On the convergence of data assimilation for the one-dimensional shallow water equations with sparse observations

The shallow water equations (SWE) are a widely used model for the propagation of surface waves on the oceans. We consider the problem of optimally determining the initial conditions for the one-dimensional SWE in an unbounded domain from a small set of observations of the sea surface height. In the linear case, we prove a theorem that gives sufficient conditions for convergence to the true initial conditions. At least two observation points …