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The Lovelock-Watson model of ``Daisyworld''

The original LWM is a zero-dimensional caricature of a planet which is illuminated by the sun and which is able to support merely two different types of vegetation cover.

The surface of the ``naked'' planet, i.e., the planet without vegetation, is characterized by an overall albedo tex2html_wrap_inline477. The equilibrium temperature tex2html_wrap_inline479 depends on the insolation S and the black-body radiation according to
 equation21
where tex2html_wrap_inline483 is the Stephan-Boltzmann constant. As mentioned above, the toy biosphere consists of two components only:

The temperature-dependent growth rate tex2html_wrap_inline497 of species i is a unimodular function with a maximum at tex2html_wrap_inline501:
 equation27
The dynamics of our model biosphere is governed by a system of two coupled nonlinear differential equations:
 eqnarray36
Here tex2html_wrap_inline503 denotes a constant mortality rate and x, the uncovered area, is trivially given by
equation41

This feedback system has been analyzed by several authors [7, 8, 9, 10] in great detail. One remarkable result is that, in contrast to the uncovered planet, the ``bioplanet'' is able to keep the global temperature relatively constant when the external ``control parameter'' S is varied within a rather wide range. This property of self-regulation is referred to as ``homeostasis''. As a matter of fact, homeostasis is achieved here by a rather simple mechanism: white (black) daisies are fitter in hot (cold) climates as their comparatively high (low) albedo tends to reduce (increase) the local temperature.


next up previous
Next: Introducing spatial dependencecompetition, Up: Modelling the geosphere-biosphere feedback Previous: Modelling the geosphere-biosphere feedback

Werner von Bloh (Data & Computation)
Thu Jul 13 14:36:30 MEST 2000