each other.
I intend to wait a little bit longer to see if the averages graph gets updated, if they don't at the next update I will do my own recalculation.

Meanwhile, I have included a Gompertz curve fit to my multiple curve fitting graph of September ice volume:

As discussed before, I do not see any convincing physical reason why ice-melting should so dramatically slow down when ice volume get low. For now the more "alarming" curves, give better R2 scores than the Gompertz curve but probably not significantly yet. That could change this year.


Wipneus, yes, I remarked a little while back that PIOMAS had been rebaselined. I hadn't noticed the averages plot was unchanged, so well spotted.

As it happens, that I hadn't noticed didn't affect the data I've posted since. Faced with the prospect of reworking 30 years of data, I've tweaked their more recent data to fit their old baseline. I suppose eventually, I'll need to redo the whole thing :-(

I take your point on the merits of a Gompertz fit - my thinking: now we have two curves that are a better fit than linear, and we can see which (if either) holds up over time. And if neither, then we learned something from that, too.

Hopefully, they'll post a new version of the graph soon (its been stuck on Feb 28) and we can see how March stacks up.


Thanks a lot, Gas Glo. That deserves to be a blog post.


With MODIS down I've been following a large, rounded chunk of ice shelf (I think) on DMI.
It may still be caught in the gyre in front of Petermann Fjord and could again smash into Petermann's now fractured ice shelf.


is the latest image, but it's easier to track using MODIS

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