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.

[This post published 9/05/2014 was made “sticky” during early April 2018 to show the inclusion of Gail Tverberg’s recent graph of world energy consumption.]

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.

Note added April 2018.
The two episodes of low rate of growth of carbon emissions, from 1913 to 1945 and from 1973 to 2009, relate to times of low growth in world energy consumption. This graph by Gail Tverberg shows that world energy consumption grew so slowly from 1920 to 1940 and from 1980 to 2000 that it did not keep up with the growth of population.

Trends in world surface air temperature

For time intervals of about three decades, world surface air temperatures tend to increase or decrease along straight lines. The tendency is very strong at the times of most rapid temperature rise: from 1909 to 1943 and from 1975 to 2005. All four dates mark points of abrupt change. I also recognise an abrupt change point at 1879. Linear trends in temperature change that join the five change points are:

From 1850: +0.72°/century;
From 1879: -0.97°/century;
From 1909: +1.47°/century;
From 1943: -0.37°/century;
From 1976: +1.91°/century;
From 2005: negative (?).

Linear trends of the whole record

In the whole 160-year period, world surface air temperature increased by 0.85 degrees and fossil fuel carbon emissions increased by 2.15 log units, that is by 162 times. Put another way, emissions doubled each 22.4 years, while the temperature rose by 0.12 degrees. (This relation is not the same as “climate sensitivity”. See Note 5. below.)

Discussion

The well-known decrease in world surface air temperature from 1943 to 1975, called a “pause” or a “hiatus”, has always complicated the attribution of climate change to carbon emissions. This graph shows that there are two such pauses to be explained, with perhaps a third beginning now. Not only that, the two pauses in the warming came at times of fast growth of emissions, and the most rapid warming came at times of slow growth of emissions.
The relation between emissions and temperature is direct at a century scale, but inverse at a decadal scale.

[In later posts, I show how several changes in the value of the Inter-decadal Pacific Oscillation (IPO) coincide with times of changing trend in global warming and how the more recent part of the global warming record can be straightened using IPO data. More recently, in May 2017, I posted “Global Warming Bent-line Regression” , referring to similar prior work by Thayer Watkins.]

Postings elsewhere

I posted this material previously in two forums: Weatherzone, thread (CLOSED) “Inter-decadal climate cycles or shifts”, Post #1191136 (25/4/13), and Alternative Technology Association (Australia), thread “Climate Change – Scientific Discussion”, Post #45773 (28/7/13).

In each forum there was constructive criticism that is worth reading. I have improved this post as a result.

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Notes

1. Source for HadCRUT4 world surface temperature data (smoothed): Source.
2. One tonne of carbon is equivalent to 3.67 tonnes of carbon dioxide.
3. Source for global fossil-fuels emissions data: Source. CITE AS: Boden, T.A., G. Marland, and R.J. Andres. 2012. Global, Regional, and National Fossil-Fuel CO2 Emissions. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A. doi 10.3334/CDIAC/00001_V2012
4. Data Format. For the temperature data, I adopt the authors’ “decadally smoothed” data set. To remove short period fluctuations (mainly noise, but also the Southern Oscillation) they smoothed the raw annual data values with a 21-point binomial filter. The annual carbon emissions data needs no smoothing. These fossil fuel emissions include: combustion of solid, liquid, and gas fuels, gas flaring, and cement production. Because growth in emissions has been exponential (so far), I have converted data to logarithms. (The 2009 estimate of 8,738,000,000 tonnes of carbon emitted becomes 9.941 expressed as a logarithm to the base 10.)
5. “Climate sensitivity.” Warming of 1.5° to 4.5°* can be expected to result from each doubling of the concentration of carbon dioxide in the atmosphere. This graph does not show that concentration. Concentration figures from Mauna Loa, which go back only to 1958, show an upward trend that accelerates, even as a logarithmic plot. The concentration increased by 3.5% in the decade from 1958, and by 5.5% in the decade to 2010.
By contrast, the carbon emissions (graphed here) increased at a compounding average rate of 36% per decade: almost ten times faster.

* IPCC Working Group I contribution to 5th Assessment Report (AR5). I have cited only the long-term equilibrium climate sensitivity.