• Aksoy, A., , F. Zhang, , and J. W. Nielsen-Gammon, 2006: Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model. Mon. Wea. Rev., 134, 29512970, doi:10.1175/MWR3224.1.

    • Search Google Scholar
    • Export Citation
  • 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, doi:10.1175/2008MWR2691.1.

    • 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, doi:10.1175/2009MWR3086.1.

    • Search Google Scholar
    • Export Citation
  • Aksoy, A., , S. D. Aberson, , T. Vukicevic, , K. J. Sellwood, , S. Lorsolo, , and X. Zhang, 2013: Assimilation of high-resolution tropical cyclone observations with an ensemble Kalman filter using NOAA/AOML/HRD’s HEDAS: Evaluation of the 2008–11 vortex-scale analyses. Mon. Wea. Rev., 141, 18421865, doi:10.1175/MWR-D-12-00194.1.

    • Search Google Scholar
    • Export Citation
  • Albers, S. C., , J. A. McGinley, , D. L. Birkenheuer, , and J. R. Smart, 1996: The Local Analysis and Prediction System (LAPS): Analysis of clouds, precipitation, and temperature. Wea. Forecasting, 11, 273287, doi:10.1175/1520-0434(1996)011<0273:TLAAPS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Amezcua, J., , K. Ide, , E. Kalnay, , and S. Reich, 2014: Ensemble transform Kalman–Bucy filters. Quart. J. Roy. Meteor. Soc., 140, 9951004, doi:10.1002/qj.2186.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 28842903, doi:10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2003: A local least squares framework for ensemble filtering. Mon. Wea. Rev., 131, 634642, doi:10.1175/1520-0493(2003)131<0634:ALLSFF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2007: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D, 230, 99111, doi:10.1016/j.physd.2006.02.011.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2009: Spatially and temporally varying adaptive covariance inflation for ensemble filters. Tellus, 61A, 7283, doi:10.1111/j.1600-0870.2008.00361.x.

    • Search Google Scholar
    • Export Citation
  • 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.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2016: Reducing correlation sampling error in ensemble Kalman filter data assimilation. Mon. Wea. Rev., 144, 913925, doi:10.1175/MWR-D-15-0052.1.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., , and S. L. Anderson, 1999: A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Wea. Rev., 127, 27412758, doi:10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., , T. Hoar, , K. Raeder, , H. Liu, , N. Collins, , R. Torn, , and A. Avellano, 2009: The Data Assimilation Research Testbed: A community facility. Bull. Amer. Meteor. Soc., 90, 12831296, doi:10.1175/2009BAMS2618.1.

    • Search Google Scholar
    • Export Citation
  • Annan, J. D., 2004: On the orthogonality of bred vectors. Mon. Wea. Rev., 132, 843849, doi:10.1175/1520-0493(2004)132<0843:OTOOBV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Annan, J. D., , J. C. Hargreaves, , N. R. Edwards, , and R. Marsh, 2005: Parameter estimation in an intermediate complexity earth system model using an ensemble Kalman filter. Ocean Modell., 8, 135154, doi:10.1016/j.ocemod.2003.12.004.

    • Search Google Scholar
    • Export Citation
  • Aravéquia, J. A., , I. Szunyogh, , E. J. Fertig, , E. Kalnay, , D. Kuhl, , and E. J. Kostelich, 2011: Evaluation of a strategy for the assimilation of satellite radiance observations with the local ensemble transform Kalman filter. Mon. Wea. Rev., 139, 19321951, doi:10.1175/2010MWR3515.1.

    • Search Google Scholar
    • Export Citation
  • Ballish, B., , X. Cao, , E. Kalnay, , and M. Kanamitsu, 1992: Incremental nonlinear normal-mode initialization. Mon. Wea. Rev., 120, 17231734, doi:10.1175/1520-0493(1992)120<1723:INNMI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Barker, D. M., 2005: Southern high-latitude ensemble data assimilation in the Antartic mesoscale prediction system. Mon. Wea. Rev., 133, 34313449, doi:10.1175/MWR3042.1.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Bergemann, K., , and S. Reich, 2010: A mollified ensemble Kalman filter. Quart. J. Roy. Meteor. Soc., 136, 16361643, doi:10.1002/qj.672.

    • Search Google Scholar
    • Export Citation
  • Berner, J., , G. J. Shutts, , M. Leutbecher, , and T. N. Palmer, 2009: A spectral stochastic kinetic energy backscatter scheme and its impact on flow-dependent predictability in the ECMWF ensemble prediction system. J. Atmos. Sci., 66, 603626, doi:10.1175/2008JAS2677.1.

    • Search Google Scholar
    • Export Citation
  • Bishop, C. H., , and Z. Toth, 1999: Ensemble transformation and adaptive observations. J. Atmos. Sci., 56, 17481765, doi:10.1175/1520-0469(1999)056<1748:ETAAO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bishop, C. H., , and D. Hodyss, 2009: Ensemble covariances adaptively localized with ECO-RAP. Part 1: Tests on simple error models. Tellus, 61A, 8496, doi:10.1111/j.1600-0870.2008.00371.x.

    • Search Google Scholar
    • Export Citation
  • Bishop, C. H., , B. J. Etherton, , and S. J. Majumdar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420436, doi:10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bloom, S. C., , L. L. Takacs, , A. M. da Silva, , and D. Ledvina, 1996: Data assimilation using incremental analysis updates. Mon. Wea. Rev., 124, 12561271, doi:10.1175/1520-0493(1996)124<1256:DAUIAU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bonavita, M., 2011: Impact and diagnosis of model error in the ECMWF ensemble of data assimilations. Proc. ECMWF Workshop on Representing Model Uncertainty and Error in Numerical Weather and Climate Prediction Models, Shinfield Park, Reading, United Kingdom, ECMWF, 303318.

  • Bonavita, M., , L. Torrisi, , and F. Marcucci, 2010: Ensemble data assimilation with the CNMCA regional forecasting system. Quart. J. Roy. Meteor. Soc., 136, 132145, doi:10.1002/qj.553.

    • Search Google Scholar
    • Export Citation
  • Bonavita, M., , L. Isaksen, , and E. Hólm, 2012: On the use of EDA background error variances in the ECMWF 4D-Var. Quart. J. Roy. Meteor. Soc., 138, 15401559, doi:10.1002/qj.1899.

    • Search Google Scholar
    • Export Citation
  • Bonavita, M., , M. Hamrud, , and L. Isaksen, 2015: EnKF and hybrid gain ensemble data assimilation. Part II: EnKF and hybrid gain results. Mon. Wea. Rev., 143, 48654882, doi:10.1175/MWR-D-15-0071.1.

    • Search Google Scholar
    • Export Citation
  • Bonavita, M., , E. Hólm, , L. Isaksen, , and M. Fisher, 2016: The evolution of the ECMWF hybrid data assimilation system. Quart. J. Roy. Meteor. Soc., 142, 287303, doi:10.1002/qj.2652.

    • Search Google Scholar
    • Export Citation
  • Bormann, N., , and P. Bauer, 2010: Estimates of spatial and interchannel observation-error characteristics for current sounder radiances for numerical weather prediction. I: Methods and application to ATOVS data. Quart. J. Roy. Meteor. Soc., 136, 10361050, doi:10.1002/qj.616.

    • Search Google Scholar
    • Export Citation
  • Bowler, N. E., , A. Arribas, , K. R. Mylne, , K. B. Robertson, , and S. E. Beare, 2008: The MOGREPS short-range ensemble prediction system. Quart. J. Roy. Meteor. Soc., 134, 703722, doi:10.1002/qj.234.

