We noted earlier that the Artic sea-ice is approaching a record minimum. The record is now broken, almost a month before the annual sea-ice minima usually is observed, and there is probably more melting in store before it reaches the minimum for 2012 – before the autumn sea-ice starts to form.
The figure shows annual variations in the area of sea-ice extent, and the x-axis marks the time of the year, starting on January 1st and ending on December 31st (for the individual years). The grey curves show the Arctic sea-ice extent in all previous years, and the red curve shows the sea-ice area for 2012.
(The figure is plotted with an R-script that takes the data directly from NSIDC; the R-environment is available from CRAN)
UPDATE on the update The National Snow and Ice Data Center announced today (August 27th, 2012) that the 2007 record has now been broken by their more conservative 5-day running average criterion. They also note that “The six lowest ice extents in the satellite record have occurred in the last six years (2007 to 2012).”
I just posted the following message at the White House website.
The GOP platform criticizes President Obama for describing climate change as a severe threat. I hope that President Obama speaks very forcefully about this in his acceptance speech at the Democratic convention on September 6.
The NSIDC has recently announced that arctic sea ice extent has shrunk to a record level. The PIOMAS updated estimate for arctic sea ice volume might be released early enough in September to be included in the acceptance speech, also. The decline in volume is even more dramatic than the shrinking of arctic sea ice extent.
The threat posed by climate change and extreme weather is highlighted by the impact of this year’s drought and heat on agricultural production. The United States military has described climate change as an “accelerant of instability and conflict.”
sidd @143 & 144 — One might begin with the
http://en.wikipedia.org/wiki/Logistic_function
to develop a justification (of a crude4 sort) for the exponential nature of the fit.
[Response: Hmm.. What justifies using an exponential fit? –eric]
Well, when scientists have NO CLUE what sort of fit is appropriate, the fit that fits reality best is by definition the default fit. So, Eric, either provide some evidence that the exponential fit is wrong, or….
[Response: We discussed this before. Exponential fits don’t have any basis in physics, and don’t even give the smallest residuals. No model simulation indicates that an exponential fit is a good prediction – even when you know the answer! No peer reviewed paper has supported this with any, err… actual evidence. So, no, the burden of proof is not on those who don’t think this is justified, but rather is on those who seek to persuade others it is justifiable. – gavin]
Gavin,
Thanks for the response, and I accept that I’m likely wrong. “Denialism” is rampant both on the low and high side.
Thanks for the explanations re the antartic, appreciated
Norman this should help with a few of your questions
http://www.skepticalscience.com/print.php?r=288
Norman @145/148
Further to Tamino @147, the DMI graph you link to is produced for air temperatures above 80ºN. That bit of the Arctic still remains essentially ice-covered. Indeed, this year of dramatic melt it is about the only bit remaining ice-covered. That is why the temperature tends to hover where it does.
When I witnessed Lindzen using these DMI graphs at the talk he gave in the Palace of Westminster a few months back (he actually shuffled them up so even a proper sequence of yearly graphs was not presented), it spurred me to produce some arctic temperature graphs to illustrate the warming that Lindzen said didn’t exist.
Arctic air temperatures essentially the graph linked @146 but also showing winter & summer anomalies since 1979.
Monthly Arctic air temperatures since 1979.
Monthly sea-surface temperatures for Arctic & for above 80ºN The lower trace is thus the SST for the area in the DMI air temp graphs.
(Note usually 2 clicks to ‘download your attachments’)
I’ve been drawing simple bar graphs that track the minimum ice extent, area or volume for each year to date. With the PIOMAS August update (through 8/25) the results are striking:
http://img.photobucket.com/albums/v224/Chiloe/12_Climate/sea_ice_PIOMAS_min_to_date.png
Gavin said :
I am just an amateur, and I think you are right that an pure exponential fit has no physical basis.
However, I did put my money on the reasoning that there is a physical basis for the observed non-linear decline at least until ice area gets really small :
http://scienceblogs.com/stoat/2011/06/26/betting-on-sea-ice-10000/
My reasoning goes as follows, and I would love to hear your opinion on where this reasoning goes wrong (if anywhere) :
1) Assume that starting ice volume (thickness*area) is the same each year, and assume a given amount of heat during summer that melts ice to a certain minimum extent at the end of the season. During freezing season, that volume grows back to same volume it started with the year before. So system is in equilibrium.
