Climate simulations in a global coupled model are investigated using a dynamic-thermodynamic sea ice and snow model with sophisticated thermodynamics and a subgrid scale parameterization for multiple ice thicknesses. In addition to the sea ice component, the model includes a full primitive-equation ocean and a simple energy-moisture balance atmosphere. We introduce a formulation of the ice thickness distribution that is Lagrangian in thickness-space. The method is designed to use fewer thickness categories because it adjusts to place resolution where it is needed most and it is free of diffusive effects that tend to smooth Eulerian distributions. Experiments demonstrate that the model does reasonably well in simulating the mean Arctic climate. We find the climate of the Arctic and northern North Atlantic is sensitive to resolving the ice-thickness distribution when comparing the model results to a simulation with a two-level sea ice model. The ice-thickness distribution causes ice export through Fram Strait to be more variable and more strongly linked to meridional overturning in the North Atlantic Ocean. The Lagrangian formulation of the ice-thickness distribution allows for the inclusion of a vertical temperature profile with relative ease compared to an Eulerian method. We find ice growth rates and ocean surface salinity differ in our model with a well-resolved vertical temperature profile in the ice and snow and an explicit brine-pocket parameterization compared to a simulation with Semtner zero-layer thermodynamics. Although these differences are important for the climate of the Arctic, the effects of an ice thickness distribution are more dramatic and extend into the northern North Atlantic. Sensitivity experiments indicate that five ice-thickness categories with ~50-cm vertical temperature resolution capture the effects of the ice-thickness distribution on the heat and freshwater exchange across the surface in the presence of sea ice in these simulations. ¿ 2001 American Geophysical Union