• Anderson, J. L., 2012: Localization and sampling error correction in ensemble Kalman filter data assimilation. Mon. Wea. Rev., 140, 23592371, doi:10.1175/MWR-D-11-00013.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Asai, T., 1965: A numerical study of the air-mass transformation over the Japan Sea in winter. J. Meteor. Soc. Japan, 43, 115.

  • Aydin, K., T. A. Seliga, and V. Balaji, 1986: Remote sensing of hail with a dual linear polarization radar. J. Climate Appl. Meteor., 25, 14751484, doi:10.1175/1520-0450(1986)025<1475:RSOHWA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Aydin, K., Y. Zhao, and T. A. Seliga, 1990: A differential reflectivity radar hail measurement technique: Observations during the Denver hailstorm of 13 June 1984. J. Atmos. Oceanic Technol., 7, 104113, doi:10.1175/1520-0426(1990)007<0104:ADRRHM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Barker, D. M., W. Huang, Y. R. Guo, and Q. N. Xiao, 2004: A three-dimensional data assimilation system for MM5: Implementation and initial results. Mon. Wea. Rev., 132, 897914, doi:10.1175/1520-0493(2004)132<0897:ATVDAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Barker, D. M., and Coauthors, 2012: The Weather Research and Forecasting Model’s Community Variational/Ensemble Data Assimilation System: WRFDA. Bull. Amer. Meteor. Soc., 93, 831843, doi:10.1175/BAMS-D-11-00167.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brandes, E., and K. Ikeda, 2004: Freezing-level estimation with polarimetric radar. J. Appl. Meteor., 43, 15411553, doi:10.1175/JAM2155.1.

  • Brandes, E., G. Zhang, and J. Vivekanandan, 2002: Experiments in rainfall estimation with a polarimetric radar in a subtropical environment. J. Appl. Meteor., 41, 674685, doi:10.1175/1520-0450(2002)041<0674:EIREWA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi, V., V. Chandrasekar, J. Hubbert, E. Gorgucci, W. L. Randeu, and M. Schoenhuber, 2003: Raindrop size distribution in different climatic regimes from disdrometer and dual-polarized radar analysis. J. Atmos. Sci., 60, 354365, doi:10.1175/1520-0469(2003)060<0354:RSDIDC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carey, L., and S. Rutledge, 1998: Electrical and multiparameter radar observations of a severe hailstorm. J. Geophys. Res., 103, 13 97914 000, doi:10.1029/97JD02626.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carey, L., S. Rutledge, D. A. Ahijevych, and T. D. Keenan, 2000: Correcting propagation effects in C-band polarimetric radar observations of tropical convection using differential propagation phase. J. Appl. Meteor., 39, 14051433, doi:10.1175/1520-0450(2000)039<1405:CPEICB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Caya, A., J. Sun, and C. Snyder, 2005: A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation. Mon. Wea. Rev., 133, 30813094, doi:10.1175/MWR3021.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., V. Bringi, N. Balakrishnan, and D. Zrnić, 1990: Error structure of multiparameter radar and surface measurements of rainfall. Part III: Specific differential phase. J. Atmos. Oceanic Technol., 7, 621629, doi:10.1175/1520-0426(1990)007<0621:ESOMRA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chang, S.-F., Y.-C. Liou, J. Sun, and S.-L. Tai, 2016: The implementation of the ice-phase microphysical process into a four-dimensional Variational Doppler Radar Analysis System (VDRAS) and its impact on parameter retrieval and quantitative precipitation nowcasting. J. Atmos. Sci., 73, 10151038, doi:10.1175/JAS-D-15-0184.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Deierling, W., W. Petersen, J. Latham, S. Ellis, and H. Christian, 2008: The relationship between lightning activity and ice fluxes in thunderstorms. J. Geophys. Res., 113, D15210, doi:10.1029/2007JD009700.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dowell, D., F. Zhang, L. Wicker, C. Snyder, and A. Crook, 2004: Wind and temperature retrievals in the 17 May 1981 Arcadia, Oklahoma, supercell: Ensemble Kalman filter experiments. Mon. Wea. Rev., 132, 19822005, doi:10.1175/1520-0493(2004)132<1982:WATRIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dowell, D., L. Wicker, and C. Snyder, 2011: Ensemble Kalman filter assimilation of radar observations of the 8 May 2003 Oklahoma City supercell: Influences of reflectivity observations on storm-scale analyses. Mon. Wea. Rev., 139, 272294, doi:10.1175/2010MWR3438.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107, doi:10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, J., and D. Stensrud, 2012: Assimilation of reflectivity data in a convective-scale, cycled 3DVAR framework with hydrometeor classification. J. Atmos. Sci., 69, 10541065, doi:10.1175/JAS-D-11-0162.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, J., and D. Stensrud, 2014: Some observing system simulation experiments with a hybrid 3DEnVAR system for storm-scale radar data assimilation. Mon. Wea. Rev., 142, 33263346, doi:10.1175/MWR-D-14-00025.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ge, G., J. Gao, and M. Xue, 2012: Diagnostic pressure equation as a weak constraint in a storm-scale three-dimensional variational radar data assimilation system. J. Atmos. Oceanic Technol., 29, 10751092, doi:10.1175/JTECH-D-11-00201.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hall, M., J. Goddard, and S. Cherry, 1984: Identification of hydrometeors and other targets by dual-polarization radar. Radio Sci., 19, 132140, doi:10.1029/RS019i001p00132.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hascoet, L., and V. Pascual, 2004: TAPENADE 2.1 user’s guide. France INRIA Tech. Rep. 0300, 78 pp. [Available online at https://hal.inria.fr/inria-00069880/document.]

  • Hong, S.-Y., J. Dudhia, and S.-H. Chen, 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103120, doi:10.1175/1520-0493(2004)132<0103:ARATIM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, doi:10.1175/MWR3199.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hu, M., and M. Xue, 2007: Impact of configurations of rapid intermittent assimilation of WSR-88D radar data for the 8 May 2003 Oklahoma City tornadic thunderstorm case. Mon. Wea. Rev., 135, 507525, doi:10.1175/MWR3313.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hu, M., M. Xue, and K. Brewster, 2006a: 3DVAR and cloud analysis with WSR-88D level-II data for the prediction of the Fort Worth, Texas, tornadic thunderstorms. Part I: Cloud analysis and its impact. Mon. Wea. Rev., 134, 675698, doi:10.1175/MWR3092.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hu, M., M. Xue, J Gao, and K. Brewster, 2006b: 3DVAR and cloud analysis with WSR-88D level-II data for the prediction of the Fort Worth, Texas, tornadic thunderstorms. Part II: Impact of radial velocity analysis via 3DVAR. Mon. Wea. Rev., 134, 699721, doi:10.1175/MWR3093.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hubbert, J., V. Bringi, and L. Carey, 1998: CSU-CHILL polarimetric radar measurements from a severe hail storm in eastern Colorado. J. Appl. Meteor., 37, 749775, doi:10.1175/1520-0450(1998)037<0749:CCPRMF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Janjić, Z., 1994: The step-mountain eta coordinate model: Further developments of the convection, viscous sublayer, and turbulence closure schemes. Mon. Wea. Rev., 122, 927945, doi:10.1175/1520-0493(1994)122<0927:TSMECM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, T., J. Otkin, D. Stensrud, and K. Knopfmeier, 2014: Forecast evaluation of an observing system simulation experiment assimilating both radar and satellite data. Mon. Wea. Rev., 142, 107124, doi:10.1175/MWR-D-13-00151.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, G. Zhang, and J. Straka, 2008a: Assimilation of simulated polarimetric radar data for a convective storm using the ensemble Kalman filter. Part I: Observation operators for reflectivity and polarimetric variables. Mon. Wea. Rev., 136, 22282245, doi:10.1175/2007MWR2083.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, G. Zhang, and J. Straka, 2008b: Assimilation of simulated polarimetric radar data for a convective storm using the ensemble Kalman filter. Part II: Impact of polarimetric data on storm analysis. Mon. Wea. Rev., 136, 22462260, doi:10.1175/2007MWR2288.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, and G. Zhang, 2010: Simulations of polarimetric radar signatures of a supercell storm using a two-moment bulk microphysics scheme. J. Appl. Meteor. Climatol., 49, 146163, doi:10.1175/2009JAMC2178.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulation. Meteor. Monogr., No. 32, Amer. Meteor. Soc., 84 pp.

    • Crossref
    • Export Citation
  • Li, X., and J. Mecikalski, 2010: Assimilation of the dual-polarization Doppler radar data for a convective storm with a warm-rain radar forward operator. J. Geophys. Res., 115, D16208, doi:10.1029/2009JD013666.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, X., and J. Mecikalski, 2012: Impact of the dual-polarization Doppler radar data on two convective storms with a warm-rain radar forward operator. Mon. Wea. Rev., 140, 21472167, doi:10.1175/MWR-D-11-00090.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, X., and J. Mecikalski, 2013: Evaluation of the sensitivity of the dual-polarization Doppler radar data assimilation to radar forward operator. J. Meteor. Soc. Japan, 91, 287304, doi:10.2151/jmsj.2013-304.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, Y., and K. E. Mitchell, 2005: The NCEP stage II/IV hourly precipitation analysis: Development and applications. Preprints, 19th Conf. on Hydrology, San Diego, CA, Amer. Meteor. Soc., P1.2. [Available online at https://ams.confex.com/ams/pdfpapers/83847.pdf.]

  • Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the long-wave. J. Geophys. Res., 102, 16 66316 682, doi:10.1029/97JD00237.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., and J. A. Milbrandt, 2015: Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part I: Scheme description and idealized tests. J. Atmos. Sci., 72, 287311, doi:10.1175/JAS-D-14-0065.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Navon, I, X. Zou, J. Derber, and J. Sela, 1992: Variational data assimilation with an adiabatic version of the NMC spectral model. Mon. Wea. Rev., 120, 14331446, doi:10.1175/1520-0493(1992)120<1433:VDAWAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Otkin, J., 2012: Assessing the impact of the covariance localization radius when assimilating infrared brightness temperature observations using an ensemble Kalman filter. Mon. Wea. Rev., 140, 543561, doi:10.1175/MWR-D-11-00084.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oye, R., C. Mueller, and S. Smith, 1995: Software for radar translation, visualization, editing, and interpolation. Preprints, 27th Conf. on Radar Meteorology, Vail, CO, Amer. Meteor. Soc., 359–361.

  • Parrish, D. F., and J. C. Derber, 1992: The National Meteorological Center’s spectral statistical-interpolation analysis system. Mon. Wea. Rev., 120, 17471763, doi:10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Payne, C., T. Schuur, D. MacGorman, M. Biggerstaff, K. Kuhlman, and W. Rust, 2010: Polarimetric and electrical characteristics of a lightning ring in a supercell storm. Mon. Wea. Rev., 138, 24052425, doi:10.1175/2009MWR3210.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Petersen, W. A., K. R. Knupp, D. J. Cecil, and J. R. Mecikalsi, 2007: The University of Alabama Huntsville THOR Center instrumentation: Research and operational collaboration. Preprints, 33rd Int. Conf. on Radar Meteorology, Cairns, QLD, Australia, Amer. Meteor. Soc., 5.1. [Available online at https://ams.confex.com/ams/pdfpapers/123410.pdf.]

  • Posselt, D., X. Li, S. Tushaus, and J. Mecikalski, 2015: Assimilation of dual-polarization radar observations in mixed- and ice-phase regions of convective storms: Information content and forward model errors. Mon. Wea. Rev., 143, 26112636, doi:10.1175/MWR-D-14-00347.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pu, Z., X. Li, and J. Sun, 2009: Impact of airborne Doppler radar data assimilation on the numerical simulation of intensity change of Hurricane Dennis near a landfall. J. Atmos. Sci., 66, 33513365, doi:10.1175/2009JAS3121.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rinehart, R. E., 1997: Radar for Meteorologists. Rinehart Publications, 428 pp.

