# 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

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Bayesian Networks

#### 2.2. Data Collection

^{2}) exposed to intense rainfall events from local convective storms, large-scale frontal systems, and torrential rainfall brought by tropical cyclones. Historical records of flood events reported as major by the Federal Emergency Management Agency (FEMA) indicate a relatively equal importance of these different flood sources [18]. The response of the catchment to extreme rainfall has been further exacerbated by rapid development which has occurred over the century [63], leading to faster runoff rates and larger flood volumes [64,65].

**Discharge:**Mean daily discharges were collected from the U.S. Geological Survey at the locations shown in Figure 2a. The available period of data varied significantly per station, with records starting between 1936 and 1971. Abrupt changes in the discharge data series indicate a possible sign of anthropogenic influences on the hydrologic response of the catchment [66,67]. We identified the most important change in mean in the data series (function findchangepts() in MATLAB), which, at most stations, was found to be located between 1970 and 1980 (for details see Section S1.1 in Supplementary Material). Therefore, we selected data from 1 January 1980 onwards to represent the current developed state of the catchment and assumed stationary conditions between 1980 and 2016. Of the seven stations, four stations had a very high temporal coverage for this period (>97%), and three had a limited to poor coverage (9–43%).

**Storm surge:**Hourly water levels and astronomical tide projections were obtained from the National Oceanic and Atmospheric Administration (NOAA) for the LL and Galveston Pier 21 (GP) tide stations, Figure 2a,b. The LL tide station has a limited record length, about 11 years worth of data scattered between 1995 and 2014, compared to 113 years from 1904 to 2016 at GP. At both stations, hourly non-tidal residuals were calculated by subtracting the measured water level from the predicted astronomical tide. The maximum hourly non-tidal residuals in a day is set to be the daily non-tidal residual, what is referred to the storm surge in this study. Data for GP were further corrected for mean sea-level rise using a linear regression of the hourly non-tidal residuals of the whole record length, 1904–2016. This was not possible for the LL tide station, so we assumed stationarity of the available data.

#### 2.3. Bayesian Network Construction

#### 2.4. 1D Hydraulic Model

^{2}> 0.98) [79]. Moreover, the model was also validated for Tropical Storm Frances (11 September 1998) and Tropical Storm Allison (6 June and 9 June 2001) and showed a reasonable performance, considering that water level observations from tropical cyclone events often have high uncertainty [80]. Results and figures from the runs are shown in Sections S4.2 and S4.3 in Supplementary Material.

## 3. Results

- Case A: The 100-year marginal return period for each discharge variable and the storm surge variable is calculated and modeled. This represents the (untrue) assumption of full dependence.
- Case B: The boundary conditions of the model are set to the marginal 100-year return period for the storm surge downstream, and the distribution mean for the upstream boundary conditions. This represents the (untrue) assumption of physical ‘independence’ between the downstream water level and the discharge. Such an approach is comparable to a bathtub approach [84], even though in the latter method discharges are usually completely neglected and not modeled.

