Discrete wavelet-based trend identification in hydrologic time series
Trend identification is a substantial issue in hydrologic series analysis, but it is also a difficult task in practice due to the confusing concept of trend and disadvantages of methods. In this article, an improved definition of trend was given as follows: ‘a trend is the deterministic component in...
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| Published in | Hydrological processes Vol. 27; no. 14; pp. 2021 - 2031 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Blackwell Publishing Ltd
01.07.2013
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| Abstract | Trend identification is a substantial issue in hydrologic series analysis, but it is also a difficult task in practice due to the confusing concept of trend and disadvantages of methods. In this article, an improved definition of trend was given as follows: ‘a trend is the deterministic component in the analysed data and corresponds to the biggest temporal scale on the condition of giving the concerned temporal scale’. It emphasizes the intrinsic and deterministic properties of trend, can clearly distinguish trend from periodicities and points out the prerequisite of the concerned temporal scale only by giving which the trend has its specific meaning. Correspondingly, the discrete wavelet‐based method for trend identification was improved. Differing from those methods used presently, the improved method is to identify trend by comparing the energy difference between hydrologic data and noise, and it can simultaneously separate periodicities and noise. Furthermore, the improved method can quantitatively estimate the statistical significance of the identified trend by using proper confidence interval. Analyses of both synthetic and observed series indicated the identical power of the improved method as the Mann–Kendall test in assessing the statistical significance of the trend in hydrologic data, and by using the former, the identified trend can adaptively reflect the nonlinear and nonstationary variability of hydrologic data. Besides, the results also showed the influences of three key factors (wavelet choice, decomposition level choice and noise content) on discrete wavelet‐based trend identification; hence, they should be carefully considered in practice. Copyright © 2012 John Wiley & Sons, Ltd. |
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| AbstractList | Trend identification is a substantial issue in hydrologic series analysis, but it is also a difficult task in practice due to the confusing concept of trend and disadvantages of methods. In this article, an improved definition of trend was given as follows: ‘a trend is the deterministic component in the analysed data and corresponds to the biggest temporal scale on the condition of giving the concerned temporal scale’. It emphasizes the intrinsic and deterministic properties of trend, can clearly distinguish trend from periodicities and points out the prerequisite of the concerned temporal scale only by giving which the trend has its specific meaning. Correspondingly, the discrete wavelet‐based method for trend identification was improved. Differing from those methods used presently, the improved method is to identify trend by comparing the energy difference between hydrologic data and noise, and it can simultaneously separate periodicities and noise. Furthermore, the improved method can quantitatively estimate the statistical significance of the identified trend by using proper confidence interval. Analyses of both synthetic and observed series indicated the identical power of the improved method as the Mann–Kendall test in assessing the statistical significance of the trend in hydrologic data, and by using the former, the identified trend can adaptively reflect the nonlinear and nonstationary variability of hydrologic data. Besides, the results also showed the influences of three key factors (wavelet choice, decomposition level choice and noise content) on discrete wavelet‐based trend identification; hence, they should be carefully considered in practice. Copyright © 2012 John Wiley & Sons, Ltd. |
| Author | Wang, Zhonggen Liu, Changming Sang, Yan-Fang |
| Author_xml | – sequence: 1 givenname: Yan-Fang surname: Sang fullname: Sang, Yan-Fang email: Correspondence to: Yan-Fang Sang, Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China. , (Yan-Fang Sang); (Zhonggen Wang), sangyf@igsnrr.ac.cnsunsangyf@gmail.comwangzg@igsnrr.ac.cn organization: Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, 100101, Beijing, China – sequence: 2 givenname: Zhonggen surname: Wang fullname: Wang, Zhonggen organization: Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, 100101, Beijing, China – sequence: 3 givenname: Changming surname: Liu fullname: Liu, Changming organization: Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, 100101, Beijing, China |
