When stratospheric volcanos erupt, there are identifyable exogenous perturbations. But, right now, I agree there are no obvious ones (and likely, in reality, there are none.)

I’m perfectly willing to believe that the process is not AR(anything)! If the system is not stationary in moments higher than the mean I’m not sure any statistical analysis can be done at all. Can it?

Ocean fluid dynamics is a very high order process and Gavin knows it. He has no more clue than I or you do what to do about it.

Brigg’s chart is generated data.

Yes. My point was that there are certain trends that would “falsify” the known trend for the data. Take 1975 to 1985 for instance.

The result I am posting absolutely does not falsify the 50 year trend. It falsifies the IPCC projected trend, which exceeds the 50 years trend, and pretty much any long term trend since the thermometer record begins.

My uncertainty intervals also contain the 100 year trend.

When doing hypothesis tests for claims, you use the uncertainty interval for the trend. Generally speaking the data themselves fall outside these trends.

As to your underlying question, which presumably related to my conclusions:

If the IPCC claim of 2C/century were true, less than 5% of 10 year trends exhibit trends lower than the trend determined based on the actual measured monthly data since the time the IPCC made their projections. (I think the value is actually less than 1%. I’d check further for you, but my sister and I have tickets to the Lyric Opera, and I need to leave soon.)

Or course, it takes a long time for weather to average out. That is why the confidence intervals associated with the trend I obtained are so wide. The 1 σ is 1.1 C/century, which is huge compared to the trend of -1.1C/century.

I am rather surprised we had such a strong excursion into colling, but it happened. It may be the 2.5 σ event. But it happened. No pointing at the distinction between weather and climate makes this go away. Climate is an average of weather. There is no specific number of years that defines a cut-off.

The weather noise you are discussing falls inside the red bands. Yes, the weather noise will fall outside the uncertainty bands for the mean.

Yes, and if you calculate trends based on short snippets, you get values that are sometimes far from the true trend.

In other words, the short term variations in weather are defining the trend right now and not the changes in radiative forcing (whatever they may be). It takes longer than 7 years for the weather noise to “average out.” This is why the IPCC makes projections for thirty years.

How many ten year trends from Briggs’ figure would falsify the actual 50 year trend?

When testing the difference in mean trends (or just means of any sort), we are comparing the error band represented by blue lines in graphs like this:
to the predicted trend and it’s uncertainty.

The weather noise you are discussing falls inside the red bands. Yes, the weather noise will fall outside the uncertainty bands for the mean.

It’s conventional when testing hypotheses to compare the mean trend to the predicted mean trend. This averages out the weather noise.

Of course, if you are suggesting that the IPCC bands include the weather noise, then the falsification I did is even stronger than I stated.

As you can see quite clearly, both the near term IPCC projections and their stated uncertainty intervals fall outside the uncertainty bands for the data.

I think this needs some clarification. Perhaps it is partly the IPCC’s fault for not making their graphic clear, but if they were including short term variability into the uncertainties, we would see huge error bars immediately after 2001 (I’d guess these would be on the order of +/- 0.3`C at one year out–just a guess, however) The error bars would then shrink until we reach the 30 year projection. All in all, it would not be as pretty a presentation, but it would be better for discussions of this kind.

Comparing an 8 year trend to a 30 year projection is bound to give weird results, not matter what the data are. We know based on the Jan07 to Jan08 swing that internal variability can be at least 0.5`C (Unless someone wants to suggest an external cause, which is highly implausible.) Such apples and oranges comparisons don’t, I contend, allow such a conclusion as:

So, looked at both ways, IPCC near term prediction of 2C/century for the trend appears provisionally falsified.

“provisionally” or not.

Not to say that the analysis isn’t interesting.