From the “(pick one: 90% 95% 97%) certainty department, comes this oopsie:
Via Bishop Hill:
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Doug Keenan has just written to Julia Slingo about a problem with the Fifth Assessment Report (see here for context).
Dear Julia,
The IPCC’s AR5 WGI Summary for Policymakers includes the following statement.
The globally averaged combined land and ocean surface temperature data as calculated by a linear trend, show a warming of 0.85 [0.65 to 1.06] °C, over the period 1880–2012….
(The numbers in brackets indicate 90%-confidence intervals.) The statement is near the beginning of the first section after the Introduction; as such, it is especially prominent.
The confidence intervals are derived from a statistical model that comprises a straight line with AR(1) noise. As per your paper “Statistical models and the global temperature record” (May 2013), that statistical model is insupportable, and the confidence intervals should be much wider—perhaps even wide enough to include 0°C.
It would seem to be an important part of the duty of the Chief Scientist of the Met Office to publicly inform UK policymakers that the statement is untenable and the truth is less alarming. I ask if you will be fulfilling that duty, and if not, why not.
Sincerely, Doug
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To me, this is just more indication that the 95% number claimed by IPCC wasn’t derived mathematically, but was a consensus of opinion like was done last time.
Your article asks “Were those numbers calculated, or just pulled out of some orifice?” They were not calculated, at least if the same procedure from the fourth assessment report was used. In that prior climate assessment, buried in a footnote in the Summary for Policymakers, the IPCC admitted that the reported 90% confidence interval was simply based on “expert judgment” i.e. conjecture. This, of course begs the question as to how any human being can have “expertise” in attributing temperature trends to human causes when there is no scientific instrument or procedure capable of verifying the expert attributions.
So it was either that, or it is a product of sleep deprivation, as the IPCC vice chair illustrated today:
There’s nothing like sleep deprived group think under deadline pressure to instill confidence, right?
lund@clemson.edu
Yes, a fractionally integrated solution would be correct. I linked you to a peer-reviewed paper that showed when accounting for the fractionally integrated component, the 95% confidence intervals expand to include zero. I told you to read that paper and warned of the dangers (and difficulty) in estimating this value.
In summary: you claimed using such a model would have no effect, and I linked you to a peer-reviewed paper that does the calculation that shows it has a very large effect.
And without answering the scientific points I raise, you announce you are dropping out of the discussion at this point.
What a surprise.
Bart, the “quasi-periodic” cycles you describe are almost certainly a consequence of fractionally integrated random variations, and not deterministic cycles at all.
Unfortunately you plot your PSD on a linear scale. The CIs of a PSD become very large on this type of scale so the uncertainty is unclear. You should (generally) plot PSD on a log-log or semi-log Y scale. The CIs are fixed width on this type of scale and it is easier to determine if those “quasi periodic cycles” are actually anything of interest.
Spence_UK says:
October 1, 2013 at 6:15 am
“Bart, the “quasi-periodic” cycles you describe are almost certainly a consequence of fractionally integrated random variations, and not deterministic cycles at all.”
They are definitely not deterministic cycles. I never suggested they were. But, they are very likely representative of ordinary resonant systems driven by random excitation.
The ~21 year cycles are likely due to quasi-periodic variations in solar activity. The Hale cycle has a nominal period of about this duration corresponding to oscillation of magnetic polarity (now that I think of it, this might be a manifestation of Svensmark-type cosmic ray modulation). A model for the sunspots, which displays characteristics very similar to observations, can be found here. See, for example, the simulations here and here, and compare to actual sunspot data here. Note, I am pointing out qualitative similarity, not quantitative replication. That analysis is TBD.
Partial differential equations on bounded domains typically produce solutions which can be expanded in a series of normal modes. Random excitation of these normal modes, with some inherent energy dissipation leading to damping, can be represented using a system model such as proffered above for the sun spots. This is standard operating procedure in, e.g., modeling structural vibrations, and is very widespread and well-established.
IMO, the ~65 year process is very likely such a normal mode excitation of the oceanic-atmospheric system. The random excitation doesn’t even actually have to be wideband – just nominally stationary with repeatable energy levels at the resonant frequency.
“Unfortunately you plot your PSD on a linear scale.”
It is better for seeing the spikes indicative of the resonances. A log-log scale is useful for observing power-law types of noise, but not very good for picking out resonances, as the varying scale distorts the Cauchy peaks.
Bart, natural variability *is* a power law. The variability extends across nine orders of magnitude (see here: https://itia.ntua.gr/en/docinfo/1297/)
Your 20 year and 65 year cycle fits right in to that relationship. And yes, pretty much any cycle you can come up with can be matched to some physical phenomenon.
Spence_UK: I must apologize. Your cited paper is certainly relevant. I didn’t read it the first two times you mentioned it. Perhaps I was misled by a lot of the misinformation here. I don’t normally look at this page. You have to yell pretty loud to be heard over all the noise. There is so much to correct.
But your reference contains exactly the type of analysis that I would think is hard to refute. The ARIMA(3,1,0) stuff is going the wrong way. While, I have not read your citation in detail, if the fractionally differenced p-value is .07, I would say okay, that increased the p-value way way more than I expected for the value of d quoted. This is not quite the case for the Continental US Series, which I have examined. I’m going to guess there are specifics (yearly instead of monthly series, interval of observation (does it contain the last few years, etc.) to dicker around, but I believe you.
BTW, I am still here. I just don’t have time to reply to everything.
Spence_UK says:
October 1, 2013 at 1:26 pm
“Bart, natural variability *is* a power law.”
