降雨沖蝕指數R30為USLE公式中用來描述一個地區降雨和逕流對土壤沖擊能力的指標，其定義為降雨動能E和最大30分鐘降雨強度的乘積，即R30 = EI30。本文係探討降雨沖蝕指數R30在水庫淤積、崩塌地面積以及土石流等土砂災害行為之中所扮演的角色。然而有很多地方的降雨歷史資料，常缺乏短於30分鐘的雨量紀錄資料，而只有時雨量資料，造成R30在計算上的困難。有鑑於此，研究中首先定義出擬似降雨沖蝕指數R60 為以時雨量資料所計算的降雨動能和最大時降雨強度的乘積，即R60 = E60I60，並收集曾文地區的十分鐘雨量和時雨量資料，進行R30和R60的計算，再以陳有蘭溪流域為對照組，建構出時雨量資料對降雨沖蝕指數的推估模式，以解決雨量資料的缺乏問題。研究的結果顯示，R30和R60之間呈現高度的相關，相關係數高達0.98，且可以表示為R30 = 1.5R60 (單場與年均適用)。
本文以台灣中南部的曾文溪集水區為主要的研究區域，藉由對災害資料的蒐集，以及利用統計迴歸分析的方式，探討在時間和空間R30的變化對水庫淤積、崩塌以及土石流等災害的影響，並建立土砂災害的經驗關係式。分析結果顯示，在時間變化上，相較於降雨量，單場極端颱風的R30和水庫淤積量之間存在高度的相關性，相關係數為0.92，可以表示為水庫淤積量RS (104 m3) = 0.67R30 (10 MJ-mm/ha-hr) – 96，且當R30超過580 (10MJ-mm/ha-hr)的時候，該年的淤積量便會大於300 (104 m3)。在空間變化方面，經由比較不同降雨特性發現，R30更能掌握集水區新生崩塌率的變化，因此本文利用打荻式的概念，建立R30和集水區新生崩塌率的經驗關係式，即Y = α(R30-Rc)β，其中，Rc為觸發崩塌的臨界降雨沖蝕指數，而土石流的發生則以840 (10MJ-mm/ha-hr)為臨界降雨線，1400 (10MJ-mm/ha-hr)為受災降雨線；同樣地，卡玫基和莫拉克颱風的案例分析顯示，重大災情的發生集中於降雨沖蝕指數達4000左右的地區，周圍區域僅有零星的小災情發生，故而能解釋在莫拉克時期，小林村與新開、新發等地區發生大規模崩塌和土石流之因。
本研究所提出的降雨沖蝕指數推估模式具有理論的可行性及創新性，且應用於研究區域中能夠有效的反應土砂災害的行為。相較於以往，以R30建立的土砂災害經驗式對於以單一的降雨指標所建立的經驗式已提出具體有效之改善，未來可依據本文的研究結果做為在防災、減災時候的參考。

Sediment hazards on hillslope in Taiwan have been widely analyzed in relation to hydrological factors. Despite qualitative and quantitative analysis of sediment hazards can be concluded from rainfall amount, but a more complete assessment of the con-trols on hazards behavior requires the investigation of more detailed rainfall characte-ristics. This study uses the rainfall erosivity index R30 (= kinetic energy E × maximum 30-min rainfall intensity I30) which can simultaneously reflect the responses of soil to precipitation and runoff, to investigate reservoir sedimentation, new landslide rate and the occurrence of debris flows in the Watershed Tseng-Wen River. Additionally, the pseudo-rainfall erosivity R60 (= calculated kinetic energy by hourly rainfall data E60 × maximum hourly rainfall intensity I60) was computed by hourly rainfall data from six rainfall stations, instead of R30 for the lack of 10-min or min rainfall data in many places, establishing the assessment model as R30 = 1.5 R60, which concluded from the Watershed of Tseng-Wen Reservoir and Chenyulan Watershed.
As a Result, the rainfall erosivity index R30 can characterize the behaviors of sedi-ment hazards on hillslope more pertinently then other rainfall indices. In a temporal analysis, annual reservoir sedimentation can be commanded by the R30, associating with significant typhoon events for the correlation coefficient being 0.92. The empiri-cal equation can be represented as reservoir sedimentation RS (104 m3) = 0.67 R30 (10 MJ-mm/ha-hr) – 96, moreover, the sedimentation will be greater than 300 (104 m3) when the R30 exceed 580 (10MJ-mm/ha-hr) in a typhoon event. In a spatial analysis, the rainfall erosivity index R30 was recognized as a key factor to describe new landslide rate induced by a heavy rainfall in a watershed. The results were used to ca-librate the Uchihugi’s empirical model. Debris flows linked to rain are likely to be triggered when the R30 exceeds 840 (10MJ-mm/ha-hr) and totally above 1400 (10MJ-mm/ha-hr). Finally, the case study of Typhoon Kalmegi and Morakot indicated that kinetic energy center accompany the occurrence of catastrophic disasters. In Ty-phoon Morakot, record-breaking rainfall resulted in the R30 distributing over the Wa-tershed of Tseng-Wen River greater than the center of Typhoon Kalmegi, and may be used to explain the deep-seated landslide in Xiaolin village.