Now if due to some external forcing, like planetary GHG forcing or ocean current heat, the amount of heat input during the melting season starts to increase linearly, then we would expect the minimum ice area at the end of the melting season to reduce linearly as well. That’s the first order.
2) Of course, ice-water albedo feedback will kick in during the melting season, which means a second order term appears in the ‘minimum ice area’ function.
3) Now, if the negative feedback during freeze-up (lower ice insulation leads to faster ice growth) is not as large as the positive feedback in (2), then next year ice will be thinner. Warmer winters don’t help restore original volume here. That means that (1) will progress faster, which leads to the third order term.
Note that PIOMAS results suggest that year-over-year ice volume declined linearly by 400 km^3/year over the past 30 years. This means that (3) is certainly present, although most volume reduction so far was in thick MYI. So we did not see this third term expressed in sea ice area/extent reduction…until this year ?
4) Finally, and likely most important : possibly due to the same external forcing in (1), summer snow cover (over land) starts to reduce rapidly, especially over the past decade :
http://nsidc.org/arcticseaicenews/files/2012/07/Figure5a.png
Since albedo effect is largest in June, when the sun is brutal in the Arctic, snow-albedo effect should be much larger than ice-albedo effect in (2) :
For example, in June, 60 deg North the record 6 million km^2 in June suggests something like a 1000 TW heat input anomaly on the land directly bordering still pristine Arctic sea ice. If even 25 % of that heat causes ice melt, then snow anomaly in June 2012 alone will cause a 2000 km^2 ice volume anomaly w.r.t. year 2000.
Since that heat entered early in the melting season, this heat goes right back into (1), for further amplification.
Models seems to support a soft landing more or less like a Gompertz curve, and that is how most smaller water basins melt out (such as Hudson Bay). So I think models are going to be proven correct qualitatively.
But so far, PIOMAS still shows loss of volume (despite a harsh winter) and thus we do not seemed to have reached the soft landing part of that Gompertz curve yet…
So AFAIK the question is thus not if there is a physical basis for a near-exponential decline (there is), nor if Arctic sea ice extent decline follows that function (it does so far), but the question is when (which sea ice area minimum, and over which timeframe) and how will it ‘land’ and what will happen after that ?
MARodger @ 157
Thanks for the graphs. They do show a warmer temperature in the summer as well that would cause greater ice melt.
I was doing more research on this topic.
This link provides information on Arctic Warming from 1920-1940.
http://mclean.ch/climate/Arctic_1920_40.htm
From Skeptical Science posted by Daniel Bailey @83 he provides a graphic of Arctic ice in 1938 compared to 2012.
http://www.skepticalscience.com/news.php?p=2&t=83&&n=1589
If you compare August 1919 to August 1980 they are fairly close, both are during cold times in the Arctic.
http://brunnur.vedur.is/pub/trausti/Iskort/Pdf/1919/
http://arctic.atmos.uiuc.edu/cryosphere/IMAGES/ARCHIVE/19800830.png
Taking in all this information and then looking at this graph of the North Atlantic temperatures.
http://i52.tinypic.com/72yjwj.jpg
It may be possible that a warmer North Atlantic water temp is responsible for a lot of the Arctic melting and the warmer Arctic temperatures.
Then there is this article to consider.
http://www.eurekalert.org/pub_releases/2008-01/du-naw010308.php
Typo : replace “2000 km^2 ice volume” by “2000 km^3 (2000 Gton) ice volume”.
Also, I did not want to single out Gavin for a response.
Please feel free to shoot down my explanation of why Arctic sea ice decline is on a near-exponential decline, still pointing at near-ice-free conditions in summer in a few years.
Also, please let us know what you think would happen with excess heat in the Arctic after a seasonally ice free ocean is common. Will it simply raise ocean temperatures ? Will ice free conditions expand quickly to August and July (or October and November) ? And how much will it enhance Greenland ice sheet melting ?
