Sea Ice Bet: Atmoz Challenge (try 3)
Atmoz proposed a bet on the summer sea ice extent and placed his bet at 7.7 million km^2, using an ordinary least squares (OLS) regression on data from 1950 to last year. This means he is predicting the ice will be well above last years record low of 5.557 million km^2.
I predict 7.4 million km^2 using Cochrane-Orcutt, applied to the same years. My calculation assumes an autocorrelation for the residuals of ρ=0.11. My prediction is illustrated by the yellow triangle in this graphic:
Caption: The solid blue line indicates the best-fit regression for the temperature as a function of year, not knowing the temperature for the previous year. My predicted value, shown in yellow, falls below the value predicted using the best-fit trend line due to the effect of the autocorrelation of ρ=0.11 and the summer 2007’s low value for ice extent. The dashed blue curves represent the bounds for the best-fit regression, accounting for the uncertainty in the slope and intercept. The error bars represent the ±95% bounds for the ice extent, which I added to the uncertainty in the best-fit regression. As you can see, the uncertainty in this estimate is rather large. Atmoz’s prediction not only falls inside my uncertainty intervals, but were it not for the correlation of ρ=0.11, our predictions would be identical. Note also: Last year’s summer ice extent was a major outlier.
Are you wondering why I used C-O? The reason is simple: I would have used Atmoz’s method, except he already used it!
Is C-O likely to give a better prediction? Nope! As it happens, the autocorrelation of the residuals (ρ) that best fits the data during this period is statistically indistinguishable from zero. When the autocorrelation is zero, C-O and OLS are identical methods and using non-zero value for ρ introduces noise.
However, I will pretend I believe the slight positive correlation is positive by advancing the following argument: Since the ice formed since last summer is thin. So, all things being equal, we would expect it to melt more quickly than thicker ice. In fact, this is generally the case, and so we expect some positive autocorrelation in the residuals for ice extent.
If you don’t buy my physical argument, you are permitted to believe I am using the non-zero autocorrelation only because it lets me do something almost as easy OLS, yet predict a different amount of sea ice than Atmoz. (You are also permitted to accuse me of cherry picking 1950 to get a positive autocorrelation for the residuals. I will claim that I picked 1950 because Atmoz did.)
In case you are wondering, the standard error in the residuals for “ice extent” based on OLS is 0.53 million km^2.
Disclaimers
To avoid punishment for placing a bad bet based on misunderstanding the rules, I will state that my bet is based on my understanding of the rules are as follows:
- We are betting on the value that will be posted for “summer 2008″ in this file: The Cryosphere Today’s Northern Hemisphere Ice Extents.
- We are to project an area for the ice extent, not just “break the record” or “don’t break the record”.
- We can use any method we wish to make our predictions. I guess we’ll see if voodoo or astrology can beat curve fitting or climatology.
- Atmoz hasn’t announced a deadline for entry. Presumably, he or she will limit entries to some reasonable period, so early entrants aren’t competing with others who wait until minutes before the summer data are posted.
- No prizes have been offered. Losers will, evidently, be punished in some unspecified way.
People in comments are discussing side-bets denominated in Quatloos or Fizbins. Even if Atmoz doesn’t set a deadline for entry, the bookies might set some for the purposes of betting. So, you may want to whip out your climate-blog-wallets and get your bets in now!
Data to consider when betting
When placing your bets, it might be useful to ponder the trends during all seasons.
It appears the summer ice extent has been dropping at a fairly rapid clip since 1950, but the ice extent during other seasons are less affected. Why? Beats me! (Still, I’m always eager to speculate. I’d guess a thin layer of ice will always tend to form when the air is cold enough. This would make the winter ice extent less variable than the summer extent. )
Note: This is republished. Something odd happened with the first attempt.
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43 Responses to “Sea Ice Bet: Atmoz Challenge (try 3)”
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Al May 1st, 2008 at 3:52 pm
Jim H told me to say that the ice has almost completely melted so I will say 2.5 - thats close enough and should keep me in the media
steven mosher May 1st, 2008 at 5:22 pm
Boris
Ya, Part of me wanted to say we would match last year, especially since the ice is new.
steven mosher May 1st, 2008 at 5:26 pm
Phil. I was going to guess last years extent, but I’m betting 2008 will come in slightly cooler
than 2007, but I dont see how any of that new ice has a chance. I just wanted to beat boris.