    • Search Google Scholar
    • Export Citation
  • Brankart, J.-M., , C. Ubelmann, , C.-E. Testut, , E. Cosme, , P. Brasseur, , and J. Verron, 2009: Efficient parameterization of the observation error covariance matrix for square root or ensemble Kalman filters: Application to ocean altimetry. Mon. Wea. Rev., 137, 19081927, doi:10.1175/2008MWR2693.1.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., 2012: Evaluation of a spatial/spectral covariance localization approach for atmospheric data assimilation. Mon. Wea. Rev., 140, 617636, doi:10.1175/MWR-D-10-05052.1.

    • Search Google Scholar
    • Export Citation
  • 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, doi:10.1175/2009MWR3157.1.

    • 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, doi:10.1175/2009MWR3158.1.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., and Coauthors, 2015: Implementation of deterministic weather forecasting systems based on ensemble–variational data assimilation at Environment Canada. Part I: The global system. Mon. Wea. Rev., 143, 25322559, doi:10.1175/MWR-D-14-00354.1.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., , M. Miller, , and T. N. Palmer, 1999: Stochastic representation of model uncertainties in the ECMWF ensemble prediction system. Quart. J. Roy. Meteor. Soc., 125, 28872908, doi:10.1002/qj.49712556006.

    • Search Google Scholar
    • Export Citation
  • Burgers, G., , P. J. van Leeuwen, , and G. Evensen, 1998: Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev., 126, 17191724, doi:10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Campbell, W. F., , C. H. Bishop, , and D. Hodyss, 2010: Vertical covariance localization for satellite radiances in ensemble Kalman filters. Mon. Wea. Rev., 138, 282290, doi:10.1175/2009MWR3017.1.

    • Search Google Scholar
    • Export Citation
  • Candille, G., 2009: The multiensemble approach: The NAEFS example. Mon. Wea. Rev., 137, 16551665, doi:10.1175/2008MWR2682.1.

  • Candille, G., , and O. Talagrand, 2005: Evaluation of probabilistic prediction systems for a scalar variable. Quart. J. Roy. Meteor. Soc., 131, 21312150, doi:10.1256/qj.04.71.

    • Search Google Scholar
    • Export Citation
  • Candille, G., , and O. Talagrand, 2008: Impact of observational error on the validation of ensemble prediction systems. Quart. J. Roy. Meteor. Soc., 134, 959971, doi:10.1002/qj.268.

    • Search Google Scholar
    • Export Citation
  • Cardinali, C., 2009: Monitoring the observation impact on the short-range forecast. Quart. J. Roy. Meteor. Soc., 135, 239250, doi:10.1002/qj.366.

    • Search Google Scholar
    • Export Citation
  • Caron, J.-F., , T. Milewski, , M. Buehner, , L. Fillion, , M. Reszka, , S. Macpherson, , and J. St-James, 2015: Implementation of deterministic weather forecasting systems based on ensemble-variational data assimilation at Environment Canada. Part II: The regional system. Mon. Wea. Rev., 143, 25602580, doi:10.1175/MWR-D-14-00353.1.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Chang, C.-C., , S.-C. Yang, , and C. Keppenne, 2014a: Applications of the mean recentering scheme to improve typhoon track prediction: A case study of typhoon Nanmadol (2011). J. Meteor. Soc. Japan, 92, 559584, doi:10.2151/jmsj.2014-604.

    • Search Google Scholar
    • Export Citation
  • Chang, W., , K.-S. Chung, , L. Fillion, , and S.-J. Baek, 2014b: Radar data assimilation in the Canadian high-resolution ensemble Kalman filter system: Performance and verification with real summer cases. Mon. Wea. Rev., 142, 21182138, doi:10.1175/MWR-D-13-00291.1.

    • Search Google Scholar
    • Export Citation
  • Charron, M., , G. Pellerin, , L. Spacek, , P. L. Houtekamer, , N. Gagnon, , H. L. Mitchell, , and L. Michelin, 2010: Toward random sampling of model error in the Canadian Ensemble Prediction System. Mon. Wea. Rev., 138, 18771901, doi:10.1175/2009MWR3187.1.

    • 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, doi:10.1002/qj.2054.

    • Search Google Scholar
    • Export Citation
  • Cohn, S. E., , and D. F. Parrish, 1991: The behavior of forecast error covariances for a Kalman filter in two dimensions. Mon. Wea. Rev., 119, 17571785, doi:10.1175/1520-0493(1991)119<1757:TBOFEC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Cohn, S. E., , A. da Silva, , J. Guo, , M. Sienkiewicz, , and D. Lamich, 1998: Assessing the effects of data selection with the DAO physical-space statistical analysis system. Mon. Wea. Rev., 126, 29132926, doi:10.1175/1520-0493(1998)126<2913:ATEODS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Compo, G. P., , J. S. Whitaker, , and P. D. Sardeshmukh, 2006: Feasibility of a 100-year reanalysis using only surface pressure data. Bull. Amer. Meteor. Soc., 87, 175190, doi:10.1175/BAMS-87-2-175.

    • Search Google Scholar
    • Export Citation
  • Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • Daley, R., 1995: Estimating the wind field from chemical constituent observations: Experiments with a one-dimensional extended Kalman filter. Mon. Wea. Rev., 123, 181198, doi:10.1175/1520-0493(1995)123<0181:ETWFFC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Daley, R., , and T. Mayer, 1986: Estimates of global analysis error from the global weather experiment observational network. Mon. Wea. Rev., 114, 16421653, doi:10.1175/1520-0493(1986)114<1642:EOGAEF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., 1995: On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Rev., 123, 11281145, doi:10.1175/1520-0493(1995)123<1128:OLEOEC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., 2005: Bias and data assimilation. Quart. J. Roy. Meteor. Soc., 131, 33233343, doi:10.1256/qj.05.137.

  • Derber, J. C., , and W.-S. Wu, 1998: The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system. Mon. Wea. Rev., 126, 22872299, doi:10.1175/1520-0493(1998)126<2287:TUOTCC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Derber, J. C., , and F. Bouttier, 1999: A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus, 51A, 195221, doi:10.1034/j.1600-0870.1999.t01-2-00003.x.

    • Search Google Scholar
    • Export Citation
  • Desroziers, G., , L. Berre, , B. Chapnik, , and P. Poli, 2005: Diagnosis of observation, background and analysis-error statistics in observation space. Quart. J. Roy. Meteor. Soc., 131, 33853396, doi:10.1256/qj.05.108.

    • Search Google Scholar
    • Export Citation
  • Dillon, M. E., and Coauthors, 2016: Application of the WRF-LETKF data assimilation system over southern South America: Sensitivity to model physics. Wea. Forecasting, 31, 217236, doi:10.1175/WAF-D-14-00157.1.

    • Search Google Scholar
    • Export Citation
  • Dong, J., , and M. Xue, 2013: Assimilation of radial velocity and reflectivity data from coastal WSR-88D radars using an ensemble Kalman filter for the analysis and forecast of landfalling hurricane Ike (2008). Quart. J. Roy. Meteor. Soc., 139, 467487, doi:10.1002/qj.1970.

    • Search Google Scholar
    • Export Citation
  • Dowell, D. C., , F. 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, doi:10.1175/1520-0493(2004)132<1982:WATRIT>2.0.CO;2.

    • 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, doi:10.1175/2010MWR3438.1.

    • Search Google Scholar
    • Export Citation
  • ECMWF, 2011: Proceedings of the ECMWF Workshop on Representing Model Uncertainty and Error in Numerical Weather and Climate Prediction Models, 20–24 June 2011. ECMWF, 370 pp.

