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

  • Barker, D. M., 1998: Var scientific development paper 25: The use of synoptically-dependent error structures in 3DVAR. UK MET Office Tech. Rep., 2 pp.

  • Bishop, C. H., , and Z. Toth, 1999: Ensemble transformation and adaptive observations. J. Atmos. Sci., 56 , 17481765.

  • 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
  • Burgers, G., , P. J. van Leeuwen, , and G. Evensen, 1998: Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev., 126 , 17191724.

  • Cohn, S. E., , D. M. da Silva, , J. Guo, , M. Sienkiewiez, , and D. Lamich, 1998: Assessing the effects of data selection with the DAO physical space statistical analysis system. Mon. Wea. Rev., 126 , 29132926.

    • 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
  • Courtier, P., and Coauthors, 1998: The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: Formulation. Quart. J. Roy. Meteor. Soc., 124 , 17831807.

    • Search Google Scholar
    • Export Citation
  • Daley, R., 1985: Analysis of synoptic-scale divergence by a statistical interpolation procedure. Mon. Wea. Rev., 113 , 10661079.

  • Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • Daley, R., , and E. Barker, 2001: NAVDAS: Formulation and diagnostics. Mon. Wea. Rev., 129 , 869883.

  • Dee, D. P., 1995: Online estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Rev., 123 , 11281196.

  • Etherton, B. J., , and C. H. Bishop, 2004: Resilience of hybrid ensemble/3DVAR analysis schemes to model error and ensemble covariance error. Mon. Wea. Rev., 132 , 10651080.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99 , C5. 1014310162.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53 , 343367.

  • 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. C., , L. Cherette, , L. Fillion, , P. Koclas, , and S. Laroche, 1998: Implementation of a 3D variational data assimilation system at the Canadian Meteorological Centre. Part I: The global analysis. Atmos.–Ocean, 37 , 103156.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., 2006: Ensemble based atmospheric data assimilation. Predictability of Weather and Climate, R. Hagedorn and T. N. Palmer, 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 , 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 forecast from bred, singular vector, and perturbed observation ensembles. Mon. Wea. Rev., 128 , 18351851.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Hanea, R. G., , G. J. M. Velders, , A. J. Segers, , M. Verlaan, , and A. W. Heemink, 2007: A hybrid Kalman filter algorithm for large-scale atmospheric chemistry data assimilation. Mon. Wea. Rev., 135 , 140151.

    • 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.

  • Houtekamer, P. L., , H. L. Mitchell, , G. Pellerin, , M. Buehner, , and M. Charron, 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133 , 604620.

    • Search Google Scholar
    • Export Citation
  • Kepert, J. D., 2004: On ensemble representation of the observations-error covariance in the ensemble Kalman filter. Ocean Dyn., 54 , 561569.

    • Search Google Scholar
    • Export Citation
  • Liu, H., , M. Xue, , J. R. Purser, , and D. F. Parrish, 2005: Retrieval of moisture from GPS slant-path water vapor observations using 3DVAR with isotropic and anisotropic recursive filters. Preprints, 17th Conf. on Numerical Weather Prediction, Washington, DC, Amer. Meteor. Soc., CD-ROM, 14B.6.

  • Lorenc, A. C., 1981: A global three-dimensional multivariate statistical interpolation scheme. Mon. Wea. Rev., 109 , 701721.

  • 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
  • Lynch, P., , and X-Y. Huang, 1992: Initialization of the HIRLAM model using a digital filter. Mon. Wea. Rev., 120 , 10191034.

  • Majumdar, S. J., , C. H. Bishop, , B. J. Etherton, , I. Szunyogh, , and Z. Toth, 2001: Can an ensemble transform Kalman filter predict the reduction in forecast-error variance produced by targeted observations? Quart. J. Roy. Meteor. Soc., 127 , 28032820.

    • Search Google Scholar
    • Export Citation
  • Majumdar, S. J., , C. H. Bishop, , B. J. Etherton, , and Z. Toth, 2002a: Adaptive sampling with the ensemble transform Kalman filter. Part II: Field program implementation. Mon. Wea. Rev., 130 , 13561369.

    • Search Google Scholar
    • Export Citation
  • Majumdar, S. J., , C. H. Bishop, , R. Buizza, , and R. Gelaro, 2002b: A comparison of ensemble transform Kalman filter targeting guidance with ECMWF and NRL total-energy singular vector guidance. Quart. J. Roy. Meteor. Soc., 128 , 25272549.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Ott, E., and Coauthors, 2004: A local ensemble Kalman filter for atmospheric data assimilation. Tellus, 56A , 415428.

  • Palmer, T. N., , R. Gelaro, , J. Barkmeijer, , and R. Buizza, 1998: Singular vectors, metrics, and adaptive observations. J. Atmos. Sci., 55 , 633653.

    • 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
  • Purser, J. R., , W. S. Wu, , D. F. Parrish, , and N. M. Roberts, 2003: Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: Spatially inhomogeneous and anisotropic general covariances. Mon. Wea. Rev., 131 , 15361548.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., , J. N. Thepaut, , and P. Courtier, 1998: Extended assimilation and forecast experiments with a four-dimensional variational assimilation system. Quart. J. Roy. Meteor. Soc., 124 , 139.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., , H. Jarvinen, , 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.

    • Search Google Scholar
    • Export Citation
  • Riishøjgaard, L-P., 1998: A direct way of specifying flow-dependent background error correlations for meteorological analysis systems. Tellus, 50A , 4257.

    • Search Google Scholar
    • Export Citation
  • Ross, S., 1998: A First Course in Probability. Prentice Hall, 514 pp.

  • Schlatter, T. W., 1975: Some experiments with a multivariate statistical objective analysis scheme. Mon. Wea. Rev., 103 , 246257.

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

    • Search Google Scholar
    • Export Citation
  • Szunyogh, I., , E. J. Kostelich, , G. Gyarmati, , D. J. Patil, , B. R. Hunt, , E. Kalnay, , E. Ott, , and J. A. York, 2005: Assessing a local ensemble Kalman filter: Perfect model experiments with the NCEP global model. Tellus, 57A , 528545.

    • 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.

    • 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
  • Toth, Z., , and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer. Meteor. Soc., 74 , 23172330.

  • Toth, Z., , and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125 , 32973319.

  • Wang, X., , and C. H. Bishop, 2003: A comparison of breeding and ensemble transform Kalman filter ensemble forecast schemes. J. Atmos. Sci., 60 , 11401158.

    • Search Google Scholar
    • Export Citation
  • Wang, X., , C. H. Bishop, , and S. J. Julier, 2004: Which is better, an ensemble of positive–negative pairs or a centered spherical simplex ensemble? Mon. Wea. Rev., 132 , 15901605.

    • 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
  • Whitaker, J. S., , and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130 , 19131924.

  • Wu, W. S., , J. R. Purser, , and D. F. Parrish, 2002: Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon. Wea. Rev., 130 , 29052916.

    • 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, S., , and J. L. Anderson, 2003: Impact of spatially and temporally varying estimates of error covariance on assimilation in a simple atmospheric model. Tellus, 55A , 126147.

    • Search Google Scholar
    • Export Citation
  • Zou, X., , A. Barcilon, , I. M. Navon, , J. Whitaker, , and D. G. Cacuci, 1993: An adjoint sensitivity study of blocking in a two-layer isentropic model. Mon. Wea. Rev., 121 , 28332857.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 86 86 8
PDF Downloads 65 65 7

A Comparison of Hybrid Ensemble Transform Kalman Filter–Optimum Interpolation and Ensemble Square Root Filter Analysis Schemes

View More View Less
  • 1 CIRES Climate Diagnostics Center, University of Colorado, and Physical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado
  • | 2 Physical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado
  • | 3 Naval Research Laboratory, Monterey, California
© Get Permissions
Restricted access

Abstract

A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A two-layer primitive equation model was used under perfect-model assumptions. A simplified observation network was used, and the OI method utilized a static background error covariance constructed from a large inventory of historical forecast errors. The hybrid scheme updated the ensemble mean using a hybridized ensemble and static background-error covariance. The ensemble perturbations in the hybrid scheme were updated by the ETKF scheme. The EnSRF ran parallel data assimilation cycles for each member and serially assimilated the observations. The EnSRF background-error covariance was estimated fully from the ensemble.

For 50-member ensembles, the analyses from the hybrid scheme were as accurate or nearly as accurate as those from the EnSRF, depending on the norm. For 20-member ensembles, the analyses from the hybrid scheme were more accurate than analyses from the EnSRF under certain norms. Both hybrid and EnSRF analyses were more accurate than the analyses from the OI. Further reducing the ensemble size to five members, the EnSRF exhibited filter divergence, whereas the analyses from the hybrid scheme were still better than those updated by the OI. Additionally, the hybrid scheme was less prone to spurious gravity wave activity than the EnSRF, especially when the ensemble size was small. Maximal growth in the ETKF ensemble perturbation space exceeded that in the EnSRF ensemble perturbation space. The relationship of the ETKF ensemble variance to the analysis error variance, a measure of a spread–skill relationship, was similar to that of the EnSRF ensemble. The hybrid scheme can be implemented in a reasonably straightforward manner in the operational variational frameworks, and the computational cost of the hybrid is expected to be much less than the EnSRF in the operational settings.

Corresponding author address: Dr. Xuguang Wang, Physical Sciences Division, NOAA/Earth System Research Laboratory, 325 Broadway, R/PSD1 Boulder, CO 80305-3328. Email: xuguang.wang@noaa.gov

Abstract

A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A two-layer primitive equation model was used under perfect-model assumptions. A simplified observation network was used, and the OI method utilized a static background error covariance constructed from a large inventory of historical forecast errors. The hybrid scheme updated the ensemble mean using a hybridized ensemble and static background-error covariance. The ensemble perturbations in the hybrid scheme were updated by the ETKF scheme. The EnSRF ran parallel data assimilation cycles for each member and serially assimilated the observations. The EnSRF background-error covariance was estimated fully from the ensemble.

For 50-member ensembles, the analyses from the hybrid scheme were as accurate or nearly as accurate as those from the EnSRF, depending on the norm. For 20-member ensembles, the analyses from the hybrid scheme were more accurate than analyses from the EnSRF under certain norms. Both hybrid and EnSRF analyses were more accurate than the analyses from the OI. Further reducing the ensemble size to five members, the EnSRF exhibited filter divergence, whereas the analyses from the hybrid scheme were still better than those updated by the OI. Additionally, the hybrid scheme was less prone to spurious gravity wave activity than the EnSRF, especially when the ensemble size was small. Maximal growth in the ETKF ensemble perturbation space exceeded that in the EnSRF ensemble perturbation space. The relationship of the ETKF ensemble variance to the analysis error variance, a measure of a spread–skill relationship, was similar to that of the EnSRF ensemble. The hybrid scheme can be implemented in a reasonably straightforward manner in the operational variational frameworks, and the computational cost of the hybrid is expected to be much less than the EnSRF in the operational settings.

Corresponding author address: Dr. Xuguang Wang, Physical Sciences Division, NOAA/Earth System Research Laboratory, 325 Broadway, R/PSD1 Boulder, CO 80305-3328. Email: xuguang.wang@noaa.gov

Save