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Kron, W. Coasts: The high-risk areas of the world. Nat. Hazards
**2013**, 66, 1363–1382. [Google Scholar] [CrossRef] - Rueda, A.; Camus, P.; Tomás, A.; Vitousek, S.; Méndez, F.J. A multivariate extreme wave and storm surge climate emulator based on weather patterns. Ocean Model.
**2016**, 104, 242–251. [Google Scholar] [CrossRef] - Neumann, B.; Vafeidis, A.T.; Zimmermann, J.; Nicholls, R.J. Future coastal population growth and exposure to sea-level rise and coastal flooding—A global assessment. PLoS ONE
**2015**, 10. [Google Scholar] [CrossRef] - Hallegatte, S.; Green, C.; Nicholls, R.J.; Corfee-Morlot, J. Future flood losses in major coastal cities. Nat. Clim. Chang.
**2013**, 3, 802–806. [Google Scholar] [CrossRef] - Sebastian, A.; Dupuits, E.J.C.; Morales-Nápoles, O. Applying a Bayesian network based on Gaussian copulas to model the hydraulic boundary conditions for hurricane flood risk analysis in a coastal watershed. Coast. Eng.
**2017**, 125, 42–50. [Google Scholar] [CrossRef] - Svensson, C.; Jones, D.A. Dependence between sea surge, river flow and precipitation in south and west Britain. Hydrol. Earth Syst. Sci.
**2004**, 8, 973–992. [Google Scholar] [CrossRef][Green Version] - Saleh, F.; Ramaswamy, V.; Wang, Y.; Georgas, N.; Blumberg, A.; Pullen, J. A Multi-Scale Ensemble-based Framework for Forecasting Compound Coastal-Riverine Flooding: The Hackensack-Passaic Watershed and Newark Bay. Adv. Water Resour.
**2017**, 110, 371–386. [Google Scholar] [CrossRef] - Needham, H.F.; Keim, B.D.; Sathiaraj, D. A review of tropical cyclone-generated storm surges: Global data sources, observations, and impacts. Rev. Geophys.
**2015**, 53, 545–591. [Google Scholar] [CrossRef][Green Version] - Karl, T.R.; Melillo, J.M.; Peterson, T.C. Global Climate Change Impacts in the United States; Cambridge University Press: Cambridge, UK; New York, NY, USA, 2009; ISBN 9780521144070. [Google Scholar]
- Pielke, J.R.; Roger, A.; Gratz, J.; Landsea, C.W.; Collins, D.; Saunders, M.A.; Musulin, R. Normalized Hurricane Damage in the United States: 1900–2005. Nat. Hazards Rev.
**2008**, 9, 29–42. [Google Scholar] [CrossRef] - Zheng, F.; Leonard, M.; Westra, S. Application of the design variable method to estimate coastal flood risk. J. Flood Risk Manag.
**2015**. [Google Scholar] [CrossRef] - Klerk, W.J.; Winsemius, H.C.; van Verseveld, W.J.; Bakker, A.M.R.; Diermanse, F.L.M. The co-incidence of storm surges and extreme discharges within the Rhine–Meuse Delta. Environ. Res. Lett.
**2015**, 10, 035005. [Google Scholar] [CrossRef][Green Version] - Allen, G.H.; David, C.H.; Andreadis, K.M.; Hossain, F.; Famiglietti, J.S. Global Estimates of River Flow Wave Travel Times and Implications for Low-Latency Satellite Data. Geophys. Res. Lett.
**2018**. [Google Scholar] [CrossRef] - Zscheischler, J.; Westra, S.; van den Hurk, B.J.J.M.; Seneviratne, S.I.; Ward, P.J.; Pitman, A.; AghaKouchak, A.; Bresch, D.N.; Leonard, M.; Wahl, T.; et al. Future climate risk from compound events. Nat. Clim. Chang.
**2018**, 8, 469–477. [Google Scholar] [CrossRef] - Field, C.B.; Barros, V.; Stocker, T.F.; Dahe, Q.; Dokken, D.J.; Ebi, K.L.; Mastrandrea, M.D.; Mach, K.J.; Plattner, G.-K.; Allen, S.K.; et al. Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation. A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change; Cambridge University Press: Cambridge, UK, 2012; ISBN 978-1-107-60780-4. [Google Scholar]
- Wahl, T.; Jain, S.; Bender, J.; Meyers, S.D.; Luther, M.E. Increasing risk of compound flooding from storm surge and rainfall for major US cities. Nat. Clim. Chang.
