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

HadCRUT Global Temperature Smoothing

Graph of recent HadCRUT4

As a long-term instrumental record of global temperature, the HadCRUT4 series may be the best we have. [See Ole Humlum’s blog in the notes below.]
I like to use the published smoothed annual series of HadCRUT4.  I find that this smoothing gets rid of the “noise” that makes graphs about global warming needlessly hard to read. I used the smoothed HadCRUT series to point out the curious inverse relation between the rate of warming and the rate of carbon emissions in this post from 2014.  I will refer again to that post in discussing the use of bent-line regression to describe global warming.

The Met Office Hadley Centre published the smoothing procedure that they used for the time series of smoothed annual average temperature in the HadCRUT3 data set. The smoothing function used is a 21-point binomial filter. The weights are specified in the link above.
The authors discuss the fudge that they use to plot smoothed values up to the current year, even though a validly smoothed value for that year would require ten years of data from future years. Their method is to continue the series by repeating the final value. They had added to the uncertainty by using a final value from just part of a year.
They relate how this procedure had caused consternation when the smoothed graph published in March 2008 showed a curve towards cooling, due to the final value used being very cool.
They show the effect by displaying the graph for that date.
They maintain that the unacceptable smoothed curve (because it shows cooling, not warming) is due mainly to using a final value from an incomplete year, saying:
“The way that we calculate the smoothed series has not changed except that we no longer use data for the current year in the calculation.”
That web-page is annotated:
“Last updated: 08/04/2008 Expires: 08/04/2009”
However, this appears to be the current procedure, used with the HadCRUT4 data set.

For my own interest, I plotted the values from 1990 to 2016 of the annual series of HadCRUT4, averaged over northern and southern hemispheres. [Data sources below.]

On my graph (above), all points 1990 to 2016 are as sourced. I have plotted raw values 2017 to 2026 (uncoloured) as I believe they are used in the smoothing procedure. I have also left uncoloured the smoothed data points from 2007 to 2016, to indicate that their values are not fully supported by data.

I agree with Ole Humlum that it is very good of the Met Office to come clean on the logical shortcomings of their procedure for smoothing, but it would be even better if they ceased plotting smoothed points when the smoothing depends on data points for future years.
In my monthly series of parametric plots of smoothed monthly values of climate anomaly variables, I have faced the same problem. I smooth using a 13-point Gaussian curve. My solution is to plot “fully-smoothed” data points (in colour) up to six months ago. That gives a consistent mapping up to that date. The fifth month before now (plotted uncoloured) is smoothed with an 11-point Gaussian and so on, up to the latest month with a necessarily unsmoothed value.


Notes

1.
Ole Humlum’s blog “Climate4you”

[See: Index\Global Temperature\Recent global air temperature change, an overview\]

2.
HadCRUT4 data
Source of raw annual values:

Source of smoothed annual values:

Hammering Global Warming Into Line

Global temp and IPO graph

In my post of 18 Sep 2014 “The record of the IPO”, I showed a graph of the Inter-decadal Pacific Oscillation,plotted as a cumulative sum of anomalies (CUSUM). This CUSUM plot has a shape that makes it seem that it could be used to straighten the dog-leg (zig-zag) trace of global temperature that we see. A straighter trace of global warming would support the claim that a log-linear growth in carbon dioxide emissions is the main cause of the warming.

My attempt to straighten the trace depends on the surmise (or conjecture) that the angles in the global temperature record are caused by the angles in the IPO CUSUM record. That is, the climatic shifts that appear in the two records are the same shifts.
I have adopted an extremely simple model to link the records:
1. Any global temperature changes due to the Inter-decadal Pacific Oscillation are directly proportional to the anomaly. (See Note 1.);
2. Temperature changes driven by the IPO are cumulative in this time-frame.

To convert IPO CUSUM values to temperature anomalies in degrees, they must be re-scaled. By trial and error, I found that dividing the values by 160 would straighten most of the trace – the part from 1909 to 2008. (See Note 2.) The first graph shows (i) the actual HadCRUT4 smoothed global temperature trace, (ii) the re-scaled IPO CUSUM trace, and (iii) a model global temperature trace with the supposed cumulative effect of the IPO subtracted.


The second graph compares the actual and model temperature traces. I note, in a text-box, that the cooling trend of the actual trace from 1943 to 1975 has been eliminated by the use of the model.
The graph includes a linear trend fitted to the model trace for the century 1909 to 2008, with its equation: y = 0.0088x – 0.9714 and R² = 0.9715.

