(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 should be withdrawn before it causes you more embarrassment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 rvarious 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.