Flood Discharge Prediction using Two-Dimensional Inverse Modeling

A new approach to estimate flood discharges in complex river geometries is presented. Discharges are determined through the combination of nonintrusive measurements of surface velocities and water levels with a Navier–Stokes solver and an inverse optimization algorithm. The numerical model is based on a finite-element solution of the two-dimensional Reynolds-averaged Navier–Stokes equations with a $k-\epsilon$ turbulence model, allowing for computation of the free water surface on adaptive, unstructured grids. The inverse modeling technique uses the Levenberg–Marquardt minimizing algorithm. In order to rule out uncertainties from the numerical model and to strictly quantify the effect of measuring errors, measurements are generated synthetically through forward computations. The methodology is illustrated for the gaging station of the Saltina River at Brig, Switzerland, which involves a complex bed geometry and where laboratory measurements for transcritical flows were available. For perfect measurements the discharge can in principle be estimated to an accuracy of ≈2%, independently of the number of measurements. Measurement errors in the water level have a small influence on the estimated discharge, whereas errors in velocity lead to a major discharge error. This error can be minimized by increasing the number of measurement points and choosing appropriate measurement positions.