  • English, S. J., , R. J. Renshaw, , P. C. Dibben, , A. J. Smith, , P. J. Rayer, , C. Poulsen, , F. W. Saunders, , and J. R. Eyre, 2000: A comparison of the impact of TOVS and ATOVS satellite sounding data on the accuracy of numerical weather forecasts. Quart. J. Roy. Meteor. Soc., 126, 29112931, doi:10.1002/qj.49712656915.

    • Search Google Scholar
    • Export Citation
  • Errico, R. M., , R. Yang, , N. C. Privé, , K.-S. Tai, , R. Todling, , M. E. Sienkiewicz, , and J. Guo, 2013: Development and validation of observing-system simulation experiments at NASA’s Global Modeling and Assimilation Office. Quart. J. Roy. Meteor. Soc., 139, 11621178, doi:10.1002/qj.2027.

    • 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, doi:10.1029/94JC00572.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53, 343367, doi:10.1007/s10236-003-0036-9.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2004: Sampling strategies and square root analysis schemes for the EnKF. Ocean Dyn., 54, 539560, doi:10.1007/s10236-004-0099-2.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2009: The ensemble Kalman filter for combined state and parameter estimation. IEEE Control Syst., 29, 83104, doi:10.1109/MCS.2009.932223.

    • Search Google Scholar
    • Export Citation
  • Fertig, E. J., , J. Harlim, , and B. R. Hunt, 2007: A comparative study of 4D-VAR and a 4D ensemble Kalman filter: Perfect model simulations with Lorenz-96. Tellus, 59A, 96100, doi:10.1111/j.1600-0870.2006.00205.x.

    • Search Google Scholar
    • Export Citation
  • Fillion, L., , H. L. Mitchell, , H. Ritchie, , and A. Staniforth, 1995: The impact of a digital filter finalization technique in a global data assimilation system. Tellus, 47A, 304323, doi:10.1034/j.1600-0870.1995.t01-2-00002.x.

    • Search Google Scholar
    • Export Citation
  • Fisher, M., 2004: Background error covariance modelling. Proc. ECMWF Seminar on Recent Developments in Data Assimilation for Atmosphere and Ocean, Shinfield Park, Reading, United Kingdom, ECMWF, 4563.

  • Fisher, M., , and H. Auvinen, 2012: Long window 4D-Var. Proc. ECMWF Seminar on Data Assimilation for Atmosphere and Ocean, Shinfield Park, Reading, United Kingdom, ECMWF, 189202.

  • Fishman, G. S., 1996: Monte Carlo: Concepts, Algorithms and Applications. Springer, 698 pp.

  • Fitzgerald, R. J., 1971: Divergence of the Kalman filter. IEEE Trans. Automat. Control, 16, 736747, doi:10.1109/TAC.1971.1099836.

  • Flowerdew, J., 2015: Towards a theory of optimal localisation. Tellus, 67A, 25257, doi:10.3402/tellusa.v67.25257.

  • Frehlich, R., 2006: Adaptive data assimilation including the effect of spatial variations in observation error. Quart. J. Roy. Meteor. Soc., 132, 12251257, doi:10.1256/qj.05.146.

    • Search Google Scholar
    • Export Citation
  • Fujita, T., , D. J. Stensrud, , and D. C. Dowell, 2007: Surface data assimilation using an ensemble Kalman filter approach with initial condition and model physics uncertainties. Mon. Wea. Rev., 135, 18461868, doi:10.1175/MWR3391.1.

    • 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, doi:10.1002/qj.49712555417.

    • Search Google Scholar
    • Export Citation
  • Gauthier, P., , and J.-N. Thépaut, 2001: Impact of the digital filter as a weak constraint in the preoperational 4DVAR assimilation system of Météo-France. Mon. Wea. Rev., 129, 20892102, doi:10.1175/1520-0493(2001)129<2089:IOTDFA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gauthier, P., , M. Tanguay, , S. Laroche, , S. Pellerin, , and J. Morneau, 2007: Extension of 3DVAR to 4DVAR: Implementation of 4DVAR at the Meteorological Service of Canada. Mon. Wea. Rev., 135, 23392354, doi:10.1175/MWR3394.1.

    • Search Google Scholar
    • Export Citation
  • Geer, A. J., , and P. Bauer, 2011: Observation errors in all-sky data assimilation. Quart. J. Roy. Meteor. Soc., 137, 20242037, doi:10.1002/qj.830.

    • Search Google Scholar
    • Export Citation
  • Ghil, M., , and P. Malanotte-Rizzoli, 1991: Data assimilation in meteorology and oceanography. Advances in Geophysics, Vol. 33, Academic Press, 141–266.

  • Ghil, M., , S. Cohn, , J. Tavantzis, , K. Bube, , and E. Isaacson, 1981: Applications of estimation theory to numerical weather prediction. Dynamic Meteorology—Data Assimilation Methods, L. Bengtsson, M. Ghil, and E. Källén, Eds., Springer-Verlag, 139–224.

  • Gilleland, E., , D. A. Ahijevych, , B. G. Brown, , and E. E. Ebert, 2010: Verifying forecasts spatially. Bull. Amer. Meteor. Soc., 91, 13651373, doi:10.1175/2010BAMS2819.1.

    • Search Google Scholar
    • Export Citation
  • Golub, G. H., , and C. F. Van Loan, 1996: Matrix Computations. 3rd ed. Johns Hopkins University Press, 694 pp.

  • Gorin, V. E., , and M. D. Tsyrulnikov, 2011: Estimation of multivariate observation-error statistics for AMSU-A data. Mon. Wea. Rev., 139, 37653780, doi:10.1175/2011MWR3554.1.

    • Search Google Scholar
    • Export Citation
  • Grell, G. A., , and D. Dévényi, 2002: A generalized approach to parameterizing convection combining ensemble and data assimilation techniques. Geophys. Res. Lett., 29, doi:10.1029/2002GL015311.

    • 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, doi:10.1175/2010MWR3328.1.

    • Search Google Scholar
    • Export Citation
  • Ha, S., , J. Berner, , and C. Snyder, 2015: A comparison of model error representations in mesoscale ensemble data assimilation. Mon. Wea. Rev., 143, 38933911, doi:10.1175/MWR-D-14-00395.1.

    • Search Google Scholar
    • Export Citation
  • Hager, G., , and G. Wellein, 2011: Introduction to High Performance Computing for Scientists and Engineers. Chapman & Hall/CRC, 330 pp.

  • Hamill, T. M., 2001: Interpretation of rank histograms for verifying ensemble forecasts. Mon. Wea. Rev., 129, 550560, doi:10.1175/1520-0493(2001)129<0550:IORHFV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., 2006: Ensemble-based atmospheric data assimilation. Predictability of Weather and Climate, T. Palmer and R. Hagedorn, Eds., Cambridge University Press, 124–156.

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

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., , and J. S. Whitaker, 2011: What constrains spread growth in forecasts initialized from ensemble Kalman filters? Mon. Wea. Rev., 139, 117131, doi:10.1175/2010MWR3246.1.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., , J. S. Whitaker, , and C. Snyder, 2001: Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev., 129, 27762790, doi:10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hamrud, M., , M. Bonavita, , and L. Isaksen, 2015: EnKF and hybrid gain ensemble data assimilation. Part I: EnKF implementation. Mon. Wea. Rev., 143, 48474864, doi:10.1175/MWR-D-14-00333.1.

