Calculating global emissions of carbon

Our recent energy consumption is about 518 EJ (10¹⁸ J). Let’s calculate the emissions of CO₂ caused by this energy consumption, given the values for CO₂/MJ given above and the current proportions of energy sources — 33% oil, 27% coal, 21% gas, and 19% other non-fossil fuel sources. The way to do this is to first figure out how many grams of CO₂ are emitted per MJ given this mix of fuel sources, and then scale up from 1 MJ to 518 EJ. Let’s look at an example of how to do the math here — let r_1-4 in the equation below be the rates of CO₂ emission per MJ given above, and let f_1-4be the fractions of different fuels given above. So r₁ could be the rate for oil (65.7) and f₁ would be the fraction of oil (.33). You can get the composite rate from:

$r_{c} = r_{1} f_{1} + r_{2} f_{2} + r_{3} f_{3} + r_{4} f_{4}$

Plugging in the numbers, we get:

$65.7 \times .33 + 62.2 \times .27 + 103.7 \times .21 + 6.2 \times .19 = 61.4 [\frac{{gCo}_{2}}{MJ}]$

What is the total amount of CO₂ emitted? We want the answer to be in Gigatons — that’s a billion tons, and in the metric system, one ton is 1000 kg (1e6 g or 10⁶ g), which means that 1Gt = 10¹⁵ g (1e15 g).

$1 [EJ] = 1 e 12 [MJ], so, 518 [EJ] = 518 e 12 [MJ]$

$518 e 12 [MJ] \times 61.4 [\frac{{gCO}_{2}}{MJ}] = 31.7 e 15 [{gCO}_{2}] = 31.8$

So, the result is 31.8 Gt of CO₂, which is very close to recent estimates for global emissions.

It is more common to see the emissions expressed as Gt of just C, not CO₂, and we can easily convert the above by multiplying it by the atomic weight of carbon divided by the molecular weight of CO₂, as follows:

$31.8 [{GtCO}_{2}] \times \frac{12 [gC]}{44 [{gCO}_{2}]} = 8.7 [GtC]$

And remember that this is the annual rate of emission.

Let’s quickly review what went into this calculation. We started with the annual global energy consumption at the present, which we can think of as being the product of the global population times the per capita energy consumption. Then we calculated the amount of CO₂ emitted per MJ of energy, based on different fractions of coal, oil, gas, and non-fossil energy sources — this is the emissions rate. Multiplying the emissions rate times the total energy consumed then gives us the global emissions of either CO₂ or just C.

We now see what is required to create an emissions scenario:

A projection of global population
A projection of the per capita energy demand
A projection of the fractions of our energy provided by different sources
Emissions rates for the various energy sources

In this list, the first three are variables — the 4^th is just a matter of chemistry. So, the first three constitute the three principal controls on carbon emissions.

Here is a diagram of a simple model that will allow us to set up emissions scenarios for the future:

Stella model as discussed earlier in the course. Important information in caption

Figure 8. Stella model of the emissions' calculation part of the model. This looks more complex than it really is due to the addition of 10 converters that enable the user to change the fraction of energy coming from different sources. The key result from this model is Total Emissions, in Gt C per year, which then controls the flow of carbon into the atmosphere of the global carbon cycle part of the model (see Figure 9).

Click for a text description of Figure 8.

The image is a complex systems diagram titled "System Dynamics Model of Energy Consumption and Emissions," which illustrates the relationships and feedback loops between various factors related to energy consumption, population, and emissions. Here's a detailed breakdown:

Components:

Population: Represented by a rectangular box labeled "Population," which has arrows indicating influence from and to other components.
Pop Limit: A cloud-shaped symbol labeled "Pop Limit" with an arrow pointing to the "Population" box, indicating a limit or constraint on population growth.
net change: An arrow labeled "net change" connects from "Population" to a circular node, indicating the net change in population affecting other variables.
r: A circular node labeled "r" connected to "Population," representing the growth rate of the population.
per capita energy: Connected to "Population" with an arrow, indicating per capita energy consumption.
global energy consumption: A circular node connected to "per capita energy," representing the total global energy consumption.
Total Emissions: A rectangular box connected to "global energy consumption," representing the total emissions resulting from energy consumption.
RC: A central circular node labeled "RC," which seems to be a key regulatory or control factor influencing various energy sources.

