Editorial Type:
Article
Article Type:
Research Article

An Efficient Dual-Resolution Approach for Ensemble Data Assimilation and Tests with Simulated Doppler Radar Data

Jidong Gao Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, Oklahoma

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Ming Xue Center for Analysis and Prediction of Storms and School of Meteorology, University of Oklahoma, Norman, Oklahoma

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Print Publication:
01 Mar 2008
DOI:
https://doi.org/10.1175/2007MWR2120.1
Page(s):
945–963
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Abstract

A new efficient dual-resolution (DR) data assimilation algorithm is developed based on the ensemble Kalman filter (EnKF) method and tested using simulated radar radial velocity data for a supercell storm. Radar observations are assimilated on both high-resolution and lower-resolution grids using the EnKF algorithm with flow-dependent background error covariances estimated from the lower-resolution ensemble. It is shown that the flow-dependent and dynamically evolved background error covariances thus estimated are effective in producing quality analyses on the high-resolution grid.

The DR method has the advantage of being able to significantly reduce the computational cost of the EnKF analysis. In the system, the lower-resolution ensemble provides the flow-dependent background error covariance, while the single-high-resolution forecast and analysis provides the benefit of higher resolution, which is important for resolving the internal structures of thunderstorms. The relative smoothness of the covariance obtained from the lower 4-km-resolution ensemble does not appear to significantly degrade the quality of analysis. This is because the cross covariance among different variables is of first-order importance for “retrieving” unobserved variables from the radar radial velocity data.

For the DR analysis, an ensemble size of 40 appears to be a reasonable choice with the use of a 4-km horizontal resolution in the ensemble and a 1-km resolution in the high-resolution analysis. Several sensitivity tests show that the DR EnKF system is quite robust to different observation errors. A 4-km thinned data resolution is a compromise that is acceptable under the constraint of real-time applications. A data density of 8 km leads to a significant degradation in the analysis.

Corresponding author address: Dr. Jidong Gao, Center for Analysis and Prediction of Storms, National Weather Center, Suite 2500, 120 David L. Boren Blvd., Norman, OK 73072. Email: jdgao@ou.edu

Abstract

A new efficient dual-resolution (DR) data assimilation algorithm is developed based on the ensemble Kalman filter (EnKF) method and tested using simulated radar radial velocity data for a supercell storm. Radar observations are assimilated on both high-resolution and lower-resolution grids using the EnKF algorithm with flow-dependent background error covariances estimated from the lower-resolution ensemble. It is shown that the flow-dependent and dynamically evolved background error covariances thus estimated are effective in producing quality analyses on the high-resolution grid.

The DR method has the advantage of being able to significantly reduce the computational cost of the EnKF analysis. In the system, the lower-resolution ensemble provides the flow-dependent background error covariance, while the single-high-resolution forecast and analysis provides the benefit of higher resolution, which is important for resolving the internal structures of thunderstorms. The relative smoothness of the covariance obtained from the lower 4-km-resolution ensemble does not appear to significantly degrade the quality of analysis. This is because the cross covariance among different variables is of first-order importance for “retrieving” unobserved variables from the radar radial velocity data.

For the DR analysis, an ensemble size of 40 appears to be a reasonable choice with the use of a 4-km horizontal resolution in the ensemble and a 1-km resolution in the high-resolution analysis. Several sensitivity tests show that the DR EnKF system is quite robust to different observation errors. A 4-km thinned data resolution is a compromise that is acceptable under the constraint of real-time applications. A data density of 8 km leads to a significant degradation in the analysis.

Corresponding author address: Dr. Jidong Gao, Center for Analysis and Prediction of Storms, National Weather Center, Suite 2500, 120 David L. Boren Blvd., Norman, OK 73072. Email: jdgao@ou.edu

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  • 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 , 2741–2758.

    • 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 , 1719–1724.

  • 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 , 1367–1387.

    • Search Google Scholar
    • Export Citation

  • Crook, A., and J. D. Tuttle, 1994: Numerical simulations initialized with radar-derived winds. Part II: Forecasts of three gust-front cases. Mon. Wea. Rev., 122 , 1204–1217.

    • 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

  • Du, J., 2004: Hybrid ensemble prediction system: A new ensembling approach. Preprints, Symp. 50th Anniversary Operational Numerical Weather Prediction, College Park, MD, Amer. Meteor. Soc., P4.2.

  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99 , 10143–10162.

    • Search Google Scholar
    • Export Citation

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

  • Gal-Chen, T., 1978: A method for the initialization of the anelastic equations: Implications for matching models with observations. Mon. Wea. Rev., 106 , 587–606.

    • Search Google Scholar
    • Export Citation

  • Gao, J., M. Xue, Z. Wang, and K. K. Droegemeier, 1998: The initial condition and explicit prediction of convection using ARPS adjoint and other retrieval methods with WSR-88D data. Preprints, 12th Conf. on Numerical Weather Prediction, Phoenix, AZ, Amer. Meteor. Soc., 176–178.

  • Gao, J., M. Xue, A. Shapiro, Q. Xu, and K. K. Droegemeier, 2001: Three-dimensional simple adjoint velocity retrievals from single-Doppler radar. J. Atmos. Oceanic Technol., 18 , 26–38.

    • Search Google Scholar
    • Export Citation

  • Gao, J., M. Xue, K. Brewster, and K. K. Droegemeier, 2004: A three-dimensional variational data analysis method with recursive filter for Doppler radars. J. Atmos. Oceanic Technol., 21 , 457–469.

    • 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

  • 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

  • Hu, M., M. Xue, and K. Brewster, 2006a: 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 , 675–698.

    • Search Google Scholar
    • Export Citation

  • Hu, M., M. Xue, J. Gao, and K. Brewster, 2006b: 3DVAR and cloud analysis with WSR-88D level-II data for the prediction of the Fort Worth, Texas, tornadic thunderstorms. Part II: Impact of radial velocity analysis via 3DVAR. Mon. Wea. Rev., 134 , 699–721.

    • Search Google Scholar
    • Export Citation

  • Ide, K., P. Courtier, M. Ghil, and A. Lorenc, 1997: Unified notation for data assimilation: Operational, sequential and variational. J. Meteor. Soc. Japan, 75 , 181–189.

    • Search Google Scholar
    • Export Citation

  • Lazarus, S., A. Shapiro, and K. K. Droegemeier, 2001: Application of the Zhang–Gal-Chen single-Doppler velocity retrieval to a deep convective storm. J. Atmos. Sci., 58 , 998–1016.

    • Search Google Scholar
    • Export Citation

  • Lin, Y., P. S. Ray, and K. W. Johnson, 1993: Initialization of a modeled convective storm using Doppler radar-derived fields. Mon. Wea. Rev., 121 , 2757–2775.

    • Search Google Scholar
    • Export Citation

  • Lin, Y-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22 , 1065–1092.

    • Search Google Scholar
    • Export Citation

  • Lord, S. J., E. Kalnay, R. Daley, G. D. Emmitt, and R. Atlas, 1997: Using OSSEs in the design of the future generation of integrated observing systems. Preprints, First Symp. on Integrated Observing Systems, Long Beach, CA, Amer. Meteor. Soc., 45–47.

  • 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 , 1143–1170.

    • Search Google Scholar
    • Export Citation

  • Ray, P. S., B. C. Johnson, K. W. Johnson, J. S. Bradberry, J. J. Stephens, K. K. Wagner, R. B. Wilhelmson, and J. B. Klemp, 1981: The morphology of several tornadic storms on 20 May 1977. J. Atmos. Sci., 38 , 1643–1663.

    • Search Google Scholar
    • Export Citation

  • 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

  • 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 , 1642–1661.

    • Search Google Scholar
    • Export Citation

  • Tong, M., 2006: Ensemble Kalman filter assimilation of Doppler radar data for the initialization and prediction of convective storms. Ph.D. dissertation, University of Oklahoma, 243 pp.

  • 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 , 1789–1807.

    • Search Google Scholar
    • Export Citation

  • Weygandt, S. S., A. Shapiro, and K. K. Droegemeier, 2002: Retrieval of model initial fields from single-Doppler observations of a supercell thunderstorm. Part I: Single-Doppler velocity retrieval. Mon. Wea. Rev., 130 , 433–453.

    • Search Google Scholar
    • Export Citation

  • Whitaker, J. S., and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130 , 1913–1924.

  • Xu, Q., C-J. Qiu, H-D. Gu, and J-X. Yu, 1995: Simple adjoint retrievals of microburst winds from single-Doppler radar data. Mon. Wea. Rev., 123 , 1822–1833.

    • Search Google Scholar
    • Export Citation

  • Xue, M., K. K. Droegemeier, and V. Wong, 2000: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification. Meteor. Atmos. Phys., 75 , 161–193.

    • Search Google Scholar
    • Export Citation

  • Xue, M., and Coauthors, 2001: The Advanced Regional Prediction System (ARPS)—A multi-scale nonhydrostatic atmospheric simulation and prediction tool. Part II: Model physics and applications. Meteor. Atmos. Phys., 76 , 143–165.

    • Search Google Scholar
    • Export Citation

  • Xue, M., D-H. Wang, J. Gao, K. Brewster, and K. K. Droegemeier, 2003: The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation. Meteor. Atmos. Phys., 82 , 139–170.

    • 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 , 46–66.

    • Search Google Scholar
    • Export Citation

  • Zupanski, M., S. J. Fletcher, I. M. Navon, B. Uzunoglu, R. P. Heikes, D. A. Randall, T. D. Ringler, and D. Daescu, 2006: Initiation of ensemble data assimilation. Tellus, 58A , 159–170.

    • Search Google Scholar
    • Export Citation
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