« The bunny explains | Main | Arctic snow cover shows steep decline »


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

Chris Reynolds

Bob Wallace,

As I explain to Crandles above. The major reason I see a rapid crash is that I think the pack is mainly young ice, I think the old ice is mainly gone. If I am wrong then the continuing loss of volume could be coming from the demise of the remaining old ice, which having a longer time constant has memory of perturbations. Whereas young ice, particularly FYI, can recover far more quickly so has less memory. If the current volume loss is coming from old ice as almost all of the loss of PIOMAS volume has, then we may still face a long(ish) tail as the regional warming shifts the winter equilibrium growth of ice to be thin enough for all the ice to be lost in one melt season.

Because I could be wrong I'm not writing the Armour paper off yet. As for ice surviving into the middle of the 21st century - that's bordering on the inherently improbable. But ice surviving into next decade could still be feasible, even if I personally doubt it.


Fully agree with that Bob. That "rate of change of Arctic sea ice area decreases late in the simulation" is leaving it awfully late before making an appearance and maybe it won't make an appearance. So we should be doing some risk assessment of the consequences of it not appearing.

Chris Reynolds

Correction to previous post to Crandles, inclosing para:

" then the conclusion I draw is that the volume loss rate is likely to abate and a longer tail will emerge."

should read

" then the conclusion I draw is that the volume loss rate COULD abate and a longer tail COULD emerge."

Bob Wallace

I don't think it's any longer an "old ice/new ice" issue. It's more a "piled ice".

The ice shoved against the north coast of Greenland and the CAA was supposed to produce the tail that drags out the melt. And now we're seeing it start to get blown away from the coast at some times and through the various channels at others. And we're seeing the land that the ice is piled up against loosing its snow cover and heating, apparently causing some close to shore melting.

If we were to melt away most of the Central Basin it could take only a few days of strong southerly wind to move the last crust of piled ice out where it could get transported/quickly melted. If the first "almost total meltout" occurs a month before the beginning of the next freeze season I'd give that crust only a slight chance of holding on.

I put the likelihood of a prolonged multi-year final melt fairly low. But I also don't totally dismiss the possibility of a long tail melt. Weather variability could drag things on for a year or three.


BTW, I'm uncomfortable with the use of "memory" to describe a physical process.

Older/thicker ice seems to have more resistance to melting due to its ability to block transmission of light/energy to the water below. It seems to have more resistance to melting because of a lower salt content. Those things are not memory.

(And I'll repeat for those who are new or have leaky memories like mine. I'm way out of my depth here. Very interested but I lack a lot of the scientific background to fully understand everything. So if I say something stupid I won't be surprised. Teach me better.)


OK, if you are thinking about enough MYI to bias the thickness high then your 2m+/2m- split makes sense. I think I would prefer to call that something like mechanical process thickened ice (MPTI) rather than old/young description. I expect MPTI to be denser than first year ice. A lot of MPTI will be MYI because it takes time to build up volume of MPTI. So it obviously takes more energy to melt MPTI then the same volume of FYI.

When MPTI was disappearing before 2010, we had the heat budget imbalance to melt it. After 2010 that heat budget imbalance appears to still be present as we are now melting larger volumes.

Why is this concentrated 20 April to 29 June rather than when the albedo effect occurs later in the season? I suggest a possibility is that there is still a noticable volume of MYI as per my suggested calculated earlier. The volume is less and this is partly because the MYI is thinner now so FYI is added to the bottom of the MYI. This means that early in the melt season, the water only has to get up to -1.5C to start melting this FYI rather than higher temperatures to melt purer MYI. So it starts occurring earlier. Perhaps by 29 June we are melting mainly MYI as the FYI stuck to bottom of MYI has all been melted. The 29 June date should get later as the MYI gets thinner but does not appear to be doing so. So this explanation is likely flawed or at least incomplete.

Anyway the MYI continues to decline by getting both thinner and less area, the energy imbalance is still there and can melt an increased total volume because there is less MYI. When it is all FYI it will all be meltable, otherwise there will be some MYI.


We had a thread on modelling, “Models are improving, but can they catch up?” back in September. Wipneus’ 2046 CMIP5 projection recalls a lot of what was discussed.

From WCRP ( http://cmip-pcmdi.llnl.gov/cmip5/ ):
“ CMIP5 promotes a standard set of model simulations in order to:
• evaluate how realistic the models are in simulating the recent past,
• provide projections of future climate change on two time scales, near term (out to about 2035) and long term (out to 2100 and beyond), and
• understand some of the factors responsible for differences in model projections, including quantifying some key feedbacks such as those involving clouds and the carbon cycle “

And the National Academy of Sciences (http://dels.nas.edu/Report/Seasonal-Decadal-Predictions-Arctic/13515), November 29, 2012:
“However, gaps in understanding the interactions between Arctic sea ice, oceans, and the atmosphere, along with an increasing rate of change in the nature and quantity of sea ice, is hampering accurate predictions.”

On 11 April I wrote: “I’m afraid most scientists will, for varying reasons, stubbornly measure, model and figure out into the detail ‘how it ticks’, while their object is vanishing.”

Consuming all that, Wipneus, I suppose you presented the 2046 graph with irony. While I am impressed one can run a ‘professional’ model ‘at home’.

Chris Reynolds


After 2010 we have much more young ice and less old ice, or as you put it MPTI, ice that is outside the thickness range of thermodynamic thickening. I wonder if MPTI and TTI (thermodynamically thickened ice) would be the best demarcation for my argument to avoid future confusion?

The paper I linked to on the previous page (Perovitch & Polashenski) implies that the albedo change happens from around June 1, although figure 2 shows a small drop in albedo at some sites from mid May. Prior to June 1 temperatures are below zero so liquid water on ice or as wet snow can't cause the albedo drop. But a role for albedo changes may be argued using that paper for the period from 1/6. This leaves around mid April to late may unexplained. However it also begs the question why do anomalies rise during July when a) albedo is lower b) the summer Arctic Dipole should be having an effect post 2007 c) July volume loss is the highest of the year implying (as I've read somewhere) that insolation is at its highest so any albedo change driven loss should also be at its highest.

I'll be blogging about all this in more detail as for the last few weeks I've been ploughing through all my Arctic sea ice related data: Trying to get my head around the changes in the seasonal cycle.

