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Sequential, adaptive, and gradient diffusion filters are implemented into spatial multiscale three-dimensional variational data assimilation (3DVAR) as alternative schemes to model background error covariance matrix for the commonly used correction scale method, recursive filter method, and sequential 3DVAR. The gradient diffusion filter (GDF) is verified by a two-dimensional sea surface temperature (SST) assimilation experiment. Compared to the existing DF, the new GDF scheme shows a superior performance in the assimilation experiment due to its success in extracting the spatial multiscale information. The GDF can retrieve successfully the longwave information over the whole analysis domain and the shortwave information over data-dense regions. After that, a perfect twin data assimilation experiment framework is designed to study the effect of the GDF on the state estimation based on an intermediate coupled model. In this framework, the assimilation model is subject to “biased” initial fields from the “truth” model. While the GDF reduces the model bias in general, it can enhance the accuracy of the state estimation in the region that the observations are removed, especially in the South Ocean. In addition, the higher forecast skill can be obtained through the better initial state fields produced by the GDF

Diffusion Filters for Variational Data Assimilation of Sea Surface Temperature in an Intermediate Climate Model