Mapping and pseudo-inverse algorithms for data assimilation

TitleMapping and pseudo-inverse algorithms for data assimilation
Publication TypeJournal Article
Year of Publication2002
AuthorsFieguth, P., D. Menemenlis, and I. Fukumori
JournalIEEE International Geoscience and Remote Sensing Symposium
Pagination3221 - 3223
Keywordsbathymetry, closed dynamical system, coarse state, computational bottleneck, data assimilation, FFT, GCM grid, general circulation model, geophysical signal processing, implicit methods, interpolation, interpolation operators, irregular coastlines, iterative approach, Kalman filters, mapping algorithms, ocean data assimilation methodologies, oceanographic techniques, pseudo-inverse algorithms, reduced order systems, reduced-state filters, reduced-state Kalman filters, state-reduction, subsampling methods

Among existing ocean data assimilation methodologies, reduced-state Kalman filters are a widely-studied compromise between resolution, optimality, error specification, and computational feasibility. In such reduced-state filters, the measurement update takes place on a coarser grid than that of the general circulation model (GCM); therefore, these filters require mapping operators from the GCM grid to the reduced state and vice-versa. The general requirements are that the state-reduction and interpolation operators be pseudo-inverses of each other, that the coarse state defines a closed dynamical system, that the mapping operations be insensitive to noise, and that they be appropriate for regions with irregular coastlines and bathymetry. In this paper we investigate a variety of approaches, including computing the pseudoinverse by brute force, using the FFT, subsampling methods, implicit methods, and finally develop a novel iterative approach. We also evaluate the mapping performance of eleven interpolation kernels; surprisingly, common kernels such as bilinear, exponential, Gaussian, and sinc, performed only moderately well. This comprehensive study greatly reduces the computational bottleneck and guesswork of pseudo-inverse algorithms, making possible the application of reduced-state filters to global problems at state-of-the-art resolution.