LETKF Perturbations by Ensemble Transform in a Cloud Resolving Model

In ensemble data assimilation, the forecast error is estimated by perturbations of the ensemble forecast, while characteristics of the ensemble forecast strongly depend on how the initial ensemble was generated. The ensemble transform (ET), eigenvalue decomposition of the analysis error covariance matrix, is widely used as the initial ensemble perturbation generator for the most ensemble data assimilation including LETKF and the ensemble variational method (EnVAR). However, in our previous studies for the mesoscale ensemble system (Saito et al. 2011, 2012; Duc et al. 2015), perturbations from LETKF were not necessarily better than other methods as the initial perturbations. Non-diagonal components in the transform matrix likely contaminate the synoptic scale structure of the bred vectors in the ensemble forecast in the assimilation window.

Recently, Duc et al. (2018) presented the diagonally predominance property of the positive symmetric ensemble transform matrix and reported that initial perturbations obtained from a diagonal matrix produce better ensemble forecasts than the ones obtained from the conventional ET in experiments using real observations. In this paper, we show detailed structures of perturbations by LETKF and by diagonal transform matrix, and compare their evolution in a cloud resolving model with deep convection.

References

Duc, L., T. Kuroda, K. Saito and T. Fujita, 2015: Ensemble Kalman Filter data assimilation and storm surge experiments of tropical cyclone Nargis. Tellus A, 67, 25941, doi: 10.3402/tellusa.v67.25941.

Duc, L., K. Saito and D. Hotta, 2018: The diagonally predominant property of the positive symmetric ensemble transform matrix and its application in ensemble forecast. Mon. Wea Rev. (in revision, presented by a poster in AMS2019)

Saito, K., M. Hara, M. Kunii, H. Seko, and M. Yamaguchi, 2011: Comparison of initial perturbation methods for the mesoscale ensemble prediction system of the Meteorological Research Institute for the WWRP Beijing 2008 Olympics Research and Development Project (B08RDP). Tellus, 63A, 445-467.

Saito, K., H. Seko, M. Kunii and T. Miyoshi, 2012: Effect of lateral boundary perturbations on the breeding method and the local ensemble transform Kalman filter for mesoscale ensemble prediction. Tellus. 64, 11594, doi:10.3402/tellusa.v64i0.11594.

Key words: perturbation method, ensemble transform, LETKF, cloud resolving model