    • Search Google Scholar
    • Export Citation
  • Hersbach, H., 2000: Decomposition of the continuous ranked probability score for ensemble prediction systems. Wea. Forecasting, 15, 559570, doi:10.1175/1520-0434(2000)015<0559:DOTCRP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., 1993: Global and local skill forecasts. Mon. Wea. Rev., 121, 18341846, doi:10.1175/1520-0493(1993)121<1834:GALSF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., 2011: The use of multiple parameterizations in ensembles. Proc. ECMWF Workshop on Representing Model Uncertainty and Error in Numerical Weather and Climate Prediction Models, Shinfield Park, Reading, United Kingdom, ECMWF, 163173.

  • Houtekamer, P. L., , and L. Lefaivre, 1997: Using ensemble forecasts for model validation. Mon. Wea. Rev., 125, 24162426, doi:10.1175/1520-0493(1997)125<2416:UEFFMV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., , and H. L. Mitchell, 1998: Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev., 126, 796811, doi:10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., , and H. L. Mitchell, 2001: A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Wea. Rev., 129, 123137, doi:10.1175/1520-0493(2001)129<0123:ASEKFF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., , and H. L. Mitchell, 2005: Ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc., 131, 32693289, doi:10.1256/qj.05.135.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., , L. Lefaivre, , J. Derome, , H. Ritchie, , and H. L. Mitchell, 1996: A system simulation approach to ensemble prediction. Mon. Wea. Rev., 124, 12251242, doi:10.1175/1520-0493(1996)124<1225:ASSATE>2.0.CO;2.

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

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., , H. L. Mitchell, , and X. Deng, 2009: Model error representation in an operational ensemble Kalman filter. Mon. Wea. Rev., 137, 21262143, doi:10.1175/2008MWR2737.1.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., , X. Deng, , H. L. Mitchell, , S.-J. Baek, , and N. Gagnon, 2014a: Higher resolution in an operational ensemble Kalman filter. Mon. Wea. Rev., 142, 11431162, doi:10.1175/MWR-D-13-00138.1.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., , B. He, , and H. L. Mitchell, 2014b: Parallel implementation of an ensemble Kalman filter. Mon. Wea. Rev., 142, 11631182, doi:10.1175/MWR-D-13-00011.1.

    • 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, doi:10.1175/MWR3092.1.

    • Search Google Scholar
    • Export Citation
  • Hu, X.-M., , F. Zhang, , and J. W. Nielsen-Gammon, 2010: Ensemble-based simultaneous state and parameter estimation for treatment of mesoscale model error: A real-data study. Geophys. Res. Lett., 37, L08802, doi:10.1029/2010GL043017.

    • Search Google Scholar
    • Export Citation
  • Huang, X.-Y., , and P. Lynch, 1993: Diabetic digital-filtering initialization: Application to the HIRLAM model. Mon. Wea. Rev., 121, 589603, doi:10.1175/1520-0493(1993)121<0589:DDFIAT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hunt, B. R., and Coauthors, 2004: Four-dimensional ensemble Kalman filtering. Tellus, 56A, 273277, doi:10.1111/j.1600-0870.2004.00066.x.

    • Search Google Scholar
    • Export Citation
  • Hunt, B. R., , E. J. Kostelich, , and I. Szunyogh, 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 230, 112126, doi:10.1016/j.physd.2006.11.008.

    • Search Google Scholar
    • Export Citation
  • Isaksen, L., 2012: Data assimilation on future computer architectures. Proc. ECMWF Seminar on Data Assimilation for Atmosphere and Ocean, Shinfield Park, Reading, United Kingdom, ECMWF, 301322.

  • Jones, R. H., 1965: Optimal estimation of initial conditions for numerical prediction. J. Atmos. Sci., 22, 658663, doi:10.1175/1520-0469(1965)022<0658:OEOICF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Jung, Y., , M. Xue, , and G. Zhang, 2010a: 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.

    • Search Google Scholar
    • Export Citation
  • Jung, Y., , M. Xue, , and G. Zhang, 2010b: 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, doi:10.1175/2009MWR2748.1.

    • Search Google Scholar
    • Export Citation
  • Kalman, R. E., 1960: A new approach to linear filtering and prediction problems. J. Basic Eng., 82, 3545, doi:10.1115/1.3662552.

  • Kalman, R. E., , and R. S. Bucy, 1961: New results in linear filtering and prediction theory. J. Basic Eng., 83, 95108, doi:10.1115/1.3658902.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., , and A. Dalcher, 1987: Forecasting forecast skill. Mon. Wea. Rev., 115, 349356, doi:10.1175/1520-0493(1987)115<0349:FFS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., , and S.-C. Yang, 2010: Accelerating the spin-up of ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc., 136, 16441651, doi:10.1002/qj.652.

    • Search Google Scholar
    • Export Citation
  • Kang, J.-S., , E. Kalnay, , J. Liu, , I. Fung, , T. Miyoshi, , and K. Ide, 2011: “Variable localization” in an ensemble Kalman filter: Application to the carbon cycle data assimilation. J. Geophys. Res., 116, D09110, doi:10.1029/2010JD014673.

    • Search Google Scholar
    • Export Citation
  • Kang, J.-S., , E. Kalnay, , T. Miyoshi, , J. Liu, , and I. Fung, 2012: Estimation of surface carbon fluxes with an advanced data assimilation methodology. J. Geophys. Res., 117, D24101, doi:10.1029/2012JD018259.

    • Search Google Scholar
    • Export Citation
  • Kelly, D., , A. J. Majda, , and X. T. Tong, 2015: Concrete ensemble Kalman filters with rigorous catastrophic filter divergence. Proc. Natl. Acad. Sci. USA, 112, 10 58910 594, doi:10.1073/pnas.1511063112.

    • 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, doi:10.1002/qj.443.

    • Search Google Scholar
    • Export Citation
  • Kleist, D. T., , and K. Ide, 2015a: An OSSE-based evaluation of hybrid variational-ensemble data assimilation for the NCEP GFS. Part I: System description and 3D-hybrid results. Mon. Wea. Rev., 143, 433451, doi:10.1175/MWR-D-13-00351.1.

    • Search Google Scholar
    • Export Citation
  • Kleist, D. T., , and K. Ide, 2015b: An OSSE-based evaluation of hybrid variational-ensemble data assimilation for the NCEP GFS. Part II: 4DEnVar and hybrid variants. Mon. Wea. Rev., 143, 452470, doi:10.1175/MWR-D-13-00350.1.

    • Search Google Scholar
    • Export Citation
  • Krishnamurti, T. N., , H. S. Bedi, , W. Heckley, , and K. Ingles, 1988: Reduction of the spinup time for evaporation and precipitation in a spectral model. Mon. Wea. Rev., 116, 907920, doi:10.1175/1520-0493(1988)116<0907:ROTSTF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Krishnamurti, T. N., , C. M. Kishtawal, , T. E. LaRow, , D. R. Bachiochi, , Z. Zhang, , C. E. Williford, , S. Gadgil, , and S. Surendran, 1999: Improved weather and seasonal climate forecasts from multimodel superensemble. Science, 285, 15481550, doi:10.1126/science.285.5433.1548.

    • Search Google Scholar
    • Export Citation
  • Kumjian, M. R., 2013: Principles and applications of dual-polarization weather radar. Part III: Artifacts. J. Oper. Meteor., 1, 265274, doi:10.15191/nwajom.2013.0121.

    • Search Google Scholar
    • Export Citation
  • Kunii, M., 2014: The 1000-member ensemble Kalman filtering with the JMA nonhydrostatic mesoscale model on the K computer. J. Meteor. Soc. Japan, 92, 623633, doi:10.2151/jmsj.2014-607.

