Variational assimilation of Lagrangian data in oceanography

We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at a fixed depth. We aim at reconstructing the four-dimensional spacetime circulation of the ocean. This problem is solved using the four-dimensional variational technique and the adjoint method. In this problem, the control vector is chosen as being the initial state of the dynamical system. The observed variables, namely the positions of the floats, are expressed as a function of the control vector via a nonlinear observation operator. This method has been implemented and has the ability to reconstruct the main patterns of the oceanic circulation. Moreover, it is very robust with respect to increase of the time-sampling period of observations. We have run many twin experiments in order to analyse the sensitivity of our method to the number of floats, the time-sampling period and the vertical drift level. We also compare the performances of the Lagrangian method to that of the classical Eulerian one. Finally, we study the impact of errors on observations.