Performance Analysis and Validation of Modified Singular Spectrum Analysis based on Simulation Torrential Rainfall Data

Shazlyn Milleana Shaharudin, Norhaiza Ahmad, Nur Syarafina Mohamed, Nazrina Aziz


A popular method for time series analysis to extract the components of noise and trend from the time series data is called the singular spectrum analysis (SSA). However, the drawback of SSA is its problem in determining the appropriate window length, L for certain data set in confirming patent separation of the components of trend and noise. Another issue that crops up when using SSA is that, over time, the sum of day-to-day rainfall becomes nearly comparable. In this case, disjoints sets of singular values and distinctive series components could essentially be intermixed, resulting in poor separability between trend and noise components. The introduction of modified SSA is to mitigate the problems efficiently. The performance of modified SSA is measured by using w-correlation and RMSE based on simulated data. These results show that the parameter L = T/5 was suitable to use in short time series rainfall data. It can be proved by the plot of the extracted trend for modified SSA that appears to conform to the original data configuration for time series rainfall however there is the omission of components of noise predominantly for L = T/5 in detecting the uncharacteristically heavy downpour which could potentially initiate the occurrence of torrential rainfall. In addition, the result shows that average RMSE for reconstructed time series components of modified SSA is much smaller than SSA for each L


singular spectrum analysis; trend; simulation; iterative o-ssa; robust sparse k-means; window length; modified singular spectrum analysis.

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F.W. Githui, A. Opere, and W. Bauwens, “Statistical and trend analysis of rainfall and river discharge: Yala River Basin, Kenya,” in Proc. International Conference of UNESCO, 2005.

M. Khaleghi, H. Zeinivand, and S. Moradipour, “Rainfall and river discharge trend analysis: a case study of Jajrood Watershed, Iran,” International Bulletin of Water Resources and Development, vol.2, pp. 1-2, Sept. 2014.

A. Mondal, S. Kundu, and A. Mukhopadhyay, “Rainfall trend analysis by mann-kendall test: a case study of north-eastern part of cuttack district, Orissa,” International Journal of Geology, Earth and Environmental Sciences, vol.2, pp. 70-78, April 2012.

T. Alexandrov, N. Golyandina, and A. Spirov, “Singular spectrum analysis of gene expression profiles of early drosophila embryo: exponential-in-distance patterns,” Research Letters in Signal Processing, vol. 2008, pp. 1-5, June 2008.

H. Hu, S. Guo, R. Liu, and P. Wang, “An adaptive singular spectrum analysis method for extracting brain rhythms of electroencephalography,” PeerJ, June, 2017. [Online]. Available: DOI 10.7717/peerj.3474.

S.M. Shaharudin, N. Ahmad, F. Yusof, “Effect of window length with singular spectrum analysis in extracting the trend signal on rainfall data,” AIP Conf. Proc., vol. 1643, pp. 321-326, 2015.

N. Golyandina, V. Nekrutkin, and A. Zhigljavsky, “Analysis of time series structure:ssa and the related technique,” 1th ed., New York: Chapman &Hall/CRC, 2001.

S.M. Shaharudin, N. Ahmad, F. Yusof, X.Q. Yap, “The comparison of t-mode and pearson correlation matrices in classification of daily rainfall patterns in Peninsular Malaysia,” Matematika, vol.29, pp. 187-194, 2013.

E. Barton, B. Al-Sarray, S. Chretien, K. Jagan, “Decomposition of dynamical signals into jumps, oscillatory patterns and possible outliers,” Mathematics, vol. 6(7), pp.124-137, July 2018.

S.M. Shaharudin, N. Ahmad, N.H. Zainuddin, N.S. Mohamed, “Identification of rainfall patterns on hydrological simulation using robust principal component analysis,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 11, pp. 1162-1167, Sept. 2018.

H-K. Cho, K.P. Bowmanand, and G.R. North, “A comparison of gamma and log-normal distribution for characterizing satellite rain rates from the tropical rainfall measuring mission,”Journal of Applied Meteorology, vol. 43, pp.1586-1597, 2004.

R.H. Al-Suhili, and R. Khanbilvardi, “Frequency analysis of the monthly rainfall data at sulaimania region, Iraq,” American Journal of Engineering Research, vol.3, pp. 212-222, 2014.

N.O.S. Alghazali, and D.A.H. Alawadi, “Fitting statistical distributions of monthly rainfall for some Iraqi stations,” Civil and Environmental Research, vol. 6, pp. 40-47, 2014.

O.I. Traore, L. Pantera, N. Favretto-Cristini, P. Cristini, S. Viguier-Pla, and P. Vieu, “Structure analysis and denoising using Singular Spectrum Analysis: Application to acoustic emission signals from nuclear safety experiment,” Measurement, vol.104,pp.78-88, Feb. 2017.

M. B. Priestley, Spectral Analysis and Time Series, London: Academic Press., 1981.

Y. Kondo, M. Salibian-Barrera, and R. Zamar, A Robust and Sparse K-means Clustering Algortihm, arXiv:1201.6082v1.

S. M. Shaharudin et al., “Modified singular spectrum analysis in identifynig rainfall trend over Peninsular Malaysia,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 15, No. 1, pp. 283-293, 2019.



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