# A User-Oriented Local Coastal Flooding Early Warning System Using Metamodelling Techniques

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Site Description: Physical Setting, User Practices and Needs

^{2}) is a small territory; hence, within our exploratory work, the interactions with the potential users of the FEWS are more manageable, and coastal flood modelling can account for wave overtopping phenomena (see Section 4.2 for further details).

#### 2.2. Methodology

- •
- Define the indicators (I
_{j}, with j = 1:N) (Section 2.3); - •
- Set up the process-based model that will be used to build the learning dataset for the metamodels (Section 2.4);
- •
- Build (and validate) the metamodels Y
_{i}= f_{i}(X) (with i = 1:M) that are needed to estimate the indicators I_{j}(j = 1:N) (Section 2.5); - •
- Implement the post-processing of the metamodel outputs (including the computation of Z
_{k}indicators) to estimate the indicators I_{j}(Section 2.6); and - •
- Deploy the FEWS, which downloads the forecasted conditions X and returns the indicators I
_{j}(j = 1:N) for the next 6 tides (Section 2.7).

#### 2.3. Indicators and Classes

_{j}, with j = 1:14. Other indicators may have been considered, such as the trafficability on every road or the water depth at each building. However, in the present research work, we first aim to test the skills of the entire process in predicting different types of information. Thus, we focus on the most critical indicators for each type of need (e.g., for the roads, the parts affecting crisis management buildings; for the buildings, only the crisis management buildings). In the list of Table 1, some indicators have no units, and others are physical quantities. Regardless of the type of indicator, one important issue when building an FEWS is that the provided information can be directly interpreted. Thus, even for indicators referring to physical quantities, instead of providing a quantitative value, we provide the class in which the indicator falls. These classes are defined in different ways depending on the indicators. Figure 2 and Figure 3 show the locations of the physical quantities on which each indicator is based and the associated classes, respectively.

_{2}–I

_{6}), we rely on studies of the loss of human stability as a function of the water depth and velocity (see, e.g., [30]); moreover, as these survey points are located either on coastal defences or on the upper beach, we assume that the velocity is greater than 1 m/s when water is present. This assumption is confirmed by analysing the results obtained with the numerical model presented in the next section. For the classes of the maximal water height (I

_{14}) over the tide, at the 989 points, we rely mainly on the national flood hazard recommendations [31], and we include the 0.1 m class, as this threshold of 0.1 m is important for emergency services. This approach allows us to provide information with which the users are familiar, as they are used to seeing flood hazard maps. For the water discharge (I

_{7}and I

_{8}), the classes are built based on the capacities of the available pumping engines of the emergency service (SDIS56, which is located outside Gâvres) to help them plan which types of engines they should bring to the site before the flood. For the intensity (I

_{1}), 6 classes are defined based on thresholds of the flooded surface (percentage of the area: 5%, 10%, 30%), thereby ensuring that the Johanna-induced flood (10 March 2008), the last major flooding event to affect the demonstrate site (see Figure A1 in Appendix A), falls in the high-intensity class. An additional class is included to distinguish events where only few waves overtopped the coastal defences from real flood events. It is important to note that the colour scale in Figure 3 is indicator specific, i.e., that just because indicator I

_{2}would fall in the higher (purple) class does not mean that the other indicators should fall in their higher classes. Indeed, I

_{2}–I

_{6}focus on human risks, while the water discharge classes are designed based on the pumping engine capacities, and I

_{1}focuses on the intensity of the flood over the entire territory.

