Impact of Observation Operators on Low-Level Wind Speed Retrieved by Variational Multiple-Doppler Analysis

Transcription

1 215 Impact of Observation Operators on Low-Level Wind Speed Retrieved by Variational Multiple-Doppler Analysis Ken-ichi Shimose, Shingo Shimizu, Takeshi Maesaka, Ryohei Kato, Kaori Kieda, and Koyuru Iwanami National Research Institute for Earth Science and Disaster Resilience, Tsukuba, Japan Abstract This study investigated the impact of observation operators on low-level wind speed analysis. An evaluation of wind speeds retrieved by variational multiple-doppler analyses using radial velocities (V r ) based on the formats of both a Plan Position Indicator (PPI) (hereafter, PPI-VAR) and a Constant Altitude Plan Position Indicator (CAPPI) (hereafter, CAPPI-VAR) was performed for comparison with wind speeds observed by a wind profiler during the warm season of three consecutive years. The statistical analysis showed that PPI-VAR was more accurate than CAPPI-VAR at 500 m above ground level (AGL). The error of CAPPI-VAR at 500 m AGL was caused by a representative error of CAPPI-formatted V r derived from a certain radar whose beam height was far from the analysis level, and this error became more obvious the greater the vertical difference in wind speed across the analysis level. CAPPI-VAR uses CAPPI-formatted V r from each radar equally; thus, the representative error might cause performance degradation of CAPPI-VAR at 500 m AGL. Conversely, PPI-VAR uses PPI-formatted V r from each radar with appropriate weighting based on the beam height distance from the analysis level. PPI-VAR showed better results at 500 m AGL because the observation grid points were dense around 500 m AGL. (Citation: Shimose, K., S. Shimizu, T. Maesaka, R. Kato, K. Kieda, and K. Iwanami, 2016: Impact of observation operators on low-level wind speed retrieved by variational multiple-doppler analysis. SOLA, 12, , doi: /sola ) 1. Introduction To prevent loss of life by strong winds and to control transportation infrastructure safely and efficiently, it is necessary to monitor low-level wind speed accurately. This can be achieved via the retrieval of three-dimensional wind velocity using dual- or multiple-doppler wind analysis. This method was first proposed by Armijo (1969) and various multiple-doppler wind analysis procedures have been developed and evaluated subsequently (e.g., Ray et al. 1975, 1978, 1980; Doviak et al. 1976; Chong and Testud 1983; Chong et al. 1983, Testud and Chong 1983; Bousquet and Chong 1998; Shapiro and Mewes 1999; Gao et al. 1999, 2004; Liou and Chang 2009; Shapiro et al. 2009; Liou et al. 2012; Potvin et al. 2012a, b, c). Potvin et al. (2012c) reported that the variational multiple-doppler wind analysis proposed by Gao et al. (1999) is more accurate than the multiple-doppler wind analysis that explicitly integrates the continuity equation vertically, such as that by Ray et al. (1980). Therefore, the variational multiple-doppler wind analysis has become the method commonly used for wind-field retrieval. Considering the observation operator of the variational method, there are two types of radar radial-velocity data format: one based on a Plan Position Indicator (PPI) and the other based on a Constant Altitude Plan Position Indicator (CAPPI). The variational multiple-doppler wind analysis using radial velocity based on the PPI format (hereafter, PPI-VAR) has been used by Gao Corresponding author: Ken-ichi Shimose, Storm, Flood and Landslide Research Division, National Research Institute for Earth Science and Disaster Resilience (NIED), 3-1, Tennodai, Tsukuba, Ibaraki, , Japan. kshimose@bosai.go.jp. 2016, the Meteorological Society of Japan. et al. (1999, 2004), Shapiro et al. (2009), and Potvin et al. (2012a, b, c). Gao et al. (1999) mentioned that one advantage of PPI- VAR is that it is a single-step method that combines interpolation and analysis. The analysis is performed directly in a Cartesian coordinate system; only interpolation from the Cartesian (analysis) coordinate grid point to the polar (radar) coordinate grid point is needed. Therefore, PPI-VAR can avoid errors due to interpolation from the radar coordinate grid point to the analysis coordinate grid point, which should be larger than when interpolation is done in reverse (Gao et al. 1995). Variational multiple-doppler wind analysis using radial velocity based