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viddaloo

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Re: The Slow Transition
« Reply #250 on: December 02, 2014, 08:02:13 PM »
Cool. I'm sure Jai will be interested in using this formula.
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ghoti

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Re: The Slow Transition
« Reply #251 on: December 02, 2014, 08:13:24 PM »
Looks like for horizontal surface ignoring transmission coefficient through atmosphere.
I used to have that calculation in a fortran program that created 3D plots of irradiance on surfaces of different orientations - unfortunately long lost code (1980s were a long time ago) Figure from http://www.ehleringer.net/uploads/3/1/8/3/31835701/071.pdf page 9 of pdf
« Last Edit: December 02, 2014, 08:21:35 PM by ghoti »

ChrisReynolds

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Re: The Slow Transition
« Reply #252 on: December 02, 2014, 09:45:04 PM »
Ghoti, Viddaloo,

Yes, I am also ignoring transmission through the atmosphere. That's mainly because I don't have cloud data, and even if I did, handling that is very daunting (scattered vs direct insolation, LW and SW etc).

What I want to do is calculate the amount of open water through the spring/summer season on a per-grid-box basis day by day using NSIDC gridded concentration (which I can already process). Then weight the open water by insolation, which I may just handle as a percentage of peak insolation.

So...

On a grid box basis.

1) Calculate the open water fraction for each day.

2) Multiply that by the insolation (or percentage insolation?) for each day.

3) Sum the results per grid box and calculate a grid box area weighted average for the whole Arctic Ocean.

The resulting index should better represent the warming effect of the sun on open water. I hope it will give improved correlation with autumn surface warming. And as the process of ice loss proceeds in decades to come it should better represent the effect of larger amounts of open water under peak insolation in June and July.

Cracking this in a spreadsheet means I can now easily write a module in VBA to handle this and feed it the latitude coordinates of each grid box (and date) as I process the sea ice concentration.

I'll write a blog post explaining how that equation was calculated, but the core of it is in the PDF linked to above, it's above the plot of insolation vs latitude, the function for H is explained a couple of pages prior. The trickiest part is handling the inverse cosine and tangents used to calculate H. Initially all around the poles I was getting numerical errors caused by ACOS being fed numbers greater than 1.

If anyone using Excel wants me to share the spreadsheet just ask.

jdallen

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Re: The Slow Transition
« Reply #253 on: December 03, 2014, 10:35:34 AM »
Woo Hooo!!!

With the help of a pdf of lecture notes...
http://nit.colorado.edu/atoc5560/week13.pdf

I am now able to calculate insolation (ignoring the variation in sun-earth distance and Milankovitch type cycles) for any latitude on any day of the year.  ;D 8) ;D

Here's the Excel equation.

=($O$5/PI())*(ACOS(IF(ABS(-1*TAN(DR$7)*TAN($N10))>1,SIGN(-1*TAN(AT$7)*TAN($N10)),-1*TAN(AT$7)*TAN($N10)))*SIN($N10)*SIN(AT$7)+SIN(ACOS(IF(ABS(-1*TAN(DR$7)*TAN($N10))>1,SIGN(-1*TAN(AT$7)*TAN($N10)),-1*TAN(AT$7)*TAN($N10))))*COS($N10)*COS(AT$7))

Horrible isn't it?  ;)
Nice! And Lordy!

I wonder if I can make that work with open office....

Might be worth it just to shell out to the evil empire...
Thinking about the "daunting" part - sorting in albedo and cloud scattering - seems this automated could produce a nice cell-by-cell matrix which could be mated with a similar cloud scattering algorithm.  KISS at first, not worrying about multiple cloud layers and the kind, but total insolation + angle of incidence could create some very interesting energy density maps.

Additional edit - orbital variation & Milankivitch can probably be dealt with via simply applying some constant to the base insolation calc. You'd only really need to do that once at the start and feed it in as a parameter.  That said, the variation probably will just ge lost as noise when compared to the feast of the inputs... ;)
« Last Edit: December 03, 2014, 10:48:55 AM by jdallen »
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ChrisReynolds

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Re: The Slow Transition
« Reply #254 on: December 03, 2014, 04:26:20 PM »
JD Allen,

Issues like precession, obliquity and orbital variations can be addressed with the information in that PDF. Having considered today I might try to incorporate optical depth of the atmosphere. Cloud is trickier, I might be able to use cloud cover from ZNCEP/NCAR but what of cloud depth?

The earliest calculation of solar radiation used measurement of the rate of melt of an ice block. My plot of ten day rate of change of PIOMAS volume suggests that, at least in PIOMAS, cloud has a limited impact on melt and seasonal insolation changes dominate.

ghoti

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Re: The Slow Transition
« Reply #255 on: December 04, 2014, 03:35:52 AM »
Doesn't cloud cover work both ways? It blocks/reflects incoming visible but also traps long wave energy loss. The buoy webcam images in the summer almost always seem to show more obvious melting under overcast conditions and refreeze under clear skies. So I'd agree that cloud cover might not add much to your calculations.

LRC1962

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Re: The Slow Transition
« Reply #256 on: December 04, 2014, 04:01:26 AM »
ghoti you are right. used to live at 8,000' on sunny days in direct sunlight it got very warm, shade though was cool. when it was cloudy temperatures were more uniform, although cooler than direct sunlight still warmer then shaded areas. Granted this was at high altitude which is much different then sea level, but I think the principle still applies.
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ChrisReynolds

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Re: The Slow Transition
« Reply #257 on: December 04, 2014, 07:52:30 AM »
Ghoti,

I agree, thiis may be a reason for the behavior of PIOMAS rate of change described above.

ChrisReynolds

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Re: The Slow Transition
« Reply #258 on: December 21, 2014, 11:01:54 PM »
New blog post:
The Slow Transition: Arctic Ocean Energy Gain.
http://dosbat.blogspot.co.uk/2014/12/the-slow-transition-arctic-ocean-energy.html

...Once this state is reached, autumn/winter volume gains will oppose the continuing ice/ocean albedo feedback, and as I argue has happened in from 2010 to 2014, winter volume will peak out to the expected for ice of around 2m thick. A mainly first year ice pack will then decline at a slower rate than previously, with April volume being held high by autumn/winter ice growth, and the thermodynamic thickening of ice through the autumn/winter dictating April volume, and in turn dictating open water formation efficiency through maintaining April volume and stopping the long term decline seen in recent decades.