Andrew May 1st, 2008 at 5:45 pm
Lucia, you might not be able to answer this, but there is something non-nonsensical about the chart above, to me at least: The ice does not appear to have responded to the warm Arctic 30’s at all! Why is that? I would think that it would have some impact. It sure makes me doubt sea ice as a thermometer.
lucia May 1st, 2008 at 7:12 pm
Yes Andrew, there are many funny things about that chart. For example, the autumn and winter ice extent is almost supernaturally constant long ago. Either it was, or they didn’t measure it very precisely. I don’t happen to know. That’s just the data I found!
Phil. May 1st, 2008 at 8:35 pm
Lucia, I suspect that the reason is related to the fact that the Arctic ocean is rather close to a bowl surrounded by land, in the winter once the bowl is full of ice there’s no room for any more. As to its reaction to earlier warm periods that would rather depend on the ice thickness, the present situation is the culmination of several decades of ice loss.
Raven May 1st, 2008 at 9:15 pm
I don’t think sea is a particularly good proxy for global temperature because other types of pollution such as black carbon also have a significant effect. Peike Sr. has a good post on the topic here: http://climatesci.org/2008/04/.....ike-smith/
terry (25 comments.) May 2nd, 2008 at 5:53 am
Sea Ice Bet Haiku (I’m really getting into these!)
the world is watching
how much will the sea ice melt?
terry bets 6.
(better then last years 5.57, but somewhat unsure about the AO and PDO and stuff like that.)
Martin Ringo May 2nd, 2008 at 11:47 am
Lucia,
Thanks for the site to the data. And just because you diligent in these areas, I will give you a pure time series forecast: no physics, no climatology, no understanding of what is going on. Just a simple — or not so simple depending on your point of view — ARMA(3,3) with lagged seasonal explanatory. Note this is an iterative process, where one forecasts for each series one step ahead, and then uses the forecast variables for the missing explanatory in the next forecast with the whole thing starting at the first month. (I didn’t actually do all that but cheated a bit for the fall, winter, and spring, but that is part of the idea behind dynamic time series forecasting. There are better ways, but for an exercise they are not worth the effort.)
And so with process and a lag-3 structure (of the dependent variable) along with an ARMA(3,3) error term, I get a 6.8 (million square kilometers).
Let me suggest that part of the reason for the difference is that a first order autoregressive process does not fit the summer ice data very well, but at the same time there is significant serial correlation which could come from higher order autoregressive terms or moving average terms or combinations. My estimate of the process suggests that it has significant autoregressive coefficient only at AR2, but it has a very significant, negative MA(3) coefficient (-0.94) with is in conjunction with a not-quite-so-significant positive coefficient for the lagged summer ice variable of +0.54. Additionally, there is a stability problem with the coefficients although not the structure of the error term. Thus, I would be very skeptical about the calculated confidence bounds: in my estimate there were roughly +/- 1 million km^2 and I would probably close to double it, which leaves the times series forecast too wide — 5 to 8.5 — to have much merit for trend analysis. That is a nasty fact for many time series, and the best we can do is get an idea of the structure of the variation, e.g. U.S. Dept. of Agriculture weather simulations which are useful for the probability of extreme dry or wet or cold or hot seasons, but nothing in terms of what the next season will be. One thing is interesting though, the forecast predicts a drop of over a half million km^2 for 2009 from the 2008 value. I won’t tell you the predictive accuracy of forecasted sign changes, but it does say that the order two or higher lags, etc. have a noticeable effect which is in accordance with the significance of some of those terms in the estimate.
lucia May 2nd, 2008 at 11:57 am
Martin– Cool! I still need to learn the ARMA. The pesky safety stuff at work is making me more busy than usual. GRRR.. (Oh well. It’s part time, and I do make money when something comes up. That’s the way I like it.)
I see you edged out Moscher on the low side. I’m going to have to make a big table of all these prediction/projections.
Raven– I agree that the Arctic ice may not be as great a “detector” of the reason for warming as some claim. On the one hand, it is an integrator but so are the oceans. On the other hand, the snow is particularly susceptible to effects like haze, particulates and what not.
I do think setting bets introduces some levity into the often grim an ill tempered subject of climate blogging. So, I’m glad Atmoz suggested it. Maybe in the fall, we can switch to Antarctic melting.
steven mosher May 2nd, 2008 at 12:03 pm
I read somewhere over at ATMOZ that ods were 3/5 on beating last years low.
I shoulda guessed 5.5. Oh well, die is cast.
Andrew May 2nd, 2008 at 7:49 pm
There are some caveats about the data here may explain the discrepancy:
http://arctic.atmos.uiuc.edu/S.....ce.doc.txt
I’m also told there is some under recognized Russian data which shows more variability. I’m dubious of the pre 1970’s (pre-satellite) data, personally.
