I have been asked by a number of people to comment on a new paper that purportedly shows that “statistical tests for global warming fails to find statistically significantly anthropogenic forcing.” This paper was highlighted over at Watts Up With That. Money quote from “Polynomial cointegration tests of anthropogenic impact on global warming”:
…We show that although these anthropogenic forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance. Therefore, greenhouse gas forcing, aerosols, solar irradiance and global temperature are not polynomially cointegrated. This implies that recent global warming is not statistically significantly related to anthropogenic forcing. On the other hand, we find that greenhouse gas forcing might have had a temporary effect on global temperature.
As I have been saying for years, it makes little or no physical sense to say that temperatures have or have not “statistically significantly” increased or decreased. I understand what those (classically trained, frequentist) statisticians mean when they make statements like this, but that doesn’t imply these statements have any real, i.e. non-metaphysical, meaning.
Assume first we have unambiguously defined what a “global mean temperature” is. Whether or not a GAT makes physical sense is not important, so please no more emails informing me of this (I get many). What is indisputable is that I can operationally define a GAT. This can be as simple as, “The annual GAT shall be what the NWS thermometer reads in Central Park on 4 July at noon,” to more complicated functions of observed data (say those which incorporate more than one station and time, or that use satellite or buoy numbers). I just don’t care here what those functions are. Any operationally defined GAT is okay with me.
Next, I assume the GAT is measured without error. That is, the operationally definition itself has no uncertainty in it. If you, or some authority like my pal Gav, tells me the GAT last year was 15.42oC, then I accept that it was 15.42oC and that we are 100% sure of it.
Now let’s play with an (imaginary) plot of GAT by time. Some years it’s up, others down, and in still more it darts around some middle. I won’t draw this because I’m lazy; but you’ve seen hundreds of these plots.
I have real difficulty convincing people of what I say next. For some reason the simplicity of the answer is not compelling.
Given what I’ve said thus far (agreed upon operational GAT, no measurement error), then if we want to ascertain whether temperatures have increased, decreased, or stayed the same, all we have to do is look. We will always be 100% sure of our answer. If the temperatures between two dates have increased, a glance will show it. If somebody instead claims that it has decreased between these two dates, or that it has stayed the same, then we are right to refer this person to an optometrist or a psychologist.
That’s the final answer, too. We are done with a plot.
But we can get physical. We can additionally ask what caused the observed changes. Something caused the changes (and it isn’t measurement error, as we’ve agreed). Some real, physical thing or things caused the changes. Tangible entities like the sun’s rays, or even human beings exhaling. One thing is certain: “chance” did not cause the observed changes, because “chance” does not cause anything. It just makes no logical or physical sense to say “the observed temperature changes are consistent with chance.” What a person always means—whether or not they know it—when they utter phrases like that is, “Something caused the observed changes, but I have no or little idea what it was.” Nothing in the world wrong with admitting what you don’t know, but we shouldn’t try to make our ignorance sound scientific by adding p-values.
Differing people posit different physical causes for the observed changes. How many different possible causes are there for any set of observed data? An infinity, which is quite a lot of culprits to check. So people have to narrow it down some to get on. No matter how this is done, in the end there will be a set of possible explanations, or “models”.
Because there are so many models to choose from, we can always find some which explain the observed GAT well. But we can also find just as many alternate models which won’t be at all consistent with the observed GAT. Classical statisticians touting the close-fitting models will say their model statistically significantly “proves” whatever theory led them to choose their model; thus their model is right. Classical statisticians trumpeting the ill-fitting models will counter that the fit is statistically insignificant, and therefore their model is to be preferred.
When this isn’t nuts, it’s backwards. Go ahead and tout which model you will, but understand that fitting the current data well or ill is only of little help in ascertaining whether the model best describes uncertainty in GATs we have not yet observed. The model or models which do this well are those that should be trusted. Everything else is not interesting.
Logic and induction can whittle down a set of models. Prior experience shows that it makes no sense, for example, for a star 100 million light years away to cause changes in our GAT. So we won’t include that star in our model. Another example: Any organism which moves in and on the surface of the planet, since this movement changes the composition and placement of air, necessarily cause changes to the GAT. Thus it makes sense to ask how much—not if, but how much—influence human beings have on the GAT.
