The theoretical impact of remotely sensed sea surface salinity observations in a multi-variate assimilation system

The global ocean observing system is soon to be expanded to include two satellite missions SMOS and Aquarius that will provide the first global observations of sea surface salinity (SSS). Since the ocean responds to gradients in mass the need to more adequately observe salinity is not debatable. Previous studies for these missions have estimated that SSS observations will have a large expected error. Large observation error variance limits the potential impact for analyses of the full ocean state and even SSS itself. Estimating the impact of remotely sensed SSS on an ocean data assimilation system must be cast in the context of multi-variate contributions from both sea surface temperature and sea level anomaly. A simple analytical formulation for a multi-variate analysis of SSS is presented and used to derive diagnostics that estimate the magnitude of observation error variance that can be expected to contribute to the analysis of SSS. The diagnostics assess the likely impact of new observations in a multi-variate scheme where the forecast error covariance and observation error covariance have been estimated. As an example the diagnostics are applied to a specific ensemble optimal interpolation scheme, which has been used for eddy resolving reanalyses and operational predictions in the Asian–Australian region. This scheme dependent result indicates that sea surface temperature and sea level anomalies effectively constrain the forecast error variance of SSS in the mid- to high-latitudes. We conclude that remotely sensed SSS observations are expected to positively contribute to a multi-variate analysis in the tropical Indo–Pacific, but more modestly in the mid- to high-latitudes.