Yesterday I posted the betting script for bets on September NH Ice Extent. For clarification: we are using the values for ‘NSIDC September- average NH Ice Extent’ which will be published here: ftp://sidads.colorado.edu/DATASETS/NOAA/G02135/Sep/N_09_area.txt. This matches ARCUS sea ice bets. Results can be announced when NSIDC updates in early October.
When I first posted the script I tested it out snapping up the ice level for last year: 4.61 million km^2. But I don’t believe that’s the most probable value. This morning, I downloaded some data, and did a quick fiddle. When I’d finished I entered 4.411 km^2. Since this is betting, my bet provides no uncertainty intervals and I am overly precise.
Below I plotted the my “best fit” curve fit and it’s 1.96*sigma uncertainty intervals:
As some might recall, last year I played around with fits that I concocted by:
- Concocting a bunch of candidate regressions forms and assuming the “correct” fit must be one of those fits.
- Determining the probability that each fit is “the” correct one based on AIC.
- Creating a best fit by taking the probability weighted sum of the candicate fits. Uncertainties were similarly computed based on these.
There were a number of tweaks last year (because I had lots of candidate fits!) But so far this year, the “candidates” are: a) Linear, b) Quadratic, c) Cubic, d) 4rth Order, and e) Gompretz fit of September NH ice extent to year. Weighting all together, I predict a “best” value of 4.411 km^2 and a ±1.96 sigma range of [3.27, 5.55]. So, according to my statistical model, there is a decent chance the ice extent will fall below the 2007 minimum. Mind you: I haven’t taken into account information on current ice volume, April extents, population of Leprechauns or the numbers of nails in Lukewarmer coffins. We can start to expand my method of predicting the ice level later on.
With this, I invite people to enter their bets on extent and, if you wish, explain how you obtain your estimate.
If your “best” value is 4.411, then why did you bet on 4.111?
Typo?
Skeptical— Typo in post. I bet 4.411.
I bet 4.29.
Lets see. Nothing in the state of the ice suggests that we will
see a better year than last year ( 4.61 ) so I’d take the under bet, that is under 4.61.
looking at concentrations versus 2007 I note that the concentrations appear lower. but 2007 had some freaky winds.. so I’d take the hunch that the two will balance and we’d hit around the 2007 number of 4.3. I pick 4.29 just in case we do crush the record and I can say that I predicted below the record.
In short: only a fool would bet above 4.61. all the betting action
will take place between 4.3 and 4.6, for psychological reasons I choose below the record.
Steven Mosher
Well not everyone may agree with that:
Heavy ice could delay start of Shell Alaska’s Arctic drilling
“In short: only a fool would bet above 4.61.”
Why would a reasonable person make an arrogant statement like that?
Barry, hush! Keep them low ball. 😉
Don B,
A reasonable person wouldn’t. You haven’t figured out Mosher yet? 😉
Foolish me, I’m going with 4.8 x 10^16 cm^2. I’ll take home field advantage on the Bering Sea heavy ice this year. Does ARCUS have wishcast as an option for a type of prediction?
Earle Williams –
Mosher said that only a fool would bet above 4.61.
He didn’t say the sea ice wouldn’t be above 4.61. 🙂
this is great! not a hint of any pseudo-scientific input a la Arthur Smith.
anteros is spoiling my game.
Based on last year’s september extent ending just above the linear trend for the last twelve years. I’m going to bet on 4.393 million km^2 (the straight 12 year linear trend projection minus just a tiny skosh).
But with normal variability I wouldn’t be terribly surprised at anything between 3.9 and 4.9 (although I would tend to think low in that range is more likely than high based on the current ice extent).
I think that’s on of the many methods lumped under “heuristic”.
Mind you: Statistical can also be “wishcasting” if you change your method to get the answer you “like”.
Benjamin, I don’t think a linear trend is the best way to model recent ice loss. Not even linear trend + noise. There’s a definite breakpoint around 2002, and a phase change in the annual cycle that happens around 2007.