Energy Sources and Emissions:

f_gas: Connected to "RC," representing emissions from gas.
f_oil: Connected to "RC," representing emissions from oil.
f_coal: Connected to "RC," representing emissions from coal.
er_gas: Connected to "f_gas," representing the energy ratio or efficiency for gas.
er_oil: Connected to "f_oil," representing the energy ratio or efficiency for oil.
er_coal: Connected to "f_coal," representing the energy ratio or efficiency for coal.
er_renew: Connected to "RC," representing the energy ratio or efficiency for renewable energy.
f_renew: Connected to "er_renew," representing emissions from renewable energy sources.

Switches and Reductions:

Gas Switch: A diamond-shaped decision node connected to "f_gas," "f_change 3," and "gas red time," indicating a decision point for switching to or from gas.
Oil Switch: Similar to Gas Switch, connected to "f_oil," "f_change 2," and "oil red time," for oil.
Coal Switch: Connected to "f_coal," "f_change 1," and "coal red time," for coal.
gas red time: Connected to "Gas Switch," indicating the time frame for gas reduction.
f_gas reduction: An arrow from "Gas Switch" indicating the reduction in gas emissions.
oil red time: Connected to "Oil Switch," indicating the time frame for oil reduction.
f_oil reduction: An arrow from "Oil Switch" indicating the reduction in oil emissions.
coal red time: Connected to "Coal Switch," indicating the time frame for coal reduction.
f_coal reduction: An arrow from "Coal Switch" indicating the reduction in coal emissions.

Feeddack Loops:

f_change 1, f_change 2, f_change 3: These nodes are connected to the respective switches (Coal, Oil, Gas) and "star," indicating changes or feedback loops affecting the energy mix over time.
star: A central node labeled "star" with a value of 0.1, connected to "f_change 1," "f_change 2," and "f_change 3," possibly representing a rate of change or a multiplier effect in the system.

Connections:

Arrows with labels like "er_gas," "er_oil," "er_coal," "er_renew" indicate the flow of influence from energy efficiency ratios to emissions.
The diagram shows a network of interconnections where changes in one part of the system can influence others, particularly through the "RC" node, which seems to be a regulatory center affecting all energy sources and their emissions.

This diagram visualizes how population growth, energy consumption per capita, and the choice of energy sources (gas, oil, coal, renewable) interact to influence total emissions, with various feedback loops and decision points affecting the dynamics over time.

Credit: David Bice @ Penn State is licensed under CC-BY-NC-4.0

In this model, the per capita energy (a graph that you can change) is multiplied by the Population to give the global energy consumption, which is then multiplied by RC (the composite emissions rate) to give Total Emissions. Just as we saw in the sample calculation above, RC is a function of the fractions and emissions rates for the various sources. Note that the non-fossil fuel energy sources (nuclear, solar, wind, hydro, geothermal, etc.) are all lumped into a category called renew, because they are mostly renewable. The model includes a set of additional converters (circles) that allow you to change the proportional contributions from the different energy sources during the model run.

