Data assimilation into a numerical equatorial ocean model. II. Assimilation experiments

Abstract A sequence of numerical experiments is conducted using a linear, semi-spectral equatorial ocean model and an advanced data assimilation scheme. The numerical model is based on decomposition of the oceanic fields into Kelvin and Rossby waves belonging to the baroclinic modes of a stratified equatorial ocean. The assimilation procedure finds that solution to the model equations that best fits, in the generalized least-squares sense, all observations made within some specified space-time interval. All experiments are of the ‘identical twin’ type; synthetic data are generated by sampling the observable fields produced by a control run of the model, then the data are assimilated using the same model. The sequence of numerical experiments serves two purposes; to demonstrate the performance of the assimilation procedure in the context of a fully three-dimensional, time-varying equatorial ocean model; and to examine the utility of specified data sets, in particular, observations of sea level, in estimating the state of the equatorial ocean. The results indicate that the assimilation procedure works very well when sufficient data are provided. However, sea-level data alone are not sufficient and must be supplemented with subsurface observations if more than a few baroclinic modes are allowed in the model ocean. The required amount of supplementary subsurface data (in the form of density profiles in these experiments) can be reduced by imposing smoothness contraints on the recovered model solution.