台灣地區近年來氣候變化異常，降雨量極不穩定，對台灣社會造成嚴重的影響。許多文獻均指出受到氣候變遷的影響，極端氣候發生的強度與頻率會增加，若降雨減少可能造成供水不足影響日常用水，但過度集中的降雨亦會造成洪水災害，因此了解降雨特性的趨勢變化對水資源規劃與管理而言是一項很重要的工作。
本文以統計方法探討台灣地區年雨量的趨勢與分佈變化，採用台灣地區23個雨量測站1947年到2000年共54年資料，分別利用線性迴歸、Mann-Kendall檢定及分量迴歸(quantile regression)探討各測站年雨量的可能變化趨勢。由於分量迴歸可得到不同分量下之線性迴歸線，本研究整合不同分量之資訊轉換為近似的機率密度函數(probability density function, PDF)，並比較資料始末年(1947、2000年)年雨量的機率密度函數之變化，即可了解年雨量分佈的變化情形。
線性迴歸與Mann-Kendall檢定結果顯示台北站年雨量有上升趨勢，五塊、里港與大武站有下降趨勢，分量迴歸分析結果顯示前述4站之部份分量有明顯變化趨勢。線性迴歸與Mann-Kendall檢定結果有19站沒有顯著變化趨勢，但分量迴歸顯示此19站中有7站之分量有變化趨勢。若以年雨量機率密度函數的變化來判斷則台灣北區年雨量沒有趨勢，中、南區降雨範圍將更加集中且年雨量有減少趨勢，東區降雨量不變與減少趨勢各佔一半。

Extreme climatic events have frequently observed in Taiwan recently. Such unusual extreme events often cause severe economic damages. Many studies report that intensified events caused by climate change are occurred frequently. Declining rainfall would induce insufficient water supplies, while increasing rainfall would cause flooding. Understanding trend of rainfall characteristics thus becomes an important task in water resources planning and management.
This study aims to detect trend and distribution-change of annual rainfall by using statistical methods, including linear regression, Mann-Kendall test, and quantile regression. The data used in this study is the annual rainfall with at least 54 years (from 1947 to 2000) of 23 rainfall gauge stations in Taiwan. Quantile regression can identify the linear regression lines at various quantiles. An approach is proposed in this study to integrate changes of all quantiles from quantile regression model in terms of changes of probability density function (PDF) to detect distributional changes of annual rainfall.
Linear regression and Mann-Kendall test show that the Taipei station has an increasing trend, while Wukuai, Likang, and Tawu have descending trend. The results of quantile regression also show that the above 4 stations have significant trend at some quantiles. There are 19 stations exhibit non-significant trend by the linear regression model and Mann-Kendall test. However, significant trend at some quantiles are observed by quantile regression for 7 stations. That is, such trends are not detected by linear regression model and Mann-Kendall test. In terms of PDF-change, the PDF of annual rainfall in North region has no shift, the PDF in Central and South regions has leftward shift and concentrates in a narrower rage, and half of PDF in East region has no shift and the other half PDF has left shift.

Al-Ahmadi, K. and Al-Ahmadi, S., Rainfall-Altitude Relationship in Saudi Arabia. Advances in Meteorology 2013, 363029, 2013.
Alexander, L. V., Zhang, X., Peterson, T. C., Caesar, J., Gleason, B., Klein Tank, A. M. G., Haylock, M., Collins, D., Trewin, B., Rahimzadeh, F., Tagipour, A., Rupa Kumar, K., Revadekar, J., Griffiths, G., Vincent, L., Stephenson, D. B., Burn, J., Aguilar, E., Brunet, M., Taylor, M., New, M., Zhai, P., Rusticucci, M., and Vazquez-Aguirre, J. L., Global observed changes in daily climate extremes of temperature and precipitation. Journal of Geophysical Research 111(D5), D05109, 2006.
Barbosa, S. M., Quantile trends in Baltic sea level. Geophysical Research Letters 35(22), L22704, 2008.