Bob Wallace,

I don't have any substantial disagreement with what you say, except.

"BTW, I'm uncomfortable with the use of "memory" to describe a physical process."

Memory in all sorts of physical systems is critical. I think it is in sea ice too.

Sea ice thickens thermodynamically by growing ice onto the base due to heat flux through the ice to the surface. So if warm weather 'perturbs' the thickness of young ice to below that for a typical winter, it only takes another winter of more normal cold for that ice to grow back to the thickness it normally has. This is why young ice has little memory, the physical impact of a perturbation is wiped by the next year's growth.

However it takes years to compress and ridge ice into thicker old ice. So the same melt event causing the same percentage loss of volume per cubic meter of the ice has an impact that can be seen many years later as reduced volume.

This in a nutshell is why thin ice has less memory than thick ice. I don't want to patronise you but this might make more sense -

Think of two bank accounts. A Current Account and a Savings Account. The current account has wages of £1000 per month going in, from which £100 is diverted into the savings account. If the TV breaks one month you use the current account to buy a new one. You feel this financially for perhaps one or two months (one or two additions of £1000 wages). But if you paid out of the savings account for the TV you'd be able to trace that deficit into the future.

i.e. the current account has a short memory, the savings account has a long memory. The current account is like younger ice, the savings account like older multi year ice. It may take years, but given time the savings account can come to dwarf the current account balance.

The volume loss has been almost totally coming from the loss of old ice, PIOMAS shows this, the submarine data does to.

Whilst each winter puts wages into the ice balance, as new ice. The old ice sticks around. Even though the deficit is small the multi year ice (savings account) has had more going out than in, so its previously massive balance has dwindled to very low levels today. Memory is another way of looking at the issue.


Dr. Zhang has added the 2012 PIOMAS thickness and ice concentration data files.


Werther, Chris, Crandles, and all,

I have updated the Arctic sea ice concentration and thickness maps imagery through January 20, and will update next weekend for January 25.

Here is what changed:

The UK Met/NCOF and MMAB SSMIS are updated:


The comparison of the U Bremen SSMIS and AMSR2 with the ifremer SSMIS reprocessed imagery:


The ifremer SSMIS runs show the fracturing and thinning of ice in the CAB given the wind patterns around the dominant high pressure.

Finally, I have matched the comparison of the HYCOM-CICE ice thickness data and the UK Met NCOF ice thickness modeling. The scale of the UK Met/NOCF has been changed to 0-5 meters of ice thickness to match the HYCOM-CICE, beginning from January 1, 2013.

The new UK Met ice thickness model, based upon CICE, begins its imagery on January 16, 2013 and is a dramatic change from the prior used LIM based model. the most significant change is that the polar "hole" in the LIM model is gone.

Also, the images are turned to roughly the same orientation.

The UK Met model is more detailed, and reflects much slimmer ice thickness than the HYCOM model.

The effects of wind and current on ice movement is more apparent in comparing day to day ice thickness changes.

Most of the Arctic is below 2 meters in lengthy strands, which seem to be shaped by the dominant wind patterns.

The only MYI over 5 meters thick is on the northeast Greenland coast near Station Nord. See:


Tor Bejnar

Whoops: I wrote about stacked FYI getting over 2 m think in Open Thread #1, which probably belongs here.

Bob Wallace

Chris, it's the use of a term that describes an animate feature to describe something happening in inanimate objects. It's a minor gripe on my part and it may already be in too wide use to reverse.

I'd rather we use other terms for physical conditions. Next thing we may be talking about ice's heart, soul or ego.... ;o)

" I don't want to patronise you "

A politely presented explanation is never patronizing.


Don't anthropomorphize inanimate objects, they hate it when you do that. ;o)

Jim Hunt

@Werther - I fear my initial excitement was misplaced. It seems Wipneus is in fact crunching the numbers output by a "professional" CMIP5 model.

@crandles - I'm afraid it's not obvious to me how to pressure the powers that be to fund the "professional modellers" so that they can attempt to catch up with reality. That's why I got excited at the thought of an open source "amateur" project to do so instead, unconstrained by Myles Allen et. al.! In this day and age my mobile phone has more number crunching power than my laptop. Unfortunately climate models seem largely to be written in Fortran rather than Java.

I certainly haven't seen any model runs from any source that reproduce what's happening at the moment, then follow it with a guaranteed happy ending.


Fram Strait transport graph updated with 2012 data:


Andy Lee Robinson

As promised, at last!

PIOMAS Arctic Sea Ice animated graph: http://www.youtube.com/watch?v=GetB-xs9D_A

800 frames, 30 mins per frame...


Projected September Sea Ice Disappearance using gridded exponential fit to PIOMAS was updated.



- PIOMAS 2012 data included
- improvements of the robustness of the fitting algorithm
- dropped 1978 PIOMAS gridded data file, it seems to be too much of an outlier in many respects

As noted before, uncertainties in extrapolations like these are large and grow rapidly the longer you take them in the future.


Calculating and analyzing the extent for the gridded exponential fit to the PIOMAS data has turned out not to be as straight forward as the volume. Let me explain with the graph:

Here I compare several possibilities with the NSIDC September data ( thick black line with ditto dots).

The red line is extent calculated the usual way, every grid cell with concentration over 15 % is included. Up to 2006 PIOMAS extent is about 15% higher than NSIDC, after 2007 the values are close. This can partly be explained by different grids, NSIDC uses 25x25 km squared, PIOMAS grid cells vary in size the smaller cells closer to Greenland.

Now my fits have only thickness, not concentration so I have to in- or exclude cells according to the thickness. The blue thick line includes cells with 15cm ice or more. The result is convincing, it lies even closer to the NSIDC data as before.
The same calculation, thickness over 15cm, used on the fitted data comes out larger. This is a consequence of the noise in the real data, cells can be excluded during low fluctuations where the smoothed value is over the cut-off value. The effect seems to be quite small in the last 4 years.
I have include different cut-off values to see how that effects the "zero ice" date.
As can be seen, probably less than a year.


The schweiger paper
PIOMAS appears to overestimate thin ice thickness and underestimate thick ice

Your calculation of extent is all about thin ice so the red line being above NSIDC extent seems to be as expected for the piomas bias.

