Extraction of Nonlinear Rainfall Trends Using Singular Spectrum Analysis
Publication: Journal of Hydrologic Engineering
Volume 20, Issue 12
Abstract
Rainfall plays a crucial role in the socioeconomic development of a country. Knowledge of both the amount of rainfall and its pattern of distribution are equally important for proper management of water resources systems. In the present study, trends of two rainfall series from different locations having different time periods and time steps have been extracted using the singular spectrum analysis (SSA) method. Data analyzed include monthly data of England and Wales precipitation (EWP) from 1766 to 2002 in which no periodic component is prevailing and daily rainfall data of Koyna watershed, Maharashtra, India from 1961 to 2009, which shows a strong periodic component of 365 days. Method of periodogram analysis has been used in order to select the components corresponding to trend in the grouping stage of SSA. The Mann–Kendall (MK) test is also used to detect trends in EWP monthly series and the performance of SSA and MK test is compared. The result showed that the MK test could detect the presence of a positive or negative trend at a significant level, whereas the proposed SSA method could extract the nonlinear trend present in the series along with its shape. Trends extracted from the England and Wales precipitation are compared with a previously published EWP trend extraction study. The comparison shows that the method of SSA in trend extraction could extract nonlinear trends along with its shape whereas the previous study extracted linear trends. The EWP monthly rainfall series showed an increasing trend during the winter season and a decreasing trend during summer. The trend extracted for the Koyna series has very small values (almost constant), implying that the rainfall series is almost stationary. The study proves the applicability of SSA for extracting nonlinear trends that provide more insight into the observed time series.
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References
Alexander, L., and Jones, P. D. (2001). “Updated precipitation series for the U.K. and discussion of recent extremes.” Atmos. Sci. Lett., 1(2), 142–150.
Alexandrov, T. (2009). “A method of trend extraction using singular spectrum analysis.” Revstat Stat. J., 7(1), 1–22.
Alexandrov, T., and Golyandina, N. (2006). “Automatic trend extraction and forecasting for a family of time series.” Int. Symp. on Forecasting, International Institute of Forecasters, Medford, MA.
Birsan, M. V., Molnar, P., Burlando, P., and Pfaundler, M. (2005). “Streamflow trends in Switzerland.” J. Hydrol., 314(1–4), 312–329.
Bojar, K. (2011). “Trend extraction from noisy discrete signals by means of singular spectrum analysis and morphological despiking.” Przeglad Elektrotechniczny, 87(6), 241–244.
Bonaccorso, B., Cancelliere, A., and Rossi, G. (2005). “Detecting trends of extreme rainfall series in Sicily.” Adv. Geosci., 2, 7–11.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (2003). Time series analysis- Forecasting and control, Pearson Education, New Delhi, India, 1–598.
Broomhead, D., and King, G. P. (1986). “Extracting qualitative dynamics from experimental data.” Phys. D: Nonlinear Phenomena, 20(2–3), 217–236.
Brunetti, M., Colacino, M., Maugeri, M., and Nanni, T. (2001). “Trends in the daily intensity of precipitation in Italy from 1951 to 1996.” Int. J. Climatol., 21(3), 299–316.
Burn, D. H., and Elnur, M. A. H. (2002). “Detection of hydrologic trends and variability.” J. Hydrol., 255(1–4), 107–122.
CDO (Central Design Organisation). (1992). “Final report on revised flood study for Koyna Dam.” Goverment of Maharashtra, Irrigation Dept.
Chau, K. W., and Wu, C. L. (2010). “A hybrid model coupled with singular spectrum analysis for daily rainfall prediction.” J. Hydroinf., 12(4), 458–473.
Damberg, L., and Agha Kouchak, A. (2014). “Global trends and patterns of drought from space.” Theor. Appl. Climatol., 117(3–4), 441–448.
Elsner, J. B., and Tsonis, A. A. (1996). Singular spectrum analysis—A new tool in time series analysis, Plenum, New York, 1–160.
Golyandina, N., and Zhigljavsky, A. (2013). Singular spectrum analysis for time series, Springer, New York, 1–118.
