We begin with the carbon cycle in its natural, equilibrium state. The concentration of CO2 in the atmosphere is 300 ppm, which means it contains 650 Pg of carbon. The oceanic carbon reservoir, meanwhile, contains 77,000 Pg. Each year, the ocean emits 37 Pg into the atmosphere, and absorbs 37 Pg from the atmosphere. But now we start adding an extra 10 Pg/yr to the atmosphere by burning fossil fuels. In the the numerical equations that describe our carbon cycle, we set mF = 10 Pg/yr. You can download our carbon cycle spreadsheet here. In it, you will find the following plot, along with our calculations.
Figure: Atmospheric and Oceanic Carbon Mass versus Time, with Ten Petagrams per Year Fossil Fuel Emissions. The time scale is logarithmic. Note that 1 Eg = 1,000 Pg. Click to enlarge.
During the first ten years, the total mass of carbon entering the atmosphere each year is 47 Pg/yr. But the mass absorbed by the oceans remains 37 Pg/yr. The mass of carbon in the atmosphere increases by 10 Pg/yr.
After ten years, we have emitted 100 Pg by burning fossil fuels. The mass of carbon in the atmosphere has increased by 80 Pg to 730 Pg. The rate at which carbon is absorbed by the ocean has increased in proportion, because there are more CO2 molecules available to absorb. The ocean now absorbs 41 Pg/yr. With 37 Pg/yr emitted by the ocean, and 10 Pg/yr emitted by burning fossil fuels, the carbon mass of the atmosphere increases by 6 Pg/yr.
After a hundred years, we have emitted 1,000 Pg by burning fossil fuels. The mass of carbon in the atmosphere has increased by 180 Pg to 830 Pg. The rate at which atmospheric carbon enters the oceanic reservoir is 47 Pg/yr. The mass of the oceanic reservoir itself has increased by 820 kg to 77,820 kg, which is only 1%. The rate at which oceanic carbon emerges into the atmosphere is still close to 37 Pg/yr. The atmosphere is in equilibrium: carbon enters at 47 Pg/yr and leaves at 47 Pg/yr. Its carbon mass increases only by 0.1 Pg/yr.
After one thousand years, the mass of carbon in the oceanic reservoir has increased by 13% to 87,000 Pg. The rate at which the ocean emits carbon into the atmosphere has increased by 13% to 42 Pg/yr. The mass of carbon in the atmosphere has risen to 910 Pg, and every year 52 Pg of atmospheric carbon is absorbed by the oceanic reservoir. The atmosphere is still in equilibrium with the ocean: each year 52 Pg enters and 52 Pg leaves. Its carbon mass continues to increase by only 0.1 Pg/yr, while the carbon in the oceanic reservoir increases by 10 Pg/yr.
After six thousand years, the mass of carbon in the atmosphere has doubled, and the mass in the oceanic reservoir has almost doubled. The plot below shows how atmospheric CO2 concentration increases with time for the same scenario.
Figure: Atmospheric CO2 Concentration in Response to Emission of 10 Pg/yr of Carbon by Burning Fossil Fuels. Units are parts per million by volume. Click to enlarge.
Burning fossil fuels at the rate we are going today, it would take 100 years to raise the concentration of CO2 in our natural, equilibrium atmosphere from 300 ppmv to 400 ppmv, and 6,000 years to raise it from 300 ppmv to 600 ppmv.