We describe a three-dimensional (3D) finite-element ocean model designed for investigating the largescale ocean circulation on time scales from years to decades. The model solves the primitive equations in the dynamical part and the advection-diffusion equations for temperature and salinity in the thermodynamical part. The time-stepping is implicit. The 3D mesh is composed of tetrahedra and has a variable resolution. It is based on an unstructured 2D surface mesh and is stratified in the vertical direction. The model uses linear functions for horizontal velocity and tracers on tetrahedra, and for surface elevation on surface triangles. The vertical velocity field is elementwise constant. An important ingredient of the model is the Galerkin least-squares stabilization used to minimize effects of unresolved boundary layers and make the matrices to be inverted in time-stepping better conditioned. The model performance was tested in a 16-year simulation of the North Atlantic using a mesh covering the area between 7°and 80°N and providing variable horizontal resolution from 0.3°to 1.5°.

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Abstract. The quality of the prediction of dynamical system evolution is determined by the accuracy to which initial conditions and forcing are known. Availability of future observations permits reducing the effects of errors in assessment the external model parameters by means of a filtering algorithm. Usually, uncertainties in specifying internal model parameters describing the inner system dynamics are neglected. Since they are characterized by strongly nonGaussian distributions (parameters are positive, as a rule), traditional Kalman filtering schemes are badly suited to reducing the contribution of this type of uncertainties to the forecast errors. An extension of the Sequential Importance Resampling filter (SIR) is proposed to this aim. The filter is verified against the Ensemble Kalman filter (EnKF) in application to the stochastic Lorenz system. It is shown that the SIR is capable of estimating the system parameters and to predict the evolution of the system with a remarkably better accuracy than the EnKF. This highlights a severe drawback of any Kalman filtering scheme: due to utilizing only first two statistical moments in the analysis step it is unable to deal with probability density functions badly approximated by the normal distribution.

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Currently there are different approaches to filter algorithms based on the Kalman filter. One of the most used filter algorithms is the Ensemble Kalman Filter (EnKF). It uses a Monte Carlo approach to the filtering problem. Another approach is given by the Singular Evolutive Extended Kalman (SEEK) and Singular Evolutive Interpolated Kalman (SEIK) filters. These filters operate explicitly on a low-dimensional error space which is represented by an ensemble of model states. The EnKF and the SEIK filter have been implemented within a parallel data assimilation framework in the Finite Element Ocean Model FEOM. In order to compare the filter performances of the algorithms, several data assimilation experiments are performed. The filter algorithms have been applied with a model configuration of FEOM for the North Atlantic to assimilate the sea surface height in twin experiments. The dependence of the filter estimates on the represented error subspace is discussed. In the experiments the SEIK algorithm provides better estimates than the EnKF. Furthermore, the SEIK filter is much cheaper in terms of computing time.

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[1] Estimating unobserved quantities such as velocities and transports indirectly from temperature and salinity measurements is one of the best studied problems in physical oceanography. It is ill posed. The ill posedness is traditionally removed by adding prior information such as a level of no motion or a set of conservation principles. We propose to use the deep pressure gradient taken from a prognostic integration of an ocean general circulation model in primitive equations as a weak constraint when using the stationary inverse of the same model to derive transports. First results for the western boundary currents in the North Atlantic compare well with previous estimates from several studies including direct measurements.