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When will the Arctic Extent dip below 1,000,000 Km^2

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Voting closed: July 27, 2018, 07:46:32 AM

Author Topic: When will the Arctic Go Ice Free?  (Read 130488 times)

Tor Bejnar

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Re: When will the Arctic Go Ice Free?
« Reply #1300 on: November 07, 2019, 03:36:52 PM »
I concur.  The freeze chart show the influence of thicker ice insulating the freezing water from the cold air.  FDD (freezing degree days) is pretty much the only input.  Melt, on the other hand, is more directly related to the energy received. 

Melting snow atop of ice is almost totally independent of how thick supporting ice is.

In a simplistic model with snow-free ice, the 2nd meter of growth requires many more FDDs than the 1st meter.  Melting the 1st meter of ice will use more energy than the 2nd because the ice will be colder to start with.

Maybe the question is: if two floes, side by side have the same snow cover at the beginning of the melting season and have the same salt content, etc., but one floe is 2 m thick while the other is 1 m thick [e.g., near the end of the winter, the thicker floe was created by a rafting event, and enough time elapsed to even out its temperature gradient], will it take more or less than twice the energy (as delivered by natural forces) to melt the thicker floe?  (This gets rid of the temperature gradient difference between the 2 ice thicknesses at the start of the melt season.)  The melting energy is delivered by solar gain, wind, rain and whatever is happening in the water under the ice.
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Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1301 on: November 07, 2019, 05:29:18 PM »
I concur.  The freeze chart show the influence of thicker ice insulating the freezing water from the cold air.  FDD (freezing degree days) is pretty much the only input.  Melt, on the other hand, is more directly related to the energy received. 

Melting snow atop of ice is almost totally independent of how thick supporting ice is.
etc...

Maybe the question is: if two floes, side by side have the same snow cover at the beginning of the melting season and have the same salt content, etc., but one floe is 2 m thick while the other is 1 m thick ... etc.

 The melting energy is delivered by solar gain, wind, rain and whatever is happening in the water under the ice.

And RE Oren "Also a lot of the melting is due to direct insolation while the temperature stays near zero."

1.  RE freezing energy out and melting energy back in. 
     I see what you are saying about the solar aspect, but I still suspect that it simply comes down energy in vs. energy out, regardless of how that energy travels in or out.  If so, then the Thorndike curve would work in reverse, giving much faster melt for the final 1 meter of ice.

2.  RE Melting snow on top of ice being independent of ice thickness below. 
    That one I agree with.  What portion of the summer melt season energy input is used up by melting snow on top of the ice?  That's a question, not a comment posing as a question.  I truly have no clue about that.  But even if snow cover uses up a significant portion of the summer melt energy, that would only dilute the effect of the final-meter-melting-faster regime, not counteract it.  Once the snow is melted off, then you still have the issue of whether the remaining ice will melt faster if it is 1 meter vs. 2 meters thick.

3. RE "and have the same salt content". 
     But it seems realistic to assume that 2M thick ice does in fact, on average, have a higher portion of MYI (and thus fresher, and mechanically stronger with fewer voids) that is more resistant to melt, on average, than 1-meter-thick ice.  So it seems that qualitative characteristics of the final 1 meter of ice will indeed be a contributing factor for accelerated final melt.

----------
    As shown on the CAB volume chart, even with an eyeball-drawn straight line trend it reaches zero (2048?) about 16 years after the Wipneus whole Arctic Ocean volume chart.  (Polynomial regression curves get you into trouble when extending beyond data used to define a relationship, And the higher the exponent value, i.e. X2 to X3, the greater the hazard.  Given enough exponents you can make a curve do anything. So I am not moved by the X3 extrapolation curve for the CAB volume data.)  If somebody is willing, it wouldn't take long to add a straight line trend to that chart.  The point being that the CAB volume trend does not demonstrate a high degree of additional resistance to melt.

    Another factor not mentioned earlier -- CAB losses might accelerate as the peripheral seas around the CAB no longer provide an ice wall barricade against melting energy.  Also, even at 90N, the encroaching loss of albedo in the waters surrounding the CAB will contribute to greater and proximate summer solar radiation melting energy getting into the CAB.

    All that said, there is a very strong argument against my rambling associations that I failed to mention -- The experts who actually study this stuff.  They continue to publish estimates showing September ASI extent and volume lasting late into the 21st century.  For example, the recent IPCC cryosphere report. 

     So I can't be too adamant in defending my fast-final-meter-melt thesis because I at least know that I don't know the details.  But lest you think I am humble and wise in saying that, let me exemplify opposite characteristics by stating an unfair and baseless suspicion that the experts may be so engaged, enmeshed and enthralled with their models that they don't see what seems obvious to a simpler minded observer like me - the Arctic sea ice is taking a beating.  That charge may not be entirely baseless in that the earlier expert model predictions greatly overestimated how much ASI would remain by 2019.  I am loathe trod down this path, as it is exactly what the climate change deniers do.  But at least in this case I am basing spurious accusation on some concrete observations.  Maybe sometimes the Emperor does have no clothes.  But let's move on, because the "experts are wrong!" line of argument really is on "thin ice." 

     Even without last-meter volume loss acceleration, there is what is to me the bedrock evidence of the Wipneus straight line volume trend.  It looks like a robust trend and it hits zero, nada, zip, in 2032.  Maybe somebody smarter than me will do the math to show at what volume, and thus roughly what year, we can expect rapid acceleration of Extent losses.   Zero Volume requires 0 Extent, but proportional Extent losses have so far lagged behind Volume losses.  Given that we have already lost ca. 3/4 of the September minimum volume, but only 1/2 of the Sept. minimum Extent, even if Volume loss rate remains stable the Extent loss rate would have to accelerate within the next decade.

     Countervailing forces of increased Arctic warming; more fractured, thinner ice; more storms, polar cell weakening; Atlantification/Pacification of Arctic ocean SST  vs.  higher latitude for the final ice; could result in the Volume loss trend continuing on a straight line trend.  If that happens, or even if Volume losses slowed down a bit, the requirement for % Extent losses to eventually catch up to % Volume losses means that Extent loss acceleration may not be far off, if not underway already.  (Which I acknowledge is a different question than the final-meter melt rate question which is the topic at hand.)  If so, then gerontocrat's CAB open water chart will be an interesting metric to watch in next few years.

PS Tor, sorry for misspelling your name in previous post, now corrected. 
« Last Edit: November 08, 2019, 08:31:32 PM by Glen Koehler »

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Re: When will the Arctic Go Ice Free?
« Reply #1302 on: November 07, 2019, 05:34:42 PM »
The area is also important when answering the question. The larger the area the more the thin floe will break, increasing surface area, albedo and melting. So an apples to apples comparison requires a fixed area too.

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Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1303 on: November 07, 2019, 09:01:34 PM »
One more...
RE Oren "The physical behaviors of melting and freezing in the Arctic are different due to the effect of the buffer of the water below the ice."
     That factor is beyond my understanding.  Maybe that is why the experts show such a prolonged persistence of the final ice despite current trends.  Nothing I can say because I don't know nuthin' about it and too lazy/ not enough time to read up on it right now.  It may be the Achilles heel of my thesis.

RE GoSouthYoungins "freezing season near the pole brings a darkness and cold that is hard to comprehend". 
     No doubt it is still wicked cold up there.  But it is only the current vs past relative temperatures that count.  Arctic winter cold is not a new factor, and despite still being very cold, the freezing season, like the melting season, is getting warmer.  The equilibrium level for both seasonal max and min amounts of ASI has to decline with both ends of the Arctic seasonal temperature cycle warming.
« Last Edit: November 07, 2019, 10:57:39 PM by Glen Koehler »

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Re: When will the Arctic Go Ice Free?
« Reply #1304 on: November 07, 2019, 10:29:20 PM »
There must be some good research that settles the question nicely. I can't find it. In the meantime, some clarification.

First-year ice most certainly is more prone to melt than multi-year ice.
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kassy

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Re: When will the Arctic Go Ice Free?
« Reply #1305 on: November 08, 2019, 12:03:56 AM »
Maybe there is none.

