Editorial Type:
Article
Article Type:
Research Article

Parameter Estimation Using Ensemble-Based Data Assimilation in the Presence of Model Error

Juan Ruiz Centro de Investigaciones del Mar y la Atmósfera (CIMA/CONICET-UBA), DCAO/FCEyN-Universidad de Buenos Aires, UMI-IFAECI/CNRS, Buenos Aires, Argentina, and AICS/RIKEN, Kobe, Japan

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Manuel Pulido Department of Physics, Universidad Nacional del Nordeste, IMIT (UNNE-CONICET), Corrientes, and UMI-IFAECI/CNRS, Buenos Aires, Argentina

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Print Publication:
01 May 2015
DOI:
https://doi.org/10.1175/MWR-D-14-00017.1
Page(s):
1568–1582
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Abstract

This work explores the potential of online parameter estimation as a technique for model error treatment under an imperfect model scenario, in an ensemble-based data assimilation system, using a simple atmospheric general circulation model, and an observing system simulation experiment (OSSE) approach. Model error is introduced in the imperfect model scenario by changing the value of the parameters associated with different schemes. The parameters of the moist convection scheme are the only ones to be estimated in the data assimilation system. In this work, parameter estimation is compared and combined with techniques that account for the lack of ensemble spread and for the systematic model error. The OSSEs show that when parameter estimation is combined with model error treatment techniques, multiplicative and additive inflation or a bias correction technique, parameter estimation produces a further improvement of analysis quality and medium-range forecast skill with respect to the OSSEs with model error treatment techniques without parameter estimation. The improvement produced by parameter estimation is mainly a consequence of the optimization of the parameter values. The estimated parameters do not converge to the value used to generate the observations in the imperfect model scenario; however, the analysis error is reduced and the forecast skill is improved.

Corresponding author address: Juan Ruiz, CIMA (CONICET-Universidad de Buenos Aires), Ciudad Universitaria, Buenos Aires, CABA C1428EGA, Argentina. E-mail: jruiz@cima.fcen.uba.ar

Abstract

This work explores the potential of online parameter estimation as a technique for model error treatment under an imperfect model scenario, in an ensemble-based data assimilation system, using a simple atmospheric general circulation model, and an observing system simulation experiment (OSSE) approach. Model error is introduced in the imperfect model scenario by changing the value of the parameters associated with different schemes. The parameters of the moist convection scheme are the only ones to be estimated in the data assimilation system. In this work, parameter estimation is compared and combined with techniques that account for the lack of ensemble spread and for the systematic model error. The OSSEs show that when parameter estimation is combined with model error treatment techniques, multiplicative and additive inflation or a bias correction technique, parameter estimation produces a further improvement of analysis quality and medium-range forecast skill with respect to the OSSEs with model error treatment techniques without parameter estimation. The improvement produced by parameter estimation is mainly a consequence of the optimization of the parameter values. The estimated parameters do not converge to the value used to generate the observations in the imperfect model scenario; however, the analysis error is reduced and the forecast skill is improved.

Corresponding author address: Juan Ruiz, CIMA (CONICET-Universidad de Buenos Aires), Ciudad Universitaria, Buenos Aires, CABA C1428EGA, Argentina. E-mail: jruiz@cima.fcen.uba.ar
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  • Aksoy, A., 2015: Parameter estimation. Encyclopedia of Atmospheric Sciences, 2nd ed. G. R. North, J. Pyle, and F. Zhang, Eds., Vol. 4, Academic Press, 181–186.

  • Aksoy, A., F. Zhang, and J. Nielsen-Gammon, 2006a: Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model. Mon. Wea. Rev., 134, 2951–2969, doi:10.1175/MWR3224.1.

    • Search Google Scholar
    • Export Citation

  • Aksoy, A., F. Zhang, and J. Nielsen-Gammon, 2006b: Ensemble-based simultaneous state and parameter estimation with MM5. Geophys. Res. Lett., 33, L12801, doi:10.1029/2006GL026186.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 2884–2903, doi:10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., 2009: Spatially and temporally varying adaptive covariance inflation for ensemble filters. Tellus, 61A, 72–83, doi:10.1111/j.1600-0870.2008.00361.x.

    • Search Google Scholar
    • Export Citation

  • Annan, J. D., 2005: Parameter estimation using chaotic time series. Tellus, 57A, 709–714, doi:10.1111/j.1600-0870.2005.00143.x.

  • Annan, J. D., J. C. Hargreaves, N. R. Edwards, and R. Marsh, 2005: Parameter estimation in an intermediate complexity earth system model using an ensemble Kalman filter. Ocean Modell., 8, 135–154, doi:10.1016/j.ocemod.2003.12.004.

    • 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, 293–306, doi:10.1111/j.1600-0870.2006.00178.x.

    • Search Google Scholar
    • Export Citation

  • Bellsky, T., J. Berwald, and L. Mitchell, 2014: Nonglobal parameter estimation using local ensemble Kalman filtering. Mon. Wea. Rev., 142, 2150–2164, doi:10.1175/MWR-D-13-00200.1.

    • Search Google Scholar
    • Export Citation

  • Buizza, R., M. Miller, and T. N. Palmer, 1999: Stochastic representation of model uncertainties in the ECMWF ensemble prediction system. Quart. J. Roy. Meteor. Soc., 125, 2887–2908, doi:10.1002/qj.49712556006.

    • Search Google Scholar
    • Export Citation

  • Cornick, M., B. Hunt, E. Ott, H. Kurtuldu, and M. F. Schatz, 2009: State and parameter estimation of spatiotemporally chaotic systems illustrated by an application to Rayleigh–Bénard convection. Chaos, 19, 013108, doi:10.1063/1.3072780.

    • Search Google Scholar
    • Export Citation

  • Danforth, C., E. Kalnay, and T. Miyoshi, 2007: Estimating and correcting global weather model error. Mon. Wea. Rev., 135, 281–299, doi:10.1175/MWR3289.1.

    • Search Google Scholar
    • Export Citation

  • Dee, D., and A. da Silva, 1998: Data assimilation in the presence of forecast bias. Quart. J. Roy. Meteor. Soc., 124, 269–295, doi:10.1002/qj.49712454512.

    • Search Google Scholar
    • Export Citation

  • Fertig, E., B. Hunt, E. Ott, and I. Szunyogh, 2007: Assimilating non-local observations with a local ensemble Kalman filter. Tellus, 59A, 719–730, doi:10.1111/j.1600-0870.2007.00260.x.

    • Search Google Scholar
    • Export Citation

  • Greybush, S. J., E. Kalnay, T. Miyoshi, K. Ide, and B. R. Hunt, 2011: Balance and ensemble Kalman filter localization techniques. Mon. Wea. Rev., 139, 511–522, doi:10.1175/2010MWR3328.1.

    • Search Google Scholar
    • Export Citation

  • Greybush, S. J., R. J. Wilson, R. N. Hoffman, M. J. Hoffman, T. Miyoshi, K. Ide, T. McConnochie, and E. Kalnay, 2012: Ensemble Kalman filter data assimilation of Thermal Emission Spectrometer temperature retrievals into a Mars GCM. J. Geophys. Res., 117, E11008, doi:10.1029/2012JE004097.

    • Search Google Scholar
    • Export Citation

  • Hamill, T., J. S. Whitaker, and C. Snyder, 2001: Distance-dependent filtering of background-error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev., 129, 2776–2790, doi:10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • 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, doi:10.1175/2008MWR2737.1.

    • Search Google Scholar
    • Export Citation

  • Hunt, B. R., E. J. Kostelich, and I. Szunyogh, 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 77, 437–471, doi:10.1016/j.physd.2006.11.008.

    • Search Google Scholar
    • Export Citation

  • Jakob, C., 2010: Accelerating progress in global atmospheric model development through improved parameterizations. Bull. Amer. Meteor. Soc., 91, 869–875, doi:10.1175/2009BAMS2898.1.

    • Search Google Scholar
    • Export Citation

  • Jazwinski, A. H., 1970: Stochastic and Filtering Theory. Mathematics in Sciences and Engineering Series, Vol. 64, Academic Press, 376 pp.

  • Jung, Y., M. Xue, and G. Zhang, 2010: Simultaneous estimation of microphysical parameters and the atmospheric state using simulated polarimetric radar data and an ensemble Kalman filter in the presence of an observation operator error. Mon. Wea. Rev., 138, 539–562, doi:10.1175/2009MWR2748.1.

    • Search Google Scholar
    • Export Citation

  • Kang, J. S., E. Kalnay, J. Liu, I. Fung, T. Miyoshi, and K. Ide, 2011: “Variable localization” in an ensemble Kalman filter: Application to the carbon cycle data assimilation. J. Geophys. Res.,116, D09110, doi:10.1029/2010JD014673.

    • Search Google Scholar
    • Export Citation

  • Kondrashov, D., C. Sun, and M. Ghil, 2008: Data assimilation for a coupled ocean–atmosphere model. Part II: Parameter estimation. Mon. Wea. Rev., 136, 5062–5076, doi:10.1175/2008MWR2544.1.

    • Search Google Scholar
    • Export Citation

  • Koyama, H., and W. Watanabe, 2010: Reducing forecast errors due to model imperfections using ensemble Kalman filtering. Mon. Wea. Rev., 138, 3316–3332, doi:10.1175/2010MWR3067.1.

    • Search Google Scholar
    • Export Citation

  • Li, H., E. Kalnay, T. Miyoshi, and C. M. Danforth, 2009: Accounting for model errors in ensemble data assimilation. Mon. Wea. Rev., 137, 3407–3419, doi:10.1175/2009MWR2766.1.

    • Search Google Scholar
    • Export Citation

  • Meng, Z., and F. Zhang, 2007: Test of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part II: Imperfect model experiments. Mon. Wea. Rev., 135, 1403–1423, doi:10.1175/MWR3352.1.

    • Search Google Scholar
    • Export Citation

  • Miyoshi, T., 2005: Ensemble Kalman filter experiments with a primitive-equation global model. Ph.D. thesis, University of Maryland, College Park, 197 pp.

  • Miyoshi, T., 2011: The Gaussian approach to adaptive covariance inflation and its implementation with the local ensemble transform Kalman filter. Mon. Wea. Rev., 139, 1519–1535, doi:10.1175/2010MWR3570.1.

    • Search Google Scholar
    • Export Citation

  • Miyoshi, T., and S. Yamane, 2007: Local ensemble transform Kalman filtering with an AGCM at a T159/L48 resolution. Mon. Wea. Rev., 135, 3841–3861, doi:10.1175/2007MWR1873.1.

    • Search Google Scholar
    • Export Citation

  • Miyoshi, T., S. Yamane, and T. Enomoto, 2007: Localizing the error covariance by physical distances within a local ensemble transform Kalman filter (LETKF). SOLA, 3, 89–92, doi:10.2151/sola.2007-023.

    • Search Google Scholar
    • Export Citation

  • Molteni, F., 2003: Atmospheric simulations using a GCM with simplified physical parametrizations. I: Model climatology and variability in multi-decadal experiments. Climate Dyn., 20, 175–191, doi:10.1007/s00382-002-0268-2.

    • Search Google Scholar
    • Export Citation

  • Pulido, M., and J. Thuburn, 2006: Gravity wave drag estimation from global analyses using variational data assimlation principles. Part II: Case study. Quart. J. Roy. Meteor. Soc., 132, 1527–1543, doi:10.1256/qj.05.43.

    • Search Google Scholar
    • Export Citation

  • Ruiz, J., M. Pulido, and T. Miyoshi, 2013a: Estimating model parameters with ensemble-based data assimilation: A review. J. Meteor. Soc. Japan, 91, 79–99, doi:10.2151/jmsj.2013-201.

    • Search Google Scholar
    • Export Citation

  • Ruiz, J., M. Pulido, and T. Miyoshi, 2013b: Estimating model parameters with ensemble-based data assimilation: Parameter covariance treatment. J. Meteor. Soc. Japan, 91, 453–469, doi:10.2151/jmsj.2013-403.

    • Search Google Scholar
    • Export Citation

  • Schirber, S., D. Klocke, R. Pincus, J. Quaas, and J. L. Anderson, 2013: Parameter estimation using data assimilation in an atmospheric general circulation model: From a perfect towards the real world. J. Adv. Model. Earth Syst., 5, 58–70, doi:10.1029/2012MS000167.

    • Search Google Scholar
    • Export Citation

  • Shutts, G., 2005: A kinetic energy backscatter algorithm for use in ensemble prediction systems. Quart. J. Roy. Meteor. Soc., 131, 3079–3102, doi:10.1256/qj.04.106.

    • Search Google Scholar
    • Export Citation

  • Stainforth, D. A., and Coauthors, 2005: Uncertainty in predictions of the climate response to rising levels of greenhouse gases. Nature, 433, 403–406, doi:10.1038/nature03301.

    • Search Google Scholar
    • Export Citation

  • Tong, M., and M. Xue, 2008: Simultaneous estimation of microphysical parameters and atmospheric state with simulated radar data and ensemble square root Kalman filter. Part II: Parameter estimation experiments. Mon. Wea. Rev., 136, 1649–1668, doi:10.1175/2007MWR2071.1.

    • Search Google Scholar
    • Export Citation

  • Whitaker, J. S., and T. M. Hamill, 2012: Evaluating methods to account for system errors in ensemble data assimilation. Mon. Wea. Rev., 140, 3078–3089, doi:10.1175/MWR-D-11-00276.1.

    • Search Google Scholar
    • Export Citation

  • Whitaker, J. S., T. M. Hamill, X. Wei, Y. Song, and Z. Toth, 2008: Ensemble data assimilation with the NCEP global forecasting system. Mon. Wea. Rev., 136, 463–482, doi:10.1175/2007MWR2018.1.

    • Search Google Scholar
    • Export Citation

  • Wu, X., S. Zhang, Z. Liu, A. Rosati, T. L. Delworth, and Y. Liu, 2012: Impact of geographic dependent parameter optimization on climate estimation and prediction: Simulation with an intermediate coupled model. Mon. Wea. Rev., 140, 3956–3971, doi:10.1175/MWR-D-11-00298.1.

    • Search Google Scholar
    • Export Citation

  • Yang, S.-C., E. Kalnay, and T. Miyoshi, 2012: Improving EnKF spin up for typhoon assimilation and prediction. Wea. Forecasting, 27, 878–897, doi:10.1175/WAF-D-11-00153.1.

    • Search Google Scholar
    • Export Citation

  • Zhang, S., Z. Liu, A. Rosati, and T. Delworth, 2012: A study of enhancive parameter correction with coupled data assimilation for climate estimation and prediction using a simple coupled model. Tellus, 64A, 10963, doi:10.3402/tellusa.v64i0.10963.

    • Search Google Scholar
    • Export Citation
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