Sains Malaysiana 50(7)(2021): 2035-2045

http://doi.org/10.17576/jsm-2021-5007-18

Understanding the Behaviour of Wind Direction in Malaysia during Monsoon Seasons using Replicated Functional Relationship in von Mises Distribution

(Pemahaman Tingkah Laku Arah Angin di Malaysia ketika Musim Tengkujuh menggunakan Hubungan Fungsian yang Direplikasi dalam Pengedaran von Mises)

NOR HAFIZAH MOSLIM¹, NURKHAIRANY AMYRA MOKHTAR², YONG ZULINA ZUBAIRI³* & ABDUL GHAPOR HUSSIN⁴

¹Institute of Advanced Studies, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

²Faculty of Computer and Mathematical Sciences,Universiti Teknologi MARA, Cawangan Johor, Kampus Segamat, 85000 Segamat, Johor Darul Takzim, Malaysia

³Centre for Foundation Studies in Science, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

⁴Faculty of Defence Sciences and Technology, National Defence University of Malaysia, Kem Sungai Besi, 57000 Kuala Lumpur, Federal Territory, Malaysia

Received: 23 June 2020/Accepted: 19 November 2020

ABSTRACT

In studies of potential wind energy, knowing statistical distribution of wind direction provides useful information in making predictions and gives a better understanding of the behavior of the wind direction. Malaysia experiences two monsoon seasons per year, namely Southwest Monsoon and Northeast Monsoon and in this paper, our interest is to investigate whether the direction of wind data in monsoon seasons can be modelled using replicated LFRM with von Mises distribution. The beauty of this model is that it considers the error terms in both x and y variables. This study considers the bivariate relationship of directional wind data where errors are present in both. Here, we propose a replicated functional relationship model, with the von Mises distribution to describe the relationship of the wind direction data. In the parameter estimation, maximum likelihood method is considered with pseudo-replicated group of the replicated form of the functional relationship. The novelty of this approach is that assumption on the ratio of concentration parameters is no longer deemed necessary. Also, we derive the covariance matrix of the parameters based on Fisher Information. From the Monte Carlo simulation study, small bias measures were obtained, suggesting the viability of the model. Based on the simulation study, it can be concluded that the wind direction of the two monsoons in Malaysia can be modelled using replicated linear functional relationship model.

Keywords: Circular data; Monte Carlo simulation; parameter estimation; von Mises distribution; wind direction data

ABSTRAK

Dalam kajian tentang potensi tenaga angin, mengetahui pengedaran statistik arah angin memberikan maklumat yang berguna dalam membuat ramalan dan memberikan pemahaman yang lebih baik mengenai tingkah laku arah angin. Malaysia mengalami dua musim tengkujuh setiap tahun, iaitu Monsun Barat Daya dan Monsun Timur Laut dan dalam makalah ini, minat kami adalah untuk mengkaji apakah arah data angin pada musim tengkujuh dapat dimodelkan menggunakan LFRM yang direplikasi dengan pengedaran von Mises. Keindahan model ini adalah bahawa ia menganggap istilah kesalahan dalam kedua-dua pemboleh ubah x dan y. Kajian ini mempertimbangkan hubungan bivariat data angin arah dan terdapat kesilapan pada kedua-duanya. Di sini, kami mencadangkan model hubungan fungsian yang direplikasi, dengan pengedaran von Mises untuk menggambarkan hubungan data arah angin. Dalam perkiraan parameter, kaedah kemungkinan maksimum dipertimbangkan dengan kumpulan pseudo-replikasi bentuk replikasi hubungan fungsian. Kebaruan pendekatan ini adalah bahawa anggapan mengenai nisbah parameter kepekatan tidak lagi dianggap perlu. Juga, kami memperoleh matriks kovarians parameter berdasarkan Maklumat Fisher. Daripada kajian simulasi Monte Carlo, ukuran bias kecil diperoleh, menunjukkan keberlangsungan model. Berdasarkan kajian simulasi, dapat disimpulkan bahawa arah angin dua monsun di Malaysia dapat dimodelkan dengan menggunakan model hubungan fungsian linear yang direplikasi.

Kata kunci: Anggaran parameter; data arah angin; data berkeliling; pengedaran von Mises; simulasi Monte Carlo

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*Corresponding email; email: yzulina@um.edu.my