  • Rutledge, S., and P. Hobbs, 1983: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. VIII: A model for the “seeder-feeder” process in warm-frontal rainbands. J. Atmos. Sci., 40, 11851206, doi:10.1175/1520-0469(1983)040<1185:TMAMSA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A., D. Zrnić, and B. A. Gordon, 1998: Polarimetric method for ice water content determination. J. Appl. Meteor., 37, 125134, doi:10.1175/1520-0450(1998)037<0125:PMFIWC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sachidananda, M., and D. S. Zrnić, 1987: Rain rate estimates from differential polarization measurements. J. Atmos. Oceanic Technol., 4, 588598, doi:10.1175/1520-0426(1987)004<0588:RREFDP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schaefer, J. T., 1990: The critical success index as an indicator of warning skill. Wea. Forecasting, 5, 570575, doi:10.1175/1520-0434(1990)005<0570:TCSIAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schenkman, A., M. Xue, A. Shapiro, K. Brewster, and J. Gao, 2011a: Impact of CASA radar and Oklahoma Mesonet data assimilation on the analysis and prediction of tornadic mesovortices in an MCS. Mon. Wea. Rev., 139, 34223445, doi:10.1175/MWR-D-10-05051.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schenkman, A., M. Xue, A. Shapiro, K. Brewster, and J. Gao, 2011b: The analysis and prediction of the 8–9 May 2007 Oklahoma tornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVAR. Mon. Wea. Rev., 139, 224246, doi:10.1175/2010MWR3336.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Seliga, T. A., and V. N. Bringi, 1976: Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation. J. Appl. Meteor., 15, 6976, doi:10.1175/1520-0450(1976)015<0069:PUORDR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., doi:10.5065/D68S4MVH.

    • Crossref
    • Export Citation
  • Snook, N., M. Xue, and Y. Jung, 2011: Analysis of a tornadic mesoscale convective vortex based on ensemble Kalman filter assimilation of CASA X-band and WSR-88D radar data. Mon. Wea. Rev., 139, 34463468, doi:10.1175/MWR-D-10-05053.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Snyder C., and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131, 16631677, doi:10.1175//2555.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Straka, J., D. Zrnić, and A. Ryzhkov, 2000: Bulk hydrometeor classification and quantification using polarimetric radar data: Synthesis of relations. J. Appl. Meteor., 39, 13411372, doi:10.1175/1520-0450(2000)039<1341:BHCAQU>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sugimoto, S., A. Crook, J. Sun, Q. Xiao, and D. Barker, 2009: An examination of WRF 3DVAR radar data assimilation on its capability in retrieving unobserved variables and forecasting precipitation through observing system simulation experiments. Mon. Wea. Rev., 137, 40114029, doi:10.1175/2009MWR2839.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., 2005: Initialization and numerical forecasting of a supercell storm observed during STEPS. Mon. Wea. Rev., 133, 793813, doi:10.1175/MWR2887.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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, 16421661, doi:10.1175/1520-0469(1997)054<1642:DAMRFD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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, 835852, doi:10.1175/1520-0469(1998)055<0835:DAMRFD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., and Y. Zhang, 2008: Analysis and prediction of a squall line observed during IHOP using multiple WSR-88D observations. Mon. Wea. Rev., 136, 23642388, doi:10.1175/2007MWR2205.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., and H. Wang, 2013: Radar data assimilation with WRF-4D-Var. Part II: Comparison with WRF 3D-Var. Mon. Wea. Rev., 141, 22452264, doi:10.1175/MWR-D-12-00169.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., M. Chen, and Y. Wang, 2010: A frequent-updating analysis system based on radar, surface, and mesoscale model data for the Beijing 2008 Forecast Demonstration Project. Wea. Forecasting, 25, 17151735, doi:10.1175/2010WAF2222336.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., S. Trier, Q. Xiao, M. Weisman, H. Wang, Z. Ying, M. Xu, and Y. Zhang, 2012: Sensitivity of 0–12-h warm-season precipitation forecasts over the central United States to model initialization. Wea. Forecasting, 27, 832855, doi:10.1175/WAF-D-11-00075.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., H. Wang, W. Tong, Y. Zhang, D. Xu, C.-Y. Lin, 2016: Comparison of the impact of momentum control variables in limited-area high-resolution variational data assimilation. Mon Wea. Rev., 144, 149169, doi:10.1175/MWR-D-14-00205.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tong, M., and M. Xue, 2005: Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS experiments. Mon. Wea. Rev., 133, 17891807, doi:10.1175/MWR2898.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vivekanandan, J., S. M. Ellis, R. Oye, D. S. Zrnić, A. V. Ryzhkov, and J. Straka, 1999: Cloud microphysics retrieval using S-band dual-polarization radar measurements. Bull. Amer. Meteor. Soc., 80, 381388, doi:10.1175/1520-0477(1999)080<0381:CMRUSB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vivekanandan, J., G. Zhang, and E. Brandes, 2004: Polarimetric radar estimators based on a constrained gamma drop size distribution model. J. Appl. Meteor., 43, 217230, doi:10.1175/1520-0450(2004)043<0217:PREBOA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, H., J. Sun, S. Fan, and X. Huang, 2013a: Indirect assimilation of radar reflectivity with WRF 3D-Var and its impact on prediction of four summertime convective events. J. Appl. Meteor. Climatol., 52, 889902, doi:10.1175/JAMC-D-12-0120.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, H., J. Sun, X. Zhang, X. Huang, and T. Auligne, 2013b: Radar data assimilation with WRF-4DVAR. Part I: system development and preliminary testing. Mon. Wea. Rev., 141, 22242244, doi:10.1175/MWR-D-12-00168.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weygandt, S., A. Shapiro, and K. Droegemeier, 2002: Retrieval of model initial fields from single-Doppler observations of a supercell thunderstorm. Part II: Thermodynamic retrieval and numerical prediction. Mon. Wea. Rev., 130, 454476, doi:10.1175/1520-0493(2002)130<0454:ROMIFF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xiao, Q., and J. Sun, 2007: Multiple-radar data assimilation and short-range quantitative precipitation forecasting of a squall line observed during IHOP_2002. Mon. Wea. Rev., 135, 33813404, doi:10.1175/MWR3471.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xiao, Q., Y.-H. Kuo, J. Sun, W.-C. Lee, E. Lim, Y.-R. Guo, and D. Barker, 2005: Assimilation of Doppler radar observations with a regional 3DVAR system: Impact of Doppler velocities on forecasts of a heavy rainfall case. J. Appl. Meteor., 44, 768788, doi:10.1175/JAM2248.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xiao, Q., and Coauthors, 2006: Doppler radar data assimilation with WRF-VAR: Current status and future plan. Preprints, Seventh WRF Users’ Workshop, Boulder, CO, National Center for Atmospheric Research. [Available online at http://www2.mmm.ucar.edu/wrf/users/workshops/WS2006/abstracts/PSession04/P4_7_Xiao.pdf.]

  • Xiao, Q., Y.-H. Kuo, J. Sun, W.-C. Lee, D. Barker, and E. Lim, 2007: An approach of radar reflectivity data assimilation and its assessment with the inland QPF of Typhoon Rusa (2002) at landfall. J. Appl. Meteor. Climatol., 46, 1422, doi:10.1175/JAM2439.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xiao, Q., and Coauthors, 2008: Doppler radar data assimilation in KMA’s operational forecasting. Bull. Amer. Meteor. Soc., 89, 3943, doi:10.1175/BAMS-89-1-39.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xue, M., M. Hu, and A. Schenkman, 2014: Numerical prediction of the 8 May 2003 Oklahoma City tornadic supercell and embedded tornado using ARPS with the assimilation of WSR-88D data. Wea. Forecasting, 29, 3962, doi:10.1175/WAF-D-13-00029.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., C. Snyder, and J. Sun, 2004: Impact of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 132, 12381253, doi:10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., Y. Weng, J. A. Sippel, Z. Meng, and C. Bishop, 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 137, 21052125, doi:10.1175/2009MWR2645.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G., J. Vivekanandan, and E. Brandes, 2001: A method for estimating rain rate and drop size distribution from polarimetric radar measurements. IEEE Trans. Geosci. Remote Sens., 39, 830841, doi:10.1109/36.917906.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, Q., J. Cook, Q. Xu, and P. Harasti, 2008: Improving short-term storm predictions by assimilating both radar radial-wind and reflectivity observations. Wea. Forecasting, 23, 373391, doi:10.1175/2007WAF2007038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zrnić, D. S., and A. V. Ryzhkov, 1996: Advantages of rain measurements using specific differential phase. J. Atmos. Oceanic Technol., 13, 454464, doi:10.1175/1520-0426(1996)013<0454:AORMUS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • View in gallery

    Data assimilation increment at 0730 UTC 15 Mar 2008 at model level 8 (near 2-km altitude) in cloud water [qc (g kg−1)] and rainwater [qr (g kg−1)] from the (a),(b) WRM_SINGLE and (c),(d) ICE_SINGLE experiments with assimilation of single-radar reflectivity of 56 dBZ at 2-km height. The contour lines for the cloud water increment are 0.005, 0.01, 0.02, and 0.04 g kg−1. The contour lines for the rainwater increment are 0.01, 0.05, 0.1, 0.15, and 0.3 g kg−1.

  • View in gallery

    Data assimilation increment at model level 15 (near 7.2-km altitude) in (a) cloud water, (b) rainwater, (c) water vapor [qυ (g kg−1)], and (d) temperature [T(K)] from the WRM_SINGLE experiment, and (e) cloud ice [qi (g kg−1)], (f) snow [qs (g kg−1)], (g) water vapor, and (h) temperature from the ICE_SINGLE experiment with assimilation of single-radar reflectivity of 32 dBZ at 7-km height. For cloud water and cloud ice increment, the contour lines are 0.001, 0.005, 0.01, 0.02, and 0.03 g kg−1. For rainwater and snow increment, the contour lines are 0.001, 0.01, 0.05, 0.1, and 0.15 g kg−1. For the water vapor increment, the contour lines are 0.005, 0.01, 0.02, 0.04, and 0.06 g kg−1. For the temperature increment, the contour lines are 0.005, 0.01, 0.02, 0.1, 0.15, and 0.3 K.

  • View in gallery

    Cross sections of the analysis increment from the WRM_SINGLE experiment in (a) rainwater and (b) water vapor, and the ICE_SINGLE experiment in (c) snow and (d) water vapor with assimilation of single-radar reflectivity of 32 dBZ at 7-km height. For the rainwater and snow increment, the contour lines are 0.001, 0.01, 0.05, 0.1, and 0.15 g kg−1. For the water vapor increment, the contour lines are 0.005, 0.01, 0.02, 0.04, and 0.06 g kg−1.

  • View in gallery

    (a) First-guess fields of water vapor mixing ratio, total water mixing ratio [qt (g kg−1)], and temperature at 0730 UTC 15 Mar 2008 from the CTRL experiment, (b) the increment fields in the WRM experiment, and (c) the increment fields in the ICE experiment at 7-km altitude.

  • View in gallery

    Comparison of reflectivity results at 7-km height from (a) KHTX observations, (b) WRF Model forecasts in CTRL, and data assimilation analysis fields from (c) WRM and (d) ICE at 0730 UTC 15 Mar 2008.

  • View in gallery

    West–east vertical cross sections of reflectivity at (left) 0730 and (right) 0830 UTC 15 Mar 2008 from (a),(b) KHTX radar observations; (c),(d) the CTRL experiment overplotted with vertical velocity; and data assimilation analysis fields from (e),(f) WRM and (g),(h) ICE. The cross sections are along 34.0°N for plots at 0730 UTC and along 33.85°N for 0830 UTC.

  • View in gallery

    Histogram plots of OB, where B is from the background, at (a) 0730 and (c) 0830 UTC 15 Mar 2008, and OA, where A is from data assimilation analysis at (b) 0730 and (d) 0830 UTC 15 Mar 2008.

  • View in gallery

    Vertical distribution of the RMSD between the observations and the background from the CTRL experiment, and difference between the observations and the data assimilation analysis fields from the WRM and ICE experiments calculated at (a) 0730 and (b) 0830 UTC 15 Mar 2008.

  • View in gallery

    As in Fig. 5, but at 0830 UTC 15 Mar 2008.

  • View in gallery

    Comparison of reflectivity at 2-km altitude from (a) the KHTX radar observations with (b) the 9.5-h forecast field from the CTRL experiment, and 1-h forecast fields from the (c) WRM and (d) ICE experiments at 0930 UTC 15 Mar 2008.

  • View in gallery

    As in Fig. 10, but at 1030 UTC 15 Mar 2008.

  • View in gallery

    Comparison of 1-h rainfall (mm) from (a) the stage IV accumulated precipitation analysis with forecasts from the (b) CTRL, (c) WRM, and (d) ICE experiments at 1000 UTC 15 Mar 2008.

  • View in gallery

    Threat scores of horizontal reflectivity for the CTRL, WRM, and ICE experiments for thresholds of (a) 10, (b) 20, (c) 35, and (d) 45 dBZ from 0730 to 1030 UTC 15 Mar 2008.

