Fig. 1
Comparison of standard 4DVAR with 4DVAR-QSVA both fixed and non-fixed background error covariance.
Fig. 2
RMSE (y-axis) for different hybrid methods (and the ETKF) as a function of ensemble size (different lines) and observation periods (x-axis). Each panel shows a different data assimilation method (Each y-axis has a different scale).
Fig. 3
Cluster Degree (CD, y-axis) for different observation periods for a 50 member ETKF with no inflation.
Fig. 4
Performance of each data assimilation method analysis as a function of window lengths and observation periods (x-axis); y-axis is the RMSE (scale in both panels are different). In Fig. 4a, 4DENVAR is under 4DVAR-BEN.
Fig. 5
(a), (c) and (e) are the ensemble-based background error covariances calculated before assimilation, and (b), (d) and (f) are the ensemble-based background error covariance matrices after assimilation. The ensemble-based background error covariance matrices are taken at observation time for different observation periods.
Fig. 6
Performance of each data assimilation method analysis as a function of window lengths and observation periods (x-axis); y-axis is the RMSE. These plots show longer windows without (top row) and with (bottom row) QSVA.
Fig. 7
RMSE (y-axis) for 4DVAR and different variational hybrid methods as a function of window length (x-axis). Each panel shows a different observation period. Note: (d) has a longer y-axis than the others.
ETKSSimilar to the ETKF but the smoother version which applies the weight to the whole ensemble trajectory. The background error covariance matrix is calculated from ensemble members, B e .4DVARTraditional non-incremental strong constraint 4DVAR. Uses an adjoint model and a full climatologic background error covariance matrix, B c .4DVAR-ETKFUses ETKF to generate a flow-dependent background error covariance matrix in the 4DVAR framework. Combines flow-dependent B e matrix with the climatological B c matrix.4DVAR-BENThe same method as 4DVAR-ETKF but uses a full flow-dependent B e matrix without the climatology.4DENVAR4DVAR framework but replaces the adjoint model in the cost function gradient with cross state covariances. Background error covariance matrix is generated from an ensemble of model trajectories.