A Statistical Modeling of Extreme Rainfall in Peninsular Malaysia Using the Generalized Extreme Value (Gev) Distribution

採用廣義極值分布對馬來半島極端降雨進行統計模擬

10.6234/JGR.2015.63.02

黃燕儀(Yuen-Yi Ng)；翁叔平(Shu-Ping Weng)

極端降雨 ； 廣義極值分布（GEV） ； 重現期 ； 時空變化 ； Extreme rainfall ； Generalized Extreme Value (GEV) ； Return period ； spatial-temporal variability

地理研究

63期（2015 / 11 / 01）

33 - 53

英文

本研究採用時間序列為1971－2007年，馬來西亞水利灌溉局22個自動降雨測站之日降水資料，取年最大值及季最大值對馬來半島極端降雨的變化進行分析，進一步擬合廣義極值分布模式（GEV），計算出極端降雨的重現水平。根據研究結果顯示，半島東部地區的年最大降雨強度最高，而半島中部地區為低強度的極端降雨，但是在近年來有上升的趨勢，表示此區在未來可能面臨過去所未曾遭遇到的極端洪災事件。在季節分析上，中部地區春秋二季在未來可能遭受更頻繁的水患事件，而北部地區在秋季時則可能面臨乾旱的災害。本研究以GEV分布模式推估出50年和100年極端降雨的重現水平。在參數估計上，根據最佳配適度檢定結果顯示最大似然估計法（MLE）的配適度優於線性動差估計（LM）。我們發現半島西部和東部極端降雨重現水平的推估值具有明顯的空間差異，其中東岸地區重現水平的變化明顯高於半島西部地區，表示西部地區極端降雨實際觀測值很容易就超越了百年重現水平。上述的研究結果也透露出GEV分布模式對於半島西部地區極端降雨的重現水平估計依然難以掌握，雖然在配適度上得到了不錯的配適成效，這值得讓我們做進一步地思考。在極端降雨的空間分布特徵上，這樣的結果也暗示了近年馬來半島極端降雨的趨勢在空間分布上的轉變。

In this study, we have used the maximum daily rainfall data from a total of 22 automatic rainfall stations obtained from Department of Irrigation and Drainage Malaysia (DIDM) during 1971-2007. We have made use of the annual and seasonal maximum daily rainfall data to analyze extreme rainfall in Malaysia. We have also applied the generalized extreme value (GEV) distribution to model the occurrence probability of extreme rainfall in Peninsular Malaysia. The results showed that the greatest rainfall intensity was found in the east coast of Malaysia, while the lowest extreme rainfall intensity was found in the west central areas. Besides, our study also highlights a positive trend of extreme rainfall event that occurred at west central region in recent year. This result also suggests a likely increase of extreme flooding events in Malaysia in the coming years. For seasonal analysis, it is suggested that a rising flood disaster would possibly be affecting west central areas during the spring (MAM) and autumn (SON), while the northern part of Peninsula would probably suffered from the drought disaster during SON. We have also used the GEV distribution to calculate the return value for the 50-year and 100-year return periods. The maximum likelihood estimation (MLE) is suggested to be the best estimation in this study based on the result of goodness-of-fit. In this study, we have also noticed an apparent difference between the western and eastern parts of Peninsular Malaysia on the variation scale of return level, in which the variation recorded in the eastern region was greater than that of the western region. In addition, the observed rainfall level in the western region had exceeded the 100-year return level estimation. Our results suggest that deliberation is needed in the use of the GEV distribution for the estimation of the return levels of extreme rainfall in the western part of Peninsular Malaysia. For the spatial pattern of the extreme rainfall, our results also suggest that there is a shift in the spatial distribution of the extreme rainfall in recent years.