  • View in gallery

    Data assimilation increment in rainwater mixing ratio at 2 km and snow mixing ratio at 7-km altitude from the ICE_KDP experiment at 0730 UTC 15 Mar 2008. The ring shows ARMOR coverage and the triangle shows the radar site.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 436 277 7
PDF Downloads 3083 2962 2

An Ice-Phase Microphysics Forward Model and Preliminary Results of Polarimetric Radar Data Assimilation

View More View Less
  • 1 University of Alabama in Huntsville, Huntsville, Alabama
  • | 2 University of Michigan, Ann Arbor, Michigan
Full access

Abstract

In this study, an ice-phase microphysics forward model has been developed for the Weather Research and Forecasting (WRF) Model three-dimensional variational data assimilation (WRF 3D-Var) system. Radar forward operators for reflectivity and the polarimetric variable, specific differential phase (KDP), have been built into the ice-phase WRF 3D-Var package to allow modifications in liquid (cloud water and rain) and solid water (cloud ice and snow) fields through data assimilation. Experiments have been conducted to assimilate reflectivity and radial velocity observations collected by the Weather Surveillance Radar-1988 Doppler (WSR-88D) in Hytop, Alabama, for a mesoscale convective system (MCS) on 15 March 2008. Numerical results have been examined to assess the impact of the WSR-88D data using the ice-phase WRF 3D-Var radar data assimilation package. The main goals are to first demonstrate radar data assimilation with an ice-phase microphysics forward model and second to improve understanding on how to enhance the utilization of radar data in numerical weather prediction. Results showed that the assimilation of reflectivity and radial velocity data using the ice-phase system provided significant improvement especially in the mid- to upper troposphere. The improved initial conditions led to apparent improvement in the short-term precipitation forecast of the MCS. An additional experiment has been conducted to explore the assimilation of KDP data collected by the Advanced Radar for Meteorological and Operational Research (ARMOR). Results showed that KDP data have been successfully assimilated using the ice-phase 3D-Var package. A positive impact of the KDP data has been found on rainwater in the lower troposphere and snow in the mid- to upper troposphere.

Current affiliation: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Dr. Xuanli Li, xuanli@nsstc.uah.edu

Abstract

In this study, an ice-phase microphysics forward model has been developed for the Weather Research and Forecasting (WRF) Model three-dimensional variational data assimilation (WRF 3D-Var) system. Radar forward operators for reflectivity and the polarimetric variable, specific differential phase (KDP), have been built into the ice-phase WRF 3D-Var package to allow modifications in liquid (cloud water and rain) and solid water (cloud ice and snow) fields through data assimilation. Experiments have been conducted to assimilate reflectivity and radial velocity observations collected by the Weather Surveillance Radar-1988 Doppler (WSR-88D) in Hytop, Alabama, for a mesoscale convective system (MCS) on 15 March 2008. Numerical results have been examined to assess the impact of the WSR-88D data using the ice-phase WRF 3D-Var radar data assimilation package. The main goals are to first demonstrate radar data assimilation with an ice-phase microphysics forward model and second to improve understanding on how to enhance the utilization of radar data in numerical weather prediction. Results showed that the assimilation of reflectivity and radial velocity data using the ice-phase system provided significant improvement especially in the mid- to upper troposphere. The improved initial conditions led to apparent improvement in the short-term precipitation forecast of the MCS. An additional experiment has been conducted to explore the assimilation of KDP data collected by the Advanced Radar for Meteorological and Operational Research (ARMOR). Results showed that KDP data have been successfully assimilated using the ice-phase 3D-Var package. A positive impact of the KDP data has been found on rainwater in the lower troposphere and snow in the mid- to upper troposphere.

Current affiliation: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Dr. Xuanli Li, xuanli@nsstc.uah.edu

1. Introduction

Many studies have showed that radar data assimilation is an effective tool for improving the initialization of mesoscale features of severe weather, leading to improved forecast skill (Weygandt et al. 2002; Sun 2005; Hu et al. 2006a; Zhao et al. 2008; Hu and Xue 2007; Pu et al. 2009). Radar data assimilation has been studied in numerous research efforts with various methods and techniques. Sun and Crook (1997, 1998) developed the four-dimensional Variational Doppler Radar Analysis System (VDRAS) using a cloud-scale model to indirectly assimilate radar reflectivity and radial velocity data. In their studies, reflectivity data only contributed to liquid water through a warm-rain physics scheme. Ice-phase physics processes were neglected in order to reduce the computational cost and nonlinearities during the data assimilation procedure. Sun (2005), Sun and Zhang (2008), and Sun et al. (2010) demonstrated that radar data assimilation with VDRAS has significantly improved the initialization of severe storms, although the effect was limited to the atmosphere below 8-km altitude owing to the lack of ice physics in the cloud-scale model. In a recent study, Chang et al. (2016) made an upgrade to include ice-phase microphysics processes in the VDRAS and added control variables that related to ice physics within the 4D-Var framework. The results indicated that the modification yielded significant improvements in the description of hydrometers and in the kinematic and thermodynamic structure of deep convection, as well as benefits in precipitation forecast skill. The ensemble Kalman filter (EnKF) has been used in many radar data assimilation research efforts (Zhang et al. 2004; Caya et al. 2005; Tong and Xue 2005; Zhang et al. 2009; Dowell et al. 2011). Snyder and Zhang (2003) was the first to assimilate radar radial velocity data using EnKF. Later studies (e.g., Dowell et al. 2004; Tong and Xue 2005; Dowell et al. 2011; Snook et al. 2011) included multiclass microphysics schemes and developed radar forward operators to incorporate both radial velocity (VR) and reflectivity. With the use of flow-dependent model error covariances estimated from the ensemble members in EnKF, the radar observations significantly improved the numerical weather prediction (NWP) at cloud scale. However, it is worth noting that EnKF is computationally costly as a result of the need for 101–102 ensemble forecasts, and the computation of flow-dependent error covariance from the ensemble members. EnKF methods also suffer from sampling errors because of their reduced rank representation of the background error covariances, and because the ensembles are typically underdispersive. These latter issues are commonly addressed using covariance localization and inflation techniques (Anderson 2012).

Another commonly used method for radar data assimilation is the three-dimensional variational data assimilation (3D-Var) technique. Unlike 4D-Var, 3D-Var does not involve the integration of a numerical model over time. Therefore, 3D-Var is a more flexible technique requiring much less computational cost than 4D-Var or EnKF. Many previous studies have demonstrated the successful assimilation of radar observations using 3D-Var. For example, Hu et al. (2006a,b) and Hu and Xue (2007) developed a cloud analysis procedure in the Advanced Regional Prediction System (ARPS)’s 3D-Var system to estimate the cloud type, cloud water and ice mixing ratios, and in-cloud thermal fields from radar observations. These studies showed that forecasts of supercell storm characteristics were improved in terms of timing and location. The spinup problem for tornadic storms was also reduced. Similarly, Schenkman et al. (2011a,b) and Xue et al. (2014) showed that small-scale features of tornadic storms were significantly improved with the assimilation of high temporal (5 min) and spatial (100-m gate spacing) resolution radar data within an 80-min window using the ARPS 3D-Var system. However, these above-mentioned studies also indicated that the impact of radar data assimilation at cloud scale could be highly sensitive to the assimilation strategy. For example, Ge et al. (2012) added a pressure equation as a weak constraint to the ARPS 3D-Var radar data assimilation system, which accelerated the spinup of convective cells and enhanced the low-level rotation in a tornadic supercell. Gao and Stensrud (2014) conducted sensitivity experiments to compare the effects of static and ensemble-derived flow-dependent forecast error covariances in 3D-Var. They found that the impact of radar data on low-level flow, cold pool structure, and the reflectivity pattern of a supercell storm were quite sensitive to the error covariances. Furthermore, the parameters that contributed to the error covariances including ensemble sizes, weightings of ensemble covariance, and selection of control variables could also make a big difference.

The community Weather Research and Forecasting (WRF) Model and its 3D-Var system have been used in numerous data assimilation studies. The WRF 3D-Var system was originally developed to assimilate conventional observations, and currently it has the ability to assimilate data from multiple platforms including surface and upper-air in situ observations, satellite retrievals and radiances, radar, and lidar (Barker et al. 2004, 2012). The radar data assimilation package in the community WRF 3D-Var system was developed by Xiao et al. (2005, 2007). This package uses a warm-rain moist-physics scheme, which was based on Asai (1965), Kessler (1969), and Dudhia (1989) to describe condensation, accretion, autoconversion, and evaporation processes. The relationship between reflectivity and rainwater content developed by Sun and Crook (1997) has been used as the radar forward operator. Xiao et al. (2005, 2006, 2008) and Xiao and Sun (2007) evaluated the WRF 3D-Var radar data assimilation package based on case studies and statistics from the operational implementation at the Korea Meteorological Administration. They demonstrated the positive impacts of radar data on initialization, especially moisture, hydrometeors, and wind fields and hence improved quantitative precipitation forecasts of severe storms. Sugimoto et al. (2009) and Sun et al. (2012) made modifications to the above-mentioned radar assimilation package by including a cloud analysis scheme. Before radar data assimilation, the cloud analysis made slight modifications to the background thermodynamic and hydrometeor fields to activate the microphysics processes in regions where precipitation was observed but being missed in the background. This enhanced the hydrometeor and moisture fields and produced stronger updrafts in the analyses, which led to improved precipitation forecasts for up to 9 h. Another study by Wang et al. (2013a) indicated that the use of a linearized reflectivity–rain relationship could result in significant errors for the cost function calculations when the amount of rainwater in the background is very small. They developed a scheme to first retrieve rainwater and water vapor from radar reflectivity and then to assimilate the retrieved variables with WRF 3D-Var. The result showed that rapid update cycled assimilation of radar data significantly improved the precipitation forecast skill for up to 7 h. Overall, the above studies indicate that the assimilation of radar data using WRF 3D-Var improves forecasts at the convective scale. However, with the warm-rain-only microphysics, ice-phase particles and processes have been excluded from the radar assimilation procedure, the above-mentioned studies indicated that the most significant impact of the radar observations was constrained within the lower to midtroposphere, and the value of radar reflectivity data in the upper troposphere was largely lost. Restriction of radar assimilation to regions containing only liquid hydrometeors could cause misrepresentation of cloud and precipitation structures for deep convective storms. Gao and Stensrud (2012) adopted a temperature-based hydrometeor classification approach to distinguish liquid water, snow, and hail. A radar reflectivity forward operator was developed to partition the contribution of reflectivity to rain, snow, and hail. They found that such a technique helped to produce a more reasonable precipitation distribution and the temperature field was improved with a deeper cold pool near the surface. Chang et al. (2016) compared radar data assimilation results found when using warm-rain physics with assimilation results when using the ice-phase microphysics scheme in the VDRAS system. The inclusion of ice-phase physics produced more latent heat release and triggered a stronger updraft at upper levels. When compared with the warm-rain VDRAS, a better prediction of storm evolution with an improved precipitation prediction capability was produced by the ice-phase VDRAS.

In the present study, the forward model of a simple ice microphysics scheme and its tangent linear and adjoint codes were developed for the WRF 3D-Var system to replace the existing warm-rain-only microphysics. This allows for the existence and adjustment of ice particles (i.e., the cloud ice and snow mixing ratios) in the data assimilation procedure. The radar forward operator was updated in order to relate reflectivity to snow amount at levels near and above the 0°C isotherm. With these modifications, the assimilation of reflectivity is hypothesized to bring additional improvements to the initialization of severe storms, especially in the middle to upper troposphere.

Another component of this study is the assimilation of dual-polarimetric (or simply “polarimetric”) radar observations. In June 2013, the National Weather Service (NWS) completed their upgrades to the operational Weather Surveillance Radar-1988 Doppler (WSR-88D) system to include dual-polarimetric capabilities for the continental U.S. radar network. The polarimetric radar simultaneously transmits and receives radio waves at both horizontal and vertical polarizations. This enhancement provides additional information to help identify the type, shape, size, density, and orientation of precipitation particles (Seliga and Bringi 1976; Sachidananda and Zrnić 1987; Rinehart 1997; Straka et al. 2000). In addition to reflectivity and radial velocity, typical variables obtained from the polarimetric radar also include differential reflectivity ZDR, correlation coefficient ρHV, differential phase ΦDP, specific differential phase KDP, linear depolarization ratio (LDR), and spectral width (SW). Many studies have shown that the polarimetric radar can provide estimates of hydrometeor type and mass content with higher accuracy than the nonpolarimetric radar (Hall et al. 1984; Chandrasekar et al. 1990; Zrnić and Ryzhkov 1996; Carey et al. 2000; Zhang et al. 2001; Vivekanandan et al. 2004). Polarimetric radar observations also improve precipitation classification (Aydin et al. 1986, 1990; Carey and Rutledge 1998; Hubbert et al. 1998), identification of the freezing level and melting layer (Brandes and Ikeda 2004), and detection and prediction of tornadoes and lightning activities (Deierling et al. 2008; Payne et al. 2010).

