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>"I would advise against using the graph as an indication of anything"

Yes, care is needed. e.g. Thickness wasn't growing into August 2008. It is because thin ice was melting that the remainder calculates to a higher average.

Still, there is a very noticable change in peak date from early August to late May in just a few years!

Volume reaches its peak in only about a week, while it is likely to be another 6 weeks before PICT maximum. So should we guess that about 3 or 4 weeks after volume max, thickness in central arctic stops growing and for next 2 or 3 weeks thickness in central arctic is marginally declining but the melt of thin ice is proceeding at a faster rate so that PICT continues rising?

Chris Reynolds


Actually I don't think it's much to do with actual changes in growth/loss. As I see it, as the ice recedes towards the central Arctic the influence of the thicker sea-ice off the Canadian Arctic Archipelago has a larger bias on calculated thickness because it occupies a proportionately larger area of the remaining sea-ice.

So the thickness (thickness caculated by PIOMAS volume and observed area) metric shows a peak in the Spring and Summer. After which the minimum is in the Autumn where a large area of new thin ice growth biasses the calculated thickness low.

I've got a plot of volume anomaly here:

We're a month away from initial indications of whether we'll see a repeat of the massive Spring volume losses of 2010 and 2011.

The impact of these losses can be seen in the third of Neven's graphics. The 'roof' seen from June to September in previous years shows that during that period volume loss was largely accounted for by change in area. This has been a robust feature right back to 1979.

However in the last two years something radical has happened, and (if we are to believe PIOMAS) reduction of thickness has been 'needed' to account for the change in PIOMAS volume. Hence the different behaviour shown in Neven's third graph.

Andrew Piccirillo

I created a different version of this graph which uses a formula to exclude all area over 10,000 km2 as if it were .5m thick. In winter and spring this yields an estimate of the thickness of only the more northern sea ice by excluding peripheral sea ice volume and area from the calculation.

As you can see it reduces the current disparity in thickness between 2012 and 2011, which makes sense given the volumes remain nearly identical.

Here it is:



>"Actually I don't think it's much to do with actual changes in growth/loss" ... "The 'roof' seen from June to September in previous years shows that during that period volume loss was largely accounted for by change in area."

for 2011
PIOMAS 1 June 18.66 min in Sept 4.017
CT Area 1 June 10.06 min in Sept 2.917
So Piomas falls to 21.5% while area falls to 29%. Maybe that doesn't seem much, but it can be expressed as a 35% more fall for PIOMAS (calculated on end %ages) as the ice is losing thickness as well as area.

Volume anomaly may well not change as much during that period. (because it is an anomaly it shows less seasonal change?)

Anyway, I think you do need to think about both volume or growth/loss as well as area (and I was trying to say this earlier). In the time period you picked both area and volume were falling. However, there are other times when one is rising and the other falling. (I tried to concentrate on this earlier but we seem to have come to different conclusions so my explanation probably wasn't what was needed.)

Chris Reynolds


But my point is that the last two years are different from the preceding years. Yes during the last two years there has been a fall in thickness from June to September.

Thickness = Volume / Area.

Therefore if thickness doesn't change then the change in volume has to be accounted for by the change in area. Previously the June - Sept period has been typified by less change in area calculated thickness, i.e. a 'roof' in the calculated thickness. So the change of volume during the roof had to be mostly accounted for by the change in area.

Both volume and area are always changing, except for small periods around max and min. What the loss of the 'roof' is telling us is that in the last two years there has been a loss of volume between June & Sept which cannot be largely accounted for by the change in area. Mathematically it must imply a loss of thickness. This is new.


I've pondered something similar but trying to remove the high bias due to thick ice in Summer. Can't get a satisfying method though.

I don't want to remove the difference in calculated thickness between now and last year. Volume is around the same as last year, but area is greater, which implies a component of thinner ice. That being what NSIDC have recently stated and other posters here have suggested.

Chris Reynolds

Actually it might help to make things more clear if I refer to some other graphics.

See this page,

The first 4 graphics show the average seasonal cycles for 1980-99, 1980s, 1990, 2000, and 2010/2011.

You can ignore the extent and area-extent plots, I'm not using extent any more. But basically the graphs show that the 'roof' in area calculated thickness is a persistent feature prior to 2010/2011. It's only in those two most recent years that this persistent feature is absent.


Sorry, I mis-understood what you were driving at Chris.

Another feature of the graph is the remarkably straight decline in PICT over that June to September period. I am wondering if that tells us something about the frequencies of different thickness of ice in those two year.

If the rate of melt was the same for whole of this period and at all locations then the straight decline in PICT in those two years would appear to be telling us there is equal amounts of all thicknesses of ice and this wouldn't have been true in previous years. However, I doubt that the equal rate of melt for all of the June to Aug time and for all locations is true.

Not really sure how far out that assumption is. Nevertheless the different shape of PICT seems to me to be saying the frequencies of different ice thicknesses has changed.

Another silly pair of hand drawn graphs probably won't help explain. But is meant to be histogram of ice thicknesses so vertical is thickness and area is volume and under silly assuption melting moves the x axis upward. Last two years on left, previous year on right.

Chris Reynolds

I'll have to think about what you suggest Crandles.

I've not even really worked out what the cause of the 2010 and 2011 Spring volume losses is. 2010 seems to have been associated with an early high pressure system that was present during the volume loss. The weather during Spring 2011 wasn't exceptional.

I'm not sure this does require equal melt over all areas (which implies all categories of ice and hence all thicknesses). I don't even know where the loss is coming from, either geographically or in terms of FY/MY ice. That's a question I'll be asking the PIOMAS team if there's a repeat this year.

If you look at the daily volume anomalies:
It can be seen that the most recent years are'nt really in isolation. There is a suggestion of an increasing tendency to such melts in the preceding years. So if 2010 was a 'primer' with weather causing the volume loss then 2011 may have been thinner ice being subject to more rapid melt. Otherwise I can't figure out why you'd have such a step change in behaviour.

It all depends on what happens this year. But, tentatively, I expect this to repeat. I don't know what's going on but the tendency in years before 2010/11 for a Spring volume loss leads me to expect this to be a new mode.


Chris: I'm not sure this does require equal melt over all areas (which implies all categories of ice and hence all thicknesses).

To my way of thinking this is the whole point. Of course, we are working with limited data here, but this is how I interpret that graph.

Prior to 2009 the melt was mostly confined to ice at the fringe, with less thinning of ice at the core (still some, as old thick ice is transported out). As the thinner-than-average ice at the fringe melts out and the thick core remains solid, we see the increase in the average thickness measure, even while both volume and area are decreasing. After minimum we see a rapid increase of thin ice jacking up area without increasing volume as much, and thus the average thickness drops.

Chris ponders the cause of the sping ice loss for the last two seasons, but we have to understand what happened before we can expect to understand how it happened. Only at the very beginning of the melt do we see the old regime of growing average thickness while volume and area are falling, but we quickly move to a different situation. What is that different situation? I think the steady decline in thickness, in contrast to previous seasons, implies thinning over a much greater area.

We still see melting at the edges, of course, but rather than a solid core remaining I infer a larger area of ice that is thinner than in previous years and now lacking the mechanical strength to hold together. That now readily spreads to refill that boundary area. There is still a strong core, but its getting ever smaller, and between that smaller core and relatively unchanged boundary there is a wider area of mobile ice that will spread to re-cover areas of melt.

One might imagine the old cross section of the ice across the whole Arctic at minimum as being like a mesa, but we have moved towards a profile that is more like that of a old eroded hill.

2 cents worth...

Lloyd Smith

Would boots on the ice drilling samples during this melt season help answer questions about volume? If so, are any planned? Also, is speedup of Greenland glacier melt impacting the volume of sea ice?

Kevin O'Neill

I distill the essence of the thickness graphs down to one main idea: Prior to 2009 the period from the end of May until the end of Sept. was characterized by equivalent changes in volume and area. Since 2009 volume has been decreasing at a faster rate than area during this period.

The best explanation I can come up with is that the thick ice is now being exposed to heavy volume losses, but (because it's initially thick) it is not completely disappearing so it still 'counts' as area. When thick ice is no longer undergoing volume losses we should see a resumption of the previous ratio changes. The most likely scenario for this to occur is for all the thick ice to become *thin* ice.

Chris Reynolds

Frank D.

Before moving onto 'how' here's "What happened?"

With regards 2010 all we have is a model output showing a significant loss of volume in Spring 2010 that rivals 2007.

We know that PIOMAS has in the past performed well against observations of thickness (Schweiger et al), and we know it performed well during the crash of 2007. So I am minded to take the 2010 volume loss in PIOMAS seriously.

The above is a plot of volume from PIOMAS, and it can be seen that the volume deviates from the region of previous values and onto the same track as 2011 from around day 109 to 169 (about 20/4/2010 to 19/6/10), That's the Spring volume loss of 2010.

The anomalies however show a similar Spring deviation for 2011. The following graph being volume anomalies from the daily average for 1980 to 1999.

Is this a new process of volume loss in the Spring, or is it just the 'hangover' from the volume loss in Spring 2010 i.e. deviation from previous seasonal shape due to lower levels. I had thought the former, now I'm wondering if it's the latter, and I can't at present figure out which it is.

The implications of this for thickness calculated from PIOMAS and CT area are substantial.

The above are the daily calculated thickness anomalies from the daily average for 1980 to 1999. The red line is the date of minima for 2010/11, actually it's a bit early should be days 252 and 254 respectively. The implied reduction in thickness at minima is of the order of 50cm. Due to the lack of observational data from before or after Spring 2010 I have been unable to confirm even this massive reduction.

