Making Sense of Bifurcation Diagrams: A New Framework to Understand the Roles of Clouds and Bare Sea Ice for Waterbelt States

Earth has experienced several pan-glaciations in its history, often interpreted as hard Snowball Earth periods with global ice cover. Alternatively, waterbelt states with a narrow equatorial strip of ice-free ocean provide a compelling explanation for the survival of life during these extreme glaciations. In this study, we establish a framework to quantify three atmospheric factors that influence waterbelt states: the spatial extent of bare dark sea ice set by the pattern of surface precipitation and evaporation, cloud masking of the ice-albedo feedback, and cloud shortwave feedback. We first explore these factors in the Budyko-Sellers energy balance model, and then investigate them in simulations with three versions of the ICON global climate model. This allows us to relate differences in the waterbelt states between ICON versions to the three factors. A broader Hadley circulation shifts the boundary between snow-covered and bare sea ice poleward, leading to waterbelt states whose ice lines are at higher latitudes. Cloud masking always works in favor of stable waterbelt states by weakening the ice-albedo feedback. The role of the cloud shortwave feedback, in contrast, depends on the ICON version: in one version, increasing cloud condensate over the low-latitude open ocean destabilizes waterbelt states and creates an additional small hysteresis. In the other two versions, the cloud shortwave feedback is stabilizing. While our study does not answer which of the model versions is most realistic, it provides a quantitative framework for understanding the atmospheric mechanisms that govern the existence and hysteresis of waterbelt states.