    • Search Google Scholar
    • Export Citation
  • Lang, S. T. K., , M. Bonavita, , and M. Leutbecher, 2015: On the impact of re-centering initial conditions for ensemble forecasts. Quart. J. Roy. Meteor. Soc., 141, 25712581, doi:10.1002/qj.2543.

    • Search Google Scholar
    • Export Citation
  • Lange, H., , and G. C. Craig, 2014: The impact of data assimilation length scales on analysis and prediction of convective storms. Mon. Wea. Rev., 142, 37813808, doi:10.1175/MWR-D-13-00304.1.

    • Search Google Scholar
    • Export Citation
  • Lavaysse, C., , M. Carrera, , S. Bélair, , N. Gagnon, , R. Frenette, , M. Charron, , and M. K. Yau, 2013: Impact of surface parameter uncertainties within the Canadian regional ensemble prediction system. Mon. Wea. Rev., 141, 15061526, doi:10.1175/MWR-D-11-00354.1.

    • Search Google Scholar
    • Export Citation
  • Lawson, W. G., , and J. A. Hansen, 2004: Implications of stochastic and deterministic filters as ensemble-based data assimilation methods in varying regimes of error growth. Mon. Wea. Rev., 132, 19661981, doi:10.1175/1520-0493(2004)132<1966:IOSADF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lei, L., , and J. L. Anderson, 2014: Empirical localization of observations for serial ensemble Kalman filter data assimilation in an atmospheric general circulation model. Mon. Wea. Rev., 142, 18351851, doi:10.1175/MWR-D-13-00288.1.

    • Search Google Scholar
    • Export Citation
  • Lei, L., , and J. S. Whitaker, 2015: Model space localization is not always better than observation space localization for assimilation of satellite radiances. Mon. Wea. Rev., 143, 39483955, doi:10.1175/MWR-D-14-00413.1.

    • Search Google Scholar
    • Export Citation
  • Lei, L., , D. R. Stauffer, , and A. Deng, 2012: A hybrid nudging-ensemble Kalman filter approach to data assimilation in WRF/DART. Quart. J. Roy. Meteor. Soc., 138, 20662078, doi:10.1002/qj.1939.

    • Search Google Scholar
    • Export Citation
  • Leith, C. E., 1974: Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev., 102, 409418, doi:10.1175/1520-0493(1974)102<0409:TSOMCF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lewis, J. M., , S. Lakshmivarahan, , and S. K. Dhall, 2006: Dynamic Data Assimilation: A Least Squares Approach. Cambridge University Press, 654 pp.

  • Li, X., , M. Charron, , L. Spacek, , and G. Candille, 2008: A regional ensemble prediction system based on moist targeted singular vectors and stochastic parameter perturbations. Mon. Wea. Rev., 136, 443462, doi:10.1175/2007MWR2109.1.

    • Search Google Scholar
    • Export Citation
  • Lien, G.-Y., , E. Kalnay, , and T. Miyoshi, 2013: Effective assimilation of global precipitation: Simulation experiments. Tellus, 65A, 19915, doi:10.3402/tellusa.v65i0.19915.

    • Search Google Scholar
    • Export Citation
  • Lien, G.-Y., , E. Kalnay, , T. Miyoshi, , and G. J. Huffman, 2016a: Statistical properties of global precipitation in the NCEP GFS model and TMPA observations for data assimilation. Mon. Wea. Rev., 144, 663679, doi:10.1175/MWR-D-15-0150.1.

    • Search Google Scholar
    • Export Citation
  • Lien, G.-Y., , T. Miyoshi, , and E. Kalnay, 2016b: Assimilation of TRMM multisatellite precipitation analysis with a low-resolution NCEP global forecast system. Mon. Wea. Rev., 144, 643661, doi:10.1175/MWR-D-15-0149.1.

    • Search Google Scholar
    • Export Citation
  • Lindskog, M., , K. Salonen, , H. Järvinen, , and D. B. Michelson, 2004: Doppler radar wind data assimilation with HIRLAM 3DVAR. Mon. Wea. Rev., 132, 10811092, doi:10.1175/1520-0493(2004)132<1081:DRWDAW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Liu, C., , Q. Xiao, , and B. Wang, 2008: An ensemble-based four-dimensional variational data assimilation scheme. Part I: Technical formulation and preliminary test. Mon. Wea. Rev., 136, 33633373, doi:10.1175/2008MWR2312.1.

    • Search Google Scholar
    • Export Citation
  • Liu, Z.-Q., , and F. Rabier, 2003: The potential of high-density observations for numerical weather prediction: A study with simulated observations. Quart. J. Roy. Meteor. Soc., 129, 30133035, doi:10.1256/qj.02.170.

    • Search Google Scholar
    • Export Citation
  • Liu, Z.-Q., , C. S. Schwartz, , C. Snyder, , and S.-Y. Ha, 2012: Impact of assimilating AMSU-A radiances on forecasts of 2008 Atlantic tropical cyclones initialized with a limited-area ensemble Kalman filter. Mon. Wea. Rev., 140, 40174034, doi:10.1175/MWR-D-12-00083.1.

    • Search Google Scholar
    • Export Citation
  • Lorenc, A. C., 1986: Analysis methods for numerical weather prediction. Quart. J. Roy. Meteor. Soc., 112, 11771194, doi:10.1002/qj.49711247414.

    • 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, doi:10.1256/qj.02.132.

    • Search Google Scholar
    • Export Citation
  • Lorenc, A. C., , N. E. Bowler, , A. M. Clayton, , S. R. Pring, , and D. Fairbairn, 2015: Comparison of hybrid-4DEnVar and hybrid-4DVar data assimilation methods for global NWP. Mon. Wea. Rev., 143, 212229, doi:10.1175/MWR-D-14-00195.1.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1965: A study of the predictability of a 28-variable atmospheric model. Tellus, 17A, 321333, doi:10.1111/j.2153-3490.1965.tb01424.x.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1982: Atmospheric predictability experiments with a large numerical model. Tellus, 34A, 505513, doi:10.1111/j.2153-3490.1982.tb01839.x.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 2005: Designing chaotic models. J. Atmos. Sci., 62, 15741587, doi:10.1175/JAS3430.1.

  • Lynch, P., , and X.-Y. Huang, 1992: Initialization of the HIRLAM model using a digital filter. Mon. Wea. Rev., 120, 10191034, doi:10.1175/1520-0493(1992)120<1019:IOTHMU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Machenhauer, B., 1977: On the dynamics of gravity oscillations in a shallow water model, with application to normal mode initialization. Contrib. Atmos. Phys., 50, 253271.

    • Search Google Scholar
    • Export Citation
  • Mandel, J., 2006: Efficient implementation of the ensemble Kalman filter. Center for Computational Mathematics Rep. 231, University of Colorado at Denver and Health Sciences Center, Denver, CO, 9 pp.

  • Mass, C. F., , D. Ovens, , K. Westrick, , and B. A. Colle, 2002: Does increasing horizontal resolution produce more skillful forecasts? Bull. Amer. Meteor. Soc., 83, 407430, doi:10.1175/1520-0477(2002)083<0407:DIHRPM>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • McNally, T., 2004: The assimilation of stratospheric satellite data at ECMWF. Proc. ECMWF/SPARC Workshop on Modelling and Assimilation for the Stratosphere and Tropopause, Shinfield Park, Reading, United Kingdom, ECMWF, 103106.