I think that just flipping the graph is not valid but could we think of the curve for melting. What would it look like?

Thinner ice is more effected by the sum melt (top and bottom) and at some point it breaks up and fractures which accelerates melt.

Then there is the factor of location (cold north) and the deep seas beneath and what that possibly does to the currents and we have to consider that a lot of ice that ends up in the central arctic seas was made somewhere else and that might fail so who knows what happens next.

We don´t know what the worst case effect of the weather could be with prolonged open weather mixing up the outer arctic seas or the precise effects of atlantification and pacification going forward.

There are simply to much variables to settle the question.
 
My first question would be at which thickness will melting ice break up. At some point it becomes   less rigid and waves will damage it more. That should be an important point.

Þetta minnismerki er til vitnis um að við vitum hvað er að gerast og hvað þarf að gera. Aðeins þú veist hvort við gerðum eitthvað.

Richard Rathbone

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Re: When will the Arctic Go Ice Free?
« Reply #1306 on: November 08, 2019, 04:01:23 AM »
The latent heat doesn't get conducted through ice when it melts, but it does when it freezes.

Consequently thicker ice freezes slower, but it doesn't melt slower.


Tor Bejnar

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Re: When will the Arctic Go Ice Free?
« Reply #1307 on: November 08, 2019, 03:49:34 PM »
Thanks, Richard: I think you've referenced the 'science' I was looking for.  (I have functionally no thermodynamics formal education.)  Can you say more about the melting process?  About how and why the temperature gradient changes in ice as it melts? 

As I wrote these questions, I realized that for freezing sea ice, all the heat exchange is from the water, through the ice and into the air.  During the melting season, the heat exchange is from both the 'air' and from the water below.  In a colloquial sense, the 'cold' enters the ice only from above and leaves the ice in both directions.
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Richard Rathbone

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Re: When will the Arctic Go Ice Free?
« Reply #1308 on: November 08, 2019, 09:21:04 PM »
If you go and look at old posts in What the buoys are showing, you can find plenty of temperature profile data of how the temperature profiles through the ice change during the season.

There's all sorts of stuff that matters a little, but the big effect that breaks symmetry between freeze and thaw, is as you note, the cold enters from above and leaves in both directions.

In a simple model the temperature profile is linear during freeze (from -1.8 at the bottom to -20 or whatever you pick as the representative freezing season temperature at the top). In the later part of thaw its also linear, (from -1.8 to 0) but although the top increases to zero fairly fast, it takes several months during which there is a gradually decreasing bump in the middle for the whole profile to flatten out.

The big transfer is the latent heat, but when that isn't being conducted through the ice, the profile is set by conducting heat into the ice to heat up the middle from its winter temperature to its late summer temperature.

Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1309 on: November 08, 2019, 09:54:44 PM »
Ditto that request Tor.
 
RE: 
Gerontocrat, your graphs has gotten me thinking.  What if the open water in the peripheral seas is contributing to larger heat losses, resulting in faster refreeze of the CAB?  Widespread ice cover in the past may have kept more heat bottled up beneath the ice.

Uh oh, another possible Achilles heel.  And maybe that was part of the Chris Reynolds 'Slow Transition' hypothesis that I missed.  I can see how ASI refreeze declines could slow as diminishing ice cover allows more ocean heat to escape to the atmosphere during the winter.  That would stall declines in April Maximum.  But even with a semi-stabilized April max, increasing warming of the summer melt seasons would still progress toward a September minimum reaching the BOE threshold of 1M km2 Extent.

    Just to clarify, my proposition that the final meter would melt out faster is not saying that the Arctic is going to ice free year round anytime soon.  It would apply sequentially to each month as its monthly average thickness got to and below 1 meter.  Thus, September Volume and Extent losses would transition from a straight line trend down to a downward bending curve as average thickness declines.  If that is true, then it should start becoming apparent pretty soon (i.e in next 5 years) because Sept. average thickness is getting close to 1 meter.   

      See the Wipneus average montlhly Volume graph at
https://14adebb0-a-62cb3a1a-s-sites.googlegroups.com/site/arctischepinguin/home/piomas/grf/piomas-trnd2.png?attachauth=ANoY7coD8qak1Y1OxDoPDEijpxlR44NBQbsfo1c5i4-Bk1Zvmt1qUiw2vkca4klldt_5e_ZfGwzmI0esENnfeDW9sXTTdna3Brr9mvGsVbPuI1oD5uyzvq7Z3D8zf2EfMCy9nnbKl45gFjfDbj6kZwFDFybvy9yhahjUNE5xVFrB84O_dzfeIEwDQDZXZVbi5nZDn9-9IBKLLbEeSE4eAnkpqcVVwWYWMVXq9QGC-BVCpuGpLMcrTZJ1srgqcr6Ut-8eYoiJQg0L&attredirects=0

      As shown on the Wipneus graph - August and October volumes only trail September by a few years.   But then there is a big jump to July and November, another big jump to December, and another to January and June.  So those later months would still have large amounts of ice for many years to come even if the fast-final-meter hypothesis is correct.

     The Wipneus graph provides some evidence to evaluate the notion that as a month reaches and goes below 1m average thickness, its losses accelerate.   The graph applies X2 curves to monthly average ASI volumes.  According to my reasoning, September should have the steepest downward curve since it is the closest to crossing the 1 meter average thickness threshold (not that there is a discrete threshold to cross). 

     And lo, the Sept. curve does bend down at a steeper rate than the July or June curves.  (August and October curves have essentially same curvature as September, Nov and Dec curves not posted for 2019 yet).  I measured curvature by comparing the left axis 1975 amount vs. the 2020 right axis amount for September vs. June or July curves.  The Sept curve is farther below June or July in 2020 than it was in 1975, so it is bending downward at a steeper rate. This is hardly a Nobel prize winning observation, but at least it fits with my hypothesis.

     But it is also true that while I am not ready throw in the towel quite yet, the more I think about this, the more I realize I am dabbling in concepts I know too little about to make meaningful conclusions.  There are books and articles to explain things like this.  We don't have to figure it out by ourselves because other people have thought about it in a lot more depth. 

      I read through the recent IPCC Cryosphere report looking for a mechanistic explanation and found surprisingly little exposition on this critically important issue.   If you know of a good summary that addresses how ASI loss trends are likely to evolve in the coming 20 years please share citation or link.  Here is one I read a while back, but need to re-read:
    Overland, J. E., and M. Wang (2013), When will the summer Arctic be nearly sea ice free?, Geophys. Res. Lett., 40, 2097–2101, doi:10.1002/grl.50316.  https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/grl.50316
   
     Even though it is getting a bit dated now, it was written right after the 2012 minimum at which time ASI declines were greatly exceeding expectations.  Thus, awareness was high that the Arctic was not behaving as had been predicted.

    I wonder how many of the experts at NSIDC, NASA etc. read the ASIF.  Maybe professional etiquette prevents them from zooming in and correcting the half baked-theories posted by non-experts like me.  (Some of the folks that do post here give the appearance of being professional ASI scientists.  There is tremendous knowledge embedded in ASIF.  If the experts aren't reading it, they should because they could learn a lot too.)  But just saying "Wrong" isn't enough.  What I would like is for somebody with expertise to provide a summary of how ASI loss dynamics are likely to behave over the coming 10-30 years. 

    Specifically, I would like to read an expert opinion on whether the Wipneus volume straight line trend is expected to continue.  And if not, why not.  Because if it continues, we will reach zero average ASI in September 2032, and rapidly declining Sept. average Extent over the next 10 years as Extent losses catch up to Volume losses.  With August and October not far behind September.  That scenario has consequences for the habitability of our planet.  So it is not simply an intellectual exercise.  We really need to understand this stuff.

    Sorry for another long post.  Just trying to get it down in words.  Guess I wasn't born for Twitter times.

   
« Last Edit: November 08, 2019, 10:12:02 PM by Glen Koehler »

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Re: When will the Arctic Go Ice Free?
« Reply #1310 on: November 08, 2019, 11:27:20 PM »
That’s fine, Glen. Meaty subjects need long posts.
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Re: When will the Arctic Go Ice Free?
« Reply #1311 on: November 08, 2019, 11:52:00 PM »

 I can see how ASI refreeze declines could slow as diminishing ice cover allows more ocean heat to escape to the atmosphere during the winter. 
   


