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A new method for detecting abrupt changes in the dependence among multivariate hydrological series based on moving cut total correlation

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Abstract

Knowledge of how to define and estimate the dependence among multivariate hydrological series is essential for detecting abrupt changes in the dependence. In this paper, a new method (BMCTC) is proposed to detect all possible abrupt change points in the dependence among multivariate hydrological series. The total correlation estimated by the matrix-based Renyi's alpha-order entropy functional is firstly introduced to define and measure the dependence strength among multivariate hydrological series. Then, the moving cut total correlation (MCTC) sequence is built by the moving window technique, which is used to measure changes in the dependence strength among multivariate hydrological series. Finally, the Bernaola-Galvan algorithm is used to detect all change points of the MCTC sequence. Simulations are performed to compare the effectiveness of BMCTC with Pearson correlation (BMCPC) and Spearman correlation (BMCSC), Cramer-von Mises (CvM) and copula-based likelihood-ratio (CLR). The results show that all change points are detected by BMCTC regardless of the samples size, but wrong change points or no change points are detected by other methods in most cases. BMCTC is applied to detect change points in the dependence among annual runoff, precipitation and sediment discharge series in the Xiliugou and the Kuyehe River, China. It is found that the dependence among runoff, precipitation and sediment discharge changed abruptly in 1980 and 1996 in the Kuyehe River and in 1999 in the Xiliugou River. These changes are mainly caused by human activities such as construction of water conservancy projects and coal mining.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The study was supported by National Natural Science Foundation of China (Grant Nos. 52279005 and 51609254), the Belt and Road Special Foundation of the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (Grant No. 2020nkms03), and NUPTSF (Grant Nos. NY219161 and NY220035).

Author information

Authors and Affiliations

  1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Longxia Qian & Nanjun Liu

  2. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, 210098, China

    Guangqiu Jin

  3. Environmental Science Division, Argonne National Laboratory, Lemont, IL, 60439, USA

    Cheng Wang

  4. Water Resources and Reservoir Dispatching Center of Shanxi Province, Xian, 710004, China

    Jianhong Yang

  5. College of Water Sciences, Beijing Normal University, Beijing, 100875, China

    Hongrui Wang

Authors
  1. Longxia Qian
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  2. Guangqiu Jin
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  3. Cheng Wang
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  4. Nanjun Liu
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  5. Jianhong Yang
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  6. Hongrui Wang
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Contributions

LQ: Writing-original draft, Modelling, Methodology, Conceptualization. GJ: Writing-review & editing, Supervision. CW: Funding acquisition, Investigation. NL: Writing-review & editing, Software, Methodology. JY: Writing-review & editing, Validation. HW: Writing-review & editing, Data curation, Methodology.

Corresponding author

Correspondence to Guangqiu Jin.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Appendix

Appendix

See Figs. 14, 15, 16, 17, 18, 19 and Tables 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.

Fig. 14
figure 14

Comparison of MCTC, MCPC and MCSC sequences with a size of 50: a Gumbel copula; b Clayton copula; c Frank copula; d Different copulas

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Fig. 15
figure 15

Comparison of MCTC, MCPC and MCSC sequences with a size of 150: a Gumbel copula; b Clayton copula; c Frank copula; d Different copulas

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Fig. 16
figure 16

Comparison of MCTC, MCPC and MCSC sequences with a size of 300: a Gumbel copula; b Clayton copula; c Frank copula; d Different copulas

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Fig. 17
figure 17

Comparison of MCTC, MCPC and MCSC sequences with a size of 500: a Gumbel copula; b Clayton copula; c Frank copula; d Different copulas

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Fig. 18
figure 18

Comparison of MCTC, MCPC and MCSC sequences with different sample sizes when each segment obeys bivariate t distribution: a 50; b 90; c 150; d 250; e 300; f 500

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Fig. 19
figure 19

Comparison of MCTC, MCPC and MCSC sequences with different sample sizes when each segment obeys Wishart distribution: a 50; b 90; c 150; d 250; e 300; f 500

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Table 5 Comparison of BMCTC for detection of change points and confidence probability with other methods at a sample size of 50
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Table 6 Comparison of BMCTC for detection of change points and confidence probability with other methods at a sample size of 150
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Table 7 Comparison of BMCTC for detection of change points and confidence probability with other methods at a sample size of 300
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Table 8 Comparison of BMCTC for detection of change points and confidence probability with other methods at a sample size of 500
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Table 9 Comparison of BMCTC for detection of change points and confidence probability with other methods in the case of different sample size when each segment obeys bivariate normal distribution
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Table 10 Comparison of BMCTC for detection of change points and confidence probability with other methods in the case of different sample size when each segment obeys bivariate t distribution
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Table 11 Comparison of BMCTC for detection of change points and confidence probability with other methods in the case of different sample size when each segment obeys Wishart distribution
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Table 12 Comparison of the detection of abrupt change points when each segment obeys Clayton copula
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Table 13 Comparison of the detection of abrupt change points when each segment obeys Frank copula
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Table 14 Comparison of the detection of abrupt change points when each segment obeys different copulas
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Table 15 Comparison of the detected change points at different values of \(\alpha\) when each segment obeys Clayton copula
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Table 16 Comparison of the detected change points at different values of \(\alpha\) when each segment obeys Frank copula
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Table 17 Comparison of the detected change points at different values of \(\alpha\) when each segment obeys different copulas
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Qian, L., Jin, G., Wang, C. et al. A new method for detecting abrupt changes in the dependence among multivariate hydrological series based on moving cut total correlation. Stoch Environ Res Risk Assess 38, 467–488 (2024). https://doi.org/10.1007/s00477-023-02580-4

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