Abstract
Two-sided extreme conditional sampling regularly is coupled with copula theory to assess the dependence between flood-risk drivers such as extreme precipitation or river discharge and storm surge. The approach involves many subjective choices, including sampling techniques used to identify extreme events [block maxima or peaks-over-threshold (POT)], whether to account for the fit of marginal distributions, and time-lags considered between the two drivers. In this study, estimates of the potential for compound events at three sites along the Texas Gulf Coast, where the USACE is undertaking coastal storm risk management (CSRM) projects, were shown to be highly sensitive to the setup of the statistical model. A pragmatic approach accounting for marginal fit in a POT framework is proposed and was shown to provide stable estimates of the compounding potential for high discharge and storm surge events. We also explored the effect of using precipitation as a proxy for discharge in the absence of sufficiently long discharge records.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The first and second authors acknowledge financial support from the USACE Climate Preparedness and Resilience Community of Practice and Programs. This material is based in part on work supported by the National Science Foundation under Grant AGS-192938.
References
Arns, A., T. Wahl, I. D. Haigh, J. Jensen, and C. Pattiaratchi. 2013. “Estimating extreme water level probabilities: A comparison of the direct methods and recommendations for best practise.” Coastal Eng. 81 (Nov): 51–66. https://doi.org/10.1016/j.coastaleng.2013.07.003.
Arns, A., T. Wahl, C. Wolff, A. T. Vafeidis, I. D. Haigh, P. Woodworth, S. Niehüser, and J. Jensen. 2020. “Non-linear interaction modulates global extreme sea levels, coastal flood exposure, and impacts.” Nat. Commun. 11 (Apr): 1918. https://doi.org/10.1038/s41467-020-15752-5.
Balkema, A. A., and L. De Haan. 1974. “Residual life time at great age.” Ann. Probab. 2 (5): 792–804. https://doi.org/10.1214/aop/1176996548.
Bender, J., T. Wahl, A. Müller, and J. Jensen. 2016. “A multivariate design framework for river confluences.” Hydrol. Sci. J. 61 (3): 471–482. https://doi.org/10.1080/02626667.2015.1052816.
Bevacqua, E., D. Maraun, I. Hobæk Haff, M. Widmann, and M. Vrac. 2017. “Multivariate statistical modelling of compound events via pair-copula constructions: Analysis of floods in Ravenna (Italy).” Hydrol. Earth Syst. Sci. 21 (6): 2701–2723. https://doi.org/10.5194/hess-21-2701-2017.
Bevacqua, E., D. Maraun, M. I. Vousdoukas, E. Voukouvalas, M. Vrac, L. Mentaschi, and M. Widmann. 2019. “Higher probability of compound flooding from precipitation and storm surge in Europe under anthropogenic climate change.” Sci. Adv. 5 (9): eaaw5531. https://doi.org/10.1126/sciadv.aaw5531.
Bevacqua, E., M. I. Vousdoukas, T. G. Shepherd, and M. Vrac. 2020a. “Brief communication: The role of using precipitation or river discharge data when assessing global coastal compound flooding.” Nat. Hazards Earth Syst. Sci. 20 (6): 1765–1782. https://doi.org/10.5194/nhess-20-1765-2020.
Bevacqua, E., M. I. Vousdoukas, G. Zappa, K. Hodges, T. G. Shepherd, D. Maraun, L. Mentaschi, and L. Feyen. 2020b. “More meteorological events that drive compound coastal flooding are projected under climate change.” Commun. Earth Environ. 1 (1): 1–11. https://doi.org/10.1038/s43247-020-00044-z.
Bilskie, M. V., and S. C. Hagen. 2018. “Defining flood zone transitions in low-gradient coastal regions.” Geophys. Res. Lett. 45 (6): 2761–2770. https://doi.org/10.1002/2018GL077524.
Blake, E. S., and D. A. Zelinsky. 2018. Hurricane Harvey (National Hurricane center tropical cyclone report). Washington, DC: National Oceanic and Atmospheric Administration.
BRA (Brazos River Authority). 2019. Lower Brazos flood protection planning study. Richardson, TX: Halff Associates.
