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That is quite a lot of text to include on a graph. So what should we put? Perhaps:

Data Source
Data retrieved
Graph created by
The past is not necessarily a guide to the future see http://neven1.typepad.com/blog/2012/03/use-of-graphs.html.

Kevin McKinney

Well-said, Neven.

Of course, some of the 'usual suspects' would feel that all of these fits are wrong, since said suspects are still hopefully awaiting the 'inevitable' recovery of SIE.


Now I wonder if Wipneus can/will/should change the trnd2 graph to a notice and graph saying:

Note: To avoid misleading parliament
The graph that was here has been moved to
https://sites.google.com/site/arctischepinguin/_/rsrc/1331361080527/home/piomas/piomas-trnd9.png while this location adds extra information to clarify the situation.

This graph was created by [name] not by the PIOMAS team. Dr Axel Schweiger is chair of PSC which created the PIOMAS data.

The past is not necessarily a guide to the future.

Dr Schweiger has written
"I disagree with the extrapolation of PIOMAS data and I am glad you are pointing it out. I think there is little basis for using an exponential. At least if there is, I haven't seen it.

[The following graph is] a nice figure which demonstrates a number of different functions fitted to PIOMAS data. It clearly illustrates the sensitivity of the "ice free summer" prediction to the choice of extrapolation function and suggests the need for some solid scientific reasoning for choosing one over another. I haven't seen that reasoning."

followed by the trnd1 graph.

Wayne Kernochan

Following up on @Neven's comment about the lack of a model behind these graphs: it does seem to me to be possible to connect our models of Arctic sea ice to these graphs. Skipping a lot of argument: the combined effects assumed in a PIOMAS-type model would result in volume that initially (up to now) fits the gompertz curve. The resulting pack of curves would posit (linear or exponential) decrease in volume at maximum and exponential decrease in volume at minimum, as per the data. They would posit a normal, skewed normal, or bimodal distribution of volume values in sub-areas at any time, with the same distribution at all times of the year, and include a corrector for "negative volume" sub-areas to account for sub-areas with sustained periods of zero thickness. These volume curves, aside from the parameters mentioned above, could also vary based on projections for various types of multi-year ice (more many-year ice would increase the "flatness" of the normal curve), projections on the speed of movement of the ice into and out of colder parts of the Arctic (lower speed would also "flatten" the distribution curve), and projections as to multi-year ice exit from the Arctic (more exit would increase the exponential rate of the minimum curve, and the rate of linear decrease of the maximum curve). Effects of increased "heat storage" in new open water during the summer (which would increase the rate of decrease) and of other side-effects such as NAO change, methane release, and albedo-change effects on temperature should be regarded as having much less effect, but can be varied as a second pass.

L. Hamilton

It's a small thing and certainly not foolproof, but for just this reason I make a habit of including little notes at lower left in my graphs, e.g.,

graph: L Hamilton 1/28/2012
data: PIOMAS (Zhang & Rothrock 2003)

Occasionally I've seen my graphs (not just the ice ones) show up in other people's slide shows or blog posts without mention of the source, except for whatever I had placed within the image itself. From that, an interested reader could probably track the graph back to its source if questions arose.

I like Neven's point about not giving scientists (like the PIOMAS team) blame for how other folks graph their data. Again, an argument for making clear within the image itself who authored the data, who authored the graph.

Bob Wallace

"said suspects are still hopefully awaiting the 'inevitable' recovery of SIE"

Waiting for the U-shaped curve to appear?

"U" as in Unicorn....

Lou Grinzo

Good points, as always, Neven.

On the data itself, as displayed in these graphs, I have to say that I find the more "official" pronouncements we sometimes hear about hitting the (virtually) zero ice point after 2040, say, to be a bit odd. Looking at the first graph posted above, it seems clear that making such a prediction is tantamount to saying that either PIOMAS is wildly wrong or it's right and the curve is about to take a truly astonishing left-hand turn very soon.

This is reminiscent of those calculations and curves showing how quickly we'll have to cut CO2 emissions as a function of when those emissions peak -- later means a much steeper reduction is needed. In this case, the lower that curve goes, the more of an Arctic miracle (possibly aided by a unicorn, as suggested above) we'll need to avoid even a very short period of Blue Arctic every summer.

Bob Wallace

Seems like if we calculated the amount of energy needed for the average annual volume loss we could estimate the size of the unicorn that we're watching for.

A great big unicorn, likely it could sneak us on us unobserved?

Outside of perhaps a bit more ice-insulating snowfall have we heard any hoofbeats off in the distance?



As some of you may remember, I first posted links to these graphs two years ago. This was after FrankD had shown first that the PIOMAS data, then only available as an anomaly graphic, was far more alarming when graphed as absolute volumes.
The data seemed to show that collapse of the minimum ice could be well before 2020 , much faster than the area/extent graphs indicated not to mention most of the 'offical' predictions.
I have stayed on this party, to witness the outcome. I updated the graphs, and occasionally polished them up in the process.
I gave them a more permanent place, 'arctischepinguin', for convenience.

