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標題: 以擴散波模式進行漫地流之水理分析
Hydraulic Analysis of Overland Flow by a Diffusion Wave Model
作者: 王鼎佑
Ding-You Wang
關鍵字: 擴散波方程式;漫地流;質量守恆定律;時變性降雨;Diffusion wave equation;Overland flow;Law of mass conservation;Time-varying rainfall
引用: 1. 石棟鑫(2001),「台灣地區颱風與降雨型態之分析研究」,碩士論文,中央大學土木工程研究所,中壢。 2. 吳宏義(2013),「降雨強度對屋頂排水量影響之研究」,碩士論文,中國科技大學建築研究所,文山。 3. 黃靖倫(2015),「海岸地區潮汐與降雨和土壤差異對非拘限含水層的地下水變化」,碩士論文,中興大學水土保持研究所,台中。 4. Bajracharya K., Barry D. A. (1997), 'Accuracy criteria for linearised diffusion wave flood routing' Journal of Hydrology, 195(1-4):200-217. 5. Bell, N. C., Wheater H .S. and Johnston P. M. (1989), 'Evaluation of overland flow models using laboratory catchment data II. Parameter identification of physically based (kinematic wave) models' Hydrological Sciences Journal, 34(3): 289-317. 6. Brutsaert W. (2005), Hydrology: An Introduction, Cambridge Univ. Press, New York. 7. Cappelaere B. (1997), 'Accurate diffusion wave routing' Journal of Hydraulic Engineering, 123(3): 174-181. 8. Chow V. T. (1959), Open Channel Hydraulics, McGraw-Hill, New York. 9. De Lima J. L. M. P., Singh V. P. (2002), 'The influence of the pattern of moving rainstorms on overland flow' Advances in Water Resources, 25(7):817-828. 10. Fan P., Li J. C. (2002), 'Diffusive wave solutions for open channel flows with uniform and concentrated lateral inflow' Advances in Water Resources, 29:1000-1019. 11. Hayami S. (1951), 'On the propagation of flood waves' Bulletin No. 1, Disaster Prevention Research Institute, Kyoto University, Japan , December 1951. 12. Henderson F. M. (1966), Open Channel Flow, Macmillan, New York. 13. Jain M. K., Singh V. P. (2005), 'DEM-based modelling of surface runoff using diffusion wave equation' Journal of Hydrology, 302(1-4): 107-126. 14. Kazezyılmaz-Alhan C. M. (2012), 'An improved solution for diffusion waves to overland flow' Applied Mathematical Modelling, 36(9): 4165-4172. 15. Kazezyılmaz-Alhan C. M., Medina M. A. (2007), 'Kinematic and Diffusion Waves: analytical and numerical solutions to Overland and Channel Flow' Journal of Hydrologic Engineering, 133(2): 217-228. 16. Nazari B. (2017), 'Toward high-resolution flood forecasting for large urban areas - new solutions for 1D routing', Thesis of doctor, The University of Texas at Arlington, Arlington, May 2017. 17. Özisik, M.N. (1968), Boundary value problems of heat conduction, Dover Publications, INC., New York. 18. Ponce, V.M. (1989), Engineering hydrology, principles and practices. Prentice-Hall, Englewood Cliffs, N.J. 19. Ponce, V.M., Klabunde A.C. (1999), 'Parking lot storage modeling using diffusion waves' Journal of Hydrologic Engineering, 4(4): 371-376. 20. Shen B., Shen J. (1990), 'Experimental and numerical study of overland flow induced by rainfall on the loess slope' Hydraulic Engineering, Published by American Society of Civil Engineers, New York., 151-156. 21. Wallach, R., Grigorin G. and Rivlin J. (1997), 'The errors in surface runoff prediction by neglecting the relationship between infiltration rate and overland flow depth' Journal of Hydrology, 200(1-4): 243-259. 22. Wang, L., Wu J. Q., Elliot W. J., Fiedler F. R. and Lapin S. (2014), 'Linear diffusion-wave channel routing using a discrete Hayami convolution method' Journal of Hydrology, 509(1-4): 282-294. 23. Yang, Y., Endreny T. A. (2013), 'Watershed hydrograph model based on surface flow diffusion' Water Resources Research, 49(1): 507-516. 24. Yang, Y., Endreny T. A. and Nowak D. J. (2015), 'Simulating the effect of flow path roughness to examine how green infrastructure restores urban runoff timing and magnitude' Urban Forestry & Urban Greening, 14(2): 361-367. 25. Yen, B. C., Tsai C. W. –S. (2001), 'On noninertia wave versus diffusion wave in flood routing' Journal of Hydrology, 244(1-4): 97-104. 26. Zhao, P. Y., Xu X. X., Liu P. L., Chen T. L., Liao X. and Li. B.(2009), 'Infiltration Characteristics Under Different Land Uses in the Loess Hilly Area' Bulletin of Soil and Water Conservation, 29(1): 40-44.

In recent years, various hillslopes in Taiwan have been developed and large amounts of materials such as cement, asphalt, etc. were used to cover the original ground surface. This not only causes the decrease in surface friction and permeability, but also increases the velocity and runoff of overland flow, which in turn increases the frequency and scale of flooding. For this reason, the prediction of change of the overland flow caused by rainfall has become an important issue.
The purpose of this study is to simulate the differences in overland flow under different rainfall patterns. Simulations are based on the theory of the diffusion wave model. The diffusion wave equations studied by previous studies are used to derive the analytical solution to the water depth of overland flow by using the generalized integral transform technique. In addition, because the previous studies on the diffusion wave use a large number of parameters only by empirical judgement, this study proposes an algorithm of parameter correction using the law of mass conservation to enhance the rationality of the overall simulation results. In the same case, compared with the parameters used by previous studies, about 20% mass shift can be reduced, and the simulation results of the overland flow through each location along the slope can be greatly improved.
In the case of uniform rainfall, this study confirms that under a continuous rainfall event, the flow will reach a stable state and no longer change over time. From the results of time-varying rainfall analysis, it can be known that the peak at last section rainfall has the maximum peak depth and peak discharge. It followed by the peak at the third quarter section rainfall. However, the average overland flow velocity of the peak at center rainfall is the largest, followed by the peak at the first quarter section rainfall. The peak depth, peak flow, and average flow rate of the double peak rainfall are the smallest of all rainfall patterns. The assumptions of this study may make the research results slightly different from the actual physical phenomena, but we still hope that this study can provide a reference for watershed management work.
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