Case Studies
Dec 7, 2018

Bivariate Frequency Analysis of Hydrological Drought Using a Nonstationary Standardized Streamflow Index in the Yangtze River

Publication: Journal of Hydrologic Engineering
Volume 24, Issue 2

Abstract

In order to reassess the hydrological drought in the Yangtze River under changing environment, a nonstationary standardized streamflow index was proposed in this study to fit the streamflow series at Yichang station; time and a modified reservoir index were introduced as covariates to assess the effect of reservoir regulation. The copula method was applied for bivariate modeling of drought duration and severity, in which joint and conditional return periods were considered for drought risk assessment. The results indicated that the monthly streamflow series at Yichang station have undergone great changes and the stationary assumption is no longer valid. The drought severity was more severe with its marginal distribution changed from the generalized extreme value to gamma when considering nonstationary properties. The Joe copula was selected for bivariate frequency analysis, and the correlation coefficient between drought characteristics increased in nonstationary models. Using the conditional return period, the model with reservoir index as covariate reported a worse drought condition compared with the stationary model, implying that the reservoirs may deteriorate the downstream hydrological drought at the Yichang station. By contrast, the time covariate may underestimate the drought risk. The nonstationary index is capable for drought modeling in the Yangtze River, and can be a useful tool in further research.

Get full access to this article

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

Acknowledgments

This work is supported by the National Key Research and Development Program of China (No. 2016YFC0402204) and the Fundamental Research Funds for the Central Universities (No. 5003271021).

