Guest Post By Javier
We define “warming” as a positive rate of temperature change over time. According to the main hypothesis, warming since 1951 has been due almost exclusively to the increase in GHGs (greenhouse gases), of which CO2 is the most important one. The IPCC does not find anything else that has contributed to the observed warming.
Figure 1. IPCC attribution of warming. AR5 SPM.
According to the IPCC at least 77%, but more probably 120%, and up to 200% of the observed warming, has been caused by GHGs.
The rate of CO2 change (the atmospheric increase in CO2 every year) has been increasing almost linearly since 1959 and is currently ~2.4 ppm/year.
Figure 2. Mauna Loa rate of increase in CO2 (ppm/year). Thin line, 12-month increase. Thick line, gaussian smoothing. Red line, 2nd order polynomial least-squares fit to the yearly increase.
If the IPCC hypothesis was correct, the warming rate should increase (accelerate) if CO2 is increasing rapidly. The warming rate can only decrease (decelerate) if CO2 is increasing more slowly and can only turn into cooling (negative rate) if CO2 is decreasing.
But the hypothesis doesn’t fit the observations. The HadCRUT 4 rate of temperature change (°C/year) is no longer increasing. In fact, it stopped increasing ~1994 and has been decreasing since. Global warming has been decelerating for over 20 years despite CO2 levels increasing at the same rapid rate.
Figure 3. HadCRUT 4 rate of temperature change (°C/year). Thin line, 12-month rate of change. Thick line, gaussian smoothing. Red line, 2nd order polynomial least-squares fit to the yearly increase.
Since 2017, the rate of temperature change has become negative.
Figure 4. Zoom of the HadCRUT 4 rate of temperature change (°C/year). The best fit polynomial (black line) shows the long-term evolution in the rate of temperature change.
The global warming deceleration since 1994, and cooling since 2017 are incompatible with the hypothesis that the increase in CO2 is driving global warming. Other factors must be more important than CO2.
The Mauna Loa CO2 data can be downloaded here and the HadCRUT 4 global temperature data can be downloaded here.
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Oh, I forgot. Ever heard of overfitting? It plagues most naive attempts at statistics. I see it all the time.
Ever heard of some doctors using jargon to appear more knowledgeable than they actually are about the patient’s problem? It also afflicts some statisticians that like to thrown names of specific tests even if they don’t know how to spell them correctly, like the Maclaurin (not MacLauren) series.
Myself coming from statistical physics and having worked for nearly 20 years as a quant in the finance sector I think the argument of Javier could be made more catchy as follows:
(1) Assuming equilibrium thermodynamics being applicable here, the change of heat $$Q$$ is proportional to the change of temperature $$T$$ or as formula
$$ \Delta Q = c \Delta T$$
with some appropriate positive specific heat capacity $$c$$, depending on the material to be warmed up (water, air, soil).
(2) Take the HadCRUT4 monthly temperature set and compute the first difference of this time series, i.e. $$Delta T$$. Doing a statistical analysis of this, we obtain for the entire data set (starting January 1850 and ending December 2018) the expectation of $$Delta T$$ to be approx. 0.000645 (i.e. 0) and the standard deviation approx. 0.138482. It seems that a random walk without drift is a good proxy for the stochastic process describing $$Delta T$$. (I have not done the further statistical tests yet to confirm this with a statistical significance of 6 sigma, say.)
As a consequence from (1) and (2) we conclude that also $$Delta Q$$ follows a random walk without drift, i.e. it is not getting warmer over the observed time horizon. Interestingly, this result also holds if we only look at the time interval from January 1950 until December 2018. If this time series was a stock chart, the trend would be so insignificant that one could not benefit from it as an investor .
The mathematicians amongst the readers may recall the famous reflection principle for Wiener processes: at any time a driftless random walk can be reflected on a horizontal line going through the “last point” and the continuation of the mirror image is equally likely as the original random path.
A final caveat: it is not clear if methods of equilibrium thermodynamics for such a complex system can be applied so far away from equilibrium.
Do you mean ‘it is not getting warmer’ or do you mean ‘the rate at which it is getting warmer is negligible’?
I think you mean the latter – temperatures are rising, but the rate at which temperatures are rising is not increasing.