**2015**, 5, 1093–1097. [Google Scholar] [CrossRef] - Federal Emergency Management Agency. Guidance for Flood Risk Analysis and Mapping; Combined Coastal and Riverine; Federal Emergency Management Agency: Washington, DC, USA, 2015. [Google Scholar]
- Federal Emergency Management Agency. Flood Insurance Study. Harris County, Texas and Incorporated Areas; Federal Emergency Management Agency: Washington, DC, USA, 2017; Volumes 1–2. [Google Scholar]
- Ward, P.; Jongman, B.; Salamon, P.; Simpson, A.; Bates, P.; De Groeve, T.; Muis, S.; de Perez, E.C.; Rudari, R.; Trigg, M.A.; Winsemius, H. Usefulness and limitations of global flood risk models. Nat. Clim. Chang.
**2015**, 5, 712–715. [Google Scholar] [CrossRef] - Muis, S.; Verlaan, M.; Winsemius, H.C.; Aerts, J.C.J.H.; Ward, P.J. A global reanalysis of storm surges and extreme sea levels. Nat. Commun.
**2016**, 7, 11969. [Google Scholar] [CrossRef] [PubMed][Green Version] - Cid, A.; Camus, P.; Castanedo, S.; Méndez, F.J.; Medina, R. Global reconstructed daily surge levels from the 20th Century Reanalysis (1871–2010). Glob. Planet. Chang.
**2017**, 148, 9–21. [Google Scholar] [CrossRef] - Vousdoukas, M.I.; Voukouvalas, E.; Mentaschi, L.; Dottori, F.; Giardino, A.; Bouziotas, D.; Bianchi, A.; Salamon, P.; Feyen, L. Developments in large-scale coastal flood hazard mapping. Nat. Hazards Earth Syst. Sci.
**2016**, 16, 1841–1853. [Google Scholar] [CrossRef][Green Version] - Winsemius, H.C.; Van Beek, L.P.H.; Jongman, B.; Ward, P.J.; Bouwman, A. A framework for global river flood risk assessments. Hydrol. Earth Syst. Sci.
**2013**, 17, 1871–1892. [Google Scholar] [CrossRef][Green Version] - Ward, P.; Jongman, B.; Weiland, F.; Bouwman, A.; van Beek, R.; Bierkens, M.; Ligtvoet, W.; Winsemius, H. Assessing flood risk at the global scale: Model setup, results, and sensitivity. Environ. Res. Lett.
**2013**, 8, 44019. [Google Scholar] [CrossRef][Green Version] - Maskell, J.; Horsburgh, K.; Lewis, M.; Bates, P. Investigating River-Surge Interaction in Idealised Estuaries. J. Coast. Res.
**2014**, 294, 248–259. [Google Scholar] [CrossRef] - Ray, T.; Stepinski, E.; Sebastian, A.; Bedient, P.B. Dynamic Modeling of Storm Surge and Inland Flooding in a Texas Coastal Floodplain. J. Hydraul. Eng.
**2011**, 137, 1103–1111. [Google Scholar] [CrossRef] - Kumbier, K.; Carvalho, R.C.; Vafeidis, A.T.; Woodroffe, C.D. Investigating compound flooding in an estuary using hydrodynamic modelling: A case study from the Shoalhaven River, Australia. Nat. Hazards Earth Syst. Sci.
**2018**, 2, 463–477. [Google Scholar] [CrossRef] - Bevacqua, E.; Maraun, D.; Hobæk Haff, I.; Widmann, M.; Vrac, M. Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy). Hydrol. Earth Syst. Sci.
**2017**, 21, 2701–2723. [Google Scholar] [CrossRef][Green Version] - Zheng, F.; Leonard, M.; Westra, S. Efficient joint probability analysis of flood risk. J. Hydroinform.
**2015**, 17, 584–597. [Google Scholar] [CrossRef] - Hawkes, P.J.; Gouldby, B.P.; Tawn, J.A.; Owen, M.W. The joint probability of waves and water levels in coastal engineering design. J. Hydraul. Res.
**2002**, 40, 241–251. [Google Scholar] [CrossRef] - Leonard, M.; Westra, S.; Phatak, A.; Lambert, M.; van den Hurk, B.; Mcinnes, K.; Risbey, J.; Schuster, S.; Jakob, D.; Stafford-Smith, M.A. Compound event framework for understanding extreme impacts. Wiley Interdiscip. Rev. Clim. Chang.