The utilization of polarimetric radar data remains a vibrant research area. Jung et al. (2008a,b, 2010) directly assimilated simulated polarimetric variables in observing system simulation experiments (OSSEs) with an EnKF system. Using a sophisticated microphysical scheme, the ZDR, reflectivity difference ZDP, and KDP data were incorporated into the ARPS model. The studies of Jung et al. demonstrated significant improvements from polarimetric variables to vertical velocity, water vapor, and hydrometeor fields. Our previous studies (Li and Mecikalski 2010, 2012, 2013) also demonstrated significant impacts of polarimetric radar observations on storm initialization and the short-term prediction of precipitation. Posselt et al. (2015) found that polarimetric radar observations contain information on ice- and mixed-phase hydrometeors, but noted that the constraint provided by the measurements can be highly sensitive to changes in the parameters defining the ice particle density and ice and rain particle size distribution. This present study extends our prior research by conducting polarimetric radar data assimilation using the newly developed ice-phase WRF 3D-Var package, and seeks further enhancement in short-term quantitative precipitation estimates (QPEs) and quantitative precipitation forecasts (QPFs). The main goal of this study is to demonstrate and discuss the technique used to assimilate reflectivity and radial velocity observations employing a newly developed ice-phase microphysics forward model and an ice-phase radar operator in WRF 3D-Var for a real case study. Preliminary results are also presented from the assimilation of KDP data using the same microphysics forward model, yet with a different radar forward operator in WRF 3D-Var.

This paper is organized as follows. Section 2 will introduce the ice-phase microphysics forward model and the radar forward operator developed in WRF 3D-Var. In section 3, a brief review will be given of the observational data used, the model configuration, and of the experiment design. In section 4, the result from single data test will be discussed. The comparison experiments for a real MCS event will be examined to evaluate radar data assimilation with the ice-phase microphysics forward model; the result of polarimetric radar data assimilation will also be analyzed. Section 5 will provide a summary and addresses some unresolved questions.

2. Data assimilation procedure

The current community WRF 3D-Var system uses a warm-rain moist-physics forward model that was based on Dudhia (1989) with some parameters and processes adopted from Asai (1965) and Kessler (1969). The processes represented in the warm-rain model include condensation of water vapor into cloud water, accretion of clouds by rain, automatic conversion of cloud water to rainwater, and evaporation of rain to water vapor. More details about processes in this warm-rain scheme can be found in Xiao et al. (2005, 2007).

In the present study, an ice-phase microphysics forward model was developed for inclusion in the WRF 3D-Var to allow the influence of radar data on cloud ice and snow fields when near and above the freezing level during the data assimilation procedure. The forward model developed in our study was based on the simple ice microphysics scheme employed by Dudhia (1989) and Rutledge and Hobbs (1983). This scheme was adopted because of its relative simplicity when compared to the more sophisticated schemes that include hail or graupel. The noise and error generated and accumulated during the computation of ice processes in those sophisticated schemes can easily cause the cost function computation to fail or to greatly increase the difficulty of convergence (i.e., as the cost function reaches a required value). The simple ice scheme considers the existence of cloud ice and snow above the freezing level, as well as cloud water and rainwater below. The following ice-phase processes have been added on top of the existing warm-rain microphysics forward model of WRF 3D-Var: initiation of ice crystals (IINT), vapor deposition of ice crystals (IDEP), conversion of ice to snow (SCON), collection of ice by snow (SACI), collection of cloud water by snow (SACW), melting of snow (SMLT), deposition/sublimation for snow (SDEP), evaporation of melting snow (SEVP), and melting of cloud ice (IMLT). The latent heat computation was updated to include each of the above processes:
e1
In Eq. (1), Lυ is the latent heat of the condensation of liquid water, Ls is the latent heat of sublimation, and Lf is the latent heat of fusion. The warm-rain condensation (COND) and rain evaporation (REVP) processes already exist in the publicly released community WRF 3D-Var moist-physics forward model.
In this study, the freezing level was defined by the 0°C temperature from the background field. For the simple ice scheme, latent heat change due to phase changes at 0°C can be abrupt. Therefore, the Dudhia (1989) scheme was modified to include a melting layer that allows the melting process to occur within a layer between −5° and 5°C instead of at a single level of 0°C. A linear melting function was used between −5° and 5°C to define the percentage of melting from snow to rain. It is assumed that snow decreases linearly downward, and rain decreases linearly upward, in the melting layer. The modified snow mixing ratio is defined as
e2
where T is the temperature (in °C), qs is the snow mixing ratio, and qr is the rainwater mixing ratio. The modified rain content is
e3
The ratio of rain in the mixture is
e4
A critical value for snow (0.05 g kg−1) is added in the tangent linear and adjoint codes to avoid an excessively large gradient of the cost function during minimization for small values of snow. In the current WRF 3D-Var, the fall velocity for rain is defined based on Sun and Crook (1997) as
e5
where p0 is the surface pressure, is the base-state pressure, and ρ is the air density. This equation was used in our package for calculation of rainwater fall velocity. Assuming the intercept of snow N0s = 2 × 107 m−4, and density of snow ρs = 100 kg m−3, the fall velocity of snow is defined based on Dudhia (1989) and Chang et al. (2016) as
e6
Further description of the simple ice microphysics scheme can be found in the appendix.
The tangent linear and adjoint models of the microphysics processes were developed with the aid of the automatic differentiation tool, Tapenade (Hascoet and Pascual 2004), following a careful manual check for the correctness of the models. The accuracy of the tangent linear model of the microphysics processes was verified by evaluating the ratio of the linear and nonlinear perturbation solutions. When various small perturbations were applied to the tangent linear model, the ratio stayed very close to 1 (e.g., for perturbation of 10−7, the ratio was 1.002 056). The adjoint code of the microphysics processes was verified by the following adjoint relation from Navon et al. (1992):
e7
In Eq. (7), is the input of the original code, is either a single do loop or a subroutine, and T represents the transpose. The adjoint of the simple ice microphysics scheme passed the check by satisfying Eq. (7).
In the community WRF 3D-Var radar data assimilation package, the moisture control variable is the pseudo–total water, which includes the water vapor mixing ratio qυ, cloud water qc, and rainwater qr. With our modifications to the microphysics forward model in WRF 3D-Var, the moisture control variable has been updated to the pseudo–total water that includes qυ, qc, qr, snow qs, and cloud ice qi. Following Barker et al. (2004), the background error statistics were estimated for the horizontal covariance and vertical error correlations of the new control variable using the National Meteorological Center [NMC, now known as the National Centers for Environmental Prediction (NCEP)] method (Parrish and Derber 1992), with 24- and 12-h WRF forecasts of the month of March 2008 for all three model domains:
e8
Radar observations were assimilated through an observational operator that describes the relationship between the reflectivity and the liquid or solid water content. The current WRF 3D-Var employs the radar forward operator in Sun and Crook (1997), which assumes a Marshall–Palmer distribution of drop size for liquid water, and N0r = 8 × 106 m−4. The reflectivity is estimated from rainwater content qr by
e9
where ZH is the radar reflectivity (in dBZ), ρ is the air density (in kg m−3), and qr is the rainwater mixing ratio (in g kg−1). This operator was used in the current study to assimilate reflectivity data for rain. For solid water content, the mass of snow from Straka et al. (2000) is
e10
where ZH is in mm6 m−3 and Ms is the snow water content (in g m−3). After conversion, the mass of the snow is expressed in WRF 3D-Var as
e11
where ZH is in dBZ and qs is the snow mixing ratio (in g kg−1). At the melting layer, the forward operator is defined as
e12
where qrm and qsm are calculated from Eqs. (2) and (3).
Radial velocity data were assimilated into the model fields with the operator from Xiao et al. (2005):
e13
where (x, y, z) is the radar site and (xi, yi, zi) is the location of the radar data, (u, υ, w) is the 3D wind field, ri is the distance between the radar site and the location of the radar data, and VT is the terminal velocity of rain or snow particles.
One of the most important recent updates to the NWS radar system is the inclusion of the polarimetric capability to the WSR-88D network. Many studies have indicated that polarimetric radar observations provided more accurate measurements of liquid and solid cloud and precipitation particles than nonpolarimetric weather radars (Aydin et al. 1990; Chandrasekar et al. 1990; Zrnić and Ryzhkov 1996; Rinehart 1997; Ryzhkov et al. 1998; Vivekanandan et al. 1999; Carey et al. 2000; Zhang et al. 2001; Brandes et al. 2002; Bringi et al. 2003; Vivekanandan et al. 2004). Therefore, it is worthwhile to examine the value of polarimetric radar variables in NWP and data assimilation. In this study, we tested the assimilation of KDP data for this MCS event. The radar forward operator for KDP was based on the relationships described in Straka et al. (2000). For liquid water, the relationship is written in the form of
e14
For solid water, the forward operator of KDP is
e15
where KDP is in degrees per kilometer, and qr and qs are in grams per kilogram. In the melting layer, the forward operator is
e16

The observational errors for reflectivity and KDP were defined as 2 dBZ and 0.1° km−1, respectively. The radial velocity data were assumed to have a Gaussian distribution with a maximum value of 2 m s−1 and a standard deviation of 1 m s−1. To remove the clear-air echoes in the storm region, reflectivity observations less than 5 dBZ in the lower troposphere (<2 km) were not assimilated [Eq. (9) or (11)], and qr values at these locations were set to zero. As discussed in Sugimoto et al. (2009) and our previous study (Li and Mecikalski 2010), it is difficult to turn on the microphysics processes when there is no convection in the background. Therefore, three outer loops were used in the radar data assimilation of the case study. In addition, before the radar data were assimilated, an adjustment was applied to the background field by giving qr a small value (5% of the observed value if the background qr is zero) when below the freezing level, and 5% of the observed value for qs when above the freezing level. The temperature field was then modified accordingly by the latent heat from the changes in qr and qs.

3. Numerical experiments and data assimilation methodology

Reflectivity and radial velocity observations used in this study were collected by the WSR-88D in Hytop, Alabama (KHTX). A quality control procedure was employed before the KHTX radar data were assimilated. The radar data were initially converted into sweep data using the NCAR Radx software (http://www.ral.ucar.edu/projects/titan/docs/radial_formats/radx.html). The NCAR Solo software (Oye et al. 1995) was used to manually clean the sweep data in order to correct for velocity folding, removing noise, etc. Then, the polar coordinate sweep data were interpolated onto Cartesian coordinate grids using the Radx software. The gridded data have horizontal resolutions of 1 km and vertical resolutions of 0.5 km.

The MCS event on 15 March 2008 was previously investigated in Li and Mecikalski (2010) to explore the assimilation of polarimetric radar observations collected by the Advanced Radar for Meteorological and Operational Research (ARMOR). ARMOR (Petersen et al. 2007) is a C-band Doppler radar located at Huntsville International Airport (34.6804°N, 86.7743°W). The observation data for this MCS case have been shown in Li and Mecikalski (2010, 2012), in which a more detailed description of the quality and the limitation of the observational data can be found.

Two-way interactive nested domains were adopted in the numerical simulations of the WRF model (Skamarock et al. 2008). As in Li and Mecikalski (2010), the model domains have horizontal resolutions of 12, 4, and 1.33 km, respectively. The model physics options in all experiments included the Rapid Radiative Transfer Model (RRTM; Mlawer et al. 1997) longwave radiation, Dudhia shortwave radiation (Dudhia 1989), Betts–Miller–Janjić cumulus parameterization (Janjić 1994), and Yonsei University (YSU) PBL schemes (Hong et al. 2006). Since hail and graupel particles were observed in this storm (Li and Mecikalski 2010), the WRF single-moment 6-class (WSM6) microphysics scheme (Hong et al. 2004) was adopted. The cumulus parameterization was used only in the outer domain with 12-km resolution. The model initial conditions were interpolated from the NCEP North American Mesoscale Forecast System (NAM) analysis with a 12-km resolution. The boundary conditions were also interpolated from the NAM analysis and were updated every 6 h.

Four numerical experiments were conducted for the MCS event (see Table 1). The experiment CTRL is a WRF control simulation initialized using NAM analysis with no data assimilation. Two experiments WRM and ICE have been conducted to assimilate radar observations with different WRF 3D-Var packages. In the experiment WRM, reflectivity and radial velocity data from the KHTX radar were assimilated using the warm-rain WRF 3D-Var package. In ICE, reflectivity and radial velocity data were assimilated using the ice-phase assimilation package. An additional experiment, ICE_KDP assimilated KDP and radial velocity data collected by ARMOR using the ice-phase assimilation package. The ARMOR data were used because the KHTX radar did not have the polarimetric capability at that time. All simulations began at 0600 UTC 15 March 2008. In all experiments, the radar data were assimilated between 0730 and 0830 UTC 15 March 2008 with a 30-min interval. After the cycled data assimilation, a forecast was made from 0830 to 1200 UTC 15 March 2008. For all experiments, the radar observations were assimilated into all three domains of the WRF Model with different data-thinning procedures. Since the gridded radar data have a horizontal resolution of 1 km, the data were averaged at two adjacent points prior to being assimilated into the innermost domain (1.33 km). For the two outer domains, the observational data were thinned by averaging values (weighted by the distance) within 2- or 6-km distance from the radar grids to fit the 4- or 12-km resolution.