NOAA DFO Site CH01 (ref) is a sea bottom moored upward looking sonar that measures ice draft. It would appear to be ideally placed to observe sea-ice draft changes due to ocean heat influx. Its results do not show the impact of 2007, or any impact in Spring 2010. However as the source page notes, the Chucki Sea is mainly first year sea-ice that has not changed substantially in response to the changes in the Arctic. The growth of first year sea-ice is still dominated by the cold of winter, whilst the winter has warmed (NCEP/NCAR - as much as 5degC in winter) it has not warmed so much that seasonal growth of sea-ice has been retarded. In terms of the heat flux through ice and its insulating effect, the issues determining how thick the ice can grow over Winter, the difference between -30degC and -25degC is not significant. It is worth noting the peak drafts of ice are around 15m (seems large to me), this will probably be due to thick multi-year ice from the central Arctic off the Canadian Arctic Archipelago being entrained into the Beaufort Gyre. Are there fewer of these high peak drifts? Well the second link above shows 5 day segments, and there don't seem to be fewer post 2007 or 2010...

However if these results can be extrapolated to the other regions dominated by first year sea-ice, such as the seas of the Siberian coast, then it would seem that these areas are not the source of the volume loss. To look for the volume loss we must look towards the central Arctic, the area left at the end of the Summer.

Arctic mass balance bouys may provide another option. However they don't generally have ice thickness data available. Using the start thicknesses (in April) doesn't suggest such a large thickness loss. However bouys are placed deliberately on thicker ice flows, so there may be a sampling bias there - I'm sure I've read of problems finding ice thick enough to put bouys on, but can't recall where right now.

If anyone has any ideas I'd be grateful.

Chris Reynolds

Lloyd Smith,

The area is so massive that boots on the ground might be of no use. The US and UK Navies have produced significant amounts of data on sea ice thickness by many transits under the sea ice. If they're still doing so to the same degree then the data hasn't been compiled in a proper study since 2008, when Kwok added ICESat to that data.

To put things in context, in 2008 at the end of Kwok's series the thickness in the Submarine DRA was reckoned to be around 2m in March and 1m in September.

Icebridge is supposed to fill the gap, but at present I can't work out how to use it to get data. Evene if I could the data seems to be in raw form, I'm not capable of producing a dataset comparable with Kwok's.

I'd tend to agree, but as I outline in my previous post, the implications are such that I really need observational data. What's available doesn't seem able to confirm or refute PIOMAS.

Maybe it's time to email a scientist? Dr Kwok? Dr Wadhams? Both have access to submarine thickness data. Perhaps also the PIOMAS team?


I find it difficult to get my head around this, but I remember reading somewhere that PIOMAS overestimates thin ice. Could it be that the model sees vast regions of thin ice of a certain (overestimated) thickness, but then in Spring this ice goes poof, leading to very large reductions in volume. In other words, if they wouldn't overestimate the thickness of thin ice, the 2010 and 2011 trends would be more in line with other years?

Hmm, that's not really a good explanation, is it? :-)


Chris, you of course have already touched on this in a sense in your recent PIOMAS calculated thickness post:

Schweiger et al carried out validation against Kwok and Rothrock's work finding that in Autumn PIOMAS, using ice concentration and sea surface temperature assimilation, had a trend of -0.38m/decade, whereas Kwok & Rothrock had a trend of -0.50m/decade. However this validation was in the DRA and outside of that region there has been a lot of thinning of thick ice off the CAA (PIOMAS underestimates thick ice), while in the Siberian sector there has been an unknown change of what has always been relatively younger, hence thinner, ice due to the divergent effect of the transpolar drift (and PIOMAS overestimates the thickness of thin ice). So perhaps the discrepancy can be explained at least in a qualitative sense, indeed Schweiger et al conclude as much with respect to thickness trends.

Although I believe you try to explain the discrepancy between volume/area and volume/extent here.

BTW, I apologize if I'm saying things some of you have already said or explained. Like I said, I'm having a hard time getting my head around this, because it's already around many things lately (one third ice, one third work, one third life in general, oh, and books).

Chris Reynolds

Neven, from the Schweiger paper: "the model tends to overestimate the thickness of thinner ice and underestimate the thickness of thick ice." This should really be a stabilising influence. As the sea ice is now mainly FY PIOMAS should be stating more volume than there really is.

If anything the scenario of the ice crashing should result in a real crash that PIOMAS misses or underestimates.


I feel uncomfortable flaunting my intellectual inadequacies, but Socrates would probably say: out with it, boy, if only to learn you know nothing. However, getting your head (somewhat) around something is one thing, explaining it quite another. Ah well, here goes.

As the sea ice is now mainly FY PIOMAS should be stating more volume than there really is.

Exactly. And thus PIOMAS overestimating the thickness of thinner ice could explain the crashes.

Let's say you have 3 square meters of thin ice. PIOMAS says the volume is 1.5 m3. This means the thickness is 0.5 meters. However, the ice is in reality 0.2 meters thick, thus the volume is 0.6 m3.

When this ice goes, and it's most probably the first to go (thus in Spring), there is nothing there for PIOMAS to overestimate, and the volume 'crashes'. In other words, the jump from 0.6 m3 (/0.2 m thickness) to 0 is much smaller than 1.5 m3 (/0.5 m thickness).

Neven, from the Schweiger paper: "the model tends to overestimate the thickness of thinner ice and underestimate the thickness of thick ice." This should really be a stabilising influence.

This stabilising or compensating factor - underestimated thickness of thick ice - kicks in later, which explains why the gap between the 2010 and 2011 thickness trend lines and the other trend lines gets smaller towards the minimum. Also because the amount of overestimated thin ice is getting smaller.

I probably didn't explain this well, or made a very simple error, but I think the clue to the 2010 and 2011 spring crashes lies in this overestimating of thickness of thin ice.

Now I can't get my head around the question: why the difference with other years?


It would appear that the April PIOMAS numbers will be eagerly awaited by several bloggers.

Looking further out, I haven't seen any comment (on this thread, anyway) on the implications of Wipneus' expected 2012 values later on. It seems to my untutored eyeball that if the actual figures hit the projections at any point in September, then either:
- The average thickness at that point will be significantly lower than even 2010/2011, or
- The 2007 minimum area/extent is going to be beaten by a LARGE margin.

Or both.

Artful Dodger

Hi folks, how was your Winter / Summer? ;^)

There is an interesting pre-press paper available now titled "Evaluation of Arctic sea ice thickness simulated by AOMIP mode" (more detail on AOMIP below*). The list of Authors of this paper reads like a virtual directory of modern cryosphere science:

Mark Johnson, Andrey Proshutinsky, Yevgeny Aksenov, An T. Nguyen, Ron Lindsay, Christian Haas, Jinlun Zhang, Nikolay Diansky, Ron Kwok, Wieslaw Maslowski, Sirpa
Hakkinen, Igor Ashik, Beverly de Cuevas

Here is a quote from the paper relevant to Neven's point above:

"Despite an assessment of six models that differ in numerical methods, resolution, domain, forcing, and boundary conditions, the models generally overestimate the thickness of measured ice thinner than ~2 m and underestimate the thickness of ice measured thicker than about ~2 m."

BTW, this paper rates the two best performing models as ECCO2 (from JPL) and PIOMAS (from UWash).

The final paper should be published in the Journal of Geophysical Research on about Apr 25, 2012.

*The Arctic Ocean Model Intercomparison Project (AOMIP) is an international effort to identify systematic errors in Arctic Ocean models and to reduce uncertainties in model results and climate predictions.

Cheers, Lodger


Neven wrote:

Let me know if captcha returns

The "captcha", the joke with the illegable characters has returned. I had to redo again 3 times while hoping my PC wouldn't crash meanwhile. Boy, this really is a joy spoiler.

I wonder, till the week before we had to cope with a quite doable tric (gray scale panel and only one word). Is the change due to typepad or to you? Can the system be reverted to the "gray scale" panel thing? If so, PLEASE!

BTW, it looks very mich like Artful D in the previous message has forgotten to close the black


HTML fixed.

Is the change due to typepad or to you?

It looks like TypePad has gone for the Google reCaptcha system 6 days ago. I'm sorry, Kris, there's nothing I can do about it, I think.


Kris, from that link above this comment:

Hi Sean! The CAPTCHA should only appear if: (1) you are not logged into Typepad or your OpenID account (e.g. Twitter, Facebook, Yahoo, Google, etc); or (2) the blog owner has set it up so that all commenters are required to see the CAPTCHA. Above the comment form there should be a section that says, "sign in with..." and a list of the main OpenID options, including Typepad and a "more" link. If you click one of those, sign in to the service, you'll be taken back to the comment form where you can write and submit your comment. Doing that will authenticate you as a commenter, meaning you won't see the CAPTCHA screen.

Chris Reynolds


No worries about going over things again, in discussion here I've managed to make more progress with this than looking at it on my own.

Now I see what you're saying. The PIOMAS data we have is from runs that assimilate sea ice concentration, in view of that your suggestion makes even more sense. As the sea-ice retreats areas that are estimated as being say 0.5m thick could suddenly disappear due to concentration drops as the 'real' ice recedes.

