The three-parameter gamma distribution n(D) ϭ N 0 D exp(Ϫ⌳D) is often used to characterize a raindrop size distribution (DSD). The parameters and ⌳ correspond to the shape and slope of the DSD. If and ⌳ are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified, which facilitates retrieval of rain parameters from remote measurements. It is important to determine whether the-⌳ relation arises from errors in estimated DSD moments, or from natural rain processes, or from a combination of both statistical error and rain physics. In this paper, the error propagation from moment estimators to rain DSD parameter estimators is studied. The standard errors and correlation coefficient are derived through systematic error analysis. Using numerical simulations, errors in estimated DSD parameters are quantified. The analysis shows that errors in moment estimators do cause correlations among the estimated DSD parameters and cause a linear relation between estimators and. However, the slope and intercept of the error-induced relation depend on the expected values and ⌳, ⌳ and it differs from the-⌳ relation derived from disdrometer measurements. Further, the mean values of the DSD parameter estimators are unbiased. Consequently, the derived-⌳ relation is believed to contain useful information in that it describes the mean behavior of the DSD parameters and reflects a characteristic of actual raindrop size distributions. The-⌳ relation improves retrievals of rain parameters from a pair of remote measurements such as reflectivity and differential reflectivity or attenuation, and it reduces the bias and standard error in retrieved rain parameters.

A unique dataset consisting of high-resolution polarimetric radar measurements and dense rain gauge and disdrometer observations collected in east-central Florida during the summer of 1998 was examined. Comparison of the radar measurements and radar parameters computed from the disdrometer observations supported previous studies, which indicate that oscillating drops in the free atmosphere have more spherical apparent shapes in the mean than equilibrium shapes. Radar-disdrometer comparisons improved markedly when using an empirical axis ratio relation developed from observational studies and representing more spherical drop shapes. Fixedform power-law rainfall estimators for radar reflectivity (Z H ), specific differential phase (K DP ), specific differential phase-differential reflectivity (K DP , Z DR ), and radar reflectivity-differential reflectivity (Z H , Z DR ) were then determined using the disdrometer observations. Relations were produced for both equilibrium shapes and the empirical axis ratios. Polarimetric rainfall estimators based on more spherical shapes gave significantly improved performance. However, the improvement was largely in bias mitigation. Rainfall estimates with the Z H -Z DR measurement pair had the highest correlation with rain gauge observations, the smallest range in bias factors from storm to storm, and the smallest root-mean-square error.

Winter-storm hydrometeor distributions along the Front Range in eastern Colorado are studied with a ground-based two-dimensional video disdrometer. The instrument provides shape, size, and terminal velocity information for particles that are larger than about 0.4 mm. The dataset is used to determine the form of particle size distributions (PSDs) and to search for useful interrelationships among the governing parameters of assumed distribution forms and environmental factors. Snowfalls are dominated by almost spherical aggregates having near-exponential or superexponential size distributions. Raindrop size distributions are more peaked than those for snow. A relation between bulk snow density and particle median volume diameter is derived. The data suggest that some adjustment may be needed in relationships found previously between temperature and the concentration and slope parameters of assumed exponential PSDs. A potentially useful relationship is found between the slope and shape terms of the gamma PSD model.

In this paper, data from three 2-dimensional video disdrometers (2DVDs) and an S-band polarimetric radar are used to characterize rain microphysics in Oklahoma. Sampling errors from the 2DVD measurements are quantified through side-by-side comparisons. In an attempt to minimize the sampling errors, a method of sorting and averaging based on two parameters (SATP) is proposed. The shape-slope (-⌳) relation of a constrained gamma (C-G) model is then refined for the retrieval of drop size distributions (DSDs) from polarimetric radar measurements. An adjustable term that is based on observed radar reflectivity and differential reflectivity is introduced to make the C-G DSD model more applicable. Radar retrievals using this improved DSD model are shown to provide good agreement with disdrometer observations and to give reasonable results, including in locations near the leading edge of convection where poorly sampled large drops are often observed.

