Overlap statistics of cumuliform cloud fields in large-eddy simulations

Cumuliform clouds are irregular in shape at a range of different length-scales, due to their turbulent nature. This range stretches from very small values (e.g. the edge of an individual shallow cumulus cloud) to very large values (complete deep convective clouds). Given the significant impact of clouds on the earth's radiative budget, a key question for the numerical prediction of weather and climate is how this irregularity at a range of scales affects the effective vertical overlap of cumuliform clouds. Although recent observational studies have revealed much about cloud overlap in general on scales of about 0.5km and larger, a quantification of overlap statistics on smaller scales in exclusively cumuliform cloud fields is still lacking. This study makes use of numerical large-eddy simulations at high temporal and spatial resolutions to investigate the cloud overlap statistics of boundary layer cumuliform cloud fields. Specific questions that are addressed are; i) what is the impact of the typical small-scale irregularity of cumuliform clouds on the vertical overlap, and ii) how do large-scale conditions such as vertical wind shear affect these statistics. To this purpose the effective cloud overlap in a certain layer is expressed as the ratio of the mean cloud fraction to the projected cloud cover. This “overlap ratio” is diagnosed for a range of layer thicknesses, varying from zero to full cloud layer depth. The resulting probability density function suggests that overlap is very efficient at small depth-scales, becoming less efficient above layer thicknesses of 300 m. Various axis transformations are applied to establish which functional relationship provides the best fit to the diagnosed probability density. A double exponential fit is found to be most applicable, including a small-scale component covering the first 300m with an e-folding depth of 220 m, and a second component covering greater thicknesses with an e-folding depth of 800 m (see Fig. 1, showing an example log-linear plot of the BOMEX shallow cumulus case). The sensitivity of these results to vertical discretization in LES as well as cumulus cloud regime is assessed.