A model of the seasonal variation of the mixed layer and the pycnocline under polar sea ice is compared with observations during the Arctic Ice Dynamics Joint Experiment (AIDJEX) 1975-1976. The model is of the Kraus-Turner type, extended to include mixed layer and pycnocline. The forcing mechanisms are the mechanical mixing due to ice keel stirring and the surface buoyancy flux due to melting and freezing of sea ice. The model is designed to be used for climate studies in conjunction with atmospheric and oceanic general circulation models and with sea ice models.