Barbosa, S. M., Scotto, M. G., and Alonso, A. M., Summarising changes in air temperature over Central Europe by quantile regression and clustering. Natural Hazards and Earth System Sciences 11(12), 3227–3233, 2011.
Bari Abarghouei, H., Asadi Zarch, M. A., Dastorani, M. T., Kousari, M. R., and Safari Zarch, M., The survey of climatic drought trend in Iran. Stochastic Environmental Research & Risk Assessment 25(6), 851–863, 2011.
Barreto, R. A. and Hughes, A. W., Under performers and over achievers: A quantile regression analysis of growth. Economic Record 80(248), 17–35, 2004.
Baur, D. G., Dimpfl, T., and Jung, R. C., Stock return autocorrelations revisited: A quantile regression approach. Journal of Empirical Finance 19(2), 254–265, 2012.
Biggs, E. M. and Atkinson, P. M., A characterisation of climate variability and trends in hydrological extremes in the Severn Uplands. International Journal of Climatology 31(11), 1634–1652, 2011.
Birsan, M.-V., Molnar, P., Burlando, P., and Pfaundler, M., Streamflow trends in Switzerland. Journal of Hydrology 314(1–4), 312–329, 2005.
Buchinsky, M., Changes in the U.S. Wage Structure 1963-1987: Application of Quantile Regression. Econometrica 62(2), 405–458, 1994.
Buchinsky, M., Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research. The Journal of Human Resources 33(1), 88–126, 1998.
Burn, D. H. and Elnur, M. A. H., Detection of hydrologic trends and variability. Journal of Hydrology 255(1-4), 107–122, 2002.
Cade, B. S. and Noon, B. R., A gentle introduction to quantile regression for ecologists. Frontiers in Ecology and the Environment 1(8), 412–420, 2003.
Chamaille-Jammes, S., Fritz, H., and Murindagomo, F., Detecting climate changes of concern in highly variable environments: Quantile regressions reveal that droughts worsen in Hwange National Park, Zimbabwe. Journal of Arid Environments 71(3), 323–329, 2007.
Chamaillé-Jammes, S. and Blumstein, D., A case for quantile regression in behavioral ecology: getting more out of flight initiation distance data. Behavioral Ecology and Sociobiology 66(6), 985–992, 2012.
Chernozhukov, V. and Hansen, C., Instrumental quantile regression inference for structural and treatment effect models. Journal of Econometrics 132(2), 491–525, 2006.
Cheung, W. H., Senay, G. B., and Singh, A., Trends and spatial distribution of annual and seasonal rainfall in Ethiopia. International Journal of Climatology 28(13), 1723–1734, 2008.
De Toffol, S., Laghari, A., Rauch, W., et al., Are extreme rainfall intensities more frequent? Analysis of trends in rainfall patterns relevant to urban drainage systems. Water Science and Technology 59(9), 1769–1776, 2009.
del Rio, S., Herrero, L., Fraile, R., and Penas, A., Spatial distribution of recent rainfall trends in Spain (1961-2006). International Journal of Climatology 31(5), 656–667, 2011.
Dodet, G., Bertin, X., and Taborda, R., Wave climate variability in the North-East Atlantic Ocean over the last six decades. Ocean Modelling 31(3–4), 120–131, 2010.
Gadgil, A. and Dhorde, A., Temperature trends in twentieth century at Pune, India. Atmospheric Environment 39(35), 6550–6556, 2005.
Geraci, M. and Bottai, M., Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics 8(1), 140–154, 2007.
Gould, W., Quantile regression with bootstrapped standard errors. Stata Technical Bulletin 2(9), 2012.
Hayashi, M., The effects of medical factors on transfer deficits in Public Assistance in Japan: a quantile regression analysis. International Journal of Health Care Finance & Economics 11(4), 287–307, 2011.
He, X., Quantile Curves without Crossing. The American Statistician 51(2), 186–192, 1997.
Hess, A., Iyer, H., and Malm, W., Linear trend analysis: a comparison of methods. Atmospheric Environment 35(30), 5211–5222, 2001.
