Abstract
A coupled climate model with idealized representations of atmosphere, ocean, sea ice, and land is used to investigate transitions between global climate equilibria. The model supports the presence of climates with limited ice cover (Warm), a continuum of climates in which sea ice extends down into the midlatitudes and the tropics (Cold), together with a completely ice-covered earth (Snowball). Transitions between these states are triggered through volcanic eruptions, where the radiative effect of stratospheric sulfur emissions is idealized as an impulse reduction in incoming solar radiation. Snowball transitions starting from the Cold state are more favorable than from the Warm state, because less energy must be extracted from the system. However, even when starting from a Cold climate, Toba-like volcanic events (cooling of order −100 W m−2) must be sustained continuously for several decades to glaciate the entire planet. When the deep ocean is involved, the volcanic response is characterized by relaxation time scales spanning hundreds to thousands of years. If the interval between successive eruptions is significantly shorter (years to decades) than the ocean’s characteristic time scales, the cumulative cooling can build over time and initiate a state transition. The model exhibits a single hysteresis loop that connects all three climate equilibria. When starting from a Snowball, the model cannot access the Cold branch without first transitioning to an ice-free climate and completing the hysteresis loop. By contrast, a Cold state, when warmed, transitions to the Warm equilibrium without any hysteresis.
Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-18-0883.1.s1.
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