Thickness of tropical ice and photosynthesis on a snowball Earth

On a completely ice-covered "snowball" Earth the thickness of ice in the tropical regions would be limited by the sunlight penetrating into the ice cover and by the latent heat flux generated by freezing at the ice bottom--the freezing rate would balance the sublimation rate from the top of the ice cover. Heat transfer models of the perennially ice-covered Antarctic dry valley lakes applied to the snowball Earth indicate that the tropical ice cover would have a thickness of 10 m or less with a corresponding transmissivity of > 0.1%. This light level is adequate for photosynthesis and could explain the survival of the eukaryotic algae.