Empirical determination of the basic modes of cumulus heating and drying profiles

The constraint on the coupled vertical profiles of cumulus heating and dryi ng, which can be used as a partial closure in cumulus parameterization, is examined using observational data from convectively active regions in the s ummertime. The data used in this study include those derived from Global At mospheric Research Programme (GARP) Atlantic Tropical Experiment Phase III, Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experim ent over The intensive flux array region, and four subsets of the European Centre for Medium-Range Weather Forecasts Re-Analysis data that cover areas ranging from tropical to midlatitude continents. The profiles of Q(1) and Q(2) calculated from those data are analyzed using a statistical method. Th e proposed method is a revised version of the rotated principal component a nalysis based on the Promax rotation (RPCA(Promax)), which is believed suit able for identifying basic structures embedded within a given dataset. It i s designed in such a way that the distortion of identified structures due t o the use of a linear model is minimized. The revised RPCA(Promax). togethe r with some selected statistical tools, are evaluated using synthetic datas ets before they are applied to observations. The analysis of the observational data shows that, for all the convectively active regions examined, most of the variance of observed Q(1) and Q(2) ca n be explained by retaining only two modes. Moreover, while these two modes have different amplitudes in time and space, the shapes of the Q(1) and Q( 2) profiles associated with each mode are similar from one region to anothe r. In this sense, they are analogous to the cloud types in the spectral cum ulus ensemble model of the Arakawa-Schubert cumulus parameterization, in wh ich the spectral distribution of cloud-base mass flux varies with large-sca le conditions while the vertical profile of normalized mass flux is fixed f or each cloud type. It is suggested that, as far as deep convection is conc erned, the cloud model in cumulus parameterization probably can be construc ted based on the empirically determined Q(1) and Q(2) profiles.