# Coastal Flooding Hazard Due to Overflow Using a Level II Method: Application to the Venetian Littoral

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. GPU-Based Swallow Water Equation Model

#### 2.2. Procedure for the Assessment of Coastal Flooding Hazard Maps

**X**is ${f}_{x}(\mathbf{X})$, the probability of failure is evaluated as:

**(a) Definition of the offshore marine loads**. The coastal flooding may be forced by a combination of several variables that contribute to the rise of the water level at the domain boundary. The rise of water level is due to: (1) the sea level $\zeta $ formed by the astronomical tide (${\zeta}_{A}$) and the meteorological contribution (storm surge, ${\zeta}_{S}$) caused by wind and pressure effects; and (2) the wave contribution, i.e., breaking waves contribute to the water level rise through wave run up and wave set-up Z, which mainly depend on wave height, period, and direction.

**X**can be studied in terms of significant wave height ($Hs$), peak period ($Tp$), mean wave direction, sea level $\zeta $ (tide + surge) and storm duration. This information can be derived from direct measures (e.g., from buoys) or computed dataset (from numerical model such as WAM [41]). From these data, a homogeneous and independent sample can be derived by identification of sea storms.

**X**can be analyzed to find their joint statistics. Note that the variations of some input variables, such as the wave period (or, better, the wave steepness) and the storm duration, induce low variability on the model output and the associated sensitivity is very low. Their mean value can be considered as model input. Therefore, the joint statistics is limited to wave height $Hs$ and sea level $\zeta $. The final step is to transform these random variables

**X**= [$Hs$, $\zeta $] to equivalent standard normal random variables, finding the transformation function

**U**= ${F}_{T}(\mathbf{X})$.

**(b) Definition of the boundary conditions at the shoreline**. A wave transformation model from offshore to onshore needs to be applied to a set of offshore conditions to estimate the value of the set-up Z and the residual wave height at the shoreline refereed to the Mean Sea Level (MSL). The wave transformation model used is the “Dally, Dean and Dalrymple model” [47] for breaker decay that is capable of describing wave transformation across beaches of irregular profile shape. It considers that the wave breaking starts when $H>0.78d$ (d is the water depth) and continues until some stable wave height is attained (usually $H>0.4d$). An example of its application is shown in Figure 2.

**(c) Coastal inundation modeling**. The model for coastal flooding propagation, presented in Section 2.1, can be applied introducing the following essential data: the position of the shoreline refereed to the MSL (or the shoreline position in MSL condition); the inland topography; and the roughness ${K}_{s}$. For each of the boundary conditions selected, the propagation model is run. The maximum water depth reached in each grid cell of the domain is saved and the obtained maps are flooding maps relative to each couple of $Hs$ and $\zeta $.

**(d) Reliability analysis**. The probability of failure is defined as the probability that a portion of inland is flooded under certain values of wave height and sea level. Therefore, the limit state $g(\mathbf{X})=0$ is evaluated through an interpolation with the obtained results. In each cell of the domain, the maximum water level reached during the simulation for a fixed value of $\zeta $ is plotted against different values of $Hs$ (Figure 4a). Then, two couples that correspond to a water level in the cell equal to ${h}_{F}$ (in Figure 4a ${h}_{F}$ = 0.5 m) are extrapolated. Finally, the transformation of the two couples from the physical space to the standard space is applied and the minimum distance $\beta $ (and consequently the ${p}_{f}$) from the limit state to the origin of the standard space is computed (Figure 4b).

