• Aksoy, A., D. C. Dowell, and C. Snyder, 2009: A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part I: Storm-scale analyses. Mon. Wea. Rev., 137, 18051824, https://doi.org/10.1175/2008MWR2691.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Aksoy, A., D. C. Dowell, and C. Snyder, 2010: A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part II: Short-range ensemble forecasts. Mon. Wea. Rev., 138, 12731292, https://doi.org/10.1175/2009MWR3086.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Auligné, T., A. Lorenc, Y. Michel, T. Montmerle, A. Jones, M. Hu, and J. Dudhia, 2011: Toward a new cloud analysis and prediction system. Bull. Amer. Meteor. Soc., 92, 207210, https://doi.org/10.1175/2010BAMS2978.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ballard, S. P., Z. Li, D. Simonin, and J.-F. Caron, 2016: Performance of 4D-Var NWP-based nowcasting of precipitation at the Met Office for summer 2012. Quart. J. Roy. Meteor. Soc., 142, 472487, https://doi.org/10.1002/qj.2665.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brewster, K., M. Hu, M. Xue, and J. Gao, 2005: Efficient assimilation of radar data at high resolution for short-range numerical weather prediction. WWRP Int. Symp. Nowcasting Very Short Range Forecasting, WSN05, Toulouse, France, 3.06.

  • Buehner, M., P. L. Houtekamer, C. Charette, H. L. Mitchell, and B. He, 2010a: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: Description and single-observation experiments. Mon. Wea. Rev., 138, 15501566, https://doi.org/10.1175/2009MWR3157.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Buehner, M., P. L. Houtekamer, C. Charette, H. L. Mitchell, and B. He, 2010b: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part II: One-month experiments with real observations. Mon. Wea. Rev., 138, 15671586, https://doi.org/10.1175/2009MWR3158.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carley, J. R., 2012: Hybrid ensemble-3DVar radar data assimilation for the short-term prediction of convective storms. Ph.D. dissertation, Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, 205 pp.

  • Clark, A. J., J. Gao, P. T. Marsh, T. Smith, J. S. Kain, J. Correia, M. Xue, and F. Kong, 2013: Tornado pathlength forecasts from 2010 to 2011 using ensemble updraft helicity. Wea. Forecasting, 28, 387407, https://doi.org/10.1175/WAF-D-12-00038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Clayton, A. M., A. C. Lorenc, and D. M. Barker, 2013: Operational implementation of a hybrid ensemble/4D-Var global data assimilation system at the Met Office. Quart. J. Roy. Meteor. Soc., 139, 14451461, https://doi.org/10.1002/qj.2054.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dawson, D. T., M. Xue, J. A. Milbrandt, and A. Shapiro, 2015: Sensitivity of real-data simulations of the 3 May 1999 Oklahoma city tornadic supercell and associated tornadoes to multimoment microphysics. Part I: Storm- and tornado-scale numerical forecasts. Mon. Wea. Rev., 143, 22412265, https://doi.org/10.1175/MWR-D-14-00279.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dixon, M., Z. Li, H. Lean, N. Roberts, and S. Ballard, 2009: Impact of data assimilation on forecasting convection over the United Kingdom using a high-resolution version of the Met Office Unified Model. Mon. Wea. Rev., 137, 15621584, https://doi.org/10.1175/2008MWR2561.1.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dowell, D. C., L. J. 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, https://doi.org/10.1175/2010MWR3438.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Du, N., M. Xue, K. Zhao, and J. Min, 2012: Impact of assimilating airborne Doppler radar velocity data using the ARPS 3DVAR on the analysis and prediction of Hurricane Ike (2008). J. Geophys. Res., 117, D18113, https://doi.org/10.1029/2012JD017687.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Etherton, B. J., and C. H. Bishop, 2004: Resilience of hybrid ensemble/3DVAR analysis schemes to model error and ensemble covariance error. Mon. Wea. Rev., 132, 10651080, https://doi.org/10.1175/1520-0493(2004)132<1065:ROHDAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10 14310 162, https://doi.org/10.1029/94JC00572.

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

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, J., M. Xue, K. Brewster, and K. Droegemeier, 2004: Three-dimensional variational data analysis method with recursive filter for Doppler radars. J. Atmos. Oceanic Technol., 21, 457469, https://doi.org/10.1175/1520-0426(2004)021<0457:ATVDAM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, J., M. Xue, and D. J. Stensrud, 2013: The development of a hybrid EnKF-3DVAR algorithm for storm-scale data assimilation. Adv. Meteor., 2013, 512656, https://doi.org/10.1155/2013/512656.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, J., C. H. Fu, D. J. Stensrud, and J. S. Kain, 2016: OSSEs for an ensemble 3DVAR data assimilation system with radar observations of convective storms. J. Atmos. Sci., 73, 24032426, https://doi.org/10.1175/JAS-D-15-0311.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gaspari, G., and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723757, https://doi.org/10.1002/qj.49712555417.

    • 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, https://doi.org/10.1175/JTECH-D-11-00201.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ge, G., J. Gao, and M. Xue, 2013: Impacts of assimilating measurements of different state variables with a simulated supercell storm and three-dimensional variational method. Mon. Wea. Rev., 141, 27592777, https://doi.org/10.1175/MWR-D-12-00193.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Greybush, S. J., E. Kalnay, T. Miyoshi, K. Ide, and B. R. Hunt, 2011: Balance and ensemble Kalman filter localization techniques. Mon. Wea. Rev., 139, 511522, https://doi.org/10.1175/2010MWR3328.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grzych, M. L., B. D. Lee, and C. A. Finley, 2007: Thermodynamic analysis of supercell rear-flank downdrafts from project ANSWERS. Mon. Wea. Rev., 135, 240246, https://doi.org/10.1175/MWR3288.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gustafsson, N., and Coauthors, 2018: Survey of data assimilation methods for convective-scale numerical weather prediction at operational centres. Quart. J. Roy. Meteor. Soc., 144, 12181256, https://doi.org/10.1002/qj.3179.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., and C. Snyder, 2000: A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon. Wea. Rev., 128, 29052919, https://doi.org/10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hirth, B. D., J. L. Schroeder, and C. C. Weiss, 2008: Surface analysis of the rear-flank downdraft outflow in two tornadic supercells. Mon. Wea. Rev., 136, 23442363, https://doi.org/10.1175/2007MWR2285.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., H. L. Mitchell, G. Pellerin, M. Buehner, M. Charron, L. Spacek, and M. Hansen, 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133, 604620, https://doi.org/10.1175/MWR-2864.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hu, M., M. Xue, and K. Brewster, 2006: 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, https://doi.org/10.1175/MWR3092.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, G. Zhang, and J. M. Straka, 2008: 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, https://doi.org/10.1175/2007MWR2288.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, and G. Zhang, 2010: Simultaneous estimation of microphysical parameters and the atmospheric state using simulated polarimetric radar data and an ensemble Kalman filter in the presence of an observation operator error. Mon. Wea. Rev., 138, 539562, https://doi.org/10.1175/2009MWR2748.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, and M. Tong, 2012a: Ensemble Kalman filter analyses of the 29–30 May 2004 Oklahoma tornadic thunderstorm using one- and two-moment bulk microphysics schemes, with verification against polarimetric radar data. Mon. Wea. Rev., 140, 14571475, https://doi.org/10.1175/MWR-D-11-00032.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jung, Y., M. Xue, Y. Wang, Y. Pan, and K. Zhu, 2012b: Tests of a cycled EnKF data assimilation and forecasts for the 10 May 2010 tornado outbreak in the central US domain. 26th Conf. on Severe and Local Storms, Nashville, TN, Amer. Meteor. Soc., 8A.4, https://ams.confex.com/ams/26SLS/webprogram/Paper211285.html.

  • Jung, Y., M. Xue, Y. Wang, S. Wang, F. Kong, Y. Pan, and K. Zhu, 2013: Multi-scale ensemble Kalman filter data assimilation and forecasts of the 10 May 2010 tornado outbreak in central United States. Sixth Conf. on Data Assimilation, College Park, MD, WMO, https://das6.umd.edu/program/Posters/uploads/Bp09-Jung_Youngsun.pdf.

  • Kain, J. S., and Coauthors, 2008: Some practical considerations regarding horizontal resolution in the first generation of operational convection-allowing NWP. Wea. Forecasting, 23, 931952, https://doi.org/10.1175/WAF2007106.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kain, J. S., and Coauthors, 2010: Assessing advances in the assimilation of radar data and other mesoscale observations within a collaborative forecasting-research environment. Wea. Forecasting, 25, 15101521, https://doi.org/10.1175/2010WAF2222405.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., 2009: Covariance localisation and balance in an ensemble Kalman filter. Quart. J. Roy. Meteor. Soc., 135, 11571176, https://doi.org/10.1002/qj.443.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kong, R., M. Xue, and C. Liu, 2018: Development of a hybrid En3DVar data assimilation system and comparisons with 3DVar and EnKF for radar data assimilation with observing system simulation experiments. Mon. Wea. Rev., 146, 175198, https://doi.org/10.1175/MWR-D-17-0164.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, Y., X. Wang, and M. Xue, 2012: Assimilation of radar radial velocity data with the WRF hybrid ensemble-3DVAR system for the prediction of Hurricane Ike (2008). Mon. Wea. Rev., 140, 35073524, https://doi.org/10.1175/MWR-D-12-00043.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, Y., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 10651092, https://doi.org/10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, C., and M. Xue, 2016: Relationships among four-dimensional hybrid ensemble-variational data assimilation algorithms with full and approximate ensemble covariance localization. Mon. Wea. Rev., 144, 591606, https://doi.org/10.1175/MWR-D-15-0203.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, C., M. Xue, and R. Kong, 2019: Direct assimilation of radar reflectivity data using 3DVAR: Treatment of hydrometeor background errors and OSSE tests. Mon. Wea. Rev., 147, 1729, https://doi.org/10.1175/MWR-D-18-0033.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, C., M. Xue, and R. Kong, 2020: Direct variational assimilation of radar reflectivity and radial velocity data: Issues with nonlinear reflectivity operator and solutions. Mon. Wea. Rev., 148, 14831502, https://doi.org/10.1175/MWR-D-19-0149.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, H., and M. Xue, 2008: Prediction of convective initiation and storm evolution on 12 June 2002 during IHOP_2002. Part I: Control simulation and sensitivity experiments. Mon. Wea. Rev., 136, 22612282, https://doi.org/10.1175/2007MWR2161.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lorenc, A. C., 2003: The potential of the ensemble Kalman filter for NWP—A comparison with 4D-Var. Quart. J. Roy. Meteor. Soc., 129, 31833203, https://doi.org/10.1256/qj.02.132.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Manobianco, J., S. Koch V. M. Karyampudi, and A. J. Negri, 1994: The impact of assimilating satellite-derived precipitation rates on numerical simulations of the ERICA IOP 4 cyclone. Mon. Wea. Rev., 122, 341365, https://doi.org/10.1175/1520-0493(1994)122<0341:TIOASD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., and Y. P. Richardson, 2014: The Influence of environmental low-level shear and cold pools on tornadogenesis: Insights from idealized simulations. J. Atmos. Sci., 71, 243275, https://doi.org/10.1175/JAS-D-13-0159.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., J. M. Straka, and E. N. Rasmussen, 2002: Direct surface thermodynamic observations within the rear-flank downdrafts of nontornadic and tornadic supercells. Mon. Wea. Rev., 130, 16921721, https://doi.org/10.1175/1520-0493(2002)130<1692:DSTOWT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Noilhan, J., and S. Planton, 1989: A simple parameterization of land surface processes for meteorological models. Mon. Wea. Rev., 117, 536549, https://doi.org/10.1175/1520-0493(1989)117<0536:ASPOLS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pan, Y., and Coauthors, 2014: A GSI-based coupled EnSRF-En3DVar hybrid data assimilation system for the operational rapid refresh model: Tests at a reduced resolution. Mon. Wea. Rev., 142, 37563780, https://doi.org/10.1175/MWR-D-13-00242.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simonin, D., C. Pierce, N. Roberts, S. P. Ballard, and Z. Li, 2017: Performance of Met Office hourly cycling NWP-based nowcasting for precipitation forecasts. Quart. J. Roy. Meteor. Soc., 143, 28622873, https://doi.org/10.1002/qj.3136.

    • Crossref
    • Search Google Scholar
    • 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, https://doi.org/10.1175/MWR-D-10-05053.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Snook, N., M. Xue, and Y. Jung, 2012: Ensemble probabilistic forecasts of a tornadic mesoscale convective system from ensemble Kalman filter analyses using WSR-88D and CASA radar data. Mon. Wea. Rev., 140, 21262146, https://doi.org/10.1175/MWR-D-11-00117.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Snook, N., M. Xue, and Y. Jung, 2019: Tornado-resolving ensemble and probabilistic predictions of the 20 May 2013 Newcastle–Moore EF5 tornado. Mon. Wea. Rev., 147, 12151235, https://doi.org/10.1175/MWR-D-18-0236.1.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stensrud, D. J., and Coauthors, 2013: Progress and challenges with warn-on-forecast. Atmos. Res., 123, 216, https://doi.org/10.1016/j.atmosres.2012.04.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stratman, D. R., N. Yussouf, Y. Jung, T. A. Supinie, M. Xue, P. S. Skinner, and B. J. Putnam, 2020: Optimal temporal frequency of NSSL phased array radar observations for an experimental warn-on-forecast system. Wea. Forecasting, 35, 193214, https://doi.org/10.1175/WAF-D-19-0165.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sugimoto, S., N. A. Crook, J. Sun, Q. N. Xiao, and D. M. 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, https://doi.org/10.1175/2009MWR2839.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., and N. A. Crook, 1994: Wind and thermodynamic retrieval from single-Doppler measurements of a gust front observed during Phoenix II. Mon. Wea. Rev., 122, 10751091, https://doi.org/10.1175/1520-0493(1994)122<1075:WATRFS>2.0.CO;2.

    • 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, https://doi.org/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, https://doi.org/10.1175/1520-0469(1998)055<0835:DAMRFD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, J., and Coauthors, 2014: Use of NWP for nowcasting convective precipitation: Recent progress and challenges. Bull. Amer. Meteor. Soc., 95, 409426, https://doi.org/10.1175/BAMS-D-11-00263.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, W., and C. Chang, 1986: Diffusion-model for a convective layer. Part I: Numerical simulation of convective boundary-layer. J. Climate Appl. Meteor., 25, 14451453, https://doi.org/10.1175/1520-0450(1986)025<1445:DMFACL>2.0.CO;2.

    • 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, https://doi.org/10.1175/MWR2898.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tong, M., and M. Xue, 2008: Simultaneous estimation of microphysical parameters and atmospheric state with simulated radar data and ensemble square root Kalman filter. Part I: Sensitivity analysis and parameter identifiability. Mon. Wea. Rev., 136, 16301648, https://doi.org/10.1175/2007MWR2070.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, H., J. Sun, and Y.-R. Guo, 2011: Radar reflectivity data assimilation with the four-dimensional variational system of the Weather Research and Forecast Model. 15th Symp. on Integrated Observing and Assimilation Systems for the Atmosphere, Oceans and Land Surface (IOAS-AOLS), Seattle, WA, Amer. Meteor. Soc., J17.4, https://ams.confex.com/ams/91Annual/webprogram/Paper185272.html.

  • Wang, H., J. Sun, S. Fan, and X. Huang, 2013: 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, https://doi.org/10.1175/JAMC-D-12-0120.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, W., and T. T. Warner, 1988: Use of four-dimensional data assimilation by Newtonian relaxation and latent-heat forcing to improve a mesoscale-model precipitation forecast: A case study. Mon. Wea. Rev., 116, 25932613, https://doi.org/10.1175/1520-0493(1988)116<2593:UOFDDA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, X., T. A. Hamill, J. S. Whitaker, and C. H. Bishop, 2007: A comparison of hybrid ensemble transform Kalman filter-optimum interpolation and ensemble square root filter analysis schemes. Mon. Wea. Rev., 135, 10551076, https://doi.org/10.1175/MWR3307.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, Y., and X. Wang, 2017: Direct assimilation of radar reflectivity without tangent linear and adjoint of the nonlinear observation operator in the GSI-based EnVar system: Methodology and experiment with the 8 May 2003 Oklahoma city tornadic supercell. Mon. Wea. Rev., 145, 14471471, https://doi.org/10.1175/MWR-D-16-0231.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 19131924, https://doi.org/10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and T. M. Hamill, 2012: Evaluating methods to account for system errors in ensemble data assimilation. Mon. Wea. Rev., 140, 30783089, https://doi.org/10.1175/MWR-D-11-00276.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • WSEC, 2006: A recommendation for an enhanced Fujita scale (EF-scale). Texas Tech University Wind Science and Engineering Center Rep., 95 pp., www.depts.ttu.edu/weweb/pubs/fscale/efscale.pdf.

  • Wu, W.-S., R. J. Purser, and D. F. Parrish, 2002: Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon. Wea. Rev., 130, 29052916, https://doi.org/10.1175/1520-0493(2002)130<2905:TDVAWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xiao, Q., Y. Kuo, J. Sun, W. C. Lee, E. Lim, Y. Guo, and D. M. 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, https://doi.org/10.1175/JAM2248.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xiao, Q., Y. H. Kuo, J. Sun, W. C. Lee, D. M. 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, https://doi.org/10.1175/JAM2439.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xue, M., and W. J. Martin, 2006: A high-resolution modeling study of the 24 May 2002 dryline case during IHOP. Part I: Numerical simulation and general evolution of the dryline and convection. Mon. Wea. Rev., 134, 149171, https://doi.org/10.1175/MWR3071.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xue, M., K. K. Droegemeier, and V. Wong, 2000: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification. Meteor. Atmos. Phys., 75, 161193, https://doi.org/10.1007/s007030070003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xue, M., and Coauthors, 2001: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction tool. Part II: Model physics and applications. Meteor. Atmos. Phys., 76, 143165, https://doi.org/10.1007/s007030170027.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xue, M., D. Wang, J. Gao, K. Brewster, and K. K. Droegemeier, 2003: The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation. Meteor. Atmos. Phys., 82, 139170, https://doi.org/10.1007/s00703-001-0595-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xue, M., M. Tong, and K. K. Droegemeier, 2006: An OSSE framework based on the ensemble square root Kalman filter for evaluating the impact of data from radar networks on thunderstorm analysis and forecasting. J. Atmos. Oceanic Technol., 23, 4666, https://doi.org/10.1175/JTECH1835.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xue, M., M. Tong, and G. Zhang, 2009: Simultaneous state estimation and attenuation correction for thunderstorms with radar data using an ensemble Kalman filter: Tests with simulated data. Quart. J. Roy. Meteor. Soc., 135, 14091423, https://doi.org/10.1002/qj.453.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xue, M., F. Kong, K. W. Thomas, J. Gao, Y. Wang, K. Brewster, and K. K. Droegemeier, 2013: Prediction of convective storms at convection-resolving 1km resolution over continental United States with radar data assimilation: An example case of 26 May 2008 and precipitation forecasts from spring 2009. Adv. Meteor., 2013, 259052, https://doi.org/10.1155/2013/259052.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xue, M., M. Hu, and A. D. 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, https://doi.org/10.1175/WAF-D-13-00029.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yussouf, N., and D. J. Stensrud, 2010: Impact of phased-array radar observations over a short assimilation period: Observing system simulation experiments using an ensemble Kalman filter. Mon. Wea. Rev., 138, 517538, https://doi.org/10.1175/2009MWR2925.1.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, M., F. Zhang, X. Huang, and X. Zhang, 2011: Intercomparison of an ensemble Kalman filter with three- and four-dimensional variational data assimilation methods in a limited-area model over the month of June 2003. Mon. Wea. Rev., 139, 566572, https://doi.org/10.1175/2010MWR3610.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, M., M. Zupanski, M. J. Kim, and J. A. Knaff, 2013: Assimilating AMSU-A radiances in the TC core area with NOAA operational HWRF (2011) and a hybrid data assimilation system: Danielle (2010). Mon. Wea. Rev., 141, 38893907, https://doi.org/10.1175/MWR-D-12-00340.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, K., and M. Xue, 2009: Assimilation of coastal Doppler radar data with the ARPS 3DVAR and cloud analysis for the prediction of Hurricane Ike (2008). Geophys. Res. Lett., 36, L12803, https://doi.org/10.1029/2009GL038658.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Comparisons of Hybrid En3DVar with 3DVar and EnKF for Radar Data Assimilation: Tests with the 10 May 2010 Oklahoma Tornado Outbreak

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  • 1 Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, Oklahoma
  • 2 University of Oklahoma, Norman, Oklahoma
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Abstract

In this study, a hybrid En3DVar data assimilation (DA) scheme is compared with 3DVar, EnKF, and pure En3DVar for the assimilation of radar data in a real tornadic storm case. Results using hydrometeor mixing ratios (CVq) or logarithmic mixing ratios (CVlogq) as the control variables are compared in the variational DA framework. To address the lack of radial velocity impact issues when using CVq, a procedure that assimilates reflectivity and radial velocity data in two separate analysis passes is adopted. Comparisons are made in terms of the root-mean-square innovations (RMSIs) as well as the intensity and structure of the analyzed and forecast storms. For pure En3DVar that uses 100% ensemble covariance, CVlogq and CVq have similar RMSIs in the velocity analyses, but errors grow faster during forecasts when using CVlogq. Introducing static background error covariance B at 5% in hybrid En3DVar (with CVlogq) significantly reduces the forecast error growth. Pure En3DVar produces more intense reflectivity analyses than EnKF that more closely match the observations. Hybrid En3DVar with 50% B outperforms other weights in terms of the RMSIs and forecasts of updraft helicity and is thus used in the final comparison with 3DVar and EnKF. The hybrid En3DVar is found to outperform EnKF in better capturing the intensity and structure of the analyzed and forecast storms and outperform 3DVAR in better capturing the intensity and evolution of the rotating updraft.

© 2020 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: Ming Xue, mxue@ou.edu

Abstract

In this study, a hybrid En3DVar data assimilation (DA) scheme is compared with 3DVar, EnKF, and pure En3DVar for the assimilation of radar data in a real tornadic storm case. Results using hydrometeor mixing ratios (CVq) or logarithmic mixing ratios (CVlogq) as the control variables are compared in the variational DA framework. To address the lack of radial velocity impact issues when using CVq, a procedure that assimilates reflectivity and radial velocity data in two separate analysis passes is adopted. Comparisons are made in terms of the root-mean-square innovations (RMSIs) as well as the intensity and structure of the analyzed and forecast storms. For pure En3DVar that uses 100% ensemble covariance, CVlogq and CVq have similar RMSIs in the velocity analyses, but errors grow faster during forecasts when using CVlogq. Introducing static background error covariance B at 5% in hybrid En3DVar (with CVlogq) significantly reduces the forecast error growth. Pure En3DVar produces more intense reflectivity analyses than EnKF that more closely match the observations. Hybrid En3DVar with 50% B outperforms other weights in terms of the RMSIs and forecasts of updraft helicity and is thus used in the final comparison with 3DVar and EnKF. The hybrid En3DVar is found to outperform EnKF in better capturing the intensity and structure of the analyzed and forecast storms and outperform 3DVAR in better capturing the intensity and evolution of the rotating updraft.

© 2020 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: Ming Xue, mxue@ou.edu
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