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.
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
Abdelkader M, Yerdelen C (2022) Hydrological drought variability and its teleconnections with climate indices. J Hydrol 605:127290. https://doi.org/10.1016/j.jhydrol.2021.127290
Aghelpour P, Bahrami-Pichaghchi H, Varshavian V (2021) Hydrological drought forecasting using multi-scalar streamflow drought index, stochastic models and machine learning approaches, in northern Iran. Stochastic Environ Res Risk Assess 35(8):1615–1635. https://doi.org/10.1007/s00477-020-01949-z
Ahmed K, Shahid S, Chung ES, Wang XJ, Harun SB (2019) Climate change uncertainties in seasonal drought severity-area-frequency curves: case of arid region of Pakistan. J Hydrol 570:473–485. https://doi.org/10.1016/j.jhydrol.2019.01.019
Altn TB, Sar F, Altn BN (2020) Determination of drought intensity in Seyhan and Ceyhan River basins, Turkey, by hydrological drought analysis. Theor Appl Climatol 139(1–2):95–107. https://doi.org/10.1007/s00704-019-02957-y
Boone AA, Habets F, Noilhan J, Clark D, Yang ZL (2004) The rhône-aggregation land surface scheme intercomparison project: an overview. J Clim 17(1):187–208. https://doi.org/10.1175/1520-0442(2004)017%3c0187:TRLSSI%3e2.0.CO;2
Chatterjee S, Khan A, Akbari H, Wang Y (2016) Monotonic trends in spatio-temporal distribution and concentration of monsoon precipitation (1901–2002) West Bengal. India.Atmos Res 182(12):54–75. https://doi.org/10.1016/j.atmosres.2016.07.010
Chen X, Li FW, Li JZ, Feng P (2019) Three-dimensional identification of hydrological drought and multivariate drought risk probability assessment in the Luanhe River basin, China. Theor Appl Climatol 137:3055–3076. https://doi.org/10.1007/s00704-019-02780-5
Diaz V, Corzo G, Lanen HV, Solomatine DP, Varouchakis EA (2019) Characterization of the dynamics of past droughts. Sci Total Environ 718:134588. https://doi.org/10.1016/j.scitotenv.2019.134588
Dikshit A, Pradhan B, Alamri AM (2021) Long lead time drought forecasting using lagged climate variables and a stacked long short-term memory model. Sci Total Environ 755(2):142638. https://doi.org/10.1016/j.scitotenv.2020.142638
Ding YH, Li Y, Wang ZY, Si D, Liu YJ (2020) Interdecadal variation of Afro-Asian summer monsoon: coordinated effects of AMO and PDO oceanic modes. Trans Atmos Sci 43(1):20-32 (In Chinese) https://d.wanfangdata.com.cn/periodical/njqxxyxb202001005
Ding YB, Xu JT, Wang XW, Cai HJ, Zhou ZQ, Sun YA, Shi YH (2021) Propagation of meteorological to hydrological drought for different climate regions in China. J Environ Manage 283:111980. https://doi.org/10.1016/j.jenvman.2021.111980
Fischer T, Gemmer M, Su B, Scholten T (2013) Hydrological long-term dry and wet periods in the Xijiang River basin. South China Hydrol Earth Syst Sci 17(1):135–148. https://doi.org/10.5194/hess-17-135-2013
Gu L, Chen J, Yin JB, Xu CY, Chen H (2020) Drought hazard transferability from meteorological to hydrological propagation. J Hydro 585:124761. https://doi.org/10.1016/j.jhydrol.2020.124761
Han ZM, Huang SZ, Huang Q, Leng GY, Liu Y, Bai QJ, He PX, Liang H, Shi WZ (2021) Grace-based high-resolution propagation threshold from meteorological to groundwater drought. Agric for Meteorol 307:108476. https://doi.org/10.1016/j.agrformet.2021.108476
Hansen MC, Defries RS, Townshend J, Sohlberg R (2000) Global land cover classification at 1 km spatial resolution using a classification tree approach. Int J Remote Sens 21(6–7):1331–1364. https://doi.org/10.1080/014311600210209
