“Tamino” has made a couple of posts on how the last 10 year drop in temperature is not statistically significant, so it isn’t real. He went too far in his last one and began claiming it was a tactic of some kind of creature called a denialist to confuse and confound the public.

Let’s see what Tamino has been saying on his blog link HERE.

Some of you might wonder why I make so many posts about the impact of noise on trend analysis, and how it can not only lead to mistaken conclusions about temperature trends, it can be abused by those who wish deliberately to mislead readers. The reason is that this is still a common tactic by denialists to confuse and confound the public.

I just hate bad science. First he points out how Bjorn Lomborg made some comments about temperature decreasing, after placing the ever more popular label of denialist on him implying Lomborg’s statements were intended to confound and confuse the public. Heres the main point of what Bjorn Lomborg said.

They (temperatures) have actually decreased by between 0.01 and 0.1C per decade.

Ok, so graphs like the one below are the reason Bjorn Lomborg is a denialist.

I copied this graph from Digital Diatribes of a Random Idiot - A great unbiased site for trends (link on the right). Note the slope of -.0082 (.01C/month units or .00098 degC/year - Thanks to digitial diatribes comment below) in the equation on the graph. Most of us know this is actual data and is correct, in fact every measure is showing similar results. The earth stopped warming- a very inconvenient truth. So Tamino what’s the argument, why are the evil and uncooperative denialists wrong?

Statistics of course.

Here comes the numbers from Tamino.

The most natural meaning of “this decade” is — well, this decade, i.e., the 2000’s. So I computed the trend and its uncertainty (in deg.C/decade) for three data sets: NASA GISS, RSS TLT, and UAH TLT, using data from 2000 to the present. To estimate the uncertainties, I modelled the noise as an ARMA(1,1) process. Here are the results:

Data	Rate (deg.C/decade)	Uncertainty (2-sigma)
GISS	+0.11	0.28
RSS	+0.03	0.40
UAH	+0.05	0.42

All three of these show warming during “this decade,” although for none of them is the result statistically significant.

Ok Tamino has calculated GISS, RSS and UAH. One ground measurement and two satellite. For those of you who don’t spend their afternoons and weekends digging into this. ARMA is a fancy sounding method for what ends up being a simple process Tamino has used to estimate the standard deviation of the temperature. Sometimes it seems the global warming guys believe the more complicated the better, but no matter. He has a 2 sigma column which represents about 95%. He then goes on to say that because of the sigma 0.28 or 0.40 is bigger than the trend, the trend is not statistically significant. He repeats the comment below.

Let’s make the same calculation using data from January 1998 to the present:

Data	Rate (deg.C/decade)	Uncertainty (2-sigma)
GISS	+0.10	0.22
RSS	-0.07	0.38
UAH	-0.05	0.38

Finally one can obtain negative trend rates, but only for 2 of the 3 data sets. But again, none of the results is statistically significant. Even allowing this dreadfully dishonest cherry-picked start date, the most favorable

Now Tamino claims to be a statistician so I can’t see how he made such a simple boneheaded error but if he wants to pitch softballs, I’ll hit em. Just to make sure he’s in good and deep here’s one more quote.

I’ve previously said “Those who point to 10-year “trends,” or 7-year “trends,” to claim that global warming has come to a halt, or even slowed, are fooling themselves.” I may have been mistaken; is Lomborg fooling himself, or does he know exactly what he’s doing?

So, Mr. Lomborg, we’re all very curious: how did you get those numbers?

Wrong turns everywhere

The first and really obvious error Tamino makes is referring to the short term variation in temperature as noise. Noise in the context of sigma is related to measurement error. How can we determine the measurement error of the three methods GISS, RSS and UAH. Well the graph of the three is below.

The first thing you notice from this graph is that the 3 measurements track each other pretty well. The signal is therefore not completely noise. Well what is the level of noise? We have above 12 measurements per year times 29 years. So we don’t need ARMA or other BS we can simply subtract the data. I put the numbers in a spreadsheet and calculated the difference between RSS and GISS, RSS and UAH and UAH and GISS. With 348 measurments for each type of instrument I was able to get a very good estimate of standard deviation of the actual measurements. Again, no ARMA, just using the difference between the graphs.

GISS - RSS one sigma 0.099 Two sigma 0.198

RSS-UAH one sigma 0.101 Two sigma 0.202

GISS-UAH one sigma 0.058 Two sigma 0.116

These are actual numbers and are substantially lower than the estimated two sigma by Tamino but still bigger than the 0.1 C per decade although the two sigma GISS - UAH is within a 90% confidence interval already!

This isn’t the end though. Tamino ended his discussion there implying shenanigans and other things of those who see a trend.

Both of our standard deviation calcs are for a SINGLE measurement NOT a trend.

This is a big screw up. How can a self proclaimed statistical expert miss this, it’s beyond me. Anyway, none of us is universally right every day but most hold their tongue rather than post a big boner on the internet. Well most scientists realize that when you take more than one measurement of a value you improve the accuracy. So being a non-genius, I used R to calculate what the statistical certainty of the slope is when taken over 10 year trends. Thanks again to Steve McIntyre for pointing me to this software. I don’t love it but it is convenient.

t=read.csv(”c:/agw/giss data/10 year variation.csv”, header=FALSE)

x = (1:length(t[,1]))

y=t[,1]

a=gls(y ~x)
confint(a)

confint(a)[2,1]-confint(a)[2,2]

y=t[,2]

a=gls(y ~x)
confint(a)
confint(a)[2,1]-confint(a)[2,2]

y=t[,3]

a=gls(y ~x)
confint(a)
confint(a)[2,1]-confint(a)[2,2]

What this script does is load the difference files i.e. GISS-UAH, fits a line to them and presents a number for the statistical confidence interval of the slope coefficient at 95 percent confidence which is about two sigma. The confidence of the slope of the trend is as follows

GISS - RSS Two sigma 0.00108 DegC/year

RSS-UAH Two sigma 0.001068 DegC/year

GISS-UAH Two sigma 0.0005154 DegC/year

Despite a standard deviation of .02 We have a twenty times more accurate slope measurement of 0.001degC/year !

Conclusions

1. We can say with a high degree of certainty that we know the trend of temperature for any ten year plot to within .01 degC/decade.

2. We can say that temperatures have dropped this past decade, just as our eyes looking at the graphs had already told us.

3. We can also say that Tamino owes a few more apologies.

He and Real Climate still don’t let me post on their blogs!

I wonder why?