I've done a rough model on a spreadsheet of the down slope. Taking two sets of 8 columns, the first set being 'real' the second set 'modelled' Both have a loss of -0.1 as they go down each column, real starts from 1, modelled from 1.3. Each column represents a 'box' of ice that will melt out prior to the end of the season. The modelled columns set to zero when corresponding real figure is zero. I then sum the modelled and real in two seperate columns to represent total ice area, real and modelled. With the initial value at 1.3 for modelled the slope is greater, because at the end both modelled and real end up at zero - all the boxes are 'ice free' at the end of the season. The modelled result is stepped, due to the 'set to zero' action as each real column reaches zero. I suppose I ought to use a segment of a sinusoid, but I'm making the assumption that over the period concerned ice loss follows a roughly linear line.

The important thing here is that as the total area (sums of each set; real and model) nears zero the difference between them reduces as there are less boxes to introduce an error. when I introduce a constant offset by adding 4 to the sum of the real columns, and 4.4 to the sum of the model columns to simulate a remaining level of sea ice, this convergence still happens. Each 'modelled' box still introduces an error that won't there when that box is ice free (reaches zero). This might seem obvious but I'd suggest that whilst your proposal could account for some of the slope of the Spring volume loss it doesn't account for the magnitude of the loss. This might seem odd, but the modelled sea-ice volume is already higher at the start of the season, so the action of setting volumes in boxes to zero as observed concentration in those boxes hits zero can't IMO account for the reported volume loss itself.

Perhaps a neater way of cutting through the complexity is to note that the factor you describe is happening during seasons before 2010 and 2011. So as you say, why the difference with other years? The answer, it seems to me, has to be that PIOMAS is reporting an actual volume loss, not an artefact of the assimilation of sea-ice concentration - whether this relates to a real volume loss in the real world is the key issue.


Thanks for that paper. The weather here in the UK has now reverted to seasonal norm, although it's interesting that the low we have is part of a trough system going right up to Siberia and on to the Bering Strait. It's part of a +ve Arctic Dipole anomaly and is reminiscent of the Summer pattern that's dominated most of the UK during Summer since 2007.


Neven wrote:

Hi Sean! The CAPTCHA should only appear if: (1) you are not logged into Typepad or your OpenID account

That has no sense, as prior to be able to write a comment, one has to log in with his Typepad or with his OpenId account.
Che burocrazia!

And btw, I'm logging always in with a Typedad account.

Neven wrote too:

2) the blog owner has set it up so that all commenters are required to see the CAPTCHA.

So it should be you then, shouldn't it?

Anyway, to repeat myself once more again, the "captcha" till it was gave no problems. The new one nothing but problems.
You should try it yourself.


Thanks, Chris. Like you wrote in a comment on Dosbat:

PIOMAS is driven by the atmospheric state as represented by NCEP/NCAR, the ocean element is driven by assimilation of sea ice concentration and SSTs. There is no specific 'forcing' by externally specified ocean currents.

Maybe this is the reason why the thickness of thinner ice at the margins is overestimated. And maybe this overestimation has become bigger in 2010 and 2011 than in previous years, because 'warm' ocean currents have gnawed more at the first year ice from below?


Kris, I'm going to ask TypePad support about this. I really don't have a clue why you're getting these reCaptcha problems.

BTW, let's take this to the Open Thread. :-)


Always bothered me that Piomas didn't seem to correlate very well to changes in area.

However, assuming the models have remained the same throughout the all the data, then it should still be very good for identifying trends, it just may be over estimating or under estimating the exact values at some parts of the year.

I noticed on the volume / area chart that just eye-balling it, would take another 7 years for the annual maximum average thickness to get below the 2005 minimum average thickness.

This would be a complete bifurcation in 14 years.

This corresponds nicely to the Barrow, Alaska CO2 curve, which has a complete bifurcation, i.e. annual minimum exceeding the old annual maximum, every 12 to 14 years.

so while it's not literally correct, assuming PIOMAS is at least properly identifying the annual trend, it makes perfect sense given other GW related data.


I am wondering why you would predict the loss this year to be equal to the highest loss ever? Why not take a 4 year average instead of 18.25?
There doesn't seem to be much of a steady trend. 16.5 average from 2002-6. 2007 a big anomaly year. Then a step up since 2007 to an approximate 18.25 average. If you wanted to be even more conservative you could say that volume loss peaked in 2010 and might revert further to the historical trend to be below 18 this year.
Based on the numbers I think 18 is a safer guess than 19, but I'm only looking at the graphs to try to eyeball any trends.

I just guessed the numbers off the graph but they are probably close.

2002-27.6--- 10.8 --- 16.8
2003-27.3--- 10.3 --- 17
2004-25.8---- 9.9 --- 15.9
2005-26.2---- 9.2 --- 17
2006-25.1---- 9.0 --- 16.1
2007-23.9---- 6.5 --- 17.4
2008-25 ------ 7.1 --- 17.9
2009-25 ------ 6.9 --- 18.1
2010-23.4 --- 4.4 ---- 19
2011-22 ------- 4 ---- 18
2012-22 ------- 3 ---- 19

Chris Reynolds


Not clear to whom you're speaking. But if we're talking about taking PIOMAS as a good proxy for volume then the last two years have shown odd behaviour - massive loss of volume in the Spring. That's odd in the context of 1979 to present.

So I'm not convinced taking a 4 year average is the best thing to do.

Rob Dekker

Chris, I agree.
I never really understood the physical causes of the 2010 PIOMAS ice loss. Or the seemingly strange change in rate of volume loss during spring over the past few years.

Maybe PIOMAS also does not quite know what is happening, only that MYI is getting thinner and reduces in coverage....


On Real Climate, a guest commentary by Axel Schweiger, Ron Lindsay, and Cecilia Bitz "PIOMAS, Prediction, and the Perils of Extrapolation":

Kevin McKinney

Yes. In pursuing a comment on that RC thread, I came across this blog, which I am sure will be of interest to many here:


(A link! Now let's see if I get a Captcha...!)

Kevin McKinney

Nope, no Captcha.

Yvan Dutil

Speeking of PIOMAS, there is this nice post about it on Realclimate:



My first reaction on the Schweiger, Lindsay and Bitz RealClimate contribution is simple. 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. Interesting, but meanwhile I don’t feel appealed when they use the word ‘misdirected’.
I cannot direct my concern for the planet in the scientific method. I think information, measurement can be useful in a restricted time and place. Beyond that, I can only ‘feel’ what it’s all about.


Some remarks on the above:

‘Because sea ice is strongly driven by the atmosphere’
I’m aware they address sea ice variability. But lately I attained much more info on the role of the seas in transferring energy surplus. I wonder if their point isn’t overstated here.

‘coupled model simulations have shown that even removing all the sea ice in a particular July has little lasting impact on the trajectory of the ice after a few years’
I wish them the best in virtually recreating our world, but this is probably one of the most difficult problems to solve: they’re other worlds.

‘First, an appropriate function for the extrapolation should be chosen.’
Our graphics specialists on the blog now that their method is statistic. So the word ‘misdirected’ can only apply to the writers’ determination to direct themselves to evaluating physics and justifying appropriateness... that's okay, we'll ring the bells.

‘CCSM4 (Fig 3). The characteristic flattening of this trajectory, at first order, arises from the fact that there is an increasingly negative (damping) feedback as the sea ice thins’
That’s a subject we often discussed on the blog. I still wonder whether that would be ‘appropriate’

‘Periods of rapid decline are followed by slower periods of decline or increases.’
This one really boggles me... Do they mean a geological scale? I can’t remember having witnessed general increases since I took an interest in this around 2003. As for slower periods of decline: it’s been going down steady ever since 2003, with an unforeseen smash in 2007.

‘We have to remember that part of the observed trend is likely due to natural variability’
I wonder what Hansen would say on this...

Bob Wallace

I've giving the paper only a quick once-over. A couple of things -

1) "Clearly, linear, quadratic or exponential functions do not properly reflect the flattening of the trajectory in the next few decades seen for example in the CCSM4 (Fig 3). The characteristic flattening of this trajectory, at first order, arises from the fact that there is an increasingly negative (damping) feedback as the sea ice thins described by Bitz and Roe (2004) and Armour et al. (2011)."

Does anyone know what those increasingly negative feedbacks are that Bitz - Armour describe?

2) The CCSM4 model runs stretch the survival of the ice out to well past 2060. Assuming that the PIOMAS numbers are roughly correct why does Schweiger not raise a red flag and pull his graph? It clearly is doing something different that what is happening.

It seems to me that he has made an assumption that the ice will survive because it's been long thought that the ice will survive. This assumption looks to be inconsistent with PIOMAS reality.

(I suppose if you can see those unspecified dampening forces charging in from over the far ridge....)

Bob Wallace

"Because low clouds have a net warming effect at the surface, October cloud increases may be responsible for the enhanced autumnal warming in surface air temperature, which effectively prolong the melt season and lead to a positive feedback to Arctic sea ice loss."

Wu, D. L., and J. N. Lee (2012)

Sounds like increased cloud cover is not one of the dampening forces which will help save the ice.


(Will Typepad auto-shorten links? Some blog software does.)


I don't know the details of how the various models do and don't include some features. But it struck me that they didn't explicitly mention warm ocean currents.

So either I'm missing something because I don't know what is/n't included in the modelling, or they're excluding or overlooking what appears to me to be the big invisible effect on ice volume. The warmer oceans thinning, or at least inhibiting thickening, of the surface ice from below.

Someone? Anyone?

Chris Biscan


Yes, that is definitely happening, the shallower sea's have rivers of heat under the ice. There is much buoy data out there from the Russians(1950s-1970s) Then more internationally afterwards, and many sources from the 90s to now. But even more post 2004.

