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# Three-Dimensional Wind Field Retrieved from Dual-Doppler Radar Based on a Variational Method: Refinement of Vertical Velocity Estimates

• In this paper, a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps. First, the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method, avoiding a weighting parameter specification step. Compared with conventional dual-Doppler wind synthesis approaches, this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process, which is one of the main sources of errors. Then, through the accelerated Liebmann method, the vertical velocity is further re-estimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause. The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation. Compared with the method proposed by O'Brien, this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability. Furthermore, the method proposed in this paper is applied to Doppler radar observation of a squall line process. It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display (VAD) method, and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations. There is a good correspondence between the divergence field of the derived wind field and the vertical velocity. And, the horizontal and vertical circulations within and around the squall line, as well as strong updrafts, the associated downdrafts, and associated rear inflow of the bow echo, are analyzed well. It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations.
摘要: 本文提出了一种基于变分法的双多普勒雷达反演三维风场的分析方案。首先，在笛卡尔坐标系下，采用标准共轭梯度法极小化由三维格点风场与雷达径向速度的强约束关系构建的代价函数，直接求解得到水平风场。与传统方法相比，该变分法避免了迭代求解过程中从雷达观测位置到分析网格的多次插值带来的误差，这通常是误差的主要来源之一。然后，采用加速利布曼方法求解由垂直速度的二阶导数构成的泊松方程，直接得到垂直速度。该方法不采用质量连续性方程进行显式垂直积分，避免了传统方法积分过程中的误差积累以及对垂直速度的任意订正。与O'Brien提出的方法相比，该方法对边界的不确定性较不敏感，具有较好的稳定性和可靠性。最后，应用本文提出的方法对一次飑线过程进行风场反演，结果表明反演的风场垂直廓线与VAD风廓线有很好的一致性，反演的径向速度基本保留了实际观测到的飑线正负速度中心和水平风切变。反演风场的散度场和垂直速度有很好的对应关系，并且很好地分析出了飑线内部和周围的环流，包括强上升气流、相关的下降气流和弓形回波顶端后部的强后侧入流，得到了合理的飑线动力结构。值得一提的是，本文的反演方法可以同时对两部及两部以上的雷达进行风场反演。
• Figure 1.  A schematic view of the geometry of a ground-based radar in the Cartesian coordinate system (r is the distance between the target and the radar, $\theta$ is the azimuth angle, $\varphi$ is the elevation angle, and $u$, v, and ${w}'$ are the velocity components in the x, y, and z directions, respectively).

Figure 2.  WRF model domain (solid box), dual-Doppler analysis domain (dashed box), and positions of two assumed radars (marked by hollow five-pointed star).

Figure 3.  The WRF model-simulated supercell storm (a, b) at 30 min and retrieved field (c, d) from two virtual Doppler radars denoted in Fig. 2. (a, c) Horizontal wind vectors (arrow, m s−1; the scale is in the bottom-left corner), vertical velocity (contours every 3 m s−1) and simulated reflectivity (shaded, dBZ) at 2.5 km above ground level (AGL). (b, d) Vertical cross section of synthesized wind field (horizontal and vertical wind vectors projected onto the cross section, arrow, m s−1), vertical velocity (contours, solid line for upward every 3 m s−1 and dashed line for downward every 2 m s−1) and simulated reflectivity (shaded, dBZ) along line A–B in (a, c).

Figure 4.  Error distribution of vertical velocity obtained from model-simulated horizontal wind by scheme SO, DO, SP, DP, and DPE compared with simulated vertical velocity at each level. (a) Mean absolute error MAE (m s−1). (b) Correlation coefficient CC. (c) Root-mean-square error RMS_W (m s−1). (d) Relative root-mean-square error RRE_W.

Figure 5.  As in Fig. 4, but for vertical velocity derived from two virtual Doppler radars denoted in Fig. 2.

Figure 6.  Locations of Nanchang and Fuzhou radar stations (solid five-pointed star) that observed the squall line on 11 May 2017 and the dual-Doppler analysis domain (solid box) with terrain heights (shaded and contoured every 250 m). The dotted circles denote the 150 km range of measurement while it is suitable to perform wind synthesis in the non-overlapping domain of two solid cycles. The grid point marked with an asterisk represents the position 47 km away from the Nanchang radar. The red dots indicate the mosaic of composite radar reflectivity greater than or equal to 45 dBZ at 1242 UTC 11 May 2017.

