>The Matthews Factor


The press release for Matthews et al (2009) “The Proportionality of Global Warming to Cumulative Carbon Emissions” includes the statement, “These findings mean that we can now say: if you emit that tonne of carbon dioxide, it will lead to 0.0000000000015 degrees of global temperature change.” For the sake of simplicity, I’ll refer to that 13-figure multiplier as the “Matthews Factor”, though they refer to it as the carbon-climate response (CCR). Matthews Factor has a much nicer ring to it than the acronym CCR.

Link to Matthews et al abstract at “Nature”:

Link to press release:

The Matthews et al (2009) abstract reads, “Here we generalize these results and show that the carbon–climate response (CCR), defined as the ratio of temperature change to cumulative carbon emissions, is approximately independent of both the atmospheric CO2 concentration and its rate of change on these timescales. From observational constraints, we estimate CCR to be in the range 1.0–2.1 deg C per trillion tonnes of carbon (Tt C) emitted (5th to 95th percentiles), consistent with twenty-first-century CCR values simulated by climate–carbon models.” [Bold Face Added]

So the Matthews factor is approximately the midpoint of the Carbon-Climate Response range of 1.0–2.1 deg C per trillion tonnes of carbon (Tt C) emitted.

My Figure 1 is Matthews et al Figure 4, available here:

The description of the Matthews et al graph reads, “CCR was estimated for each decade of the twentieth century after 1910 by scaling an observationally constrained estimate of greenhouse-gas-attributable warming relative to 1900–09 by the ratio of CO2 forcing to total greenhouse gas forcing, and dividing by cumulative anthropogenic carbon emissions over the same period. This observationally constrained estimate of CCR is both stable in time and consistent with the estimates derived from model simulations.”

Figure 1


The Global CO2 Emissions from Fossil-Fuel Burning, Cement Manufacture, and Gas Flaring (1751-2006) is available from the Carbon Dioxide Information Analysis Center (CDIAC):

Let’s limit the period in question to a good portion of the last 30 years. The reason for limited time period is the length of a dataset used later in this post. Figure 2 illustrates the CDIAC Total Annual Global CO2 Emissions from 1979 to 2006. (CDIAC is lax in updating their data files.) As you can see, the CO2 emissions have been accelerating lately, or at least through 2006, so relying on an extension of the trend for 2007 and 2008 should be conservative.
Figure 2

And plotting a running total of the total annual CO2 emissions illustrates the Cumulative Carbon Emissions, Figure 3, which are the focus of Matthews et al.
Figure 3

To show the impact of the Cumulative Carbon Emissions on global temperature, simply multiply that data by the Matthews factor of 0.0000000000015 deg C/Ton of CO2 Emissions. Refer to Figure 4. There can only be one reason for the simple multiplier and that is to place cause and effect in very easy-to-understand terms.
Figure 4

Figure 5 compares the Impact of the Cumulative Carbon Emissions, based on the Matthews Factor, to RSS MSU TLT anomalies. It illustrates the substantial impact Matthews et al are attempting to attribute to cumulative carbon emissions.
Figure 5

At first glance, it almost appears logical. Until one remembers that…


Of course, this is something that Matthews et al account for. Refer again to their description of their Figure 4. In it, they wrote, “CCR was estimated for each decade of the twentieth century after 1910 by scaling an observationally constrained estimate of greenhouse-gas-attributable warming relative to 1900–09 by the ratio of CO2 forcing to total greenhouse gas forcing, and dividing by cumulative anthropogenic carbon emissions over the same period.”

So let’s examine the difference between CO2 and total greenhouse gas forcings.