**2014**, 5, 113–128. [Google Scholar] [CrossRef] - Zheng, F.; Westra, S.; Leonard, M.; Sisson, S.A. Modeling dependence between extreme rainfall and storm surge to estimate coastal flooding risk. Water Resour. Res.
**2014**, 50, 2050–2071. [Google Scholar] [CrossRef][Green Version] - Kew, S.F.; Selten, F.M.; Lenderink, G.; Hazeleger, W. The simultaneous occurrence of surge and discharge extremes for the Rhine delta. Nat. Hazards Earth Syst. Sci.
**2013**, 13, 2017–2029. [Google Scholar] [CrossRef] - Zheng, F.; Westra, S.; Sisson, S.A. Quantifying the dependence between extreme rainfall and storm surge in the coastal zone. J. Hydrol.
**2013**, 505, 172–187. [Google Scholar] [CrossRef] - Ward, P.J.; Couasnon, A.; Eilander, D.; Haigh, I.; Hendry, A.; Muis, S.; Veldkamp, T.I.E.; Winsemius, H.; Wahl, T. Dependence between high sea-level and high river discharge increases flood hazard in global deltas and estuaries. Environ. Res. Lett.
**2018**. [Google Scholar] [CrossRef] - Salvadori, G.; De Michele, C.; Kottegoda, N.T.; Rosso, R. Extremes in Nature: An Approach Using Copulas; Springer Science & Business Media: Berlin, Germany, 2007; pp. 1–294. ISBN 978-1-4020-4415-1. [Google Scholar]
- Salvadori, G.; Durante, F.; De Michele, C.; Bernardi, M.; Petrella, L. A multivariate copula-based framework for dealing with hazard scenarios and failure probabilities. Water Resour. Res.
**2016**, 52, 3701–3721. [Google Scholar] [CrossRef] - Moftakhari, H.R.; Salvadori, G.; AghaKouchak, A.; Sanders, B.F.; Matthew, R.A. Compounding effects of sea level rise and fluvial flooding. Proc. Natl. Acad. Sci. USA
**2017**, 114, 9785–9790. [Google Scholar] [CrossRef] [PubMed][Green Version] - Van den Hurk, B.; van Meijgaard, E.; de Valk, P.; van Heeringen, K.-J.; Gooijer, J. Analysis of a compounding surge and precipitation event in the Netherlands. Environ. Res. Lett.
**2015**, 10, 035001. [Google Scholar] [CrossRef][Green Version] - Neal, J.; Keef, C.; Bates, P.; Beven, K.; Leedal, D. Probabilistic flood risk mapping including spatial dependence. Hydrol. Process.
**2013**, 27, 1349–1363. [Google Scholar] [CrossRef] - Keef, C.; Tawn, J.A.; Lamb, R. Estimating the probability of widespread flood events. Environmetrics
**2013**, 24, 13–21. [Google Scholar] [CrossRef] - Bender, J.; Wahl, T.; Müller, A.; Jensen, J. A multivariate design framework for river confluences. Hydrol. Sci. J.
**2016**, 61, 471–482. [Google Scholar] [CrossRef] - Apel, H.; Thieken, A.H.; Merz, B.; Blöschl, G. Flood risk assessment and associated uncertainty. Nat. Hazards Earth Syst. Sci.
**2004**, 4, 295–308. [Google Scholar] [CrossRef][Green Version] - Lamb, R.; Keef, C.; Tawn, J.; Laeger, S.; Meadowcroft, I.; Surendran, S.; Dunning, P.; Batstone, C. A new method to assess the risk of local and widespread flooding on rivers and coasts. J. Flood Risk Manag.
**2010**, 3, 323–336. [Google Scholar] [CrossRef] - Port of Houston Authority. Available online: http://www.porthouston.com/ (accessed on 27 March 2018).
- Davlasheridze, M.; Atoba, K.O.; Brody, S.; Highfield, W.; Merrell, W.; Ebersole, B.; Purdue, A.; Gilmer, R.W. Economic impacts of storm surge and the cost-benefit analysis of a coastal spine as the surge mitigation strategy in Houston-Galveston area in the USA. Mitig. Adapt. Strateg. Glob. Chang.