While we are at it, does anyone know of a study that shows why glacial/inter-glacial cycles did NOT occur until CO2 levels declined to some 300-400 ppm during the late Pliocene (3 million years ago) ?
http://en.wikipedia.org/wiki/File:Five_Myr_Climate_Change.svg
Could it be that the positive feedbacks in the Arctic that I mention above (snow albedo, ice albedo, ocean temperature forcing on sea ice) are strong enough to prevent a 40 W/m^2 insolation drop to create a glacial period ?
If so, then why would we think that a similar small forcing would not knock out the remainder of Arctic sea ice ? And what would prevent us from going back to that late-Pliocene climate, and corresponding sea levels ?
Mr. Dekker: Right now we are all amateurs. Looking at PIOMAS noise variation shows there is approx 1e21J heat sloshing yearly around the icepack. Seasonally gone in a decade to within the noise.
Now consider Prof. Box estimate of 1e20J extra from albedo flip in GRIS this July, and his argument as to erosion of “cold content.” And the fact that, as attested to by many (Nansen for example, Mr. Lewis on this blog more recently,) that warm ice flows much better than cold.
What will happen when the ocean has no more ice to melt ? A hard rain gonna fall on GRIS every warmth. Ablation line going up, ice surface going down. What will it do ? GRACE will tell the sad tale.
sidd
> what will happen
The End of a Glaciation”
Focus September 2012 Volume 5 No 9 pp585-674
“… the transitions from glacial maximum to interglacial conditions generally occurred over about 10,000 years. In this web focus, we present a collection of overview, primary research and opinion pieces that explore the links between solar radiation, ice-sheet melting, ocean circulation and climate that govern the transition from glacial maximum to interglacial warmth….”
…
“… Past transitions from glacial to interglacial climates have not been smooth. It would be wise to prepare for similarly sudden episodes of ice loss in future climate changes.”
#145 et seq.: It’s interesting to line this development up against natural influences. While we are higher in the solar cycle than in 2007, the current solar cycle is still one of the lowest on record. 2007 was a cooling year in the ENSO cycle, whereas this year we’re had a bit of the El Niño phase of the cycle, but not a strong one. There isn’t anything to suggest from this that any natural influence should be causing unusual warming. Next time the solar cycle goes back to its more usual maximum or next time we have a strong El Niño 1998-style, we could see a very rapid loss of sea ice extent.
However: we should be careful of looking for instantaneous connections.
What we are seeing this time is most likely the effect of long-term loss of multi-season ice depth that doesn’t in the short term decrease sea ice extent, but results in needing a year that’s not exceptionally above the norm to drive back ice area a long way, once the multi-season ice has thinned enough. GISS shows northern hemisphere summer is one of the warmest on record, but not the warmest. Local Arctic conditions could also be warmer (I can’t find data specific to that on a quick search), but you wouldn’t expect this much ice to go away all at once. Arctic sea ice volume is another trend you should relate to sea ice extent.
Have been reading in sections of the media that the Arctic ice loss is due to a natural cycle of ocean currents, and something similer happened in the 1930’s. What is the background to this?
[Response: It’s true that there was Arctic warming in the 1920s and 1930s, and this was noted in the records of the time, but the losses of sea ice pale in magnitude compared to what is being seen now. I suggest that you compare any specific mentions of some change in a part of the Arctic with maps from today – there is a huge difference. – gavin]
#81, Allen W., 28 Aug, 8:35 AM
To continue walloping a point with more info, here’s further follow up on heavy rain along the eastern coast of the southern Chukchi Sea. The accompanying photo, taken on the 25th, is probably worth a click just for novelty by anyone.
http://www.thearcticsounder.com/article/1235flood_plagues_region
Norman @160
Your first link I have recently visited (spurred by the John Christy garbage) & was less than impressed by the bit that I was interested in – Russian Northern Sea Route shipping. The link says that the 1930s have to have been less icy than the early 1900s because the shipping using the N.S.R. in the 1930s contrasts with the likes of the St Anna in 1912 that was caught in ice & carried off into the central Arctic.
Most of the specific assertions are iffy enough to ring loud alarm bells. And I was amused to read elsewhere that, like the St Anna, the Russian icebreaker Sedov was caught in ice in 1937. Two other breakers with her were rescued but the Sedov was carried off into the central Arctic, eventually being resucued only in 1940 when the Russians sent the biggest icebreaker they had to free her.