_{i}, with i = 1:N) predicted with metamodels. Table 2 provides a list of these metamodels and for which indicator I

_{j}they are used. Metamodels Y

_{7}to Y

_{18}are designed to use functional inputs (i.e., time-varying forcing conditions), while metamodels Y

_{1}to Y

_{6}use scalar inputs (i.e., steady forcing conditions). Indeed, metamodels Y

_{1}to Y

_{6}aim mainly to predict whether water will enter inland (Y

_{1}) or to predict the water depth on the upper part of the beach/coastal defence (Y

_{2}to Y

_{6}); hence, we can use these metamodels to make quasi-steady computations, i.e., discretise the time window of interest (here, (HT − 3 h:HT + 3 h), with HT referring to high tide) in smaller windows and perform computations with steady forcing conditions in each sub-window. For the road practicability (I

_{11}–I

_{13}), a decision tree is used, where the threshold is defined by the fording depths of the considered cars (e.g., 0.3 m for passenger cars and 0.6 m for emergency vehicles; [29]).

#### 2.4. Process-Based Model Setup and Validation

_{1}–Y

_{6}) and (2) another focused more on estimating the inland impact. To support the learning of these two types of metamodels, two types of numerical simulations are performed: (Sim1) simulations on 15 min (+spin up) with scalar (i.e., steady) forcing conditions X that are repeated 20 times each with randomly selected seed values and (Sim2) simulations on 6 h (+spin up) with functional (i.e., unsteady) forcing conditions X and a constant seed value. These two types of simulations are performed for hundreds of scenarios (see Section 2.5.2). Then, the numerical results (spatio-temporal fields of the water height and velocity) are post-processed to provide the Y

_{i}values. It should be noted that except for Y

_{2}–Y

_{6}, which are computed using a 1 s sampling (numerical) model output, all the other Y

_{i}values are computed based on 1 min sampling outputs.

#### 2.5. Metamodels

#### 2.5.1. Principles of Metamodelling

_{1},…, X

_{n}(a design of experiments) is obtained. Second, the corresponding set of output values $f$(X

_{1}),…,$f$(X

_{n}) is computed. The second step requires the “true” model to be evaluated n times, so n may be limited to a small value (10 to 100, for instance). Finally, the metamodel is a function $\widehat{f}$ of X defined on the input space covered by X

_{1},…, X

_{n}and learns from $f$(X

_{1}),…,$f$(X

_{n}). There are many standard methods for constructing a metamodel, such as linear or polynomial regression, polynomial chaos expansion [38], Gaussian processes (GPs) [39], random forests (RFs) [40], and kernel smoothing [41]. The common desirable feature among these methods is that evaluating $\widehat{f}$(X) does not require calling the “true” model and has a negligible computational cost (within a few minutes). Hence, analyses that would be too costly to apply directly to the “true” model (for instance, the Monte Carlo propagation of uncertainty studies or the estimation of sensitivity indices, both of which typically require thousands of function calls to yield meaningful results) may be applied to the metamodel function instead.

#### 2.5.2. Design of Experiments

#### 2.5.3. Metamodelling Technique

_{1}–Y

_{6}. To improve the prediction of the cases without flooding (i.e., Y

_{1}= 0), the GP-based metamodel (see, e.g., [39]) is combined with a classification RF model [48], which aims at predicting the probability of flooding P

_{f}(i.e., Y

_{1}> 0). When P

_{f}is predicted to be below 50%, the predicted value of Y

_{1}is set to zero. Further details are provided by [22], who applied this approach using the same numerical modelling chain but with a different grid experiment and DEM2008 instead of DEM2015–2018.

