Page 406 - Contributed Paper Session (CPS) - Volume 2

CPS1911 Nurkhairary A. M. et al.

Modelling Wind Direction Data in Kota Kinabalu
Coastal Station Using Simultaneous Linear
Functional Relationship Model
1
2
1
Nurkhairany Amyra Mokhtar , Yong Zulina Zubairi , Abdul Ghapor Hussin ,
2
Rossita Mohamad Yunus
1 National Defence University of Malaysia
2 University of Malaya

Abstract
Wind direction data is important in meteorological studies as the knowledge
of wind direction may contribute to accurate estimation of real power
transmission capacity. The nature of the data is circular and is represented in
the form of degree or radians. This paper discusses on modelling simultaneous
linear functional relationship for multivariate circular wind direction data in
Kota Kinabalu coastal station in Malaysia during northeast monsoon for three
consecutive years. The three variables of the wind direction data are
considered with the von Mises distribution. The rotation parameter and the
concentration parameter are estimated using the maximum likelihood
estimation. It is found that the error concentration of wind direction is less
concentrated and dispersed over the three-year period.

Keywords
wind direction data; multivariate circular data; rotation parameter; error
concentration parameter; statistical modelling

1. Introduction
Unlike many other linear variables such as the wind speed and ozone level,
the wind direction has to be dealt differently in statistical analysis
(Jammalamadaka and Lund (2006)). The circumference of circular random
variables is a bounded closed space and different from the usual Euclidean
type variables (Hussin et al. (2004)). This is because a two-dimensional
direction of circular variable is represented as a point on the circumference of
a circle. The application of the conventional linear techniques on circular data
may result paradoxes (Lovell et al. (1991)). A circular observation may be
regarded as a unit vector in a plane, or as a point on a circle of unit radius.
Each circular observation may be specified by the angle from the initial
direction to the point on the circle corresponding to the observation once an
initial direction and an orientation of the circle have been chosen. Data are
usually measured in degrees or in radians. Because of the wrapped around
nature of angles, circular data cannot escape very far from each other and
certainly not able to hide from view (Fisher (1993), Mardia and Jupp (2000)).

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