« September 2011 sea ice extent, looking back | Main | PIOMAS September 2011 (volume record lower still) »


Feed You can follow this conversation by subscribing to the comment feed for this post.

Rob Dekker

Thanks Larry,
It's a humbling thought that indeed despite less than ice-export-favorable wind conditions, 2011 volume by PIOMAS still hit an all-time low. Some questions and comments remain :

- Why did 2010 show such a huge drop in volume ? Were the winds more favorable for ice export, or was the solar irradiance higher, causing more ice to melt ? Or was the winter of 2009/2010 much milder that the 2010/2011 winter ?
Somehow I doubt either of these explanations. What's your take on this, and did you see the guys at PIOMAS giving an explanation ?

- Regarding the Gompertz curve fitting over ice volume, did you attempt to put the extent (or area) Gompertz curve (shown by Neven in the previous post) over the volume Gompertz curve, to see how the ice thickness should develop if all these Gompertz curves are indeed an accurate reflection of what's to come over the next decade ?

Chris Biscan

The models show a classic beautiful DPA anomaly coming.

We will see how a thin ice pack in early to mid October can handle this kind of pattern.

If it happens.

A Facebook User


Good question! We don't have an explanation of the processes that lead to the reduction of sea ice from one year to another. One thing to keep in mind is that the 280 km^3 in annual sea ice volume loss we show in our volume record, corresponds to a change in energy of roughly 0.4 Wm2. That's a very small number to try to track down. Yes, we can conjecture about the role of winds, ocean heat fluxes, ice export, clouds, feedbacks etc. and sometimes those things line up in a way that allow you to draw some fairly strong conclusions(e.g. 2007) but I think it will remain difficult to come up with solid explanations about year to year changes.

Appreciating the 0.4 Wm-2, I think we are better off looking at the longer term changes. Doing so, and that's my personal bias, we have a better chance in getting a handle at the mechanisms that drive the changes in Arctic sea ice.

Note also that scientific papers discussing the role of the contribution of various processes in 2007 are still coming out in 2011, and I doubt we are done quite yet.

Nonetheless, its fun to follow what's happening in any one year and speculate about what's going on. Sometimes those ideas can inspire more detailed investigations that firm up those ideas.

Axel Schweiger


Is it worth using data up to 1995 to make 1996 predictions using gompertz and exponential (and possible also quadratic and linear) extrapolations? Then predict 1997 using data to 1996 and so on to see which method has been closer for most years in the 1996-2011 period?

Doing this for Uni Bremen, PIOMAS, and CT area sounds like a lot of work if it will just give an even split between Gompertz and exponential or wouldn't really tell us anything that we could believe anyway. So it may well not be worth doing. So I thought it might be worth asking before trying to get stuck in.

L. Hamilton

Crandles, I think the Gompertz and exponential are so close in recent years that you couldn't make a decision between them on that basis. I like the Gompertz not because it's fitting better right now, but because it behaves more reasonably for the early and later years.

Rob Dekker

Thank you for stopping by and offering your perspective on volume decline short/long term.

I understand that even with a model (like PIOMAS) it may be hard to track down where exactly a small change comes from, especially a year-to-year variation. However, PIOMAS shows a drop of some 1500 km^3 from 2009 to 2010, which should be somewhere in the 2.5 W/m^2 range, which seems significant w.r.t. the long term down trend of 250 km^2/yr.

So my question is : to which extent was the 2010 drop caused by PIOMAS 'free-running' as a model, and to which extent was it the result of observational constraints imposed on the model ?

Also, for long term projections, Tietsche et al 2010 (using GCMs) obtain a fairly strong (interannual) ice recovery to a long term mean, mainly caused by increased fall IR losses outperforming summer albedo effect.

Could you give us your perspective on how PIOMAS would respond to year with ultra-low ice cover, and what the level of ice-volume would be that it 'recovers' to after a few years ?

Once again, thank you for your insights and please keep up the great work you guys are doing at PSC.

L. Hamilton

Axel, thanks for dropping by. I agree that the longer-term questions are the big ones, and perhaps most tractable, although humans (especially those living or working in the North) wish the short-term predictions were better too.

And perhaps illogically, the outcome of short-term predictions is widely viewed by non-scientists as a criteria for whether long-term predictions should be taken seriously.

L. Hamilton

Looking back at my April graph with its 5.2 prediction, I realize that I had based that prediction on a different version of the PIOMAS data, before the daily dataset became public. The new graph on this page, on the other hand, was calculated from the now-public daily data, so my 5.2 April prediction and the 4.2 September result are not strictly comparable.