on the CAPPI format (hereafter, CAPPI-VAR) has been used by Shimizu et al. (2008) and Kim et al. (2012). One of the advantages of CAPPI-VAR is the spatial continuity of the analysis. The CAPPI-formatted radial velocity (CAPPI-V r ) is produced by a Cressman-type interpolation (Cressman 1959) of PPI-formatted radial velocity (PPI-V r ). Therefore, CAPPI-VAR can provide a wind field that has spatial continuity, which might provide a better solution. The spatial continuity of CAPPI-V r is also suitable for traditional multiple- Doppler wind analysis that explicitly integrates the continuity equation vertically and therefore, traditional multiple-doppler wind analyses commonly use CAPPI-V r (e.g., Ray et al. 1980; Sun and Crook 1997, 1998). However, the process of derivation of CAPPI-V r includes a spatial interpolation procedure, and errors associated with this procedure could affect CAPPI-VAR accuracy. This study focused on the region near the atmospheric boundary layer where the observation grid points of PPI-V r are rather dense and thus, PPI-VAR should be capable of retrieving accurate lowlevel wind speeds. Therefore, it is important to comprehend the quantitative difference between PPI-VAR and CAPPI-VAR in the lower-level atmosphere. The purpose of this work is to investigate the quantitative analysis error of low-level wind speeds retrieved by PPI-VAR and CAPPI-VAR (hereafter, WS PPI-VAR and WS CAPPI-VAR, respectively). PPI-V r obtained from three Doppler radars was used for the lowlevel wind speed analyses. For the evaluation of error, horizontal wind speed observations were obtained from a wind profiler (hereafter, WPR) located close to the three radars. In order to conduct a robust evaluation, the statistical analysis was based on data from the warm seasons of three consecutive years. 2. Data and methods WS PPI-VAR and WS CAPPI-VAR were analyzed for precipitation systems that passed over WPR (see Fig. 1 for its location) at Nagoya in Japan during the warm seasons (April September) of three consecutive years ( ). WPR was installed by the Japan Meteorological Agency. There were three X-band multi-parameter (MP) radars operated by the Ministry of Land, Infrastructure, Transport and Tourism (MLIT) located around the WPR and their respective locations (Anjo, Bisai, and Suzuka) and observational ranges are presented in Fig. 1. The data resolution of MLIT X-band MP radar was 150 m for range and 1.2 for azimuth, and the observational range was 80 km (Maesaka et al. 2011). The number of elevation angles for a single volume scan was 12 (1.0, 1.6, 2.7, 3.8, 5.1, 6.5, 8.1, 10.0, 12.0, 14.3, 17.0, and 20.0 ), and it took 5 min to make one volume scan. The time interval of WPR observation was 10 min (details of WPR observations are described below) and thus, CAPPI-V r, WS PPI-VAR, and WS CAPPI-VAR were evaluated every 10 min. WPR was located within the observation range of each MLIT X-band MP radar. Hence, the

2 216 Shimose et al., Observation Operators on Wind Speed Retrieved by Multiple-Doppler Analysis Fig. 1. Distribution of the observation network around Nagoya, Japan. The star indicates the location of the wind profiler. The crosses denote the locations of the MLIT X-band MP radars, and the large open circles indicate their observational ranges. Color shading denotes terrain height. location was considered suitable for the evaluation of wind analysis derived from these three radars. The distances from WPR to the radars were 32, 26, and 44 km for Anjo, Bisai, and Suzuka, respectively. To produce CAPPI-V r, PPI-V r was interpolated to a Cartesian (analysis) coordinate system using the Cressman weighting function (Cressman 1959). The grid spacing of the analysis coordinate system was 1 km in the horizontal and 500 m in the vertical. The radius of influence ellipsoid in the weighting function was 1.5 km in the horizontal and 0.5 km in the vertical. CAPPI-V r was produced every 5 min using one volume scan of PPI-V r before 5 min of analysis time. The variational method of PPI-VAR and CAPPI-VAR was based on Gao et al. (1999). Here, the background and smoothing terms in the cost function, which have the effect of smoothing the characteristics of the observation, were not used. For the observation operator that transforms the analysis grid variable into the form of an observation grid variable, a bilinear interpolation operator was used, such