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Thanks Neven. And the volume is? They're not saying, and the one published ref (Laxton et al 2013 in GRL -- on the data page) isn't all that helpful:

"[16] Ice volume is computed using CS-2 over the 'ICESat domain' (Figure 1). The domain covers the central Arctic Ocean and has an area of 7.2 million km2. Values for grid cells north of the CS-2 latitudinal limit (88N for CS-2 and 86N for ICESat) are obtained by substituting values from the nearest grid cells that include thickness data. ...

"[17] In common with earlier satellite radar altimeters CS-2 sea ice thickness estimates exclude open water. To compute sea ice volume, we therefore take the product of the area, the thickness excluding open water obtained from CS-2 and the ice concentration obtained from SSM/I [Meier et al., 2006]."


"[20] Table 1 shows the average ice volumes computed for the ICESat period and for the two CS-2 winters. Also shown is the change in ice volume between the two time periods for
both the satellite and model estimates. We include the “unadjusted” ice volumes for comparison with K09 ... but consider the adjusted volumes as more representative since they account for changing ice concentration between the two periods."

One is tempted to just multiply the CS-2 thickness by the Cryosphere Today area (which is already "concentration adjusted"), but that might be biased high because of the coverage differences?

Jim Hunt

Gergyl - Perhaps you'd like to take a look at the ongoing discussion about these matters over on the Arctic Sea Ice Forum?

Piomas vs. CryoSat

The "ICESat domain" at 7.2 million km2 is very much smaller than the complete "Cryosphere Today domain", and the CT "Central Arctic Basin" is smaller still.

If we're lucky perhaps "Wipneus" is computing the appropriate mask as we speak? He has tantalisingly stated over there:

"I might add Cryosat later"

Chris Reynolds


The ICESat domain is simply Beaufort/Chukchi/ESS/Laptev/Central and can readily be calculated from my regional PIOMAS data.

Chris Reynolds

Thanks Neven,

So the intrusion of MYI into Beaufort/Chukchi is modelled in PIOMAS and HYCOM, is seen in ASCAT, and now in Cryosat 2. Hope for an exciting season looks like residing from Laptev to Barents and towards the Pole.


>"And the volume is? They're not saying,"

"This February, Cryosat saw average sea-ice floe thicknesses of just over 1.7m, giving a volume across the Arctic of nearly 24,000 cubic km. Back in the winter of 2013, following strong melting during the previous summer, floe thicknesses averaged 1.5m and the volume fell below 21,000 cu km."

For comparison

2015 32 20.348
2015 60 22.524
avg 21.502

2013 avg Feb 19.376
so Cryosat continues to have more volume in winter.


...but not by much.

Jim, the ICESat domain was used for some comparisons in Laxton et al 2013; it seems no longer relevant, given that the new CS-2 data is much more extensive.

Seems to me the problem with getting a realistic total volume estimate from CS-2 is mostly to do with the edges, where the thickness data drops out well inside the area / extent limits (at least in many pixels). That isn't going to be well-solved by any sort of masking; it needs an interpolation / extrapolation scheme.


Does anyone know why Cryosat only reports (Arctic) data from mid-October to mid-April?


Magma: because they can't distinguish Summer's melt ponds from open water.


Re: volume

201110 5285.7710
201111 10393.6171
201112 14260.6350
201201 19034.4468
201202 21914.0118
201203 25264.4449
201204 25277.3580
201210 5419.6971
201211 10169.5799
201212 14236.0916
201301 18041.6983
201302 20869.0761
201303 24601.5179
201304 24265.1174
201310 8879.8820
201311 13095.3897
201312 17235.3437
201401 21020.1913
201402 23995.5547
201403 26838.7185
201404 26420.0175
201410 7632.6782
201411 13032.8434
201412 16795.5443
201501 20503.3015


Unless I missed something, it is all quit about the Antarctic Sea Ice.
Have they given up getting meaningful numbers from there?


Wipneus, stupid question from me, but are there any distribution maps available. I mean, like the 28-day one, but for the past couple of years?

Protege Cuajimalpa

Thank you. Even that I haven't write on the last couple of years, Neven's Blog and Forum are the best source of information, so thanks everybody for all your work.


Thanks, PC! It takes a community to raise a blog.



My 13h or more annual April summer/fall climate projection based on refraction methods is the most comprehensive one ever done.

Less sea ice extent than 2012 is foreseen, would have been worse if La-Nina was rising instead of El-Nino. I also agree, all eyes on the North Pole!

Jim Hunt

Neven - At the moment only the most recent maps and underlying data seem to be available via the new NRT page. However the overview page states that:

Monthly thickness and volume maps from the archive (2010-2015) will be released in the next few months.

Gergyl - There seem to be gaps in coverage even in the depths of the basin on the 28 day map shown above, as well as a big "Pole Hole". How thick are the white areas near Ellesmere for example?

My overly brief comment was intended to indicate that Wipneus has much experience dealing with that sort of thing, along with calculating daily regional area. However no historical data seems to be available, so an additional complication would involve grabbing the data on a daily basis while it lasts. The data is in a non standard (one dimensional) format also.

If you want to try and compare like with historical like then leaving the peripheral regions out of the calculations would seem to be a good idea?


Thanks a lot, Jim. I thought I was overlooking something.


Jim - What I didn't write, because its very new and a bit perplexing, is that about 4 hours under-melt a day stalls accretion fully (verified manually). The way I see this is that when ice forms it releases 334 KJ/Kg , this heat should "stall" or slow further ice reforming quite a lot by warming sea water. Too bad buoys have a resolution of 10 cm. there should be sea water underside temperature increase But I wonder if that makes sense? Can you see underside warming after the sun lowers?


Elementary thermodynamics: ice formation does not "warm" adjacent waters (zeroeth law: thermal equilibrium). The ice forms in a sub-freezing environment and the water molecule is at 0C immediately before, during, and after the freezing process. The enthalpy of freezing the water molecule is considerable (equivalent to heating the water to 70C after melting) but the "heat released" in freezing only dissipates into the sub-freezing environs (i.e., sub-zero air or ice). The released heat could help to keep adjacent water at 0C (so stalling additional freezing) but cannot warm it above that -- zeroeth law of thermodynamics.


Volume: tks Wipneus; method?


