Nullis in Verba

Box -Jenkins time series analysis assumes that the time series is stationary; ie mean and variance do not change with time and there is no trend.

This is not true for the temperature record, which shows a statistically significant warming trend. The Box and Jenkins method does not apply.

"Box -Jenkins time series analysis assumes that the time series is stationary; ie mean and variance do not change with time and there is no trend."

No it doesn't.

Chapter 4 covers linear non-stationary series, chapter 9 covers seasonal models and trends, chapter 10 covers non-linear models and long-term persistence.
http://onlinelibrary.wiley.com/book/10.1002/9781118619193

Keenan was explicitly comparing trend-stationary models with non-stationary ones, and got heavily criticised for using the latter, so quite where you get this one from I can't imagine. Cut-n-paste?

Micky H Corbett

If you get a discontinuous event as in you recalibrate your sensor after 6 months and realise it's out you don't know when it happened or how the drift looks which means that particular sample has an n of 1 and a large uncertainty i.e half of the difference. You can get round this by multiple recalibrations.

This is how the satellite microwave sensors operate. There are a fewsensors, which are recalibrated using an onboard reference source. Their internal vulnerability is that if the reference sources are unstable, their calibration will drift. With no external check available there is no way to detect the drift.

Surface temperatures are measured by a large number of sensors. Apart from routine calibration, each station can be checked against its neighbours. Part of the adjustment process is to look for stations whose output drifts relative to those adjacent to it. If the problem is something temporary like shading from growing trees or a calibrationroblem it can be corrected.

If the problem is permanent, such as a new building neaby, a correction factor can be applied to future measurements.

Mickey,

You need to know what the drift looks like to know when to recalibrate.

A measurement process has to have a known bound on its errors to be useful. Sometimes that error bound is known to expand over time. You schedule recalibrations at an interval over which the expanded error should not exceed the required accuracy. You can then use the maximum expected error for your error bars, and so long as measurement errors are independent, the error in the average is bounded by a quantity that shrinks as 1/sqrt(n).

The classic example of a drifting error is a clock, which has a systematic (trend) component, and a random-walk component that accumulates the effects of noise and temperature changes, etc. You would model its error as something like A*t+B*sqrt(t), where A is the systematic rate error, B is the random-walk drift, and t is the time since the last synchronisation. You solve A*t+B*sqrt(t)=requirement for t to figure out the maximum time between recalibrations you can allow, and you use either the maximum error expected just before recalibration if you want to be conservative, or your modeled error if you want a bit more precision for your individual measurement accuracy.

Of course, it's obvious in this case that the errors in successive measurements are not independent. You can measure time differences more accurately, but you can't improve the absolute accuracy of your times by simply averaging successive measurements. They've all got substantially the same offset.

However, if you was to average the measurements made by several different clocks, there's more hope for them being independent, and the CLT applies approximately. It doesn't matter that the error distribution isn't known precisely, or that it changes over time. It's still of finite variance, so averaging multiple measurements does still give an approximate 1/sqrt(n) improvement in error bound compared to a single measurement.

NiV,

Anyone can make a silly mistake

Of course, but if you're going to claim statisticians trumps astrophysicists, maybe you should find an example without an elementary error.

It's not nonsense. It's standard mathematics - time series analysis as done in Box & Jenkins.

And if we were talking mathematics or pure time series analysis, maybe you'd have a point, but we're not, so you really don't. In this context, it's nonsense. And I had thought you weren't one of those who would go on to misrepresent what others said, but I guess I was wrong.

"Of course, but if you're going to claim statisticians trumps astrophysicists, maybe you should find an example without an elementary error."

Which is?

"And if we were talking mathematics or pure time series analysis, maybe you'd have a point, but we're not, so you really don't."

The original context of Keenan's work was a response to a pure time series analysis offered by the Met Office as an explanation for their claims of "statistically significant global warming". In context, it demonstrated the purely mathematical point being made. Some people assumed additional physical claims were being made that weren't. But whatever.