Note the unsubtracted annual variability post 2007 in the anomalized data here and the “cliff” the anomalized series falls off circa 2002.
Nonetheless, it will be fun to see how close you are!
Carrick, I agree that it is likely underestimating the long term loss of ice
because the loss isn’t linear but rather accelerating. But the breakpoint wasn’t 2002. It was about 1994. If you examine the ‘trend of the trends‘ it is clear that the fundamental change happened about 1993/1994. Since then it there has been a relatively steady acceleration in the trend rates.
But trying to predict any single year is fundamentally a game of plausible guessing. The annual noise in the system is much larger than the long term rate of ice loss per annum no matter what (physically reasonable) model you choose to use.
Hi Benjamin,
Thanks for the comments, but do you have the correct axis there?
Your graph says “Antarctic Sea Ice Extent”.
I notice you also just are picking September. Likely that is injecting noise because technically what you appear to be doing is decimating a series without first applying a dealiasing filter—and what that does is take high-frequency noise and alias it into the low-frequency part of the spectrum that you’re trying to analyze.
In any case, derivatives are pretty noisy, so you’d need to put error bars on that quantity before we could know whether they were significant.
I’ve also looked at the rate of ice loss, and while it’s pretty clear that 2002-2007 is a period of accelerated ice loss, I’m not sure it’s defendable to claim either that the rate of ice loss 2007-2012 is greater than 2002-2007 (which is what would be implied by a “steady acceleration in the trend rates”) or that 1993/1994 is even a particularly interesting year.
This is what I get for the rate of ice extent loss using 5-year window with a sliding rectangular window.
The period 2002-2007 stands as an outlier compared to the rest of the data set (well outside of the 95% CL range), however, prior to 2002 and post 2007, the main feature looks to be an ENSO-related oscillation, and possibly a tiny linear acceleration that I believe fails to achieve significance.
Of course I agree with your comment about inter-annual noise being much larger than the effect associated with secular ice loss.
Speculation alert level orange:
I don’t know how much validity to assign to them, but the rates I found in this graph were systematically at a minimum during El Niño intervals, and near a maximum in La Niña intervals. Since we’re currently sliding out of a La Niña, perhaps that suggests we should expect somewhat less ice loss than we saw last year (during a strong La Niña period)?
Related brain-food here.
My bet is going to be a WAG, so I’ll take Steven Mosher’s advice and bet above 4.61… I think 4.66 sounds good.
It appears to me that 2012 will see a new low, based on only the extent and shape of the multi-year ice:
http://www.aari.ru/odata/_d0015.php?lang=1&mod=0&yy=2012
The ice age chart raises questions, though.
Why, if the Arctic sea ice loss is due to warming, is the multi-year ice so asymmetric – nearly all the multi-year ice in the western arctic?
Were the ice loss thermodynamic, wouldn’t one expect a more or less symmetric ever shrinking remainder of ice centered on the pole?
On the other hand, if the ice loss is dynamic, when will it cease?
I’m not sure what you mean by “ice loss thermodynamic”. But we don’t necessarily expect ice to bet totally and completely centered on the pole. Geography and wind do matter. There are places where warm water can flow is and places where ice can exit. In other spots, land prevents flow. If climate were not variable we’d see the September minimum vary and ice coverage would not be perfectly concentric around the pole, but the Sept minimum would tend to oscillate up and down around some preferred average level.
Assuming there is a warming trend, the September minimum will cease to decline after it hits zero and stays there for a while. When that will happen I don’t know.
This is a mugs game. If, as is suspected, the amount of ice is due primarily to ice export winds (or lack of), and secondarily to temperature.
.
In other words, to get an accurate number, we have to accurately predict the WEATHER for the next 3 1/2 months.
.
But, a I am a mug (or a fool, according to Mosh), and down for 4.85….
Climate weenie: the Artic Gyre is now counter clockwise. Ice is tranported to the islands and northern Greenland, and piles up there. As the ice melting in situ is less than what piles up, the next year it is “old ice”. That is why it looks asymetric.
