降雨-逕流模式可供估算集水區的流出過程與洪峰流量，提供水資源工程及規劃所需的水文資訊。模式建置必須考量現地氣象、水文及地文基本資料的合理性與精確性，才能建立正確的降雨-逕流模式，例如，曾文水庫集水區歷年許多大尺度暴雨事件之逕流係數均大於1，根據現地經驗，觀測雨量低估主要原因為電傳雨量計受遮蔽效應所致；而暴雨期間集水區內之崩坍及野溪沖刷，使得流出水量中含有相當數量的泥砂，造成觀測流量高估。上述這些因素將影響集水區降雨-逕流模式之建置及模擬的正確性。
以單位歷線模擬集水區暴雨轉換逕流之過程在工程界仍然廣泛使用，然而，單一單位歷線難以兼顧不同降雨強度及總雨量的非線性流出型態，特別是防洪工程所關注的大洪峰流量，本研究採用雙單位歷線分別模擬大小雨量之流出過程，以有效模擬洪峰流量。建置過程採用完整的降雨-逕流模擬，包含針對可能低估之觀測雨量逐時增補修正，應用懸浮載泥砂率定曲線推估水庫入砂量，另利用單一水筒模擬地表下逕流，並於檢定過程使用信賴域反射牛頓法優選各項待定參數，包括雙單位歷線。
應用上述模擬方法於曾文水庫集水區歷史暴雨事件，可優選出基期為8小時的大雨量強度單位歷線及基期16小時的小雨量強度單位歷線。結果顯示，採用雙單位歷線配合完整降雨-逕流過程模擬，可使模擬流出歷線更貼近觀測流量，模式檢定成果之整體效率係數為0.87，驗證事件效率係數達0.89至0.94。可知配合完整降雨-逕流過程模擬可建置合理之雙單位歷線，可供工程設計上推估降雨形成之流量歷程。

Because of the special geographical location, geologic conditions, and climatic conditions of Taiwan, we require an accurate rainfall-runoff model to handle the preceding operations of water resources planning and hydraulic engineering at the catchment. Nonetheless, to construct a rational rainfall-runoff model, we should concern the accuracy and reasonableness of the in-situ observational data. Take the typhoon-flood events happened at Zengwun reservoir catchment as an example, there were lots of large scale events’ runoff coefficients over 1. Actually, the underestimation of the observed precipitation and the overestimation of the streamflow could give rise to the events’runoff coefficients over 1. According to the in-situ experiences, during the typhoon-flood events period, the reason of underestimated precipitation could be attributed to the errors of the rainfall measurements at rainfall gauge stations. On the other hand, the landslide of catchment and the scour of torrent could contribute to the watershed outflow containing amounts of sediment which lead to the overestimation of the observed outflow. The aforementioned factors and uncertainties have impacts on estimating more accurate outflow at the catchment. Consequently, we have to consider all of the above-mentioned factors into the process of analyzing rainfall-runoff model. For the sake of assessing effective rainfall and direct runoff meticulously to develop double unit hydrograph, this study simulates the comprehensive rainfall-runoff process at the catchment which includes the compensating for the probable-underestimated rainfall hourly, applying the suspended load rating curve to estimate the sediment inflow into the reservoir, and simulating the subsurface flow with single tank model. Furthermore, in order to simulate the peak discharge more effectively, we adopt the double unit hydrograph to conduct the simulation. Meanwhile, we apply the trust-region reflective newton method to optimum every undetermined parameters in the calibration. Apply above mentioned method into typhoon-flood events at Zengwun reservoir catchment, we could obtain the heavy-rain unit hydrograph with base period 8 hours as well as light-rain unit hydrograph with base period 16 hours. The result demonstrates that the simulated streamflow are closed to the observed streamflow highly once containing comprehensive rainfall-runoff process in the simulated procedure and adopting double unit hydrograph. The integral coefficient efficiency (CE) of the calibration cases is 0.87 and the CE in validation cases are from 0.89 to 0.94. In addition, it could simulate the peak discharge precisely and the average percent error of peak discharge (EQP) is -0.3 %. In a nutshell, it could build a proper double unit hydrograph to forecast the streamflow yielded form the precipitation in the future once it contained the comprehensive rainfall-runoff process in the modelling.

