Bishop Hill reports that Doug Keenan’s article about statistical significance in the temperature records seems to have had a response from the Met Office.
WUWT readers may recall our story here: Uh oh, the Met Office has set the cat amongst the pigeons:
===========================================
The Parliamentary Question that started this was put by Lord Donoughue on 8 November 2012. The Question is as follows.
To ask Her Majesty’s Government … whether they consider a rise in global temperature of 0.8 degrees Celsius since 1880 to be significant. [HL3050]
The Answer claimed that “the temperature rise since about 1880 is statistically significant”. This means that the temperature rise could not be reasonably attributed to natural random variation — i.e. global warming is real.
…
The issue here is the claim that “the temperature rise since about 1880 is statistically significant”, which was made by the Met Office in response to the original Question (HL3050). The basis for that claim has now been effectively acknowledged to be untenable. Possibly there is some other basis for the claim, but that seems extremely implausible: the claim does not seem to have any valid basis.
=============================================
The Met office website text is here and there is a blog post here.
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
“The idea of testing for significant trend, or increase, is to see if something has changed.”
The idea of testing for a significant trend is to see if there is evidence for a trend. Change can occur for other reasons besides trends.
“There wasn’t a trend before, now there is. It doesn’t suggest that there has always been a trend, or always will be.”
How do you know there was no trend before? How do you know there is one now?
“But the purpose of Keenan’s analysis has been to suggest that nothing has changed. It’s just random variation like we’ve always had.”
No, the purpose of Keenan’s analysis was to show that the Met Office analysis claiming that there was a significant trend, based on the data not fitting a driftless AR(1) model, was invalid. Keenan’s position is, as I understand it, that there is no evidence in either direction. The Met Office’s claim that there is was bogus.
“But random walk variation can’t have been the regular state of affairs. So if you want to adopt it as a local model, you need an idea of when it became a random walk and why.”
I just said. The model says that over the short term the behaviour is indistinguishable from random walk because the restoring forces are drowned out by the amplitude of the year-to-year noise. You have weather each year that adds or subtracts a random chunk of energy to the climate system. The temperature this year will be the temperature last year plus some multiple of this random chunk. The distribution of the chunk has to vary with temperature to keep the accumulated temperature within bounds, but this shift in the mean is small compared to the spread, and so, like the curvature of a short-enough segment of curve, can be safely neglected.
It’s approximately random walk, and the approximation is good enough over periods short enough such that the average of the accumulated noise is smaller than the restoring forces pushing the climate back to the equilibrium.
That there’s a unit root in the statistics is a thoroughly mainstream result.
nullifies in verba says:
“Cange can occur for other reasons besides trends.”
This is the first time I have ever seen a trend being claimed as a cause of change. I was under the impression that the trend was the manifestation of that change. When I turn the kettle on, the trend is for the temperature of the water to increase. It tells me nothing about the cause, just the a change is occurring over time.
Sorry, typo crept in. It should have been Nullius in verba, not nullifies.
Nullius in Verba says: May 31, 2013 at 3:28 pm
“The idea of testing for a significant trend is to see if there is evidence for a trend. Change can occur for other reasons besides trends.”
The emphasis was meant to be on “significant”. If you’re testing for significance, you’re testing whether you have identified a change from a normal, which can’t have had that trend indefinitely.
“How do you know there was no trend before?”
A fixed trend can’t have been the normal state of affairs, just as with random walk.
“It’s approximately random walk, and the approximation is good enough over periods short enough”
But short periods won’t do. If you want to say that the present observation is natural variation and nothing has changed, then you need a model of that variation which doesn’t change. If you have to postulate that random walk just applies during the period, then that needs explaining just as a trend would.
In fact, a random walk with autocorrelation 1 would be a straight line.
From Nick Stokes on May 31, 2013 at 3:16 pm:
This is the point where Smokey would start slapping you around the room, because the Null Hypothesis states the warming is natural variability, the onus is on YOU to prove it is not. The Null Hypothesis does not require proving. It does not require one to “propose something that would work without changing”. Climate skeptics have nothing to prove. If you want to say it’s not natural, than YOU prove otherwise.
You’re a smart guy, Nick. You know how the Null Hypothesis works. You’re being disingenuous to act like you don’t. Why are you coming here to the World’s Most Viewed Climate Website and trying to deceive others? Go back to RC and impress your pal Gavin with your antics.
