The basic goal of physical oceanography is to obtain a quantitative description of the ocean. Data collected from the ocean is sparse, but it can be assimilated into a partial differential equation by inverse methods to get a better understanding of the ocean. Many indirect inverse methods minimize an objective function, which describes the discrepancy between observed values and values obtained by the governing equations, by gradient search methods. This is very inefficient when the number of data is small, as compared to the number of unknowns in the discretization of the governing equations (as is the case with ocean data). The representer method is an efficient way to minimize the objective function because the search space is only as large as the number of data. However, this method requires a linear model. The tangent linear form of the Lagrangian shallow water equations is used, and the inversion is iterated, to obtain a nonlinear fit of the model and data. In this talk we will show results from an inversion with simulated float data.