The representativeness of the a priori database is responsible for the prior probability distribution function (pdf) in our Bayesian methodology. In this study, we construct a database of rain profiles measured by TRMM Precipitation Radar (PR) to constrain the CRM database. For each raining scene identified by PR, TMI measurements provide candidate profiles based on the CRM database. Rainfall profiles given by either PR or TMI have both merits and demerits which can be compensated by combining PR and TMI. For instance, PR directly profiles rainfall but is insensitive to ice particles aloft. The opposite is true for TMI. Therefore, those profiles which are consistent both with PR and TMI measurements would constitute a more realistic database properly representing the natural variety in rain profiles.
For determining the conditional pdf in the Bayesian theory, it is crucial to adequately model the uncertainties in assumptions for unmeasurable quantities. A largest uncertainty comes from drop size distribution (DSD). Uncertainties in DSD associated with PR measurements could be modeled using ground observations by polarimetric radars etc. Once a set of DSDs is measured for a large number of rain profiles, the DSD parameters with their statistical dispersions are categorized in terms of various characteristics prescribing rain-profile types. Given other uncertainties (those in the surface condition, instrument noise, and so on), propagation of errors through the retrieval procedure is formulated in a statistically unbiased manner in the Bayesian framework.
This work is a part of a project to update the current TMI level-2 algorithm toward a future version, which would be designed also for radiometers to be participated in Global Precipitation Measurement (GPM) mission.