The continued volume loss would then be determined by winter temperatures, not by summer ice/ocean albedo feedback, and will decline at a slower rate.

Another angle:
Quote
Given the strong thickness–growth feedback of sea ice (Bitz and Roe 2004), where in a warming climate we can expect the thicker MY ice to thin at a greater rate than the thinner FY ice, and the fact that the ratio of MY to FY ice entering into the MY ice category each year is decreasing, it is likely that the difference between FY and MY ice survival ratios will decrease in a warming climate. If this occurs, the Arctic sea ice system would move toward a regime of decreased memory and decreased sensitivity to climate forcing...
Armour et al 2010, "Controls on Arctic Sea Ice from First-Year and Multiyear Ice Survivability"
http://faculty.washington.edu/luanne/mypapers/Armouretal2011.pdf

In other words, MYI remembers the insults upon it. FYI forgets each freeze season. Therefore as the pack transitions to a FYI state the memory declines and the persistence of volume loss declines, the trend of loss relaxes.

ghoti

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Re: The Slow Transition
« Reply #259 on: December 22, 2014, 12:28:36 AM »
Plus export or lack there of seems to accentuate the year to year variability. It seems like 2014 minimum was as high as it was because of the wind patterns that  seemed to stop Fram export.

jai mitchell

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Re: The Slow Transition
« Reply #260 on: December 22, 2014, 10:58:10 PM »
Cool. I'm sure Jai will be interested in using this formula.

it would help if you described the values and formats for the following four inputs

O5 - Latitude?
DR7 - declination?
N10 - date?
AT7 -???

or, just share the spreadsheet :-)

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ChrisReynolds

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Re: The Slow Transition
« Reply #261 on: December 27, 2014, 08:01:04 PM »

jai mitchell

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Re: The Slow Transition
« Reply #262 on: December 27, 2014, 09:17:13 PM »
That is interesting and colourful!

I also was looking at this:

http://www.cgd.ucar.edu/cas/catalog/reanalysis/ecmwf/era40/daily_othr.html

as referenced here:

http://polar.erdc.dren.mil/people/personnel_sid/perovichweb/DKPpdf/2007GL031480.pdf

They have TOP and Surface gridded historic data by second and day.

So a simple summation of cumulative data within the desired grids will produce the result.  They even include cloud cover and clear sky data (I believe)  I have not downloaded the data set tho.

using the spreadsheet, how do you intend to include cumulative irradiance between periods and latitudes, knowing that the current values are daily average insolation values?
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Steven

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Re: The Slow Transition
« Reply #263 on: July 16, 2015, 10:07:38 PM »
The following new paper seems interesting:

The Impact of Stored Solar Heat on Arctic Sea-ice Growth
http://onlinelibrary.wiley.com/doi/10.1002/2015GL064541/full

Abstract:

Quote
High-resolution measurements of ocean temperature and salinity in the Arctic Ocean's Canada Basin reveal the importance of the release of solar-derived stored ocean heat on sea-ice growth.

Locally-absorbed summer solar heat is stored in a Near Surface Temperature Maximum (NSTM) layer underlying the mixed layer.

The heat content of the NSTM layer was anomalously large following summer 2007, which saw considerable sea-ice losses and intense solar absorption into the exposed surface ocean.

Measurements provide evidence for the entrainment of NSTM-layer heat in fall/winter 2007–08 by shear-driven mixing, and convective mixing by the release of dense, salty plumes during sea-ice growth. While at least a portion of the NSTM-layer was eroded, deeper warm ocean layers remained unaffected.

It is shown that the release of solar heat stored following summer 2007 was sufficient to have reduced sea-ice thickness at the end of the 2008 growth season by about 25%.
« Last Edit: July 16, 2015, 11:04:17 PM by Steven »

Neven

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Re: The Slow Transition
« Reply #264 on: July 16, 2015, 10:24:40 PM »
Wow, that sounds exciting. Thanks, Steven.  :)
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ChrisReynolds

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Re: The Slow Transition
« Reply #265 on: July 16, 2015, 10:45:56 PM »
Thanks Steven,

It should be borne in mind that 2008 still saw a rebound in volume in PIOMAS. And less it be thought that PIOMAS was wrong in this. Despite a Dipole index of around that of 2007, extent in the summer of 2008 was far higher than 2007.

Steven

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Re: The Slow Transition
« Reply #266 on: July 17, 2015, 04:53:35 PM »
Chris,

Is that the Arctic dipole index for June only?  Anyway, 2007 was much warmer than 2008 in the Arctic, and there was exceptionally early widespread melt pond formation in early June 2007:

http://onlinelibrary.wiley.com/doi/10.1029/2011JC007869/full


And les[t] it be thought that PIOMAS was wrong in this.

Generally I guess PIOMAS is (broadly) correct, and I have more confidence in PIOMAS than in other models for sea ice thickness such as hycom/cice.

Incidentally: the graphic below compares FYI vs. MYI thickness estimates from ICESat for Mar-Apr 2007 and Feb-Mar 2008:



(link).

That link also suggests that the snow depth on the sea ice in winter/spring 2008 was relatively low compared to other years.  If so, this enhanced first-year ice thickening during that freezing season.

Another factor that may have played a role is widespread fracturing of sea ice in Jan/Feb 2008 (somewhat similarly to Feb 2013).  At least, that's what I remember from earlier discussions. The fracturing in winter helps Arctic ocean heat to vent and escape to the atmosphere.


I'm not sure how much of a role these factors played, and whether this affects the analysis in the Timmermans 2015 paper which I linked yesterday.

 
« Last Edit: July 17, 2015, 11:52:57 PM by Steven »

ChrisReynolds

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Re: The Slow Transition
« Reply #267 on: July 18, 2015, 09:11:29 AM »
Steven,

That image is for June only, but the AD index can be calculated for any period. However it relies on EOFs, and my maths isn't up to calculating an index myself. 2008 and 2009 were colder, after the 2012 crash similarly 2013 and 2014 were cold. Here it gets complex, and I don't have a clear answer. This summer pattern that gives rise to the AD is in part driven by sea ice loss (Bluthgen 2011 Atmospheric response to the extreme Arctic sea ice conditions in 2007). Summer temperatures at the surface tell us more about loss of ice revealing open water which can warm above 0degC than they do about processes driving loss of sea ice.

