Skip to main content

Advertisement

Log in

Hydrological drought dynamics and its teleconnections with large-scale climate indices in the Xijiang River basin, South China

  • Original Paper
  • Published:
Theoretical and Applied Climatology Aims and scope Submit manuscript

Abstract

Hydrological drought is a highly complex and extreme natural disaster, which has increased in deficit, areal extent, and frequency with the penetration of climate change impact. For better anticipating hydrological droughts, it is crucial to evaluate hydrological drought and its teleconnections with large-scale climate indices (LSCI) effectively. This study estimated the dynamics and patterns of hydrological drought in the near-real river networks by virtue of the standardized runoff index (SRI) based on VIC and large-scale routing model in the Xijiang River basin, and revealed their teleconnections with the climate indices. Results show that model simulation can reasonably reveal the hydrological drought evolutions in near-real river networks and effectively expose the drought downward spread along main channels. The drought spread distances in Hongshuihe and Yujiang Rivers are farther under the comprehensive influence of climate, topography, and watershed shape. Hydrological drought evolutions in the upper reaches are mainly manifested as three patterns, including S12 (simultaneous significant changes in drought intensity, concentration degree, and frequency), S7(simultaneous significant changes in drought intensity and frequency), and S1(single significant change in drought intensity). These drought dynamic patterns are majority affected by climate variation patterns M1 (warm and cold AMO), M3 (cold PDO), and M7 (warm AMO/AO). For decision-makers, this work is beneficial for understanding and anticipating hydrological droughts in the river networks, and further selecting management strategies for water resources.

Highlights

  • The quantitative results of model simulation are reliable for drought evaluation.

  • Drought concentration period delays and drought risk increases significantly.

  • Dynamic evolutions of drought mainly manifest as three combinations patterns.

  • Upstream drought is mainly affected by AMO, PDO, and AMO/AO.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

The raw datasets used for model establishment are open source. The meteorological data are available on the Internet at http://data.cma.cn/. The global 10-km soil profile dataset and global 1-km land cover classification dataset can refer to Reynolds et al (2000) and Hansen et al (2000), respectively. However, the model output dataset cannot be shared at this time as the data also forms part of an ongoing study.

References

Download references

Acknowledgements

The authors sincerely acknowledge the insightful comments and corrections of editors and reviewers. Meanwhile, the technical guidance of consultant Dr. Seyed Hamidreza Sadeghi is highly acknowledged.

Funding

This work was jointly supported by the National Natural Science Foundation of China (Grant number 52009065), the Natural Science Foundation of Hubei province, China (Grant number 2020CFB293), and the NSFC-MWR-CTGC Joint Yangtze River Water Science Research Project (Grant number U2240225).

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the study conception and design. Qingxia Lin performed the data analysis and drafted the paper; Zhiyong Wu designed the study and improved the manuscript; Jingjing Liu committed to data acquisition; Vijay P. Singh improved the manuscript revision; Zheng Zuo edited the writing.

Corresponding author

Correspondence to Zhiyong Wu.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix

1.1 Drought concentration degree (DCD) and Drought concentration period (DCP)

Referring to the concepts of precipitation concentration degree and concentration period, the calculation formula of drought concentration degree, and concentration period is as follows:

$${C}_{i}=\frac{\sqrt{{S}_{xi}^{2}+{S}_{yi}^{2}}}{{S}_{i}}$$
(1)
$${P}_{i}=\mathrm{arctan}\left(\frac{{S}_{xi}}{{S}_{yi}}\right)$$
(2)
$${S}_{xi}={\sum }_{j=1}^{N}{s}_{ij}\times \mathrm{sin}{\theta }_{j}$$
(3)
$${S}_{yi}={\sum }_{j=1}^{N}{s}_{ij}\times \mathrm{cos}{\theta }_{j}$$
(4)

where i is the year, j is the month. \({C}_{i}\) and \({P}_{i}\) are the concentration degree (DCD) and concentration period (DCP) of hydrological drought in the year, respectively. \({S}_{i}\) is the drought severity of year i, and \({s}_{ij}\) is the drought severity of month j in the specified year i. The \({s}_{xi}\) and \({s}_{yi}\) represent the horizontal and vertical components of the vector \({s}_{ij}\). The \({\theta }_{j}\) is the representative degree of each month (Fig. 9), e.g., the \({\theta }_{j}\) of January and February are 0° and 30°. After vector calculation, the \({P}_{i}\) has different values. When the \({P}_{i}\) falls between \(15^\circ \sim 45^\circ\), it means that drought concentrates in February, and the angle range of other months can be analogized in turn.

