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Data assimilation for non‐linear tidal models
Author(s) -
Heemink A. W.,
Kloosterhuis H.
Publication year - 1990
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650110804
Subject(s) - kalman filter , data assimilation , discretization , mathematics , ensemble kalman filter , euler equations , filter (signal processing) , extended kalman filter , mathematical analysis , computer science , meteorology , statistics , physics , computer vision
A data assimilation procedure to incorporate measurements into a non‐linear tidal model by using Kalman‐filtering techniques is developed. The Kalman filter is based on the two‐dimensional shallow water equations. To account for the inaccuracies, these equations are embedded into a stochastic environment by introducing a coloured system noise process into the momentum equations. The continuity equation is assumed to be perfect. The deterministic part of the equations is discretized using an ADI method, the stochastic part using the Euler scheme. Assuming that the system noise is less spatially variable than the underlying water wave process, this stochastic part can be approximated on a coarser grid than the grid used to approximate the deterministic part. A Chandrasekhar‐type filter algorithm is employed to obtain the constant‐gain extended Kalman filter for weakly non‐linear systems. The capabilities of the filter are illustrated by applying it to the assimilation of water level measurements into a tidal model of the North Sea.