that for PPI-VAR, the observation grid variable was interpolated linearly from the nearest eight analysis grid point values (for CAPPI-VAR, the observation grid point value corresponded to the analysis grid point value). The analysis grid spacing for PPI-VAR and CAPPI-VAR was 1 km in the horizontal and 500 m in the vertical and the analysis time interval was 5 min; both identical to CAPPI-V r. The same volume scan was used for both PPI-VAR and CAPPI-VAR. Because of the limitation of analysis accuracy, the region where the intersection angle between each radar was < 20 was not used for the analysis. It is noted that PPI-VAR at 500 m above ground level (AGL) only used PPI-V r between 500 and 1000 m AGL because of the limitation of the bilinear interpolation operator. The horizontal wind speed observed by WPR (hereafter, WS WPR ) was used for the evaluation. A detailed description of WPR can be found in Kato et al. (2003). The observation time interval was 10 min and the vertical observation spacing was about 300 m (the lowest observation level is 450 m AGL). Because the horizontal coverage of WPR was increased in the vertical direction (about 1 km at 3000 m AGL), the evaluation was performed for heights below 3000 m AGL. WS WPR was interpolated linearly at 500-m intervals after ensuring its accuracy. WS WPR was averaged over 10 min; thus, WS PPI-VAR and WS CAPPI-VAR were also averaged over the same period. To evaluate the wind speed error quantitatively, the root mean square error (RMSE), relative RMSE (RRMSE; RMSE as a percentage of root mean square WS WPR ), mean bias error (MBE), and relative MBE (RMBE; MBE as a percentage of mean WS WPR ) were calculated between the analysis and observed wind speed. These values were averaged at each level for the three warm seasons. 3. Results and discussions Vertical profiles of the RMSE and RRMSE of WS PPI-VAR and WS CAPPI-VAR from the warm seasons of three years ( ) are presented in Fig. 2. Vertical profiles of the MBE and RMBE of WS PPI-VAR and WS CAPPI-VAR for the same period are shown in Fig. 3. The vertical profile of the mean WS WPR is also shown in Figs. 2 and 3. A sample size of at least 4400 (about 30 days) was used for calculating the averaged error value; the sample size was varied according to the altitude and method used. Figure 2 shows that at 500 m AGL, the RMSE and RRMSE of WS PPI-VAR (1.6 m s 1 and 24%, respectively) are smaller than those of WS CAPPI-VAR (2.0 m s 1 and 29%, respectively). The mean WS WPR at 500 m AGL was smaller than that above 500 m AGL (see Figs. 2 and 3) and therefore, the RRMSE of wind speed at 500 m AGL was relatively larger than that above 500 m AGL. Figure 3 shows that the MBE and RMBE of WS PPI-VAR and WS CAPPI-VAR at 500 m AGL are both Fig. 2. Vertical profiles of RMSE and RRMSE of WS PPI-VAR and WS CAPPI-VAR, and mean WS WPR for warm seasons of three consecutive years ( ). Red circles and blue triangles denote the results from PPI-VAR and CAPPI-VAR, respectively. Black squares indicate the mean WS WPR.

3 217 Fig. 3. Same as Fig. 2 except for the MBE and RMBE of WS PPI-VAR and WS CAPPI-VAR. positive values, and that WS CAPPI-VAR is overestimated considerably with respect to WS WPR. At 1000 m AGL, the RMSE and RRMSE of WS PPI-VAR were comparable with those of WS CAPPI-VAR, whereas above 1000 m AGL, the RMSE and RRMSE of WS PPI-VAR were larger than the RMSE and RRMSE of WS CAPPI-VAR. At 3000 m AGL, however, the RMSE and RRMSE of WS PPI-VAR were once again seen to be comparable with those of WS CAPPI-VAR. The MBEs of WS CAPPI-VAR were relatively small above 1000 m AGL, while the MBEs of WS PPI-VAR were considerably positive and negative at 2000 and 2500 m AGL, respectively. Because surface wind damage is frequently caused by microbursts and tornadoes, whose wind speeds attain maximum values at around 200 m AGL and decrease with altitude (Wilson et al. 1984; Wurman and Kosiba 2013), it is important to monitor the wind field at altitudes that are as low as possible. Therefore, the error factors of WS PPI-VAR and WS CAPPI-VAR at the lowest level (500 m AGL) are discussed in detail. To understand which observation grid points had the greatest effect on the analysis accuracy at 500 m AGL, the distribution of observation grid points around WPR was investigated. Figure 4a shows the observation grid points of PPI-V r from each radar around a 2 2 km horizontal square