One solution to this connundrum is that volume increase during autumn/winter following a crash leads to retarded loss in the summers afterwards, that means more ice and colder summers. However I have not viewed 2013/14 as such a crash response because volume only increased in 2013 during the summer. This perspective might be wrong, it could be that PIOMAS is somewhat understating winter volume growth after 2012, it might be that one wouldn't expect the volume increase to happen until the following summer in such a rebound. Anyway, the pattern of crash, followed by two muted melt years is suggested by 2007 and now by 2012. Of course it could just be a coincidence.

Your presentation of the graph from the Kwok paper and comparison with the 25% decrease of thickness from Timmermans 2015 is useful. Kwok finds that Feb/Mar 2006 FYI thickness was 1.7m, while in Feb/Mar of 2008 it was 1.6m. Mar/April 2007 isn't comparable as the growth rate in winter will affect the difference between Feb/Mar and Mar/Apr. However another Kwok paper
"Thinning and volume loss of the Arctic Ocean sea ice cover: 2003–2008" from which I think that graphic is adapted, shows: (FM = Feb/Mar, MA = March April)

FM04 1.91
FM05 2.29
FM06 2.00
MA07 2.18 - later in winter/spring
FM08 1.94

I suspect that the reasons the drop of 25% found by Timmermans 2015 is not seen here might be due to the sort of factors you outline. Thanks for the copy of that paper.

It is worth pointing out that in my blog posts on the 'Slow Transition' using a thermodynamic model of sea ice growth I pointed out that ocean heat flux would reduce growth, and that this would be factored into the model as:

k(To-Ts) / h = p l dh/dt +Oflux. [eq. 2]
http://dosbat.blogspot.co.uk/2015/01/the-simplest-model-of-sea-ice-growth.html

The ocean heat flux (Oflux) would essentially take the place of some of the heat flux that would have gone into melting ice, resulting in less ice growth. That model wouldn't really take into account bottom melt in winter, it is the simplest possible model. However Timmermans equation 3 could be used to add that factor into the equation.

I see nothing wrong with what Timmermans is arguing, however a 25% thickness decrease from the FM07 thickness of 2m, would be 1.5m, and in Kwok's ICESat data, which I view as a good empirical measure, the decrease of thickness for first year ice was 0.06m, not 0.50m.

So Timmermans results suggest that while the NSTM heat content had the potential to reduce thickening by 25%, the available evidence suggests that this did not actually happen. That doesn't mean it couldn't in future.
« Last Edit: July 19, 2015, 08:31:27 AM by ChrisReynolds »

Steven

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Re: The Slow Transition
« Reply #268 on: July 18, 2015, 09:03:56 PM »
Chris,

Thanks for the reference to the Kwok et al. paper.  It seems that you accidentally swapped the 2006 and 2007 months and numbers in your above list of first-year ice thicknesses.

Figure 5c of the Kwok et al. paper:


Anyway, looking at the FebMar and MarApr data, this confirms that the first-year ice thicknesses in spring 2007 and spring 2008 were very similar.

Incidentally, part (b) of that Figure also shows that snow depth on the sea ice in winter/spring 2008 was lower than in the other years.



Having read the Timmermans 2015 paper in more detail now, I see that she uses data from Ice-Tethered Profilers deployed in multi-year ice floes in the Canada Basin.

Drift tracks of the ITP's shown in Fig 1a of the Timmermans paper: 

For comparison, here is a map showing the sea ice extent on 9 September 2007.

Regarding the potential 25% reduction in thickening due to NSTM heat content, the paper says:

Quote
Time series [...] indicate a loss of stored ocean heat from fall 2007 to winter 2008 of around 36 MJ m-2 (Figure 4). This heat is equivalent to around 15 cm of ice melt, about 1/4 of the total sea ice growth (~60 cm) measured over the 2008 season. By contrast, the ~8 MJ m-2 stored ocean heat loss the previous year is equivalent to around 3 cm of ice melt. Coupled with observations that show the release of stored heat (to the surface ocean in contact with sea ice), it is reasonable to conclude that sea ice in May 2008 was a significant fraction thinner than it would have been in the absence of an ocean heat source in winter.

Link to Figure 4.

It seems that all the numbers in the above quote refer to the specific ITP data used in the paper.  I think the "25%" should not be taken too literally, and can be viewed as an upper bound.  Anyway, I think it's interesting that the paper has some empirical data about this subject.
« Last Edit: July 18, 2015, 11:59:14 PM by Steven »

ChrisReynolds

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Re: The Slow Transition
« Reply #269 on: July 19, 2015, 08:41:25 AM »
I have corrected the error in my list, which is from figure 6. Thanks.

I did notice the use of Canada Basin data, and was going to post some data for PIOMAS in Beaufort. However I cannot reliably extract FYI from MYI in PIOMAS, so in the end didn't do so. I remain sceptical of these ITPs, as they only give a single point dataset.

Timmermans is a paper worth noting. But I think a study of more years would be needed, and for extreme examples the only years are 2007 and 2012 (perhaps 2011?).

Anyway, in the 2020s I suspect that this phenomemon will be more apparent, and a more important factor in the thinning of winter ice.

Steven

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Re: The Slow Transition
« Reply #270 on: July 19, 2015, 06:51:26 PM »
I remain sceptical of these ITPs, as they only give a single point dataset.

Timmermans is a paper worth noting. But I think a study of more years would be needed, and for extreme examples the only years are 2007 and 2012 (perhaps 2011?).

Anyway, in the 2020s I suspect that this phenomemon will be more apparent, and a more important factor in the thinning of winter ice.

Yes, I agree.

Nightvid Cole

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Re: The Slow Transition
« Reply #271 on: July 20, 2015, 03:07:32 AM »
I think the argument that the decline in max volume will flatten is likely correct.

But that's the only part I agree with. If increases in melt are due to more open water, are you claiming that there will be less open water? Because it seems the opposite is what is happening and will continue to happen. More open water earlier in the season, as well as many other factors all pushing the system towards more melt.

It seems to me that the argument that increased melt is caused by declining max volumes is putting the cart before the horse.

I agree it is putting the cart before the horse.

