We investigate the representation of convective transport of atmospheric compounds by boundary layer clouds. We focus on three key parameterizations that, when combined, express this transport: the area fraction of transporting clouds, the upward velocity in the cloud cores and the chemical concentrations at cloud base. The first two parameterizations combined represent the kinematic mass flux by clouds. To investigate the key parameterizations under a wide range of conditions, we use large-eddy simulation model data for 10 meteorological situations, characterized by either shallow cumulus or stratocumulus clouds. The parameterizations have not been previously tested with such large data sets. In the analysis, we show that the parameterization of the area fraction of clouds currently used in mixed-layer models is affected by boundary layer dynamics. Therefore, we (i) simplify the independent variable used for this parameterization, Q1, by considering the variability in moisture rather than in the saturation deficit and update the parameters in the parameterization to account for this simplification. We (ii) next demonstrate that the independent variable has to be evaluated locally to capture cloud presence. Furthermore, we (iii) show that the area fraction of transporting clouds is not represented by the parameterization for the total cloud area fraction, as is currently assumed in literature. To capture cloud transport, a novel active cloud area fraction parameterization is proposed. Subsequently, the scaling of the upward velocity in cloud cores by the Deardorff convective velocity scale and the parameterization for the concentration of atmospheric reactants at cloud base from literature are verified and improved by analysing six shallow cumulus cases. For the latter, we additionally discuss how the parameterization is affected by wind conditions. This study contributes to a more accurate estimation of convective transport, which occurs at sub-grid scales.