Abstract:
The Budyko climate model is an energy balance model that considers how variations in radiative forcing affect the presence and growth of ice sheets on Earth. This conceptual model has three key terms representing energy received from the sun, energy re-radiated into space in the form of outgoing long-wave radiation and energy transport between latitudinal layers. Previously, an evolving ice line equation was coupled with the Budyko model and the behaviour of the resulting system was investigated. It was shown that this coupled climate model could be reduced to a single differential equation. In later work, a second slow-varying parameter representing CO2 concentration in the atmosphere was coupled with the reduced Budyko-ice line equation and the behaviour of this model in a physical setting was explored. It was found that small stable ice caps and large amplitude oscillations between ice-free and ice-covered climate regimes were possible attracting states for the system. We extend this work further by investigating the dynamics of the coupled Budyko-ice line-CO2 model upon the addition of an equation for a slowly varying silicate weathering parameter. An increase in silicate weathering rate is believed to have been a key reason for the Earth's climate system entering a completely glaciated state. We use geometric singular perturbation theory to determine how the behaviour depends on the dynamic silicate weathering related parameter. It was found that the speed at which silicate weathering rate increases determines the systems possible behaviour. Trajectories that remained indefinitely in an ice-free state with a constant silicate weathering rate are now capable of being reinjected into an ice cap regime. We also find that small amplitude oscillating ice caps before a snowball Earth event is a possibility.