Continue reading

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

Warming and Carbon Emissions: Shifting Trends

Log from 1850 of world surface air temperature and carbon emissions

Trends in global temperature and in carbon emissions changed sharply several times during the last 160 years.
One question is at the heart of concern about human influence on climate: how does global temperature relate to human-caused emissions of carbon dioxide?
This graph shows that relation: it does not explain it.

Data

I display two well-established data sets:
1. The HadCRUT4 record of estimated global surface air temperature. Values are expressed as the anomaly from 1961-1990 mean values in degrees celsius.(See Note 1. below.)
2. Global Fossil Fuel Carbon Dioxide Emissions, tabulated and graphed as tonnes of carbon (See Note 2. below.)) by the Carbon Dioxide Information Analysis Center, Oak Ridge.(See Note 3. below.)

The format of the data is given in Note 4. below.

Multi-decadal linear trends

Trends in carbon emissions

Throughout this time, the rate of carbon emissions increased exponentially, but at rates that changed abruptly at certain dates. In units of log-cycles per century, the rates were:

From 1850: 1.97 units;
From 1913: 0.28 units;
From 1945: 2.14 units;
From 1973: 0.77 units. Continue reading

Manilla in Global Warming Context: II

Logs of smoothed world and local temperatures. (25/7/14)

This post updates a similar post that was based on data available in July 2011. I now have data from three more years.

World surface air temperature

The blue line shows how the air has warmed and cooled during the 21st century. It is based on GISS, which is one of three century-long records that estimate the surface air temperature of the whole earth. The other two are HadCRUT and NCDC.
Monthly values of GISS vary wildly, and I have smoothed them with a 37-month moving average. Ole Humlum uses 37-month smoothing in many graphs on his website.

The 37-month smoothing allows plotting only up to 18 months ago, in December 2012. As you see, the GISS air temperature anomaly (See Note 1.), when smoothed in this way, moves rather steadily in one direction for years at a time.

The world’s surface air warmed rapidly from early 2000 to late 2002, then warmed slowly to a peak in early 2006. This is the warmest the world surface air has been in hundreds of years. After that peak, the air cooled rapidly by two-thirtieths of a degree to a trough in late 2007. It warmed again slowly to a lower peak in early 2010, steadied for a year, then fell to a trough in January 2012 that was like the previous trough. The air warmed rapidly through 2012. Continue reading

Manilla NSW in Global Warming Context

Logs of smoothed world and local temperatures.

[I posted an Up-dated version of this graph in July 2014]

Up-to -date data on global temperature change can easily be down-loaded from Ole Humlum’s website “climate4you“.
Humlum favours sampling windows 37 months wide. For my own data at Manilla, NSW, I have always used windows about six months wide, which show up Australia’s vigorous Quasi-biennial oscillations of climate. I tried Humlum’s 37-month window on my data, with quite startling results, as shown in the graph above.

Humlum re-presents three records since 1979 of global monthly air surface temperature anomalies:
* HadCRUT3: by the (UK Met Office) Hadley Centre for Climate Prediction and Research, and the University of East Anglia’s Climatic Research Unit (CRU), UK.
* NCDC: National Climatic Data Centre, NOAA, USA.
* GISS: Goddard Institute for Space Studies, Columbia University, New York, NASA, USA.
When smoothed by a 37-month running average, these data sets give very similar results. I use the GISS data because it matches my data best.

The match is very good, particularly in the sharp fall from the maximum in April 2006 to the minimum in September 2007. Where my data begins in September 2000, both curves rise steeply from low values, but mine peaks in August 2001, more than a year before a corresponding peak in global temperature (September 2002). After that, there is a plateau, where the graphs rise together to the highest peak (April 2006).
The other global data sets, HadCRUT and NCDC, have temperature falling or steady along the 2002-2006 plateau.
There are two reasons for plotting my data on a separate axis (on the right). First, the reference periods are different: GISS uses 1951-1980, while I use the decade from April 1999. Second, temperature varies much more at a single station than in the average of many stations around the world. I use a scale six times larger.

It turns out that the cold time in Manilla in late 2007, which I had mentioned in several contexts, was a cold time world-wide.

Home-made thermometer screen

Giant Mixing Bowl Thermometer Screen

I am over the moon at getting agreement between data from my home-made thermometer screen and the best that world climatologists can do. It makes me inclined to believe some of the things they say.


This article and graph were posted on 18th August 2011 in a weatherzone forum: General Weather/ Observations of Climate Variation.