The theory of Anthropogenic Global Warming, so far as we understand it, consists of the following two assertions.
(1) If we increase the concentration of CO2 in the atmosphere to 600 ppmv, we will cause the world to warm up by at least 2°C. (The concentration in pre-industrial times was 300 ppmv and is currently 400 ppmv, where ppmv is parts per million by volume.)
(2) If we continue burning fossil fuels at our current rate, emitting 10 petagrams of carbon into the atmosphere every year, we will raise the concentration of CO2 in the atmosphere to 600 ppmv within the next one hundred years.
We can falsify the second assertion using our observations of the carbon-14. We present a detailed analysis of atmospheric carbon-14 in a series of posts starting with Carbon-14: Origins and Reservoir. Here we present a summary, with approximate numerical values that are easy to remember.
Each year, cosmic rays create 8 kg of carbon-14 in the upper atmosphere. If carbon-14 were a stable atom, all carbon in the Earth's atmosphere would be carbon-14. But carbon-14 is not stable. One in eight thousand carbon-14 atoms decays each year. The rate at which the Earth's inventory of carbon-14 decays must be equal to the rate at which it is created. There must be 64,000 kg of carbon-14 on Earth.
The Earth's atmosphere contains 800 Pg of carbon (1 Pg = 1 Petagram = 1012 kg) bound up in gaseous CO2. One part per trillion of this carbon is carbon-14 (1 ppt = 1 part in 1012). There are 800 kg of carbon-14 in the atmosphere. That leaves 63,200 kg of the total inventory somewhere else. We'll call this "somewhere else" the carbon-14 reservoir.
Each year, 8 kg of carbon-14 is created in the atmosphere by cosmic rays, and each year the atmosphere loses 8 kg of carbon-14 to the reservoir. (Here we are ignoring the 0.1 kg of atmospheric carbon-14 that decays each year.) There is no chemical reaction that can separate carbon-14 from normal carbon. Every 1 kg of carbon-14 that leaves the atmosphere for the reservoir will be accompanied by 1 Pg of normal carbon.
Consider the atmosphere before we began to add 10 Pg of carbon to it each year. The mass of carbon in the atmosphere is constant. If 1 Pg of carbon leaves the atmosphere and enters the reservoir, 1 Pg of carbon must go in the opposite direction, leaving the reservoir and entering the atmosphere.
The only way for there to be a net loss of carbon-14 from the atmosphere to the reservoir is if the concentration of carbon-14 in the reservoir is lower than in the atmosphere. The only place on Earth that is capable of acting as the reservoir is the deep ocean, in which the concentration of carbon-14 is 80% of the concentration in the atmosphere. Each year 40 Pg of carbon leaves the atmosphere and enters the deep ocean, carrying with it 40 kg of carbon-14, while 40 Pg of carbon leaves the ocean and enters the atmosphere, carrying with it 32 kg of carbon-14. The result is a net flow of 8 kg/yr of carbon-14 into the ocean. Furthermore, the ocean contains 63,200 kg of carbon-14 in concentration 0.8 ppt, so the total mass of carbon in the oceans is roughly 80,000 Pg.
With the ocean and the atmosphere in equilibrium, 40 Pg of carbon is absorbed by the ocean each year, and 40 kg is released by the ocean. If we were to double the quantity of carbon in the atmosphere, we would double the amount absorbed by the ocean each year. Instead of 40 Pg being absorbed each year, 80 Pg would be absorbed. We could double the concentration of carbon in the atmosphere by emitting 40 Pg/yr. But we emit only 10 Pg/yr. Our emissions are sufficient to increase the mass of carbon in the atmosphere by 25%, after which everything we emit will be absorbed by the oceans. The oceans contain 80,000 Pg of carbon. If we add 10 Pg/yr, it will take roughly eight thousand years to double the carbon concentration in the oceans, after which the concentration in the atmosphere will double also.
Back in the 1960s, atmospheric nuclear bomb tests doubled the concentration of carbon-14 in the atmosphere. Such tests stopped in 1967. In our more precise calculation we predict that the concentration of carbon-14 must relax after 1967 with a time constant of 17 years, so that it would be 1.37 ppt in 1984 and 1.05 ppt in 2018. The concentration did relax afterwards, with a time constant of roughly 15 years, and in 2016, the carbon-14 concentration in the atmosphere is indistinguishable from its value before the bomb tests. During that time, almost every CO2 molecule that existed in the atmosphere in 1967 passed into the ocean and was replaced by another from the ocean. Anyone claiming that our carbon emissions will remain in the atmosphere for thousands of years, such as the author of this article, is wrong. If we stopped burning fossil fuels tomorrow, the CO2 concentration of the atmosphere would return to its pre-industrial value within fifty years.
When carbon is absorbed or emitted by the ocean, it does so as a molecule of CO2. Statistical mechanics dictates that the rate of absorption is weakly dependent upon temperature, but the rate of emission is strongly dependent upon temperature. When we calculate the effect of temperature upon the equilibrium between the ocean and the atmosphere, we conclude that a 1°C warming of the oceans will cause a 10 ppmv increase in the concentration of CO2 in the atmosphere. When we look back at the record of CO2 concentration and temperature over the past 400,000 years, we see the correlation we expect, with the magnitude of the changes in good agreement with our prediction. For a 12°C increase in temperature, for example, the concentration of CO2 increases by 110 ppmv.
If we consider the atmosphere of the Earth in pre-industrial times, its atmospheric CO2 concentration was roughly 300 ppmv. A more exact value for the creation of carbon-14 is 7.5 kg/yr and we conclude that 37 Pg/yr or carbon was being absorbed and emitted by the ocean. When we add 10 Pg/yr human emissions from burning fossil fuels, we expect the concentration of CO2 in the atmosphere to rise by 27% to 380 ppmv, which is close to the 400 ppmv we observe.
Our analysis of the carbon cycle makes three independent and unambiguous predictions all of which turn out to be correct to within ±10%. Our analysis is reliable, and it tells us that it will take roughly eight thousand years to double the CO2 concentration of the atmosphere if we continue burning fossil fuels at our current rate. Assertion (2) above is wrong by two orders of magnitude. The theory of Anthropogenic Global Warming, as stated above, is untrue.
POST SCRIPT: Assertion (1) is harder to falsify, and we do not claim to have done so in a manner convincing to all readers. Nevertheless, we did conclude that assertion (1) had to be wrong in our series of posts on the greenhouse effect, which we summarize in Anthropogenic Global Warming. We calculated that doubling the CO2 concentration of the atmosphere will cause the Earth to warm up by 1.5°C, provided we ignore changes in water vapor and cloud cover. As the world warms up, however, water evaporates more quickly from the oceans, and we get more clouds. Clouds reflect sunlight. The warming effect of doubling CO2 concentration is reduced by an increase in cloud cover. Clouds stabilize the Earth's temperature because they become more frequent as the Earth warms up, and less frequent as it cools down. Our simulation of the atmosphere with clouds suggests that the actual warming caused by a doubling of CO2 will be 0.9°C. So far as we can tell, the climate models used by the majority of climate scientists do not account for the increase in cloud cover that occurs as the world warms up. But they do account for the increase in water vapor in the atmosphere. Clouds cool the world, but water vapor is another greenhouse gas, and warms the world. By including water vapor but excluding the increasing cloud cover, these climate models conclude that the effect of doubling CO2 concentration will be 2°C or larger.
POST POST SCRIPT: Some readers suggest that the atmosphere-ocean system cannot be modeled with linear diffusion because the dissolved CO2 does not increase in proportion to atmospheric CO2 concentration. We address and reject their claim in an update to Probability of Exchange.