Hirsch, R. M., Slack, J. R., and Smith, R. A., Techniques of trend analysis for monthly water quality data. Water Resources Research 18(1), 107–121, 1982.
Hirschi, M., Seneviratne, S. I., Alexandrov, V., Boberg, F., Boroneant, C., Christensen, O. B., Formayer, H., Orlowsky, B., and Stepanek, P., Observational evidence for soil-moisture impact on hot extremes in southeastern Europe. Nature Geoscience 4(1), 17–21, 2011.
Huth, R. and Pokorná, L., Parametric versus non-parametric estimates of climatic trends. Theoretical and Applied Climatology 77(1-2), 107–112, 2004.
IPCC, Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Geneva, Switzerland, 2007.
Jiang, F.-q., Hu, R.-J., Wang, S.-P., Zhang, Y.-W., and Tong, L., Trends of precipitation extremes during 1960–2008 in Xinjiang, the Northwest China. Theoretical and Applied Climatology 111(1-2), 133–148, 2013.
Kendall, M. G., Rank Corelation Measures (1 ed.). London: Charles Griffin, 1975.
Kim, J. S. and Jain, S., Precipitation trends over the Korean peninsula: typhooninduced changes and a typology for characterizing climate-related risk. Environmental Research Letters 6(3), 2011.
Koenker, R. and Bassett, G., Regression Quantiles. Econometrica 46(1), 33–50, 1978.
Koenker, R. and Machado, J. A., Goodness of fit and related inference processes for quantile regression. Journal of the american statistical association 94(448), 1296–1310, 1999.
Koenker, R., Ng, P., and Portnoy, S., Quantile smoothing splines. Biometrika 81(4), 673–680, 1994.
Koenker, R. and Xiao, Z., Inference on the quantile regression process. Econometrica 70(4), 1583–1612, 2002.
Koenker, R. W. and D’Orey, V., Algorithm AS 229: Computing Regression Quantiles. Journal of the Royal Statistical Society. Series C (Applied Statistics) 36(3), 383–393, 1987.
Kuglitsch, F. G., Toreti, A., Xoplaki, E., Della-Marta, P. M., Zerefos, C. S., Türkeş, M., and Luterbacher, J., Heat wave changes in the eastern Mediterranean since 1960. Geophysical Research Letters 37(4), L04802, 2010.
Longobardi, A. and Villani, P., Trend analysis of annual and seasonal rainfall time series in the Mediterranean area. International journal of Climatology 30(10), 1538–1546, 2010.
Luce, C. H. and Holden, Z. A., Declining annual streamflow distributions in the Pacific Northwest United States, 1948-2006. Geophysical Research Letters 36, L16401, 2009.
Ma, L. and Pohlman, L., Return forecasts and optimal portfolio construction: a quantile regression approach. European Journal of Finance 14(5), 409–425, 2008.
Mann, H. B., Nonparametric Tests Against Trend. Econometrica 13(3), 245–259, 1945.
Mazvimavi, D., Investigating changes over time of annual rainfall in Zimbabwe. Hydrology and Earth System Sciences 14(12), 2671–2679, 2010.
Melly, B., Estimation of counterfactual distributions using quantile regression. Review of Labor Economics 68, 543–572, 2006.
Muhlbauer, A., Spichtinger, P., and Lohmann, U., Application and comparison of robust linear regression methods for trend estimation. Journal of Applied Meteorology and Climatology 48(9), 1961–1970, 2009.
Nunes, P. M., Mendes, S., and Serrasqueiro, Z., SMEs’ investment determinants: empirical evidence using quantile approach. Journal of Business Economics and Management 13(5), 866–894, 2012.
Piccarreta, M., Capolongo, D., and Boenzi, F., Trend analysis of precipitation and drought in Basilicata from 1923 to 2000 within a southern Italy context. International Journal of Climatology 24(7), 907–922, 2004.
Portnoy, S. and Koenker, R., The Gaussian Hare and the Laplacian Tortoise: Computability of squared- error versus absolute-error estimators. Statistical Science 12(4), 279–296, 1997.