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When the arctic gyre is clockwise, ice is exported out via the Fram Strait. It dosen’t get a chance to become old ice. Most ice loss is thought to be from this process. There are some good time lapse views of the gyre, but I don’t have a link, sorry.
It is the correct axis. It was just mis-labeled. I’ve fixed the label now.
I am a bit bemused by your moving from my 5 year averages of 11 year trends to simple 5 year trends because that makes the noise problem significantly worse, not better. Instead of a clean chart stripped of high frequency noise you end up with a very noisy chart with the underlaying trends obscured.
My long windows with averaging remove high frequency noise quite efficiently (as is reflected in the smoothness of the final curve) while your 5 year trends are extremely noisy (also reflected in the jaggedness of your final curve).
I’ve run the same procedure on August, September and October as a three month average and it tells the same story – there is an inflection point around 1993/1994 and an accelerating rate of loss since then.
If the effect was just some kind of very high frequency noise ‘sloshing’ loss around from nearby months around you would expect to see severely different results from averaging in the three months versus the single month.
And you don’t.
Addendum for clarity: When I said ‘inflection point’ above I was referring to the acceleration of the rate of loss. It changed from a decreasing rate of loss to an increasing rate of loss.
Lucia, regarding loss to melting versus loss to advection, there is some suggestion that the last few decade’s loss in Arctic sea ice is due more to export to the Atlantic than it is to increased melting in place.
Certainly that’s the impression I get from staring at the movie:
http://seaice.apl.washington.edu/IceAge&Extent/Rigor&Wallace2004_AgeOfIce1979to2007.mpg
It is a key question, though a dynamic explanation argues for an eventual reversion to the mean of circulation and an increase ( if not back to normal ) of sea ice.
I’m curious, what do you, and what do readers make if the DMI data?
http://ocean.dmi.dk/arctic/meant80n.uk.php
If the DMI data are accurate, then looking back from the 1950s, there is not a particularly good correlation between temperature and sea ice changes.
Les, it very much appears from the axis of older ice protruding southward along Greenland’s East Coast, that export of Arctic sea ice is still occurring.
Climate Weenie–
Could you explain why you think “If the DMI data are accurate, then looking back from the 1950s, there is not a particularly good correlation between temperature and sea ice changes.”. The link just goes to a page with a graph of the annual cycle, the current trace and a bunch of other links.
Yes. Some people think ice loss is due to export. Others don’t.
Nevertheless, I think it is clearly true that if the earth surface temperature oscillated around something 5C higher we would see less ice at the pole and if it oscillated around something 5C lower we would tend to see more ice at the pole. We would still see oscillations about the respective average levels due to transport (or other variability). With respect to my current comment, I’m not making any claims about the time scale for various oscillations.
What I’m saying is more inline with saying something like “because it’s close to the sun, all other things being equal, we expect Mercury to be hotter than Mars. ” We do.
Lucia, since 2000, the Arctic sea ice has continued to decline, but the melt season temperatures since 2000 appear normal, with 2003, 2004, 2005, 2006, 2009, and 2010 melt season temperatures appearing to be slightly lower than the long term average.
Compare those years with 1958,1959,1960,1961,1962 which appear to have melt season temperature slightly higher than the long term average.
To the extent that the DMI data are correct, it is evidence contrary to ‘warming’ causing the sea ice loss. On the other hand, in place buoy motion provides evidence that loss to the Atlantic has and is taking place.
It will be interesting to see what happens in the coming decades.
Benjamin:
You shouldn’t be. 5 years is the ENSO period. Going to 11 years smears out physics, not just noise.
Not really true.
Going to a longer window smears out events with a shorter duration, which is all you’ve done. You’ve then misattributed the smearing of your filter to real physical processes.
The criticism I had with you pulling just September I guess you didn’t understand. You are giving up approximately a factor of sqrt(12) in SNR by just using September instead of using anomalizing data (as I have done). That more than offsets the sqrt(11/5) factor that you are so bemused about.