Henriques A, Santos M (1999) Regional drought distribution model. Phys Chem Earth Part B Hydrol. Oceans Atmos 24:19–22. https://doi.org/10.1016/S1464-1909(98)00005-7
Huang SZ, Huang Q, Chang JX, Leng GY (2016) Linkages between hydrological drought, climate indices and human activities: a case study in the Columbia River basin. Int J Climatol 36(1):280–290. https://doi.org/10.1002/joc.4344
Huang SZ, Li P, Huang Q, Leng GY, Hou BB, Ma L (2017) The propagation from meteorological to hydrological drought and its potential influence factors. J Hydro 547:184–195. https://doi.org/10.1016/j.jhydrol.2017.01.041
Huang Y, Wang H, Xiao WH, Chen LH, Yan DH, Zhou YY, Jiang DC, Yang MZ (2018) Spatial and temporal variability in the precipitation concentration in the upper reaches of the Hongshui River basin, southwestern China. Adv Meteorol 1:1–19. https://doi.org/10.1155/2018/4329757
Kambombe O, Ngongondo C, Eneya L, Monjerezi M, Boyce C (2021) Spatio-temporal analysis of droughts in the Lake Chilwa Basin, Malawi. Theor Appl Climatol 144:1219–1231. https://doi.org/10.1007/s00704-021-03586-0
Katipolu OM, Acar R, Senocak S (2021) Spatio-temporal analysis of meteorological and hydrological droughts in the Euphrates basin. Turkey Water Sci Technol Water Supply 21(4):1657–1673. https://doi.org/10.2166/ws.2021.019
Kumar KS, Anandraj P, Sreelatha K, Sridhar V (2021) Regional analysis of drought severity-duration-frequency and severity-area-frequency curves in the Godavari River basin. India Int J Climatol 41(12):5481–5501. https://doi.org/10.1002/joc.7137
Li SL, Bates GT (2007) Influence of the Atlantic multidecadal oscillation on the winter climate of east China. Adv Atmos Sci 24(1):126–135. https://doi.org/10.1007/s00376-007-0126-6
Li Z, Su YX (2009) The analysis on precipitation variation characteristic in Guangxi from 1961 to 2004. Chin Agric Sci Bull 25(15):268–272 (In Chinese) https://d.wanfangdata.com.cn/periodical/zgnxtb200915059
Li DP, Mu PF, Bai T, Huang Q, Huang SZ, Zhang Y (2020) Meteorological drought characteristics and driving force analysis of Xijiang River Basin based on variable scale SPI. J Xi’an Univ Technol 36(1):41–50 (In Chinese) https://doi.org/10.19322/j.cnki.issn.1006-4710.2020.01.006
Li ZL, Quan XS, Tian QY, Zhang LY (2020b) Copula-based drought severity-area-frequency curve and its uncertainty, a case study of Heihe River basin. China Hydrol Res 51(2):867–881. https://doi.org/10.2166/nh.2020.173
Li JY, Wu CH, Xia CA, Yeh PJF, Hu BX, Huang GR (2021) Assessing the responses of hydrological drought to meteorological drought in the Huai River Basin, China. Theor Appl Climatol 144:1043–1057. https://doi.org/10.1007/s00704-021-03567-3
Li YL, He R, Qin WJ (2010) Influence of climate change on drought disaster in Guangxi. Meteorol environ res. 1(6):62–65 (In Chinese) https://doi.org/10.3969/j.issn.0517-6611.2010.21.098
Liang X, Lettenmaier DP, Wood EF, Burges SJ (1994) A simple hydrologically based model of land surface water and energy fluxes for general circulation models. J Geophys Res Atmos 99(D7):14415–14428. https://doi.org/10.1029/94JD00483
Lin QX, Wu ZY, Singh VP, Sadeghi S, He H, Lu GH (2017) Correlation between hydrological drought, climatic factors, reservoir operation, and vegetation cover in the Xijiang basin, South China. J Hydrol 549:512–524. https://doi.org/10.1016/j.jhydrol.2017.04.020
Lin QX (2018) Analysis of Hydrological drought evolution and its interaction with environment factors in the Xijiang River basin. Dissertation, Hohai University (In Chinese)