_{7}–Y

_{18}). To reduce both the memory and the processing requirements of the metamodel, we implement the B-spline [49] and principal component analysis (PCA) [50] dimension reduction techniques, as thoroughly explained in [23], who tested this method using a simplified flood model (relying on the use of an overtopping formula over a single cross-shore profile). Compared to alternative dimension reduction approaches such as the polynomial or Fourier bases of functions, one advantage is that the basis functions from PCA are orthogonal, and those from B-splines have many zero scalar products, which can be beneficial for least square procedures when the decomposition dimension is large. In many studies, the structural characteristics of the metamodels are chosen beforehand (e.g., PCA decomposition in [51], B-spline decomposition in [52], the Matérn 5/2 covariance function in [53]) without a specific sensitivity analysis or benchmarking. In the present work, we use the ant colony-based optimisation algorithm ACO-Gp proposed in [54] to fix several structural characteristics of each metamodel, such as the set of inputs to use for prediction and the type of kernel function of the model. This algorithm helps to efficiently explore the space of potential metamodel configurations while optimising the prediction quality. Implementations for functional input GP-based metamodelling and structural optimisation supported on ACO-Gp are available through the R [55] funGp package [56], which is freely accessible from CRAN at https://cran.r-project.org/package=funGp and GitHub at https://github.com/djbetancourt-gh/funGp, accessed on 25 July 2021. Alternatives to ant colony-based optimisation could be other methods for combinatorial optimisation, such as simulated annealing or genetic algorithms. Here, ant colony-based optimisation is adapted to the tree structure of the decision space (see [54]). For instance, whether a functional input is active affects the dimension of the rest of the decision parameter to be selected. This tree structure is naturally exploitable with the pheromone paths of ant colony-based optimisation, whereas it is much less clear how to exploit this tree structure with simulated annealing or genetic algorithms.

_{18}), we rely on the work of [24], the method of which is summarised as follows. Y(X,s) depends on both hydro-meteorological conditions (functional inputs) X and spatial coordinates s = (longitude, latitude). For the GP-based metamodel, we place a (zero-mean) GP prior on Y, where (1) the covariance function k is given by the separable kernel k((X,s), (X′,s′)) = k

_{X}(X,X′)k

_{s}(s,s′) and (2) the sub-kernels k

_{X}and k

_{s}evaluate the correlation between the functional inputs (X,X′) and that between the spatial coordinates (s,s′), respectively. Since k is attenuated by the spatial correlation, nearby values X and X’ can result in small correlations for distant values of s and s′, and vice versa. As Y is GP-distributed, the predictions can be performed then for classical GP-based metamodels (see, e.g., [39]). Furthermore, using a separable kernel considerably eases the implementation. As shown by [24], the resulting GP model can also be written as a multi-output model where the outputs are driven by a given set of functions. Implementations in both Python and R are freely available at https://github.com/anfelopera/spatfGPs, accessed on 25 July 2021. In the present work, we use 1003 spatially designed points. Those points are selected based on a dedicated k-means-based methodology accounting for both the spatial locations (i.e., longitude, latitude) and the flood ratios (see Section 3.1 and [24], for a further discussion). For a comparison with the more classic multi-output GP method based on linear models of coregionalisation, see also [24].

#### 2.6. Requirements, Combination Rules of the Metamodel-Based Predictions, Optimisation, and Validation Procedure

_{1}metamodel is used to force the indicators relying on the GP-based metamodels to 0 (i.e., class 1) when Z

_{1}= 0, with Z

_{1}being the maximum of Y

_{1}over the tide. In addition, Z

_{1}is used to discriminate between events at the flood limit (i.e., few wave overtopping events may occur; Z

_{1}< V1) and events corresponding to minor flooding (Z

_{1}≥ V1) such that if Z

_{1}< V1, then the intensity (I

_{1}) falls in the second class (Figure 3). At this stage, the threshold V1 is not defined; this is accomplished by optimising the numbers of true and false alarms (Section 3.3). For this optimisation step, we employ a damage database covering the period 1900–2010 together with the oceanographic forcing database [7]. These corrections can be seen as hierarchical constraints (Figure 5). In addition, some physically logical constraints are considered. For instance, the locations of indicators I

_{9}(town hall), I

_{10}(gymnasium), and I

_{12}(road2) are such that they cannot be flooded if the intensity of the flood is too small (typically for Z

_{7}< S1 with S1 = 29,200 m

^{2}, S1 corresponding to the upper limit of class no. 3 of intensity indicator I

_{1}, Figure 3). This has been checked by analysing the numerical model results for the grid experiment (see Section 3.1). Thus, an additional constraint based on Z

_{7}is imposed to improve the prediction of indicators I

_{9}, I

_{10}, and I

_{12}. For I

_{9}and I

_{10}, an additional constraint is imposed: if Z

_{10}< H1 (with H1 = 0.01 m), then C(I

_{9}) = 1 considering that 1 cm of water is included in the model uncertainties. We also have knowledge of some physical relationships between a few indicators. This knowledge is taken into account, again relying on the reliability of Z

_{1}(Figure 5, bottom-left insert). Finally, in terms of visualisation in the FEWS, indicators I

_{7}, I

_{8}, and I

_{14}are shown only if the flood intensity triggers a flood alarm, i.e., only if C(I

_{1}) ≥ 3. The predicted indicators I

_{j}are validated for the period from September 2019 to March 2021 (Section 3.4).