That’s what Smokey would have said. With many links including many links to graphs. You’re really having fun taking advantage of his absence so you can pull out the cheap tricks that he never fell for, I can tell.
Null hypothesis: [statistics] A statement that essentially outlines an expected outcome when there is no pattern, no relationship, and/or no systematic cause or process at work; any observed differences are the result of random chance alone. The null hypothesis for a spatial pattern is typically that the features are randomly distributed across the study area. Significance tests help determine whether the null hypothesis should be accepted or rejected.
From GIS dictionary
“This is the first time I have ever seen a trend being claimed as a cause of change.”
You’re right. That’s not clear.
There are two separate aspects to consider: the objective truth about the physical system, and our subjective estimate of it filtered through the murky lens of observation.
An objective trend in a physical system is understood to mean that the reality is some deterministic function of time (the first derivative of which is the trend) plus random noise from other unspecified causes.
But the random noise can cause change too. And if the random noise is such that neighbouring values are correlated, this can give rise to successive values all going up or all going down more than you would expect, given that most of our intuitions are built on results about uncorrelated noise. If you take a short segment of the output, it changes in a way that looks like an objective underlying trend. It isn’t though, it’s a random outcome that could equally well have come out going the other way.
Take a sequence of random numbers, and then compute a moving average of them, taking blocks of a hundred or so consecutive values. Look at a short section of this moving average series. Does it look like there’s a trend in them? The numbers will start low and gradually rise, or start high and gradually fall. From the point of view of subjective observation, you could call that a ‘trend’. But the underlying objective reality is that there is no difference in how they’re generated over time. The distribution is always the same, and the true average is a constant, neither rising nor falling.
In the case of the weather, we do actually know that there is an underlying trend (the greenhouse effect is real physics) but we don’t know how big, or whether it is big enough to show up against the background noise. The idea of this sort of test is to show that the observations are feasible as the outcome of a process with no underlying trend, and therefore we cannot say we know for a fact that the rise has shown up. It doesn’t say that there’s no rise, or that the trendless model is the truth. It’s only a null hypothesis that hasn’t been rejected.
… “Looking at the Thames we know it isnt frozen.” …
Wow with such “heavy weight” argument what else to say… But maybe there is a few “good ones” sourced direct from warming consensus biased Wikipedia:
Wikipedia(River Thames frost fairs)
”
However, the colder climate was not the only factor that allowed the river to freeze over in the city: the Thames was broader and shallower in the Middle Ages – it was yet to be embanked, meaning that it flowed more slowly.[5] Moreover, old London Bridge, which carried a row of shops and houses on each side of its roadway, was supported on many closely spaced piers; these were protected by large timber casings which, over the years, were extended – causing a narrowing of the arches below the bridge, thus concentrating the water into swift-flowing torrents. In winter, large pieces of ice would lodge against these timber casings, gradually blocking the arches and acting like a dam for the river at ebb tide.[6][7]
”
“The last frost fair”
”
The frost fair of 1814 began on 1 February, and lasted four days. An elephant was led across the river below Blackfriars Bridge. A printer named “Davis” published a book, Frostiana; or a History of the River Thames in a Frozen State. This was to be the last frost fair. The climate was growing milder; also, old London Bridge was demolished in 1831[12][13][14] and replaced with a new bridge with wider arches, allowing the tide to flow more freely;[15] additionally, the river was embanked in stages during the 19th century, which also made the river less likely to freeze.
”
January 1814 mean temperature: -2.9 degC [*]
“The Thames freezes over upstream, beyond the reach of the tide, more often – above the weir near Windsor for example. The last great freeze of the Thames upstream was in 1963”
January 1963 mean temperature: -2.1 degC [*]
January 1684 mean temperature: -3 degC (Great Frost) [*]
AFAIK The Great Freeze of ’63 did not involve London. Only at Windsor and upstream (beyond the reach of the tide). 1776 is reported to have frozen at London w/t only -1.6degC mean for january.
—
Philosophical question directly related to the thread:
What or how we define “Normality”?
Was those time colder than actual? Was it colder than normal?
Is actual time warmer than the “colder” refered period? Is it warmer than normal?
All those techno babling on statistics is simply offuscation of this central question of definition of normality. Sometimes you can look at a data graph and see trends w/o doing a damn statistic test of the null hypothesis.
