Forming sea ice incorporates salt from the ocean into microscopic brine inclusions. Over time, this brine drains out in a process known as gravity drainage, resulting in a desalination of the sea ice. This drainage sets up a circulating flow of brine with the ocean, which is an important source of nutrients for biology living in the ice in the brine inclusions. In this DOE funded research, we develop a new thermodynamic module for the Los Alamos sea-ice model, CICE, which simultaneously determines both the time varying temperature and bulk salinity of the sea ice. This improves on the currently released version of CICE, which has a fixed salinity profile. Observational data from both tank experiments and fieldwork are used to guide and test the development of a simple parameterization of the gravity drainage suitable for inclusion in a global climate model. We find that gravity drainage consists of two modes: a rapid desalination near the base of the ice and a slower desalination throughout the ice. The rapid mode is parameterized as an upward vertical flow of brine through the connected brine inclusions and a return downward flow through evacuated channels. The slow mode is parameterized as a relaxation of salinity to a critical porosity. The model results fit both the experimental and fieldwork data well.