Biology · Introductory biology · Worked example

Balance the global carbon budget

In 2022 fossil fuels and cement released $9.9 Gt C$ and land clearing $1.2 Gt C$ . The ocean took up $2.8 Gt C$ and land $3.8 Gt C$ . How much should the atmosphere have gained? Compare that with the measured gain of $4.6 Gt C$ , and express the gain in $ppm$ of ${CO}_{2}$ .

Add the sources

Both sources release carbon into the atmosphere, so they add.

9.9 + 1.2 = 11.1

Subtract the sinks

The ocean and land each remove carbon from the air. What is left is the predicted gain of the atmosphere, by inflows minus outflows.

11.1 - 2.8 - 3.8 = 4.5

Find the imbalance

The measured gain was $4.6 Gt C$ . Sources minus everything that took up carbon leaves the budget imbalance. It is $- 0.1 Gt C$ , so the estimated sources were slightly too low or the sinks slightly too high.

11.1 - (4.6 + 2.8 + 3.8) = - 0.1

\begin{array}{l} 11.1 - (4.6 + 2.8 + 3.8) \\ = - 0.1 \end{array}

Convert to $ppm$

Each $ppm$ of ${CO}_{2}$ in the air is $2.124 Gt C$ , so the gain was about $2.17 ppm$ . The measured rise was $2.18 ppm$ , and the small gap comes from rounding $4.6$ .

\frac{4.6}{2.124} \approx 2.17

Read the result

Of every $10$ tonnes of carbon released, about $4$ stayed in the air and about $6$ went into the ocean and land. Those sinks slow the rise of ${CO}_{2}$ but do not stop it.

Result

The atmosphere should have gained $11.1 - 2.8 - 3.8 = 4.5 Gt C$ . It gained $4.6 Gt C$ , about $2.2 ppm$ , so the budget balances within $0.1 Gt C$ .

Your turn

1. One like the example

In a model year, emissions are $10.0 Gt C$ , the ocean takes $2.5$ and land $3.0$ . How much does the atmosphere gain, in $Gt C$ and in $ppm$ ?

Show the answer and explanation

$4.5 Gt C$ , about $2.12 ppm$ .

$10.0 - 2.5 - 3.0 = 4.5 Gt C$ , and $4.5 / 2.124 \approx 2.12 ppm$ .

\begin{array}{l} 10 - 2.5 - 3 = 4.5 \\ \frac{4.5}{2.124} \approx 2.12 \end{array}

2. A variation

What fraction of the $11.1 Gt C$ released in 2022 stayed in the atmosphere?

Show the answer and explanation

About $0.414$ , or $41 %$ .

$4.6 / 11.1 \approx 0.414$ . This share is called the airborne fraction. The rest, about $59 %$ , went into the ocean and land.

\frac{4.6}{11.1} \approx 0.414

3. Somewhere new

Climate pledges often count tonnes of ${CO}_{2}$ , not tonnes of carbon. Using $C = 12.01 g / mol$ and ${CO}_{2} = 44.01 g / mol$ , convert the $11.1 Gt C$ released in 2022 into $Gt$ of ${CO}_{2}$ .

Show the answer and explanation

About $40.7 Gt$ of ${CO}_{2}$ .

Each tonne of carbon becomes $44.01 / 12.01 \approx 3.664$ tonnes of ${CO}_{2}$ , because each carbon atom carries two oxygen atoms. Then $11.1 \times 3.664 \approx 40.67$ , which the Global Carbon Budget reports as $40.7$ .

\begin{array}{l} \frac{44.01}{12.01} \approx 3.664 \\ 11.1 (3.664) \approx 40.67 \end{array}

Keep exploring

The carbon cycle opens in Biogeochemical cycles, in Biology, with its $9$ fluxes. Combustion matches the fossil source, ocean carbon uptake the ocean sink and photosynthesis the land sink.

Return to the concept →

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After reading

Study it, then try it

Practice the key terms as flashcards, then open the example in its tool, change a value and keep a useful result on your board.

Study the 11 key terms Open the carbon cycle Balance the budget in Math Open worked example on a board Biogeochemical processes in Biology Reference

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Add the sources

Subtract the sinks

Find the imbalance

Convert to ppmppm

Read the result

Result

Your turn

1. One like the example

4.5 Gt C4.5 Gt C, about 2.12 ppm2.12 ppm.

2. A variation

About 0.4140.414, or 41⁢%41%.

3. Somewhere new

About 40.7 Gt40.7 Gt of CO2CO2​.

Keep exploring

Study it, then try it

Convert to $ppm$

$4.5 Gt C$ , about $2.12 ppm$ .

About $0.414$ , or $41 %$ .

About $40.7 Gt$ of ${CO}_{2}$ .