The evaluation of several climatological background-error covariance matrix (defined as the B matrix) estimation methods was performed using the ALADIN limited-area modeling data-assimilation system at a 4 km horizontal grid spacing. The B matrices compared were derived using the standard National Meteorological Center (NMC) and ensemble-based estimation methods. To test the influence of lateral boundary condition (LBC) perturbations on the characteristics of ensemble-based B matrix, two ensemble prediction systems were established: one used unperturbed lateral boundary conditions (ENS) and another used perturbed lateral boundary conditions (ENSLBC). The characteristics of the three B matrices were compared through a diagnostic comparison, while the influence of the different B matrices on the analysis and quality of the forecast were evaluated for the ENSLBC and NMC matrices. The results showed that the lateral boundary condition perturbations affected all the control variables, while the smallest influence was found for the specific humidity. The diagnostic comparison showed that the ensemble-based estimation method shifted the correlations toward the smaller spatial scales, while the LBC perturbations gave rise to larger spatial scales. The influence on the analysis showed a smaller spatial correlation for the ensemble B matrix compared to that of the NMC, with the most pronounced differences for the specific humidity. The verification of the forecast showed modest improvement for the experiment with the ensemble B matrix. Among the methods tested, the results suggest that the ensemble-based data-assimilation method is the favorable approach for background-error covariance calculation in high-resolution limited-area data assimilation systems.
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