Sains Malaysiana 43(9)(2014): 1451–1460

Penentuan Taburan Terbaik daripada Hujan Maksimum Bagi Tempoh Ribut (Storm)

yang Panjang Melebihi 48 Jam (MR) dan Hujan Maksimum Tahunan (MT)

(The Best Fitting Distribution of Maximum Storm Rainfall with Long Duration with More than 48 H (MR) and Maximum Rainfall Annualy (MT))

R. YENDRA¹*, A.A. JEMAIN² & W.Z. WAN ZIN³

¹Department of Mathematics, Faculty of Science and Mathematics

Universitas Islam Negeri Sultan Syarif Kasim Riau, 28293, Pekanbaru, Riau

Indonesia

²School of Mathematical Sciences, Faculty of Science and Technology

Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia

³School of Mathematical Sciences, Faculty of Science and Technology

Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia

Received: 2 April 2013/Accepted: 2 January 2014

ABSTRAK

Kajian ini tertumpu kepada penentuan taburan terbaik untuk memodelkan siri data maksimum tahunan (MT) dan siri maksimum hujan dalam tempoh ribut yang melebihi 48 jam (MR). Data hujan setiap jam dari tahun 1970 hingga 2008 dari 4 stesen hujan di Semenanjung Malaysia telah digunakan dalam kajian ini. Kedua jenis data maksimum ini mempunyai kegunaan yang sangat baik bagi mengesan banjir di kawasan bandar terutama yang disebabkan oleh kegagalan sistem perparitan dalam menampung hujan lebat semasa tempoh ribut yang panjang, manakala kajian yang boleh meramalkan ketahanan empangan dalam masa 50 atau 100 tahun kehadapan sangat bergantung kepada penentuan taburan hujan maksimum tahunan. Pelbagai taburan yang sering digunakan bagi kajian pemodelan ekstrim digunakan untuk mendapatkan taburan yang terbaik bagi menerangkan taburan kedua jenis data hujan maksimum tersebut. Dua ujian kebagusan model telah digunakan iaitu kaedah bergraf dan kaedah PRKD. Hasil menunjukkan bahawa taburan Pearson Jenis 3 adalah yang terbaik untuk menerangkan taburan hujan maksimum tahunan pada kesemua stesen hujan yang digunakan pada kajian ini. Taburan Pareto dan Gama adalah taburan yang terbaik bagi menerangkan taburan hujan maksimum yang berlaku pada tempoh ribut yang panjang. Hasil kajian penentuan taburan terbaik bagi hujan maksimum tahunan di atas juga telah berjaya dalam meramalkan hujan maksimum yang akan berlaku untuk masa 50 dan 100 tahun yang akan datang.

Kata kunci: Gama; hujan ribut; maksimum tahunan; Pareto; Pearson jenis 3; RMSE

ABSTRACT

The focus of this study was to determine the best distribution to represent the annual series of maximum hourly rainfall and the maximum series rainfall from the storm exceeding 48 h. Data from 1970 to 2008 for 4 rain gauge stations in Peninsular Malaysia is used. Both types of maximum data series used in the detection of flood at urban areas, especially those caused by the failure of the drainage system to, while the study to predict the resistance of dam over 50 or 100 years’ time is very dependent on the determination of the best fitting distribution for annual maximum rainfall. Various distributions which are often used for modeling extreme events are used to obtain the best distribution for two types of data. The goodness of fit test performed are the graphical and RMSE methods have identified Pearson Type 3 distribution is the best model to explain the annual maximum rainfall at all stations used in this study. On the other hand Pareto and Gamma distribution are the best distribution to describe the maximum rainfall occurring during storm period. The study is successful in predicting the maximum rainfall at 50 and 100 years from now.

Keywords: Annual maximum; gamma; pareto; Pearson type 3; RMSE; storm rainfall

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*Corresponding author; email: yendra_75@yahoo. com.sg