Sains Malaysiana 38(5)(2009): 751–760

A Comparative Study of Extreme Rainfall in Peninsular Malaysia:

with Reference to Partial Duration and Annual Extreme Series

(Kajian Perbandingan Siri Tempoh Separa dan Maksimum Tahunan

Bagi Hujan Ekstrem di Semenanjung Malaysia)

Wan Zin Wan Zawiah*, Abdul Aziz Jemain & Kamarulzaman Ibrahim

School of Mathematical Sciences, Faculty of Science and Technology

Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D.E., Malaysia

Jamaludin Suhaila

Department of Mathematics, Faculty of Science

Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia

Mohd Deni Sayang

Center of Statistical Studies, Faculty of Information Technology and Quantitative Science

Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia

Received: 24 October 2008 / Accepted: 2 March 2009

ABSTRACT

Statistical distributions of annual extreme (AE) and partial duration (PD) for rainfall events are analysed using a database of 50 rain-gauge stations in Peninsular Malaysia, involving records of time series data which extend from 1975 to 2004. The generalised extreme value (GEV) and generalised Pareto (GP) distributions are considered to model the series of annual extreme and partial duration. In both cases, the three parameter models such as GEV and GP distributions are fitted by means of L-moments method, which is one of the commonly used methods for robust estimation. The goodness-of-fit of the theoretical distribution to the data is then evaluated by means of L-moment ratio diagram and several goodness-of-fit (GOF) tests for each of the 50 stations. It is found that for the majority of stations, the AE and PD series are well fitted by the GEV and GP models, respectively. Based on the models that have been identified, we can reasonably predict the risks associated with extreme rainfall for various return periods.

Keywords: Annual extreme series; extreme rainfall events, generalised extreme value distribution; generalised pareto distribution; L-moments; partial duration series

ABSTRAK

Taburan statistik bagi siri ekstrim tahunan (AE) dan tempoh separa (PD) bagi kejadian hujan dianalisis menggunakan pengkalan data 50 stesen sukatan hujan di Semenanjung Malaysia, merangkumi rekod yang berlanjutan dari 1975 ke 2004. Taburan nilai ekstrim teritlak (GEV) dan Pareto teritlak (GP) telah dicadangkan bagi pemodelan siri ekstrim tahunan and tempoh separa. Dalam kedua-dua kes, model tiga-parameter seperti taburan GEV dan GP, dipadankan menggunakan kaedah momen-L, yang merupakan salah satu kaedah yang sering digunakan bagi penganggaran teguh. Keserasian padanan diantara taburan secara teori kepada data kemudiannya dinilai dengan menggunakan rajah nisbah momen-L dan beberapa ujian kebagusan penyuaian (GOF) bagi setiap stesen. Didapati bahawa bagi kebanyakan stesen yang dikaji, siri AE mengikut model GEV manakala siri PD mengikut model GP. Berdasarkan model-model yang telah dikenal pasti, kita dapat membuat penganggaran yang munasabah mengenai risiko berhubung dengan hujan ekstrim bagi beberapa tempoh pulangan.

Kata kunci: Kejadian hujan ekstrem; momen-L; siri maksimum tahunan; siri tempoh separa; taburan nilai ekstrem teritlak; taburan pareto teritlak

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*Corresponding author; e-mail: w_zawiah@ukm.my