A more detailed reply to Pat Frank – Part 1
Posted by Jeff Id on August 8, 2011
We’ve been discussing Pat Franks recent temperature uncertainty publications for quite some time on this other thread. I’m not pleased to say that nearly zero ground has been made in understanding the problems in this work and even some very sharp people have missed the mark. I’ll give it an hour this morning, and work away at it for a bit until I’m finished. Math isn’t always boring but we have already covered this stuff so you guys might not like it. The paper being discussed is online here.
There are multiple problems with the paper but I’ll start from the beginning and work my way through. There are several statistical analyses presented which are broken into different cases. Case 1 is fine, Case 2 has some problems. Case 2 however, is not used in the conclusions but is merely presented as an example. However, the error in the example is repeated throughout the paper.
Note the definition of tau at the beginning, N true temperature magnitudes. Not N temperature measurements with error but ‘true’ temperatures. Equations 4 and 5 are non-controversial for noise which is normally distributed and random. No disagreements here.
The problem with Case 2 starts on page 972 word three “‘further’ source of uncertainty” now emerges from the condition that tau’s are different. Equation 6 takes the spread of individual temperature stations and incorporates them into an error calculation s which is the standard deviation of inherently different temperatures. In other words, Pat is accidentally making the claim that there is an uncertainty s created by the delta tau from the mean of the TRUE temperature magnitudes. This is weather noise, and this is false.
This equation is apparently not used in calculating the uncertainty though so my recommendation is to ignore section 2 entirely.
Later in case 3 we have this:
Note the statement of lack of knowledge concerning stationarity and true magnitudes of noise variance. The problem here though is i n the final paragraph where again the ‘true’ temeprature magnitudes have a standard deviation which is represented again as s. This standard deviation is the difference betweeen true temepratures at different stations so it is again ‘weather noise’. Again, ‘s’ is defined as a ‘magnitude’ uncertainty and is incorrectly calculated. Having known magnitudes for tau that are different does not create uncertainty and sigma bar total in this equation includes the different true temperature magnitudes as an uncertainty, this is both confusing and incorrect.
Then we get this quote farther along:
This is where Pat makes the claims that stationary noise variances are unjustified. This is key to the conclusions and equations presented throughout the paper. I also believe that has problems but they are more subtle than the more obvious problems of the previous equations. We’ll get into that tomorrow.
I get that Pat hasn’t included weather noise in his final calculations for Table 1,2 and the figures, but he has incorrectly defined ‘s’ throughout the paper – and that does include the distributions of true temperature anomaly magnitude, and thus ‘weather noise’. What’s more is that the lack of improvement in uncertainty of the mean is a powerful assumption which can be disproven as time permitting, I will show next time.