1. Ng, Yuen Yi(2013)。An analysis of rainfall periodicity of maritime continent: a case study in Peninsular Malaysia (1971-2007)。Journal of Geographical Science，71，93-111。
   連結：
2. Aryal, Santosh K.,Bates, Bryson C.,Campbell, Edward P.,Li, Yun,Palmer, Mark J.,Viney, Neil R.(2009).Characterizing and modeling temporal and spatial trends in rainfall extremes.Journal of Hydrometeorology,10,241-253.
3. Azpurua, Marco,Dos Ramos, Karina(2010).A comparison of spatial interpolation methods for estimation of average electromagnetic field magnitude.Progress In Electromagnetics Research M,14,135-145.
4. Beirlant, Jan,Vynckier, Petra,Teugels, Jozef L.(1996).Excess functions and estimation of the extreme-value index.Bernoulli,2(4),293-318.
5. Chang, Chih-Pei,Wang, Zhuo,McBride, John,Liu, Ching-Hwang(2005).Annual cycle of Southeast Asia-maritime continent rainfall and the asymmetric monsoon transition.Journal of Climate,18,287-301.
6. Chen, Tsing-Chang,Tsay, Jenq-Dar,Yen, Ming-Cheng,Matsumoto, Jun(2013).The winter rainfall of Malaysia.Journal of Climate,26,936-958.
7. Chu, Pao-Shin,Zhao, Xin,Ruan, Ying,Grubbs, Melodie(2009).Extreme rainfall events in the Hawaiian Islands.Journal of Applied Meteorology and Climatology,48,502-516.
8. Coles, Stuart,Pericchi, Luis R.(2003).Anticipating catastrophes through extreme value modelling.Applied Statistics,52,405-416.
9. Coles, Stuart,Pericchi, Luis R.,Sisson, Scott(2003).A fully probabilistic approach to extreme rainfall modelling.Journal of Hydrology,273,35-50.
10. Fredolin, T. Tangang,Alui, Bahari(2002).Enso influences on precipitation and air temperature variability in Malaysia.Proceedings of the Regional Symposium on Environment and Natural Resources, April 10-11, Kuala Lumpur
11. Hershfiels, David M.(1973).On the probability of extreme rainfall events.Bulletin American Meteorological Society,54(10),1013-1018.
12. Hosking, J. R. M.(1990).L-moments: analysis and estimation of distributions using linear combinations of order statistics.Journal of the Royal Statistical Society B,52,105-124.
13. Hosking, J. R. M.,Wallis, James R.,Wood, Eric. F.(1985).Estimation of the generalised extreme value distribution by the method of probability-weighted moments.Technometrics,27,251-261.
14. Intergovernmental Panel on Climate Change=IPCC(2007).Climate change 2007: Synthesis Report.
15. Jenkinson, A. F.(1955).The frequency distribution of the annual maximum (or minimum) values of meteorological elements.Quarterly Journal of the Royal Meteorological Society,81(348),158-171.
16. Juneng, Liew,Tangang, Fredonlin T.,Kang, Hongwen,Lee, Woo-Jin,Yap, Kok Seng(2010).Statistical downscaling forecasts for winter monsoon precipitation in Malaysia using multimodel output variables.Journal of Climate,23,17-27.
17. Juneng, Liew,Tangang, Fredonlin T.,Reason, Chris J. C.(2007).Numerical case study of an extreme rainfall event during 9-11 December 2004 over the east coast of Peninsular Malaysia.Meteorology and Atmospheric Physics,98,81-98.
18. Justel, Ana,Peña, Daniel,Zamar, Rubén(1997).A multivariate Kolmogorov-Smirnov test of goodness of fit.Statistics & Probability Letters,35,251-259.
19. Kottek, Markus,Griesek, Jürgen,Beck, Christoph,Rudolf, Bruno,Rubel, Franz(2006).World map of the Köppen-Geiger climate classification updated.Meteorologische Zeitschrift,15(3),259-263.
20. Koutsoyiannis, Demetris(2004).Statistics of extremes and estimation of extreme rainfall: I. Theoretical investigation.Hydrological Sciences Journal,49(4),575-590.
21. Koutsoyiannis, Demetris,Baloutsos, George(2000).Analysis of a long record of annual maximum rainfall in Athens, Greece, and design rainfall inferences.Natural Hazards,29,29-48.
22. Lavenda, Bernard H.,Cipollone, Elvio(2000).Extreme value statistics and thermodynamics of earthquakes: aftershock sequences.Annali Di Geofisica,43(5),967-982.
23. Liew, Juneng,Fredolin, T. Tangang(2008).Level and source of predictability of seasonal rainfall anomalies in Malaysia using canonical correlation analysis.International Journal of Climatology,28,1255-1267.
24. Liew, Juneng,Fredolin, T. Tangang(2002).Malaysia northeast monsoon precipitation variability and its relationships with tropical sea level pressure.Proceedings of the Regional Symposium on Environment and Natural Resources, April 10-11, Kuala Lumpur
25. Madsen, Henrik,Rasmussen, Peter F.,Rosbjerg, Dan(1997).Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events, 1, At-site modeling.Water Resources Research,33(4),747-758.