To me, a power law is something which manifests as a linear slope in a log-log plot, generally indicative of red or pink noise. Spurious peaks may appear in a PSD analysis performed on such data, but they are generally amorphous and fail to be persistent.
“Your 20 year and 65 year cycle fits right in to that relationship.”
These are concentrated regions of elevated “energy” with common morphology. They indicate distinct processes above and beyond any background variability.
The ~65 year quasi-cycle is of particular interest, because it was the upswing of that cycle which was interpreted as accelerated warming due to CO2, and which has now got the climate community tied up in knots as it shifts into the downward cycle, spoiling their expectations, and poised to bring the entire house of cards tumbling down.
There was a time in which it could be argued that the ~65 year process was a fluke, and just a mirage of random variability. However, when the cycle turned in in mid-two-ohs right on schedule, that contention became a lot less tenable.
Lund@clemson.edu
In which case I should apologise back for allowing my frustrations to cause me to question your motivations. Sorry for that. I’m glad you found the paper interesting.
Bart,
To me, a power law is something which manifests as a linear slope in a log-log plot
Yes indeed – and that is exactly what the paper I link above demonstrates, across nine orders of magnitude (out to millions of years). The peaks you show are not special in this context.
Spence_UK says:
October 2, 2013 at 5:55 am
“The peaks you show are not special in this context.”
I always used to tell my students, you can’t rely on all this fancy math. It’s all based on models, and the models aren’t always applicable. You have to dig down into the actual data and do sanity checks.
If you can really look at this plot and not see the ~65 year component blazing in your eyes, then you need to take a break, and drop down to your local pub for a glass of perspective and soda.
Spence_UK says:
October 2, 2013 at 5:54 am
“In which case I should apologise…”
Frankly, I don’t see any reason to apologize. Lund came in swinging with some very churlish comments. Now, he is apologizing to you because he sees that you are sympathetic to his point of view. So, only people sharing his outlook and priorities deserves respect and a fair hearing. Pshaw.
http://stevengoddard.files.wordpress.com/2013/09/screenhunter_1013-sep-28-00-13.jpg
Add a bit of explanation and it makes a great
tee-shirtsweatshirt.Bart: You are the one who has spewed a ton of misinformation here. Learn what a random walk is.
Lund – charming. You need to learn that there are other conventions in other disciplines than the one in which you are engaged, and expand your mind.
“Learn what a random walk is.”
If you have an objection, state it clearly. My definition is standard, and consonant with descriptions widely available on the web.
Bart: all fractionally integrated time series will show strong “quasi-periodic” cycles near to the length of the time series. You can demonstrate this yourself easily by generating random fractionally integrated time series of a similar length.
Spence_UK says:
October 2, 2013 at 1:47 pm
” …all fractionally integrated time series will show strong “quasi-periodic” cycles near to the length of the time series.”
But, not all quasi-periodic cycles are phantoms of a power law process. Furthermore, you appear to be glossing over the fact that the ~65 year quasi-periodic cycle is half the length of the modern instrument record. There are very nearly two full cycles in evidence here.
This argument has been going on here longer than you may realize. Back in the early 2000’s, many people noticed that there appeared to be a ~65 year cyclicality to the temperature data. In particular, the run-up in temperatures from about 1910-1940 was almost precisely the same as that between about 1970-2000.
Even greater force was given to the argument when the turning point came roughly in 2005, right on schedule.
Fractionally integrated noise is a Martingale – the future does not depend on the past. These two events, the replication of the 1910-1940 and 1970-2000 increases and the turnabout in roughly 2005, would be astounding coincidences under the assumption that this is a figment of fractionally integrated noise.
“Fractionally integrated noise is a Martingale…”
This is incorrect. I am looking for the property which will convey my intention. That is basically that there is no compelling reason for fBm to exhibit repeating coherent patterns, and it is unlikely among all the paths that it could take for it to do so.
Bart,
It is easy to see patterns in fractionally integrated noise, especially when you get to interpret those patterns post hoc.
Spence_UK says:
October 2, 2013 at 3:25 pm
“…especially when you get to interpret those patterns post hoc.”
A) But, I did not see them post hoc. As I stated, many people were waiting to see if the turnaround would come after 2000 as would be expected for a persistent quasi-cyclical process. It did.
B) These patterns would then be uncannily precise. The increase from about 1910-1940 is virtually identical to that from 1970-2000. The turnaround came at exactly the right time.
Put Spence my team,dawg.. Bart, ???????, this is out of control.
[“on” my team? “in” ? Mod]
(Another fake identity -mod)
Bart,
Please, then give us, your altenative def of a random walk, replete with frequency reasoning.
[How many screen names are you using? ~ mod.]
At least 20:
Bart says:
October 2, 2013 at 3:06 pm
(This sockpuppet can’t keep his screen names straight. -mod)
[1. The repeated STFU’s in repeated replies are not needed, nor useful, nor desired. Cut them out.<
2. What did you mean by “for fBm to exhibit repeating coh” ? Mod]
bart@hotmail.com says:
October 2, 2013 at 5:55 pm
“Please, then give us, your altenative def of a random walk, replete with frequency reasoning.”
This has been done upthread. Don’t be so lazy.
“Folks: do we blather on or STFU?”
Oh, great. The feces flinging monkeys have arrived.
I would recommend you STFU, since you evidently have nothing to contribute.
carol@stat.usc.edu says:
October 2, 2013 at 5:39 pm
If you are confused, perhaps you should ask actual questions. I am not equipped to interpret “?????”.
Fake name. -mod.
[When cursing the world, it is usually best to tell the un-cursed-at rest of the world, which other person the writer is mad at. Mod]
(Fake name. -mod)