Polarimetric radars use differential reflectivity (Z_dr) in addition to the radar reflectivity (Z_h) to determine the two main parameters governing rain drop size distributions (DSD), typically the mass-weighted mean diameter, D_m, and the normalized intercept parameter (N_W). One built-in assumption is that the drops are oblate and that the minor-to-major axis ratios reduce with increasing size in accordance with theoretically- based approximations. For light rain, however, the Z_dr approaches 0 dB because of the dominance of the small drops (D<0.8 mm) which are spherical in shape. Our scattering calculations using measured DSDs in light rain and drizzle show that for DSDs with D_m < 0.8 mm, the S-band Z_dr tends to be < 0.2 dB and that using Z_dr to retrieve D_m will have large uncertainties due to measurement errors as well as parameterization errors. On the other hand, D_m shows a more gradual variation with Z_h for light rain and drizzle DSDs. Simulations of Z_h and Z_dr using measured DSDs with optical array probe and 2D-video disdrometer located inside a Double Fence International Reference (DFIR) wind shield were used to develop an algorithm to estimate D_m=f(Z_h) for light rain. For drizzle, the fitted equation was derived using aircraft-based data in stratocumulus rain. Validation of the D_m retrievals was performed using Z_h measured by scanning S-band polarimetric radars (CSU-CHILL in Colorado and NPOL in Delmarva peninsula) over two DFIR locations versus D_m from disdrometer measurements in the two locations. Consistent results were obtained but only for reflectivity less than 18 dBZ for light rain and 5 dBZ for drizzle. Finally, 500m by 500m gridded data from NPOL, are used to identify light rain and drizzle regions and their D_m histograms are compared with those derived from stratiform and convective rain regions. Comparisons are also made for the histograms of the normalized intercept parameter (N_W).