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"Arctic sea ice extent for December 2012 remained far below average, driven by anomalously low ice conditions in the Kara, Barents, and Labrador seas.

The average sea ice extent for December 2012 was 12.20 million square kilometers (4.71 million square miles). This is 1.16 million square kilometers (448,000 square miles) below the 1979 to 2000 average for the month, and is the second-lowest December extent in the satellite record."


Andy Lee Robinson

Great, now that 2012's data is complete, I'll make another animated graph.

Ac A

And do not forget those cracks in winter Arctic ice: http://3.bp.blogspot.com/-SdFxR-nRppE/UOoTroAZh0I/AAAAAAAAAfU/DIrlHKGj20k/s1600/hrpt_dfo_ir_100.jpg

Vadim Frolov

Two cents for winter weirdness: heavy rains lashing Israel.

Possibly, it comes in the same trend as cold weather in Russia, warm weather in Europe, e.t.c.

Jim Williams

There might be time, but it doesn't look like there's a whole lot of cold to work with. Seems that this year the polar vortex fell into Siberia and China.

Tim D

"the error bar for the 2013 minimum goes below zero, ....but it's interesting to see that it's possible from a statistical point of view."

Not really. From a statistical point of view it suggests that using a real numbered estimation is becoming inappropriate, and using a positive distribution would be better.

I think that the 2013 minimum estimate is too low. We have had an extreme value this year and regression to the mean would suggest that it should be quite close to this years minimum. The same graph shows this effect the last 2 years following a large drop in sea ice (2008 and 2011).


Why noone discuss strange antarctic wheather? It is weird enouph also. There is big positive ice anomaly all last year, even now, in summer it is almost at record high values http://arctic.atmos.uiuc.edu/cryosphere/IMAGES/seaice.recent.antarctic.png Also it is cold there last monthes http://www.esrl.noaa.gov/psd/map/images/fnl/sfctmpmer_30b.fnl.html Any versions why?


Damn points at the end of links. How to edit posts here?

[Fixed the links, N.]

Ghoti Of Lod

Tim D:
"We have had an extreme value this year and regression to the mean would suggest that it should be quite close to this years minimum."

That's a really good point. When the variation is an oscillation around a stable mean an extreme low would be more likely to be followed by a value closer to the mean.

Looking at the PIOMAS anomaly trend suggests instead that the we aren't looking at variation around a stable mean but at a steadily declining mean. If there is regression to the mean it is to an ever decreasing one.


Antarctic cold. Ozone compared to base period?

Positive ice anomaly - there was a recent paper by Holland and Kwok suggesting stronger winds.

The bunny seems to be suggesting this is also linked to ozone


Tim, Ghoti,

You can also calculate a negative one year lag auto-correlation. I think some papers have noted it is significant.


I would find the "regression to the mean" point to be more useful if I thought we knew what "the mean" means! As Ghoti Of Lod points out, when there is reason to believe that data are distributed randomly about a stable mean, "regression to the mean" is expected after a year like 2012. We don't have a stable mean. For all we know, 2008 was anamalously high.



stronger winds in summer must cause negative anomaly, but it is positive all the year round. And there is less ozone hole this year than before.


I agree Lavevn, wierd weather on Antactica should not go unnoticed like it often does. And it is not just the cold that is gripping the continent, take a look at the temperatures in the polynia outside of West-Antarctica http://www.dmi.dk/dmi/en/index/hav/sst.htm
Surface temperatures that are 4 degrees celsius above average. That can't be very healthy, can it?


4C above average but SST looks close to 0C. If it is normally ice covered and averages -4C when ice covered and the ice is in slightly different places than usual then won't it be normal for polynias to look 4C above average?

No negative anomalies for over a year - yes it does look like first time that has happened.

With a slight upward trend we are going to get records like that from time to time. No year with all negative anomalies early in record either so yes somewhat unusual. A peculiarity of lack of noise in the noise perhaps?

I think GHGs are causing a different seasonal pattern than the base period so it is now normal to be colder than normal this time of year and warmer than normal ~Jul-Oct
180 day average warm
90 day average cold

Aaron Lewis

In a time of global warming, we have a non-linear feedback system (climate) that is out of control.

Nonlinar feedback systems that go out of control regress AWAY from previous states.

This system is nonlinear, and has discontinuous processes such as melting ice and so it can regress away from previous states suddenly. This makes it very hard to (statistically) separate actual system behaviors from noise. In fact, much of what a statistician would call "noise" is internal work (weather) as the system comes to local or temporary equilibrium. These local and temporary equilibriums propagate through the system and ultimately drive other feedback loops that push the system away from its previous states.

90% of the heat from AGW goes into the oceans, and mostly we measure global warming with air temperatures. Our big temperature regulators are the heat of fusion and heat of vaporization of water. Air temps are a poor indicator of these effects.

Aaron Lewis

PIOMAS did not give a hint of current behavior in the Arctic Basin see http://www.iup.uni-bremen.de:8084/ssmis/arctic_SSMIS_nic.png .

We can be pretty sure that the Barents, Kara, Laptev, ESS, and Chukchi seas will melt next summer. This January breakup of the Arctic Basin makes it very likely that everything will melt. Sorry!

R. Gates

Jim Williams said:

"There might be time, but it doesn't look like there's a whole lot of cold to work with. Seems that this year the polar vortex fell into Siberia and China."


The Arctic vortex indeed is very disrupted. We had a Sudden Stratopsheric warming event beginning about a week ago, and saw both the Arctic stratosphere warm, along with the reversal of winds as the vortex began to break apart:



An overview of the NH from ECMWF shows the story very well. Warmer temps over the N. pole proper, with cold air masses being pushed toward each side of the N. Hemisphere:


The vortex has just sort of fallen apart as is typical with a SSW event. The vortex may reform some, but certainly not as strongly before the springtime weather patterns begin to take over.

The current warmth in the SH, especially over Australia can be traced back to an SSW event that occurred over the S. Pole in mid-July and slowly worked its way down to the troposphere along with the associated higher pressure anomaly.

R. Gates

Aaron Lewis said:

"90% of the heat from AGW goes into the oceans, and mostly we measure global warming with air temperatures. Our big temperature regulators are the heat of fusion and heat of vaporization of water. Air temps are a poor indicator of these effects."

Good reminder Aaron. Too bad certain so-called AGW skeptics can't grasp this basic physical fact.

R. Gates

Doomcomesoon said:

"I agree Lavevn, wierd weather on Antactica should not go unnoticed like it often does."


The story of Antarctica this year is the SSW event that took place back in mid-July, during the middle of the Antarctic winter:


You'll notice that warming event (caused by a plantary wave breaking at the tropopause in the SH)trickled all the way down (along with the associated shift in winds and higher pressure) over the following months to cause a warming troposphere anomaly which continued into the current SH summer and is one of the reason for the anomalous warmth in Australia right now. This same high pressure anomaly that started with the SSW event in mid-July:


Caused a net outflow of wind from the center of Antarctica outward, toward the sea ice edge. This colder outflow helped to cause the growth of sea ice. Thus, several things can be related directly to the SH SSW event of mid-July:

1) Anomalous warmth in the stratosphere that slowly moved down into the troposphere over a period of months causing a anomalous surface warmth in the SH.
2) Higher pressure over Antarctica causing at net outflow of winds toward the sea ice edge leading to more sea ice growth

R. Gates

Just to add, the extreme high pressure anomaly that began last July with the SSW event over Antarctica, and worked it's way down to the troposphere over the ensuing months continues:


In looking back at many decades of data, I find it hard to see any similarly long-standing and intense period of high-pressure anomaly over the Southern Hemisphere.

dominik lenné

shows consistently warmer winters the last years which cost us 5 - 10% freeze rate.

