The Earth's CO2 System-Let the Data Speak

By Guus Berkhout

Prologue

In short, there are two different ways of improving our knowledge of a system.

1) Traditionally, we use an initial theoretical model, simulate measurements, and then compare the simulated measurements with real measurements. By updating the model parameters, we bring simulated and modeled measurements closer together. The updated model can be used for a better understanding of the systems behavior and for making model-driven projections into the future.

2) Second, we don’t start with a theoretical model, but we do start with the measurements, analyze those measurements, construct images and search for patterns in these images. Results are used for a quantitative description of the systems behavior and for making datadriven projections into the future.

My scientific career was in geophysical imaging.

With measurements we made images of the complex geology of the upper lithosphere worldwide.

Together with the geologists, we compared their geological models with our images.

This interaction led to improved models and updated measurement instrumentation.

Our slogan was and is: “Let the data speak’.

My experience is, if we deal with complex systems, it is wise to start with measurements and find out what the measurements try to tell us (‘squeezing information out of the data’).

My experience is also system images provide invaluable information about the level at which theoretical models and real measurements can be best compared and, last but not least, whether the available measurements allow us to estimate the model parameters with any statistical significance.

In the following, I will summarize the properties of the complex CO₂-system with the above in mind. I hope it will help in bringing the different CO₂-schools closer together.

Introduction

During the past 30 years, we see three topics that are most often discussed in climate science and climate policy circles:

1. What is the cause of the increased CO₂-concentration in the atmosphere and what is the role of humans in this process
2. What is the influence of the increased atmospheric CO₂-concentration on the temperature in the atmosphere, particularly in the lower troposphere
3. Using the information from topics 1 and 2, what is the most sensible climate policy

The main stream climate theory states:

(1) the increasing CO₂ is fully caused by human activities and 

(2) the increasing CO₂ in the atmosphere is the principal cause of global warming. This belief explains current climate policies

(3) mankind has the capability to significantly lower the global warming by decreasing its CO₂-emission. Looking at the socalled catastrophic consequences of global warming (“There is a climate crisis”), the mainstream message is that CO₂-reduction must be done in a great hurry (“It is five minutes to twelve”).

In CLINTEL, we  point out that there is NOT enough scientific knowledge and, therefore, NO scientific proof to declare CO₂ is the dominant factor in global warming.

Here, it is relevant to point at the research of Will Happer and William van Wijngaarden. They show the more CO₂ in the atmosphere, the smaller the increase in global warming ('decreased warming returns').

In CLINTEL, we also argue, apart from greenhouse gases, changes in the solar irradiation, changes in the cloud cover, and changes in the big ocean circulations, must be included in the research on climate change. Climate change is a multifactor phenomenon.

The overall message of CLINTEL to climate alarmists is there is no scientific argument to spend billions of dollars to reduce the amount of CO₂ in the atmosphere to stop the global warming.

This means the answer of question 1 is actually not relevant for global warming policies if the answer of question 2 is the CO₂ contribution is most likely to be small.

If we also look at the fact more CO₂ is beneficial for nature and mankind, any CO₂-reduction policy is highly debatable. 

By the way, for those who still are worried about the large anthropogenic CO₂-emission, if we would move to nuclear power plants, that problem is solved as well.

Let the data speak

Summarizing, please look at the CO₂-data in Figure 1: 

Figure 1: a) Full measurements, b) trend data and c) ratios.

Explanation of Figure 1

Red curve: yearly human emission (in GtCO₂/yr)) is large and increases fast (based on measurements in the past 60 years)

Blue curve: yearly atmospheric accumulation (in GtCO₂/yr) is much smaller – about a factor two – and increases less fast (also based on measurements in the past 60 years) 

Green curve: yearly natural absorption (in GtCO₂/yr) is computed by obeying the mass balance equation, i.e., human emission – atmospheric accumulation = absorption by the total natural system (land + marine). 

If we look at the trend data (b), we see the total natural system is a big absorber of CO₂. The amount of absorption is almost half the amount of human emission. We also see in the past 60 years, the ratio absorption/emission increased (green curve in c).

In the following, we will see in the CO₂-cycle the amount of CO₂ that moves between the atmosphere and the natural system is about 20 times larger (!) than the human emission.

From Figure 1 we may conclude of the total amount of CO₂ humans yearly emit in the atmosphere ~ 50% stays in the atmosphere and ~ 50% is absorbed by the natural system.

