A Direct Inverse Method for Inferring Open Boundary Conditions of a Finite-Element Linear Harmonic Ocean Circulation Model

Abstract

Abstract A direct inverse method is presented for inferring numerical model open boundary conditions from interior observational data. The dynamical context of the method is the frequency-domain 3D linear shallow water equations. A set of weight matrices is derived via finite-element discretization of the dynamical equations. The weight matrices explicitly express any interior solution of elevations or velocities as a weighted sum of boundary elevations. The interior data assimilation is then cast as a regression problem. The weight matrix may be singular, which implies there may be an infinite set of boundary conditions that fit the data equally well. With the singular value decomposition technique, a general solution is provided for this infinite set of minimum-squared-misfit boundary conditions. Among them, a particular boundary condition, which minimizes potential energy on the boundary (hence the whole domain), is studied in detail: its confidence interval is defined and a way to smooth it is discuss...