Nigel,
modelling the temperature $$T$$ (actually the anomaly) by a stochastic process whose first difference seems to be a random walk without drift (meanwhile I have done Dickey-Fuller unit root test for stationarity and a t-test for the mean -it appears the hypothesis that the drift is zero cannot be rejected within the usual confidence levels), then the actual trajectory of the stochastic process for $$T$$ is increasing to the current levels. However, the expectation of $$T$$ is unchanged because the expectation of $$Delta T$$ is zero. In other words, rather then going up from where we actually are, in the next time steps $$T$$ could equally go down – it follows a Martingale process where the best estimate for the expectation is the last observed value!
In finance it is likewise difficult to find out whether a stock goes up because there really is a trend significantly different from zero (and positive) or whether the stock price is there where it actually is due to a sequence of random fluctuations which happened to go up. In finance we call it the search of “alpha”.
As a consequence of my reasoning I expect $$Delta T$$ equal zero and thus the expectation of heat change would be also zero (provided the heat capacity is a nonstochastic function or at least cadlag and in the natural filtration of the stochastic process for $$T$$). Thus my statement would be ‘it is not getting warmer’.
Best regards, Markus
P.S.: I have only looked at the problem from a stochastic process viewpoint. A theory which models the time-change of a physical observable such as a temperature by a stochastic process is not as “good” as a theory modelling the observable starting ab initio from first principles. But then again non-equilibrium thermodynamics or even non-equilibrium quantum statistical physics to derive some forecasting formulae for any macroscopic observable is still quite a challenge.
Thank you for trying to see through this mist. My only comment is that the first difference is pretty random, but there is a small upwards drift. Whether that drift is rising or falling is very debateable, the data simply does not provide the information.
I guess it’s the same in the finance world – short term it is a random walk, but over a 20 year period you expect to see an upward drift.
I agree entirely, it is much better to have an underlying model of the physics and look at the uncertainty in that. Actually, now i mention it….let me post something….
I’m sorry for the slow response, I have been doing some real work….
I don’t think Javier has made a substantive response to any of my concerns. Overfitting is a very real concern, it plagues many areas of statistics and data science. Making conclusions based on minute R^2 for data which is almost pure noise is another very common mistake.
But, let us try this. Let us assume that the plots in fig 3 and 4 had data to which a second degree polynomial had an excellent fit, with an R^2 of around 0.8 rather than the actual 0.001 or so. What would our conclusions be?
Before 1969 the temperature was falling (the first derivative was negative). However, the upwards acceleration was very large, so much so that if the behaviour in 1960 continued we would now be in a situation where the temperature increases (the first derivative of temperature) would be very high, reaching maybe around 0.2 degrees C per year by 2019, and hence the actual temperatures would be so high that disaster would be imminent.
By 1994 the acceleration (second derivative of temperature) had fallen to zero, but the temperature was still rising at a rate of 0.02 degrees C per year.
By 2019, the acceleration had reversed enough that the temperature rise (first derivative of temperature) had fallen to zero. Temperatures were no longer rising.
However, if the behaviour continues, the reversal of acceleration will be so great that by 2015 temperatures will be falling at a disasterous rate, and the rate of falling temperatures will be accelerating in a downward spiral at ever more precipitous rates.
Overall in the period 1960 – 2019, on average the rate of temperature rise was positive, the acceleration in temperature rise was positive (the rate of temperature rise was increasing) and the temperature in 2019 was significantly higher than in 1960.
How does that work for you?
I’m sorry, a typo, I meant 2050, not 2015. Hell has not yet frozen over.
Let me go off slightly from the track, but it may bring some intuition.
In my day job I am an expert in probabilistic uncertainty quantification of oil and gas reservoirs, where you use historical data as an input to a Bayesian prodeiction. You have to construct an ensemble of models, using a likelihood function and applying full Bayesian Markov Chain Monte Carlo methods. random walk methods are hopeless, so I use Hamiltonian methods.
Some of the early work I did on history matching was based on work done by Durham University. History matching of climate is, in principle, no different to history matching of oil and gas resevrvoirs, but climate models are much more complex. My [battle the last 20 years has been to convince reservori engineers that they need to include realistic uncertainty, and a good match does not necessarily mean a good prediction.
Good stuff you are working on! A first and maybe naive analysis of the data using first-order differences to obtain a stationary time series and modelling this by a random walk (a valid hypothesis not rejected by a suit of tests) does not provide the desired insight. Maybe a Bayesian approach is more appropriate – but then I must confess I am a frequentist…
Some of the people I worked with have worked on climate models. Here are some references. You will see they are not gullible, and somewhere they talk about IPCC as a beauty parade.
https://projecteuclid.org/download/pdf_1/euclid.ba/1340370559
https://people.maths.bris.ac.uk/~mazjcr/
Hmmmm – lots of reference, I have some of the papers, but most seem to be for purchase only.