The problem with Chris's argument in post #49 exemplified by the correlations in the first plot therein, is that *of course* spring volume loss correlates with year-on-year volume loss; spring is part of the year! What Chris should be doing is comparing de-trended spring max volume to de-trended spring-to-summer volume loss; if there is a statistically significant correlation, it supports Chris's hypothesis, if no significant correlation, the hypothesis is unsupported.

Chris argues also based on open water formation efficiency, which includes physically plausible assumptions, however, one must not confuse area/extent loss increasing with volume loss increasing. While volume loss can certainly increase as a result of lower albedo of a fragmented pack, as Chris rightly points out, it does not follow that other factors such as June snow cover can't have a similar effect; thus the conclusion of a "slow transition" is not justified.
« Last Edit: July 20, 2015, 03:21:11 AM by Nightvid Cole »

ChrisReynolds

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Re: The Slow Transition
« Reply #272 on: July 20, 2015, 09:42:36 AM »
Y'know, I am bored of this subject now and am happy to let the ice adjudicate.

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Re: The Slow Transition
« Reply #273 on: July 24, 2015, 11:14:07 AM »
At the risk of polluting this thread, and with apologies in advance for not following this thread as carefully as I should...

I've been working on a theory that degree-days are of primary importance in determining arctic ice growth and ice melt.  See for example NSIDC Ice Growth and Modeling Glacier Melt.

Jim Hunt kindly gave me the DMI 80N temperature data since 1958.  [I had to interpolate data for a small number of dates for which there was no data.]  For each date, if the temperature was below 271.35 degrees kelvin (-1.8C) I counted the degrees below 271.35 as freezing degree days.  Similarly, if the daily temperature was above freezing, the degrees above freezing were counted as thawing degree days.  This gives the following graph:
80N Saltwater Degree Days

In this graph, the freezing degree days is on the left and the thawing degree days in on the right.  There are far more freezing days than thawing days.  Ice freezes down from the bottom and builds insulation as it grows, but melts from the top.

As expected, the number of freezing degree days drops over time.  Unexpectedly, the thawing degree days also drops, although slower, over time as well.  I'm guessing the explanation for this is that Multiyear Ice has been melting.  Multiyear ice contains less salt and melts at a higher temperature.  The air temperature is driven toward the temperature of the ice.  With lots of Multiyear Ice in the CAB, the average summer temperature should be close to the freezing point of fresh water, as that melts the average temperature should drop toward the freezing point of salt water.

Next, we can use degree days to estimate the amount of ice that will freeze or melt.  NSIDC kindly provides a formula for ice growth at the above link: 1.33*(degree_days^0.58) gives centimeters of ice growth.

For melting, the above glacier link suggests a range of multiplicative factors for glaciers and suggests that oceans have higher multiplicative factors.  I arbitrarily chose 1 cm of melt per degree day.  This seems to be roughly in the right ballpark, but we may want to mentally slide the line showing melted ice up or down.  We get the following graph for the amount of ice grown and melted:
80N Ice Growth and Melt

The graph of course just gives a rough estimate.  As ice is pushed toward the archipelago, thinner ice may be left behind causing more ice to grow than is estimated here.  We start the freezing season with quite a bit of ice in place already, so we may overestimate the amount of ice that grows.  And, of course, I pretty much totally made up the amount of melt.  But the graphs are roughly in the right place: the growth and melt must have been in rough equilibrium in past decades or we would have seen rapid accumulation or loss of ice.

Finally, we can add the growth and melt for each year:
80N Ice Change

This has a large dip in 1998, and more recent dips in 2002, 2007, 2011, and 2012.  So the result seems to correlate roughly with extent graphs.  (These graphs are using calendar year freezing as opposed to seasonal freezing, which might produce a slightly different picture.)

So far in 2015 (as of a few days ago, day 203), we've had 123 saltwater thawing degree days, the same as we had in 2012.

To extrapolate into the future, we would expect thawing degree days to continue to drop, and thus ice growth would continue to slowly drop.  I would expect thawing degree days to level out now that most multiyear ice has been lost from the CAB.  But I wouldn't expect thawing degree days to rise much unless we start to melt out the periphery of the CAB relatively early in the melting season.

Wipneus

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Re: The Slow Transition
« Reply #274 on: July 24, 2015, 11:42:51 AM »

As expected, the number of freezing degree days drops over time.  Unexpectedly, the thawing degree days also drops, although slower, over time as well.  I'm guessing the explanation for this is that Multiyear Ice has been melting.  Multiyear ice contains less salt and melts at a higher temperature.  The air temperature is driven toward the temperature of the ice.  With lots of Multiyear Ice in the CAB, the average summer temperature should be close to the freezing point of fresh water, as that melts the average temperature should drop toward the freezing point of salt water.


Another explanation is a discontinuity in 2002 (and 2006 and 2010) due to the change from ERA40 to NWP model T511/T799/T1279. I guess slight differences between the reanalysis's make big changes in degree-days.

Andreas T

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Re: The Slow Transition
« Reply #275 on: July 24, 2015, 02:14:26 PM »
Cesium62, there are a few issues with your method which should be taken into consideration when interpreting what this shows.
(BTW the labeling on the right hand scale has got lost, and the left hand scale is too large to be days in a year?)
Ice does melt at the bottom as well as the top. That is because short wave radiation from the sun can pass through ice and transfer energy to water below ice as well as the ice itself. This transfer causes melting with very little change (theoretically no change) in temperature.
Because saltwater melts ice at lower temperatures than pure ice would, saltwater inclusions (which make first year ice salty) melt surrounding ice as the melting temperature is approached. This drains saltwater from the ice (and makes multiyear ice less salty).
sea ice is therefore less salty on the top than at the bottom. Also there is snow on the ice to start with. Ice floes can therefore be warmer on the top surface than the surrounding sea water. Early in the season that can be observed in IR satellite images. It can also be seen in IMB temperature profiles.
So you can have melt when air temperatures are below melting temp. (fresh and salty) on sunny days, when the energy input happens over a larger thickness but energy output (longwave IR) happens at the surface.
You can also have very little melt melt when surface temp are above saltwater melting temp.
Bottom melt continues into September when temperatures at the surface are alredy well below freezing, because there is a lot of water very slightly above the melting temperature below  the ice.
I do not claim this includes all the complications, it is just what I can think of at the moment.

