Inverse Modeling for Open Boundary Conditions in Channel Network

An inverse modeling problem for systems of networked one dimensional shallow water equations subject to periodic forcing is investigated. The problem is described as a PDE-constrained optimization problem with the objective of minimizing the norm of the difference between the observed variables and model outputs. After linearizing and discretizing the governing equations using an implicit discretization scheme, linear constraints are constructed which leads to a quadratic programming formulation of the state estimation problem. The usefulness of the proposed approach is illustrated with a channel network in the Sacramento San-Joaquin Delta in California, subjected to tidal forcing from the San Francisco Bay. The dynamics of the hydraulic system are modeled by the linearized Saint-Venant equations. The method is designed to integrate drifter data as they float in the domain. The inverse modeling problem consists in estimating open boundary conditions from sensor measurements at other locations in the network. It is shown that the proposed method gives an accurate estimation of the flow state variables at the boundaries and intermediate locations.