We perform global simulations of the Los Alamos sea‐ice model, CICE, with a new thermodynamics component that has a fully prognostic, variable bulk salinity vertical profile based on mushy layer physics. The processes of gravity drainage, melt‐water flushing and snow‐ice formation are parameterized to allow the bulk salinity to evolve with time. We analyze the seasonal and spatial variation of sea‐ice bulk salinity, area, volume and thickness and compare these quantities to simulations using the previous thermodynamic component. Adjusting one of the gravity drainage parameters, we find good agreement between simulation results and fieldwork ice‐core observations of sea‐ice bulk salinity. As expected, bulk salinity is highest during periods of ice growth and lowest after periods of ice melt. In the northern hemisphere the new thermodynamics component produces thicker ice than the previous thermodynamics component. Of the nine major differences between the two models, differences in how salinities are calculated and how melt‐pond flushing is parameterized are the principal causes of this thickness difference. Thickness differences are smaller in the southern hemisphere than in the northern hemisphere since a greater fraction of ice melts, and differences cannot accumulate year‐on‐year. Model differences in how ice thickness changes and snow‐ice formation are calculated are the most important causes of the different thickness between the two thermodynamic components in the southern hemisphere. The melt‐pond area and volume are found to be highly sensitive to a parameter choice controlling drainage through macroscopic holes in the ice, in both hemispheres. Key Points: Sea‐ice salinity is simulated in the CICE global sea‐ice model Gravity drainage, melt pond flushing and snow‐ice formation determine salinity Reasonable agreement found between simulation results and sea‐ice core data