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The shallow water equations (SWE) model a variety of geophysical flows. Flowsin channels with rectangular cross sections may be modelled with a simplifiedone-dimensional SWE with varying width. Among other model parameters,information about the bathymetry and friction coefficient is needed for thecorrect and precise prediction of the flow. Although synthetic values of themodel parameters may suffice for testing numerical schemes, approximations ofthe bathymetry and other parameters may be required for applications.Estimations may be obtained by experimental methods but some of thosetechniques may be expensive, time consuming, and not always available. In thiswork, we propose to solve the inverse problem to estimate the bathymetry andthe Manning's friction coefficient from transient velocity data. This is donewith the aid of a cost functional which includes the SWE through Lagrangemultipliers. The solution is obtained by solving the constrained optimizationproblem by a continuous descent method. The direct and the adjoint problems areboth solved numerically using a second-order accurate Roe-type upwind scheme.Numerical tests are included to show the merits of the algorithm.

Bathymetry and friction estimation from transient velocity data for 1D shallow water flows in open channels with varying width