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Re: The Slow Transition
« Reply #276 on: July 24, 2015, 03:16:00 PM »
At the risk of polluting this thread, and with apologies in advance for not following this thread as carefully as I should...

Note that (where relevant) the GWC IMB buoy maps for 2015 include FDD. Currently they are based on air temperature, but it did occur to me that temperature at the snow/ice interface might actually be more relevant?

http://GreatWhiteCon.info/resources/ice-mass-balance-buoys/summer-2015-imbs/#2013F
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cesium62

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Re: The Slow Transition
« Reply #277 on: July 24, 2015, 07:16:49 PM »
(BTW the labeling on the right hand scale has got lost, and the left hand scale is too large to be days in a year?)
The right hand scale should be Thawing Degree Days.  There are multiple degrees in a day.

there are a few issues with your method...
Ice does melt at the bottom as well as the top. ...

I wasn't saying "all ice growth and melt can be explained by degree days".  I was saying, degree days is a big component and we may be able to qualitatively understand the CAB better by looking at degree days.  A model doesn't have to be perfect in order to lend insight.

If you want to pursue this critique, you would need to directly spell out why thawing degree day models are useful for thinking about glacier melt but not sea ice melt.

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Re: The Slow Transition
« Reply #278 on: July 24, 2015, 07:33:13 PM »
Caesium,

My calculation of FDDs (I didn't do MDDs) was done using gridded NCEP/NCAR Reanalysis 2 data. I calculated FDDs on a per-grid box basis and area weighted the final stage calculation of FDDs for a given region.



Sorry, but I didn't find as much of a decline as you did for the region north of 80degN. I am unaware of issues with Reanalysis 2, that does not mean to say there are no issues that would reduce the trend of FDDs at high latitude.

BTW, like yourself I used -1.8degC. If it helps here is a core code part.

Quote
For DayNum = 1 To 120
  For Lat = 1 To 11
    For Lon = 1 To 192
       Temperature = Worksheets("air").Cells(Lat + 3 + (94 * DayNum), Lon + 3).Value
       '271.35 = 273.15 - 1.8
          If Temperature < 271.35 Then 'temperature below -1.8 degC freezing point of sea water
            If LandMask(Lat, Lon) = 0 Then 'ocean only
               TemperatureArea = TemperatureArea + (Temperature - 271.35) * GridAreas(Lat) 'sum up the product of temp and area
               TotalArea = TotalArea + GridAreas(Lat) 'total area to make area weighted average
            End If
          End If
    Next Lon
  Next Lat
  FDD = FDD + TemperatureArea / TotalArea 'area weighted average of FDD north of 70degN over ocean
Next DayNum
That's for the early part of the year, another identical set calculated for the latter part of the year, days 244 to 365.

I reformulated the equation for ice growth to produce it in terms of autumn/winter thickness growth based on initial thickness.
http://dosbat.blogspot.co.uk/2015/01/the-slow-transition-thickness-growth.html
And obtained a good agreement between Central Arctic volume gain, and calculations via my model using north of 80degN FDDs.


This is not necesarily in support of what I have done regards FDDs because NCEP/NCAR Reanalysis is used by PIOMAS, so such an argument would be essentially circular. The valid closed loop argument I make is that ice growth physics explain the increase in PIOMAS volume gain over autumn/winter.
« Last Edit: July 24, 2015, 07:39:30 PM by ChrisReynolds »

cesium62

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Re: The Slow Transition
« Reply #279 on: July 25, 2015, 08:15:10 AM »
My calculation of FDDs (I didn't do MDDs) was done using gridded NCEP/NCAR Reanalysis 2 data. I calculated FDDs on a per-grid box basis and area weighted the final stage calculation of FDDs for a given region.

My apologies.  I didn't intend to revisit a subject that had already been thoroughly explored with a better data set.

[In addition to the different data sets, and between gridded vs ungridded data, I'm summing calendar years and not freezing seasons, and I'm summing freezing degree days between days 120 and 244.]

I think we'ld have to pull out some heavier statistics to decide which graph shows a steeper reduction in freezing degree days.  You have the CAB consistently peaking at 5000 in the 80s and 90s and peaking at 4000 in the 2010s.  I have the CAB consistently peaking at around 5500 falling to about 4500 in the 2010s.

We agree that freezing degree days would have to fall a lot to have any real effect on the ice thickening.  If the degree days are falling by about 1,000 over two decades, it might be forty years before we see a good-sized fall off in thickening.

The FDD above 70N seems to be falling even more slowly, which doesn't bode well for us seeing peripheral seas open up early in the year thus allowing the Thawing Degree Days to greatly increase at least around the periphery of the CAB.

So...  we have a simple model for ice growth that seems to produce at least good qualitative results.  Do we have an equivalent simple model for ice melt?

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Re: The Slow Transition
« Reply #280 on: July 25, 2015, 11:21:08 AM »
Following Chris's important work of the freezing model, the reduction of MYI, and the resultant prediction of a slow transition, we are kind of "stuck" in a very slow timetable, as opposed to the simple extrapolation graphs that show an ice-free state by 2016 or 2020.
So as we all await the coming decades to see how slow would be the transition of the CAB to a seasonally ice-free state, I think we could greatly benefit from an analysis of other areas that have undergone or currently undergoing this transition, due to the shortening of the freezing season.

Are there any peripheral seas that used to have perennial ice in decades past and are now seasonally ice free? Admittedly peripheral seas are more affected by winds and currents causing import and export, but still if it's possible to take such a sea, analyse the historical trend of freezing degree days, MYI trend, ice volume growth etc., I think it could give us an empirical test of the theory and maybe a better understanding of what to expect of the CAB transition.
Beyond floating this idea I can do zilch about the subject, lacking any and all required knowledge. I would love some feedback by the experts as to the validity and usefulness of such an analysis.

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Re: The Slow Transition
« Reply #281 on: July 25, 2015, 12:12:51 PM »
So...  we have a simple model for ice growth that seems to produce at least good qualitative results.  Do we have an equivalent simple model for ice melt?

Simple model = Energy absorbed by ice. But that means: start with incoming solar radiation, albedo of atmosphere and surface and re-radiation of heat by atmosphere some of which reaches surface where it is reflected or absorbed. Then you have to do this in small cells which have different conditions and then there is heat transport by atmosphere and ocean and how much of that heat gets absorbed by the ice .....

