2021-07-20[Event Report]DA Seminar on July 16, 2021

Dr. Milija Zupanski of Colorado State University gave a presentation on a new ensemble data assimilation method with state-space covariance localization and global numerical optimization.

In ensemble-based data assimilation method, covariance localization is required in order to address the problem of insufficient degrees of freedom due to the use of small ensemble size. In these methods, covariance localization is often formulated in observation space based on distances between observations and model variables. It has been shown that localization in observation space can be problematic for spatially-integrated observations such as satellite radiances, aerosol optical depth, or liquid water path. These observations do not have a clear definition of their vertical locations, which makes it difficult to define distance between the observation and model variables.

Motivated by this challenge and the accompanied minimization inconsistency introduced by nonlinear problems, Dr. Zupanski proposed a method that employs covariance localization in state space and finds an optimal analysis solution with global optimization. This method is referred to as the MLEF with State Space Localization (MLEF-SSL), where MLEF stands for Maximum Likelihood Ensemble Filter. MLEF-SSL is similar to the concept of modulated ensemble method proposed by Bishop et al, but is different from the modulated ensemble method in the calculation of a reduced-rank localized forecast error covariance. MLEF-SSL uses random projection for the calculation of forecast error covariance, which is considered one important novelty introduced in this new method. Using random projection, the analysis dimension can be reduced to a manageable size, thus allows direct matrix operation for high-dimensional applications. The sensitivity of the MLEF-SSL method to the rank of random matrix is examined by a series of experiments with the Lorenz model II. Dr. Zupanski presented results from the Lorenz model and showed that the MLEF-SSL method, in general, is more skillful than the observation-space approach, especially when the rank of random matrix is small.

In summary, the MLEF-SSL method is computationally efficient and easy to implement due to the use of random projection. In addition, although this state-space localization is introduced in the MLEF, the main ideas are general and can be extended to other ensemble methods. For more details about MLEF-SSL method, please see Dr. Zupanski's new paper titled "The Maximum Likelihood Ensemble Filter with State Space Localization" by Monthly Weather Review (2021).

Author: Ting-Chi Wu

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