ERAD THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

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1 Multi-beam raindrop size distribution retrieals on the oppler spectra Christine Unal Geoscience and Remote Sensing, TU-elft Climate Institute, Steinweg 1, 68 CN elft, Netherlands, Christine Unal 1. Introduction Acquiring the raindrop size distribution from radar data is still a challenge. Generally this distribution is retrieed using the reflectiity, Z, and the differential reflectiity, Z dr, at S-band. The specific differential phase, K dp, proides a third radar obserable in the case of heay precipitation to strengthen the retrieal technique. For S-band profiling radars, K dp cannot be used, mainly because of the limited number of range bins containing rain. The Z dr urement cannot be employed when the eleation is near the ertical, or in the case of drizzle and light rain. Therefore retrieals hae to be performed on the ured oppler spectra. For this purpose, the oppler spectra of rain are eled using Rayleigh scattering, the gamma distribution for the raindrop size, a size-shape relationship and a Gaussian kernel for the turbulence. Comparing the ured oppler spectrum with the eled one, a non-linear least-square fit technique is employed to obtain the parameters of the raindrop size distribution ( 0, and the turbulence broadening factor of the raindrop size spectrum (σ 0. The intercept parameter (N w and the radial wind component ( 0 are estimated by scaling the broadened drop size distribution (S along the spectral reflectiity axis and the oppler elocity axis respectiely. This approach has been proposed in (Moissee et al, 006. So far, this technique has not been further deeloped, exploited and alidated. It is our intention to inestigate this methodology using the oppler-polarimetric TARA radar to retriee raindrop size distribution from drizzle to heay precipitation with high spatial and time resolution. Since TARA can profile in three directions, three raindrop size distribution profiles are estimated, which can gie insight in the microphysical homogeneity of the precipitation.. Microphysical el of raindrops The oppler spectrum, or spectral reflectiity sz HH (, can be expressed as the oppler spectrum resulting from the raindrop size distribution, sz HH (, conoluted by a Gaussian-shaped kernel of width σ 0 eling spectral broadening. Spectral broadening has seeral causes, among them turbulence and wind shear in the radar resolution olume. 1 ( szhh, ( = exp sz HH ( d (mm 6 m -3 (1 πσ σ 0 0 where and are oppler elocities and d szhh ( = N( { } σ HH ( {} d d ( The radar cross section, σ HH, is calculated using Rayleigh-Gans scattering of spheroidal hydrometeors. It strongly depends on the raindrop equiolume diameter,. The raindrop size distribution, N(, follows the gamma distribution: ( = N f ( exp ( 3.67 N f ( = w 6 ( ( 3.67 Γ ( 4 4 (mm -1 m -3 (3 where the triplet ( 0, N w, characterize the distribution. 0 is the median olume diameter and the shape parameter. Finally, due to the contribution of the radial ambient wind, the oppler spectrum experiences a shift of length 0 along the oppler elocity axis. A complete el schematic is gien in Fig. 1. When the parameters of the S are known, the reflectiity (Eq. 5, the liquid water content (Eq. 6 with ρ w =10-3 g mm -3 and the number of raindrops (Eq. 7 can be calculated: Γ ( 7 7 Z = Nw f ( 7 0 (mm 6 m -3 ( ( π 4 LWC = ρ 4 wnw0 (g m -3 ( Γ ( 1 Nt = Nwf ( 1 0 (m -3 ( ( (4

2 Fig. 1 Model schematic: this el simulates the oppler spectra of rain for the polarization settings HH and VV at the eleation α. 3. Retrieal of the raindrop size distribution, the spectral broadening, and the radial wind elocity The retrieal algorithm obtains the three parameters of the S ( 0, N w, and the dynamic parameters ( 0, σ 0 by fitting eled spectra to ured spectra. An optimization procedure has to minimize the difference (or error between the fitted spectrum and the ured spectrum by arying the fie input parameters. = max ( szhh ( ( szhh ( Ψ (8 min 10 log 10 log, Ψ = min where Ψ contains all three raindrop size distribution parameters, the spectral broadening and the ambient wind elocity. The fie parameter minimization problem, Eq. (8, can be simplified by separating the retrieal of the intercept parameter: sz = sz,,1,,, σ N ε (9 ( ( HH HH w This allows the deriation of estimates of the intercept parameters without nonlinear fitting. For this linear fit, the alues of 0, and σ 0 hae to be known and 0 is set to 0. A second simplification of Eq. (8 is done on the estimation of 0. Assuming the other four parameters of the el are known, the shift between the eled and the ured spectrum can be obtained by determining the lag of the cross correlation of the ured and the eled spectrum sz,,1,,0, σ N. HH ( 0 0 w The separate estimation of the intercept parameter and the ambient wind elocity results in a three parameter nonlinear least squares problem. The three parameters are 0, and σ 0. This approach is followed in (Moissee et al, 006 and (Spek et al, 008. Because of multiple minima in the cost functions, an iteratie cascaded retrieal algorithm, like in (Spek et al, 008, is preferred to obtain them. This algorithm is illustrated in Fig.. 4. Quality of the retrieal technique To get insight in the quality of the optimization procedure, the optimization is applied on simulated oppler spectra. By comparing the input parameters used to create a simulated spectrum with the parameters obtained with the retrieal algorithm, conclusions can be drawn on their errors. To generate signals with real statistical properties, noise is added according to Chandrasekar et al. (1986. The alues of the parameters are selected randomly from the interals, gien in Table 1. Like in (Moissee et al., 30 realizations of the oppler power spectra are aeraged to obtain an estimate of the true spectrum and the retrieal algorithm is only applied on the resulting spectrum when its corresponding reflectiity is between 10 and 55 dbz. The root mean square deiation (RMS of each parameter is gien in Table 1.