I note that the denialosphere has now picked up on some of these statements in the link with the icebreaker Sibiryukov now sailing the salty seas round North of Severnaya Zemlya in 1932 with narry a whiff of any dynamite useage to shift all the ice.
Judging from the configuration of the sea ice extent right now, The Gulf Stream may go more northward,the sinking point also moving northward.
The final scenario I thought up is The stream stops sinking in The Arctic Sea, instead goes through Bering Strait to The Pacific.
The situational evidence looks looming. In the last winter,SIE covered the strait on a two decades ago basis.
My guess is the stream pushed SIE forward toThe Pacific.If realized, global oceanic current system would change drastically.
How long has it been since the last time arctic sea ice extent-area-volume were as low as they are now? How long has it been since the last time the Arctic ocean was ice free? Is there a link to a good reference on that?
Thanks everyone for pointing out “anomaly”. Two months ago we were 4 standard deviations below trend, 4!!, and no-one thought it worthy of mention.
If you’ve been at all interested in Arctic ice conditions lately you would have read of ships cruising through 2 meters of “ice” without the crash and bang of ice breaking because the “ice” was the consistency of a slushy. When a floating slushy is agitated by stormy seas is it any wonder that it disappears?
> ships cruising through 2 meters of “ice” without the crash
Help me out here, as Google hasn’t been able
to find a source for that, for me, today.
Where’d you learn about that?
PS for Cowichan
> two months ago
The June anomaly was mentioned in widely read sources, for example, here:
http://nsidc.org/arcticseaicenews/2012/07/rapid-sea-ice-retreat-in-june/
#165, DP. If there was a warming in the Arctic it was not extensively measured due to lack of weather stations especially on the North American side of the Arctic. However a good way to judge the sea ice melt would be to look at end of August 1938 extent map as recorded by DMI
http://brunnur.vedur.is/pub/trausti/Iskort/Pdf/1938/1938_08.pdf
and compare with end of august Cryosphere today:
http://arctic.atmos.uiuc.edu/cryosphere/NEWIMAGES/arctic.seaice.color.000.png
As it all melts the tides-current and dominant winds eventually force the ice to ridge to the Greenland North American sid. In effect, more observations from the Russian side basically show a vast area of ice still present and surviving till the beginning of the 21st Century.
Kozo Nagase @168 — First heck the volumetric constraint on currents through the Bering Strait. It is narrow and shallow.
John Kintree @169
This link comes from the answer question page of the National Snow and Ice Data Center that produces the graphs used in many arctic climate studies.
The ice may have been less than today about 5500 years ago.
“Based on the paleoclimate record from ice and ocean cores, the last warm period in the Arctic peaked about 8,000 years ago, during the so-called
Holocene Thermal Maximum. Some studies suggest that as recent as 5,500 years ago, the Arctic had less summertime sea ice than today. However, it is not clear that the Arctic was completely free of summertime sea ice during this time.”
http://nsidc.org/arcticseaicenews/faq/#summer_ice
So? You do understand that the current human population is orders of magnitudes greater than then?
Or are you suggesting that since, in the past, natural causes dominated, that today, our CO2 emissions don’t? That would be lame, surely you’re not *that* lame, are you?
And, of course, our main worry is going forward … as things are shaping up, we’re going to blow out any semi-recent comparisons right out of the water in the next few decades.
Question
http://www.nature.com/ngeo/journal/v5/n9/full/ngeo1528.html
Why did glaciers not cover Siberia? Or is it just not shown?
=======
Question
“[T]he Laurentide Ice Sheet residing in the Hudson Bay marine basin collapsed”
“However, once the Laurentide Ice Sheet became predominately marine-based over Hudson Bay during TI, it underwent a relatively rapid reduction in area5, 74, 75 (Fig. 5e), analogous to a lagged-nonlinear response.”
So “collapsed” doesn’t mean all in one day? “Collapse” is such a dramatic word to use instead of “melt.”
I see that the authors of the article are working on the second question.
