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Chris Reynolds


What I was referring to is my ongoing attempt to say something meaningful about the transition - whether we face a crash or a tail.

What I've been trying to do is to find a way in which having separated the melt an growth seasons I can use functions derived from data to examine the strengths of feedbacks in those periods.

My main issue is simple. To get to zero by September one would need either:

Thinner starting ice (April average).

Or more seasonal melt.

The starting thickness is a function of growth after the previous year's minimum. Thermodynamic thickness is around 2m thick. Most of that ice is within the Arctic Ocean, and early June area gives us the rough area of this ice: around 10M km^2. 2m thick ice over 10m km^2 gives a volume of about 20k km^3. So in a regime where there's a regular summer ice free period you would need to melt 20k km^3 of ice (roughly) to get zero sometime later in the melt season.

OK? So that's the freeze season. But what of the melt?

The converse applies there, without winter thinning one would need to lose about 20k km^3 in the Arctic basin to get a period with zero volume later in the season. My question is this:

Autumn/winter volume gain is increasing due to lower sea ice area. It can increase up to about 20k km^3.

Both 2007 and 2010 have seen increases in spring/summer melt amount, related to loss of MYI and general thinning. Can this seasonal loss meet 20k km^3 under current CO2 and ocean/atmosphere warming levels?

How do these two seasons interplay? Do they result in a steeply accelerating crash to zero volume in September or do they result in a tail of remnant volume?

If there is a tail of remnant volume then it could take some time to remove this, that would be because thermodynamic growth of ice would peg peak volume at around 20k km^3, and it would require a change to winter thermodynamics to bring about sufficient volume loss to create open water at the end of the season with an invariant volume loss during the melt season.



I would like to ask you to think about the processes and not the numbers - it makes things clearer if you can name them and you can easily model them.

In summer - it is albedo feedback melting the ice. Integration of that differential equation results in the exponential Wipneus uses to fit the data. That function is not rejected by fitting - so everything concerning this is fine.

The tail - it may have reasons because it is positive definite. Put in a base line to adress that.
It may be due to a negative feed back - please name it and then we can calculate the function for that by integration of the rate equation.

In winter I think the ocean currents will play the game and they are changing. I will not integrate that for you since I allready badly took it wrong with my stupid evaporation idea. Maybe a better idea can be found here: https://forum.arctic-sea-ice.net/index.php/topic,80.msg3774.html#msg3774

The seasons will not interplay from summer to winter after Sept. value touches zero (this year or 2018). And interplay from winter to summer will do some up and down - so that is that base line I was talking about. You may call it tail. But it is not a new process - we can ignore that difference without any consequence. That is why I call such an approach futile.

Chris Reynolds


I disagree.

Going the way you suggest is already done in numerical models.

Working on the assumption that all the feedbacks are now at play, I think it should be possible to use empirical data (with PIOMAS as a good proxy for volume) to determine the interplay between melt and freeze season processes.

"The seasons will not interplay from summer to winter after Sept. value touches zero (this year or 2018)."

They will because this will produce more vigorous ice growth in the autumn, which in following years may be delayed by increasing open water earlier in the season.


Chris Reynolds,

I remember reading your "Long Tail or Fast Crash?" and "March 2013 Status" blog posts back when you first posted them. Some of the conclusions that you made were based on the decline in thickness (as calculated by PIOMAS volume divided by CT area) being much faster in Winter than the incline in seasonal thinning, as you showed in this graph.

When I first saw this, I realized that there was a problem with simply using the PIOMAS volume to compare winter and summer thickness loss, but for some reason I never got around to mentioning it. The problem is that PIOMAS is overestimating winter volume loss and underestimating summer volume loss.

This was one of the findings when the measurements of CryoSat-2 were compared to those of ICESat. Neven's blog post on this contained a link to a BBC article in which Katharine Giles was quoted as saying, "The decline predicted by PIOMAS is slightly less in the autumn and slightly more in winter, but broadly speaking there's good agreement".

Since summer volume has declined more and winter volume declined less than predicted by PIOMAS, the decline in winter thickness will be smaller and the increase in seasonal thinning will be greater than indicated in your graph.

The NERC press release on the same subject also quoted Professor Christian Haas as saying, "While two years of CryoSat-2 data aren't indicative of a long-term change, the lower ice thickness and volume in February and March 2012, compared with same period in 2011, may have contributed to the record minimum ice extent during the 2012 autumn". The lower volume in winter 2012 as compared to winter 2011 is in contrast with PIOMAS indicating essentially the same volume during those two time periods. In other words, contrary to what PIOMAS shows, winter volume did not plateau.

These differences may be small (I still need to check the actual paper), but they nonetheless have important implications for your conclusions about a potentially long tail. Much of your argument for a potentially log tail was based on winter volume potentially plateauing a bit, and decline in winter thickness playing a much greater role than an increase in seasonal thinning. The CryoSat-2 results seem to indicate that PIOMAS has gotten these details at least partially incorrect, i.e., winter volume is not plateauing, winter thickness is not declining as quickly, and seasonal thinning is increasing more quickly. This could greatly undermine your argument for a potentially long tail.




""The seasons will not interplay from summer to winter after Sept. value touches zero (this year or 2018)."

They will because this will produce more vigorous ice growth in the autumn, which in following years may be delayed by increasing open water earlier in the season."

Now I agree - that is exactly the topic (change of ice-volume in winter and spring) I think we should address now. That is the task I was talking about in my comments. Modelling of Sept. volume is completed, winter and spring are of main interest.

Chris Reynolds


I have considered this, it's a minor reason why I haven't been too worried about getting a profile that matches PIOMAS volume.

However I perhaps wasn't clear enough about length of tail. I don't expect decades of tail. One flaw with my approach is that it doesn't factor in system energy gain due to large amounts of open water, at what would probably be progressively earlier dates in the year. So when the 'model' shows an oscillating tail it should not be taken as indicating reality.

What I see the tail as indicating is a state where autumn/winter ice growth is able to at least match spring/summer ice loss. With the growth being determined by thermodynamic ice growth, which under current winter temperatures is around 2m thick. So until the region had warmed enough to reduce winter thermodynamic equilibrium thickness, allowing summer to open up more water, the rapid volume loss would reduce and there would be a tail. Actually, if the modellers are right and CO2 is the main issue in winter I suppose that could persist. Then again there would be some residual warming of the ocean... So much to consider.

I posted that post before having seen the recent PIOMAS gridded data. With sight of that it shows that this year included the apparent levelling in volume hides potentially significant declines in thick ice.

However I still wonder if the autumn/winter thermodynamic growth has the potential to draw things out. Or if we will see a succession of crashes culminating in a sea ice free state.


Crandles has been talking about trying to make a 'toy model' that's more physically based than my attempt using curves derived from data.

I still think that re-doing PIOMAS or NAME would be futile. But Crandles may have a point - what has deterred me is that when I tried a similar approach around the time I changed opinion on a rapid loss, everything I did either crashed to zero, or zoomed to +/- infinity.

I keep meaning to do a further blog post, but have been pondering doing a thread over on the forum.



Ah, now I understand. Thanks for the clarifications.


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