A major question concerning how severe, and how long-lasting, human induced climate change might be is the lifetime of carbon dioxide (CO2) in the atmosphere. Worst case projections of climate change often invoke a lifetime of centuries or more, which makes sense for this must lead to very high accumulations of the gas for very long periods of time. But is this invocation correct? Fortunately, we already possess sufficient data, or sufficient quality, to answer the question at least reasonably well, and test alternative answers to it.
But first, we must answer a more basic question: what is meant by lifetime? Thinking about it, a CO2 molecule might spend many millennia in the atmosphere, even longer in fact, or it might last only a few seconds before being retaken back into one the several surface sinks on the planet. What is needed is some kind of average lifetime, and not just any average but one that allows for straightforward calculations pertaining to global warming and climate change. The lifetime generally preferred in science for these kinds of purposes is called the half-life.
For a complete discussion on half-life, see http://amedleyofpotpourri.blogspot.com/2017/11/half-life.html, or https://en.wikipedia.org/wiki/Half-life. Half-life is commonly encountered in measurements of radioactive decay, and is easiest to describe in this context. The half-life of a quantity of radioactive atoms is the time required for half the atoms to decay into other atoms (which may or may not be radioactive themselves). For example, starting with X number of uranium atoms, the half-life is the time it takes until only X/2 uranium atoms are left. The important point here is that it is not possible to say when a specific atom will decay; thus, we can only speak in terms of probabilities. Another way of expressing half-life is the number of years that must elapse for there to be a 50% chance that a specific atom will decay -- or, more generally, for a specific process to occur.
Applied to CO2 in the atmosphere, half-life refers to the time needed for a specific CO2 molecule to leave the atmosphere and enter a surface or oceanic sink; alternatively, it is the time over which half the CO2 residing in the atmosphere will leave it. The estimate of this half-life used here is 27 years (http://amedleyofpotpourri.blogspot.com/2017/11/the-half-life-of-co2-in-earths.html). Here there is an important point: if CO2 levels are constant, as they have apparently been for about the last 10,000 years up to human industrialization beginning 150-200 years ago (at around 280 ppm, or 2.1 trillion tonnes), then over this half-life an equal amount of CO2 must have been entering the atmosphere as leaving it over any time period.
Given the half-life of atmospheric CO2, we can calculate the percentage of the gas that leaves the atmosphere per year. The necessary calculation is given in the reference above, and it turns out to be about 2.5%. That is, when the atmosphere contained 280 ppm of CO2 (or 2.1 trillion tonnes), some 7.0 ppm / 52.5 billion tonnes were taken up by sinks every year. Again, assuming CO2 levels constant, that means an equal amount of the gas moved from those sinks back into the atmosphere / year.
I will make an assumption now, but, as we shall see, it is a reasonable assumption because calculations based on it fit current data, while significant deviations from it do not. That assumption is that natural sources of CO2 today are close to those 150-200 years ago; that is, they still amount to about 52.5 billion tonnes of the gas transported into the atmosphere every year. Remember, these are natural sources. Adding in anthropogenic sources yields a total of about 90 billion tonnes of CO2 transported into the atmosphere yearly.
How well does this assumption work? Go back to the 2.5% / year removal of atmospheric CO2. Applied to the ~400 ppm -- 3 trillion tons of the gas today, this means some 75 billion tonnes / year are being taken up by surface sinks.
If 90 billion tonnes of CO2 are entering the atmosphere every year, while 75 billion tonnes are leaving, then this gives a net increase of 90-75 = 15 billion tonnes / year. 15 billion tonnes equals 2 ppm, which is very close to the average increase of CO2 per year over the last several decades. This strongly indicates that the assumption of CO2 outgassing from natural sinks having changed little over the last 150-200 years is at least approximately correct, even with the 1 degree C temperature increase over that period.
If the above analysis is correct, we can posit some reasonable speculations about future levels of atmospheric CO2 , and their possible effects on warming and climate change. For example, if the current 90 billion tonne atmospheric influx per year is maintained, then levels of the gas will increase until its 27 year half-life leads to an equal amount leaving annually, bringing the system to equilibrium. It turns out that that 90 billion is 2.5% of 3.6 trillion tonnes, or 480 ppm. That is, in approximately a century (about 3.7 half-lives), atmospheric CO2 will almost level out at 480 ppm, which is 20% greater than current levels.
There is considerable disagreement about the climate effect of such an increase. I'm going to take the most straightforward approach, which is that since the Earth has experienced a 40% increase in over the last ~150 years, accompanied by a ~1 degree C increase in temperature, a 20% rise should lead to about another ~0.5 degree C of further warming. Again though, I emphasize that this is by no means certain.
What about other scenarios? While there is no way emissions could be reduced to zero now or in the immediate future, we can also calculate how long it would take for CO2 to return to pre-industrial levels, or close to them if that did happen. If emissions were to suddenly decrease to the natural 52.5 billion tonnes / year, the current uptake of 75 billion tonnes would mean a first year decrease of atmospheric CO2 of 22.5 billion tonnes, reducing the current level from 400 ppm down to about 397 ppm. Now, as this difference will decrease as CO2 diminishes, to an average of around 11.5 billion tonnes -- 1.5 ppm, in about 80 years, or three half-lives -- up to the year 2100 -- we would be close to the pre-industrial level of 280 ppm.
If emissions were to gradually drop to zero during the coming century, how would this scenario change? I calculate we would then reach approximately half-way toward pre-industrial CO2 levels from today during that period, or about 340 ppm.
On the other hand, what if emissions double over the course of this century; how much would levels rise? A doubling of emissions means increasing them from 90 billion tonnes / year to around 125-130 billion tonnes. Again, we ask what would the atmospheric level of CO2 have to be for this amount to be equal to 2.5% of that level? The answer is at least five point two trillion tonnes, or 680--700 ppm. Such an increase could represent a 1 degree C temperature increase above the emissions unchanged scenario (i.e., 1.5 degrees), perhaps even more.
Raising global temperatures should increase CO2 atmospheric half-life, as the solubility of gasses in water decreases with increasing temperature. As we see, however, a rise of 1 degree doesn't appear to have much effect, so another 0.5-1.5 C should not drastically increase half-life either.
Assuming the analysis here holds up, it means that claims of having to reduce carbon emissions to zero by 2100 or even 2050 are pure hyperbole, without scientific basis. Yet developing energy sources with lower or zero emissions compared to fossil fuels should have high priority, as increasing CO2 sufficiently could have unpleasant consequences, some of which we are not yet aware of.