#### 2.7. Implementation in an FEWS

_{i}falls) over the next six tides. This requires the use of forecasted data X. The FEWS relies on the X forecasted data provided by the MARC (https://marc.ifremer.fr/, accessed on 15 July 2021) and DATASHOM (https://data.shom.fr/, accessed on 15 July 2021) platforms. These X data are pre-processed by extracting the data at the location of interest (Figure 1a), harmonising the time steps between the different variables originating from the data suppliers (the tide T, atmospheric surge S, wave height Hs, wave peak period Tp, wave direction Dp, wind speed U, and wind direction Du). A unified time step of 10 min is used to properly account for the tide-induced sea-level variations. In a second step, the automatic detection of high tides is performed on the dataset, and then, the X data are extracted over the 6 h windows centred on the high tides for the 6 next tides. Then, the metamodels (Y

_{i,i=1:18}) are run, providing the 18 outputs for each tide. These outputs are post-processed (providing Z

_{i,i=1:15}) and aggregated into the specific indicators (I

_{i,1:14}). Finally, the I

_{i}indicators are published through the FEWS.

^{©}software suite supports the FEWS web platform. To guarantee the scalability and shareability of the system, dedicated application programming interfaces (APIs) have been developed for the data processing chain. Finally, the accessibility of the FEWS is restricted to the members of the consortium and the final beneficiaries (the local user group) via secured access.

## 3. Results

#### 3.1. Grid Experiment and Numerical Modelling Results: Preliminary Analysis

_{Num}for the Y values extracted directly from the numerical results, i.e., to avoid misunderstanding with the Y metamodels); these are the (X,Y

_{Num}) datasets used to build the metamodels. The cross-validation figures provided in the next section illustrate the domain covered by Y

_{Num}in comparison with the defined indicator classes. As a preliminary analysis of the numerical results, for the scalar (functional) input grid experiments Sim1 and Sim2 defined in Section 2.5.2, numerical modelling indicates that floods occur (i.e., water enters into the inland domain of analysis) in 105 (155) scenarios out of the total number of scenarios, i.e., 144 (174). Thus, the functional inputs include fewer cases without floods than the scalar inputs. Regarding the numerical results obtained from the functional input grid experiment, the ratio of the number of scenarios where the pixel is flooded to the total number of scenarios is mapped (Figure 8), illustrating the range of flood events (in terms of the flooded area) covered by the numerical simulations: from non-flood events to severe flooding (with a computed maximal flooded surface area of 312 309 m

^{2}, i.e., 55% of the studied area).

#### 3.2. Metamodel Cross-Validation

_{1}to Y

_{6}), the widely used 10-fold cross-validation method is performed (see [40]). Figure 9 provides a comparison between the observations (the numerically calculated Y

_{num}values) and the predictions of the GP-based metamodels; their agreement reflects a highly satisfactory prediction quality. This consistency is further confirmed by the high coefficient of determination Q

^{2}calculated using the residuals derived from the cross-validation procedure. The closer Q

^{2}is to one, the more satisfactory the capability of the GP-based metamodel to predict the considered Y. In our case, Q

^{2}is not lower than 95%, and hence, it is considered satisfactory. The predictive capability of the RF model for Y

_{1}is measured by the accuracy of the classification (denoted ACC), which is defined as the ratio of the number of events correctly classified by the RF model to the total number of events. In our case, ACC reaches 92%, which can be considered satisfactory.

