Bivariate Flood Frequency Analysis of Nonstationary Flood Characteristics
Publication: Journal of Hydrologic Engineering
Volume 24, Issue 4
Abstract
Modeling the simultaneous behavior of flood characteristics, namely peak, volume, and duration, is essential for water resource planning and management. A multivariate probability approach, which provides a comprehensive understanding of flood characteristics and their relationship, may estimate flood magnitude more accurately than a univariate approach. Most previous studies related to the multivariate frequency analysis of extreme events assumed temporal stationarity. However, several recent studies show that flood characteristics exhibit nonstationary behavior due to climate change, urbanization, land-use change, or water resource structures. Therefore, it is necessary to perform multivariate frequency analysis in a nonstationary condition. In this study, nonstationary bivariate models, where the parameters of the marginal distribution vary with possible physical covariates (i.e., precipitation, urbanization, and deforestation), are developed to understand/model the nonstationary behavior of the flood characteristics of the Dongnai River in Vietnam. This study indicates that the assumption of temporal stationarity in flood characteristics leads to an underestimation of flood risk. For example, the flood characteristics’ quantiles estimated for a 50-year return period in a stationary condition is nearly equal to flood characteristics’ quantiles estimated for a 10-year return period in a nonstationary condition. Specifically, the volume and peak pair calculated for a nonstationary condition for the 10-year joint return period (OR) is (625.8, 147.8). The volume and peak pair calculated for a stationary condition for the 50-year joint return period (OR) is (620.1, 148.8).
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors gratefully acknowledge the National Hydro–Meteorological Service and Ministry of Natural Resources and Environment, Vietnam, for providing hydrometeorological data.
References
Aghakouchak, A., G. Ciach, and E. Habib. 2010. “Estimation of tail dependence coefficient in rainfall accumulation fields.” Adv. Water Resour. 33 (9): 1142–1149. https://doi.org/10.1016/j.advwatres.2010.07.003.
Agilan, V., and N. V. Umamahesh. 2017. “What are the best covariates for developing non-stationary rainfall intensity-duration-frequency relationship?” Adv. Water Resour. 101: 11–22. https://doi.org/10.1016/j.advwatres.2016.12.016.
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.
Bender, J., T. Wahl, and J. Jensen. 2014. “Multivariate design in the presence of non-stationarity.” J. Hydrol. 514: 123–130. https://doi.org/10.1016/j.jhydrol.2014.04.017.
Berg, P., C. Moseley, and J. O. Haerter. 2013. “Strong increase in convective precipitation in response to higher temperatures.” Nat. Geosci. 6 (3): 181–185. https://doi.org/10.1038/ngeo1731.
Blöschl, G., et al. 2015. “Increasing river floods: Fiction or reality?” Wiley Interdisciplinary Rev.: Water 2 (4): 329–344. https://doi.org/10.1002/wat2.1079.
Chebana, F., and T. B. Ouarda. 2011. “Multivariate quantiles in hydrological frequency analysis.” Environmetrics 22 (1): 63–78. https://doi.org/10.1002/env.1027.
Cheng, L., and A. Aghakouchak. 2014. “Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate.” Sci. Rep. 4: 7093. https://doi.org/10.1038/srep07093.
Cheng, L., A. AghaKouchak, E. Gilleland, and R. W. Katz. 2014. “Non-stationary extreme value analysis in a changing climate.” Clim. Change 127 (2): 353–369. https://doi.org/10.1007/s10584-014-1254-5.
Coles, S., J. Bawa, L. Trenner, and P. Dorazio. 2001. An introduction to statistical modeling of extreme values. London: Springer.
Coles, S., J. Heffernan, and J. Tawn. 1999. “Dependence measures for extreme value analyses.” Extremes 2 (4): 339–365. https://doi.org/10.1023/A:1009963131610.
Condon, L. E., S. Gangopadhyay, and T. Pruitt. 2015. “Climate change and non-stationary flood risk for the upper Truckee River basin.” Hydrol. Earth Syst. Sci. 19 (1): 159–175. https://doi.org/10.5194/hess-19-159-2015.