“For the lagged-nonlinear model, the Barents-Kara Ice Sheet may have taken several millennia to fully collapse63, 64, 65, 66, a significantly longer period than present concerns over future eustatic sea-level rise98. However, the final collapse of the marine portion of the Laurentide Ice Sheet at ~8.2 kyr ago occurred in less than 130 years and raised eustatic sea level 0.8–2.2 m75, which is a timescale of more importance to global society98.”
Some studies suggest that as recent as 5,500 years ago, the Arctic had less summertime sea ice than today.
Begging the question, when was “today?”
In the holocene optimum, insolation in the northern hemisphere was much higher in summer, as earth was in its perihelion then at this time. This has been abundantly pondered on in this blog. That we see similar conditions with the opposite orbital forcing is quite remarkable, and not a good reason to downplay things in lukewarmer lingo.
Marcus
Sidd said :
Sidd, climate models seem to indeed project a steep decline in Arctic sea ice extent, but actual ice losses are now 4 sigmas (SD’s) below model projections. This seems to suggest that the Arctic in reality is much more sensitive than IPCC model projections indicate.
[Response: This is no longer true. See Stroeve et al referenced above. – gavin]
Some scientific papers suggest that “internal variability” of Arctic climate is responsible for the larger-than-expected drops in ice extent.
And these may indeed be right, but there comes a point where the probability of “internal variability” as the cause of sea ice decline is no longer statistically reasonable, and we would have to look at other causes, such as snow albedo effect and ice-thinning due to warmer ocean currents, and the 4th order ice reduction function I suggested in post 159.
Incidentally, does anyone have any data on the snow anomaly that is projected in GCM simulations, and if this anomaly even remotely resembles the actual snow anomaly in June 2012 of 6 million km^2, which adds an extra 1000 TW into the melting season ?
The putative warming imbalance of the planet is 0.9W/sq.m of 145E20 Joules/year.
Arctic sea ice reduction accounts for about 1E20 Joules/year – 1/145th of the planet’s supposed energy gain or 0.7%.
This is from a surface area inside the Arctic circle (66 degN) of about 4% of the Earth’s surface.
Could someone explain why we are so worried about the Arctic rather than any other 4% patch of the Earth’s surface?
dhogaza @176
I was not making any suggestions with my reponse. I was answering questions from John Kintree @169. He asked for some links on past ice cover and I provided him with them.
Rob Dekker@180
Regarding Snow Cover projections from models. AR4 give figures from Chapter 6 of ACIA which ACIA break down into quarterly anomalies for 2071-2099 (fig 6.5 p200). Given the spectacular anomalies of early summer in the last few years graphed here (usually 2 clicks to ‘download your attachment’), the projected end-of-century figures do suggest an underestimation (in a similar way to sea ice). So far winters have been getting snowier which masks the annual averages, but the summer snow cover is the factor for the fragile Arctic climate. This year’s MAM anomaly was -2.2, about a third of the max projected for 2100 & this year’s JJA anomaly will probably exceed the max end-of-century projection!
AVERAGE SEASONAL ANOMALIES (M sq km)
SEASON . ACIA AVE . (ACIA MAX) . 2010-2012
DJF . . . . . . -3.8 . . . . . . . . . (-5,8) . . . . . . +1.7
MAM . . . . . -4.9 . . . . . . . . . (-6.8) . . . . . . . -1.8
JJA . . . . . . .-1.1 . . . . . . . . . (-3.2) . . . . . . . -2.6
SON . . . . . . .-3.3 . . . . . . . . . (-4.6) . . . . . . . +0.7
It’s a bit of untold Northern drama that I came across just a few weeks ago.
178 dbostrom: Good point Doug. There seems to be persistent interest in 5500 YBP, various interglacials, the PETM, you name it. Here’s the problem with that: we don’t live in the PETM, or whenever else. We live here and now and this is the only climate we’ve got. The world’s societal and agricultural infrastructure has developed in response to the climate we have (or perhaps more appropriately, used to have…) . It’s worth repeating the closing statement from the recent AMS Climate Change Statement: Prudence dictates extreme care in accounting for our relationship with the only planet known to be capable of sustaining human life.
> Norman says:
> … I was not making any suggestions …. I was answering questions …. He
> asked for some links on past ice cover and I provided him with them.
Well, you provided him with some, but not particularly recent ones.
He presumably wanted sources from current science.
