Abstract

Few studies have focused on the multivariate joint design of drought properties. Using daily streamflow data, this paper analyzes the impacts of pooling and exclusion of drought events in determining hydrological drought properties. The bivariate joint distributions of droughts were determined by using copulas. A novel method for bivariate design, the most-likely weight function, was applied to select design pairs for drought properties. The confidence interval of design curves of a given joint return period was limited by the measure of the joint probability density function due to the uncertainty of the estimated copula parameter. By comparing subseries separated by the low-flow change point, drought properties and their joint distributions, and designs were investigated under changing environment. Results showed that it was appropriate to set the pooling and excluding ratios as 0.2 and 0.41, respectively. The dependences of drought properties were positive and Archimedean copulas fitted well the bivariate joint distribution of droughts. The uncertainty of design duration–peak was remarkably greater than that of duration–severity and severity–peak. The design duration–severity was considerably stationary. Under changing environment, drought duration, severity, and peak remarkably decreased.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

Supported by the National Key R&D Program of China (2017YFC0405900) and the National Natural Science Foundation of China (51479217; 51879288) are gratefully acknowledged.

References

Chen, L., V. P. Singh, S. L. Guo, J. Z. Zhou, and J. H. Zhang. 2015. “Copula-based method for multisite monthly and daily streamflow simulation.” J. Hydrol. 528: 369–384. https://doi.org/10.1016/j.jhydrol.2015.05.018.
Chen, Y. D., Q. Zhang, M. Z. Xiao, and V. P. Singh. 2013. “Evaluation of risk of hydrological droughts by the trivariate Plackett copula in the East River basin (China).” Nat. Hazard. 68 (2): 529–547. https://doi.org/10.1007/s11069-013-0628-8.
De Michele, C., G. Salvadori, R. Vezzoli, and S. Pecora. 2013. “Multivariate assessment of droughts: Frequency analysis and dynamic return period.” Water Resour. Res. 49 (10): 6985–6994. https://doi.org/10.1002/wrcr.20551.
Dobric, J., and F. Schmid. 2007. “A goodness of fit test for copulas based on Rosenblatt’s transformation.” Comput. Stat. Data Anal. 51 (9): 4633–4642. https://doi.org/10.1016/j.csda.2006.08.012.
Dupuis, D. J. 2007. “Using copulas in hydrology: Benefits, cautions and issues.” J. Hydrol. Eng. 12 (4): 381–393. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(381).
Favre, A., S. E. Adlouni, L. Perreault, N. Thiemonge, and B. Bobee. 2004. “Multivariate hydrological frequency analysis using copulas.” Water Resour. Res. 40 (1): 290–294. https://doi.org/10.1029/2003WR002456.
Genest, C., B. Remillard, and D. Beaudoin. 2009. “Goodness-of-fit tests for copulas: A review and a power study.” Insurance Math. Econ. 44 (2): 199–213. https://doi.org/10.1016/j.insmatheco.2007.10.005.
Genest, C., and L. P. Rivest. 1993. “Statistical inference procedures for bivariate Archimedean copulas.” J. Am. Stat. Assoc. 88 (423): 1034–1043. https://doi.org/10.1080/01621459.1993.10476372.
Jiang, C., L. H. Xiong, C. Y. Xu, and S. Guo. 2015. “Bivariate frequency analysis of nonstationary low-flow series based on the time-varying copula.” Hydrol. Process. 29 (6): 1521–1534. https://doi.org/10.1002/hyp.10288.
Li, T., S. Guo, B. Yan, and L. Chen. 2013. “Derivative design flood hydrograph based on trivariate joint distribution.” [In Chinese.] J. Hydroelectr. Eng. 32 (3): 10–14.
Madsen, H., and D. Rosbjerg. 1995. “On the modelling of extreme droughts.” In Proc., Boulder Symp. on Modelling and Management of Sustainable Basin-Scale Water Resource Systems. Wallingford, UK: IAHS Publication.
Massey, F. J. 2012. “The Kolmogorov-Smirnov test for goodness of fit.” J. Am. Stat. Assoc. 46 (253): 68–78. https://doi.org/10.1080/01621459.1951.10500769.
Milly, P. C., J. Betancourt, M. Falkenmark, R. M. Hirsch, Z. M. Kundzewicz, D. P. Lettenmaier, and R. J. Stouffer. 2008. “Stationarity is dead: Whither water management?” Science 319 (5863): 573–574. https://doi.org/10.1126/science.1151915.
Mishra, A. K., and V. P. Singh. 2010. “A review of drought concepts.” J. Hydrol. 391 (1–2): 202–216. https://doi.org/10.1016/j.jhydrol.2010.07.012.
Mishra, A. K., and V. P. Singh. 2011. “Drought modeling—A review.” J. Hydrol. 403 (1–2): 157–175. https://doi.org/10.1016/j.jhydrol.2011.03.049.
Nalbantis, I., and G. Tsakiris. 2009. “Assessment of hydrological drought revisited.” Water Resour. Manage. 23 (5): 881–897. https://doi.org/10.1007/s11269-008-9305-1.
Pettitt, A. N. 1979. “A non-parametric approach to the change-point problem.” J. R. Stat. Soc. 28 (2): 126–135.
Salvadori, G., and C. De Michele. 2007. “On the use of copulas in hydrology: Theory and practice.” J. Hydrol. Eng. 12 (4): 369–380. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(369).
Salvadori, G., C. De Michele, and F. Durante. 2011. “On the return period and design in a multivariate framework.” Hydrol. Earth Syst. Sci. 15 (11): 3293–3305. https://doi.org/10.5194/hess-15-3293-2011.