Figure 7.  Hodographs showing the wind profile (black solid line) retrieved from dual-Doppler radar observations and the VAD wind profile (grey solid line) of the Nanchang radar at 1242 UTC 11 May 2017. The black dashed and gray dashed lines represent the vertical 1–3.5 km wind shear based on the retrieved wind profile and the VAD wind profile, respectively. The position of the retrieved wind profile is shown in Fig. 6.

Figure 8.  The observed radial velocity (a, c, shaded, m s−1, positive away from and negative toward the radar) at 1.45° elevation angle from the Nanchang (a, b) and Fuzhou (c, d) radars and the retrieved radial velocity (b, d, shaded, m s−1) based on the derived wind from dual-Doppler radar data according to Eq. (1) at 1242 UTC 11 May 2017. The locations of the Nanchang and Fuzhou radars are shown in Fig. 6. The black arrow represents the heading of the squall line while the red ellipse indicates the positions of the positive and negative velocity centers and the horizontal wind shear. The negative values of x- and y-axis represent the west and south sides of the radar.

Figure 9.  Scattergraph of the observed–retrieved radial velocity comparisons from all elevation angles of the Nanchang (a) and Fuzhou (b) radars, with the concentration (0–1) represented by different colors of the scatters.

Figure 10.  Evolution of the squall line together with radar reflectivity, horizontal storm-relative wind field, horizontal divergence, and vertical velocity retrieved from dual-Doppler radar observations at (a–c) 1224 UTC 11 May, (d–f) 1242 UTC 11 May, and (g–i) 1300 UTC 11 May. (a), (d), (g) Horizontal storm-relative wind vectors (arrow, m s−1; the scale is in the bottom-right corner) and radar reflectivity (shaded, dBZ) at 2.5 km AGL. The blue solid lines describe horizontal storm-relative winds of 20 m s−1 and 24 m s−1. (b), (e), (h) Vertical velocity (shaded, m s−1; positive for upward and negative for downward) and horizontal divergence (contours, 10−4 s−1; dashed line for convergence, solid line for divergence) at 2.5 km AGL. (c), (f), (i) Vertical cross section of the synthesized wind field (storm-relative wind vectors projected onto the cross section, arrow, m s−1), vertical velocity (contours, solid line for upward and dashed line for downward; every 5 m s−1), and radar reflectivity (shaded, dBZ) along line A–B in (a), respectively. The thick gray solid line represents the updraft and downdraft.

