Salinity estimation using the T‐S relation in the context of variational data assimilation

Abstract

A salinity adjustment scheme using statistics of the temperature‐salinity (T‐S) relationship is proposed in the framework of variational data assimilation. The scheme not only considers the mean T‐S diagram but also takes the variance of the T‐S relations into consideration. To test performance of the scheme, a 1‐D mixed layer model of the Mellor‐Yamada type and a conductivity‐temperature‐depth (CTD) data set in the western tropical Pacific are used in two experiments. The CTD data set contains intensive temperature and salinity observations. In the experiments, first, the mean T‐S diagram and its variance are obtained from temperature and salinity observations over the assimilation period; then, temperature and salinity profiles are adjusted by minimizing a cost function that contains four terms: the temperature observation term, the background terms for both temperature and salinity, and a term measuring the distance between the salinity and the inferred salinity from the temperature via the mean T‐S diagram. A simpler scheme, which first adjusts the temperature profile by assimilating temperature data and then replaces the model salinity profile using the mean T‐S diagram and the newly updated temperature profile, is also tested for comparison. The proposed scheme shows good skill in reconstructing salinity variations at most levels and performs slightly better than the simpler scheme with overall improvements of 4–10%. The applicability of the method is also discussed.