Liu Z, Huang Q, Yang YY, Huang SZ (2020) Diagnosis and driving force analysis of variations in precipitation-temperature relation of Xijiang River basin. J Hydroelectric Eng 39(10):57–71 (In Chinese) https://doi.org/10.11660/slfdxb.20201004
Lu GH, Liu JJ, Wu ZY, He H, Xu HT, Lin QX (2015) Development of a large-scale routing model with scale independent by considering the damping effect of sub-basins. Water Resour Manage 29(14):5237–5253. https://doi.org/10.1007/s11269-015-1115-7
Mahmoudi P, Rigi A, Kamak MM (2019) A comparative study of precipitation-based drought indices with the aim of selecting the best index for drought monitoring in Iran. Theor Appl Climatol 147:3123–3138. https://doi.org/10.1007/s00704-019-02778-z
Margariti J, Rangecroft S, Parry S, Wendt DE, Van Loon AF (2019) Anthropogenic activities alter drought termination. Elem Sci Anth 7:27. https://doi.org/10.1525/elementa.365
Melsen LA, Guse B (2019) Hydrological drought simulations: how climate and model structure control parameter sensitivity. Water Resour Res 55(12):10527–10547. https://doi.org/10.1029/2019WR025230
Meng CQ, Zhou JZ, Muhammad T, Shuang Z, Zhang HR (2016) Integrating artificial neural networks into the VIC model for rainfall-runoff modeling. Water 8(9):407. https://doi.org/10.3390/w8090407
Mishra A, Desai V (2005) Spatial and temporal drought analysis in the Kansabati river basin. India Int J River Basin Manag 3:31–41. https://doi.org/10.1080/15715124.2005.9635243
Mishra AK, Singh VP (2009) Analysis of drought severity–area–frequency curves using a general circulation model and pattern uncertainty. J Geophys Res 114:D06120. https://doi.org/10.1029/2008JD010986
Monjo R, Royé D, Martin-Vide J (2020) Meteorological drought lacunarity around the world and its classification. Earth Syst Sci Data 12(1):741–752. https://doi.org/10.5194/essd-12-741-2020
Nahler G (2009) Pearson Correlation Coefficient Springer Vienna. Chapter 1025:132–132. https://doi.org/10.1007/978-3-211-89836-9
Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models: part I-A discussion of principles. J Hydrol 10(3):282–290. https://doi.org/10.1016/0022-1694(70)90255-6
Niu J (2013) Precipitation in the Pearl River basin, South China: scaling, regional evolutions, and influence of large-scale climate anomalies. Stochastic Environ Res Risk Assess 27(5):1253–1268. https://doi.org/10.1007/s00477-012-0661-2
Niu J, Chen J (2014) Terrestrial hydrological responses to precipitation variability in Southwest China with emphasis on drought. Hydrol Sci J 59(2):325–335. https://doi.org/10.1080/02626667.2013.822641
Niu J, Chen J, Sun L (2015) Exploration of drought evolution using numerical simulations over the Xijiang (West River) basin in South China. J Hydrol 526:68–77. https://doi.org/10.1016/j.jhydrol.2014.11.029
Noorisameleh Z, Gough WA, Mirza M (2021) Persistence and spatial–temporal variability of drought severity in Iran. Environ Sci Pollut Res 28:48808–48822. https://doi.org/10.1007/s11356-021-14100-4
Qian CC, Yu JY, Chen G (2014) Decadal summer drought frequency in China: the increasing influence of the Atlantic Multi-decadal Oscillation. Environ Res Lett 9:124004. https://doi.org/10.1088/1748-9326/9/12/124004
Rangecroft S, Van Loon AF, Maureira H, Verbist K, Hannah DM (2019) An observation-based method to quantify the human influence on hydrological drought: upstream downstream comparison. Hydrol Sci J 64:276–287. https://doi.org/10.1080/02626667.2019.1581365
Reynolds CA, Jackson TJ, Rawls WJ (2000) Estimating soil water-holding capacities by linking the Food and Agriculture Organization soil map of the world with global pedon databases and continuous pedotransfer functions. Water Resour Res 36(12):3653–3662. https://doi.org/10.1029/2000WR900130
