Abstract
The main aim of this study is to perform a time series frequency analysis and assessment for stream flow over the Johor River using a comparative method between wavelet transform (WT) and Fourier transform (FT). One of the wavelet analyses used was the discrete wavelet transform (DWT), which revealed the periodic wavelet components responsible for the trend detection. Using the FT, the periodicities that governed the trend can be obtained; however, in terms of the time domain analysis, FT seems to be lacking compared to the WT. The conditions for using DWT are discussed, and the selection decisions for such discretization are considered. Besides, using the global wavelet spectrum (GWS) and the continuous wavelet transform (CWT), the dominant periodicity components can be further well described in time frequency characteristic. In addition, the integration of the WT and Mann–Kendall (MK) test allows the determination of possible trends present in the stream flow dataset series. It is shown that the wavelet analysis is more suitable than the Fourier analysis as it exhibits good extraction of the time and frequency characteristics, especially for a nonstationary data series.
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References
Ahmad I, Tang D, Wang T, Wang M, Wagan B (2015) Precipitation trends over time using Mann-Kendall and spearman’s rho tests in swat river basin, Pakistan. Advances in Meteorology, 2015
Amin M, Shaaban A, Ercan A, Ishida K, Kavvas M, Chen Z, Jang S (2017) Future climate change impact assessment of watershed scale hydrologic processes in Peninsular Malaysia by a regional climate model coupled with a physically-based hydrology modelo. Sci Total Environ 575:12–22
Aminikhanghahi S, Cook DJ (2017) A survey of methods for time series change point detection. Knowl Inf Syst 51(2):339–367
Bae D-H, Koike T, Awan JA, Lee M-H, Sohn K-H (2015) Climate change impact assessment on water resources and susceptible zones identification in the Asian monsoon region. Water Resour Manag 29(14):5377–5393
Bayazit M (2015) Nonstationarity of hydrological records and recent trends in trend analysis: a state-of-the-art review. Environmental Processes 2(3):527–542
de Artigas MZ, Elias AG, de Campra PF (2006) Discrete wavelet analysis to assess long-term trends in geomagnetic activity. Physics and Chemistry of the Earth, Parts A/B/C 31(1-3):77–80
Delgado JM, Apel H, Merz B (2010) Flood trends and variability in the Mekong river. Hydrol Earth Syst Sci 14(3):407–418
Fathian F, Morid S, Kahya E (2015) Identification of trends in hydrological and climatic variables in Urmia Lake basin, Iran. Theor Appl Climatol 119(3-4):443–464
GenerPianosi F, Wagener T (2016) Understanding the time-varying importance of different uncertainty sources in hydrological modelling using global sensitivity analysis. Hydrol Process 30(22):3991–4003
Kendall M (1975) Rank Correlation Methods, Charles Griffin, London. Google Scholar
Kundzewicz ZW, Graczyk D, Maurer T, Pińskwar I, Radziejewski M, Svensson C, Szwed M (2005) Trend detection in river flow series: 1. Annual maximum flow/Détection de tendance dans des séries de débit fluvial: 1. Débit maximum annuel. Hydrol Sci J 50(5)
Lehmann E (1975) Nonparametrics: statistical methods based on ranks Holden-Day. Inc., San Francisco
Machiwal D, Jha MK (2009) Time series analysis of hydrologic data for water resources planning and management: a review. Journal of Hydrology and Hydromechanics 54(3):237–257
Mehala N, Dahiya R (2008) A comparative study of FFT, STFT and wavelet techniques for induction machine fault diagnostic analysis. Paper presented at the Proceedings of the 7th WSEAS international conference on computational intelligence, man-machine systems and cybernetics, Cairo
Mondal A, Kundu S, Mukhopadhyay A (2012) 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 2(1):70–78
Morán-Tejeda E, Ceballos-Barbancho A, Llorente-Pinto JM (2010) Hydrological response of Mediterranean headwaters to climate oscillations and land-cover changes: The mountains of Duero River basin (Central Spain). Glob Planet Chang 72(1-2):39–49
Nalley D, Adamowski J, Khalil B (2012) Using discrete wavelet transforms to analyze trends in streamflow and precipitation in Quebec and Ontario (1954–2008). J Hydrol 475:204–228
Nason GP (2006) Stationary and non-stationary time series. Statistics in Volcanology. Special Publications of IAVCEI, vol 1, pp 000–000
Pohlert T (2016). Non-parametric trend tests and change-point detection. CC BY-ND, 4
Sethi R, Pandey BK, Krishan R, Khare D, Nayak P (2015) Performance evaluation and hydrological trend detection of a reservoir under climate change condition. Modeling Earth Systems and Environment 1(4):33
Shadmani M, Marofi S, Roknian M (2012) Trend analysis in reference evapotranspiration using Mann-Kendall and Spearman’s Rho tests in arid regions of Iran. Water Resour Manag 26(1):211–224
Sneyers R, Vandiepenbeeck M, Vanilierde R, Demarée G (1990) Climatic changes in Belgium as appearing from the homogenized series of observations made in Brussels–Uccle (1933-1988) In: SCHIETECAT, GD. Contributions à l’etude des changements de climat. Bruxelles: Institut Royal Meteorologique de Belgique, Publications Série 124:17–20
Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79(1):61–78
Wong C, Venneker R, Uhlenbrook S, Jamil A, Zhou Y (2009) Variability of rainfall in Peninsular Malaysia. Hydrol Earth Syst Sci Discuss 6(4):5471–5503
Wu J, Wei S (1989) Time series analysis. Hunan Science and Technology Press, ChangSha
Yue S, Pilon P, Cavadias G (2002) Power of the Mann–Kendall and Spearman's rho tests for detecting monotonic trends in hydrological series. J Hydrol 259(1-4):254–271
Yue S, Wang C (2004) The Mann-Kendall test modified by effective sample size to detect trend in serially correlated hydrological series. Water Resour Manag 18(3):201–218
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The authors would like to appreciate so much the financial support received from the University of Malaya Research Grant (UMRG) coded RP025A-18SUS University of Malaya, Malaysia.
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Chong, K.L., Lai, S.H. & El-Shafie, A. Wavelet Transform Based Method for River Stream Flow Time Series Frequency Analysis and Assessment in Tropical Environment. Water Resour Manage 33, 2015–2032 (2019). https://doi.org/10.1007/s11269-019-02226-7
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DOI: https://doi.org/10.1007/s11269-019-02226-7