Bishop Hill More from the Beddington FOI
May 27, 2011 Climate: Statistics Climate: Surface Here is another interesting document from the Beddington FOI I mentioned last week.
This was sent in February 2010 when the furore over Climategate was still at its peak and before the inquiries got under way. It consists of a summary of the science of global warming sent to Beddington by Julia Slingo, the chief scientist at the Met Office. Slingo, you may remember, later appeared at the SciTech committee hearings alongside Beddington.
What is interesting about Slingo's take on climate science is all the statements of statistical significance she makes:
For the last 3 decades the rate of temperature increase is significant even when uncertainties in the observations are factored in (Fig. 3).
Every year since 1998 (in fact every single year for the past three decades) has been significantly warmer than the temperatures you'd expect if there was no warming [baseline of 1861-1900]. The last ten years have all been among the 15 warmest in the historical record ; it is just that these years have not been quite as warm as 1998.
From the 1980s onwards each decade has been significantly warmer than the previous decade.
The overwhelming majority of leading climate scientists agree on the fundamentals - that the Earth is definitely warming
As readers here know, the claims of statistical significance in the global temperature records are based on an assumption that the Earth's temperature can be approximated by the AR1 statistical model, an assumption that can apparently be readily shown to be incorrect. As Doug Keenan points out in an email, Slingo's final claim - that the overwhelming majority of leading climate scientists agree that the Earth is definitely warming - is 'technically true, but irrelevant if none of those scientists knows how to determine whether such warming is significant'.
What is so frustrating about this is that the question of model selection for the temperature records doesn't appear to be a particularly abstruse bit of statistics, as this excerpt from an undergraduate textbook on time series analysis shows (see also here):
So I must confess that I am a little mystified as to why the AR1 assumption is made. Nobody seems willing to say anything in favour of it, but nobody within the climate science or statistical mainstream seems willing to say it's wrong.
Reader Comments (18)
"the temperatures you'd expect if there was no warming"
Does she mean arithmetical warming, or warming over and above what one might expect when moving out of a period of significant cold (the LIA)? What temperatures would she expect, I wonder..?
Of course we're getting warmer. My Phil says so, and he's a good boy.
He was on the telly with a Sir a few weeks ago. I had the neighbours round to watch and we had special biscuits. It was ever so good, but he looks a bit thin.
Phil's Mum
Didn't your boy also say that there had not been any statistically significant warming in the last 15 years? I wish he'd make his mind up.
I missed that bit because I had to help Mrs Cresswell from number 27 to the lav......I think the camomile tea disagreed with her.
In a temperature signal that shows around 0.1C baseline change each and every decade (it is 1/f noise), the simple fact is that cooling or warming is normal. Therefore cooling or warming of the same magnitude is not significant because it is normal.
Only if you define normal as being abnormal can the insignificant change be described as significant ...
Item 4 in the covering letter from Slingo indicates a hope that Muir Russell will NOT call in the statisticians to check the Met Office's work. Presumably she was not confident that the MO's conclusions would stand up to such additional scrutiny.
Messenger
I agree. That statement in Item 4 is most peculiar -- implying a fear should statisticians check the methodology. But isn't that a basic problem in the climate science industry? (Lack of participation/imput by competent statisticians.)
"From the 1980s onwards each decade has been significantly warmer than the previous decade."
From the 1940s onwards each decade was significantly cooler than the previous decade.
If I pick the right time to stop!
"If you had invested 1000$ with us in 19xx it would be worth..."
Extrapolation has no scientific validity.
It looks to me as if Slingo was sending information to Beddington so that he could pass it on to his buddy Muir Russell to assist his inquiry (i.e. tell him he doesn't need to look at the statistics), to which HM Government had no input, according to Beddington.
The Met Office Climate science Briefing Paper is a litany of garbage. It must have been written by a summer student in his spare time one evening down the pub.
An AR1 model is an ARIMA model.
Mike N
I take your point, but why do they assume AR1?
To elaborate a little on the textbook exercise (3.33)…. An ARIMA(p,d,q) model has three components: AR(p), I(d), MA(q). An ARIMA(1,0,0) model is the same as an AR(1) model is the same as AR1.
The most commonly used method to fit a straight line to data is the method of least squares. That method is equivalent to fitting a straight line where the residuals (how far away from the line the data points are) are assumed to be from iid [independent identically-distributed] Gaussian distributions.
A generalization of that method is to assume that the residuals are AR(1). That generalization is used by the IPCC, and several climatologists.
What the textbook exercise (3.33) is asking students to do is fit an ARIMA model without a straight line. I.e. assuming that temperature variations have no deterministic trend. Other portions of the textbook that consider this issue include Example 2.5 and exercise 5.3. The authors strongly indicate that a deterministic trend is neither needed or desirable in modeling the data.
As His Eminence notes, the really startling issue here is that nobody has ever attempted to justify using a straight line with AR1 residuals. Climate scientists just assume that they can use it. The fact that that they should not use it is actually secondary, and requires doing some statistical calculations. Basing their analyses on an unchecked assumption is the primary error—and that requires no statistics to understand.
The same point was made in my WSJ article. That article shows that an ARIMA(3,1,0) model is far better than the IPCC model. Other people have made similar observations. (I sent His Eminence the textbook exercise to illustrate this.)
__________________________________________________
The d in ARIMA(p,d,q)
If the time series is x1, x2, x2, x4, …, then the we can subtract adjacent elements to obtained the differenced series: x2−x1, x3−x2, x4−x3, ….
With an ARIMA(p,0,q) model, no differencing is done. With an ARIMA(p,1,q) model, the series is differenced, and then that differenced series is modeled via ARIMA(p,0,q). With an ARIMA(p,2,q) model, the series is twice differenced, and then the resultant series is modeled via ARIMA(p,0,q). Etc.
An ARIMA(p,0,q) model is usually called “ARMA(p,q)”.
An AR(1) model is another name for an ARIMA(1,0,0) model. The temperature is not ARIMA(1,0,0) but it may still be ARIMA(p,d,q) for some suitable set of parameters p, d, and q.
The famous VS 'unit root thread' was effectively arguing that d = 1, for example.
Or it might not be ARIMA at all. ARIMA is a very wide class of models, but it doesn't fit everything.
“The time has come” the Slingo said
To talk of many things
“Of tricks and trends and tipping points
And early coming springs
And why the sea is boiling hot
And whether pigs have wings...”
If it was written down the pub, as Phillip Bratby suggests, the subheadings on pp 6-10 dealing with sceptical points appear to be in a different hand to the text, with sometimes little relation between the two. The hockeystick and the absent troposphere hotspot in particular are dealt with in a language apparently aimed at primary school children.
So, in fact, fascism.
Well it might appear off-topic, but read and you see why it isn't.
http://wattsupwiththat.com/2009/06/20/the-met-office-brings-doom-to-a-place-near-you/
Prof Slingo doesn't seem to have any hard and fast ideas, except warmism that is.
I am reminded of VS