  • McTaggart-Cowan, R., , C. Girard, , A. Plante, , and M. Desgagné, 2011: The utility of upper-boundary nesting in NWP. Mon. Wea. Rev., 139, 21172144, doi:10.1175/2010MWR3633.1.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., , and F. Zhang, 2007: Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part II: Imperfect model experiments. Mon. Wea. Rev., 135, 14031423, doi:10.1175/MWR3352.1.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., , and F. Zhang, 2008a: Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part III: Comparison with 3DVAR in a real-data case study. Mon. Wea. Rev., 136, 522540, doi:10.1175/2007MWR2106.1.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., , and F. Zhang, 2008b: Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part IV: Comparison with 3DVAR in a month-long experiment. Mon. Wea. Rev., 136, 36713682, doi:10.1175/2008MWR2270.1.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., , and F. Zhang, 2011: Limited-area ensemble-based data assimilation. Mon. Wea. Rev., 139, 20252045, doi:10.1175/2011MWR3418.1.

    • Search Google Scholar
    • Export Citation
  • Mitchell, H. L., , and P. L. Houtekamer, 2000: An adaptive ensemble Kalman filter. Mon. Wea. Rev., 128, 416433, doi:10.1175/1520-0493(2000)128<0416:AAEKF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mitchell, H. L., , and P. L. Houtekamer, 2009: Ensemble Kalman filter configurations and their performance with the logistic map. Mon. Wea. Rev., 137, 43254343, doi:10.1175/2009MWR2823.1.

    • Search Google Scholar
    • Export Citation
  • Mitchell, H. L., , P. L. Houtekamer, , and G. Pellerin, 2002: Ensemble size, balance, and model-error representation in an ensemble Kalman filter. Mon. Wea. Rev., 130, 27912808, doi:10.1175/1520-0493(2002)130<2791:ESBAME>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., 2011: The Gaussian approach to adaptive covariance inflation and its implementation with the local ensemble transform Kalman filter. Mon. Wea. Rev., 139, 15191535, doi:10.1175/2010MWR3570.1.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., , and K. Kondo, 2013: A multi-scale localization approach to an ensemble Kalman filter. SOLA, 9, 170173, doi:10.2151/sola.2013-038.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., , Y. Sato, , and T. Kadowaki, 2010: Ensemble Kalman filter and 4D-Var intercomparison with the Japanese operational global analysis and prediction system. Mon. Wea. Rev., 138, 28462866, doi:10.1175/2010MWR3209.1.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., , E. Kalnay, , and H. Li, 2013: Estimating and including observation-error correlations in data assimilation. Inverse Probl. Sci. Eng., 21, 387398, doi:10.1080/17415977.2012.712527.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., , K. Kondo, , and T. Imamura, 2014: The 10,240-member ensemble Kalman filtering with an intermediate AGCM. Geophys. Res. Lett., 41, 52645271, doi:10.1002/2014GL060863.

    • Search Google Scholar
    • Export Citation
  • Molteni, F., 2003: Atmospheric simulations using a GCM with simplified physical parametrizations. I: Model climatology and variability in multi-decadal experiments. Climate Dyn., 20, 175191.

    • Search Google Scholar
    • Export Citation
  • Morrison, H., , A. Morales, , and C. Villanueva-Birriel, 2015: Concurrent sensitivities of an idealized deep convective storm to parameterization of microphysics, horizontal grid resolution, and environmental static stability. Mon. Wea. Rev., 143, 20822104, doi:10.1175/MWR-D-14-00271.1.

    • Search Google Scholar
    • Export Citation
  • Murphy, J., and Coauthors, 2011: Perturbed parameter ensembles as a tool for sampling model uncertainties and making climate projections. Proc. ECMWF Workshop on Representing Model Uncertainty and Error in Numerical Weather and Climate Prediction Models, Shinfield Park, Reading, United Kingdom, ECMWF, 183208.

  • Mylne, K. R., , R. E. Evans, , and R. T. Clark, 2002: Multi-model multi-analysis ensembles in quasi-operational medium-range forecasting. Quart. J. Roy. Meteor. Soc., 128, 361384, doi:10.1256/00359000260498923.

    • Search Google Scholar
    • Export Citation
  • Nerger, L., 2015: On serial observation processing in localized ensemble Kalman filters. Mon. Wea. Rev., 143, 15541567, doi:10.1175/MWR-D-14-00182.1.

    • Search Google Scholar
    • Export Citation
  • Newton, C. W., 1954: Analysis and data problems in relation to numerical prediction. Bull. Amer. Meteor. Soc., 35, 287294.

  • Oczkowski, M., , I. Szunyogh, , and D. J. Patil, 2005: Mechanisms for the development of locally low-dimensional atmospheric dynamics. J. Atmos. Sci., 62, 11351156, doi:10.1175/JAS3403.1.

    • Search Google Scholar
    • Export Citation
  • Ott, E., and Coauthors, 2004: A local ensemble Kalman filter for atmospheric data assimilation. Tellus, 56A, 415428, doi:10.1111/j.1600-0870.2004.00076.x.

    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., 2012: Towards the probabilistic earth-system simulator: A vision for the future of climate and weather prediction. Quart. J. Roy. Meteor. Soc., 138, 841861, doi:10.1002/qj.1923.

    • Search Google Scholar
    • Export Citation
  • Pan, Y., , K. Zhu, , M. Xue, , X. Wang, , M. Hu, , S. G. Benjamin, , S. S. Weygandt, , and J. S. Whitaker, 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, doi:10.1175/MWR-D-13-00242.1.

    • Search Google Scholar
    • Export Citation
  • 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.

    • Search Google Scholar
    • Export Citation
  • Pennell, C., , and T. Reichler, 2011: On the effective number of climate models. J. Climate, 24, 23582367, doi:10.1175/2010JCLI3814.1.

  • Penny, S. G., 2014: The hybrid local ensemble transform Kalman filter. Mon. Wea. Rev., 142, 21392149, doi:10.1175/MWR-D-13-00131.1.

  • Penny, S. G., , D. W. Behringer, , J. A. Carton, , and E. Kalnay, 2015: A hybrid global ocean data assimilation system at NCEP. Mon. Wea. Rev., 143, 46604677, doi:10.1175/MWR-D-14-00376.1.

    • Search Google Scholar
    • Export Citation
  • Petersen, D. P., 1968: On the concept and implementation of sequential analysis for linear random fields. Tellus, 20A, 673686, doi:10.1111/j.2153-3490.1968.tb00410.x.

    • Search Google Scholar
    • Export Citation
  • Pires, C., , R. Vautard, , and O. Talagrand, 1996: On extending the limits of variational assimilation in nonlinear chaotic systems. Tellus, 48A, 96121, doi:10.1034/j.1600-0870.1996.00006.x.

    • Search Google Scholar
    • Export Citation
  • Plant, R. S., , and G. C. Craig, 2008: A stochastic parameterization for deep convection based on equilibrium statistics. J. Atmos. Sci., 65, 87105, doi:10.1175/2007JAS2263.1.

    • Search Google Scholar
    • Export Citation
  • Polavarapu, S., , M. Tanguay, , and L. Fillion, 2000: Four-dimensional variational data assimilation with digital filter initialization. Mon. Wea. Rev., 128, 24912510, doi:10.1175/1520-0493(2000)128<2491:FDVDAW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Polavarapu, S., , S. Ren, , A. M. Clayton, , D. Sankey, , and Y. Rochon, 2004: On the relationship between incremental analysis updating and incremental digital filtering. Mon. Wea. Rev., 132, 24952502, doi:10.1175/1520-0493(2004)132<2495:OTRBIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., , and F. Zhang, 2014: Intercomparison and coupling of ensemble and four-dimensional variational data assimilation methods for the analysis and forecasting of Hurricane Karl (2010). Mon. Wea. Rev., 142, 33473364, doi:10.1175/MWR-D-13-00394.1.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., , and F. Zhang, 2015: Systematic comparison of four-dimensional data assimilation methods with and without the tangent linear model using hybrid background error covariance: E4DVar versus 4DEnVar. Mon. Wea. Rev., 143, 16011621, doi:10.1175/MWR-D-14-00224.1.