Protege Cuajimalpa

News from Nasa on the topic of Sea Ice Volume and PIOMAS:
InSIE, it seems important:
"The September mean ice extent for the corrected model were slightly closer to the actual result than the control forecast run, but both were fairly far off from the actual record minimum. This may have been due to unusual weather over the summer, including a large Arctic storm in August, or to deficiencies in the model simulation of the new very thin ice conditions of the Arctic. Lindsay said winds have a bigger impact on the thinner ice of recent years than on thick ice. It may be possible to redo this experiment, using this summer's atmospheric conditions in the forecasts. "This would tell us the impact of the observations for the weather we actually experienced," said Lindsay."


I'm a macro kind of guy, which is a long way of writing lazy.
Can someone with more patience explain whether the SSW event in the NH now will also ripple through and cause a July heat wave in corresponding latitudes. Are South Africa and Argentina also experiencing the ripple of the SH SSW in the same manner as Oz now?


Glenn Tamblyn

We are hoping to do a post at SkepticalScience in the next few weeks about PIOMAS and the trends. If Wipneus is out there, is there any chance we could get the eqns values for the exponential trends for each month that you put into your graph - notjust the Sept values.

Hopefully we will produce an animated version of that as part of the post - with attribution to you of course.

With so much of the world thinking only about the area trends - including the IPCC seemingly - the more we can highlight the volume trends the better.




v(t) ~ v0*(1-e^((t-t0)/tau)))

v=volume [1000 km3]
t=time [years CE]

regression parameters:

v0 t0 tau
Jan 26.68750 2023.452 13.05362
Feb 29.27269 2024.912 12.93910
Mar 31.35182 2026.857 13.60483
Apr 32.46496 2027.741 14.01682
May 31.49572 2024.364 11.95467
Jun 28.47878 2020.459 10.64559
Jul 22.19606 2017.448 10.55969
Aug 17.38218 2015.904 11.35588
Sep 16.00322 2015.140 11.19265
Oct 17.36760 2015.908 11.41174
Nov 19.94483 2018.682 11.97795
Dec 23.10602 2021.147 12.34412

v0 : volume at the start
t0 : time the curve crosses the x-axis
tau: time constant

You can contact me "wipneus" on "freenet.de"

Glenn Tamblyn


Thank you. It might be a week or 2 before I can get time to work on this but I will keep you posted and look for any feedback you might have.



Dear Wipneus and Glenn,

since it is not very convincing to present a fit without a reason I would like you to consider a very simple linear rate equation for albedo-feedback as possible basis for the function:
If loss-rate is proportional to negative volume (the more open sea - the more melt), than integration leads to above exponential function. Konstant V0 is then the starting volume and the last year is the fitting parameter.
If you allready did mind such a reason I am sorry for disturbing.
Best regards,


I suggest that to get a physical basis you need to model freeze volume and melt volume separately.

For melt volume I get:
-0.21*Max vol+22.78+correct max vol to trend max vol

This seems to work well.

For freeze volume, possible something like
if you think the level of the minimum is relevant.

I am not sure that I do think that, so an alternative is to use an exponential extrapolation of the maximum. The reason I would give for the downward acceleration in the maximum despite GHG levels being rather linear would be thermal inertia of oceans meaning that upward heat flux would be expected to accelerate upwards. That is difficult to quantify unless you have some suitable data.

Integrating such formula leaves me with the impression that a physically based extrapolation is going to have at least a linear component and constant as well as an exponential part. Perhaps there would even be two exponential components and a quadratic.

More free parameters just for the sake of a better fit is usually a bad idea. Doing so to get the extrapolation physically based may be OK if there aren't too many good fits with future extrapolations varying markedly.


Sorry but I'm not a believer in Piomas for end-game prediction. First, it was always a bad idea to reduce a very complex situation to a single variable (ice volume) because that meant other very instructive data series -- gathered at great expense, validated and analyzed in considerable detail -- are discarded. Think for a minute about the ambiguity of inversion: if I give you the sea ice volume, you can't give me the sea ice extent nor the distribution in thickness classes nor export out the Fram.

It's never a good idea to discard information. However it's also fair to say that volume, area, extent, thickness, ice salinity, melt ponds, fractures, land snow pack, open reach, changed inflows from the Bering Strain etc etc are not altogether independent of sea ice volume. Under these circumstances, the modern approach is principle component analysis. That reduces the dimensionality to a small number of independent variables that account for the lion's share of variance. While volume might be a substantial contributor, PCA will always outperform a single variable or subjective mix of them.

(The hastily composed 'Great Cyclone of 2012' paper -- which did not consider sea-ice imagery showing breakup in motion days *before* the storm -- also used a 1950's sidewalk metric of central low, its laplacian, radius, and pressure differential to score historic cyclones. Since these are hardly independent, again this called for principle component analysis.)

Second, the end-game of sea ice involves very different ice physics from the early rounds, effects that did not need to be modeled -- and were not -- in Piomas (who besides Chris, Aaron and myself has read these difficult papers?). The emphasis now might be on longer open water reach for longer times, wave fracture, lower mean freeboard, smaller floes with high melt perimeters, ice salinity, and induced advective heat transfer changes above and below on the preponderance of young, thin, structurally weak ice.

Although everyone shipboard this summer has commented on worsening ice fragility, that hasn't resulted in a numerical map for the Arctic Ocean, much less the all-important trend. Thus even PCA on what we have is not going to be enough.

It's actually quite hard to quantitate ice strength because of the dominant effect of bubbles, salt content, pre-existing cracks, refrozen melts, annual layering history, salt extrusion channels, and crystal grain size and degree of interlocking. I could find only a few studies and these involved unworkable techniques or just practical considerations (US army recommendations on loads, from skier to snowmobile to small tanks).





>"Think for a minute about the ambiguity of inversion: if I give you the sea ice volume, you can't give me the sea ice extent nor the distribution in thickness classes nor export out the Fram."

How does that come out if instead of sea ice, I substitute weather and for another example substitute climate. Wouldn't we end up deciding weather is chaotic? Does that mean a simple one dimensional climate model cannot be used for anything?

With regards to discarding information, don't discard it keep it for work that needs it. i.e. use multiple approaches some that use lots of datasets and some that try to simplify down to the important components.

Aaron sees non linear system presumably with chaotic interplay. Yet the downward trend seems rather smooth. It seem to me that there is a possibility that it is an easier boundary condition problem than a chaotic initial condition problem. I could well be wrong an chaotic effects may start or already be present.

Ruling out a method without showing it doesn't work seems a bad idea. If there is enough evidence that it doesn't work then that is a completely different matter.

Principal component analysis may well be better. I am reasonably happy with the melt volume formula which used area for a handle on the albedo feedback works reasonably well. The sensitivity of the area to volume may be changing so certainly improvements may well be possible even without adding other components. I am much less happy with the freeze up. An analysis with uses more components and determines which are important sounds a very good idea.

Chris Reynolds


I suggest that to get a physical basis you need to model freeze volume and melt volume separately.

Except that the melt period feeds forward into the early freeze season...

Partly due to being intrigued by the discussion you had with SATire recently I've started getting to grips with the volume and area ice data, and NCEP/NCAR temperature and TOA OLR. There's a lot in there I hadn't seen before.

First line of attack, after an unplanned splatter of graphing and correlations, is to try to identify the changes in the seasonal cycle and produce a robustly argued/evidenced narrative of the changes in the annual cycle. To remain data-centric and data-driven (IMO the first step in analysis) I'm trying as much as possible to avoid reference to scientific papers.

I must confess that the maths to model the Arctic, even simplistically is probably beyond my competence. I could try but would be plagued by stupid mistakes.

