Spatial regression and multiscale approximations for sequential data assimilation in ocean models

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Abstract
Effects of spatial regularity and locality assumptions in the extended Kalman filter are examined for oceanic data assimilation problems. Biorthogonal wavelet bases are used to implement spatial regularity through multiscale approximations, while a Markov random field (MRF) is used to impose locality through spatial regression. Both methods are shown to approximate the optimal Kalman filter estimates closely, although the stability of the estimates can be dependent on the choice of basis functions in the wavelet case. The observed filter performance is nearly constant over a wide range of values for the scalar weights (uncertainty variances) given to the model and data examined here. The MRF‐based method, with its inhomogeneous and anisotropic covariance parameterization, has been shown to be particularly effective and stable in assimilation of simulated TOPEX/POSEIDON altimetry data into a reduced‐gravity, shallow‐water equation model.