淹水模擬對於都市地區的淹水風險評估非常重要，目前世界上常用的淹水模式，主要採用淺水波方程式，同時模擬一維下水道水流和二維地表逕流，進行細緻化的都市淹水模擬。本研究利用擴散波、局部慣性波和動力波三種不同動量方程式，分別探討淺水波方程式中，慣性力對地表逕流模式和下水道模式的影響，以2012年6月12日和2012年6月16日在臺北市文山區發生的豪雨事件，進行模擬與比較。
研究結果顯示，在淹水範圍的驗證當中，由於擴散波忽略了水體流動慣性，在流向與坡向相反的管道中，基於擴散波的下水道模式容易高估下水道流量與地表交換量，導致流量變化量發生劇烈震盪，產生不合理的下水道逆流和溢淹循環；而使用動力波和局部慣性波的結果相似，同時顯示較擴散波更佳的結果，雖然無法從肉眼判斷兩者的優劣，但是性能指標顯示動力波模式有較高的命中率，此乃因為當下水道洪水波在傳遞的過程中，水體斷面積在空間上的變化與其在時間上的變化相互抵消，造成對流慣性項顯得微不足道。
與下水道模式相比，忽略地表逕流模式的慣性項對淹水模擬結果的影響不明顯，這可能是因為慣性力的影響主要來自下水道滿管時快速提高的水壓，而地表水體並不會發生壓力快速提高的現象，所以導致地表逕流模式的差異不明顯。整體而言，簡化淺水波動量方程式中的慣性力，對於都市地表逕流模擬影響不大，但對於下水道管流，則容易造成逆流與震盪的現象，低估下水道的通洪能力，進而高估了淹水範圍。

Flood simulation is an important reference for the disaster prevention in urban area. In this study, a coupled flood model based on shallow water equations is adopted to simulate the one-dimensional sewer flow and two-dimensional overland flow in urban areas simultaneously. Different momentum equations including diffusion wave, local inertial wave, and dynamic wave are employed to discover the influence of inertial forces in overland flow model and sewer flow model. The simulation results were compared with a high-intensity rainstorm event that occurred on June 12th in 2012 in Taipei City. In the verification of the maximum flood extent, the sewer flow models based on diffusion wave perform the worst due to the ignorance of sewer flow inertia in pipes with adverse slopes. The models using dynamic wave and local inertial wave show similar results whereas the former performs slightly better in predicting the depth and extent of flooding. The convective inertial term becomes trivial because the increase in flow cross-sections and the decrease in flow velocity canceling out each other. The influence of different momentum considerations in the overland flow model is insignificant on flood extents in comparison with those in the sewer flow model because . The results show that the simplification of momentum equations in sewer flow model has a negative influence on flood simulation accuracy.

1. 吳書幃。「即時降雨資料應用於淹水預報之研究」。碩士論文，國立臺灣大學生物環境系統工程學研究所，2007。
2. 呂玟潔。「雷達降雨應用於農業災害預警之可行性研究」。碩士論文，淡江大學水資源及環境工程學系碩士班，2018。
3. 陳欣怡。「台南科學工業園區暴雨排水之動態模擬」。碩士論文，國立臺灣大學農業工程學研究所，2001。
4. 蔡世瑛。「市區街道系統淹排水模式之研究」。碩士論文，國立成功大學水利及海洋工程學系，1998。
5. 謝宗霖。「都會區淹水模式之比較與應用」。碩士論文，國立臺灣大學生物環境系統工程學研究所，2013。
6. 簡名毅。「鹽水溪流域洪水與淹水演算模式」。碩士論文，國立臺灣大學農業工程學研究所，1999。
7. Al-Maliki, A., EZZELDIN M., Al-Ghamdi, A. (2014). Numerical Solution for Diffusion Waves equation using Coupled Finite Difference and Differential Quadrature Methods. International Journal of Civil & Environmental Engineering IJCEE-IJENS, 14, 03.
8. Bates, P.D., Horritt, M.S., Fewtrell, T.J., (2010). A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling. Journal of Hydrology, 387, 33–45.
9. Cea, L., Garrido, M., Puertas, J. (2010). Experimental validation of two-dimensional depth-averaged models for forecasting rainfall–runoff from precipitation data in urban areas. Journal of Hydrology, 382, 1-4, 88-102.
10. Chang, T.J., Wang, C.H., Chen, A.S., Djordjević, S., 2018. The influence of inlet drainage in modelling flow interactions between storm sewer system and overland surface. J. Hydro. http://dx.doi.org/10.1016/j.jhydrol.2018.01.066.
11. Chen, A.S., Djordjević, S., Leandro, J., Savić, D. (2007). The urban inundation model with bidirectional flow interaction between 2D overland surface and 1D sewer networks. NOVATECH 2007, Lyon, France, 465–472.
