Observation space localizations for the maximum likelihood ensemble filter

The maximum likelihood ensemble filter (MLEF) can handle nonlinearity of observation operators more appropriately than conventional ensemble Kalman filters. Here we consider the observation space localization method for MLEF to enable application to large-scale problems in the atmosphere. Optimization of the cost function in MLEF, however, impedes local analysis, suitable for massive parallel computers, in the same manner as the local ensemble transform Kalman filter (LETKF). In this study two approaches to observation space localization for MLEF (LMLEF) are compared. The first method introduces local gradients to minimize the global cost function (Yokota et al. 2016). An alternative approach, proposed here, defines a local cost function for each grid assuming a constant ensemble weight in the local domain to enable embarrassingly parallel analysis. The two approaches are compared to LETKF in cycled data assimilation experiments using the Lorenz-96 and the SPEEDY models. LMLEFs are found to be more accurate and stable than LETKF when nonlinear observations are assimilated into each model. Our proposed method is comparable to Yokota's global optimization method when dense observations are assimilated into the Lorenz-96 model. This result is consistent with the fact that ensemble weights have high spatial correlations with those at neighboring grids. Although our method also yields similar analysis in the SPEEDY experiments with a more realistic observation network, Yokota’s global optimization method shows faster error convergence in the earlier cycles. The error convergence rate seems to be related to the difference between global and local optimization and the validity of the assumption of constant weights, which depends strongly on the observation density.