Table 1.

Numerical experiments setup.

Table 1.

4. Results

a. Single-data test

The newly developed ice-phase WRF 3D-Var package was first evaluated using single-data test experiments. The single pseudo-observation of reflectivity at 0730 UTC 15 March 2008 was assimilated in two experiments, WRM_SINGLE and ICE_SINGLE, using the warm-rain and ice-phase 3D-Var packages, respectively. For both single-data test experiments, five outer loops were used in the radar data assimilation. In the first test, an observation with reflectivity of 56 dBZ at 2-km altitude at 35.7°N, 89.93°W was assimilated using Eq. (9). The background qr is 3.25 g kg−1 at the observation location, which is equivalent to a reflectivity of 47 dBZ when being calculated using Eq. (9). Figure 1 shows the analysis increment fields in qr and qc at model level 8 (the level closest to 2-km height) from the two experiments. It is shown that WRM_SINGLE and ICE_SINGLE created very similar increments in the qr and qc fields at model level 8 in terms of magnitude and the pattern of the data impact.

Fig. 1.
Fig. 1.

Data assimilation increment at 0730 UTC 15 Mar 2008 at model level 8 (near 2-km altitude) in cloud water [qc (g kg−1)] and rainwater [qr (g kg−1)] from the (a),(b) WRM_SINGLE and (c),(d) ICE_SINGLE experiments with assimilation of single-radar reflectivity of 56 dBZ at 2-km height. The contour lines for the cloud water increment are 0.005, 0.01, 0.02, and 0.04 g kg−1. The contour lines for the rainwater increment are 0.01, 0.05, 0.1, 0.15, and 0.3 g kg−1.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

The second test was performed to assimilate single-reflectivity data of 32 dBZ at 7-km altitude using Eq. (9) in WRM_SINGLE and Eq. (11) in ICE_SINGLE. The background qs is 1.04 g kg−1 at the observation location, equivalent to a reflectivity of 23 dBZ when calculated using Eq. (11). Figure 2 compares the analysis increment fields in qr, qc, qυ, and temperature T from WRM_SINGLE with increments in qs, qi, qυ, and T from ICE_SINGLE at model level 16 (the level closest to 7-km height). From Fig. 2, the reflectivity observation generated a larger increment in ICE_SINGLE than in WRM_SINGLE. The maximum increments in qc and qr in WRM_SINGLE are 0.006 and 0.012 g kg−1, respectively. In ICE_SINGLE, the reflectivity observation produces a change in qi with a maximum value of 0.033 g kg−1 and in qs with a maximum increment of 0.17 g kg−1, centered at the observed location. The increments in the T and qυ fields in ICE_SINGLE also have higher magnitudes with a broader area than those in WRM_SINGLE. Figure 3 compares the vertical structure of the increment fields in qr and qυ from WRM_SINGLE with qs and qυ from ICE_SINGLE when the reflectivity of 32 dBZ at 7 km was assimilated. In ICE_SINGLE, the impact of the reflectivity data on the snow field can be found from 3.5- to 9.5-km altitude, centered at the observation height. The impact on the moisture field can be seen from the low to upper levels with a stronger impact at 4–9-km height. Consistent with Fig. 2, Fig. 3 indicates that a stronger impact on the hydrometeor and moisture fields was created in ICE_SINGLE than WRM_SINGLE.

Fig. 2.
Fig. 2.

Data assimilation increment at model level 15 (near 7.2-km altitude) in (a) cloud water, (b) rainwater, (c) water vapor [qυ (g kg−1)], and (d) temperature [T(K)] from the WRM_SINGLE experiment, and (e) cloud ice [qi (g kg−1)], (f) snow [qs (g kg−1)], (g) water vapor, and (h) temperature from the ICE_SINGLE experiment with assimilation of single-radar reflectivity of 32 dBZ at 7-km height. For cloud water and cloud ice increment, the contour lines are 0.001, 0.005, 0.01, 0.02, and 0.03 g kg−1. For rainwater and snow increment, the contour lines are 0.001, 0.01, 0.05, 0.1, and 0.15 g kg−1. For the water vapor increment, the contour lines are 0.005, 0.01, 0.02, 0.04, and 0.06 g kg−1. For the temperature increment, the contour lines are 0.005, 0.01, 0.02, 0.1, 0.15, and 0.3 K.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

Fig. 3.
Fig. 3.

Cross sections of the analysis increment from the WRM_SINGLE experiment in (a) rainwater and (b) water vapor, and the ICE_SINGLE experiment in (c) snow and (d) water vapor with assimilation of single-radar reflectivity of 32 dBZ at 7-km height. For the rainwater and snow increment, the contour lines are 0.001, 0.01, 0.05, 0.1, and 0.15 g kg−1. For the water vapor increment, the contour lines are 0.005, 0.01, 0.02, 0.04, and 0.06 g kg−1.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

b. Case study of the MCS on 15 March 2008

The thermodynamic and hydrometeor fields from the two data assimilation experiments, WRM and ICE, were compared to understand how the WRF initial fields were changed by assimilating KHTX reflectivity and radial velocity data using different 3D-Var packages. As indicated by the single-data test experiments, the most significant difference between the warm-rain and ice-phase package occurs at mid- to high altitudes, while the data impact discussion in this section focuses more on the upper troposphere. Figure 4 shows the qυ, total water qt, and T fields at 7-km height in the CTRL, WRM, and ICE experiments after the first cycle of radar data assimilation. Comparing with the background fields in Fig. 4a, the radar data intensified the storm in the model initial conditions with increased qt over the observed storm region. An increase in T was generated by the latent heat release as a result of the production of the liquid and solid water content. A positive increment in qυ was also found over the storm region with maximum values in the southern part of the storm over central Alabama. Comparing Fig. 4b with Fig. 4c, it is found that a stronger impact on thermodynamic fields was created when the ice-phase package was used. Specifically, ICE produced higher values, with a slightly larger area of positive qt increment over central Alabama. The increments in qυ and T in ICE were also stronger over the storm region with larger maximum positive values. This result indicates that a more significant impact on the moisture and cloud microphysical properties was produced at high levels when the ice-phase 3D-Var package was used to assimilate the reflectivity and radial velocity data.

Fig. 4.
Fig. 4.

(a) First-guess fields of water vapor mixing ratio, total water mixing ratio [qt (g kg−1)], and temperature at 0730 UTC 15 Mar 2008 from the CTRL experiment, (b) the increment fields in the WRM experiment, and (c) the increment fields in the ICE experiment at 7-km altitude.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

Figure 5 gives a direct comparison of the reflectivity field before and after the first assimilation cycle (0730 UTC 15 March 2008) with a radar image from KHTX. As shown in Fig. 5, radar data assimilation greatly intensified the cloud and precipitation particles in the storm area. Specifically, the most distinguishing feature in the WSR-88D observations was the well-organized convective storm over northern and central Alabama (Fig. 5a). Compared with the KHTX observations, before radar data assimilation, CTRL produced strong false alarm convection over the northwest corner of the domain and did not capture the MCS (Fig. 5b). After assimilating the reflectivity and radial velocity data using the warm-rain radar package, WRM produced a weak storm with maximum reflectivity of 18 dBZ at the observed storm area (Fig. 5c). Using the ice-phase package, ICE produced a stronger storm than WRM, although it was still weaker than the observed one (Fig. 5d). This is in agreement with the results in Figs. 24. The stronger impact in ICE can be attributed to the inclusion of the ice microphysics processes to allow the existence of cloud ice and snow and the involvement of related processes. Figure 6 shows more details on the radar data impact via the vertical structure of reflectivity and vertical motion during different data assimilation cycles. At 0730 UTC, Fig. 6c shows that the MCS storm was not captured in CTRL and the vertical velocity was very weak. Figures 6e and 6g indicate that both WRM and ICE created a storm near the observed location after the first cycle of radar data assimilation at 0730 UTC. Comparing with the result shown for the KHTX radar, assimilation of the radar data greatly helped with constructing the stratiform precipitation region. The convective core region with high reflectivity, however, was underdeveloped in both WRM and ICE. A maximum reflectivity of 32 dBZ was produced in WRM at around 2-km height above ground and 34 dBZ in ICE near 2.5-km height, with values that were around 20 dBZ lower than the observed reflectivities over the convective core region. In WRM (Fig. 6e), the region of reflectivity above 15 dBZ was mostly below 6-km altitude. While in ICE (Fig. 6g), the region of reflectivity above 15 dBZ extended to 8-km height. Maximum updrafts of 2.8 m s−1 at 2.5-km height in WRM and 3.4 m s−1 at 4 km height in ICE were created. ICE produced a stronger storm than WRM, especially at the mid- to high levels above 4 km. After three cycles of radar data assimilation, the storm structure at 0830 UTC was further improved (Figs. 6b,d,f,h) in both WRM and ICE. Convection was built up in both WRM and ICE, with maximum updrafts of 11.5 m s−1 during WRM and 18.3 m s−1 during ICE. When comparing with WRM, ICE produced a more realistic vertical storm structure with a maximum reflectivity of 52 dBZ in the low troposphere, which is very close the observed result of 54 dBZ.

Fig. 5.
Fig. 5.

Comparison of reflectivity results at 7-km height from (a) KHTX observations, (b) WRF Model forecasts in CTRL, and data assimilation analysis fields from (c) WRM and (d) ICE at 0730 UTC 15 Mar 2008.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

Fig. 6.
Fig. 6.

West–east vertical cross sections of reflectivity at (left) 0730 and (right) 0830 UTC 15 Mar 2008 from (a),(b) KHTX radar observations; (c),(d) the CTRL experiment overplotted with vertical velocity; and data assimilation analysis fields from (e),(f) WRM and (g),(h) ICE. The cross sections are along 34.0°N for plots at 0730 UTC and along 33.85°N for 0830 UTC.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

A more quantitative evaluation on different radar assimilation experiments was performed by examining OB and OA at the observational locations. Here, OB represents the difference between the KHTX observed reflectivity and the reflectivity calculated from the background field from the experiment CTRL. In this case, OA represents the difference in reflectivity between the KHTX observations and the analysis fields from the WRF 3D-Var analysis in experiments WRM or ICE. The reflectivity fields used in B and A are taken from the simulations of the innermost domain. The statistics for OB and OA at 0730 and 0830 UTC 15 March 2008 are displayed in Fig. 7 via histogram plots of the percentage of the grid points. The positive values in Fig. 7 represent the reflectivity values that were underestimated in the model fields. The negative values, especially the large negative ones, represent the overestimate of the reflectivity, indicating cloud/precipitation particles that were generated at incorrect locations. At 0730 UTC, only a small portion (10%) of observation grid points had OB values smaller than −5 dBZ (Fig. 7a), representing the false alarm convection produced by CTRL over the northwest corner of the domain. Most of the observation grid points (62%) had positive OB values greater than 5 dBZ, indicating that CTRL fails in generating the MCS storm at 0730 UTC. After assimilation of the KHTX data, WRM and ICE have greatly improved the initial conditions. The differences between the observations and the analysis fields from WRM and ICE were much smaller than those between the observations and the background from CTRL. Specifically, in Fig. 7b, the ratio of the observation grid points that had OA values greater than 5 dBZ was 36% in the experiment WRM and 23% in ICE. The mean of the OB value was 9.5 dBZ. After assimilation, the mean OA values were 5.3 and 3.2 dBZ for WRM and ICE, respectively. These results indicate that the assimilation of the radar data helped build cloud and precipitation particles of the MCS over the observed location. In addition, the positive impact of using the ice-phase 3D-Var assimilation can be seen in Fig. 7b by more grid points with small OA values (−6 to 15 dBZ) in ICE than in WRM. There were also fewer grid points with large OA values (>15 dBZ), indicating the benefit of assimilation of KHTX data with the ice-phase assimilation package in correcting the strong echo region. However, it is also indicated in Fig. 7b by the positive skewness in both of the OA histogram plots that neither WRM nor ICE could correctly build the convective core region through 3D-Var. The storm was further improved by the cycled data assimilation. After two cycles of radar data assimilation, the background fields at 0830 UTC in both WRM and ICE had fewer grids with OB value above 10 dBZ (Fig. 7c) than those at 0730 UTC, indicating the development of the MCS in both WRM and ICE. However, there were more grids at 0830 than 0730 UTC having OB values of −14 dBZ or less, which indicates the growing false alarm convection over the northwest corner of the domain. The last cycle of radar data assimilation managed to correct the overestimate of the false alarm convection and the underestimate of the convection in the MCS. Both Figs. 7b and 7d indicate that ICE performed better than WRM in correcting the hydrometeor fields.

