Comment on ``Snowball Earth: A thin-ice solution with flowing sea glaciers'' by David Pollard and James F. Kasting

[1] Pollard and Kasting [2005] (hereinafter referred to as PK) have coupled an energy-balance climate model to an ice-shelf flow model, to investigate the Snowball Earth episodes of the Neoproterozoic, 600–800 million years ago, when the ocean apparently froze all the way to the equator [Hoffman and Schrag, 2002]. PK’s particular concern was to investigate the possibility that over a wide equatorial band where sublimation exceeded snowfall, the bare ice may have been thin enough to permit transmission of sunlight to the water below, providing an extensive refugium for the photosynthetic eukaryotes that survived the Snowball events. This possibility was first proposed by McKay [2000], whose model of radiative transfer and heat conduction predicted tropical ice only a few meters thick for ice albedo up to 0.7, under assumed conditions of sunlight and temperature at the Snowball equator. However, when spectral resolution was incorporated into the radiative transfer model [Warren et al., 2002], the ice albedo had to be reduced below 0.4 to obtain the thin-ice solution under otherwise identical conditions. It seemed unlikely that such dark sea ice could avoid melting under the equatorial Sun. But even if it could avoid melting, the thin ice would risk being crushed by the inflow of kilometer-thick ‘‘sea glaciers’’ from higher latitudes [Goodman and Pierrehumbert, 2003]. To further investigate the feasibility of tropical thin ice, it was therefore necessary to couple a climate model to models of sea-ice thermodynamics and sea-glacier flow. This is what PK have done. Surprisingly, they conclude that thin ice (<3 m thick) ‘‘may have prevailed’’ in a 20-degree latitude band centered on the equator. We argue here that this conclusion is too optimistic, because PK’s thin-ice solution apparently required that several controlling variables be set outside their measured ranges: the albedo of cold glacier ice, the depth of transition from snow to ice, and the thermal conductivity of ice. We then raise the more general question of how wide is the thin-ice domain in the parameter-space of model variables. 2. Choices of Model Variables That Favor Thin Ice 2.1. Albedo of Cold Glacier Ice [2] As sea glaciers flowed equatorward into the tropical region of net sublimation, their surface snow and subsurface firn would sublimate away, exposing bare glacier ice to the atmosphere and solar radiation. This ice would be freshwater (meteoric) ice, which originated from compression of snow, so it would contain numerous bubbles, giving a high albedo. The albedo of cold (nonmelting) glacier ice exposed by sublimation (Antarctic ‘‘blue ice’’) has been measured as 0.55–0.65 in four experiments in the Atlantic sector of Antarctica [Bintanja and van den Broeke, 1995; Bintanja et al., 1997; Liston et al., 1999; Reijmer et al., 2001], 0.63 in the Transantarctic Mountains [Warren et al., 2002], and 0.66 near the coast of East Antarctica [Weller, 1968]. (Weller’s blue-ice albedo is often quoted as 0.69 [e.g., Weller, 1980; King and Turner, 1997], but that is an average value, which included a few times with patchy snow cover on the ice.) Not all glacier ice is bubbly: under several hundred meters of ice thickness, the pressure becomes so great that each air bubble dissolves in the ice to form a clathrate crystal, and the ice becomes relatively clear [Price, 1995]. However, when this ice becomes depressurized as its cover sublimates away (as in the Antarctic blue-ice areas where the albedos were measured), the bubbles reform [Lipenkov, 2000], so that the albedo of 0.55–0.66 is observed at the surface. [3] In contrast to glacier ice, which forms by compression of snow, sea ice forms by freezing of liquid water. In their model, PK tried two values of scattering coefficient, each of which they applied uniformly to both sea ice and glacier ice. With albedo 0.47 (a reasonable value for meter-thick snowfree sea ice [Brandt et al., 2005, Figure 1]), the sea glaciers terminated at 9 degrees latitude, leaving an equatorial strip of thin ice. But with albedo 0.64 (i.e., within the measured range for glacier ice), the sea glaciers advanced to the equator, with a thickness of 1 km. To add realism to the model, it would be good to assign different values of scattering coefficient to these two very different types of ice.