Article Type:
Review Article

Limited-Area Ensemble-Based Data Assimilation

Zhiyong Meng Laboratory for Climate and Ocean–Atmosphere Studies, Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing, China

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Fuqing Zhang Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

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Print Publication:
01 Jul 2011
Collections:
Intercomparisons of 4D-Variational Assimilation and the Ensemble Kalman Filter, Review Articles in Monthly Weather Review
DOI:
https://doi.org/10.1175/2011MWR3418.1
Page(s):
2025–2045
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Abstract

Ensemble-based data assimilation is a state estimation technique that uses short-term ensemble forecasts to estimate flow-dependent background error covariance and is best known by varying forms of ensemble Kalman filters (EnKFs). The EnKF has recently emerged as one of the primary alternatives to the variational data assimilation methods widely used in both global and limited-area numerical weather prediction models. In addition to comparing the EnKF with variational methods, this article reviews recent advances and challenges in the development and applications of the EnKF, including its hybrid with variational methods, in limited-area models that resolve weather systems from convective to meso- and regional scales.

Corresponding author address: Dr. Fuqing Zhang, Department of Meteorology, The Pennsylvania State University, University Park, PA 16802. E-mail: fzhang@psu.edu

This article is included in the Intercomparisons of 4D-Variational Assimilation and the Ensemble Kalman Filter special collection.

Abstract

Ensemble-based data assimilation is a state estimation technique that uses short-term ensemble forecasts to estimate flow-dependent background error covariance and is best known by varying forms of ensemble Kalman filters (EnKFs). The EnKF has recently emerged as one of the primary alternatives to the variational data assimilation methods widely used in both global and limited-area numerical weather prediction models. In addition to comparing the EnKF with variational methods, this article reviews recent advances and challenges in the development and applications of the EnKF, including its hybrid with variational methods, in limited-area models that resolve weather systems from convective to meso- and regional scales.

Corresponding author address: Dr. Fuqing Zhang, Department of Meteorology, The Pennsylvania State University, University Park, PA 16802. E-mail: fzhang@psu.edu

This article is included in the Intercomparisons of 4D-Variational Assimilation and the Ensemble Kalman Filter special collection.

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  • Aksoy, A., F. Zhang, J. W. Nielsen-Gammon, and C. C. Epifanio, 2005: Ensemble-based data assimilation for thermally forced circulations. J. Geophys. Res., 110, D16105, doi:10.1029/2004JD005718.

    • Search Google Scholar
    • Export Citation

  • Aksoy, A., F. Zhang, and J. W. Nielsen-Gammon, 2006a: Ensemble-based simultaneous state and parameter estimation with MM5. Geophys. Res. Lett., 33, L12801, doi:10.1029/2006GL026186.

    • Search Google Scholar
    • Export Citation

  • Aksoy, A., F. Zhang, and J. W. Nielsen-Gammon, 2006b: Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model. Mon. Wea. Rev., 134, 2951–2970.

    • 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, 1805–1824.

    • 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, 1273–1292.

    • Search Google Scholar
    • Export Citation

  • Ancell, B., and G. J. Hakim, 2007: Comparing adjoint- and ensemble-sensitivity analysis with applications to observation targeting. Mon. Wea. Rev., 135, 4117–4134.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 2884–2903.

  • Anderson, J. L., 2006: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D, 230, 99–111.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., 2009: Spatially and temporally varying adaptive covariance inflation for ensemble filters. Tellus, 61A, 72–83.

  • Anderson, J. L., and N. Collins, 2007: Scalable implementations of ensemble filter algorithms for data assimilation. J. Atmos. Oceanic Technol., 24, 1452–1463.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., B. Wyman, S. Zhang, and T. Hoar, 2005: Assimilation of surface pressure observations using an ensemble filter in an idealized global atmospheric prediction system. J. Atmos. Sci., 62, 2925–2938.

    • Search Google Scholar
    • Export Citation

  • Annan, J. D., D. J. Lunt, J. C. Hargreaves, and P. J. Valdes, 2005: Parameter estimation in an atmospheric GCM using the ensemble Kalman filter. Nonlinear Processes Geophys., 12, 363–371.

    • Search Google Scholar
    • Export Citation

  • Aravéquia, A. J., 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, 1932–1951.

    • Search Google Scholar
    • Export Citation

  • Barker, D. M., 2005: Southern high-latitude ensemble data assimilation in the Antarctic Mesoscale Prediction System. Mon. Wea. Rev., 133, 3431–3449.

    • Search Google Scholar
    • Export Citation

  • Barnes, S. L., 1964: A technique for maximizing details in numerical weather map analysis. J. Appl. Meteor., 3, 396–409.

  • Beezley, J., and J. Mandel, 2008: Morphing ensemble Kalman filters. Tellus, 60A, 131–140.