**2018**, 1–26. [Google Scholar] [CrossRef] - Christian, J.; Fang, Z.; Torres, J.; Deitz, R.; Bedient, P. Modeling the Hydraulic Effectiveness of a Proposed Storm Surge Barrier System for the Houston Ship Channel during Hurricane Events. Nat. Hazards Rev.
**2015**, 16, 04014015. [Google Scholar] [CrossRef] - Torres, J.M.; Bass, B.; Irza, J.N.; Proft, J.; Sebastian, A.; Dawson, C.; Bedient, P. Modeling the Hydrodynamic Performance of a Conceptual Storm Surge Barrier System for the Galveston Bay Region. J. Waterw. Port Coast. Ocean Eng.
**2017**, 143, 05017002. [Google Scholar] [CrossRef] - Niedermayer, D. An Introduction to Bayesian Networks and Their Contemporary Applications; Innovations in Bayesian Networks; Springer: Berlin/Heidelberg, Germany, 2008; pp. 117–130. ISBN 9783540850656. [Google Scholar]
- Vogel, K.; Riggelsen, C.; Korup, O.; Scherbaum, F. Bayesian network learning for natural hazard analyses. Nat. Hazards Earth Syst. Sci.
**2014**, 14, 2605–2626. [Google Scholar] [CrossRef][Green Version] - Weber, P.; Medina-Oliva, G.; Simon, C.; Iung, B. Overview on Bayesian networks applications for dependability, risk analysis and maintenance areas. Eng. Appl. Artif. Intell.
**2012**, 25, 671–682. [Google Scholar] [CrossRef] - Hanea, A.; Morales Napoles, O.; Ababei, D. Non-parametric Bayesian networks: Improving theory and reviewing applications. Reliab. Eng. Syst. Saf.
**2015**, 144, 265–284. [Google Scholar] [CrossRef] - Hanea, A.M.; Kurowicka, D.; Cooke, R.M. Hybrid Method for Quantifying and Analyzing Bayesian Belief Nets. Qual. Reliab. Eng. Int.
**2006**, 22, 709–729. [Google Scholar] [CrossRef] - Salvadori, G.; De Michele, C. Frequency analysis via copulas: Theoretical aspects and applications to hydrological events. Water Resour. Res.
**2004**, 40, 1–17. [Google Scholar] [CrossRef] - Genest, C.; Favre, A.-C. Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask. J. Hydrol. Eng.
**2007**, 12, 347–368. [Google Scholar] [CrossRef][Green Version] - Joe, H. Dependence Modeling with Copulas; Chapman & Hall/CRC: London, UK, 2015; ISBN 9781466583221. [Google Scholar]
- Graler, B.; Van Den Berg, M.J.; Vandenberghe, S.; Petroselli, A.; Grimaldi, S.; De Baets, B.; Verhoest, N.E.C. Multivariate return periods in hydrology: A critical and practical review focusing on synthetic design hydrograph estimation. Hydrol. Earth Syst. Sci.
**2013**, 17, 1281–1296. [Google Scholar] [CrossRef][Green Version] - Sklar, A. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris
**1959**, 8, 229–231. [Google Scholar] - Nelsen, R.B. An Introduction to Copulas, 2nd ed.; Springer Science & Business Media: New York, NY, USA, 2006. [Google Scholar]
- Joe, H. Multivariate Models and Multivariate Dependence Concepts; CRC Press: London, UK, 1997. [Google Scholar]
- Wang, W.; Wells, M.T. Model Selection and Semiparametric Inference for Bivariate Failure-Time Data. J. Am. Stat. Assoc.
**2000**, 95, 62–72. [Google Scholar] [CrossRef] - Paprotny, D.; Morales-Nápoles, O. Estimating extreme river discharges in Europe through a Bayesian network. Hydrol. Earth Syst. Sci.
**2017**, 21, 2615–2636. [Google Scholar] [CrossRef][Green Version] - Qian, Z. Without zoning: Urban development and land use controls in Houston. Cities
**2010**, 27, 31–41. [Google Scholar] [CrossRef] - Gori, A.; Blessing, R.; Juan, A.; Brody, S.; Bedient, P. Characterizing urbanization impacts on floodplain through integrated land use, hydrologic, and hydraulic modeling. J. Hydrol.
**2018**, in press. [Google Scholar] - Gori, A. Quantifying Impacts of Development on Floodplain Evolution and Projection of Future Flood Hazard: Applications to Harris County. Master’s Thesis, Rice University, Houston, TX, USA, 2018. [Google Scholar]
- Mallakpour, I.; Villarini, G. The changing nature of flooding across the central United States. Nat. Clim. Chang.
