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Jim Williams

Sure makes the change in 2010 stand out.

R. Gates

Great job!

Actually, both 2007 and 2010 stand out if you pause the video on the side view and look at the relative drops those two years. In relation to those years, while 2012,was the lowest ever, it was not the biggest relative drop from the previous year.

Chris Reynolds

Thanks Andy, great video.

Andy Lee Robinson

Neven, thanks for posting, and to everyone for nice feedback!

I'm toying with the idea of including monthly-averaged regression series at 90°, to project when we can expect a month to be ice-free.
Tamino has done some great work on this.

The trend for all Septembers seems to indicate a >50% probability of breaking 2012's record. We start this year with 1,058 cubic km less ice than the same time last year - that's about one trillion tonnes not needing to be melted this year. That a lot of surplus energy.

Are we taking bets yet on how 2013 will turn out?


A PayPal betting pool for Sept NSIDC minimum? I'm in.

For your collective amusement: I came across this 39-year-old satellite photo in the course of looking at a 28-year-old paper on Arctic Ocean sea ice conditions, melt ponds, and albedo (we're still at this?!?).

The coloration is a bit unfamiliar but after staring at it for a while, it appears that peak melt didn't amount to a whole lot back then, just the Bering Sea and Laptev.

Otherwise it looks rather like 25 Jan 2013 except the latter is fracturing by the day (that huge new triangle above Greenland is a major anomaly in the ice velocity vector field).


 photo 1974SeaIce_zps8855a151.jpg

 photo 25Jan13Fractures_zpsa8929fcb.jpg


I realize it is not the politically correct thing to say, but for the sake of any hope of action to preserve the long term climate, the faster Arctic sea ice volume and extent hit zero, the better.
Nothing else will change the mind of the average Joe (and most of the MSM). After an absolutely mind blowing 2012 in the US, CNN still felt the need to give a blatantly lying, professional climate denier the same amount of time as the pro-science side (on Piers Morgan the other night). Even though the science side has gotten more support from the US based public after being hammered with AGW related disasters all year, the exact opposite is true for Europe, and especially Northern Europe, where four winters in a row with severe Arctic blasts have swayed opinion in anti-science direction better than any well paid denier could have dreamed of doing.
The melt records in the Arctic have had some impact, but I think that the impact of images of the North Pole being pretty much completely melted away will have a much stronger effect on public opinion than all other climate related catastrophes that we have seen so far combined.
The deniers will try to spin it wildly, but I think that will be the moment when the majority of the public finally wakes up. The denial industry knows this all too well, so they will be prepared.


@ Esop:
"denial industry" as you name it sounds funny to me - here they blame the "AGW industry" to waste poeples money for reducing CO2 in vain...

@ Andy:
are you thinking to a simillar thing Wipneaus did in the latest PIOMAS-thread? (exponential fits to all the grids of ice volume - very nice): Most areas are projected to be ice-free around 2017 - some seem to last longer, but that is probably only to transport via Fram street.

Tommi Kyntola

SATire: I don't think the Wipneus grid graph can be used to make such lengthy predictions. As I understood how it was done, it's accurate in showing what melts next, but beyond that it goes astray. It doesn't transport ice and it doesn't take into account non-local feed-backs, most notably the albedo change as there's no heat transfer either. Those areas still frozen and not quite yet next to open ocean have hardly any indication of that in their history and thus cannot accurately predict their demise on their own.

It's a great chart for sure, but in my opinion one should be cautious with it. The overall PIOMAS data and the monthly averages show clearly how the individual grid extrapolation is likely to be inaccurate after a year or two.

It might be interesting to plot the average of the grid approach into the overall graph and see how it fares.



It might be interesting to plot the average of the grid approach into the overall graph and see how it fares.

Do you mean something like https://sites.google.com/site/arctischepinguin/home/piomas/grf/pgd-volsep1.png ?

Could you explain a bit more what it is that "show clearly how the individual grid extrapolation is likely to be inaccurate after a year or two"?

Andy Lee Robinson

Wipneus, yes exactly like that!
I can make arrays of monthly averages easily enough, and create bsplines and beziers, but those only interpolate.
All I'd need is some perl or php code to write regressed values into new arrays, spline them into a collection of objects to make smooth ribbons and transform to map to the right 3D locations, and animate them...
I love these challenges!

Tommi Kyntola

Nice one Wipneus. The gompertz tail comes out as expected. That's the inaccuracy I'm referring to.

Now, I know some people except that to happen for physical reasons and model simulations. Be that as it may, in this particular case that comes out for the wrong reasons. In your grid graph the cells are not connected. Thus any future feedback of albedo change as a result of ice loss does not affect anything outside its own cell. Also ice transport is not there either. The ice thickness stays relatively constant in those areas through which it's transported elsewhere to melt. Hence those regions right now not yet melting, or through which ice of constant thickness passes, will produce a fit that predict a longer life time than it should based on this data. Of course it worth a note to realize that all negative future feedbacks are not at play either, but I think we all agree that right now the positives reign supreme.