The number of cells with thin ice may have increased over time so it might be expected that this gap would get larger, which it hasn't. I guess if it was that predictable then PIOMAS would have found better parameters to match the data more accurately.

Is this evidence for PIOMAS being more accurate recently than further ago? Only for extent? Or perhaps there is other better evidence?

(The paper (or at least the graphs as I haven't reread the paper recently) seems more aimed at finding thickness bias relative to actual thickness than the level of error over time. I suspect PIOMAS is more accurate now than in the past when volume was understated and extent a little overstated but this is little more than a guess.)


Intended to add : Great work both Andy and Wipneus.

Nightvid Cole

Chris Reynolds,

The paper I linked to on the previous page (Perovitch & Polashenski) implies that the albedo change happens from around June 1, although figure 2 shows a small drop in albedo at some sites from mid May. Prior to June 1 temperatures are below zero so liquid water on ice or as wet snow can't cause the albedo drop.

Not true necessarily - ice and snow may still melt due to direct solar heating even if the surface air temp. is slightly below freezing.

I suspect much of the reason for the PIOMAS volume anomaly being the most extreme around July 1st may be accounted for by ice outside the Arctic Ocean proper. With climate warming the ice in areas such as Kara Sea and Hudson Bay becomes thin enough to start transmitting appreciable amounts of light to the water below, earlier than it would have without that climate warming, thus increasing its thinning rate and volume loss over what would otherwise occur at that point in the season.

Once that thickness reaches zero, it cannot contribute anymore to the volume loss and as a result the anomaly goes back up again, toward zero.

Chris Reynolds

Thanks Nightvid Cole,

I have considered this, but in April NCEP/NCAR average surface temperature N of 70degN is about -14degC, in May it's about -5degC. So in the early part of the spring volume loss temperatures are (I suspect) so far below zero that insolation driven melt or sublimation isn't a major factor. It probably is a larger factor in more southerly locations as you state. After all the regional average covers a large difference in insolation, hence temperature.

Dave C

Arctic Sea Ice Volume by PIOMAS

I expanded Donald's numbers to include recoveries. A few things stick out to me.

-Recovery in winter is counter-cyclical. The years following big volume losses have tended to have larger gains.
-Melt does not seem to be counter-cyclical, but fairly steadily increasing.
-Recovery has been increasing, not decreasing. Volume losses are occurring because summer melt is increasing even faster.
-2007 and 2010 were anomalous years. Much of their volume loss occurred due to lack of recovery during the winter.
-It probably means nothing because the sample size is too small, but if we take this chart literally then every third year has a weak winter recovery. So if 2013 is going to follow the chart pattern then we would see an unusually weak winter Gain followed by a much lower Min. My guess is that the pattern will be broken this year and volume Min will just be similar to 2012.


>"-Recovery in winter is counter-cyclical."

Yes speed of growth is fast when thickness unusually thin. So perturbation to minimum level makes little difference to max volume.

Data is available easily enough to extend the sample backwards. The one in 3 years pattern does not continue and I think we can already see that recovery after 2012 will be around 17.7.


Extra parameters are probably a bad idea. It seemed as if it might be more physical to have a linear component as well as an exponential component.

The fit is bound to improve with 5 parameters rather than 3, and the fit isn't much better at all. Also seems more difficult to optimize the fit, but if anyone want to know the fit I ended up with was:

Lin slope -0.042957759
Constant 84.08769516
Exp P1 1.107519017
Exp P2 -1988.295189
Exp P3 16.5949083

Year Min Exponetial + linear fit
1979 16.855 15.28216596
1980 16.139 15.19759486
1981 12.589 15.10854954
1982 13.395 15.01454892
1983 15.077 14.91506023
1984 14.48 14.80949339
1985 14.475 14.69719489
1986 15.935 14.57744093
1987 15.176 14.44942992
1988 14.853 14.31227407
1989 14.649 14.16499014
1990 13.679 14.00648915
1991 13.476 13.83556507
1992 14.864 13.65088218
1993 12.234 13.45096115
1994 13.611 13.23416357
1995 11.185 12.99867491
1996 13.715 12.74248552
1997 13.178 12.46336967
1998 11.512 12.15886233
1999 10.916 11.82623344
2000 10.954 11.4624594
2001 12.179 11.0641915
2002 10.792 10.62772101
2003 10.24 10.14894042
2004 9.881 9.623300581
2005 9.159 9.045763241
2006 8.993 8.41074843
2007 6.458 7.712076227
2008 7.072 6.942902252
2009 6.893 6.095646223
2010 4.428 5.161912835
2011 4.017 4.132404126
2012 3.261 2.99682243
2013 ----- 1.743762881
2014 ----- 0.360594378
2015 ----- -1.166672267

This is more rapid a decline than just the exponential fit. Interesting to see the data perfers this more rapid than exponential decline side than the less rapid gompertz side of the exponential.


Seeing if the peaks and troughs of maximum volume can be predicted by Pacific and Atlantic water temperatures sounds like an interesting exercise after looking at


Betting pool on 2014 maximum volume anyone?

Tommi Kyntola

Dave C, how do you get "min similar to 2012"? Smaller melt? If so, why? Because the freeze doesn't seem to amount to that much higher this year. I'm only curious as my guess would be the exact opposite (even bigger melt) based on little more than a hunch from this fractured freeze and just continuation of recent years.

Jim Williams

crandles, I don't know about 2014 but I'll bet on "essentially 0" for the 2015 maximum volume. I think by then there'll be a little bit of fast ice and either some bergs or a lot of bergs.

I'm expecting the crash to be late this year from the current look of things. That means there'll still be enough cold left to do some freezing over 2013-2014.

And yes, I'm guessing. I'm pretty well convinced of a fast transition from seasonally free to annually free, but don't have a feel for when seasonally free becomes early enough in the season.

Dave C

Mostly a guess. Here's my reasoning.

Everyone knows that 07 and 10 were monster years. What people don't notice as much is that 06 and 09 were very poor years for volume melt. So both 07 and 10 benefited from a counter-cyclical reversion to the mean. 12 had a much higher melt than 06/09 so 2013 will not be benefiting from this effect.