Er no. No signal processing background I presume? Otherwise you’d know this isn’t true.
The high frequency noise is (nearly) white after spectral alasing. Selecting one month raises your noise floor by sqrt(12). (Indeed, it gets whiter as the decimation factor you use increases.)
I take it you’re grumpy because my results contradict yours (and probably your prior expectations), but what I have done is completely defensible, and doesn’t suffer from the warts that are present in your processing.
Another thing—Changing the filter window size doesn’t magically make an effect that was not significant suddenly significant. If you perform the statistical analysis correctly, when you smooth, you introduce autocorrelation which of course reduces your ability to resolve features like acceleration in trend from noise. Typically the two effects just trade off.
There are specific cases where pre-smoothing followed by a polynomial fit can give you an improvement in the SNR of the metric of interest (I guess second derivative here). A particularly example is the presence of blue noise ($latex S(f) = S_0 f^\alpha$ with $latex \alpha > 0$).
If you look at the spectrum of the anomalized series, it’s red ($latex \alpha < 0$) not blue. Pre-smoothing has no beneficial effect on SNR of a linear (or quadratic) trend estimation in this case.
The reasonable thing to do here is fit the entire anomalized series to a quadratic polynomial, then verify that the residuals make sense (e.g., that they are stationary, if they are correlated, autocorrelation-corrected). There is a problem here, because if you do look at the residuals of the fit (yes I've done this), you'll find the residuals aren't stationary, and that puts a bit of a crimp on performing significance testing for this data.
The nonstationarity arises principally for reasons I pointed out above: The 2002-2007 "what the heck" period and the post 2007 change in phase of the annual cycle.
I love the way skeptical people conclude that the wind dunnit.
in some sense that is true. When rotten ice is compacted by winds and currents.. ya, the wind dunnit.. not the rotten part, but the compaction. And when wind/currents move ice to warmer waters where it melts.. ya the wind dunnit. sorta.
which makes me wonder what secular change has there been in wind since 1979. It would appear that the ‘winds” been doing it for some time.. just how? numbers help..
Smart money is down around the 2007 record. dont everybody bet there at once.
Steven Mosher:
Got it. You’re betting around 4.8
Ice betting and using and explaining models. That I like. Lucia, as a neophyte bettor I need to know how I obtain some Quatloos for placing bets. I am hoping for a good exchange rate.
Kenneth: Triskelion.
Kenneth –
I can loan you some, but I’m afraid I take interest on a weekly basis, and it’s not cheap 🙂
Carrick –
My thinking as well.
Perhaps we should have side bets on Mosher’s bet?
Anteros:
Actually, I want to bracket his bet (I’ll be Mosher + 1e-6 and you be Mosher – 1e-6)…
^_^
Arrrrrrg.
http://www.youtube.com/watch?v=nOQTApMvIqY&feature=related
Steven Mosher
Don’t worry, your triple bluff is safe with me 😉
I’ve been looking as anomaly plots. They are currently quite high relative to recent years.
Nick–
Are you going to place a bet? Obviously, it’s a crap shoot for most of us. I try to make ‘better’ predictions later on– but we never know until we know!
Lucia,
It would be a SWAG for me too. Last year drummed into me how things can change. But it’s running high at the moment.
I’ll make a bet in the morning if inspiration strikes 🙂
OK, I made a modest bet. And followed Mosh’s advice in a roundabout way:
“In short: only a fool would bet above 4.61. all the betting action
will take place between 4.3 and 4.6, for psychological reasons I choose below the record.”
If you bet where angel’s rush in, you get a smaller spread for your quatloos. So I bet 4.62.
looks like all the action will take place below the
record and above last year.
lucia there is still time to change your
bet
Mosher:
“which makes me wonder what secular change has there been in wind since 1979. It would appear that the ‘winds†been doing it for some time.. just how? numbers help..”
