Climate change is especially pronounced over the Arctic Ocean, where the atmosphere warmed twice as fast as in lower latitudes in the last few decades. This warming is associated with a rapid decline of the Arctic sea ice cover. For future predictions of changes in the Arctic climate system, profound knowledge of all processes influencing the surface energy budget in polar regions is essential. The focus of this thesis lies on improving our current understanding of convective processes and the related turbulent fluxes in the polar atmospheric boundary layer (ABL) over both the sea ice covered regions and over the open ocean at the sea ice edge. A major part of the analysis is based on aircraft measurements from the campaign STABLE, which was carried out over the pack ice in the northern Fram Strait in March 2013. These results are supplemented by modeling studies using a simple boxmodel and a one-dimensional mesoscale model. For the first time, comprehensive aircraft measurements over leads were conducted during the campaign STABLE. They are used to study the formation of convective plumes over leads and their impact on the polar ABL. It is found that the conditions over four wide leads are highly variable with respect to turbulent fluxes, as well as to the mean variables temperature, humidity, and wind. In one of the cases large entrainment fluxes exceeding 30 % of the surface fluxes are observed. The convective plumes over leads have a large influence on the vertical profiles of sensible heat and momentum fluxes, which are non-linear downstream of the leads with a distinct flux maximum in the core of the convective plumes. For the first time, it it shown based on measurements that the plume also affects the wind field by diminishing low level jets in the region influenced by the plume. In addition to the small scale impact of individual leads the regional impact of lead ensembles is studied using long transect flights. The analysis shows that near-surface atmospheric temperatures are clearly related to the ice concentration in the considered region. The impact of a heterogeneous sea ice cover and of the related surface temperature changes on atmospheric temperatures is also analysed using a Lagrangian box model. The model uses reanalysis winds as well as sea ice concentration and surface temperature from satellites as input data. The box model is used to calculate the evolution of the near-surface air temperature along backward-trajectories, which are then compared to measured temperatures at three different Arctic sites. The results suggest that a large amount of the observed air temperature variability can be attributed to heterogeneous surface temperatures and that the characteristic length of the upstream region influencing air temperatures at a specific location is 200 km. Convection during cold air outbreaks at the sea ice edge has a much stronger impact on the polar ABL than convective plumes over leads. Dropsonde measurement of four cold air outbreaks during STABLE are used to analyse the downstream development of meteorological variables and the ABL growth. Two of the considered cases are influenced by the size of the Whaler's Bay polynya north of Svalbard, which was unusually large in the three winters from 2012 to 2014 compared to the previous 20 years. The analysis of the dropsonde measurements shows that the unusual ice conditions lead to strong atmospheric convection in a region north of Svalbard that was typically ice-covered in the last decades. This leads to extreme convective ABL heights and modifies local temperature conditions considerably. Convective processes in the ABL have to be parametrised in climate models. Therefore, in addition to the measurements, the performance of three different sensible heat flux parametrisations is tested in a 1D mesoscale model and results are compared to those of a large eddy simulation model (LES). Both the considered counter-gradient and eddy-diffusivity mass-flux (EDMF) approach reproduce the shape of the temperature profile of the LES better than a classical mixing length approach. A sensitivity analysis shows that the EMDF approach is the least sensitive to changes of the vertical grid spacing, which can be attributed to the derivation of the ABL height using a diagnostic equation of the updraft velocity. The sensitivity of the counter-gradient closure to the grid spacing can be significantly reduced when the updraft velocity equation of the EDMF approach is included and used to derive the ABL height.