Also, 07 had an extremely low winter recovery while 10 had a very low winter recovery. At current levels 13's winter recovery is running close to average. So it is looking unlikely that 13 will have the massive head start that the two recent big years did.

It's not conclusive, but just for the last 5 years Melt seems to have hit a slight plateau. Intuitively this makes sense since it seems that ice gets harder to melt the further north you go. I'm sure oceanic/atmospheric effects eventually will overcome the lack of sunlight but I would guess that melting might slow slightly because oceanic mixing needs time to overcome the relative lack of insolation.

At this point no one has much authority when it comes to arctic ice, but I am also reluctant to go against the large majority of scientists. I don't think there are very many scientists predicting that arctic ice will be virtually gone in 3 years. The volume trend has to reverse really soon for the scientific community to avoid being overwhelmingly wrong. Still, as of today it has not.

Right now that quoted statement does not have numerical evidence to back it up. So far the trends seem to predict an average volume year, which would result in a drop to about 2.5. So if pressed I guess that is my real prediction, although I will be hypersensitive to any signs of slowing.


Jim wrote
"I don't know about 2014 but I'll bet on "essentially 0" for the 2015 maximum volume."


What is "essentially zero"?

The exponential fit gives max volume fit for 2015 of 19.4 K Km^3 and I think somewhere around 19 K Km^3.

If you want to split the difference and bet on max volume 2015 being below 12 K Km^3, then I will take you on. How much do you want to bet? Would you be willing to do it via intrade (currently excludes USA residents) if such a contract was created?



the fits do not "know" about bifurcations (see e.g. the Eisenman paper). If the odds are reasonable, I would go with such a bet, since it seams so unlikely ;-)

Chris Reynolds

Dave C,

I generally agree with your findings, you'll find this blog post about 2010 interesting, if you've not already seen it.

I'm not convinced about next year seeing a further significant loss of volume below 2012 though.

It's true that we will see more thickening by April, the month of maximum. However I don't expect this to remove the current deficit, and the large expanse of thin ice seen in gridded PIOMAS for December.

Ice grows by basal accretion according to a 1/thickness relationship, so initial thickening is the fastest period of growth, with thickness of the order of 2m being equilibrium thickness for themodynamic growth. This initial thickening is very temperature dependent, NCEP/NCAR shows that Nov & December temperatures were no higher than the other post 2007 years (these have actually levelled recently), NCEP/NCAR - give time to process as it's a direct link. Whilst the average for the January so far remains about -20deg, significant areas are around 3 to 6 degC above the long term average.

I really think the ice is nearing critical thickness, where we'll see the volume losses increasing.

Jim Williams

I'm A U.S. Resident. I'm also poor. Besides, I'm making it a habit to lowball; which, I'll point out, worked out fine this year.


>"If the odds are reasonable"

Well quite, at what odds, strike volume, and amounts would you want to bet on:
a) more ice
b) less ice

Let see for me betting on more ice
Even money, 14K Km^3 per piomas 2015 daily minimum for fun money US$10-40
even money, 12 K Km^2 US$41-200
even money, 8 K Km^3 US$201-1000

For me betting on less ice (not that I expect to get takers at these figures):

Even money, 20K Km^3 per piomas 2015 daily minimum for fun money US$10-40
even money, 21 K Km^2 US$41-200
even money, 22 K Km^3 US$201-1000

So 14 to 20 K Km^3 is too close to what I expect to want to bet.

I am in UK and would prefer it done through intrade or in pounds sterling as currency though I am willing to consider it being denominated in another currency to be paid by paypal.

If there is a rush to take me on then I might try to get better term than these rough suggestions which should not be considered as firm offers. Mainly I would like to see what people would bet on and to expect that well someone has to make a move suggesting odds, strike volume, and amounts they are willing to bet first.


One thing I've learned is there have been multiple drivers of volume loss active at different time. Always present in the background is Arctic Amplification with raising temperatures. Until 2007 it was mainly export of MYI through Fram Strait. The ice got continuously younger and younger and thus doubled overall drift speed.

An unknown is the inflow of warm Atlantic water supporting bottom melt, if the halocline mixes. Barents Sea is now still ice free, which might be a sign.

In 2007 the Arctic Dipole demonstrated massive melting of MYI as it combined a static wind pattern with clear sky. A new chapter was started then with FYI as the dominant ice type, which absorbs even more heat through melting ponds and is very vulnerable to late season storms, we saw it last year.

An Arctic with predominant FYI becomes boring in terms of volume, because max height will be 2m or less. Thickness is then merely a function of month and latitude. Interestingly Chris has already found a max thickness of 3m in latest PIOMAS data.

This was the situation Nov 2007 (week 48):

This is where we have been last November, same week:

I would call this a complete new and unknown setup. Let's see how PIOMAS will model all that seasonal ice. Now more than 60% of the ice cover depends on the weather in Summer _and_ Winter and a whole bunch of new variables step in (e.g. accumulated snow load, SSW events)

To summarize, 2013 becomes exciting because the range of possible outcomes is vast and greater than in any year before. Considering 2012 as a normal year in terms of weather and seeing its impact, I don't want to watch an action replay of 2007.

The point is nobody can exclude an ice free Arctic this year.

The most positive result of such a catastrophe would be the GCM guys undergoing a reality check and recalling all 'mid century' projections.

Bob Wallace

Does anyone know what year to year salinity looks like?

Is there enough mixing of incoming fresh water due to more open water and storms to cause the FYI to have an increasing salt content and melt easier? Or would this be a weak forcing?

Bob Wallace

Sorry, I think I got that backwards. Saltier surface water slowing freezing.

Chris Reynolds


"Interestingly Chris has already found a max thickness of 3m in latest PIOMAS data."

I've merely used >3.5m as a final category that includes all thicker ice.

Actually the maximum thickness reported by grid boxes is much thicker. PS - all the following figures are for January - I'd forgotten that they're tabulated for each month down the page. 1980 was a notable year, 1 to 3 grid boxes showed thicknesses up to 8m, however the surrounding years had ice only up to about 7m thick. As these are averages for a grid box, some sub grid ice will have been thicker.

However once volume comes into the equation the volume of these thick grid boxes becomes vanishingly small. 3.5m was chosen to bring out the recent changes and behaviour of bulk volume.

