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MARCH 2004 BRANDES ET AL. 461 Drop Size Distribution Retrieval with Polarimetric Radar: Model and Application EDWARD A. BRANDES,GUIFU ZHANG, AND J. VIVEKANANDAN National Center for Atmospheric Research,* Boulder, Colorado (Manuscript received 24 February 2003, in ®nal form 30 September 2003) ABSTRACT Polarimetric radar measurements are used to retrieve properties of raindrop distributions. The procedure assumes that drops are represented by a gamma distribution and retrieves the governing parameters from an empirical relation between the distribution shape and slope parameters and measurements of radar re¯ectivity and differential re¯ectivity. Retrieved physical characteristics of the drop size distribution (DSD) were generally well matched with disdrometer observations. The method is applied to select storms to demonstrate utility. Broad DSDs were determined for the core (high re¯ectivity) regions of thunderstorms. Largest drop median volume diameters were at the leading edge of the storm core and were displaced slightly downwind from updrafts. Rainy downdrafts exhibited what are believed to be equilibrium DSDs in which breakup and accretion are roughly in balance. DSDs for stratiform precipitation were dominated by relatively large drops. Median volume diameters at the ground were closely related to the intensity of an overlying bright band. The radar measurements suggest that, although DSDs in stratiform rain were also broad and nearly constant in the rain layer, they were not at equilibrium but were merely steady. DSD invariance is attributed to small total drop numbers, which result in few collisions. 1. Introduction using measurements of radar re¯ectivity and differential re¯ectivity. Subsequent research suggests that, for short Dual-polarization radars typically transmit horizon- time periods commensurate with radar measurements, tally and vertically polarized electromagnetic waves and DSDs are more typically represented by a gamma dis- receive backscattered signals. Because illuminated hy- tribution (Ulbrich 1983), drometeors are not exactly spherical and are not simi- m larly oriented, wave scattering is different for the two N(D) 5 ND0 exp(2LD), (1) polarizations. Waves propagating through precipitation 2m21 23 are subject to scattering, attenuation, phase shifts, and where N 0 (mm m ) is a number concentration pa- depolarization. Signal properties change continuously rameter, m is a distribution shape parameter, L (mm21) as the waves propagate, yielding information regarding is a slope term, and D (mm) is the drop equivalent particle size, shape, and orientation that can be used to volume diameter. Because the gamma DSD is described estimate the governing parameters of assumed drop size by three parameters, three measurements or relations are distribution (DSD) models (Seliga and Bringi 1976; required. The retrieval technique used here, an adap- Zhang et al. 2001; Gorgucci et al. 2002; Bringi et al. tation of that proposed by Zhang et al. (2001), is based 2002). A capability to retrieve DSD information would on measurements of radar re¯ectivity at horizontal po- be important for studying precipitation processes and larization (ZH) and differential re¯ectivity (ZDR), and an the hydrometeor properties of storms, for validating mi- empirical constraining relationship between the drop crophysical parameterizations within numerical models, size distribution shape and slope parameters. The m±L and for improving rainfall estimates. relation was derived from drop size distribution mea- Seliga and Bringi (1976, 1978) retrieved two param- surements. Concern has been raised as to the in¯uence eters de®ning an exponential DSD, that is, a concen- of measurement errors on such relations (Chandrasekar tration parameter and the drop median volume diameter, and Bringi 1987). This issue is addressed by Zhang et al. (2003), who show that the m±L relation is intrinsi- cally different than the linear relation associated with * The National Center for Atmospheric Research is sponsored by measurement error and that retrieved m and L values the National Science Foundation. are not biased by statistical errors. Gorgucci et al. (2002) and Bringi et al. (2002) propose Corresponding author address: Dr. Edward A. Brandes, National to retrieve the DSD from re¯ectivity, differential re- Center for Atmospheric Research, P.O.Box 3000, Boulder, CO 80307. ¯ectivity, and speci®c differential phase (KDP). The pro- E-mail: [email protected] cedure yields the mean axis ratio of the drops, the DSD q 2004 American Meteorological Society Unauthenticated | Downloaded 09/25/21 08:53 PM UTC 462 JOURNAL OF APPLIED METEOROLOGY VOLUME 43 shape factor, a normalized number concentration, and work and the disdrometer. [For instrument locations see the DSD median volume diameter. There is some ques- Brandes et al. (2002, their Fig. 1).] tion with regard to the use of KDP for DSD