  • Berre, L., and G. Desroziers, 2010: Filtering of background error variances and correlations by local spatial averaging: A review. Mon. Wea. Rev., 138, 3693–3720.

    • Search Google Scholar
    • Export Citation

  • Bishop, C. H., and D. Hodyss, 2007: Flow-adaptive moderation of spurious ensemble correlations and its use in ensemble-based data assimilation. Quart. J. Roy. Meteor. Soc., 133, 2029–2044.

    • 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, 420–436.

    • Search Google Scholar
    • Export Citation

  • Bonavita, M., L. Torrisi, and F. Marcucci, 2008: The ensemble Kalman filter in an operational regional NWP system: Preliminary results with real observations. Quart. J. Roy. Meteor. Soc., 134, 1733–1744.

    • Search Google Scholar
    • Export Citation

  • Bonavita, M., L. Torrisi, and F. Marcucci, 2010: Ensemble data assimilation with the CNMCA regional forecasting system. Quart. J. Roy. Meteor. Soc., 136, 132–145.

    • Search Google Scholar
    • Export Citation

  • Buehner, M., 2005: Ensemble-derived stationary and flow-dependent background-error covariances: Evaluation in a quasi-operational NWP setting. Quart. J. Roy. Meteor. Soc., 131, 1013–1043.

    • 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, 1550–1566.

    • 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, 1567–1586.

    • 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, 3081–3094.

    • Search Google Scholar
    • Export Citation

  • Charron, M., P. L. Houtekamer, and P. Bartello, 2006: Assimilation with an ensemble Kalman filter of synthetic radial wind data in anisotropic turbulence: Perfect model experiments. Mon. Wea. Rev., 134, 618–637.

    • Search Google Scholar
    • Export Citation

  • Chen, Y., and C. Snyder, 2007: Assimilating vortex position with an ensemble Kalman filter. Mon. Wea. Rev., 135, 1828–1845.

  • Dévényi, D., and T. W. Schlatter, 1994: Statistical properties of three-hour prediction “errors” derived from the Mesoscale Analysis and Prediction System. Mon. Wea. Rev., 122, 1263–1280.

    • Search Google Scholar
    • Export Citation

  • Dirren, S., R. D. Torn, and G. J. Hakim, 2007: A data assimilation case study using a limited-area ensemble Kalman filter. Mon. Wea. Rev., 135, 1455–1473.

    • Search Google Scholar
    • Export Citation

  • Dowell, D. C., and L. J. Wicker, 2009: Additive noise for storm-scale ensemble data assimilation. J. Atmos. Oceanic Technol., 26, 911–927.

    • 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, 1982–2005.

    • Search Google Scholar
    • Export Citation

  • Ehrendorfer, M., 2007: A review of issues in ensemble-based Kalman filtering. Meteor. Z., 16, 795–818.

  • Etherton, B. J., 2007: Preemptive forecasts using an ensemble Kalman filter. Mon. Wea. Rev., 135, 3484–3495.

  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10 143–10 162.

    • Search Google Scholar
    • Export Citation

  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53, 343–367.

  • Evensen, G., 2007: Data Assimilation: The Ensemble Kalman Filter. Springer, 279 pp.

  • 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, 1846–1868.

    • Search Google Scholar
    • Export Citation

  • Fujita, T., D. J. Stensrud, and D. C. Dowell, 2008: Using precipitation observations in a mesoscale short-range ensemble analysis and forecasting system. Wea. Forecasting, 23, 357–372.

    • Search Google Scholar
    • Export Citation

  • Gao, J., and M. Xue, 2008: An efficient dual-resolution approach for ensemble data assimilation and tests with simulated Doppler radar data. Mon. Wea. Rev., 136, 945–963.

    • 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, 723–757.

    • Search Google Scholar
    • Export Citation

  • Hacker, J. P., and C. Snyder, 2005: Ensemble Kalman filter assimilation of fixed screen-height observations in a parameterized PBL. Mon. Wea. Rev., 133, 3260–3275.

    • Search Google Scholar
    • Export Citation

  • Hacker, J. P., J. L. Anderson, and M. Pagowski, 2007: Improved vertical covariance estimates for ensemble-filter assimilation of near-surface observations. Mon. Wea. Rev., 135, 1021–1036.

    • Search Google Scholar
    • Export Citation

  • Hakim, G. J., and R. D. Torn, 2008: Ensemble synoptic analysis. Synoptic–Dynamic Meteorology and Weather Analysis and Forecasting: A Tribute to Fred Sanders, L. F. Bosart and B. Bluestein, Eds., Amer. Meteor. Soc., 147–162.

    • 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.

    • 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, 2905–2919.

  • Hamill, T. M., and C. Snyder, 2002: Using improved background error covariances from an ensemble Kalman filter for adaptive observations. Mon. Wea. Rev., 130, 1552–1572.