Rosenbrock HH (1960) An automatic method for finding the greatest or least value of a function. Comput J 3(3):175–184. https://doi.org/10.1093/comjnl/3.3.175
Scheidegger JM, Jackson CR, Muddu S, Tomer SK, Filgueira R (2021) Integration of 2D lateral groundwater flow into the variable infiltration capacity (VIC) model and effects on simulated fluxes for different grid resolutions and aquifer diffusivities. Water 13(5):663. https://doi.org/10.3390/w13050663
Shan CH, Yuan F, Sheng D, Zhou L, Liu YP (2016) A simulation of climate change features under pattern to A1B in West River basin by PRECIS. China Rural Water Hydropower. 84–87 (In Chinese) http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZNSD201612018.htm
Shukla S, Wood AW (2008) Use of a standardized runoff index for characterizing hydrologic drought. Geophys Res Lett 35(2):226–236. https://doi.org/10.1029/2007GL032487
Talaee PH, Tabari H, Ardakani SS (2014) Hydrological drought in the west of Iran and possible association with large-scale atmospheric circulation patterns. Hydrol Processes 28(3):764–773. https://doi.org/10.1002/hyp.9586
Touseef M, Chen LH, Yang KP, Chen YY (2020) Long-term rainfall trends and future projections over Xijiang River Basin, China. Adv Meteorol 2020:1–18. https://doi.org/10.1155/2020/6852148
Vazifehkhah S, Kahya E (2019) Hydrological and agricultural droughts assessment in a semi-arid basin: inspecting the teleconnections of climate indices on a catchment scale. Agric Water Manage 217:413–425. https://doi.org/10.1016/j.agwat.2019.02.034
Veettil AV, Mishra AK (2020) Multiscale hydrological drought analysis: role of climate, catchment and morphological variables and associated thresholds. J Hydrol 582(4):124533. https://doi.org/10.1016/j.jhydrol.2019.124533
Venegas-Cordero N, Birkel C, Giraldo-Osorio JD, Correa-Barahona A, Nauditt A (2021) Can hydrological drought be efficiently predicted by conceptual rainfall-runoff models with global data products? J Nat Resour Dev 11(2):1–18. https://doi.org/10.5027/jnrd.v11i0.02
Wada Y, Van Beek LP, Wanders N, Bierkens MF (2013) Human water consumption intensifies hydrological drought worldwide. Environ Res Lett 8:034036. https://doi.org/10.1088/1748-9326/8/3/034036
Wang YM, Li SL, Luo DH (2009) Seasonal response of Asian monsoonal climate to be the Atlantic Multidecadal Oscillation. J Geophys Res 114:D02112. https://doi.org/10.1029/2008jd010929
Wu ZY, Lin QX, Lu GH, He H, Qu JJ (2015) Analysis of hydrological drought frequency for the Xijiang River Basin in South China using observed streamflow data. Nat Hazards 77(3):1655–1677. https://doi.org/10.1007/s11069-015-1668-z
Wu JF, Chen XH, Yu ZX, Yao HX, Li W, Zhang DJ (2019a) Assessing the impact of human regulations on hydrological drought development and recovery based on a ‘simulated-observed’ comparison of the SWAT model. J Hydrol 577:123990. https://doi.org/10.1016/j.jhydrol.2019.123990
Wu JF, Chen XW, Chang TJ (2019b) Correlations between hydrological drought and climate indices with respect to the impact of a large reservoir. Theor Appl Climatol 139(1):727–739. https://doi.org/10.1007/s00704-019-02991-w
Wu ZY, Lin QX (2016) Analysis on spatial and temporal characteristics of hydrological drought in Xijiang River basin. Water resour. Prot. 32(1): 51–56 (In Chinese) https://doi.org/10.3880/j.issn.1004-6933.2016.01.008
Wu ZY, Liu QT, Liu JJ, Xu ZG (2021) Construction and validation of 10 km grid routing model in China. J China Hydrol 41(3):75–81 (In Chinese) https://doi.org/10.19797/j.cnki.1000-0852.20190369
