In polar regions with large sea ice cover there is always an open water fraction arranged in small channels called leads. The large temperature difference between the lead surface and the near-surface air causes strong turbulent heat fluxes with convective plumes penetrating into the atmospheric boundary layer. The goals of this project, carried out as a joint work at the Alfred Wegener Institute for Polar and Marine Research (AWI) in Bremerhaven and at the Institute for Meteorology and Climatology (IMUK) at the Leibniz University Hannover, were to get a better understanding of lead effects on the ABL and to develop turbulence parameterizations for models with different grid sizes applied to the polar atmosphere over sea ice with leads. The basic tool for this investigation was the large eddy simulation (LES) model PALM run by IMUK on a massively parallel computer which allowed a very high resolution. It was used to resolve turbulent eddies over leads with grid spacings between 0.25 m and 10 m. Parameterizations of the turbulent processes over leads were developed and tested in the mesoscale model METRAS which was run with different resolutions but in most studies with a grid spacing of 100 m, allowing to resolve the internal ABL over leads. The development of a turbulence parameterization for this microscale led to a deepened insight into the governing processes over leads. It can be seen as an intermediate step towards the development of a parameterization of the lead impact in climate models. LES runs helped first to identify the necessary resolution for the modelling of turbulence over leads. It was found that much smaller grid spacings are necessary than those used in the literature before the current project. A large number of case studies with extremely high resolution was only possible by implementing a new initialization procedure in PALM allowing inflow with already developed turbulence. This procedure has proven to be a powerful method for the future modelling of similar cases. Our investigations showed that convective roll-like structures near the surface, described in earlier publications, occur as a numerical artefact when the turbulence is not fully resolved. Another important part of the LES studies addressed the dependence of heat fluxes on lead width, wind speed and domain size. The result of this study was that a non-monotonic dependence of heat fluxes on lead width λ with a maximum flux at λ = 1 km is also only a numerical artefact, circumvented by a very high resolution. The new results shows that fluxes decrease monotonically with increasing lead size. This finding agrees better with observations. A new closure for the microscale was developed. It consists of a combination of a nonlocal and local closure, allowing countergradient transport in the core of the convective region over leads and local transport in the outer region governed by the local vertical gradients of temperature and wind. The new closure accounts for the dependence of turbulence downstream of leads on the conditions over the leads which were ignored in all closures being available before this project. Other project studies aimed to analyze the lead impact as obtained by climate models. First, a coupled sea ice atmosphere 1D version of METRAS was used accounting for leads as climate models are doing. Results showed that the lead impact can be larger than known from previous studies. For winterly clear-sky conditions the near-surface temperature is modified by up to 3.5 K per 1 % change in sea ice concentration. Finally, the microscale model was applied with the new closure in 2D to large domains with several leads. It was found that for a given domain averaged sea ice concentration the domain averaged fluxes depend on the lead width and even on the distance between leads. Another result was that climate models underestimate the turbulent fluxes of heat and overestimate the fluxes of momentum, when they are used with the traditional turbulence closures over sea ice with leads. Results obtained by our studies with LES and the microscale model give a line to improve parameterizations in climate models. They could be constructed by accounting for the fetch dependence of fluxes and by a modification of characteristic surface layer values.