• Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129 , 28842903.

  • Anderson, J. L., 2003: A local least squares framework for ensemble filtering. Mon. Wea. Rev., 131 , 634642.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Berre, L., O. Pannekoucke, G. Desroziers, S. E. Stefanescu, B. Chapnik, and L. Raynaud, 2007: A variational assimilation ensemble and the spatial filtering of its error covariances: Increase of sample size by local spatial averaging. Proc. ECMWF Workshop on Flow-Dependent Aspects of Data Assimilation, Reading, United Kingdom, ECMWF, 151–168. [Available online at http://www.ecmwf.int/publications/library/do/references/list/14092007.].

    • Search Google Scholar
    • Export Citation
  • Buehner, M., 2005: Ensemble-derived stationary and flow-dependent background error covariances: Evaluation in a quasi-operation NWP setting. Quart. J. Roy. Meteor. Soc., 131 , 10131043.

    • Search Google Scholar
    • Export Citation
  • Courtier, P., J. N. Thepaut, and A. Hollingsworth, 1994: A strategy for operational implementation of 4D-Var, using an incremental approach. Quart. J. Roy. Meteor. Soc., 120 , 13671387.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46 , 30773107.

    • 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 , 1014310162.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., and P. J. van Leeuwen, 2000: An ensemble Kalman smoother for nonlinear dynamics. Mon. Wea. Rev., 128 , 18521867.

  • Fertig, E. J., J. Harlim, and B. R. Hunt, 2007: A comparative study of 4D-VAR and a 4D ensemble filter: Perfect model simulations with Lorenz-96. Tellus, 59A , 96100.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Gilbert, J. C., and C. Lemarechal, 1989: Some numerical experiments with variable storage quasi-Newton algorithm. Math. Programm., 45B , 407435.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., and C. Snyder, 2000: A hybrid ensemble Kalman filter–3D variational analysis scheme. Mon. Wea. Rev., 128 , 29052919.

  • 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 , 31323147.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., C. Snyder, and R. E. Morss, 2000: A comparison of probabilistic forecasts from bred, singular-vector, and perturbed observation ensembles. Mon. Wea. Rev., 128 , 18351851.

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

    • 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.

    • 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.

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

  • Hunt, B. R., and Coauthors, 2004: Four-dimensional ensemble Kalman filtering. Tellus, 56A , 273277.

  • Kain, J. S., 2004: The Kain–Fritsch convective parameterization: An update. J. Appl. Meteor., 43 , 170181.

  • 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.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Liu, Z., 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.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Mitchell, H. L., P. L. Houtekamer, and G. Pellerin, 2002: Ensemble size and model-error representation in an ensemble Kalman filter. Mon. Wea. Rev., 130 , 27912808.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the long-wave. J. Geophys. Res., 102 , (D14). 1666316682.

    • Search Google Scholar
    • Export Citation
  • Pu, Z-X., E. Kalnay, J. Sela, and I. Szunyogh, 1997: Sensitivity of forecast errors to initial conditions with a quasi-inverse linear method. Mon. Wea. Rev., 125 , 24792503.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., and A. Hollingsworth, 2002: Some aspects of the improvement in skill of numerical weather prediction. Quart. J. Roy. Meteor. Soc., 128 , 647677.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, W. Wang, and J. G. Powers, 2005: A description of the Advanced Research WRF version 2. NCAR Tech. Note NCAR/TN-468+STR, 88 pp.

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

    • Search Google Scholar
    • Export Citation
  • Xiao, Q., X. Zou, M. Pondeca, M. A. Shapiro, and C. S. Velden, 2002: Impact of GMS-5 and GOES-9 satellite-derived winds on the prediction of a NORPEX extratropical cyclone. Mon. Wea. Rev., 130 , 507528.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., 2005: Dynamics and structure of mesoscale error covariance of a winter cyclone estimated through short-range ensemble forecasts. Mon. Wea. Rev., 133 , 28762893.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., C. Snyder, and R. Rotunno, 2002: Mesoscale predictability of the “surprise” snowstorm of 24–25 January 2000. Mon. Wea. Rev., 130 , 16171632.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., Z. Meng, and A. Aksoy, 2006: Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part I: Perfect model experiments. Mon. Wea. Rev., 134 , 722736.