A better comparison to the observed 4.2 would have been a prediction based on the same data through 2010. That prediction would have been 4.9, somewhat closer to the observed 4.2.

Artful Dodger

Hi Axel,

Welcome back, Iceman! Appreciate you dropping in, your words are always an inspiration.

I wonder, how does PIOMAS handle ice age/brine content and it's effect on the melting point of sea ice?


Account Deleted

Using Gompertz curves is a complete non-sense.
Because in this kind of curves, there is an inflexion in the curve, which implies a combination of to opposite processes, and cannot be applied to the ice melting process.

In the case of ice melting, it has necessary an exponential trend like in the following graph http://neven1.typepad.com/.a/6a0133f03a1e37970b0153920dd89a970b-pi
as the more the ice melts, the more it heats and then the more it melts, so is an accelerating process until complete melting.


Congratulations, Hugues. That was the ten thousandth comment on this blog. :-)

Artful Dodger


Melting is not the only process involved in the decline of Arctic Sea-ice. There is also refreezing, changing salinity, and sea ice advection. It is not the simple High School physics experiment you imply.

The Gompertz curve currently provides the best fit to observed data. The exponential trend you prefer does not fit well with observations from 1972 until the mid-90's, where the Gompertz curve fits very well.

In short, your comments are "complete non-sense", lol. Welcome to the 'blog ;^)


Account Deleted

Dear lodger,

Thank you a lot for making me laugh so much. In fact I was expecting such kind of reaction, an boastful one of a specialist who doesn't have any consideration about people who are not specialist at all.
In fact I'm a 40 year old engineer with 15 years of experience, and not a 'poor' student in physics who would like to proof he knows a lot. And in my experience, I've met a lot of arrogant people who are so sure of themselves that they need to depreciate others. And I'm able to think logically without your help.

I'm telling all this because the trend of the ice melting is an accelerating trend (and every year the reality is worse than expected), and not a trend as shown in Gompertz curve. And I don't care if the Gompertz curve fits well for the past, the fact is that it cannot fit for the future, because of very simple logic.
And if we compare the graph I added in my post (I didn't invent it, just found it on the web), with your's, there is no visible difference. And you know that many experts agree with the fact that the arctic sea could by free in 2015-16, +- 2 years. And in fact in an accelating process, it is evident (the process of melting of an ice cube in warming water).
You cannot use a curve just because it fits to previous data. You absolutely need a reason for using this curve and not another.
So how can you explain, that in your curve not only the acceleration is stopped, but also the speed of melting decreases to almost zero i in 2022-23 ?
As I said in my precedent message, in this case, there MUST be a extremely strong counteracting process in order to invert the tendency. So please, tell me what is this process that is able to delay for 7-8 years (from 2015 to 2022-23 as in your graph) this incredibly strong process that is ice melting (and generally global warming). In fact, and you can't not know, many experts in climate change agree to say that the trend of complete melting in 2015-16, with 2-3 years error do to variability).

Frankly, I'm bored of this kind of reaction saying 'Please let me explain you, I'm a specialist, you don't know anything, so shut up and let me do my job.'


Wayne Kernochan

@Hugues Hi to you, and let me try to give you an alternate explanation. In this case, there are not two competing processes -- there is, instead, an underlying exponential trend of decreasing thickness, where thickness is (perhaps) normally distributed around the average -- and what happens when thickness hits zero.

What happens as volume (the best measure) approaches zero (in this case, at the minimum, each season)? Some of the ice melts out. If we were to assume that the melted ice "continued melting", then our volume figure would continue decreasing at an exponential rate, straight into negative territory, around 2014-2016. But instead, we measure volume as the volume of the ice that's left. On average, half of that ice will therefore be melted to zero thickness in, say, 2015. If it's a "tight" normal curve, we might expect 70% the next year, 90% the year after, and 99% the year after that. In other words, the volume we actually see does indeed decelerate its loss. It's not two processes -- it's the way we measure what's going on.

That volume trend, in turn, drives the area and extent losses. According to my own mental model, a lot of volume loss is "bottom melt", not melt from above or along the edges. The result is that until the ice is melted "all the way to the top", it still has area and extent. Thus, the area and extent also follow a curve of accelerating loss followed by deceleration, but accelerating much more slowly at the start, much more quickly before half the ice is melted, and decelerating much more slowly right after, much quicker at the end.

