A simple parameterization, called the Cumulus Potential (CuP) scheme, has been developed to predict size distributions of boundary-layer clouds. The premise of the scheme is that cumuli are made of buoyant parcels that rise, largely undiluted, from near the surface. Each cloud has its own unique buoyancy and lifting condensation level. If the water vapor in a rising parcel condenses, then a cloud forms; however if the water vapor does not condense, then the parcel remains a clear-air updraft.
In the CuP scheme, the properties of a parcel are determined from a discrete joint frequency distribution (JFD) of virtual-potential temperature and lifting condensation level (LCL). The scheme determines which bins of the JFD contain rising parcels and which bins contain sinking parcels, by comparing the virtual-potential temperature of each bin to the mean mixed-layer virtual-potential temperature. If a virtual-potential temperature of a bin is less than that of the environment, then all parcels in that bin would not rise out of the surface layer. If a virtual-potential temperature is greater than that of the environment, then all parcels in that bin rise to their level of neutral buoyancy.
The scheme determines cloud properties by comparing the LCL of each bin of rising air with the level of neutral buoyancy calculated for that bin. If the level of neutral buoyancy is less than the LCL then the parcels remain clear. If the level of neutral buoyancy is greater than the LCL then the parcels become cloudy and will continue to rise, moist adiabatically, to a new, higher altitude. Total cloud cover is simply the fraction of parcels that become saturated, cloud bases are the LCL of the cloudy bins, and cloud tops are the level at which these cloudy parcels stop rising.
The CuP model results are compared to data collected during Boundary Layer Experiment 1996 (BLX96). Twelve research flights were conducted during BLX96 during which we measured JFDs of buoyancy and humidity at five different levels in the convective mixed layer.