What to do about global warming - 2: The carbon dioxide life cycle

This article continues a series. The first article is here.

Reports from the Intergovernmental Panel on Climate Change (IPCC) document the history of human-generated carbon-dioxide emissions into the atmosphere (IPCC, 2014). In Figure 1 we show the published history of annual carbon dioxide (CO2) emissions and the cumulative CO2 emissions since the beginning of the industrial revolution.

Figure 1. Annual and cumulative CO2 emissions (IPCC, 2014, Figure 1.d)

As of 2011, the total amount of carbon dioxide emitted into the atmosphere is about 2050 Gt (Gigatonnes or trillion kilograms). These cumulative emissions have resulted in increasing the pre-industrial levels of CO2 from 280 ppm (parts per million) to greater than 400 ppm (2184 Gt of additional CO2 corresponds to doubling CO2 from 280 ppm).

What happens to the CO2 in the atmosphere? It’s complicated. However, three things happen concurrently, but with different time scales (Archer, 2009):

• CO2 dissolves into the ocean (decades to hundreds of years)
• CO2 is taken up by plants (decades to hundreds of years)
• CO2 is removed by geologic processes, combining to create calcium carbonate (CaCO3) and calcium oxide (CaO) (thousands to tens of thousands of years).

(Archer, 2009) notes that CO2 effects depend on the quantity release (1000 Petagram (10^15 g, or 1000 Gt) Carbon vs. 5000 Pg (1 Pg of Carbon is 1 Gt of Carbon or 3.67 Gt of CO2):

"The equilibration time scale for ocean invasion, calculated by a least squares fit of an exponential to the CO2 concentration trajectory, is about 250 ± 90 years for the 1000 Pg C release spike, and 450 ± 200 years for the 5000 Pg C release." (Archer, 2009)

We display in Figure 2 a rendering and curve-fit of this, with the curve fit as

Fraction Remaining=-0.8120*ln(t) 0.800273.

Figure 2. Fraction of CO2 remaining vs. time for Archer (1000 Pg case), and a best-fit.

The adopted curve fit is between the 1000 Pg and 5000 Pg cases of (Archer 2009) at the century mark, and underestimates the residual amount after a few thousand years (which may cause us to slightly underestimate the temperature effects in that time period). As one can see, even after two hundred years there remains about 30% of the initial CO2 added. Put another way, even if carbon dioxide emissions could cease abruptly, they remain in the atmosphere long after we are told we “must do something”.

Let us then consider a thought experiment: suppose we were able, by some means, to eliminate all human-generated carbon dioxide emissions beginning in 2020. Then the annual emissions from the beginning of the industrial revolution about 1850 would look like Figure 3 (the annual emissions growth rate from the IPCC is approximately 1.5%):

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

The cumulative CO2 emissions would then look like Figure 4.

Figure 4. Cumulative CO2 emissions (Gt) from 1850 assuming zero emissions beginning in 2020.

We apply the decay model of Figure 2 to the annual emissions each year and determine the residual carbon dioxide based on the emissions and decay of all prior years. Given the decay rate of CO2 in Figure 2 and the annual emissions of Figure 3, the amount of CO2 remaining in the atmosphere each year is displayed in Figure 5:

Figure 5. Net CO2 (Gt) remaining in the atmosphere assuming emissions cease in 2020.

The peak occurs in 2020 with about 50% of the total amount of carbon dioxide emitted still remaining, and slowly decays thereafter. However, even after 1000 years (2850) 50% of the peak (or about a quarter of all emissions) remains in the atmosphere, even if emissions cease in 2020! The equilibration with the ocean is occurring as expected.

A more realistic time frame for reducing CO2 emissions might be that, beginning in 2020, we cease increasing CO2 emissions and begin reducing CO2 emissions exponentially with a 100-year decay constant, as in Figure 6:

Figure 6. Annual CO2 emissions (Gt) from 1850 with decrease beginning in 2020.

While this approach would seem to satisfy the urgency to “do something”, this scenario reduces human-generated CO2 emissions to pre-industrial levels in about 300 years (2350). What would be the effect on human-generated carbon dioxide in the atmosphere? Figure 7 displays the total cumulative carbon dioxide emissions for this scenario:

Figure 7. Cumulative CO2 emissions (Gt) from 1850 assuming peak emissions in 2020 and 100-year exponential decay).

In this scenario CO2 emissions continue, though at a decreasing rate, and the cumulative carbon dioxide continues to increase for another 500 years or so to a level about double that of the “hard cutoff” scenario.

The effect on the level of CO2 remaining in the atmosphere can be calculated using the same decay model in Figure 2 for each years' emissions, and yields remaining atmospheric CO2 as in Figure 8:

Figure 8. Net CO2 (Gt) remaining in the atmosphere assuming emissions begin an exponential decrease in 2020.

As indicated in Figure 8, the peak level of CO2 occurs about the year 2250 and is about twice the value see with the sharp cutoff model. After a thousand years (2850) there remains about 80% of the peak value.

What does all this mean? As can be seen in the analysis and figures, it’s difficult to get the carbon dioxide out of the atmosphere once it’s put there. So, even if we cease emissions immediately (extremely unlikely) or begin reducing our carbon dioxide emissions immediately (possible), the atmosphere will continue to hold significant human-generated CO2 for hundreds to thousands of years. This presents a significant challenge for any approach to managing global warming that relies primarily on eliminating or reducing the use of fossil fuels.

But what about the effect on global average temperatures? After all, it was previously stated that the focus should be on temperature not carbon dioxide. If the level of carbon dioxide in the atmosphere determines the future global average temperature, then the slow decay of carbon dioxide suggests that there is a long-range effect on global average temperature. We take this up in the next installment.

Works Cited

• Archer, D. e. (2009). "Atmospheric lifetime of fossil fuel carbon dioxide", Annual Review of Earth Planet Science, 37, 117-134. [preprint]
• IPCC (2014). Climate Change 2014 Synthesis Report Summary for Policymakers. Intergovernmental Panel on Climate Change.

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