Monday, March 19, 2007

Once more dear Prof. Keller

(cont., cont., cont., cont.,.cont., and oh yes ..

Dear Prof. Keller, you have no doubt read our previous letters, but we think this missive will present the clearest reasons why the paper by Essex, McKitrick and Andresen that appeared in the February issue of the Journal of Non-Equilibrium Thermodynamics entitled "Does a Global Temperature Exist?" should be withdrawn before it causes you more embarrassment
(but thanks for the fish).

Again we start from the definition of r-averages given in the paper

r-mean Average = [1/N (x1^r + x2^r+ ....... +xN^r)]^(1/r) for all r
various values of r. Using their own data set, it will now be shown how a failure to consider the nature of their own data renders their conclusions in Part 4 of the paper moot (ROTFLMAO quality). Essex et al., calculate monthly means across 12 stations and fit a linear trend to the to this as a function of time. Groups that compile global temperature anomaly data first find an average value across a region for some climatologically relevant period, generally 30 years) Monthly temperatures anomalies are calculated as the difference between the monthly temperature and the average temperature for the base period. You can find details of procedure in Ref 1 and 2 of the Essex, et al. paper. Let us examine why this is done
The blue line is the Essex, et al. raw temperature monthly average. The purple line shows the anomalies. If you calculate anomalies you can directly compare trends at places that are at different latitudes. The Essex, et al. data is dominated by the the eliptical nature of the earth's orbit assuming their sample balanced stations at northern and southern latitude. If not it would also result from some combination of the two factors. The GISS and Hadley Center global temperature anomalies deal with this by taken weighted averages of tempertures from individual stations on a grid overlayed on the earth, the weightings are taken from distance to the grid point. This is another factor that EMA appear not to have appreciated.

This should not be a surprise (although it might have been to Essex and Andresen, we suspect that McKitrick did not think it mattered). The ratio of standard deviations (blue/purple) =3.1/0.6. The ratio of slopes is (1.62 + 1.48 x 10^-2 C/Year) : (1.58 + 0.28 x 10^-2 C/Year). At least for this set of linear averages, the difference in the slope is well within the error bounds, but for a larger data set this may not be so. The error in the slope is about a factor of five smaller.

Now let us examine what happens if one sets r=3

Joel Shore informs me that Essex, et al. used Kelvin for these calculations, which would make a small difference in the above chart for the temperature data, but none for the anomalies which are differences of temperatures and independent of the zero of the temperature scale.

12 comments:

Anonymous said...

Monthly temperatures anomalies are calculated as the difference between the monthly temperature and the average temperature for the base period. You can find details of procedure in Ref 1 and 2 of the Essex, et al. paper. Let us examine why this is done"

Hey, who really cares why this is done?

It's much more fun to engage in endless mathematical exercises -- playing with the value of parameters in formulas -- than to read and critique what climatologists have actually done.

Besides, that makes the "critique" infinitely easier, since one is free to imply climatologists have done and claimed things that they have not.

ankh said...

This may be helpful:

http://boingboing.net/images/BLOGGERSTICKERprototype.gif

Anonymous said...

Did Mr. Keller already answer?

EliRabett said...

Well actually Eli did not send this yet. It has to be reformulated and tightened up (kinda sprawling right now, but such a target rich environment...)and there are a few more points to be made and some comments from the comments to be included.

Anonymous said...

But, Eli, wouldn't that mean you'd lose your ananemone?

God knows there's nothing worse.

I once lost mine and had to go all the way to the Maine coast to find a new one.

Anonymous said...

Forgive me for changing the subject hare, but those graphs look suspiciously like the ones here

Now I'm not superstitious or anything, but you be careful, now Rabett, it could be a sign ...that the lynx is in waiting.

An what then? Where would we anonymice go?

Joel Shore said...

Eli:

I guess the problem with a paper that is wrong-headed in so many ways is that it is hard to agree on what the most fundamental error is!

I do agree with you that their method, by keeping in the seasonal cycle, looks at averages over a much more variable quantity than if they had taken that cycle out (e.g., by looking at temperature anomalies or, alternatively, by averaging over the months to get yearly data).