**2015**, 5, 250–254. [Google Scholar] [CrossRef] - Villarini, G.; Smith, J.A.; Baeck, M.L.; Krajewski, W.F. Examining Flood Frequency Distributions in the Midwest US. JAWRA J. Am. Water Resour. Assoc.
**2011**, 47, 447–463. [Google Scholar] [CrossRef] - Serinaldi, F. Can we tell more than we can know? The limits of bivariate drought analyses in the United States. Stoch. Environ. Res. Risk Assess.
**2015**, 30, 1691–1704. [Google Scholar] [CrossRef] - Claps, P.; Laio, F. Can continuous streamflow data support flood frequency analysis? An alternative to the partial duration series approach. Water Resour. Res.
**2003**, 39, 1–11. [Google Scholar] [CrossRef] - Hobaek Haff, I.; Frigessi, A.; Maraun, D. How well do regional climate models simulate the spatial dependence of precipitation? An application of pair-copula constructions. J. Geophys. Res. D Atmos.
**2015**, 120, 2624–2646. [Google Scholar] [CrossRef][Green Version] - Serinaldi, F.; Bárdossy, A.; Kilsby, C.G. Upper tail dependence in rainfall extremes: would we know it if we saw it? Stoch. Environ. Res. Risk Assess.
**2015**, 29, 1211–1233. [Google Scholar] [CrossRef] - Morales-Nápoles, O.; Worm, D.; van den Haak, P.; Hanea, A.; Courage, W.; Miraglia, S. Reader for Course: Introduction to Bayesian Networks; TNO-060-DTM-2013-01115; TNO: Delft, The Netherlands, 2013. [Google Scholar]
- Mutua, F.M. The use of the Akaike Information Criterion in the identification of an optimum flood frequency model. Hydrol. Sci. J.
**1994**, 39, 235–244. [Google Scholar] [CrossRef][Green Version] - Morales-Nápoles, O.; Steenbergen, R.D.J.M. Large-Scale Hybrid Bayesian Network for Traffic Load Modeling from Weigh-in-Motion System Data. J. Bridg. Eng.
**2014**, 20, 1–10. [Google Scholar] [CrossRef] - McLachlan, G.; Peel, D. Finite Mixture Models; Wiley Interscience: Hoboken, NJ, USA, 2000. [Google Scholar]
- NOAA National Oceanic and Atmospheric Administration. Tides and Currents. Annual Exceedance Probability Curves 8771450 Galveston Pier 21, TX. Available online: https://tidesandcurrents.noaa.gov/est/curves.shtml?stnid=8771450 (accessed on 15 December 2017).
- Henderson, F.M. Open Channel Flow; Prentice-Hall: Upper Saddle River, NJ, USA, 1966; ISBN 0023535105. [Google Scholar]
- Brunner, G.W. HEC-RAS River Analysis System. Hydraulic Reference Manual; US Army Corps of Engineers, Institute for Water Resources, Hydrologic Engineering Center: Davis, CA, USA, 2016. [Google Scholar]
- Harris County Flood Control District Model and Map Management System. Available online: http://www.m3models.org/ (accessed on 1 July 2016).
- Landsea, C.W.; Franklin, J.L. Atlantic Hurricane Database Uncertainty and Presentation of a New Database Format. Mon. Weather Rev.
**2013**, 141, 3576–3592. [Google Scholar] [CrossRef] - Arns, A.; Wahl, T.; Haigh, I.D.; Jensen, J.; Pattiaratchi, C. Estimating extreme water level probabilities: A comparison of the direct methods and recommendations for best practise. Coast. Eng.
**2013**, 81, 51–66. [Google Scholar] [CrossRef] - Arns, A.; Dangendorf , S.; Jensen, J.; Talke, S.; Bender, J.; Pattiaratchi, C. Sea-level rise induced amplification of coastal protection design heights. Sci. Rep.
**2017**, 7, 40171. [Google Scholar] [CrossRef] [PubMed][Green Version] - Vitousek, S.; Barnard, P.L.; Fletcher, C.H.; Frazer, N.; Erikson, L.; Storlazzi, C.D. Doubling of coastal flooding frequency within decades due to sea-level rise. Sci. Rep.