Fig. 7.
Fig. 7.

Histogram plots of OB, where B is from the background, at (a) 0730 and (c) 0830 UTC 15 Mar 2008, and OA, where A is from data assimilation analysis at (b) 0730 and (d) 0830 UTC 15 Mar 2008.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

To investigate the impact of the radar assimilation at different vertical levels, Fig. 8 shows the root-mean-square difference (RMSD) in reflectivity between the observations and experiments CTRL, WRM, and ICE during different radar data assimilation cycles. At 0730 UTC, the maximum RMSD value in CTRL was 12.9 dBZ at 2-km altitude. Large values of RMSD were found in the low- to midtroposphere levels, between 1- and 4-km altitudes. The RMSD value decreased with height from 2 to 10 km with a sharp decrease above 6 km, since the majority of the ice particles above the freezing level were snow that produced weaker radar echoes than rain particles. After the assimilation of the KHTX data at 0730 UTC, the differences between the observation and model fields in both WRM and ICE became much smaller. The maximum RMSD of 6.1 dBZ in both WRM and ICE occurred at 3-km height. Furthermore, Fig. 8a shows that after the first radar data assimilation cycle, RMSD values in WRM and ICE were similar below 3-km altitude. Above 3 km, the RMSD values in ICE were smaller than in WRM. This became apparent above 6 km (with maximum difference of 1.6 dBZ at 8-km height) where the ice-phase microphysics processes played a major role in the storm. Figure 8b shows the RMSD from CTRL, WRM, and ICE at 0830 UTC 15 March 2008. The impacts of radar data accumulated when more observation data were incorporated with the cycled data assimilation. At 0830 UTC, the maximum RMSD was 4.82 dBZ in WRM at 2-km height, 1.3 dBZ smaller than that at 0730 UTC. The RMSD in ICE was about 1 dBZ smaller than WRM from the lower through the upper troposphere at 0830 UTC. This verifies that the assimilation of radar data using the ice-phase package provided more improvement in storm structure.

Fig. 8.
Fig. 8.

Vertical distribution of the RMSD between the observations and the background from the CTRL experiment, and difference between the observations and the data assimilation analysis fields from the WRM and ICE experiments calculated at (a) 0730 and (b) 0830 UTC 15 Mar 2008.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

Figure 9 compares the structure of the storm in the upper troposphere from KHTX with the results from the experiment CTRL, along with analysis fields from experiments WRM and ICE at 0830 UTC 15 March 2008. As in Fig. 9b, the false alarm storm over the northwest corner in CTRL intensified, yet the MCS was still not captured in CTRL. The false alarm storm still existed in both data assimilation experiments WRM and ICE since reflectivity data below 5 dBZ were not assimilated. With cycled radar data assimilation, the MCS was generated in both WRM and ICE, indicating the significant impact of the radar data assimilation in building cloud and precipitation particles at the observed location. In addition, the intensity of the MCS over northern/central Alabama in both WRM and ICE was comparable to the observed one. The location and general pattern of the MCS storm in WRM and ICE were also close to the observations. However, neither WRM nor ICE produced the high-reflectivity bow echo as it appeared in the observations. This high-reflectivity region in the upper-level atmosphere in the observations was related to the production of hail in the storm. The warm-rain radar assimilation only benefits the qr and qc fields. Using the new ice-phase data assimilation, the reflectivity data can help improve the distribution of snow and cloud ice particles, but not hail or graupel. In addition, as shown in Fig. 5, it is difficult for 3D-Var to construct a strong convective core region, and it had to rely on the WRF Model to build up strong vertical motion and to spin up the microphysics for graupel or hail to form and mature. This might take a longer time than the period of the data assimilation window. These may be the possible reasons why the high-reflectivity region was not easily captured in the 3D-Var analysis fields at this time. Comparing with WRM, ICE produced the MCS with a wider horizontal span, and the intensity and precipitation patterns were closer to those of the observed storm. This is consistent with Figs. 5 and 6, which indicate the benefit of the assimilation of KHTX radar data using the ice-phase package. This benefit can also be attributed to the use of the observational operator [Eq. (11)] in introducing and distributing snow and cloud ice near and above the freezing level, which again improves the hydrometeor and cloud fields in the mid- to upper troposphere.

Fig. 9.
Fig. 9.

As in Fig. 5, but at 0830 UTC 15 Mar 2008.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

With better storm initialization from radar assimilation, the following will discuss how the short-term precipitation forecast of the MCS has been influenced. Since strong echoes relating to heavy precipitation are usually concentrated in the lower troposphere, low-level reflectivity fields from different experiments were compared with to evaluate the precipitation forecast of the MCS. Figures 10 and 11 show reflectivity at 2-km height from the KHTX observations, CTRL, WRM, and ICE at 0930 and 1030 UTC 15 March 2008, respectively. As in Fig. 10, the assimilation of KHTX data improved the prediction of the MCS. Comparing to Fig. 10a, the forecast in CTRL missed the well-organized bow-shaped echo over northern Alabama and Georgia. The false alarm convection in CTRL developed further over northern Alabama–southern Tennessee. This storm can also be seen in Figs. 10c and 10d, but both show weaker intensity than in CTRL. With the cycled assimilation of the radar data, the forecast of the MCS in WRM was much better represented than CTRL in terms of location and storm intensity, although the region with reflectivity above 30 dBZ was broader than the one observed (Fig. 10c). The strong echo region, with values above 40 dBZ, was to the south of the observed one. ICE also produced an overestimate in the MCS intensity (Fig. 10d). Comparing with WRM, ICE provided a better prediction of the MCS in terms of the storm pattern and convective center location. Figures 11a–d compare the forecasts of the MCS at 1030 UTC 15 March 2008. Consistent with Fig. 10, ICE and WRM produced precipitation structures that are in good agreement with what actually occurred. The location and propagation speed of the storms in WRM and ICE are also close to the observations. The storm pattern produced by ICE appears to be better than that produced by WRM. The MCS results in both WRM and ICE showed a broader storm coverage than in the observations, probably due to the fact that the 3DVAR system was able to build the stratiform region, but could not produce an intense enough convective line in the initial conditions. Figure 12 provides further evaluation of the precipitation forecasts with hourly rainfall from stage IV analysis (Lin and Mitchell 2005) compared with the WRF forecasts from CTRL, WRM, and ICE at 1000 UTC 15 March 2008. As shown in Figs. 12c and 12d, WRM and ICE produced rainfall patterns of the MCS that were similar to those of the stage IV analysis. However, an overestimate in surface precipitation can be found in both WRM and ICE for the region with a rainfall rate above 10 mm h−1. This may highlight the need for evaluation of the WRF microphysics scheme for midlatitude MCS storms during the springtime.

Fig. 10.
Fig. 10.

Comparison of reflectivity at 2-km altitude from (a) the KHTX radar observations with (b) the 9.5-h forecast field from the CTRL experiment, and 1-h forecast fields from the (c) WRM and (d) ICE experiments at 0930 UTC 15 Mar 2008.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

Fig. 11.
Fig. 11.

As in Fig. 10, but at 1030 UTC 15 Mar 2008.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

Fig. 12.
Fig. 12.

Comparison of 1-h rainfall (mm) from (a) the stage IV accumulated precipitation analysis with forecasts from the (b) CTRL, (c) WRM, and (d) ICE experiments at 1000 UTC 15 Mar 2008.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

The quantitative evaluation of the effect of the radar data assimilation with different packages is displayed in Fig. 13 with the threat score (TS) calculated for experiments CTRL, WRM, and ICE. The TS was calculated based on Xiao et al. (2005) by
e17
where C is the number of correct forecast events, F is the number of forecast events, and R is the number of events detected by the KHTX radar. TS and other similar indices (e.g., equitable threat score, critical success index, etc.) are widely used in research and operational studies (Schaefer 1990; Hu et al. 2006a,b; Sun and Zhang 2008) to provide a point-by-point assessment of the quality of the numerical precipitation forecasts at cloud scale.
Fig. 13.
Fig. 13.

Threat scores of horizontal reflectivity for the CTRL, WRM, and ICE experiments for thresholds of (a) 10, (b) 20, (c) 35, and (d) 45 dBZ from 0730 to 1030 UTC 15 Mar 2008.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

Figure 13 shows the TSs from 0730 to 1030 UTC with thresholds of 10, 20, 35, and 45 dBZ. Generally, TSs of WRM and ICE were much higher than CTRL, indicating the significant positive impact of the improved initialization. In addition, ICE generated higher TS values than WRM at most times. This was especially apparent at 0830 UTC. The much higher values of the TSs at all four thresholds verify the benefit of cycled assimilation of radar data using the ice-phase 3D-Var package. Comparing Figs. 13d with 13a, the TS values in WRM and ICE were 0.4–0.6 for a threshold of 10 dBZ, and less than 0.2 for a threshold of 45 dBZ. This indicates that the radar data were effective in creating the hydrometeor fields at observed locations, while it was difficult for WRF 3D-Var to generate the convective center with a strong radar echo during the first assimilation cycle at 0730 UTC. Generally, the TS values became highest at 0830 UTC with the cycled assimilation, and then had a decreasing trend within the 2 h afterward. The decrease was more apparent for strong echoes with a reflectivity threshold of 45 dBZ (Fig. 13d) than weak echoes with a threshold of 10 dBZ (Fig. 13a). This indicates that the WRF model showed good skill in predicting the location of the MCS, while it was difficult for the model to capture the strong convective features.

c. Assimilation of polarimetric radar variables

The above results demonstrated the impact of the KHTX radar reflectivity and radial velocity observations on storm structure as well as on the short-term forecast of the MCS event. It is of interest to investigate the assimilation of the polarimetric radar observations using the new ice-phase WRF 3D-Var package. The experiment ICE_KDP was conducted to explore the assimilation of KDP data for the MCS event. The radar forward operators of KDP for qr and qs were described in section 2. As mentioned above, the observational data used in ICE_KDP were collected by ARMOR since the KHTX radar did not have the polarimetric capability at that time. [Plots of ARMOR observational data of the MCS can be found in Li and Mecikalski (2010).] As a C-band radar, ARMOR has a smaller measurement range than the S-band WSR-88D, and is more vulnerable to attenuation. Therefore, the main purpose of showing the results from this experiment was not to compare the impact of the KDP data to reflectivity data, but to demonstrate the capability of the new ice-phase WRF 3D-Var package to assimilate the polarimetric radar data.

Figure 14 displays the analysis increments of qr at 2-km height and qs at 7-km height after the first data assimilation cycle at 0730 UTC, from the experiment ICE_KDP. Comparing with the background field in Fig. 4, the assimilation of KDP has generated a significant amount of rain at low levels and snow at high levels across the observed area. The pattern of the data impact in Fig. 14b was slightly different from that created in the ICE experiment (Fig. 4c). This can be attributed to a couple of factors: KDP data have better accuracy for heavy precipitation than reflectivity observations and the ICE_KDP experiment used different radar forward operators: Eqs. (14) and (15) versus Eqs. (9) and (11) used by ICE. The small measurement region of the ARMOR C-band radar (the black circle in Fig. 14b) is another limitation of this particular instrument. Specifically, for the MCS case, the southern part of the storm over central Alabama is beyond the coverage of ARMOR (outside the ring in Fig. 14b). This caused the radar data impact to be constrained to the northern half of the storm, while the southern half of the storm over central Alabama was missed. Therefore, the results from the ICE_KDP experiment were not comparable to WRM or ICE. Since the northern part of the storm was significantly improved, Fig. 14 indicates that the polarimetric ARMOR data can be successfully assimilated into the WRF Model using the ice-phase 3D-Var package, to improve the storm structure from the low- to the upper-tropospheric atmosphere. However, more experiments and case studies are needed to further quantitatively evaluate the polarimetric radar data assimilation with the ice-phase 3D-Var package.

Fig. 14.
Fig. 14.

Data assimilation increment in rainwater mixing ratio at 2 km and snow mixing ratio at 7-km altitude from the ICE_KDP experiment at 0730 UTC 15 Mar 2008. The ring shows ARMOR coverage and the triangle shows the radar site.

Citation: Monthly Weather Review 145, 2; 10.1175/MWR-D-16-0035.1

5. Discussion and conclusions

In this research, an ice-phase moisture microphysics forward model and its tangent linear and adjoint model were developed in the WRF 3D-Var data assimilation system to assimilate the Doppler radar data (reflectivity and radial velocity) and polarimetric radar variable KDP, with the goal of improving WRF Model initial conditions and subsequent forecasts of convection. The study’s first goal was to examine the benefits associated with the assimilation of the radar data using the ice-phase package, and second was to show how the radar assimilation influenced the short-term precipitation forecast. An MCS that occurred on 15 March 2008 was selected to examine the performance of the new ice-phase 3D-Var package in assimilating the reflectivity and radial velocity data collected by the KHTX WSR-88D and KDP data collected by ARMOR. The impacts of the radar data on storm structure and short-term forecast were then quantified.

