ABSTRACT
Dynamical models are used to calculate estimates of the state of the ocean, however, they require accurate inputs; such as initial conditions, boundary conditions, and parameterizations. Data collected from the ocean can provide estimates of these inputs, but it is sparse. In order to get good estimates, the model and data are combined in an optimal way, via inverse methods. We may view this process as the model guiding the interpolation of the data.
The inverse method I will discuss is one type of `adjoint optimization` technique, which finds the best fit of the data and model in a least squares sense. The optimal solution is found by solving the Euler-Lagrange equations, a coupled two point boundary value problem in time. `Representers' decouple these equations, and search the data space for the best fit.
I will also show some results from assimilating data from ocean `floats', into the Lagrangian form of the shallow water equations.