Ocean Spectral Data Assimilation Without Background Error Covariance Matrix
Naval Postgraduate School Monterey United States
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Predetermination of background error covariance matrix B is challenging in existing oceandata assimilation schemes such as the optimal interpolation OI. An optimal spectraldecomposition OSD has been developed to overcome such difficulty without using the Bmatrix. The basis functions are eigenvectors of the horizontal Laplacian operator, pre-calculatedon the base of ocean topography, and independent on any observational data and backgroundfields. Minimization of analysis error variance is achieved by optimal selection of the spectralcoefficients. Optimal mode truncation is dependent on the observational data and observationalerror variance and determined using the steep-descending method. Analytical 2D fields of largeand small mesoscale eddies with white Gaussian noises inside a domain with 4 rigid and curvedboundaries are used to demonstrate the capability of the OSD method. The overall errorreduction using the OSD is evident in comparison to the OI scheme. Synoptic monthly griddedworld ocean temperature, salinity, and absolute geostrophic velocity datasets produced with theOSD method and quality controlled by the NOAA National Centers for EnvironmentalInformation NCEI are also presented.