Salvadori, G., and C. DeMichele. 2004. “Frequency analysis via copulas: Theoretical aspects and applications to hydrological events.” Water Resour. Res. 40 (12): 229–244. https://doi.org/10.1029/2004WR003133.
Salvadori, G., F. Durante, and C. De Michele. 2013. “Multivariate return period calculation via survival functions.” Water Resour. Res. 49 (4): 2308–2311. https://doi.org/10.1002/wrcr.20204.
Serinaldi, F. 2013. “An uncertain journey around the tails of multivariate hydrological distributions.” Water Resour. Res. 49 (10): 6527–6547. https://doi.org/10.1002/wrcr.20531.
Serinaldi, F., and C. G. Kilsby. 2015. “Stationarity is undead: Uncertainty dominates the distribution of extremes.” Adv. Water Resour. 77: 17–36. https://doi.org/10.1016/j.advwatres.2014.12.013.
Shiau, J. T. 2006. “Fitting drought duration and severity with two dimensional copulas.” Water Resour. Manage. 20 (5): 795–815. https://doi.org/10.1007/s11269-005-9008-9.
Singh, V. P., and L. Zhang. 2007. “IDF curves using the Frank Archimedean copula.” J. Hydrol. Eng. 12 (6): 651–662. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:6(651).
Song, S., and V. P. Singh. 2010a. “Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm.” Stochastic Environ. Res. Risk Assess. 24 (5): 783–805. https://doi.org/10.1007/s00477-010-0364-5.
Song, S., and V. P. Singh. 2010b. “Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data.” Stochastic Environ. Res. Risk Assess. 24 (3): 425–444. https://doi.org/10.1007/s00477-009-0331-1.
Tallaksen, L. M., H. Madsen, and B. Clausen. 1997. “On the definition and modelling of streamflow drought duration and deficit volume.” Hydrol. Sci. J. 42 (1): 15–33. https://doi.org/10.1080/02626669709492003.
Tu, X., V. P. Singh, X. Chen, L. Chen, Q. Zhang, and Y. Zhao. 2015. “Intra-annual distribution of streamflow and individual impacts of climate change and human activities in the Dongijang River basin, China.” Water Resour. Manage. 29 (8): 2677–2695. https://doi.org/10.1007/s11269-015-0963-5.
Tu, X., V. P. Singh, X. Chen, M. Ma, Q. Zhang, and Y. Zhao. 2016. “Uncertainty and variability in bivariate modeling of hydrological droughts.” Stochastic Environ. Res. Risk Assess. 30 (5): 1317–1334. https://doi.org/10.1007/s00477-015-1185-3.
Tu, X., Q. Zhang, V. P. Singh, X. Chen, C. Liu, and S. Wang. 2012. “Space-time changes in hydrological processes in response to human activities and climatic change in the south China.” Stochastic Environ. Res. Risk Assess. 26 (6): 823–834. https://doi.org/10.1007/s00477-011-0516-2.
Vicente-Serrano, S. M., J. I. Lopez-Moreno, S. Begueria, J. Lorenzo-Lacruz, C. Azorin-Molina, and E. Moran-Tjeda. 2012. “Accurate computation of a streamflow drought index.” J. Hydrol. Eng. 17 (2): 318–332. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000433.
Volpi, E., and A. Fiori. 2012. “Design event selection in bivariate hydrological frequency analysis.” Hydrol. Sci. J. 57 (8): 1506–1515. https://doi.org/10.1080/0262667.2012.726357.
Volpi, E., and A. Fiori. 2014. “Hydraulic structures subject to bivariate hydrological loads: Return period, design, and risk assessment.” Water Resour. Res. 50 (2): 885–897. https://doi.org/10.1002/2013WR014214.
Zelenhasic, E., and A. Salvai. 1987. “A method of streamflow drought analysis.” Water Resour. Res. 23 (1): 156–168. https://doi.org/10.1029/WR023i001p00156.
Zhang, Q., Y. D. Chen, X. Chen, and J. Li. 2011. “Copula-based analysis of hydrological extremes and implications of hydrological behaviors in the Pearl River basin, China.” J. Hydrol. Eng. 16 (7): 598–607. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000350.
Zhang, Q., X. H. Gu, V. P. Singh, D. D. Kong, and X. Chen. 2015a. “Spatiotemporal behavior of floods and droughts and their impacts on agriculture in China.” Global Planet. Change 131: 63–72. https://doi.org/10.1016/j.gloplacha.2015.05.007.
Zhang, Q., T. Y. Qi, V. P. Singh, Y. D. Chen, and M. Z. Xiao. 2015b. “Regional frequency analysis of droughts in China: A multivariate perspective.” Water Resour. Manage. 29 (6): 1767–1787. https://doi.org/10.1007/s11269-014-0910-x.
Zhang, Q., V. P. Singh, K. Li, and J. Li. 2014. “Trend, periodicity and abrupt change in streamflow of the East River, the Pearl River basin, China.” Hydrol. Process. 28 (2): 305–314. https://doi.org/10.1002/hyp.9576.
Zhang, Q., P. Sun, J. Li, V. P. Singh, and J. Liu. 2015c. “Spatiotemporal properties of droughts and related impacts on agriculture in Xinjiang, China.” Int. J. Climatol. 35 (7): 1254–1266. https://doi.org/10.1002/joc.4052.
Zhang, Q., M. Xiao, and V. P. Singh. 2015d. “Uncertainty evaluation of copula analysis of hydrological droughts in the East River Basin, China.” Global Planet. Change 129: 1–9. https://doi.org/10.1016/j.gloplacha.2015.03.001.
Zhang, Q., M. Xiao, V. P. Singh, and X. Chen. 2013. “Copula-based risk evaluation of hydrological droughts in the East River basin, China.” Stochastic Environ. Res. Risk Assess. 27 (6): 1397–1406. https://doi.org/10.1007/s00477-012-0675-9.