    • Search Google Scholar
    • Export Citation
  • Poterjoy, J., , and F. Zhang, 2016: Comparison of hybrid four-dimensional data assimilation methods with and without the tangent linear and adjoint models for predicting the life cycle of Hurricane Karl (2010). Mon. Wea. Rev., 144, 14491468, doi:10.1175/MWR-D-15-0116.1.

    • Search Google Scholar
    • Export Citation
  • Potter, J. E., 1964: W matrix augmentation. MIT Instrumentation Laboratory, Memo. SGA 5-64, Massachusetts Institute of Technology, Cambridge, MA.

  • Press, W. H., , S. A. Teukolsky, , W. T. Vetterling, , and B. P. Flannery, 1992: Numerical Recipes in FORTRAN: The Art of Scientific Computing. 2nd ed. Cambridge University Press, 933 pp.

  • Putnam, B. J., , M. Xue, , Y. Jung, , N. Snook, , and G. Zhang, 2014: The analysis and prediction of microphysical states and polarimetric radar variables in a mesoscale convective system using double-moment microphysics, multinetwork radar data, and the ensemble Kalman filter. Mon. Wea. Rev., 142, 141162, doi:10.1175/MWR-D-13-00042.1.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., , H. Järvinen, , E. Klinker, , J.-F. Mahfouf, , and A. Simmons, 2000: The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics. Quart. J. Roy. Meteor. Soc., 126, 11431170, doi:10.1002/qj.49712656415.

    • Search Google Scholar
    • Export Citation
  • Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding. World Scientific, 240 pp.

  • Ruiz, J., , and M. Pulido, 2015: Parameter estimation using ensemble-based data assimilation in the presence of model error. Mon. Wea. Rev., 143, 15681582, doi:10.1175/MWR-D-14-00017.1.

    • Search Google Scholar
    • Export Citation
  • Rutherford, I. D., 1976: An operational 3-dimensional multivariate statistical objective analysis scheme. Proc. JOC Study Group Conf. on Four-Dimensional Data Assimilation, Rep. 11, Paris, France, WMO/JCSU, 98121.

  • Ryzhkov, A. V., 2007: The impact of beam broadening on the quality of radar polarimetric data. J. Atmos. Oceanic Technol., 24, 729744, doi:10.1175/JTECH2003.1.

    • Search Google Scholar
    • Export Citation
  • Sakov, P., , and L. Bertino, 2011: Relation between two common localisation methods for the EnKF. Comput. Geosci., 15, 225237, doi:10.1007/s10596-010-9202-6.

    • Search Google Scholar
    • Export Citation
  • Schraff, C., , H. Reich, , A. Rhodin, , A. Schomburg, , K. Stephan, , A. Periáñez, , and R. Potthast, 2016: Kilometre-scale ensemble data assimilation for the COSMO model (KENDA). Quart. J. Roy. Meteor. Soc., 142, 14531472, doi:10.1002/qj.2748.

    • Search Google Scholar
    • Export Citation
  • Schwartz, C. S., , G. S. Romine, , R. A. Sobash, , K. R. Fossell, , and M. L. Weisman, 2015: NCAR’s experimental real-time convection-allowing ensemble prediction system. Wea. Forecasting, 30, 16451654, doi:10.1175/WAF-D-15-0103.1.

    • Search Google Scholar
    • Export Citation
  • Shutts, G., 2005: A kinetic energy backscatter algorithm for use in ensemble prediction systems. Quart. J. Roy. Meteor. Soc., 131, 30793102, doi:10.1256/qj.04.106.

    • Search Google Scholar
    • Export Citation
  • Shutts, G., , and A. Callado Pallares, 2011: Tracking down the origin of NWP model uncertainty: coarse-graining studies. Proc. ECMWF Workshop on Representing Model Uncertainty and Error in Numerical Weather and Climate Prediction Models, Shinfield Park, Reading, United Kingdom, ECMWF, 221231.

  • Simmons, A. J., 1996: The skill of 500 hPa height forecasts. Proc. ECMWF Seminar on Predictability, Shinfield Park, Reading, United Kingdom, ECMWF, 1968.

  • Sippel, J. A., , F. Zhang, , Y. Weng, , L. Tian, , G. M. Heymsfield, , and S. A. Braun, 2014: Ensemble Kalman filter assimilation of HIWRAP observations of Hurricane Karl (2010) from the unmanned Global Hawk aircraft. Mon. Wea. Rev., 142, 45594580, doi:10.1175/MWR-D-14-00042.1.

    • Search Google Scholar
    • Export Citation
  • Sluka, T. C., , S. G. Penny, , E. Kalnay, , and T. Miyoshi, 2016: Assimilating atmospheric observations into the ocean using strongly coupled ensemble data assimilation. Geophys. Res. Lett., 43, 752759, doi:10.1002/2015GL067238.

    • 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, doi:10.1175/MWR-D-10-05053.1.

    • Search Google Scholar
    • Export Citation
  • Snook, N., , M. Xue, , and Y. Jung, 2015: Multiscale EnKF assimilation of radar and conventional observations and ensemble forecasting for a tornadic mesoscale convective system. Mon. Wea. Rev., 143, 10351057, doi:10.1175/MWR-D-13-00262.1.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., 2015: Introduction to the Kalman filter. Les Houches 2012: Advanced Data Assimilation for Geosciences, E. Blayo et al., Eds., Oxford University Press, 75–120.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Steinhoff, J., , and D. Underhill, 1994: Modification of the Euler equations for “vorticity confinement”: Application to the computation of interacting vortex rings. Phys. Fluids A Fluid Dyn., 6, 27382744, doi:10.1063/1.868164.

    • Search Google Scholar
    • Export Citation
  • Stewart, L. M., , S. L. Dance, , and N. K. Nichols, 2013: Data assimilation with correlated observation errors: Experiments with a 1-D shallow water model. Tellus, 65A, 19546, doi:10.3402/tellusa.v65i0.19546.

    • Search Google Scholar
    • Export Citation
  • Strohmaier, E., , J. Dongarra, , H. Simon, , and M. Meuer, 2015: The Top500 list: Twenty years of insight into HPC performance. Accessed December 2015. [Available online at www.top500.org/lists/2015/11.]

  • Swinbank, R., and Coauthors, 2015: The TIGGE project and its achievements. Bull. Amer. Meteor. Soc., 97, 4967, doi:10.1175/BAMS-D-13-00191.1.

    • Search Google Scholar
    • Export Citation
  • Szunyogh, I., , E. J. Kostelich, , G. Gyarmati, , E. Kalnay, , B. R. Hunt, , E. Ott, , E. Satterfield, , and J. A. Yorke, 2008: A local ensemble transform Kalman filter data assimilation system for the NCEP global model. Tellus, 60A, 113130, doi:10.1111/j.1600-0870.2007.00274.x.

    • Search Google Scholar
    • Export Citation
  • Tarantola, A., 1987: Inverse Problem Theory. Elsevier, 613 pp.

