Obstacles and benefits of the implementation of a reduced-rank smoother with a high resolution model of the tropical Atlantic Ocean

Abstract. Most of oceanographic operational centers use three-dimensional data assimilation schemes to produce reanalyses. We investigate here the benefits of a smoother, i.e. a four-dimensional formulation of statistical assimilation. A square-root sequential smoother is implemented with a tropical Atlantic Ocean circulation model. A simple twin experiment is performed to investigate its benefits, compared to its corresponding filter. Despite model's non-linearities and the various approximations used for its implementation, the smoother leads to a better estimation of the ocean state, both on statistical (i.e. mean error level) and dynamical points of view, as expected from linear theory. Smoothed states are more in phase with the dynamics of the reference state, an aspect that is nicely illustrated with the chaotic dynamics of the North Brazil Current rings. We also show that the smoother efficiency is strongly related to the filter configuration. One of the main obstacles to implement the smoother is then to accurately estimate the error covariances of the filter. Considering this, benefits of the smoother are also investigated with a configuration close to situations that can be managed by operational center systems, where covariances matrices are fixed (optimal interpolation). We define here a simplified smoother scheme, called half-fixed basis smoother, that could be implemented with current reanalysis schemes. Its main assumption is to neglect the propagation of the error covariances matrix, what leads to strongly reduce the cost of assimilation. Results illustrate the ability of this smoother to provide a solution more consistent with the dynamics, compared to the filter. The smoother is also able to produce analyses independently of the observation frequency, so the smoothed solution appears more continuous in time, especially in case of a low frenquency observation network.

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