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# Climate, vegetation, and global carbon cycle: the simplest zero-dimensional model

**Yuri M. Svirezhev and Werner von Bloh **

Potsdam Institute for Climate Impact Research (PIK)

Telegrafenberg, P.O. Box 601203, D-14412 Potsdam

Germany

Ecological Modelling 101, 79-96 (1997)

### Abstract:

The mechanisms of interaction between climate and biosphere are studied for some
hypothetical zero-dimensional (``point'' planet, where all parameters are globally averaged over the 2-dimensional surface of the planet, which is without ocean.
These mechanisms are formed by two causal loops:

and
.

with a strong non-linear interaction. Using the conservation law for the total amount
of carbon in the system and taking into account the assumption about quasi-stationary evolution of the
system under anthropogenic emission, we reduce the dimension of the basic system
of differential equations to 2. The reduced system is then studied by
qualitative methods. The system can have up to five equilibria, three of them
can be stable. Here there are two bifurcation parameters: total amount of carbon
(*A*) and product of maximal plant productivity and residence time of carbon in
the biota. Considering the system evolution under increase of *A*, we can observe the
change of the planet ``status'' from ``cold desert'' to ``green cold planet'' (first
bifurcation), then a "tropical planet'' arises (second bifurcation), and, as a
result of further increase of carbon in the system, the planet transforms to a
``hot desert'' In conclusion the model was calculated for ``quasi-Earth'' values
of parameters.

__Keywords:__ Minimal model, biosphere, carbon cycle.

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*Werner von Bloh (Data & Computation) *

Thu Jul 13 11:24:58 MEST 2000