centered on WPR, which are projected to a west east cross section. Figure 4b shows the relative vertical distance from an analysis grid point to the centroid of the observation grid points inside the influence ellipsoid of CAPPI-V r for each radar (hereafter, RVD). The lowest observation grid point of Anjo, Bisai, and Suzuka was located at around 500, 500, and 800 m AGL, respectively (Fig. 4a); thus, at 500 m AGL, RVD of Anjo and Bisai was small (0.11 and 0.17 km, respectively), while that of Suzuka was relatively large (0.34 km). Figure 4c shows the mean vertical distance between an analysis grid point and observation grid points inside the analysis grid of PPI-VAR from all radars (hereafter, MVD). MVD was small (0.19 km) at 500 m AGL and the observation grid points were dense in the vicinity of 500 m AGL (Fig. 4a). The relationship between the error factor of WS CAPPI-VAR and the distribution of observation grid points at 500 m AGL mentioned above is discussed. CAPPI-V r was produced by a Cressman-type interpolation of PPI-V r. In general, the centroid of observation grid points inside the influence ellipsoid represents CAPPI-V r at the analysis grid point. The error of CAPPI-V r tends Fig. 4. (a) Observation grid points of PPI-V r from each radar around a 2 2 km horizontal square centered on the wind profiler (WPR), projected to a west east cross section. Red squares, green circles, and blue triangles denote the observation grid points from Anjo, Bisai, and Suzuka, respectively. Black asterisks and gray rhombuses indicate the observation grid points of WPR and the analysis grid points of PPI-VAR and CAPPI-VAR, respectively. (b) Mean relative vertical distance from an analysis grid point to centroid of observation grid points inside the influence ellipsoid of CAPPI-V r for each radar (red squares: Anjo, green circles: Bisai, blue triangles: Suzuka). (c) Mean vertical distance between an analysis grid point and observation grid points inside the analysis grid of PPI-VAR from all radars.

4 218 Shimose et al., Observation Operators on Wind Speed Retrieved by Multiple-Doppler Analysis to be larger when RVD becomes large, i.e., when the observation grid points are distributed unevenly and are far from the analysis grid point inside the influence ellipsoid. This error is the so-called representative error and it is likely to appear when PPI-V r inside the influence ellipsoid is not uniform. Actually, when RVD of Suzuka at 500 m AGL was large and there was a difference in the mean WS WPR at m AGL (2.7 m s 1 ), the error of WS CAPPI-VAR at 500 m AGL was large. This result suggested that the representative error of CAPPI-V r from Suzuka at 500 m AGL was probably large. CAPPI-VAR used CAPPI-V r from each of the three radars equally; thus, CAPPI-V r from Suzuka might have caused the performance degradation of CAPPI-VAR at 500 m AGL. The relationship between the error factor of WS PPI-VAR and the distribution of observation grid points at 500 m AGL is discussed. Unlike CAPPI-VAR, PPI-VAR used PPI-V r inside the analysis grid from all radars, simultaneously. The small MVD at 500 m AGL, as shown in Fig. 4c, indicates that observation grid points were dense in the vicinity of 500 m AGL. Specifically, the numbers of observation grid points from Anjo and Bisai in the vicinity of 500 m AGL were larger than from Suzuka and Bisai around 800 m AGL (Fig. 4a). Therefore, PPI-VAR was much affected from PPI-V r in the vicinity of 500 m AGL rather than around 800 m AGL. For PPI-VAR, the contamination of the representative error caused by PPI-V r around 800 m AGL could be reduced; therefore, the accuracy of WS PPI-VAR was better than that of WS CAPP-VAR. To verify the above discussions can be identified in actuality, two cases were investigated in detail (the detailed results are described in the supplementary materials). One case involved a large difference in wind speed at m AGL (hereafter, LD case) and the other involved a small difference in wind speed at m AGL (hereafter, SD case). In the LD case, the error of WS CAPPI-VAR at 500 m AGL was larger than that of the warm seasons of the three years, whereas the error of WS PPI-VAR at 500 m AGL was similar to that of the warm seasons of the three years. In the SD case, the errors of WS PPI-VAR and WS CAPPI-VAR at 500 m AGL were small and similar to the error of WS PPI-VAR at 500 m AGL of the warm seasons