Brauer, N. S., J. B. Basara, C. R. Homeyer, G. M. McFarquhar, and P. E. Kirstetter. 2020. “Quantifying precipitation efficiency and drivers of excessive precipitation in post-landfall Hurricane Harvey.” J. Hydrometeorol. 21 (3): 433–452. https://doi.org/10.1175/JHM-D-19-0192.1.
Brazos BBEST (Brazos River Basin and Bay Expert Science Team). 2012. Brazos River basin and bay expert science team environmental flow regime recommendations report. Austin, TX: Environmental Flows Advisory Group and the Texas Commission on Environmental Quality.
Bunya, S., et al. 2010. “A high-resolution coupled riverine flow, tide, wind, wind wave, and storm surge model for southern Louisiana and Mississippi. Part I: Model development and validation.” Mon. Weather Rev. 138 (2): 345–377. https://doi.org/10.1175/2009MWR2906.1.
Camus, P., I. Haigh, T. Wahl, A. Nasr, S. E. Darby, and R. J. Nicholls. 2021. “Regional analysis of multivariate compound coastal flooding potential around Europe and environs: sensitivity analysis and spatial patterns.” Nat. Hazards Earth Syst. Sci. 21 (2). https://doi.org/10.5194/nhess-21-2021-2021.
Couasnon, A., D. Eilander, S. Muis, T. I. E. Veldkamp, I. D. Haigh, T. Wahl, H. C. Winsemius, and P. J. Ward. 2020. “Measuring compound flood potential from river discharge and storm surge extremes at the global scale.” Nat. Hazards Earth Syst. Sci. 20 (2): 489–504. https://doi.org/10.5194/nhess-20-489-2020.
Couasnon, A., A. Sebastian, and O. Morales-Nápoles. 2018. “A copula-based Bayesian network for modeling compound flood hazard from riverine and coastal interactions at the catchment scale: An application to the Houston ship channel, Texas.” Water 10 (9): 1190. https://doi.org/10.3390/w10091190.
Duong, T. 2007. “ks: Kernel density estimation and kernel discriminant analysis for multivariate data in R.” J. Stat. Software 21 (7): 1–16. https://doi.org/10.18637/jss.v021.i07.
FEMA. 2015. Guidance for flood risk analysis and mapping; combined coastal and riverine floodplain. Washington, DC: FEMA.
Ganguli, P., and B. Merz. 2019. “Extreme coastal water levels exacerbate fluvial flood hazards in northwestern Europe.” Sci. Rep. 9 (1): 1–14. https://doi.org/10.1038/s41598-019-49822-6.
Ghanbari, M., M. Arabi, S.-C. Kao, J. Obeysekera, and W. Sweet. 2021. “Climate change and changes in compound coastal-riverine flooding hazard along the U.S. coasts.” Earth’s Future 9: e2021EF002055. https://doi.org/10.1029/2021EF002055.
Gnedenko, B. V. 1943. “Sur la distribution limite du terme maximum d’une serie aleatoire.” Ann. Math. 44 (3): 423–453. https://doi.org/10.2307/1968974.
Gori, A., N. Lin, and J. Smith. 2020. “Assessing compound flooding from landfalling tropical cyclones on the North Carolina coast.” Water Resour. Res. 56 (4): e2019WR026788. https://doi.org/10.1029/2019WR026788.
Gräler, B., M. J. van den Berg, S. Vandenberghe, A. Petroselli, S. Grimaldi, B. De Baets, and N. E. C. 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.
Hendry, A., I. D. Haigh, R. J. Nicholls, H. Winter, R. Neal, T. Wahl, A. Joly-Laugel, and S. E. Darby. 2019. “Assessing the characteristics and drivers of compound flooding events around the UK coast.” Hydrol. Earth Syst. Sci. 23 (7): 3117–3139. https://doi.org/10.5194/hess-23-3117-2019.
Jane, R., L. Cadavid, J. Obeysekera, and T. Wahl. 2020. “Multivariate statistical modelling of the drivers of compound flood events in South Florida.” Nat. Hazards Earth Syst. Sci. Discuss. 20 (10): 2681–2699. https://doi.org/10.5194/nhess-2020-82.
