Sains Malaysiana 41(11)(2012): 1389–1401

Analysis of T-Year Return Level for Partial Duration Rainfall Series

(Analisis Tahap Ulangan T-Tahun bagi Siri Hujan Tempoh Separa)

Wendy Ling Shin Yie* & Noriszura Ismail

School of Mathematical Sciences, Faculty of Science and Technology,

Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia

Diserahkan: 30 September 2011 / Diterima: 29 Mei 2012

ABSTRACT

This paper aims to estimate the Generalized Pareto Distribution (GPD) parameters and predicts the T-year return levels of extreme rainfall events using the partial duration series (PDS) method based on the hourly rainfall data of five stations in Peninsular Malaysia. In particular, the GPD parameters are estimated using five methods namely the method of Moments (MOM), the probability weighted moments (PWM), the L-moments (LMOM), the trimmed L-moments (TLMOM) and the maximum likelihood (ML) and the performance of the T-year return level of each estimation method is analyzed based on the RMSE measure obtained from Monte Carlo simulation. In addition, we suggest the weighted average model, a model which assigns the inverse variance of several methods as weights, to estimate the T-year return level. This paper contributes to the hydrological literatures in terms of three main elements. Firstly, we suggest the use of hourly rainfall data as an alternative to provide a more detailed and valuable information for the analysis of extreme rainfall events. Secondly, this study applies five methods of parametric approach for estimating the GPD parameters and predicting the T-year return level. Finally, in this study we propose the weighted average model, a model that assigns the inverse variance of several methods as weights, for the estimation of the T-year return level.

Keywords: Generalized Pareto Distribution; parameter estimation; partial duration series; T-year return level

ABSTRAK

Kajian ini bertujuan menganggar parameter Taburan Pareto Teritlak (GPD) dan meramal tahap ulangan T-tahun bagi kejadian hujan melampau menggunakan kaedah siri tempoh separa (PDS) berdasarkan data hujan per jam untuk lima stesen di Semenanjung Malaysia. Secara khususnya, parameter GPD dianggar melalui lima kaedah iaitu momen (MOM), momen kebarangkalian berpemberat (PWM), L-momen (LMOM), TL-momen (TLMOM) dan kebolehjadian maksimum (ML) dan prestasi tahap ulangan T-tahun untuk setiap kaedah dianalisis berdasarkan ukuran RMSE yang diperoleh melalui simulasi Monte Carlo. Selain itu, kajian ini mencadangkan model purata berpemberat, iaitu suatu model yang mewakilkan pemberat setiap kaedah dengan songsangan varian untuk menganggar tahap ulangan T-tahun. Kajian ini menyumbang kepada literatur hidrologi melalui tiga elemen utama. Pertama, kami mencadangkan penggunaan data hujan per jam sebagai alternatif untuk memberikan maklumat yang lebih bermakna dan menyeluruh bagi analisis kejadian hujan melampau. Kedua, dalam kajian ini kami menggunakan lima kaedah daripada pendekatan berparameter untuk menganggar parameter GPD dan meramal tahap ulangan T-tahun. Akhir sekali, kami mencadangkan model purata berpemberat, iaitu suatu model yang mewakilkan pemberat setiap kaedah dengan songsangan varian untuk penganggaran tahap ulangan T-tahun.

Kata kunci: Penganggaran parameter; siri tempoh separa; Taburan Pareto Teritlak; tahap ulangan T-tahun

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*Pengarang untuk surat-menyurat; email: lingshinyie@gmail.com