parameter retrieval; K is computed from measurements of dif- DP 3. DSD parameter retrieval ferential propagation phase, which can be noisy, partic- ularly at lower rain rates. To reduce the uncertainty in The method for retrieving the DSD governing param- eters follows that of Zhang et al. (2001) as modi®ed by KDP, the differential phase measurements are ®ltered in range, often over several kilometers (e.g., Ryzhkov and Brandes et al. (2003). The procedure uses the de®nitions Zrnic 1996; Hubbert et al. 1993). Retrievals of drop of radar re¯ectivity and differential re¯ectivity ex- pressed in terms of the DSD parameters (N , m, and L) mean shape with KDP can produce large variations in 0 space and time, which have not been independently ver- and drop backscattering amplitudes and an empirical i®ed. Further, Illingworth and Blackman (2002) argue relation between m and L determined from drop ob- servations: that the redundancy among ZH, ZDR, and KDP precludes the retrieval of the three DSD parameters in Eq. (1) with L51.935 1 0.735m 1 0.0365m2. (2) this parameter set. Rather, KDP is used here for verifying the radar calibration (Vivekanandan et al. 2003). Bringi This relation is based upon a representative cross section et al. (2002) apply the method only to situations in of storms that included light stratiform to heavy con- 21 vective precipitation. Drop axis ratios are calculated which KDP $ 0.38 km (rain rates of greater than 20 mm h21). Hence, the technique has limited application with for general DSD retrieval. r 5 0.9951 1 0.025 10D 2 0.036 44D2 This paper gives an overview of the available data 0.005 030D340.000 249 2D , (3) and the DSD retrieval procedure. The method is then 1 2 applied to moderate thunderstorms, a stratiform rain where r is the axis ratio (vertical axis divided by the event, and a strong multicellular thunderstorm. Re- horizontal axis). This expression was used by Brandes trieved total drop concentrations, mass-distribution et al. (2002) for rainfall estimation. Bias factors for spectral widths, drop median volume diameters, rain- polarimetric rainfall estimators using ZH, KDP, KDP and water content, and rain rates are compared with com- ZDR, and ZH and ZDR converged to a similar value, in- putations with disdrometer observations and are used to dicating the validity of the relation. The DSD can be examine the spatial and temporal characteristics of found by using the de®nition of ZDR and the empirical DSDs within the selected storms. relation [Eq. (2)] to retrieve m and L by iteration and then using the de®nition of radar re¯ectivity at hori- zontal polarization to ®nd N 0. 2. Data Once the governing parameters of the DSD are known, other attributes can be computed. The total drop Radar measurements used in this study were collected concentration (N ,m23) is given by with the National Center for Atmospheric Research's S- T band, dual-polarization Doppler radar (S-Pol) in east- Dmax N 5 N(D) dD, (4) central Florida during a special ®eld experiment (``PRE- T E CIP98'') to evaluate the potential of polarimetric radar 0 to estimate rainfall (Brandes et al. 2002). Measurements where Dmax, the diameter of the largest drop (mm), is were obtained at high temporal and spatial resolution estimated from radar re¯ectivity (Brandes et al. 2003). The over a special rain gauge network installed by the Na- drop median volume diameter (D0, mm) is de®ned as tional Aeronautics and Space Administration as part of DD0 max its Tropical Rainfall Measuring Mission. The network EEDN33(D) dD 5 DN(D) dD, (5) included a video disdrometer (Kruger and Krajewski 0 D0 2002) located 38 km from the radar. One-minute ob- servations were available. Re¯ectivity and differential and one-half of the rainwater content is contained in drops smaller and one-half in drops larger than D .A re¯ectivity measurements from the radar were averaged 0 closely related parameter, the mass-weighted average (linear units) over ®ve range gates. Each gate was 0.15 diameter (D , mm), is computed from km in length. For comparison with the disdrometer (sec- m tions 3 and 4), the smoothed radar measurements for Dmax range bins containing the disdrometer and for 0.58 an- E DN4 (D) dD tenna elevation were used. Gridded values of DSD pa- 0 Dm 5 . (6) rameters (section 4) were found by averaging retrieved Dmax 3 DSD parameters over a volume having a radius of 0.75 E DN(D) dD km. Proximity to the Weather Surveillance Radar-1988 0 2 2 Doppler (WSR-88D) at Melbourne, Florida, (KMLB) The variance of the mass spectrum (s m , mm ) is given gave dual-Doppler radar coverage over the gauge net- either by (Ulbrich 1983) Unauthenticated | Downloaded 09/25/21 08:53 PM UTC MARCH 2004 BRANDES ET AL. 463 Dmax el [Eq. (1)] associate with high concentrations of small (D 2 D )23DN(D) dD E m dropsÐnot usually observed at the leading edge of 0 2 strong convection. The constrained-gamma model [Eq.

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