The Canadian Arctic Archipelago (CAA) connects the Arctic Ocean and Baffin Bay through narrow channels and is one of the key gateways where freshwater leaves the Arctic. It has therefore the potential to affect the deep convection in the northern North Atlantic. Representing the CAA in traditional global models still poses a challenge due to the small scale nature of the narrow passages. In this study we apply a global, multi-resolution sea ice ocean model (the Finite Element Sea ice Ocean Model, FESOM) with refinement in the CAA up to 5 km, while keeping a coarse resolution setup otherwise. With this model setup, a hindcast simulation for the period 1968-2007 was performed. The first goal of this thesis is to assess the model behavior in the CAA region and in the Arctic Ocean. The model assessment revealed good agreement with sea ice conditions in the Arctic Ocean and with fluxes through the main gates of the Arctic Ocean. During the period 1968-2007 the mean volume transports through Lancaster Sound and Nares Strait amount to 0.86 Sv (1 Sv = 10^6 m^3/s) and 0.91 Sv, respectively. The monthly mean volume transport through western Lancaster Sound is highly correlated with the observational estimate (r=0.81). A comparison of simulated sectionally averaged velocities in Nares Strait with observational estimates reveals good agreement (r=0.57). The simulated mean CAA freshwater export rate is 123 mSv, slightly higher than the observational estimate (101+-10 mSv). The local refinement of 5 km allows to investigate the freshwater contribution of individual narrow straits to the Parry Channel. In the second part of the thesis, the mechanisms driving the interannual variability of freshwater transports through the CAA are analyzed. The interannual variability is determined by sea surface height (SSH) gradients between the Arctic Ocean and northern Baffin Bay. The variability of fluxes through Lancaster Sound and Nares Strait is mainly determined by that of the SSH on the shelf along the Beaufort Sea coast and in the northeastern Baffin Bay, respectively. Sea level variations north of the CAA are explained by changes in the wind regimes (cyclonic vs. anticyclonic) associated to release or accumulation of freshwater from the Beaufort Gyre, whereas sea level in the northeastern Baffin Bay can be attributed to ocean-atmosphere heat fluxes over the Labrador Sea. Both processes are linked with the North Atlantic Oscillation type of atmospheric variability. In the last part of the thesis, the effect of mesh resolution in the CAA area is evaluated by performing experiments with and without highly resolved archipelago (5 km vs. 24 km resolution). Increased resolution in the CAA leads to higher freshwater transports through the CAA; at the same time transports on the eastern side of Greenland are reduced. The `redirection' of Arctic freshwater affects convection in the Labrador Sea and thus the Atlantic meridional overturning circulation. We conclude that multi-resolution models like FESOM are promising tools for global climate modeling, as they are able to present small scale processes in a global setup.