 More open water means more time for heat to escape but it also means more heat gets into the oceans.  It seems to me that as long as there is significant ice in September the ice extent will grow, sometimes furiously fast and heat will be trapped in. The top layer of the ocean, when frozen, keeps the heat in.
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uniquorn

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Re: When will the Arctic Go Ice Free?
« Reply #1312 on: November 09, 2019, 12:40:28 AM »
When looking at buoys for verification of 'trapped heat' it is nearly always at 25m-75m depth depending on pacific or atlantic side.
13 operational whoi itp buoy data are available here https://www.whoi.edu/page.do?pid=165676

Tor Bejnar

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Re: When will the Arctic Go Ice Free?
« Reply #1313 on: November 09, 2019, 05:57:48 AM »
What I hear Glen asking for, Neven, is for you to ask for some ASIB posts written by experts in the fields of sea ice dynamics and the like.  For example, Richard Rathbone just referenced "all sorts of stuff that matters a little" associated with sea ice melt.  On the other hand, ASIFers with some pertinent knowledge could offer to write a guest ASIB post.  These people will have a handle on what we can handle.  (Many a scientific paper quickly flies over my head.)
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Klondike Kat

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Re: When will the Arctic Go Ice Free?
« Reply #1314 on: November 09, 2019, 03:27:18 PM »

 I can see how ASI refreeze declines could slow as diminishing ice cover allows more ocean heat to escape to the atmosphere during the winter. 
   


 More open water means more time for heat to escape but it also means more heat gets into the oceans.  It seems to me that as long as there is significant ice in September the ice extent will grow, sometimes furiously fast and heat will be trapped in. The top layer of the ocean, when frozen, keeps the heat in.

True, but much depends on when the open water occurs.  During the spring and summer, full sun will heat up the open water.  However during the autumn, there is more darkness than light, and consequently, more loss of heat than gain. 

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Re: When will the Arctic Go Ice Free?
« Reply #1315 on: November 09, 2019, 04:59:24 PM »
My 2 cents worth which, due to market demand, is only worth a penny.

Thinner ice is more fragmented, mobile, dispersed and saline IMHO. All of these would cause this ice to go poof faster than thicker ice.

Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1316 on: November 09, 2019, 06:46:53 PM »
http://psc.apl.washington.edu/zhang/IDAO/multi.html
Animation of ASI Thickness out to 2050 by Dr. Zhang at Polar Science Center.  Shows first BOE by the 1m km2 definition around 2032 (eyeball estimate) with some recovery years in mid-2030s.  By 2040 September min is essentially a BOE every every year and August almost as low.  By 2046 August is at or near BOE every year.  Still plenty of Extent into July even by 2050.

The page and animations are not dated.  Because they use an older emissions-warming scenario (B2) and start future projections in 2005  I assume they were created before the most recent full IPCC reports in 2013-14 (which used RCP scenarios), and probably been created ca. 2004.  A lot has happened since then.  But the animations are still interesting to watch if only too see what state of the art was at that time.

    The files ran on Windows Media Player when viewed through Google Chrome browser over home wifi.  For unknown reasons I could not view  with Firefox. First time through it had some long pauses.  Playing through 2nd time is smoother.  If you are quick with the mouse you can stop and view any single month as freeze frame.
« Last Edit: November 10, 2019, 01:11:08 PM by Glen Koehler »

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Re: When will the Arctic Go Ice Free?
« Reply #1317 on: November 09, 2019, 08:23:30 PM »
RE Overland, J. E., and M. Wang (2013), When will the summer Arctic be nearly sea ice free?, Geophys. Res. Lett., 40, 2097–2101, doi:10.1002/grl.50316.  https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/grl.50316

     Overland and Wang (O&W) look at 3 methods to project when the Arctic will go below 1m km2 ice extent.  The 3 methods (trend extrapolation, stochasitc events, model estimates) come up with dates of 2020, 2030, and 2040 respectively.  There are strengths and weaknesses for each, though the weaknesses of the model  approach are the most defined (which is to be expected in that multi-model estimates provide the most data upon which to measure performance.  It will be interesting to see how much improvement the new generation of CMIP6 models - which I think will have better ocean-atmosphere coupling and cloud physics -  will provide.)   

    The 2020 estimate based on trend was made right after the unprecedented 2012 Extent losses.  (O&W note that Volume loss in 2012 was not so extreme.  I think we worship at the feet of Extent and 2012 too much, no doubt because that is the measure we have best access to.  That is kind of like the drunk looking for his car keys under the street lamp.  But I digress...)  As I have repeated ad nauseum, the volume trend estimate as shown by Wipneus has Sept. volume reaching zero around 2032, so presumably 1m km2 Extent would occur several years before that.

    So if you update the O&W trend estimate from 2020 to 2030, and as per O&W comments, discount the model estimate of 2040 due to a poor track record, then you have two estimates to consider, 2030 by the stochastic approach, and 2030 by an updated trend extrapolation.  Looks like 2030 is the winner.

    Overland and Wang mention the final ice being at higher latitude could be more resistant to melt, but they also point to the CAA as the last refuge.  The CAA as last refuge factor also shows up in the Zhang animation link given in previous post.  To me it looks like the "high latitude = slower final losses" argument does not fit with the CAA as final refuge prediction.  The projected location for the final ice is not centered around 90N.  It occurs in a band around 75-85N.  The land mass effects of CAA apparently greatly exceeds any latitude effect. 

     We already have open water occurring at above 80N as shown in the Sept. 2019 Extent map at http://nsidc.org/arcticseaicenews/files/2019/10/Figure-1.png.  I don't think the high latitude effect is going to provide much added melt resistance.  And whatever high latitude effect there is seems likely to overwhelmed by continued high GHG emissions, Atlantification / Pacification, mechanical weakness, surface area, dispersal, mobility and export.  And as somebody noted above, in the past the CAB ice volume was replenished from peripheral seas.  As those supply lines diminish, the CAB gets indirectly affected by losses in those lower latitude areas that we already have seen are vulnerable to today's level of Arctic warming, and even moreso with continued warming. 
« Last Edit: November 10, 2019, 01:35:27 AM by Glen Koehler »

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Re: When will the Arctic Go Ice Free?
« Reply #1318 on: November 09, 2019, 09:12:45 PM »
http://psc.apl.washington.edu/zhang/IDAO/multi.html
Interesting animation of ASI Thickness out to 2050 by Dr. Zhang at Polar Science Center. 
I looked at the Winter Sea Ice Animation.

The Bering sea ice in March 2018 & March 2019 was less than that shown in the last frame of the movie.

Huh! he said.
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Re: When will the Arctic Go Ice Free?
« Reply #1319 on: November 09, 2019, 10:06:00 PM »
Global warming hasn't stopped. In many ways, the entire globe is going through a cold phase. Soon the record hot cold phase will become an even more record hot hot phase. Rinse and repeat.

Since 2007 the date of the first BOE has been getting closer and closer. Then it stopped at 2032 for the last few years.

Global warming is not stopping any time soon, why should the melt stop? Can fall snow lower albedo enough to counteract the warm oceans and wobbly polar vortex? Has winter ice hit a new minimum due to a very fast ice extent allowing more time for thickening? For how long? CO2 is still up there making everything warmer.
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kassy

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Re: When will the Arctic Go Ice Free?
« Reply #1320 on: November 09, 2019, 11:02:13 PM »
Arctic Shifts To a Carbon Source Due to Winter Soil Emissions
https://eurekalert.org/pub_releases/2019-11/nsfc-ast110819.php

A NASA-funded study suggests winter carbon emissions in the Arctic may be adding more carbon into the atmosphere each year than is taken up by Arctic vegetation, marking a stark reversal for a region that has captured and stored carbon for tens of thousands of years.

Researchers estimate a yearly loss of 1.7 billion metric tons of carbon from the permafrost region during the winter season from 2003 to 2017 compared to the estimated average of 1 billion metric tons of carbon taken up during the growing season.