Gerg, the numbers are from the Cryosat Team. Latest description is Laxon at al., 2013. Of course with "lots of useful improvements".

Jim Hunt

Cincinnatus - At the risk of repeating myself, please desist. Here's a link I seem to recall pointing you at previously. Sea ice thermodynamics for dummies:


Have you read this bit yet?

The freezing temperature of ocean (saline) water is typically -1.8 degrees Celsius (28.7 degrees Fahrenheit)

Wayne - If I've understood the effect you are seeking properly then I can see no sign of it in amongst the somewhat noisy data. Ice mass balance buoy 2015A is sat on fast ice not far from Prudhoe Bay. Would that be the best place to look?


Irrelevant strawman, Jim. My point was about thermal equilibrium in general, not about saline water specifically. I've notice strawmen are a popular tool of the inmates here. In future I won't reply to strawmen as they are easily identified by the reader.


Cincinnatus, you seem to be one of those people who maintain there is 0% chance that AGW (and Arctic sea ice loss) will have serious consequences. Perhaps you are of a different opinion, but this is how you come across. It's no wonder then that people react to you the way you do.

This is after all a blog that attracts people who don't think that there is 0% chance that AGW (and Arctic sea ice loss) will have serious consequences, and find this alarming, given the rate of loss so far, and the fact that we do not know enough.

Jim Hunt

Cincinnatus - You do a very good impersonation of a master craftsman of irrelevant strawmen!

Here's lots of pretty pictures revealing lots of sea ice floating on water at a temperature above -1.8 degrees Celsius:



What does it matter if 0C or -1.8C for the purposes of a physical explanation to give understanding at a qualitative level???? (Which by the way it is absolutely right)

Jim Hunt

navegante - Perhaps sea ice thermodynamics are somewhat more complex than the picture painted in the average classroom?



Neven, you can put me down as a "Miocene optimum" kind of a guy. The warmest periods in the geologic past are called "optimums" (or "optima" for the Jims out there) because life positively thrived in those epochs. Given that there is no "runaway greenhouse effect" -- a false alarmist stance, now discredited -- then it stands to reason that some warming is all to the good. And this is my beef with alarmists -- that they don't deliver. Where's the warming? Trenberth was right -- it's a travesty.

While I enjoy watching the Arctic ice wax & wane, I'm not an inmate at Arc-ham here. I'll stick more closely to the visiting rules (i.e., less visits) so as not to upset the inmates. Cheers.

[Well, given that I'm the doctor here (and I'm probably going to send you away to another asylum where you fit better, Dr. Watts has plenty of room for your type of D-K), I'm putting you down as a climate risk denier, because you maintain that the rate of change towards "Miocene optimum" poses no risk whatsoever to society; N]


Cincinnatus - I can understand why you'd have that opinion.

From what brief study I had in pursuit of my degree - Geology - life did thrive in the heat of the "Optimums" Eocene, Miocene, etc.

Where your analogy breaks down is when you consider the *rate* of change to reach those peaks.

To apply an imperfect but I think apt analogy, tossing a basket eggs up to a shelf vs lifting it have far different outcomes.

*IF* the changes we are seeing now took place over millenia, as they did in the past, your outcome might be more likely, and both nature and Humanity would have time to adapt to changing climate.

With a 2C rise in what is geologically a finger snap will leave a lot of yolk on the floor, and far fewer eggs. The portents for our civilization are pretty dire, let alone for nature. Who gets to choose the slain?

Bill Fothergill

Phase changes & energy release:

Way back in June 1972 - during my carefree undergrad days - I somewhat surprised the faculty, and bloody astonished myself, by somehow contriving to get a distinction in Thermodynamics. As I promptly went on a bender to celebrate, much of that learning was immediately lost. However, if I can dredge something out of the beer addled brain, perhaps I may be allowed to offer some words on the subject...

First off, for anyone trying to understand this stuff, what happens under the ice is not the best place to start. Consider instead two parcels of air that have been heated by sunlight. (OK, it's more accurate to say the air was heated by convection from the underlying surface, and it was the underlying surface that was actually heated by the sunlight. That, however, is unnecessary detail for our purposes.)

Imagine that one of the air packets was "dry", in that it formed over land, and that the second was "moist", as it had formed over an ocean surface. If the two air packets gain sufficient heat, they will become more buoyant than the surrounding air, and will therefore rise.

As each packet rises, it gradually expands, and this expansion is a form of work. In each case, energy is expended, and the packet of air will gradually cool as energy is lost to the surroundings.

However, even if they both start at the same temperature, the "moist" air packet has a higher relative humidity. As the temperature drops, the saturated vapour pressure also drops, in accordance with the Clausius Claperyon relationship.

As this happens, some of the water vapour condenses into droplets, simultaneously lowering the actual vapour pressure and converting latent heat of vaporisation into sensible heat. The result is that a moist packet of air cools more slowly as it rises, as compared to an equivalent air packet that was drier from the offset. Both air packets may experience this "latent heat to sensible heat" energy transformation, but the "moist" packet with the higher initial relative humidity will experience more such heating. If anybody wants to go further into this, look up "lapse rate" or "moist adiabat".

(This, incidentally, is thought by many to be the mechanism by which the 1997/98 super el Nino gave rise to the extremely high TLT* figures measured by UAH and RSS during 1998.)(* TLT = Temperature, Lower Troposphere - basically derived from the Oxygen radiation spectrum in the bottom 10 kms of the atmosphere, weighted towards the 0 - 4 km range.)

Moist rising air cooling more slowly than dry rising air is an example where a phase change genuinely can be categorised as "releasing heat". Under the ice, it's a bit different.

An earlier commenter introduced the subject of the Zeroth Law of Thermodynamics. This basically states that...
"If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then B and C will also be in thermal equilibrium with each other, i.e. all three will be in mutual equilibrium."

If that sounds to you like a "statement of the bleedin' obvious", then welcome to the club. I remember once spending a stupefyingly boring 15 minutes trying to convince a physics graduate that it really was that simple.

However, when we're talking about under surface ice growth, thermal equilibrium is a bit of a distraction. The very fact that the ice is growing means that we're not talking about an equilibrium situation.