Another way of looking at it would be to consider a similar graph done two or more years ago. The tail would extend out earlier. And again because the positive feedback during those two or more years would not be there in the data affecting the fit or extrapolation.

Or what if not such a large part of melt had taken place in thinning and lost MYI, i.e. what if all of the melt only took place at the ice edges? The grid graph would produce silly results in that case.

Now, like I said, the Gompertz tail has some physical backing, too, Some negative feed-backs and Greenland winds sustaining it a little longer, iirc. The explanations I've heard have been unconvincing, but whether they turn out to be true or not remains to be seen.

I can't help but think that some of the academic models have somewhat analogous problems, i.e. underestimated heat and ice transfer mechanisms.

(Disclaimer, an absolute climate amateur here, I may be wrong on some or all accounts, so feel free to teach me. Also as I've lived all my life north of 60N, I've seen my share of spring and summer ice melts. The Baltic sea and lakes are naturally different beasts, but they make me susceptible to being biased for an ever faster melt towards the very end.)


Beauford Gyre spin-up is shearing ice today from Barrow to Wrangel:

 photo WrangelShear_zps57afb076.jpg


Piomas may provide an upper bound to sea ice crash. But as Tommi notes, too many unwelcome effects aren't considered, like ice loss wind-driven spin-up of the Beaufort Gyre, whose shear effects on weak ice are so evident today (mid-winter!) around Wrangel and Morris Jesup:

"More than 70,000 km3 of freshwater are stored in the upper layer of the Arctic Ocean. Satellite measurements between 1995 and 2010 show that the dome in sea surface height associated with the Beaufort Gyre has been steepening, indicating spin-up of the gyre.

We find that the trend in wind field curl -- a measure of spatial gradients in the wind that lead to water convergence or divergence -- exhibits a corresponding spatial pattern, suggesting that wind-driven convergence controls freshwater variability. We estimate an increase in freshwater storage of 8,000 km3.

There are different potential causes for an increase in the transfer of momentum. The wind drives the surface water directly over leads, and deforms and moves the sea-ice, which drives the water beneath. Buoy observations show a large ice deformation rate in summer 2007 compared with previous summers (1979–2006), suggesting that the mechanical strength of the ice decreased, making it easier to move.

 photo BeaufortGyre_zps69a7c142.gif


Grrr, typepad. Here is the rest of that post on Beaford Gyre spin-up and doming:

"An increased ice drift speed has also been observed from 2004 onwards, which cannot be fully explained by changes in wind speed. Arctic sea-ice extent and thickness are declining and this decrease in ice thickness is a likely cause of the increase in ice deformation rate and drift speed.

Increasing ice deformation also results in more leads and ridges, increasing the area of vertical surfaces the wind can blow against, which increases the momentum transfer to the sea-ice. The atmospheric momentum flux is also influenced by the turbulent fluxes of sensible and latent heat from the surface, which depend on the presence/thickness of the sea-ice." KA Giles et al Nature Geoscience 22 January 2012


Upwelling of Arctic pycnocline associated with shear motion of sea ice (free full text):
MG McPhee et al GRL doi:10.1029/2004GL021819, 2005


Chris Reynolds

A Team, Tommi Kyntola,

Thanks for the info regards the Beaufort Gyre. Beaufort used to be a 'flywheel' circulating and aging ice before dumping it into the transpolar drift, to be partitioned between Fram outflow and further compacting off the Canadian Arctic Archipelago (CAA). Now the BG drives ice into the regions suffering the most regular greatest melt out. So an intensification of the BG in current state implies further loss of MYI (multi-year ice).

I too now see the Gompertz tail as an artefact of ice movement within the pack. Wipneus's excellent grid cell trend plot shows that the most persistent areas are associated with the transpolar drift and net movement of ice along Greenland towards Fram. Link

As Crandles has also noted, these are probably due to new ice replenishing grid cells in those areas, thus reducing the trend. On this basis I think that whilst we can expect the ice to last until after 2015, the extension of the tail beyond 2020 is an artefact of ice transport off Greenland.

Gompertz is derived, as I understand it, from studies involving natural systems. Is there any way to determine whether the Arctic ice system is of a Gompertz or an exponential type?

Chris Reynolds


I keep meaning to ask, and now I've linked to the image in question...