Keef, C., C. Svensson, and J. A. Tawn. 2009. “Spatial dependence in extreme river flows and precipitation for Great Britain.” J Hydrol. 378: 240–252. https://doi.org/10.1016/j.jhydrol.2009.09.026.
Kumbier, K., R. C. Carvalho, A. T. Vafeidis, and C. D. Woodroffe. 2018. “Investigating compound flooding in an estuary using hydrodynamic modelling: A case study from the Shoalhaven River, Australia.” Nat. Hazards Earth Syst. Sci. 18 (2): 463–477. https://doi.org/10.5194/nhess-18-463-2018.
Lian, J. J., K. Xu, and C. Ma. 2013. “Joint impact of rainfall and tidal level on flood risk in a coastal city with a complex river network: A case study of Fuzhou City, China.” Hydrol. Earth Syst. Sci. 17 (2): 679. https://doi.org/10.5194/hess-17-679-2013.
Moftakhari, H., J. E. Schubert, A. AghaKouchak, R. A. Matthew, and B. F. Sanders. 2019. “Linking statistical and hydrodynamic modeling for compound flood hazard assessment in tidal channels and estuaries.” Adv. Water Resour. 128 (Jun): 28–38. https://doi.org/10.1016/j.advwatres.2019.04.009.
Moftakhari, H. R., G. Salvadori, A. AghaKouchak, B. F. Sanders, and R. A. Matthew. 2017. “Compounding effects of sea level rise and fluvial flooding.” Proc. Natl. Acad. Sci. U.S.A. 114 (37): 9785–9790. https://doi.org/10.1073/pnas.1620325114.
Nasr, A. A., T. Wahl, M. M. Rashid, P. Camus, and I. D. Haigh. 2021. “Assessing the dependence structure between oceanographic, fluvial, and pluvial flooding drivers along the United States coastline.” Hydrol. Earth Syst. Sci. Discuss. https://doi.org/10.5194/hess-2021-268.
NOAA (National Oceanic and Atmospheric Administration). 2020a. Billion-dollar weather and climate disasters: Table of events. Washington, DC: NOAA.
NOAA (National Oceanic and Atmospheric Administration). 2020b. “Climate data online.” Accessed April 30, 2020. https://www.ncdc.noaa.gov/cdo-web.
NOAA (National Oceanic and Atmospheric Administration). 2020c. “High and low water conditions.” Accessed April 30, 2020. https://tidesandcurrents.noaa.gov.
Northrop, P. J., N. Attalides, and P. Jonathan. 2017. “Cross-validatory extreme value threshold selection and uncertainty with application to ocean storm severity.” J. R. Stat. Soc. Ser. C Appl. Stat. 66 (1): 93–120. https://doi.org/10.1111/rssc.12159.
OCDD and TWDB (Orange County Drainage District and Texas Water Development Board). 2015. Flood protection planning study, Cow and Adams Bayou, Orange County Texas. Beaumont, TX: Carroll & Blackman.
Paprotny, D., M. I. Vousdoukas, O. Morales-Nápoles, S. N. Jonkman, and L. Feyen. 2018. “Compound flood potential in Europe.” Hydrol. Earth Syst. Sci. Discuss. 1–34. https://doi.org/10.5194/hess-2018-132.
Parsons. 2006. Nonpoint source modeling of the watersheds of Adams and Cow Bayous. Austin, TX: Texas Commission on Environmental Quality.
Pettitt, A. 1979. “A non-parametric approach to the change-point problem.” J. R. Stat. Soc. Ser. C Appl. Stat. 28 (2): 126–135. https://doi.org/10.2307/2346729.
Pickands, J. 1975. “Statistical inference using extreme order statistics.” Ann. Stat. 3: 119–131. https://doi.org/10.1214/aos/1176343003.
Rahmani, V., S. L. Hutchinson, J. A. Harrington Jr., J. M. S. Hutchinson, and A. Anandhi. 2015. “Analysis of temporal and spatial distribution and change-points for annual precipitation in Kansas, USA.” Int. J. Climatol. 35 (13): 3879–3887. https://doi.org/10.1002/joc.4252.
