# 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

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## 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

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**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