Basically the arctic between 25M and 200M is warming rapidly in many places and heat is building year after year.


More on this sort of research was on our blog before: see 'Polar ice caps can recover' august 19, 2011.


The thing seems to be aspects of hysteresis, irreversible thermodynamic change, studied through modelling.
Haven't yet found what FI Armour considers 'a dampening feedback', but it's possible his models give responses that 'just' point at not yet identified processes.
It enforces my gut feel that this has very limited relations with our real world...

Peter Ellis

Werther: We've discussed the feedback ourselves multiple times, and it's covered in the papers they reference.

Simply put: thinner ice at the summer minimum allows more heat to radiate to space during the re-freeze. The more ice you lose during the summer, the more you form during the winter.


Ji Peter,
I remember that, yes. In the meantime, we saw how the Barentsz/Kara seas remained anomalously ice free, while massive OLR/radiation did not enhance refreeze, but instead 'bulged' the troposphere and reshaped the entire NH Rossby-wave configuration. The thin ice/rapid refreeze theory only works when the constant influx of heat through the ocean stops.


A few comments on the reactions to the Realclimate piece.

1. The role of natural variability in complicating efforts to extrapolate the observed trend.

This is simply a known unknown. We know that there is considerable natural variability driven by the atmosphere. One can see this on a week-by-week basis during the year, as well as on a year-to-year basis.

I thought that their example of extrapolating trends on the basis of the model results for 1979-2012, and comparing that with what the models actually did, was quite a convincing demonstration of the pitfall of relying on extrapolation.

2. Possibly negative feedbacks.

I think the issue here is that the last 2 million square km of ice, or so, could well be a lot harder to melt than suggested by an exponential trend/positive feedback arguments.

I think there's some reasonable arguments in favour of this. It's all piled up against the coast of the Greenland and the Canadian archipelago. It's much further north.

It's hard to work out how that balances against the positive feedbacks - more solar radiation absorbed by open ocean, reduction in multi-year ice.

Our "best guess" at assimilating all these processes - coupled ocean/atmosphere/sea-ice models - suggest that the negative feedbacks will delay the final loss of sea-ice.

The best guess might be wrong, but I still think that it trumps simple extrapolation.

3. Final thoughts. Let's look at this another way. Bearing in mind that Arctic temperatures are extremely anomalously high - due to AGW - that there are obvious ice-albedo positive feedbacks at play, and that the weather over the last decade or so has been more favourable for sea-ice melt...

You could argue that the sea-ice has been surprisingly robust to have not disappeared already. Using Cryosphere Today area figures, the minimum has actually declined by less than 50% from the highest minimum since 1979.

If you imagine that the weather over the next decade or so becomes generally less favourable to summer sea-ice melt, then it is not outlandish to suppose that we could have a pause in the decline of summer sea-ice, even though the underlying trend continues down.


If you imagine that the weather over the next decade or so becomes generally less favourable to summer sea-ice melt, then it is not outlandish to suppose that we could have a pause in the decline of summer sea-ice, even though the underlying trend continues down.

That's one thing, the other thing is the AMO, the third thing is that darn CT SIA maximum, that keeps me careful and conservative.

Bob Wallace

Peter -

"Simply put: thinner ice at the summer minimum allows more heat to radiate to space during the re-freeze."

But based on the Wu paper (above at 3:20) this heat radiation could be trapped by increased cloud cover. A possible partial/total cancellation.

Bob Wallace

If you imagine that the weather over the next decade or so becomes generally less favourable to summer sea-ice melt, then it is not outlandish to suppose that we could have a pause in the decline of summer sea-ice, even though the underlying trend continues down.

What might we expect from the weather over the next decade?

Might more heat/energy in the system lead to stronger storms and more heat transfer from outside the Arctic?

There seems to be an agreement that we are likely to see stronger (but not more frequent) tropical hurricanes/cyclones as the planet warms.

Those of you who have watched the Arctic weather over years, has the weather been somewhat usual and more of a contributor to the melting we've seen?

Is there any indication that we've been in a weather-melting cycle and, if so, that we might be reaching the end of that cycle?

What mechanisms might cause the weather to become more benign in its treatment of the Arctic ice?

Chris Reynolds

Bob Wallace,

The main negative feedbacks are:

1) The rapid growth of new ice over the freeze season in areas that are newly ice free at the end of the melt season. Freeze season = Oct to March. Melt season = April to Sept.

2) The increased loss of heat fromm newly open areas of ocean - the Titesche effect.


Wasn't there some paper recently that turned the whole knowledge wrt inversion upside down? What does that mean for the Tietsche effect?

What mechanisms might cause the weather to become more benign in its treatment of the Arctic ice?

The big known unknown for me is the AMO, and I still haven't looked into it, 1) because I'm lazy, 2) because I fear I won't find a conclusive answer.

Bob Wallace

We can identify several accelerating forces.

1) Thin ice has less albedo effect. The water below thin ice warms faster.

2) The freeze season is starting later.

3) Overall atmospheric temperatures are rising.

4) Snow levels seem to be declining. (The loss of an insulator and loss of albedo.)

5) Increased open water makes for stronger wave action and physical destruction of the ice. (Longer fetch.)

6) Open water allows for more spreading/melting and increased transportation out of the Arctic.

7) An overall thinner ice pack allows for more motion and more dispersion.

8) Increased organic growth makes the water darker, trapping more heat.

9) Late melt season clouds trap heat.

10) More energy in the season could/should mean stronger, more destructive storms. More ice transport out of the region.

11) Overall thinner ice means bottom melt is reaching a larger percentage of the ice.

12) Even if the amount of incoming heat remained constant there is less mass to melt. More energy will go into heating water which will delay fall freeze-up.

13) Loss of snow/ice cover on surrounding land masses. Less albedo allowing more heat build-up. And less energy going into melting that land snow/ice.

14) We've just come out of a low solar cycle and have headed into a high output cycle.

15) Surrounding oceans temperatures are increasing which means that what outside water enters the Arctic is going to be warmer.

16) Ice transported out is going to melt quicker, thus reducing resistance to the next pieces from moving out. Less for the winds to push.

While there are some 'dampening' factors seems like they would have to be quite strong to overcome the repeated melting we're observing.

1) "The increased loss of heat fromm newly open areas of ocean - the Titesche effect."

2) Possibly more melt season cloud cover.

One list is long, one short. I don't see any heavy duty factors in the short list.

(What factors have I missed? I do suffer from a leaky memory....)

Bob Wallace

Dampening factor -

3) Thinner ice at the summer minimum allows more heat to radiate to space during the re-freeze.

Bob Wallace

4) (L)arge cracks in winter’s (thinner) ice cover help create new ice, since the extremely cold air in contact with the liquid ocean promotes refreezing, which leads to a sheet with greater surface area than before."

Rampal et al. hidden behind a wall one can't even buy their way through...


Chris Reynolds

Bob Wallace,

And your model of these factors shows????

I'm sorry but counting and listing is irrelevant, you need to model the relative effects and interactions of the factors. I'm sorry if I seem terse, I really don't mean to, but do you really think counting factors is valuable?

BTW you've missed the Arctic Dipole out of your list of positive feedbacks - and it's probably the key player in recent ice losses.

I know it's not great netiquette, but on a technical note - it's 'damping'. The term is from electronics and is in turn from 'damping' a fire - like closing the flue in a chimney.


As I've blogged on one paper recently I can suggest; Boe et al, which finds that models suffer from excessively strong polar inversions meaning they have excessive cold above the sea ice making thicker sea ice than observations. There's also a paper by one of the Zhangs (IIRC) that looks at the reduction of the polar inversion due to warming at the surface.

Bob Wallace

I ain't got no stinkin' model. ;o)

I'm just trying to get a list of factors which could speed or slow the rate of melt. Someone would have to figure out the weight of each to make a model worth calling a model.

I suppose my very simplified quasi-model is that there are a lot of things on the melt side which should increase in strength as the ice lessens and not many factors which could push back. And the damping factors don't appear to be particularly strong.

I do think listing factors is important. I'm not sure how one would build a good model if things are omitted. And this spins out of the Schweiger paper on Real Climate. That model is clearly not tracking the PIOMAS data.

(No problem with correcting 'dampening'. While it seems to be correct word meaning, it probably isn't standard use. Thanks.)


As I've blogged on one paper recently I can suggest; Boe et al, which finds that models suffer from excessively strong polar inversions meaning they have excessive cold above the sea ice making thicker sea ice than observations.

I think that was the one, Chris. Thanks.


Just a few possible list item issues:

4. Albedo and insulator act in opposite directions so which list should it be on? I also suspect/guess snow is increasing volume at high latitudes while area at lower latitudes is decreasing. Reasoning here being the temperature differencials between water and land may be increasing so snow more likely to be dumped as soon as clouds go over cold land.

6. More ice area spreading out - sure. But if the ice is thinner the volume transported out could be falling even though area is increased. Also if there is less ice near Fram Straight as the ice retreats perhaps we could even get less area transported out despite more area spreading.

7. More motion but is this more area but less volume?

10. As above, more area but is it more volume?

13. As 4 above could be more snow on high lattitude land and less at lower latitudes.

If all 5 of these issues mean these items should be moved to other list, then 16-5=11 which is not much different than 4+5=9.

11v9 is certainly close enough that you need to be able to (at least roughly) assess strength of all these effects.

Daniel Bailey

A copy of Rampal et al can be found here:

Bob Wallace

Thanks for the input crandles.