Why would we get a different result than GCMs that have already done this?

The main reason for change in amount of heat absorbed looks to me as if it should be surface albedo. Start with thinner ice and the albedo drops more quickly. But if there is extra snow that can mean later drop in albedo.

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Re: The Slow Transition
« Reply #282 on: July 25, 2015, 12:19:01 PM »
Following Chris's important work of the freezing model, the reduction of MYI, and the resultant prediction of a slow transition, we are kind of "stuck" in a very slow timetable, as opposed to the simple extrapolation graphs that show an ice-free state by 2016 or 2020.
So as we all await the coming decades to see how slow would be the transition of the CAB to a seasonally ice-free state, I think we could greatly benefit from an analysis of other areas that have undergone or currently undergoing this transition, due to the shortening of the freezing season.

Are there any peripheral seas that used to have perennial ice in decades past and are now seasonally ice free? Admittedly peripheral seas are more affected by winds and currents causing import and export, but still if it's possible to take such a sea, analyse the historical trend of freezing degree days, MYI trend, ice volume growth etc., I think it could give us an empirical test of the theory and maybe a better understanding of what to expect of the CAB transition.
Beyond floating this idea I can do zilch about the subject, lacking any and all required knowledge. I would love some feedback by the experts as to the validity and usefulness of such an analysis.
Baffin bay might be a good example for that. Can this years delayed melt be "hindcast" by a model which takes melt days and other parameters as much as they are known into account?

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Re: The Slow Transition
« Reply #283 on: July 25, 2015, 12:47:47 PM »
So...  we have a simple model for ice growth that seems to produce at least good qualitative results.  Do we have an equivalent simple model for ice melt?
Why would we get a different result than GCMs that have already done this?

I felt that in this thread we were looking at simple models that we could understand and mull over as opposed to looking at the output of a GCM that we could admire without understanding how the output had been produced.

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Re: The Slow Transition
« Reply #284 on: July 25, 2015, 07:29:55 PM »
My calculation of FDDs (I didn't do MDDs) was done using gridded NCEP/NCAR Reanalysis 2 data. I calculated FDDs on a per-grid box basis and area weighted the final stage calculation of FDDs for a given region.

My apologies.  I didn't intend to revisit a subject that had already been thoroughly explored with a better data set.

No apologies needed, I just used a more similar dataset to PIOMAS...

Ice melt has beaten me it is way too complex. Blizzard of Oz gives a excellent run down of the sort of issues that had me banging my head on the desk, and outlines the sort of model I was aiming at.
http://forum.arctic-sea-ice.net/index.php/topic,1149.msg57970.html#msg57970

And yes, although I am bored of this slow transition issue and am happy to see what happens now, if you want to use simple models to expore the issue feel free to here. But pursuing simple models has to be done with caution as Eisenman found, discussed here:
http://dosbat.blogspot.co.uk/2015/05/is-arctic-sea-ice-like-cup-or-ball.html

Note, I do expect that FDD decline will accelerate, and I do expect summer melt to increase further, that's why I put the 1M km^2 at something like 2030 +/-5 years, not in the 2050s!

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Re: The Slow Transition
« Reply #285 on: July 25, 2015, 07:49:20 PM »
What I came here to post...

At the end of the comments on my Simple Model post, Chuck Simmons has come up with a very good point made with a really useful paper.
http://dosbat.blogspot.co.uk/2015/01/the-simplest-model-of-sea-ice-growth.html

Quote
Chuck Simmons said...
For an initial thickness of zero, NSIDC discussion pages reference Lebedev 1938
http://pubs.aina.ucalgary.ca/arctic/Arctic14-1-2.pdf
and give the equation: thickness (cm) = 1.33 * FDD ^ 0.58

Apparently that was obtained from the Russian side of the arctic. For 4,000 freezing degree days, that equation gives 1.63 meters of ice.

Lebedev also mentions the equation: 1.53 * FDD ^ 0.59, which comes from a Canada station. For this 4,000 freezing degree days produce 2.04 meters of ice.

Lebedev gives a few other equations which produce ice thicknesses less than the Canada station.

Your equation, when reformulated to look like a Lebedev equation, is: 3.53 * FDD ^ 0.5

I'm not sure that the above means anything; I just find the variance interesting.

My reply was...

Quote
Chuck,

Thanks, I've never come across that Bilello paper. It is meaningful, and another useful resource of spot thickness.

As stated in the derivation of my equation, my equation doesn't take into account snow (which would be modelled as a separate layer above the ice), or ocean heat flux (which would deduct from the heat flux making ice), so it pretty consistently produces thicker ice than either PIOMAS or the other thickness data I have looked at (not shown). Bilello uses observational data and fits curves to it, this approach will include such 'real world' factors.

Another issue is that Bilello does not find one set of parameters, for each area they are different. However they are all of similar magnitude, and you are right my derivation is giving a substantially greater constant 3.5. This however is offset by the exponent being lower (the greater exponents in Bilello gives thicker ice). For example 4000^0.5 = 63.25, 4000^0.58 = 122.80, that alone demands a much smaller constant.

Note that for my equation FDD=4000 gives 2.23m thick ice, which is thicker than I would expect.

Figure 7-11 shows FDDs using the -1.8degC threshold for locations in the CAA in the 1950s, the range is between 6830 and 5680.

Depending on whether one takes NCEP/NCAR Reanalysis 2, or DMI, that's a substantial drop in FDDs within the CAA (assuming that north of 80degN is similar to the CAA...

However as the 'simple model' suggests, the drop in FDDs has not led to a large drop in winter thickness (figs 7 to 11). That said there was massive variability between sample locations.


cesium62

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Re: The Slow Transition
« Reply #286 on: July 25, 2015, 09:05:28 PM »
Ice melt has beaten me it is way too complex. Blizzard of Oz gives a excellent run down of the sort of issues that had me banging my head on the desk, and outlines the sort of model I was aiming at.
http://forum.arctic-sea-ice.net/index.php/topic,1149.msg57970.html#msg57970

And yes, although I am bored of this slow transition issue and am happy to see what happens now, if you want to use simple models to expore the issue feel free to here. But pursuing simple models has to be done with caution as Eisenman found, discussed here:
http://dosbat.blogspot.co.uk/2015/05/is-arctic-sea-ice-like-cup-or-ball.html

Simple temperature models seem to work well for Glaciers, so I had some hope they would work okay for sea ice.  The issues of snow and insolation are the same.  In the CAB, bottom melt might not be too important until the concentration is relatively low and the average ice thickness is relatively thin.  Wind blowing ice in and out of the CAB is an additional factor, as is wave action at the periphery.

