Data reconciliation of an open channel flow network using modal decomposition

This article presents a method to estimate flow variables for an open channel network governed by the linearized Saint-Venant equations and subject to periodic forcing. The discharge at the upstream end of the system and the stage at the downstream end of the system are defined as the model input; the flow properties at selected internal locations, as well as the other external boundary conditions, are defined as the output. Both inputs and outputs are affected by noise and we use the model to re-estimate this data. A spatially-dependent transfer matrix in the frequency domain is constructed to relate the model input and output using modal decomposition. A data reconciliation technique is used to incorporate the error in the measured data and results in a set of reconciliated external boundary conditions; subsequently, the flow properties at any location in the system can be accurately constructed from the input measurements. The applicability and effectiveness of the method is demonstrated with a case study of the river flow subject to tidal forcing in the Sacramento-San Joaquin Delta in California. We used existing USGS sensors placed in the Delta as measurement points, and deploy our own sensors at selected locations to produce data used for the validation. The proposed method gives an accurate estimation of the flow properties at intermediate locations within the channel network.