Ice formation on the under surface normally occurs when the air temperature starts to plummet. Even though ice is a pretty poor thermal conductor, energy is still being lost from the cold water under the ice, through the ice, to the even colder air on top of the ice. (Obviously, if the ice is fractured, there can be a great deal of heat exchange at the water/air boundary - until that transforms itself into a water/ice boundary underlying an ice/air boundary.)

What we have here is the First Law of Thermodynamics in action, i.e. the conservation of energy. There is no real "release of energy", as the energy flow from the water, through the ice, to the air has already taken place. The accumulation of ice on the bottom surface therefore occurs as a direct consequence of the preceding removal of an amount of energy equivalent to the latent heat of fusion of water.

The Zeroth Law would only really enter into the equation if the total heat capacity of the air was big enough such that it would suck enough energy out of the water for the temperatures to equilibrate. As mentioned above, the fact that the ice is growing is a consequence of the fact that the system is NOT in thermal equilibrium. (And the ocean getting into thermal equilibrium with air that might be at -20C ain't happening any time soon, at least in this reality.)

cheers bill f


Density variations due to temperature and salinity with very different diffusion rates complicates fluid dynamics wrt fresh water, but directly, by thermodynamics (quasi-equilibrium states evolving extremely fast) ice cannot warm liquid water (even when releasing latent heat)

*Slow* salt migration from ice to ocean water causes sinking and transport of the latent heat released to deeper ocean levels, but the time scale of this process is much longer than what Wayne implies (I believe).

If I wanted to look for agressive, idiotic loons that ignore science, most of them on purpose, I would just visit denialist sites. I usually don't, and I dont respond to denialists because it is a stupid waste of time. However I notice here we resort to scientific knowledge because science backs AGW. I use it, incorrectly many times. But I jump to respond to what I believe is not right because here it is not a waste of time.

I suspect that you prefer this site and the likes to follow Arctic ice and melting season for the same reason as I explained, you seem to have gray matter and not be just another sheep.

Kevin McKinney

"Given that there is no "runaway greenhouse effect" -- a false alarmist stance, now discredited -- then it stands to reason that some warming is all to the good."

That is a truly spectacular non sequitur.


For ice growth process not to be in thermal (quasi) equilibrium, the ice thickness should be growing at speeds close to speed of sound (the slowest one of the media considered). That is the velocity comparable to air molecules speeds, or vibration speeds in solids.

As long as the process evolves much slower than that, you can assume the system evolves along states of themodynamic (quasi)equilibrium.

The quasi means that it evolves, hence it is not completely in equilibrium, but you can safely ignore that for most processes in planet Earth.


Like lightning, explosions blasts, shock waves in supersonic aircraft,... i believe Arctic ice changes are quieter. (Sorry post was broken)

Bill Fothergill


When one has water at, say, -1.5C separated by a body of ice from air that is much colder, say -20C, there is a thermal gradient across the ice column. When you have a thermal gradient, the various parts of the system are NOT in equilibrium.

The ice very close to the ice/water boundary will of course be at a temperature very close to that of the water, and it will be clamped there by the massive thermal inertia of the surrounding ocean. Similarly, due to advection, the ice near the air/ice boundary will have a temperature that is tied to the corresponding air temperatures.

In between these upper and lower regions, the temperature will vary gradually from one extreme to the other. This is a thermal gradient.

The original question asked by Wayne (22:52 19th April) was if the freezing of water to produce ice on the underside of the existing ice would release "heat energy" into that part of the system. The answer to that question is "no".

The reason that the answer to that question is "no", has little to do with the Zeroth Law, but is instead a direct consequence of the First Law - as explained in my earlier post.

At any phase boundary, such as ice and water, the individual molecules do not stay in a static arrangement in one or other of the phases. Instead, there is a dynamic equilibrium, whereby as one molecule goes into the ice phase, it is matched by another going the other way. Under such circumstances, there is no net transformation of energy between latent and sensible heat.

At the Triple Point, this gets really interesting, and one has freezing, boiling, melting, condensing, sublimation and deposition all happening in dynamic equilibrium.

When the overall mass of ice in the system is being increased (or decreased) it should be pretty clear that equilibrium conditions are not in force. If one has an electric kettle switched on, and it's boiling away merrily, it ain't in equilibrium. This incremental phase change is driven by the extra energy being applied from the National Grid. When ice is accumulating on the underside of existing ice, it's being driven by the energy extraction from the water, first to the ice, and ultimately to the colder air above.

BTW, I was already aware that the growth of ice did not occur at supersonic speeds, but thanks for clearing that up, just in case there had been any one here unaware of that fact.

You should also check the meaning of "quasi", because it doesn't mean what you seem to think it means.

cheers bill f

Susan Anderson

Bill Fothergill, I cannot thank you enough for explaining in what is, metaphorically speaking, words of one syllable, how things work in one part of this discussion.

For others, responding to Cincinnatus, the fact that he refers to you as "inmates" and denigrates your open attitude towards real world developments and evidence makes him part of an increasing presence all over the internet that promotes contempt for real knowledge. The attacks are getting more subtle and are intended to deceive. (In the US, they are also arming themselves, but that's another story.)

You all know more about the Arctic than I do, but I have more experience because I have made it my business to observe the tactical effort to obscure the truth. It is paramount for us all to remember that we are part of a family of humankind and take action to save ourselves and each other. They know we are tolerant and open, and they see this as something they can exploit.

It is time to stop tolerating lies in all the shapes they take, here and everywhere. This has been going on too long, and it is doing noone, not even the attackers, since they too have lives and families, any good in the scheme of eternity. Unfortunately, eternity as a form of extinction is beginning to look like decades rather than centuries. This is not OK.


Cincinnatus- In one of the following links, Dr. Suzuki was asked about the future of the earth. His answer is the earth will be fine like any other time big changes in earth's past has happened. The problem is - WE WILL NOT BE AROUND. We will all be wiped out by the changes that are coming our way unless we get our act together.
I think you somehow believe we will survive all this. Most of us believe there is actually no way we can, or if we do a very very small number. I am of the latter camp. In fact, I tend to believe that we have a very small window of time to get it right then nature will ensure that we will be one of the extinct species when the new era gets established.


"With Cryosat, we're now able to provide users of the Arctic with information on sea-ice thickness in rapid fashion, which will be a step change from what has gone before."
I will give him that it is a major step up from all previous attempts, but Arctic ice is a very complicated creature an thickness alone does not even begin to tell you what you need to know about working and travelling in the Arctic. You can travel at almost max speed in in that is metres thick over long distances because it is so rotten the get sunk by a small (by surface area) by a berg the Cryosat can not show because it is very hard ice.
Saw a doc following a very experienced Inuit hunter. There was an area he walked on the he prodded the ice ahead of him with his long spear before he took his next step. On the surface it looked all the same, Cryosat would have treated it all the same. His spear told him where to go and where to avoid.
Tech is great, but do not exaggerate what it is capable of otherwise you can kill people in the Arctic. And for the rest of us I think it still will not tell us the full picture and the Arctic will continue to spring many more surprises.


Unusual melt activity at Greenland's South-East coasts on 19th April 2015 [NSIDC}.


We agree bottom melting or freezing is not static and not in equillibrium. I mean that the system state at any location, depth and time is locally in thermodynamic equilibrium and satisfies laws fundamented on aggregation of molecular dynamics.
Heat is released when freezing, and there is temperature gradient and heat transport within the ice toward the top. There is no significant negative temperature gradient and heat transport downwards. (there can be positive gradient though but then there is heat absoption and melting).


Very good discussion Bill and and Navegante, that is like Susan suggests worth our time.

I know very well about latent heat of fusion being released upwards the ice column , I should come back on this soon. In fact it may very well be the process slowing accretion which I am looking for. If the ice warms , the total process of accretion should slow down same as ice thickness does not build up linearly over the long night by its own insulation. Top of water column also responds to temperature change of the ice either by conduction, or its own convection. And so I look for what slows accretion when Lebedev should dictate 20 cm more ice at -20 C in one week, when no ice gain has been noted. No heat transfer towards water would be a surprise to me , given ice direct contact, Not necessarily ice which melts at -1.8 , but purer in water ice say which melts at -1.7 C. or even greater temperatures, this I noted with the buoys at end of melt season. We did have ice warmer than water , so its complex, and usually good discussions makes things clearer.


Wayne, freezing itself slows down further freezing when the sink of heat ceases to exist (temperatures reach melting point on top side of ice). However, it takes several days to switch from freezing to melting in 2 m thick ice. Didnt do the math. It is the gradual shallowing of the temp profile that one observes from the buoy graphs that Jim kindly posts.

I know my view of this is simplistic but hopefully not so far from the real process.

Robert S

LRC: Having spent time on ice, albeit freshwater rather than saltwater ice, I agree that Cryosat is never going to tell you whether ice is safe to walk across... and nor is almost any other instrument I can think of - that's all down to experience. But I think the Cryosat data will help to move us forward in terms of understanding the dynamics of weather and ice development/melt... which is what I think Wayne is pointing to.


@Bill_Fothergill -

"The ice very close to the ice/water boundary will of course be at a temperature very close to that of the water, and it will be clamped there by the massive thermal inertia of the surrounding ocean"

So here's what wakes me up some nights...

If I understand it correctly, the entire arctic ocean has a temperature profile which is inverted w.r.t other bodies of water. - elsewhere, surface water is warmer that that below - but in the arctic , the surface is less dense because it has lower salinity, so it can stay at the top even though it is colder than the higher salinity water below.

...but isn't the inversion caused by the ubiquitous presence of ice on the surface? If so at some point will it flip - and all the energy that is currently lurking below 50M will suddenly become much more relevant?

Jim Hunt

Now seems as good a time as any to point out that the University of Queensland's "Making Sense of Climate Science Denial" MOOC starts on April 28th:


According to the press release:

The free Massive Open Online Course (MOOC) includes renowned researchers from universities in Canada, USA and the UK – and even Sir David Attenborough lends his support.

UQ Global Change Institute Climate Communication Fellow and MOOC coordinator John Cook said the course tackled climate myths and exposed techniques used to mislead the public.

Here's Sir David waxing lyrical about the wonders of brinicles:


Jim Hunt

navegante - Thanks for your kind words. Here's an interesting one, to me at least. A few days in the life of a (nearly) 2 m thick ice floe at the North Pole:

Click the image for a larger version.


Jim, so in two days, the heat wave (by conduction) has traveled 1/3 of ice thickness (mark 15), and with simplistic estimate it would take another four to reach bottom. If we had melting temp sustained at the surface, the gradient at the bottom mark 30 will take another week or so to become flat. Freezing ceases.

Total of two weeks. This is a long time (compared to hours), but this is less than the minimum 1-month delay of bottom melting after surface melting starts (I hear that number around). Bottom melting also needs flow of warmer waters under the ice.

Kevin McKinney

Jim, what are the units on the x-axis of your chart? And what are the dates given? (Can't quite make 'em out with certainty.)

It's indeed an interesting graphic. Thanks for sharing!

I'm a bit intrigued by the sharpness of the 'knees' at the bottom and (especially) at the top of the ice. (You know, the 6 cm/dm/ell/furlong/whatever mark…) ;-)

Jim Hunt

Kevin - Perhaps I should have added "Click the next image for a still larger version"? I've now increased the font size in the ultimate destination, which hopefully makes the legend more legible.

The x axis is thermistor number. The air above the ice is on the left. The water below the ice on the right. A more detailed explanation can be found at:


The "knee" at 6 is where air changes to snow initially and then ice. The "knee" at 31 is where ice changes to water.

The dates are April 11th (shortly after the buoy was installed), April 18th (after a very warm day for the time of year) and then April 20th (when air temperatures were cooling down again).

navegante - It was suggested on the ASIF that this might make a good real world example of the heat equation in action, but I haven't tried that experiment yet though!

The "heat wave" really got going on April 15th.


Hi Jim. Great stuff, but resolution is not expanded enough, I am looking for
small variations at bottom of ice/water limit. If you take out 3/4 's of top, there should be small very interesting variations.


The surprising reason why Arctic warming could be worse than previously thought


Chris Reynolds


The answer to your question is, as Bill explains, 'no'. This is because the very heat release from melting ice is what drives ice thickening.

Ice grows due to heat flux through the ice.

'qlatent' is the energy released from ice formation ( as the molecules of water drop from the energetic state of liquid to the less energetic state of an ice lattice they give up energy - latent heat of fusion)

'qocean' is the flux of energy from the ocean.

