Boundary Data Reconstruction for Open Channel Networks Using Modal Decomposition

This article presents a method to estimate flow variables for an open channel network governed by first-order, linear hyperbolic partial differential equations and subject to periodic forcing. The selected external boundary conditions of the system are defined as the model input; the flow properties at internal locations, as well as the other external boundary conditions, are defined as the output. A spatially-dependent transfer matrix in the frequency domain is constructed to relate the model input and output. A data reconciliation technique efficiently eliminates the error in the measured data and results in a reconciliated external boundary conditions; subsequently, the flow properties at any location in the system can be accurately evaluated. The applicability and effectiveness of the method is substantiated with a case study of the river flow subject to tidal forcing in the Sacramento-San Joaquin Delta, California. It is shown that the proposed method gives an accurate estimation of the flow properties at any intermediate location within the channel network.