Stochastic modeling of CO2 fluctuations and Snowball transitions on Earth and other planets

The question of what causes global glaciations to occur on Earth-like planets is of great importance to habitability and climate evolution. Earth itself has a complex climate history consisting of long stretches of apparently clement conditions in the Archean, a stable Proterozoic climate punctuated by major intervals of glaciation at the beginning and end, and fluctuation between warm and cool climates in the Phanerozoic without any further global glaciation events. Deterministic models of the carbonate-silicate cycle on Earth-like planets do not predict such a sequence of transitions, instead yielding either permanently clement conditions, or limit-cycle behavior only for planets receiving low stellar fluxes.

In this work, we take a stochastic approach to modeling atmospheric CO2 evolution. We present a simple model that assumes an imperfect CO2 thermostat, such that pCO2 follows a bounded random walk around a mean value that alone would maintain clement climate conditions. Because less CO2 is required to keep the planet warm as solar luminosity increases, the model predicts an increase in climate variability with time. This implies that unless some mechanism is present to decrease CO2 variance as stellar luminosity increases, the climates of Earth-like planets should become increasingly unstable as they approach the inner edge of their systems’ habitable zones. Implications for exoplanets are discussed, and the model is then applied to the specific problem of Earth’s climate history. In particular, the potential role of the biosphere in forcing and/or inhibiting Snowball transitions both in the Phanerozoic and earlier in Earth history is discussed.