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
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.