Guest essay by Jeff Patterson
In a recent post on RealClimate, the author examines the statistical significance of the “The Pause” using a technique recently in vogue called changepoint analysis (CPA). The basic idea is to subdivide a time series into intervals and determine if a statistically significant change in the regression slope can be detected at the interval breakpoints. For a given number of break points, all potential break point positions are tried and the best fit is recorded. The number of break points is increased by one and the analysis is re-run. This continues until no significant reduction in the residual is obtained. The breakpoints at which a significant change is detected are called “changepoints”.
Since CPA is designed to answer the question, “has something changed” (we use it where I work to monitor the defect rate of electronic assemblies as a process control metric), one can forgive the naive application to global temperature undertaken in the aforementioned post. The author’s basic thesis is that since a CPA analysis detects no significant recent change in the slope of the GISS dataset there is no pause. Unfortunately, the analysis is of no value because, as is commonly known, the CPA cannot be used on auto-regressive time series. This can be easily demonstrated. Here’s a random sample of an ARIMA[3,1,1] process (This is not to infer the climate can be modeled as an ARIMA process. CPA fails for any integrative process, a class which in all likelihood the climate falls within.)
Figure 1 Simulated climate data from an ARIMA process
If we run this random data through R using the standard changepoint package we get:
Figure 2 – Changepoint analysis using R
The CPA algorithm detected three significant “changepoints” in a process known to have none.
So while I place no value in the analysis, ironically I actually agree with the author’s contention that all this talk of a pause is gibberish. The fact of the matter is that there has been no statistically significant increase in the rate of warming over the entire observable temperature record. Here is yet another way to demonstrate this unassailable fact.
Start with the Cowtan and Way modified Hacdrut4 global temperature series:
Figure 3 – HadCRUT4v2
Subdivide the series into 640-month intervals, where each interval is offset 2 months from the previous interval (638 month overlap). Plot the least-squares, best-fit slope (in °C/decade) for each interval.
Figure 4 – Sliding window regression
Add the best-fit linear regression to the above.
Figure 5 – Sliding window slope regression with best-fit line
Over the 32 year period from 1963 to 1985 the rate of warming increased from .01 in °C/decade to .15 °C/decade, not significantly different from the -.03 to .1 change that occurred from 1893 to 1930.
As we decrease the interval length, the data gets noisier but we can get a better idea of the recent behavior. The conclusion remains the same.
Figure 6 – 640 and 320-month interval slope regression
Conclusion
One benefit of the recent discussions on the so called “pause” in global warming is a healthy re-focusing on the empirical data and on the failure of climate models to accurately reflect climate dynamics. Yet to speak of a pause infers that the rapid warming that occurred at the end of the last century reflects the true, post-industrial trend. As the analysis above shows, there is no empirical evidence to support the notion that that period was particularly unusual, much less that it was due to anthropogenic effects.
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.
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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.
Was there a change in the late 1800s?
The Annals of Applied Statistics
2014, Vol. 8, No. 3, 1372–1394
DOI: 10.1214/14-AOAS753
© Institute of Mathematical Statistics, 2014
CHANGE POINTS AND TEMPORAL DEPENDENCE IN
RECONSTRUCTIONS OF ANNUAL TEMPERATURE:
DID EUROPE EXPERIENCE A LITTLE ICE AGE?
BY MORGAN KELLY AND CORMAC Ó GRÁDA
University College Dublin
Some of us think so 🙂 http://wattsupwiththat.com/2013/10/04/the-great-climate-shift-of-1878/
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.
Which is of course a section of the positive phase of the ~1,000 year cycle that is responsible for the Minoan, Roman and Medieval Warm periods and the concomitant cold periods such as the Dark ages.
The late 20th century warming 1970-2000 that has so excited the AGW fantasists is the positive phase of the ~60 year cycle that correlates quite well with the North Atlantic Oscillation, and is statistically practically identical with the warming period 1910-1940, followed by the 30 year cooling period 1940-1970 – both of which periods are a considerable embarrassment to the Warmies, who claim that the advent of detectable anthropogenic influence on the Earth’s temperature was 1940.
So there has been no detectable anthropogenic influence whatsoever on the Earth’s climate – not by greenhouse gases nor by sundry aerosols – in the measured temperature record, and the billions – trillions? – of dollars, pounds or whatever that has been wasted on this utterly non-existent threat will shortly be recognised as the biggest “scientific” mistake in all of human history.
And you can take that to the bank.
I’m confused. The figures seem to show the conclusion the post is disputing. Fig4. shows the sliding slope (deg/time) of a ~50 year period average as a function of time. We see it agrees with Fig3: The climate was cooling (negative values in Fig 4) in the 1800s and warming since 1900 (positive values.) If you used a shorter trend period you might find more warming and cooling periods but the overall picture would be the same. Around 1960 the slope almost gets down to zero because of the flat or cooling trend from 1940-1970 in Fig 3, but is still positive on a 50 year average.
