Suppose atmospheric $\mathrm{CO}_{2}$ is growing at 2 ppm/yr, fossil fuel and cement emissions are 9 GtC/yr, and the airborne fraction is 38 percent. If the only other carbon emissions are associated with land use changes, estimate their net carbon emission rate.

In this exercise, we have the next value:

$\mathrm{Cement\ concentration}=9 \mathrm{Gtc}/ \mathrm{year}$

$\mathrm{Land\ usage}=2.2 \mathrm{ppm}$

$\mathrm{Airborn\ fraction}=38 \%$

Now, find $\mathrm{C\ emissions}$:

$$\begin{align*} \mathrm{X}&=\frac{2 \mathrm{ppm/year } \cdot 2.12 \mathrm{GtC} / \mathrm{ppm}}{0.38}\\ &=11.15\ \mathrm{GtC}/ \mathrm{year}\\ \end{align*}$$

So, we can calculate emissions:

$$\begin{align*} \mathrm{X}&=11.5\ \mathrm{GtC}/ \mathrm{year}-9\ \mathrm{GtC}/ \mathrm{year}\\ &=2.15\ \mathrm{GtC}/ \mathrm{year}\\ \end{align*}$$