Change points in global surface temperature: and by what magic is earth warming?

Quite often you'll read deniers claiming that the earth is warming by magic, or supernatural forces. No denier will ever use the words "magic" or "supernatural". They'll pick a euphemism, like "Little Ice Age" - though how an ice age caused warming I've yet to see anyone explain.

An ice age won't cause cooling or warming. An ice age is a state not a force. Sometimes a fake sceptic will add that it's because of a recovery from an ice age, as if warm was a natural state and cold an unnatural state. Yet that would require an explanation of how earth got into the unnatural state and what forced it out of that unnatural state. A lot of deniers think of climate as a bouncing ball minus the forcing that causes the ball to bounce. And they don't seem to mind that the bounce up in the global surface temperature is showing no sign of bouncing back down, although some of them swear that we're heading for an ice age - any day now.

Occasionally there'll be a vague explanation for the unnatural state, usually something to do with the sun - but with little enthusiasm.  (The sun may have played a minor role during the Little Ice Age, recent research points to the cause of it being heightened volcanic activity, which is thought to have driven changes in the ocean which caused more cooling. See papers below.) And when one asks, well what about the decline in solar forcing recently - why hasn't it cooled down? You'll be lucky to get a response.

The reason deniers want to reach for a non-explanation of warming, like a bounce from the Little Ice Age - is that they don't want to reduce waste CO2. Some of them know that the greenhouse effect is real and still deny it. Others just deny the greenhouse effect holus bolus.

There are deniers who go to some lengths to reject physics and chemistry. One such person, Jeff Patterson, wrote another article for WUWT today (archived here). He's been here before. Jeff likes playing with numbers but he's not very good at it. Last time he wrote that he thought there was a "parabolic temperature trend".  He didn't go so far as to predict when the parabola he sees would trend down again. Back then his conclusion was:

The climate record of the past 163 years is well explained as the integral second-order response to a triggering event that occurred in the mid-to-late 1870s, plus an oscillatory mode regulated by solar irradiance. There is no evidence in the temperature records analyzed here supporting the hypothesis that mankind has had a measurable effect on the global climate. 

Jeff declined to say what that "triggering event" was back in the mid to late 1870s. Going by his last sentence it's clear that he doesn't accept that increasing CO2 was a trigger let alone a cause.  As for his "oscillatory mode regulated by solar irradiance" - he doesn't explain himself other than to talk about some mysterious "60+ year mode", which he tries, unsuccessfully, to tie in with the eleven year solar cycle.

Today Jeff's writing about a recent article at RealClimate.org by Stefan Rahmstorf, which was a very nice illustration of the surface temperature trend. Stefan was explaining what was meant by "statistical significance" of trends and confidence intervals. It's one of the clearest explanations I've come across for the layperson. Stefan also demonstrated and described change point analysis (see also here) as applied to the GISTemp temperature anomaly record. (The realclimate.org link has some further reading listed.) Here is the result:

Fig. 4. Global temperature (annual values, GISTEMP data 1880-2014) together with piecewise linear trend lines from an objective change point analysis. (Note that the value for 2014 will change slightly as it is based on Jan-Oct data only.) 

Graph by Niamh Cahill.

Stefan said the above analysis was by Niamh Cahill. She is a PhD candidate at the School of Mathematical Sciences, University College Dublin, who specialises in developing statistical models for sea level data. Stefan wrote:

It is the proper statistical technique for subdividing a time series into sections with different linear trends. Rather than hand-picking some intervals to look at, like I did above, this algorithm objectively looks for times in the data where the trend changes in a significant way. It will scan through the data and try out every combination of years to check whether you can improve the fit with the data by putting change points there. The optimal solution found for the global temperature data is 3 change points, approximately in the years 1912, 1940 and 1970. There is no way you can get the model to produce 4 change points, even if you ask it to – the solution does not converge then, says Cahill. There simply is no further significant change in global warming trend, not in 1998 nor anywhere else. 

Jeff Patterson is disputing the use of change point analysis, arguing that to apply it to global surface temperature is "naive" and that "as is commonly known, the CPA cannot be used on auto-regressive time series".