## 3. An Application to Two Stretches of the Venetian Littoral

#### 3.1. Valle Vecchia Littoral Cell

#### 3.2. Caorle Littoral Cell

**Figure 13.**Hazard map (cell VE3): Probability that flooding level 0.5 m is exceeded, expressed as return period ${T}_{R}$.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Cazenave, A.; Cozannet, G.L. Sea level rise and its coastal impacts. Earth’s Future
**2014**, 2, 15–34. [Google Scholar] [CrossRef] [Green Version] - Pomaro, A.; Cavaleri, L.; Lionello, P. Climatology and trends of the Adriatic Sea wind waves: Analysis of a 37-year long instrumental data set. Int. J. Climatol.
**2017**, 37, 4237–4250. [Google Scholar] [CrossRef] - Rahmstorf, S. Rising hazard of storm-surge flooding. Proc. Natl. Acad. Sci. USA
**2017**, 114, 11806–11808. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Nicholls, R.J.; Cazenave, A. Sea-level rise and its impact on coastal zones. Science
**2010**, 328, 1517–1520. [Google Scholar] [CrossRef] [PubMed] - Vafeidis, A.T.; Nicholls, R.J.; McFadden, L.; Tol, R.S.; Hinkel, J.; Spencer, T.; Grashoff, P.S.; Boot, G.; Klein, R.J. A new global coastal database for impact and vulnerability analysis to sea-level rise. J. Coast. Res.
**2008**, 24, 917–924. [Google Scholar] [CrossRef] - Zanuttigh, B.; Simcic, D.; Bagli, S.; Bozzeda, F.; Pietrantoni, L.; Zagonari, F.; Hoggart, S.; Nicholls, R.J. THESEUS decision support system for coastal risk management. Coast. Eng.
**2014**, 87, 218–239. [Google Scholar] [CrossRef] - Zachry, B.C.; Booth, W.J.; Rhome, J.R.; Sharon, T.M. A national view of storm surge risk and inundation. Weather Clim. Soc.
**2015**, 7, 109–117. [Google Scholar] [CrossRef] - Wadey, M.P.; Nicholls, R.J.; Hutton, C. Coastal flooding in the Solent: An integrated analysis of defences and inundation. Water
**2012**, 4, 430–459. [Google Scholar] [CrossRef] - Spaulding, M.L.; Grilli, A.; Damon, C.; Fugate, G.; Oakley, B.A.; Isaji, T.; Schambach, L. Application of state of art modeling techniques to predict flooding and waves for an exposed coastal area. J. Mar. Sci. Eng.
**2017**, 5, 10. [Google Scholar] [CrossRef] - Aucelli, P.P.C.; Di Paola, G.; Incontri, P.; Rizzo, A.; Vilardo, G.; Benassai, G.; Buonocore, B.; Pappone, G. Coastal inundation risk assessment due to subsidence and sea level rise in a Mediterranean alluvial plain (Volturno coastal plain–southern Italy). Estuarine Coast. Shelf Sci.
**2017**, 198, 597–609. [Google Scholar] [CrossRef] - Di Luccio, D.; Benassai, G.; Di Paola, G.; Rosskopf, C.; Mucerino, L.; Montella, R.; Contestabile, P. Monitoring and modelling coastal vulnerability and mitigation proposal for an archaeological site (Kaulonia, Southern Italy). Sustainability (Switzerland)
**2018**, 10, 2017. [Google Scholar] [CrossRef] - Di Risio, M.; Bruschi, A.; Lisi, I.; Pesarino, V.; Pasquali, D. Comparative Analysis of Coastal Flooding Vulnerability and Hazard Assessment at National Scale. J. Mar. Sci. Eng.
**2017**, 5, 51. [Google Scholar] [CrossRef] - Gallien, T. Validated coastal flood modeling at Imperial Beach, California: Comparing total water level, empirical and numerical overtopping methodologies. Coast. Eng.
**2016**, 111, 95–104. [Google Scholar] [CrossRef] - Lerma, A.; Bulteau, T.; Elineau, S.; Paris, F.; Durand, P.; Anselme, B.; Pedreros, R. High-resolution marine flood modelling coupling overflow and overtopping processes: Framing the hazard based on historical and statistical approaches. Nat. Hazards Earth Syst. Sci.
**2018**, 18, 207–229. [Google Scholar] [CrossRef] - Simeoni, U.; Corbau, C. A review of the Delta Po evolution (Italy) related to climatic changes and human impacts. Geomorphology
**2009**, 107, 64–71. [Google Scholar] [CrossRef] - Carbognin, L.; Teatini, P.; Tosi, L. Eustacy and land subsidence in the Venice Lagoon at the beginning of the new millennium. J. Mar. Syst.
