Abstract
Correlation associations have been detected using Pearson’s r which aims to analyze linear correlation between two variables. It should be noted here that associations between hydro-meteorological variables are usually nonlinear. In this sense, the classical correlation analysis method cannot truly reflect the inherent associations between variables characterized by nonlinear associations. In this case, a new algorithm has been proposed by using the ideas of local correlation, detrended cross-correlation analysis and multifractals, and this novel algorithm is called as the general detrended correlation analysis. The newly-proposed algorithm was evaluated for the validity with numerically-generated time series and the real world hydrological series. The results indicate that the newly-proposed algorithm can well reflect the nonlinear and non stationary associations between two hydrological series when compared to the classical relation detection method such as the Pearson correlation analysis method, and it is particularly the case under the condition that hydrological abrupt changes of the hydrological processes occur where the classical association analysis is not appropriate.
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Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (Grant No.: 11201396), Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.: 20124301120004), The Leading Expert Program in Anhui Province and is fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK441313). The authors would like to thank Prof. Dr. George Christakos, the editor in chief, and three anonymous referees for the comments which are greatly helpful to improve this manuscript.
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Zhou, Y., Zhang, Q., Singh, V.P. et al. General correlation analysis: a new algorithm and application. Stoch Environ Res Risk Assess 29, 665–677 (2015). https://doi.org/10.1007/s00477-014-0970-8
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DOI: https://doi.org/10.1007/s00477-014-0970-8