Editorial Type:
Article
Article Type:
Research Article

Improved Vertical Covariance Estimates for Ensemble-Filter Assimilation of Near-Surface Observations

Joshua P. Hacker National Center for Atmospheric Research, * Boulder, Colorado

Search for other papers by Joshua P. Hacker in
Current site
Google Scholar
PubMed Close
,
Jeffrey L. Anderson National Center for Atmospheric Research, * Boulder, Colorado

Search for other papers by Jeffrey L. Anderson in
Current site
Google Scholar
PubMed Close
, and
Mariusz Pagowski NOAA/Forecast Systems Laboratory, and Colorado State University/Cooperative Institute for Research in the Atmosphere, Boulder, Colorado

Search for other papers by Mariusz Pagowski in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Mar 2007
DOI:
https://doi.org/10.1175/MWR3333.1
Page(s):
1021–1036
Restricted access

Abstract

Strategies to improve covariance estimates for ensemble-based assimilation of near-surface observations in atmospheric models are explored. It is known that localization of covariance estimates can improve conditioning of covariance matrices in the assimilation process by removing spurious elements and increasing the rank of the matrix. Vertical covariance localization is the focus of this work, and two basic approaches are compared: 1) a recently proposed hierarchical filter approach based on sampling theory and 2) a more commonly used fifth-order piecewise rational function. The hierarchical filter allows for dynamic estimates of localization functions and does not place any restrictions on their form. The rational function is optimized for every analysis time of day and for every possible observation and state variable combination. The methods are tested with a column model containing PBL and land surface parameterization schemes that are available in current mesoscale modeling systems. The results are expected to provide context for assimilation of near-surface observations in mesoscale models, which will benefit short-range mesoscale NWP applications. Results show that both the hierarchical and rational function approaches effectively improve covariance estimates from small ensembles. The hierarchical approach provides localization functions that are irregular and more closely related to PBL structure. Analysis of eigenvalue spectra show that both approaches improve the rank of the covariance matrices, but the amount of improvement is not always directly related to the assimilation performance. Results also show that specifying different localization functions for different observation and state variable combinations is more important than including time dependence.

Corresponding author address: Joshua Hacker, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: hacker@ucar.edu

Abstract

Strategies to improve covariance estimates for ensemble-based assimilation of near-surface observations in atmospheric models are explored. It is known that localization of covariance estimates can improve conditioning of covariance matrices in the assimilation process by removing spurious elements and increasing the rank of the matrix. Vertical covariance localization is the focus of this work, and two basic approaches are compared: 1) a recently proposed hierarchical filter approach based on sampling theory and 2) a more commonly used fifth-order piecewise rational function. The hierarchical filter allows for dynamic estimates of localization functions and does not place any restrictions on their form. The rational function is optimized for every analysis time of day and for every possible observation and state variable combination. The methods are tested with a column model containing PBL and land surface parameterization schemes that are available in current mesoscale modeling systems. The results are expected to provide context for assimilation of near-surface observations in mesoscale models, which will benefit short-range mesoscale NWP applications. Results show that both the hierarchical and rational function approaches effectively improve covariance estimates from small ensembles. The hierarchical approach provides localization functions that are irregular and more closely related to PBL structure. Analysis of eigenvalue spectra show that both approaches improve the rank of the covariance matrices, but the amount of improvement is not always directly related to the assimilation performance. Results also show that specifying different localization functions for different observation and state variable combinations is more important than including time dependence.

Corresponding author address: Joshua Hacker, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: hacker@ucar.edu

Save
Cover Monthly Weather Review
Monthly Weather Review

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

  • Anderson, J. L. , 2003: A local least squares framework for ensemble filtering. Mon. Wea. Rev., 131 , 634–642.

  • Anderson, J. L. , 2006: Exploring the need for localization in ensemble data assimilation using an hierarchical ensemble filter. Physica D, in press.

    • Search Google Scholar
    • Export Citation

  • Beljaars, A. C. M. , and A. A. M. Holtstag , 1991: Flux parameterization over land surfaces for atmospheric models. J. Appl. Meteor., 30 , 327–341.

    • Search Google Scholar
    • Export Citation

  • Ek, M. B. , K. E. Mitchell , Y. Lin , P. Grunmann , V. Koren , G. Gayno , and J. D. Tarpley , 2003: Implementation of Noah land surface model advances in the National Centers for Environmental Prediction operational mesoscale Eta model. J. Geophys. Res., 108 .8851, doi:10.1029/2002JD003296.

    • 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 , 10143–10162.

    • Search Google Scholar
    • Export Citation

  • Furrer, R. H. , and T. Bengtsson , 2007: Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants. J Multivar. Anal., 98 , 227–255.

    • 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

  • Gneiting, T. , 1999: Correlation functions for atmospheric data analysis. Quart. J. Roy. Meteor. Soc., 125 , 2449–2464.

  • 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

  • Hamill, T. M. , J. Whitaker , and C. Snyder , 2001: Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev., 129 , 2776–2790.

    • 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. , 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

  • Janjić, Z. I. , 2001: Nonsingular implementation of the Mellor–Yamada level 2.5 scheme in the NCEP meso model. National Centers for Environmental Prediction Office Note Tech. Rep. 437, 61 pp.

  • Keppenne, C. L. , and M. M. Rienecker , 2002: Initial testing of a massively parallel ensemble Kalman filter with the Poseidon isopycnal ocean general circulation model. Mon. Wea. Rev., 130 , 2951–2965.

    • Search Google Scholar
    • Export Citation

  • Mellor, G. L. , and T. Yamada , 1982: Development of turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20 , 851–875.

    • 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 , 2791–2808.

    • Search Google Scholar
    • Export Citation

  • Mitchell, K. , and Coauthors , 2000: Recent GCIP-sponsored advancements in coupled land surface modeling and data assimilation in the NCEP Eta Mesoscale Model. Preprints, 15th Conf. on Hydrology, Long Beach, CA, Amer. Meteor. Soc., 180–183.

  • Pagowski, M. , 2004: Some comments on PBL parameterizations in WRF. Preprints, Joint 5th WRF/14th MM5 Users’ Workshop, Boulder, CO, NCAR, 43–46. [Available online at http://www.mmm.ucar.edu/mm5/workshop/workshop-papers_ws04.html.].

  • Pagowski, M. , J. Hacker , and J-W. Bao , 2005: Behavior of WRF PBL schemes and land surface models in 1D simulations during BAMEX. Preprints, Joint 6th WRF/15th MM5 Users’ Workshop, Boulder, CO, NCAR, 4.6. [Available online at http://www.mmm.ucar.edu/wrf/users/workshops/WS2005/WorkshopPapers.html.].

  • 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. National Center for Atmospheric Research Tech. Rep. TN-468, 100 pp.

  • van Leeuwen, P. J. , 1999: Comment on “Data assimilation using an ensemble Kalman filter technique.”. Mon. Wea. Rev., 127 , 1374–1377.

    • Search Google Scholar
    • Export Citation

  • Weber, R. O. , and P. Talkner , 1993: Some remarks on spatial correlation function models. Mon. Wea. Rev., 121 , 2611–2617.

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

    • Search Google Scholar
    • Export Citation

  • Whitaker, J. S. , G. P. Compo , X. Wei , and T. M. Hamill , 2004: Reanalysis without radiosondes using ensemble data assimilation. Mon. Wea. Rev., 132 , 1190–1200.

    • Search Google Scholar
    • Export Citation

  • Zilitinkevich, S. S. , 1995: Non-local turbulent transport: Pollution dispersion aspects of coherent structure of convective flows. Air Pollution Theory and Simulation, H. Power, N. Moussiopoulos, and C. A. Brebbia, Eds., Vol. I, Air Pollution III, Computational Mechanics Publications, 53–60.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 147 90 7
PDF Downloads 80 34 5