Phil. May 2nd, 2008 at 9:09 pm
Martin,
What about running the analysis in two parts: the perennial ice and the one year ice?
Martin Ringo May 2nd, 2008 at 11:05 pm
Phil,
I don’t really know what perennial ice is, and so I am not sure how let alone where to get the data. If perennial is simple a constant, it doesn’t effect any of the results from regressions simple or complex. If perennial ice varies, it could be useful in that it, the perennial, could have a different error structure which if removed from the annual ice extent would leave a (presumably) more visible — and with some luck — a more traditional error structure. All that would allow for a more accurate (smaller coefficient variance) estimate and tighter forecast bounds. It might also allow for a multi-equation estimation where the error terms are correlated between equations (as well as over time). (For those of you who pay attention to the issues of estimation, the multiple equation system with cross-equation, correlated errors is where one can usefully use Feasible Generalized Least Squares or, when the dependent variables of one equation are the independents of another, Three Stage Least Squares.)
So if you can write sea ice extent as X(t) = Y(t) + Z(t), where Y and Z can be correlated but have some part of independent variation, then one can usually improve on the estimate and consequently the forecast of sea ice extent. Is there such a breakdown?
Alan S. Blue May 2nd, 2008 at 11:37 pm
Kuhnkat May 3rd, 2008 at 5:04 pm
Since the “Northwest Passage” was open during WWII and a small Canadian ship travelled it al least twice, my edumacated guess is that the data are not well. Has anyone taken their temperature?? I notice that it actually shows a greater ice cover during the period?!?!?!
http://www.athropolis.com/arct.....t-roch.htm
http://freestudents.blogspot.c.....ssage.html
http://en.wikipedia.org/wiki/St._Roch
Their first try took 2 years as they were frozen in the ice!! The second try was a real example of open water and only took 86 days.
Phil. (13 comments.) May 3rd, 2008 at 8:53 pm
Martin
The perennial ice is the ice that lasts more than one year until recently most one-year ice melts each year but relatively little perennial ice, it seems to me that their behavior could be modelled separately.
here’s some data
Cassanders May 4th, 2008 at 3:43 am
hmmm, as:
a) I’m a marine microbial ecologist, (and belong to the slightly numerically challenged)
b) The available regressions seems to have large confidence bounds, anyway
c) This thread has the form of a betting competition¨:
I’ll go on record and suggest 6.81 mill sq. Km.
I have employed what in Scandinavian is called “Bensinstasjonslokaliseringsprinsippet”. I have not been able to fins an anglophone version. (Are you up to it, Lucia?). Basically it explains why gas stations are not uniformly distributed between towns, but tends to agglomerate close to them.
Nevermind: when employng said principle, my bet is on the side I’ll find most probable, but just enough to beat Martin Ringo
I do in fact have a number of other cues.
1) To my knowledge, both the NAO and AMO are now departing from the former simultaneous positive phase towards a negative phase
2) While SST anomalies in the NW Atlantic and the Barents sea has lead to substantial ice extent anomalies around Spitzbergen, Franz Josef’s land and Novaja Semlja, the turning of NAO and AMO might reverse this trend.
3) While SST in the Baltic-, North-, Norwegian Seas as well as the Denmark Strait is above the 1978-1998 mean, the SST conditions E of the USA apperas to be cooling. This water will reach The Barents Sae and the Polar areas before anticipated ice minimum in September (and may slow the melting).
Cassanders
In Cod we trust
lucia May 4th, 2008 at 6:32 am
Hmmm… well, despite having name that sounds like I must be 100% Swedish, I’m afraid “Liljegren” was acquired by marriage, and “Lucia” comes from my Cuban grandmoterh. So… I have no idea what that word might mean in English.
Many of use are using the classic American Army method called “SWAG” (Scientific Wild Ass Guess). Could that be related to “Bensinstasjonslokaliseringsprinsippet”?
Cassanders May 5th, 2008 at 6:35 am
Thanks Lucia, your national (and other
)affiliation is duly noted.
The reason I didn’t provide a direct translation was the hope that some other scandinavian lurkers in fact knew the appropriate term in english.
But here goes:
“Bensin” = Gas, “Bensinstasjon”= Gas station,
“Lokalisering” = Localization,
“Prinsippet” = Principle
Hence: The Gas Station Localization Principle. (GSLP, hereafter)
I think we in the Scandinavian languages shun huphenations to a large extent (in contrast to anglophones). I susspect the (indeed long and cumbersome) word is coined with two objects : 1) to be descriptive, 2) to be eye-catching due to its length and cumbersome pronounciation. (It is therefore easily remembered)
The principle does indeed aspire to explain why gas stations tend to cluster themselves around town/cities rather then spreading more uniform between them (or in the middle). It also offers a strategy on where to put a new gas station (catching the largest number of potential customers) when knowing where the other gas stations are placed allready.
