Low-cost assimilation for sound speed fields in the PCA framework

Abstract

Forecast ocean sound speed fields are often inaccurate and need to be reconciled with observation data. Conventional data-assimilation methods used for this are generally quite computationally intensive. A compressed representation of the forecast sound speed fields can be obtained using principal component analysis (PCA), where the forecast fields are represented by a linear combination fo PCA modes. We develop a low-cost assimilation approach that updates the PCA compressed representation of the background forecast field, based on observation data.The approach uses Bayes‘ rule to obtain the maximum likelihood estimate for the update in the space spanned by the PCA modes. Significant cost savings come from the dimensionality reduction that is provided by PCA. Results are presented for sound speed fields derived from HYCOM ocean forecast data and expendable bathythermograph data obtained from the Scipps Institution of Oceanography.