This might mess up things a bit more.
Þetta minnismerki er til vitnis um að við vitum hvað er að gerast og hvað þarf að gera. Aðeins þú veist hvort við gerðum eitthvað.

Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1321 on: November 11, 2019, 06:52:12 PM »
     Having flaunted my ignorance in public in this thread, I am chagrined and pleased to report that the experts have in fact already spoken.  I just wasn't listening.  "Ask and ye shall find that ye have already received, ye just weren't paying attention!"
     Two excellent September 2018 articles, both online with open access:

Changing state of Arctic sea ice across all seasons
Julienne Stroeve and  Dirk Notz
2018 Environ. Res. Lett.13 103001
https://iopscience.iop.org/article/10.1088/1748-9326/aade56

The Trajectory Towards a Seasonally Ice-Free Arctic Ocean. 
Dirk Notz and Julienne Stroeve.
Current Climate Change Reports (2018) 4:407–416
https://doi.org/10.1007/s40641-018-0113-2
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6411203/pdf/40641_2018_Article_113.pdf

Excerpts from Notz and Stroeve, 2018.

“…we find that the temperature at which the Arctic first becomes ice free will have a 95% uncertainty range from internal variability of ±0.2 to 0.4◦C. These values are in line with results from large-ensemble model simulations. Combined with the temperature threshold of less than +2◦C for a near ice-free ocean during summer, this then implies low, but above zero chances for a near-ice free Arctic ocean at + 1.5◦C global warming.”

“….the 95% uncertainty range for cumulative future emissions of CO2 leading to an ice free Arctic Ocean during summer becomes 500 to 1100 Gt based on the average value of 800 Gt established above. For a given emission per year, this uncertainty range can be translated to an uncertainty range of the year when the Arctic first becomes ice free.  For today’s emission of about 40 Gt CO2per year, we get an uncertainty range of about 15 years,…”

“Based on this approach, we identify the following statements to be very likely true for the future evolution of the Arctic sea-ice cover.
1. The Arctic sea-ice cover has been and will remain linearly related to global-mean air temperature in all months. Global-mean air temperature can hence be interpreted as the most important control variable on future Arctic sea-ice evolution.

2. The observed linear relationship between Arctic sea-ice coverage and global-mean air temperature suggests Arctic sea-ice coverage to drop below 1 million km2 in more than 50% of all years for a global warming of less than 2◦C compared to pre-industrial levels.

3. The observed linear relationship between Arctic sea-ice coverage and cumulative anthropogenic emissions of CO2 suggests Arctic sea-ice coverage to below 1 million km2 for more than 50% of all years for total future anthropogenic CO2 emissions of less than 800 Gt.

4. From internal variability, September sea-ice coverage can vary by a maximum of ±1 million km2for a given global-mean air temperature.

5. This year-to-year fluctuation can directly be translated into an uncertainty of ±0.2 to 0.4C for the global warming at which the Arctic Ocean loses its summer sea ice for the first time. For CO2 emissions, the uncertainty is about ±300 Gt CO2 emissions. Hence, the Arctic Ocean can be expected to be nearly ice-free in 5% of all years for 500-Gt future CO2 emissions and in 95% of all years for 1100-Gt future CO2 emissions.

6. As the observed linear relationship between Arctic sea-ice coverage and global-mean temperature currently hold for all months, they allow us to estimate the future seasonal cycle directly from the observational record.  This is also true for the observed linear relationship between Arctic sea-ice coverage and cumulative CO2 emissions. 

Based on current emission rates of about 40-Gt CO2 per year, these findings imply a substantial likelihood of an ice-free Arctic Ocean during summer before mid-century.  The time window to prevent the loss of the Arctic summer sea-ice cover hence closes very rapidly.”

**********************
My summary of some take home messages:

    The article was written in September 2018.  At 40 GtCO2 per year, the average estimate of “less than 800” Gt CO2 for 50% chance for any single year going below 1m km2, is 20 years after 2018.  Thus, by September 2038

     Due to uncertainty in the estimate and fluctuations between individual melt years, by 2031 (500/40 = 12.5.  2018 +13 = 2031) there is at least a 5% chance for any single year going below 1m km2 Arctic sea ice cover.  With the single year chance increasing for each subsquent year.
 
     By 2046 (1100/40 = 27.5.  2018 +28 = 2046) (if emissions continue at 40 GtCO2 per year) each individual year would have at least a 95% chance of going below 1m km2.

    The Notz and Stroeve dates based on CO2 emissions also fit with dates derived from the Notz and Stroeve global average temperature - sea ice relationship (e.g. <1M km2 in more than 50% of all years at <+2◦C; 1st year <1M km2 possible at ca. +1.5C) when compared to my projection of NASS GISS global surface temperature anomalies:

Year   Projected NASA GISS vs. 1850-1900
          (Obs, ENSO and solar cycle for 2019; ENSO & solar for 2020; Solar & RCP8.5 emissions after 2020)
2019   1.20
2020   1.16
2021   1.14
2022   1.14
2023   1.19
2024   1.25
2025   1.31
2026   1.37
2027   1.42
2028   1.42
2029   1.43
2030   1.44
2031  1.45
2032   1.46
2033   1.48
2034   1.53
2035   1.59
2036   1.65
2037   1.71
2038   1.77
2039   1.78
2040   1.80
2041   1.82
2042   1.83
2043   1.85
2044   1.87
2045   1.94
2046  2.00


« Last Edit: November 11, 2019, 07:02:31 PM by Glen Koehler »

Tor Bejnar

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Re: When will the Arctic Go Ice Free?
« Reply #1322 on: November 11, 2019, 07:11:27 PM »
Thanks, Glen!  Great information.

I wonder if they considered ice floe dynamics when floes get thin - breaking apart (and flash melting) when there is a big storm (GAC - Great Arctic Cyclone).

I wonder if they considered Chris' "Slow Transition".
Arctic ice is healthy for children and other living things.

gerontocrat

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Re: When will the Arctic Go Ice Free?
« Reply #1323 on: November 11, 2019, 07:12:54 PM »
Stroeve & Notz papers

To state that the linear relationship between sea ice loss and Arctic Global-mean(?) temperatures will hold until there is no more ice is heroic indeed.

How do they deal with September sea ice loss 1979 to 2019 of around 50% and volume loss of around 75% ? If both continue at the same linear rate then an arithmetical impossibility looms.
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Stephan

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Re: When will the Arctic Go Ice Free?
« Reply #1324 on: November 11, 2019, 07:48:51 PM »
It is time for the monthly update of my extrapolation when the extent [Extent], volume [Volumen], thickness [Dicke] and area [Fläche] will reach zero. The extrapolation occured linearly and by a logarithmic function; the latter one almost constantly resulting in earlier times (valid for volume, area and thickness, not for extent in the winter months). October value now includes 2019.
Extent for October 2019 lies largely, area slightly below the long-term trend lines, volume roughly sits on the trend line, whereas thickness was above the trend line. These anomalies decreased the "BOE numbers" by averaged 4 years (extent and area) and left this number unchanged compared with October 2018 (volume and thickness).
The order (earlier → later BOE) generally is volume < thickness < area < extent.

Please note that this is not a forecast but a trend!
See attached table.
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Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1325 on: November 11, 2019, 09:04:51 PM »
Also from Notz and Stroeve 2018
“Also for the future, no substantial self amplification of the summer ice loss is expected. In particular, in all models that participated in CMIP5, the linear relationship between Arctic sea-ice cover and global-mean temperature holds until all sea ice is lost. This behavior already takes into account that in many regions, the ice-free duration during summer is becoming longer and longer, and that the ice cover as a whole is getting thinner. These factors are apparently not sufficient to overcome the stabilizing feedbacks and do not cause an acceleration of the summer sea-ice loss.”

    This seems to put to rest hope for a slowdown in ASI losses due to the final ice being at higher latitude.  Notz and Stroeve discuss and dismiss the opposite potential for reinforcing feedbacks to accelerate the rate of decline.  That does not leave much room for a slow down.
   
Stroeve & Notz papers
To state that the linear relationship between sea ice loss and Arctic Global-mean(?) temperatures will hold until there is no more ice is heroic indeed.