The principle is probably easiest demonstrated with a betting situation.
Assume that you compete with ONE opponent in guessing how many peas there are in a jar. The competitor with the most accurate number win. You opponent says 200. You judge the jar, and consider the opponents bet to be an considerable undersetimate. You suggest 350. Alas, it actually turns out to be 270 peas in the jar, and you looses, despite being correct WRT your opponent’s estimate/guess being too low..
The betting strategy according to GSLP would be to claim 201 (if you opponent says 200, and you think that is an underestimate).
I guess you see why I referred to Martin Ringo?
Cassanders
In Cod we trust
lucia May 5th, 2008 at 6:44 am
Cassanders–
Ahh… Yes, I can see you bracketed Marty. Maybe someone will show up with the English word for that. We tend to make up words constantly, so for all I know, we may have one.
It is funny about my name. When I first married, I got my university ID. I showed it at the library, the librarian looked at me and said: “Oh, I would have guessed you were Swedish just by looking!”
I laughed and said, “Funny, no one ever said that before. Last month, my last name was Tiernan and people thought I looked Irish!”
Cassanders May 5th, 2008 at 7:45 am
@ Lucia,
Here are some new interesting data for April: http://nsidc.org/data/seaice_index/
As you can see, also the april Arctic sea ice anomaly is well above the (negative) trendline, and are approaching the “normal” (i.e the 1979-2000 mean).
The Antarcic sea ice continues its growth, and have a quite impressive positive april anomaly. As far as I can see, an “all time high” since 1970.
Cassanders
In Cod we trust
lucia May 5th, 2008 at 8:11 am
Cassanders–
The April high (for April) following the all time summer low is what makes this bet interesting. We clearly have an outlier here. The ice extent is larger than normal going into summer. On the other hand, it’s thin and so more vulnerable. I’m sure if Martin does do some sort of statistics only projection taking both factors into account, he’d find the uncertainty of any prediction is higher than usual, because we have two outliers to any statistical fit! One is high; the other is low.
Reference May 5th, 2008 at 11:58 am
These are my best 22 guesses loosely based on the main GCM models:
-2.1, 0.0, 0.0001, 0.99, 3, 4 and a bit, precisely 5, six, 6.2, 6.4, 6.6, 6.8, …., more than 9
Cassanders May 5th, 2008 at 1:58 pm
@lucia
Sure, I am not putting that much weigth on the ice extent itself. I am aware that the area of >1 year ice have continued to diminish, probably leaving the ice more vulnerable to melting and other forces.
In the light of this, I do find the graph from Alan S. Blue (#2523) interesting. Despite the less amount/extent of perennial ice, the reduction rate in March and April seems less than previous years.
A possible explanation could be a period of “beneficial” wind patterns (both wind speed i.e. wave action, and/or direction governing outbound transportation).
Cassanders
In Cod we trust
Phil. (13 comments.) May 5th, 2008 at 7:00 pm
Cassanders, at this stage of the season the melting ice is first year ice so I wouldn’t expect much impact until later in the season. Except for the Greenland sea which was old ice both this year and last and is at much the same stage now as then see this graph
I’d expect about a month before any melting occurs in the regions where there have been major changes in the perennial ice, in particular the fragmented ice in the Beaufort sea should be interesting.
Phil. (13 comments.) May 5th, 2008 at 8:01 pm
NSIDC just did their April analysis basically the same as the one I did for my guess except they didn’t wimp out and add 1 million sq km^2!
Dave Andrews May 8th, 2008 at 1:45 pm
My guestimate is that whatever it turns out to be all sides will say that they were closest. LOL
Lars (1 comments.) May 9th, 2008 at 4:19 pm
I tried to estimate the September ice extent from the Jan-April air temperature from 20N to 90N. I took NCEP data and 36 years of monthly sea ice extent (merged Cavalieri et al & NSIDC data). The result is scaled to cryosphere today summer extent. Thus, my calculated estimate is: 8.5 Mio km^2
(Correlation is -0.75)
However, my gut instinct says it could be also well less than 3 Mio km^2
So long!
Lars
Nothern Hemisphere Sea Ice: How’s it going? | The Blackboard July 3rd, 2008 at 9:10 am
[...] My sea ice bet of a summer NH minimum ice extent of 7.4 million km2 is doing ok! (Recall, started all this; Atmoz bet 7.7 million km2; he’s still in the running too. ) [...]