Now if you're not a statistician you might be asking "what is an auto-regressive time series".  What I understand autoregression to mean is that past values affect current and future values. Obviously there is some autoregression in surface temperature anomalies. The global surface temperature next year will, in part, be dependent upon the global surface temperature this year (unless you are a David Archibald or a John McLean). But that's not all it depends upon. And if there were only a random fluctation about a mean, then temperatures would go up and down around a mean, they wouldn't be going up and up and up like they are. There are forces acting that are pushing the global surface temperature upwards (primarily increasing greenhouse gases) which are outweighing the forces pushing the temperature downwards (like volcanic eruptions and aerosols).

I have not come across any other article anywhere that states that you cannot apply change point analysis if there is any autoregression in the time series. I did find an article describing a technique to distinguish between shifts in the mean and autocorrelation. In any case, I would defer to an expert in statistics rather than someone who could be a process engineer (whose expertise appears to be an electronics production line), writing for a pseudo-science blog.

The "evidence" that Jeff provides seems to support the opposite of what he is claiming. He put up a random sample of an ARIMA[3,1,1] process. ARIMA stands for "autoregressive integrated moving average", although Jeff admits he is not implying that climate can be modeled as an ARIMA process, so it's not clear why he chose it. Here's his chart:

Figure 1 Simulated climate data from an ARIMA process
Source: WUWT

You'll notice that although Jeff says he is not implying that climate can be modeled as an ARIMA process, he still labelled the chart as "simulated climate data from an ARIMA process".  But compare that to the GISTemp chart above. They are nothing alike. To illustrate this, I've made an animation starting with Jeff's chart and merging through to the actual global surface temperature (GISTemp).

Sources: WUWT and NASA GISS

I don't know how many runs Jeff had to do to get so much of the chart above the zero line, but it strikes me that if he could have got a run anything like the actual surface temperature charts he would have used it. And if he did find one that looked anything like the surface temperature chart, would he have said how many runs he had to do to get it? Would he have computed the odds? Maybe, maybe not. The odds would have been very low. I haven't done it myself but if anyone has, do tell.

Jeff also claims that "CPA fails for any integrative process, a class which in all likelihood the climate falls within". I don't know that that is true, nor what he means by "in all likelihood". Someone did quiz him in the comments about this but so far Jeff hasn't elaborated.

As he did last time, Jeff makes illogical leaps. He wrote:

In short it is in my view incorrect to term the nearly 20 year slowing in the rate of warming as a pause. Rather it is the natural (and perhaps cyclical) variation around a warming trend that has remained constant at ~.008 °C/decade² since the late 1800s. There is no empirical evidence from the temperature record that mankind has had any effect one way or the other. 

Do you spot the leap of faith?

First he argues that there has been a rise in global surface temperature, a "warming trend" that has "remained constant" at around 0.008°C/decade².  He'd be wrong about that. Global surface temperatures have risen around 0.8°C since the 1920-30s. Since 1950, the global surface temperature has risen by an average of 0.122°C a decade. Since 1980 it has risen by 0.156°C a decade. It's not had a constant rate of increase of 0.008°C per decade² (nor a constant increase of 0.08°C a decade).

The leap of faith is that according to Jeff, this large rise in surface temperature must be being caused by something other than human actions. Magic? If it were random, then temperatures would have gone up and down but on balance not moved far from a mean. Instead, what is happening is that the average surface temperature is heading up and up and up. There's no going back down again. The only time in the last 130 years that the global surface temperature fell was back at the turn of last century - between 1880 and 1910. That's an awfully long time between downshifts if all that was happening was a random fluctuation.

Jeff is thinking that it's somehow normal for the earth to get hotter and hotter. But he provides no explanation. No forcing agent. It's as if he drove his car to a the top of a hill and then put it in neutral gear, turned off the brakes and gave it a shove. Then tried to claim that it rolled downhill all by itself with no forcing - ignoring his initial push and the force of gravity.