This emissions model is actually part of a much larger model that includes a global carbon cycle model and a climate model. Here is how it works — the Total Emissions transfers carbon from a reservoir called Fossil Fuels that represents all the Gigatons of carbon stored in oil, gas, and coal (they add up to 5000 Gt) into the atmosphere. Some of the carbon stays in the atmosphere, but the majority of it goes into plants, soil, and the oceans, cycling around between the reservoirs indicated below. The amount of carbon that stays in the atmosphere then determines the greenhouse forcing that affects the global temperature — you’ve already seen the climate model part of this. The carbon cycle part of the model is complicated, but it is a good one in the sense that if we plug in the known historical record of carbon emissions, it gives us the known historical CO₂ concentrations of the atmosphere. Here is a highly schematic version of the model:

$Global carbon cycle image shows how the model calculates the total carbon emissions as a function of the fractions of our energy that come from fossil fuels and renewables.$

Figure 9. Highly simplified sketch of the global carbon cycle part of the model. The global carbon cycle is essentially a set of interconnected reservoirs. Humans are affecting this cycle (red arrows), preventing it from finding a steady state. The fossil fuel burning flow (on right side above) is controlled by the part of the model that calculates the emissions.

Click for a text description of Figure 9.

The image is a flowchart diagram illustrating the global carbon cycle, showing the movement and storage of carbon in various parts of the Earth's system. Units are provided in gigatons of carbon (GT), where one gigaton equals one billion metric tons or 101510^{15}1015 grams. The diagram uses different colors to represent various carbon reservoirs and arrows to indicate the flow of carbon between these reservoirs. Red arrows indicate flows that are sensitive to human activities, while green arrows represent flows that are sensitive to temperature.

Carbon Reservoirs:

Atmosphere: Contains 750 GT of carbon. It is connected to other parts of the cycle via various processes.
Land Biota: Contains 610 GT of carbon, involved in processes like photosynthesis and respiration.
Soil: Contains 1580 GT of carbon, connected to land biota through litter fall.
Surface Oceans: Contains 970 GT of carbon, involved in ocean-atmosphere diffusion and upwelling & downwelling.
Deep Oceans: Contains 38,000 GT of carbon, connected to surface oceans through upwelling & downwelling.
Ocean Biota: Contains 3 GT of carbon, connected to surface oceans.
Sedimentary Rocks: Contains 1,000,000 GT of carbon, connected to the deep oceans through sedimentation.
Fossil Fuels: Contains 5000 GT of carbon, influencing the atmosphere through fossil fuel burning.
Mantle: Connected to sedimentary rocks through subduction.

Carbon Flows (in GT/year):

Atmosphere to Land Biota:
- Photosynthesis: 110 GT/year (green arrow, temperature sensitive)
- Burning: 50 GT/year (red arrow, human activity sensitive)
Land Biota to Atmosphere:
- Respiration: 59.4 GT/year (green arrow, temperature sensitive)
- Burning/Farming: 50 GT/year (red arrow, human activity sensitive)
Land Biota to Soil: Litter fall: 60 GT/year
Soil to Atmosphere: Respiration: 60 GT/year (green arrow, temperature sensitive)
Atmosphere to Surface Oceans: Ocean-atmosphere diffusion: 90 GT/year (green arrow, temperature sensitive)
Surface Oceans to Atmosphere: Ocean-atmosphere diffusion: 90 GT/year (green arrow, temperature sensitive)
Surface Oceans to Deep Oceans: Upwelling & downwelling: 105.6 GT/year
Deep Oceans to Surface Oceans: Upwelling & downwelling: 96.2 GT/year
Surface Oceans to Ocean Biota: 105 GT/year
Ocean Biota to Surface Oceans: 105 GT/year
Deep Oceans to Sedimentary Rocks: Sedimentation: 0.6 GT/year
Sedimentary Rocks to Mantle: Subduction: 0.6 GT/year
Fossil Fuels to Atmosphere: Fossil Fuel Burning: 9 GT/year (red arrow, human activity sensitive)
Volcanic Eruptions: 0.6 GT/year from the mantle to the atmosphere (green arrow, temperature sensitive)

Notes:

Numbers next to the arrows represent approximate annual flows in gigatons per year (GT/year).
The diagram highlights the interaction between natural processes and human-induced changes in the carbon cycle, emphasizing the impact of activities like burning fossil fuels and land use changes (farming, burning).

Credit: David Bice @ Penn State is licensed under CC-BY-NC-4.0