A toy model linking atmospheric thermal radiation and sea ice growth

A highly simplified analytical model of sea ice growth is presented in which the atmosphere is in thermal radiative equilibrium with the ice. This makes the downwelling longwave radiation reaching the ice surface an internal variable rather than a specified forcing. The ice is characterized by only two variables, thickness and surface temperature. The seasonal cycle is resolved into four steps, in which either the thickness or the temperature can vary. An ocean mixed layer of fixed depth but variable temperature provides a heat sink if the ice melts away during the summer. Analytical results show how the ice state depends on properties of the ice and on the externally specified climate. The main result is that this bare bones physics is enough to produce an annual cycle of temperature and thickness not unlike today's conditions. The results also suggest how much the climate must change to produce qualitatively different cycles. Reducing the atmospheric poleward heat transport by 20 W m −2 is enough to make the ice so thick (>12 m) that it never warms up to the melting point in summer. Increasing the poleward flux by 30 W m −2 is enough to produce an arctic ocean which stores enough heat in summer to prevent any ice forming in winter. The model predicts that today's climate can support either a perennial ice pack or an ice free Arctic. However, a winter ice pack which melts completely each summer is not possible under any climate.