Balance and Ensemble Kalman Filter Localization Techniques

Abstract

In Ensemble Kalman Filter data assimilation, localization modifies the error covariance matrices to suppress the influence of distant observations, removing spurious long distance correlations. In addition to allowing efficient parallel implementation, this takes advantage of the atmosphere's lower dimensionality in local regions. There are two primary methods for localization. In B-localization, the background error covariance matrix elements are reduced by a Schur product so that correlations between grid points that are far apart are removed. In R-localization, the observation error covariance matrix is multiplied by a distance-dependent function, so that far away observations are considered to have infinite error. Successful numerical weather prediction depends upon well-balanced initial conditions to avoid spurious propagation of inertial-gravity waves.Previous studies note that B-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 begins with a comparison of the accuracy and geostrophic balance of EnKF analyses using no localization, B-localization, and R-localization with simple onedimensional balanced waves derived from the shallow water equations, indicating that the optimal length scale for R-localization is shorter than for B-localization, and that for the same length scale R-localization is more balanced. The comparison of localization techniques is then expanded to the SPEEDY global atmospheric model. Here, natural imbalance of the slow manifold must be contrasted with undesired imbalance introduced by data assimilation. Performance of the two techniques is comparable, also with a shorter optimal localization distance for R-localization than for B-localization.

Parameter Sensitivities of the Dual-Localization Approach in the Local Ensemble Transform Kalman Filter

“…Each column of the background ensemble perturbation matrix dX f is composed of the difference between each ensemble forecast and the ensemble mean x f , and the ensemble size is N. P a , H, R and y o denote the analysis error covariance in ensemble space, the linear tangent matrix of the observation operator, observation error covariance matrix (assumed to be diagonal) and observation vector, respectively. In the LETKF we apply observation localization r short to R −1 and weigh the observation error variances depending on the distance from the analyzed grid point (Hunt et al 2007;Greybush et al 2011). trates similar analysis increments as Fig.…”

High-resolution data assimilation through stochastic subgrid tensor and parameter estimation from 4DEnVar

“…The minimization and the error covariance update steps are done around each grid point considering the flow representation and the observations within a region of small size. Within the local domain, observation error is gradually increased when further away from the analysis grid point (Greybush et al, 2011). Note that the ensemble forecast step must be done globally with the full non-linear dynamic model.…”

A suboptimal data assimilation algorithm based on the ensemble Kalman filter

“…To reduce the false covariations at long distances so-called localization is used. There are two main types of localization (Greybush et al, 2011). With one type the forecast error covariance matrix elements are multiplied by a function of the distance between grid points in such a way that the corresponding correlation at long distances tends to zero.…”