A non‐eddy‐resolving microscale model is applied to simulate convection over three different leads (elongated channels in sea ice), which were observed by aircraft over the Arctic Marginal Ice Zone in 2013. The study aims to evaluate the quality of a local and a non‐local turbulence parametrization. The latter represents a lead‐width‐dependent approach for the turbulent fluxes designed for idealised conditions of a lead‐perpendicular, near‐neutral inflow in an atmospheric boundary layer (ABL) capped by a strong inversion at around 250 to 350 m height. The observed cases considered here are also characterised by an almost lead‐perpendicular flow but, in comparison to the idealised conditions, our analysis covers effects in stable inflow conditions and a much shallower ABL. The model simulations are initialised with observed surface parameters and upwind profiles, and the results are compared with measurements obtained above and downwind of the leads. The basic observed features related to the lead‐generated convection can be reproduced with both closures, but the observed plume inclination and vertical entrainment near the inversion layer by the penetrating plume are underestimated. The advantage of the non‐local closure becomes obvious by the more realistic representation of regions with observed vertical entrainment or where the observations hint at counter‐gradient transport. It is shown by comparison with the observations that results obtained with the non‐local closure can be further improved by including the determination of a fetch‐dependent inversion height and by specifying a parameter determining the plume inclination as a function of the upwind ABL stratification. Both effects improve the representation of fluxes, boundary‐layer warming, and vertical entrainment. The model is also able to reproduce the observed vanishing of a weak low‐level jet over the lead, but its downwind regeneration and related momentum transport are not always well captured, irrespective of the closure used.