Abstract
Most flood risk studies quantify flood likelihood and damage as functions of depth. The length of time that a flood remains above a stage (duration) is also necessary to quantify infrastructure vulnerability. The proposed approach adds a second dimension, time, into flood risk studies by developing a joint distribution of flood stage and event duration. Bivariate flood frequency model metrics are developed; the metrics are illustrated using data from four gauged sites, two riverine and two tidal. It is concluded that a general joint distribution model is applicable to both riverine and tidal sites. A minimum time between events (interevent time) determines the assignment of sequential periods to a single event or multiple events; this measure is shown to affect the statistics of the tidal sites, but not the riverine sites. The flood stage-duration-frequency curves developed in this study demonstrate a new approach that allows stakeholders to consider the coupling between depth and duration, and thereby develop preparedness and response plans that address temporal aspects such as time out of service in addition to depth-dependent damages.
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Acknowledgments
This research was supported by District of Columbia Water and Sewer Authority (DC Water), through Grant No. 120809. The authors thank two anonymous reviewers for their comments and suggestions.
References
Allsop, N. W. H., Kortenhaus, A., and Morris, M. (2007). “Failure mechanisms for flood defence structures.”, HR Wallingford, Wallingford, Oxfordshire, U.K.
Bačová Mitková, V., and Halmová, D. (2014). “Joint modeling of flood peak discharges, volume and duration: A case study of the Danube River in Bratislava.” J. Hydrol. Hydromech., 62(3), 186–196.
Chang, T. J. (1990). “Effects of drought on streamflow characteristics.” J. Irrig. Drain. Eng., 332–341.
Chebana, F., and Ouarda, T. B. M. J. (2011). “Multivariate quantiles in hydrological frequency analysis.” Envirometrics, 22(1), 63–78.
Cunderlik, J. M., and Ouarda, T. B. M. J. (2006). “Regional flood-duration-frequency modeling in the changing environment.” J. Hydrol., 318(1–4), 276–291.
Davis, D., Faber, B. A., and Stedinger, J. R. (2008). “USACE experience in implementing risk analysis for flood damage reduction projects.” J. Contemp. Water Res. Educ., 140(1), 3–14.
Dutta, D., Herath, S., and Musiake, K. (2003). “A mathematical model for flood loss estimation.” J. Hydrol., 277(1–2), 24–49.
Eagleson, P. S. (1972). “Dynamics of flood frequency.” Water Resour. Res., 8(4), 878–898.
FEMA. (2006). “Overview of Hurricane Katrina in the New Orleans area.” FEMA 459, Hurricane Katrina in the Gulf Coast: Mitigation assessment team report, building performance observations, recommendations, and technical guidance. Chapter 8. ⟨https://www.fema.gov/media-library/assets/documents/4069⟩ (Apr. 2016).
FEMA. (2009). “Multi-hazard loss estimation methodology flood model, HAZUS-MH MR4 technical manual.” Washington, DC.
Ferreira, L. V., and Stohlgren, T. J. (1999). “Effects of river level fluctuation on plant species richness, diversity, and distribution in a floodplain forest in Central Amazonia.” Oecologia, 120(4), 582–587.
Griffin, J. L., and Saxton, A. M. (1988). “Response of solid-seeded soybean to flood irrigation. II: Flood duration.” Agron. J., 80(6), 885–888.
Guerrero-Salazar, P., and Yevjevich, V. (1975). “Analysis of drought characteristics by the theory of runs.”, Colorado State Univ., Fort Collins, CO.
Gumbel, E. J., and Lieblein, J. (1954). “Statistical theory of extreme values and some practical applications: A series of lectures.”, U.S. Government Printing Office, Washington, DC.
Jaffe, D. A., and Sanders, B. F. (2001). “Engineered levee breaches for flood mitigation.” J. Hydraul. Eng., 471–479.
Javelle, P., Ouarda, T. B. M. J., and Bobée, B. (2003). “Spring flood analysis using the flood-duration-frequency approach: Application to the provinces of Quebec and Ontario, Canada.” Hydrol. Process., 17(18), 3717–3736.
Javelle, P., Ouarda, T. B. M. J., Lang, M., Bobée, B., Galéa, G., and Grésillon, J. M. (2002). “Development of regional flood-duration-frequency curves based on the index-flood method.” J. Hydrol., 258(1), 249–259.
Jonkman, S. N. (2007). “Loss of life estimation in flood risk assessment—Theory and applications.” Ph.D. dissertation, Delft Univ. of Technology, Delft, Netherlands.
Kayen, R., Collins, B., and Gibbons, H. (2006). “USGS scientists investigate new Orleans levees broken by Hurricane Katrina.” ⟨https://soundwaves.usgs.gov/2006/01/⟩ (Apr. 2016).
Kent, R., and Johnson, D. (2001). “Influence of flood depth and duration on growth of lowland rice weeds, Cote d’Ivoire.” Crop Prot., 20(8), 691–694.
Kenward, A., Yawitz, D., and Raja, U. (2013). Sewage overflows from Hurricane Sandy, Climate Central, Princeton, NJ.