Beware answering by copypasting references you find elsewhere in blog argument.
Often the same stuff is “cited” over and over to spin the discussion.
Use Scholar, limit your search to recent work, look for papers that have been cited frequently and articles that review the field.
Or use Google with the same search terms;
You’ll find things like this:
http://anthro.palomar.edu/homo/images/map_of_glaciations.gif
from http://anthro.palomar.edu/homo/homo_3.htm
Confusing for some but fascinating for most here at RC is this map:
http://www.esrl.noaa.gov/psd/map/images/rnl/sfctmpmer_01a.rnl.html
even without a great deal of ice the sea surface temperatures appear mostly normal over open water, but warmer over what is left of sea ice.
Again as I predicted and always wrote: its because of the clouds:
http://www.weatheroffice.gc.ca/data/satellite/hrpt_dfo_ir_100.jpg
So much clouds that the average temperature during the last 30 days:
http://www.esrl.noaa.gov/psd/map/images/fnl/sfctmpmer_30a.fnl.html
Appears totally Normal over the Arctic Ocean even during the entire melt season:
http://www.esrl.noaa.gov/psd/map/images/rnl/sfctmpmer_90b.rnl.html
The warmest air was over the area where the ice resists melting. Meaning that there is an interesting exchange going on between open water and the near permanent cloudy Arctic ocean sky. I will have a refraction based analysis soon on this, lets see what the sun disk has to say about this.
Rasmus: thanks for posting your R code. I tweaked it a tad so I could see the text in a smaller scale and took out the background in my response to all this. Short summary: sea ice can go fast if you don’t pay attention to volume and only look at area.
And we mustn’t forget that about 90% of warming goes into the ocean, and not too big a shift in where ocean heat content ends up could make a big difference to sea ice.
@Gavin
I don’t see how your response to the following is supported by Stroeve et al.
>>
Sidd, climate models seem to indeed project a steep decline in Arctic sea ice extent, but actual ice losses are now 4 sigmas (SD’s) below model projections. This seems to suggest that the Arctic in reality is much more sensitive than IPCC model projections indicate.
[Response: This is no longer true. See Stroeve et al referenced above. – gavin]
>>
The appropriate quote from abstract:
Trends from most ensemble members and models nevertheless remain smaller than the observed value. Pointing to strong impacts of internal climate variability, 16% of the ensemble member trends over the satellite era are statistically indistinguishable from zero. Results from the CMIP5 models do not appear to have appreciably reduced uncertainty as to when a seasonally ice-free Arctic Ocean will be realized.
Another paper, by Maslowski et al. (2012) states:
The inability of climate models to adequately reproduce the recent states and trends of Arctic sea ice diminishes confidence in their accuracy for making future climate predictions. Another issue is that sea ice extent and area are parameters that only partially account for the loss of sea ice volume. An unrealistic sea ice–thickness distribution will affect the modeled ice extent and area as well as volume, which in turn may delay (or accelerate) predicted changes in seasonal sea ice cover in the Arctic Ocean. This fact emphasizes the need for detailed analyses of changes in sea ice thickness and volume to determine the actual rate of melt of Arctic sea ice.
By the way, in the earlier discussion of the ice free Arctic you (the group) concluded
It is possible that this analysis will change the predicted timing of the “ice free summers” but large uncertainties will likely remain. Until then, we believe, we need to let science run its course and let previous model-based predictions of somewhere between “2040 and 2100″ stand.
Are you entirely sure, that when the reality is more and more divergent from the models, it should be wiser to stick to data, instead of trusting the models?
[Response: You are over interpreting what I said, and your last statement is a completely nonsensical statement. That might sound a little harsh, but think about it for a minute before responding. There are two issues here: a purely factual one related to whether the CMIP5 models show a spread of declines that encompass the observed decline – and in agreement with my statement above – they do. Second there is the issue of how to make predictions in the light of the observed trend and spectrum of model results and infinite possibilities for statistical projections. Since we do not have any observations of the future (yet), any projection must require a model of some sort. There is no projection that just ‘follows’ from the observations absent some statistical model of the underlying behavior, hence your dichotomy is nonexistent- the only choice you have is in deciding what models you want to pay attention to and on what basis. – gavin]
Could someone explain why we are so worried about the Arctic rather than any other 4% patch of the Earth’s surface?
