What do about global warming - 3: The effects of CO2 on global average temperature

In our previous installment we explained the carbon dioxide (CO2) life cycle in the atmosphere for two optimistic scenarios regarding reducing carbon dioxide emissions. We noted the persistence of carbon dioxide for hundreds and thousands of years. In this installment we examine the effect this has on global average temperatures.

As discussed in the first installment we accept the premise that human-generated CO2 causes unacceptable atmospheric warming. In this article we determine the magnitude of this warming over time for the two carbon-dioxide-emission scenarios we previously developed.

What is the magnitude of the expected temperature increase? (IPCC, 2007) section 2.3 has calculated that doubling carbon dioxide atmospheric concentration from 280 ppm (parts per million) at pre-industrial levels to 560 ppm based on human-generated carbon dioxide emissions will increase the global average temperature by 3.0 °C or K (Kelvin). This is a primary basis for attempting to limit carbon-dioxide emissions. At 280 ppm the mass of CO2 in the atmosphere can be calculated as 2.184x10^3 Gt; doubling this mass yields 4.368 x 10^3 Gt. Therefore, the sensitivity of temperature change to CO2 emissions is 3.0 °C/(2.184 x 10^3 Gt), or 1.37°C/Tt (trillion tonnes CO2). This agrees within the error margin of (Leduc, 2016) with sensitivity of 1.7 ± 0.4°C/Tt.

How fast is the temperature increase realized? (Seinfeld, 2011) estimates that 40% of the CO2-induced temperature effect is realized in 5 years, with the remaining 60% realized on “century time scales”. We use 300 years for this latter quantity, and depict the temperature realization as in Figure 1.

Figure 1. Temperature realization (K/Gt CO2) vs. time (years after emission) due to carbon dioxide emissions; no additional temperature decay.

The literature is less clear about how global average temperatures might decrease as carbon dioxide is removed. (Archer, 2009) (p. 9) suggests a “1000-year response time relaxing to a target temperature determined by a deep-ocean climate sensitivity of 3°C.” (p. 9). This would be a consequence of deep-ocean mixing of the energy initially deposited in the atmosphere equilibrating with the ocean. Figure 1 displayed a situation where the resulting temperature only follows the CO2 level, i.e., there is no additional temperature decay. If we assume an additional temperature decrease due to ocean equilibration with a 1000-year exponential decay (beginning only when the peak temperature is realized), then the temperature dependence appears as in Figure 2. But we have not included "relaxing to a target temperature...of 3°C"; the temperature decays to the original, unperturbed temperature.

Figure 2. Temperature realization (K/Gt CO2) vs. time (years after emission) due to carbon dioxide emissions and 1000-year exponential temperature decay.

Since this results in a faster temperature decay, we use this to establish “best case” bounding scenarios for the effects of carbon dioxide emissions. For, if we exceed the “tipping point” with a “best case” scenario, there is by definition no other scenario that will yield a better result.

We first consider the most optimistic but unlikely scenario of complete CO2 emissions cutoff in 2020, as in Figure 3.

Figure 3. Modeled annual CO2 emissions from 1850 with emissions cutoff in 2020.

Using the CO2 sensitivity model discussed in the prior article and the temperature sensitivity developed above, this scenario yields Figure 4:

Figure 4. Net CO2 remaining in the atmosphere (red line) and resulting temperature increase (blue line) for emissions cutoff in 2020 with additional temperature decay.

The peak temperature increase is about 3.5K. The temperature “tipping point” of 2K is initially exceeded about 2060 and substantially exceeded at about year 2270 (t=420) as indicated in the expanded temperature scale in Figure 5. The temperature increase decays after a few thousand years.

Figure 5. Net CO2 remaining in the atmosphere (red line) and resulting temperature increase (blue line) for emissions cutoff in 2020 with additional temperature decay.

This must be considered the “best-best” case, and still the temperature exceeds the 2K tipping point. For completeness we consider other scenarios in the Appendix, but focus our remaining discussion on the implications of this result.

The reader will likely notice that the decay time of the temperature (blue line) in Figures 4 and 5 is much shorter than the apparent decay time of the carbon dioxide (red lines). This seems counterintuitive if carbon dioxide is the cause of global warming. The reason for this situation is that the models derived from the literature are not clearly reconciled. The decay time of carbon dioxide is based on (Archer 2009) as discussed in the prior installment, and has a very long tail, into the thousands of years.

The effect on temperature is developed by (Seinfeld 2011) as described above, with the ultimate warming effect realized "on century time scales", shorter than "thousands of years" for carbon dioxide persistence. So there is some inconsistency. If the warming truly follows the carbon dioxide concentration one would expect warming to continue as long as there is some carbon dioxide above the initial condition. However, (Archer 2009) notes that "the radiative [heating] impact of a further kilogram [of carbon dioxide] decreases, because of the absorption band saturation effect," and the reality that "the airborne fraction [of carbon dioxide] increases because of the depleted carbon buffer chemistry of the ocean," meaning that the ocean can no longer absorb as much CO2 and the atmospheric concentration is therefore higher. They also state that these two effects "largely counteract each other, so that the radiative impact of a kilogram of CO2 is nearly independent of whether that kilogram is released early or late in the fossil fuel era." So it seems to be the case that the residual carbon dioxide in later centuries does not cause additional heating and the primary effect is early heating in the initial decades as Figures 4 and 5 indicate.