3 o min o max Iteratie selection procedure estimation procedure o σ 0 Nw V 0 L L ( = max sz ( sz (, 0 HH, db HH, db 0 = min σ o min σ o max L max 0 = HH, db( HH, db(, σ0 0 = min ( σ L sz sz σ 0 min max L HH, db HH, db σ 0, 0 = min max ( = ( (, L sz sz o Final outcome Optimization procedure from cost function study (L Fitting Variable projection method (Rust, 003 Estimation from o, σ 0 and Max cross-correlation Model spectrum ured spectrum Error calculation Output of the el Non linear least-square algorithm Fig. Cascaded rain retrieal algorithm schematic where the cost function L is ealuated from spectral reflectiities expressed in dbz. The same exercise is carried out on integral parameters, the reflectiity, the liquid water content and the number of particles. The results are gien in Table. The root mean square deiations in Tables 1- are estimated errors and do not include the uncertainties of the microphysical relationships of the el. The RMS normalized to the mean (coefficient of ariation is gien for the parameters of which the alues are positie. Table 1: Regions and root mean square deiations of parameters Parameter 0 N w σ 0 0 Region 0. 3 mm mm -1 m m s m s -1 RMS 0.1 mm 1350 mm -1 m m s m s -1 CV(RMS 17% 54% 8.4% 8% Table : Root mean square deiations of integral parameters Parameter Z LWC N t RMS 0.30 db 0.13 g m m -3 CV(RMS 0.91% % 7.4% 5. Application of the retrieal technique on non-aeraged oppler spectra of rain Because TARA has 3 beams for wind profiling, the retrieal technique can be applied on HH- and VV-spectra of the main beam (MB, which is dual-polarized, and on VV-spectra of the offset beams, OB1 and OB, which are single-polarized. OB1 and OB are 15 deg. away from the main beam in two orthogonal directions. For the presented urements, the eleations of MB, OB1 and OB, are 75 o, 90 o and 69 o respectiely. Spectral polarimetric processing is performed to obtain noise- and clutter-free dealiased oppler spectra (Unal and Moissee 004; Unal 009 for the dual-polarized beam and classical spectral processing is carried out for the single-polarized beams. This full processing is implemented real-time for the TARA radar (Unal et al., 01. Output examples are gien in Fig. 3.

4 Prior to the retrieal algorithm, three supplementary processing steps are carried out. The first one consists of replacing single and dual-missing data using neighboring oppler bins. Then an automatic low clipping leel is estimated to ensure that the oppler spectra hae about the same spectral reflectiity alue at the lower parts of the spectrum. Finally a light smoothing is performed. These steps are carried out on the spectra of Fig. 3, which results in the input spectra of Fig. 4. Fig. 3 Multi-beam ured oppler spectra. The ertical beam is OB1. The height related to the radar is the same (86 m but the radar resolution olumes are separated by 14 m. This separation has to be compared with the radar resolution resulting from the antenna beamwidth, which is around 30 m for the considered ranges. The full width of the oppler spectra is about 6 m s -1 but the range of oppler elocities clearly differs of 1 m s -1 for OB1-MB and -3 m s -1 for OB1-OB due to the radial component of the wind (- 0. Fig. 4 Input oppler spectra clipped and lightly smoothed. The clipping leel is -8.3, -9.4, and db for main beam HH and VV, OB1 and OB, respectiely. The fit and the results of the retrieal algorithm are gien. Compared to the other beams, a significant oppler shift of - 0 (-.56 m s -1 is found for OB, which was expected. To strengthen the retrieal algorithm, two ifications hae been implemented. The first one is the reduction of the search interal of, which is now [-1, 5]. The second one is the reduction of the search interal of 0 using the reflectiity alue. Varying the drop size distribution parameters leads to simulated reflectiity alues. After a large number of runs, an interal of median olume diameters can be associated to an interal of reflectiity alues, assuming that N w aries from 10.5 to For example, if the ured reflectiity is between 0 and 10 dbz, like in the example of Figs. 3-4, the search interal of 0 is [0.3, 0.9] mm. Results of the retrieal algorithms are gien in Fig. 4. Note that results for the main beam oppler spectra HH and VV differ while the radar resolution olumes are the same. Those differences are comparable with the RMS estimated in Table 1, except for N w. 6. Retrieal results comparison using HH and VV oppler spectra Because the main beam probe the same medium with two different polarization settings, the retrieal algorithm is applied on the oppler spectra HH and VV. We expect the same retrieal results with an error comparable to the RMS alues of Tables 1-. The retrieal algorithm is applied on 1555 non-aeraged oppler spectra, HH and VV, acquired with a time resolution of.9 s and a height resolution of 14.5 m. They represent stratiform light rain during 3.5 min between 00 m and 1750 m. The results are gien in Fig. 5 (odd panels. The correlation coefficient (corr and the coefficient of ariation (CV of the RMS are indicated with the RMS in each scatter-plot. Concerning the microphysical retrieals, the median olume diameter is well retrieed, the error on the shape parameter is ±1 and the RMS of both the intercept parameter and the number of raindrops is much too large. espite its strong dependency in 0 ( 4 0, the liquid water content estimate is affected by the large error on N w. Concerning the dynamical retrieals, the radial wind elocity estimate is reasonable and the spectrum width broadening is not well retrieed. The inestigation of the profiles of the retrieed parameters shows that they are noisy. It is necessary to apply a heightsmoothing in order to interpret the profiles (Fig. 6. The een panels of Fig. 5 gie the scatter-plots between retrieals for the same radar resolution olume when height-smoothing has been applied. As expected, the retrieals HH and VV are better comparable. The error on the shape parameter is decreased to ±0.4, the RMS of N w and N t is still large but strongly improed. The retrieal algorithm combined with height-smoothing of the results shows a good consistency of 0,, 0 and LWC.