Aaron sees non linear system presumably with chaotic interplay. Yet the downward trend seems rather smooth. It seem to me that there is a possibility that it is an easier boundary condition problem than a chaotic initial condition problem

I too suspect that all the ingredient processes are already at play and that no novel processes will manifest, although different processes will wax and wane in importance at different times.


I have some sympathy with your comments about volume fixation. However the volume trend, when compared to area/extent, does beg the question of how the two trends will be reconciled. Naïve extrapolation of volume loss has its faults (many IMO), but the rate of change acceleration does suggest either a reduction in rate of volume loss, or a crash. I'm at a loss as to what process will rein in volume decline.



I fully agree, that things in the arctic are complicated and need a lot of work. I was fascinated by the Eisenman paper given in the other Piomas-Thread (describing possible bifurcation to whole year ice-free arctic depending on a small number of important parameters).

But I think Piomas is very useful because it is a number that was very well predictable the last 5 years - which other number did like that in those crazy years? And it could be a nice weakeup to the world to get attention. For that purpose a very simple modell could be fitted - because nearly every fit could work with very similar results, due to the fact that the number has gone allready 80% of its road. So - I think they should publish it and I agree, you should keep on working out e.g. the date Greenland's ice will slide into the sea using a holistic way.

Chris Reynolds


But I think Piomas is very useful because it is a number that was very well predictable the last 5 years - which other number did like that in those crazy years?

Could that merely be a factor of PIOMAS being a simplification?

Chris Reynolds

Actually SATire, scrub that...

Having been looking at my plots of PIOMAS thickness 'simplification' doesn't fit the bill.

I think what singles out sea ice volume over all other indices is that volume has a memory. It is integrating the other processes at play in the Arctic, and the large thermal mass of the ice (including phase transition requirements) acts to smooth the signal.



you are right, it is a drastic simplification. But it is working surprisingly well - so I am quite convinced by this number and the probable physical meaning behind it. I am now much less convinced by Monte-Carlo simulations of numerous complicated processes predicting last years ice-extent for the year 2050...

Aaron Lewis

We have a thermodynamic system and "entropy increases". However, I do not see compliance with thermodynamics as "chaotic events".

I see professional scientists in "publish or perish" mode working with air temps because they are easy to explain. In contrast,sea ice strength comes in 6 flavors and 5 colors and it is hard to tell in advance which combination will yield a good paper that will be accepted before the end of the fiscal year on September 30, or the cutoff for the next IPCC report.

If we think of the climate as a thermodynamic engine, then PIOMAS (trend) was one measure of power output, and in the past, that measure has had a certain rhythm to it. Soon PIOMAS will go to zero and we will have to find other measures of power output.

The changes are large and abrupt, because in the past, the model was too limited. The problem is not chaotic events in the sea ice system, it is a failure of the old sea ice models. They considered local insolution, rather than global heat transport. When the temperature warmed above 0C, heat transport increased dramatically.

Instead of following ice melt, we should have simply measured the Gibbs energy in the global system. (Not a paper that will get written by the end of the fiscal year, thus not likely to get done in our current research environment.) My point has always been that the Gibbs energy of the global system was increasing, so that the sea ice would melt. And, given the nature of ice, the melt would be very abrupt and surprising to anyone that was just following air temperatures.

The bottom line is that an increase in the Gibbs energy of a volume of ice means weaker ice. In practice, take a volume of ice and measure how much heat is required to melt it. More heat implies stronger ice. That value can be inserted into strength of structure formulas.

Bob Wallace

I think what singles out sea ice volume over all other indices is that volume is that it provides a measurement of all three dimensions of ice.

Neither area/extent nor thickness tells the complete story. We're watching people, right now, projecting the first summer meltout for some decades from now because they are observing only the two surface dimensions and ignoring thickness.

Anyone who looks at the PIOMAS annual minimum graph has to see that, if the data is not fake, we are 2 years, +/- 2 years, away from a summer meltout.


Since 1980 we have had 5 annual melts which, if repeated, would take us to an effective zero in 2013. We have had occasional recoveries (mostly following large melt years) which could push the first meltout a bit past 2015.

As Aaron points out we have an ever decreasing amount of ice and most of the forces which melt and transport ice are increasing.

Toss in a measurement we don't have, the quality of the remaining ice, and my guess is that the first meltout will happen sooner in the forecast window than later.

Mike Constable

Bob, I agree with your timing. Following the different threads I see some of the complexity of the maths, but most of the 'official' models are a long way behind the observed state of the ice.

"Keep It Simple, Stupid" is probably helpful in judging what the true situation is, too much complexity in models and their graphs appears to be an excuse for inaction.

Having said that, we all rely on the images we get from space, etc., obtained through complex assessments of data, interpreted by the wise, into the graphs and models we can understand!


Looking at the gompertz and exponential trend curves one could say that 2011 was a year of reverting to the mean, as was 2012 in august, and nothing out of the ordinary otherwise. That is if one accepts those curves as the new shifting mean rather than predictive. So perhaps this year we'll see a dramatic drop from those curves, 2,500km3 seems entirely possible or even 3000km3 in august.
The volume of ice is probably the most important indicator because of its ability to retain fresher water in the contours of its underside, both for rapid repairs of cracks and to prevent this 'easier to freeze' fraction escaping out the fram on the surface, things which extent and area have little impact on. Not to even think about it being replaced by warmer atlantic water. Even now the export of ice out the fram looks dramatic.

Bob Wallace

The Fram is wide open. It seems like only yesterday that we were wondering if the Svalbard fast ice would break loose and now there is none.

I wonder if there is a site that plots estimates of monthly ice flow through the Fram?

It might be very interesting to compare amounts of flow over the years. It could be that we'll start this year some distance below previous years due to higher winter transport.


Trying again...

Winter 2010/11 saw a heatwave along the West coast of Greenland.

Causing a record anomaly here:


Winter 2011/12 a heatwave much further East, in the Kara/Barentzs region.

Causing a record anomaly here:


Winter 2012/13 the heat seems to be centrally aligned, from the Fram Srait to the Pole.

This is currently causing a record (winter) anomaly here:


Five gold stars, and/or a fair fight for access to a small share of my rapidly diminishing supply of ale, for anybody who can articulate, in words or diagrams, why this might matter quite a lot over the coming summer...

Bob Wallace

The plug is getting pulled.

When the Central Basin goes soft it creates conditions which can allow the Great Flush.


Actually, with that big high over the Siberian Seas and Central Arctic Basin (that's been there for weeks now) I would think there is not so much ice transport through Fram Strait, but actually winds pushing the ice back towards the centre, perhaps causing thickening...

Jim Williams

The Navy's guestimate would agree with you Nevin: http://www7320.nrlssc.navy.mil/hycomARC/navo/arcticictn_nowcast_anim30d.gif

I don't know of any more reality based estimates myself, so I guess I'll go with them.


If you run the animation here http://polar.ncep.noaa.gov/seaice/nh.html even if you 'step' it could be deemed ambiguous until Iceland gets splatted, about 15 days back, which clearly comes from the north.

On this next one if you go through the images a couple of times they move swiftly from one to the next, and its worth looking at both the SIC and PR89 which shows openings forming to the south of Nares and at both ends of devon island implying warm water being forced to baffin


Finally if you run the 30 day gif CICE thickness from here
its clear that whilst we're getting a lot of compaction in the Beaufort that also the thicker ice,where volume can build, against the coast of the canadian archipelago / greenland waxes and wanes but is constantly driven south through the islands or Fram, and with it imho the fresh water that would aid recovery.
Compare that to the situation in antarctica where imho the fresh water eroded from the grounded ice maintains the most persistent sea ice by being available below to repair any openings http://polar.ncep.noaa.gov/seaice/sh.html


It suggests to me that unless something changes, and quick, there's no longer a home for thick ice in the arctic, and nothing to retain the fresh water of the melt or river outflows, which will get dissipated south at the whim of the weather.
Perhaps April will join May June and July in taking a dive in this graph with the melt starting at banks island

Bob Wallace

I'm not suggesting that we're going to get a large transport out in the next few months, but that conditions are setting up for much more loss from transport out during the next melt season.

