IDENTIFICATION OF RIVER GEOMETRIC-HYDRAULIC RELATIONSHIPS USING INVERSE SOLUTION OF THE SAINT-VENANT EQUATIONS AND APPLICATION OF IT

This article presents a novel method to identify geometric-hydraulic relationships in rivers. The method is based on inverse solution of the Saint-Venant equations and needs no field-surveyed data about the river cross-sections. Geometric-hydraulic relationships are extracted from cross-sections data and are important in many applications of river such as hydraulic flood routing modeling, sediment transport modeling, contaminant transport modeling, etc. Obtaining cross-sections data needs field survey which is difficult and extensive. In this article these relationships are expressed in terms of mathematical formulas between flow area, wetted perimeter and top width of the river as the dependent variables and water depth as the independent variable and are obtained by inverse problem method. An inverse problem is the process of calculating from a set of observations the causal factors that produced them. Inverse problems are some of the most important mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe or measurement of them is expensive and difficult. In this method, water level data records are used as an input of the inverse model and then by minimizing the corresponding objective function, the desired outputs will be estimated. The proposed model is validated using hypothetical and real test cases; and in each case the actual and identified geometric-hydraulic relationships are compared. Also 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. The results of the flood routing using this method are more accurate and versatile than the ordinary applicable hydrologic methods such as Muskingum. This implies the validity of the proposed inverse model; therefore it can be applied to identify the geometric-hydraulic relationships of rivers by means of easier measurable water level data records than the direct field surveying of the river cross sections.