[1] 王如意、易任，「應用水文學(上)(下)」，國立編譯館，臺北 (1992)。
[2] 徐義人，「應用水文學」，國立編譯館主編，大中國圖書公司印行，臺北 (1995)
[3] 徐百慶、周乃昉，「曾文水庫集水區梅雨期間不同入滲過程分析方法比較」，碩士論文，國立成功大學水利暨海洋工程研究所，臺南(2005)
[4] 陳岱源、顏沛華，「修正型水筒模式應用於基流分離之研究」，碩士論文，國立成功大學水利暨海洋工程研究所，臺南(2005)
[5] 馬昌鳳，「最優化方法及其MATLAB程序設計」，北京科學出版社，頁211－244，北京(2009)
[6] 賴進松，「曾文水庫庫區泥砂濃度觀測站建置及量測研判分析計畫」，國立臺灣大學水工試驗所，臺北(2013)
[7] 財團法人成大研究發展基金會，「曾文水庫集水區土地變異及土砂災害監測成果報告書」，經濟部水利署南區水資源局，臺南(2013)
[8] 南區水資源局，「曾文水庫第四次定期安全評估計畫綜合報告」，經濟部水利署南區水資源局，臺南(2014)
[9] Beven, K. J. and A. M. Binley, "The future of distributed models: model calibration and uncertainty prediction.", Hydrological Processes, 6, pp. 279–298, (1992)
[10] Cai, X., D. C. McKinney and L. S. Lasdon, "Solving Nonlinear Water Management Models Using A Combined Genetic Algorithm And Linear Programming Approach." , Advances in Water Resources, Vol. 24, issue 6, pp. 667-676, (2001)
[11] Chow, V. T., "Runoff Handbook of Applied Hydrology. ", McGraw-Hill Book Company, New York, (1964)
[12] Chow, V. T., D. R. Maidment and L. W. Mays, "Applied Hydrology", McGraw- Hill Book Company, New York, (1988)
[13] Coleman, T. F., and Yuying Li, "An interior Trust Region Approach foe Nonlinear Minimization Subject to bounds. ", SIAM Journal Optimization, 6(2), pp. 418-445, (1996)
[14] Collins, W. T., "Runoff distribution graphs from precipitation occurring in more than one time unit. ", Civil Engineering, vol. 9, no. 9, pp. 559-561, (1939)
[15] Dooge, J. C. L., "A General Theory of The Unit Hydrograph.", Journal of Geophysical Research, 64(1), pp. 241-256, (1959)
[16] Dooge, J. C. L., "Linear theory of hydrologic systems", Technology Bull. No. 1468, Agric. Res. Serv., pp. 117-124, U. S. Department of Agriculture, Washington, D. C., (1973).
[17] Dooge, J. C. L., and M. Bruen, "An efficient And robust method for estimating unit hydrograph ordinates.", Journal of Hydrology, vol. 70, pp. 1-24, (1984)
[18] Ewen, J., G. O’Donnell, A. Burton and E. O’Connell, "Error and Uncertainty in Physically-based rainfall-runoff modelling of catchment change effects.", Journal of Hydrology, vol. 330, pp. 641-650, (2006)
[19] Ghorbani, M. A. and Vijay P. Singh, " Probability distribution functions for unit hydrograph with optimization using genetic algorithm.", Applied Water Science, (2015)
[20] Kuchment, L. S., "Solution of inverse problem for linear flow models. ", Soviet Hydrology, Select. pp. 194-199, (1967)
[21] Kuczera G., and E. Parent, " Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm.", Journal of Hydrology, 211(1), pp. 69–85, (1988)
[22] Moulin, L., E. Gaume and C. Obled, "Uncertainties on mean Areal precipitation: 530 Assessment And impact on streamflow simulations.", Hydrological Earth System Science, pp. 99-114. (2009)
[23] Newton, D. S., and J. W. Vinyard, "Computer-determined unit hydrograph from floods.", Journal of Hydrology, vol. 93, no. HYS, pp. 219-235, (1967)
[24] Rodda, J. C., "Precipitation research. ", EOS(American Geophysical Union Transactions), (1985)
[25] Saghafian, B., " Nonlinear transformation of unit hydrograph. ", Journal of Hydrology, vol. 330, pp. 596-603, (2006)
[26] Sherman, L. K., "Streamflow from rainfall by the unit-graph method. ", Engineering News Record, vol. 108, pp. 501-505, (1932)
[27] Snyder, W. M., "Hydrograph Analysis by the method of least squares. ", Proce. Amer. Soc. Civ. Eng., vol. 81, pp. 1-24, (1955)
[28] Sugawara, M., "Automatic Calibration of tank model. ", Hydrological Sciences-Bulletin-des Sciences Hydrological, 24(3):pp. 375-388, (1961)
[29] Winter, T. C., "Uncertainties in Estimating the Water balance of lakes. ", Water Resources Bulletin, vol 17, pp. 82-115, (1981)
[30] Yang, Z. and D. Han, "Derivation of unity hydrograph using a transfer function approach. ", Water Resources Research, vol. 42, W01501, (2006)
[31] Zhao, B. and Y. K. Tung, "Determination of optimal unity hydrograph by linear programming.", Water Resources Management, vol. 8, pp101-119, (1994)