The Fram Straight used to be choked down with fast ice. The Kara and Barents are no longer ice filled, but will be quick-melt pools for any ice that moves into them.

We're in the middle of January and the Central Basin is not full of compacted, thick ice. It's broken up. By April the ice may be compacted but it will not have the thickness of yesteryear's ice and will be fractured more easily.

And, when the wind blows into the ice pack next season, the Fram/Barents/Kara ice blocks will not be there to stop the movement of Sun-warmed surface water into the ice pack.

I can see major losses in the Central Basin next year as fractured ice is sloshed to and fro. I can see earlier and more severe damage to the CB ice coming from the Atlantic side than from the North American/Asian front.

Chris Reynolds

Rather than waste time retyping...

My latest blog post Observations from the Brink should be of interest. This one's short.

I'd appreciate it if anyone's got any ideas for the constant relationship shown.


Hi Chris,

that slope should be 1/thickness - but that line must cross 0,0 - so while linear fit does good for the data until now, it makes no sense at all in the vicinity of 0.

The thing would be a bit clearer if you plotted volume versus area like Neven...

A fit is never a proove for something - it is just a test, if a model must be rejected. If not, the model could work, but a lot of others could do so, too. There is no "thruth" in natural science by concept.

Chris Reynolds


Just posted a PS, after posting it occurred to me that it makes more sense to do as thickness = vol/area. In that sense I think the first graphic suggests the existence of a critical thickness.

I disagree that the fit isn't significant. It's persisted throughout the events of 2007 and 2010, which staggers me! And throughout 34 data points (years at minimum). The closeness of fit is IMHO highly significant.

The question is: Why, if the fit has persisted for 34 years, is it clearly physically impossible for it to persist to zero? In terms of a model, this fit-model has worked for 34 years, but it cannot continue to work. This is telling us something.


I agreed, that the linear function with off-set fits the data. But I disagree, that it makes much sense to have this off-set. And that a function fits tha data is not a proove, that only this function describes the data well - that is in 99% just by accident. Sorry, that is live.

Chris Reynolds


We'll have to disagree on this one then. I'm not a scientist, just a calibration engineer, but for two closely related variables to exhibit such close agreement for so long doesn't seem accident to me. In my job when I see such agreement between variables one might expect to be intrinsically interlinked my task is then to understand why. I still think the implied failure of this agreement, in the near future, is important.


Chris, I described this before and used it to estimate the sept minimum:



Chris Reynolds

Thanks Wipneus,

I've posted a link in comments. I wasn't aware you'd found it before. If people are aware of it then it explains a lot of the expectation of a fast transition.

Have you a guess as to why this relationship holds?


Hi Wipneus and Chris,

since I would not like the consequence Wipneus draw in his link "[..]whole basis of this (PIOMAS) is not as reliable as I thought" I would suggest to try the other route with the exponential. I know, that this is derived only from simple albedo-feedback. For area there would be then an other exponent of the time then for the volume or for simplicity just an other tau. The ratio would be an expontial then, too.
So, if the ice-loss is driven mainly by warm atlantic water, it will be a wrong forecast. We will see that result soon.

Chris, I totally agree with you, that we should keep on disagreeing. The nature is a tough judge - observations are the natural death of all theories and models in the end...

For your last question to Wipneus: A linear extrapolation for short time is a proven way, because any function can be linear approximated in a small range. On the long run, linear approximation is _always_ false (e.g. predicting negative ice-volume...).


I was just going to mention Wipneus had discussed and used this. I think I decided it made sense to graph thickness against area.

Presumably the thinner the ice the more likely it is to break into smaller pieces. The idea of a large area (1.8 million km^2), all 1 molecule thick, all melting at the same time does not make sense.

For large pieces it may be about strength to resist waves breaking it up. Ie length of a piece reduces to half wavelength of waves if the ice isn't strong/thick enough to prevent such a breakage.

For small pieces, the tendency to roll for stability and the much larger ratio of surface area to volume may tend to keep shapes tending towards a sphere as the pieces get smaller. The thickness of each piece may then tend towards square root of the area of the piece.

The variation in the distribution of different size pieces seems key to this. Also the way surface area becomes large compared to volume as the pieces get smaller tending to eliminate smaller pieces more quickly than their volume might suggest.

Eventually you get down to one piece and thickness tends towards square root of area. That is a curve that head to the origin. Working back to larger volume, with 10, 100 or 1000 small pieces the area will be more like 10, 100 or 1000 times the thickness squared. So area grows rapidly as you add more pieces.

I see plenty of time for the relationship to evolve into a curve towards the origin as volume decreases. The typical wavelengths of waves and the thickness needed to avoid being broken by those waves might be a reasonable cause for the straight line relationship seen so far?

Chris Reynolds


Happy to disagree, and I don't take criticism personally. :)

Regards the ocean role. Given that the volume drop is mainly from around 20/4 to 5/7, and the area drop has a steeper component from 20/4 to 20/6, with a shallower component from 20/6 to 26/8. I seriously doubt a role for ocean warming in the recent acceleration, although a role in the longer term trend seems likely. (dates approximate, based on difference between 2000-2005 and 2007-2012). Most of the acceleration is due to volume & area loss from April to early July, which also means I now see the summer Arctic Dipole as a lesser factor behind albedo changes in the ice.


I don't see wave action as being a major factor in the linear trend of Volume/Area scatterplot. I read a paper last week that talked about waves penetrating hundreds of km into the pack due to low ice conc and thinner ice. Yet 2011 and 2012 were still on the trend line.

However you may have a more general point with regards proportionate thickness profiles - by which I mean proportionate to average thickness (which has changed) the profile of thickness as one proceeds across the pack (thin at edges thicker in centre) may not have changed.

I've worked too much this weekend, I'll think some more over the next few days.



Sorry, above I was wrong - the ratio V/A is not an exponential.

The differential equation for the loss of volume V ~ -V:
-d/dt V(t)= -1/tau V(t)
is solved by V(t)=Vo(1-exp (t-to)/tau)

and similarly for area A - with same t0 but different tau2. I would suggest to determine t0 from PIOMAS-fit and use this t0 to fit to area or extent to check.

The ratio (average thickness) would be
thickness = V0/A0 (1-exp (t-t0)/tau1)/(1-exp (t-t0)/tau2), with 1/tau1 larger than 1/tau2 of course...


>"However you may have a more general point with regards proportionate thickness profiles - by which I mean proportionate to average thickness (which has changed) the profile of thickness as one proceeds across the pack (thin at edges thicker in centre) may not have changed."

Re "may not have changed"
Surely if the profile hadn't changed then there would be a straight line through the origin.

I think we are running out of area faster than we are running out of thickness (when viewing this series of September minimum points). Clearly an area of 1cm^2 but 20cm thickness is not possible because it would fall on its side to make 20cm^2 area and thickness of 1cm.

So the profile is changing.
Also the way it is changing cannot continue so it must at some point start changing in a different way.


Should do the calcs before I say anything. Sorry. It seems we are running out of thickness faster than we are running out of area but only marginally. Plotting area against thickness I get the intersect at area of 0.5 million km^2 area. The origin looks to be within the margin of error. A straight line to the origin on this thickness against area graph looks more plausible now than when I looked with one less year plotted.