'qice' is the flux of energy into the ice/ocean interface from the formation of new ice due to the enthalpy of fusion.

'qsurface' is the flux of energy from the ice/atmosphere boundary into the atmosphere.

thus, considering net fluxes...

qsurface = qice = qlatent + qocean.

Incidentally, this is why heat flux from the ocean leads to thinner ice, it takes up some of the flux that would have gone into forming ice through the q latent term.

So Bill is correct, the heat produced by net ice formation through the winter does not warm the ocean/ice interface. It is actually driven by the heat flux from warmer ocean to the colder surface of the ice (where the atmosphere is frigid).

This relationship between ice thickness and heat flux through it, and basal accretion of ice gives rise to the simplest model of sea ice growth, whose general form can be seen in the core equations of models like PIOMAS and CICE. Although those far more advance models incorporate far more advanced physical modelling of further, more complex, process.

I have covered this simple model here:

And I have used that simple model to examine the thickness-growth feedback here.

Chris Reynolds


'qice' is the flux of energy through the ice driven by the temperature gradient between the ice/ocean and atmosphere/ice interfaces mediated by the thermal conductivity of the ice, it is inversely proportional to the thickness of the ice.


Chris, very nice to read the standard theory, but don't forget that this theory modeled 2007 melt was suppose to happen in 2038. The interface appears to be complex. What is observed sometimes goes like this:

Accretion happens when it is warmer outside , and no accretion happened with same ice at colder surface temperatures, even more the no accretion period occurred with less snow cover, all this contradicts the theory so skillfully presented.

Also by description from divers, the sea ice bottom can be very complex in texture and or fragility, I dwell with complexities at present. I am thinking that sea ice has many facets o be discovered. So we must look for them.

Chris Reynolds


2007 was a weather driven event, how is this relevant?

Holland et al 2006, Future abrupt reductions in summer Arctic sea ice finds an abrupt reduction around 2040. However their definition of an abrupt reduction is:

"We identify an abrupt event when the derivative of the five-year running mean smoothed September ice extent timeseries exceeds a loss of 0.5 million km2 per year, equivalent to a loss of 7% of the 2000 ensemble mean ice extent in a single year."

I have previously blogged in this in 2013. Using data to that year the post 2007 erar does not satisfy Holland et al's criterion.

At no point does the 5 year running mean smoothed September ice extent timeseries exceeds a loss of -0.5 million km2 per year, the y axis being the 5 year running mean smoothed September ice extent. So 2007 and its aftermath isn't as big as the modelled rapid ice loss events Holland et al discuss. That conclusion is based on data up to 2012, adding 2013 and 2014 would not change it, they would reinforce it.

Acretion of ice could happen when the air is warmer due to heat flux into the ice mass which may be colder than both atmosphere and ocean. Existing physics is not contradicted, although this simple model would fail.

Yes that model is more simple than reality (spherical chickens in a perfect vacuum). That is why working models factor in more complex processes. However that model accounts for the increase in autumn/winter volume gains seen after 2007, for example in the Central Arctic.
(Lack of snow and ocean heat flux mean the model grows more ice than PIOMAS, but it still shows a post 2007 increase in autumn/winter volume gain.)



"2007 was a weather driven event, how is this relevant?"

Sure was weather, but also very thick ice melting extremely rapidly. No , that is still not a good excuse, the model was certainly coupled and definitely included sea ice physics.

I like your idea about sea ice being colder than air and water, but that does not explain why sea ice with less snow cover and colder air did not expand more if thermal fluxes are all that matters.

However this said, I observed the horizon line at true astronomical horizon lasting longer when it was colder, this implied less accretion than when it was warmer with greater snow cover. I knew there was more accretion during the greater snow cover period, but I still cant explain why within the confines of present theories. What likely happened was sun rays penetrated the ice core deeper (than with more snow) and gave a negative flux from top of ice. This cancelled flux to air, and focused the bottom for melting or stalling. The only problem is that I observed about 4 hours of flux cancellation. I cant explain the 20 hours when radiation escaped to the atmosphere as per theories . there should have been some ice gain during the said period because of 1/6 negative top of ice flux doesn't compute, unless there is a complexity not quite understood, what better place than the interface where no one sees?

very good comments nevertheless!


The volumes that Wipneus obtained from the CS-2 data team are plotted here:


Pretty close, except mid-winter. Details here:


Colorado Bob

Giant Waves Quickly Destroy Arctic Ocean Ice and Ecosystems

Within an hour there was a four-meter swell. The Lance’s navigation system ultimately recorded occasional waves more than six meters in height, the largest ever measured amid Arctic ice. “And we could see even bigger waves higher than the deck of the ship—30 feet [nine meters] or more,” Marchenko says.

This incident marks the first time that scientists had recorded any waves over three meters high amid Arctic pack ice. Marchenko later gave his measurements to Clarence Collins and his colleagues at the NRL in Mississippi, who analyzed the interaction of the waves and ice. It turned out that although the ice damped incoming waves, it also contributed to its own destruction.

Ice near the outer edge of the pack absorbed some energy from arriving waves but also focused the remaining energy into pulses that could strike deeper into the pack, lifting it as the waves rolled beneath. The rise and fall strained ice to the breaking point. Once broken, the smaller ice chunks allowed the largest waves to pass almost unhindered and attack solid ice farther in. The ice went from blocking almost all the wave energy to none at all within just one hour. The process happened so fast, in fact, that Collins calculated waves were destroying the pack at a rate of over 16 kilometers of ice an hour.



[snip, more inventive insults needed + a long, hard look in the mirror; N.]

Anyway, I'll be back in September for a few well-earned jeers. See you!

Jim Hunt

Bob - For more on large swells in the Arctic see also this over on the Forum:


Jim Hunt

Wayne - I fear the 10 cm thermistor spacing is something over which I have no control!

The SIMBr style buoys have radiometers above and below the ice, but the numbers they record are "preliminary" and not currently made publicly available.



Regarding "... believe we will survive all this. Most of us believe there is actually no way we can, or if we do a very very small number.", speak for yourself. That is an extreme view.


I believe this is going to be a fascinating (likely terrifying) year.

The ice volume projections are all over the place.