You're using the proper PIOMAS grid, centred on Greenland, apparent from the graphic above! That's way ahead of me. I'm trying to work out grid box areas to improve the volume figures I've been getting. How have you worked the real grid out? And do you have an area mask with areas for grid boxes? If you have worked that out already would help me avoid hours marred by my inept attempts at programming. Otherwise any advice regards how to work out the real grid would be appreciated, bearing in mind my maths is from doing a degree in electronics nearly 30 years ago.



all functions are used to describe natural systems, if appropriate. Simple exponentials are natural, if the rate of growth of something is proportional to the same something - as melt and volume e.g.. Gompertz is very simmilar to 2 exponentials - one of growth proportional to something and one declining as in radioactive decline e.g.. I really can not see such decline type of effect in the arctic, since molten ice is just water and nothing disapears actually. Because a steady decrease of melt was not observed in the past I doubt that it will suddenly show up in the very last days of sea ice...



since you know electronics - please replace above "radioactive decline" by "capacitor discharge" for your convinience.

best regards


Regarding Tommi's comments about Wipneus's calculations, what he's describing reminds me of the reaction-diffusion models, whereby the state of neighboring cells influence their neighbors. Would it be possible to incorporate a step whereby an empty cell increased the melt rate of its neighbor (and vice-versa)?



Guys, what was a slight cough yesterday is now a 38.8 dgC fever. I am under strict orders to stay in bed, so I keep it short.

Tommi and others. I have said before that there is a distinct danger not to appreciate the nature of exponetial decline/growth. Humans are known not to understand them.

In other words I am not entirely convinced that the effect described (speedup of melt of adjacent cells, visible effects of ice transport) are not already included (causing the exponetial decline in the first place).

Chris I took examples from the provided program sources. The read_hi_uce.f program shows how the variables are read
You must have used the clat/clon coordinates of the grid cells.
These give you the SW coordinates of each grid cell, that is enough to plot them. Area is calulated from the length of the sides of the cells: HTN, HTW, HTS and HTE from the grid.dat.pop file: (HTN+HTS)*(HTE+HTW)/4


Get well soon! It is the perfect day to stay in bed.

I totally agree, that most effects are included in your fits - the Fram-issue was allready discussed. I think you have really done everything on the data that should be done. Since correlation between PIOMAS and observed data is not very strong (0.72 from Schweiger http://psc.apl.washington.edu/wordpress/wp-content/uploads/schweiger/pubs/IceVolume-2011-06-02-accepted-with-figures.pdf), more statistical magics could be chasing pavements (speaking with Adele).

Next thing could be trying to detect signs for bifurcations. That is a tough thing, because statistics are so weak. A 3 sigma effect is not very likely - and that would be the minimum for starting to think about a possible effect... Maybe in the waters of Franz Joseph Land it could be observed. The bifurcation could be triggered by the atlantic water coming in the arctic basin, since albedo-melt and water drift/mixing by the regular storms come together there allready now. So - if your fits around Franz Joseph talk about march-ice until 2030 and it vanishes allready now, that could be a test for bifurcation-detection at the north pole and in Laptev e.g. next year.

Chris Reynolds


Thanks for reminding me it's the SW corner, I'd been assuming they were centre coordinates - having myself been interrupted by illness I'd got mixed up. Should be more straightforward now.


I've previously posted some papers for Rob Decker by Livina and Lenton.
Which has previously been re-interpreted as not meaning there was a bifurcation in 2007.
This comment on the earlier paper needs to be read - Ditlevsen shows that it's not a bifurcation but a change in seasonal cycle.
I also linked to a paper from the same authors that discusses finding warning signs of bifurcations. But I can't find that right now. The point I took from that is that while bifurcations may be seen in longer (millennial) records from paleo-datasets, tracking a bifurcation as it happens may not be possible until after the event. And as the Livina/Lenton papers above show other changes like changes in a seasonal cycle could masquerade as bifurcation like events.

Bifurcations however must arise from real physical processes. In this respect we can explain away aspects of current change, like the change in the seasonal cycle. But this may not help decide if bifurcation is underway. Critical slowing...

Ahh, found that other Livina/Lenton paper:

Critical slowing may be taken as an early warning indicator, my maths isn't yet up to implementing this for myself. But longer datasets seem to be needed for statistical significance, although with a mechanistic explanation backing up a change as not being natural variability, shouldn't the length of dataset needed to attain physical (if not statistical) significance, be shortened?

I also wonder if one should expect a bifurcation to be associated with multiple changes in key metrics, like the 2007 shift in area/extent seasonal cycle, and the 2010 shift in volume seasonal cycle.

Hand-waving blather ends here...


Chris, thank you for the nice material to read - I really appreciate your links to papers.

Regarding the bifurcations - I am not so interested in a mathematical proove of a bifurcation, that looks a bit booring to me and someone more patient may do that, if everything has happened allready. I am interested in seeing, what Eisenman predicted. Since that math is simple 1D it would fit nicely to the things Wipneus is doing on the grids - he could see a hint first with that methode. A proove will be difficult because of the poor statistics, but to see the signs of an annual ice-free arctic first is something I would enjoy.
Since I am a well-bred physicist, I should be able to deal with the math - so if you need something to be computed, maybe I could help. But I quit coding some ten years ago, so my Fortran would not be that smooth anymore. But since there are enough coders anyway in the community, I would like to concentrate on the engineering perspective I am missing. So please excuse me if I am to ignorant sometimes, it is for that reason.