In Fig5 we see the linear fit to the slope as a function of time, i.e. the average slope of the slope, the average second derivative. The linear fit has a positive slope, indicating that on average the warming is accelerating. If it were constant then the linear fit would be a horizontal line (above the x-axis for warming, at zero for no change.) This is consistent with the ‘instantaneous’ slope which is more positive near the present than in the past. There are sizable oscillations around the linear trend, but the trend is there. I don’t see how you can argue based on these figures that the climate scientists are wrong. You could try and show that the linear best fit isn’t statistically significant somehow, but that is not shown here as far as I can tell.
Yes, if the results presented here show anything, its that the rate of warming accelerated in the 20th century!
So the conclusion should be that it is “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 accelerated at a constant rate of ~.008 °C/decade2 since the late 1800s.” (what else has accelerated since the late 1800’s I wonder…)
I don’t know of anyone who has seriously suggested that AGW started at the turn of the 20th century but lets pretend that’s the case and that the trend will persist unabated. If you extrapolate the parabola implied by the ~.008 °C/decade2 you get to warming <2 degsC by 2100. Since that is below the IPCC target, can we declare victory and go home?
The increase in the rate of warming has been constant and at the same value since long before GHGs could have possibly had an impact.
Your figures don’t show that. They show that the 50 year trend has considerable variation. If you model that with a straight line fit you assume a constant 2nd derivative. From your graphs we can’t tell what the 3rd derivative might be and I suspect we really would be pushing into areas of too little data/noise to measure a constant 3rd derivative. You could bound it though.
You say GHG couldn’t possibly have an impact but I don’t see how you can assume that. Industrialization was well under way by the late 1800s. You can crudely fit emissions with a parabola too. Obviously the early ones are too small to have a measurable impact under other variations by themselves, but fitting emissions and temps with a parabola doesn’t disprove AGW.
Of course, the proper way to do this isn’t to arbitrarily fit different measurements with trends, but to understand the physics that links them, model it, and see how consistent the models are with reproducing observations. The only thing you get from these graphs is: temperatures are increasing and the warming is accelerating on average so far, since the late 1800s.
” … ironically I actually agree with the author’s contention that all this talk of a pause is gibberish. The fact of the matter is that there has been no statistically significant increase in the rate of warming over the entire observable temperature record. ”
Quite right .
It’s hard to get across what a near noise level molehill this whole politically useful hysteria is all about , a change of just 0.3% in our estimated mean temperature which is only about 3% warmer than the about 279K ( varying +- 2.3K from peri- to aphelion ) of a gray ball in our orbit .
tadchem December 8, 2014 at 11:35 am wrote :
“The flaw in nearly all flawed ‘regression analysis’ studies is made before a single calculation has taken place. The most greivous error is in the selection of an inappropriate mathematical model. If the physics of the process is not reflected in the equations of the model as used for calculation, only self-delusion can result.”
Quite right .
You can do all the stats on all the observational data you want , and you still will not understand the planet’s temperature until you understand the physics I come at this as an APL programmer for whom to understand a quantitative relationship is to implement it so I can explore its parameter space
But even at this most basic level “climate science” parts paths with the classic quantitative analytical method of physics . Because it has to , because its nakedness , if not outright fraud , is quickly apparent .
But if the ~60-year cycle held (cool circa 1900, warm in mid-1930s, cooling to ~1978 when alarmist types were flapping about doom from global cooling, warming to ~1998) we should be halfway down the cooling part of a cycle.
But…. there may well be several influences of different periodicity, that will reinforce or counteract depending on where each is in its cycle at a particular time (i.e. now).
Of course your figures don’t cover recent years.
The “peak” you mentioned is a broad span of ten years – not a “point” at 1945 (up from 1910, down to 1976) but a slow sinewave-like rise from a low broad valley in 1910 to a broad curve centered about 1945. Then a slight down curve towards another valley in 1976, then a broad rise up towards the Modern Warming Period flat-topped curve between 1998 and 2010-2012. Yes, if you think of a thirty five year half-wave, we’d be halfway along (1998->2014), but that’s not the curve we follow.
And, if one assumes the Modern Warming Period is a long 200 year near-plateau between the 1000 year low point of 1650 and the Modern Ice Age of ~2500, then today’s broad MWP will probably stay near the 2000-2010 level for quite some time.
HotWhopper wrote a disparaging critique of this post. I have posted a response here (http://alturl.com/5qwnv) which also addresses similar comments above.
Jeff Patterson