Gregory, J. M., Jones, P. D., and Wigley, T. M. L. (1991). “Precipitation in Britain: An analysis of area-average data updated to 1989.” Int. J. Climatol., 11(3), 331–345.
Heng, S., and Suetsugi, T. (2013). “Coupling singular spectrum analysis with artificial neural network to improve accuracy of sediment load prediction.” J. Water Resour. Prot., 5(4), 395–404.
IPCC (Intergovernmental Panel on Climate Change). (1996). “Climate change 1995 impacts, adaptations and mitigation of climate change: Scientific-technical analyses.” Contribution of Working Group II to the Second Assessment Rep. of the Intergovernmental Panel on Climate Change, T. Watson Robert, C. Zinyowera Marufu, H. Moss Richard, and D. Dokken David, eds., Cambridge University Press, New York.
IPCC (Intergovernmental Panel on Climate Change). (2001). “Climate change 2001: Impacts, adaptation and vulnerability.” Contribution of Working Group II to the Third Assessment Rep. of the Intergovernmental Panel on Climate Change, J. McCarthy James, F. Canziani Osvaldo, A. Leary Neil, J. Doken David, and S. White Kasey, eds., Cambridge University Press, U.K.
Jia, S., Guo, Y., Wang, Q., and Zhang, J. (2009). “Trend extraction and similarity matching of financial time series based on EMD method.” 2009 WRI World Congress on Computer Science and Information Engineering, IEEE Computer Society, NJ, 526–530.
Jones, P. D., and Conway, D. (1997). “Precipitation in the British Isles: An analysis of area-average data updated to 1995.” Int. J. Climatol., 17(4), 427–438.
Jothiprakash, V., and Kote, A. S. (2011). “Improving the performance of data-driven techniques through data pre-processing for modelling daily reservoir inflow.” Hydrol. Sci. J., 56(1), 168–186.
Jothiprakash, V., and Magar, R. B. (2012). “Multi-time-step ahead daily and hourly intermittent reservoir inflow prediction by artificial intelligent techniques using lumped and distributed data.” J. Hydrol., 450–451, 293–307.
Kahya, E., and Kalayci, S. (2004). “Trend analysis of streamflow in Turkey.” J. Hydrol., 289(1–4), 128–144.
Kandlikar, M. (2007). “Air pollution at a hotspot location in Delhi: Detecting trends, seasonal cycles and oscillations.” Atmos. Environ., 41(28), 5934–5947.
Katz, R. W. (2010). “Statistics of extremes in climate change.” Clim. Change, 100(1), 71–76.
Kendall, M. (1975). Rank correlation methods, Charles Griffin, London.
Kote, A. S., and Jothiprakash, V. (2009). “Monthly reservoir inflow modeling using time lagged recurrent networks.” Int. J. Tomograp. Stat., 12(F09), 64–84.
Kumar, U., and Jain, V. K. (2010). “Time series models (Grey-Markov, Grey model with rolling mechanism and singular spectrum analysis) to forecast energy consumption in India.” Energy, 35(4), 1709–1716.
Liu, D., Guo, S., Chen, X., and Shao, Q. (2012). “Analysis of trends of annual and seasonal precipitation from 1956 to 2000 in Guangdong Province, China.” Hydrol. Sci. J., 57(2), 358–369.
Luis, M. D., Raventos, J., Hidalgo, J. C. G., Sanchez, J., and Cortina, J. (2000). “Spatial analysis of rainfall trends in the region of Valencia (East Spain).” Int. J. Climatol., 20(12), 1451–1469.
Mann, H. (1945). “Non-parametric tests against trend.” Econometrica, 13(3), 245–259.
Martino, G. De, Fontana, N., Marini, G., and Singh, V. P. (2013). “Variability and trend in seasonal precipitation in the continental United States.” J. Hydrol. Eng., 630–640.
Meteorological Office. (2001). The wet weather returns, 〈http://www.metoffice.gov.uk/climate/uk/interesting/feb2001rain.html〉 (Jun. 6, 2014).