**2017**, 7, 1399. [Google Scholar] [CrossRef] [PubMed] - Teng, J.; Jakeman, A.J.; Vaze, J.; Croke, B.F.W.; Dutta, D.; Kim, S. Flood inundation modelling: A review of methods, recent advances and uncertainty analysis. Environ. Model. Softw.
**2017**, 90, 201–216. [Google Scholar] [CrossRef] - Van Oldenborgh, G.J.; van der Wiel, K.; Sebastian, A.; Singh, R.; Arrighi, J.; Otto, F.; Haustein, K.; Li, S.; Vecchi, G.; Cullen, H. Attribution of extreme rainfall from Hurricane Harvey, August 2017. Environ. Res. Lett.
**2017**, 12, 124009. [Google Scholar] [CrossRef][Green Version] - Sebastian, A.G.; Lendering, K.T.; Kothuis, B.L.M.; Brand, A.D.; Jonkman, S.N. Hurricane Harvey Report. A Fact-Finding Effort in the Direct Aftermath of Hurricane Harvey in the Greater Houston Region; Delft University Publishers: Delft, The Netherlands, 2017. [Google Scholar]
- Jonkman, S.N.; Godfroy, M.; Sebastian, A.; Kolen, B. Brief communication: Post-event analysis of loss of life due to hurricane Harvey. Nat. Hazards Earth Syst. Sci.
**2018**, 18, 1073–1078. [Google Scholar] [CrossRef] - Serafin, K.A.; Ruggiero, P.; Stockdon, H.F. The relative contribution of waves, tides, and nontidal residuals to extreme total water levels on U.S. West Coast sandy beaches. Geophys. Res. Lett.
**2017**, 44, 1839–1847. [Google Scholar] [CrossRef] - Vousdoukas, M.I.; Bouziotas, D.; Giardino, A.; Bouwer, L.M.; Mentaschi, L.; Feyen, L. Understanding epistemic uncertainty in large-scale coastal flood risk assessment for present and future climates. Nat. Hazards Earth Syst. Sci.
**2018**, 18, 2127–2142. [Google Scholar] [CrossRef] - Melito, L.; Postacchini, M.; Sheremet, A.; Calantoni, J.; Zitti, G.; Darvini, G.; Brocchini, M. Wave-Current Interactions and Infragravity Wave Propagation at a Microtidal Inlet. Proceedings
**2018**, 2, 628. [Google Scholar] [CrossRef] - Sebastian, A.; Proft, J.; Dietrich, J.C.; Du, W.; Bedient, P.B.; Dawson, C.N. Characterizing hurricane storm surge behavior in Galveston Bay using the SWAN+ADCIRC model. Coast. Eng.
**2014**, 88, 171–181. [Google Scholar] [CrossRef] - Dietrich, J.C.; Zijlema, M.; Westerink, J.J.; Holthuijsen, L.H.; Dawson, C.; Luettich, R.A.; Jensen, R.E.; Smith, J.M.; Stelling, G.S.; Stone, G.W. Modeling hurricane waves and storm surge using integrally-coupled, scalable computations. Coast. Eng.
**2011**, 58, 45–65. [Google Scholar] [CrossRef] - Salvadori, G.; Tomasicchio, G.R.; D’Alessandro, F. Practical guidelines for multivariate analysis and design in coastal and off-shore engineering. Coast. Eng.
**2014**, 88, 1–14. [Google Scholar] [CrossRef] - Pappadà, R.; Durante, F.; Salvadori, G. Quantification of the environmental structural risk with spoiling ties: Is randomization worthwhile? Stoch. Environ. Res. Risk Assess.
**2017**, 31, 2483–2497. [Google Scholar] [CrossRef] - Emanuel, K. Assessing the present and future probability of Hurricane Harvey’s rainfall. Proc. Natl. Acad. Sci. USA
**2017**, 201716222. [Google Scholar] [CrossRef] [PubMed] - Hamilton, C.M.; Martinuzzi, S.; Plantinga, A.J.; Radeloff, V.C.; Lewis, D.J.; Thogmartin, W.E.; Heglund, P.J.; Pidgeon, A.M. Current and Future Land Use around a Nationwide Protected Area Network. PLoS ONE
**2013**, 8. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hollis, G.E. The effect of urbanization on floods of different recurrence interval. Water Resour. Res.
**1975**, 11, 431–435. [Google Scholar] [CrossRef] - Sarhadi, A. Time-varying nonstationarymultivariate risk analysis using a dynamic Bayesian copula. Water Resour. Res.
**2016**, 52, 2327–2349. [Google Scholar] [CrossRef]

