Overlap statistics of cumuliform boundary-layer clouds are studied using large-eddy simulations at high resolutions. The cloud overlap is found to be highly inefficient, due to the typical irregularity of cumuliform clouds over a wide range of scales. The detection of such inefficient overlap is enabled in this study by i) applying fine enough discretizations and ii) by limiting the analysis to exclusively cumuliform boundary-layer cloud fields. It is argued that these two factors explain the differences with some previous studies on cloud overlap. In contrast, good agreement exists with previously reported observations of cloud overlap as derived from lidar measurements of liquid water clouds at small cloud covers. Various candidate functional forms are fitted to the results, suggesting that an inverse linear function is most successful in reproducing the observed behavior. The sensitivity of cloud overlap to various aspects is assessed, reporting a minimal or non-systematic dependence on discretization and vertical wind-shear, as opposed to a strong case-dependence, the latter probably reflecting differences in the cloud size distribution. Finally, calculations with an offline radiation scheme suggest that accounting for the inefficient overlap in cumuliform cloud fields in a general circulation model can change the top-of-atmosphere short-wave cloud radiative forcing by −20 to −40 W m−2, depending on vertical discretization. This corresponds to about 50 to 100% of the typical values in areas of persistent shallow cumulus, respectively