•  Armijo, L., 1969: A theory for the determination of wind and precipitation velocities with doppler radars. J. Atmos. Sci., 26, 570−573, https://doi.org/10.1175/1520-0469(1969)026<0570:ATFTDO>2.0.CO;2. Boucher, R. J., R. Wexler, D. Atlas, and R. M. Lhermitte, 1965: Mesoscale wind structure revealed by doppler radar. J. Appl. Meteor., 4, 590−597, https://doi.org/10.1175/1520-0450(1965)004<0590:MWSRBD>2.0.CO;2. 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, 343−359, https://doi.org/10.1175/1520-0426(1998)015<0343:AMDSAC>2.0.CO;2. Caton, P. G., 1963: The measurement of wind and convergence by doppler radar. Proc. 10th Weather Radar Conf., Washington DC, Amer. Meteor. Soc., 290−296. Chong, M., and C. Campos, 1996: Extended overdetermined dual-doppler formalism in synthesizing airborne doppler radar data. J. Atmos. Oceanic Technol., 13, 581−597, https://doi.org/10.1175/1520-0426(1996)013<0581:EODDFI>2.0.CO;2. Chong, M., and S. Cosma, 2000: A formulation of the continuity equation of MUSCAT for either flat or complex terrain. J. Atmos. Oceanic Technol., 17, 1556−1565, https://doi.org/10.1175/1520-0426(2000)017<1556:AFOTCE>2.0.CO;2. Chong, M., and O. Bousquet, 2001: On the application of MUSCAT to a ground-baseddual-Doppler radar system. Meteor. Atmos. Phys., 78, 133−139, https://doi.org/10.1007/s007030170011. Cressman, G. P., 1959: An operational objective analysis system. Mon. Wea. Rev., 87, 367−374, https://doi.org/10.1175/1520-0493(1959)087<0367:AOOAS>2.0.CO;2. Foote, G. B., and P. S. Du Toit, 1969: Terminal velocity of raindrops aloft. J. Appl. Meteor., 8, 249−253, https://doi.org/10.1175/1520-0450(1969)008<0249:TVORA>2.0.CO;2. Fujita, T. T., 1978: Manual of downburst identification for Project NIMROD. SMRP Res. Paper, 156, 104 pp. Fujita, T. T., 1979: Objectives, operation, and results of Project NIMROD. Preprints, 11th Conf. on Severe Local Storms, Kansas City, Amer. Meteor. Soc., 259−266. Gao, J. D., 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, 2128−2142, https://doi.org/10.1175/1520-0493(1999)127<2128:AVMFTA>2.0.CO;2. Gao, J. D., M. Xue, A. Shapiro, Q. Xu, and K. K. Droegemeier, 2001: Three-dimensional simple adjoint velocity retrievals from single-Doppler radar. J. Atmos. Oceanic Technol., 18, 26−38, https://doi.org/10.1175/1520-0426(2001)018<0026:TDSAVR>2.0.CO;2. Klemp, J. B., and R. Rotunno, 1983: A study of the tornadic region within a supercell thunderstorm. J. Aeronaut. Sci., 40, 359−377, https://doi.org/10.1175/1520-0469(1983)040<0359:ASOTTR>2.0.CO;2. Koscielny, A. J., R. J. Doviak, and R. Rabin, 1982: Statistical considerations in the estimation of divergence from single-Doppler radar and application to prestorm boundary-layer observations. J. Appl. Meteor., 21, 197−210, https://doi.org/10.1175/1520-0450(1982)021<0197:SCITEO>2.0.CO;2. Laroche, S., and I. Zawadzki, 1994: A variational analysis method for retrieval of three-dimensional wind field from single-Doppler radar data. J. Atmos. Sci., 51, 2664−2682, https://doi.org/10.1175/1520-0469(1994)051<2664:AVAMFR>2.0.CO;2. Lateef, M. A., 1967: Vertical motion, divergence, and vorticity in the troposphere over the caribbean, August 3-5:1963. Mon. Wea. Rev., 95, 778−790, https://doi.org/10.1175/1520-0493(1967)095<0778:VMDAVI>2.3.CO;2. Lhermitte, R. M., and D. Atlas, 1961: Precipitation motion by pulse Doppler radar. Preprints, 9th Conf. on Radar Meteorology, Kansas City, KS, Amer. Meteor. Soc., 218−223. Liebmann, H., 1918: Die angenäherte Ermittelung harmonischer Funktionen und konformer Abbildungen. Sitzungsberichte der math. -phys. Klasse, Bayer. Akademie der Wissenschaften, München, 385−416. (in German) 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, 3992−4010, https://doi.org/10.1175/2009MWR2980.1. Liou, Y.-C., S.-F. Chang, and J. Z. Sun, 2012: An application of the immersed boundary method for recovering the three-dimensional wind fields over complex terrain using multiple-Doppler radar data. Mon. Wea. Rev., 140, 1603−1619, https://doi.org/10.1175/MWR-D-11-00151.1. Liou, Y.-C., P.-C. Yang, and W.-Y. Wang, 2019: Thermodynamic recovery of the pressure and temperature fields over complex terrain using wind fields derived by multiple-Doppler radar synthesis. Mon. Wea. Rev., 147, 3843−3857, https://doi.org/10.1175/MWR-D-19-0059.1. Liu, S., C. J. Qiu, Q. Xu, P. F. Zhang, J. D. Gao, and A. M. Shao, 2005: An improved method for Doppler wind and thermodynamic retrievals. Adv. Atmos. Sci., 22, 90−102, https://doi.org/10.1007/BF02930872. Meng, Z. Y., F. Q. Zhang, P. Markowski, D. C. Wu, and K. Zhao, 2012: A modeling study on the development of a bowing structure and associated rear inflow within a squall line over South China. J. Atmos. Sci., 69, 1182−1207, https://doi.org/10.1175/JAS-D-11-0121.1. Miller, L. J., and R. G. Strauch, 1974: A dual Doppler radar method for the determination of wind velocities within precipitating weather systems. Remote Sens. Environ., 3, 219−235, https://doi.org/10.1016/0034-4257(74)90044-3. O'Brien, J. J., 1970: Alternative solutions to the classical vertical velocity problem. J. Appl. Meteor., 9, 197−203, https://doi.org/10.1175/1520-0450(1970)009<0197:ASTTCV>2.0.CO;2. Ogura, Y., and N. A. Phillips, 1962: Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19, 173−179, https://doi.org/10.1175/1520-0469(1962)019<0173:SAODAS>2.0.CO;2. Qiu, C.