Simple Stochastic Modeling of Snowball Probability Throughout Earth History

Over its multibillion-year history, Earth has exhibited a wide range of climates. Its history ranges from snowball episodes where the surface was mostly or entirely covered by ice to periods much warmer than today, where the cryosphere was virtually absent. Our understanding of greenhouse gas evolution over this long history, specifically carbon dioxide, is mainly informed by deterministic models. However, the complexity of the carbon cycle and its uncertainty over time motivates the study of non-deterministic models, where key elements of the cycle are represented by inherently stochastic processes. By doing so, we can learn what models of variability are compatible with Earth's climate record instead of how exactly this variability is produced. In this study, we address why there were snowballs in the Proterozoic, but not the Phanerozoic by discussing two simple stochastic models of long-term carbon-cycle variability. The first, which is the most simple and represents CO2 concentration directly as a stochastic process, is instructive and perhaps intuitive, but is incompatible with the absence of snowballs in the Phanerozoic. The second, which separates carbon source from sink and represents CO2 outgassing as a stochastic process instead of concentration, is more flexible. When outgassing fluctuates over longer periods, as opposed to brief and rapid excursions from a mean state, this model is more compatible with the snowball record, showing only modest increases in the probability of snowball events over Earth history. The contrast between these models illustrates what kind of variability may have characterized the long-term carbon cycle.