E4DVar: Coupling an Ensemble Kalman Filter with Four-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model

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

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

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Abstract

A hybrid data assimilation approach that couples the ensemble Kalman filter (EnKF) and four-dimensional variational (4DVar) methods is implemented for the first time in a limited-area weather prediction model. In this coupled system, denoted E4DVar, the EnKF and 4DVar systems run in parallel while feeding into each other. The multivariate, flow-dependent background error covariance estimated from the EnKF ensemble is used in the 4DVar minimization and the ensemble mean in the EnKF analysis is replaced by the 4DVar analysis, while updating the analysis perturbations for the next cycle of ensemble forecasts with the EnKF. Therefore, the E4DVar can obtain flow-dependent information from both the explicit covariance matrix derived from ensemble forecasts, as well as implicitly from the 4DVar trajectory. The performance of an E4DVar system is compared with the uncoupled 4DVar and EnKF for a limited-area model by assimilating various conventional observations over the contiguous United States for June 2003. After verifying the forecasts from each analysis against standard sounding observations, it is found that the E4DVar substantially outperforms both the EnKF and 4DVar during this active summer month, which featured several episodes of severe convective weather. On average, the forecasts produced from E4DVar analyses have considerably smaller errors than both of the stand-alone EnKF and 4DVar systems for forecast lead times up to 60 h.

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

Abstract

A hybrid data assimilation approach that couples the ensemble Kalman filter (EnKF) and four-dimensional variational (4DVar) methods is implemented for the first time in a limited-area weather prediction model. In this coupled system, denoted E4DVar, the EnKF and 4DVar systems run in parallel while feeding into each other. The multivariate, flow-dependent background error covariance estimated from the EnKF ensemble is used in the 4DVar minimization and the ensemble mean in the EnKF analysis is replaced by the 4DVar analysis, while updating the analysis perturbations for the next cycle of ensemble forecasts with the EnKF. Therefore, the E4DVar can obtain flow-dependent information from both the explicit covariance matrix derived from ensemble forecasts, as well as implicitly from the 4DVar trajectory. The performance of an E4DVar system is compared with the uncoupled 4DVar and EnKF for a limited-area model by assimilating various conventional observations over the contiguous United States for June 2003. After verifying the forecasts from each analysis against standard sounding observations, it is found that the E4DVar substantially outperforms both the EnKF and 4DVar during this active summer month, which featured several episodes of severe convective weather. On average, the forecasts produced from E4DVar analyses have considerably smaller errors than both of the stand-alone EnKF and 4DVar systems for forecast lead times up to 60 h.

Corresponding author address: Dr. Fuqing Zhang, Department of Meteorology, The Pennsylvania State University, University Park, PA 16802. E-mail: fzhang@psu.edu
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  • Andersson, E., M. Fisher, R. Munro, and R. A. McNally, 2000: Diagnosis of background error for radiances and other observable quantities in a variational data assimilation scheme, and the explanation of a case of poor convergence. ECMWF Tech. Memo. 296, Reading, United Kingdom, 22 pp.

    • Search Google Scholar
    • Export Citation
  • Barker, D. M., W. Huang, Y.-R. Guo, A. J. Bourgeois, and Q. N. Xiao, 2004: A three-dimensional variational data assimilation system for MM5: Implementation and initial results. Mon. Wea. Rev., 132, 897914.

    • Search Google Scholar
    • Export Citation
  • Berre, L., 2000: Estimation of synoptic and mesoscale forecast error covariances in a limited area model. Mon. Wea. Rev., 128, 644667.

    • 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.

    • 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, 10131043.

    • 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.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Courtier, P., 1997: Dual formulation of four-dimensional variational data assimilation. Quart. J. Roy. Meteor. Soc., 123, 24492461.

  • Courtier, P., J.-N. Thépaut, 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
  • Dowell, D. C., F. Zhang, L. J. Wicker, C. Snyder, and N. A. Crook, 2004: Wind and thermodynamic retrievals in the 17 May 1981 Arcadia, Oklahoma, supercell: Ensemble Kalman filter experiments. Mon. Wea. Rev., 132, 19822005.

    • 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.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Gao, J., and M. Xue, 2008: An efficient dual-resolution approach for ensemble data assimilation and tests with assimilated Doppler radar data. Mon. Wea. Rev., 136, 945963.

    • 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
  • Gauthier, P., and J. N. Thépaut, 2001: Impact of the digital filter as a weak constraint in the preoperational 4D-Var assimilation system of Météo-France. Mon. Wea. Rev., 129, 20892102.

    • Search Google Scholar
    • Export Citation
  • Gauthier, P., M. Tanguay, S. Laroche, and S. Pellerin, 2007: Extension of 3DVAR to 4DVAR: Implementation of 4DVAR at the Meteorological Service of Canada. Mon. Wea. Rev., 135, 23392364.

    • 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, 1693, doi:10.1029/2002GL015311.

    • Search Google Scholar
    • Export Citation
  • Guo, Y.-R., Y.-H. Kuo, J. Dudhia, D. Parsons, and C. Rocken, 2000: Four-dimensional variational data assimilation of heterogeneous mesoscale observations for a strong convective case. Mon. Wea. Rev., 128, 619643.

    • 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.

  • Hayden, C. M., and R. J. Purser, 1995: Recursive filter objective analysis of meteorological fields: Applications to NESDIS operational processing. J. Appl. Meteor., 34, 315.