Law, G. S. (2002). Duration and frequency analysis of lowland flooding in western Murfreesboro, Rutherford County, Tennessee, 1998–2000, U.S. Dept. of the Interior, U.S. Geological Survey, Nashville, TN.
Leclerc, G., and Schaake, J. C. (1972). “Derivation of hydrologic frequency curves.”, Massachusetts Institute of Technology, Cambridge, MA.
Lekuthai, A., and Vongvisessomjai, S. (2001). “Intangible flood damage quantification.” Water Resour. Manage., 15(5), 343–362.
Messner, F., and Meyer, V. (2006). “Flood damage, vulnerability and risk perception–challenges for flood damage research.” Flood risk management: Hazards, vulnerability and mitigation measures, Springer, Dordrecht, Netherlands, 149–167.
Mishra, A. K., and Singh, V. P. (2011). “Drought modeling: A review.” J. Hydrol., 403(1), 157–175.
Nirupama, N., Armenakis, C., and Montpetit, M. (2014). “Is flooding in Toronto a concern?” Nat. Hazards, 72(2), 1259–1264.
NOAA (National Oceanic and Atmospheric Administration). (2016a). “The Battery, NY—Station ID: 8518750.” ⟨https://tidesandcurrents.noaa.gov/stationhome.html?id=8518750⟩ (Jan. 2015).
NOAA (National Oceanic and Atmospheric Administration). (2016b). “Washington, DC—Station ID: 8594900.” ⟨http://tidesandcurrents.noaa.gov/stationhome.html?id=8594900⟩ (Jan. 2015).
Penning-Rowsell, E. C., et al. (2003). The benefits of flood and coastal defence: Techniques and data for 2003, Flood Hazard Research Centre, Middlesex Univ., London.
Pfurtscheller, C., and Schwarze, R. (2008). “Estimating the costs of emergency services during flood events.” Proc., 4th Int. Symp. on Flood Defence, Institute for Catastrophic Loss Reduction, Toronto.
Rodríguez-Iturbe, I. (1969). “Applications of the theory of runs to hydrology.” Water Resour. Res., 5(6), 1422–1426.
Scott, H., DeAngulo, J., Daniels, M., and Wood, L. (1989). “Flood duration effects on soybean growth and yield.” Agron. J., 81(4), 631–636.
Shiau, J., and Shen, H. (2001). “Recurrence analysis of hydrologic droughts of differing severity.” J. Water Resour. Plann. Manage., 30–40.
Singh, V. P. (1998). “Generalized extreme value distribution.” Entropy-based parameter estimation in hydrology, Kluwer Academic Publishers, Dordrecht, Netherlands, 169–183.
Smith, J. A. (1987). “Estimating the upper tail of flood frequency distributions.” Water Resour. Res., 23(8), 1657–1666.
Soetanto, R., and Proverbs, D. G. (2004). “Impact of flood characteristics on damage caused to UK domestic properties: The perceptions of building surveyors.” Struct. Surv., 22(2), 95–104.
Tawn, J. A. (1992). “Estimating probabilities of extreme sea-levels.” J. R. Stat. Soc.: Series C (Appl. Statist.), 41(1), 77–93.
USACE (U.S. Army Corps of Engineers). (1995). “Flood proofing regulations.”, Washington, DC.
USEPA (U.S. Environmental Protection Agency). (2008). Methods for evaluating wetland condition: Wetland hydrology, Office of Water, Washington, DC.
USGS. (2016a). “USGS 01570500 Susquehanna River at Harrisburg, PA.” ⟨http://waterdata.usgs.gov/nwis/nwismap/?site_no=01570500&agency_cd=USGS⟩ (Jan. 2015).
USGS. (2016b). “USGS 01583500 Western Run at Western Run, MD.” ⟨http://waterdata.usgs.gov/nwis/nwismap/?site_no=01583500&agency_cd=USGS⟩ (Jan. 2015).
Wagenaar, D. J. (2012). “The significance of flood duration for flood damage assessment.” Master thesis, Delft Univ. of Technology, Delft, Netherlands.
Walshaw, D. (2013). “Generalized extreme value distribution.” Encyclopedia of environmetrics, 2nd Ed., A. H. El-Shaarawi and W. W. Piegorsch, eds., Wiley, Chichester, U.K.
Yevjevich, V. (1967). “An objective approach to definitions and investigations of continental hydrologic droughts.”, Colorado State Univ., Fort Collins, CO.
Yue, S. (2001). “A bivariate gamma distribution for use in multivariate flood frequency analysis.” Hydrol. Process., 15(6), 1033–1045.
Yue, S., Ouarda, T. B. M. J., Bobée, B., Legendre, P., and Bruneau, P. (1999). “The Gumbel mixed model for flood frequency analysis.” J. Hydrol., 226(1), 88–100.
Zhang, Z., Wu, Z., and Martinez, M. (2008). “Pavement structures damage caused by Hurricane Katrina flooding.” J. Geotech. Geoenv. Eng., 633–643.
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©2017 American Society of Civil Engineers.
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Received: May 31, 2016
Accepted: May 3, 2017
Published online: Sep 13, 2017
Published in print: Nov 1, 2017
Discussion open until: Feb 13, 2018
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