How do they deal with September sea ice loss 1979 to 2019 of around 50% and volume loss of around 75% ? If both continue at the same linear rate then an arithmetical impossibility looms.

     What got me started on all this was the discrepancy between the Extent and Volume trends.  Since Extent has to reach zero at the same time as Volume, my query was how much longer before the Extent curve bends down to a necessary eventual reckoning with zero Volume?  Shared Humanity's comment about ice going poof is worth more than what he supposes is its current market value!  It got me to realize that the Extent curve does NOT have to bend down to meet the Volume trend, at least not until the last day.

     Volume is a product of Extent x Thickness.  We've lost about 76% of Volume (based on PIOMAS Sept. Volume trend for 2019 vs.1979), but only about 42% of Extent (based on NSIDC Sept. Extent trend line for 2019 vs. 1979). 

     The Extent value gets multiplied by the Thickness value to get Volume.  So Extent can keep on floating down at a less steep slope until the point at which Thickness gets so thin that it falls prey to a warming event that takes Thickness down to zero.  That is the "poof" moment when Extent suddenly catches up to Volume, i.e. they both reach zero.   

    Figure 6 in the Strove and Notz, 2018 cited in previous post shows that 10-day Extent losses of 1M km2 have occurred, and that losses of at least 0.5M km2 are not that rare.  Thus, once Extent  gets into the range of less than 2.0M to 1.5 km2, there is a possible and increasingly likely chance of a "poof" event of 0.5 to 1.0km2 scale that takes Extent below the arbitrary 1.0M km2 BOE threshold.  That provides an indicator for how much longer Extent losses can continue at a slower pace than Volume losses before a fluctuation in Thickness creates a first time BOE.   

    The Sept. 2019 NSIDC Exent was 4.32M km2.  As per NSIDC "The linear rate of sea ice decline for September extent from 1979 to 2019 is 82,400 square kilometers per year."

    To reach the 2.0M Extent when a poof Event becomes possible, would require losing another 2.3M km2 of Sept Extent below the 2019 value of 4.3 (which is pretty much on the Trend line).  By this reasoning, at 82k per year losses, losing 2.3M km2 would take another 28 years, i.e. 2047 before Extent in 50% of years would be within plausible range of a poof event. 

    This is later than I had expected, since Notz and Stroeve put the 50% chance of any single year going below 1.0M km2 as 2038.  By 2047, Notz and Strove estimate that >95% of individual years will go below 1M km2.

    Hmmm?  So Extent trend alone does not end up at the expected date for 50% chance of BOE.  That leaves Thickness losses as the missing factor that aligns the NSIDC Extent trend with the Notz and Stroeve BOE dates.  And that makes sense. 

     Stroeve and Notz Fig. 5 show the decline of April ASI Thickness, and they cite the PIOMAS April Thickness trend as -0.28M per decade.  Looking at PIOMAS Sept. thickness linear trend, I get a very similar -0.27M/decade trend.  So by 2038, absent any acceleration or deceleration of Thickness losses, the average Sept. ice Thickness is likely to be near 0.51M.  As Thickness declines from 1.022 (Sept. 2019) to 0.51M, the frequency of 0.5 to 1.0 km2 Extent losses in a 10-day period will certainly increase, and the magnitude of infrequent large scale Extent losses will also increase. 

    That is why extrapolation of the Extent loss curve alone yields BOE dates that are artificially late.  Combine the continued Extent loss curve with an increasing (instead of static) scale for 10-day Extent losses (due to declining Thickness), then you can get dates to fit with the Notz and Stroeve estimate of 2038 for when 50% of years could reach BOE status of <1.0M km2.

     In 20 years, the Extent trend goes to 4.32M - (0.084M x 20) = 2.67M km2.  That is way too high to be taken down to 1.0 km2 by a 10-day Extent loss event if the September Thickness remained at the current ca. 1.02M.  But much more likely when the average September Thickness is down to 0.51M.

   So here we have the most likely poof moment scenario for when ASI goes below 1.0m km2.  Around 2038, with Sept. Extent at ca. 2.7M km2 and Thickness is down to 0.5M, a 10-day event removes enough ice to take Extent below 1.0M km2.  (This scenario also fits well enough with Archimid's April max vs. summer losses crossing trendlines.)

    Of course, this is an event of arbitrary significance.  The ice will begin refreezing and our long march to a hot Earth destiny will continue with ups and downs in ASI.  Deniers will cite the fact that Arctic ice coverage in October increased over September to show that there is nothing to worry about.

    As for thin ice melt acceleration, which is also where this adventure started, I stand corrected and have to yield to more educated minds that reversing the Thorndike curve is not legitimate in terms of thickness alone and thermodynamics.  But as Shared Humanity noted, my gut still says that in a real world setting, younger, saltier, highest-surface-to-volume-ratio, more fractured, dispersed, thinner ice has a higher chance in a rolling ocean exposed to currents to get melted by export or to go poof due to flash melt, and that the chances for rapid Extent loss increases faster than the linear change in thickness.  But now I'm just being stubborn. ;D

     I don't know if this convinces anybody else, and there remains the chance of some bonehead error that makes this all wrong, but thanks to the Stroeve and Notz articles I feel like I have some understanding for how the Extent, Thickness, and Volume trends will evolve over the next 20 years.  The Emperors are well dressed indeed, and I retract my arrogant and ignorant allegations to the contrary. 

     
« Last Edit: November 12, 2019, 04:59:57 AM by Glen Koehler »

Richard Rathbone

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Re: When will the Arctic Go Ice Free?
« Reply #1326 on: November 11, 2019, 09:19:49 PM »
Stroeve & Notz papers

To state that the linear relationship between sea ice loss and Arctic Global-mean(?) temperatures will hold until there is no more ice is heroic indeed.

How do they deal with September sea ice loss 1979 to 2019 of around 50% and volume loss of around 75% ? If both continue at the same linear rate then an arithmetical impossibility looms.

Its answered in the paper. Models support the linearity of extent loss.

"In particular, the linearity holds in all CMIP5 models until summer sea ice vanishes in individual simulations."

Also, they consider the volume data and models aren't good enough to do a similar analysis based on volume rather than coverage.

"Fourth, we lack a good understanding of the past and future evolution of sea-ice volume. This is related to the lack of a sufficiently long and sufficiently reliable observational record of sea-ice volume, to uncertainties in reanalyzed sea-ice volume [78], and to a failure of many CMIP5 models to reproduce the observed distribution and time evolution of sea-ice thickness"


Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1327 on: November 11, 2019, 09:38:00 PM »
It is time for the monthly update of my extrapolation when the extent [Extent], volume [Volumen], thickness [Dicke] and area [Fläche] will reach zero.

Volume is king/queen.  Extent and Thickness can't be above zero when Volume is zero.  So when I see the linear trend for Volume hitting zero for JULY in 2034, that is yet another Yikes moment.  Can you double check that?   That would bring major albdeo impact, polar cell/weather disruption, and other global consequences if that trend holds up.   This stuff is just getting too weird.  We don't need to worry about 2100. We've got to get past 2034 first. 

Klondike Kat

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Re: When will the Arctic Go Ice Free?
« Reply #1328 on: November 11, 2019, 10:07:00 PM »
It is time for the monthly update of my extrapolation when the extent [Extent], volume [Volumen], thickness [Dicke] and area [Fläche] will reach zero.

Volume is king/queen.  Extent and Thickness can't be above zero when Volume is zero.  So when I see the linear trend for Volume hitting zero for JULY in 2034, that is yet another Yikes moment.  Can you double check that?   That would bring major albdeo impact, polar cell/weather disruption, and other global consequences if that trend holds up.   This stuff is just getting too weird.  We don't need to worry about 2100. We've got to get past 2034 first.

Conversely, volume cannot be zero, if extent and thickness are not.  Volume, being three-dimensional, will always change faster than thickness (one-dimensional) or extent/area (two-dimensional).  At some point, they must converge.  What is your reasoning to believe that volume is the key metric over the others?

