Smoothing Wind and Rainfall Data through Functional Data Analysis Technique
DOI:
https://doi.org/10.11113/jt.v74.3011Keywords:
Basis function, smoothing curve, roughness penalty, functional data, fourier basisAbstract
The pattern of wind and rainfall throughout Peninsular Malaysia are varied from one region to another, because of strong influences from the monsoons. In order to capture the wind and rainfall variations, a functional data analysis is introduced. The purpose of this study is to convert the wind and rainfall data into a smooth curve by using functional data analysis method. Fourier basis is used in this study since the wind and rainfall data indicated periodic pattern. In order to avoid such overfitting data, roughness penalty is added to the least square when constructing functional data object from the observed data. Result indicated that if we use a small number of bases functions, the difference is very small between with and without roughness penalty, showing that it is safer to smooth only when required. However, when a large basis function is employed, the roughness penalty should be added in order to obtain optimal fit data. Based on the contour plot of correlation and cross-correlation functions of wind and rainfall data, the relationship between both climate functions could be determined.Â
Â
References
Cuevas, A., Febrero, M., Fraiman, R. 2003. An Anova Test for Functional Data. Comput. Stat. Data Anal. 47: 111–122.
Ferraty, F., Vieu, P., Viguier-Pla, S. 2006. Factor-based Comparison of Groups of Curve. Comput. Stat. Data Anal. 51: 4903–4910.
Hyndman, R. J., Booth, H. 2008. Stochastic Population Forecasts using Functional Data Models for Mortality, Fertility and Migration. Int. J. Forecasting. 24: 323–342.
Manteiga, W. G., Vieu, P. 2007. Statistical for Functional Data. Comput. Stat. Data Anal. 51: 4788–4792.
Nikitovic, V. 2011. Functional Data Analysis in Forecasting Serbian Fertility. Institute of Social Sciences. 2: 73–89.
Ramsay, J. O., Ramsey, J. B. 2002. Functional Data Analysis of the Dynamics of the Monthly Index of Nondurable Goods Production. J. Econometrics. 107: 327–344.
Ramsay, J. O., Hooker, G., Graves, S. 2005. Functional Data Analysis with R and Matlab. Springer. New York.
Ramsay, J. O., Silverman, B. W. 2005. Functional Data Analysis. second ed. Springer, New York.
Ratcliffe, S. J., Leader, L. R., Heller, G. Z. 2002. Functional Data Analysis With Application to Periodically Stimulated Foetal Heart Rate Data. I: Functional Regression. John Wiley & Sons, Ltd. 21. 1103–1114.
Suhaila, J., Jemain, A. A. 2011. A Comparison of the Rainfall Patterns between Stations on the East and the West coasts of Peninsular Malaysia using the Smoothing Model of Rainfall Amounts. Meteorol. Appl. 16(3): 391–401.
Suhaila, J., Jemain, A. A., Hamdan, M. F., Zin, W. Z. W. 2011. Comparing Rainfall Pattern between Regions in Peninsular Malaysia via a Functional Data Analysis. J. Hydro. 411: 197–206.
Tian, T. S. 2010. Functional Data Analysis in Brain Imaging Studies. Front Psychol. 1: 35.
Downloads
Published
Issue
Section
License
Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.
