Skip to main content

Analyzing spatial–temporal change of multivariate drought risk based on Bayesian copula: Application to the Balkhash Lake basin

Theoretical and Applied Climatology volume 149, pages 787–804 (2022)Cite this article

Abstract

In the past century, drought events were likely to be frequent and severe in the arid areas under climate change impact. In this study, a Bayesian copula multivariate analysis (BCMA) method is developed for assessing the impact of spatial–temporal variation on drought risk, through coupling Bayesian copula with multivariate analysis. BCMA can reveal the dynamic characteristics of droughts and deal with the uncertainty caused by copula parameters when modeling the dependent structures of variable pairs (duration-severity-affected area). BCMA is applied to the Balkhash Lake basin in Central Asia for assessing multivariate drought risk during 1901–2020. Some major findings can be summarized: (1) in 1901–2020, the basin suffered 53 droughts; the most severe drought occurred from October 1973 to January 1977 (39 months), and 95% of the basin was affected (335,800 km2); (2) droughts usually develop in the direction of “east–west,” and Ili River delta and alluvial plain are the most frequent areas (47.2%) in the basin; (3) droughts show significant seasonality and frequently occur in spring and summer (64.2%), and drought risks of the middle and lower reaches of Ili River are the highest in spring and summer; (4) multivariate characteristics significantly affect drought risk, and drought risk ranges from 1.9 to 18.1% when the guarantee rate is 0.99; (5) the possible causes of drought risk dynamics are meteorological factors (e.g., precipitation and evapotranspiration) and underlying surface factors (e.g., runoff and soil moisture). The findings suggest that droughts in the Balkhash Lake basin are affected by climatic factors, and BCMA can provide methodological support for the studies of drought in other arid regions.

Graphical abstract

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Data availability

The data sets supporting the results of this study are included in the article.

Code availability

Codes of the MATLAB program are provided in an individual appendix file.

References

  • Abdi A, Hassanzadeh Y, Talatahari S (2016) Parameter estimation of copula functions using an optimization-based method. Theoret Appl Climatol 129(1–2):1–12

    Google Scholar 

  • Aizhan U (2020) Save Kazakhstan’s shrinking Lake Balkhash. Science 370(6514):303

    Google Scholar 

  • Akinwale TO, Phillip GO, David AO (2019) Drought spatiotemporal characterization using self-calibrating Palmer Drought Severity Index in the northern region of Nigeria. Results Eng 3:100088

    Google Scholar 

  • Anne F, Kerstin S, Giuliano DS (2016) Drought in a human-modified world: reframing drought definitions, understanding, and analysis approaches. Hydrol Earth Syst Sci 20(9):3631–3650

    Article  Google Scholar 

  • Arbel J, Crispino M, Girard S (2019) Dependence properties and Bayesian inference for asymmetric multivariate copulas. J Multivar Anal 174:104530

    Article  Google Scholar 

  • Ault TR (2020) On the essentials of drought in a changing climate. Science 368(6488):256–260

    Article  Google Scholar 

  • Ben E, Matthew G, Boyd H (2019) The social and economic impacts of drought. Aust J Soc Issues 54(1):22–31

    Article  Google Scholar 

  • Benjamin LH (2012) A spatio-temporal structure-based approach to drought characterization. Int J Climatol 32(3):406–418

    Article  Google Scholar 

  • Bhatti MI, Do HQ (2019) Recent development in copula and its applications to the energy, forestry and environmental sciences. Int J Hydrogen Energy 44(36):19453–19473

    Article  Google Scholar 

  • Bohn VY, Raúl R, Varni M (2020) Using SPEI in predicting water table dynamics in Argentinian plains. Environ Earth Sci 79(19):1–16

    Article  Google Scholar 

  • Chen ZM (2010) An outline of Asia’s geomorphic sphere and its plate morph tectonics. Surveying and Mapping Press, Beijing

    Google Scholar 

  • Dehghan S, Salehnia N, Sayari N (2020) Prediction of meteorological drought in arid and semi-arid regions using PDSI and SDSM: a case study in Fars province. Iran J Arid Land 12(2):318–330

    Article  Google Scholar 

  • Diaz V, Perez G, Van LH (2020) An approach to characterize spatio-temporal drought dynamics. Adv Water Resour 137:103512

    Article  Google Scholar 

  • Duan W, Zou S, Chen Y (2020) Sustainable water management for cross-border resources: the Balkhash Lake basin of Central Asia, 1931–2015. J Clean Prod 263:121614

    Article  Google Scholar 

  • Dubovyk O, Ghazaryan G, González J (2019) Drought hazard in Kazakhstan in 2000–2016: a remote sensing perspective. Environ Monit Assess 191(8):510

    Article  Google Scholar 

  • Fatemeh H, Farzad H, Mostafa Y (2021) Evaluation of drought characterization using SPI and SC-PDSI drought indices in baseline and upcoming periods in Birjand region. Arab J Geosci 14(11):939

    Article  Google Scholar 

  • Guo H, Bao A, Liu T (2018) Spatial and temporal characteristics of droughts in Central Asia during 1966–2015. Sci Total Environ 624:1523–1538