-J., and Q. Xu, 1992: A simple adjoint method of wind analysis for single-Doppler data. J. Atmos. Oceanic Technol., 9, 588−598, https://doi.org/10.1175/1520-0426(1992)009<0588:ASAMOW>2.0.CO;2. Qiu, C.-J., and Q. Xu, 1996: Least squares retrieval of microburst winds from single-Doppler radar data. Mon. Wea. Rev., 124, 1132−1144, https://doi.org/10.1175/1520-0493(1996)124<1132:LSROMW>2.0.CO;2. Ray, P. S., and K. L. Sangren, 1983: Multiple-Doppler radar network design. J. Climate Appl. Meteor., 22, 1444−1454, https://doi.org/10.1175/1520-0450(1983)022<1444:MDRND>2.0.CO;2. Ray, P. S., R. J. Doviak, G. B. Walker, D. Sirmans, J. Carter, and B. Bumgarner, 1975: Dual-Doppler observation of a tornadic storm. J. Appl. Meteor., 14, 1521−1530, https://doi.org/10.1175/1520-0450(1975)014<1521:DDOOAT>2.0.CO;2. 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, 1201−1212, https://doi.org/10.1175/1520-0450(1978)017<1201:TDOOAC>2.0.CO;2. Ray, P. S., J. J. Stephens, and K. W. Johnson, 1979: Multiple-Doppler radar network design. J. Appl. Meteor., 18, 706−710, https://doi.org/10.1175/1520-0450(1979)018<0706:MDRND>2.0.CO;2. 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, 1607−1625, https://doi.org/10.1175/1520-0493(1980)108<1607:SAMDRO>2.0.CO;2. Ray, P. S., and Coauthors, 1981: The morphology of several tornadic storms on 20 May 1977. J. Atmos. Sci., 38, 1643−1663, https://doi.org/10.1175/1520-0469(1981)038<1643:TMOSTS>2.0.CO;2. Richardson, L. F., 1911: IX. The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam. Philosophical Transactions of the Royal Society A: Mathematical. Physical and Engineering Sciences, 210, 459−470, https://doi.org/10.1098/rsta.1911.0009. Schenkman, A. D., M. Xue, A. Shapiro, K. Brewster, and J. D. Gao, 2011: Impact of CASA radar and oklahoma mesonet data assimilation on the analysis and prediction of tornadic mesovortices in an MCS. Mon. Wea. Rev., 139, 3422−3445, https://doi.org/10.1175/MWR-D-10-05051.1. Shapiro, A., C. K. Potvin, and J. D. Gao, 2009: Use of a vertical vorticity equation in variational dual-Doppler wind analysis. J. Atmos. Oceanic Technol., 26, 2089−2106, https://doi.org/10.1175/2009JTECHA1256.1. Skamarock, W. C., and Coauthors, 2008: A description of the advanced research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp. Waldteufel, P., and H. Corbin, 1979: On the analysis of single-Doppler radar data. J. Appl. Meteor., 18, 532−542, https://doi.org/10.1175/1520-0450(1979)018<0532:OTAOSD>2.0.CO;2. Weisman, M. L., 1992: The role of convectively generated rear-inflow jets in the evolution of long-lived mesoconvective systems. J. Atmos. Sci., 49, 1826−1847, https://doi.org/10.1175/1520-0469(1992)049<1826:TROCGR>2.0.CO;2. Weisman, M. L., 1993: The genesis of severe, long-lived bow echoes. J. Atmos. Sci., 50, 645−670, https://doi.org/10.1175/1520-0469(1993)050<0645:TGOSLL>2.0.CO;2. Weisman, M. L., and J. B. Klemp, 1982: The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon. Wea. Rev., 110, 504−520, https://doi.org/10.1175/1520-0493(1982)110<0504:TDONSC>2.0.CO;2. Wilhelmson, R. B., and J. B. Klemp, 1981: A three-dimensional numerical simulation of splitting severe storms on 3 April 1964. J. Atmos. Sci., 38, 1581−1600, https://doi.org/10.1175/1520-0469(1981)038<1581:ATDNSO>2.0.CO;2. Xu, Q., and C.-J. Qiu, 1995: Adjoint-method retrievals of low-altitude wind fields from single-Doppler reflectivity and radial-wind data. J. Atmos. Oceanic Technol., 12, 1111−1119, https://doi.org/10.1175/1520-0426(1995)012<1111:AMROLA>2.0.CO;2. Xu, Q., C.-J. Qiu, and J.-X. Yu, 1994: Adjoint-method retrievals of low-altitude wind fields from single-doppler wind data. J. Atmos. Oceanic Technol., 11, 579−585, https://doi.org/10.1175/1520-0426(1994)011<0579:AMROLA>2.0.CO;2. Xu, Q., C.-J. Qiu, H.-D. Gu, and J.-X. Yu, 1995: Simple adjoint retrievals of microburst winds from single-Doppler radar data. Mon. Wea. Rev., 123, 1822−1833, https://doi.org/10.1175/1520-0493(1995)123<1822:SAROMW>2.0.CO;2. Zhang, J., and S. X. Wang, 2006: An automated 2D multipass Doppler radar velocity dealiasing scheme. J. Atmos. Oceanic Technol., 23, 1239−1248, https://doi.org/10.1175/JTECH1910.1.
