The Ensemble Kalman Filter (EnKF) is a promising new method for data assimilation. One of its strengths is the ability to allow estimates of the model covariance to evolve with time, as determined from an ensemble of model runs (Kalnay, 2003). Spatial localization modifies the covariance matrices to reduce the influence of distant regions (Houtekamer and Mitchell, 2001). In addition to allowing efficient parallel implementation, this takes advantage of the ensemble's lower dimensionality in local regions, removing spurious long distance correlations (Hunt et. al., 2007). There are two primary methods for localization. In B-localization, the model covariance matrix elements are reduced by a Schur product, so that grid points that are far apart show no statistical relationship (Hamill et al., 2001). In R-localization, the observation covariance matrix is multiplied by an exponential distance function, so that far away observations are considered to have infinite error.

Successful NWP depends upon well-balanced initial conditions. Lorenc (2003) and Keppert (2006) note that localization can disrupt the relationship between the height gradient and the wind speed of the analysis increments, resulting in an analysis that can be significantly ageostrophic. This study compares the differing impacts of these two localization techniques upon the balance of the analysis. The investigation begins with a simple one-dimensional balanced waveform using the shallow water equations and two ensemble members. Observations are then assimilated to explore the parameter space of the localization distance, wavelength, and distance between observations. Analyses using no localization, B-localization, and R-localization are examined for accuracy (RMSE) and geostrophic balance. Preliminary results suggest that R-localization creates a more balanced analysis than B-localization. The procedure is then expanded to include a global general circulation model, SPEEDY (Molteni, 2003), with realistic observations.

References

Hamill, T.M., 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.

Houtekamer, P.L., and H.L. Mitchell, 2001: A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation. Mon. Wea. Rev., 129, 123–137.

Hunt, Brian R., Eric J. Kostelich, and Istvan Szunyogh, 2007: Efficient Data Assimilation for Spatiotemporal Chaos: a Local Ensemble Transform Kalman Filter. Physica D: Nonlinear Phenomena, 230, 112-126.

Kalnay, Eugenia, 2003: Atmospheric Modeling, Data Assimilation, and Predictability, Cambridge University Press.

Keppert, J.: Localisation, Balance and Choice of Analysis Variable in an Ensemble Kalman Filter, 7th Adjoint Workshop, 12 Oct 2006.

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

Molteni, F., 2003: Atmospheric simulations using a GCM with simplified physical parametrizations. I: model climatology and variability in multi-decadal experiments. Climate Dynamics, 20, 175-191.