4) I was thinking that the snow would insulate the ice below from warmer air temps.

If there is more snow at higher latitudes then 'less snow' belongs on one list, 'more snow' on the other.

6. Thinner ice should be more responsive to wind. When the wind comes up the ice should start moving quicker and it should take less force from the wind to transport it out.

Wind moves surface water, not deeper water.

Toward the 'final melt' there could be far less ice to transport out, but would not the proportion transported remain somewhat steady?

7. My thinking is that thinner ice breaks easier. Those pieces are going to move around a lot. Edges grind. A higher ratio of edge to surface.

It will figure into area, but that's only a two dimensional measurement.

10. A larger ratio of area:volume can only be achieved by thinning the ice. That's not good for ice's long term survival.

13. Quite possible. But low altitude land mass is generally close to the shore where the extra heat may help melt the fast, MYI.

And there's less high altitude uncovered land mass than low altitude land mass. The high Greenland mass, for example, is well covered by ice. Some extra snow would not be covering land now exposed during the melt season. It's the low altitude parts of Greenland that are snow/ice free for part of the year.

After writing my 19:51 post I lengthened my damping list. And I can see that some of the speeding list items are not as clear cut as I originally thought.

I'm still trying to understand the factors at play. In no way can I start to give then weightings, way over my pay grade.

I think the most I can get out of this exercise (unless someone steps forwards to educate me) is that I can identify factors to keep my eye on to see how the final part of the melt curve might look.

Bob Wallace

Daniel - thanks for the Rampal link. Having that beforehand would have saved me a lot of thinking. ;o)


>"I was thinking that the snow would insulate the ice below from warmer air temps."

I was thinking of snow insulation slowing down the transfer of heat from warm water to atmosphere and less heat transfer means less ice formation. So have we now got 4 insulation issues and 2 albedo issues?

>"Thinner ice should be more responsive to wind." ... "start moving quicker "

I get lost trying to think this through. Thinner ice has less freeboard on which the wind can work but there is also less mass to accelerate so does that leave the same acceleration? The real/more significant differences being 1. Less resistance to moving out of pack due to other ice being thin and 2. Faster winds from stormier weather.

I wrote "More ice area spreading out - sure." but now think even that is at best dubious. We have ice moving faster but does this work in a Boyle Law fashion such that area including spaces between are proportion to temperature=speed of movement. So it seems possible that the ice moves faster but gaps between are larger so that area passing any point might be the same. It might not work like Boyles law so area passing through fram straight could be more or less despite the higher speed of movement. If the ice is thinner the volume moving out seems certain to be less.

>"Toward the 'final melt' there could be far less ice to transport out, but would not the proportion transported remain somewhat steady?"

Sorry, I don't know. I was thinking it spreads out more but if there is a greater distance to fram straight then I don't see how you are concluding proportion would be the same.

>"My thinking is that thinner ice breaks easier. Those pieces are going to move around a lot. Edges grind. A higher ratio of edge to surface."

Sure edges grind. Circumference of circle to area seems at first to give a higher ratio of edge to surface area as radius (R) decreases: 2.Pi.R/Pi.R.R = 2/R which increases as R decreases. However isn't the edge we are interested actually the area of the surface edge to the surface area. Modeling as shallow cylinder rather than a circle, this gives us 2*thickness/radius. As both thickness and radius decrease, I am not sure there is much effect in the way you are thinking.

However, there are other complications like the cylinders grinding might have different thicknesses when only the thinner thickness matters. ...

Think I probably need to wish you good luck with both identifying the factors and keeping your eye on them.


Bob, you asked

What mechanisms might cause the weather to become more benign in its treatment of the Arctic ice?
There doesn't have to be a mechanism, it could simply be random.

Let's imagine that the weather can either encourage sea-ice melt, not encourage sea-ice melt, or be some balance of the two, with equal one-third probability.

The probability of 5 or more years in a decade being conducive to sea-ice melt work out to be a little more than 20%. So it could simply be chance that we've had a few years that have supercharged the sea-ice death spiral, and produced a short-term trend that you can extrapolate to ice-free before the end of the decade.

My point is that there's no compelling evidence to disprove this hypothesis.

It's normally the fake sceptics who allow themselves to be blinded by the noise and ignore the signal. I don't think we should seek to balance things out by doing the same in the opposite direction.

John Christensen

Hi guys,

I will need to bother you with my uneducated comments;
- Evaluating the PIOMAS graph at the top of the post, I had the same suspicion that (as most models trying to calculate a total from an uneven structure) it would probably overestimate the lows (thickness of thin ice) and underestimate the highs (thickness of the thickest ice).
You will notice that from Feb. 1 2012 and the following couple of weeks the increase in volume departs significantly from the same period a year earlier, and as we all know the strong high-pressure over NW Siberia caused a significant concentration of sea ice in the Beaufort and Chuckchi Seas. The PIOMAS graph therefore seems to have underestimated the increase in sea ice thickness in the NA region of the Arctic, and as thin ice subsequently covered large parts of the Kara Sea, PIOMAS responded by quickly 'catching up' again on the volume chart.
I believe I saw a posting on higher than average ice thickness in some areas, but was that along the NA coastlines?
And from a 'sea ice optimist observer' perspective my hope from that sea ice concentration event, was that it would exactly expose more water to the cold air for a period and increase the heat flux.
This should have been a contributing factor to the spike in Arctic air temperatures measured for February in some regions, while temperatures stayed low where sea ice extent was at or above normal in the Bering and Baffin Seas, insulating the athmosphere from the water.

So the upside of such an ice concentration event should be that a a thicker/better protected pack is created in one place (hopefully also far away from the Fram Strait), while increasing heat flux, cooling the water and building new ice faster than would otherwise be the case.
Downside would be that the new ice is thin and quickly melts away allowing more radiation to reach the water in late spring and summer.

So is building ice volume more important than keeping water covered with ice to avoid radiation to reach the water??

Is this a valid scenario to be observing in the coming months?

John Christensen

One sea ice movement:
From childhood observations of ice being built up in fjords and coastal areas, it always seemed that both thin and thicker ice would be moved easily by the wind, maybe because the wind is moving both the top layer of the water as well as the ice being out of water.
If that is true, then wind patterns (accidental as well as those related to oscillations) should be a considerable factor in either keeping ice at protected high latitudes or pushing it to lower latitudes through the Fram or Bering Straits.
It would be interesting to see how seasons with predominantly southernly or east/west wind correlates with SIA or MYI, and also how these wind patterns correlate with AO, NAO, or the AMO, but others on this blog probably know this?
Secondly; if we have a strong positive AO (such as '88-'93) or a strong negative AO (such as '09-'11), I guess while the AO+ is protecting Arctic climate from storm systems from lower latitudes, it also reduces the Arctic heat sink effect and thereby may be a contributor to global temperature increases, while the AO- 'exposes' Arctic sea ice to a greater extent, but on the positive side increases the heat sink effect, potentially keeping global temperatures down to some extent.



Interesting questions John. Sorry no help from me.

>"Evaluating the PIOMAS graph at the top of the post, I had the same suspicion that (as most models trying to calculate a total from an uneven structure) it would probably overestimate the lows (thickness of thin ice) and underestimate the highs (thickness of the thickest ice)."

My understanding is that PIOMAS ice thickness is entirely the product of a model. Assimulation of data is limited to ice **concentration** and SST - i.e if model shows ice in an area where there is none then the assimulation changes the model information to say no ice here. So it seems to me that it isn't a matter of "trying to calculate a volume from an uneven surface".

This is my understanding of what it says at http://psc.apl.washington.edu/wordpress/research/projects/arctic-sea-ice-volume-anomaly/

Doesn't mean the bias isn't as you expect, but being as you suspect does not seem likely to be strongly supportive of the suspected PIOMAS bias.

Sorry if that is more hindrance than help.

Bob Wallace

If I'm reading the Rampal paper correctly the speed of ice drift has increased as the ice has thinned.

"From buoy data, Rampal et al. [2009] showed that the sea ice drift speed has increased at a rate of 9.0(±1.9)% per decade on average within the Arctic basin from 1979 to 2007...."

(Page 3 - link in above comment)

The ratio of freeboard:keel should stay roughly constant.

The ratio of "rough surface"/sail:keel will increase - wind will have something to push against in addition to the exposed edge/freeboard.

Water close to the surface is moved more by the wind than is water deeper. A recent articles on ice bergs stated that they are moved little by the wind since they protrude so deeply into water that is not moved by normal winds.

Bob Wallace

Misfranz - Obviously we can't predict the weather conditions coming at us well enough to see the future of the ice. But whatever happens the ice will be at the mercy of physical forces, not something called "random".

Fake skeptics, as you call them, start with a belief and then look for data/arguments they can use to "prove" their belief.

Starting with an observation that Arctic sea ice volume seems to be dropping very rapidly and then trying to list/understand the factors which could speed or slow further ice loss doesn't seem like backwards-denying.

John Christensen

Hi crandles,
From the PIOMAS model:
"The assimilation of observations into numerical models currently provides one way of estimating sea ice volume changes on a continous basis."
Does the model not provide an estimate of ice thickness based on the combination of satellite observations and the concentration of that ice as part of the assimilation?
What I have noted sometimes for the waters between Denmark and Sweden is that e.g. DMI (http://ocean.dmi.dk/satellite/index.uk.php) in dark/cold months suddenly will indicate ice cover, where there is no ice, but just no wind and low, cold clouds, and at least a couple of times on trips to Asia from the US east coast I have noticed visible sea ice from 10KM altitude, where CT has indicated open water.
So I was guessing that cold water/very thin ice is difficult to measure correctly and also that e.g. when ice reaches a certain thickness it would be more difficult for satellites to pick up that additional 50cm rather than the first 50cm for younger ice, as older packed ice potentially also with snow cover would be more similar after some time.
I may be completely mistaken, so guidance is appreciated.