Ridder, N. N., A. J. Pitman, S. Westra, A. Ukkola, H. X. Do, M. Bador, A. L. Hirsch, J. P. Evans, A. Di Luca, and J. Zscheischler. 2020. “Global hotspots for the occurrence of compound events.” Nat. Commun. 11 (1): 5956. https://doi.org/10.1038/s41467-020-19639-3.
Salas, J. D. 1993. “Analysis and modeling of hydrologic time series.” In Handbook of hydrology, edited by D. Maidment, 19.1–19.72. New York: McGraw-Hill.
Salvadori, G., and C. De Michele. 2013. “Multivariate extreme value methods.” In Vol. 65 of Extremes in a changing climate, water science and technology library, edited by A. AghaKouchak, D. Easterling, K. Hsu, S. Schubert, and S. Sorooshian, 115–162. Berlin: Springer.
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.
Santiago-Collazo, F. L., M. V. Bilskie, and S. C. Hagen. 2019. “A comprehensive review of compound inundation models in low-gradient coastal watersheds.” Environ. Modell. Software 119 (Sep): 166–181. https://doi.org/10.1016/j.envsoft.2019.06.002.
Santos, V. M., M. Casas-Prat, B. Poschlod, E. Ragno, B. van den Hurk, Z. Hao, T. Kalmár, L. Zhu, and H. Najafi. 2021a. “Statistical modelling and climate variability of compound surge and precipitation events in a managed water system: A case study in the Netherlands.” Hydrol. Earth Syst. Sci. 25 (6): 3595–3615. https://doi.org/10.5194/hess-25-3595-2021.
Santos, V. M., T. Wahl, R. Jane, S. K. Misra, and K. D. White. 2021b. “Assessing compound flooding potential with multivariate statistical models in a complex estuarine system under data constraints.” J. Flood Risk Manage. 14 (4): e12749. https://doi.org/10.1111/jfr3.12749.
Schepsmeier, U., J. Stoeber, E. Brechmann, B. Graeler, T. Nagler, T. Erhardt, C. Almeida, A. Min, C. Czado, and M. Hofmann. 2015. “Package ‘VineCopula’.” Accessed May 6, 2019. https://github.com/tnagler/VineCopula.
Sebastian, A., E. J. C. Dupuits, and P. Morales Nápoles. 2017. “Applying a Bayesian network based on Gaussian copulas to model the hydraulic boundary conditions for hurricane flood risk analysis in a coastal watershed.” Coastal Eng. 125 (Jul): 42–50. https://doi.org/10.1016/j.coastaleng.2017.03.008.
Sebastian, A., A. Gori, R. B. Blessing, K. van der Wiel, and B. Bass. 2019. “Disentangling the impacts of human and environmental change on catchment response during Hurricane Harvey.” Environ. Res. Lett. 14 (12): 124023. https://doi.org/10.1088/1748-9326/ab5234.
Serafin, K. A., and P. Ruggiero. 2014. “Simulating extreme total water levels using a time-dependent, extreme value approach.” J. Geophys. Res. Oceans 119: 6305–6329.
Serafin, K. A., P. Ruggiero, K. Parker, and D. F. Hill. 2019. “What’s streamflow got to do with it? A probabilistic simulation of the competing oceanographic and fluvial processes driving extreme along-river water levels.” Nat. Hazards Earth Syst. Sci. 19 (7): 1415–1431. https://doi.org/10.5194/nhess-19-1415-2019.
Serinaldi, F. 2015. “Dismissing return periods.” Stoch. Environmental Res. Risk A. 29 (4): 1179–1189. https://doi.org/10.1007/s00477-014-0916-1.
Sharma, S., D. Swayne, and C. Obimbo. 2016. “Trend analysis and change point techniques: A survey.” Energy Ecol. Environ. 1 (3): 123–130. https://doi.org/10.1007/s40974-016-0011-1.
Solari, S., M. Egüen, M. Polo, and M. Losada. 2017. “Peaks over threshold (POT): A methodology for automatic threshold estimation using goodness of fit p-value.” Water Resour. Res. 53 (4): 2833–2849. https://doi.org/10.1002/2016WR019426.
TIFP and BRA (Texas Instream Flow Program and Brazos River Authority). 2010. Instream flow study of the middle and lower Brazos River: Draft study design. Austin, TX: Texas Water Development Board.