This study showed that the approach of taking the pseudo rainfall erosivity index R60 as a variable to estimate the rainfall erosivity index R30 is effective and creative, also reflecting hazards processes in study area very well. Therefore, these methods can still provide information for assessing the effect of rainfall on soil failure, thereby refining hazards prediction, prevention and mitigation.

1. 伍婉貞 (1990)，台北地區自然降雨動能及其與降雨強度之關係，碩士論文，國立台灣大學農業工程學系，台北。(in Chinese)
2. 黃俊德 (1981)，台灣降雨沖蝕指數之研究，中華水土保持學報，第10卷，第1期，第127-144頁。(in Chinese)
3. 打荻珠男 (1971)，ひと雨による山腹崩壊について，新砂防，通巻79号。(in Japanese)
4. Aleotti, P. (2004). “A warning system for rainfall-induced shallow failures.” En-gineering Geology. 73, 247–265.
5. Ayalew, L, and Yamagishi, H. (2005). “The application of GIS-based logistic re-gression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains, Central Japan.” Geomorphology, 65, 15–31.
6. Wu, C. J., and Wang, A. B. (1996) “Drop Size Characteristics and Erosive Kinetic Energy of Natural Rainstorms in Pingtung Laopi Area.” Journal of Chinese Soil and Water Conservation, 27(2), 151-165. (in Chinese)
7. Caine, N. (1980). “The Rainfall Intensity Duration Control of Shallow Landslides and Debris Flows.” Geografiska Annaler, 62, 23-27.
8. Cannon, S.H., and Ellen, S. (1985). “Rainfall conditions for abundant debris avalanches in the San Francisco Bay region, California.” Geology, 38, 267–272.
9. Casadei, M., Dietrich WE, and Miller, N. L. (2003). “Testing a model for pre-dicting the timing and location of shallow landslide initiation in soil mantled landscapes.” Earth Surface Processes and Landforms, 28, 925-950.
10. Chen, J. C., Jan, C. D. (2008) “Probabilistic analysis of landslide potential of an inclined uniform soil layer of infinite length: application.” Environmental Geol-ogy, 54, 1175-1183.
11. Chen, J. C., Jan, C. D., and Lee, M. H. (2008)“Reliability analysis of design discharge for mountainous gully flow.”Journal of Hydraulic Research, 46(6), 835-838.
12. Chiang, S. H., and Lai, L. W. (2002). “Rainfall changes in Taiwan.” Journal of Chinese Soil and Water Conservation, 34 (2), 161-170. (in Chinese)
13. Ciesiolka, C. A. (1995). “Methodology for a multi-country study of soil erosion management.” Soil Technology, 8, 179-192
14. Crozier, M. J. (1999). “Prediction of rainfall-triggered landslides: a test of the antecedent water status model.” Earth Surface Processes and Landforms, 24, 825–833.
15. Dadson, S. J. et al. (2003). “Links between erosion, runoff variability and seis-micity in the Taiwan orogen.” Nature, 426, 648-651.
16. Flanagan, D. C., and Nearing, M. A. (1995). “USDA Water erosion prediction project (WEPP).”WEPP user summary. NSERL report no. 10. USDA–ARS Na-tional Soil Erosion Research Laboratory, West Lafayette, IN.
17. Guzzetti, F., Cardinali, M., Reichenbach, P., Cipolla, F., Sebastiani, C., Galli, M., and Salvati, P. (2004). “Landslides triggered by the 23 November 2000 rainfall event in the Imperia Province, Western Liguria, Italy.” Engineering Geology, 73, 229–245.
18. Hsu, H. H., Chen, C. T. (2002). “Observed and projected climate change in Tai-wan.” Meteorology Atmosphere Physics, 79, 87-104.
19. Iverson, R. M. (2000). “Landslide triggering by rain infiltration.” Water Re-sources Research, 36, 1897–1910.
20. Keefer, D. K. et al. (1987). “Real-time landslides warning during heavy rainfall.”, Science, 238, 921-925
21. Langbein, W. B., and Schumm, S. A. (1958). “Yield of sediment in relation to mean annual precipitation.” Transactions of the American Geophysical Union, 39, 1076-1084.
22. Larsen, M. C., and Simon, A. (1993). “A rainfall intensity-duration threshold for landslides in a humid-tropical environment, Puerto Rico.” Geografiska Annaler, 75A, 13–23.
23. Laws, J. O., and Parsons, D. A. (1943). ‘‘The relation of rain drop size to inten-sity.” Transactions, American Geophysical Union, 24, 452-460.
24. Lootens, M., Lumbu, S. (1986). “Suspended sediment production in a suburban tropical basin (Lubumbashi, Zaire).” Hydrology Sciences Journal, 31(1), 39–49.