Das, J., and N. V. Umamahesh. 2017. “Uncertainty and nonstationarity in streamflow extremes under climate change scenarios over a River Basin.” J. Hydrol. Eng. 22 (10): 04017042. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001571.
Du, T., L. Xiong, C. Y. Xu, C. J. Gippel, S. Guo, and P. Liu. 2015. “Return period and risk analysis of nonstationary low-flow series under climate change.” J. Hydrol. 527: 234–250. https://doi.org/10.1016/j.jhydrol.2015.04.041.
Dung, D. D., N. N. Anh, and D. T. Ha. 2014. “Evaluation of changes of water resources in the Dongnai river basin and its surrounding basins.” J. Water Resour. Environ. Eng. 47: 19–26.
Dung, N. V., B. Merz, A. Bardossy, and H. Apel. 2015. “Handling uncertainty in bivariate quantile estimation—An application to flood hazard analysis in the Mekong Delta.” J. Hydrol. 527: 704–717. https://doi.org/10.1016/j.jhydrol.2015.05.033.
Evan, E., and A. Ataur. 2018. “Characterizing changes in rainfall: A case study for New South Wales, Australia.” Int. J. Climatol. 38 (3): 1452–1462. https://doi.org/10.1002/joc.5258.
Fischer, E. M., and R. Knutti. 2015. “Anthropogenic contribution to global occurrence of heavy-precipitation and high-temperature extremes.” Nat. Clim. Change 5 (6): 560–564. https://doi.org/10.1038/nclimate2617.
Gaál, L., J. Szolgay, S. Kohnová, K. Hlavčová, J. Parajka, A. Viglione, R. Merz, and G. Blöschl. 2015. “Dependence between flood peaks and volumes: A case study on climate and hydrological controls.” Hydrol. Sci. J. 60 (6): 968–984. https://doi.org/10.1080/02626667.2014.951361.
Gobin, A., H. T. Nguyen, V. Q. Pham, and H. T. T. Pham. 2016. “Heavy rainfall patterns in Vietnam and their relation with ENSO cycles.” Int. J. Climatol. 36 (4): 1686–1699. https://doi.org/10.1002/joc.4451.
Gräler, B., M. van den Berg, S. Vandenberghe, A. Petroselli, S. Grimaldi, B. De Baets, and N. Verhoest. 2013. “Multivariate return periods in hydrology: A critical and practical review focusing on synthetic design hydrograph estimation.” Hydrol. Earth Syst. Sci. 17 (4): 1281–1296. https://doi.org/10.5194/hess-17-1281-2013.
Hao, Z., and V. P. Singh. 2016. “Review of dependence modeling in hydrology and water resources.” Prog. Phys. Geogr. 40 (4): 549–578. https://doi.org/10.1177/0309133316632460.
Ishak, E. H., A. Rahman, S. Westra, A. Sharma, and G. Kuczera. 2013. “Evaluating the non-stationarity of Australian annual maximum flood.” J. Hydrol. 494: 134–145. https://doi.org/10.1016/j.jhydrol.2013.04.021.
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.
Karmakar, S., and S. P. Simonovic. 2008. “Bivariate flood frequency analysis: Part 1. Determination of marginals by parametric and nonparametric techniques.” J. Flood Risk Manage. 1 (4): 190–200. https://doi.org/10.1111/j.1753-318X.2008.00022.x.
Katz, R. W. 2013. “Statistical methods for nonstationary extremes.” In Extremes in a changing climate: Detection, analysis and uncertainty. Edited by A. Aghakouchak, D. Easterling, K. Hsu, S. Schubert, and S. Sorooshian. Dordrecht: Springer.
Kim, H., S. Kim, H. Shin, and J. H. Heo. 2017. “Appropriate model selection methods for nonstationary generalized extreme value models.” J. Hydrol. 547: 557–574. https://doi.org/10.1016/j.jhydrol.2017.02.005.
