ABSTRACT
The goal is regional assimilation of Lagrangian data into a primitive equation model on the sphere. The primitive equation model is ill-posed as an initial-boundary value problem. However, if a boundary that moves with the flow is adopted, the problem is well-posed. Lagrangian coordinates are convenient for expressing a `comoving' boundary, and lead to linear measurement functionals for float data. We have compared the Lagrangian form of the shallow water equations to the Eulerian form and found that solutions are within 3% of each other. We assimilate synthetic data into the Lagrangian form, and determine that the model can fit the data.