No matter. The point is that some serious statisticians are looking at climate change, and they, being statisticians, are very comfortable with uncertainty and very uncomfortable with certainty.
Here we go.
http://www.mucm.ac.uk/Pages/Downloads/Reading%20List/Probabilistic%20Inference%20for%20Future%20Climate%20ROUGIER.pdf
I haven;t read it for some years, but as soon as I read ther first paragraph I saw it was relevant to our discussion here.
Thanks for the reference to Rougier 2007. He estimates a covariance structure for the Gaussian process which is quite tricky. I shall look into the details of this paper over the week-end. From EM algorithms applied on Gaussian correlated data I recall lots of problems (the MLE sometimes converges to a singular covariance matrix and special constraints need to be introduced to obtain a feasible solution).
In my own work I use Matern correlation functions i the covariance matrix, and have two orthogonal directions and different correlations lengths for the two directions. I then estimate the hyperparameters by optimising the restricted likelihood function. I use a combination of BOBYQA and GA to do this, but it is also possible to use quasi Newton methods if one can be bothered to go through all the algebra. My own work is univarariate, but Jonty did some work us on multivariate methods, where the covariance matrix takes account of correlations in time – but the matrix gets much bigger depending on how many points you choose. I preferred to have good univaraiate approximations rather than weaker multi variate.
ps. I can easily be found on LinkedIn, where I have my email address if you want some papers which may be of interest. I am also looking at Weibull. Have you come across
https://github.com/ragulpr/wtte-rnn
My current day job involves predictive asset maintenance for Shell.
http://empslocal.ex.ac.uk/people/staff/dbs202/publications/2012/stephenson.pdf
https://arxiv.org/pdf/1411.6878 – this paper is great, and almost readable!
The growth rate of atmospheric CO2 concentration is trending exponentially and at the rate we are going, we will hit 100,000 ppm in < 140 years. Plot it out yourself in Excel. OSHA exposure tables indicate convulsions and death within minutes at that level. We will probably all notice we can't breathe so good a bit earlier than that, but if there's a plus side, it's that it will affect everyone equally and there won't be a debate about climate change anymore. Hopefully we get our shit together and prevent that scenario if possible.
In fig 2 I can see that the rate of increase in CO2 is increasing – i.e. the amount of CO2 is accelerating, the second derivative is positive.
But I don’t see any exponential increase?
I am going to be critical of hyperbole on both sides !
I make no apology for preferring to use derivatives in my posts, I find when others talk about increase in CO2 or temperature the language can quickly become sloppy, as can be seen by the headline which is completely incorrect (the global temperature IS increasing, the planet IS warming’.
Definitely no criticism coming from me regarding your work. I came to my conclusions based on my personal efforts to model CO2 projections which I genuinely hope are wrong. I’m getting a year to year % growth rate in CO2 that tracks the exponential function F(x) = c^(0.01524x) where x is year. This is all from my own analysis on data from Mauna Loa. It’s been tracking on target since I stopped looking at the data in 2015. I understand the aversion to hyperbolic statements, and fear mongering. Panic is not helpful for anyone. There just shouldn’t really be “sides” or “debate” in math or science – that’s a symptom of other issues.
PS: second derivative is rate of change of the rate of change i.e “acceleration” in physics and “curl” in mathematics (dy/dx is slope and d2y/dx2 is curvature of slope). That would also support the crude Excel extrapolation.
I’m wrong about calling the 2nd derivative “the curl”. That’s from vector calculus which is not applicaple at all here. I don’t know what the 2nd derivative property is called in normal math, it may just be called the 2nd derivative.. also the calc for year over year co2 % change should be: F(x) = c exp(0.01524x).
Thanks. If I am doing anything, it is just provoking clarity. You are saying that the growth rate is exponential. That means that the first derivative of CO2 is growing exponentially. Because the derivative of an exponential is an exponential, that also means that CO2 is growing exponentially.
If you had said the CO2 growth rate fitted a second order polynomial, then that would mean the actual CO2 fitted a third order polynomial.
In any case, i think everybody agrees it is rising! The issue is simply how rapidly it is rising, and whether the rate of rise is also increasing. I haven’t downloaded CO2 data, but my guess is that the data won;t give a clear answer on those.
Hi Nigel, Yes. It looks like the growth rate of CO2 ppm is exponential (1st deriv. is exponential, rate of rise is increasing, etc) Year 2144 indicates ~100,000ppm atmospheric according to extrapolation.