  • Tarantola, A., 2006: Popper, Bayes and the inverse problem. Nature Phys., 2, 492494, doi:10.1038/nphys375.

  • Tardif, R., , G. J. Hakim, , and C. Snyder, 2015: Coupled atmosphere–ocean data assimilation experiments with a low-order model and CMIP5 model data. Climate Dyn., 45, 14151427, doi:10.1007/s00382-014-2390-3.

    • Search Google Scholar
    • Export Citation
  • Temperton, C., , and M. Roch, 1991: Implicit normal mode initialization for an operational regional model. Mon. Wea. Rev., 119, 667677, doi:10.1175/1520-0493(1991)119<0667:INMIFA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thépaut, J.-N., , and P. Courtier, 1991: Four-dimensional variational data assimilation using the adjoint of a multilevel primitive-equation model. Quart. J. Roy. Meteor. Soc., 117, 12251254, doi:10.1002/qj.49711750206.

    • Search Google Scholar
    • Export Citation
  • Thomas, S. J., , J. P. Hacker, , and J. L. Anderson, 2009: A robust formulation of the ensemble Kalman filter. Quart. J. Roy. Meteor. Soc., 135, 507521, doi:10.1002/qj.372.

    • Search Google Scholar
    • Export Citation
  • Thompson, T. E., , L. J. Wicker, , X. Wang, , and C. Potvin, 2015: A comparison between the local ensemble transform Kalman filter and the ensemble square root filter for the assimilation of radar data in convective-scale models. Quart. J. Roy. Meteor. Soc., 141, 11631176, doi:10.1002/qj.2423.

    • Search Google Scholar
    • Export Citation
  • Tippett, M. K., , J. L. Anderson, , C. H. Bishop, , T. M. Hamill, , and J. S. Whitaker, 2003: Ensemble square root filters. Mon. Wea. Rev., 131, 14851490, doi:10.1175/1520-0493(2003)131<1485:ESRF>2.0.CO;2.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Torn, R. D., , and G. J. Hakim, 2008: Performance characteristics of a pseudo-operational ensemble Kalman filter. Mon. Wea. Rev., 136, 39473963, doi:10.1175/2008MWR2443.1.

    • Search Google Scholar
    • Export Citation
  • Torn, R. D., , G. J. Hakim, , and C. Snyder, 2006: Boundary conditions for limited-area ensemble Kalman filters. Mon. Wea. Rev., 134, 24902502, doi:10.1175/MWR3187.1.

    • Search Google Scholar
    • Export Citation
  • Toth, Z., , and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125, 32973319, doi:10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Verlaan, M., , and A. W. Heemink, 2001: Nonlinearity in data assimilation applications: A practical method for analysis. Mon. Wea. Rev., 129, 15781589, doi:10.1175/1520-0493(2001)129<1578:NIDAAA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wang, S., , M. Xue, , A. Schenkman, , and J. Min, 2013: An iterative ensemble square root filter and tests with simulated radar data for storm-scale data assimilation. Quart. J. Roy. Meteor. Soc., 139, 18881903, doi:10.1002/qj.2077.

    • Search Google Scholar
    • Export Citation
  • Wang, X., , and T. Lei, 2014: GSI-based four-dimensional ensemble-variational (4DEnsVar) data assimilation: Formulation and single- resolution experiments with real data for NCEP global forecast system. Mon. Wea. Rev., 142, 33033325, doi:10.1175/MWR-D-13-00303.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., , C. Snyder, , and T. M. Hamill, 2007: On the theoretical equivalence of differently proposed ensemble-3DVAR hybrid analysis schemes. Mon. Wea. Rev., 135, 222227, doi:10.1175/MWR3282.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., , D. M. Barker, , C. Snyder, , and T. M. Hamill, 2008: A hybrid ETKF–3DVAR data assimilation scheme for the WRF model. Part I: Observing system simulation experiment. Mon. Wea. Rev., 136, 51165131, doi:10.1175/2008MWR2444.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., , D. Parrish, , D. Kleist, , and J. Whitaker, 2013: GSI 3DVar-based ensemble-variational hybrid data assimilation for NCEP global forecast system: Single-resolution experiments. Mon. Wea. Rev., 141, 40984117, doi:10.1175/MWR-D-12-00141.1.

    • Search Google Scholar
    • Export Citation
  • Wei, M., , and Z. Toth, 2003: A new measure of ensemble performance: Perturbation versus error correlation analysis (PECA). Mon. Wea. Rev., 131, 15491565, doi:10.1175//1520-0493(2003)131<1549:ANMOEP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Weng, Y., , and F. Zhang, 2012: Assimilating airborne Doppler radar observations with an ensemble Kalman filter for convection-permitting hurricane initialization and prediction: Katrina (2005). Mon. Wea. Rev., 140, 841859, doi:10.1175/2011MWR3602.1.

    • Search Google Scholar
    • Export Citation
  • Weng, Y., , and F. Zhang, 2016: Advances in convection-permitting tropical cyclone analysis and prediction through EnKF assimilation of reconnaissance aircraft observations. J. Meteor. Soc. Japan, 94, 345358, doi:10.2151/jmsj.2016-018.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., , and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 19131924, doi:10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2; Corrigendum, 134, 1722, doi:10.1175/MWR3156.1

    • 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, doi:10.1175/MWR-D-11-00276.1.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., , T. M. Hamill, , X. Wei, , Y. Song, , and Z. Toth, 2008: Ensemble data assimilation with the NCEP global forecast system. Mon. Wea. Rev., 136, 463482, doi:10.1175/2007MWR2018.1.

    • 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, doi:10.1175/JTECH1835.1.

    • Search Google Scholar
    • Export Citation
  • Xue, M., , J. Schleif, , F. Kong, , K. W. Thomas, , Y. Wang, , and K. Zhu, 2013: Track and intensity forecasting of hurricanes: Impact of convection-permitting resolution and global ensemble Kalman filter analysis on 2010 Atlantic season forecasts. Wea. Forecasting, 28, 13661384, doi:10.1175/WAF-D-12-00063.1.

    • Search Google Scholar
    • Export Citation
  • Yang, S.-C., , E. Kalnay, , B. Hunt, , and N. E. Bowler, 2009: Weight interpolation for efficient data assimilation with the Local Ensemble Transform Kalman Filter. Quart. J. Roy. Meteor. Soc., 135, 251262, doi:10.1002/qj.353.

    • Search Google Scholar
    • Export Citation
  • Yang, S.-C., , E. Kalnay, , and B. Hunt, 2012a: Handling nonlinearity in an ensemble Kalman filter: Experiments with the three-variable Lorenz model. Mon. Wea. Rev., 140, 26282646, doi:10.1175/MWR-D-11-00313.1.

    • Search Google Scholar
    • Export Citation
  • Yang, S.-C., , E. Kalnay, , and T. Miyoshi, 2012b: Accelerating the EnKF spinup for typhoon assimilation and prediction. Wea. Forecasting, 27, 878897, doi:10.1175/WAF-D-11-00153.1.

    • Search Google Scholar
    • Export Citation
  • Yang, S.-C., , E. Kalnay, , and T. Enomoto, 2015: Ensemble singular vectors and their use as additive inflation in EnKF. Tellus, 67A, 26536, doi:10.3402/tellusa.v67.26536.

    • Search Google Scholar
    • Export Citation
  • Ying, Y., , and F. Zhang, 2015: An adaptive covariance relaxation method for ensemble data assimilation. Quart. J. Roy. Meteor. Soc., 141, 28982906, doi:10.1002/qj.2576.

    • Search Google Scholar
    • Export Citation
  • Zhang, F.,