Clear-Air Radiative cooling induced by the temperature inversion at cloud top

A mixing fraction determines the relative amount of above-cloud-top air which has been mixed into a cloudy air parcel. A method, based on the use of a mixing fraction, to calculate radiative and evaporative cooling terms at cloud top is derived and discussed. We compute cooling terms for the whole range of the mixing fraction for two cases of stratocumulus-topped marine boundary layers. In both cases the total radiative cooling term is found to be the most dominant contributor to the negative buoyancy excess found at cloud top. The largest radiative cooling rates are found for clear-air parcels immediately adjacent to cloud top rather than inside the cloud. With the help of a simple longwave radiation model, we show this to be caused by clear-air cooling due to the temperature jump at cloud top. Further we argue that the mixing fraction can be used as a vertical coordinate instead of height. The advantage of this is that the position of the air parcel relative to cloud top is known and thus can be used to calculate turbulent fluxes over cloud top from a horizontal level run.