_{7}–Y

_{17}), are validated using a leave-one-out (LOO) cross-validation procedure. Here, using LOO cross-validation enables us to benefit from explicit virtual LOO formulas (Bachoc et al., 2013; Zhang and Wang, 2010). Figure 10 illustrates the performance of the metamodels on the prediction of the maximal flooded surface (Y

_{7}). The metamodelling quality is assessed by comparing the LOO predictions with the values obtained by the numerical model. As in the case of the scalar input metamodels, the results show a satisfactory prediction quality, which is further supported by a fairly high Q

^{2}value. In addition, the class is correctly predicted for the vast majority of the points (white dots). However, at this stage, we note that Y

_{7num}values equal to 0 are overestimated. Appendix B presents the validation plots for the metamodels for the prediction of Y

_{8}to Y

_{17}.

#### 3.3. Indicator Predictions: Raw Results, Optimisation, Hindcast, and Reinforced Hindcast

_{1}predictions over the continuous forcing conditions from 1900 to 2010 and the 48 damage events, together with the optimisation curve of V1, leading to V1 = 62 m

^{3}. With this value, considering that 0 < Z

_{1}< V1 leads to a simple warning and Z

_{1}≥ V1 leads to a real flood alarm, we obtain four true flood event alarms and two false alarms. Over the entire 110-year period, this threshold leads to the prediction of only nine flood events and 102 “warning” events, implying that for DEM2015–2018, there is an empirical probability of 1 “warning” (few instances of overtopping) per year and 1 “alarm” per decade. Regarding the two false alarms (1948 and 1957), it should be noted that for both events, the confidence level of the classification between no flooding and minor flooding is moderate [7] such that it is possible that minor flooding did not occur on either date. The 1904 event is classified with moderate confidence as a major flood from an analysis of the historical information [7] such that this event may have been a minor flood instead of a major flood, but we are sure that there was a flood. Thus, the number of false alarms (i.e., two) should be considered as the upper limit of the real number of false alarms. Finally, two events are not clearly identified in the damage event database: those on 18 December 1945 and 19 December 1945. However, after [60], strong erosive events may have occurred in December 1945. Focusing on the four remaining flood events of the damage database, (1) consistent with our validation assumption, Z

_{1}= 0 for two past minor flooding events and 0 < Z

_{1}< V1 for one past major flooding event (considering the less protective topo-bathymetry during the studied period), and (2) Z

_{1}= 0 for the past major flooding event on 10 January 2001. The result for this last event is not inconsistent. Indeed, in comparison to the other major flooding events, the water level, wave, and wind conditions are not exceptional (with a joint exceedance return period of the water level and significant wave height of less than 1 year); in fact, this event was caused by a coastal defence failure, which led to significant flooding [7]. The failure of coastal defences is not accounted for in our method/FEWS (see Section 4.1 for a more detailed discussion).

^{3}and the constraint scheme shown in Figure 5, we obtain predictions for all the indicators I

_{j}over the period 1900–2010. Figure 13 shows the results only for the events where Z

_{1}> 0 (i.e., the intensity indicator I

_{1}falling in a class larger or equal to 2) or Z

_{1}> V1 (i.e., such that C(I

_{1}) ≥ 3) for the sake of readability. First, we note the consistency of the predictions between the indicators: only minor flooding events are predicted, while neither the roads nor the crisis management buildings are flooded (I

_{9}to I

_{13}). The predictions indicate that the riskiest survey points are GP4 (I

_{5}) and G1 (I

_{6}). This is consistent with Figure 8 and with local knowledge, which indicates that the preferential pathway of flooding is in front of the cemetery (i.e., GP4). Furthermore, significant human risk (C(I

_{5}) and C(I

_{6}) reaching up to 4, in red) is predicted for these survey clusters (corresponding to I