The Danes (http://ocean.dmi.dk/anim/index.php Istykkelse Arktis) project the greatest ice thickness extent.

The U.S. navy Hycom (http://www7230.nrlssx.navy.mil/hycomARC/navo/arcticictn_nowcast_anim30d.gif) are next most extensive.

These contrast hugely with Cryosat (actual measurement) and the Japanese Vishop (http://ads.nipr.ac.jp/vishop/vishop-monitor.html SeaIceThickness). At least two of these are wrong. I suspect that DMI, Hycom and PIOMAS are all wrong.

I believe Cincinnatus is relying on the DMI. I believe the reality is as we see from Cryosat and Vishop.

The PIOMAS projections are likely way off the mark and have been for a couple of years. (Was there an algorithm change to PIOMAS?)

To bolster this, today the Worldview imagery is showing an ice fracture along the entire length of Ellesmere with the thick "fast ice" coming ungrounded from land.

If as in past years the 2.5 meter and less ice melts (greens and most yellows in the Vishop image) we should see a record melt.

If in addition we see large waves stirring the ocean (likely) and any major cyclonic systems (which we have seen the past several years), we may see most of the thick fast ice go as well.

The jet streams in the past month have gone bonkers. For a few days two weeks back, the jets over Europe and Central Asia looked like rorshach test. This may be indicative of the beginnings of the destabilization of the three cell atmospheric circulation into a chaotic pattern ahead of a shift to a one cell system.

Hang on to your hats. Things look to be about to get very interesting.


Jim, I agree! very bad resolution, under he is radiometer is a superb idea! kudoos to the science group making it so.

But with he resolution at hand, look carefully, I see some activity , its there and faint compared to other more stable thermistors at about the interface.


Sam, they appear way off, things are getting very prone for melting as we write, all time low extent is rather the right projection.


D_C_S: Sorry about putting words in your mouth, but I was just drawing what I thought inevitable conclusions over a period of centuries.
Is it extreme to think that over 400 years the avg global temps will rise by over 10C? Is it extreme to them conclude that the supply of clean fresh water which is in dangerously short supply in most of the world will be greatly reduced because of that heat and the demands humans will place on it as humans need more water the hotter it gets? Is it extreme to think that in 400 years the sea level will rise by over 10 feet? If all of these questions get answered with a no it is not extreme then then impact on human life will be very extreme and this is the reasoning.
Lack of water will mean lack of food as food requires water to be produced. Lack of food and water always results in mass migrations. Mas migrations always result in stresses in places to live. All these factors usually result in violence of one sort or another which usually results in more disruption in food, water and habitation supplies. On top of that disease will also become a very deadly force.
Up to now in human history these events have occurred on a local or regional level and have been contained within that area. We must remember that these disruptions when large enough also include loss of large amounts of local knowledge such as what happened at the fall of the Roman Empire when it was known to a very high degree the polar and equatorial circumference distances of the earth.
In the next 400 years though this will affect the entire globe. The question then becomes how many will die from these disruptions? Not only that will the violence be just the efforts of containing or moving on the migrations or will they spill over into efforts of disrupting those that have enough for themselves to ensure that they no longer have anything either? History is replete of examples of all these things occurring and to believe that somehow in the next 400 years with all the disruption that will happen we will avoid a repeat of history I believe is pure fantasy.
The only way I can see of avoiding all this is to get CO2 back to 300ppm within the 100 - 200 years.And get year round ice covering a minimum of 75% back on the Arctic Ocean.

Chris Reynolds


PIOMAS is on track, doing fine, and in my opinion correct. I see no substantive disagreement between PIOMAS and HYCOM. There has been no change to the PIOMAS model since V2.1 was released. Were there such a change I would see it in the data I analyse.

The increase in volume as seen in PIOMAS will preclude a crash this year mainly because multi-year ice is being exported into Beaufort and Chukchi. HYCOM shows the MYI tongue is already near Wrangle Island.
On past performance it is likely to make a significant presence in the East Siberian Sea. When I get my coding finished I suspect PIOMAS will back up HYCOM.

And for those who don't beleive the models. ASCAT shows the tongue of MYI.

Seriously good melt weather could overcome these odds. But I'm not aware of any predictive patterns at this stage of the year so am not willing to bet on that.

I think we're in for another 2010 style year, there is the chance of a good volume loss (if 2013/14 weather isn't repeated), but presence of MYI in the Pacific sector of the Arctic Ocean will probably mean persistent low concentration rotten ice holding up extent late in the summer in Beaufort/Chukchi and the ESS, as in 2010. That alone would smack down chances of a crash. :(

Neven and others have observed FYI through to the pole. But due to the transpolar drift it is not the first time we've seen that and it does not guarantee a melt through to the pole.


On the subject of PIOMAS, PIOMAS gice is the sub grid thickness distribution modelling thicknesses (metres) seen in the legend of the following plot. The plot being a plot of volumes from various gice thickness bands of ice for the Arctic Ocean (Beaufort round to Greenland Seas, Central and CAA).

The volume 'crash' years of 2007, 2010, and 2012 are indicated, the plot shows the impacts of those years on thickness distribution within PIOMAS.


Sorry, been busy writing a blog post, I think we'll have to agree to disagree.

Neven and others have observed FYI through to the pole. But due to the transpolar drift it is not the first time we've seen that and it does not guarantee a melt through to the pole.

Chris, when did we see it? At this time of year, I mean.

Chris Reynolds


Quikscat 30 April 2006.
(sorry no direct link) Broad swath of FYI from Siberia toward but not quite to pole/

ASCAT 2013 Day 116 (last week of April)
Broad swath of FYI to the pole.

ASCAT 2012 day 120 (end April)
Broad swathe of FYI to the pole.

For comparison ASCAT Day 112 of 2015.
Broad swath of FYI from Siberia encompasses the pole.

My point is that due to the transpolar drift we have precedent years that had a large expanse of FYI from the Siberian coast towards the pole. I could give other years that aren't as good due to some MYI inclusion. This year the expanse encompasses the pole, but in those other years the ice edge did not even take out all of the FYI available towards the end of April.



I agree. If PIOMAS and HYCOM are right we will likely see Sept areas of about 3 million km^2. If DMI is right, make that about 3.5 million.

But if Vishop and Cryosat are right, we are probably looking at 1.25 million.



