Recursive Upward Sweeping and Updating Method on Ensemble Based Multiscale Algorithm in Data Assimilation

Abstract

In data assimilation, it is practical and necessary to assimi-late different multisource measurements at temporal and spatial scales into dynamical models to obtain the optimal estimation of states and parameters. The Ensemble Kalman Filter (EnKF) is available but it has computational challenge when large numbers of measurements need to be processed. Spatial localization is introduced to reduce the computa-tional cost, and Ensemble multiscale Kalman filter (EnMSF) with mul-tiscale autoregressive (MAR) frame work is alternative. Another modi-fied ensemble based multiscale method, the ensemble multiscale filter using a recursive upward sweeping and updating method (Rec-EnMSF), is proposed to utilize the observational information at differ-ent scales asynchronously to get precise estimation with less computa-tional cost. The nodes are updated with measurements at the same scale if available and then they are utilized in the next upward sweep-ing step in the EnMSF. Effectiveness of the algorithm is illustrated by some numerical experiments on two-dimensional turbulent flow model with virtual measurements at different scales. The corresponding nu-merical experiments indicate that assimilation scheme with Rec-EnMSF has better and more stable performance. Therefore, Rec-EnMSF is more efficient, effective and steady than EnMSF to deal with measurements at different scales.