John, I have this critique on your 15:53 post
Why would you feel such suspicion looking at the graphs? PIOMAS puts 2012 more or less on the same level last months. Wipneus’ first graph shows volume not as low as expected. The second shows theoretical thickness and looks ‘appropriate’ (thanks to Schweiger, Lindsay and Bitz).
I see theoretical thickness getting slashed in that timeframe. If your suspicion stems from that and high-pressure over NW Siberia, than I have difficulty following you. You are right; weather during jan-mar favoured the sea ice in the Beaufort-Chukchi Seas. But that was due to regional configuration, not the single driving consequence of the configuration elsewhere, FI the Kara region.
I see where you’re going... PIOMAS missed the thickness growth you suppose in the Beaufort-Chukchi region and overvalued thin ice on the Kara Sea since a month. But your shortcut here cannot account for what you make up from PIOMAS. Both regions make up 14% of the Arctic Ocean. Without Bering/Ochotsk! PIOMAS can only be evaluated against all sea ice regions. I remember having seen a report for 2.4 m thickness in the Chukchi near Barrow. If that’s the standard, 2012 would have 1.2 million km2 x 0.6 m more volume than last year over there: 720 km3. But I think it’s justified to calculate a 1200 km3 less in the Atlantic sector (Barentsz 0,4, Kara 0,5, Laptev 0,7 and Basin 1,0 million km2 x 0,45 m; see also aari.ru).
Why would PIOMAS be equal to 2011? Plus 0,9 million km2 x 0,5 = 450 km3 in the Bering, Ochotsk and Baffin regions.
You guess thickness growth in the Beaufort-Chukchi can be attributed to concentration. To have as consequence more open ocean at the other side. IMO that doesn’t work on a scale of 1500 km. To me, it was a good, hard freeze over there during jan-march and little snow cover. And no ice growth at all at the Atlantic side. From your point of view, your mechanics should have lead to strong heat release on the Atlantic side. Again, you are right in that release, but it didn’t stem from your mechanics. It was the Atlantic Multidecadal Oscillation at work.
I think your concentration-mechanics and restrain to effects in just 14% of the Arctic lead to erroneous expectations for the melt to 'dampen' this year.


The Rampal paper is one of the few papers I have excerpted so far in the Papers subsection.

Chris Reynolds


A few points following on from Crandles...

4) Snow. Actually Cohen has done work which suggests that a lack of winter warming trend over Siberia and N Europe is due to increased snow in Siberia in Autumn, probably due to more open Arctic water. This however increases the occurrence of Warm Arctic Cold Continents patterns (e.g. 2009/10 & 2010/11) which means warmer period over winter in the Arctic due to increased heat flux from mid lattitudes.

6) Actually surface winds cause a net movement of ocean and ice to the right of the wind's direction. This is caused Ekman Transport.
e.g. http://oceanmotion.org/html/background/ocean-in-motion.htm
There is no trend in net mass of ice transported through the Fram Strait.
Although due to increase of speed of transport through Fram, area flux has increased in recent years (Smedsrud et al, 2008).
The Smedsrud paper is available in the references here:


Re sea ice speeds, they have gone up.
There's a PDF of the source paper available search string "Sea ice drift in the Arctic since the 1950s."


I don't think it is just chance weather.

The Arctic Dipole is the key to the weather issue. It's become a major player in recent years, and has a clear role in major episodes of ice loss in the 2000s, and possibly this decade. See the third and fourth posts (and if you don't believe me check the paywall free references) here:

John Christensen,

The AO has had a role in movement of sea ice, a strongly positive AO in the 1990s caused a substantial increase in export of sea ice through the Fram Strait (between Iceland and Greenland). However since then the correlation between sea ice and the AO has weakened, and before the 1990s a generally weaker correlation has been found. So it is possible that the changes in atmospheric circulation leading to the emergence to dominance of the Arctic Dipole had a role in the large 1990s Fram Strait export. More recently the Arctic Dipole is arguably seen to have a greater impact on sea ice.
That graphic shows years of ice loss (underlined in red) and the summer and winter Arctic Dipole index, named DA in that graphic.

I think the thicker ice is in the Pacific sector (Beaufort Chucki etc), with a large bite of thin ice in Barents/Kara. The February hot spot IIRC was over Barents/Kara (NCEP/NCAR) so likely was due to open water. This should mean more ice in the Beaufort Gyre Flywheel, which normally would be considered a stabilising influence. However if the Barents/Kara melts out to leave a large hole early in the season with the right winds this could fill with ice from the Siberian sector reducing the stabilisation of the gyre as it delivers the ice into the Siberian sector.

It's taken me so long to write this reply there's been a flurry of posts in the meantime. :(


Crandles is right about SST and ice concentration. I'll try to sketch a diagram of PIOMAS in words....

Atmosphere (NCEP/NCAR reanalysis)


PIOMAS (Ice and Ocean modelled).--> Modelled Volume.


SST and ice concentration (satellite observations)

Chris Reynolds


"...strong heat release on the Atlantic side. Again, you are right in that release, but it didn’t stem from your mechanics. It was the Atlantic Multidecadal Oscillation at work."

The AMO has been neutral/negative so far this year, last year it was positive.

Yet using Mercator:
The SST anomalies in the Atlantic sector are surprisingly similar.

So I don't think the AMO is involved.


>"Does the model not provide an estimate of ice thickness based on the combination of satellite observations and the concentration of that ice as part of the assimilation?"

I could be wrong. I see
"Model and Assimilation Procedure
PIOMAS is a numerical model with components for sea ice and ocean and the capacity for assimilating some kinds of observations. For the ice volume simulations shown here, sea ice concentration information from the NSIDC near-real time product are assimilated into the model to improve ice thickness estimates and SST data from the NCEP/NCAR Reanalysis are assimilated in the ice-free areas."

Note the 'some kind of observations' and the link to what is described as an ice *concentration* product. If they were assimilating ice thickness information from somewhere then I think there would be a link to such information they are assimilating.

I have also seen an explanation I think by Axel Schweiger, saying what I am trying to explain that the corrections to the model thickness are only where model has ice but observations show have no ice. Alas, I cannot remember where I saw this or when. If it was before change to version 2 then page linked seems clear about improvements brought in with v2 being assimulation of SSTs and by using a different parameterization for the strength of the ice. No indication of a change to also assimilate thickness information.

Sorry if this is all rather vague and inconclusive due to memory and potential misinterpretation issues.

Anyway to attempt an answer to your question quotes at beginning of post, I think:

Yes the model does provide an estimate of ice thickness. This model estimate is improved as a result of assimilating ice concentration information. But there is no measurement of ice thickness being assimilated into the model.

The modelling does involve calibration and verification against thickness measurments from various sources but this isn't the same as assimilating thickness information on a near real time basis to correct/improve on the model calculations.

John Christensen

Thanks crandles!

And on the factor list:

- Warmer Atlantic water entering Arctic Basin via the Fram Strait

Was just reading the 1/28/2011 Science article on "Enhanced heat transfer to the Arctic by warm Atlantic water".
Apparently water temperatures in the eastern part of the Fram Strait went up starting as early as 1850, being now around 2C warmer than in the preceding 2 ky.
Reference is made to increased CO2 and also some uncertainty around dating of the top sediment layer, but irrespective of this being solely the result of AGW or combined with other reason for sea current changes, this does not bode well for the ice sheet..

And Werther,

The sea ice concentration in Jan/Feb seemed to cover vast parts of the Arctic Basin, changing the wind pattern from its normal direction that time of year being towards east Greenland to instead go across from Eurasia towards NA, but agreed that developments in Bering/Othotsk played their part as well.


Chris Reynolds,
I may have used the term AMO wrong; it’s difficult to be exact in contributing anything within the right definition.
But do you think the anomalous heat/SST in the Barentsz/Kara region was solely induced through insolation? The whole Arthun-study was made around Atlantic influx.

Chris Reynolds


Using salinity as a proxy for influx of salty Atlantic waters: 2012 shows a substantial influx of high salinity throughout the Arctic basin. Whereas 2008 - 2011 show a similar pattern, intense salinity anomaly in the Atlantic sector, with lesser anomalies drawn into the Arctic from that; the pattern in these years is nowhere near as extreme as 2012. Notably 2007 shows much less of an anomaly (the other years have deep red anomalies, 2007 is mainly blue and yellow.

So if we can take Mercator at face value and accept salinity anomaly as indicative of Atlantic waters, there has been a substantial influx of Atlantic water into the Arctic since 2007. This makes sense because the growth of much more first year ice over the winter leads to brine rejection as the ice forms, and this brine rejection (of near freezing water) disturbs the stratification of the ocean. Atlantic influx, being salty and dense, typically falls into the Arctic abyss near the ice edge in the Atlantic sector. Cold brine rejected from the ice will allow the Atlantic water to mix upwards.

To be clear, Mercator salinity during the Autumn shows more substantial anomalies at the surface across the Arctic. So I think this is brine rejection, and the recent Atlantic influx is not an immediate matter of brine rejection.

So yes, there is a role for Atlantic waters. And no I don't see a role for insolation in that region in January/February.