Therefore there may not be much change in the proportionate thickness profile.

Looking in your plots of thickness

2009 and 2010 seem to have large area with thickness near the thickest. 2011 thickness profile is different with only a small area with near the thickest thicknesses and rather linear increases. To me this is saying the thinning is reaching a long way into the pack. Also highest thicknesses seem lower so some of the thinning covers all of the area. So I don't see much slowing of volume loss through lack of reach.

Re your first graph in
not saying anything about speed. I would say the lowest seven points are well spread out meaning an increasingly rapid rate of retreat.

Tor Bejnar

Chris's graph showing Arctic sea ice area declining at a slower rate than is volume may explain something. Scientists who watch "only" area see Arctic sea ice lasting much longer (ice-free Arctic by "mid-century") than those who watch mostly volume (ice-free later "this decade").

I expect crandles is on the right path concerning ice: when it breaks up from wave action, pieces fall over, so that area declines more slowly than does volume. This happens at the ice edge more than in the middle of the ice pack, although we have seen much more sloppy ice soup these last two years. When most of the Arctic sea ice becomes an expanse of "slush puppy" melange in September, perhaps then new data points on Chris's graph will trend toward [0,0]. But I fear there might be only one or two years of such an environment before we have a functionally ice-free Arctic (< 10^6 km^2 area).


Chris and others,

I had to be short yesterday, a bit longer reaction now.

Since you seem to have missed it, crandles and I had some more discussion here:

Like you, I think the linear relationship is remarkable. At the same time the "true" relationship must go through the origin, so extrapolating to volume=0 is bound to go dramatically wrong somewhere. There is an obvious question here.

So that makes me wander what kind of relationship between area/extent and volume you might expect. I think a power relationship is natural: tickness ~ v^n
Think of it: the function crosses the origin as expected, a small cube of ice will have n=1/3, a situation where area is confined n=1, a situation where both thickness and area/extent contribute equally n=1/2

Power relations are straight lines in log-log plots, where the angle indicates the exponent n.

Here are the log-log plots for extent and area:


As can be seen, the power relation holds well up to 2009 , with exponents nearly 1/2 for extent and a little less for area.
After that the matter is not clear. 2010 and 2011 are clearly off, 2012 might be interpreted as a return to the normal. But I can imagine as well a new trend starting with 2010-2012, or even a halt in declining thickness.

(Skipping here an explanation what happened in 2010 and how that changed the volume/area/thickness relations)

In this light the 2010 break has helped to keep the extent/volume more straight, it must bend downward soon.

That is about as far I have come. All fascinating and a reminder of the importance of volume for the future of the sea ice cover.


Large version

Data: PIOMAS Volume, CT Area.
Blue line: Area=1.72million*thickness
Graph crandles

Volume = Area * thickness
= (1.72million*thickness) * thickness

Simple - no change in relationship required.


Sorry about the obvious botch- plotted wrong way around.



Fixed ratio of area to thickness seems to make reasonable sense though I don't think it is guaranteed to follow that path.

Looking at just 3 years as I did earlier, you tend to see changes which is the noise about the trend which are likely much larger than the trend.



Just noticing that your model is the same as my case n=1/2

Or put in another way, tickness and area contribute in equal amounts to the decline in volume.



It helps to look at thickness versus area. While the actual trend (black) is not quite same as red fit, it is close. Cannot see a power significantly different to 0.5 working well.

The reason I post this, are the large volume reductions tending to be rather horizontal? I guess that is to be expected - if the season gets an early start then more albedo feedback melts lots of thin ice so the remaining ice is rather thick so there is a tendency for the average thickness not to fall.

Reason for uploading that is:

Does this help to say that plot is above line so we won't get a big volume drop this year? Or is that just another way of saying after one large drop we won't get another large drop?


I break down key characteristics between older ice of 1989 and present day sea ice, as seen from space, there are several differences especially at the coldest spot in the Northern Hemisphere, the area between Northern Ellesmere and Northern Greenland.


http://eh2r.blogspot.ca/ top of page

Chris Reynolds

I've used me previous data on PIOMAS to break down the Volume/Area plot.

Here's the original one I did.

AreaVol 1

Then I've used the thickness breakdowns I've got to calculate fraction from MYI and FYI and multiplied monthly PIOMAS volume by those fractions. I've done it this way as making close agreement with PIOMAS's series isn't possible due to problems with grid areas, and PIOMAS data implies an extent like lower threshold, so area calculated using PIOMAS grid is actually more like extent. Furthermore note that in the following I've only gone up to 2011, gridded PIOMAS data not yet available for 2012.

Area Vol 2

So here is the breakdown using thickness as a proxy for MYI and FYI, FYI mainly below 2m thick, FYI mainly above.

Trend comparison

Trend equation for linear fit, of the form bx + c.
>2m _ 3.8165 , -10.539
0 to 2m _ 0.1734 , 3.741
Sum _ 3.9899 , -6.798
Original _ 3.9403 , -6.5508

The agreement is good, the slight offset between the sum of component c for MYI and FYI is probably due to problem with PIOMAS grid area.

This doesn't answer the problem of why linear fit fits the scatterplot so well. However it can be seen as the sum of two linear fits - with FYI having a much shallower slope (nearly level) and MYI showing a massive loss that accounts for most of the downward trend of the first graphic. This also accounts for the non-zero origin of the Vol/Area scatterplot. The MYI was on such a steep trajectory it was going to hit near zero before overall ice area did. Whereas the FYI, being replenished each winter, has held the trend up.

By definition, as long as there is ice surviving the summer MYI will be present, just at a residual level. However the behaviour of the FYI is interesting. Does this mean we'll see an abatement of the rate of volume loss, or will volume loss simply transfer to FYI?

I've re-jigged the seasonal cycle of volume. Using day to day differences and summing to make an annual cumulative volume plot.

Area Vol 3

This shows what has been happening in the last couple of years, since 2010 when much of the last of the old thick ice was lost. The Spring seasonal cycle has moved back, so melt starts earlier. Given that FYI regenerates over the winter it is exactly such a change that would be needed to achieve a sea ice free state, because that state would need the seasonal melt to equal the winter maximum volume.

Chris Reynolds

Wipneus, Crandles,

Thanks for the log plots, and for reminding me of the 1/2 power issue. I've been pondering whether thickness or area losses have been dominant.

Comparing 2007 and 2010 is interesting. 2007 showing a level drop in area, without a strong thickness contribution. However 2010 showing thickness loss as well as area loss. That's a surprise to me - but I have become overly fixated on the time period of the 2010 loss and have forgotten what happened later in the season - I assume your plots are all using minima data?

I'm not so sure we can use negative one year lag autocorrelations based on past data in the years to come. The implication loss of MYI (well virtually all of it) suggests to me a new regime of extreme volatility.


Just to add to the confusion with my view (albedo-feedback is to blame) again - also with exponential fits we end up with definite thickness in the last year of ice: 1-2 m in the last year before it is gone.

For Volume I used Wipneus' fit to PIOMAS Sept.:
and for area I did a rough fit with same end-date to cryosphere today Sept. area:

V/A is decreasing slowly from V0/A0 to V0/A0*tau1/tau2=16/5*6/11.2=1.7
- that function (given in earlier post) is not much different from a straight line and could be a possible reason for your observations.

(sorry for not posting the graph - I have no webside to store it at hand...)


- I assume your plots are all using minima data?

CT area day minimum, NSIDC extent september data, as it was calculated for Neven's poll.


I have used CT area minimum - with NSIDC you would get an other slope and other thickness, therefore.