THE NOAA Annual Greenhouse Gas Index (AGGI) lists the Annual Radiative Forcing (watts/meter^2) from 1979 to 2007 for all anthropogenic greenhouse gases, not simply CO2. This is the dataset that dictated the period of time used in this post. Refer to their Table 2:

Figure 6 shows the Annual Radiative Forcings for CO2 and all anthropogenic greenhouse gases as listed in Table 2 of the AGGI webpage. CO2 does represent a major portion of the anthropogenic total, according to the AGGI.
Figure 6

And for those interested, the percentage of the AGGI represented by CO2 is shown in Figure 7. It’s risen in recent years, due in part to the increases in CO2 emissions, and due in part, as NOAA states, to “the slowdown in the methane growth rate and the decline in the CFCs”.
Figure 7


Dividing the annual Total AGGI by the annual AGGI for CO2 provides the ratio of the total AGGI radiative forcing to the AGGI radiative forcing for CO2. We can then use these ratios as annual multipliers for the Matthews Factor and determine the total impact of all anthropogenic greenhouse gases on global temperature anomaly, assuming the Matthews Factor is correct. In Figure 8, I’ve again compared it to RSS MSU TLT anomalies. It appears that Matthews et al are attempting to attribute all of the warming since 1979 to greenhouse gases.
Figure 8


In an earlier post, The Impact of the North Atlantic and Volcanic Aerosols on Short-Term Global SST Trends, I discussed the effects of volcanic aerosols and of the natural variability of the North Atlantic on Global SST anomaly trends from November 1981 to January 2009. By removing them, the linear trend plummeted from 0.095 deg C/decade to 0.037 deg C/decade. In Figure 9, I’ve combined Figures 1 and 5 from that earlier post to create a comparison graph with linear trends. It illustrates the impacts of those two natural variables on Global SST anomaly trends. Note the substantial drop in the trends.
Figure 9

Note: The post “The Impact of the North Atlantic and Volcanic Aerosols on Short-Term Global SST Trends” also ran at WattsUpWithThat:


If we assume that removing the impacts of volcanic aerosols and the natural variations of the North Atlantic would cause a proportional decrease in the trend of Global RSS MSU TLT anomalies, then the GCMs used by Matthews et al have grossly overestimated the significance of CO2 on global temperature.


About Bob Tisdale

Research interest: the long-term aftereffects of El Niño and La Nina events on global sea surface temperature and ocean heat content. Author of the ebook Who Turned on the Heat? and regular contributor at WattsUpWithThat.
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5 Responses to >The Matthews Factor

  1. kuhnkat says:

    >Hey, what do you have against CCR?!?!?!They do great music!!Credence Clearwater RevivalHAHAHAHAHAHAHA

  2. Bob Tisdale says:

    >kuhnkat: Thanks for bringing them up. I have nothing against Credence Clearwater Revival. I originally had a reference to them when I wrote that sentence in the opening paragraph, but I felt it would detract from the critique of Matthews et al.Regards

  3. >It's interesting how, even after SST during the Mt. Pinatubo eruption is corrected, SST still does not resemble ENSO during that time period.Also, OT, the 86/7 and 97/8 El Ninos were the only events not to coincide with a volcanic eruption since 76, as you have explained many times. However, they are also the only two El Ninos that were followed by strong La Ninas.When an El Nino event ends without a La Nina, perhaps the water that sloshes East merely returns West along the counter-current. But when a La Nina occurs, the flow of cold water separates the warm water North and South into the equatorial currents. Perhaps the reason that those two El Ninos caused step changes in SST is that a La Nina prevented them from merely returning to the PWP. Any thoughts?Carl

  4. Anonymous says:

    >Is this paper any better than Michael's back of the envelope post on:http://www.worldclimatereport.com/index.php/2009/04/30/what-you-cant-do-about-global-warming/?ie 1.77 tmt/Deg C.

  5. Bob Tisdale says:

    >Anonymous: The WorldClimateReport factor looks like it’s based on projections of temperature rise for a doubling of CO2, and the Matthews factor is based on historic changes in CO2 and temperature. The WorldClimateReport factor seems to assume that all of the projected warming is based on a rise in CO2, but the Matthews factor appears to consider that other greenhouse gases contributed to the past warming.

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