That is actually incorrect. For the past three years temperature has been decreasing. For the past 17 years the temperature increase from 2002 to now has been of 0.1 °C.
As 0.1°C is the measurement uncertainty, you cannot say that the global temperature has actually increased for the past 17 years.
Incorrect. Don;t keep sifting the goal posts. Since 1960 the temperature has been increasing, and if you fit a linear trendline to fig 4 you will see that it is trending upwards, which means that over the period from 1960 on average the temperature increase has been accelerating.
But as I have repeated many times and you have not acknowledged, the statistical significance is very weak or else entirely absent.
Now, of course we can take the last 3 years, but the statistical significance is even less. There are fewer degrees of freedom. Even so, if you take your fig 4 and look at the last 3 years, you will see that your trendline is above zero for most of this time, hence the temperature is increasing for the last 3 years if we are to believe your trendline, but of course no serious statistician would believe your trendline for one micro second.
Nigel Goodwin
“I don’t think Javier has made a substantive response to any of my concerns.”
Javier made extensive, polite and on topic responses which seem to have been ignored.
On a different note he has attracted some attention elsewhere which is good, as well as Nick commentating here.
This seems to indicate touching a nerve on the warmist side so well done Javier.
CO2 increase is real. [extremely likely]
Response to CO2 increase does not fit the predicted scientific expectation for atmospheric temperature.
Either science is wrong [extremely unlikely].
Or science is not fully up to speed on all the other effects that also affect the atmospheric temperature,
[very likely].
Or some scientists are using alarmist feedback expectations [extremely likely]
Good scientists would acknowledge the pause and look to the reasons why.
Very few brave and good scientists out there at the moment.
Shame.
All I am asking is for people to be a bit more precise, don’t confuse the terms ‘warming’, ‘temperature’ and ‘rate of warming’, and take a realistic view on the level of uncertainty given the very noisy nature of the data.
Not too much to ask, and it would all be assumed if an article was being submitted to a decent peer reviewed paper.
To most people, ‘it is getting warm’ means temperature is rising, the first derivative is positve.
Hence ‘the rate of warming is increasing/decreasing’ means the second derivative of temperature is positive/negative.
I think I have said all I need to say, I am starting to repeat myself.
‘The planet is no longer warming’ is not the same as ‘the rate of increase in temperature is slowing down’.
I have done my reductio ad absurdum, it shows that Javier’s conclusions are indeed worrying, we will all freeze in a few years.
I am not the only one to ask Javier for some error estimates or explain the level of uncertainty given the minute R^2. He has not responded in any way to that challenge.
> I have done my reductio ad absurdum […]
Here’s mine:
https://andthentheresphysics.wordpress.com/2019/02/17/only-connect/
Better analogies welcome.
Thank you for your comments.
Thanks for the link. I thought maybe I was going crazy, but it seems there are others who have the same doubts as me on Javier’s data analysis. One of the links led me to the following statement by Javier:
“For your information, cooling means negative change in the temperature rate.”
WTF!!!
As I have said all along, Javier gets his derivatives in a twist (I do note that he starts talking about derivatives in the links).
Temperature rate is the first derivative of temperature wrt. time.
A negative change in temperature rate is the second derivative of temperature wrt. time.
So, the temperature can have an upward trend, but the slope of that upward trend may be reducing. (I am not suggesting for one millisecond that the data supports this, the data is full of noise, but I am just using it as an example).
Cooling is not, whatever Javier insists, a negative change in the temperature rate.
Going back to the ridiculous fig. 4, even this shows that temperatures are increasing up to 2019, when the temperatures, based on the statistically insignificant curve fit, start to fall.
Pace Javier, I am not suggesting temperatures have started to fall, I am saying that there is no statistical significance, we don’t know. According to fig 4 we had better invest in wool because hell is going to freeze over in a few years.
I like the analogy, but I fear the listening has stopped. Javier is right, he knows he is right, and everybody else is wrong.
You point out Javier’s error much more eloquently than me in your blog.
The king of analogies.
That is useful if you have trouble with the analysis of reality.
Argument by analogy is one of the examples described in Thouless’s book ‘Straight and Crooked Thinking’.
https://en.wikipedia.org/wiki/Straight_and_Crooked_Thinking
But that would remove all the fun from discussions, which would become extremely dry.
> That is useful if you have trouble with the analysis of reality.
What is that, dear Javier – analogies, arguments from analogy, analogical reasoning, or the lack of your subdued machismo?