Jeff talks of "no empirical evidence" yet the temperature data itself is evidence. The warming trend in the temperature data shows that something is acting on earth to cause it to heat up. Jeff seems to think earth gets hot by magic. It makes you wonder if he puts his potatoes in a pot of water and expects them to cook and soften all by themselves, without him having to put the pot on a hotplate. Or maybe he puts instant coffee in his mug, adds cold water and wonders why the coffee doesn't dissolve. Why, when someone else makes instant coffee it comes out hot, yet he can't get it to heat up no matter how long he leaves his mug of cold water sitting still. He's done all the ARIMA time analysis of coffee and cold water and he reckons it should get hot or turn to ice just by autoregression :)

Someone might kindly tell him the trick of cooking potatoes and making instant coffee. It is to boil water - by applying heat. That is, injecting energy - adding a forcing. It doesn't happen by magic.

Before getting to the WUWT comments, I'll add that I'm not a statistician. Any stats knowledge I once had is rusty and extremely under-used. For stats I defer experts like Tamino and Niamh Cahill. I know some readers are also experts, so feel free to add commentary.

From the WUWT comments

Patrick B was the second person to comment, and asked the question about CPA supposedly failing for any integrative process etc:

December 7, 2014 at 6:22 pm
“CPA fails for any integrative process, a class which in all likelihood the climate falls within.”
These seems to be a basic assumption in your analysis. Please elaborate. Thanks.

Peterkar picked Jeff up on his misuse of the word "infer"

December 7, 2014 at 6:57 pm
Infer/imply. Get ‘em right. Please.

Martin C picked up Jeff on his mistake in the trend:

December 7, 2014 at 7:41 pm
” . . .warming trend that has remained constant at ~.008 °C/decade . . . ”
Shouldn’t that be per YEAR ? OR 0.08 °C/decade . . ? 

Martin C corrected his previous comment and wrote:

December 7, 2014 at 7:50 pm. .OK. sorry, I see it is ‘an INCREASE in the rate of warming . . not just ‘the rate of warming. I was thinking of the warming of 0.8°C over about a century, when I made the previous comment.

Bill 2

December 7, 2014 at 7:56 pmWhether it is due to humans or not, at least we all can agree that it’s been warming and there is no pause. 

And to support my long-held contention that deniers are link-averse, Typhoon replied to Bill 2

December 7, 2014 at 8:10 pmTwo words: statistical significance.

majormike1 is an historical and current and a climate ignoramus, writing:

December 7, 2014 at 8:56 pm
It has been cooling since the Holocene Climatic Maximum 6,000 years ago. Each of warming periods that followed – Minoan, Roman, Medieval, and the one we are in now – was not as warm as its predecessor. Current warming is just a natural rebound from the coldest period of the past 10,000 years, the Little Ice Age (1450-1850 AD). Historical climate “ignorati” don’t recognize that climate change did not begin with Al Gore’s birth. 

There aren't too many comments so far. Only 15 at last count. You can see the latest archive here.

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Reeves, Jaxk, Jien Chen, Xiaolan L. Wang, Robert Lund, and Qi Qi Lu. "A review and comparison of changepoint detection techniques for climate data." Journal of Applied Meteorology and Climatology 46, no. 6 (2007): 900-915. doi: http://dx.doi.org/10.1175/JAM2493.1 (open access)

Schurer, Andrew P., Simon FB Tett, and Gabriele C. Hegerl. "Small influence of solar variability on climate over the past millennium." Nature Geoscience 7, no. 2 (2014): 104-108.  doi:10.1038/ngeo2040

Lehner, Flavio, Andreas Born, Christoph C. Raible, and Thomas F. Stocker. "Amplified inception of European Little Ice Age by sea ice–ocean–atmosphere feedbacks." Journal of Climate 26, no. 19 (2013): 7586-7602. doi: http://dx.doi.org/10.1175/JCLI-D-12-00690.1  (paper here)

Miller, Gifford H., Áslaug Geirsdóttir, Yafang Zhong, Darren J. Larsen, Bette L. Otto‐Bliesner, Marika M. Holland, David A. Bailey et al. "Abrupt onset of the Little Ice Age triggered by volcanism and sustained by sea‐ice/ocean feedbacks." Geophysical Research Letters 39, no. 2 (2012). DOI: 10.1029/2011GL050168 (open access)