Chris, when I say the North Pole has my special interest this year (I believe I said so on the ASIF), I don't mean to say that I'm certain it's going to be ice-free this year. But I'm not necessarily ruling it out either, even though it will take some pretty persistent weather conditions.

Like you say, not only does the FYI expanse encompass the Pole this year (unlike in your other examples), but there was also open water all the way up to 86°N at the end of last melting season. And up to 85°N in 2013.

But again, I need to see more comparisons for the Winter Analysis. It has the potential to become one of the more interesting features of this melting season.

Jai Mitchell

It seems pretty clear to me that the minimum extent is primarily dependent on local cloud cover and regional temperatures at the onset of the summer season. Increases in mid-latitude moisture and South-East Asian aerosols into the region around may 25th-June 15th over the last 2 years seems to be a good predictor for early melt pond formation which seems to set a self-sustaining melt through the rest of the season.

So I keep my eye on the >80'N DMI temp chart. If temps suddenly drive below the seasonal average (for the first time this year!) around May 10th then we might see another "recovery" year like 2013 and 2014. If, however, the temperature moves above the freezing mark early and ins maintained, with high solar activity, then we could easily see <3K by Sept 28th.

just my .02


Jai, very little chance of a repeat, current temperatures are way to warm,. But you have a good point about the clouds.


That alleged 3-4 meter thick ice isn't looking so good in the Beaufort, Chukchi, and Western Arctic the last two days.

Actually, it looks like it is being pulverized, and it looks much more like one would expect for 1-2 meter ice.



Sam: Could it possibly have been compacted ice mounding up that did not freeze in a solid mass and is now breaking apart? Or is it a possibility of rotten ice that was thick and now weather action is acting on it?


Drones are now being used to study arctic sea ice.



I think "pulverised" is too strong a word. Remember the resolution of the techniques you're using. Even a single pixel on (say) MODIS/TERRA imaging from Worldview is 250m across - which means that the floes you're looking at are generally a minimum of 1km across, which classes as big or vast floes.

The off-shore breakup in the Beaufort is possibly a bit ahead of schedule, but that's all we can reasonably say fo far this year.



It's all relative to the size scale of the area in question. Would you prefer shattered, crushed or pounded?


Chris Reynolds


I didn't mean to imply you'd claimed that FYI meant a pole melt was a certainty. I merely wanted to point out that the FYI state from Siberia to the pole doesn't guarantee a melt out, and past years suggest such an outcome would be unlikely.


For a grid cell's area to be counted towards extent it only needs to have a concentration of over 15%. Let's look at 16.6667%, which would be counted towards extent. That state is 1/6 of area being chunks of sea ice floating in 5/6 of area open water.

What you call pulverised MYI is probably thick enough for much of it to last into the late summer. That's when the area only needs to be 1/6 of ice to keep extent up. That really did happen in 2010.
The yellow/green stuff in the top left quarter of that plot looked like it would just melt away through August. It didn't.


Jim, have they worked out the near surface thermistor/sun ray induced temperature error? This is important, otherwise the data analysis from buoys is much more difficult. Which top thermistors are considered too warmed up by solar radiation? I think we haven't discussed this subject enough.


Chris - regarding your 2010 observation - I think floe size matters, and that is now much different from 2010 I expect. Once you are down to 100M diameter and smaller, side melt becomes an increasing danger to the ice.

Less intact ice combined with increased threat from swells/wave action concerns me and I think also may present a risk not seen five years ago.

Hmmm. What *was* the average size of floes in that area in 2010? What does it appear to be currently?

Chris Reynolds

JD Allen,

I don't know the answer to your question and yes lateral melt is a concern. However as we've all seen from MODIS and IR, the pack is normally very fragmented - its natural state. So in any mass transport the floes will be broken up and fresh ice will grow in leads between them.

The PIOMAS gice data is monthly back to 1979 but the 2015 data is only daily. I haven't yet got round to coding to transform daily into my own monthly files, or to wholly use daily files (which go back to 2000).

However we have the Drift Age Model. That's not ideal because it assigns age to the oldest amount of ice with extent (>15%). Anyway the DAM shows more extent of older ice this year than in 2010, this year is more like 2014 or a pre 2007 year.
DAM images.

Week 05 2010.

Week 05 2015.


Studying the cryosphere is important in more ways than we can imagine, for instance we can eventually move to Mars because it has a permafrost! But let's literally see how much permafrost there is on Mars first.


Jim Hunt

Wayne - I'm not aware of any discussion (expert or otherwise!) about the effect of direct solar radiation on the thermistors above the snow & ice.

On the topic of sea ice thickness there's a Sea Ice Prediction Network webinar next week (14:00 EDT on May 5th) on the topic of "Observations of Arctic Snow and Sea Ice Thickness from Satellite and Airborne Surveys":


The presentation, given by Nathan Kurtz of NASA's Cryospheric Sciences Lab at Goddard, will focus on the current state and availability of snow and sea ice thickness data from NASA's Operation IceBridge airborne surveys and the European Space Agency's CryoSat-2 satellite mission. The accuracy and limitations of these operational data sets will also be discussed to place the utility of the data in context for use in a variety of study areas.

A previous SIPN webinar did cover modelling the sea ice radiation budget, amongst a variety of other things:


Chris Reynolds

Thanks Jim,

That's 1900 UK time. I'll make a note to watch it.

Time converter page:


Jim, it seems a serious problem, :

'Temperature measurements are accurate to approx. ±0.2 °C. Further, measurements in summer may be affected by solar heating of the probe."


also talked to very good field experts confirming so.

top of ice to surface thermistors are not in a stephenson screen.
Optically speaking, snow layer top of ice should read colder during the day. Otherwise, if considered accurate the horizon line would
be well below true astronomical, which has not been observed yet.
in other words top thermistors are reading too warm... I caught that with a buoy cam last year showing snow when temperature was about +2 C with no water, I presumed wrongly that water was under the snow.


Look at that! The Helheim glacier is vanishing right before our eyes.

