On Homeostasis in Daisyworld

Abstract

The steady state solution of the Daisyworld modelof Watson and Lovelock (1983) is examined in detail. Focus is on the two-daisy state, which exhibits homeostasis overa large range of solar luminosities. The analytical approach usedmakes clear the dependence of the steady state and the size of thedomain 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 basedon a priori specifying a relation between the equilibrium effectivetemperature T^eq _e and the equilibrium effective albedoA^eq _e. 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 heatin an efficient manner. It is shown that the attractivity of the steady stateis due to the temperature-dependence of the expansion rate of thedaisies, 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 modelgive 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 associatedheat transport mechanism itself do not seem to have parallels in the real Earth system.