Tosunoglu, F., F. Gürbüz, and M. N. Ispirli. 2020. “Multivariate modeling of flood characteristics using Vine copulas.” Environ. Earth Sci. 79 (19): 459–479. https://doi.org/10.1007/s12665-020-09199-6.
Valle-Levinson, A., M. Olabarrieta, and L. Heilman. 2020. “Compound flooding in Houston-Galveston Bay during Hurricane Harvey.” Sci. Total Environ. 747 (Dec): 141272. https://doi.org/10.1016/j.scitotenv.2020.141272.
Wahl, T., S. Jain, J. Bender, S. D. Meyers, and M. E. Luther. 2015. “Increasing risk of compound flooding from storm surge and rainfall for major US cities.” Nat. Clim. Change 5 (12): 1093–1097. https://doi.org/10.1038/nclimate2736.
Ward, P. J., A. Couasnon, D. Eilander, I. D. Haigh, A. Hendry, S. Muis, T. I. E. Veldkamp, H. C. Winsemius, and T. Wahl. 2018. “Dependence between high sea-level and high river discharge increases flood hazard in global deltas and estuaries.” Environ. Res. Lett. 13 (8): 084012 https://doi.org/10.1088/1748-9326/aad400.
Watson, K., G. Harwell, D. Wallace, T. Welborn, V. Stengel, and J. McDowell. 2018. Characterization of peak streamflows and flood inundation of selected areas in southeastern Texas and southwestern Louisiana from the August and September 2017 flood resulting from Hurricane Harvey. Washington, DC: USGS.
Wu, W., K. McInnes, J. O’Grady, R. Hoeke, M. Leonard, and S. Westra. 2018. “Mapping dependence between extreme rainfall and storm surge.” J. Geophys. Res. 123 (4): 2461–2474. https://doi.org/10.1002/2017JC013472.
Wu, W., S. Westra, and M. Leonard. 2021. “Estimating the probability of compound floods in estuarine regions.” Hydrol. Earth Syst. Sci. 25 (5): 2821–2841. https://doi.org/10.5194/hess-25-2821-2021.
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.
Zheng, F., S. Westra, and S. A. Sisson. 2013. “Quantifying the dependence between extreme rainfall and storm surge in the coastal zone.” J. Hydrol. 505 (Nov): 172–187. https://doi.org/10.1016/j.jhydrol.2013.09.054.
Zscheischler, J., et al. 2018. “Future climate risk from compound events.” Nat. Clim. Change 8 (6): 469–477. https://doi.org/10.1038/s41558-018-0156-3.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 27 • Issue 3 • March 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Mar 9, 2021
Accepted: Oct 19, 2021
Published online: Jan 13, 2022
Published in print: Mar 1, 2022
Discussion open until: Jun 13, 2022
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.
Cited by
- R. A. Jane, V. Malagón‐Santos, M. M. Rashid, L. Doebele, T. Wahl, S. R. Timmers, K. A. Serafin, L. Schmied, C. Lindemer, A Hybrid Framework for Rapidly Locating Transition Zones: A Comparison of Event‐ and Response‐Based Return Water Levels in the Suwannee River FL, Water Resources Research, 10.1029/2022WR032481, 58, 11, (2022).
- Avantika Gori, Ning Lin, Projecting Compound Flood Hazard Under Climate Change With Physical Models and Joint Probability Methods, Earth's Future, 10.1029/2022EF003097, 10, 12, (2022).
- Peyman Abbaszadeh, David F. Muñoz, Hamed Moftakhari, Keighobad Jafarzadegan, Hamid Moradkhani, Perspective on uncertainty quantification and reduction in compound flood modeling and forecasting, iScience, 10.1016/j.isci.2022.105201, 25, 10, (105201), (2022).
- C. Lyddon, P. Robins, M. Lewis, A. Barkwith, G. Vasilopoulos, I. Haigh, T. Coulthard, Historic Spatial Patterns of Storm-Driven Compound Events in UK Estuaries, Estuaries and Coasts, 10.1007/s12237-022-01115-4, 46, 1, (30-56), (2022).