Xing Z, Ma M, Su Z, Lv J, Song W (2020) A review of the adaptability of hydrological models for drought forecasting. Proc IAHS 383:261–266. https://doi.org/10.5194/piahs-383-261-2020
Yamazaki D, Oki T, Kanae S (2009) Deriving a global river network map and its sub-grid topographic characteristics from a fine-resolution flow direction map. Hydrol Earth Syst Sci 13(11):2241–2251. https://doi.org/10.5194/hess-13-2241-2009
Yuan X, Zhang M, Wang LY, Zhou T (2017) Understanding and seasonal forecasting of hydrological drought in the Anthropocene. Hydrol Earth Syst Sci 21:5477–5492. https://doi.org/10.5194/hess-21-5477-2017
Yuan F, Zhang YQ, Liu Y, Ma MW, Zhang LM, Shi JY (2021) Drought assessment of Xijiang River basin based on standardized Palmer drought index. Water Resour Prot 37(1):46–52 (In Chinese) https://doi.org/10.3880/j.issn.1004-6933.2021.01.007
Zhang F (2012) Research on distributed hydrological simulation and its application in Xijiang River basin. Dissertation, Donghua University (In Chinese) http://www.doc88.com/p-9488184731625.html
Zhang JP (2014) Change law and forecasting of the runoff in the Zhangze Reservoir based on nonlinear method. Doctoral dissertation. Dissertation, Xi’an University of Technology (In Chinese) https://doi.org/10.7666/d.D548827
Zhang D, Zhang Q, Qiu JM, Bai P, Kang L, Li XH (2018) Intensification of hydrological drought due to human activity in the middle reaches of the Yangtze River, China. Sci Total Environ 637–638:1432–1442. https://doi.org/10.1016/j.scitotenv.2018.05.121
Zhang RR, Wu XP, Zhou XZ, Ren BY, Zeng JY, Wang QF (2021) Investigating the effect of improved drought events extraction method on spatiotemporal characteristics of drought. Theor Appl Climatol 147:395–408. https://doi.org/10.1007/s00704-021-03838-z
Zhang LJ, Li J (2018) Spatiotemporal change of drought at various time scales indicated by SPEI and SPI in Xijiang River basin. Plateau Meteorol 37(2):560–567 (In Chinese) https://doi.org/10.7522/j.issn.1000-0534.2018.00013
Zhu Y, Liu Y, Wang W, Singh VP, Ma XY, Yu ZG (2019) Three-dimensional characterization of meteorological and hydrological droughts and their probabilistic links. J Hydrol 578:124016. https://doi.org/10.1016/j.jhydrol.2019.124016
Zhu LJ, Cooper DJ, Han SJ, Yang JW, Zhang YD, Li ZS, Zhao HY, Wang XC (2021) Influence of the Atlantic multidecadal oscillation on drought in northern Daxing’an mountains. Northeast China Catena 198:105017. https://doi.org/10.1016/j.catena.2020.105017
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
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
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:
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.
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.
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:
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:
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:
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:
Herein construct another rank statistic is as follows:
When \(n\) is an even number, the mean and variance of \(A\) are as follow:
When \(n\) is an odd number, the mean and variance values of \(A\) are as follow:
At this point, the joint statistic \(HK\) can be constructed as follows:
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:
Under the assumption of time series is random and independence, the mean and variance of \({d}_{k}\) are as follow:
Standardize the \({d}_{k}\) to the following:
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
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00704-022-04153-x