    • Search Google Scholar
    • Export Citation
  • Honda, Y., M. Nishijima, K. Koizumi, Y. Ohta, K. Tamiya, T. Kawabata, and T. Tsuyuki, 2005: A pre-operational variational data assimilation system for a non-hydrostatic model at the Japan Meteorological Agency: Formulation and preliminary results. Quart. J. Roy. Meteor. Soc., 131, 34653475.

    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., J. Dudhia, and S.-H. Chen, 2004: A revised approach to ice microphysical processes or the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103120.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Huang, X.-Y., X. Yang, N. Gustafsson, K. Mogensen, and M. Lindskog, 2002: Four-dimensional variational data assimilation for a limited area model. HIRLAM Tech. Rep. 57, 41 pp.

    • Search Google Scholar
    • Export Citation
  • Huang, X. Y., and Coauthors, 2009: Four-dimensional variational data assimilation for WRF: Formulation and preliminary results. Mon. Wea. Rev., 137, 299314.

    • 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, 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, 16871704.

    • Search Google Scholar
    • Export Citation
  • Lorenc, A. C., 2003a: 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
  • Lorenc, A. C., 2003b: Modelling of error covariances by 4D-Var data assimilation. Quart. J. Roy. Meteor. Soc., 129, 31673182.

  • Lorenc, A. C., and Coauthors, 2000: The Met. Office global three-dimensional variational data assimilation scheme. Quart. J. Roy. Meteor. Soc., 126, 29913012.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., and F. Zhang, 2007: Test 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
  • Meng, Z., and F. Zhang, 2008a: Test 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.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., and F. Zhang, 2008b: Test of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part IV: Performance over a warm-season month of June 2003. Mon. Wea. Rev., 136, 36713682.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Navon, I. M., D. N. Daescu, and Z. Liu, 2005: The impact of background error on incomplete observations for 4D-Var data assimilation with the FSU GSM. Lect. Notes Comput. Sci., 3515, 837844.

    • Search Google Scholar
    • Export Citation
  • Noh, Y., W. G. Cheon, S. Y. Hong, and S. Raasch, 2003: Improvement of the K-profile model for the planetary boundary layer based on large eddy simulation data. Bound.-Layer Meteor., 107, 421427.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., J.-N. Thépaut, and P. Courtier, 1998: Extended assimilation and forecast experiments with a four-dimensional variational assimilation system. Quart. J. Roy. Meteor. Soc., 124, 18611887.

    • 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. Quart. J. Roy. Meteor. Soc., 126, 11431170.

    • 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 TN-468+STR, 88 pp.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., and F. Zhang, 2003: Tests of an ensemble Kalman filter for convective-scale data assimilation. Mon. Wea. Rev., 131, 16631677.

    • Search Google Scholar
    • Export Citation
  • Sun, J., and N. A. Crook, 1997: Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part I: Model development and simulated data experiments. J. Atmos. Sci., 54, 16421661.

    • Search Google Scholar
    • Export Citation
  • Thépaut, J.-N., P. Courtier, G. Belaud, and G. Lemaitre, 1996: Dynamic structure functions in a four-dimensional variational assimilation: A case study. Quart. J. Roy. Meteor. Soc., 122, 535561.

    • 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.

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

    • 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.

    • 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: Observation System Simulation Experiment. Mon. Wea. Rev., 136, 51165131.

    • Search Google Scholar
    • Export Citation
  • Wang, X., D. M. Barker, C. Snyder, and T. M. Hamill, 2008b: A hybrid ETKF–3DVAR data assimilation scheme for the WRF model. Part II: Real observation experiments. Mon. Wea. Rev., 136, 51325147.

    • Search Google Scholar
    • Export Citation
  • Wang, X., T. M. Hamill, J. S. Whitaker, and C. H. Bishop, 2009: A comparison of the hybrid and EnSRF analysis schemes in the presence of model error due to unresolved scales. Mon. Wea. Rev., 137, 32193232.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Xu, L., T. Rosmond, and R. Daley, 2005: Development of NAVDAS-AR: Formulation and initial tests of the linear problem. Tellus, 57A, 546559.

    • 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., C. Snyder, and J. Sun, 2004: Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 132, 12381253.

    • Search Google Scholar
    • Export Citation
  • Zhang, F., Z. Meng, and A. Aksoy, 2006: Test 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, F., M. Zhang, and J. A. Hansen, 2009: Coupling ensemble Kalman filter with four- dimensional variational data assimilation. Adv. Atmos. Sci., 26, 18.

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

    • Search Google Scholar
    • Export Citation
  • Zou, X., 1997: Tangent linear and adjoint of “on/off” processes and their feasibility for use in 4-dimensional variational data assimilation. Tellus, 49A, 331.

    • Search Google Scholar
    • Export Citation
  • Zou, X., and Y.-H. Kuo, 1996: Rainfall assimilation through an optimal control of initial and boundary conditions in a limited-area mesoscale model. Mon. Wea. Rev., 124, 28592882.

    • Search Google Scholar
    • Export Citation
  • Zupanski, D., 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
  • Zupanski, M., D. Zupanski, T. Vukicevic, K. Eis, and T. V. Haar, 2005: CIRA/CSU four-dimensional variational data assimilation system. Mon. Wea. Rev., 133, 829843.

    • Search Google Scholar
    • Export Citation
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