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CPS1887 Sahidan A. et al.
agricultural area for rice paddy, fruit and vegetables. Those two areas have the
largest population and construction projects ongoing for instance
underground transportation systems, commercial centers and new high-rise
apartments (Ro-Ting and Chang-Chuan, 2009). As a result, those factors might
have an effect on the land surface temperature in the future. Thus, our study
emphasis on seasonal pattern and trend of average increase in LST in Taiwan.

2. Methodology
Cubic spline function was the method that applied in this study. A spline
function is also recognized as, derivatives with numeric curve fitting function
that developers able state as essential for its applications (Wahba, 1990). Not
only the degree of the spline function, but other parameters for example a
number of polynomial points for connecting with other pieces which known
as knots, the position of the knots and the free coefficients of the spline
function are the user’s choices (Wold, 1974). In order to choose an appropriate
number of the knots to be applied with LST data, it has to compromise
between smoothness of the seasonal curve and goodness of fit (Wongsai et
al., 2017).
An order 3 of cubic spline was the most commonly-used. Moreover, it is a
piecewise cubic polynomial with continuous second derivatives and is
smoothest among all functions in the sense that it has a minimal integrated
squared second derivative. Natural cubic spline was used to extract an annual
seasonal trend in temporal daytime (Wongsai et al., 2017). Furthermore, it has
been widely used for smoothing data in different areas of study for instance
real-time digital signal processing (Feng, 1998), interactive computer graphics
(Smith et al, 1994) and satellite-based time series data (Mao et al., 2017). In
addition, cubic spline can be used to fit by using linear least squares
regression. The continuous of the first and second derivatives are the key
advantages of the spline fit (Smith et al, 1994), comprising its high precision,
smoothness, good stability and simple calculation (Zhang et al, 2016).
Actually, the data from MODIS fluctuated in every season. Mostly the
seasonal pattern of LST is presumed to be the same for every year and they
have some change in other factors for example land use and land cover
change that might has a direct or indirect influence to the LST. Therefore, LST
of construction land, the development of agricultural land and the natural
disaster might change LST pattern. From those reason we suggest that the
cubic spline model is an appropriate model in modelling LST change pattern
and trend because they provide continuous seasonal pattern for each day of
the year with specific boundary conditions that certify smooth periodicity.

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