    • Search Google Scholar
    • Export Citation

  • Hamill, T. M., and J. S. Whitaker, 2005: Accounting for the error due to unresolved scales in ensemble data assimilation: A comparison of different approaches. Mon. Wea. Rev., 133, 3132–3147.

    • 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, 796–811.

    • 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, 123–137.

    • Search Google Scholar
    • Export Citation

  • Houtekamer, P. L., and H. L. Mitchell, 2005: Ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc., 131, 3269–3289.

  • 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, 1225–1242.

    • 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, 604–620.

    • 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, 2126–2143.

    • Search Google Scholar
    • Export Citation

  • Hu, X., 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., and P. Lynch, 1993: Diabatic digital-filtering initialization: Application to the HIRLAM model. Mon. Wea. Rev., 121, 589–603.

    • Search Google Scholar
    • Export Citation

  • Hunt, B. R., and Coauthors, 2004: Four-dimensional ensemble Kalman filtering. Tellus, 56A, 273–277.

  • 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, 112–126.

    • 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, 2246–2260.

    • 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 observation operator error. Mon. Wea. Rev., 138, 539–562.

    • Search Google Scholar
    • Export Citation

  • Kalman, R. E., 1960: A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng., 82D, 35–45.

  • Kalman, R. E., and R. S. Bucy, 1961: New results in linear filtering and prediction theory. Trans. ASME J. Basic Eng., 83D, 95–108.

  • Kepert, J. D., 2009: Covariance localisation and balance in an ensemble Kalman filter. Quart. J. Roy. Meteor. Soc., 135, 1157–1176.

  • 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 multi-model superensemble. Science, 285, 1548–1550.

    • Search Google Scholar
    • Export Citation

  • Lawson, W. G., and J. A. Hansen, 2005: Alignment error models and ensemble-based data assimilation. Mon. Wea. Rev., 133, 1687–1709.

  • Lei, J., P. Bickel, and C. Snyder, 2010: Comparison of ensemble Kalman filters under non-Gaussianity. Mon. Wea. Rev., 138, 1293–1306.

  • Lei, T., M. Xue, and T. Yu, 2008: Multi-scale analysis and prediction of the 8 May 2003 Oklahoma City tornadic supercell storm assimilating radar and surface network data using EnKF. Preprints, 13th Conf. on Integrated Observing and Assimilation Systems for Atmosphere, Oceans, and Land Surface (IOAS-AOLS), Pheonix, AZ, Amer. Meteor. Soc., Paper 6.4. [Available online at http://ams.confex.com/ams/89annual/techprogram/paper_150404.htm with a link to the extended abstract at http://twister.ou.edu/papers/LeiXueYu_AMS2009.pdf.]

    • Search Google Scholar
    • Export Citation

  • Li, H., E. Kalnay, T. Miyoshi, and C. M. Danforth, 2009: Accounting for model errors in ensemble data assimilation. Mon. Wea. Rev., 137, 3407–3419.

    • 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, 3363–3373.

    • Search Google Scholar
    • Export Citation

  • Liu, C., Q. Xiao, and B. Wang, 2009: An ensemble-based four-dimensional variational data assimilation scheme. Part II: Observing system simulation experiments with Advanced Research WRF (ARW). Mon. Wea. Rev., 137, 1687–1704.

    • Search Google Scholar
    • Export Citation

  • Liu, H., J. Anderson, Y. H. Kuo, C. Snyder, and A. Caya, 2008: Evaluation of a nonlocal quasi-phase observation operator in assimilation of CHAMP radio occultation refractivity with WRF. Mon. Wea. Rev., 136, 242–256.

    • Search Google Scholar
    • Export Citation

  • Liu, J., H. Li, E. Kalnay, E. J. Kostelich, and I. Szunyogh, 2009: Univariate and multivariate assimilation of AIRS humidity retrievals with the local ensemble transform Kalman filter. Mon. Wea. Rev., 137, 3918–3932.

    • 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, 3183–3203.

    • Search Google Scholar
    • Export Citation

  • Lynch, P., and X. Huang, 1992: Initialization of the HIRLAM model using a digital filter. Mon. Wea. Rev., 120, 1019–1034.

  • 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, 1403–1423.

    • 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, 522–540.

    • 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, 3671–3682.

    • Search Google Scholar
    • Export Citation

  • Mitchell, H. L., and P. L. Houtekamer, 2000: An adaptive ensemble Kalman filter. Mon. Wea. Rev., 128, 416–433.

  • 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, 2791–2808.

    • Search Google Scholar
    • Export Citation

  • Miyoshi, T., and K. Aranami, 2006: Applying a four-dimensional local ensemble transform Kalman filter (4D-LETKF) to the JMA Nonhydrostatic Model (NHM). SOLA, 2, 128–131.