The parameterization of the ice-phase microphysics processes in the physics forward model was based on a simple ice microphysics scheme. The moisture control variable in the WRF 3D-Var was updated to the pseudo–total water that includes cloud ice, snow, cloud water, and rain. The background error covariance matrix was calculated for this new control variable. Radar forward operators were updated in the WRF 3D-Var system to relate the reflectivity and KDP data to snow near and above the freezing level. Assimilation of a single reflectivity data point using the ice-phase 3D-Var package showed a reasonable impact on the hydrometeor and thermodynamic fields from the lower through the upper troposphere. The new algorithm was applied to a case study of a midlatitude MCS event and yielded the following conclusions.

  1. The reflectivity and radial velocity data from the WSR-88D can be appropriately assimilated into the WRF Model through the newly developed ice-phase 3D-Var package. It is shown by the comparison experiments that the new package for radar data assimilation was effective in assimilating radar observations to produce more realistic storm structures in the mid- to high troposphere.

  2. The cycled assimilation of reflectivity and radial velocity data using the ice-phase 3D-Var package greatly improved the location and structure of the MCS in the initial conditions. The overall results support the hypothesis that the ice-phase 3D-Var assimilation can produce better short-term precipitation and MCS forecasts as compared to the warm-rain 3D-Var radar data assimilation.

  3. The preliminary results from the experiment that assimilated KDP data indicate that polarimetric radar data can be successfully assimilated using the ice-phase 3D-Var package, leading to improved hydrometeor fields in the initial conditions.

Results from the data assimilation experiments using the new ice-phase WRF 3D-Var package are quite encouraging. However, there are still questions yet to be answered, as well as large areas for improvement. First, our current ice-phase microphysics forward model was based on a simple ice scheme. The use of a simple ice scheme can help avoid excessive nonlinearity created during the integration of the complex ice processes, and help us to obtain a relatively quick convergence of the cost function in the minimization procedure. The limitation of this simplification is also apparent. With the lack of hail or graupel in the control variable, it is difficult for 3D-Var to build large ice particles above the freezing level, which is a part of the reason why the strong convective core was not captured in Figs. 5 and 6. This can also lead to errors in the hydrometeor fields and misrepresentations in the latent heat release and, hence, can cause negative influences on the thermodynamic and kinematic fields. On the other hand, complex microphysics processes (e.g., the 6-class schemes such as the WSM6 or the more complex two-moment schemes such as the Morrison scheme) related to hail and graupel can produce a high degree of nonlinear computational noise, which could cause serious problems in data assimilation procedures. Although challenging, it would be worthwhile to develop such a sophisticated ice-phase microphysical scheme within the current WRF 3D-Var system. This work could be a focus of our future research, and indeed recent developments in microphysical schemes that depart from a traditional category-based representation of ice have shown promise for variational assimilation (e.g., Morrison and Milbrandt 2015). Second, as indicated by Figs. 5 and 9, it is difficult to remove the false alarm convection from the background using the 3D-Var package. A study by Hu et al. (2006a) used the clear-air echo to reduce the number of hydrometeors and amount of moisture over the region with overestimated precipitation. False alarm convection may also be reduced by using additional datasets. Otkin (2012) and Jones et al. (2014) showed that the assimilation of infrared brightness temperature was effective in reducing the false alarm convection, especially in the mid- to upper troposphere. These might be potential methods to test in our future studies as we search to find effective strategies for 3D-Var to correct the false alarm convection.

The ice-phase WRF 3D-Var package was also tested with the assimilation of KDP data collected from ARMOR. Because of the limited measurement coverage and characteristics of the C-band radar, the results from this experiment were not comparable to those that assimilated reflectivity data from the S-band KHTX radar. More case studies are required to explore in detail how the assimilation of the polarimetric radar data compares to traditional reflectivity data when all observations are obtained from the same radar system, especially the impact of the different observables on the structure of deep convective storms.

Polarimetric radar data assimilation is a new and challenging research area that requires further and in-depth research to explore techniques to utilize these data for better storm initialization at the convective scale (Jung et al. 2008a,b, 2010; Li and Mecikalski 2010; Posselt et al. 2015). With the recent upgrades to the polarimetric capabilities of the NWS’s WSR-88D network, it is important to direct research efforts toward understanding how to better utilize these data for high-resolution numerical simulations, to effectively incorporate these data into the high-resolution models, and hence to gain further improvements in initialization and quantitative precipitation forecasts of severe weather. A recent study by Sun et al. (2016) showed that the use of different momentum control variables in high-resolution radar data assimilation with WRF 3D-Var could largely influence the analysis of horizontal and vertical wind and, hence, the short-term precipitation forecast. Wang et al. (2013b) and Sun and Wang (2013) developed the WRF 4D-Var radar data assimilation system, which demonstrated further improvements in precipitation and thermodynamic fields, as well as storm organization, when compared with the WRF 3D-Var system. The EnKF technique (e.g., Zhang et al. (2009)) may be more flexible in handling microphysics processes in data assimilation at the convective scale, as the tangent linear and adjoint of the forward operator are not needed in EnKF, and a flow-dependent background error covariance can further improve the performance of the data assimilation. These could be potential techniques to explore in our future studies as we seek out further improvements in polarimetric radar data assimilation.

Acknowledgments

This work was supported by NSF Grant AGS-1005354. The authors thank Drs. Lawrence Carey and Walter Petersen for their help with obtaining and processing the ARMOR radar observations and the valuable comments on the radar forward operators. The authors would also like to thank the anonymous reviewers for their valuable comments and suggestions that helped improve the quality of this paper.

APPENDIX

Ice-Phase Microphysics Processes

The forward and adjoint model of the microphysics processes in the WRF 3D-Var is developed following Dudhia (1989) and Rutledge and Hobbs (1983). The hydrometeors in this simple ice scheme include cloud water qc, rainwater qr, cloud ice qi, and snow qs. The latent heat L is for vapor to liquid water (Lυ) when the temperature is above zero and for vapor to ice (Ls) when the temperature is below zero.

The saturated vapor pressure (in hPa) with respect to ice is
eq2
where T is the temperature and T0 = 273.15 K. Using the intercept of snow, N0s = 2 × 107 m−4, and the density of snow, ρs = 100 kg m−3, the slope parameter of the size distribution of snow is
eq3
where qs is the snow mixing ratio and ρ is the density of air. The initiation of ice crystals (PRI) is computed by
eq4
and it is also constrained by
eq5
where Δt is the time step, M0 is the initial mass of an ice crystal, nc is the number of ice nuclei per unit mass of air, qυ is the water vapor mixing ratio, and qsi is the saturation mixing ratio with respect to ice.
The ice deposition growth of cloud ice (IDEP) is defined as
eq6
where is the average diameter of the cloud ice particles. It is estimated by , where qi is the cloud ice mixing ratio. The saturation ratio with respect to ice is Si, and A and B are given by
eq7
eq8
in which Ka = 2.42 × 10−2 J m−1 s−1 K−1 is the thermal conductivity of air. The molecular weight of water is Mw = 18.016, the gas constant is R, and the diffusivity of water vapor in air is χ.
The accretion of cloud ice by snow is
eq9
in which E = 0.1 is the accretion efficiency for snow. The constants from Hong et al. (2004) are as =11.72 and bs = 0.41. Conversion from cloud ice to snow is
eq10
where is the critical value of ice crystal. The model time step is Δt and is set as 5 s in this study. Melting of cloud ice is given by
eq11
Melting of snow is given by
eq12
where Lf = 3.34 × 105 J kg−1 is the latent heat of fusion, a = 1.139, and μ = 1.718 × 10−5 kg m−1 s−1 is the dynamic viscosity of air. The deposition growth of snow is
eq13
The evaporation of melting snow is
eq14
where S is the saturation ratio with respect to water, with the parameters and .

REFERENCES

  • Anderson, J. L., 2012: Localization and sampling error correction in ensemble Kalman filter data assimilation. Mon. Wea. Rev., 140, 23592371, doi:10.1175/MWR-D-11-00013.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Asai, T., 1965: A numerical study of the air-mass transformation over the Japan Sea in winter. J. Meteor. Soc. Japan, 43, 115.

  • Aydin, K., T. A. Seliga, and V. Balaji, 1986: Remote sensing of hail with a dual linear polarization radar. J. Climate Appl. Meteor., 25, 14751484, doi:10.1175/1520-0450(1986)025<1475:RSOHWA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Aydin, K., Y. Zhao, and T. A. Seliga, 1990: A differential reflectivity radar hail measurement technique: Observations during the Denver hailstorm of 13 June 1984. J. Atmos. Oceanic Technol., 7, 104113, doi:10.1175/1520-0426(1990)007<0104:ADRRHM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Barker, D. M., W. Huang, Y. R. Guo, and Q. N. Xiao, 2004: A three-dimensional data assimilation system for MM5: Implementation and initial results. Mon. Wea. Rev., 132, 897914, doi:10.1175/1520-0493(2004)132<0897:ATVDAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Barker, D. M., and Coauthors, 2012: The Weather Research and Forecasting Model’s Community Variational/Ensemble Data Assimilation System: WRFDA. Bull. Amer. Meteor. Soc., 93, 831843, doi:10.1175/BAMS-D-11-00167.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brandes, E., and K. Ikeda, 2004: Freezing-level estimation with polarimetric radar. J. Appl. Meteor., 43, 15411553, doi:10.1175/JAM2155.1.

  • Brandes, E., G. Zhang, and J. Vivekanandan, 2002: Experiments in rainfall estimation with a polarimetric radar in a subtropical environment. J. Appl. Meteor., 41, 674685, doi:10.1175/1520-0450(2002)041<0674:EIREWA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi, V., V. Chandrasekar, J. Hubbert, E. Gorgucci, W. L. Randeu, and M. Schoenhuber, 2003: Raindrop size distribution in different climatic regimes from disdrometer and dual-polarized radar analysis. J. Atmos. Sci., 60, 354365, doi:10.1175/1520-0469(2003)060<0354:RSDIDC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carey, L., and S. Rutledge, 1998: Electrical and multiparameter radar observations of a severe hailstorm. J. Geophys. Res., 103, 13 97914 000, doi:10.1029/97JD02626.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carey, L., S. Rutledge, D. A. Ahijevych, and T. D. Keenan, 2000: Correcting propagation effects in C-band polarimetric radar observations of tropical convection using differential propagation phase. J. Appl. Meteor., 39, 14051433, doi:10.1175/1520-0450(2000)039<1405:CPEICB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Caya, A., J. Sun, and C. Snyder, 2005: A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation. Mon. Wea. Rev., 133, 30813094, doi:10.1175/MWR3021.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., V. Bringi, N. Balakrishnan, and D. Zrnić, 1990: Error structure of multiparameter radar and surface measurements of rainfall. Part III: Specific differential phase. J. Atmos. Oceanic Technol., 7, 621629, doi:10.1175/1520-0426(1990)007<0621:ESOMRA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chang, S.-F., Y.-C. Liou, J. Sun, and S.-L. Tai, 2016: The implementation of the ice-phase microphysical process into a four-dimensional Variational Doppler Radar Analysis System (VDRAS) and its impact on parameter retrieval and quantitative precipitation nowcasting. J. Atmos. Sci., 73, 10151038, doi:10.1175/JAS-D-15-0184.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Deierling, W., W. Petersen, J. Latham, S. Ellis, and H. Christian, 2008: The relationship between lightning activity and ice fluxes in thunderstorms. J. Geophys. Res., 113, D15210, doi:10.1029/2007JD009700.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dowell, D., F. Zhang, L. Wicker, C. Snyder, and A. Crook, 2004: Wind and temperature retrievals in the 17 May 1981 Arcadia, Oklahoma, supercell: Ensemble Kalman filter experiments. Mon. Wea. Rev., 132, 19822005, doi:10.1175/1520-0493(2004)132<1982:WATRIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dowell, D., L. Wicker, and C. Snyder, 2011: Ensemble Kalman filter assimilation of radar observations of the 8 May 2003 Oklahoma City supercell: Influences of reflectivity observations on storm-scale analyses. Mon. Wea. Rev., 139, 272294, doi:10.1175/2010MWR3438.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107, doi:10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, J., and D. Stensrud, 2012: Assimilation of reflectivity data in a convective-scale, cycled 3DVAR framework with hydrometeor classification. J. Atmos. Sci., 69, 10541065, doi:10.1175/JAS-D-11-0162.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, J., and D. Stensrud, 2014: Some observing system simulation experiments with a hybrid 3DEnVAR system for storm-scale radar data assimilation. Mon. Wea. Rev., 142, 33263346, doi:10.1175/MWR-D-14-00025.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ge, G., J. Gao, and M. Xue, 2012: Diagnostic pressure equation as a weak constraint in a storm-scale three-dimensional variational radar data assimilation system. J. Atmos. Oceanic Technol., 29, 10751092, doi:10.1175/JTECH-D-11-00201.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hall, M., J. Goddard, and S. Cherry, 1984: Identification of hydrometeors and other targets by dual-polarization radar. Radio Sci., 19, 132140, doi:10.1029/RS019i001p00132.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hascoet, L., and V. Pascual, 2004: TAPENADE 2.1 user’s guide. France INRIA Tech. Rep. 0300, 78 pp. [Available online at https://hal.inria.fr/inria-00069880/document.]