I have to think this over. At the moment I am thinking to give the page 'arctischepinguin' some textual context and on the graphs themselves a link to that page.
Link to the PIOMAS data is already there, but can be simplified.
I 'd like to avoid cluttering the graphs with caveats if possible.


Wipneus, it could be a good idea to add a bit of extra info on your graphs, just to be sure. Like Larry does it should be enough:

graph: Wipneus (of gewoon Wipperd ;-) ) 1/28/2012
data: PIOMAS (Zhang & Rothrock 2003)


Excellent post Neven: Evidence of your integrity and quality of this blog!


Oh well, Phil. Integrity and quality won't mean much if Arctic sea ice does follow one of those exponential curves, but we just don't know enough right now. Of course, this doesn't mean things are dandy. On the contrary.

Eli Rabett

You know, as a practical matter Eli finds it extremely difficult to see any difference between the extrapolations on that last graph. Somewhere between 2015 and 2030 poof

A Facebook User


Thanks for this post. It greatly helps that you have clarified the difference between PIOMAS output and the interpretations done here on this blog. To be sure, when I get a chance to stop by here, I am always amazed by the enthusiasm, energy, and expertise that is displayed here on this blog. I often see very good questions raised and frequently find myself scratching my head over one, only to find a pretty good answer posted by somebody here. So I hope it is clear that my comments about he use of the PIOMAS data were directed at their use and attribution, rather than at what people are posting here. Though, I would have hoped that before things go to parliament or to the BBC, that someone preparing the materials would catch the source and make sure that things are attributed properly. But, I think this is now all cleared up thanks in part to your post. The BBC had already corrected their article.

As to the use of extrapolations for predictions, just quickly here: The choice of function is only one issue, and as discussed here, an exponential isn't a good fit for the trajectory of ice volume under a warming scenario. Just as importantly, for a prediction based on extrapolation to be skillful, the period over which the fit is performed also must have sufficient information about the future evolution of the sea ice trajectory.

That this is indeed the case and that this information is sufficient to make a skillful prediction, in my view, needs to be clearly demonstrated before such a prediction should make it beyond experimentation and onto informing policy. I'm rather doubtful that this possible, but I'll keep an open mind.



I have modified the attribution in the graphs on https://sites.google.com/site/arctischepinguin/home/piomas to:

Data: PIOMAS (Zhang and Rothrock 2003) \nPrepared by Wipneus (https://sites.google.com/site/arctischepinguin/home/piomas) yyyy/mm/dd

Do you think that is enough?

If a caveat about extrapolations is needed, I will add one.

Kevin McKinney

Bob Wallace wrote:

Seems like if we calculated the amount of energy needed for the average annual volume loss we could estimate the size of the unicorn that we're watching for.

If I understand you correctly, this has already been done by Gareth of "Hot Topic" as what he amusingly called--and it's good to take what amusement one can here; the big picture is a bit grim--"a topologically infeasible 'back of the back of the envelope' calculation."

BOBOTE here:

I think I might be tempted to call that a 'black unicorn.'

Al Rodger

As an inveterate creator of graphs on my steam-power spreadsheets, I have always been aware that artifacts such as graphs can grow legs & travel who-knows-where across the internet.
I would thus echo L.Hamilton (& others) and advise that any creation is effectively 'signed' & 'signed' promenantly such that anyone who is more that the most casual viewer will notice. If you can read the title & so interpret the graph, the 'signature' should be visible if not readable.
I think there is also a matter of providing the right title. The graph under discussion above is titled "PIOMAS Yearly Minimum Arctic Ice Volumes" with no mention that the 'exponential trend' is not PIOMAS, but rather fitted onto PIOMAS. It may be irresponsible for other to strip a graph from its context and set it up standing alone but, hey, it's gonna happen so try and make provision for it.
Mind, I'm probably a bit too cavalier when it comes to atributing the data. "PIOMAS 2.0" is all I put for the source on my own ice volume graph. Here's hoping Zhang & Rothrock aren't agrieved by the lack of mention.

Do you think that is enough?

I think it is, Wipneus. Well done.

If a caveat about extrapolations is needed, I will add one.

No, that's the responsibility of the person using your graphs. You could put a short caveat/text on top of your web page, but that's up to you. It's good enough as is, in my opinion.

Chris Reynolds


Thanks for your graphs.

FWIW I agree with Neven, it's not your responsibility to clutter graphs up with various declarations. The place for them is on the source page. In your case that seems to be here, and the previous discussions give ample context.

It's good practice when linking to images to always link to the source page. Whenever I see images linked to without a discussion of how they were made and any potential caveats my BS meter starts to switch. There's a reason scientific papers take the space to explain their graphics. If only to avoid such a suspicious response from readers good practice needs to be followed.

If AMEG are correct, I don't think so but I could be wrong, then this performance is worrying. The potential importance of their message means they really need to start playing a more professional game. Screw ups like this do not help their case.

Al Roger,

"...an inveterate creator of graphs on my steam-power spreadsheets..."

I know that feeling, with every day from 1979 and area/extent/volume my 5Mb spreadsheet stretches Excel to its limit. But my time is limited, I know how to use Excel, and can't spare the time to learn a more appropriate solution.

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