How did the snowball earths end?
Under extreme CO2 radiative forcing (greenhouse effect), built up over millions of years because CO2 consumption by silicate weathering is slowed by the cold, while volcanic and metamorphic CO2 emissions continue unabated.

In the 1960's, the climate physicists who discovered the "white earth" instability knew of no way the climate could recover, short of waiting for billions of years of Solar evolution. They did not know about plate tectonics, a concept that revolutionized the earth sciences in the late 1960's. Plate tectonics accounts for the volcanism that delivers CO2 to the atmosphere and oceans. It also accounts for the flow (subduction) of CaCO3 and organic matter into the Earth's mantle, where it is heated and transformed back into the CO2 which exits volcanoes. This is known as the geochemical carbon cycle and a key step in the cycle is the conversion of CO2 (as carbonic acid rain) into Ca2+ and HCO3- (bicarbonate) ions through the breakdown ("weathering") of common silicate rocks like basalt. Silicate rock weathering consumes CO2 through chemical reactions that are temperature and moisture dependent. If global temperatures warm, weathering rate goes up as does the consumption of CO2. Conversely, if global climate gets colder, weathering rate goes down as does the consumption of CO2. The temperature dependence acts as a brake, or self-stabilizing mechanism, on the climate system. But like a truck with bad brakes, it cannot prevent the Earth crashing into a snowball earth because the braking (silicate weathering feedback) takes on the order of a million years to take effect. In contrast, the radiative consequences of ice sheet growth are felt in a matter of months. Fortunately for us, the slow-acting feedback won out in the end.

In the event of a snowball earth, plate tectonics would continue uninterrupted. Plate tectonics is driven by the sinking of 100-km-thick slabs of cold rock under the influence of gravity and does not care if a measely 1.0 km of ice is floating on the ocean. Consequently volcanism will continue unabated and more than 100 million years worth of CaCO3 and organic matter in sea-floor sediments would be available for CO2 generation at depth. On the other hand, if the continents are largely ice-covered and no water left the atmosphere in the form of rain, silicate weathering would be severely limited to areas of wet-base ice with neutral pH. The rate of CO2 consumption would plummet while the emissions would remain the same. CO2 would enter the ocean via sub-sea volcanoes and vents, and the atmosphere from terrestrial subglacial volcanoes like those under the present Vatnajökull in Iceland. On a geological time scale, CO2 in the ocean and atmosphere would maintain equilibrium through air-sea gas exchange in sea-ice cracks and leads (if present). Slowly, the atmospheric CO2 must build up due to an imbalance between outgassing and consumption. The only process that could prevent this is permanent deposition of CO2 ice (dry ice) in polar caps. This might limit the attainable CO2 concentration below that needed to overcome the surface albedo. The condensation temperature of dry ice rises with CO2 concentration (partial air pressure), so there is a trade-off as CO2 and consequently temperature rise. Calculations indicate that dry ice would indeed condense in the polar regions in winter, but that it would sublimate completely in summer so no lasting "sink" for CO2 would exist in polar caps.

The steady build up of CO2 will increase the radiative forcing due to the greenhouse effect, more rapidly at first because of the non-linear dependence on the CO2 concentration (i.e., approximately equal response to each CO2 doubling). Eventually, the CO2 radiative forcing begins to rival the radiative loss by the reflective surface (planetary albedo) and temperatures at the equator touch the melting point. Surface melt water darkens the ice causing more Solar radiation to be absorbed and soon areas of open water are exposed, which absorb radiation with 90% efficiency (versus 60% for bare ice and 10% for fresh snow). Now the ice-radiative (ice-albedo) feedback works in reverse and combined with other feedbacks (e.g., ice-elevation feedback: melting lowers the surface elevation of a grounded ice-sheet, increasing the melting rate due to the warmer surface air temperature) it drives a cataclysmic meltdown of the snowball earth. Climate modeling suggests that the meltdown could occur in as little as 2000 years, which would increase the global runoff by a factor of 10 assuming 2 km average ice cover on the continents and 0.4 km on the ocean. This would result in a transient stratification of the ocean, in which low-density oxic meltwater subject to surface warming caps high-density cold brine evolved for millions of years beneath an ice cover. It would also cause a rapid sea-level rise and many shelves and platforms that stood in shallow water before the glaciation would be deeply flooded due to tectonic subsidence during the long glacial period. Carbonate and silicate rock weathering would accelerate as the ice retreats, exposing a landscape of rock debris and "flour" from the grinding action of the ice. Chemical reactions would be hastened by surface warming, acidic rain and the large surface area of fresh rock available. But even with accelerated weathering rates it would take tens of thousands of years to lower the atmospheric CO2 to a steady state with the now ice-free surface. Accordingly, the immediate aftermath of a snowball earth is an ultra-greenhouse transient. In his 1992 paper introducing the snowball earth concept, Joe Kirschvink predicted that evidence would be found in the sedimentary record of sudden switching from glacial to hothouse conditions, and that these changes would be seen globally. The 1998 paper by the Harvard University group linked this climate switch to post-glacial "cap carbonates", observed globally after the Sturtian and Marinoan glaciations.