| Summary: | Vita. Phenomena associated with the small ice cap instability (SICI) are investigated using a general circulation model (GCM: NCAR Community Climate Model version 0) and a noise forced energy balance model (EBM). With idealized boundary conditions consisting of an all land planet without topography and mean annual insolation we generate four different climate regimes by altering the solar constant in the GCM: ice-free, partially ice-covered without ice-albedo feedback and with ice-albedo feedback and finally a totally ice-covered planet. The first and second moments of the resulting computed temperature fields for each case are presented. The ice-albedo feedback lengthens the characteristics scales both in spatial and temporal domains. Parameterization of the EBM is carried out by utilizing the output of GCM runs. It is found that the parameters of the EBM depend upon the solar constant. An analytical solution for the second moment statistics of temperature fields of linear EBM forced by noise which is homogeneous in space and white in time is presented and the results of numerical simulations including the nonlinear case are also presented. We find that the diffusivity of the EBM plays a similar role as the circulation strength of GCM; it modulates the equator-to-pole temperature difference and the magnitude of second moment variabilities. Non-white noises, spatially blue and temporally red, are introduced to lead to a better fit of the resulting characteristics of temperature fields generated by EBM to those by GCM. Multiple equilibrium states are found in the GCM in which, with two different initial conditions under identical boundary conditions, two different stable equilibria of partially ice-covered and totally ice-covered states are found. However for the regions where SICI might occur we do not find any multiple equilibria. The simulations with EBM have shown that SICI phenomena in the presence of fluctuations are strongly dependent on the amplitude of the noise forcing. When the strength of noise ...
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