Ah...  Your blog post is highly relevant: it contains exactly the results of the simple model that I was groping for and shows the expected future path of Thawing Degree Days (leveling off over time as the temperature gradient between the poles and equator grows smaller).

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Re: The Slow Transition
« Reply #287 on: July 26, 2015, 06:04:51 PM »
Cesium,

Regards the last paragraph, I don't get that at all, can't see which graph you mean.

I'm not sure how straightforward Glacial models of melt are.

If you're relating melt to melt degree days then a problem is that the ice pegs temperature at close to zero in summer, like ice in a drink. So there is hardly any upward trend in my calculation of melt degree days. I attach a quick plot of seasonal temperature anomalies relaive to the NASA GISS basline period of 1951 to 1980.

Anyway I recommend reading Blizzard of Oz's comment linked to above as a start to getting your head around the problem.

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Re: The Slow Transition
« Reply #288 on: July 26, 2015, 07:46:13 PM »
Cesium,

Regards the last paragraph, I don't get that at all, can't see which graph you mean.

I'm not sure how straightforward Glacial models of melt are.

If you're relating melt to melt degree days then a problem is that the ice pegs temperature at close to zero in summer, like ice in a drink. So there is hardly any upward trend in my calculation of melt degree days. I attach a quick plot of seasonal temperature anomalies relaive to the NASA GISS basline period of 1951 to 1980.

Anyway I recommend reading Blizzard of Oz's comment linked to above as a start to getting your head around the problem.

I suppose you could set the base temperature a few tenths of a degree below freezing for your melt degree days calculation - at least this relates to the amount of time the ice is in a melting state.

cesium62

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Re: The Slow Transition
« Reply #289 on: July 26, 2015, 09:56:04 PM »
Cesium,

Regards the last paragraph, I don't get that at all, can't see which graph you mean.

I'm not sure how straightforward Glacial models of melt are.

If you're relating melt to melt degree days then a problem is that the ice pegs temperature at close to zero in summer, like ice in a drink. So there is hardly any upward trend in my calculation of melt degree days. I attach a quick plot of seasonal temperature anomalies relaive to the NASA GISS basline period of 1951 to 1980.

Anyway I recommend reading Blizzard of Oz's comment linked to above as a start to getting your head around the problem.

I was referencing "figure 4b of Wagner & Eismann".  This suggests that thawing degree days (to the extent that represents heat transfer to the arctic from the tropics) will slowly linearly increase and later level off.

Glacial models based on thawing degree days are extremely straight-forward, and the referenced paper (which I might have hid as a link from the word Glaciers) states they are used successfully for many purposes.

Yes, I saw the problem that the temperature of the ice tends to cause the temperature of the air instead of vice versa, and even used that as an explanation for why I was seeing a drop in thawing degree days.  I was ignoring the problem hoping it would go away.  I think your point here is that Thawing Degree Days might be really good at explaining what happened, but be useless to understand what will happen.

Yes, I saw Blizzard of Oz's comments.  All of those apply to glaciers just as much as they apply to sea ice.  The glacier paper states that all of that correlates well with thawing degree days, at least within an individual glacier catchment area. 

Erm...  On that graph, can I pick the 'djf' line instead of the 'jja' line?  ;-)

cesium62

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Re: The Slow Transition
« Reply #290 on: July 26, 2015, 10:02:01 PM »
Cesium,

Regards the last paragraph, I don't get that at all, can't see which graph you mean.

I'm not sure how straightforward Glacial models of melt are.

If you're relating melt to melt degree days then a problem is that the ice pegs temperature at close to zero in summer, like ice in a drink. So there is hardly any upward trend in my calculation of melt degree days. I attach a quick plot of seasonal temperature anomalies relaive to the NASA GISS basline period of 1951 to 1980.

Anyway I recommend reading Blizzard of Oz's comment linked to above as a start to getting your head around the problem.

I suppose you could set the base temperature a few tenths of a degree below freezing for your melt degree days calculation - at least this relates to the amount of time the ice is in a melting state.

I kind of did cheat in that fashion.  I originally set the melt point at 0C instead of -1.8C (leaving the freeze point at -1.8C), but didn't like the results.

Andreas T

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Re: The Slow Transition
« Reply #291 on: July 27, 2015, 10:18:42 AM »
The reason why melt degree days works for glaciers but not on sea ice is probably that glacies are surrounded by land which does warm at the surface and warms the air. Even though there is radiative heating of the glacial ice without raising surface temperature above 0deg, the surrounding land does raise air temperature and gives an indication of the strength of that solar input. On ice this does not happen.
To add to Blizard of Oz's comment I have written this on OLR in the Arctic. Without looking at radiation processes sea ice can't be understood.
......
jdallen; the difference between the EBAF chart and blaine's figure is that the 0deg are more likely found at ground level. Since the chart shows monthly average it includes the tops of clouds which are much colder. Use the IR band on EOSDIS as I have described above to see how these temperatures vary for high clouds (cold) and low clouds (fog can be warmer than the ice below it)
Radiation of long wave IR down to the ground is dependent on temp of cloud bottom and can be equal, lower or higher than ice surface temp.
This isn't an external input generally unless warm air is advected and forms relatively warm clouds over the cold surface layer, but in the arctic it can lead to higher surface temperatures under clouds than under clear sky. Clear sky has much less down welling LW while outgoing LW is fairly constant (ice surface temps in summer are pretty constant (in Kelvin). incoming SW is of course higher under clear sky but as the incident angle falls it becomes less while outgoing LW is just a function of temperature.
See diurnal fluctuations in buoy air temperatures south of 80N. When the sky is clear temps drop below 0C when there are clouds they can stay more level above 0C
The other important issue is: where is the radiation emitted or absorbed. Water is largely transparent to the SW coming in (dependent on suspended solids and gases) So clear water absorbs it gradually over a thick layer, ice over a shorter thickness and snow also not purely at its surface (I don't know enough but clearly it has some translucent behaviour)
Outgoing LW is emitted at the very surface because water is not transparent at those frequencies.
This doesn't alter radiative balance but it does determine how surface temperatures respond to it and where the energy goes. Water warmed over a greater depth shows a smaller temperature rise.  That warmed water needs to be convected to the ice/ water interface to cause melting, and that takes time.
This is meant as additional aspects to Blizzard of Oz's comment which I find a  good outline of the physics

ChrisReynolds

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Re: The Slow Transition
« Reply #292 on: July 27, 2015, 07:31:05 PM »
Cesium,

Looking at figure 4 of W&E, and the plot I presented of seasonal temperature anomalies...

