Since much surface ocean data is Lagrangian in nature, its assimilation into ocean models is a key element of an ocean forecasting system. We investigate the propagation of information vertically caused by the existing vertical correlations between a stack of layers in the water column, such as the Eulerian velocity field and other dynamical variables, by observing Lagrangian data in the surface. We test the method by using different layered models with the known Lagrangian observations at discrete time intervals in the surface layer and unknown sub-surface layers. We adopt the method for assimilating Lagrangian data in which the model is augmented with drifter advection equations and track the correlations between the flow and the drifters via the Kalman Filter. The experiments show that Lagrangian data assimilation is feasible and effective for layered models.; The technique is first tested on a two layer point vortex flow: a two layer point vortex system of ( N1v, N2v ) vortices at each layer with a Gaussian white noise term is modeled by its deterministic counterpart. Positions of N1d drifter particles in the top layer are observed at regular time intervals and assimilated into the model. Numerical experiments demonstrate successful system tracking for ( N1v, N2v, N1d, N2d ) = (2; 2; 1; 0). Our numerical model simulations show that our method is capable of successful tracking of the vortices in both of the layers by observing the Lagrangian data from the top layer. It demonstrates that we can capture the Eulerian velocity field of the point vortex flow in the sub-surface layer by assimilating the Lagrangian data in the top layer. The method we have developed gives an understanding of the potential of Lagrangian data assimilation in models with vertical variation.; We further test the method on the two and a half layer reduced gravity shallow water double gyre unsteady flow configuration. Our numerical simulations show that the method is capable of correcting both of the active layers even if Lagrangian observations are only available in the top active layer and the assimilation time interval is of the order of the Lagrangian auto-correction time scale of the flow. The results clearly demonstrate that our method is effective when dealing with a more complex dynamics flow with an unknown sub-surface flow structure. The Lagrangian data assimilation method that we have developed, therefore, provides an approach that allows us to fully realize the potential of Lagrangian data for assimilation in more realistic ocean models.
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