I don't think a Gompertz curve will prove to be completely right (if my model is correct). I think that the last few years suggest that the variation of ice thickness around the median is pretty tight, and therefore we will see a steeper dive in the next few years than in the Gompertz curve. But a counter-argument is that once the ice melts, the rate of further melt slows, because much of the additional heat in the melted areas comes from albedo warming of the ocean's surface, heat which is released rapidly once the sun stops shining. So it may in fact be true that the remnant of the ice at minimum may last another 3-4 years.

Sometime in the next 3-4 years, we should be sure that a sharply accelerating model for extent is correct. Sometime in the next 3-4 years after that we should be sure whether it will continue at the same pace as "real average volume" (including the melted parts as negative) approaches zero. But unless ice thickness has zero variability, I think it's pretty unlikely that measured volume, area, or extent will reach zero by 2016 -- and I'm a pessimist.


I think there are counteracting changes in the heat budget. One is well known albedo effect that causes more melting the less ice (area) there is.

Counteracting effects include winter freezing occurs as heat is lost. The thinner the ice the more heat is lost and the more ice forms in winter once any excess temperature has been lost.

Less ice is likely to be in a smaller area that is nearer pole. Pole gets longer winter night. So while the annual heat budget may remain positive for whole Arctic, this may be badly distributed to be able to melt the last of the ice.

There is variation in thickness as mentioned by Wayne above. There might also be an effect of variation in area of pieces such that small pieces melt out but larger pieces do not. There may also be some shaded nooks and cranies. I doubt these will amount to much of a counteracting effect but the first two might.

Anyway I think we do have a combination of opposite processes which you said cannot be applied. The first one I mentioned applies to the freezing not the melting but the second one appears to me that it does apply to the melting.

I do accept that these haven't appeared in the curve fitting yet. That doesn't mean they won't appear. Of course, this does beg the question of when, if at all, they will appear.


@ Hugues
Here is a link to the expected ice loss provided by the GCM's used by scientists to predict the future of the arctic. http://www.realclimate.org/images/seaice10.jpg
This shows the same tailing off of ice loss as the Gompertz curve shows. You have to be open to the possibility that the models are picking up something that occurs at lower levels of ice. I think the exponential trend is correct but I must accept the possibility that I could be wrong.

@ Lodger
You do not have any mathamatical justification for your claims that the Gompertz curve fits better than the exponential curve. First of all the current behavior of the fitted Gompertz is exponential. Around the knee it will start to deviate from exponential. Second the RMSE differences are so small between the 2 curves that it is statistically insignificant.

David Gould

I am still unsure that there could suddenly be evidenced a counter process to the melt that has not been seen up until now.

Extent/area has declined dramatically over the last few years, leaving a lot of open water that was not there 20 years ago. No let up in the decline has appeared.

If a further, say, 20 per cent of the remaining extent went, getting us to an extent of around 3.7 square kilometres, would that extra one million of open water suddenly and dramatically slow the decline when the four million new square kilometres of open water did not slow it at all, but instead saw it speed up?

Given that the exponential curves show ice vanishing very soon, a very large effect has to come into play very quickly ...

Kevin O'Neill

Hugues - "many experts in climate change agree to say that the trend of complete melting in 2015-16, with 2-3 years error do to variability)."

I know of two: Maslowski and Barber. I'm sure there are others, but the majority, probably large majority, believe 2030 is a more likely scenario for an ice-free September.

I believe it will be sooner - and likely this decade. Having read dozens of papers regarding the arctic the one thing I know is that there are many unknowns. Weather variability could take a turn in favor of ice regrowth. A new dominant climate pattern could emerge that favors ice regrowth. Sea ice loss could reach a point (may have already reached a point) where negative feedbacks offset positive feedbacks and the arctic we see today becomes the status quo.

Curves, of any flavor, merely describe the system as it has performed in the past. They have no ability to predict changes in the system. Only when we understand the physics of how a system responds to various stimuli can we predict (model) how it will respond to changes.

If you have read Tietsche et al, then you should understand that there is a mechanism for the ice to quickly "recover". I may not put as much weight behind this work as some others might, but I do not dismiss it out of hand.

Andrew Xnn

Don't know what the best name for it is, but a significant feedback from melting sea ice is the loss of insulation that the ice provided.

With larger amounts of open water exposed or covered by thin ice, the cold of winter is able to form more ice than it would otherwise.

This was observed following 2007 record minimum area and extent. During the 2007/2008 winter, a record amount of ice formed in the arctic: 18,700 km3.

The 33 year average is 16,290km3
Between 80-82, the average was 15,600km3

David Gould

Andrew Xnn,

Yes, but that rebound did not affect the polynomial decline. The 2007 was a drop below the trend line - the rebound just brought us back up to it.