Stephan

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Re: When will the Arctic Go Ice Free?
« Reply #1329 on: November 11, 2019, 10:21:33 PM »
I don't know whether I am thinking correctly at the moment.
I just take the numbers and extrapolate them to zero resulting in the years I collected in my table. In recent time I find that extrapolated BOE dates of area and extent move to "earlier times" than last year or two years ago, while the extrapolated BOE dates for volume and thickness remain stable. If this trend continues, the "BOE times" (at least those for July to October) will get closer to each other and solving the "problem" of extent and area values well above zero while volume has already reached zero ?!?  :-\
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gerontocrat

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Re: When will the Arctic Go Ice Free?
« Reply #1330 on: November 11, 2019, 10:29:24 PM »
I always end up with the observation that nature (mostly) abhors a straight line.

For a long time the linear relationship may look the best, but it mostoften breaks down eventually. So will it be KK's long-tailed gompertz slow  / minimal decline or will it fall apart with a crash

So I just can't go along with Stroeve et al when linear is pushed out to the end. It just ain't like that.

ps: And 2007 and 2012 pushed the max dip in an annual variation well over 1 million km2 when melting conditions are almost perfect.
pps: Volume divided by extent is not a good measure of thickness at minimum, especially using NSIDC data. This is because the ice is very spread out with lots of open water at minimum, concentration getting as low as 55%. Volume divided by Area is a much better measure at minimum.
 





« Last Edit: November 11, 2019, 10:34:26 PM by gerontocrat »
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Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1331 on: November 11, 2019, 10:37:50 PM »
Edited quote
......I find that extrapolated BOE dates of area and extent move to "earlier times" than last year or two years ago, while the extrapolated BOE dates for volume and thickness remain stable. If this trend continues, the "BOE times" (at least those for July to October) will get closer to each other and solving the "problem" of extent and area values well above zero while volume has already reached zero ?!?  :-\
That part makes sense to me. They have to converge at the end.
So you are sure about the linear July volume trend hitting zero in 2034 (1 year before August, which is also odd), but the July log trend not hitting zero until 2038 (10 years AFTER August)?
« Last Edit: November 11, 2019, 11:02:39 PM by Glen Koehler »

Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1332 on: November 11, 2019, 10:47:18 PM »
I always end up with the observation that nature (mostly) abhors a straight line.

For a long time the linear relationship may look the best, but it most often breaks down eventually. So will it be KK's long-tailed gompertz slow  / minimal decline or will it fall apart with a crash

So I just can't go along with Stroeve et al when linear is pushed out to the end. It just ain't like that.

ps: And 2007 and 2012 pushed the max dip in an annual variation well over 1 million km2 when melting conditions are almost perfect.
pps: Volume divided by extent is not a good measure of thickness at minimum, especially using NSIDC data. This is because the ice is very spread out with lots of open water at minimum, concentration getting as low as 55%. Volume divided by Area is a much better measure at minimum.

I think the poof scenario meets the definition of "fall apart with a crash".
It does not rely on linear trend right to end, in fact it demonstrates why that won't be the case. 

We all agree they have to meet up at the end (i.e. Zero Volume & Extent).  And this is how it happens.  Extent decline can keep up its straight line trend that is slower than volume decline, but only for a while. When thickness gets so thin that it is susceptible to flash melt, that is when the Extent trend curves sharply downward and catches up within a single year.  Thus an Extent crash.

RE ps   I used 10-day Extent losses, but I think you are right (whether you meant to imply that or not) that it would be better to use year to year Extent changes as the indicator to estimate when Extent is low enough to suffer a within-one-year loss large enough to get below the 1M km2 threshold.  Being much larger than the 10-day losses, using the year to year losses strengthens the argument for the potential for a single year to go below the BOE threshold.

RE pps I used PIOMAS September average thickness data.  That's all I have to work with.  That is the minimum monthly average, not the minimum day.  I agree that using annual minimum thickness values from November would be unhelpful because those values are very distorted by expanding area of thin refreezing ice.  But comparing the Sept. average Thickness across years seems like a reasonable way to measure a trend for ice thickness.
« Last Edit: November 12, 2019, 05:05:16 AM by Glen Koehler »

Stephan

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Re: When will the Arctic Go Ice Free?
« Reply #1333 on: November 11, 2019, 11:02:36 PM »
So you are sure about the linear July volume trend hitting zero in 2034 (1 year before August, which is also odd), but the July log trend not hitting zero until 2038 (10 years AFTER August)?
I am certainly not sure about July / August differences. At the moment it is just numbers and slopes.
If you look at PIOMAS' volume graph you can easily see that July falls more steeply than August and any other month, the same finding I made when I calculated the slope ("Stg" in my table). It has its highest value in July which let it become zero one year before August. The log evaluation on the other hand describes the curvature of the data which in the case of July is less pronounced than in August...
As I wrote, this is not a forecast, but a trend.
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Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1334 on: November 11, 2019, 11:17:09 PM »
Conversely, volume cannot be zero, if extent and thickness are not.  Volume, being three-dimensional, will always change faster than thickness (one-dimensional) or extent/area (two-dimensional).  At some point, they must converge.  What is your reasoning to believe that volume is the key metric over the others?

I agree that "At some point, they must converge."  That was the reason for my quest -- (cue Man of La Mancha music): How/when will the Extent trend and Volume trends meet?

I suppose you can frame the same question as "When will the Volume trend flatten out so that it can meet the Extent trend?"  I don't see reason for that to happen.  The linear volume trend looks pretty inexorable.  And while, as gerontoacrat noted, Volume measurement has its problems, Extent is not so pristine either.  A pixel with 16% ice counts as 1, with 14% counts as 0; melt ponds misidentified as open water etc. 

     And even if measured perfectly, Extent in the real world is subject to being altered by wind patterns, compaction vs. dispersal.  That is also why I think 2012, while certainly an important event as we watch the ASI go down the tubes, is overrated.  It was hyuge (new American English spelling, as in 'our politics and planet are hyugely screwed up') Extent event, but a less cataclysmic Volume event, and thus less of an informative marker for progressive ASI decline.  Thus Extent is the more mercurial hare, subject to temporary conditions, while good ole Volume is the sober implacable tortoise plodding its way towards cryospheric Armageddon. 

Maybe it is arbitrary that I start with the presumption that you can't have Extent of ice without any Volume of ice to create it.  But that makes more sense to me than the other way around.  Stuff has to exist before you deal with how it is spread around.

I am more likely to buy into gerontocrat's argument that the Volume measures are more subject to error, so this discordance between the Extent and Volume trends (that I repeat, we all agree have to meet up in the end) could be due to spurious Volume measurements.
.... But not really.  Because it makes perfect sense that what we see (Extent loss) is multiplied by what we can't see (simultaneous Thickness loss) to create Volume losses that are bigger than Extent losses.  In fact, the only way Extent losses could keep up with Volume losses is if there was NO Thickness loss. So of course Extent losses lag behind Volume losses.  How could it be otherwise? 

    And it makes sense to me that Thickness is being affected by the same forces that are depleting Extent and Volume.  And it makes no sense to think that Thickness is not being depleted.  And regardless of what you or I think, hard working scientists and other folks take measurements that show that Thickness is indeed going down.

I defer to the great Juan C. Garcia.  His message tag line points to Volume losses being a more important indicator than Extent because Extent, as you noted, is missing a dimension, the key dimension of concurrent thickness losses. 
"Volume is harder to measure than extent, but 3-dimensional space is real, 2D's hide ~50% thickness gone.
-> IPCC/NSIDC trends [based on extent] underestimate the real speed of ASI lost."
« Last Edit: November 12, 2019, 12:09:01 AM by Glen Koehler »

Rodius

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Re: When will the Arctic Go Ice Free?
« Reply #1335 on: November 11, 2019, 11:43:41 PM »
I am not a scientist or expert. I love the charts and numbers and basically understand them.

I do have significant experience doing things in nature. And this has been said earlier but it bears repeating.... Nature abhors a straight line.
I tend to agree.

To me, area and extent are fun to watch, but it is giving too many nice straight lines until the ice disappears.

My bet is for the ice to disappear before 2025. And my reasoning might be far too simplistic, but this short video of ice melting explains why I think it will look basically okay in terms of area and extent right up until it isnt.


Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1336 on: November 11, 2019, 11:53:08 PM »
Edited quote
... this short video of ice melting explains why I think it will look basically okay in terms of area and extent right up until it isnt.



Nice.  Exactly!  Watch the footprint of that ice cube as it melts.  The area covered declines at a much slower rate than volume as the thickness declines.  Until the thickness gets so small that continued losses come at the expense of the area covered (Extent).  Then it rapidly declines at the very end as Extent loss (footprint) finally catches up the Volume loss (shrinking ice cube).

binntho

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Re: When will the Arctic Go Ice Free?
« Reply #1337 on: November 12, 2019, 04:29:31 AM »
The ice cube video strongly supports all of Glen's excellent postings! Having started this discussion, and then buggered off to a part of the world with minimal Internet, I've still been able to read most of it and Glen seems to have effectively put the case to rest - linearity rules ... until it doesn't.

My gut feeling has long been that global warming is the main and domineering driver of sea ice melting, i.e. if the world keeps warming up then the ice should keep smelting - and since global warming has been as close to a straight line as makes no difference for the last 30 years, ice melt should also be as close to a straight line as makes no difference over the same period. Hence no hiatus when it comes to ice loss over the same period.

As for the future - as Glen has demonstrated so well, the science tells us that ice loss and the rate of warming (and at a further remove, the increase in cumulative atmospheric CO2) have a linear relationship well into the future. And by ice loss I of course mean loss of volume (i.e. actual loss, rather than the symptomatic loss of extent).

So loss of volume, from here and down to practically nothing, should follow global warming in a linear relationship, which of course means that extent has to catch up at some point. Which Glen has covered very nicely with his discussion of how thin ice can suddenly go poof, losing a million or more KM2 in a few days.
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Klondike Kat

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Re: When will the Arctic Go Ice Free?
« Reply #1338 on: November 12, 2019, 04:39:52 AM »
The problem with the ice cube analogy is that it is not representative of sea ice.  The sea ice basically melts from two directions; the solar energy above and the water below.  Very little side melting occurs as the ice is adjacent to mostly ice.  Hence, I feel that extent (or area) is the better metric, not to mention they are measured with higher accuracy.

binntho

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Re: When will the Arctic Go Ice Free?
« Reply #1339 on: November 12, 2019, 04:43:50 AM »
I'm not sure if the old canard, that "nature abhors a straight line", can be applied to trend lines, seeing as how they are artificial products of our syntactic minds. Anyway, the correct aphorism is "nature abhors a vacuum" and it's sibling, "there are no straight lines in nature". Both of which are absolutely true.

But of course, nature is full of lines that are as close to straight as makes no difference, as in the trend in global warming over the last 30 years or so.

Any stretch of a river between two erosion-resisting points (e.g. waterfalls or rapids) will strive for an elevation profile that is a straight line. Any holes get filled in, any bumps erased away. At the end, once the flat elevation profile nears the horizontal, meandering kicks in.

So all river systems in the world are constantly striving to create straight-line elevation contours, or as close to a straight line as makes no difference. Just to mention an example of a system constantly trending to a straight line.
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KiwiGriff

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Re: When will the Arctic Go Ice Free?
« Reply #1340 on: November 12, 2019, 04:49:22 AM »
Global warming paused ....if you ignore ocean heat content.
Sea ice decline paused.... if you ignore volume.
 :D

binntho

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Re: When will the Arctic Go Ice Free?
« Reply #1341 on: November 12, 2019, 05:00:55 AM »
Global warming paused ....if you ignore ocean heat content.

I guess you mean the "hiatus" in the noughties that deniers loved to talk about. As Tamino has shown, statistically there was no hiatus - but looking at the graphs it certainly looks that way!

Quote
Sea ice decline paused.... if you ignore volume.
 :D
The same thing - some (but not all) graphs of sea ice extent decline look as if there was a pause. But as with the global warming hiatus, it's just something that looks as if ...
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binntho

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Re: When will the Arctic Go Ice Free?
« Reply #1342 on: November 12, 2019, 05:13:42 AM »
The problem with the ice cube analogy is that it is not representative of sea ice.  The sea ice basically melts from two directions; the solar energy above and the water below.  Very little side melting occurs as the ice is adjacent to mostly ice.  Hence, I feel that extent (or area) is the better metric, not to mention they are measured with higher accuracy.
I wrote some rubbish in response to this earlier, it was totally off the mark (due to severe lack of coffee), so I deleted it.

Ice melts from the surface in, whether it is a cube or a thin layer (as in sea ice). The surface-to-volume ratio is vastly different, with the cube having a much lower ratio. As the cube melts, this ratio increases rapidly and if there is enough heat available then the rate of melt should increase correspondingly.

Sea ice has a vastly higher surface-to-volume ratio, so big that I guess it's almost irrelevant. So focusing on extent is valid in the sense that the speed of melt is not dependent on the remaining volume (as is the case with the cube).

However, extent is also able to hide what is really going on, since it doesn't tell us anything about thickness. Extent is therefore able to suddenly disappear, to go "poof", while volume is not really able to go "poof".

So if we want to know when the ice is going to disappear, we cannot rely on trends in extent. It's only the trend in thickness (which implies the trend in volume) that matters. At some point, thickness gets so low (perhaps so much that we should be talking about thinness instead?)  that extent will simply vanish.

And we already know that volume is falling faster than extent, which means that thickness is falling faster than extent. So we already know that extent is hiding the real story from us.
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binntho

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Re: When will the Arctic Go Ice Free?
« Reply #1343 on: November 12, 2019, 05:17:38 AM »
One point to make about the linear relation between global warming and sea ice loss. If the current bump in global warming turns out to be an acceleration in trend, then it follows that sea ice loss should also accelerate.

Tamino is not quite ready to call it an acceleration yet, see https://tamino.wordpress.com/2019/11/08/global-temperature-update-6/
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Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1344 on: November 12, 2019, 06:11:30 AM »
Well if binntho agrees with me, he must be right! 

    But here is another perspective about a possible Extent pause.  I am (almost) sure that if Tamino bit into the Extent numbers he would, as he did with global average surface temperature faux pause, show that there is no statistical justification for the relatively small number of yearly data points in the presumed Extent hiatus period to be called a significant violation of the long term linear trend that is derived from a much larger set of of data points with considerable year to year variability.  (BTW Tamino's wife announced on his blog that he had surgery recently.  Sending him wishes for healing and good health.) 

    But I submit to the jury that even if Extent did have a statistically valid hiatus, it would not matter.  There could be a scenario where Volume losses continue their inexorable decline, yet a prolonged series of years with conditions favorable for greater ice dispersion resulted in Extent value flat-lining for enough years in sequence to pass a statistical test for truly being a hiatus.   

     But so what?  In terms of progressive ice decline, that would not change the underlying fact that Volume losses were still proceeding toward zero.  A hiatus in Exent would only temporarily increase the discordance between the Extent and Volume trends.  The increased difference would have to be compensated for at the end.  The only consequence of an Extent hiatus would be that the Extent trend would have to fall that much farther faster when the zero Volume-Thickness-Extent day of no ice reckoning finally arrived. 

    The 10-30 year lag for the majority of global warming impact from elevated greenhouse gas levels to be expressed means that the warming and ice melt trends for the next 10-30 years have already largely been set by our previous emissions.  The fact that the trend-projected date for the first zero ASI Volume event is now within the next 20 years means that it is probably unavoidable at this point even if we sharply reduced further GHG additions.  Then again, Notz and Stroeve point to an 800 Gt CO2 of additional emissions needed after 2018 for the total GHG load to be enough to result in Volume reaching zero.  So in theory at least, keeping total emissions below that amount could presumably prevent the Volume losses from reaching the zero point. 

     (On the other other hand, --- running out of hands ---, I suspect that even if emissions ceased immediately, with enough time and the slow depletion of existing CO2 from the atmosphere, even the GHG emissions already made thus far, bolstered by some permafrost thaw and other feedbacks, would eventually result in ASI Volume-Thickness-Extent reaching zero.)

