## 1. Introduction

[2] Raindrop size distributions (DSDs) describe the number and size of raindrops in precipitation. The vertical distribution and time evolution of the DSD provides information about the dynamical processes of precipitating clouds. Vertically pointing Doppler radar profilers operating at very high frequency (VHF) and ultrahigh frequency (UHF) provide information on the vertical structure of hydrometeors and the ambient air motions in the precipitating clouds that advect overhead.

[3] During the past two decades, studies using vertically pointing profilers have successfully retrieved the raindrop size distribution from precipitating clouds. Profilers observe ambient air motion characteristics due to the energy backscattering from changes in the radio refractive index (Bragg scattering) and observe the motion of the hydrometeors due to the energy backscattering off of the distributed particles (Rayleigh scattering). Using the high-transmitted-power 46.5 MHz middle and upper atmosphere (MU) profiler located near Kyoto, Japan, *Wakasugi et al.* [1986, 1987] resolved both the Bragg and Rayleigh scattering components in a single Doppler spectrum. The observed mean ambient air motion and spectral broadening information from the Bragg scattering component represented the updrafts/downdrafts and turbulence in the radar pulse volume. Raindrop size distribution retrieval models utilizing the Bragg and Rayleigh scattering components in a single Doppler spectrum are called single-Doppler-spectrum (SDS) models.

[4] Two profilers operating at two different frequencies can extend the sensitivity to the Bragg and Rayleigh scattering processes, not possible with the limited dynamic range of single-frequency profilers. Reliable air motion characteristics have been estimated from a 50 MHz (VHF) profiler at Darwin, Australia, and used as parameterizations to the DSD retrieval using the Doppler velocity spectrum from a collocated 920 MHz (UHF) profiler [*Rajopadhyaya et al.*, 1998, 1999; *Cifelli and Rutledge*, 1994, 1998; *May and Rajopadhyaya*, 1996; *Cifelli et al.*, 2000]. This type of DSD retrieval model utilizes a parameterized air motion (PAM) model.

[5] The Rayleigh scattering portion of the Doppler velocity spectrum represents the hydrometeor size distribution shifted by the ambient air motion and broadened by the turbulence and wind shear in the radar pulse volume. The sans air motion (SAM) model described in this work estimates the ambient air motion, the spectral broadening, and the hydrometeor size distribution from only the Rayleigh scattering portion of the Doppler velocity spectrum. The SAM model can be used when the Bragg scattering component cannot be resolved in the Doppler velocity spectrum (SDS method) and when the ambient air motion and spectral broadening cannot be parameterized (PAM model). *Hauser and Amayenc* [1981, 1983] developed the initial analytical description for the SAM model using an exponential form of the raindrop size distribution and ignoring the spectral broadening of the Doppler velocity spectrum. *Sangren et al.* [1984] suggested that the modeling efforts could be improved by including the spectral broadening as a fitted parameter.

[6] In this study, the SAM model is developed using two methods. The first method uses the integrated moments of reflectivity, mean Doppler velocity, and spectral width calculated from the observed Doppler spectrum. The ambient air motion and spectral broadening are not estimated but are assumed to be zero. The integrated moment version of the SAM model is useful for near-surface observations and stratiform rain regimes where the ambient air motions approach zero. The second method uses the observed Doppler velocity spectrum to determine a best fit model spectrum. The model spectrum estimates the ambient air motion, the spectral broadening, and the raindrop size distribution described by the three parameters of a modified gamma distribution.

[7] First, this paper presents the general mathematical framework to retrieve the raindrop size distribution from vertical incident profiler observations. Section 3 describes the mathematics for the integrated moment SAM model method assuming zero-mean ambient air motion and negligible spectral broadening. Section 4 develops the spectral SAM model method and presents the accuracy of the DSD retrieval using noisy simulated spectra. Section 5 presents the SAM-model-retrieved raindrop size distributions from UHF (915 MHz) profiler observations made in central Florida and compares the profiler retrievals with simultaneous surface disdrometer observations. The discussion and conclusions are presented in section 6.