•  [1] Kong Fanyou, Mao jietai, 1994: A Model Study of Three Dimensional Wind Field Analysis from Dual-Doppler Radar Data, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 162-174.  doi: 10.1007/BF02666543 [2] Guanshun ZHANG, Jiangyu MAO, Yimin LIU, Guoxiong WU, 2021: PV Perspective of Impacts on Downstream Extreme Rainfall Event of a Tibetan Plateau Vortex Collaborating with a Southwest China Vortex, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1835-1851.  doi: 10.1007/s00376-021-1027-9 [3] Hongli LI, Xiangde XU, 2017: Application of a Three-dimensional Variational Method for Radar Reflectivity Data Correction in a Mudslide-inducing Rainstorm Simulation, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 469-481.  doi: 10.1007/s00376-016-6010-5 [4] Wei Ming, Dang Renqing, Ge Wenzhong, Takao Takeda, 1998: Retrieval Single-Doppler Radar Wind with Variational Assimilation Method-Part I: Objective Selection of Functional Weighting Factors, ADVANCES IN ATMOSPHERIC SCIENCES, 15, 553-568.  doi: 10.1007/s00376-998-0032-6 [5] Ma Yimin, 1992: Preliminary Study on Vertical Velocity Caused by Katabatic Wind in Antarctica and Its Influence on Atmospheric Circulation, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 247-250.  doi: 10.1007/BF02657515 [6] SHUN Liu, QIU Chongjian, XU Qin, ZHANG Pengfei, GAO Jidong, SHAO Aimei, 2005: An Improved Method for Doppler Wind and Thermodynamic Retrievals, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 90-102.  doi: 10.1007/BF02930872 [7] ZHANG Lei, QIU Chongjian, HUANG Jianping, 2008: A Three-Dimensional Satellite Retrieval Method for Atmospheric Temperature and Moisture Profiles, ADVANCES IN ATMOSPHERIC SCIENCES, 25, 897-904.  doi: 10.1007/s00376-008-0897-4 [8] Fu Baopu, 1987: VARIATION IN WIND VELOCITY OVER WATER, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 93-104.  doi: 10.1007/BF02656665 [9] ZHAO Kun, LIU Guoqing, GE Wenzhong, DANG Renqing, Takao TAKEDA, 2003: Retrieval of Single-Doppler Radar Wind Field by Nonlinear Approximation, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 195-204.  doi: 10.1007/s00376-003-0004-9 [10] LIU Ye, YAN Changxiang, 2010: Application of a Recursive Filter to a Three-Dimensional Variational Ocean Data Assimilation System, ADVANCES IN ATMOSPHERIC SCIENCES, 27, 293-302.  doi: 10.1007/s00376-009-8112-9 [11] ZENG Zhihua, DUAN Yihong, LIANG Xudong, MA Leiming, Johnny Chung-leung CHAN, 2005: The Effect of Three-Dimensional Variational Data Assimilation of QuikSCAT Data on the Numerical Simulation of Typhoon Track and Intensity, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 534-544.  doi: 10.1007/BF02918486 [12] Chaoqun MA, Tijian WANG, Zengliang ZANG, Zhijin LI, 2018: Comparisons of Three-Dimensional Variational Data Assimilation and Model Output Statistics in Improving Atmospheric Chemistry Forecasts, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 813-825.  doi: 10.1007/s00376-017-7179-y [13] LI Yan, ZHU Jiang, WANG Hui, 2013: The Impact of Different Vertical Diffusion Schemes in a Three-Dimensional Oil Spill Model in the Bohai Sea, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1569-1586.  doi: 10.1007/s00376-012-2201-x [14] Xu Hui, Zhang Weiping, Lang Xuxing, Guo Xia, Ge Wenzhong, Dang Renqing, TakaoTakeda, 2000: The Use of Dual-Doppler Radar Data in the Study of 1998 Meiyu Frontal Precipitation in Huaihe River Basin, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 403-412.  doi: 10.1007/s00376-000-0032-7 [15] SHAO Aimei, QIU Chongjian, LIU Liping, 2004: Kinematic Structure of a Heavy Rain Event from Dual-Doppler Radar Observations, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 609-616.  doi: 10.1007/BF02915728 [16] ZHANG Chengwei, YU Fan, WANG Chenxi, YANG Jianyu, 2011: Three-dimensional Extension of the Unit-Feature Spatial Classification Method for Cloud Type, ADVANCES IN ATMOSPHERIC SCIENCES, 28, 601-611.  doi: 10.1007/s00376-010-9056-9 [17] Xin LI, Mingjian ZENG, Yuan WANG, Wenlan WANG, Haiying WU, Haixia MEI, 2016: Evaluation of Two Momentum Control Variable Schemes and Their Impact on the Variational Assimilation of Radar Wind Data: Case Study of a Squall Line, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 1143-1157.  doi: 10.1007/s00376-016-5255-3 [18] Leilei KOU, Zhuihui WANG, Fen XU, 2018: Three-dimensional Fusion of Spaceborne and Ground Radar Reflectivity Data Using a Neural Network-Based Approach, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 346-359.  doi: 10.1007/s00376-017-6334-9 [19] Xingchao CHEN, Kun ZHAO, Juanzhen SUN, Bowen ZHOU, Wen-Chau LEE, 2016: Assimilating Surface Observations in a Four-Dimensional Variational Doppler Radar Data Assimilation System to Improve the Analysis and Forecast of a Squall Line Case, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 1106-1119.  doi: 10.1007/s00376-016-5290-0 [20] Federico OTERO, Diego C. ARANEO, 2022: Forecasting Zonda Wind Occurrence with Vertical Sounding Data, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 161-177.  doi: 10.1007/s00376-021-1007-0