**2004**, 51, 345–353. [Google Scholar] [CrossRef] - Martinelli, L.; Zanuttigh, B.; Corbau, C. Assessment of coastal flooding hazard along the Emilia Romagna littoral, IT. Coast. Eng.
**2010**, 57, 1042–1058. [Google Scholar] [CrossRef] - Pescaroli, G.; Magni, M. Flood warnings in coastal areas: How do experience and information influence responses to alert services? Nat. Hazards Earth Syst. Sci.
**2015**, 15, 703–714. [Google Scholar] [CrossRef] - Wolshon, B.; Urbina, E.; Wilmot, C.; Levitan, M. Review of policies and practices for hurricane evacuation. I: Transportation planning, preparedness, and response. Nat. Hazards Rev.
**2005**, 6, 129–142. [Google Scholar] [CrossRef] - Jia, X.; Morel, G.; Martell-Flore, H.; Hissel, F.; Batoz, J.L. Fuzzy logic based decision support for mass evacuations of cities prone to coastal or river floods. Environ. Model. Softw.
**2016**, 85, 1–10. [Google Scholar] [CrossRef] - Kunreuther, H.; Pauly, M. Rules rather than discretion: Lessons from Hurricane Katrina. J. Risk Uncertain.
**2006**, 33, 101–116. [Google Scholar] [CrossRef] - Burcharth, H.F.; Zanuttigh, B.; Andersen, T.L.; Lara, J.L.; Steendam, G.J.; Ruol, P.; Sergent, P.; Ostrowski, R.; Silva, R.; Martinelli, L.; et al. Chapter 3—Innovative Engineering Solutions and Best Practices to Mitigate Coastal Risk. In Coastal Risk Management in a Changing Climate; Butterworth-Heinemann: Boston, MA, USA, 2015; pp. 55–170. [Google Scholar]
- Vanderlinden, J.P.; Baztan, J.; Coates, T.; Dávila, O.G.; Hissel, F.; Kane, I.O.; Koundouri, P.; McFadden, L.; Parker, D.; Penning-Rowsell, E.; et al. Chapter 5—Nonstructural Approaches to Coastal Risk Mitigations. In Coastal Risk Management in a Changing Climate; Butterworth-Heinemann: Boston, MA, USA, 2015; pp. 237–274. [Google Scholar]
- Kusumo, A.; Reckien, D.; Verplanke, J. Utilising volunteered geographic information to assess resident’s flood evacuation shelters. case study: Jakarta. Appl. Geogr.
**2017**, 88, 174–185. [Google Scholar] [CrossRef] - Coastal Flooding Hazard—Community information and participation. Available online: https://coastalfloodinghazard.wordpress.com/community-information (accessed on 7 January 2019).
- Hoggart, S.; Hawkins, S.J.; Bohn, K.; Airoldi, L.; van Belzen, J.; Bichot, A.; Bilton, D.T.; Bouma, T.J.; Colangelo, M.A.; Davies, A.J.; et al. Chapter 4–Ecological Approaches to Coastal Risk Mitigation. In Coastal Risk Management in a Changing Climate; Butterworth-Heinemann: Boston, MA, USA, 2015; pp. 171–236. [Google Scholar]
- Gómez-Pina, G.; Muñoz-Pérez, J.J.; Ramírez, J.L.; Ley, C. Sand dune management problems and techniques, Spain. J. Coast. Res.
**2002**, 36, 325–332. [Google Scholar] [CrossRef] - Favaretto, C.; Martinelli, L.; Ruol, P. A Model of Coastal Flooding Using Linearized Bottom Friction and its Application to a Case Study in Caorle, Venice Italy. Int. J. Off. Polar Eng.
**2019**, 29, 1–9. [Google Scholar] - Favaretto, C.; Martinelli, L.; Ruol, P. Raster Based Model of Inland Coastal Flooding Propagation Using Linearized Bottom Friction and Application to a Real Case Study in Caorle, Venice (IT). In Proceedings of the 28th International Ocean and Polar Engineering Conference, Sapporo, Japan, 10–15 June 2018. [Google Scholar]
- Bates, P.D.; Horritt, M.S.; Fewtrell, T.J. A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling. J. Hydrol.