With regards those very thick grid boxes. In the 2000s 2008 was the thickest year, with 1179 grid boxes over 3.5m thick, single digit counts of boxes up to 6.35m thick. But 14036 grid boxes of thickness 0.05 to 3.5m thick. The greatest thickness in 2011 was 3.6m, with 2 grid boxes reporting that thick.

I'm running the macro again to include 2012.

Chris Reynolds

Ahh, I've just read "latest PIOMAS data". I'll have a look at that once the macro is complete. Could even post the data online.


Jim Hunt:

NCOF ice thickness statement source request: Jim, I am sorry, but I cannot reveal that - I gave my word.

Chris Reynolds: I sent a note to NCOF in regard to the PIOMAS gridded anaylsis you have done. Also, I have added mention of your PIOMAS work/recent post in my NCOF ice thickness discussion. I hope you do not mind.

Also, Chris, may I add a couple of your modeled images to my sea ice pages - with full credit to you?

Arcticio, is there a link to the MYI imagery that you shared in your prior post? I am thinking of adding an MYI page to the sea ice concentration and thickness pages.


I have updated the sea ice concentration and thickness through January 25 on my page:


One note: the iFremer iamgery is not updated yet. Also, the U Bremen AMSR2 imagery has been removed from the main site except Jan 24 and 25.


The METOP 2/B IASI CH4 imagery has been updated through 012613 pm.

There are high methane concentrations over the Norwegian, Barents and Kara Seas for the last few weeks and several days, as high as 2140 PPBv.


Rob Dekker

Jim Williams, crandles,
Could it be that Jim in his January 26, 2013 at 17:47 post :

but I'll bet on "essentially 0" for the 2015 maximum volume.

intended to say minimum and
crandles in his January 26, 2013 at 23:55 post :
Even money, 14K Km^3 per piomas 2015 daily minimum

intended to say maximum ?
That would make a lot more sense, no ?
Forgive me if I am messing up an honest betting proposal :o)

Unrelated : Chris Reynolds, Wipneus, would it help if I send you the latest PIOMAS grid cell area data (obtained from taking the line-integral of PIOMAS grid points) that I calculated last year ?


Oops yes I did intend to say maximum. (I did wonder whether Jim meant minimum but instead of clarifying, I confused it further by my mistake.)

Jim Hunt

A4R - I'm not suggesting that you break any confidences, whether in public or in private.

I am however suggesting that I suspect I'm not the only one who finds it somewhat baffling in all the circumstances that the comment box on your site still tells me "You have no permission to add comments" and your contact details over there still say "you can comment at Neven Acropolis' Arctic Sea Ice blog where I lurk often".

I'll pursue my line of enquiry via an alternative route.

Jim Williams

I intended maximum, though I admit to being extremely aggressive. I do expect a rapid progression from ice free all Summer to ice free all year -- on the order of the following Winter to the Winter thereafter. I'm more unclear about when it goes from ice free at the end of Summer to ice free near the beginning of Summer -- though I expect that to be rather soon.

I think that once the cap is opened up one time the winds will quickly overwhelm the freshwater lens and the freeze thaw cycle will collapse.


Hi Jim Hunt,

Thanks for understanding on the sources.

Also, while I had added the comments box on my main page, the permissions to the page were still perhaps too restricted. I have changed the page permissions setting so hopefully people can comment there.

Given time constraints and the number of sites/pages I maintain, I restrict how many people can comment on and direct them here because this is the blog I check regularly.

(Neven, this blog is such a rich source of "all things Arctic", I want them to visit this site).

Chris Reynolds


Feel free to use images etc, they are in the public domain, and I'm not possessive about what I stumble upon. But read my note to Rob below - the volume data I use has a small error due (~3%) to the difficulties calculating area.


Thanks but I have the improved area grid you did, thanks for your work on that. The issue is that Wipneus sent me a breakdown by volume using a different method of area calculation. When I tallied it up and compared to monthly PIOMAS derived from the main PIOMAS series I found it was much closer than the result using your areas - from memory errors of less than 1%. It seems that Wipneus has worked out how to use the vector grid (grid.dat.pop), whereas we were only using the scalar grid (grid.dat). I've tried on and off to use the scalar grid to improve on your grid areas derived from that grid. Yesterday I realised that Wipneus was using the vector grid and tried to get my head around it. As I concluded back in June, it's really too much effort for me.

I do this as a hobby for enjoyment, and last week wasn't at all enjoyable at all! So stuff it, I'll just live with the error, which is only around 3%, given the stated uncertainties of PIOMAS (Schweiger et al 2011) a 3% error isn't worth stressing myself out over. I often have to produce results at work that have stated uncertainties of as much as 3%, the question isn't 'is it perfect enough' but 'is it fit for purpose'.

The hard work you put into this matter is good enough for my purposes. As I discovered last week the best I could achieve was an RMS error of about 5%, with larger range than your area calculations. So once again - I am in your debt.


Chris, I will put the grid area table on the net tomorrow. There is no way to get permission to get to the PC tonight
PS I do not think grid.dat.pop is 100% for vectors, just used to dump some data that was found to be missing.
PPS You are smart enough to learn programming. It is a shame it takes you so much time, to what can be done in two lines of code.

Chris Reynolds


Thanks, now I'm in your debt too! But please don't rush on my account. Get well first!

I used to programme DSP on 68000 machine code, I used to programme in C and C++. But as I've got older I've gotten rusty, and I've been realising in the last week that I've never fully recovered from my illness in the autumn..


Friends, I can do some coding if that would help get the word out that we have a problem.



A4R, you'll find all info here :


Rob Dekker

Chris Reynolds, you hold no debt to anyone. We are all trying to make sense of what is happening in the Arctic, and how the PIOMAS model can augment that understanding.

Wipneus, I'm looking forward to your PIOMAS grid cell area table.

I'd be more than happy to throw my table away, since I never figure out why my grid cell area calculations derived from the 'grid.dat' grid cell area corner points differed (1-3 %) from PIOMAS' own grid cell area assessment.



I have written it as csv file. 360 rows , 120 columns. Loads into a spreadsheet fine here.
Just mention it if the format is not covenient.


