عنوان مقاله [English]
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.
1- Abida, H., 2009. Identification of compound channel flow parameters. Journal of Hydrology and Hydromechanics, 57(3), pp.172-181.
2- Akan, A. O. 2011. Open Channel Hydraulics: Butterworth-Heinemann.
3- Barton, G.J., Moran, E.H. and Berenbrock, C., 2004. Surveying cross sections of the Kootenai River between Libby Dam, Montana, and Kootenay Lake, British Columbia, Canada (No. 2004-1045). US Geological Survey.
4- Becker, L. and Yeh, W.W.G., 1972. Identification of parameters in unsteady open channel flows. Water Resources Research, 8(4), pp.956-965.
5- Becker, L. and Yeh, W.W.G., 1973. Identification of multiple reach channel parameters. Water Resources Research, 9(2), pp.326-335.
6- Cunge, J.A., Holly, F.M. and Verwey, A., 1980. Practical aspects of computational river hydraulics.
7- D’Oria, M., Mignosa, P. and Tanda, M.G., 2014. Bayesian estimation of inflow hydrographs in ungauged sites of multiple reach systems. Advances in Water Resources, 63, pp.143-151.
8- Ding, Y. and Wang, S.S., 2005. Identification of Manning's roughness coefficients in channel network using adjoint analysis. International Journal of Computational Fluid Dynamics, 19(1), pp.3-13.
9- Eli, R.N., Wiggert, J.M. and Contractor, D.N., 1974. Reverse flow routing by the implicit method. Water Resources Research, 10(3), pp.597-600.
10- Fread, D.L. and Smith, G.F., 1978. Calibration technique for 1-D unsteady flow models. Journal of the Hydraulics Division, 104(7), pp.1027-1044.
11- Friedman, J., Hastie, T. and Tibshirani, R., 2001. The elements of statistical learning (Vol. 1, No. 10). New York: Springer series in statistics.
12- Gessese, A. and Sellier, M., 2012. A direct solution approach to the inverse shallow-water problem. Mathematical Problems in Engineering, 2012.
13- Hansen, P.C., 1998. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, SIAM, Philadelphia. Google Scholar, pp.1-214.
14- Henderson, F. M. 1996. Open channel flow: Macmillan.
15- Khatibi, R.H., Williams, J.J. and Wormleaton, P.R., 1997. Identification problem of open-channel friction parameters. Journal of Hydraulic Engineering, 123(12), pp.1078-1088.
16- Nguyen, H.T. and Fenton, J.D., 2005. Identification of roughness in compound channels. In MODSIM 2005 international congress on modelling and simulation. Modelling and Simulation Society of Australia and New Zealand (pp. 2512-2518).
17- Price, R.K., 1974. Comparison of four numerical methods for flood routing. Journal of the Hydraulics Division, 100(Proc. Paper 10659).
18- Richard, C., Borchers, B. & Thurber, C., 2004. Parameter Estimation and Inverse Problems. s.l.:Academic Press.
19- Szymkiewicz, R., 1993. Solution of the inverse problem for the Saint Venant equations. Journal of Hydrology, 147(1-4), pp.105-120.
20- Szymkiewicz, R., 2008. Application of the simplified models to inverse flood routing in upper Narew river (Poland). Publications of the Institute of Geophysics, Polish Academy of Sciences, (405), pp.121-135.
21- Westaway, R.M., Lane, S.N. and Hicks, D.M., 2000. The development of an automated correction procedure for digital photogrammetry for the study of wide, shallow, gravel‐bed rivers. Earth Surface Processes and Landforms, 25(2), pp.209-226.
22- Wormleaton, P.R. and Karmegam, M., 1984. Parameter optimization in flood routing. Journal of Hydraulic Engineering, 110(12), pp.1799-1814.
23- Wu, W., 2008. Computational River Dynamics, Sediment Laden Drainage, Betsiboka River, Madagascar. Courtesy of NASA. National Aeronautics and Space Administration, Houston, USA. Taylor & Francis Group, London. Google Scholar.
24- Wu, Q., Rafiee, M., Tinka, A. and Bayen, A.M., 2009, December. Inverse modeling for open boundary conditions in channel network. In Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on (pp. 8258-8265). IEEE.