Bo Huang;
Xuguang Wang;
Craig Bishop
University of Oklahoma, USA
The 8th EnKF Data Assimilation Workshop
High-rank Ensemble Transform Kalman Filter (HETKF)
Talk:
EnKF_Huang_Wang_final.pdf
Covariance localization is typically achieved in ETKF by inflating the observation error variance with an increasing distance from the state variable of interest (hereafter R-localization). Alternatively, it can be achieved by directly modulating the raw prior ensemble perturbations through an element-wise product of each raw prior ensemble perturbation with each column of a modulation matrix (hereafter MP-localization with MP standing for modulated perturbations). The modulation matrix is defined through the covariance localization functions. It is shown mathematically that for a given modulation matrix, the MP-localization method has a higher rank (hereafter HETKF) than the R-localization.
In this study, extensive cycling experiments are conducted to reveal the differences of the MP-localization and the R-localization for ETKF. MP-localization outperforms R-localization. The superiority of MP-localization is more obvious for smaller ensemble size. With a fixed ensemble size but increased observation densities, the advantage of MP-localization over R-localization is reduced possibly due to the systemic improvement by assimilating larger number of observations. MP-localization is less sensitive to the localization length scales.
Covariance localization is typically achieved in ETKF by inflating the observation error variance with an increasing distance from the state variable of interest (hereafter R-localization). Alternatively, it can be achieved by directly modulating the raw prior ensemble perturbations through an element-wise product of each raw prior ensemble perturbation with each column of a modulation matrix (hereafter MP-localization with MP standing for modulated perturbations). The modulation matrix is defined through the covariance localization functions. It is shown mathematically that for a given modulation matrix, the MP-localization method has a higher rank (hereafter HETKF) than the R-localization.
In this study, extensive cycling experiments are conducted to reveal the differences of the MP-localization and the R-localization for ETKF. MP-localization outperforms R-localization. The superiority of MP-localization is more obvious for smaller ensemble size. With a fixed ensemble size but increased observation densities, the advantage of MP-localization over R-localization is reduced possibly due to the systemic improvement by assimilating larger number of observations. MP-localization is less sensitive to the localization length scales.
Thanks to McGill's Atmospheric and Oceanic Sciences department for hosting this web-site.