[*] MANLEY, G. Central England temperatures: monthly means 1659 to 1973
kadaka (KD Knoebel) says: May 31, 2013 at 3:53 pm
“the Null Hypothesis states the warming is natural variability, the onus is on YOU to prove it is not. The Null Hypothesis does not require proving.”
But it does require stating. And it has to be plausible enough that rejecting it, which is the objective, is an interesting result.
The usual null here is stationary process with noise of some sort. Keenan wants to substitute random walk as the model of natural variation. But that isn’t sustainable.
It also isn’t physical for another reason. Earth’s temperature is determined by a balance between incoming and outgoing radiation. That fixes it because of the S-B law. There can be temporary variations where heat accumulates for a while, and the effect at the surface can change because of GHGs etc. But it can’t just drift. A random walk has no fixed point.
” If you want to say that the present observation is natural variation and nothing has changed, then you need a model of that variation which doesn’t change.”
That’s what we’ve got. The model doesn’t change over time, but it’s only valid for a short segment. Any short segment.
It’s the same reasoning by which you would analyse the behaviour of a curve by fitting a straight line to a part of it. Your ‘it’s a straight line’ model doesn’t change, and applies to any short segment. Pick a different segment, and it’s still ‘a straight line’ – just a slightly different one. We don’t have to explain why the curve is ‘straight’ just in that period we’re analysing. It’s ‘straight’ in any sufficiently short segment. Nothing changes in that regard.
“Null hypothesis: [statistics] A statement that essentially outlines an expected outcome when there is no pattern, no relationship, and/or no systematic cause or process at work; any observed differences are the result of random chance alone.”
That definition is not quite right. The null hypothesis is the hypothesis that you are trying to demonstrate is false. Usually you are interested in showing the existence of a new or previously unknown deterministic effect, and so the default position you are trying to disprove is generally that there is no such effect. But you can also do it the other way round.
You could, for example, take a 3C/century trend plus some noise model as your null hypothesis, and then try to reject it. If you succeed, we would know that 3C/century plus that noise model was untenable. If you fail, we would know no more than we did to start with.
Nullius in Verba says: May 31, 2013 at 4:32 pm
“That’s what we’ve got. The model doesn’t change over time, but it’s only valid for a short segment.”
???
I’d like to see such a model fully specified.
kadaka (KD Knoebel) says:
May 31, 2013 at 3:53 pm
From Nick Stokes on May 31, 2013 at 3:16 pm:
As I said above, if you want to say that it’s just natural variation and nothing has changed, then you have to propose something that would work without changing.
(Kadaka) This is the point where Smokey would start slapping you around the room, because the Null Hypothesis states the warming is natural variability, the onus is on YOU to prove it is not. The Null Hypothesis does not require proving. It does not require one to “propose something that would work without changing”. Climate skeptics have nothing to prove. If you want to say it’s not natural, than YOU prove otherwise.
Ahhhh Grass Hopper, you have learned well the lessons taught by Master Smokey!
MtK
“I’d like to see such a model fully specified.”
???
It’s just ARIMA(3,1,0). I get the feeling you’re still not understanding my point.
In the mean time, Delingpole writes a cracker.
http://blogs.telegraph.co.uk/news/jamesdelingpole/100219218/trougher-yeo-recants-on-global-warming/
Regarding…
http://wattsupwiththat.com/2013/05/29/its-official-we-are-all-climate-sceptics-now/
OK, help me out here. I was under the impression that random walks do, in fact have a centroid, ala the drunk and the lampost. Am I thinking of another phenomenon?
More accurately, any (and every) proponent of the current CAGW=CO2 Hypothesis MUST be able to explain why the climate – across every earlier period of interest – has varied by as and more of today’s random changes: Specifically, what has caused the Roman Warming Period, the Dark Ages, the Medieval Warming Period, the Little Ice Age, and today’s Modern Warming Period; and then, why such changes no longer occur .
“OK, help me out here. I was under the impression that random walks do, in fact have a centroid, ala the drunk and the lampost.”
The mathematical model extends infinitely far both forwards and backwards in time. Because it’s hard to get your head round the idea of something with no defined distribution at any point, introductory explanations usually start with the rooted random walk, which is specified to be at position zero at time zero. Then at any subsequent or previous time there is a definite position distribution, with mean zero, that gets broader with time. Once you’ve got your head round that, you take away the coordinate system, and point out that things look exactly the same if you pick any other point on the path as the origin.