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| References_xml | – reference: Sang YF, Wang D, Wu JC. 2010. Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising. Entropy 12: 1499-1513. – reference: Kahya E, Kalayci S. 2004. Trend analysis of streamflow in Turkey. Journal of Hydrology 289: 128-144. – reference: Shao QX, Li M. 2011. A new trend analysis for seasonal time series with consideration of data dependence. Journal of Hydrology 396: 104-112. – reference: Macdonald RW, Harner T, Fyfe J. 2005. Recent climate change in the Arctic and its impact on contaminant pathways and interpretation of temporal trend data. Science of the Total Environment 342: 5-86. – reference: Adam JC, Lettenmaier DP. 2008. Application of new precipitation and reconstructed streamflow products to streamflow trend attribution in northern Eurasia. Journal of Climate 21: 1807-1828. – reference: Mann H. 1945. Non-parametric tests against trend. Econometrica 13: 245-259. – reference: Schreiber T. 1993. Extremely simple nonlinear noise-reduction method. Physics Review E47: 2401-2404. – reference: Hamed KH. 2009. Enhancing the effectiveness of prewhitening in trend analysis of hydrologic data. Journal of Hydrology 368: 143-155. – reference: Torrence C, Compo GP. 1998. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 79: 61-78. – reference: Yevjevich V. 1987. Stochastic models in hydrology. Stochastic Hydrology and Hydraulics 1: 17-36. – reference: Jung HY, Choi Y, Oh JH, Lim GH. 2002. Recent trends in temperature and precipitation over South Korea. International Journal of Climatology 22: 1327-1337. – reference: Adamowski K, Prokoph A, Adamowski J. 2009. Development of a new method of wavelet aided trend detection and estimation. Hydrological Processes 23: 2686-2696. – reference: Kundzewicz ZW, Graczyk D, Maurer T, Pinskwar I, Radziejewski M, Svensson C, Szwed M. 2005. Trend detection in river flow series: 1. Annual maximum flow. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques 50: 797-810. – reference: Flandrin P, Goncalves P, Rilling G. 2005. In Hilbert-Huang Transform: Introduction and Applications, Huang NE, Shen SS-P (eds). World Scientific: Teaneck, NJ; 57-74. – reference: Yevjevich V. 1972. Stochastic Process in Hydrology. Water Resources Publications: Colorado, USA. – reference: Percival DB, Walden AT. 2000. Wavelet Methods for Time Series Analysis. Cambridge University Press: Cambridge, UK. – reference: Hamed KH. 2008. Trend detection in hydrologic data: The Mann-Kendall trend test under the scaling hypothesis. Journal of Hydrology 349: 350-363. – reference: Rivard C, Vigneault H. 2009. Trend detection in hydrological series: when series are negatively correlated. Hydrological Processes 23: 2737-2743. – reference: Sang YF, Wang D, Wu JC, Zhu QP, Wang L. 2009b. The relation between periods' identification and noises in hydrologic series data. Journal of Hydrology 368: 165-177. – reference: Partal T, Kucuk M. 2006. Long term trend analysis using discrete wavelet components of annual precipitation measurements in Marmara region (Turkey). Physics and Chemistry of the Earth 31: 1189-1200. – reference: Kendall M. 1975. Rank Correlation Methods. Charles Griffin: London. – reference: Pisoft P, Kalvova J, Brazdil R. 2004. Cycles and trends in the Czech temperatures series using wavelet transform. International Journal of Climatology 24: 1661-1670. – reference: Craigmile PF, Guttorp P, Percival DB. 2004. Trend assessment in a long memory dependence model using the discrete wavelet transform. Environmentrics 15: 313-335. – reference: Donoho DH. 1995. De-noising by soft-thresholding. IEEE Transactions on Information Theory 41: 613-617. – reference: Khaliq MN, Ouarda TBMJ, Gachon P, Sushama L, St-Hilaire A. 2009. Identification of hydrological trends in the presence of serial and cross correlations: A review of selected methods and their application to annual flow regimes of Canadian rivers. Journal of Hydrology 368: 117-130. – reference: Taleb EH, Druyan LM. 2003. Relationship between rainfall and West African wave disturbances in station observation. International Journal of Climatology 23: 305-313. – reference: Kuczera G. 1992. Uncorrelated measurement error in flood frequency inference. Water Resources Research 28: 183-188. – reference: Sang YF, Wang D, Wu JC. 2011. Comparison of the Wavelet Characters of Various Noises by Discrete Wavelet Transform. Hydrological Cycle and Water Resources Sustainability in Changing Environments. IAHS Publication 350: 622-626. – reference: Xu ZX, Li JY, Liu CM. 2007. Long-term trend analysis for major climate variables in the Yellow River basin. Hydrological Processes 21: 1935-1948. – reference: Almasri A, Locking H, Shukar G. 2008. 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