Rana, A., Uvo, C., Bengtsson, L., and Parth Sarthi, P., Trend analysis for rainfall in Delhi and Mumbai, India. Climate Dynamics 38(1-2), 45–56, 2012.
Rio, S. d., Penas, A., and Fraile, R., Analysis of recent climatic variations in Castile and Leon (Spain). Atmospheric Research 73(1–2), 69–85, 2005.
Sansigolo, C. and Kayano, M., Trends of seasonal maximum and minimum temperatures and precipitation in Southern Brazil for the 1913–2006 period. Theoretical and Applied Climatology 101(1-2), 209–216, 2010.
Serrasqueiro, Z., Nunes, P. M., Leitao, J., and Armada, M., Are there nonlinearities between SME growth and its determinants? A quantile approach. Industrial and Corporate Change 19(4), 1071–1108, 2010.
Shahid, S., Trends in extreme rainfall events of Bangladesh. Theoretical and Applied Climatology 104(3-4), 489–499, 2011.
Sousa, P., Trigo, R., Aizpurua, P., Nieto, R., Gimeno, L., and Garcia-Herrera, R., Trends and extremes of drought indices throughout the 20 th century in the Mediterranean. Natural Hazards and Earth System Sciences 11(1), 33–51, 2011.
Verropoulou, G. and Tsimbos, C., Modelling the effects of maternal sociodemographic characteristics on the preterm and term birth weight distributions in Greece using quantile regression. Journal of Biosocial Science 45(03), 375–390, 2013.
Villarini, G., Smith, J. A., Baeck, M. L., Vitolo, R., Stephenson, D. B., and Krajewski, W. F., On the frequency of heavy rainfall for the Midwest of the United States. Journal of Hydrology 400(1-2), 103–120, 2011.
Wu, Y. and Liu, Y., Variable selection in quantile regression. Statistica Sinica 19(2), 801–817, 2009.
Yu, K. and Jones, M., Local linear quantile regression. Journal of the American Statistical Association 93(441), 228–237, 1998.
Yu, K., Lu, Z., and Stander, J., Quantile regression: applications and current research areas. Journal of the Royal Statistical Society: Series D (The Statistician) 52(3), 331–350, 2003.
Yu, K. and Moyeed, R. A., Bayesian quantile regression. Statistics & Probability Letters 54(4), 437–447, 2001.
Yu, M., Li, Q., Hayes, M. J., Svoboda, M. D., and Heim, R. R., Are droughts becoming more frequent or severe in China based on the Standardized Precipitation Evapotranspiration Index: 1951–2010? International Journal of Climatology, 2013.
Zhang, Q., Xu, C.-Y., Zhang, Z., and Chen, Y. D., Changes of temperature extremes for 1960-2004 in Far-West China. Stochastic Environmental Research and Risk Assessment 23(6), 721–735, 2009.
宋嘉文，氣候變遷對台灣西半部地區降雨及乾旱影響之研究，國立成功大學水利及海洋工程學系碩士論文，2003。
朱蘭芬、陳永明、張靜貞，近百年台灣極端降雨量之變化情形-以端值理論為例，建國百年天氣分析預報與地震測報研討會，421–426，2011。
汪中和，台灣降雨的長期變化及對環境的衝擊，自然與文化研討會，農委會林試所，50–54，2004。
王婕妤，臺灣地區區域降雨總量及極端降雨與乾旱之變遷特性，國立中央大學土木工程學系碩士論文，2010。
蕭政宗、楊欣怡、馬家驎，台灣地區降雨特性趨勢分析，第十三屆水利工程研討會，B–1–B–8，2002。
許晃雄、陳正達、盧孟明、陳永明、周佳、吳宜昭，台灣氣候變遷科學報告，行政院國家科學委員會，362 頁，2011。
錢滄海、楊孟叡、曹舜評、李汴軍，台北測站長時間降雨之趨勢檢定， 水土保持學報42(3)，285–304，2010。
鍾侑達、郭峻菖、陳昶憲，台灣區域降雨趨勢分析， 農業工程學報55(4)，1–18，2009。