Because quite a lot of research suggests that weather over much of the northern hemisphere is heavily influenced by that little patch at the top of the planet. You probably already knew that but what the heck, a rhetorical Hail Mary in a tight spot might be distracting to a few people.
I used to think I wouldn’t care when I went bald. The reality proved different to what I imagined might happen as I followed my genetic heritage. What I didn’t realize was how much worse it would be to have a wee little bald patch surrounded by a generous tonsure; changes the whole look of things, quite disproportionate to area. :-)
An empirical equation for arctic sea ice volume:
V — Annual average sea ice volume
V’ — Rate of change of V
Somewhere somebody posted a link to a paper which contained phase diagrams (V on the horizontal axis and V’ on the vertical axis) derived from several different GCMs projections to century’s end. The general shape of these diagrams gives rise to a particular equation for
V’ = f(V,dT/dt)
where dT/dt is the rate of change of arctic (surface air) annualized average temperature. We take dT/dt = k (approximately 0.053 degrees Celcius per annum).
Now clearly V’=0 when V=0 but also V’=0 when the Arctic Ocean is full of ice (any overflow leaving via Fram Strait is ignored). Let m denote the maximum sea ice volume.
The resulting equation (to approximately match the phase diagrams) is
V’ = kV(V-m)
which integrates to a qubic equation for V.
Statistican George Box said words to the effect that all models are wrong but some are useful. This model is presented to stimulate discussion.
Followup From #186 , Satellites seem OK, http://eh2r.blogspot.ca/ , it is not an anomaly, malfunction or misread, the arctic atmosphere appears to have an “average” temperature. More reading will reconfirm.
{Oops. An oversight, apologies.]
The integrated solution is
V = m/{exp(kmt)-1}
which is much more interesting.
Ken Lambert:
Ken’s asked this question elsewhere. Maybe he’s hoping to get an answer he likes better here. Nah, he’s probably just trolling.
Jim Larsen: “Well, when scientists have NO CLUE what sort of fit is appropriate, the fit that fits reality best is by definition the default fit.”
Uh, no. There are other criteria, as well. Otherwise, the “model” would change any time you had a fluctuation. Simplicity (which corelates to predictive power) and physical reasonableness are also important criteria.
An exponential fit simply is not reasonable, as the amount of sea ice lost would have to be proportional to the amouth of sea ice lost in the recent past. For an exponential fit to have a chance, YOU would have to show us at least a plausible argument for why dx~axdt.
Ken Lambert,
The answer to your question is that this 4% of the planet has an outsized influence on the climate of much of the northern hemisphere, has very high abedo at present that will decrease dramatically once the ice melts, And has so damn much carbon under the ice that if it is realesed, for all practical purposes its “GAME OVER”. That help?
That’ll confuse everybody: my 5:57 pm comment is to correct my 5:37 pm comment (which is still in moderation).
Is there some common defining characteristic for the models that do roughly correspond to observed decline rates. For example, in these models, can we compute the oceanic heat flux across say the 70th or the 80th parallel to see if the ‘better’ models transport more heat into the Arctic icecap ?
sidd
MARodger,
Thank you very much for your post at Neven’s on the “untold drama” of snow cover anomalies.
Since snow cover anomalies happen when the Arctic sun is brutal (May/June/July), as opposed to ice cover anomalies (which tend to maximize in August/September, when the strength of the sun is much reduced) and they affect a larger are than ice cover anomalies, it seems that snow anomalies are the 600 pound gorilla in the room that few talk about.
Also thank you very much for the link to the AR4 model projections for snow cover anomalies. It seems odd to me that the simulated snow cover anomaly in May, using AR4 models, is lower than the anomaly in June.
Basic physics of polar amplification would suggest that if the May anomaly is X, that the June anomaly would be larger than X. After all, when snow disappears at some latitude, the albedo difference should cause a significant additional forcing to occur, which should make the snow anomaly at higher latitude larger, as long as insolation is larger.
Does anyone know if there is a paper that explains why the MAM snow anomaly in AR4 models is smaller than JJA snow anomaly ?
Which physical effect could be responsible for that inconsistency ?