Example

In the year 2020, the emission by humans was ~ 40 Gt CO₂, ~ 20 Gt stayed behind in de atmosphere and ~ 19 Gt was absorbed by the natural system. This is exactly what you see in my data picture (see the year 2020). Also look at the other years.

To further explain the numbers in Figure 1, let me introduce the cyclic double-reservoir system by showing the CO₂-flows for the year 2020 in Figure 2.

Figure 2: The flow of CO₂ between the atmospheric reservoir and the land-marine reservoir, together with the anthropogenic and natural sources.

Notation

• S = symbol for carbon dioxide Source: S_ant for anthropogenic and S_nat for natural
• A = symbol for atmospheric carbon dioxide: A⁺ for the incoming atmospheric flow and A^– for the outgoing atmospheric flow
• N = symbol for natural (land-marine) carbon dioxide: N⁺ for the incoming land-marine flow and N^– for the outgoing land-marine flow
• C = symbol for carbon, capture and storage (CCS): C_ant for the anthropogenic sequestration and C_nat for the natural sequestration

All flows are in Gt/yr.

Closed-loop Architecture 

We will use the closed-loop architecture in Figure 2 for the description of the flow dynamics in the atmospheric CO₂-system. This architecture – also used for analyzing up- and down-going waves in seismic imaging theory (Berkhout, 2018) – allows us to recognize two internal flows to (F⁺) and from (F^–) the atmosphere:

• The bio-driven circulation flow generated by the continents (‘biological pump’). On the one hand this CO₂-flow is due to absorption by plants (inhalation) and on the other hand it is due to emission by plants (exhalation) and decomposition of dead plants. The greener the Earth, the more CO₂ is stored in the Earth’s bio system.
• The physics-driven circulation flow generated by oceans (‘physical pump’). Henry’s law tells us the physics-driven flow is influenced by the CO₂-concentration in the atmosphere and in the oceans. The higher the concentration in the atmosphere, the more CO₂ flows into the oceans and vice versa (combination of Raoult’s and Henry’s law). In addition to concentration, ocean temperature is an important parameter. The colder/warmer the water, the more/less CO₂ can be stored.

In addition, the architecture allows us to properly position two external CO₂-sources that generate an incoming flow into the closed loop:

• The human-driven flow, caused by the anthropogenic source (S_ant). Think of the mass burning of fossil fuels.
• The nature-driven flow, caused by the natural source (S_nat). Think of the volcanic eruptions worldwide.

We show the orders of magnitude of these CO₂-flows and CO₂-sources in Figure 2 for the year 2020. The amount of CO₂ is expressed in ‘GtCO₂’ (gigaton CO₂) per year, 1 gigaton being one billion (10⁹) metric tonnes. In the literature these quantities are often expressed in ‘GtC’ (gigaton carbon). the GtC values are 12/44 = 0.27 smaller. Today, PgC (Petagram carbon) is often used.

Looking at Figure 2, the total yearly incoming CO₂ flow from continents and oceans, volcanos and human activities into the atmosphere is ~ 807 Gt/yr (A⁺). And the total outgoing CO₂ flow by the continents and oceans is ~ 787 Gt/yr (A^–). This means that there is an increase of CO₂ in the atmosphere of ~ 20 Gt/yr (‘atmospheric accumulation’). 

Of the total annual absorption by nature (N⁺ = 786 Gt/yr), 767 Gt is again emitted by nature (continents and oceans) into the atmosphere (N^–). This means there is an annual increase of CO₂ in the land-ocean system of +19 Gt/yr (‘land-marine absorption). 

In Figure 2 we see where the yearly 40 Gt injection is leading to (A⁺–A^–) = 807–787 = +20 Gt/yr accumulation in the atmosphere and (N⁺–N^–) = 786–767 = +19 Gt/yr absorption in the landocean system.

We see that anthropogenic emission S_ant is very small (about 5%) compared to the incoming and outgoing flows A⁺ and A^–.

This means that S_ant is a perturbation on the internal incoming atmospheric flow A⁺. On the other hand, S_ant is twice the accumulation (A⁺– A^–)!

It is important to realize that many incoming (F⁺) and outgoing (F^–) internal flows satisfy the emission, atmospheric accumulation and land-ocean absorption measurements.

