On the nature of the sea ice albedo feedback in simple models

We examine the nature of the ice-albedo feedback in a long-standing approach used in the dynamic-thermodynamic modeling of sea ice. The central issue examined is how the evolution of the ice area is treated when modeling a partial ice cover using a two-category-thickness scheme; thin sea ice and open water in one category and "thick" sea ice in the second. The problem with the scheme is that the area evolution is handled in a manner that violates the basic rules of calculus, which leads to a neglected area evolution term that is equivalent to neglecting a leading-order latent heat flux. We demonstrate the consequences by constructing energy balance models with a fractional ice cover and studying them under the influence of increased radiative forcing. It is shown that the neglected flux is particularly important in a decaying ice cover approaching the transitions to seasonal or ice-free conditions. Clearly, a mishandling of the evolution of the ice area has leading-order effects on the ice-albedo feedback. Accordingly, it may be of considerable importance to reexamine the relevant climate model schemes and to begin the process of converting them to fully resolve the sea ice thickness distribution in a manner such as remapping, which does not in principle suffer from the pathology we describe.