Roles of vertical correlations of background error and T‐S relations in estimation of temperature and salinity profiles from sea surface dynamic height

Abstract

A data assimilation scheme based on three‐dimensional variational analysis (3DVAR) is proposed to estimate temperature and salinity profiles from surface dynamic height information. The scheme takes into consideration vertical correlations for both temperature and salinity background errors and the nonlinear temperature‐salinity (T‐S) relation. In this study we designed some one‐dimensional test cases to examine the separate and combined impacts of the vertical correlations and the nonlinear T‐S relation on estimations of temperature and salinity profiles in comparison with a simplified scheme that considers neither vertical correlations nor T‐S relations. Results show that the simplified scheme cannot simultaneously improve temperature and salinity profiles over their backgrounds in some cases and could make the correction seriously nonsmooth at different depths. The consideration of vertical correlations helps to balance the magnitude of the profile correction among all depths and produce smoother results. However, consideration of vertical correlations cannot help much in reducing the root‐mean square error of estimation. The consideration of the nonlinear T‐S relation can improve both temperature and salinity estimations in all test cases and can significantly reduce the root‐mean square error of estimations. The combined effects of both vertical correlations and the nonlinear T‐S relation are similar to those of the latter but with vertically smoother results.