Weak constraint data assimilation for tides in the Arctic Ocean

Estimation of the open-boundary inputs solving a weak constraint variational formulation for an Arctic tide model is considered as an ill-posed problem in the sense that the solution is very sensitive to the data noise and to grid size. Mathematically, spatial discretization of a cost function to be minimized and penalization of normal flow through the open boundary act as regularization of the problem. An heuristic choosing rule for the regularization parameter is applied to assess a suitable spatial resolution and the weight referred to the open boundary penalty. It is shown that these provide a better fit of the solution to a control data set compared with a finer grid, the value of the energy flux through the open boundary being in agreement with other model estimates. The M₂ solution obtained is much closer to the control data than other modern solutions while the accuracy of the simulated K₁ constituent is within the same error level. The tidal maps for these waves exhibit certain distinctions in comparison with other charts.