**2010**, 387, 33–45. [Google Scholar] [CrossRef] - Hunter, N.M.; Bates, P.D.; Horritt, M.S.; Wilson, M.D. Simple spatially-distributed models for predicting flood inundation: A review. Geomorphology
**2007**, 90, 208–225. [Google Scholar] [CrossRef] - Khorshid, S.; Mohammadian, A.; Nistor, I. Extension of a well-balanced central upwind scheme for variable density shallow water flow equations on triangular grids. Comput. Fluids
**2017**, 156, 441–448. [Google Scholar] [CrossRef] - Brodtkorb, A.R.; Sætra, M.L.; Altinakar, M. Efficient shallow water simulations on GPUs: Implementation, visualization, verification, and validation. Comput. Fluids
**2012**, 55, 1–12. [Google Scholar] [CrossRef] - Liang, W.Y.; Hsieh, T.J.; Satria, M.T.; Chang, Y.L.; Fang, J.P.; Chen, C.C.; Han, C.C. A GPU-based simulation of tsunami propagation and inundation. In Proceedings of the International Conference on Algorithms and Architectures for Parallel Processing; Springer: Berlin/Heidelberg, Germany, 2009; pp. 593–603. [Google Scholar]
- Synolakis, C. The runup of solitary waves. J. Fluid Mech.
**1987**, 185, 523–545. [Google Scholar] [CrossRef] - Briggs, M.J.; Synolakis, C.E.; Harkins, G.S.; Green, D.R. Laboratory experiments of tsunami runup on a circular island. Pure Appl. Geophys.
**1995**, 144, 569–593. [Google Scholar] [CrossRef] - Kottegoda, N.; Rosso, R. Probability, Statistics, and Reliability for Civil and Environmental Engineers; McGraw-Hill: New York, NY, USA, 1997. [Google Scholar]
- Madsen, H.O.; Krenk, S.; Lind, N.C. Methods of Structural Safety; Courier Corporation: North Chelmsford, MA, USA, 2006. [Google Scholar]
- Du, X. First order and second reliability methods. In Probabilistic Engineering Design; John Wiley & Sons Inc.: Hoboken, NJ, USA, 2005; pp. 1–33. [Google Scholar]
- Hasofer, A.M.; Lind, N.C. Exact and invariant second-moment code format. J. Eng. Mech. Div.
**1974**, 100, 111–121. [Google Scholar] - Group, T.W. The WAM model—A third generation ocean wave prediction model. J. Phys. Oceanogr.
**1988**, 18, 1775–1810. [Google Scholar] [CrossRef] - Armaroli, C.; Ciavola, P.; Perini, L.; Calabrese, L.; Lorito, S.; Valentini, A.; Masina, M. Critical storm thresholds for significant morphological changes and damage along the Emilia-Romagna coastline, Italy. Geomorphology
**2012**, 143, 34–51. [Google Scholar] [CrossRef] - Boccotti, P. On coastal and offshore structure risk analysis. Excerpta Ital. Contrib. Field Hydraul. Eng.
**1986**, 1, 19–36. [Google Scholar] - Mendoza, E.; Jimenez, J.; Mateo, J.; Salat, J. A coastal storms intensity scale for the Catalan sea (NW Mediterranean). Nat. Hazards Earth Syst. Sci.
**2011**, 11, 2453–2462. [Google Scholar] [CrossRef] [Green Version] - Archetti, R.; Paci, A.; Carniel, S.; Bonaldo, D. Optimal index related to the shoreline dynamics during a storm: The case of Jesolo beach. Nat. Hazards Earth Syst. Sci.
**2016**, 16, 1107–1122. [Google Scholar] [CrossRef] - Lin-Ye, J.; García-León, M.; Gràcia, V.; Ortego, M.I.; Stanica, A.; Sánchez-Arcilla, A. Multivariate hybrid modelling of future wave-storms at the northwestern Black Sea. Water
**2018**, 10, 221. [Google Scholar] [CrossRef] - Dally, W.R.; Dean, R.G.; Dalrymple, R.A. Wave height variation across beaches of arbitrary profile. J. Geophys. Res. Oceans
**1985**, 90, 11917–11927. [Google Scholar] [CrossRef] - Ruol, P.; Martinelli, L.; Favaretto, C. Vulnerability Analysis of the Venetian Littoral and Adopted Mitigation Strategy. Water
**2018**, 10, 984. [Google Scholar] [CrossRef] - Ruol, P.; Martinelli, L.; Favaretto, C. Gestione Integrata Della Zona Costiera. Studio e Monitoraggio per la Definizione Degli Interventi di Difesa dei Litorali Dall’Erosione Nella Regione Veneto—Linee Guida; Edizioni Libreria Progetto; University of Padua: Padova, Italy, 2016. [Google Scholar]
- Nataf, A. Determination des Distribution don’t les marges sont Donnees. C. R. Acad. Sci.
**1962**, 225, 42–43. [Google Scholar] - Prinos, P.; Kortenhaus, A.; Swerpel, B.; Jiménez, J.A. Review of Flood Hazard Mapping; Floodsite Report, No. T03-07-01,54; University of Athens: Athens, Greece, 2008. [Google Scholar]