EM, I've just tried to read that article you linked earlier [it keeps crashing shockwave on my computer] but, whether I agree with it or not, I simply fail to see its relevance. The device used for measuring something, or the adjustments made to the data for instrumental reasons, should have no bearing on the physical validity of the parameter being measured. We seem to be talking at cross purposes.

Michael hart

Sorry about that. I always have trouble with PDFs.

In a perfect world you could measure a physical parameter without having to worry about technique or sample size.

Unfortunately reality is less user-friendly.

A planet does not have a single point at which a thermometer can be inserted to take its temperature Instead you have to take measurements using uncertain instruments, build up samples large enough to be reliable and then use statistical methods to analyse your data. This applies to most science, though some measurements are easier than others.

Raff, once again you have evaded the issue.

I linked to a paper which emphasised that an average temperature for the whole planet is probably physically meaningless in the context of the variation being displayed. With such a simple description, accumulating energy can also be associated with a declining average temperature, and vice versa. You only need a high school-level of Stefan-Boltzman physics to demonstrate that. I suggest you try it for yourself. Also, the concept of equilibrium is certainly taught in high school, though often not properly grasped by people with a Ph.D. Perhaps that is why aTTP ignored it. Here's another clue: it was published in the Journal of Non-Equilibrium Thermodynamics [The above is by no means the only argument in the paper. I actually gave the paper to EM, again, because he was seemingly sold on the virtues of inappropriately averaging things that probably shouldn't be averaged, to support spurious precision.]

One of your other 'criticisms' was that one of the authors was only an Economist Professor, when the other two authors are
a) Professor of Applied Mathematics at the University of Western Ontario (who started in climate modeling decades ago) and
b) Professor of Physics at the Niels Bohr Institute in Copenhagen.

Their paper also acknowledged distinguished Russian scientist and Atmospheric Physicist Kirill Kondratyev (who had also presumably been round the block a couple of times with atmospheric models) as encouraging them to write the paper. Your attempts to discredit the paper's authors fail, yet you pay deference to an activist wannabe who teaches astrobiology, starts malicious blogs on the internet, trolls for internet traffic on other people's blogs, and also conveniently appeared to wholly miss the point of the paper. [That's Ken Rice=aTTP]

As an extra criticism you invited my explanation of a graph that was not in the paper I linked to, and without context.
WTF?

You've reminded me why I usually skip over a lot of your posts here at BH. They are often uninformative, ignorant, seemingly designed to distract, and probably often derived from opinions cut-and-pasted from elsewhere. At least aTTP has the ability to know when he is dissembling and disseminating to the point of lying [You can fight amongst yourselves for who has the lowest ethical and moral standards]. The virtue of BH is that we are allowed to say what we think with some latitude, and hence make fools of ourselves if that be the case. You frequently fit the mold of someone who thinks they know the answer when they they don't even understand the question. Worse than that, your criticisms of individuals sometimes appear to not even know what the subject under discussion is: There is much mathematics in the paper that requires no knowledge of physics at all.

Worse than that, your criticisms of individuals sometimes appear to not even know what the subject under discussion is:

Truly an illustration of the beauty of online climate debates. Well done.

Michael hart

In some things I agree with you.

Surface temperature averages vary with latitude ,so a raw average gives little information.

Anomalies are better, since they give more information about temperature trends in the surface and atmosphere overall.

From the scientific perspective the best indicator is ocean heat content. 95% of the heat capacity of the whole climate system in the oceans. Monitoring how that increases gives the clearest indication of how the system is behaving.

What a lovely appeal to authority. So we have a blog commenter of unknown but doubtful training, a physicist, an economist and a mathematician...

You only need a high school-level of Stefan-Boltzman physics to demonstrate that.

...and none appears to have this high school level S-B physics. The figure is there in the paper you link, Figure 1.

3.1.2 A Physical Example of Contradictory Trends

Let’s consider a specific example involving temperature. A glass of ice water at 2 ◦C is sitting beside a cup of coffee at 33 ◦C. ...etc

and then these three authorities discuss their four curves, where the fourth:

R4 would appear in connection with black body radiation.