My understanding being that - this influx of warm Atlantic waters probably lead to the recent loss of ice in Barents/Kara. That loss of ice lead to surface heat fluxes; NCEP/NCAR shows +15degC anomalies very localised where the ice was missing but a less localised warming anomaly of only +5degC at 500mb. Crucially there was a strong positive anomaly of specific humidity right where the ice was missing in B/K. The surface heating anomalies drove the development of the high pressure. And, as an aside, that high pressure lead to a cold outbreak of Arctic air into Europe.

John Christensen


To understand your argument correctly; Are you saying that since the summer SIA anomaly is higher than the winter SIA anomaly, then that increased building of sea ice (compared to prior summers with lower summer SIA anomalies) has caused increased brine rejection, subsequently disturbing the water column bringing warmer water towards the surface?

Chris Reynolds



Tim Lenton has been arguing recently that the seasonal cycle has increased since 2007's crash. We know from the drift age model and QuickScat satellite observations over the last decade that the ice pack has transitioned from a mainly multi-year ice pack to a mainly first year ice pack. So each year more ice grows in the Winter than was previously the case.

As there is an increased amount of sea ice growth there is increased amount of brine rejection. From what I've read it is thought that this is responsible for changes in the cold halocline in some parts of the Arctic Ocean.

I've been looking for a reference for this, the nearest I've come to it is an article based on work by Catlin Survey.
Although I've definitely read this explanation in another paper, as an aside in that paper so I can't find it at present.

There is a paper by Bourgain & Gascard that attributes changes in the halocline in the Canada Basin and Makarov Basins to the AO and AD, those basins being where the ice hasn't receded so much.
While that source states: "some observations point out that salt/heat diffusion from the Atlantic water
underneath and brine rejection during sea ice formation from above could be
responsible for salt content variability within the halocline and, as a consequence,
being influential for the variability of the halocline."

That paper's abstract concludes that changes in the halocline did not drive the recession of sea-ice.

Veli Kallio

We at FIPC (Frozen Isthmuses Protection Campaing of the Arctic and North Atlatic Oceans) use indice of melt day ratio.

We monitor the area of melted sea ice each day if the sea ice melt during the day is greater or lesser than one required for the complete disappearance of sea ice by the end of the current melting season.

Like the other indicators, the number of days in excess of ice melting to induce complete disappearance of the remaining sea ice is rising. We can also say how many days too short is the season this year.

The indice uses the average annual minimum point and the number of days until it dividing the remaining sea ice area. If the melting exceeds the required rate, then sea ice was on course that particular date for complete disappearance of all ice being lost.

The number of melting days when the speed of melting is above rate of complete loss is rising and PIOMAS indicators must be right.

Chris Reynolds

Hello Veli Kallio,

Due to language difficulties I don't follow your explanation of how this works. Paragraph 3. But I'm interested.

As the profile of both area and volume change through the year is approximately a sinusoid, the rate of change will vary with time. I don't understand how you account for this.

Are you using some index of area or extent to work out melting days? If so you are missing out on melt in areas that doesn't impact area/extent immediately, but may have a delayed impact on area/extent later in the season.

I know I am late in answering you. But if you do see this reply, feel free to answer in your own language and I'll use Bing Translator.
Hope you don't mind this Neven.

You can contact me in comments at my blog.

Artful Dodger

The trend in the lengthening of the Arctic melt season is a key metric for predicting the transition to ice-free summers.
Arctic 'Melt Season' Is Growing Longer, New Research Demonstrates published in JGR in Jan 2010.

Rob Dekker

I've been reading many of your posts about my favorite topic : under-ice ocean heat flux and how it affects MYI.

I've been studying the physics of that in the past couple of weeks, and would like to share some of my thoughts with you.

For starters, I realized that due significant ice insulation, a thick MYI pack does neither grow very much in winter, nor does it bottom-melt much in summer, simply because its heat flux reduces so much.

However, ocean heat flux does not care about the thickness. This means that a small amount of ocean-heat flux will have a more significant long term effect on MYI than on FYI.

I did some calculations, which show that FYI (under ERA 40 climate) grows to about 1.6 meters. Any MYI will grow less than that.

Now, we know (physics) that 1 W/m^2 sustained ocean heat flux will knock out 10cm/year from the bottom of ice.

Thus, once ocean heat flux reaches 16 W/m^2, MYI will essentially melt out in September, and become FYI.

In reality, the 'danger' point will probably be achieved much earlier, because MYI still needs to survive summer positive feedbacks once it thins that much.

So I tentatively set the danger point (of collapsing MYI) at some 8 W/m^2 ocean heat flux.

Knowning that AW is warming up, that is scaringly small...

Before I continue, please debunk my logic...


>"However, ocean heat flux does not care about the thickness."

Ocean heat flux does not care but I think there are effects on the ice.

If the ice is thin then the heat can travel through the ice faster than heat is arriving and extra ice forms at bottom ofice. If the ice is thick then the heat cannot escape through ice fast enough and heat builds up and there is bottom melt of ice through the year.

We know MYI tends to get thicker so this melt effect of thin ice is smaller than effect of crushing thickening the ice.

An increase in upward heat flux will do more melting but does the resulting thinner ice just get crushed more to thicken it up. That would also create more area in leads where more ice is formed.

So I think there may be a few negative feedbacks on what you are thinking.


The 40% upward flux increase in the science paper was a temperature rise from 5 to 7C. That was in subsurface water entering Arctic via Fram Strait. I expect that spreads out a lot and will be a long time before there is anywhere near a 40% increase in upward heat flux over large areas in the Arctic basin. Anyone got any different ideas on the time delay or size of upward heat flux increase over most of the Arctic?

Chris Reynolds


Sorry, in the process of replying I've rambled, I post it all in the hope that some will be of use.

There is a continuing loss of MYI older than 4 years and its replacement by FYI (Maslanik - Drift Age Model). And the addition to the MYI reserves by FYI. That MYI older than four years is continuing to decline whereas MYI younger than four years seems to have arguably stabilised.
As an aside, it staggers me that this implies the typical cycling times of Arctic sea ice are now as low as three years. This is probably in large part due to the failure of the Beaufort Flywheel - that's my WAG anyway. Crandle's recent graphic of the safe zone is bang on. I should stress here that we don't really know how much MYI there is in different year categories, because each 'pixel' of ice is assigned the age of the oldest ice within it there may be a further decline of ice with age in the actual proportions of ice ages within each pixel.

I get your argument right up to where you say: "Thus, once ocean heat flux reaches 16 W/m^2, MYI will essentially melt out in September, and become FYI."
Surely, in this idealised 'model', all the FYI will melt out at that stage, 10cm/Wm^-2 X 16Wm^-2 = 160cm, the thickness you calculated from thermodynamics. But this doesn't help re the MYI. My concern here is that as the MYI store of up to four years old is continually being refreshed by additions of FYI which is then thickened by thermodynamic growth and mechanical compression. This replenishment doesn't mean it can survive indefinitely.

Then we have the interplay between energy gains due to ice albedo feedback with much of the ocean ice free - based on recent years that implies surface warming of around 5degC (above zero). And the loss of heat in the Autumn as the re-freeze is later. With possible retarded net growth through the winter due to the time taken for the ocean to cool to freezing.

Crandles, and Rob,

This post from Diablobanquisa is excellent.
IIRC it states that it takes around 2 years for Atlantic Water to get from Svalbard to the Siberian coast. As I've said before Atlantic water tends to drop deep once it gets into the Fram Basin, which is poleward of the chain of islands from Severnya Zemlya to Svalbard. However Atlantic water temperatures near Svalbard are the warmest in 2000 years (Spielhagen 2011 - is this 'the science paper'?), I think it's inconceivable that this isn't having an impact, the question is how much. I suspect that the impact is slow in nature due to the depth of Atlantic influx. More a gradual warming of the entire basin than a surface effect. This leaves the Pacific where Bering Strait influx remains at the surface, is related to the AD, and had a role in 2007.

Figure 12 in the Arctic Report Card 2011 could help get a handle on the scale of Arctic warming from Atlantic waters.
Although in terms of heat flux the key issue there is the temperature of water in contact with the sea ice.

Have both of you read "The Arctic’s rapidly shrinking sea ice cover: a research synthesis." Stroeve et al 2011?
As usual I came across it on a site (AMEG in fact) and thought I must read it, only to find I've been sitting on a copy for months. I recommend it to everyone here.

Rob Dekker

crandles An increase in upward heat flux will do more melting but does the resulting thinner ice just get crushed more to thicken it up. That would also create more area in leads where more ice is formed.

I hear you. But I think once ice gets to the point where it gets crushed and forms more leads in winter, the positive feedbacks in summer may very simply obliterate it.

So, overall (on a full annual basis), I doubt that thin ice would be still show any form of 'negative feedback' process. On the contrary : it's probably doomed to be reduced to FYI.

Rob Dekker

Chris Reynolds,
Thanks for the links to these papers.
With my theoretical estimate of 8 - 16 W/m^2 for complete demise of MYI, I was trying to point out that very little heating from below may be enough to get the Arctic into an ice-free state (at least in summer).

As you mention :

I think it's inconceivable that this isn't having an impact, the question is how much. I suspect that the impact is slow in nature due to the depth of Atlantic influx. More a gradual warming of the entire basin than a surface effect.

Even after reading many papers on AW warming, it seems to me that we actually know rather little about how much of a warming Atlantic eventually makes it to heat flux into the bottom of sea ice.