Rob: I am just guessing, did you realize that the cell edges are not "great circles", iow not the shortest paths between the corners?



Thanks for the info, you have a great website!


Chris Reynolds

Thanks Wipneus,

I'll convert to single precision binary and re run the thickness/volume breakdowns. Then post a csv format of the volume breakdown on a subpage of my blog. That should make it easy for anyone programming or spreadsheeting to access the data. It'll be done sometime in the next two days - work allowing.


This just in:

"Satellite records show a decline in ice extent over more than three decades, with a record minimum in September 2012. Results from the Pan-Arctic Ice-Ocean Modelling and Assimilation system (PIOMAS) suggest that the decline in extent has been accompanied by a decline in volume, but this has not been confirmed by data. Using new data from the ESA CryoSat-2 (CS-2) mission, validated with in-situ data, we generate estimates of ice volume for the winters of 2010/11 and 2011/12. We compare these data with current estimates from PIOMAS and earlier (2003-8) estimates from the NASA ICESat mission. Between the ICESat and CryoSat-2 periods the autumn volume declined by 4291 km3 and the winter volume by 1479 km3. This exceeds the decline in ice volume in the central Arctic from the PIOMAS model of 2644 km3 in the autumn, but is less than the 2091 km3 in winter, between the two time periods."



Thanks, Boa05att. That's the paper the late Dr. Seymour Laxon worked on.

Rob Dekker


Thank you so much for that PIOMAS grid area table. That's great work !

I ran a sanity check by calculating monthly volume using your table with the PIOMAS heff files, and found that your table results in only a 0.4-0.7 % underestimate of monthly volume (compared to the PIOMAS daily.1979.2012.Current.v2.dat results).

That is much better than the 2 % underestimate that I get with my grid area table.

I will still investigate where in the grid my table ended up most inaccurate (and find out why). It should have made no difference with method or grid source file was used. The remaining 0.4-0.7 % volume underestimate in Wipneus' table is negligent and may very well come from compounding uncertainties in floating point numbers through all the programs that the numbers went through, but I'll see if I can track down the source of that inaccuracy.
It would have been so much easier if the PIOMAS team has simply posted the cell area table :o|

So, Chris, I officially would like to declare Wipneus' table superior to mine, so please discard my table.
For your convenience, I converted Wipneus 120x360 matrix into the PIOMAS 360x120 float matrix used in the heff files and the grid area file that you have been using. That way you can simply replace the grid file that I sent you last year.

Thanks guys ! Great progress !

Rob Dekker

Wipneus said :

I am just guessing, did you realize that the cell edges are not "great circles", iow not the shortest paths between the corners?

Yes. I first used a 'planar' method, but when Chris Reynolds found the 2-3 % error in volume that caused, I searched for a spherical polygon solution. I found (and implemented) this really cool algorithm that calculates area-of-polygon-on-a-sphere :


This algorithm uses great circles as polygon edges, is accurate and general for any polygon on a sphere, and is easy to program.
Incidentally, the difference with a prior 'planar' version I used was only 0.2 % or so, and thus could not explain the 2-3 % error.

It's still a mystery to me, but with your table as reference, I feel confident that I'll find out where the inaccuracy came from.

Rob Dekker

Maybe I misunderstood you, Wipneus. Did you deliberately say not great circles, or was that a typo ? If not great circles, then what are the cell edges ?


NOT great circles indeed.

You can get in idea of the grid from Smith ans Kortas 1995, " Curvilinear Coordinates for Global Ocean Model". It is available from the Los Alamos national laboratory. Go to the technical library and search for the title.

Nightvid Cole


Where did you find that map of November age of ice? I've been looking everywhere to no avail!

Rob Dekker

Ah ! Now I understand. Yes, the PIOMAS curvilinear coordinate system creates cells that are not aligned along great circles.

However, I calculate area for each cell (polygon) separately, so as to be independent of the exact grid cell alignment configuration. Incidentally, this (working with individual line segments of individual cells) also means that it should not matter if we use the scalar grid.dat file or the vector grid.dat.pop file.

In my first analysis of where grid cell area calculations may differ, I looked at three effects :
- Curvature of Earth over a grid cell
- Choice of radius of planet Earth
- Eccentricity of planet Earth

The first effect I analyzed in detail (by going from a planar cell algorithm to the polygon-on-a-sphere algorithm) and I found that it adds about 0.2 % to grid cell areas. Did you take this effect into consideration in the vector field calculations ? If not, it may explain at least a part of the already small remaining difference between volume derived from your area numbers and the reported PIOMAS volume numbers.

For the second effect, I found that I chose a radius smaller than the one that PIOMAS team uses (I used 6353.0 km while the PIOMAS team seems to use 6378.273 km (from their LLtoXY.pro program). This explained 1 % of the 2-3 % error I made.
Which radius did you choose ?

The third effect I did not include at all, and it may be that that is the explanation to the remaining difference.

For example, taking your area table as a reference, I found that in my (scalar) field calculation, I overestimate the area of 'inner' (closer to the Greenland center) cells and underestimate the area of the 'outer' cells, which suggests that IF your numbers have eccentricity built-in, then indeed eccentricity of planet Earth is important, and cannot be discarded as I did.

I do not know if the vector field that you used (grid.dat.pop) has eccentricity inherently included or not. Could you please comment ?


I follow your conversation on these statistic calculations with interest (though without the mathematical background). It's good to see how the blog helps each other forward.

Is there any chance these grid cells can be presented cartographical? When I'm done with the GIS, I'd like to put that in CAD. Just to be able to compare PIOMASS to MODIS on an enhanced scale.


Rob, I used length x width = area. The grid.dat.pop gives the sizes of the cell edges. I think the "vector data" is not the most accurate description. This is academic software, true documentation can sometimes only be found in the program sources.

When applied to a known grid, the lat.lon system that we normaly use, this approach (length x widt) leads to much smaller erors than the 0.2%. So I doubt we can improve.



All data is laid out in 360x120 tables, the grid cells.
To map the cells there are the tables clon and clat with the lon and lat coordinates of the lower-left corner of each cell.
Ice data (thickness,concentration) comes in a 360x120 table per month.

How would you need to have that data organized?


