### Calculating global emissions of carbon

Our recent energy consumption is about 518 EJ (10^{18} J). Let’s calculate the emissions of CO_{2} caused by this energy consumption, given the values for CO_{2}/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 CO_{2} 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 CO_{2} emission per MJ given above, and let f_{1-4 }be the fractions of different fuels given above. So r_{1} could be the rate for oil (65.7) and f_{1} would be the fraction of oil (.33). You can get the composite rate from:

$${\text{r}}_{\text{c}}{\text{=r}}_{\text{1}}{f}_{1}{\text{+r}}_{\text{2}}{f}_{2}{\text{+r}}_{\text{3}}{f}_{\text{3}}{\text{+r}}_{\text{4}}{f}_{\text{4}}$$

Plugging in the numbers, we get:

$$\text{65.7}\times \text{.33+62.2}\times \text{.27+103.7}\times \text{.21+6.2}\times \text{.19=61.4}\left[\frac{gC{o}_{2}}{MJ}\right]$$

What is the total amount of CO_{2} 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 10^{6} g), which means that 1Gt = 10^{15} g (1e15 g).

$$\text{1[EJ]=1e12[MJ],so,518[EJ]=518e12[MJ]}$$

$$\text{518e12[MJ]}\times \text{61.4}\left[\frac{{\text{gCO}}_{\text{2}}}{\text{MJ}}\right]{\text{=31.7e15[gCO}}_{\text{2}}\text{]=31.8}$$

So, the result is 31.8 Gt of CO_{2}, 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 CO_{2}, and we can easily convert the above by multiplying it by the atomic weight of carbon divided by the molecular weight of CO_{2}, as follows:

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

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 CO_{2} 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 CO_{2} 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:

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 CO_{2} concentrations of the atmosphere. Here is a highly schematic version of the model: