| Auligné, T., 2014: Multivariate minimum residual method for cloud retrieval. Part I: Theoretical aspects and simulated observation experiments. Mon. Wea. Rev., 142, 4383−4398, https://doi.org/10.1175/MWR-D-13-00172.1. |
| 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, 207−210, https://doi.org/10.1175/2010BAMS2978.1. |
| Barker, D. M., W. Huang, Y. R. Guo, A. J. Bourgeois, and Q. N. Xiao, 2004: A three-dimensional variational data assimilation system for MM5: Implementation and initial results. Mon. Wea. Rev., 132, 897−914, https://doi.org/10.1175/1520-0493(2004)132<0897:ATVDAS>2.0.CO;2. |
| Bauer, P., and Coauthors, 2011: Satellite cloud and precipitation assimilation at operational NWP centres. Quart. J. Roy. Meteor. Soc., 137, 1934−1951, https://doi.org/10.1002/qj.905. |
| Bishop, C., 1995: Neural Networks for Pattern Recognition. Oxford University Press, 482 pp. |
| Bocquet, M., C. A. Pires, and L. Wu, 2010: Beyond Gaussian statistical modeling in geophysical data assimilation. Mon. Wea. Rev., 138, 2997−3023, https://doi.org/10.1175/2010MWR3164.1. |
| Boukabara, S. A., and Coauthors, 2011: MiRS: An all-weather 1DVAR satellite data assimilation and retrieval system. IEEE Trans. Geosci. Remote Sens., 49(9), 3249−3272, https://doi.org/10.1109/TGRS.2011.2158438. |
| Bridle, J. S., 1990: Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. Neurocomputing: Algorithms, Architectures and Applications, F. F. Soulie and J. Hérault, Eds., Springer, 227−236, https://doi.org/10.1007/978-3-642-76153-9_28. |
| Buehner, M., and D. Jacques, 2020: Non-Gaussian deterministic assimilation of radar-derived precipitation accumulations. Mon. Wea. Rev., 148, 783−808, https://doi.org/10.1175/MWR-D-19-0199.1. |
| Chen, H. Q., Y. D. Chen, J. D. Gao, T. Sun, and J. T. Carlin, 2020: A radar reflectivity data assimilation method based on background-dependent hydrometeor retrieval: An observing system simulation experiment. Atmospheric Research, 243, 105022, https://doi.org/10.1016/j.atmosres.2020.105022. |
| Chen, Y. D., H. L. Wang, J. Z. Min, X. Y. Huang, P. Minnis, R. Z. Zhang, J. Haggerty, and R. Palikonda, 2015: Variational assimilation of cloud liquid/ice water path and its impact on NWP. J. Appl. Meteorol. Climatol., 54, 1809−1825, https://doi.org/10.1175/JAMC-D-14-0243.1. |
| Chen, Y. D., R. Z. Zhang, D. M. Meng, J. Z. Min, and L. N. Zhang, 2016: Variational assimilation of satellite cloud water/ice path and microphysics scheme sensitivity to the assimilation of a rainfall case. Adv. Atmos. Sci., 33(10), 1158−1170, https://doi.org/10.1007/s00376-016-6004-3. |
| D′Agostino, R. B., 1970: Transformation to normality of the null distribution of g1. Biometrika, 57, 679−681, https://doi.org/10.1093/biomet/57.3.679. |
| 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, 272−294, https://doi.org/10.1175/2010MWR3438.1. |
| Errico, R. M., L. Fillion, D. Nychka, and Z. Q. Lu, 2000: Some statistical considerations associated with the data assimilation of precipitation observations. Quart. J. Roy. Meteor. Soc., 126, 339−359, https://doi.org/10.1002/qj.49712656217. |
| Errico, R. M., P. Bauer, and J. Mahfouf, 2007: Issues regarding the assimilation of cloud and precipitation data. J. Atmos. Sci., 64, 3785−3798, https://doi.org/10.1175/2006JAS2044.1. |
| Fabry, F., 2010: For how long should what data be assimilated for the mesoscale forecasting of convection and why? Part II: On the observation signal from different sensors Mon. Wea. Rev., 138, 256−264, https://doi.org/10.1175/2009MWR2884.1. |
| Fabry, F. and J. Z. Sun, 2010: For how long should what data be assimilated for the mesoscale forecasting of convection and why? Part I: On the propagation of initial condition errors and their implications for data assimilation Mon. Wea. Rev., 138, 242−255, https://doi.org/10.1175/2009MWR2883.1. |
| Fletcher, S. J., and M. Zupanski, 2007: Implications and impacts of transforming lognormal variables into normal variables in VAR. Meteorol. Z., 16, 755−765, https://doi.org/10.1127/0941-2948/2007/0243. |
| Gao, J. D., and D. J. Stensrud, 2012: Assimilation of reflectivity data in a convective-scale, cycled 3DVAR Framework with hydrometeor classification. J. Atmos. Sci., 69, 1054−1065, https://doi.org/10.1175/JAS-D-11-0162.1. |
| Gao, J. D., 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, 3326−3346, https://doi.org/10.1175/MWR-D-14-00025.1. |
| Hólm, E., and J. D. Gong, 2010: Use of cloud condensate in the background error formulation. ECMWF-JCSDA Workshop, June 2010, 111−119. |
| Hólm, E. V., E. Andersson, A. Beljaars, P. Lopez, J. F. Mahfouf, A. Simmons, and J. N. Thépaut, 2002: Assimilation and modelling of the hydrological cycle: ECMWF’s status and plans. European Centre for Medium-Range Weather Forecasts (ECMWF), Technical Memorandum, https://doi.org/10.21957/kry8prwuq. |
| 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, 675−698, https://doi.org/10.1175/MWR3092.1. |
| Huang, Y. J., and Coauthors, 2018: Forecasting severe convective storms with WRF-based RTFDDA radar data assimilation in Guangdong, China. Atmospheric Research, 209, 131−143, https://doi.org/10.1016/j.atmosres.2018.03.010. |
| Jones, T. A., D. J. Stensrud, P. Minnis, and R. Palikonda, 2013: Evaluation of a forward operator to assimilate cloud water path into WRF-DART. Mon. Wea. Rev., 141, 2272−2289, https://doi.org/10.1175/MWR-D-12-00238.1. |
| Kawabata, T., and G. Ueno, 2020: Non-Gaussian probability densities of convection initiation and development investigated using a particle filter with a storm-scale numerical weather prediction model. Mon. Wea. Rev., 148, 3−20, https://doi.org/10.1175/MWR-D-18-0367.1. |
| Kerr, C. A., D. J. Stensrud, and X. G. Wang, 2015: Assimilation of cloud-top temperature and radar observations of an idealized splitting supercell using an Observing System Simulation Experiment. Mon. Wea. Rev., 143, 1018−1034, https://doi.org/10.1175/MWR-D-14-00146.1. |
| Kotsuki, S., T. Miyoshi, K. Terasaki, G. Y. Lien, and E. Kalnay, 2017: Assimilating the global satellite mapping of precipitation data with the Nonhydrostatic Icosahedral Atmospheric Model (NICAM). J. Geophys. Res., 122, 631−650, https://doi.org/10.1002/2016JD025355. |
| Lawson, W. G. and J. A. Hansen, 2005: Alignment error models and ensemble-based data assimilation. Mon. Wea. Rev., 133, 1687−1709, https://doi.org/10.1175/MWR2945.1. |
| Legrand, R., Y. Michel, and T. Montmerle, 2016: Diagnosing non-Gaussianity of forecast and analysis errors in a convective-scale model. Nonlinear Processes in Geophysics, 23, 1−12, https://doi.org/10.5194/npg-23-1-2016. |
| Li, X. L., J. R. Mecikalski, and D. Posselt, 2017: An ice-phase microphysics forward model and preliminary results of polarimetric radar data assimilation. Mon. Wea. Rev., 145, 683−708, https://doi.org/10.1175/MWR-D-16-0035.1. |
| Lien, G. Y., E. Kalnay, and T. Miyoshi, 2013: Effective assimilation of global precipitation: Simulation experiments. Tellus A, 65, 19915, https://doi.org/10.3402/tellusa.v65i0.19915. |
| Liu, C. S., 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, 1483−1502, https://doi.org/10.1175/MWR-D-19-0149.1. |
| Liu, Z. Q., X. Y. Zhang, T. Auligné, and H. C. Lin, 2009. Variational analysis of hydrometeors with satellite radiance observations: A simulated study. Proc. 10th WRF Users’ Workshop, 23−26 June 2009, Boulder, CO. |
| Meng, D. M., Y. D. Chen, H. L. Wang, Y. F. Gao, R. Potthast, and Y. B. Wang, 2019: The evaluation of EnVar method including hydrometeors analysis variables for assimilating cloud liquid/ice water path on prediction of rainfall events. Atmospheric Research, 219, 1−12, https://doi.org/10.1016/j.atmosres.2018.12.017. |
| Michel, Y., T. Auligné, and T. Montmerle, 2011: Heterogeneous convective-scale background error covariances with the inclusion of hydrometeor variables. Mon. Wea. Rev., 139, 2994−3015, https://doi.org/10.1175/2011MWR3632.1. |
| Montmerle, T., and L. Berre, 2010: Diagnosis and formulation of heterogeneous background-error covariances at the mesoscale. Quart. J. Roy. Meteor. Soc., 136, 1408−1420, https://doi.org/10.1002/qj.655. |
| Pan, S. J., J. D. Gao, D. J. Stensrud, X. G. Wang, and T. A. Jones, 2018: Assimilation of radar radial velocity and reflectivity, satellite cloud water path, and total precipitable water for convective-scale NWP in OSSEs. J. Atmos. Oceanic Technol., 35, 67−89, https://doi.org/10.1175/JTECH-D-17-0081.1. |
| Putnam, B., Xue, M., Jung, Y., Snook, N., and Zhang, G., 2019: Ensemble Kalman Filter Assimilation of Polarimetric Radar Observations for the 20 May 2013 Oklahoma Tornadic Supercell Case. Mon. Wea. Rev., 147, 2511−2533, https://doi.org/10.1175/MWR-D-18-0251.1. |
| Poterjoy, J., 2016: A localized particle filter for high-dimensional nonlinear systems. Mon. Wea. Rev., 144, 59−76, https://doi.org/10.1175/MWR-D-15-0163.1. |
| Ravela, S., K. Emanuel, D. McLaughlin, 2007: Data assimilation by field alignment. Physica D: Nonlinear Phenomena, 230(1−2), 127−145, https://doi.org/10.1016/j.physd.2006.09.035. |
| Shen, Y., P. Zhao, Y. Pan, and J. J. Yu, 2014: A high spatiotemporal gauge-satellite merged precipitation analysis over China. J. Geophys. Res., 119, 3063−3075, https://doi.org/10.1002/2013JD020686. |
| Skamarock, W. C., and Coauthors, 2008: A description of the advanced research WRF version 3. NCAR/TN-475+STR, 113 pp. https://doi.org/10.5065/D68S4MVH. |
| Sun, J. Z., 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, 1642−1661, https://doi.org/10.1175/1520-0469(1997)054<1642:DAMRFD>2.0.CO;2. |
| Thode, H. C. Jr., 2002: Testing for Normality. Marcel Dekker, 368 pp. |
| Tong, M. J., and M. Xue, 2005: Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS experiments. Mon. Wea. Rev., 133, 1789−1807, https://doi.org/10.1175/MWR2898.1. |
| Toth, Z., S. Albers, and Y. F. Xie, 2012: Analysis of fine-scale weather phenomena. Bull. Amer. Meteor. Soc., 93, ES35−ES38, https://doi.org/10.1175/BAMS-D-11-00148.1. |
| Wang, H. L., J. Z. Sun, S. Y. Fan, and X. Y. Huang, 2013: Indirect assimilation of radar reflectivity with WRF 3D-var and its impact on prediction of four summertime convective events. J. Appl. Meteorol. Climatol., 52, 889−902, https://doi.org/10.1175/JAMC-D-12-0120.1. |
| Wang, H. L., and Coauthors, 2018: Incorporating geostationary lightning data into a radar reflectivity based hydrometeor retrieval method: An observing system simulation experiment. Atmospheric Research, 209, 1−13, https://doi.org/10.1016/j.atmosres.2018.03.002. |
| Wang, Y. M., and X. G. 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, 1447−1471, https://doi.org/10.1175/MWR-D-16-0231.1. |
| Xiao, Q. N., Y. H. Kuo, J. Z. 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. Meteorol. Climatol., 46, 14−22, https://doi.org/10.1175/JAM2439.1. |
| Yang, C., Z. Q. Liu, J. Bresch, S. R. H. Rizvi, X. Y. Huang, and J. Z. Min, 2016: AMSR2 all-sky radiance assimilation and its impact on the analysis and forecast of Hurricane Sandy with a limited-area data assimilation system. Tellus A, 68, 30917, https://doi.org/10.3402/tellusa.v68.30917. |