of the three years. These results suggested that the error of WS CAPPI-VAR at 500 m AGL became larger for greater differences in wind speed at m AGL. From the above discussions considering wind retrieval at 500 m AGL, PPI-VAR should be more accurate than CAPPI-VAR when the representative error of CAPPI-V r from a certain radar is large. This error becomes large when values of PPI-V r from a certain radar inside the influence ellipsoid are distributed unevenly and are far from the analysis level, and when greater vertical differences in wind speed exist across the analysis level. The error factor above 1000 m AGL could be explained by the similar error factor at 500 m AGL; hence, this subject will be discussed in future work. 4. Summary To investigate the impact of observation operators on the analysis of low-level wind speed, an evaluation of wind speeds retrieved by variational multiple-doppler analyses using radial velocities based on the formats of both a Plan Position Indicator (PPI-VAR) and a Constant Altitude Plan Position Indicator (CAPPI-VAR) was performed for comparison with wind speeds observed by a wind profiler during the warm seasons of three consecutive years. The statistical analysis showed that PPI-VAR was more accurate than CAPPI-VAR at 500 m AGL, where the observation grid points were dense, and the RMSE of WS PPI-VAR and WS CAPPI-VAR at this level were 1.6 and 2.0 m s 1, respectively. One of the error factors of WS CAPPI-VAR at 500 m AGL was the representative error of CAPPI-V r. Although the analysis grid point at 500 m AGL, used for the evaluation in this study, was not far from each radar, the centroid of the observation grid points inside the influence ellipsoid of CAPPI-V r for one radar was far from the analysis grid point. Therefore, CAPPI-V r at 500 m AGL from one radar could have been affected by the representative error through the interpolation procedure. This error became more obvious the greater the vertical difference in wind speed across the analysis level. CAPPI-VAR used CAPPI-V r from each of the three radars equally; hence, CAPPI-V r from one radar might have caused the performance degradation of CAPPI-VAR at 500 m AGL. Conversely, PPI-VAR used PPI-V r inside the analysis grid from all radars, simultaneously. Observation grid points were dense in the vicinity of 500 m AGL; thus, PPI-VAR was much affected by PPI-V r in the vicinity of 500 m AGL rather than far from the analysis grid point. In PPI-VAR, the contamination of the representative error caused by PPI-V r far from 500 m AGL might be reduced; therefore, the accuracy of WS PPI-VAR was better than that of WS CAPP-VAR. To reduce the analysis error caused by the representative error, radar volume scans with a large number of elevation angles from at least two radars is required. In the near future, if radar volume scans with suitably large numbers of elevation angles could be achieved using phased-array Doppler radar, it is expected that wind speeds could be obtained more accurately at any level. Acknowledgements The authors, as part of the research consortium on the technological development of MLIT s X-band multi-parameter radar, thank the Ministry of Land, Infrastructure, Transport, and Tourism (MLIT) for providing data from the MLIT s X-band radars. The DIAS data set is archived and provided under the framework of the Data Integration and Analysis System (DIAS), through the National Key Technology, Marine Earth Observation Exploration System. This work was supported by the Council for Science, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), and Enhancement of societal resiliency against natural disasters (Funding agency: JST). Edited by: H. Hashiguchi References Armijo, L., 1969: A theory for the determination of wind and precipitation velocities with Doppler radars. J. Atmos. Sci., 26, Bousquet, O., and M. Chong, 1998: A multiple-doppler synthesis and continuity adjustment technique (MUSCAT) to recover wind components from Doppler radar measurements. J. Atmos. Oceanic Technol., 15, Chong, M., and J. Testud, 1983: Three-dimensional wind field analysis from dual-doppler radar data. Part III: The boundary condition: An optimum determination based on a variational concept. J. Climate Appl. Meteor., 22, Chong, M., J. Testud, and F. Roux, 1983: Three-dimensional wind field analysis from dual-doppler radar data. Part II: Minimizing the error