In that regard, did you guys read this (2012) presentation by Polyakov ? :

I specifically were intrigued by his assessment of "double-diffusive heat flux" which gets heat up from the depths of the Arctic :

Double-diffusive heat fluxes across several diffusive layers occupying the 150–250-m depth range and overlying the AW core from the eastern Eurasian Basin are ~8 W/m^2

If AW warming water makes it under the ice, then, without a significant change in salinity gradient, we may wonder where else but to the underside of the ice that increased heat may go...
And if that happens, how we would know (other than by getting thinner MYI overall)...

Mike Constable

If deep"warm" Atlantic Water sneaks up on methane clathrate it will break that down, giving rise to lighter products (fresh water and methane) to help break down the stratification of the sea. (I see that methane clathrate has a density of about 0.9, so would float to the surface anyway if free to do so, not weighted down with sediment). I wonder if that explains some of the observations in Siberian seas . . ?

Chris Reynolds


I'm in the process of reading the Polyakov article. One reference struck me as important.

Polyakov et al 2010, "Arctic Ocean Warming Contributes to Reduced Polar Ice Cap"

"...The AW warming was associated with a substantial (up to 75–90 m) shoaling of the upper AW boundary in the central Arctic Ocean and weakening of the Eurasian Basin upper-ocean stratification. Taken together, these observations suggest that the changes in the Eurasian Basin facilitated greater upward transfer of AW heat to the ocean surface layer..."

Chris Reynolds

Oops, forgot to add.

I take it you read my recent post on models, the salient point is below the first blockquote after the first two graphics; regarding ocean heat transport in models and its relationship to rapid ice loss events in the models.


Yes Spielhagen et al 2011 was the paper I was referring to


Chris Reynolds


Wang shows that the Arctic Dipole has a role in major ice loss events. I still see it as a key factor. However I've mainly concentrated on the atmosphere - drawing in warmer air - and the ice movement - Fram Strait export. Whereas a +ve AD also implies imflux of warm water through the Bering Strait.

The Polyakov paper states that thinning of fast ice in Siberia shows that the ocean is not the sole player as the waters there are too shallow for Atlantic Water to have a major role.

However the current anomalously large Atlantic water warming, anomalous in the last 2000 years, and presumably due to Atlantic warming through AGW, and an increase of heat flux through Bering, raises the possibility that the loss of Arctic ice is at least as much due to ocean warming as due to atmospheric warming.

This however could raise a problem with PIOMAS and NPS. PIOMAS is forced by NCEP/NCAR atmospheric data, NPS by ECWMF data. The question is - is the Atlantic influx driven by winds within the Arctic region or by the Meridional Overturning Processes, such as thermohaline sinking? I don't know what the answer is. But if these assimilating models don't include the deeper Atlanic flow then either they're underpresenting the changes that are happening or the Atlantic Water is playing less of a role. In the Bering Strait Arctic Dipole driven inflow will be modelled by the assimilating models as its shallow and wind driven.

Rob Dekker

Chris said But if these assimilating models don't include the deeper Atlanic flow then either they're underpresenting the changes that are happening or the Atlantic Water is playing less of a role.

Thanks Chris. That is certainly a valid point, and also re-emphesized by the notion of the PIOAS team that they overestimate thin FYI and underestimate thick MYI. If ocean heat were more of a factor than they modeled, it would have been the other way around.

Still, one may ask why they "overestimate" thin ice and "underestimate" thick ice...
Which variables caused that bias ?
Also, I'm not sure how PIOMAS or NPS 'model' ocean heat, and how much a change in AW temperature would affect their estimates of ice thickness and cover in the vacinity. For example, would PIOMAS in free-running mode (forced only by NCEP/NCAR atmospheric variables) indeed project that ice north of Svalbard would be driven to 82.5 deg alll through winter ?

So many unknowns, so little data...

Rob Dekker

Another thing to mention : if there was ever a year when winter AW warming would have caused a pronounced effect under the Eurasian basin ice, and thus caused thinning that was not observable, then it must be this past winter of '11/'12.

Warm Atlantic water was driven high into the Arctic by persistent southern winds driven by the highs over Siberia and the lows over Greenland over the winter. Neven's latest post on the past winter give a very good overview of that effect, which also caused the western side of the Arctic to be anomalously cold.

So that AW water went under the ice, and affected the thermocline, then the East side of the North Pole (Eurasian Basin) should now have thinner than 'modeled' ice. That ice should thus be more mobile, more fragile and easier to melt or export than models assume. Not sure if we will ever know how much that effect is/was, but it will be interesting to watch that ice over the melting season.

Rob Dekker

One last thing I wanted to show you :
Polyakov mentions this 8 W/m^2 heat flux at depth under the ice in the Eurasian basin.
It would be interesting to watch the flux bouy26 (at the NP) for upward heat flux :
It has just been installed two weeks ago, and not much is going on there yet.

However, last years NP bouy started to show very significant ocean heat flux through the summer :

And, interestingly enough, bouy25 in the Beaufort shows some small but very interesting heat (peaking at some 5 W/m^2) bubbling up from the deep at semi-regular times lasting a couple of days, all through the winter.

Rob Dekker

In summary, it would have been very nice if PIOMAS would produce a 'map' of how ice volume is distributed across the Actic, rather than just a summary of total volume.
Especially this season.


>"it would have been very nice if PIOMAS would produce a 'map' of how ice volume is distributed across the Actic, rather than just a summary of total volume."

i.e. you want
to be updated to show the 2012 seasonal outlook.

Chris Reynolds


"Which variables caused that bias ?"

In the Schweiger paper there are 3 runs, all use NCEP/NCAR for atmosphere, the three options are:
Model Only - no assimilation of ice concentration (IC) or sea surface temperature (SST).
IC - assimilation of IC only.
IC-SST - assimilation of IC and SST.

Model Only and IC have long term thickness trends that closest match Kwok/Rothrock 2009. Whereas IC-SST has less of a loss trend, and being the most conservative, in the absence of strong reasons to prefer the other runs, is selected by the authors as the most conservative - therefore the run to be preferred. Counterintuitively this suggets the assimilation of SST actually retards ice loss! As to why PIOMAS has the thick/thin bias - the authors of Schweieger et al do not say, and I don't recall reading about a reason for this in the other papers I've read on PIOMAS. However in its development the model was 'tuned' to data from the SCICEX Data Release Area (DRA), data not used in the tuning was then used for validation.

The DRA doesn't cover the Siberian Coast and the Canadian Arctic Archipelago, where the thinnest and thickest ice is found. I suspect that it's possible that this is the reason for the thick/thin bias.

With regards ocean heat flux. I'll get back to you on that. Just downloaded every month's Mercator salinity anomaly plots from 2007, I suspect that changes in the model make them useless for tracking interannual changes in AW intrusion. If you've read my Musings On Models post you'll be aware that my argument is that if we want to foresee crashes like 2007, we need to keep an eye on AW and Bering Stait influxes as they lead crashes in the models and if 2007 is anything to go by may do so in the real world.

Rob Dekker

Thanks Chris,

I just checked out the Mercator site, and it looks pretty cool ! But what are we looking at here ? I understand that this is a model running, but do you know how it is forced (or at least constrained) by observations ?

I see that you focused on the 'salinity' numbers, and I admit that the surface salinity animation over the Arctic in the Mercator model looks convincing and realistic. But is there really any merit in Mercator's ability to "foresee" anything for the 2012 melting season (even w.r.t. the 2007 season) ? For example, do they have a sea-ice module in this model and what is it based upon ?

Rob Dekker

crandles said

i.e. you want http://psc.apl.washington.edu/zhang/IDAO/seasonal_outlook.html to be updated to show the 2012 seasonal outlook.

That would be nice, but rather than the hind-casts and fore-casts, a regular up-to-date map of the ice-distribution "now" as estimated by the PIOMAS model would probably be much more useful than the single-scalar volume number we get now.

But that 2011 animation DOES remind me of the issue I noted last year with the PIOMAS fore- and hind-cast maps : Keep your finger at one point on one of the animations, and watch the ice thickness decrease over 'time'. Do you notice that ice in the middle of the pack that is 2-3 meters thick reduces very rapidly until it is some 0.5 meters ? And that after that it takes an aweful long time to disappear altogether ?

That seems to suggest that PIOMAS heavily overestimates ice-melting rate (in the middle of the pack) and underestimates melting at the ice margin.

Which is kind of opposite of their assessment that they over-estimate thin ice and under-estimate thick ice.

Rob Dekker

Regarding ocean heat flux again, did you guys see this publication by Kwok and Understeiner ? :

With the header :
The surplus heat needed to explain the loss of Arctic sea ice during the past few decades is on the order of 1 W/m^2. Observing, attributing, and predicting such a small amount of energy remain daunting problems.

Here, I would like to note that this heat either came from above the ice, or from below (or a combination of both, of course).

If it came from above, then thin ice would be mostly affected. After all, ice thickness increases heat insulation and thus any heat-from-above would not directly affect thick ice.

However, again because of ice heat insulation, if that 1 W/m^2 came from below (ocean heat flux) then thick ice would be mostly affected and thin ice much less.

If Atlantic water caused only a 1 W/m^2 heat flux increase over the past decades, all volume reductioin is explained.

Incidentally, ocean heat flux change of that small a magnitude over such a long period are very difficult to measure (beyond the capabilities of the FLUX buoys) and also incidentally, that 1 W/m^2 is about as much as AGW forcing over the past 50 years that occurred across the planet (including the Arctic)...

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