    • Search Google Scholar
    • Export Citation

  • Miyoshi, T., and Y. Sato, 2007: Assimilating satellite radiances with a local ensemble transform Kalman filter (LETKF) applied to the JMA Global Model (GSM). SOLA, 3, 37–40.

    • Search Google Scholar
    • Export Citation

  • Miyoshi, T., and S. Yamane, 2007: Local ensemble transform Kalman filtering with an AGCM at a T159/L48 resolution. Mon. Wea. Rev., 135, 3841–3861.

    • Search Google Scholar
    • Export Citation

  • Orlanski, I., 1975: A rational subdivision of scales for atmospheric processes. Bull. Amer. Meteor. Soc., 56, 527–530.

  • Ott, E., and Coauthors, 2004: A local ensemble Kalman filter for atmospheric data assimilation. Tellus, 56A, 415–428.

  • Palmer, T. N., and Coauthors, 2004: Development of a European Multimodel Ensemble System for Seasonal-to-Interannual Prediction (DEMETER). Bull. Amer. Meteor. Soc., 85, 853–872.

    • Search Google Scholar
    • Export Citation

  • Peña, M., Z. Toth, and M. Wei, 2010: Controlling noise in ensemble data assimilation schemes. Mon. Wea. Rev., 138, 1502–1512.

  • Sippel, J. A., and F. Zhang, 2010: Factors affecting the predictability of Hurricane Humberto (2007). J. Atmos. Sci., 67, 1759–1778.

  • Snyder, C., and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131, 1663–1677.

    • Search Google Scholar
    • Export Citation

  • Snyder, C., T. Bengtsson, P. Bickel, and J. Anderson, 2008: Obstacles to high-dimensional particle filtering. Mon. Wea. Rev., 136, 4629–4640.

    • Search Google Scholar
    • Export Citation

  • Stensrud, D. J., J.-W. Bao, and T. T. Warner, 2000: Using initial condition and model physics perturbations in short-range ensemble simulations of mesoscale convective systems. Mon. Wea. Rev., 128, 2077–2107.

    • Search Google Scholar
    • Export Citation

  • Stuart, A. L., A. Aksoy, F. Zhang, and J. W. Nielsen-Gammon, 2007: Ensemble-based data assimilation and targeted observation of a chemical tracer in a sea breeze model. Atmos. Environ., 41, 3082–3094.

    • 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, 113–130.

    • 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, 1485–1490.

    • Search Google Scholar
    • Export Citation

  • Tong, M., and M. Xue, 2005: Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSSE experiments. Mon. Wea. Rev., 133, 1789–1807.

    • Search Google Scholar
    • Export Citation

  • Tong, M., and M. Xue, 2008a: 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, 1630–1648.

    • Search Google Scholar
    • Export Citation

  • Tong, M., and M. Xue, 2008b: Simultaneous estimation of microphysical parameters and atmospheric state with simulated radar data and ensemble square root Kalman filter. Part II: Parameter estimation experiments. Mon. Wea. Rev., 136, 1649–1668.

    • Search Google Scholar
    • Export Citation

  • Torn, R. D., 2010: Ensemble-based sensitivity analysis applied to African easterly waves. Wea. Forecasting, 25, 61–78.

  • Torn, R. D., and G. J. Hakim, 2008a: Performance characteristics of a pseudo-operational ensemble Kalman filter. Mon. Wea. Rev., 136, 3947–3963.

    • Search Google Scholar
    • Export Citation

  • Torn, R. D., and G. J. Hakim, 2008b: Ensemble-based sensitivity analysis. Mon. Wea. Rev., 136, 663–677.

  • Torn, R. D., and G. J. Hakim, 2009a: Ensemble data assimilation applied to RAINEX observations of Hurricane Katrina (2005). Mon. Wea. Rev., 137, 2817–2829.

    • Search Google Scholar
    • Export Citation

  • Torn, R. D., and G. J. Hakim, 2009b: Initial condition sensitivities of western Pacific extratropical transitions determined using ensemble-based sensitivity analysis. Mon. Wea. Rev., 137, 3388–3406.

    • 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, 2490–2502.

    • Search Google Scholar
    • Export Citation

  • Wang, W., and N. L. Seaman, 1997: A comparison study of convective parameterization schemes in a mesoscale model. Mon. Wea. Rev., 125, 252–278.

    • 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, 222–227.

    • Search Google Scholar
    • Export Citation

  • Wang, X., D. M. Barker, C. Snyder, and T. M. Hamill, 2008a: A hybrid ETKF–3DVAR data assimilation scheme for the WRF model. Part I: Observing System Simulation Experiment. Mon. Wea. Rev., 136, 5116–5131.

    • Search Google Scholar