I assume you’ve read the book:
http://seaice.apl.washington.edu/IceAge&Extent/Rigor&Wallace2004.pdf
and seem the movie:
http://seaice.apl.washington.edu/IceAge&Extent/Rigor&Wallace2004_AgeOfIce1979to2007.mpg
It’s kinda like the icicle as the perfect murder weapon, because the evidence disappears.
The animation indicates that is not the ‘rotten’ ice that’s leaving, but the good stuff and that’s the problem.
It’s not unreasonable to suspect global wurmin for ice decline – global air temperatures are up, oceanic heat content is up.
It’s just that in the Arctic during melt season, temperature doesn’t appear to correlate very well with ice loss, while advection of ice does correlate with ice loss.
When one looks back at the peak in Arctic temperatures in the 1930s and 1940s, one can imagine a similar dynamic ice loss having occurred, releasing ocean heat and accounting for the higher temperatures ( similar to the fall through spring peak now ).
Recall also that the coldest North American winter on record was 1979 (giving rise to the birth of the SUV and costing mayors their jobs when they couldn’t keep the trains running in the ice and snow). Multiple factors are involved for such events, but among them
could very well have been a maximum in Arctic sea ice, allowing for colder air mass formation because the ocean heat was better sealed off. And 1979 is when numerous satellite records began.
Speculative? yes, but so is ascribing warming for the Arctic ice loss.
The problem is that tying events to global warming that are not ‘unreasonable’ may also be wrong.
Remember the frogs dying? Global warming is killing the frogs! Seemed reasonable, but it was wrong – fungus spread by those studying frogs.
Remember the bees dying? Global warming is killing the bees!
Seemed reasonable, but it was wrong – parasites.
Remember the Hurricanes? Katrina was the poster girl for a record year. Seemed reasonable – hurricanes increase strength when they traverse warmer waters. But wrong. ACE is down with increased warmth and moving from cooler to warmer waters for a tropical cyclone is not the same as gradually warming the water and atmosphere across the tropics.
Is Arctic sea ice another example of chasing the hypothesis?
I dunno, but I’ll wager one quatloo that Arctic sea ice will by up by 2020.
Oh my,
I should of course have betted 4.30 to hedge for Stephen Moshers bet.
However I’m happy to jump into the fools line, and when applying the gas-station-localization-principle, I go for 4.62(hedging for those eventually betting on the upper limit).
Cassanders
In Cod we trust
Parsomatics has been renamed reflexive nanoscale fisking. Just thought you needed to know
My Eli!
You are inventive.
By the way I can invent words too. I coined the word “sockulator”. Some people other than me actually use it.
Ms. Rabett prefers counted cross stitch.
weanie. Neither of those papers answer the question I asked.
If you want to attribute all of the ice loss from 1979 to today to “wind” then you will have to better than that. Does the wind play a role. sure. But when you have a model that can predict the ice area and volume as a function of the wind step up and get your nobel.
Woke up this morning, cold, rainy, pain in the broken bones and in the mood for more ice ! 4.666 million km^2, final offer.
5.56 million ;P
4.9 million because I dont see many others at that level so far.
I have bet 4.32, based on least-squares fit to a logistic function. (The logistic function I use is the cumulative Gaussian normal distribution.)
FWIW, the least-squares fit shows a maximum of 7.47 (pre-industrial) and goes to zero at 2028, with an inflection point reached in 2025. Which means we’re still in a downward-acceleration phase.
nice KAP.
show your work. I wanna steal it
No inflection until 2025? Interesting.
Nick Stokes (Comment #96744)
May 31st, 2012 at 1:53 am
I’ve been looking as anomaly plots. They are currently quite high relative to recent years.
————————————————-
I think the volume anomalies are more pertinent to predicting extent.
Only if they can be measured accurately.
Owen #97424
Volume anomalies are now shown here.
FWIW, Cryosphere Today shows Arctic sea ice area (not extent) is now at an all-time low for this date (June 13).
http://arctic.atmos.uiuc.edu/cryosphere/arctic.sea.ice.interactive.html