12. Chen, A.S., Evans, B., Djordjević, S., Savić, D.A. (2012). A coarse-grid approach to representing building blockage effects in 2D urban flood modelling. J. Hydrol, 426–427, 1–16.
13. Courant, R., Friedrichs, K., Lewy, H., (1967). On the partial difference equations of mathematical physics. IBM J. Res. Dev. 11 (2), 215–234.
14. Cunge, J.A., Wegner, M., (1964). Numerical Integration of Bane de Saint Venant’s Flow Equations by Means of an Implicit Scheme of Finite Differences. Applications in the Case of Alternately free and Pressurized Flow in a Tunnel. La Houille Blanche, No. 1, 33–39.
15. Djordjević, S., Prodanović, D., Makismović, C. (1999). An approach to stimulation of dual drainage. Water Sci. Technol., 39, 95–103.
16. Halcrow, (2012). ISIS 2D User Manual.
17. Hsu, M.H., Chen, S.H., Chang, T.J., (2000). Inundation simulation for urban drainage basin with storm sewer system. J. Hydrol., 234, 21–37.
18. Hunter, N.M., Bates, P.D., Horritt, M.S., Wilson, M.D. (2007). Simple spatially-distributed models for predicting flood inundation: a review. Geomorphology, 90, 3–4, 208–225.
19. Jahanbazi, M., Egger, U. (2014). Application and comparison of two different dual drainage models to assess urban flooding. Urban Water J., 11, 584–595.
20. Jang, J.H., Yu, P.S., Yeh, S.H., Fu, J.C., Huang, C.J. (2012). A probabilistic model for realtime flood warning based on deterministic flood inundation mapping. Hydrol. Process., 26, 7, 1079–1089.
21. Jang, J.H. (2015). An advanced method to apply multiple rainfall thresholds for urban flood warnings. Water, 7, 6056–6078.
22. Jang, J.H., Chang, T.H., Chen, W.B. (2018). Effect of inlet modelling on surface drainage in coupled urban flood simulation. Journal of Hydrology., 562, 168-180
23. Kuiry, S.N., Sen, D., Bates, P.D. (2010). A coupled 1D-quasi 2D flood inundation model with unstructured grids. J. Hydraul. Eng., 136, 8, 493–506.
24. Leandro, J., Martins, R. (2016) A methodology for linking 2D overland flow models with the sewer network model SWMM 5.1 based on dynamic link libraries. Water Sci. Technol., 73, 3017.
25. Leandro, J., Chen, A.S., Djordjević, S., Savić, D.A. (2009). Comparison of 1D/1D and 1D/2D coupled (sewer/surface) hydraulic models for urban flood simulation. J. Hydraul. Eng., 135, 495–504.
26. Leandro, J., Chen, A.S., Schumann, A. (2014). A 2D parallel diffusive wave model for floodplain inundation with variable time step (P-DWave). J. Hydrol., 517, 250–259.
27. Maksimović, C., Prodanović, D., Boonya-Aroonnet, S., Leitao, J.P., Djordjević, S., Allitt, R., (2009). Overland flow and pathway analysis for modelling of urban pluvial flooding. J. Hydraul. Res., 47, 512–523.
28. Mark, O., Weesakul, S., Apirumanekul, C., Aroonnet, S.B., Djordjević, S. (2004). Potential and limitations of 1D modelling of urban flooding. J. Hydrol., 299, 284–299.
29. Mason, S.J., (1982). A model for assessment of weather forecasts. Aust. Meteorol. Mag. 30, 291–303.
30. Martins, R., J.L., s.D. (2018). Influence of sewer network models on urban flood damage assessment based on coupled 1D/2D models, J. Flood Risk Management, 11, S717–S728.
31. Morales-Hernández, M., García-Navarro, P., Burguete, J., Brufau, P. (2013). A conservative strategy to couple 1D and 2D models for shallow water flow simulation. Computers & Fluids, 81, 26-44.
32. Reza, B., Rahimi, S., Akbari, G. H. (2012). Analysis of dynamic wave model for flood routing in natural rivers. Water Science and Engineering, 5, 3, 243-258.
33. Russo, B., Sunyer, D., Velasco, M., Djordjević, S. (2015). Analysis of extreme flooding events through a calibrated 1D/2D coupled model: the case of Barcelona (Spain). J. Hydroinformatics, 17, 473.
34. Schmitt, T.G., Thomas, M., Ettrich, N. (2004). Analysis and modelling of flooding in urban drainage systems. J. Hydrol., 299, 300–311.
35. Seyoum, S.D., Vojinovic, Z., Price, R.K., Weesakul, S. (2012). Coupled 1D and Noninertia 2D flood inundation model for simulation of urban flooding. J. Hydraul. Eng., 138, 23–34.
36. Smith, M.B. (2006). Comment on ‘analysis and modelling of flooding in urban drainage systems’. J. Hydrol., 317, 355–363.