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

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

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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.

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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

Authors

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.

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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

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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

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