  • Hong, S.-Y., J. Dudhia, and S.-H. Chen, 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103120, doi:10.1175/1520-0493(2004)132<0103:ARATIM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, doi:10.1175/MWR3199.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hu, M., and M. Xue, 2007: Impact of configurations of rapid intermittent assimilation of WSR-88D radar data for the 8 May 2003 Oklahoma City tornadic thunderstorm case. Mon. Wea. Rev., 135, 507525, doi:10.1175/MWR3313.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hu, M., M. Xue, and K. Brewster, 2006a: 3DVAR and cloud analysis with WSR-88D level-II data for the prediction of the Fort Worth, Texas, tornadic thunderstorms. Part I: Cloud analysis and its impact. Mon. Wea. Rev., 134, 675698, doi:10.1175/MWR3092.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hu, M., M. Xue, J Gao, and K. Brewster, 2006b: 3DVAR and cloud analysis with WSR-88D level-II data for the prediction of the Fort Worth, Texas, tornadic thunderstorms. Part II: Impact of radial velocity analysis via 3DVAR. Mon. Wea. Rev., 134, 699721, doi:10.1175/MWR3093.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hubbert, J., V. Bringi, and L. Carey, 1998: CSU-CHILL polarimetric radar measurements from a severe hail storm in eastern Colorado. J. Appl. Meteor., 37, 749775, doi:10.1175/1520-0450(1998)037<0749:CCPRMF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Janjić, Z., 1994: The step-mountain eta coordinate model: Further developments of the convection, viscous sublayer, and turbulence closure schemes. Mon. Wea. Rev., 122, 927945, doi:10.1175/1520-0493(1994)122<0927:TSMECM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jones, T., J. Otkin, D. Stensrud, and K. Knopfmeier, 2014: Forecast evaluation of an observing system simulation experiment assimilating both radar and satellite data. Mon. Wea. Rev., 142, 107124, doi:10.1175/MWR-D-13-00151.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, G. Zhang, and J. Straka, 2008a: Assimilation of simulated polarimetric radar data for a convective storm using the ensemble Kalman filter. Part I: Observation operators for reflectivity and polarimetric variables. Mon. Wea. Rev., 136, 22282245, doi:10.1175/2007MWR2083.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, G. Zhang, and J. Straka, 2008b: Assimilation of simulated polarimetric radar data for a convective storm using the ensemble Kalman filter. Part II: Impact of polarimetric data on storm analysis. Mon. Wea. Rev., 136, 22462260, doi:10.1175/2007MWR2288.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, and G. Zhang, 2010: Simulations of polarimetric radar signatures of a supercell storm using a two-moment bulk microphysics scheme. J. Appl. Meteor. Climatol., 49, 146163, doi:10.1175/2009JAMC2178.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulation. Meteor. Monogr., No. 32, Amer. Meteor. Soc., 84 pp.

    • Crossref
    • Export Citation
  • Li, X., and J. Mecikalski, 2010: Assimilation of the dual-polarization Doppler radar data for a convective storm with a warm-rain radar forward operator. J. Geophys. Res., 115, D16208, doi:10.1029/2009JD013666.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, X., and J. Mecikalski, 2012: Impact of the dual-polarization Doppler radar data on two convective storms with a warm-rain radar forward operator. Mon. Wea. Rev., 140, 21472167, doi:10.1175/MWR-D-11-00090.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, X., and J. Mecikalski, 2013: Evaluation of the sensitivity of the dual-polarization Doppler radar data assimilation to radar forward operator. J. Meteor. Soc. Japan, 91, 287304, doi:10.2151/jmsj.2013-304.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, Y., and K. E. Mitchell, 2005: The NCEP stage II/IV hourly precipitation analysis: Development and applications. Preprints, 19th Conf. on Hydrology, San Diego, CA, Amer. Meteor. Soc., P1.2. [Available online at https://ams.confex.com/ams/pdfpapers/83847.pdf.]

  • Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the long-wave. J. Geophys. Res., 102, 16 66316 682, doi:10.1029/97JD00237.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., and J. A. Milbrandt, 2015: Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part I: Scheme description and idealized tests. J. Atmos. Sci., 72, 287311, doi:10.1175/JAS-D-14-0065.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Navon, I, X. Zou, J. Derber, and J. Sela, 1992: Variational data assimilation with an adiabatic version of the NMC spectral model. Mon. Wea. Rev., 120, 14331446, doi:10.1175/1520-0493(1992)120<1433:VDAWAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Otkin, J., 2012: Assessing the impact of the covariance localization radius when assimilating infrared brightness temperature observations using an ensemble Kalman filter. Mon. Wea. Rev., 140, 543561, doi:10.1175/MWR-D-11-00084.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oye, R., C. Mueller, and S. Smith, 1995: Software for radar translation, visualization, editing, and interpolation. Preprints, 27th Conf. on Radar Meteorology, Vail, CO, Amer. Meteor. Soc., 359–361.

  • Parrish, D. F., and J. C. Derber, 1992: The National Meteorological Center’s spectral statistical-interpolation analysis system. Mon. Wea. Rev., 120, 17471763, doi:10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Payne, C., T. Schuur, D. MacGorman, M. Biggerstaff, K. Kuhlman, and W. Rust, 2010: Polarimetric and electrical characteristics of a lightning ring in a supercell storm. Mon. Wea. Rev., 138, 24052425, doi:10.1175/2009MWR3210.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Petersen, W. A., K. R. Knupp, D. J. Cecil, and J. R. Mecikalsi, 2007: The University of Alabama Huntsville THOR Center instrumentation: Research and operational collaboration. Preprints, 33rd Int. Conf. on Radar Meteorology, Cairns, QLD, Australia, Amer. Meteor. Soc., 5.1. [Available online at https://ams.confex.com/ams/pdfpapers/123410.pdf.]

  • Posselt, D., X. Li, S. Tushaus, and J. Mecikalski, 2015: Assimilation of dual-polarization radar observations in mixed- and ice-phase regions of convective storms: Information content and forward model errors. Mon. Wea. Rev., 143, 26112636, doi:10.1175/MWR-D-14-00347.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pu, Z., X. Li, and J. Sun, 2009: Impact of airborne Doppler radar data assimilation on the numerical simulation of intensity change of Hurricane Dennis near a landfall. J. Atmos. Sci., 66, 33513365, doi:10.1175/2009JAS3121.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rinehart, R. E., 1997: Radar for Meteorologists. Rinehart Publications, 428 pp.

  • Rutledge, S., and P. Hobbs, 1983: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. VIII: A model for the “seeder-feeder” process in warm-frontal rainbands. J. Atmos. Sci., 40, 11851206, doi:10.1175/1520-0469(1983)040<1185:TMAMSA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A., D. Zrnić, and B. A. Gordon, 1998: Polarimetric method for ice water content determination. J. Appl. Meteor., 37, 125134, doi:10.1175/1520-0450(1998)037<0125:PMFIWC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sachidananda, M., and D. S. Zrnić, 1987: Rain rate estimates from differential polarization measurements. J. Atmos. Oceanic Technol., 4, 588598, doi:10.1175/1520-0426(1987)004<0588:RREFDP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schaefer, J. T., 1990: The critical success index as an indicator of warning skill. Wea. Forecasting, 5, 570575, doi:10.1175/1520-0434(1990)005<0570:TCSIAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schenkman, A., M. Xue, A. Shapiro, K. Brewster, and J. Gao, 2011a: Impact of CASA radar and Oklahoma Mesonet data assimilation on the analysis and prediction of tornadic mesovortices in an MCS. Mon. Wea. Rev., 139, 34223445, doi:10.1175/MWR-D-10-05051.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schenkman, A., M. Xue, A. Shapiro, K. Brewster, and J. Gao, 2011b: The analysis and prediction of the 8–9 May 2007 Oklahoma tornadic mesoscale convective system by assimilating WSR-88D and CASA radar data using 3DVAR. Mon. Wea. Rev., 139, 224246, doi:10.1175/2010MWR3336.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Seliga, T. A., and V. N. Bringi, 1976: Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation. J. Appl. Meteor., 15, 6976, doi:10.1175/1520-0450(1976)015<0069:PUORDR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., doi:10.5065/D68S4MVH.

    • Crossref
    • Export Citation
  • Snook, N., M. Xue, and Y. Jung, 2011: Analysis of a tornadic mesoscale convective vortex based on ensemble Kalman filter assimilation of CASA X-band and WSR-88D radar data. Mon. Wea. Rev., 139, 34463468, doi:10.1175/MWR-D-10-05053.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Snyder C., and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131, 16631677, doi:10.1175//2555.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Straka, J., D. Zrnić, and A. Ryzhkov, 2000: Bulk hydrometeor classification and quantification using polarimetric radar data: Synthesis of relations. J. Appl. Meteor., 39, 13411372, doi:10.1175/1520-0450(2000)039<1341:BHCAQU>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sugimoto, S., A. Crook, J. Sun, Q. Xiao, and D. Barker, 2009: An examination of WRF 3DVAR radar data assimilation on its capability in retrieving unobserved variables and forecasting precipitation through observing system simulation experiments. Mon. Wea. Rev., 137, 40114029, doi:10.1175/2009MWR2839.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., 2005: Initialization and numerical forecasting of a supercell storm observed during STEPS. Mon. Wea. Rev., 133, 793813, doi:10.1175/MWR2887.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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, 16421661, doi:10.1175/1520-0469(1997)054<1642:DAMRFD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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, 835852, doi:10.1175/1520-0469(1998)055<0835:DAMRFD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., and Y. Zhang, 2008: Analysis and prediction of a squall line observed during IHOP using multiple WSR-88D observations. Mon. Wea. Rev., 136, 23642388, doi:10.1175/2007MWR2205.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., and H. Wang, 2013: Radar data assimilation with WRF-4D-Var. Part II: Comparison with WRF 3D-Var. Mon. Wea. Rev., 141, 22452264, doi:10.1175/MWR-D-12-00169.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., M. Chen, and Y. Wang, 2010: A frequent-updating analysis system based on radar, surface, and mesoscale model data for the Beijing 2008 Forecast Demonstration Project. Wea. Forecasting, 25, 17151735, doi:10.1175/2010WAF2222336.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., S. Trier, Q. Xiao, M. Weisman, H. Wang, Z. Ying, M. Xu, and Y. Zhang, 2012: Sensitivity of 0–12-h warm-season precipitation forecasts over the central United States to model initialization. Wea. Forecasting, 27, 832855, doi:10.1175/WAF-D-11-00075.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., H. Wang, W. Tong, Y. Zhang, D. Xu, C.-Y. Lin, 2016: Comparison of the impact of momentum control variables in limited-area high-resolution variational data assimilation. Mon Wea. Rev., 144, 149169, doi:10.1175/MWR-D-14-00205.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tong, M., and M. Xue, 2005: Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS experiments. Mon. Wea. Rev., 133, 17891807, doi:10.1175/MWR2898.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vivekanandan, J., S. M. Ellis, R. Oye, D. S. Zrnić, A. V. Ryzhkov, and J. Straka, 1999: Cloud microphysics retrieval using S-band dual-polarization radar measurements. Bull. Amer. Meteor. Soc., 80, 381388, doi:10.1175/1520-0477(1999)080<0381:CMRUSB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vivekanandan, J., G. Zhang, and E. Brandes, 2004: Polarimetric radar estimators based on a constrained gamma drop size distribution model. J. Appl. Meteor., 43, 217230, doi:10.1175/1520-0450(2004)043<0217:PREBOA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, H., J. Sun, S. Fan, and X. Huang, 2013a: Indirect assimilation of radar reflectivity with WRF 3D-Var and its impact on prediction of four summertime convective events. J. Appl. Meteor. Climatol., 52, 889902, doi:10.1175/JAMC-D-12-0120.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, H., J. Sun, X. Zhang, X. Huang, and T. Auligne, 2013b: Radar data assimilation with WRF-4DVAR. Part I: system development and preliminary testing. Mon. Wea. Rev., 141, 22242244<