A new turbulence parametrization is developed for a non-eddy-resolving microscale model to study the effects of leads (elongated open-water channels in sea ice) of different width on the polar atmospheric boundary layer (ABL). Lead-dominated sea ice regions are characterized by large horizontal inhomogeneities of the surface temperature causing strong convection. Therefore, the new parametrization is based on a previous formulation where inhomogeneous conditions of dry convection over leads and nonlocal effects on heat fluxes had already been taken into account for a fixed lead width. A nonlocal lead width dependent approach is applied now for both heat fluxes and momentum fluxes in the convective region. Microscale model results obtained with the new, the previous nonlocal, and a local parametrization are shown, where 10 idealized cases of a lead-perpendicular, near-neutral ABL-flow below a strong capping inversion are considered. Furthermore, time-averaged large eddy simulation (LES) results of those cases are considered for analyzing the integrated effects of the dry convection on ABL characteristics. Microscale model results obtained with the new nonlocal parametrization agree well with the LES for variable lead widths and different atmospheric forcing although there is a room for further improvement. Furthermore, several features obtained with a local closure clearly disagree with LES. Thus, the microscale study also points to difficulties that might occur in mesoscale studies over regions where leads dominate the flow regime when local closures are applied.