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Tsuyuki, T., 2014: Deterministic predictability of the most probable state and reformulation of variational data assimilation. J. Meteor. Soc. Japan, 92, 599-622.
Special Edition on AICS International Workshop on Data Assimilation
https://doi.org/10.2151/jmsj.2014-606

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Highlights:

• Conditions for the forecast state starting from the mode of a PDF of the state variables to remain sufficiently close to the mode of the PDF at forecast time are derived under assumption of a small forecast error.
• A new formulation of 4DVar is presented, which reveals that a non-Gaussian prior PDF which evolves according to the Liouville equation is implicitly used in 4DVar.
• Results from data assimilation experiments with toy models demonstrate that 4DVar cycles with some modifications outperform EnKF cycles in terms of the accuracy of analysis in strong nonlinearity as well as in weak nonlinearity.