Friday
Dec182009
by 
Bishop Hill
Bishop Hill JG-C is worried
Dec 18, 2009 Climate: CRU Climate: Surface John Graham-Cumming is worried he may have found an error in the CRU temperature series algorithm.
Read it here.
Dec 18, 2009 Climate: CRU Climate: Surface
Reader Comments (7)
What a refreshing post. Uncertainty about the uncertainty seems warranted.
So which was right? Using standard deviation or standard error? Or neither?
The standard error IMHO shows the likelihood that observations in a single station are correct: e.g. the difference between using a continuous digital thermometer in a stevenson screen and a mercury thermometer on a north facing wall. That likelihood is indeed fairly high You can see the predicting skill of one long record against another one here
The standard deviation OTOH demonstrates the likelihood that a randomly selected station on the world will end up in the sampled uncertainty range. This likelihood drops rapidly as the sample size diminishes. So for that purpose the standard deviation is IMHO the preferred metric and not the standard error.
Please correct me if I'm wrong here.
Speaking of Standard Error, the east coast of the US is expecting several inches, if not feet of snow in the next day
http://www.weather.com/maps/geography/eastcentralus/index_large.html
Truly an "Inconvenient Truth".
Note to Al Gore -- please turn up the heat in Washington. Obama wants to come home and land. Harry (not of the READ_ME files) needs him to beat back the liberal (but not far left wing) Democratic senators into shape.
My, my, poor Obama. Goes to Copenhagen twice and gets nothing for it. Maybe he should stay home and try to run the country. Pero apenas mis dos centavos.
Hans,
I think he means standard error of the mean. And since he's plotting a mean, that does seem the right error range to cite.
IMHO that is misleading, as the sampling is not random, and not constant. The likelihood that a random location in the world would fit in the standard errorband is way smaller that the errorband of the sampled mean suggests.
The issue of errors has been troubling me since I read JGC's blog and I'm still not sure I have a firm enough grip on it. My inclination is to say that we should be quoting the standard deviation and not the standard error when computing the global average. I take Nick's point that what is being computed is a mean of a series of grid cell temperatures. However, these grid cell temperatures are not all measurements of the same grid cell. They are measurements of different grid cells that exhibit a range of different temperatures. Accordingly we should propagate the standard deviation associated with each grid cell across the summation and then divide by the number of grid cells. This will give us the standard deviation of the 'global average temperature'. This tells us we are 95% (or whatever interval one cares to use) confident that the estimate we have come up with lies within (say 2 sigma) of the true global temperature..
For us to use the standard error we would have to take n independent estimates of the global mean temperature, average these and divide the standard deviation of these estimates by sqrt (n-1). I don't think this is done with the global average temperature measurements. Therefore I conclude that the appropriate measure is the standard deviation and not the standard error.
If my conclusion is correct then our estimate of the global temperature in 1880 is not significantly different from our estimate of the 2008 global temperature.
What we need is a statistician to review the Brohan paper. Hans also makes some very relevant points about sampling distributions not being random that need to be considered. There is also the issue of propagating errors through to cells with missing values etc. I think there are something like 2592 5 x 5 degree cells yet in 1880 there were less than 200 stations reporting temperature. No doubt these were not randomly distributed either.