Here it is, if you can bear to look: http://snag.gy/hrU9Q.jpg

R4 starts just below 28C, as I described before:

fourth_root( (33^4 +2^4) / 2 ) = 27.75

They used Celsius. Now anyone can make a mistake, although for a eminent physicist to make this particular mistake is embarrassing if nothing else. But you just go on making the same mistake of promoting this nonsense even when it has been pointed out to you? What does that make you?

Raff, no it is not the same the graph, which suggests that you haven't read the paper, just some rejection of it. That much was immediately obvious. Now, if you make a case for it being similar, I might have looked and agreed to look further, but your history here suggests that following you or your words is waste of time. You still haven't made a case why I should.

You started the appeals to authority, not me.

And you still haven't said why you think it makes a difference in this case. It appears to me as an illustrative example.

..and by illustrative example I mean that the absolute numbers are irrelevant in this case. The same underlying principle applies whether you set a "zero" in Celsius , Kelvin, Fahrenheit, or whatever.

Oh...And you apparently started the appeals to authority by appealing to your own authority, which is curious for person who doesn't post under their real name.

Michael, the grap is a screen grab from the top of page 13 of the pdf of Essex, McKitrick, Andresen: "Does a Global Temperature Exist?"in the link you gave on page 1 of this thread

I was rude about your level of training before, you are now displaying championship-level denial.

Raff, that is precisely the same one as I linked to. If you had really read the paper I linked, why did you link to somewhere else? Because you didn't read the paper I linked to?
(And, if you wish to split hairs, it was on page 2, not page 1, as you stated. You appear to be descending to the level of 'spelling mistakes' to have the last word, yet still failing). For crying out loud, try to make an actual point.

Back to the substance, I am used to your deflections, but still, please tell us why absolute temperatures make a difference here? The mathematics of something times T*(10^4) do not materially matter to the argument.

I get the feeling I am going to be waiting a long time for a convincing argument from you. And in the mean time you will still have completely ignored the physics of intensive vs. extensive properties of matter.

michael, E&M write a book and a paper (the paper with the physicist, which you referenced). In both they use the example of the coffee at 33C and ice water at 2C. In both they screw up. So their idea that there are many averages and some can show cooling while others show warming (figure 1 in the paper) can be rejected because they used the wrong numbers.

They could of course have used Fahrenheit and got another result:
fourth_root( (91.4^4 + 35.6^4) / 2) = 77.2F == 25.1C
and in C
fourth_root( (33^4 + 2^4) / 2 ) = 27.75C

And as I said a long time ago, their idea that Earth doesn't have one temperature because its spectrum doesn't match that of a black body ... etc, is irrelevant to surface temperature indices.

Go and read the Rabett's article that I linked to. It covers intensive/extensive properties as well and would clear up your evident confusion.

Since we're discussing Essex & McKitrick, I happened to find this review of their book, "Taken by Storm: The troubled science, policy and politics of global warming". It ends with:

One hesitates to comment on these authors, given their one-size-fits-all reaction to those who disagree: all are simply dupes of the doctrine. But I cannot remember a book that combines so thoroughly tendentiousness with pretensionst of objectivity. Readers will search in vain for reasoned discussion of climate policy, or even glimmers of awareness of the large literature in this field. There is no examination of the elementary concept of economic externalities, or "no regrets" climate policies, or the complexities of agricultural adjustment to climate change. The precautionary principle is dismissed, using only the hoariest of objections. Most crucially, the book simply ignores the key policy debates about climate change, such as its economic costs and benefits. Instead, all arguments are bent in support of the well-worn conservative doctrine that environmental action is some kind of terrifying harbinger of collectivism. Among conservative commentators, Essex and McKitrick distinguish themselves only by the extreme nature of their views. What can one say about authors that view even a benign activity like planting trees as "crazy"( p. 284)?