In this Part 1 paper concerning a new Cloud Dynamics and Radiation Database (CDRD) algorithm, improvements in obtaining satellite retrievals of rainfall from multispectral passive microwave (PMW) radiometer measurements are obtained by transforming a conventional Cloud Radiation Database (CRD) algorithm. The improvements arise by combining parameter constraints derived from model-based dynamical-thermodynamical-hydrological (DTH) meteorological profile variables and additional geographical-seasonal (GS) factors, together with multispectral PMW brightness temperatures (TBs), into a specialized knowledge database underpinning a Bayesian retrieval algorithm. The so-called knowledge variables are produced by a high-resolution nonhydrostatic cloud-resolving model (CRM). The associated knowledge TBs are produced by a calibrated PMW radiative-transfer-equation model system (RMS) that relates CRM environments to expected satellite-view top-of-atmosphere TBs. By first applying the RMS to thousands of meteorological-microphysical situations simulated by the CRM and then by marshaling into the specialized database all the concomitant modeled microphysical profiles, TBs, and linked DTH/GS profiles/factors (from which optimal constraint tags can be derived), it becomes possible to use the database for the Bayesian interpretation of analogous measured TBs and tags. The main purpose of the new algorithm is to reduce ambiguity (nonuniqueness) effects that plague predecessor CRD algorithms. Such schemes restrict the interpretation of observed TBs by ignoring observable DTH/GS parameters that help constrain the influence microphysical profile sets (i.e., the associated hydrometeors, their size distributions, and their concomitant vertical distributions) that feed into the retrieval solutions. A Version 1 CDRD algorithm is tested against its CRD predecessor on two case studies of precipitation over Italy's Lazio region which were observed with various satellite PMW radiometers. The - easured TBs and corresponding tags obtained from gridded operational global model analyses are used in juxtaposition to produce the final rainfall retrievals. The retrievals are verified against coincident precision polarimetric C-band radar measurements. Skillful improvement is found for a case of intense convective rainfall where even CRD-type algorithm accuracy should be expected, as well as for a case of mixed convective-stratiform rainfall where either algorithms might otherwise be expected to be somewhat inaccurate.