Lima, C. H., U. Lall, T. J. Troy, and N. Devineni. 2015. “A climate informed model for nonstationary flood risk prediction: Application to Negro River at Manaus, Amazonia.” J. Hydrol. 522: 594–602. https://doi.org/10.1016/j.jhydrol.2015.01.009.
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.
Merz, B., S. Vorogushyn, S. Uhlemann, J. Delgado, and Y. Hundecha. 2012. “HESS Opinions more efforts and scientific rigour are needed to attribute trends in flood time series.” Hydrol. Earth Syst. Sci. 16 (5): 1379–1387. https://doi.org/10.5194/hess-16-1379-2012.
Milly, P. C., J. Betancourt, M. Falkenmark, R. M. Hirsch, Z. W. Kundzewicz, D. P. Lettenmaier, R. J. Stouffer, M. D. Dettinger, and V. Krysanova. 2015. “On critiques of Stationarity is dead: Whither water management?” Water Resour. Res. 51 (9): 7785–7789. https://doi.org/10.1002/2015WR017408.
Min, S. K., X. Zhang, F. W. Zwiers, and G. C. Hegerl. 2011. “Human contribution to more-intense precipitation extremes.” Nature 470 (7334): 378–381. https://doi.org/10.1038/nature09763.
Mondal, A., and P. P. Mujumdar. 2015. “Modeling non-stationarity in intensity, duration and frequency of extreme rainfall over India.” J. Hydrol. 521: 217–231. https://doi.org/10.1016/j.jhydrol.2014.11.071.
Montanari, A., and D. Koutsoyiannis. 2014. “Modeling and mitigating natural hazards: Stationarity is immortal!.” Water Resour. Res. 50 (12): 9748–9756. https://doi.org/10.1002/2014WR016092.
Nguyen, D. Q., J. Renwick, and J. McGregor. 2014. “Variations of surface temperature and rainfall in Vietnam from 1971 to 2010.” Int. J. Climatol. 34 (1): 249–264. https://doi.org/10.1002/joc.3684.
Obeysekera, J., and J. D. Salas. 2016. “Frequency of recurrent extremes under nonstationarity.” J. Hydrol. Eng. 21 (5): 04016005. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001339.
O’Brien, N. L., and D. H. Burn. 2014. “A nonstationary index-flood technique for estimating extreme quantiles for annual maximum streamflow.” J. Hydrol. 519: 2040–2048. https://doi.org/10.1016/j.jhydrol.2014.09.041.
Ouarda, T. B. M. J., and S. El-Adlouni. 2011. “Bayesian nonstationary frequency analysis of hydrological variables.” J. Am. Water Resour. Assoc. 47 (3): 496–505. https://doi.org/10.1111/j.1752-1688.2011.00544.x.
Prosdocimi, I., T. R. Kjeldsen, and J. D. Miller. 2015. “Detection and attribution of urbanization effect on flood extremes using nonstationary flood-frequency models.” Water Resour. Res. 51 (6): 4244–4262. https://doi.org/10.1002/2015WR017065.
Reddy, M. J., and P. Ganguli. 2012. “Bivariate flood frequency analysis of upper Godavari River flows using archimedean copulas.” Water Resour. Manage. 26 (14): 3995–4018. https://doi.org/10.1007/s11269-012-0124-z.
Salas, J. D., and J. Obeysekera. 2014. “Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events.” J. Hydrol. Eng. 19 (3): 554–568. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000820.
Sarhadi, A., D. H. Burn, M. Concepción Ausín, and M. P. Wiper. 2016. “Time varying nonstationary multivariate risk analysis using a dynamic Bayesian copula.” Water Resour. Res. 52 (3): 2327–2349. https://doi.org/10.1002/2015WR018525.
Serinaldi, F., A. Bárdossy, and C. G. Kilsby. 2015. “Upper tail dependence in rainfall extremes: Would we know it if we saw it?” Stochastic Environ. Res. Risk Assess. 29 (4): 1211–1233. https://doi.org/10.1007/s00477-014-0946-8.
Serinaldi, F., C. G. Kilsby, and F. Lombardo. 2018. “Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology.” Adv. Water Resour. 111: 132–155. https://doi.org/10.1016/j.advwatres.2017.10.015.
