The Arctic is currently warming faster than other regions of the Earth. Many processes and feedbacks contribute to the enhanced warming. Among these are the radiative effects of clouds. Arctic mixed-phase clouds, which contain both liquid and ice condensate, have high longevity and can exert significant surface warming since the amount of solar radiation in the region is relatively low and the surface reflectivity often is high. In this thesis, we study these clouds utilizing a large-eddy model coupled with one-dimensional thermodynamic sea ice model. The main aim is to understand the interactions between cloud dynamics, microphysics, radiation, and turbulent processes and how these together govern the life cycle and surface warming of the clouds. By comparing a group of models with observations from the summertime high Arctic, we confirm the hypothesis that when aerosol concentrations are low, a small increase in their number concentration can increase the liquid water content of the cloud and in turn, the surface warming. Idealized simulations of moist intrusions into the Arctic show that the surface temperature may increase by more than 15^o C if we allow clouds to form during a moist intrusion compared to if the atmosphere is cloud free. The simulations also show that the large-scale divergence rate strongly impacts the maintenance of the liquid layer at the top of these clouds. A main finding of the thesis is that the temperature of the cloud that forms during a moist intrusion is close to the initial dew point temperature. Thus, the surface warming induced by the clouds depends mostly on the initial humidity of the air mass rather than the initial temperature. In addition, the stability of the initial dew point temperature profile largely controls the turbulent state of the cloud. If the profile is unstable, then the cloud can transform from a thin, stable stratus to a deeper stratocumulus cloud, which also enhances the surface warming. Consequently, both the initial amount and the vertical structure of the initial moisture of the intrusion are important for the warming of the sea ice. A change in the number of cloud condensation nuclei does not affect the cloud evolution considerably provided that there is a continuous supply of these nuclei. However, if cloud condensation nuclei sources are absent then the cloud may remain in its stable state. Furthermore, a decrease in the cloud ice condensate, which may be caused by a lack of ice nucleation particles, may delay the transformation of the cloud into a stratocumulus. These results suggest that any future change in aerosol loading and atmospheric moisture transport into the Arctic may alter the surface longwave cloud radiative effect and cause changes in the sea ice evolution.