Fig. 9
figure 9

The representative degree \({\theta }_{j}\) of each month

Moving t-test method

The criterion of the moving t-test is whether the significant difference exists in sequence means. If the time series \(x\) has \(n\) variables, a certain time can be arbitrarily set as the test cut-off point, and the sequence sizes of sub-sequence \({x}_{1}\) and \({x}_{2}\) before and after the cut-off point are \({n}_{1}\) and\({n}_{2}\), the mean values are \(\overline{{x }_{1}}\) and \(\overline{{x }_{2}}\), and the variances are \({s}_{1}^{2}\) and\({s}_{2}^{2}\), respectively.

$$t=\frac{\overline{{x}_{1}}-\overline{{x}_{2}}}{s\sqrt{\frac{1}{{n}_{1}}+\frac{1}{{n}_{2}}}}$$
(5)
$$s=\sqrt{\frac{{n}_{1}{s}_{1}^{2}+{n}_{2}{s}_{2}^{2}}{{n}_{1}+{n}_{2}-2}}$$
(6)

The sliding method is used to set the cut-off points and the responding statics \({t}_{i}\) are calculated. The critical value \({t}_{\alpha }\) can be obtained with a given significance level. If \(\left|{t}_{i}\right|>{t}_{\alpha }\) occurs show mutations exist in the sequence.

Cramer method

The difference between the Cramer method and the moving t-test is that t-test uses the mean difference of sub-sequence as the criterion, while the Cramer rule uses the mean difference of sub-sequence and total sequence as the criterion. If \(\overline{x }\) and \(\overline{{x }_{i}}\) are the mean values of the total sequence \(x\) and its sub-sequence \({x}_{i}\), and \(s\) is the variance of the total sequence, the statistics \(t\) are:

$$t=\sqrt{\frac{{n}_{1}\left(n-2\right)}{n-{n}_{1}\left(1+{\tau }^{2}\right)}}\tau$$
(7)
$$\tau =\frac{\overline{{x}_{i}}-\overline{x}}{s}$$
(8)

where n and \({n}_{1}\) represent the sequence length and the sub-sequence sequence length. The sequence of statistics \({t}_{i}\) (\(i\)=1, 2, …, \({n-n}_{1}+1\)) can be obtained by sliding after determining \({n}_{1}\). Similar to the moving t-test, if \(\left|{t}_{i}\right|>{t}_{\alpha }\) occurs show mutations exist in the sequence.

Yamamoto method

Yamamoto method determines whether mutations exist by testing whether the difference between the sequence means is significant. The SNR is defined as follows:

$$\mathrm{SNR}=\frac{\left|\overline{{x}_{1}}-\overline{{x}_{2}}\right|}{{s}_{1}+{s}_{2}}$$
(9)

In the formula, \(\overline{{x }_{1}}\) and \(\overline{{x }_{2}}\) are the mean values of the two sub-sequences \({x}_{1}\) and \({x}_{2}\), and \({s}_{1}\) and \({s}_{2}\) are the standard deviations, respectively. Mutation and strong mutation exist when SNR is greater than 1 and 2, respectively.

