Empirical Determination of the Basic Modes of Cumulus Heating and Drying Profiles

Abstract

The constraint on the coupled vertical profiles of cumulus heating and drying, which can be used as a partial closure in cumulus parameterization, is examined using observational data from convectively active regions in the summertime. The data used in this study include those derived from Global Atmospheric Research Programme (GARP) Atlantic Tropical Experiment Phase III, Tropical Ocean Global Atmosphere Coupled Ocean?Atmosphere Response Experiment 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 Q1 and Q2 calculated from those data are analyzed using a statistical method. The proposed method is a revised version of the rotated principal component analysis based on the Promax rotation (RPCAPromax), which is believed suitable for identifying basic structures embedded within a given dataset. It is designed in such a way that the distortion of identified structures due to the use of a linear model is minimized. The revised RPCAPromax, together with some selected statistical tools, are evaluated using synthetic datasets 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 Q1 and Q2 can be explained by retaining only two modes. Moreover, while these two modes have different amplitudes in time and space, the shapes of the Q1 and Q2 profiles associated with each mode are similar from one region to another. In this sense, they are analogous to the cloud types in the spectral cumulus ensemble model of the Arakawa?Schubert cumulus parameterization, in which the spectral distribution of cloud-base mass flux varies with large-scale conditions while the vertical profile of normalized mass flux is fixed for each cloud type. It is suggested that, as far as deep convection is concerned, the cloud model in cumulus parameterization probably can be constructed based on the empirically determined Q1 and Q2 profiles.