due to temporal variation. J. Climate Appl. Meteor., 22, Cressman, G. P., 1959: An operational objective analysis system. Mon. Wea. Rev., 87, Doviak, R. J., P. S. Ray, R. G. Strauch, and L. J. Miller, 1976: Error estimation in wind fields derived from dual-doppler radar measurement. J. Appl. Meteor., 15, Gao, J., J. Chou, and L. Zhi, 1995: A method for determining the spatial structure of meteorological variable from the temporal evolution of observational data. Chinese J. Atmos. Sci., 19, (in Chinese). Gao, J., M. Xue, A. Shapiro, and K. K. Droegemeier, 1999: A variational method for the analysis of three-dimensional wind fields from two Doppler radars. Mon. Wea. Rev., 127, Gao, J., M. Xue, K. Brewster, and K. K. Droegemeier, 2004: A three-dimensional variational data analysis method with recursive filter for Doppler radars. J. Atmos. Oceanic Technol., 21,

5 219 Kato, Y., T. Abo, K. Kobayashi, Y. Izumikawa, and M. Ishihara, 2003: The wind profiler network of the Japan Meteorological Agency. Tenki, 50, (in Japanese). Kim, D.-S., M. Maki, S. Shimizu, and D.-I. Lee, 2012: X-band dual-polarization radar observations of precipitation core development and structure in a multi-cellular storm over Zoshigaya, Japan, on August 5, J. Meteor. Soc. Japan, 90, Liou, Y.-C., and Y.-J. Chang, 2009: A variational multiple-doppler radar three-dimensional wind synthesis method and its impacts on thermodynamic retrieval. Mon. Wea. Rev., 137, Liou, Y.-C., S.-F. Chang, and J. Sun, 2012: An application of the immersed boundary method for recovering the threedimensional wind fields over complex terrain using multiple- Doppler radar data. Mon. Wea. Rev., 140, Maesaka, T., M. Maki, K. Iwanami, S. Tsuchiya, K. Kieda, and A. Hoshi, 2011: Operational rainfall estimation by X-band MP radar network in MLIT, Japan. Proc. 35th Conf. on Radar Meteorology, PA, Amer. Meteor. Soc Potvin, C. K., A. Shapiro, and M. Xue, 2012a: Impact of a vertical vorticity constraint in variational dual-doppler wind analysis: Tests with real and simulated supercell data. J. Atmos. Oceanic Technol., 29, Potvin, C. K., L. J. Wicker, and A. Shapiro, 2012b: Assessing errors in variational dual-doppler wind syntheses of supercell thunderstorms observed by storm-scale mobile radars. J. Atmos. Oceanic Technol., 29, Potvin, C. K., D. Betten, L. J. Wicker, K. L. Elmore, and M. I. Biggerstaff, 2012c: 3DVAR vs. traditional dual-doppler wind retrievals of a simulated supercell thunderstorm. Mon. Wea. Rev., 140, Ray, P. S., R. J. Doviak, G. B. Walker, D. Sirmans, J. Carter, and B. Bumgarner, 1975: Dual-Doppler observations of a tornadic storm. J. Appl. Meteor., 14, Ray, P. S., K. K. Wagner, K. W. Johnson, J. J. Stephens, W. C. Bumgarner, and E. A. Mueller, 1978: Triple-Doppler observations of a convective storm. J. Appl. Meteor., 17, Ray, P. S., C. L. Ziegler, W. Bumgarner, and R. J. Serafin, 1980: Single- and multiple-doppler radar observations of tornadic storms. Mon. Wea. Rev., 108, Shapiro, A., and J. J. Mewes, 1999: New formulations of dual- Doppler wind analysis. J. Atmos. Oceanic Technol., 16, Shapiro, A., C. K. Potvin, and J. Gao, 2009: Use of a vertical vorticity equation in variational dual-doppler wind analysis. J. Atmos. Oceanic Technol., 26, Shimizu, S., H. Uyeda, Q. Moteki, T. Maesaka, M. Takaya, K. Akaeda, T. Kato, and M. Yoshizaki, 2008: Structure and formation mechanism of 24 May 2000 supercell-like thunderstorm observed over Kanto plain, Japan. Mon. Wea. Rev., 136, Sun, J., and N. A. Crook, 1997: Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part I: Model development and simulated data experiments. J. Atmos. Sci., 54, Sun, J., and N. A. Crook, 1998: Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part II: Retrieval experiments of an observed Florida convective storm. J. Atmos. Sci., 55, Testud, J. D., and M. Chong, 1983: Three-dimensional wind field analysis from dual-doppler radar data. Part I: Filtering, interpolation and differentiating the raw data. J. Climate Appl. Meteor., 22, Wilson, J. W., R. D. Roberts, C. Kessinger, and J. McCarthy, 1984: Microburst wind structure and evaluation of Doppler radar for airport wind shear detection. J. Appl. Meteor., 23, Wurman, J., and K. Kosiba, 2013: Finescale radar observations of tornado and mesocyclone structures. Wea. Forecasting, 28, Manuscript received 7 April 2016, accepted 27 June 2016 SOLA: jstage. jst. go. jp/browse/sola/