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## Manuscript History

Manuscript received: 25 January 2021
Manuscript revised: 21 June 2021
Manuscript accepted: 30 June 2021
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

## Three-Dimensional Wind Field Retrieved from Dual-Doppler Radar Based on a Variational Method: Refinement of Vertical Velocity Estimates

###### Corresponding author: Zhiying DING, dingzhiying@nuist.edu.cn;
• 1. Key Laboratory of Meteorological Disaster, Ministry of Education/Joint International Research Laboratory of Climate and Environment Change/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China
• 2. Jiangxi Meteorological Observatory, Nanchang 330096, China
• 3. Guangdong Province Key Laboratory of Regional Numerical Weather Prediction, Institute of Tropical and Marine Meteorology, CMA, Guangzhou 510080, China
• 4. Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519082, China
• 5. Jiangxi Institute of Land and Space Survey and Planning/Jiangxi Geomatics Center, Nanchang 330000, China

Abstract: In this paper, a scheme of dual-Doppler radar wind analysis based on a three-dimensional variational method is proposed and performed in two steps. First, the horizontal wind field is simultaneously recovered through minimizing a cost function defined as a radial observation term with the standard conjugate gradient method, avoiding a weighting parameter specification step. Compared with conventional dual-Doppler wind synthesis approaches, this variational method minimizes errors caused by interpolation from radar observation to analysis grid in the iterative solution process, which is one of the main sources of errors. Then, through the accelerated Liebmann method, the vertical velocity is further re-estimated as an extra step by solving the Poisson equation with impermeable conditions imposed at the ground and near the tropopause. The Poisson equation defined by the second derivative of the vertical velocity is derived from the mass continuity equation. Compared with the method proposed by O'Brien, this method is less sensitive to the uncertainty of the boundary conditions and has better stability and reliability. Furthermore, the method proposed in this paper is applied to Doppler radar observation of a squall line process. It is shown that the retrieved vertical wind profile agrees well with the vertical profile obtained with the velocity–azimuth display (VAD) method, and the retrieved radial velocity as well as the analyzed positive and negative velocity centers and horizontal wind shear of the squall line are in accord with radar observations. There is a good correspondence between the divergence field of the derived wind field and the vertical velocity. And, the horizontal and vertical circulations within and around the squall line, as well as strong updrafts, the associated downdrafts, and associated rear inflow of the bow echo, are analyzed well. It is worth mentioning that the variational method in this paper can be applied to simultaneously synthesize the three-dimensional wind field from multiple-Doppler radar observations.

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