Slushball Earth equilibria in a one-dimensional energy balance model

Understanding the widespread glaciations of the late Neoproterozoic era (715–635 Ma) is important for understanding the evolution of life on Earth. A Waterbelt state has been proposed as a more biologically friendly alternative to the Snowball Earth hypothesis. It was subsequently shown that an open tropical ocean can be sustained by a so-called “Jormungand mechanism”, where darker, bare sea ice at the descending edge of the Hadley cell halts the runaway ice-albedo feedback synonymous with Snowball Earth. However, the geological evidence for thick, active glaciers at sea level in the deep tropics during these glaciations presents a problem for the Waterbelt hypothesis that has received limited attention in the literature. We study a diffusive, one-dimensional energy balance model (EBM) with a Jormungand mechanism, where also the effects at the ascending edge of the Hadley cell are included. The EBM is solved using an analytical approach, the boundary integral method. The modified Jormungand mechanism produces several unstable Slushball Earth states in the EBM, in addition to the Waterbelt states. These Slushball Earth states are similar to Snowball Earth, but with a series of water belts over lower latitudes. Implications for the Neoproterozoic glaciations are discussed.