Editorial Type:
Article
Article Type:
Research Article

An Examination of the Incremental Balance in a Global Ensemble-Based 3D-Var Data Assimilation System

Jean-François Caron Meteorological Research Division, Environment Canada, Dorval, Québec, Canada

Search for other papers by Jean-François Caron in
Current site
Google Scholar
PubMed Close
and
Luc Fillion Meteorological Research Division, Environment Canada, Dorval, Québec, Canada

Search for other papers by Luc Fillion in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Oct 2010
DOI:
https://doi.org/10.1175/2010MWR3339.1
Page(s):
3946–3966
Restricted access

Abstract

This study examines the modification to the balance properties of the analysis increments in a global three-dimensional variational data assimilation scheme when using flow-dependent background-error covariances derived from an operational ensemble Kalman filter instead of static homogenous and isotropic background-error covariances based on lagged forecast differences. It is shown that the degree of balance in the analysis increments is degraded when the former method is used. This change can be attributed in part to the reduced degree of rotational balance found in short-term ensemble Kalman filter perturbations as compared to lagged forecast differences based on longer-range forecasts. However, the use of a horizontal and vertical localization technique to increase the rank of the ensemble-based covariances are found to have a significant deleterious effect on the rotational balance with the largest detrimental impact coming from the vertical localization and affecting particularly the upper levels. The examination of the vertical motion part of the analysis increments revealed that the spatial covariance localization technique also produces unrealistic vertical structure of vertical motion increments with abnormally large increments near the surface. A comparison between the analysis increments from the ensemble Kalman filter and from the ensemble-based three-dimensional variational data assimilation (3D-Var) scheme showed that the balance characteristics of the analysis increments resulting from the two systems are very similar.

Corresponding author address: Jean-François Caron, Met Office, Joint Centre for Mesoscale Meteorology, Meteorology Building, University of Reading, P.O. Box 243, Reading RG6 6BB, United Kingdom. Email: jean-francois.caron@metoffice.gov.uk

Abstract

This study examines the modification to the balance properties of the analysis increments in a global three-dimensional variational data assimilation scheme when using flow-dependent background-error covariances derived from an operational ensemble Kalman filter instead of static homogenous and isotropic background-error covariances based on lagged forecast differences. It is shown that the degree of balance in the analysis increments is degraded when the former method is used. This change can be attributed in part to the reduced degree of rotational balance found in short-term ensemble Kalman filter perturbations as compared to lagged forecast differences based on longer-range forecasts. However, the use of a horizontal and vertical localization technique to increase the rank of the ensemble-based covariances are found to have a significant deleterious effect on the rotational balance with the largest detrimental impact coming from the vertical localization and affecting particularly the upper levels. The examination of the vertical motion part of the analysis increments revealed that the spatial covariance localization technique also produces unrealistic vertical structure of vertical motion increments with abnormally large increments near the surface. A comparison between the analysis increments from the ensemble Kalman filter and from the ensemble-based three-dimensional variational data assimilation (3D-Var) scheme showed that the balance characteristics of the analysis increments resulting from the two systems are very similar.

Corresponding author address: Jean-François Caron, Met Office, Joint Centre for Mesoscale Meteorology, Meteorology Building, University of Reading, P.O. Box 243, Reading RG6 6BB, United Kingdom. Email: jean-francois.caron@metoffice.gov.uk

Save
Cover Monthly Weather Review
Monthly Weather Review

  • Bannister, R. N., 2008: A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances. Quart. J. Roy. Meteor. Soc., 134 , 1951–1970.

    • Search Google Scholar
    • Export Citation

  • Bélair, S., M. Roch, A-M. Leduc, P. A. Vaillancourt, S. Laroche, and J. Mailhot, 2009: Medium-range quantitative precipitation forecasts from Canada’s new 33-km deterministic global operation system. Wea. Forecasting, 24 , 690–708.

    • 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/ecpublications/_pdf/workshop/2007/Data_assimilation/Berre.pdf].

    • 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 , 1013–1043.

    • 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 , 1550–1566.

    • 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 , 1567–1586.

    • Search Google Scholar
    • Export Citation

  • Caron, J-F., and L. Fillion, 2010: An examination of background error correlations between mass and rotational wind over precipitation regions. Mon. Wea. Rev., 138 , 563–578.

    • Search Google Scholar
    • Export Citation

  • Caron, J-F., P. Zwack, and C. Pagé, 2006: DIONYSOS: A diagnostic tool for numerically-simulated weather systems. Tech. Memo., 45 pp. [Available online at http://www.dionysos.uqam.ca/documentation_e.html].

    • Search Google Scholar
    • Export Citation

  • Caron, J-F., M. K. Yau, S. Laroche, and P. Zwack, 2007: The characteristics of key analysis errors. Part I: Dynamical balance and comparison with observations. Mon. Wea. Rev., 135 , 249–266.

    • Search Google Scholar
    • Export Citation

  • Charney, J., 1955: The use of the primitive equations of motion in numerical prediction. Tellus, 7 , 22–26.

  • Derber, J. C., and F. Bouttier, 1999: A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus, 51A , 195–221.

    • Search Google Scholar
    • Export Citation

  • Fillion, L., and Coauthors, 2007: Case dependent implicit normal mode balance operators. Proc. ECMWF Workshop on Flow-Dependent Aspects of Data Assimilation, Reading, United Kingdom, ECMWF, 125–142. [Available online at http://www.ecmwf.int/publications/library/ecpublications/_pdf/workshop/2007/Data_assimilation/Fillion.pdf].

    • Search Google Scholar
    • Export Citation

  • Fillion, L., and Coauthors, 2010: The Canadian regional data assimilation and forecasting system. Wea. Forcasting, in press.

  • Gaspari, G., and S. E. Cohn, 1999: Contruction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125 , 723–757.

    • Search Google Scholar
    • Export Citation

  • Gauthier, P., M. Tanguay, S. Laroche, S. Pellerin, and J. Morneau, 2007: Extension of 3DVAR to 4DVAR: Implementation of 4DVAR at the Meteorological Service of Canada. Mon. Wea. Rev., 135 , 2339–2354.

    • Search Google Scholar
    • Export Citation

  • Gustafsson, N., L. Berre, S. Hornquist, X-H. Huang, M. Lindskog, B. Navascues, K. S. Mogensen, and S. Thorsteinsson, 2001: Three-dimensional variational data assimilation for a limited area model. Part I: General formulation and the background error constraint. Tellus, 53A , 425–446.

    • 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 , 2905–2919.

  • Hamill, T. M., C. Snyder, and R. E. Morss, 2002: Analysis-error statistics of a quasi-geostrophic model using three-dimensional variational assimilation. Mon. Wea. Rev., 130 , 2777–2790.

    • Search Google Scholar
    • Export Citation

  • Hello, G., and F. Bouttier, 2001: Using adjoint sensitivity as a local structure function in variational data assimilation. Nonlinear Processes Geophys., 8 , 347–355.

    • Search Google Scholar
    • Export Citation

  • Holton, J. R., 1992: An Introduction to Dynamic Meteorology. 3rd ed. Academic Press, 511 pp.

  • Houtekamer, P. L., and H. L. Mitchell, 2005: Ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc., 131 , 3269–3289.

  • Houtekamer, P. L., H. L. Mitchell, and X. Deng, 2009: Model error representation in an operational ensemble Kalman filter. Mon. Wea. Rev., 137 , 2126–2143.

    • Search Google Scholar
    • Export Citation

  • Kepert, J. D., 2009a: Covariance localisation and balance in an ensemble Kalman filter. Quart. J. Roy. Meteor. Soc., 135 , 1157–1176.

  • Kepert, J. D., 2009b: Change-of-variable in an ensemble Kalman filter. Extended Abstracts, Fifth WMO Int. Symp. on Data Assimilation in Meteorology, Oceanography and Hydrology, Melbourne, Australia, WMO, CD-ROM.

    • Search Google Scholar
    • Export Citation

  • Kleist, D. T., D. F. Parrish, J. C. Derber, R. Treadon, R. M. Errico, and R. Yang, 2009: Improving incremental balance in the GSI 3DVAR analysis system. Mon. Wea. Rev., 137 , 1046–1060.

    • Search Google Scholar
    • Export Citation

  • Kucukkaraca, E., and M. Fisher, 2006: Use of analysis ensembles in estimating flow-dependent background error variances. ECMWF Tech. Memo. 492, Reading, United Kingdom, 18 pp. [Available online at http://www.ecmwf.int/publications/library/ecpublications/_pdf/tm/401-500/tm492.pdf].

    • Search Google Scholar
    • Export Citation

  • Lorenc, A. C., 2003: The potential of the ensemble Kalman filter for NWP—A comparison with 4D-Var. Quart. J. Roy. Meteor. Soc., 129 , 3183–3203.

    • Search Google Scholar
    • Export Citation

  • Parrish, D., and J. Derber, 1992: The National Meteorological Centre’s spectral statistical interpolation analysis system. Mon. Wea. Rev., 120 , 1747–1763.

    • 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 , 1143–1170.

    • Search Google Scholar
    • Export Citation

  • Räisänen, J., 1995: Factors affecting synoptic-scale vertical motions: A statistical study using a generalized omega equation. Mon. Wea. Rev., 123 , 2447–2460.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 70 25 0
PDF Downloads 27 11 1