    • Search Google Scholar
    • Export Citation
  • Zhang, H., J. Xue, S. Zhuang, G. Zhu, and Z. Zhu, 2004: GRAPeS 3D-Var data assimilation system ideal experiments. Acta Meteor. Sin., 62 , 3141.

    • Search Google Scholar
    • Export Citation
  • Zupanski, D., 1997: A general weak constraint applicable to operational 4DVAR data assimilation systems. Mon. Wea. Rev., 125 , 22742292.

    • Search Google Scholar
    • Export Citation
  • Zupanski, M., 2005: Maximum likelihood ensemble filter: Theoretical aspects. Mon. Wea. Rev., 133 , 17101726.

  • Zupanski, M., D. Zupanski, D. F. Parrish, E. Rogers, and G. DiMego, 2002: Four-dimensional variational data assimilation for the Blizzard of 2000. Mon. Wea. Rev., 130 , 19671988.

    • Search Google Scholar
    • Export Citation
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An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part II: Observing System Simulation Experiments with Advanced Research WRF (ARW)

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  • 1 LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China, and ESSL/MMM, National Center for Atmospheric Research,* Boulder, Colorado
  • | 2 ESSL/MMM, National Center for Atmospheric Research,* Boulder, Colorado
  • | 3 LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
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Abstract

An ensemble-based four-dimensional variational data assimilation (En4DVAR) algorithm and its performance in a low-dimension space with a one-dimensional shallow-water model have been presented in Part I. This algorithm adopts the standard incremental approach and preconditioning in the variational algorithm but avoids the need for a tangent linear model and its adjoint so that it can be easily incorporated into variational assimilation systems. The current study explores techniques for En4DVAR application in real-dimension data assimilation. The EOF decomposed correlation function operator and analysis time tuning are formulated to reduce the impact of sampling errors in En4DVAR upon its analysis. With the Advanced Research Weather Research and Forecasting (ARW-WRF) model, Observing System Simulation Experiments (OSSEs) are designed and their performance in real-dimension data assimilation is examined. It is found that the designed En4DVAR localization techniques can effectively alleviate the impacts of sampling errors upon analysis. Most forecast errors and biases in ARW are reduced by En4DVAR compared to those in a control experiment. En3DVAR cycling experiments are used to compare the ensemble-based sequential algorithm with the ensemble-based retrospective algorithm. These experiments indicate that the ensemble-based retrospective assimilation, En4DVAR, produces an overall better analysis than the ensemble-based sequential algorithm, En3DVAR, cycling approach.

Corresponding author address: Dr. Qingnong Xiao, ESSL/MMM, National Center for Atmospheric Research, Boulder, CO 80307-3000. Email: hsiao@ucar.edu

Abstract

An ensemble-based four-dimensional variational data assimilation (En4DVAR) algorithm and its performance in a low-dimension space with a one-dimensional shallow-water model have been presented in Part I. This algorithm adopts the standard incremental approach and preconditioning in the variational algorithm but avoids the need for a tangent linear model and its adjoint so that it can be easily incorporated into variational assimilation systems. The current study explores techniques for En4DVAR application in real-dimension data assimilation. The EOF decomposed correlation function operator and analysis time tuning are formulated to reduce the impact of sampling errors in En4DVAR upon its analysis. With the Advanced Research Weather Research and Forecasting (ARW-WRF) model, Observing System Simulation Experiments (OSSEs) are designed and their performance in real-dimension data assimilation is examined. It is found that the designed En4DVAR localization techniques can effectively alleviate the impacts of sampling errors upon analysis. Most forecast errors and biases in ARW are reduced by En4DVAR compared to those in a control experiment. En3DVAR cycling experiments are used to compare the ensemble-based sequential algorithm with the ensemble-based retrospective algorithm. These experiments indicate that the ensemble-based retrospective assimilation, En4DVAR, produces an overall better analysis than the ensemble-based sequential algorithm, En3DVAR, cycling approach.

Corresponding author address: Dr. Qingnong Xiao, ESSL/MMM, National Center for Atmospheric Research, Boulder, CO 80307-3000. Email: hsiao@ucar.edu

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