5 Fig. 5 Scatter plots of the retrieal results for the same radar resolution olume. The ariations of the microphysical and dynamical parameters are rather large (odd panel. The een panels show the height-smoothed retrieed results. Fig. 6 Example of multi-beam profiles of median olume diameter 7. Retrieal results: first multi-beam comparisons At the start of the radar far-field (00 m, we expect to obtain retrieal results similar for the three probing beams. At 300 m, the radar resolution olumes are separated by 79 m. The parameters of the 3-beams raindrop size distributions are gien in Fig. 7. They reasonably agree. Howeer, the retrieal of 0 for the beam OB differs in absolute alue from the 0 alues of the two other beams. Because wind urements can be performed with TARA, we can compare the 3.5 min aeraged radial wind component retrieed (- 0 with the radial component of the mean horizontal wind. This is done in Fig. 9. The retrieal (- 0 is clearly underestimated. Consequently, the retrieal of 0 is expected to be oerestimated for OB and underestimated for MB. This can be already seen in Fig. 7. If the contribution of the 10.5 min aeraged horizontal wind radial component is subtracted to the oppler elocities of the oppler spectrum before the retrieal procedure, the retrieal of 0 may be improed. This is demonstrated in Fig. 8, where the agreement of the multi-beam raindrop size distributions is much better.

6 Fig. 7 Comparison of the multi-beam raindrop size distributions at the height 300 m. The time resolution is.9 s. Fig. 8 Comparison of the multi-beam raindrop size distributions at the height 300 m when the mean horizontal wind radial component has been remoed in the oppler spectrum before the retrieal procedure. Fig. 9 Radial component of ured mean horizontal wind (aeraged on 3.5 and 10.5 min and retrieed radial wind 8. Preliminary conclusions When the differential reflectiity cannot be used because of single-polarized beam, near-ertical profiling or ery light precipitation, the raindrop size distribution results obtained from the urement of oppler spectra show that two many ariables need to be retrieed ( 0, N w,, 0, σ 0. With the proposed retrieal technique, the correct estimation of 0 is crucial. A good candidate to replace Z dr is the radial component of the mean horizontal wind. With this knowledge, the oppler spectra can be compensated for the horizontal wind influence. This strongly improes the estimation of 0. Consequently the other parameters to retriee are directly improed as well. References Chandrasekar, V., V. Bringi, and P. Brockwell, 1986: Statistical properties of dual-polarized radar signals. Preprints, 3d Conf. on Radar Meteorology, Snowmass, CO, Amer. Meteor. Soc., Moissee,. N., V. Chandrasekar, C. M. H. Unal, and H. W. J. Russchenberg, 006: ual-polarization spectral analysis for retrieal of effectie raindrop shapes. J. Atmos. Oceanic Technol., 3, Spek, A., C. Unal,. Moissee, H. Russchenberg, V. Chandrasekar, and Y. ufournet, 008: A new technique to categorize and retriee the microphysical properties of ice particles aboe the melting layer using radar dual polarization spectral analysis. J. Atmos. Oceanic Technol., 5, Unal, C., 009: Spectral polarimetric radar clutter suppression to enhance atmospheric echoes. J. Atmos. Oceanic Technol., 6, Unal, C. M. H., and. N. Moissee, 004: Combined oppler and polarimetric radar urements: correction for spectrum aliasing and non simultaneous polarimetric urements. J. Atmos. Oceanic Technol., 1, Unal C., Y. ufournet, T. Otto, and H. Russchenberg, 01: The new real-time urement capabilities of the profiling TARA radar. Preprints, Seenth European Conf. on Radar in Meteorology and Hydrology (ERA, Toulouse, France.