Global Warming Bent-Line Regression

HadCRUT global near-surface temperatures

HadCRUtemp2lineThis graph, posted with permission, shows a bent line fitted to the HadCRUT annual data series for global near-surface temperature. Professor Thayer Watkins of San Jose State University Department of Economics posted it on his blog about 2009.

HadCRUTsmoothWithout knowing of this work, I constructed the second graph. I used data from the same HadCRUT source, but a data set smoothed by the authors.

In April 2013 I posted it to a forum thread in”weatherzone”.

Next, I added to that graph a logarithmic plot of global carbon emissions, similarly fitted with a series of straight trend lines.

Log from 1850 of world surface air temperature and carbon emissionsThis I included in posts to several forums: in a post to “weatherzone”, in a post to the Alternative Technology Association forum, and finally in a post to this blog.

Both Professor Watkins and I have fitted bent lines to the data. I fitted the lines by eye (for which I was accused of “cherry-picking”). Professor Watkins used an explicit process of Bent-Line Regression, minimising the deviations by the method of least-squares. Like me, he initially chose by eye the dates of the change points where the straight lines meet. But he then adjusted them so as to minimise the least squares deviations.
[See notes below on the method of Bent-Line Regression.]

The trend lines and change points are practically the same in the Thayer Watkins and the “Surly Bond” graphs:
1. (Up to Down) TW: 1881; SB: 1879.
2. (Down to Up) TW: 1911; SB: 1909.
3. (Up to Down) TW: 1940; SB: 1943.
4. (Down to Up) TW: 1970; SB: 1975.
As I said at the time, once straight trend lines are chosen, the dates of change points to fit this data series closely do not allow of much variation.

Relation to the IPO (or PDO) of the Pacific

Not by coincidence, Watkins and I both went on to relate the multi-decadal oscillations of Pacific Ocean temperatures to the global near-surface average temperatures.

My approach

I merely plotted my chosen global temperature change points on to the Pacific graphs (I chose to cite the IPO (Inter-decadal Pacific Oscillation)). In two posts I noted (i) the way the change points in the HadCRUT global temperature series were close to those in the IPO, and (ii) the way the IPO seemed able to explain why the trend in global warming was “bent” in 1943 and 1975 but, in that case, could only sharpen the bends of 1910 and 1880.

Professor Watkins’ approach

AGT_PDO7Professor Watkins did a separate Bent Line Regression Analysis on the Pacific graphs (He chose to cite the earlier-developed PDO (Pacific inter-Decadal Oscillation)). His analysis “A Major Source of the Near-Sixty Year Cycle in Average Global Temperatures is the Pacific (Multi)Decadal Oscillation” is here.

He admits the match is poor, with various lags and a different period. He concludes:
“Thus while the Pacific (Multi)Decadal Oscillation appears to be involved in the cycles of the average global temperature there have to be other factors also involved.”

The significance of the IPO

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The record of the IPO

Graphical record of the IPO, plus CUSUM plot and climate shift dates

My post showing shifting trends in world surface temperature and in carbon emissions brought a suggestion from Martin Shafer that allowing for the PDO could straighten the trend. I think that perhaps it could, but I have tried the IPO (Inter-decadal Pacific Oscillation) rather than the PDO (Pacific inter-Decadal Oscillation). (See below.)

Along the top of the graph I have marked in the climate shifts that prevent the trace of world temperature from being anything like a straight line. The blue line is the IPO, as updated to 2008.
The IPO is positive in the space between the last two climate shifts, negative in the next earlier space, and positive in part of the space before that. By plotting the CUSUM values of the IPO (red), it is clear that the pattern of the IPO relates very closely to the climate shift dates. Four of the seven extreme points of the IPO CUSUM trace match climate shifts. In addition, since 1925, the CUSUM trace between the sharply-defined extreme points has been a series of nearly straight lines. These represent near-constant values of the IPO, a rising line representing a positive IPO and a falling line a negative one.

As shown by the map in the Figure copied below, a positive extreme of the IPO has higher than normal sea surface temperatures in the equatorial parts of the Pacific. Could the transfer of heat from the ocean to the atmosphere be enhanced at such times?

This conjecture is developed in the post “Hammering Global Warming Into Line”.


The PDO and the IPO

The PDO is the Pacific Decadal Oscillation (or Pacific inter-Decadal Oscillation). It is one of a number of climate indicators that rise and fall over periods of a decade or more. These indicators have been introduced by different research groups at different times.
A current list of such indicators is in the contribution of Working Group I to the Fifth Assessment Report (5AR) of the Intergovernmental Panel on Climate Change (IPCC). The list is in Chapter 2 (38MB). It is at the end, in a special section: “Box 2.5: Patterns and Indices of Climate Variability”. Continue reading