Derivation of River’s Cross-Section Hydraulic Relationships Using Inverse Modeling

In this study, a methodology is presented in which hydraulic relationships including mathematical formulas for the variations of the flow area, the wetted perimeter and the flow top width with the depth are computed by inverse solution of the Saint-Venant equations. The main focus is on the comprehensiveness and applicability of the method in practical conditions. Also, one application of the presented method in the case of flood routing is presented. In the context of river hydraulics, inverse modeling usually refers to the estimation of the Manning roughness coefficient via calibration process or identifying boundary conditions by measuring the flow properties inside the domain i.e. water level or flowrate records ( Ding and Wang, 2005, Fread and Smith, 1978, Khatibi et al., 1997, Nguyen and Fenton, 2005). Inverse problems are often inherently ill-posed; and this leads to some difficulties in solving them in comparison with forward problems. Some essential issues must be considered in solving inverse problems including solution existence, solution uniqueness and solution stability (Hansen, 1998). The underlying idea of the present research is to identify the mathematical formulas of geometric-hydraulic relationships for river cross sections. In this case, the unknown parameters are determined in the functional form by inverse solution of the Saint-Venant equations. The proposed model is validated using hypothetical and real test cases; and in each case the actual and identified geometric-hydraulic relationships are compared. Additionally, application of the method is showed for the case of hydraulic flood routing in conditions where no information is available about river cross sections; and water level data records are used instead of river cross sections data.