The time-space exchangeability of satellite retrieved relations between cloud top temperature and particle effective radius

A 3-minute 3-km rapid scan of the METEOSAT Second Generation geostationary satellite over southern Africa was applied to tracking the evolution of cloud top temperature ( T) and particle effective radius (r(e)) of convective elements. The evolution of T - r(e) relations showed little dependence on time, leaving re to depend almost exclusively on T. Furthermore, cloud elements that fully grew to large cumulonimbus stature had the same T - r(e) relations as other clouds in the same area with limited development that decayed without ever becoming a cumulonimbus. Therefore, a snap shot of T - r(e) relations over a cloud field provides the same relations as composed from tracking the time evolution of T and re of individual clouds, and then compositing them. This is the essence of exchangeability of time and space scales, i.e., ergodicity, of the T - r(e) relations for convective clouds. This property has allowed inference of the microphysical evolution of convective clouds with a snap shot from a polar orbiter. The fundamental causes for the ergodicity are suggested to be the observed stability of re for a given height above cloud base in a convective cloud, and the constant renewal of growing cloud tops with cloud bubbles that replace the cloud tops with fresh cloud matter from below.