It should be pointed out that Tietsche's thesis is that the Arctic can rebound from *anomalous* declines and that there is likely to be no tipping point. I do not think that the polynomial decline is anomalous.

Bob Wallace

I keep trying to imagine some new "large effect" which might come into play to turn the positive acceleration melt into negative acceleration.

I can't see how it would be a change in ocean current. During the winters before the melt out it would still be very cold in the Arctic and that cold water would still be sinking, making room for the import of warmer water. During the last years of ice there will still be lots of summer melt to supply cold input.

With the early season ocean still covered with a layer ice, thin as it might be, there shouldn't be a huge increase in cloud cover from rapidly evaporating exposed water.

The air about the ice should be about a cold as it has been early in the melt season. Any additional water warmth would be largely trapped below the ice layer. That should mean about the same amount of air exchange with areas outside the zone.

Short of a decrease in warm water or warm air import or a blocking of income solar energy, what could there be? A decrease in summer storms as the temperature differential between within- and without- decreases?

I'm having trouble seeing the cloud of dust that tells us that the cavalry is on the way....

David Gould

Looking at the NSIDC extent data, there is a strong correlation between melt and freeze - the larger the melt of year N, the greater the freeze in year N+1.

I have not checked for autocorrelation or anything like that, but the r^2 value is 0.77 and the slope is 0.87, meaning that for every increase in melt by 1 million square kilometres means a corresponding increase in freeze by .87 million square kilometres. Note that this still sees an increasing gap between melt and freeze.

It would thus seem to me that the effects of rapid re-freeze are already built into the extent data. So no cavalry there.

(And, yes, extent data does not show meltout until around 2030. But we all agree that volume is the main game here - just looking at the extent data for clues as to behaviour).

Based on this, the data predicts that 2012 will see the third largest freeze in the NSIDC record - close to 9.8 million square kilometres of new ice. It is predicted, however, to still be the lowest March extent.

Bob Wallace

Looking at the last 30 years of melt/refreeze in the ten years of greatest melt the following winter refreeze was only 94% of what was lost. Only in 2007 was more ice made (102%) than lost in the previous summer.

In the ten years of least melt the refreeze slightly exceeded (101%) the amount lost.

When I look at the PIOMAS volume graph what I think I see following deep thaws is a short term rapid refreeze, but after a few weeks the rate of freeze drops and rarely is there a full recovery.

Since 1997 there has been only one year (2007) in which the following winter freeze was greater than the summer melt.

I think we can forget about a 'superball' effect saving the ice.



The Gompertz curve currently provides the best fit to observed data. The exponential trend you prefer does not fit well with observations from 1972 until the mid-90's, where the Gompertz curve fits very well.

Both assertions are incorrect for the PIOMAS minimum ice volume data.

Here is the spaghetti graph of fits to the data: https://sites.google.com/site/arctischepinguin/home/piomas/piomas-trnd1.png

- Exponential fit is better than Gompertz fit over all available years (by an insignificant, yet increasing margin), see R2 scores;
- The fit of data on the 1979-1995 data is better (still by an insignificant margin) for the exponential over Gompertz fit: sum(residuals^2) are 1.239 for exponential and 1.248 for Gompertz curve.

The differences between the curves are now and have been totally insignificant and will likely stay that way for the coming years. In fact if in 2015 when the exponential fit predicts "zero ice", the ice volume is right what the Gompertz curve "predicts", that will still fall in the 95% confidence margin of the exponential curve. See those margins here: https://sites.google.com/site/arctischepinguin/home/piomas/piomas-trnd6.png

So by the stats the two curves cannot be distinguished, that leaves only physical arguments. And I have seen few for the Gompertz curve yet, I am with Hugues on that.

Andrew Xnn

The melting of sea ice in response to climate forcings is an extremely complex process. To accurately model it requires a super computer loaded with a 3D model of the entire planet and all the various feedbacks and interactions between the oceans, land and atmosphere.

The most sophisticated models tend to follow a curve resembling a Compertz curve:

This doesn't mean that a Compertz curve is best, but it is convenient.

David Gould

Andrew Xnn,

I will point out that the most sophisticated models project that the ice will be gone at the end of the melt season by around 2070, which appears to be contradicted by current observations. Most scientists looking at this believe that 2030 is a more reasonable time frame, with some looking at much earlier dates.

Andrew Xnn

They guys that are getting published and cited in peer reviewed journals, are projecting ice free arctic summers within 30 years (and maybe sooner):


Curve fitters are pointing this decade.

The comments to this entry are closed.