This dissertation describes the development and application of a combined radar-radiometer rainfall retrieval algorithm for the Tropical Rainfall Measuring Mission (TRMM) satellite. A retrieval framework based upon optimal estimation theory is proposed wherein three parameters describing the raindrop size distribution (DSD), ice particle size distribution (PSD), and cloud water path (cLWP) are retrieved for each radar profile. The retrieved rainfall rate is found to be strongly sensitive to the a priori constraints in DSD and cLWP; thus, these parameters are tuned to match polarimetric radar estimates of rainfall near Kwajalein, Republic of Marshall Islands. An independent validation against gauge-tuned radar rainfall estimates at Melbourne, FL shows agreement within 2% which exceeds previous algorithms' ability to match rainfall at these two sites.

The algorithm is then applied to two years of TRMM data over oceans to determine the sources of DSD variability. Three correlated sets of variables representing storm dynamics, background environment, and cloud microphysics are found to account for approximately 50\% of the variability in the absolute and reflectivity-normalized median drop size. Structures of radar reflectivity are also identified and related to drop size, with these relationships being confirmed by ground-based polarimetric radar data from the North American Monsoon Experiment (NAME). Regional patterns of DSD and the sources of variability identified herein are also shown to be consistent with previous work documenting regional DSD properties. In particular, mid-latitude regions and tropical regions near land tend to have larger drops for a given reflectivity, whereas the smallest drops are found in the eastern Pacific Intertropical Convergence Zone. Due to properties of the DSD and rain water/cloud water partitioning that change with column water vapor, it is shown that increases in water vapor in a global warming scenario could lead to slight (1%) underestimates of a rainfall trends by radar but larger overestimates (5%) by radiometer algorithms.

Further analyses are performed to compare tropical oceanic mean rainfall rates between the combined algorithm and other sources. The combined algorithm is 15% higher than the version 6 of the 2A25 radar-only algorithm and 6.6% higher than the Global Precipitation Climatology Project (GPCP) estimate for the same time-space domain. Despite being higher than these two sources, the combined total is not inconsistent with estimates of the other components of the energy budget given their uncertainties.