What does all this mean? My interpretation is that “you can’t get there from here” by relying solely on reducing CO2 emissions on any time scale. Given the amount of human-generated carbon dioxide already emitted, the persistence of CO2 in the atmosphere, and the time scales for temperature following the CO2 (both increase and decrease), controlling CO2 emissions, by itself, is inadequate to prevent exceeding the tipping point. So we have established that the “something” we must do must be more than controlling CO2 emissions. But if 2060 is a valid estimate of when the “tipping point” will be exceeded, we must do something immediately to prevent the expected but unacceptable temperature increase.

Are we then, as the climate alarmists note, “doomed”? Are there any options for controlling catastrophic global warming? As we have shown, simply controlling carbon dioxide emissions is inadequate (ineffective with respect to the stated goal). And it doesn’t matter how much money we might spend on controlling future emissions. By focusing on the perceived root cause of carbon dioxide we can miss the corrective action of controlling temperature: "The good news, Mrs. Patient, is that we found the infection. The bad news is that Mr. Patient died from high fever before the antibiotics began working. Sorry." The basic physics dictates these results given the emissions to date.

However, we are not yet without options (enter “engineering”). We next examine active reduction of carbon dioxide by various methods of sequestering (capturing) the CO2 into a form permanently removed from the atmosphere. These are discussed in the next installment.

Works Cited

Archer, D., et al., (2009). Atmospheric lifetime of fossil fuel carbon dioxide. Annual Review of Earth Planet Science, 37, 117-134. [preprint]

IPCC. (2007). Climate Change 2007: Synthesis Report. Intergovernmental Panel on Climate Change. https://www.ipcc.ch/report/ar4/syr/

Leduc, M., et al., (2016). Regional estimates of the Transient Climate Response to cumulative CO2 Emissions. Nature Climate Change, 6, 474-478. doi:10.1038/nclimate291

Seinfeld, J. H. (2011). Insights on Global Warming. AIChE Journal, 3259-3284. doi:10.1002/aic.12780

Appendix 3A

This appendix analyzes other, non-bounding scenarios for carbon dioxide emissions and temperature decay. They generally result in either slower temperature decay, higher peak temperatures, or both compared with the results in Figures 4 and 5.

For the CO2 “cutoff scenario” of Figure 3 and the temperature profile of Figure 2 (no additional temperature decay), the net CO2 and temperature levels for this case are displayed in Figure A1:

Figure A1. Net CO2 remaining in the atmosphere (red line) and resulting temperature increase (blue line) assuming emissions begin to decrease in 2020 with no additional temperature decay.

As the figure indicates, even with a complete cutoff in 2020, the 2°C “tipping point” is exceeded shortly after the CO2 emissions are eliminated. The temperature continues to rise for another 250 years (2270), with an ultimate 3.5°C temperature increase, even if all CO2 emissions are terminated in 2020, a very unlikely scenario. The peak temperature is similar to Figures 4 and 5, though the decay is extended.

We also consider a possible realistic scenario that postulates reducing CO2 emissions exponentially beginning in 2020, with a 100-year decay constant, as in Figure A2:

Figure A2. Annual CO2 emissions from 1850 with exponential decrease beginning in 2020 (year 170).

Using the CO2 sensitivity model discussed in the prior article and the temperature sensitivity of Figure 1, this CO2 emission scenario yields the net temperature change indicated in Figure A3.

Figure A3. Net CO2 remaining in the atmosphere (red line) and resulting temperature increase (blue line), assuming emissions begin to decrease in 2020 and no additional temperature decay.

Peak temperatures increase nearly 10°C about 250 years (2500) after the peak emissions in 2250, even for a relatively optimistic scenario of exponential reduction of CO2 emissions beginning in 2020, assuming no additional temperature decay.

For this scenario (possible CO2 reduction beginning in 2020 and additional exponential temperature decay), the net CO2 and temperature vs. time are displayed in Figure A4:

Figure A4. Net CO2 remaining in the atmosphere (red line) and resulting temperature increase (blue line) assuming emissions begin to decrease in 2020 with additional temperature decay.

Compared with Figure A3, the temperature drops relatively rapidly (to no net increase at about 4500 years). The peak temperature increase is slightly lower (8.5K vs. about 9K) and still well above the 2K postulated “tipping point”.

This 8.5K peak temperature increase is probably the most optimistic possible result based on carbon dioxide emissions to date, current emissions, possible emission reductions, and eventual temperature decay. If (Archer, 2009) is correct, then deep ocean mixing yields a temperature in Figure A4 that relaxes to a net 3°C increase for times after about 2000 years. But the peak temperature increase would be similar.

(c) 2019. Ronald S. Carson. All rights reserved.