This thesis deals with Large Eddy Simulations (LES) of the Atmospheric Boundary Layer (ABL), focusing on studying the resolution dependence of turbulent passive scalar transport within the layer. The ABL is the lowest part of the atmosphere, where humans live and conduct most of their daily activities. Here, a scalar was injected at four different heights in a mixed shear- and convective-driven ABL, which was simulated using the Spectral Element Method (SEM) code Nek5000. The statistics of the four scalars were analysed and their resolution dependence was studied and compared to that of non-scalar quantities. No significant resolution dependence was found with regards to non-scalar quantities, while scalar quantities show a rather strong dependence on resolution especially in the first quarter of the simulation. Negative concentration values are found within the layer and some approaches to solve the problem are proposed. Statistics alone provide an accurate description of the general ABL behaviour, but are found to be insufficient to capture the dynamics of the scalar injection, which ought to be analysed with more advanced methods (e.g. modal decomposition). The structures arising within the layer are also analysed, and further work regarding the study of scalar fronts is suggested.