Lepage method

The Lepage method is a two-sample nonparametric test whose statistics consist of the sum of standard Wilcoxon and Ansarity-Bradley tests. The \({n}_{1}\) and \({n}_{2}\) are assumed to be the variables of sub-sequence in the left and right of the reference point, and the total sample size is \(n\). The rank statistics are as follows:

$$W={\sum }_{i=1}^{n}i{U}_{i}$$
(10)

In the formula, the \({U}_{i}\) equals to 1 and 0 when the minimum value is before and after the reference point, respectively. The \(W\) is the cumulative number of two sub-sequences, its mean and variance are as follow:

$$E\left(W\right)=\frac{1}{2}{n}_{1}\left({n}_{1}+{n}_{2}+1\right)$$
(11)
$$V\left(W\right)=\frac{1}{12}{n}_{1}{n}_{2}\left({n}_{1}+{n}_{2}+1\right)$$
(12)

Herein construct another rank statistic is as follows:

$$A={\sum }_{i=1}^{{n}_{1}}i{U}_{i}+{\sum }_{i={n}_{1}+1}^{n}\left(n-i+1\right){U}_{i}$$
(13)

When \(n\) is an even number, the mean and variance of \(A\) are as follow:

$$E\left(A\right)=\frac{1}{4}{n}_{1}\left({n}_{1}+{n}_{2}+2\right)$$
(14)
$$V\left(A\right)=\frac{{n}_{1}{n}_{2}\left({n}_{1}+{n}_{2}-2\right)\left({n}_{1}+{n}_{2}+2\right)}{48\times \left({n}_{1}+{n}_{2}-1\right)}$$
(15)

When \(n\) is an odd number, the mean and variance values of \(A\) are as follow:

$$E\left(A\right)=\frac{{n}_{1}{\left({n}_{1}+{n}_{2}+1\right)}^{2}}{4\left({n}_{1}+{n}_{2}\right)}$$
(16)
$$V\left(A\right)=\frac{{n}_{1}{n}_{2}\left({n}_{1}+{n}_{2}+1\right)\left({\left({n}_{1}+{n}_{2}\right)}^{2}+3\right)}{48\times {\left({n}_{1}+{n}_{2}\right)}^{2}}$$
(17)

At this point, the joint statistic \(HK\) can be constructed as follows:

$$HK=\frac{{\left(W-E\left(W\right)\right)}^{2}}{V\left(W\right)}+\frac{{\left(A-E\left(A\right)\right)}^{2}}{V\left(A\right)}$$
(18)

When \({HK}_{i}\) exceeds the critical value, it indicates that there is a significant difference between the samples before and after time i and the mutation occurred.

5.1 Mann–Kendall test method

As a common nonparametric statistical test method, the Mann–Kendall test has the advantage that it does not require the test samples to follow a specific distribution and is not disturbed by a few outliers. Suppose there is a climate series \({x}_{1}, {x}_{2}, {x}_{N}, {m}_{i}\) represents the cumulative number of \({x}_{i}>j (1\le j\le i)\) and defines the statistic:

$${d}_{k}={\sum }_{i=1}^{k}{m}_{i}$$
(19)

Under the assumption of time series is random and independence, the mean and variance of \({d}_{k}\) are as follow:

$$E\left({d}_{k}\right)=\frac{k\left(k-1\right)}{4}$$
(20)
$$\mathit{var}\left({d}_{k}\right)=\frac{k\left(k-1\right)\left(2k+5\right)}{72}\hspace{0.33em}\left(2\le k\le N\right)$$
(21)

Standardize the \({d}_{k}\) to the following:

$$u\left({d}_{k}\right)=\frac{\left({d}_{k}-E\left({d}_{k}\right)\right)}{\sqrt{\mathit{var}\left({d}_{k}\right)}}$$
(22)

When \(\left|u\right|>{u}_{\alpha }\), it shows that there is an obvious change trend in the sequence with the given significance level \(\mathrm{\alpha }\). Reference this method to the inverse sequence to get \(\overline{u }({d}_{i})\), if the intersection of \(u\left({d}_{k}\right)\) and \(\overline{u }({d}_{i})\) curve is between the reliability lines, then it is the mutation point.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, Q., Wu, Z., Liu, J. et al. Hydrological drought dynamics and its teleconnections with large-scale climate indices in the Xijiang River basin, South China. Theor Appl Climatol 150, 229–249 (2022). https://doi.org/10.1007/s00704-022-04153-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00704-022-04153-x

Keywords

Navigation