Actually that effect of reduced equator to pole heat transport (for the atmosphere) would be strongest in  SON, DJF, and MAM. I have plotted Pole-Equator temperature difference some years ago.



I think that is the difference between the zonal average for 20N to 65 N, and the zonal average for 65N to 90N, but can't put my hands on the blog post I used it in right now.

Data from here
http://www.esrl.noaa.gov/psd/cgi-bin/data/timeseries/timeseries1.pl
If you (or anyone else) want advice on using that page just ask.

TDDs will go up. With more open water the potential for warming increases, and that is going to be a very real effect. My problem is...

OK, we know that melting ice pegs the temperature near zero.

Let's say there was no ice. The ocean/air would warm. This is a though experiment, forget the conditions you'd need to actually remove the ice. I'm talking about waving a magic wand on 1 June and whoosh! No ice!

The amount that it would warm above zero with no ice in the Arctic Ocean tells us a lot about the sort of energy fluxes going into the region. But we don't see that warming in the real world when the ice is there because melt pegs the temperature to zero. Thus we have almost no idea what those energy fluxes are and how they might be changing.

I say almost because we can hazzard a guess as to what's going on from extent, area, thickness, and work on albedo critical processes like melt ponds, and we have models like the DMI one and PIOMAS - volume loss during the summer is related to energy gain during the summer.

I'll have to look at the glacier model paper tomorrow, I'm too tired right now.

I'm having a night off sea ice, and I'm going to start by watching Dr Strangelove (Or How I Learned to Love the Bomb), what a treat.  ;D

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Re: The Slow Transition
« Reply #293 on: August 21, 2015, 09:57:15 PM »
This is a bit silly, but just for fun ...

Assume that the IJIS September daily minimum for 2015 will be around 4.38 million km2 (see the IJIS thread for details).

The linear trend 2002-2015 is then -0.116 million km2 per year, and the standard deviation of the residuals is 0.565 million km2.

Extrapolating into the future, that trend would cross the semi-canonical 1.0 million km2 line in 2042.  But due to the interannual variability (that 0.565 million km2) there is a 50% chance of an ice-free day (sub-1.0 million km2) by approx. 2037, a 10% chance of an ice-free day by 2033, and a 1% chance of an ice-free day by 2029.

That is all predicated on the assumption that in the future the rate of decline and the amount of "noise" are both similar to what they have been in the past.  Arguments could be made that the rate will either increase or decrease.   Seeing no particular reason in favor of a speed-up or slow-down, my default assumption is that the Arctic Ocean's first nearly-ice-free day will come in September of 2034 to 2040

But I would not be at all surprised to be wrong.

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Re: The Slow Transition
« Reply #294 on: August 21, 2015, 11:02:00 PM »
Assuming PIOMAS september volume of 5500 km^3 for 2015

A linear fit for volume takes til 2030 to get under 1000 km^3 and 2033 to lose it all.

With a gompertz fit, it takes til 2024 to get under 1000 km^3 and 2031 to get under 100 km^3

A 4 parameter gompertz sets a minimum ice volume of 5144km^3 and we get close to that in 2016.

All sorts of choices for such fun and games.

Using volume still gets earlier dates than using extent. Using extent doesn't seem very logical to me  as volume declines faster than extent because thickness is also declining. So why extent rather than volume?

OTOH a levelling off, gompertz like shape does seem better established and likely given what models produce and 2013-2015 each having higher volume than any of 2010 to 2012. Far to short to suggest an upward trend but as some evidence of a slow down in the rate of loss, how much is needed to establish such a slowdown?


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Re: The Slow Transition
« Reply #295 on: August 22, 2015, 03:18:44 AM »
how much is needed to establish such a slowdown?

Just one data point. Volume = zero => Slowdown confirmed

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Re: The Slow Transition
« Reply #296 on: August 22, 2015, 04:37:07 PM »

Using volume still gets earlier dates than using extent. Using extent doesn't seem very logical to me  as volume declines faster than extent because thickness is also declining. So why extent rather than volume?

OTOH a levelling off, gompertz like shape does seem better established and likely given what models produce and 2013-2015 each having higher volume than any of 2010 to 2012. Far to short to suggest an upward trend but as some evidence of a slow down in the rate of loss, how much is needed to establish such a slowdown?

I agree on all points.  I have always felt that the use of extent was really an anachronism of the satellite image-based observation era.  Now that we have microwave sounding and piomas models volume is the best indicator of the state of the arctic. 

2013-2014 are extreme outliers.  The global weather difference between these years and the behavior of 2012 and 2015 show extreme variability that is not likely driven by natural forces.  I have theorized about geoengineering and the impacts of south-east asian aerosols contributing to the slowdown period in those cooler years.  However, there is no real causation yet determined, just speculation.

It is clear to me that within the next 4-6 years we will have a major collapse in the arctic sea ice.
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Re: The Slow Transition
« Reply #297 on: August 22, 2015, 05:24:44 PM »
"It was geoengineering" is no proper defense. It would mean they found something that works against melting, and then they would use it massively and stop their other reform attempts.

(Edit:) And if in the end it would turn out to be natural variations after all, valuable time and resources will have been wasted.
« Last Edit: August 22, 2015, 05:37:19 PM by AmbiValent »
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Re: The Slow Transition
« Reply #298 on: August 22, 2015, 06:20:14 PM »
it was not geoengineering, it was weather. and the whole point of this thread is that once most of the multiyear ice is gone, there will be a long tail, so extrapolations based on past rates of ice loss, extent or volume, will be wrong

Neven

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Re: The Slow Transition
« Reply #299 on: August 22, 2015, 09:18:11 PM »
I don't think jai meant conscious geoengineering, but rather the effect of Southeast-Asian aerosols.
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