| In this dissertation are developed three specific models intended to study two separate problems in the hydrological cycle. The first model modifies the Daisyworld model of Watson and Lovelock [128] to include a more realistic heat transport, effectively adding a degree of freedom. Results from this model include the establishment of a curve of approximately equivalent steepness in the two daisy state, despite removal of an assumption that led to proscribed local homeostasis, and the appearance of a new oscillatory phenomenon. The second model builds on the first, adding a hydrological cycle with oceans and ice caps to test the influence of biota on a more earth-like climate. Biota is found to have a nontrivial influence on the evolution of model temperature, while the hydrological cycle is shown to have a perhaps unrealistically strong one. The third model is developed from physical principles to reproduce the scaling statistics found in tropical oceanic convective rainfall. Data from this model is shown to obey the Taylor hypothesis for periods of at least 20 minutes, and to obey scaling under two separate analyses, albeit with different scaling exponents. |