At the first link you can navigate through images from September 2014 till 29th april 2015. Mind, some images are hidden behind others, so you have to click onto the tiny rectangles to the left and the right of the image in order to see it all [at least, at my system it's like that].
We know speed is at it highest in the middle of the glacier. So in theory in the middle the glacier should be longer than at the banks, creating something like a 'tongue'. But it is completely the other way around (do have a close look at the March 28th 2015 image]. IMHO meaning the glacier is already highly fragmented and collapsing under it's own speed. And remember, this has been the recession in Winter, and Summer has yet to come.

Incedentally, looks like we are facing a combined 2007 and 2012 situation: extent is extremely low as in 2007, and there is already a considerable melt in the Mac Kenzie-Amundson street-East Beaufort Sea [as in 2012}.

Jim Hunt

Kris - See also the Helheim Gletscher thread on the Arctic Sea Ice Forum for some satellite images from above:


At this juncture I reckon the East Beaufort situation is due to wind rather than "considerable melt":

It will certainly be interesting to watch where things go from here though!


Jim, you would get an idea of how unstable he bottom of ice can be with http://imb.erdc.dren.mil/irid_data/2015D_clean.csv
2015d near the pole now, the ice depth is varying like crazy, while
surface temperatures are very close to top of snow/ice.

I imagine ice forming , melting, reforming likely creating very interesting bottom geometry.


Jim Hunt wrote:

East Beaufort situation is due to wind rather than "considerable melt"

Right, on condition high temperatures allow the wind to chop the ice into pieces. So probably the wind indeed has aggravated the situation but can't be seen as the cause. And as we all are aware of, mean temperature this winter in Alaska and NW Canada has been far above average.
Another factor could be that high amounts of fresh water already are plunging into the Beaufort Sea. But that's just my guess for now ...

Chris Reynolds


I agree with Jim.

Temperatures have little to do with whether the wind can open up that region of Beaufort. The ice in that area is likely to open up parallel leads and even tracts of open water when the wind blows away from Banks Island.

What has been going on in that region is shown in the HYCOM model:

I discussed a similar break up in February 2013 on this page:

Now in early May there is not the time for ice to thicken, temperatures are too high and there isn't enough time until summer sets in, so it may have an impact on the early summer in Beaufort. However even in February 2013 under far colder conditions a similar wind driven break up occurred.

Extent at this time of year is set by seas outside of the Arctic Ocean basin. But the minimum is set by seas within the Arctic Ocean basin. I am not aware of detrended March or April extent holding any information about the following summer minimum.

Jim Hunt


Re: "high amounts of fresh water" here's the confluence of the Liard and Mackenzie Rivers on Worldview on April 29th:


It's a bit cloudy this year but flip between 2014/15. It looks like the Liard is breaking up earlier this year than last, but the Mackenzie hasn't really got going as yet.


I followed up on actions recorded by buoy 2015d, which are fascinating, its like noon march 21 here stretched out the entire day giving a good chance to analyze what happens when solar rays lowers the horizon to astronomical horizon.



Would be good to know if there is a problem with mass buoy thermistors or surface mass buoy temperature readings,
Some data match optical refraction observations quite well,
then some others clash quite a lot, especially when its sunny.

this quote from anonymous 'referee #3' sums up my misgivings exactly;

"My feeling is that the thermistors are not accurate, although sensitive, meaning that they give good relative values but poor absolute ones."


I deal with absolute values which have to be extremely accurate,
otherwise there is no correlation between buoy data and the horizon line location.

Most mass buoys temperature readings are confirmed better visually when there is no sun. However there is the question of accretion, when the ice temperature entire column is warmer than the air, as most ice buoy in the sun suggests, there is a great loss of heat, therefore accretion potential, by thermal flux upwards to
the air especially by convection, but the mass buoys indicate no accretion. Which is a bit suspicious.

My last post deals with likely visual confirmations, next weekend subject will be about refraction observations clashing with ice buoy data. Essentially helping to determine whether buoy data is flawed.

Jim Hunt

The slides for the SIPN webinar later today have already been released:


Amongst other things they include the following preliminary March 2015 snow depth information:

Click the image for a larger version.

Jim Hunt

Wayne - I'm afraid I still haven't got a grip on what you're expecting/hoping to see from the ice mass balance buoys. I thought it was some sort of evidence for diurnal bottom melting/freezing once "surface" temperatures got sufficiently high, hence I'm bemused by your interest in 2015D near the North Pole at this time of year!

The "signal" from bottom sounders often seems to be very "noisy". I idly speculate what sort of physical mechanism might account for this. Hence my interest in brinicles. See the Attenborough video above and also:


As I suggested previously, wouldn't a close examination of 2015A be better for your purposes? The rather noisy bottom sounder "signal" suggests that bottom melt may have already begun. Here's what the thermistors reveal:

As always, click through the successive images to get to the largest version.

Ghoti Of Lod

Clearly the temperature sensor and thickness sensors aren't sufficient to really see what is going on. Seems unfortunate given how much time, effort, and money go into placing and maintaining these buoys.

Look at the sudden 50cm jump in ice thickness shown by 2015A.
Seems like if we really want to know what is going on they'll have to add under ice cameras to supplement the data.


Wow no snow in Laptev and ESS whatsoever. That is gonna hurt, if true


Jim, Great suggestion, I will do something on A this weekend, I have been studying its data with big interest. And I am wondering if they are looking at the horizon from the coast, a double whammy, NOAA should be there by now.

Near North Pole buoy is very interesting and basically provides totally different data than all others. There is hardly a "normal" day there. Is more like a long prolonged noon.

Melting at bottom precedes melt Ponds by months, although I am not sure if Mass Buoys are set to deal with this, underwater camera would be essential to have a better understanding. The earlier the melting in bottom the greater the melt, especially if consistent after first sighting. There is also the issue of thermistors either accurate and showing +2 C without water, or inaccurate which would send your work to imagine some other thermal process.


Snow is a melting killer with the sun up, as it is an accretion slower during the long night. Optical observations have confirmed this. One significant spring snow fall and all melting stops for days (was confirmed the auger way as well).


Amongst other things they include the following preliminary March 2015 snow depth information:

Thanks for the link, Jim! I didn't have time to watch the SIPN webinar live, but hopefully they'll put up the recording (they usually do).

Jim Hunt

Neven - They said that a recording will be available in due course. I even got to ask a question!

My brief report can be seen on the forum: http://forum.arctic-sea-ice.net/index.php/topic,8.msg51329.html#msg51329

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