Snowball Earth: Ice thickness on the tropical ocean

[1] On the tropical oceans of a neo-Proterozoic Snowball Earth, snow-free ice would have existed in regions of net sublimation. Photosynthesis could have continued beneath this bare ice if it was sufficiently thin and sufficiently clear. The steady state ice thickness is determined by the necessity to balance the upward conduction of heat with three subsurface heating rates: the heat flux from the ocean to the ice base, the latent heat of freezing to the ice base, and the solar energy absorbed within the ice. A preliminary study, using a broadband model for solar radiation and assuming a large freezing rate, had indicated that tropical ice might be only a few meters thick. Here we show that the vertical throughput of ice by surface sublimation and basal freezing would be too slow to keep the ice thin and that the broadband model had exaggerated the absorption depth of sunlight. We use a spectral model for solar absorption, computing radiative transfer at 60 wavelengths, considering absorption by the ice, and scattering by bubbles. With the spectral model, the computed ice thickness is much greater. For a solar flux of 320 W m(-2) at the equatorial surface and expected albedo of 0.5 for bare sea ice, we find that surface temperatures below 12 degreesC generate ice layers too thick for photosynthesis (> 100 m). If the albedo were as low as 0.4, thick ice would occur only for surface temperatures below 25 degreesC, but such low temperatures would be difficult to maintain with such low albedo. For surface temperatures warmer than these limits, the ice becomes thin (< 1 m) and is unlikely to represent a coherent ice layer. However, glacial deformation of thick floating ice from nearby oceanic regions may preclude the existence of thin or ice-free patches.