Chih-Chien Chang;
Stephen G. Penny;
Shu-Chih Yang
National Central University
The 8th EnKF Data Assimilation Workshop
Exploring the impacts of orthogonal updates in Hybrid Gain Data Assimilation
Talk:
Hybrid_20180507.pptx
Hybrid Data Assimilation has been widely used in numerical weather prediction. Unlike the traditional covariance hybrid scheme, Penny (2014) proposed the hybrid-gain data assimilation (HGDA) to blend the gain matrix derived from the variational method (VAR) and the ensemble-based Kalman filter (EnKF). HGDA has shown an excellent scalability and performance. With the hybrid schemes, we expect that the VAR is able to compensate the insufficient corrections from the EnKF and vice versa, and thus the correction from either system is better to be independent to each other. With the two-step update property of HGDA, we extract the component, which is orthogonal to the ensemble perturbation subspace, from the VAR’s analysis as a correction to the EnKF. By adding the orthogonal component into the analysis of EnKF directly, it is possible to avoid using the hybrid weight, which is not trivial to be optimized.
This idea is implemented in the quasi-geostrophic (QG) model and the results indicate that the orthogonal component not only retains good information that is missed in the EnKF, but also increases the impact of inaccuracies in the VAR solution. The quality of both the background and observation error covariance matrices is the key of the effectiveness of such corrections from the orthogonal component. We find that the standard HGDA, using a hybrid weighting parameter, mitigates the detrimental effect of the inaccuracies introduced by the VAR. Such inaccurate correlation mainly comes from the noise in the observation. When the observations are very accurate, the performance of using orthogonal component is superior to either the LETKF or the VAR system and performs better than the standard HGDA.
Hybrid Data Assimilation has been widely used in numerical weather prediction. Unlike the traditional covariance hybrid scheme, Penny (2014) proposed the hybrid-gain data assimilation (HGDA) to blend the gain matrix derived from the variational method (VAR) and the ensemble-based Kalman filter (EnKF). HGDA has shown an excellent scalability and performance. With the hybrid schemes, we expect that the VAR is able to compensate the insufficient corrections from the EnKF and vice versa, and thus the correction from either system is better to be independent to each other. With the two-step update property of HGDA, we extract the component, which is orthogonal to the ensemble perturbation subspace, from the VAR’s analysis as a correction to the EnKF. By adding the orthogonal component into the analysis of EnKF directly, it is possible to avoid using the hybrid weight, which is not trivial to be optimized.
This idea is implemented in the quasi-geostrophic (QG) model and the results indicate that the orthogonal component not only retains good information that is missed in the EnKF, but also increases the impact of inaccuracies in the VAR solution. The quality of both the background and observation error covariance matrices is the key of the effectiveness of such corrections from the orthogonal component. We find that the standard HGDA, using a hybrid weighting parameter, mitigates the detrimental effect of the inaccuracies introduced by the VAR. Such inaccurate correlation mainly comes from the noise in the observation. When the observations are very accurate, the performance of using orthogonal component is superior to either the LETKF or the VAR system and performs better than the standard HGDA.
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