Sorry for answering when actually not asked :-~


Yes, I was using minimum data for both PIOMAS volume CT area even though these are typically a few days apart.

I was looking at 2007 and 2012 having large area drop and little thickness decrease in those two years. This doesn't look like it holds. For 11 largest area drops the thickness decreases average 8cm whereas the 11 smallest area drops years the thickness drops average 4cm. Middle 11 years average 3cm.

Trying volume (as I stated) works better as the reverse of what I said: For largest 11 volume drops average thickness decline is 15cm, smallest 11 volume drops average -4cm thickness drop and middle 11 years average 5cm drop.

Sorry for confusing you with that.

Chris Reynolds


I've got a problem with extrapolating fits like this. The fit I started all this off with was a past fit to data that didn't have a physically tenable extension into the future, and didn't give information about rate of progression or future trajectory. That was my problem.

The problem I have with extrapolation at present is that we seem to be on the verge of a shift in the ice, probably going through it right now. So the past may not be of much help with regards the future. Although I live in hope that sufficient clues are buried in the data we have.

The middle graph in my above post (of three graphs) suggests that most of the decline rate between Vol and Area has been due to loss of MYI, as of 2011 that seemed to have hit the floor, although basic reasoning shows a residual will remain. That leaves FYI.

FYI is declining at a far lower rate, due to replenishment in winter. In the second graph I've shown that there is a shift to earlier melt. Anomalies show this has happened in the last three years, since the crash of 2010 which killed most of the remaining MYI.
That's an old graph but it shows the anomalies from the 1980-99 mean, and the early spring crashes of the last three years.

These advances are just what is needed to reduce FYI, which has been replenished (to some degree) over winter, to zero by September. But will they? If as I suspect the spring crashes are due to a shift to FYI from MYI, with a consequent drop in albedo and increased absorption of insolation, then there may not be much more of an advance to come. The shift that has caused the advances has already happened. If that is the case then we may indeed see what the models show - a slow final retreat of sea ice. Going back to the first two graphics in that post: Graphic 1 - physicality demands that the data points track along the area axis to a greater degree until we meet volume=area=zero. And graphic two seems to suggest just this. We may see the spreading caused by 2007 and 2010 being replaced by a greater proximity of data points as the ice pack idles down to a slow end. The coming years having summers resembling the region that got wiped out by the Arctic Storm in August.

The question I'm banging my head on the desk over is this: Is there any way to determine if we face a crash, or a slow slide of gradually reducing FYI thicknesses? I've got a stack of data, a stack of correlations of varying degrees, a stack of graphs. I'm convinced that the answer is in there somewhere, but I'm not sure where, or how to encourage it out of the data. :(

Maybe the answer isn't in the data because we're in totally new territory. But after seeing that second graphic I doubt it.

Chris Reynolds

Thanks Crandles,

I need to take a few days to think about all this. I had missed the conversations you'd had with Wipneus. It can be hard sometimes ploughing through everything on here to find the interesting bits.

I am seriously starting to doubt that we face a crash though.



you know that I do not believe in fits - they have really no meaning other than a test, if a model is wrong. So - what really is the trouble of all of us understanding, what is going on. I agree with you, that first year ice is different from multi years ice (albedo, salinity, thicknes,...). Our cruel fits do not account for that. Also not for all the other features. The exponential fit comes from linear approximation of albedo-feedback - of course, that is not true but could be working for simplicity. Any linear trend must come from integration of a constant force (if not just a short term approximation of something more complex).
- Do you consider e.g. CO2-forcing allready as a constant force? I do not think so, because CO2 stays ~100 years in atmosphere - so accumulated heating force should be the medium of the last 100 years CO2-content. This is not a constant value for at least the next 100 years... Do you have anything other in mind as reason for constant force? It must be something very simple, I have overlooked. I think, the present changes are very non-linear and not constant - so if all processes cancel out to a linear trend, that would be very surprising to me...

So - to conclude my view: As volume decreases so does area with other time constant but same date of disappearence, of course. Thickness decreases - but with lower rate to a positive value. The last piece of ice would have a thickness of 1-2m before it melts or just got lost from the view of satellites. The crash will surely happen - in 1 or in 5 years. The question is, will it turn to all-year ice-free state by bifurcation (the Eisenman-article)?

R. Gates

SATire said:

"The crash will surely happen - in 1 or in 5 years."


I agree with this. Even if the AMO peeks in 2020, the crash will happen before then. The warmth being driven into the Arctic is only partially driven by the warm AMO cycle, with the other part of course being the higher heat content in general of the oceans driven by higher GHG levels. Thus, even if the AMO starts to show some cooling, it will come way too late to prevent an ice free summer Arctic. Also, it seems very probable that the higher anthropogenic GHG levels are affecting the AMO, such that there is long term upward trend overall, so that even if the next "cool" phase of the AMO hits, it won't be as cool as the previous cool phase.

Finally, related to the crash-- we may get a 2008/2009 "recovery" or slowdown in the decline or we may not. Considering the deeply disrupted Arctic vortex that we've seen occur this month and the generally higher temps north of 80 degrees as a result, we could also get another big melt.

It will be an interesting melt season and this blog is the best front row seat. Unfortunately, what will be witnessing over the next few years will be a tragedy.


>" Graphic 1 - physicality demands that the data points track along the area axis to a greater degree until we meet volume=area=zero."

That doesn't say whether we start losing area faster or start losing volume more slowly. I don't see the argument for volume more slowly but possibly see argument for area faster:

So far we have been losing thickness at almost the same rate as we are losing area. The relationship could change but suppose it doesn't. If we split that down into 3 dimensions then we see we are losing thickness faster than we are losing length or breadth of the ice pack. This means that the effects are reaching all the way to the thickest ice. If there were parts that were not being affected then I could understand an argument that the rate of volume loss would slow. With thickness declining more than length or breadth then the ratio of surface area to volume is increasing. i.e. getting easier to get at the volume. Therefore a similar rate of volume loss can now more easily cause the rate of area loss to increase.

Will a faster rate of of area loss cause higher volume loss through albedo feedback? It has in the past and everyone recognises this as a strong feedback so that seems soundly based.

I think it all points to area loss acceleration rather than volume loss slowing down.

So I am as convinced as ever that if volume at maximum keeps declining at least at the rates seen recently, we will have ice area under 200k km^2 for a few days in September before 2020.

>"Do you consider e.g. CO2-forcing allready as a constant force?"

Probably weren't asking me but...

it depends what effects you are thinking about:

The effect of slowing heat loss to space happens immediately the CO2 increases. Therefore the difference between March 2012 and March 2013 will be pretty similar to the difference between other consecutive years. That isn't the only effect of CO2 though. If warmer waters flow into arctic, upward heat flux is likely to increase. Because the ocean has lots of heat capacity the effect of CO2 is going to be significantly delayed and we are likely getting an acceleration in the rate of increase of upward heat flux.

"CO2 stays ~100 years in atmosphere" does not seem relevant if the co2 concentration is increasing in a fairly linear manner over the 1979 to 2013 period we are looking at. Ocean water temps are going to take several decades to fully reflect increased CO2 levels. (Perhaps even 1000 years for water to fully circulate but I suggest vast majority of effect will have occurred by 50 years.)

Aaron Lewis

The system is changing. Atmospheric circulation is changing. Ocean currents are Changing. Right now the ice going around in a spiral - in the past it did not spiral that fast. PIOMAS describes the old system, it does not tell us what tomorrow's system is going to do.

Volume and area of sea ice do not matter because the ice is getting weak, and one good storm will turn the whole mass into slush. This is not chaotic, because it is a system moving to thermodynamic equilibrium, but it is not the system that was there 5 years ago.