    Article  Google Scholar 

  • Haario H, Marko L, Antonietta M (2006) Dram: efficient adaptive MCMC. Stat Comput 16(4):339–354

    Article  Google Scholar 

  • Hamal K, Sharma S, Khadka N (2020) Assessment of drought impacts on crop yields across Nepal during 1987–2017. Meteorol Appl 27(5):1–18

    Article  Google Scholar 

  • Herrera JE, Satoh Y, Sheffield J (2017) Spatiotemporal dynamics of global drought. Geophys Res Lett 44:2254–2263

    Article  Google Scholar 

  • Hu ZY, Chen X, Chen DL (2019) “Dry gets drier, wet gets wetter”: a case study over the arid regions of central Asia. Int J Climatol 39(2):1072–1091

    Article  Google Scholar 

  • Huang GH, Qin XS, He L (2015) Nonstationary desertification dynamics of desert oasis under climate change and human interference. J Geophys Res 120(23):11878–11888

    Article  Google Scholar 

  • Huang K, Fan YR (2021) Parameter uncertainty and sensitivity evaluation of copula-based multivariate hydroclimatic risk assessment. J Environ Inf 38(2):131–144

  • Isbekov KB, Tsoy VN, Crétaux J (2019) Impacts of water level changes in the fauna, flora, and physical properties over the Balkhash Lake watershed. Lakes & Reservoirs 24(2):195–208

    Article  Google Scholar 

  • Jin YF, Yin ZY, Zhou WH (2019) Identifying parameters of advanced soil models using an enhanced transitional Markov chain Monte Carlo method. Acta Geotech 14(6):1925–1947

    Article  Google Scholar 

  • Li Z, Huang GH, Fan YR (2015) Hydrologic risk analysis for nonstationary streamflow records under uncertainty. J Environ Inf 26(1):41–51

    Google Scholar 

  • Liu YR, Li YP, Ma Y (2020) Development of a Bayesian-copula-based frequency analysis method for hydrological risk assessment – the Naryn River in Central Asia. J Hydrol 580:124349

    Article  Google Scholar 

  • Liu YR, Li YP, Yang X (2021) Development of an integrated multivariate trend-frequency analysis method: spatial-temporal characteristics of climate extremes under global warming for Central Asia. Environ Res 195:110859

    Article  Google Scholar 

  • Liu Z, Zhang X, Fang R (2018) Multi-scale linkages of winter drought variability to ENSO and the Arctic Oscillation: a case study in Shaanxi, North China. Atmos Res 200:117–125

    Article  Google Scholar 

  • Mellak S, Souag GD (2020) Spatio-temporal analysis of maximum drought severity using copulas in northern Algeria. J Water Clim Change 11:68–84

    Article  Google Scholar 

  • Montaseri M, Amirataee B, Rezaie H (2018) New approach in bivariate drought duration and severity analysis. J Hydrol 559:166–181

    Article  Google Scholar 

  • Neisi M, Bijani M, Abbasi E (2020) Analyzing farmers’ drought risk management behavior: evidence from Iran. J Hydrol 590:125243

    Article  Google Scholar 

  • Nelsen RB (2006) An introduction to copulas. Springer, New York

    Google Scholar 

  • Palmer WC (1968) An index of agricultural drought. B Am Meteorol Soc 49(3):295

  • Sadegh M, Ragno E, Aghakouchak A (2017) Multivariate copula analysis toolbox (MvCAT): describing dependence and underlying uncertainty using a Bayesian framework. Water Resour Res 53(6):5166–5183

    Article  Google Scholar 

  • Sedgwick P (2012) Pearson’s correlation coefficient. BMJ 345:4483–4483

    Article  Google Scholar 

  • Sheng Y, Paul P, George C (2002) Power of the Mann-Kendall and Spearman’s rho tests for detecting monotonic trends in hydrological series. J Hydrol 259:254–271

    Article  Google Scholar 

  • Soumia M, Doudja S (2020) Spatio-temporal analysis of maximum drought severity using Copulas in Northern Algeria. J Water Clim Change 11(1):68–84

    Google Scholar 

  • Vernieuwe H, Baets BD, Verhoest NE (2019) A mathematical morphology approach for a qualitative exploration of drought events in space and time. Int J Climatol 40:1–14

    Google Scholar 

  • Wang L, Yu H, Yang ML (2019) A drought index: the standardized precipitation evapotranspiration runoff index. J Hydrol 571:651–668

    Article  Google Scholar 

  • Xu K, Yang DW, Yang HB (2015) Spatio-temporal variation of drought in China during 1961–2012: A climatic perspective. J Hydrol 526:253–264

    Article  Google Scholar 

  • Yang X, Li YP, Liu YR (2020) A MCMC-based maximum entropy copula method for bivariate drought risk analysis of the Amu Darya River Basin. J Hydrol 590:125502

    Article  Google Scholar 

  • Yue P, Lee H (2020) Drought-induced spatio-temporal synchrony of plague outbreak in Europe. Sci Total Environ 698:134138

