Abstract
Empirical orthogonal function (EOF) analysis of radiance vectors associated with emission and scattering indices for the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) has been performed to examine the regional variability in relations between brightness temperature and rain rate over portions of the tropical oceans known to exhibit regional differences due to different thermodynamic environments and different large-scale forcing. The TMI indices and rain rates used in this study are the products of the Goddard profiling algorithm (GPROF), version 6. The EOF framework reduces the nine-dimensional space of the brightness temperatures and their polarizations to just two dimensions associated with the EOF coefficients. Vertical profiles of reflectivity from the TRMM precipitation radar (PR) are used to show that the statistically obtained EOFs represent bulk physical characteristics of raining clouds. Hence, EOF analysis provides an efficient framework for diagnosing regional differences in cloud structures that affect brightness temperature–rain-rate relations. The EOF framework revealed fundamental differences in the behavior of TMI surface rain-rate retrievals versus retrievals that are based on the PR aboard the TRMM satellite. In EOF space, TMI rain rates were bimodally distributed, with one mode indicating higher rain rates with greater high-density ice and rainwater content in the cloud and the other mode being consistent with moderately heavy warm rain from shallow convection. In contrast, the PR rain-rate distribution showed high rain rates being assigned over a much greater diversity of cloud structures. The manifold of EOF space constructively shows that, of the regions examined here, the tropical northwestern Pacific Ocean region produces the greatest occurrence of particularly strong cumulonimbus clouds.
