In the polar ocean regions, the Earth’s climate system is characterised by many different interaction processes between atmosphere, ocean, and sea ice. Especially between late autumn and spring, the sea ice cover plays a very important role in this system due to its mainly insulating effect, which minimises the exchange of energy between the ocean and the atmosphere. Nonetheless, also in the cold season with large sea ice cover, a strong turbulent transport of heat and moisture is possible between the relatively warm ocean and the cold atmosphere, for example, through elongated open-water channels in sea ice, which are called leads. The convective atmospheric transport over leads is driven mainly by large spatial temperature differences causing plumes with enhanced turbulent transport, which strongly affect the characteristics of the atmospheric boundary layer (ABL) depending on both lead geometry and meteorological forcing. Understanding and quantifying these rather small-scale physical processes is crucial for improving model results also on larger scales and for obtaining accurate projections of the future climate. The focus of this thesis lies on a detailed investigation of the atmospheric processes related to the flow over leads, predominantly by means of small-scale numerical modelling. The applied model uses grid sizes so that the convective plume but not the single turbulent eddies are resolved, which requires turbulence parametrization and validation of the corresponding results. The central part of this thesis is the derivation of an improved parametrization to describe the turbulent fluxes over leads of different width. The new parametrization follows a non-local approach and it is derived based on an already existing closure, but, as a new feature, the lead width is included as a parameter. Small-scale model results obtained with the new parametrization as well as with already existing approaches are evaluated in this thesis for different idealised and observed situations. As a first step, for the idealised cases, the corresponding model results are compared with new time-averaged large eddy simulation results. It is shown that an improved representation of several ABL patterns is obtained when using the new approach for situations of a lead-perpendicular flow in a neutrally stratified ABL below a strong capping inversion. As a second step, small-scale model results are validated using airborne observations. As compared with the idealised cases, also stable inflow conditions and shallower boundary layers are considered. A basic representation of the observed patterns is obtained by the model also for these situations, but some effects remain underestimated. Therefore, further modifications of the new parametrization are introduced, which cause an improved agreement between model results and observations. Besides the new parametrization, also model results obtained with a local turbulence closure are evaluated for the idealised and observed cases. Several drawbacks are shown in the corresponding results, especially for the idealised cases, whereas some of the observed ABL characteristics can be basically reproduced also with this closure type. However, the advantage of applying a non-local approach is clearly shown by the physically most reasonable representation of atmospheric processes, especially in regions of both upward heat transport in neutral or even slightly stable conditions (counter-gradient transport) and vertical entrainment. Finally, a preliminary study is carried out to point at potential implications of small-scale lead-generated atmospheric effects on larger scales. The small-scale model is applied to simulate the flow over different spatial distributions of sea ice and leads and over a region of continuous fractional sea ice cover representing a few grid cells of a regional climate model with the same sea ice concentration in each cell. It is shown by comparison of domain-averaged profiles that the distribution of leads and their geometry has a profound impact on ABL characteristics also on a larger scale. Moreover, differences are obtained depending on the applied turbulence parametrization. Although at the moment this result cannot be validated by observations, it points clearly to the necessity of an improved treatment of leads in large-scale models.