Steep-Descending Mode Truncation in Ocean Spectral Data Assimilation with Comparison to Optimal Interpolation

Optimal mode truncation is the key to the success of ocean spectral data assimilation. Low mode-truncation does not represent the reality well, while high mode-truncation may contain too many noises. A new steep-descending mode method is presented. The observational innovation is represented at the grid points without using any weight matrix. Minimization of analysis error variance is achieved by optimal selection of the spectral coefficients with absence of background and observational error covariance matrices (B, R). The basis functions are pre-calculated and independent on any observational data and background fields. This spectral ocean data assimilation method is a fully objective ocean data assimilation method without 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 its capability.