Analogies are useful to explore our intuitions. They can also help theorical thinking – doing physics without thought experiments would be quite hard. They are also useful to explore alternative realities, like the one you’re trying to sell right now, in which what does not exist is backed up by spurious results.
Your main claim rests on a shift from multiple frames of reference. All one needs to see the trick is to understand the concept of temperature anomaly. Analogies are useful to illustrate that concept, e.g.:
https://andthentheresphysics.wordpress.com/2019/02/17/only-connect/#comment-143676
See? It’s not that complex.
Since you reject both statistics and common sense, how do you access the reality to which you appeal right now?
I agree with that.
I also agree with that. They are different postulates that are not mutually exclusive.
The rate of increase in temperature has slowed down since 1997.
The planet is no longer warming since February 2016.
Both are real observations.
That’s silly. The data supports a ~65-yr oscillation in global temperature well described in the literature. We will go through a period of a couple of decades of no warming or slight cooling.
Glad to hear we can agree on some points.
I am not a climate scientist, as you know, I am a statistician, data scientist and physicist. I take problems and analyse them.
If there is a 65 year oscillation, driven by something of which I know nothing, then if we are looking at climate change we need to look at deviations from that cyclical behaviour.
Is that analysis beyond us?
I am very used to looking at data and correlations between predictors and regressors. Some regressors give good correlation to the predictor, but other regressors give a good correlation to the error once you have fitted using the high correlation data.
I am not explaining this very well.
Let us say Temp = alpha*sin(2*pi/65* something). Then this gives you the 65 year oscillations.
Now, if you are looking at other effects, you have to look estimate alpha and then look at
temp – alpha*sin(2*pi/65* something) = beta*something else.
It would be incorrect to try to fit
temp = beta*something else.
Of course it is best to estimate alpha and beta together
temp = alpha*sin(2*pi/65* something) + beta*somethingelse.
What we are interested in, if we are going to take account of 65 year oscillations, is the value of beta and what the ‘somethingelse’ is.
This would be an interesting exercise which I assume has already been done by somebody, but it is not done in your article.
What is clearly incorrect is to say that we are at the peak of an oscillation, and then do a regression on the temperature for the last few years and ascribe that peak to the lack of evidence of ‘somethingelse’. Indeed, if you are arguing that we are at the peak of an oscillation, then I will rapidly become an alarmist based on the data I see.
“Very few brave and good scientists out there at the moment. Shame”
Endangered species perhaps?
Right, these silly “warmists” and their “oxygen breathing” and aversion to “economics” in favor of the “planet” we supposedly live on that apparently has something called an “ecosystem” and “living things”.
Angech, I’d strongly encourage you to calculate the error bars of Fig 4 for yourself. Actually check the math for that polynomial.
It should be extremely apparent that we can draw no robust conclusions about whether the warming is accelerating or decelerating.
Windchasers, check this figure:
https://imgur.com/V5RZaPJ
It is a gaussian smoothing of temperature and temperature rate of change.
I think we can draw conclusions that warming has been decelerating for two decades from the data. How robust they are statistically it is of secondary importance. The abundant scientific literature on the pause indicates lots and lots of scientists agree with me that the warming decelerated in the 21st century.
/laugh-cry emoji
…no, no this isn’t correct. If your error bars are large enough to drive a truck through, as here, then you can’t say “the planet is no longer warming”. You can’t draw much conclusions at all from data with such large uncertainties.
This work is simply not rigorous. It doesn’t hold up.
LOL, you definitely cannot robustly show that warming has dropped to zero. I don’t think you can even show a statistically robust change in trend at all from before 1998 vs after 1998, much less show that the trend has decreased to zero.
Why don’t you publish the error bars for your work here? Show us how the uncertainty compares to the estimates of deceleration that you’re claiming.
Thank you Angech. That is exactly what I am doing. A big climate shift has been on the making since early 21st century. The warmists are taking refuge on inconclusive statistics ignoring that it is a damning situation. The statistics would not be inconclusive if it was CO2. Ergo, it is not CO2.
A slow motion train-wreck is coming their way. As I did with the Arctic sea-ice extent pause, I am just pointing the direction it is coming from. It is going to be a lot of fun to watch.
In due time the statistics will become significant, but that only happens afterwards. Science is about learning how change occurs to be able to predict it, not about statistically certifying that change has occurred.
> In due time the statistics will become significant, but that only happens afterwards. Science is about learning how change occurs to be able to predict it, not about statistically certifying that change has occurred.
Javier, meet Javier (h/t PaulS):
https://wattsupwiththat.com/2017/10/30/some-failed-climate-predictions/