Gavin, with all due respect, but I think that “pohjois” and “sidd” have a point.
You are correct that Stroeve et al 2012 show that “the CMIP5 models show a spread of declines that encompass the observed decline – and in agreement with my statement above – they do”.
Still, Dr. Stroeve explained on a different blog (where people are not by far as nice as here) the following caviats :
Such statements, combined with the statement in the abstract :
http://www.agu.org/pubs/crossref/2012/2012GL052676.shtml
seem to suggest that Stoeve et al suggests that we are simply still running in a ‘low’ probability area of the CMIP5 simulations. In other words, this (below 4 million km^2) 2012 minimum may still be an artifact of “internal variability”, albeit at a low probability curve…
Now, Stoeve et al may be right or not, but at least is that a correct summary of what Stroeve et al 2012 are telling us ?
If this is the message from Stoeve et al 2012, the question that emerges is : how high is the probability is that reality is indeed a artifact of “internal variability”, and that thus a “recovery” may be imminent ?
And how high is the probability that this trend is NOT due to internal variability ?
And how do we know if it is, or is not ?
What is the probability that the decline of Arctic sea ice is NOT a result of internal variability, but in fact a result of high sensitivity of the Arctic to small forcing perturbations, such as what Maslowski’s models project ?
And what is your opinion on other papers, such as Massonnett et al 2012, who state :
http://www.atmos.washington.edu/~bitz/massonnet_etal_GRL_SUBMITTED.pdf
Would that not suggest that we have just entered a timeframe where Arctic sea ice is susceptible to “elevated rate of decline” ?
Thus, when you say “your dichotomy is nonexistent- the only choice you have is in deciding what models you want to pay attention to and on what basis.” would it not be rational to pay attention to Maslowski’s models, and to address the physical basis of a 4th order polynomial decline in Arctic sea ice as I suggested in post 159 ?
whether the CMIP5 models show a spread of declines that encompass the observed decline – and in agreement with my statement above – they do. Second there is the issue of how to make predictions … There is no projection that just ‘follows’ from the observations absent some statistical model of the underlying behavior, …. – gavin]
Yep, we know you guys are hot on the trail and will eventually nail sea ice loss to within natural variability, and will be able to predict or explain the results of that variability to great accuracy. We also know that current models’ median runs underestimate sea ice loss to the extent that multiple papers have been published noting it, with one using that fact as the lead, even separated by white space and worded like a newspaper headline. You can understand how that doesn’t bestow confidence in short term results of current models.
So, when scientists are essentially saying that reality is 2-3(?) sigma off median, and those same scientists were saying a few years ago that reality is 4(?) sigma off (as always, counting data through today), then I’ve got to wonder if you guys are “there” yet. Anything over 1 sigma maintained for many years is a serious red flag unless it is explicitly explained. If one can’t explain natural variability after it happened, then one’s model isn’t done yet.
I would love to see median runs for current models, as well as 3 sigma low runs (how many runs are done?). I’m guessing 100% of the readers here would also love it. Then we would know what you mean by “encompass”. if one model’s lowest run matched reality, I wouldn’t be convinced the models were reasonable representations yet, especially if reality’s “input variables” didn’t match the low run’s randomly generated inputs.
Science strives for bottom-up solutions, as that’s the way to get to “proof”. But humans are designed for top-down thinking. Calculating the distance a ball will fly when propelled by a complex mechanism of bone and tissue is near impossible for nearly anybody except an average math-illiterate kid.
10 years ago I top-down figured the ice would be essentially gone (below 1) by 2020, so I made a bet on 2025. Perhaps the residual ice pack will be larger than the bet’s arbitrary definition, but the appropriate “model” to use is often the most complete one, and currently I’m guessing that no computer model can “throw an ice ball” as well as the one we were born with – not a simple fit/extrapolation, but a holistic solution which includes things like scientists’ personalities in the analysis.
You said exponential fits have no basis in physics. OK, but they sure can be approximations for results caused by multiple linear forcings which are seasonal and were/will be initiated at different times and act on different variables (area, volume, flow rate, etc), especially when the need for accuracy ends with such a large ice pack (1 at minimum).
As I said before, I accept I’m likely wrong – but my wallet is feeling pretty comfortable right now.