    Article  Google Scholar 

  • Zger M, Baakn EE, Ekmekciolu M (2020) Comparison of wavelet and empirical mode decomposition hybrid models in drought prediction. Comput Electron Agric 179:105851

    Article  Google Scholar 

  • Zhang YM, Li YM, Shen GM (2013) Plant resources and utilization in Central Asia. China Meteorological Press, Beijing

    Google Scholar 

  • Zhang DJ, Lin QY, Yao HX (2021) Accelerating SWAT simulations using an in-memory NoSQL database. J Environ Inf 37(2):142–152

  • Zhao H, Gao G, An W (2017) Timescale differences between sc-PDSI and SPEI for drought monitoring in China. Phys Chem Earth 102:48–58

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

Funding

This research was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA20060302).

Author information

Authors and Affiliations

  1. State Key Joint Laboratory of Environmental Simulation and Pollution Control, School of Environment, Beijing Normal University, Beijing, China

    X. Yang, Y. P. Li, G. H. Huang & S. Q. Zhang

  2. Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina, Sask, S4S 0A2, Canada

    Y. P. Li & G. H. Huang

Authors
  1. X. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. P. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. H. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Q. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

X. Yang: conceptualization, methodology, data collection, writing original draft, writing review and editing. Y. P. Li: supervision, writing review and editing, project administration, and funding acquisition. G. H. Huang: modifying the manuscript and polishing English. S. Q. Zhang: data collection, graph editing, and reference checking.

Corresponding author

Correspondence to Y. P. Li.

Ethics declarations

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

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.

Highlights

• A BCMA method is developed for analyzing multivariate drought risk.

• BCMA can reveal the static and dynamic characteristics of droughts.

• BCMA can handle the uncertainty caused by copula parameters.

• Droughts show significant seasonality and directionality.

• Meteorological factors are the key reason that brings the drought risk.

Appendix (Method details)

Appendix (Method details)

MATLAB program for self-calibrating PDSI extraction and visualization.

Step 1: Model sample data

  1. 1.

    ncdisp('H:\Global\PDSI\scPDSI.cru.3.25.bams2018.GLOBAL.1901.2017.nc');

  2. 2.

    data1=ncread('H:\Global\PDSI\scPDSI.cru.3.26.bams2018.GLOBAL.1901.2017.nc','scpdsi');

  3. 3.

    data3=data1(:,:,1);

  4. 4.

    data4=rot90(data3);

  5. 5.

    data5=flipud(data4);

  6. 6.

    data5(isnan(data5))=-999;

  7. 7.

    dlmwrite('sample_1.txt',data5,'\t',1,1)

Step 2: Add latitude and longitude information to sample_1.txt

  1. 1.

    ncols 720

  2. 2.

    nrows 360

  3. 3.

    xllcorner -180

  4. 4.

    yllcorner -90

  5. 5.

    cellsize 0.5

  6. 6.

    NODATA_value -999

Step 3: Rasterize the sample_1.txt by ASCII code in ArcGIS, and output it as sample_1.tif

Step 4: Load a raster file with projection information, and define the projection on the example_1.tif

Step 5: Batch processing

  1. 1.

    [aaaaa,R]=geotiffread('H:\Global\PDSI\example_1.tif');

  2. 2.

    info=geotiffinfo('H:\Global\PDSI\example_1.tif');

  3. 3.

    data=ncread('H:\Global\PDSI\scPDSI.cru.3.26.bams2018.GLOBAL.1901.2017.nc','scpdsi');

  4. 4.

    for year=1901:2017

  5. 5.

    data1=data(:,:,1+12*(year-1901):12*(year-1900));

  6. 6.

    data3=sum(data1,3)/12;

  7. 7.

    data4=rot90(data3);

  8. 8.

    data5=flipud(data4);

  9. 9.

    filename=strcat('H:\Global\PDSI\yearly_pdsi\global',int2str(year),'yearly_PDSI.tif');

  10. 10.

    geotiffwrite(filename, data5, R, 'GeoKeyDirectoryTag', info.GeoTIFFTags.GeoKeyDirectoryTag);

  11. 11.

    for mon=1:12

  12. 12.

    data2=data1(:,:,mon);

  13. 13.

    data4=rot90(data2);

  14. 14.

    data5=flipud(data4);

  15. 15.

    filename=strcat('H:\Global\PDSI\monthly_pdsi\global', int2str(year), '_', int2str(mon), 'monthly_PDSI.tif');

  16. 16.

    geotiffwrite(filename, data5, R, 'GeoKeyDirectoryTag', info.GeoTIFFTags.GeoKeyDirectoryTag);

  17. 17.

    end

  18. 18.

    end

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yang, X., Li, Y.P., Huang, G.H. et al. Analyzing spatial–temporal change of multivariate drought risk based on Bayesian copula: Application to the Balkhash Lake basin. Theor Appl Climatol 149, 787–804 (2022). https://doi.org/10.1007/s00704-022-04062-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00704-022-04062-z