Incorporating state-dependent temperature-salinity constraints in the background error covariance of variational ocean data assimilation

Several studies have illustrated how the univariate assimilation of temperature data can have a detrimental effect on the ocean-state variables (salinity, currents, etc.) not directly constrained by the data. In this paper, the authors describe how the salinity adjustment method proposed by Troccoli and Haines can be included as a multivariate temperature-salinity (T-S) constraint within a background-error covariance model for variational data assimilation. The method is applied to a three-dimensional variational assimilation (3DVAR) system for a tropical Pacific version of the Ocean Parallelise (OPA) ocean general circulation model. An identical twin experiment is presented first to illustrate how the method is effective in reconstructing a density profile using only temperature observations from that profile. The 3DVAR system is then cycled over the period 1993-98 using in situ temperature data from the Global Temperature and Salinity Pilot Programme. Relative to a univariate (T) 3DVAR, the multivariate (T, S) 3DVAR significantly improves the salinity mean state. A comparison with salinity data that are not assimilated is also presented. The fit to these observations is improved when the T-S constraint is applied. The salinity correction leads to a better preservation of the salinity structure and avoids the development of spurious geostrophic currents that were evident in the univariate analysis. The currents at the surface and below the core of the undercurrent are also improved. Examination of the heat budget highlights how the temperature increment must compensate for a perpetual degradation of the temperature field by abnormally strong advection in the univariate experiment. When the T-S constraint is applied, this spurious advection is reduced and the mean temperature increment is decreased. Examination of the salt budget shows that spurious advection is also the main cause of the upper-ocean freshening. When the T-S constraint is applied, the salinity structure is improved allowing for a better representation of the advection term and better preservation of the salt content in the upper ocean. The T-S constraint does not correct for all problems linked to data assimilation: vertical mixing is still too strong, and the surface salinity state and currents still have substantial errors. Improvements can be expected by including additional constraints in the background error covariances and by assimilating salinity data.