Wipneus, hi,
I think I'm beginning to understand part of the conversation. First, I assume the grid cells measure 360x120 km1. But, second, as the discussion mentioned calcs on spheres/circles, the grids are based on the parallels/meridionals (so they're not 43200 km2 square).
To adapt to the archaïc fashion I calibrated to a plane in CAD, I suppose I could start at the NP(90N 0E), plane out and array the resulting square.
A crude check can be made through the MODIS tile structure and the coastlines.

Of course, I could 'raster image' the map you produced in CAD, and use that to compare to MODIS. How did your program modulate that out of the tables? Were the data maybe derived from a GIS (geographic info system, not Greenland Ice Sheet...) program?

But, second, as the discussion mentioned calcs on spheres/circles, the grids are based on the parallels/meridionals (so they're not 43200 km2 square).

Kind of. Think of it as the traditional lon/lat grid but bended and distorted to make the North Pole lie in the centre of Greenland (where is no ocean or sea ice). There are some nice graphs in the Zhang and Rothrock 2003 paper that show this: http://psc.apl.washington.edu/zhang/IDAO/ZhangModelingGlobalIce.pdf

To adapt to the archaïc fashion I calibrated to a plane in CAD, I suppose I could start at the NP(90N 0E), plane out and array the resulting square.

The natural way to process such data is to start with i=1,j=1:
Cell corners longitude are clon[i,j] , clon[i,j+1] , clon [i+1,j+1] and clon[i+1,j]
Cell corners latitude are clat[i,j] , clat[i,j+1] , clat [i+1,j+1] and clat[i+1,j]

Map the lon's and the lat's using some carthografic projection to your drawing sheet.

The proceed with next air of i and j, until all 360x120 cells are done.

How did your program modulate that out of the tables? Were the data maybe derived from a GIS (geographic info system, not Greenland Ice Sheet...) program?

It is one line in "R" :

mapproject( clon, clat, proj="perspective",parameters=3,orient=c(88,-40,0))

With it I specify projection, in this case "perspectve", but there are numerous other
choices like mercator, aequidistant etc.

Parameter 3 means the perspective origin is 3 earth radia away, and 88,-40 is the lat/lon of the origin.


Perhaps this might help understand the piomas grid:



Thanks Wipneus, Crandles,

...for picking up my feet and run. I'll think twice before entering on this one.
The graph you show, Crandles, reminds me of a worm-hole I'd have to enter, but reversely consuming time instead of erasing it.
The projection is related to the satellite orbit, isn't it?


The projection is related to the satellite orbit, isn't it?

No it is related to ocean modelling where grids like this are common. It avoid a singularity in the computations (think 0 by 0 division) at a most important point, the North Pole.


Of course...PIOMAS is based on modelling, not satellite data...thanks for reminding me Wipneus!


Probably not very interesting but since I have done it, I may as well share.

PIOMAS Volume gain by month:


The gain in volume in each month of the freeze season do not appear to be changing much and no nonlinear trends are apparent.

Jan, Feb and March are changing least.
Dec gain is increasing modestly
Oct gain is increasing quite a bit more
Nov gain is increasing most.

Fairly boring result?

Given that there are competing effects:
1. Extra heat in the water to be lost that could cause delay before freeze up begins.
2. Lower starting volume could cause a faster rate of gain in volume.

Perhaps it is rather surprising?

Not sure if there is any significance to Nov increasing more than the two adjacent months. Perhaps there is a suggestion that the response to lower minimum volumes is faster growth in Oct to Dec so even if there is a lot more heat in the water at the end of the melt season, there is still plenty of time for the ice to get up towards thermodynamic equilibrium thickness.

Perhaps the small linear tends suggest that although the minimums are much lower, at the start of the freeze season the volume is not much further below the thermodynamic equilibrium volume than several years ago because the thermodynamic equilibrium volume is also decreasing rapidly.

The increase in the amount below the thermodynamic equilibrium volume is small therefore perhaps the non linear effects cannot be distinguished from noise from a linear trend.

I don't know if breaking it down by region or latitude band might reveal anything.


Crandles, does the CryoSat-2 data as reported in Laxon et al. (2013; linked by Boa05att in this comment) explain anything (can't wrap my head around it at the moment)?

"Between the ICESat and CryoSat-2 periods the autumn volume declined by 4291 km3 and the winter volume by 1479 km3. This exceeds the decline in ice volume in the central Arctic from the PIOMAS model of 2644 km3 in the autumn, but is less than the 2091 km3 in winter, between the two time periods."


It could well be explaining that I am expecting too much of the data because I am looking for subtle changes that are almost bound to be hidden by the noise.

Oh well, I suppose that without looking I wouldn't be sure the changes would be too subtle to spot.

Tor Bejnar

I'm curious about the Central Arctic Basin - how its sea ice volume growth/shrinking has been changing, per the PIOMAS model. Unless all that ice flushes out Fram Strait or is moved towards Siberia (to melt there), the "last stand" will be in the CAB.

Thanks for all your work on this.

That quote from Laxon, et. al. (2013) is a reminder that each data system we look at is useful for internal comparison purposes and not as absolutely correct numbers.


Here this PIOMAS thickness change map complements nicely the ice age images I've posted above.

Now that the Beaufort Sea is mainly FYI it will be interesting to see how the melting develops once started in the McKenzie Delta. And yes, PIOMAS models up to 4 meters loss North of the Archipelago and Greenland after 2007.

Rob Dekker


The Central Arctic Basin, according to the PIOMAS model, has been loosing very significant ice volume over time.

Most of the really thick MYI ice is gone, and is replaced by 1st or 2nd year ice which is much thinner.
PIOMAS shows an 80 % reduction in September ice volume over the past 3 decades, and since most ice remaining in September is in the CAB, that pretty much shows how much of this "last stand" is left over.

Chris Reynolds has a pretty good overview of the devastation in the CAB using PIOMAS model :

Chris Reynolds


Re autumn:

I'll be blogging on this data, but you'll find it helpful, I think.

Here are correlations between area at min and date of reaching various threshold areas.
Stat sig @ 95% is over 0.31.

i.e. for 10M it's the date 10M km^2 is reached versus the area at minimum (both detrended using differences).

