Observation and Model Bias Estimation in the Presence of Either or Both Sources of Error

Raquel Lorente-Plazas Research Application Laboratory, National Center for Atmospheric Research, Boulder, Colorado, and Department of Civil and Environmental Engineering and Earth Science, University of Notre Dame, Notre Dame, Indiana

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

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Abstract

In numerical weather prediction and in reanalysis, robust approaches for observation bias correction are necessary to approach optimal data assimilation. The success of bias correction can be limited by model errors. Here, simultaneous estimation of observation and model biases, and the model state for an analysis, is explored with ensemble data assimilation and a simple model. The approach is based on parameter estimation using an augmented state in an ensemble adjustment Kalman filter. The observation biases are modeled with a linear term added to the forward operator. A bias is introduced in the forcing term of the model, leading to a model with complex errors that can be used in imperfect-model assimilation experiments.

Under a range of model forcing biases and observation biases, accurate observation bias estimation and correction are possible when the model forcing bias is simultaneously estimated and corrected. In the presence of both model error and observation biases, estimating one and ignoring the other harms the assimilation more than not estimating any errors at all, because the biases are not correctly attributed. Neglecting a large model forcing bias while estimating observation biases results in filter divergence; the observation bias parameter absorbs the model forcing bias, and recursively and incorrectly increases the increments. Neglecting observation bias results in suboptimal assimilation, but the model forcing bias parameter estimate remains stable because the model dynamics ensure covariance between the parameter and the model state.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Raquel Lorente-Plazas, lorente.plazas@gmail.com

This article is included in the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) special collection.

Abstract

In numerical weather prediction and in reanalysis, robust approaches for observation bias correction are necessary to approach optimal data assimilation. The success of bias correction can be limited by model errors. Here, simultaneous estimation of observation and model biases, and the model state for an analysis, is explored with ensemble data assimilation and a simple model. The approach is based on parameter estimation using an augmented state in an ensemble adjustment Kalman filter. The observation biases are modeled with a linear term added to the forward operator. A bias is introduced in the forcing term of the model, leading to a model with complex errors that can be used in imperfect-model assimilation experiments.

Under a range of model forcing biases and observation biases, accurate observation bias estimation and correction are possible when the model forcing bias is simultaneously estimated and corrected. In the presence of both model error and observation biases, estimating one and ignoring the other harms the assimilation more than not estimating any errors at all, because the biases are not correctly attributed. Neglecting a large model forcing bias while estimating observation biases results in filter divergence; the observation bias parameter absorbs the model forcing bias, and recursively and incorrectly increases the increments. Neglecting observation bias results in suboptimal assimilation, but the model forcing bias parameter estimate remains stable because the model dynamics ensure covariance between the parameter and the model state.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Raquel Lorente-Plazas, lorente.plazas@gmail.com

This article is included in the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) special collection.

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  • Aksoy, A., F. Zhang, and J. W. Nielsen-Gammon, 2006: Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model. Mon. Wea. Rev., 134, 29512970, doi:10.1175/MWR3224.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 28842903, doi:10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2003: A local least squares framework for ensemble filtering. Mon. Wea. Rev., 131, 634642, doi:10.1175/1520-0493(2003)131<0634:ALLSFF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2009: Spatially and temporally varying adaptive covariance inflation for ensemble filters. Tellus, 61A, 7283, doi:10.1111/j.1600-0870.2008.00361.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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, 27412758, doi:10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., T. Hoar, K. Raeder, H. Liu, N. Collins, R. Torn, and A. Avellano, 2009: The Data Assimilation Research Testbed: A community facility. Bull. Amer. Meteor. Soc., 90, 12831296, doi:10.1175/2009BAMS2618.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Auligné, T., A. McNally, and D. Dee, 2007: Adaptive bias correction for satellite data in a numerical weather prediction system. Quart. J. Roy. Meteor. Soc., 133, 631642, doi:10.1002/qj.56.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Baek, S.-J., B. R. Hunt, E. Kalnay, E. Ott, and I. Szunyogh, 2006: Local ensemble Kalman filtering in the presence of model bias. Tellus, 58A, 293306, doi:10.1111/j.1600-0870.2006.00178.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bédard, J., S. Laroche, and P. Gauthier, 2015: A geo-statistical observation operator for the assimilation of near-surface wind data. Quart. J. Roy. Meteor. Soc., 141, 28572868, doi:10.1002/qj.2569.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dee, D. P., 2004: Variational bias correction of radiance data in the ECMWF system. Proc. ECMWF Workshop on Assimilation of High Spectral Resolution Sounders in NWP, Vol. 28, Reading, United Kingdom, ECMWF, 97–112. [Available online at https://www.ecmwf.int/sites/default/files/elibrary/2004/8930-variational-bias-correction-radiance-data-ecmwf-system.pdf.]

  • Dee, D. P., 2005: Bias and data assimilation. Quart. J. Roy. Meteor. Soc., 131, 33233344, doi:10.1256/qj.05.137.

  • Dee, D. P., and A. M. Da Silva, 1998: Data assimilation in the presence of forecast bias. Quart. J. Roy. Meteor. Soc., 124, 269296, doi:10.1002/qj.49712454512.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and R. Todling, 2000: Data assimilation in the presence of forecast bias: The GEOS moisture analysis. Mon. Wea. Rev., 128, 32683282, doi:10.1175/1520-0493(2000)128<3268:DAITPO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and S. Uppala, 2009: Variational bias correction of satellite radiance data in the ERA-Interim reanalysis. Quart. J. Roy. Meteor. Soc., 135, 18301841, doi:10.1002/qj.493.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Derber, J. C., and W.-S. Wu, 1998: The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system. Mon. Wea. Rev., 126, 22872299, doi:10.1175/1520-0493(1998)126<2287:TUOTCC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eyre, J. R., 1992: A bias correction scheme for simulated TOVS brightness temperatures. Tech. Memo. 186, European Centre for Medium-Range Weather Forecasts, 34 pp. [Available online at https://www.ecmwf.int/sites/default/files/elibrary/1992/9330-bias-correction-scheme-simulated-tovs-brightness-temperatures.pdf.]

  • Eyre, J. R., 2016: Observation bias correction schemes in data assimilation systems: A theoretical study of some of their properties. Quart. J. Roy. Meteor. Soc., 142, 22842291, doi:10.1002/qj.2819.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fertig, E. J., and Coauthors, 2009: Observation bias correction with an ensemble Kalman filter. Tellus, 61A, 210226, doi:10.1111/j.1600-0870.2008.00378.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Friedland, B., 1969: Treatment of bias in recursive filtering. IEEE Trans. Auto. Control, 14, 359367.

  • Gaspari, G., and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723757, doi:10.1002/qj.49712555417.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lei, L., and J. P. Hacker, 2015: Nudging, ensemble, and nudging ensembles for data assimilation in the presence of model error. Mon. Wea. Rev., 143, 26002610, doi:10.1175/MWR-D-14-00295.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 2005: Designing chaotic models. J. Atmos. Sci., 62, 15741587, doi:10.1175/JAS3430.1.

  • Pauwels, V., G. De Lannoy, H.-J. Hendricks Franssen, and H. Vereecken, 2013: Simultaneous estimation of model state variables and observation and forecast biases using a two-stage hybrid Kalman filter. Hydrol. Earth Syst. Sci., 17, 34993521, doi:10.5194/hess-17-3499-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., doi:10.5065/D68S4MVH.

    • Crossref
    • Export Citation
  • Tenenbaum, J., 1996: Jet stream winds: Comparisons of aircraft observations with analyses. Wea. Forecasting, 11, 188197, doi:10.1175/1520-0434(1996)011<0188:JSWCOA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, J., H. L. Cole, D. J. Carlson, E. R. Miller, K. Beierle, A. Paukkunen, and T. K. Laine, 2002: Corrections of humidity measurement errors from the Vaisala RS80 radiosonde—Application to TOGA COARE data. J. Atmos. Oceanic Technol., 19, 9811002, doi:10.1175/1520-0426(2002)019<0981:COHMEF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
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