Penggunaan Taburan Pareto Umum dalam Menganalisis Nilai Ekstrim Banjir Menggunakan Siri Aliran Puncak Melebihi Paras

Abstract

Siri banjir tahunan maksimum (Annual Maximum, AM) merupakan pendekatan yang begitu terkenal dalam analisis frekuensi banjir. Siri puncak melebihi paras (peaks over threshold, POT) telah digunakan sebagai alternatif kepada siri banjir tahunan maksimum. Masalah utama dalam pendekatan POT adalah berkaitan pemilihan paras yang sesuai. Dalam kajian ini, kesan perubahaan paras bagi siri POT ke atas nilai anggaran dikaji. Model POT dengan andaian bahawa bilangan puncak melebihi paras bertabur secara Poisson dan magnitud puncak melebihi paras tertabur secara Pareto Umum (General Pareto Distribution, GPD) dibincangkan. Parameter taburan GPD dianggar menggunakan kaedah kebarangkalian pemberat momen (Probability Weighted Moment, PWM) untuk paras yang diketahui. Perbandingan kesesuaian model POT dan model AM dalam menganggarkan nilai hujung atas taburan dibuat. Hasil kajian menunjukkan bahawa apabila paras siri POT boleh disuaikan oleh taburan Pareto dengan proses Poisson, model POT didapati dapat menghasilkan anggaran nilai hujung atas taburan lebih baik berbanding model aliran maksimum. Kata kunci: Siri puncak melebihi paras, proses poisson, taburan pareto umum, GEV, hujung atas taburan Annual maximum flood series remains the most popular approach to flood frequency analysis. Peaks over threshold series have been used as an alternative to annual maximum series. One specific difficulty of the POT approach is the selection of the threshold level. In this study the effect of raising the threshold of the POT series on heavy-tailed distributions estimation is investigated. The POT model described by the generalized Pareto distribution for peak magnitudes with the Poisson process for the occurrence of peaks is discussed. Estimation of the GPD parameters by the method of probability weighted moment (PWM) is formulated for known thresholds. A comparison of the efficiencies of the POT and AM models in heavy-tailed distributions is made. The result showed that when the threshold of POT series can be fitted by GPD with the Poisson process, the POT model is more efficient than the annual maximum (AM) model in estimating the highest extreme value. Key words: Peaks over threshold, poisson process, pareto distribution, GEV, heavy tailed distributions