A radar simulator for polarimetric radar variables, including reflectivities at horizontal and vertical polarizations, the differential reflectivity, and the specific differential phase, has been developed. This simulator serves as a test bed for developing and testing forward observation operators of polarimetric radar variables that are needed when directly assimilating these variables into storm-scale numerical weather prediction (NWP) models, using either variational or ensemble-based assimilation methods. The simulator takes as input the results of high-resolution NWP model simulations with ice microphysics and produces simulated polarimetric radar data that may also contain simulated errors. It is developed based on calculations of electromagnetic wave propagation and scattering at the S band of wavelength 10.7 cm in a hydrometeor-containing atmosphere. The T-matrix method is used for the scattering calculation of raindrops and the Rayleigh scattering approximation is applied to snow and hail particles. The polarimetric variables are expressed as functions of the hydrometeor mixing ratios as well as their corresponding drop size distribution parameters and densities. The presence of wet snow and wet hail in the melting layer is accounted for by using a new, relatively simple melting model that defines the water fraction in the melting snow or hail. The effect of varying density due to the melting snow or hail is also included. Vertical cross sections and profiles of the polarimetric variables for a simulated mature multicellular squall-line system and a supercell storm show that polarimetric signatures of the bright band in the stratiform region and those associated with deep convection are well captured by the simulator.

The characteristics of raindrop size distributions (DSDs) and vertical structures of rainfall during the Asian summer monsoon season in East China are studied using measurements from a ground‐based two‐dimensional video disdrometer (2DVD) and a vertically pointing Micro Rain Radar (MRR). Based on rainfall intensity and vertical structure of radar reflectivity, the observed rainfall is classified into convective, stratiform, and shallow precipitation types. Among them, shallow precipitation has previously been ignored or treated as outliers due to limitations in traditional surface measurements. Using advanced instruments of 2DVD and MRR, the characteristics of shallow precipitation are quantified. Furthermore, summer rainfall in the study region is found to consist mainly of stratiform rain in terms of frequency of occurrence but is dominated by convective rain in terms of accumulated rainfall amount. Further separation of the summer season into time periods before, during, and after the Meiyu season reveals that intrasummer variation of DSDs is mainly due to changes in percentage occurrence of the three precipitation types, while the characteristics of each type remain largely unchanged throughout the summer. Overall, higher raindrop concentrations and smaller diameters are found compared to monsoon precipitation at other locations in Asia. Higher local aerosol concentration is speculated to be the cause. Finally, rainfall estimation relationships using polarimetric radar measurements are derived and discussed. These new relationships agree well with rain gauge measurements and are more accurate than traditional relations, especially at high and low rain rates.

The evolution of microphysical characteristics of a rainband in Typhoon Matmo (2014) over eastern China, through its onset, developing, mature, and dissipating stages, is documented using observations from an S band polarimetric Doppler radar and a two‐dimensional video disdrometer (2DVD). The drop size distributions observed by the 2DVD and retrieved from the polarimetric radar measurements indicate that the convection in the rainband generally contains smaller drops and higher number concentrations than the typical maritime type convection described in Bringi et al. (2003). The average mass‐weighted mean diameter (Dm) of convective precipitation in the rainband is about 1.41 mm, and the average logarithmic normalized intercept (Nw) is 4.67 log10 mm−1 m−3. To further investigate the dominant microphysical processes, the evolution of the vertical structures of polarimetric variables is examined. Results show that complex ice processes are involved above the freezing level, while it is most likely that the accretion and/or coalescence processes dominate below the freezing level throughout the rainband life cycle. A combined examination of the polarimetric measurements and profiles of estimated vertical liquid and ice water contents indicates that the conversion of cloud water into rainwater through cloud water accretion by raindrops plays a dominant role in producing heavy rainfall. The high estimated precipitation efficiency of 50% also suggests that cloud water accretion is the dominant mechanism for producing heavy rainfall. This study represents the first time that radar and 2DVD observations are used together to characterize the microphysical characteristics and precipitation efficiency for typhoon rainbands in China.

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