**Figure 1.**(

**a**) Joint probability density function in X-plane and performance function $g({X}_{1},{X}_{2})=0$; and (

**b**) joint pdf in U-plane and performance function $g({U}_{1},{U}_{2})=0$.

**Figure 2.**Example of the wave transformation model results and definition of the boundary conditions at the isobath 0 m.

**Figure 3.**Example of final boundary condition at the shoreline refereed to the Mean Sea Level (MSL).

**Figure 4.**(

**a**) Example of evaluation of the limit state in the physical space; and (

**b**) limit state in standard space g(

**U**) and evaluation of the distance $\beta $.

**Figure 5.**The northern part of the Venetian littoral and its subdivision into coastal cells: VE1, Bibione; VE2, Valle Vecchia; VE3, Caorle; VE4, Porto Santa Margherita–Duna Verde–Eraclea; VE5, Jesolo.

**Figure 6.**Time series of significant wave height $Hs$ (black line), where dots represent the 974 storms: green dots are peak over threshold 1 m, while red dots are peak over threshold 2.5 m.

**Figure 8.**Red dots are the couple $Hs$–$\zeta $ chosen as input for the models (ZMPS is a reference level for Venice).

**Figure 10.**Hazard map (cell VE2): Probability that flooding level 0.5 m is exceeded, expressed as return period ${T}_{R}$.

© 2019 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/).

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**MDPI and ACS Style**

Favaretto, C.; Martinelli, L.; Ruol, P.
Coastal Flooding Hazard Due to Overflow Using a Level II Method: Application to the Venetian Littoral. *Water* **2019**, *11*, 134.
https://doi.org/10.3390/w11010134

**AMA Style**

Favaretto C, Martinelli L, Ruol P.
Coastal Flooding Hazard Due to Overflow Using a Level II Method: Application to the Venetian Littoral. *Water*. 2019; 11(1):134.
https://doi.org/10.3390/w11010134

**Chicago/Turabian Style**

Favaretto, Chiara, Luca Martinelli, and Piero Ruol.
2019. "Coastal Flooding Hazard Due to Overflow Using a Level II Method: Application to the Venetian Littoral" *Water* 11, no. 1: 134.
https://doi.org/10.3390/w11010134