25. Lu, C. Y., Su, C. C., and Wu, Y. Y. (2005). “Revision of the Isoerodent Map for the Taiwan Area.” Journal of Chinese Soil and Water Conservation. 36(2), 159-172. (in Chinese)
26. Lu, K. H. (1999). “Re-evaluation of Rainfall Erosivity Factor.” Journal of Chinese Soil and Water Conservation, 30(2), 87-94. (in Chinese)
27. Ma, M. M. (1995) “The Rainfall Characteristics and Erosivity in Central and Northern Areas of Taiwan.” Master thesis. Department of Civil Engineering. Na-tional Chung Hsing University, Taichung. (in Chinese)
28. Montgomery, D. R., and W. E. Dietrich, (1994) “A physically based model for the topographic control on shallow landsliding.” Water Resource Research, 30, 1153–1171.
29. Morgan, R. C. P. (1995). “Soil erosion and conservation.” Longman Group UK Limited, London.
30. Morgan, R. P. C. (1995). “The European soil erosion model (EUROSEM): a dy-namic approach for predicting sediment transport from fields and small catch-ments” Earth Surface Process and Landforms, 23, 527–544.
31. Ohlmacher, G. C., and Davis, J. C. (2003). “Using multiple logistic regression and GIS technology to predict landslide hazard in northeast Kansas, USA.” En-gineering Geology, 69, 331-343.
32. Oldeman, L., Hakkeling, R., and Sombroek, W. (1990). “World map of the status of soil degradation, an explanatory note.” International soil reference and in-formation center, Wageningen, The Netherlands and the United Nations Envi-ronmental Program, Nairobi, Kenya.
33. Renard, K. G., Foster, G. R., Weesies, G. A., and Porter, J. P. (1991). “RUSLE. Revised Universal Soil Loss Equation.” Journal of Soil and Water Conservation, 46, 30–33.
34. Renard, K. G., Foster, G. R., Weesies, G. A., McCool, D. K., and Yoder, D.C. (1997). “Predicting soil erosion by water - a guide to conservation planning with the Revised Universal Soil Loss Equation (RUSLE).”United States Department of Agriculture, Agricultural Research Service (USDA-ARS) Handbook No. 703. United States Government Printing Office, Washington, DC.
35. Rickenmann, D. (1999). “Empirical relationships for debris flows.” Natural Ha-zards, 19, 47-77.
36. Ritter, D. F., Kochel, R. C., and Miller, J. R. (1995). “The drainage ba-sin-development, morphometry, and hydrology.” In: Process Geomorphology, 3rd ed. Dubuque Iowa, Wm.
37. Schawb, G., and Fangmeier, D. (1993). “Soil and water conservation engineer-ing.” John Wiley and Sons, Inc., New York, 507.
38. Seeger, M., Errea, M. P., Begueria, S., Arnaez, J., Marti, C., and Garcia-Ruiz, J. M. (2004). “Catchment soil moisture and rainfall characteristics as determinant factors for discharge/suspended sediment hysteretic loops in a small headwater catchment in the Spanish Pyrenees.” Journal of Hydrology, 288(3-4), 299-311.
39. Sidle, R. C. (1992) “A theoretical model of the effects of timber harvesting on slope stability.” Water Resource Research, 28, 1897–1910.
40. Stephen, R. C. (1992). “Global change and freshwater ecosystems.” Annual Re-view Ecology System, 23, 119-139.
41. Walter, H. W., and Dwight, D. S. (1978). “Predicting rainfall erosion losses-A guide to conservation planning.” U.S. Department of Agriculture, Agricultural Handbook No. 282.
42. Walter, H. W., Dwight, D. S., and Uhland, R. E. (1958). “Evaluation of factors in the soil loss equation,” Agricultural Engineering, 39, 458-462
43. Whiteman, C. D. (2000). “Mountain Meteorology. Fundamental and applica-tions.” Oxford University Press, NY, 355.
44. Williams, J. R. (1975). “Sediment yield prediction with Universal Equation using runoff energy factor. In: Present and Prospective Technology for Predicting Se-diment Yields and Sources.” ARS-S-40, Agricultural Research Service, US De-partment of Agriculture, 244–252.
45. Williams, J. R., and Berndt, H. D. (1977). “Sediment yield prediction based on watershed hydrology.” Transaction American Society Agriculture Engineering, 20(6), 1100–1104.
46. Wilson, R. C. (1997). “Normalizing rainfall/debris-flow thresholds along U. S. pacific coast for long-term variation in precipitation climate.” Proceedings of the First International Conference on Debris-Flow Hazards Mitigation, ed. Chen, C-L, Hydraulic Division, American Society of Civil Engineers, August 7-9, 1997, San Francisco, 32-43.
47. Wu, M. C., and Tung C. B. (2000). “Environmental Changes of Taiwan and the Assessment of Valner ability to the Impacts of Global Change – Water Resources (Ⅱ).”National Science Council, Taiwan. NSC 89-2621-Z-002-015.
48. Young, R. A., Onstad, C. A., Bosch, D.D., and Anderson, W.P. (1987). “AGNPS, Agricultural Non-Point Source Pollution Model—A watershed analysis tool.” United States Department of Agriculture, Conservation Research Report 35.