The residence times of carbon dioxide are 16 and 55 years

August 29, 2016

The model 1DAOBM-2, which I have developed, can be used to simulate the way carbon dioxide behaves in the atmosphere-ocean-biosphere system. In the former post I showed the simulation results of the yearly and cumulative CO2 flux rates. The 1DAOBM-2 can be used to simulate residence times and the future scenarios of different CO2 emission rates.

There is a real test carried out in the atmosphere nearing an end and it can be used to check the residence time of the anthropogenic CO2 in the atmosphere. The isotope 14C is also called “bomb 14C” or radiocarbon, because it originates from the nuclear bomb tests in the atmosphere from 1945 to 1964 and it is radioactive by nature. The isotopes of 13C and 14C can be labelled, because their concentrations can be measured in the reservoirs of the CO2 recycling system. This property gives an opportunity to track their transfer rates between the reservoirs and to check the calculations of any models to see, if they really match the observations. The total CO2 amounts can be checked very accurately in the atmosphere with direct concentration measurements. The anthropogenic CO2 amounts in the ocean are also based on the measurements but these amounts are not so accurate. 

 Fig. 1. Residence time of radiocarbon 14C.


The decay curve of the 14C can be combined with some of the worldwide measurements carried out since 1950s, which are illustrated in Fig. 1. The measured permille values differed in the northern and southern hemisphere in the beginning, because the nuclear tests were carried out in the northern hemisphere until 1964, but after 1968 there is no essential difference.


The simulated decay rate with a residence time of 16 years gives a very good fit. This result shows the important feature of the CO2 recycling system, that a relatively small increase of radiocarbon is flushed away from the atmosphere into the ocean and into the biosphere. This is based on the fact that the removal processes – i.e. the fluxes from the atmosphere into the ocean and into the biosphere remove or flush a huge amount of CO2 from the atmosphere into the other reservoirs (today about 25 % of the total mass of the atmosphere each year), because they do not make practically any difference between the different CO2 isotopes. It is true that the plants prefer the 12C isotopes although this effect is fairly small.

In the beginning of the nuclear tests, the radiocarbon concentrations were at the natural level in the ocean and in the biosphere and therefore only very tiny amounts of radiocarbon returned back into the atmosphere. This also means that the deep ocean is the main sink for radiocarbon, because 80 % of radiocarbon will recycle back from the biosphere in 60 years, while the rest will stay for more than 250 years. The direct measurements show that radiocarbon has almost totally disappeared from the atmosphere. This is evidence that the ocean can be a real sink, at least for labelled CO2 fluxes.


An essential question is, whether the anthropogenic CO2 is behaving in the same way as the radiocarbon. Both isotope fluxes were added into the atmosphere, where these fluxes created an anomaly. The anthropogenic CO2 flux into the atmosphere started around 1750 when the burning of coal was started. Because this anthropogenic CO2 flux started from zero, the behaviour of anthropogenic concentration in the atmosphere is similar to the radiocarbon behaviour. Therefore a conclusion can be drawn that the decay rate of anthropogenic CO2 cannot be quicker than that of radiocarbon, but the residence time of the anthropogenic CO2 decay process should be the same as the decay rate of 14C.


Segalstadt has carried out a survey consisting of 34 residence time studies, in which six different methods were applied. The average value is 7.6 years among the studies showing residence times from 2 to 15 years. All these studies were published before 1990 starting from 1957. One common feature seems to be that the results are not based only on the direct measurements, but a model has also been applied in calculating the residence times. A rather amazing realization is that 12 of these referred papers have used radiocarbon measurements in getting the residence times from 2 years to 12.5 years. The spread of the results also show that these results are not reliable. The author’s conclusion is that the radiocarbon decay observation rate from 1964 to the present day without any models as depicted in Fig. 1 is so reliable that the results shorter than about 16 years residence time cannot be correctly calculated or evaluated. These results of a short residence time above also contain another serious common source of error that they are usually addressed to be applicable to the total CO2 decay rate in the atmosphere.


The decay rate according to 1DAOBM-2 simulations

In Fig. 2 the decay rates of anthropogenic and total CO2 concentration in the atmosphere are depicted. The simulations start from the year 1964, which is the same year the nuclear tests were stopped.


Fig. 2. The decay rates of the anthropogenic and the total CO2 in the atmosphere.


The decay rate of anthropogenic CO2 in the atmosphere is depicted with the brown graph. The residence time of 16 years gives a very good result. It is the exact residence time as measured for 14C decay rate.

The black dashed graph is the fitting with the residence time of 55 years resulting to 220 years adjustment time. The blue dashed line is a graph depicted as reference, which is the decay rate according to the Bern model. In the beginning of the change it gives much lower values than 1DAOMB-2 and in the end it stays at the level of 290.5 ppm.

There are no measured values for the total CO2 residence time. Because 1DAOBM-2 simulates accurately the anthropogenic CO2 residence time, it is a positive sign, that it could also simulate accurately the total CO2 decay rate.