Here are scatters between area at min and date of reaching thresholds (not detrended).
10M km^2
9M km^2
8M km^2
7M km^2
6M km^2

These are for area, so will precede the thickening of volume. Ice grows rapidly but is initially thin. Between 8 and 9M km^2 the ice fills the Arctic and the ice edge moves out into areas that have long been totally seasonal ice. Hence the break in correlations between 8 and 9M km^2 and the shift in behaviours since then.

Regards November volume, the ice edge leaves the Arctic in that month (8 to 9Mkm^2), I presume that thin ice area growth adds little to volume, while wide area thickening within the Arctic is rapid (thin ice responds more quickly) and tapers off during the lead up to maximum (visual examination of PIOMAS thickness plots).

Chris Reynolds

Sorry, should have been more clear re the correlations.

They're based on anomalies of date - i.e. deviation from the average for the whole series. So for example a later attainment of 7Mkm^2 will produce a positive anomaly. Therefore those negative correlations correspond to - The lower the sea ice area at minimum, the later the refreeze, although the scatter plots suggest that this is a non linear process.

Rob Dekker

Thanks for posting that volume gain by month graph.
I found that one very interesting. May mean good news or bad news.

On the one hand, it seems that indeed summer volume loss during summer causes increased ice growth in Oct Nov Dec.
Beyond that, we end up in noise.
This suggests that the Arctic is indeed responding with increased ice growth, which is a negative feedback to summer ice melt.

On the other hand, one may wonder why it took 80 % summer ice loss for autumn ice growth to increase just slightly above the noise.
That does not create much confidence that the negative feedback of thinner ice growing faster will be able to compensate for an increasingly more positive summer albedo feedback created by reduced ice extent.


Thanks for all the replies. All very interesting.

Arcticio, great map. :)

Can I just clarify, does 2012-11 delta 2007-11 mean it is average thickness for recent year (2011/12) compared to 2007/8?

There appear to be areas of thickening in the middle. Is this just because 2007 was an exceptional year?

I don't think I have really decided what I want to see for thickness maps. Perhaps trend ie (April 2012 thickness minus April 2002 thickness)/10 and anomalies from trend ie ((April 2012 thickness minus April 2011) minus trend change).

Chris, interesting correlations and scatter graphs. As my volume gain by month graph shows little response to lower minimums, it isn't greatly surprising that lower minimum means later reaching a fixed area size. You do see a non-linear effect in your scatter plots; I think that is consistent with a slight increase in volume gain in response to lower minimum.

I think I still expect Oct gain to be driven by heat in water delaying start of the freeze while November and subsequent months to be driven by how low the volume is compared to a thermodynamic equilibrium thickness derived volume. March volume gain is smaller than Feb volume gain which is in turn st Jan st Dec which is larger than Nov and that is larger than Oct.

I wonder if there is anything to tease out of the ratio of sizes of Jan Feb Mar volume gains to try to reconstruct a measure of thermodynamic equilibrium thickness derived volume and see how that is changing over time.


Mar gain has changed from 73.3% of Feb gain to 75.2%. Feb gain has changed from 72.2% of Jan gain to 72.8%.

Taking that and extrapolating as a series would end with a huge volume that would be highly error prone so that is a bad idea.

In short I am not finding anything to improve on follow previous years Jan, Feb, Mar & Apr to estimate maximum volume nor finding any hint of what is driving maximum volumes downwards.


Crandles, it displays the difference between November 2012 and November 2007. The patch with a positive delta measures between 0cm and 50cm I would explain with the higher SST in 2007, and the ones colored in light blue, possibly represent some scattered floes having survived the great storm in 2012.

Do you have a formula for thickness trend over latitude, longitude?

FYI thickness in March surely changed, but stays below equilibrium anyway. However, snow load plays a role and I would suspect the more moisture in the Arctic the more snow covers the ice, I don't know how to properly attribute changes in FYI thickness to either snow or available heat. It seams snow is the most nasty unknown appearing everywhere when it comes to sea ice thickness. The GFS model has a variable (analysis) with accumulated precipitation, possibly helpful.


Thanks Arcticio, I should have realised 11 was Nov not the year.

>Do you have a formula for thickness trend over latitude, longitude?

Looking at Chris Reynolds thickness plots, I see a disc with roughly linear declines in thicknesses towards edges other than Greenland and CAA. I haven't got formulas for this thickness profile shape.

Is that what you are asking or is it about what I think I want to see? If I want to see it I really ought to plot it myself. I was just suggesting calculating average change over last 10 year and was wrongly abbreviating that to 'trend'.

i.e. just (April 2012 thickness minus April 2002 thickness)/10

for each cell and plot those values on a map as different colours for different values.

Wipneus' fitting exponential trends to each cell is beyond my programming ability. I want to wish him well and do not want to appear impatient for more of his wonderful graphs.

Don't worry about it. Not sure I even know what I would want to look for in such graphs and Wipneus is likely to present it better without me wittering on. I should have realized your map was November instead of adding comments trying to understand it.

Chris Reynolds

I've put a page up with the PIOMAS volume broken down by thickness. Check my blog, top right panel, link entitled "PIOMAS volume breakdown by grid cell thickness."


"Do you have a formula for thickness trend over latitude, longitude?"

Not sure what you mean by this. One of the jobs on my list is to add to the new area mask and the existing lat/lon masks, a mask giving sea ice region for each grid cell. I need to do that to look at open water formation efficiency.* However dependent on what you're thinking a quick method would be to trace along lines of PIOMAS longitude and produce transects of thickness.

*Actually a quick way would be to select grid cells to segment. e.g 90 to 200 lon by 65 and above would segment out the region enclosing the most aggressive sea ice loss...


Crandles, don't censor yourself. It just wasn't clear to me, whether you're looking for the month or the region most off the trend.


I guess I was mainly wondering about regions where 'trend' is high and low and regions that are accelerating downwards versus and regions where the trend is rather linear. I am interested in April mainly at the moment as we already have Wipneus' nice time to zero trend for September.

Looking at gains split between months doesn't look like it offers much to me (so I am thinking probably leave possibility that it gets more interesting when split into regions until later).


First year-round ice free region? I think Barents is close. But projecting PIOMAS would assume a static ice sheet without any drift. Isn't Wipneus' chart highly optimistic regarding Fram Strait?

The comments to this entry are closed.