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We review most of the modelling studies performed to date to understand the initiation and melting of a Snowball Earth, as well as to describe the glacial environment during the glaciation itself. All the described scenarios explaining the onset of glaciation rely on a sufficient decrease in the concentrations of atmospheric greenhouse gases (GHGs), typically resulting from the equatorial palaeogeography of the late Proterozoic. It is still heavily debated whether or not the oceanic ice cover was thick during the glaciation itself. However, a consensus has arisen that the most climatically stable scenarios imply the existence of a globally frozen ocean, with a thick ice cover caused by the flowing of high-latitude sea-ice glaciers towards the equator. Depending on the characteristics of the ice, a thin ice layer may have persisted along the equator, but this numerical solution is rather fragile. During the snowball event itself, model results suggest the existence of wet-based continental glaciers. Some parts of the continents may have remained ice-free. From the modelling perspective, the most significant problem in the snowball hypothesis, particularly in its ‘hard snowball’ version (the most stable numerically), is the melting phase. With improved modelling, the CO2 threshold required to melt the snowball is much higher than initially thought, significantly above 0.29 bar. Indeed, because of the very cold conditions prevailing at the surface of the Earth during the glacial event, the atmosphere becomes vertically isothermal, strongly limiting the efficiency of the greenhouse effect. This melting problem is further highlighted by geochemical modelling studies that show that weathering of the oceanic crust might be an active sink of CO2 during the glacial event, limiting the rise in atmospheric CO2. The solution might be found by considering the input of dark dust from catastrophic volcanic eruptions that would efficiently decrease the albedo of the ice. Finally, modelling studies also explore the aftermath of the glaciation. The world might have been drier than initially anticipated, resulting in the persistence of the supergreenhouse effect for at least one million years after the melting phase.

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