CO2 is not a big deal in the Arctic, because suddenly the atmosphere is above freezing and saturated with H2O. In the Arctic that is a bigger difference than the changes in CO2 over the same period. And, locally there are plumes of CH4. 2ppm of CH4 is not a big deal, but the trend is in the wrong direction.

In some places the Gulf stream flows at 2.5 m/s , so there is the potential to move heat from the surface of the Caribbean to the Arctic in a season. It carries on the order of a petawatt of heat. If more of the North Atlantic is warmer, then more of that heat may reach the Arctic. I am not saying that it will, I am saying the old rules do not hold. The atmospheric circulation patterns that drove and cooled the Gulf Stream are changing.

In the last couple of years, we have started to see large scale latent heat transport into the Arctic. The Arctic Basin warming in the first couple weeks of 2013 is the scariest thing I have ever seen - It looks to me like North Atlantic Drift Water was poking into the Arctic in January. And there was water vapor in the atmosphere over it.

If more NAD water flows into the Arctic, then more heat will be radiated out, but the sea ice is going to melt earlier and the open water will be able to absorb sunlight all summer.

Everything that I see points to a very rapid (5 years) transition from substantially ice free in the summer to substantially ice free year around. A year ago, I though the transition would take at least 20 years.

I think we will see substantially ice free in the summer of 2016, so I expect to see warm oceans/cold continents with very little sea ice in the Arctic by 2020.


My formula for melt is 22.8 - 0.213 * Max Vol

This suggests a heat absorbtion equivalent to 22.8 K Km^3 of ice to water latent heat. If temperatures rise, some of that heat will be lost but ignore that for now.

Last 3 years see ~17.8 K Km^3 of freeze. So with ice free conditions heat imbalance could be 5K Km^3 worth of heat compared to ~1K km^3 worth now.

21.9K Km^3 at maximum now divide by average of 1K and 5K Km^3 heat imbalance for conditions between now and ice free conditions gives a very approximate 7 years from now.

If you think latent heat of water vapour and other heat transport in from lower latitudes is becoming a really important effect, I haven't accounted for that and 7 years might be too long. OTOH I tend to think the 17.8K Km^3 of ice latent heat worth being lost to space in winter will increase substantially if there is no ice in the way. So I tend to think much longer than 7 years.

That is almost certainly attaching far too much importance to the 22.8 K Km^3 max melt per my formula. However Rob's calculations did seem to imply the forcing from ice free would be stronger than current forcing effect by a factor of a few times.

5 years would be a scarily short transition time. I hope it does turn out to be longer. Seems like a lot could change and very rough calculations like these could be miles out. I may as well say I haven't a clue and it might be more sensible not to show such wild workings as these. Unfortunately, while 5 years is scarily short it doesn't seem silly like half of Greenland ice sheet melting in 5 years.

Chris Reynolds


I accept what you're saying. Such reasoning has been part of what's changed my mind to expecting a crash. However...

Consider my breaking the relationship into two components: MYI and FYI.

Why would they behave so differently?

MYI has a memory, it takes years to build up, so has a long time constant. By virtue of this it has a memory that integrates losses or gains of ice. In our situation we have net loss, so it integrates that, a behaviour apparent in the changes of volume which implies something with a memory of past impacts (e.g. retaining and not recovering from 2007 and 2010). That volume & area are at present linearly related would be because area melt depends on initial thickness.

FYI, if it can be shown to have a memory at all, doesn't integrate as strongly. Its recovery time from impact is of the order of one year - it can regrow fast over one season.

This is why while the thicker ice (MYI ~>2m) has dropped substantially the thinner (FYI ~<10m) has shown less of a drop.

What that graphic implies to me is that we may see a transition from one rate of change to another, i.e. a reduction of volume loss, due to a transition from an integrating dominant factor to a non integrating dominant factor. However that graph still implies unphysicality as it tends to zero area. This I think is solved by the non linear nature of open water formation efficiency. The scatter plot will relax like an inverse log to zero. With the final years resembling the area of low concentration hit by the August storm of 2012.

Having just read your reply above I think we may not disagree in terms of timescale. When I'm talking of a longer persistence of the ice I mean until nearing 2020, possibly later but not by much.

The graphic I link to in this post doesn't include 2012, but as can be seen from this graphic:
2012 is right on trend, yet the MYI has largely gone. So perhaps the energy used in melting MYI has transferred to FYI. But perhaps this is a coincidence - 2012 was due to be a new record, but its magnitude was amplified by the August storm.


Hi Crandles,

"Will a faster rate of of area loss cause higher volume loss through albedo feedback?"

Of course in simplest relationtship - that rate should be proportional to open-sea area (and a bit to thiner FYI), that is the basis of the exponential function. Area loss causes melt. Melt reduces volume and area.

"The effect of slowing heat loss to space happens immediately the CO2 increases"

What happens imidiatly is the rate of energy input is increased. But the temperature will rise as long as the higher input is there, because the earth is big. Again, you have to integrate that rate to get the energy - e.g. to sum it up as long as it acts. So - averaging 100 years is reasonable, because that is the CO2 time scale. Methane would be only 10-15 years, so that would be more close to "imidiatly".


Looks like Aaron has pretty much laid out the long and the short of it.


@ Aaron Lewis, who says, "CO2 is not a big deal in the Arctic, because suddenly the atmosphere is above freezing and saturated with H2O. In the Arctic that is a bigger difference than the changes in CO2 over the same period. And, locally there are plumes of CH4. 2ppm of CH4 is not a big deal, but the trend is in the wrong direction."

I think, Aaron, you meant 2PPBv CH4 is not a big deal. I would think differently on this.

CO2 in the Arctic still has an impact on atmospheric and thus ice conditions as an element that contributes to warming. I will be adding additional CO2 concentration imagery during the week. Currently (01/13/13 am) the global CO2 average is 394 PPMv. In some areas of the CAB it is averaging 398-402+ PPM.

CH4 has more than plumes on a local basis - significant areas have been above 1950-2100 PPBv in the last few weeks.


Jim Hunt

A4R - If I click your link Google tells me "You don't have permission to access this item. You can request access from the owner".

I don't know whether this is by accident or design, but can I have access please!


A4R -- I received the same result as Jim. You might have posted an administrative link. In any event, the page is not accessible to the public.



>"Consider my breaking the relationship into two components: MYI and FYI."

Yes, but,

1. That split is an over 2m / under 2m split and those components are bound to behave very differently if the pack has thinned so that there is now little ice over 2m. This is a last 2 cm of pencil is staying the same length so it will never run out conclusion.

2. Yes MYI takes more energy to melt than FYI. Since we are increasing left with just FYI, that means the melt volume should go up as MYI disappears. FYI equivalent volumes should be more than actual volumes.

Taking this graph:

To convert to FYI equivalent volume, the graph should be skewed by stretching the left (1979) side up more than the right (2012) side which should only very slightly be stretched up. The fits are then nearer to linear, but the conclusions from extrapolations of skewed curves are the same as the right side is barely altered. If anything the downward slope of maximum ice volume is made steeper by this skewing. The volume to be lost before ice free is reached is on right side of graph and is barely altered.

I don't see how your argument works whether it is a MYI/FYI split or a over2m/under2m split. The heat budget imbalance is still there and as there does not appear to be any important limit to the reach of the net melt, that heat budget imbalance will go into melting ice. When there is only FYI present then virtually all that heat budget imbalance goes into melting FYI.


Has anyone quantified the increase in energy required to melt FYI, 2nd yr ice, 3d yr ice & so on?

I'd assume the greatest jump would be FYI to 2nd yr ice with ever smaller changes as brine is forced out. If the greatest change is between 1st & 2nd year, how many years would it take for a doubling to occur?


