The sub-ice platelet layer (SIPL) under fast ice is most prevalent in McMurdo Sound, Antarctica. Using a modified plume model, we investigated the responses of SIPL thickening rate and frazil concentration to variations in ice shelf water supercooling in McMurdo Sound. It would be key to parameterizing the relevant process in more complex three-dimensional, primitive equation ocean models, which relies on the knowledge of the suspended frazil size spectrum within the ice–ocean boundary layer.