It explains why so many theories about what happens with the CO₂ in the land-marine system fits the measurements and the mass balance equation.

CO₂ mass balance

In the proposed closed-loop CO₂-system all values should adhere to the CO₂ mass balance equation at any time (whatever the source and system changes are):

(1a)  where A⁺ is the total incoming atmospheric flow per year:

 (1b) with F⁺(t) = N^–(t) + S_nat(t).

Similarly, A^– is the total outgoing atmospheric flow per year:

(1c) with F^–(t) = N⁺(t) + C_nat(t).

Equation (1a) may also be rewritten as:

(all quantities in Gt/y)

Equations (2a) and (2b) show how the yearly atmospheric accumulation (A⁺–A^–) is affected by the yearly net anthropogenic emission [S_ant – C_ant], the yearly land-marine absorption (N⁺–N^–) and the yearly net natural emission (S_nat – C_nat).

Note from (2b) small changes in F⁺ or F^– – due to internal changes in the land-marine reservoir – may lead to large changes in the atmospheric accumulation.

For the past 60 years (1960 – 2020), the net anthropogenic emission is much larger than the net volcanic contribution, i.e. [S_ant – C_ant]>>[S_nat– C_nat].

In addition, C_antS_ant, meaning that we may simplify equation (2a) for this period to:

                                                   (2c)

Bear in mind that in expression (2c) S_ant is the superposition of many anthropogenic sources, N^– is the result of many internal natural sources and N⁺ is the result of many internal natural sinks.

We assume that the values of S_ant and (A⁺–A^–) are reliable input quantities for this period.

By substituting these empirical quantities in the material balance equation (2c), the land-ocean absorption data (N⁺–N^–) is also known, being the residue [S_ant – (A⁺–A^–)]. 

In Figure 2 we showed for 2020: S_ant = 40 Gt/yr and (A⁺–A^–) = 20 Gt/yr and therefore residue (N⁺–N^-) = 19 Gt/yr.

If (S_nat – C_nat) cannot be neglected, then we need to replace (N⁺–N^–) by (F^––F⁺).

Similarly, if C_ant would give a significant contribution, then we need to replace S_ant by [S_ant – C_ant]. 

It is interesting, if we make S_ant = 0 and C_ant = 0, equations (1a,b,c) and (2a,b) describe the pre-industrial era.

Note, if we want to know the amount of total CO₂ in the atmosphere and in the natural system (in GtCO₂), we must know two initial values (A₀ and N₀), and need to integrate the yearly contributions (A⁺–A^–) and (N⁺–N^-). Note that N₀>>A₀.

Conclusions

1. Of the anthropogenic CO₂-flow (S_ant) into the atmosphere (in 2020 ~40 Gt/yr), about 50% stays in the atmosphere. The other 50% is taken up by the natural system (continents + oceans).
2. The anthropogenic CO₂-flow (S_ant) is only ~5% of the total CO₂-flow (A⁺). Small changes in the outgoing flow of the natural system (N^–) has a large influence on the atmospheric accumulation (A⁺ – A^–). For instance, if N^– is increasing by only a few percent, then the change in (A⁺ – A^–) is in the same order as the human contribution. The same applies to changes in A^–.
3. If the total yearly flows A⁺ and A^– are not measured but modelled, then the modeled accumulation (A⁺ – A^–) must be compared with the measured accumulation (A⁺ – A^–).
4. If the total yearly flows N⁺ and N^– are not measured but modelled, then the modeled absorption (N⁺ – N^– ) must obey the mass balance equation.

It is scientifically a commendable and also desirable step to split the natural system in continents and oceans.

However, we should realise if we split the natural system into subsystems the estimation problem becomes significantly more complex, because of the dynamic interrelationships between the subsystems. Altogether, a major task.

Anyway whatever we do, the condition must be the combined behavior of all (local) subsystems must obey the behavior of the total system at all times.

This means: 'yearly human emission – yearly atmospheric accumulation = yearly absorption of the total natural system'.

Measurements do tell us that today, the total natural system behaves as a big CO₂ absorber that increases its relative capacity.

Of course, all numbers can be enriched by uncertainty information.

Finally, the above conclusions are based on measurements and the mass balance equation. If critics do not accept the conclusions, they must make clear why they don’t trust the measurements, and/or why they don’t accept the mass balance equation. That would be an interesting discussion indeed.

Guus Berkhout, September 28, 2022