A comparison of the local ensemble transform Kalman filter and ensemble square root filter data assimilation schemes

Several ensemble-based data assimilation schemes (EDA) have been either implemented operationally or are being tested extensively as potential alternatives to current operational data assimilation schemes. Among EDA, the ensemble square root filter (EnSRF) and the local ensemble transform Kalman filter (LETKF) are two popular schemes. This study focused on revealing and understanding the differences between the two schemes.

The schemes were first compared using an observation system simulation experiment (OSSE) running the 40-variable Lorenz model and a two-layer primitive equation general circulation model with a perfect model assumption. In the experiment using the Lorenz model, the optimal localization scale of the LETKF was shorter and the optimal inflation was higher than the EnSRF, although the optimal analysis error among the two was similar. In the experiment using the two layer primitive equation model, the LETKF produced lower root mean square analysis errors than the EnSRF for the surface Exner function variable (equivalent to surface pressure). The mean hourly surface “pressure” tendency suggested that the LETKF analysis was more balanced than that of the EnSRF. A single observation increment experiment revealed that for a given localization length scale, the effective localization is harsher in the EnSRF than the LETKF and that the difference of the increments between the two schemes depends on the relative magnitude of the observation error variance (R) and the forecast error variance (Pf). An imperfect model OSSE is being conducted where the ratio of R over Pf is different from the perfect model OSSE. These results will be presented in the conference.