26. Martins, Eduardo S.,Stedinger, Jery R.(2000).Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data.Water Resources Research,36(3),737-744.
27. McNeil, Alexander J.,Frey, Rüdiger(2000).Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach.Journal of Empirical Finance,7,271-300.
28. Nadarajah, Saralees,Choi, Dongseok(2007).Maximum daily rainfall in South Korea.Journal of Earth System Science,116(4),311-320.
29. Nieuwolt, Simon(1968).Diurnal rainfall variation on Malaya.Annals of the Association of American Geographers,58(2),313-326.
30. Pagliara, Stefano,Viti, Cecilia,Gozzini, Bernardo,Meneguzzo, Francesco,Crisci, Alfonso(1998).Uncertainties and trends in extreme rainfall series in Tuscany, Italy: effects on urban drainage networks design.Water Science and Technology,37(11),195-202.
31. Parida, Bhagabat P.(1999).Modelling of Indian summer monsoon rainfall using a four-parameter Kappa distribution.International Journal of Climatology,19,1389-1398.
32. Park, Jeong-Soo,Jung, Hyun-Sook(2002).Modelling Korean extreme rainfall using a Kappa distribution and maximum likelihood estimate.Theoretical and Applied Climatology,72,55-64.
33. Park, Jeong-Soo,Jung, Hyun-Sook,Kim, Rae-Seon,Oh, Jai-Ho(2001).Modelling summer extreme rainfall over the Korean peninsula using Wakeby distribution.International Journal of Climatology,21,1371-1384.
34. Raynal-Villasenor, Jose A.(2012).Maximum likelihood parameter estimators for the two populations GEV distribution.International Journal of Research & Reviews in Applied Sciences,11(3),350-357.
35. Sobey, Rodney J.(2005).Extreme low and high water levels.Coastal Engineering,52,63-77.
36. Sugahara, Shigetoshi,da Rocha, Rosmeri P.,Silveira, Reinaldo(2009).Non-stationary frequency analysis of extreme daily rainfall in Sao Paulo, Brazil.International Journal of Climatology,29,1339-1349.
37. Suhaila, Jamaludin,Deni, Sayang Mohd,Wan Zin, Wan Zawiah,Jemain, Abdul Aziz(2010).Spatial patterns and trend of daily rainfall regime in Peninsular Malaysia during the southwest and northeast monsoons: 1975-2004.Meteorology and Atmospheric Physics,110,1-18.
38. Suhaila, Jamaludin,Jemain, Abdul Aziz(2012).Spatial analysis of daily rainfall intensity and concentration index in Peninsular Malaysia.Theoretical and Applied Climatology,108,235-245.
39. Suhaila, Jamaludin,Jemain, Abdul Aziz(2007).Fitting daily rainfall amount in Malaysia using the normal transform distribution.Journal of Applied Sciences,7(14),1880-1886.
40. Wan Zin, Wan Zawiah,Jamaludin, Suhaila,Deni, Sayang Mohd,Jemain, Abdul Aziz(2010).Recent changes in extreme rainfall events in Peninsular Malaysia: 1971-2005.Theoretical and Applied Climatology,99,303-314.
41. Wan Zin, Wan Zawiah,Jemain, Abdul Aziz(2010).Statistical distribution of extreme dry spell in Peninsular Malaysia.Theoretical and Applied Climatology,102,253-264.
42. Wan Zin, Wan Zawiah,Jemain, Abdul Aziz,Ibrahim, Kamarulzaman(2009).The best fitting distribution of annual maximum rainfall in Peninsular Malaysia based on methods of LQ-moment.Theoretical and Applied Climatology,96,337-344.
43. Wang, B.(Ed.)(2005).The Asian Monsoon.UK:Springer.
44. Wilks, Daniel S.(1993).Comparison of three-parameter probability distribution for representing annual extreme and partial duration precipitation series.Water Resources Researces,29,3543-3549.
45. Zakaria, Zahrahtul Amani,Shabri, Ani,Ahmad, Ummi Nadiah(2012).Regional frequency analysis of extreme rainfalls in the west coast of Peninsular Malaysia using partial L-moments.Water Resour Manage,26,4417-4433.
46. Zalina, Mohd Daud,Desa, Mohd Nor Mohd,Nguyen, Van-Thanh-Van,Kassim, Amir Hashim Mohd(2002).Selecting a probability distribution for extreme rainfall series in Malaysia.Water Science & Technology,45(2),63-68.
47. Zalina, Mohd Daud,Kassim, Amir Hashim Mohd,Desa, Mohd Nor Mohd,Nguyen, Van-Thanh-Van(2002).Statistical analysis of at-site extreme rainfall processes in Peninsular Malaysia.FRIEND 2002: Regional Hydrology: Bridging the Gap between Research and Practice,Wallingford:
48. Zhao, Er-Xu、Lu, Jun-Mei、Ju, Jian-Hua(2006)。Impacts of onset of summer monsoon over Southeast Asia on the rainy season in Yunnan。Journal of Tropical Meteorology，22(3)，209-216。
49. Zwiers, Francis W.,Zhang, Xuebin,Feng, Yang(2011).Anthropogenic influence on long return period daily temperature extremes at regional scales.Journal of Climate,24,881-892.