     That is a moot point for the real world situation.  It does not seem at all likely that humans will cut emissions sharply enough and soon enough to prevent exceeding the 800 additional Gt CO2 after late 2018 threshold.  And therefore, assuming the Notz and Stroeve relationship between total CO2 emissions and ASI Volume is correct, the Extent trend will meet up with the Volume trend at the zero point.  Which year that happens depends on how fast we move towards that 800 Gt CO2 post 2018 threshold.  This being the end of 2019, we have probably reduced the remaining budget to 760 already. 

     Extent can go where it will prior to the zero day of reckoning, but when the Volume trend reaches the point where there is no ice to spread around, Extent will also be at zero.

   Edited quote
And we already know that volume is falling faster than extent, which means that thickness is falling faster than extent.
    I don't agree with the second part, "... which means that thickness is falling faster than extent. " 
    Yes, we know that Volume is falling faster than Extent.  Because Volume is the product of Extent x Thickness, Volume has to fall faster than Extent unless there is either Thickness gain or zero loss.  But Thickness does not have to fall faster than Extent for Volume loss to be less than Extent loss.  It does not matter which of two (Extent or Thickness loss) is greater, or if they are exactly equal, all that matters is the product of Extent x Thickness, because that is what defines Volume.

   
« Last Edit: November 12, 2019, 06:36:50 AM by Glen Koehler »

binntho

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Re: When will the Arctic Go Ice Free?
« Reply #1345 on: November 12, 2019, 06:35:34 AM »
Well if binntho agrees with me, he must be right! 
I'm sure I am!   8)
Quote
   Edited quote
And we already know that volume is falling faster than extent, which means that thickness is falling faster than extent.
    I don't agree with the second part, "... which means that thickness is falling faster than extent. " 
    Yes, we know that volume is falling faster than Extent.  Because Volume is the product of Extent x Thickness, Volume has to fall faster unless there is either thickness gain or zero loss.  But thickness does not have to fall faster than Extent for Volume loss to be less than Extent loss.  It does not matter which is greater, or if they are exactly equal, all that matters is the product of Extent x Thickness, because that is what defines Volume.

Although I've had quite a few cups by now, coffee alone does not really help me out here - some sort of higher mathematics is needed. However, a bit of playing around with Excel shows that if both extent and volume are falling, and volume is falling faster than extent, then thickness is going to fall faster than extent.

That was also my gut feeling, i.e. that thickness had to decrease faster than extent if volume was decreasing faster than extent. But the difference is not necessarily very big. As an example, if extent is falling by 1% per year, and volume by 2%, then thickness falls by very close to, but ever so slightly above, 1%. If extent is at 1% and volume at 3%, thickness clocks in at slightly above 2%.

So until proven wrong by somebody better at mathematics than me, I'll state that if volume is falling faster than extent then thickness has by necessity to fall faster than extent - but not necessarily by a measurable amount! It all depends on the difference between the other two rates of decline.
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Glen Koehler

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Re: When will the Arctic Go Ice Free?
« Reply #1346 on: November 12, 2019, 06:54:21 AM »
Edited quote
As an example, if extent is falling by 1% per year, and volume by 2%, then thickness falls by very close to, but ever so slightly above, 1%. If extent is at 1% and volume at 3%, thickness clocks in at slightly above 2%.

Try one more cup of coffee and you may reach a level of caffeine induced enlightenment where this becomes obvious. ;D

Using your example, but merely flipping Thickness and Exent:
If Thickness is falling by 1% per year, and volume by 2%, then Extent falls by very close to, but ever so slightly above, 1%.
If Thickness loss is at 1% and volume at 3%, then Extent clocks in at slightly above 2%.

In your example, Thickness loss is always a bit greater than Extent loss.  In my flipped version, Extent loss is always a bit greater than Thickness loss.  You say TomAto, I say ToMAHto! :o

The point being that either the Thickness term or the Extent term can be the larger of the two.  It does not matter.  Either way, when they are both are negative, the resulting product of their multiplication (i.e. Volume) is smaller than either of them individually.  So when Extent trend is negative, AND the Thickness trend is also negative, then the Volume loss has to be more negative than either the Extent or Thickness trend individually.  But as for Extent and Thickness, either one of them could more more negative than the other.
« Last Edit: November 12, 2019, 07:00:18 AM by Glen Koehler »

binntho

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Re: When will the Arctic Go Ice Free?
« Reply #1347 on: November 12, 2019, 07:26:43 AM »
More caffeine, and here comes - we have two measures, Extent (E) and Volume (V). A simple ratio of the two (V/E) gives us average thickness (Tav).

Since the third term is a calculated average (and not a finite measure as the other two) then flipping them around makes no sense.

My original statement was that if volume is declining faster than extent then thickness is also declining faster than extent. Glen disputed this. I played around in Excel and came to the conclusion that I was right.

More coffee has then helped me tease out the following:

E  = 1 - percentage rate of extent loss (i.e. for 1% rate of extent decline E = 0.99)
V = 1 - percentage rate of volume loss (i.e. for 2% rate of volume decline V = 0.98)
Tav = E - (E - V)/100

So in the above example, at 1% and 2%, Tav = 0.99 - (0.99 - 0.98)/100 = 0.9899

Which is very close to 0.99 but not quite. So what are the actual percentage loss rates? Ball park figures are a decline in volume from 15 to 5 thousand km3 in 40 years which gives us a value of V at 0.973 and a decline in extent from 7 to 4.3 over the same period, giving a value of E at 0.988.

The resulting value for Tav = (0.988 - (0.988 - 0.973)/100 = 0.98785

So obviously, while thickness is declining faster then extent, the difference is exceedingly small and can be ignored.
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oren

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Re: When will the Arctic Go Ice Free?
« Reply #1348 on: November 12, 2019, 03:24:47 PM »
Binntho I think you are wrong. Volume could be declining at 1.3% per year, and extent at 1%. Volume is declining faster than extent, and yet thickness is declining slower than extent at only 0.3% per year.

BTW, this whole discussion should be area and not extent, which has an additional component of dispersion (which has been trending upwards IIRC).

And it's quite obvious that extent and area will eventually catch up with volume, once typical thickness becomes too low.

Klondike Kat

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Re: When will the Arctic Go Ice Free?
« Reply #1349 on: November 12, 2019, 04:02:26 PM »
More caffeine, and here comes - we have two measures, Extent (E) and Volume (V). A simple ratio of the two (V/E) gives us average thickness (Tav).

Since the third term is a calculated average (and not a finite measure as the other two) then flipping them around makes no sense.

My original statement was that if volume is declining faster than extent then thickness is also declining faster than extent. Glen disputed this. I played around in Excel and came to the conclusion that I was right.

More coffee has then helped me tease out the following:

E  = 1 - percentage rate of extent loss (i.e. for 1% rate of extent decline E = 0.99)
V = 1 - percentage rate of volume loss (i.e. for 2% rate of volume decline V = 0.98)
Tav = E - (E - V)/100

So in the above example, at 1% and 2%, Tav = 0.99 - (0.99 - 0.98)/100 = 0.9899

Which is very close to 0.99 but not quite. So what are the actual percentage loss rates? Ball park figures are a decline in volume from 15 to 5 thousand km3 in 40 years which gives us a value of V at 0.973 and a decline in extent from 7 to 4.3 over the same period, giving a value of E at 0.988.

The resulting value for Tav = (0.988 - (0.988 - 0.973)/100 = 0.98785

So obviously, while thickness is declining faster then extent, the difference is exceedingly small and can be ignored.

I do not think that more caffeince was the answer.  Glen is still correct.  If volume is decreasing faster than extent, all that tells you is that thickness must be decreasing (If thickness were held constant, then the volume would be decreasing at the same rate as extent). 

Using the actual values, sea ice extent has decreased to 58% of the 1979-83 average (a 5-year average just smoothes out the bumps).  Oren suggests we use area, which is probably more relevant to the discussion at hand.  The area has declined slightly more to 54% of the average.  Thickness calculations have yielded a drop to approximately 57%.  Volume calculations are about 28%.  Using the mathematical equation that area x thickness = volume, then the area percentage multiplied by the thickness percentage should equal (more or less) the volume percentage.  Multiplying 54% x 57% = 31%, not too far off from the PIOMAS value.