Growing‐error correction of ensemble Kalman filter using empirical singular vectors

Abstract

In this study, a new Ensemble Kalman Filter (EnKF) algorithm called EnKF with growing-error correction (EnKF-GEC) is developed for minimizing the growing component of the forecast error; for this purpose, prospective observations are assimilated using empirical singular vectors (ESVs). Unlike the Ensemble Kalman Smoother (EnKS) or four-dimensional EnKF (4DEnKF), the EnKF-GEC is designed to reduce the analysis error at the last analysis time (errors of initial condition for prediction). By performing assimilation experiments using the CZ-SPEEDY coupled model within a perfect model framework, it is shown that the analysis errors obtained using the EnKF-GEC are significantly reduced as compared to those obtained using the conventional EnKF until the last analysis time as well as during the middle of analysis time. This indicates that the new algorithm is beneficial for prediction. Seasonal prediction results show that the prediction skill when initial conditions are generated by the EnKF-GEC is superior to when initial conditions are generated by the conventional EnKF or EnKS, particularly during the early forecast lead month. For example, correlation skill improvement with 16 ensemble members is about 0.1 for a 3-month lead forecast. In addition, it is shown that the new EnKF algorithm is more effective for unpredictable regions, where the value of the unstable singular vector is robust.

Development of the Nonstationary Incremental Analysis Update Algorithm for Sequential Data Assimilation System

“…The main goal is to filter out the unphysical components (e.g., inertia-gravity waves in the numerical weather prediction) in the NIAU increment, which might ruin the forecast [14]. For this purpose, the TLM to propagate single time step (M ) in (2) is decomposed using the singular value decomposition (SVD) as follows [15][16][17][18][19]:…”