Estimation of the tropical Atlantic circulation from altimetry data using a reduced-rank stationary Kalman filter

Abstract

Abstract In this study, a reduced-rank stationary Kalman filter is used to assimilate TOPEX/Poseidon sea-surface height anomaly (SHA) data into a realistic model of the tropical Atlantic Ocean. The goal is to assess how the interhemispheric transports between the Atlantic subtropics and tropics are affected by the assimilation of TOPEX/Poseidon altimetry and how the subsurface thermocline structure is dynamically constrained by SHA. The model is a reduced-gravity primitive equation GCM of the upper Atlantic ocean between 30°S and 30°N. It is forced by momentum and heat fluxes at the surface and constrained by climatological fields at the northern and southern boundaries. The assimilation scheme is an approximation to the extended Kalman filter in which the error covariances of the state estimates are only calculated in a reduced-dimension subspace. We use O(10 2 ) of the leading empirical orthogonal functions calculated from an unconstrained model run to define the subspace. The error covariances are assumed to be stationary, resulting in an assimilation procedure that requires just slightly more computational effort than a simple model integration. The model error covariances are assumed to be proportioned to the model's temporal variability with the seasonal cycle removed. The filtering of the seasonal cycle results in a more horizontally localized covariance structure in the forecast error statistics and therefore a more localized impact from the observations. Both an identical twin experiment using simulated SHA observations and an assimilation experiment with TOPEX/Poseidon altimetry data were performed. Results from using simulated SHA data demonstrate the ability of the method to constrain the ocean circulation and subsurface temperature structure (with a 50% reduction in the subsurface error). Assimilation of TOPEX/Poseidon SHA data reduces the root-mean-square misfit with observed SHA by 23.6% relative to the control model run. The variability at timescales less than one year is also increased, resulting in an improved agreement between the power spectra of the observed and estimated SHA. The impact on the subsurface temperature field from assimilating SHA was assessed using data from expendable bathythermographs (XBT). This showed a substantial improvement in the estimated temperature variability only within 3° latitude of the equator, with no improvements beyond this equatorial band. The impact of SHA altimetry assimilation on the zonally integrated meridional transport across three latitudes in the equatorial band was also examined. Both the mean amplitude and interannual variability of the surface and subsurface transports were significantly enhanced. The meridional transports were only sensitive to SHA assimilation between 10° north and south of the equator. The conclusion is that SHA is a powerful constraint for the subsurface thermal structure and interhemispheric transport exchange only in a narrow equatorial band.