Shiau, J. T. 2003. “Return period of bivariate distributed extreme hydrological events.” Stochastic Environ. Res. Risk Assess. 17 (1–2): 42–57. https://doi.org/10.1007/s00477-003-0125-9.
Šraj, M., A. Viglione, J. Parajka, and G. Blöschl. 2016. “The influence of non-stationarity in extreme hydrological events on flood frequency estimation.” J. Hydrol. Hydromech. 64 (4): 426–437. https://doi.org/10.1515/johh-2016-0032.
Sugahara, S., R. P. Da Rocha, and R. Silveira. 2009. “Non-stationary frequency analysis of extreme daily rainfall in Sao Paulo, Brazil.” Int. J. Climatol. 29 (9): 1339–1349. https://doi.org/10.1002/joc.1760.
Tan, X., and T. Y. Gan. 2015. “Nonstationary analysis of annual maximum streamflow of Canada.” J. Climate 28 (5): 1788–1805. https://doi.org/10.1175/JCLI-D-14-00538.1.
Tawn, J. A. 1988. “Bivariate extreme value theory: Models and estimation.” Biometrika 75 (3): 397–415. https://doi.org/10.1093/biomet/75.3.397.
Trenberth, K. E. 2011. “Changes in precipitation with climate change.” Clim. Res. 47 (1): 123–138. https://doi.org/10.3354/cr00953.
Um, M. J., Y. Kim, M. Markus, and D. J. Wuebbles. 2017. “Modeling nonstationary extreme value distributions with nonlinear functions: An application using multiple precipitation projections for US cities.” J. Hydrol. 552: 396–406. https://doi.org/10.1016/j.jhydrol.2017.07.007.
Villarini, G., J. A. Smith, F. Serinaldi, J. Bales, P. D. Bates, and W. F. Krajewski. 2009. “Flood frequency analysis for nonstationary annual peak records in an urban drainage basin.” Adv. Water Resour. 32 (8): 1255–1266. https://doi.org/10.1016/j.advwatres.2009.05.003.
Vittal, H., J. Singh, P. Kumar, and S. Karmakar. 2015. “A framework for multivariate data-based at-site flood frequency analysis: Essentiality of the conjugal application of parametric and nonparametric approaches.” J. Hydrol. 525: 658–675. https://doi.org/10.1016/j.jhydrol.2015.04.024.
Yan, L., L. Xiong, S. Guo, C. Y. Xu, J. Xia, and T. Du. 2017a. “Comparison of four nonstationary hydrologic design methods for changing environment.” J. Hydrol. 551: 132–150. https://doi.org/10.1016/j.jhydrol.2017.06.001.
Yan, L., L. Xiong, D. Liu, T. Hu, and C. Y. Xu. 2017b. “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.
Yue, S. 1999. “Applying bivariate normal distribution to flood frequency analysis.” Water Int. 24 (3): 248–254. https://doi.org/10.1080/02508069908692168.
Yue, S. 2000. “The bivariate lognormal distribution to model a multivariate flood episode.” Hydrol. Process. 14 (14): 2575–2588. https://doi.org/10.1002/1099-1085(20001015)14:14%3C2575::AID-HYP115%3E3.0.CO;2-L.
Zhang, Q., X. Gu, V. P. Singh, M. Xiao, and X. Chen. 2015. “Evaluation of flood frequency under non-stationarity resulting from climate indices and reservoir indices in the East River basin, China.” J. Hydrol. 527: 565–575. https://doi.org/10.1016/j.jhydrol.2015.05.029.
Zheng, F., S. Westra, M. Leonard, and S. A. Sisson. 2014. “Modeling dependence between extreme rainfall and storm surge to estimate coastal flooding risk.” Water Resour. Res. 50 (3): 2050–2071. https://doi.org/10.1002/2013WR014616.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 24 • Issue 4 • April 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jan 5, 2018
Accepted: Nov 8, 2018
Published online: Feb 15, 2019
Published in print: Apr 1, 2019
Discussion open until: Jul 15, 2019
Authors
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.