Inhomogeneous Background Error Modeling for WRF-Var Using the NMC Method

Hongli Wang National Center for Atmospheric Research, Boulder, Colorado

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Xiang-Yu Huang National Center for Atmospheric Research, Boulder, Colorado

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Juanzhen Sun National Center for Atmospheric Research, Boulder, Colorado

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Dongmei Xu Nanjing University of Information Science and Technology, Nanjing, China

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Man Zhang University of Colorado Boulder, Boulder, Colorado

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Shuiyong Fan Beijing Meteorological Bureau, Beijing, China

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Jiqin Zhong Beijing Meteorological Bureau, Beijing, China

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Abstract

Background error modeling plays a key role in a variational data assimilation system. The National Meteorological Center (NMC) method has been widely used in variational data assimilation systems to generate a forecast error ensemble from which the climatological background error covariance can be modeled. In this paper, the characteristics of the background error modeling via the NMC method are investigated for the variational data assimilation system of the Weather Research and Forecasting (WRF-Var) Model. The background error statistics are extracted from short-term 3-km-resolution forecasts in June, July, and August 2012 over a limited-area domain. It is found 1) that background error variances vary from month to month and also have a feature of diurnal variations in the low-level atmosphere and 2) that u- and υ-wind variances are underestimated and their autocorrelation length scales are overestimated when the default control variable option in WRF-Var is used. A new approach of control variable transform (CVT) is proposed to model the background error statistics based on the NMC method. The new approach is capable of extracting inhomogeneous and anisotropic climatological information from the forecast error ensemble obtained via the NMC method. Single observation assimilation experiments show that the proposed method not only has the merit of incorporating geographically dependent covariance information, but also is able to produce a multivariate analysis. The results from the data assimilaton and forecast study of a real convective case show that the use of the new CVT improves synoptic weather system and precipitation forecasts for up to 12 h.

Current affiliations: Cooperative Institute for Research in the Atmosphere, Colorado State University, and NOAA/Earth System Research Laboratory, Boulder, Colorado.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Dr. Hongli Wang, NOAA/ESRL, 325 Broadway, Boulder, CO 80305. E-mail: hongli.wang@noaa.gov

Abstract

Background error modeling plays a key role in a variational data assimilation system. The National Meteorological Center (NMC) method has been widely used in variational data assimilation systems to generate a forecast error ensemble from which the climatological background error covariance can be modeled. In this paper, the characteristics of the background error modeling via the NMC method are investigated for the variational data assimilation system of the Weather Research and Forecasting (WRF-Var) Model. The background error statistics are extracted from short-term 3-km-resolution forecasts in June, July, and August 2012 over a limited-area domain. It is found 1) that background error variances vary from month to month and also have a feature of diurnal variations in the low-level atmosphere and 2) that u- and υ-wind variances are underestimated and their autocorrelation length scales are overestimated when the default control variable option in WRF-Var is used. A new approach of control variable transform (CVT) is proposed to model the background error statistics based on the NMC method. The new approach is capable of extracting inhomogeneous and anisotropic climatological information from the forecast error ensemble obtained via the NMC method. Single observation assimilation experiments show that the proposed method not only has the merit of incorporating geographically dependent covariance information, but also is able to produce a multivariate analysis. The results from the data assimilaton and forecast study of a real convective case show that the use of the new CVT improves synoptic weather system and precipitation forecasts for up to 12 h.

Current affiliations: Cooperative Institute for Research in the Atmosphere, Colorado State University, and NOAA/Earth System Research Laboratory, Boulder, Colorado.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Dr. Hongli Wang, NOAA/ESRL, 325 Broadway, Boulder, CO 80305. E-mail: hongli.wang@noaa.gov
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  • Bannister, R. N., 2008a: 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, 19511970, doi:10.1002/qj.339.

    • Search Google Scholar
    • Export Citation
  • Bannister, R. N., 2008b: A review of forecast error covariance statistics in atmospheric variational data assimilation. II: Modelling the forecast error covariance statistics. Quart. J. Roy. Meteor. Soc., 134, 19711996, doi:10.1002/qj.340.

