A simple model for multiple equilibria in ice-covered oceans

The existence of multiple equilibria (ice-covered and ice-free states) is explored using a set of coupled, nondimensional equations that describe the heat and salt balances in basins, such as the Arctic Ocean, that are subject to atmospheric forcing and two distinct water mass sources. Six nondimensional numbers describe the influences of: atmospheric cooling; evaporation minus precipitation; solar radiation; atmospheric temperature, diapycnal mixing, and the temperature contrast between the two water masses. It is shown that multiple equilibria resulting from the dependence of albedo on ice cover exists over a wide range of parameter space, especially so in the weak mixing limit. Multiple equilibria can also occur if diapycnal mixing increases to O(10−4 m2 s−1) or larger under ice-free conditions due to enhanced upward mixing of warm, salty water from below. Sensitivities to various forcing parameter are discussed.