That means that any statistical model which says humans don’t “statistically significantly” change the GAT aren’t saying anything that makes physical sense. Of course human beings change the GAT. The real question is whether this change is “significant” in some operationally defined physical, not statistical sense. Maybe “significant” mean “Percentage of polar bears decreases by 8%” or something else entirely. Either way, the answer to whether humans “significantly” effect the GAT must be either yes or no (or only a probability if the definition of “significant” cannot be made without error or is itself subject to uncertainty) because we already know they do effect it, though perhaps not “significantly”.
The paper which Anthony highlighted is just one more which claims not to explain how the observed changes occurred. (Re-read that sentence). Whether it is useful in explaining—projecting, forecasting, prognosticating, etc.—future GAT is an open question. I’m guessing, just from the structure of the model, that it wouldn’t do too well. But that, dear reader, is just my opinion.
I’ve often been asked by less statistically inclined friends to help them analyze some data. I always start by looking at it (if it’s easy to plot) or ideally having them look at it. They somehow think that being able to apply some obscure test and give them a 0.05 p-value creates useful meaning.
Of course, it’s never been anything like a GAT.
PAY NO ATTENTION TO THE DATA BEHIND THE CURTAIN
Great post. The p-value for a linear regression is a little disapointing (how different from no slope must my line be?)..
Sadly few people want to show forecast skill (model x versus model y) when predicting new data.
I would like to see folk fit multiple curves, using different parameters, to the same data and show the results for each. For kicks I once built a predictive model of GAT using Bigfoot sightings, tax rates, and a few other weird tidbits– it did a pretty decent job, despite being total fantasy.
I thought the point was that the GAT measurements (as it might be) do contain uncertainty so that it’s legitimate to ask, “did it go up or did it go down?”
Thank you.
The Berkeley Earth project provide a nice fit between sulpher, Co2 and their measure of GAT (with errors of course). Prof Briggs – how useful do you expect that correlation to be in “explaining—projecting, forecasting, prognosticating, etc.—future GAT”
Re:”Classical statisticians touting the close-fitting models will say their model statistically significantly “proves†whatever theory led them to choose their model; thus their model is right. Classical statisticians trumpeting the ill-fitting models will counter that the fit is statistically insignificant, and therefore their model is to be preferred.”
I guess if you talk in general terms like that noone can sue you for libel, but I would strongly deny that any competent statistician, classical or otherwise, would take either of those positions. Statisticians don’t “tout” models; they just express whether and to what extent they would find the observed results surprising if the models were true – and they certainly wouldn’t claim to “prove” any model, no matter how “close-fitting”.
Readers of my paper “Planetary Surface Temperatures. A Discussion of Alternative Mechanisms” will realise that it is merely a review paper of other studies. Some of the references do in fact refer to papers published in, for example, The Journal of Atmospheric and Solar Terrestrial Physics. Another reference is to work done by Hans Jelbring whose 1998 thesis was Wind Controlled Climate. Paleogeophysics & Geodynamics, Stockholm University. 111pp.
The concept of the temperature gradient in an atmosphere developing at the molecular level is not my original work by any means. Hans Jelbring (in my Ref [11]) wrote “Hence, the atmospheric mass exposed to a gravity field is the cause …”
Either you accept the fact, first postulated by Loschmidt in the 19th century, that the requirements of both the First and Second Laws of Thermodynamics dictate that an autonomous thermal gradient must develop in a still gas in a gravitational field, or you accept the naïve conjecture of climatologists, who usually have little understanding of physics, that there would have been an isothermal atmosphere in the absence of water vapour and so-called greenhouse gases. The latter requires a blatant violation of both the First and Second Laws of Thermodynamics because it assumes that, every time a molecule moves upwards, energy is created and entropy decreases.
Doug Cotton
By the way, I agree with your criticism of the phrase “statistically significantly related”. Thanks for showing equal skepticism towards the significance of analysis which purports to support a view which (I have been led to surmise) you might be inclined to share.
Alan Cooper: statisticians may not, but most model builders aren’t statisticians. A biologist will use statistics as part of their job, for example.