Ensemble Filter on dynamically driven RKHS: Application to a Multilayer Quasi-Geostrophic ocean model
Résumé
Estimating the ocean’s dynamic state, particularly at the mesoscale, is challenging due to the non-linear nature of ocean processes. Traditional data assimilation methods like optimal interpolation (OI) and four-dimensional variational assimilation (4D-Var) improve ocean state estimates but face trade-offs: OI is computationally efficient but struggles with small-scale features, while 4D-Var is more accurate but computationally demanding. Ensemble methods offer a compromise, with ensemble Kalman filters assuming Gaussianity and particle filters limited by high-dimensional systems.
This article introduces a novel ensemble filter using a Reproducing Kernel Hilbert Spaces (RKHS) framework, embedding observables in time-evolving RKHSs to relax Gaussianity assumptions and provide computational efficiency comparable to 3D-Var while addressing 4D-Var problems. A key innovation is a tiled assimilation approach that enhances the ensemble's physical properties over time. Applied to a quasi-geostrophic model of the North Atlantic with synthetic sea surface height (SSH) data, this RKHS-based filter accurately assimilates observations with non-Gaussian noise, improving both the accuracy and efficiency of ocean state estimations in complex systems.
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