Convective Meteorology (Mesoscale Dynamics)

A comparison of three ensemble filter variants: theoretical analysis and idealized tests

Bo Huang
OU School of Meteorology

10 April 2015, 2:00 PM

National Weather Center, Room 5600
120 David L. Boren Blvd.
University of Oklahoma
Norman, OK

The Ensemble Filters have received an increasing attention in data assimilation community because of its computational efficiency and flexibility. To further reduce the computational cost, the Ensemble Square Root Filter (EnSRF) and the Local Ensemble Transform Kalman Filter (LETKF) were designed and are commonly used. EnSRF assimilates observations serially to avoid the inverse of the large gain matrix and LETKF has a high degree of computational scalability by updating each model variable independently of the update of other variables. A hybrid ensemble-variational method has also become popular as it can combine the best aspects of the ensemble filter and variational method. A Consistent Hybrid Ensemble Filter (CHEF) is recently proposed (Bishop et al, 2015). It maintains the advantages of and overcomes the deficiencies of the existing ensemble filters. The primary goal of this study is to understand the difference among CHEF, EnSRF and LETKF using theoretical analysis and idealized tests.

Theoretical analysis shows that CHEF could overcome the deficiencies in both EnSRF and LETKF, thus achieving the best performance. Unlike EnSRF, the posterior from CHEF will not be affected by the order in which observations are assimilated, because CHEF is consistent with the minimum error variance estimate for the localized ensemble covariance. In the case where no localization function is applied in the ensemble error covariance EnSRF would give exactly the same analysis as CHEF. Compared with CHEF, the localized ensemble covariance of LETKF is inherently of much lower rank, which means for a given ensemble size LETKF has less degree of freedom to represent information from high-density observation networks.

Non-cycling and cycling idealized experiments were designed and conducted. For both the non-cycling and cycling experiments, CHEF gives the more accurate analysis. The non-cycling experiments reveal that when the ensemble size is not too small relative to the observation density, the performance of LETKF is better than or similar to that of EnSRF, otherwise EnSRF outperforms LETKF. The cycling experiments are being conducted to reveal the difference between EnSRF and LETKF and the results are planned to be discussed in the seminar.

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