On homeostasis in Daisyworld

The steady state solution of the Daisyworld model of Watson and Lovelock (1983) is examined in detail. Focus is on the two-daisy state, which exhibits homeostasis over a large range of solar luminosities. The analytical approach used makes clear the dependence of the steady state and the size of the domain over which it exists on the various parameters of the system as well as the mechanism for its attractivity. It is shown that the self-regulatory effect of the biota is based on a priori specifying a relation between the equilibrium effective temperature T-e(eq) and the equilibrium effective albedo A(e)(eq). This relation originates first, from the assumption that the local temperature contrast between the black and white daisies is given by the local albedo contrast, and second, from the requirement that the equilibrium expansion rates of the black and white daisies are equal. The regulation is found to work best when the local albedo contrast is large and when the system is capable of redistributing heat in an efficient manner. It is shown that the attractivity of the steady state is due to the temperature-dependence of the expansion rate of the daisies, i.e., the close-coupling between climate and the biota. Some aspects of the Daisymodel seem fairly realistic, such as the conditions for optimal temperature regulation. On the other hand, the basic assumptions of the model give rise to local temperatures (of the regions of black daisies, white daisies and uncovered ground) which are independent of the incoming radiation. This property of fixed local temperatures and the associated heat transport mechanism itself do not seem to have parallels in the real Earth system.