A framework for estimation of river characteristics from observational data is presented using model inversion methodology. At the center of the method is a cost function defined by the error in observational versus modeled data (e.g., velocity). This cost function is extended through the use of Lagrange multipliers such that an inverse (or `adjoint') model is developed, which is used to obtain a gradient of the cost function with respect to the river characteristic that is to be estimated. Using an appropriate descent algorithm, a model result fitting the data best and constrained by the original model equations is obtained. For this work, the model equations are the shallow water equations describing the flow of water in an open channel, in two-dimensions. The specific characteristic to be estimated is bathymetry. The observational data is in the form of simulated pseudo-steady-state velocity measurements (either surface or depth-averaged), and may be either sparse or full-field. A correlation between surface velocity and depth-averaged velocity is used to allow the use of two-dimensional modeling with three-dimensional data. The hydrostatic assumption inherent in the shallow water equations is shown to have an impact on the ability of the algorithm to accurately estimate the bathymetry; this impact is not more than that of resolution and noise typical of most experimental data. The ability of the algorithm to estimate bathymetry given different types, quantity and quality of velocity data is quantified. The bathymetry estimation is shown to be accurate and robust for multiple observational surface velocity data configurations on two different rivers.
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