Sea Ice Bet: Atmoz Challenge (try 3)
Atmoz proposed a bet on the summer sea ice extent and placed his best 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 predicged 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. Assuming 95% confidence interval based for an i
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 sidebets 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 extents have 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.
Previous Post:
« Easterbrook Projection of Temperatures
Next Post:
Chileans Flee Volcanic Eruption. »
42 Responses to “Sea Ice Bet: Atmoz Challenge (try 3)”
You can leave a response, or trackback from your own site.
lucia April 30th, 2008 at 11:04 am
Alan S. Blue emailed in this comment:
Here’s what I submitted:
8.0 ±0.2 via the SWAG method.
NCDC 2008 March Sea Ice More data.
Basically a bet that this winter’s cold snap - an outlier - might cause an
outlier in Sea Ice.
Boris April 30th, 2008 at 3:53 pm
Hmmm….My guess is 6.6
steven mosher April 30th, 2008 at 5:30 pm
6.5 for me Hey lucia trick atmoz in to keeping track of the all the guesses. hehe.
lucia April 30th, 2008 at 6:16 pm
SteveM. Guesses? These aren’t guesses, they are “projections”. If Mars attacks, or a volcano erupts or something, we can all patiently explain that we can’t be held to them. But even better if Mars does not attack, we can explain that, because our projections were contingent on something, you can’t compare them to data. No…. not even if it turns out Mars did not attack. After all, what if Mars had attacked. Got that?
Anyway, I figure I can keep track easily enough. I’ll make a table, and even log the date when people made their “projections”. Looks like you edged Boris out on the low side.
Today I read that there is haze over the Arctic, which may be the cause of the ultra high melt rate. (Or not.)
Philip_B April 30th, 2008 at 8:35 pm
Atmoz thought my predictions for SH winter 2008 sea ice extent were OT. Although, I’ll admit my motivation was to draw attention to the record increase in sea ice over the last 12 months. An increase which has been resolutely ignored, while we still see press releases and news items about the record NH sea ice minimum from November 2007 which has now dissapeared.
My predictions for 2008 SH winter sea ice are,
A record anomaly of 2.5 million sq kilometers.
http://arctic.atmos.uiuc.edu/c......south.jpg
An absolute record at winter sea ice extent maximum of 16.5 million sq kilometers.
http://arctic.atmos.uiuc.edu/c......south.jpg
Phil. May 1st, 2008 at 9:16 am
Lucia, at the beginning of the winter I thought that we’d probably have something of a reversion to the mean trend this summer. However, having watched the huge flow of perennial sea ice out of the Fram strait and the major breakup of perennial sea ice in the Beaufort sea I’ve revised my opinion that we will probably see a new record this year.
I’ve attached the current Quikscat photo and one from last spring, the white is the perennial ice.
Day 121, 08
Day121, 07
There’s no longer perennial sea ice at the North Pole at the 1st of May, a first in the limited data set of Quikscat.
My guessimate is that we might get as low as 4.5 this summer.
lucia May 1st, 2008 at 9:21 am
Phil–
There are evidently people guessing ice free this summer. (Just not here yet.)
I’ve got your bet noted. You’ve edged out Steve m on the low side!
I need to go see if Atmoz has indicated a deadline for entries.
Phil. May 1st, 2008 at 9:39 am
Lucia, first of all I think belated happy birthday wishes are in order. While I wouldn’t be shocked if we were ice-free this summer I think that’s more likely next year, the reported change in the Arctic Oscillation appears to be pushing the perennial ice out of the Fram through the winter, at week 11 this year 72% was new ice and it’s significantly increased since then!
lucia May 1st, 2008 at 9:48 am
Phil–
Thanks for the best wishes.
It’s funny predicting the ice melt. My husband once got stuck on an icebreaker when perennial ice melted the summer of 1998. (See http://www.ameslab.gov/news/he.....delay.html ) What with this bet, I’ll probably be watching the data this summer too.
Obviously, after a big outlier, it’s difficult to guess precisely what might happen. I think the factors I’ve read are: a) thin ice b) polar vortex and c) last summer had unusually warm winds into the arctic. Sooo…
But, given the need to make a prediction quickly for Atmoz’ challenge, I’m going with curve fitting. (Just like Atmoz did.)
Phil. May 1st, 2008 at 10:12 am
My ’scientific’ method was to estimate how much perennial ice was left, assume that it stays and add to that 13% of the new ice, that seemed too little so I added 1 for luck!
Atmoz (10 comments.) May 1st, 2008 at 10:30 am
Regarding a deadline,
How about the end of next week, Friday May 9th?
lucia May 1st, 2008 at 10:36 am
Friday sounds good to me. That way, people who want to bet all have roughly the same amount of information.