Development of Ocean Spectral Data Analysis/Assimilation without Background and Observational Error Covariance Matrices

Predetermination of background and observational error covariance matrices (B, R) is challenging in existing ocean data assimilations such as optimal interpolation (OI), Kalman fileter (KF), and variational method (3DVAR or 4DVAR). An optimal spectral decomposition (OSD) has been developed to represent the observational innovation at the grid points without using any weight matrix. Minimization of analysis error variance is achieved by optimal selection of the spectral coefficients with the absence of B and R matrices The basis functions are pre-calculated and independent on any observational data and background fields. The mode truncation depends on the observational data and is objectively determined via the steep-descending method. The OSD is a fully objective ocean data assimilation method without using any user-defined parametrical covariance functions for the (B, R) matrices. An analytical 2D streamfunction fields of large and small mesoscale eddies inside a domain with 4 rigid and curved boundaries with white Gaussian noises is used to demonstrate the capability of the OSD method. A completely gridded, optimally-estimated (T, S) data set has been established for ocean model assimilation and assessment. Furthermore, application to climatic and oceanic studies is also presented.