Meteorological Office, and CEH (Centre for Ecology and Hydrology). (2014). The recent storms and floods in the U.K., U.K., 1–27.
Mhamdi, F., Jaidane-Saidane, M., and Poggi, J.-M. (2010). “Empirical mode decomposition for trend extraction. Application to electrical data.” Compstat, Physica, Heidelberg, Germany, 1–11.
Mills, T. C. (2005). “Modelling precipitation trends in England and Wales.” Meteorol. Appl., 12(2), 169–176.
New, M., Todd, M., Hulme, M., and Jones, P. (2001). “Precipitation measurements and trends in the twentieth century.” Int. J. Climatol., 21(15), 1889–1922.
Osborn, T. J., and Hulme, M. (2002). “Evidence for trends in heavy rainfall events over the United Kingdom.” Philos. Trans. R. London: Ser. A Math. Phys. Eng. Sci., 360(1796), 1313–1325.
Osborn, T. J., Hulme, M., Jones, P. D., and Basnett, T. A. (2000). “Observed trends in the daily intensity of United Kingdom precipitation.” Int. J. Climatol., 20(4), 347–364.
Sang, Y.-F., Wang, Z., and Liu, C. (2014). “Comparison of the MK test and EMD method for trend identification in hydrological time series.” J. Hydrol., 510, 293–298.
Schuster, A. (1898). “On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena.” Terr. Magn., 3(1), 13–41.
Sivapragasam, C., Liong, S., and Pasha, M. (2001). “Rainfall and runoff forecasting with SSA-SVM approach.” J. Hydroinf., 3(3), 141–152.
Solow, A. R., and Patwardhan, A. (1996). “Extracting a smooth trend from a time series: A modification of singular spectrum analysis.” J. Clim., 9(9), 2163–2166.
Tzagkarakis, G., Papadopouli, M., and Tsakalides, P. (2009). “Trend forecasting based on singular spectrum analysis of traffic workload in a large-scale wireless LAN.” Perform. Eval., 66(3–5), 173–190.
Vautard, R., Yiou, P., and Ghil, M. (1992). “Singular-spectrum analysis: A toolkit for short, noisy chaotic signals.” Physica D, 58(1–4), 95–126.
Vitanov, N. K., Sakai, K., and Dimitrova, Z. I. (2008). “SSA, PCA, TDPSC, ACFA: Useful combination of methods for analysis of short and nonstationary time series.” Chaos, Solitons Fractals, 37(1), 187–202.
Wigley, T. M. L., and Jones, P. D. (1987). “England and Wales precipitation: A discussion of recent changes in variability and an update to 1985.” J. Climatol., 7(3), 231–246.
Wigley, T. M. L., Lough, J. M., and Jones, P. D. (1984). “Spatial patterns of precipitation in England and Wales and a revised homogeneous England and Wales precipitation series.” J. Climatol., 4(1), 1–25.
Wu, C. L., and Chau, K. W. (2011). “Rainfall-runoff modeling using artificial neural network coupled with singular spectrum analysis.” J. Hydrol., 399(3–4), 394–409.
Yue, S., and Pilon, P. (2004). “A comparison of the power of the T test, Mann-Kendall and bootstrap tests for trend detection.” Hydrol. Sci. J., 49(1), 21–37.
Yue, S., and Wang, C. Y. (2002). “Applicability of prewhitening to eliminate the influence of serial correlation on the Mann-Kendall test.” Water Resour. Res., 38(6), 4-1–4-7.
Zhang, Q., Wang, B.-D., He, B., Peng, Y., and Ren, M. (2011). “Singular spectrum analysis and ARIMA hybrid model for annual runoff forecasting.” Water Resour. Manage., 25(11), 2683–2703.
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Journal of Hydrologic Engineering
Volume 20 • Issue 12 • December 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jul 28, 2014
Accepted: Mar 24, 2015
Published online: May 8, 2015
Discussion open until: Oct 8, 2015
Published in print: Dec 1, 2015
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