Editorial Type:
Article
Article Type:
Research Article

Experimental Implementation of an Ensemble Adjustment Filter for an Intermediate ENSO Model

Alicia R. Karspeck National Center for Atmospheric Research, Boulder, Colorado

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Jeffrey L. Anderson National Center for Atmospheric Research, Boulder, Colorado

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Print Publication:
15 Sep 2007
DOI:
https://doi.org/10.1175/JCLI4245.1
Page(s):
4638–4658
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Abstract

The assimilation of sea surface temperature (SST) anomalies into a coupled ocean–atmosphere model of the tropical Pacific is investigated using an ensemble adjustment Kalman filter (EAKF). The intermediate coupled model used here is the operational version of the Zebiak–Cane model, called LDEO5. The assimilation is applied as a means of estimating the true state of the system in the presence of incomplete observations of the state.

In the first part of this study assimilation is performed under the “perfect model” assumption, where SST observations are synthetically derived from a trajectory of the model. The focus is on how and why changes in the filter parameters (ensemble size, covariance localization, and covariance inflation) affect the quality of the analysis. It is shown that isotropic covariance localization does not benefit the analysis even when a small number of ensemble members are used. These results suggest that destruction of the “balance” between variables caused by localization is more detrimental than spurious correlation due to small ensemble size.

In the second part of this study the EAKF is used to assimilate an independent dataset of SST observations. The EAKF/Zebiak–Cane assimilation system is able to correctly estimate the phase and intensity of ENSO, as measured by the average SST anomaly in the eastern equatorial Pacific. A comparison of the analysis herein to independent wind stress and thermocline depth datasets suggests that even with the assimilation of only SST observations it is possible to reproduce over 70% of the interannual variability of thermocline depth in the eastern equatorial Pacific and off the coast of the Philippine Islands. The interannual variability of zonal wind stress in the central and western equatorial Pacific is also well correlated with independent observations (R > 0.75).

Corresponding author address: Alicia R. Karspeck, National Center for Atmospheric Research, Box 3000, Boulder, CO 80307. Email: aliciak@ucar.edu

Abstract

The assimilation of sea surface temperature (SST) anomalies into a coupled ocean–atmosphere model of the tropical Pacific is investigated using an ensemble adjustment Kalman filter (EAKF). The intermediate coupled model used here is the operational version of the Zebiak–Cane model, called LDEO5. The assimilation is applied as a means of estimating the true state of the system in the presence of incomplete observations of the state.

In the first part of this study assimilation is performed under the “perfect model” assumption, where SST observations are synthetically derived from a trajectory of the model. The focus is on how and why changes in the filter parameters (ensemble size, covariance localization, and covariance inflation) affect the quality of the analysis. It is shown that isotropic covariance localization does not benefit the analysis even when a small number of ensemble members are used. These results suggest that destruction of the “balance” between variables caused by localization is more detrimental than spurious correlation due to small ensemble size.

In the second part of this study the EAKF is used to assimilate an independent dataset of SST observations. The EAKF/Zebiak–Cane assimilation system is able to correctly estimate the phase and intensity of ENSO, as measured by the average SST anomaly in the eastern equatorial Pacific. A comparison of the analysis herein to independent wind stress and thermocline depth datasets suggests that even with the assimilation of only SST observations it is possible to reproduce over 70% of the interannual variability of thermocline depth in the eastern equatorial Pacific and off the coast of the Philippine Islands. The interannual variability of zonal wind stress in the central and western equatorial Pacific is also well correlated with independent observations (R > 0.75).

Corresponding author address: Alicia R. Karspeck, National Center for Atmospheric Research, Box 3000, Boulder, CO 80307. Email: aliciak@ucar.edu

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  • Anderson, J. L., 1996: A method for producing and evaluating probabilistic forecasts from ensemble model integrations. J. Climate, 9 , 1518–1530.

    • Search Google Scholar
    • Export Citation

  • 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., 2007: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D, 230 , 99–111.

    • 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 , 2741–2758.

    • Search Google Scholar
    • Export Citation

  • Behringer, D. W., M. Ji, and A. Leetmaa, 1998: An improved coupled model for ENSO prediction and implications for ocean initialization. Part I: The ocean data assimilation system. Mon. Wea. Rev., 126 , 1013–1021.

    • Search Google Scholar
    • Export Citation

  • Bishop, C. H., B. J. Etherton, and S. J. Majumdar, 2001: Adaptive sampling with the ensemble transform Kalman Filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129 , 420–436.

    • Search Google Scholar
    • Export Citation

  • Cane, M. A., and R. J. Patton, 1984: A numerical model for low-frequency equatorial dynamics. J. Phys. Oceanogr., 14 , 1853–1863.

  • Cane, M. A., S. E. Zebiak, and S. C. Dolan, 1986: Experimental forecast of El Niño. Nature, 321 , 827–832.

  • Cañizares, R., A. Kaplan, M. A. Cane, D. Chen, and S. E. Zebiak, 2001: Use of data assimilation via linear low-order models for the initialization of El Niño–Southern Oscillation predictions. J. Geophys. Res., 106 , 30947–30959.

    • Search Google Scholar
    • Export Citation

  • Chen, D., S. E. Zebiak, A. J. Busalacchi, and M. A. Cane, 1995: An improved procedure for El Niño forecasting: Implications for predictability. Science, 269 , 1699–1702.

    • Search Google Scholar
    • Export Citation

  • Chen, D., M. A. Cane, A. Kaplan, S. E. Zebiak, and D. Huang, 2004: Predictability of El Niño over the past 148 years. Nature, 428 , 733–736.

    • Search Google Scholar
    • Export Citation

  • Derber, J., and A. Rosati, 1989: A global oceanic data assimilation system. J. Phys. Oceanogr., 19 , 1333–1347.

  • Epstein, E., 1969: Stochastic dynamic prediction. Tellus, 21 , 739–759.

  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99 , C5. 10143–10162.

    • Search Google Scholar
    • Export Citation

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

    • Search Google Scholar
    • Export Citation

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

    • Search Google Scholar
    • Export Citation

  • Gill, A. E., 1980: Some simple solutions for heat induced tropical circulation. Quart. J. Roy. Meteor. Soc., 106 , 447–462.

  • Hakim, G., and R. Torn, 2008: Ensemble synoptic analysis. Sanders Symposium Monograph, Meteor. Monogr., No. 55, Amer. Meteor. Soc., in press.

  • Hamill, T. M., 2001: Interpretation of rank histograms for verifying ensemble forecasts. Mon. Wea. Rev., 129 , 550–560.

  • Hamill, T. M., and J. S. Whitaker, 2005: Accounting for the error due to unresolved scales in ensemble data assimilation: A comparison of different approaches. Mon. Wea. Rev., 133 , 3132–3147.

    • Search Google Scholar
    • Export Citation

  • Houtekamer, P. L., 1993: Global and local skill forecasts. Mon. Wea. Rev., 121 , 1834–1846.

  • 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

  • Jazwinski, A. H., 1970: Stochastic Processes and Filtering Theory. Academic Press, 376 pp.

  • Ji, M., A. Leetmaa, and J. Derber, 1995: An ocean analysis system for seasonal to interannual climate studies. Mon. Wea. Rev., 123 , 460–481.

    • Search Google Scholar
    • Export Citation

  • Kaplan, A., M. A. Cane, Y. Kushnir, A. C. Clement, M. B. Blumenthal, and B. Rajagopalan, 1998: Analyses of global sea surface temperature 1856–1991. J. Geophys. Res., 103 , 18567–18589.

    • Search Google Scholar
    • Export Citation

  • Kaplan, A., Y. Kushnir, and M. Cane, 2003: Reduced space approach to the optimal analysis interpolation of historical marine observations: Accomplishments, difficulties, and prospects. Advances in the Applications of Marine Climatology: The Dynamic Part of the WMO Guide to the Applications of Marine Climatology, World Meteorological Organization, WMO Tech. Doc. 1081, 99–216.

  • Karspeck, A. R., A. Kaplan, and M. A. Cane, 2006: Predictability loss in an intermediate ENSO model due to initial error and atmospheric noise. J. Climate, 19 , 3572–3588.

    • Search Google Scholar
    • Export Citation

  • Keenlyside, N., M. Latif, M. Botzet, J. Jungclaus, and U. Schulzweida, 2005: A coupled method for initializing El Niño Southern Oscillation forecasts using sea surface temperature. Tellus, 57A , 340–356.

    • Search Google Scholar
    • Export Citation

  • Kleeman, R., A. M. Moore, and N. R. Smith, 1995: Assimilation of subsurface thermal data into a simple ocean model for the initialization of an intermediate tropical coupled ocean–atmosphere forecast model. Mon. Wea. Rev., 123 , 3103–3114.

    • Search Google Scholar
    • Export Citation

  • Lee, T., J-P. Boulanger, A. Foo, L-L. Fu, and R. Giering, 2000: Data assimilation by an intermediate coupled ocean-atmosphere model: Application to the 1997–1998 El Niño. J. Geophys. Res., 105 , 26063–26087.

    • Search Google Scholar
    • Export Citation

  • Morss, R. E., and D. S. Battisti, 2004: Evaluating observing requirements for ENSO prediction: Experiments with an intermediate coupled model. J. Climate, 17 , 3057–3073.

    • Search Google Scholar
    • Export Citation

  • Stricherz, J. N., D. M. Legler, and J. O’Brien, 1997: TOGA Pseudo-Stress Atlas, 1985–1994. II: Tropical Pacific Ocean. Center for Ocean–Atmosphere Prediction Studies Rep. 97–2, 155 pp.

  • Sun, C., Z. Hao, M. Ghil, and J. D. Neelin, 2002: Data assimilation for a coupled ocean–atmosphere model. Part I: Sequential state estimation. Mon. Wea. Rev., 130 , 1073–1099.

    • Search Google Scholar
    • Export Citation

  • van Leeuwen, P. J., and G. Evensen, 1996: Data assimilation and inverse methods in terms of an probabilistic formulation. Mon. Wea. Rev., 124 , 2898–2913.

    • Search Google Scholar
    • Export Citation

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

  • Wilks, D. S., 2004: The minimum spanning tree histogram as a verification tool for multidimensional ensemble forecasts. Mon. Wea. Rev., 132 , 1329–1340.

    • Search Google Scholar
    • Export Citation

  • Zebiak, S. E., 1986: Atmospheric convergence feedback in a simple model for El Niño. Mon. Wea. Rev., 114 , 1263–1271.

  • Zebiak, S. E., and M. A. Cane, 1987: A model El Niño–Southern Oscillation. Mon. Wea. Rev., 115 , 2262–2278.

  • Zhang, S., M. J. Harrison, A. T. Whittenberg, A. Rosati, J. L. Anderson, and V. Balaji, 2005: Initialization of an ENSO forecast system using a parallelized ensemble filter. Mon. Wea. Rev., 133 , 3176–3201.

    • Search Google Scholar
    • Export Citation
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