@Nick Stokes: “The usual null here is stationary process with noise of some sort. Keenan wants to substitute random walk as the model of natural variation. But that isn’t sustainable.”
Why not?
Steven Mosher says:
May 31, 2013 at 11:20 am
Keenan’s statistical model is physically wrong.
When you analyze data you choose a model. picking a model that is physically wrong ( for example a random walk for temperature) can get you a better fit, but it’s a mistake.
In a causal universe, randomness does not exist, at least at the macro level.
When we talk about randomness, as in random walk, we mean the causes are unknown.
If a random model fits the data better than a proposed physical model. This is proof the proposed physical model is wrong.
Keenan’s statistical model proves your physical model is wrong.
Nullius in Verba says: May 31, 2013 at 4:49 pm
“It’s just ARIMA(3,1,0). I get the feeling you’re still not understanding my point.”
You’re right. Where is the short period specified in ARIMA(3,1,0)?
D.J. Hawkins says: May 31, 2013 at 5:21 pm
“I was under the impression that random walks do, in fact have a centroid, ala the drunk and the lampost. Am I thinking of another phenomenon?”
I think so. A random walk has no memory. Ir doesn’t know where to go back to. A gas molecule prtetty much follows a random walk.
@Mike Jonas says 2:52 pm and Nick Stokes
My First Off was poorly phrased. What I said:
was very poorly phrased.
A better phrased point:
Keenan’s model would be wrong if it leads to physically impossible scenarios and violates boundary conditions. Instead, you [Steven Mosher] discard this predicate and say instead it is wrong because by “looking” at the data it doesn’t support the conclusion you prefer, not because it leads to impossible physics. A failure in logic. A failure in simile. A slight of hand with predicate.
But the third point is the stronger. Of course Keenan is wrong. All models are wrong. But is it wronger than a linear fit the MET uses? Which one leads toward more impossibilities?
Slingo’s anwer is weak and verbose.
“Where is the short period specified in ARIMA(3,1,0)?”
When people say that a sufficiently short segment of any smooth curve looks straight, where is “sufficiently short” defined?
“A gas molecule prtetty much follows a random walk.”
Good example!
A gas molecule cannot actually follow a random walk because it’s behaviour is bounded in both space and time. Gases have to be confined to act as gases, and the confinement prevents it moving arbitrarily far. For example, gas molecules in the atmosphere are gravitationally bound to the Earth.
The caveats are hidden in your words “pretty much”. It’s the same sort of “pretty much” that I’m using. Over short enough periods of time, gas molecules do indeed follow “pretty much” a random walk. Over a long enough time, gravity will pull it back towards the average. But the forces on a molecule from its impacts with it’s neighbouring molecules are much larger than the gravitational forces keeping it on the Earth, and so the latter can be ignored.
Stephen Rasey says: May 31, 2013 at 6:06 pm
“But is it wronger than a linear fit the MET uses?”
Well, have you ever heard the Met, or anyone else, spontaneously talk about the trend since 1880 as evidence of anything. They were clearly not keen to do so here, and only did when asked. Apart from anything else, the further back you go, the lower the trend. But more importantly, and related, the less the notion of linear rise makes sense. The forcing history is nothing like what would be needed.
The MO and others talk of the increase since 1970, 1950 or whatever. This is the period clearly influenced by anthrops, and there are no obvious non-linear effects to take into account (well, since 1975 at least). If they have to answer a question like is the rise since 1880 significant, and are pushed to quantify it, then their choice of model is a sensible one to use.
A question – is the temperature rise over the last 20,000 years statistically significant? What test would you use?
Nullius in Verba says: May 31, 2013 at 6:18 pm
“When people say that a sufficiently short segment of any smooth curve looks straight, where is “sufficiently short” defined?”
I doubt if they do say that. Any examples? I think people look at sections where they think there might be reason to expect a trend. Or possibly limited by what they have. But I can’t imagine shortness on its own being a sought after feature.
Re gas etc – these processes don’t have time boundaries. Argon atoms have been following a random walk for billions of years. They have physical boundaries, enforced by gravity (with path length) at the upper. If the model of “natural variability” includes such boundaries, it should identify them.
Mac the Knife says:
May 31, 2013 at 4:49 pm
Many times Smokey has put Nick Stokes in his place. But some folks are impervious to reason.