However, I would point out that even if they did take that variability out by starting with yearly average temperature (where this average was obtained from the monthly temperatures, by a simple arithmetic average) and they then applied the same procedure that they used with the monthly means to these yearly means (i.e., performing r-means on the absolute temperatures), they would still be able to produce a funky plot like that in Fig. 2. (It would look somewhat different but it would still show a large variability in the temperature trend with time when r ranges over the ridiculously broad range of values they look at.)

As I see it, their fundamental error is the claim that because one may not be able to rigorously define and prove EXACTLY what sort of average is optimal, any method of averaging is as good as any other. This notion is just goofy beyond belief! If all the scientific knowledge that is knocked out by this sort of logic were to disappear, we'd be back in the dark ages (or maybe earlier)!

What they need to show to prove a valid point is that within the range of reasonably-defined averages, you can still get a significantly different result for the temperature trend. E.g., they might be able to argue that it makes as much sense to weight the temperature anomalies not just by the earth's surface area that they represent but also by the (average)density of the air in that region...and if that gave a very different result from just weighting by the surface area, we might get worried. But, it won't.

I believe it is only by going to totally stupid definitions of "average" that they are going to see any significant differences in global temperature trends and, in fact, their results in Fig. 2 actually support this hypothesis since even the difference in the temperature trend between the r=1 and r==4 means is pretty small in this very contrived example...and would probably get even smaller once they did their procedure over a larger data set.

Anonymous said...

Their fundamental error is that they wrote the paper.

Anonymous said...

Arguing that "Anthropogenic global warming is not real because CO2 increases follow temperature increases" is more than a little like arguing that "The hare chases the lynx".

...which is only true in a very few (and very weird) cases -- eg, Monty Python's "Holy Grail" and Rabett Run.

TimC said...

A few years ago, I was doing a stint as a programmer at a state department of transportation. The program I was working with used formulas for calculating averages in order to measure the overall performance of the highway system or parts of the system for different periods. For example, average speed at the aggregate level was taken by weighting the speed for each vehicle by vehicle miles traveled.

Given the fact that I had worked with enough of the equations, at one point they suggested that I come up with a new measure that people might be interested in. So I started futzing around with the equations. However, the more I played with them, the less they made sense to me - until I finally discovered that virtually all of the equations were weighting individual measures incorrectly. The reason? The individual who first "derived" the equations for averaging measures thought that such averages were largely subjective.

They are not.

When you calculate the actual average speed for an aggregate, you take, you calculate things as aggregates, then once you have the appropriate aggregate measures calculated arriving at normalized measures is a simple matter of division. For example, average speed at the aggregate level is vehicle-miles traveled divided by vehicle-hours of travel.

Moreover, this makes quite a difference. Taking the original, incorrect weighting, if a single vehicle travels for 5 hours at 10 mph, then for 1 hour at 50 mph, since both legs are the same length, the average speed is calculated as the simple arithematic average of both speeds: 30 miles an hour. However, the vehicle has traveled 100 miles in 6 hours, so the average speed is actually 16.67 mph. This is what you would get by weighting by vehicle hours of travel. However, weighting is generally a bad idea: it obscures the mathematics and makes one more likely to make these sorts of mistakes. (Moreover, it makes the calculations more time consuming for the computer, but that is a different matter.)

In any case, without digging into it myself, I suspect that the same thing holds true for temperature. There is most likely an objective definition of average temperature at the aggregate level. It may be more difficult to calculate than the simple arithematic average you are used to working with. However, if you can identify the equation for this average, you should also be able to estimate the extent to which the arithematic average deviates from this average, and as I suspect that this deviation is quite small, this would be a definitive argument against the view that such an average is subjective.

Hank Roberts said...

The last link in the title seems to have defunked.
http://www2.blogger.com/post-edit.g?blogID=16612221&postID=8892613890266826309

Hat tip to http://rhinohide.wordpress.com/2011/01/23/willard-opens-a-can-of-worms/ for mentioning this thread

EliRabett said...

Corrected. It was actually a link to the edit part of blogger, but thanks for this, it gave Eli time to go back when he was young and the snark strong. Esp good was this comment about the many errors in Essex and friends
-----------------------------
If this is the case, we are forced to invoke the McKitrick/McIntyre rule which requires that the paper be withdrawn forthwith and the authors offer ritual apologies, burn their PhD degrees and retire to a life of flipping burgers at McDonalds for having shattered scientific regulations established by the Climate Audit Institute.