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

Continue reading


3-year trends to August 2010

Parametric plots of smoothed climate variables at Manilla
“Summer retreated from drought”

Trends to August 2010.

Manilla’s recent climate continues to be marked mainly by cloudier skies and a narrower daily temperature range than in the 12-year averages.
In the current plots we see final smoothed trends for summer (DJF) of 2009-10.

Daily maximum temperature anomaly is shown on the x-axis of each plot. The minimum value in Feb 2008 (-1.61) and maximum value in Nov 2009 (+1.35) are also the extremes (in blue) of the smoothed data set. In summer 2009-10 the smoothed temperature anomaly fell much faster than it had risen in the previous winter and spring. During autumn the max temp anomaly was near zero, and the raw value for August is so low (cold) the scale has had to be extended.

Monthly total rainfall anomaly is on the y-axis (inverted) of the first graph. It showed a very mild drought throughout the last winter, spring, and summer. Autumn seems to have been less droughty, much like the previous autumn, but with the opposite trend. Recently, July 2010 was very wet, but August rainfall was normal.

The anomaly of per cent cloudy mornings fell during winter 2009 as the maximum temperature anomaly rose. During summer 2009-10 it rose again as the maximum temperature anomaly fell. However, for a given maximum temperature anomaly the cloudiness anomaly was now more positive (it was cloudier). Since the end of summer, skies have been extremely cloudy

On the graph for early morning dew point anomaly, the final year’s data plots like that of the cloudiness graph. However, dew point anomalies were not so positive: in winter and spring 2009 they were quite strongly negative. By autumn 2010, dew points seem normal, and recent values are high (humid climate).

For daily temperature range anomaly, again, the last year’s pattern on this graph is like that on the previous two graphs. In this case, values low on the graph are negative anomalies, representing narrow daily temperature ranges. For a given maximum temperature anomaly, the anomaly of daily temperature range was lower during the summer than it had been the previous winter.

(Note on the “Macquarie Island” label. This August  Manilla’s anomalously low maximum temperature (16.8°) is actually much higher than that of Macquarie Island (5.0°), and the anomalously narrow daily temperature range (11.9°) is still much wider than that of Macquarie Island (3.5°).)

In the case of daily minimum temperature anomaly, summer 2010 began with a maximal value, and the value stayed high through the season. Values may have been lower in autumn, then they seem to have risen even higher (very warm nights).

World-wide low temperature

At Manilla, in early 2008  there were record low values of daily minimum temperature, daily maximum temperature and subsoil temperature. These did NOT come with high rainfall and high dew point as would occur in a “flooding rains” peak of the quasi-biennial oscillation. They match low temperature at that time world-wide.

Subsoil temperature anomalies have remained close to zero for 17 months, despite big changes in the anomalies of other temperatures.

Fully smoothed data – Gaussian smoothing with half-width 6 months – are plotted in red, partly smoothed data uncoloured, and raw data for the last data point in orange. January data points are marked by squares.
Blue diamonds and the dashed blue rectangle show the extreme values in the fully smoothed data record since September 1999.