CASE STUDY: Terrestrial Carbon Cycle

Source:

"Modelling the Human Impact on Nature", Richard John Huggett, Oxford University Press, 1993.

WARNING: THIS IS A LARGE PROJECT, REQUIRING TEAMWORK!

Background:

The purpose of this model is to evaluate the flow of carbon through one of two different types of ecosystems -- a tropical rainforest and a temperate forest. The driving variable is the amount of carbon (in the form of carbon dioxide) that is available in the atmosphere. For each of the two different ecosystems, we are assuming that the amount of carbon available for distribution is fixed, and is not influenced by any other factors.

In the model, a terrestrial ecosystem is represented as seven interacting components -- plants (divided into leaves, branches, stems, and roots), litter lying on the ground, humus, and stable humus charcoal. The amount of carbon stored in each of these components is a state variable, and is initialized at 0 at the beginning of the simulation.

The seven state variables are linked by a continuous circulation of carbon. Carbon enters the system as the gas carbon dioxide through the plant leaves, and is incorporated into the plants (leaves, branches, stems, and roots) as primary production. Some of the primary production is burnt up in respiration; the remainder constitutes the net primary production of the ecosystem. The model is driven by the net primary production, which may be partitioned among the four components of the plants: leaves, branches, roots, and stems. (A partitioning factor for each of these components for each of the six ecosystems is found as a table at the end of this reading.) You should notice that the four partition coefficients add up to a value of 1.0. For each of the four plant components, carbon uptake is calculated by multiplying the amount of carbon available by its partitioning coefficient. Since the partition coefficient adds up to 1.0, all of the available carbon (for example 27.8 Gt. C/year) should be taken up by the plants.

Carbon moves through the system. Once carbon is taken up by one of the four plant components, it is transformed and transmitted to the other components of the model -- litter on the ground, which in turn is transformed to humus, which is in turn transformed to stable humus charcoal. Note one exception to this; roots are transformed directly into humus, and do not contribute to the litter on the ground. We can categorize each of the processes according to the following table:

Component	Transforms to:	Process name
Leaves	litter	leaf fall
Branches	litter	timber fall
Stems	litter	timber fall
Roots	humus	sloughage (humification)
Litter	humus
Humus	stable humus charcoal carbonization

For each transmission or transformation, a "flux" number reflects the fraction of carbon that is passed from one state variable to another. Each of the fluxes for these processes is mathematically defined by multiplying the current value of the state variable by a fractional "transfer coefficient", also found on the data table. For example, the process of transformation from leaves to litter is defined as follows:

Leaf fall = leaves * leaves to litter coefficient

Note from the table that the leaves to litter coefficient for most of the ecosystems is 1.0, which implies that all of the carbon found in leaves is fluxed to the state variable of litter.

For the processes of humification and carbonization, values labeled "transfer factors" are shown on the data table. These values are used in a similar manner to the transfer coefficients. They are separated on the data table due to differences in units.

Modeling Task:

As you might suspect, this is a relatively large and complicated model. We want to simulate the carbon flow over a fairly long period of time, such as 500 years. You might wish to experiment with length of dt and integration method.

In order to make your model look uncluttered, you will need to design your model carefully.

Extra challenge: how might you develop this model so that the user can change ONE variable to run the simulation for each of the two different ecosystem types? As a hint, you do not necessarily have to use an "if...then" construct to implement this improvement.

Dataset for Terrestrial Carbon Cycle

	Units	Tropical Forest Ecosystem 1	Temperate Forest Ecosystem 2
Carbon Dioxide Production	Gt C/yr	27.8	8.7
Partition Coefficients	fraction
Leaves		0.3	0.3
Branches		0.2	0.2
Stems		0.3	0.3
Roots		0.2	0.2
Transfer Coefficients (rate constants)	per year
Leaves to Litter		1	0.5
Branches to Litter		0.1	0.1
Stems to Litter		0.033	0.0166
Roots to Humus		0.1	0.1
Litter to Humus		1	0.5
Humus to Charcoal		0.1	0.02
Charcoal to Environment		0.002	0.002
Transfer Factors	fraction
Hummification Factors		0.4	0.6
Carbonization factor for		0.05	0.05
Humus Decomposition		0.005	0.005
Other Values	fraction
Humus Respiration		0.995	0.995
Litter Respiration		0.6	0.6
Stable Humus Respiration		0.002	0.002

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