Ensemble Transform Kalman Incremental Smoother and Its Application to Data Assimilation and Prediction

Zhe Hui Lin, Shu Chih Yang, Eugenia Kalnay

Research output: Contribution to journalArticlepeer-review


The analysis correction made by data assimilation (DA) can introduce model shock or artificial signal, leading to degradation in forecast. In this study, we propose an Ensemble Transform Kalman Incremental Smoother (ETKIS) as an incremental update solution for ETKF-based algorithms. ETKIS not only has the advantages as other incremental update schemes to improve the balance in the analysis but also provides effective incremental correction, even under strong nonlinear dynamics. Results with the shallow-water model show that ETKIS can smooth out the imbalance associated with the use of covariance localization. More importantly, ETKIS preserves the moving signal better than the overly smoothed corrections derived by other incremental update schemes. Results from the Lorenz 3-variable model show that ETKIS and ETKF achieve similar accuracy at the end of the assimilation window, while the time-varying increment of ETKIS allows the ensemble to avoid strong corrections during strong nonlinearity. ETKIS shows benefits over 4DIAU by better capturing the evolving error and constraining the over-dispersive spread under conditions of long assimilation windows or a high perturbation growth rate.

Original languageEnglish
Article number687743
JournalFrontiers in Applied Mathematics and Statistics
StatePublished - 21 Jul 2021


  • data assimilation
  • ensemble Kalman filter
  • incremental update method
  • nonlinear dynamics
  • numerical weather prediction


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