_{5}and I

_{6}), while the intensity (I

_{1}) is small (C(I

_{1}) = 2 most of the time, in blue). This can physically be explained by the fact that both survey clusters are located in areas more subject to wave overtopping, i.e., locations where individual waves overtop the defences. Due to the stochastic behaviour of waves, in the (HT − 3 h:HT + 3 h) time window, only a single wave (or a few waves) may overtop the defences, leading to a local instantaneous water depth of a few tens of centimetres (i.e., C(I

_{5}) or C(I

_{6}) = 3 (0.1 to 0.25 m, in orange) or 4 (0.25 to 0.5 m, in red)), but they may move only a limited volume of water onto land (e.g., <V1, with V1 = 62 m

^{3}); consequently, the flood intensity remains small (C(I

_{1}) = 2, blue class, Figure 3).

_{1}, I

_{7}through I

_{13}), numerical simulations are performed for the nine events where the predicted class of indicator I

_{1}is larger than or equal to 3 (Figure 14). The comparison with the predicted values (Figure 13) shows that our predictions are relatively coherent with the “truth” (here, the direct numerical results Y

_{num}), even for these “on the edge” events, i.e., events that are difficult to properly predict with metamodels. For this hindcast, there are no cases where the intensity I

_{1}is large enough to fulfil the visualisation conditions of the I

_{14}indicator.

#### 3.4. FEWS: Operational Use of the FEWS and First Feedbacks

_{7}, I

_{8}, and I

_{14}, which are provided only when a flood event (alarm) is predicted (C(I

_{1}) ≥ 3). In addition, for I

_{14}, the cross-validation reveals a non-negligible confidence interval (e.g., ±40 cm, Figure A4 in Appendix C); in comparison with the water height classes (Figure 3), we stipulate that the I

_{14}predictions are of low confidence. Access to the FEWS interface was provided to the local users in December 2020. According to the users’ first feedback, they found it very easy to use and to understand.

_{1}) should be 2. Over the study period, the FEWS predicts C(I

_{1}) = 1 most of the time. Table 3 lists all the events for which either the FEWS predicted C(I

_{1}) > 1 or an official VVS warning was issued by Meteo-France at the department scale. With X

_{MARC}(X

_{DATASHOM}), the FEWS predicts eight (1) events “close to flood” (C(I

_{1}) = 2); i.e., the FEWS issued only warnings but no alarms for flooding events. Such predictions (i.e., usually C(I

_{1}) = 1, a few cases with C(I

_{1}) = 2, and no cases where C(I

_{1}) > 2) are in fair agreement with the information provided by the town hall. To complement the town hall information, photos were gathered on the internet. For the events for which we found photos (Table 3), they allowed the identification of high water levels in the study area and a few instances of overtopping events either within or near the study area. These photos confirm the good agreement between the predictions and observations. The only “discrepancy” is discovered for the last event (30 January 2021), where few instances of overtopping were captured in a photograph, while the FEWS predicts C(I

_{1}) = 1. As the numerical modelling with the X

_{MARC}input provides C(I

_{1}) = 2, this finding implies that improved metamodels for such types of events could lead to C(I

_{1}) = 2.

_{1}performed 3 days in advance is, for most events, equal to that performed 1 day in advance); consequently, we can trust the predictions obtained 3 days in advance for the validation period. Table 3 also includes the VVS warnings over the study period. The FEWS issues more warnings than the VVS, albeit with a lower level (blue level, “close to flood” events) than those issued by the VVS (orange level). The VVS has four warning levels (in increasing severity: green, yellow, orange, red). The recommendation associated with the orange level is that dangerous phenomena are expected and that the population should be very vigilant, stay up to date with developments, and follow the safety advice issued by authorities. Thus, our FEWS predictions seem closer to what happens locally (either nothing or only a few instances of overtopping), at least over the investigated time span from September 2019 to March 2021.

_{MARC}data are used; if these data are not available, the X

_{DATASHOM}(which are always available) are used. This allows a small security margin to be adopted but still limits the number of false alarms (as highlighted in the validation for the period 2019–2021 where the FEWS, even with the X

_{MARC}data

_{,}provided no alarms and only a few blue warnings).

## 4. