A comparison of EnKF localization techniques on balance

Successful NWP depends upon well-balanced and accurate initial conditions. One of the strengths of data assimilation with the Ensemble Kalman Filter (EnKF) is the ability of estimates of the model covariance to evolve with time, using the flow-dependent information inherent in an ensemble of model runs (Kalnay, 2003). Spatial localization modifies the covariance matrices to reduce the influence of distant regions (Houtekamer and Mitchell, 2001), removing spurious long distance correlations (Anderson, 2007). In addition to allowing efficient parallel implementation, this takes advantage of the ensemble's lower dimensionality in local regions (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 (Hamill et al., 2001) so that grid points that are far apart show no statistical relationship. In R-localization, the observation covariance matrix is multiplied by a distance-dependent function, so that far away observations are considered to have infinite error (Hunt et al. 2007; Miyoshi 2005).

Previous experiments we made with one-dimensional balanced shallow water waveforms suggested that both methods of localization can introduce imbalance, as the relationship between the height gradient and the wind speed of the analysis increments is disrupted, but that the R-localization imbalance is typically less severe than B-localization for the same localization length scale (Greybush et al., 2009). Here, this investigation is extended to use the Simplified Parametrizations, primitivE-Equation DYnamics, or SPEEDY, model (Molteni 2003), an atmospheric global circulation model of intermediate complexity. The performance of a serial EnSRF using B-localization and LETKF using R-localization are compared on the basis of both accuracy and balance. Additionally, a discussion of various metrics of imbalance, including the ageostrophic wind, second derivative of surface pressure, and comparison with a digitally filtered field (Lynch and Huang, 1992) will be included.