References

Ahn, K.-H., and R. N. Palmer. 2016. “Use of a nonstationary copula to predict future bivariate low flow frequency in the Connecticut River basin.” Hydrol. Process. 30 (19): 3518–3532. https://doi.org/10.1002/hyp.10876.
Akaike, H. 1974. “A new look at the statistical model identification.” IEEE Trans. Autom. Control 19 (6): 716–723. https://doi.org/10.1109/TAC.1974.1100705.
Chen, L., V. P. Singh, G. Shenglian, Z. Hao, and T. Li. 2012. “Flood coincidence risk analysis using multivariate copula functions.” J. Hydrol. Eng. 17 (6): 742–755. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000504.
Galiano, S. G. G., P. O. Giménez, and J. D. G. Osorio. 2015. “Assessing nonstationary spatial patterns of extreme droughts from long-term high-resolution observational dataset on a semiarid Basin (Spain).” Water 7 (10): 5458–5473. https://doi.org/10.3390/w7105458.
Gao, B., D. Yang, and H. Yang. 2013. “Impact of the Three Gorges Dam on flow regime in the middle and lower Yangtze River.” Q. Int. 304: 43–50. https://doi.org/10.1016/j.quaint.2012.11.023.
Genest, C., B. Rémillard, 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.
Heim, R. R., Jr. 2002. “A review of twentieth-century drought indices used in the United States.” Bull. Am. Meteorol. Soc. 83 (8): 1149–1166. https://doi.org/10.1175/1520-0477-83.8.1149.
Hong, X., S. Guo, Y. Zhou, and L. Xiong. 2015. “Uncertainties in assessing hydrological drought using streamflow drought index for the upper Yangtze River basin.” Stochastic Environ. Res. Risk Assess. 29 (4): 1235–1247. https://doi.org/10.1007/s00477-014-0949-5.
Huang, S., Q. Huang, J. Chang, and G. Leng. 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.
Jiang, C., L. 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.
Kendall, M. G. 1975. Rank correlation measures. London: Charles Griffin.
Keyantash, J. A., and J. A. Dracup. 2004. “An aggregate drought index: Assessing drought severity based on fluctuations in the hydrologic cycle and surface water storage.” Water Resour. Res. 40 (9): W09304. https://doi.org/10.1029/2003WR002610.
Kwon, H.-H., and U. Lall. 2016. “A copula-based nonstationary frequency analysis for the 2012–2015 drought in California.” Water Resour. Res. 52 (7): 5662–5675. https://doi.org/10.1002/2016WR018959.
Li, J., Z. Xia, and Y. Wang. 2013a. “Impact of the Three Gorges and Gezhouba Reservoirs on Ecohydrological Conditions for Sturgeon in the Yangtze River, China.” J. Hydrol. Eng. 18 (12): 1563–1570. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000759.
Li, S., L. Xiong, L. Dong, and J. Zhang. 2013b. “Effects of the three gorges reservoir on the hydrological droughts at the downstream Yichang station during 2003–2011.” Hydrol. Process. 27 (26): 3981–3993. https://doi.org/10.1002/hyp.9541.
López, J., and F. Francés. 2013. “Non-stationary flood frequency analysis in continental Spanish rivers, using climate and reservoir indices as external covariates.” Hydrol. Earth Syst. Sci. 17 (8): 3189–3203. https://doi.org/10.5194/hess-17-3189-2013.
Mann, H. B. 1945. “Nonparametric tests against trend.” Econometrica 13 (3): 245–259. https://doi.org/10.2307/1907187.
McKee, T. B., N. J. Doesken, and J. Kleist. 1993. “The relationship of drought frequency and duration to time scales.” In Proc., 8th Conf. on Applied Climatology, 179–183. Boston: American Meteorological Society.
Milly, P. C. D., J. Betancourt, M. Falkenmark, R. M. Hirsch, Z. W. 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): 202–216. https://doi.org/10.1016/j.jhydrol.2010.07.012.
Rajib, M., R. Meenu, and R. S. Govindaraju. 2013. “Identification of hydrologic drought triggers from hydroclimatic predictor variables.” Water Resour. Res. 49 (7): 4476–4492. https://doi.org/10.1002/wrcr.20346.
Rigby, R. A., and D. M. Stasinopoulos. 2005. “Generalized additive models for location, scale and shape.” J. R. Stat. Soc. Ser. C-Appl. Stat. 54 (3): 507–554. https://doi.org/10.1111/j.1467-9876.2005.00510.x.
Salvadori, G., C. De Michele, N. T. Kottegoda, and R. Rosso. 2007. “Extremes in nature: An approach using copulas.” Vol. 49 of Extremes in nature an approach using copulas, edited by G. Salvadori, C. de Michele, N. T. kottegoda, and R. Rosso, 5–89. Berlin: Springer.
Shafer, B. A., and L. E. Dezman. 1982. “Development of a surface water supply index (SWSI) to assess the severity of drought conditions in snowpack runoff areas.” In Proc., Western Snow Conf., 164–175. Fort Collins, CO: Colorado State Univ.
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.
Sklar, M. 1959. “Fonctions de repartition a n dimensions et leurs marges.” Publ. Inst. Stat. Univ. Paris 8: 229–231.
Su, B., J. Huang, X. Zeng, C. Gao, and T. Jiang. 2016. “Impacts of climate change on streamflow in the upper Yangtze River basin.” Clim. Change 141 (3): 533–546. https://doi.org/10.1007/s10584-016-1852-5.
Türkeş, M., and H. Tatlı. 2009. “Use of the standardized precipitation index (SPI) and a modified SPI for shaping the drought probabilities over Turkey.” Int. J. Climatol. 29 (15): 2270–2282. https://doi.org/10.1002/joc.1862.
Wang, Y., J. Li, P. Feng, and R. Hu. 2015. “A Time-dependent drought index for non-stationary precipitation series.” Water Resour. Manage. 29 (15): 5631–5647. https://doi.org/10.1007/s11269-015-1138-0.
Yan, L., L. Xiong, D. Liu, T. Hu, and C.-Y. Xu. 2017. “Frequency analysis of nonstationary annual maximum flood series using the time-varying two-component mixture distributions.” Hydrol. Process. 31 (1): 69–89. https://doi.org/10.1002/hyp.10965.
Yevjevich, V. M. 1967. An objective approach to definitions and investigations of continental hydrologic droughts. Fort Collins, CO: Colorado State Univ.
Yu, F., Z. Chen, X. Ren, and G. Yang. 2009. “Analysis of historical floods on the Yangtze River, China: Characteristics and explanations.” Geomorphology 113 (3–4): 210–216. https://doi.org/10.1016/j.geomorph.2009.03.008.
Yu, M., Q. Li, G. Lu, T. Cai, W. Xie, and X. Bai. 2013. “Investigation into the impacts of the Gezhouba and the Three Gorges reservoirs on the flow regime of the Yangtze River.” J. Hydrol. Eng. 18 (9): 1098–1106. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000545.

Information & Authors

Information

Published In

Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 24Issue 2February 2019

History

Received: Mar 2, 2018
Accepted: Aug 31, 2018
Published online: Dec 7, 2018
Published in print: Feb 1, 2019
Discussion open until: May 7, 2019

Permissions

Request permissions for this article.

Authors

Affiliations

Professor, School of Hydropower and Information Engineering, Huazhong Univ. of Science and Technology, Wuhan 430074, China. Email: [email protected]
Ph.D. Candidate, School of Hydropower and Information Engineering, Huazhong Univ. of Science and Technology, Wuhan 430074, China (corresponding author). ORCID: https://orcid.org/0000-0003-4494-2772. 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