Information & Authors

Information

Published In

Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 24Issue 6June 2019

History

Received: Jan 31, 2018
Accepted: Dec 17, 2018
Published online: Mar 25, 2019
Published in print: Jun 1, 2019
Discussion open until: Aug 25, 2019

Permissions

Request permissions for this article.

Authors

Affiliations

Professor, Center of Water Resources and Environment, School of Civil Engineering, and Center of Water Security Engineering and Technology in South China of Guangdong, Sun Yat-sen Univ., Guangzhou 510275, China (corresponding author). ORCID: https://orcid.org/0000-0002-8256-8358. Email: [email protected]
Graduate Student, School of Geography and Planning, Sun Yat-sen Univ., Guangzhou 510275, China. Email: [email protected]
Vijay P. Singh, Dist.M.ASCE [email protected]
Distinguished Professor, Regents Professor, and Caroline & William N. Lehrer Distinguished Chair in Water Engineering, Dept. of Biological and Agricultural Engineering, and Zachry Dept. of Civil Engineering, Texas A&M Univ., 2117, College Station, TX 77843. Email: [email protected]
Xiaohong Chen [email protected]
Professor, Center of Water Resources and Environment, School of Civil Engineering, Sun Yat-sen Univ., Guangzhou 510275, China. Email: [email protected]
Professor, State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China. Email: [email protected]
Lecturer, School of Water Conservancy, North China Univ. of Water Resources and Electric Power, Zhengzhou 450045, China. Email: [email protected]
Senior Engineer, School of Geography and Planning, Sun Yat-sen Univ., Guangzhou 510275, China. Email: [email protected]
Graduate Student, School of Geography and Planning, Sun Yat-sen Univ., Guangzhou 510275, China. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share