- now absent and reading ;-)

Chris Reynolds



I've only looked at grid.dat - the scalar grid!

I've never looked at the vector stuff in gridded PIOMAS, not being a programmer, and not being mathematically adept I decided I wasn't up to it.

Wipneus, I know you've got a better grid area worked out - congratulations etc. But I'm stuffed if I can do it. So I'll be sticking with what I have. A week's worth of long evenings followed by a weekend trying to improve on Rob's original grid area calculations and I've got nowhere. That's enough time wasted.


Brian Hansen at the Danish Meteorological Institute gave me a helpful update yesterday about AVHRR imagery concerning Nares Strait ice export and Petermann glacier calving ... once the photo pipeline coordinate error is fixed, 3x daily pictures of this region will be under 'Kennedy' at the link below. Unfortunately the higher resolution ASAR image series ended when the Envisat satellite tanked on 8 April 2012. However Modis visible spectrum will resume in the spring with more sunlight at high latitudes.


I came across this remarkable ASAR image from 2008. Each radar shot is a grayscale, so to make a time series RGB, they assigned 3 shots taken over the melt season to the green, red and blue layers of an RGB image. Everything that moves or melts shows up as a color shift (departure from gray).

The original gorgeous high-resolution 69 Mb file won't display here, but I've provided an overview of the Nares Strait region and a blow-up of Petermann to pixellation that shows a great deal of structure (in case you were wondering where it was going to calve next).

I wasn't expecting any action in the Nares Strait in late January -- especially given the static ice arch below Kane Bay -- but the Navy sea ice thickness animation has been showing quite a bit of thickness variation in the Strait, seemingly associated with flushing from the synoptic-scale shear event.



 photo petermann_zps98c96a78.jpg

Andy Lee Robinson

What's notable, and not obvious unless looking carefully at the start/end points in the graph, is that this year starts with 1,058km³ less ice volume than this time last year.
That's approximately a trillion tonne deficit.

Will the ice be able to catch up, what will the maximum look like in March/April, and are we looking at another record minimum this year?

My guess is that the odds are against recovery.

Chris Reynolds

Wipneus has helped with recalculation of the area of each PIOMAS grid box. Rob Decker spared me the minor bother of converting to the format we use. My laptop has re-run the appropriate macro...

All I had to do was paste onto my blog. :)

Top right of the main page here:
You'll find a tab 'pages', where I've posted "PIOMAS volume breakdown by grid cell thickness." In a format anyone with a spreadsheet can download without much hassle.

So that's a breakdown of the PIOMAS volume into the contribution of areas reporting ice thickness, with the thickness broken down into 25cm bands, up to 3.5m thick and over.

Sorry but blogger won't allow me to post as a bare text file, it insists on putting all the blogger stuff around the data, so it's a minor hassle to highlight down using the mouse.

Crozet Dutchie

A bit off-topic but Revkin at the NYTimes (DotEarth) posted something on the Arctic storm in August: http://dotearth.blogs.nytimes.com/2013/01/31/study-finds-arctic-cyclone-had-insignificant-impact-on-2012-ice-retreat/

Eli Rabett

Really well done. thanks

Al A

Sorry that the reason for my question is my total ignorance in both the climate and computer graphics areas, but can you give some detail on the "800 frames, 30 minutes of work per frame"? Was this in analyzing data or generating graphics, man-hours or cpu time, etc? It seems a huge amount of time, and I wonder, for instance, if this was in setup, so that subsequent years will be quick to produce, or if it will be just as manually intensive each year. Any information on the actual method of generating the graphics would be interesting too.

Andy Lee Robinson

Al A, thanks for asking - Peter Sinclair just did a write up from my post on Tamino's site, where I explain how it came about, and some of the hoops I jumped.


Of course, the amount of time programming in perl to create the objects, sequences and motion during the discovery phase took about 100 hours or more until I was satisfied enough to be able to sleep!

The graphs were done at 1920x1080 using a raytracer so reflection, ocean and cloud effects and thousands of objects to describe the graph functions add to the render time - this was per-core time, paralleled up 20x with a mixed bag of servers.

It is now just a one line command to rerun with new data that is downloaded, unpacked and converted into the graphic primitives automatically.
With a bit of extra optimization, render time is now around 8 hours, but I may tweak and extend it if any new ideas come up.
The task scheduler is flexible, and could handle 100 or more machines if I could get hold of any... This is what a botnet would be really useful for!

Video downsampled to 1280x720 25fps for youtube.

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