Aaron Lewis

What is different in the Arctic between yesterday and today? H2O vapor/latent heat. What is likely to be different between today and tomorrow? CH4!

CO2 was, is, and will be a factor. It requires mental fortitude, but it does not require mental gymnastics to change the paradigm.

We measure CO2 in ppmv. I just put CH4 in the same units. Might as well get accustomed to measuring CH4 in ppmv.

Considering the size of the areas showing CH4 at 1,900 ppbv (and above), then the local concentrations near the sources are high enough that ppmv is the appropriate unit.

When we see videos of folks lighting off plumes of methane, we know the local concentration is greater than 50,000,000 ppbv (5%v).


>>"Will a faster rate of of area loss cause higher volume loss through albedo feedback?"

>"Of course in simplest relationtship - that rate should be proportional to open-sea area (and a bit to thiner FYI), that is the basis of the exponential function. Area loss causes melt. Melt reduces volume and area."

It is a little more complex than that. Albedo of ice varies with thickness and with whether it is FYI or MYI and the age of MYI.

>"What happens imidiatly is the rate of energy input is increased. But the temperature will rise as long as the higher input is there, because the earth is big. Again, you have to integrate that rate to get the energy - e.g. to sum it up as long as it acts. So - averaging 100 years is reasonable, because that is the CO2 time scale. Methane would be only 10-15 years, so that would be more close to "imidiatly". "

You need something more like the leaky bathtub analogy. Water (Heat) flow out depends on how much water/pressure (sensible heat/temperature) there is in the system. This finds a natural level where water (heat) in matches water (heat) flowing out. Sealing some of the leaks reduces heat flow out and the level rises but not indefinitely. The heat flow out increases as you get higher water level/pressure(temperature) and a new equilibrium is reached.

The time to reach equilibrium depends on the system. With land, the equilibrium is reached quickly - a couple of years at most because of the noise. Water has higher heat capacity and the time to equilibrium is around 50 to 70 years for top 1000m. Really deep water requires thermohaline circulation circa 1000 years.

It is this time to equilibriate that matters not lifetime of CO2:

What matters is the CO2 levels. The circa 100 year lifetime of CO2 only matters if you are considering a pulse of CO2 and you are expecting CO2 levels to relax back to former levels. Our big experiment with this planet is not considering emissions being dropped to zero to allow relaxation to former levels but instead continued emissions at hopefully much lower levels than now which will keep CO2 at the higher level.


I assume FYI has lower mass per volume due to brine rejection channels. I don't know numbers for energy requirements but if the numbers are per mass then we would also need mass per volume numbers.

Chris Reynolds


I agree that the heat budget imbalance leading to loss of volume, from whatever category, will remain. However my point is that the FYI that is left is better able to recover over the winter than is MYI. It is that crucial difference between MYI and FYI that is at the core of my argument, and I see it as explaining why the MYI Vol/Area plot trend is steep, while the FYI is not - I still think this is an important insight. However I no longer see it as enough to stop a crash.

PIOMAS anomalies 2003 up to 2012.

I've been pondering this over work today, and have come home to check some graphs, notably volume anomaly plots. We're still left with a physically untenable end to the FYI trend line on the Vol/area plot. We have a massive change in the seasonal cycle since the volume crash of 2010 that cleared out much of the remaining MYI. A change that puts volume loss at the start of the melt season right where it can do the most damage. Last year finished about 1M km^3 down from 2010 and 2011, and we were at 3.261 M km^3 minimum last year. The August storm had a negligible effect on volume (a small tick around day 210), so if we carry the current 1M km^3 deficit through to the summer we can expect a bit over 2M km^3, and it will come with a crash in area. It's hard to see what can stop it now.

So I'm back to thinking that after 2007 and 2010 didn't put a dent in the Vol/Area trend, as massive as those events were, what is coming won't just change the trend, it will smash it into a terminal decline.

Sorry if I've wasted your time, I must admit to having done something similar with Dr Jennifer Francis - when I get new evidence I tend to let it carry me before I reach a new equilibrium.


"The circa 100 year lifetime of CO2 only matters if you are considering a pulse of CO2 and you are expecting CO2 levels to relax back to former levels. Our big experiment with this planet is not considering emissions being dropped to zero to allow relaxation to former levels but instead continued emissions at hopefully much lower levels than now which will keep CO2 at the higher level."

That is the point. 20 % of countries agreed to reduce CO2-level to stabilize temperature at +2K - the later they start reduction the more they have to reduce - probably soon to zero. 80 % of countries disagreed and even convinced others to cancel the agreement recently. So - it will still rise with nearly no hope. If we would drop emission to zero now, temperatures will rise next 100 years. If we do not, it will rise longer. This is without any feed-backs, which probably make the future situation much worse. From point of Germany - we have got our share of CO2-emission/person allready. From point of USA - no chance to pay it back anymore - it must compensate for that somehow differently.

Anyway - if you talk about a rate, you have to integrate that for the effect, because any rate is a derivative by definition.

Chris Reynolds


Not quite the answer to your question, but closely related.

Taken over the melt season a meter squared of FYI gains 1/3 more energy when it replaces MYI over the same square meter. That's from 900MJ/m^2 to 1200MJ/m^2. As this factor applies mainly from June to Sept it's an increase of about 38W/m^2 - see note below. This changes the seasonal behaviour of the ice:

More here, and link to source paper which should be paywall free.

Note #1.
900MJ/m^2 cumulative energy gain for MYI, 1200MJ/m^2 over the melt season, June to Sept is around 90 days, 1 watt is 1J/second.
90 days = 90 X 24 X 60 X 60 = 7,776,000 seconds.
Therefore as the difference in cumulative energy gain per m^2 is 1200 - 900 = 300MJ/m^2. That figure divided by the number of seconds in a season...
300MJ/m^2 implies 38.6W/m^2 gain when ice cover transitions from MYI to FYI.


After superficially following the conversation on the MYI/FYI area-volume graphs, I got to Chris’ latest, sighing insight that a crash is to be expected.

While reading, I continually recall the real-time, MODIS images. I took in a lot, trough ’10, ’11 and ’12. I’ve been copying them on CAD. I’ve calculated floes and leads, examining lead-structure, much like Wayne does in his last blog-post.

What was left of the ‘structured sheet’ in the CAB was app. 1 MKm2 on 3 September, just before the (tropospheric) thaw-period ended. It contains the last bit of significant MYI, 40% more or less consistent floes up to 1500 km2.

The ‘slush’, good for 1,4 MKm2 area, surrounding it offered some sort of protection against the fickleness of weather and the tides. It also took out the lower tropospheric warmth, adding to keep the ocean surface below -1,5 dC.

There’s the part that, in my take, could be the ‘missing-link’ that hides a predictive analysis of the graphs.
It’s not the MYI, it is the structure that holds up area while volume is dwindling now. It hides the crash, but it is built-in to come.

Next summer could very well be the year this FYI slush melts out far enough in August. Then it could trigger the dispersion of the ‘structured sheet’. Not the complete ‘wipe-out’, yet, as the remains could be frozen in for winter ’13-’14.
Extent would fall to 1,8 MKm2, area to 1,2 MKm2, volume to 1300 km3. Hard to believe, awe, terror, whatever we may call it. Ensuring our fear.
Mind, I dismiss anything not in the CAB. What is left in the East Greenland Sea is irrelevant.

One of the drivers now may be too small ‘freezing-power’ through winter. I did a sort of warmth-volume check on the DMI plus 80 dG North temp graphs in August. It showed the relative warmth of last winter compared to ’10 and ’11: 1,81:1,07:1.
It will be illustrative to fill in this winter and see whether it is a preparation.

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