    • 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, doi:10.1175/1520-0493(2004)132<0897:ATVDAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Barker, D. M., and Coauthors, 2012: The Weather Research and Forecasting (WRF) Model’s Community Variational/Ensemble Data Assimilation System: WRFDA. Bull. Amer. Meteor. Soc., 93, 831843, doi:10.1175/BAMS-D-11-00167.1.

    • Search Google Scholar
    • Export Citation
  • Chen, M., S. Fan, J. Zhong, X.-Y. Huang, Y.-R. Guo, W. Wang, Y. Wang, and B. Kuo, 2009: A WRF-based rapid updating cycling forecast system of BMB and its performance during the summer and Olympic Games 2008. Extended Abstracts, 10th WRF Users’ Workshop, Boulder, CO, University Corporation for Atmospheric Research, P3B.37. [Available online at http://www2.mmm.ucar.edu/wrf/users/workshops/WS2009/abstracts/P3B-37.pdf.]

  • Chen, Y., S. R. H. Rizvi, X.-Y. Huang, J. Min, and X. Zhang, 2013: Balance characteristics of multivariate background error covariance and their impact on analyses and forecasts in tropical and Arctic regions. Meteor. Atmos. Phys., 121, 7998, doi:10.1007/s00703-013-0251-y.

    • 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, doi:10.1002/qj.49712455002.

    • Search Google Scholar
    • Export Citation
  • Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • Fischer, C., T. Montmerle, L. Berre, L. Auger, and S. E. Ştefănescu, 2005: An overview of the variational assimilation in the ALADIN/France numerical weather prediction system. Quart. J. Roy. Meteor. Soc., 131, 34773492, doi:10.1256/qj.05.115.

    • Search Google Scholar
    • Export Citation
  • Fisher, M., 2003: Background error covariance modelling. ECMWF Seminar on Recent Developments in Data Assimilation for Atmosphere and Ocean, Reading, United Kingdom, European Centre for Medium-Range Weather Forecasts, 45–64. [Available online at http://old.ecmwf.int/newsevents/meetings/annual_seminar/seminar2003_presentations/Fisher.pdf.]

  • Gustafsson, N., X.-Y. Huang, X. Yang, K. S. Mogensen, M. Lindskog, O. Vignes, T. Wilhelmsson, and S. Thorsteinsson, 2012: Four-dimensional variational data assimilation for a limited area model. Tellus, 64A, 14 985, doi:10.3402/tellusa.v64i0.14985.

    • Search Google Scholar
    • Export Citation
  • Ha, J.-H., and D.-K. Lee, 2012: Effect of length scale tuning of background error in WRF-3DVAR system on assimilation of high-resolution surface data for heavy rainfall simulation. Adv. Atmos. Sci., 29, 11421158, doi:10.1007/s00376-012-1183-z.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., L. Lefaivre, J. Derome, H. Ritchie, and H. L. Mitchell, 1996: A system simulation approach to ensemble prediction. Mon. Wea. Rev., 124, 12251242, doi:10.1175/1520-0493(1996)124<1225:ASSATE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hsiao, L.-F., D.-S. Chen, Y.-H. Kuo, Y.-R. Guo, T.-C. Yeh, J.-S. Hong, C.-T. Fong, and C.-S. Lee, 2012: Application of WRF 3DVAR to operational typhoon prediction in Taiwan: Impact of outer loop and partial cycling approaches. Wea. Forecasting, 27, 12491263, doi:10.1175/WAF-D-11-00131.1.

    • 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, doi:10.1175/2008MWR2577.1.

    • Search Google Scholar
    • Export Citation
  • Huang, X.-Y., and Coauthors, 2013: The 2013 WRFDA overview. Extended Abstracts, 14th WRF Users’ Workshop, Boulder, CO, University Corporation for Atmospheric Research, 1.2. [Available online at http://www2.mmm.ucar.edu/wrf/users/workshops/WS2013/extended_abstracts/1.2.pdf.]

  • Ingleby, N., 2001: The statistical structure of forecast errors and its representation in The Met. Office Global 3-D Variational Data Assimilation Scheme. Quart. J. Roy. Meteor. Soc., 127, 209231, doi:10.1002/qj.49712757112.

    • Search Google Scholar
    • Export Citation
  • Li, Y., X. Wang, and M. Xue, 2012: Assimilation of radar radial velocity data with the WRF hybrid ensemble–3DVAR system for the prediction of Hurricane Ike (2008). Mon. Wea. Rev., 140, 35073524, doi:10.1175/MWR-D-12-00043.1.

    • Search Google Scholar
    • Export Citation
  • Parrish, D., and J. Derber, 1992: The National Meteorological Center’s spectral statistical-interpolation analysis system. Mon. Wea. Rev., 120, 17471763, doi:10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rawlins, F., S. P. Ballard, K. J. Bovis, A. M. Clayton, D. Li, G. W. Inverarity, A. C. Lorenc, and T. J. Payne, 2007: The Met Office global four-dimensional variational data assimilation scheme. Quart. J. Roy. Meteor. Soc., 133, 347362, doi:10.1002/qj.32.

    • Search Google Scholar
    • Export Citation
  • Roberts, N. M., and H. W. Lean, 2008: Scale-selective verification of rainfall accumulations from high-resolution forecasts of convective events. Mon. Wea. Rev., 136, 7897, doi:10.1175/2007MWR2123.1.

    • Search Google Scholar
    • Export Citation
  • Sugimoto, S., N. A. Crook, J. Sun, Q. Xiao, and D. M. Barker, 2009: An examination of WRF 3DVAR radar data assimilation on its capability in retrieving unobserved variables and forecasting precipitation through observing system simulation experiments. Mon. Wea. Rev., 137, 40114029, doi:10.1175/2009MWR2839.1.

    • Search Google Scholar
    • Export Citation
  • Sun, J., S. B. Trier, Q. Xiao, M. L. Weisman, H. Wang, Z. Ying, M. Xu, and Y. Zhang, 2012: Sensitivity of 0–12-h warm-season precipitation forecasts over the central United States to model initialization. Wea. Forecasting, 27, 832855, doi:10.1175/WAF-D-11-00075.1.

    • Search Google Scholar
    • Export Citation
  • Wang, H., J. Sun, X. Zhang, X.-Y. Huang, and T. Auligné, 2013a: Radar data assimilation with WRF 4D-Var: Part I. System development and preliminary testing. Mon. Wea. Rev., 141, 22242244, doi:10.1175/MWR-D-12-00168.1.

    • Search Google Scholar
    • Export Citation
  • Wang, H., J. Sun, S. Fan, and X.-Y. Huang, 2013b: Indirect assimilation of radar reflectivity with WRF 3D-Var and its impact on prediction of four summertime convective events. J. Appl. Meteor. Climatol., 52, 889902, doi:10.1175/JAMC-D-12-0120.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X., D. M. Barker, C. Snyder, and T. M. Hamill, 2008: A hybrid ETKF–3DVAR data assimilation scheme for the WRF Model. Part I: Observing system simulation experiment. Mon. Wea. Rev., 136, 51165131, doi:10.1175/2008MWR2444.1.

    • Search Google Scholar
    • Export Citation
  • Xiao, Q., and J. Sun, 2007: Multiple-radar data assimilation and short-range quantitative precipitation forecasting of a squall line observed during IHOP_2002. Mon. Wea. Rev., 135, 33813404, doi:10.1175/MWR3471.1.

    • Search Google Scholar
    • Export Citation
  • Xie, Y., and A. E. MacDonald, 2012: Selection of momentum variables for a three-dimensional variational analysis. Pure Appl. Geophys., 169, 335351, doi:10.1007/s00024-011-0374-3.

    • Search Google Scholar
    • Export Citation
  • Zupanski, M., D. Zupanski, T. Vukicevic, K. Eis, and T. Vonder Haar, 2005: CIRA/CSU four-dimensional variational data assimilation system. Mon. Wea. Rev., 133, 829843, doi:10.1175/MWR2891.1.

    • Search Google Scholar
    • Export Citation
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