**Figure 1.**Schematic workflow for generating stochastic water surface profiles in a coastal catchment.

**Figure 2.**Location of the case study area, the Buffalo Bayou catchment (

**a**) which drains into the Galveston Bay (

**b**) and connected to the Gulf of Mexico (

**c**). The discharge stations (filled circles in black) and the tide station (empty circles) Galveston Pier 21 are used to construct the BN and model water surface elevations along the main stem of the Buffalo Bayou catchment (red line). Water level stations (green) were used for the comparison with the modeled extreme water levels.

**Figure 3.**The Bayesian Network model for the Buffalo Bayou catchment. The boxes represent the nodes and the arrows the arcs. The values of the (conditional) rank correlation coefficient are shown on each arc. The histogram in the node shows the empirical probability distribution function for each variable and the values below represent the mean and standard deviation, respectively. Units are in m

^{3}s

^{-1}for discharge and in m for the storm surge.

**Figure 4.**Maximum (red), minimum (blue) water surface elevations and percentiles (90th, 95th, 99th, and 99.99th) of daily water levels at each river calculation point obtained by inferring the BN 182,500 times and modeling the resulting water surface profile.

**Figure 5.**Comparison of the annual exceedance probability distributions from observed and modeled annual maxima at stations HM (

**a**), HTB (

**b**) and HBB (

**c**). The dashed lines indicate the fit of the 95% confidence interval from the empirical GEV distribution parameters. The stations are presented from downstream to upstream along the Buffalo Bayou river, with stations HM and HTB located in the Port of Houston, see also Figure 1 and Figure 4 for their exact location.

**Figure 6.**Sensitivity of the multivariate dependence assumptions. The 100–year water level obtained from the current model framework is represented by the black full line. Case A and B represent full dependence and ‘independence’ of the boundary conditions, respectively (see text).

**Figure 7.**Similar to Figure 6 but in the transverse direction at stations HM (

**a**), HTB (

**b**) and HBB (

**c**). The location of the bank stations is extracted from the regulatory HEC-RAS riverine flood model and roughly indicates the change in channel conveyance.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Couasnon, A.; Sebastian, A.; Morales-Nápoles, O. 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* **2018**, *10*, 1190.
https://doi.org/10.3390/w10091190

**AMA Style**

Couasnon A, Sebastian A, Morales-Nápoles O. 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*. 2018; 10(9):1190.
https://doi.org/10.3390/w10091190

**Chicago/Turabian Style**

Couasnon, Anaïs, Antonia Sebastian, and Oswaldo 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, no. 9: 1190.
https://doi.org/10.3390/w10091190