The behaviour of the total CO2 increase in the atmosphere behaves differently in comparison to radiocarbon and to the anthropogenic concentrations. The difference originates from the recycling fluxes of the ocean and from the biosphere back into the atmosphere. The recycling fluxes in and out between the reservoirs are essentially at the same level, which means that almost the same amount of the total CO2 is leaving and entering the atmosphere. Because there is only a minor dilution effect for the total CO2, the residence time of the total CO2 in the atmosphere must essentially be longer than that of radiocarbon and anthropogenic CO2. The dynamic delays depend on the flux rate into the deep ocean and the possible increase of the biosphere mass.


We can make a simple theoretical experiment. Let us think about what would happen if the fossil fuel emissions of 10 GtC yr-1 were stopped totally. What would happen to the fluxes into the ocean and into the biosphere? We could expect that the average removal flux rate from the atmosphere during the next year would continue at about the present level, which would mean almost 4.5 GtC yr-1 (=45 % from the 10 GtC yr-1) in the next year. Thereafter the removal rate would gradually decrease. The ocean or the biosphere can only react on the concentration of the total atmospheric CO2 amount.


What could be the first approximation of the adjustment time required for the atmospheric CO2 concentration come back to the CO2 concentration of 280 ppm? Actually the concentration would be a little bit higher. The atmospheric concentration of 280 ppm was in balance with the CO2 amount in the ocean in 1750. An estimate of the CO2 in 1750 is 38000 GtC. Using the relationship of 280 ppm / 38000 GtC would mean a new balance value of 283 ppm of CO2 in the atmosphere. The first rough adjustment time approximation would be the same time as required to get the present concentration of  about 400 ppm, which would be 2016 – 1750 = 266 years. This calculation is based on the assumption that the ocean has a capacity to absorb the rest of the present “extra” atmospheric mass 256 GtC in 2015 (= 854 GtC – 597 GtC).


There are research studies showing the residence times of around 200 years. O’Neill et al. have calculated the adjustment time of about 175 years. Lashof and Ahuja have estimated the adjustment time to be about 230 years. The residence time of 7.5 years would mean that the present amount of 854 GtC of the total CO2 should come to 597 GtC during the adjustment time of 4*7.5 = 30 years. It would mean a linear decay rate of 29 GtC yr-1, which is impossible.


IPCC has taken another “extreme” approach to the question of the anthropogenic CO2 residence times in the atmosphere, when compared to the residence time of 7.5 years only. In AR4 IPCC applied the Bern model, which states that there are three residence times of 1.2, 18.5 and 173 years, and about 22 % of any CO2 input will stay in the atmosphere. In AR5 there is no specific lifetime formula. According to the IPCC calculation method, after 2000 thousand years, the atmosphere will still contain between 15 % and 40 % of those initial emissions. This feature can be clearly seen in the RCP simulations, which show that the atmospheric CO2 concentrations do not start to decrease even though the emissions decrease.


The mixing capability of the atmosphere explains the sharp changes in the atmospheric CO2 concentration but the recycling fluxes and the delays in the other reservoirs explain the long residence time of the system. This means that the total flush rate from the atmosphere is not the flux rate of removing the total CO2 into the sink (as assumed in the residence time of 4 years only). The removing rate is controlled by the flux from the surface ocean into the deep sea.


The simulations confirm the fact that the emission rate change to the CO2 concentration changes does not take place in one ideal mixing chamber. The atmosphere and the surface ocean can be described as an ideal mixer, as the biosphere with four parallel plug flow reactors with four different residence times, and the intermediate & deep ocean as an outlet of the system. Three of these boxes/reactors have recycling fluxes.


Simulation of the projection RCP4.5

IPCC has used projections to estimate the future warming values depending on the assumed CO2 emissions. One of these projections is the RCP4.5 projection. In this projection the fossil fuel emission reach a maximum of 11.5 GtC yr-1 in 2030. The results are depicted in Fig. 3.


Fig. 3.  The RCP4.5 projections by IPCC and 1DAOBM-2.


The CO2 concentration of 1DAOBM-2 behaves differently in comparison to the RCP4.5 simulation by IPCC. The essential difference is that according to the IPCC the anthropogenic CO2 of the present atmosphere cannot be flushed into any sink when it has reached its maximum value. The total CO2 will increase to 538 ppm and it will stay there for centuries.


According to the 1DAOBM-2 model, the total CO2 concentration starts to gradually decrease in 2060 and will come finally to the balance value. The IPCC’s way to keep the antropogenic amount at the same level, is possible only by utilizing the very long residence time of the CO2. According to IPCC, the oceans can absorb about 55 % of the yearly CO2 emissions in the present climate but as soon as the fossil fuel emission rate starts to decrease, the ocean can not do it anymore! This is very difficult to understand. It is not reasonable to believe that the CO2 amount would not to start decrease, even though the CO2 emissions have been reduced 65 % as shown in the RCP4.5 simulation.


The several hundred years residence time of CO2 is the third false assumption, which is needed in IPCC’s AGW theory. The first false assumption is the constant relative humidity in the atmosphere. In both cases the direct measurements show that these assumptions are not correct. The third element, which is not correct, is the strength of CO2 according to the equation of Myhre et al.


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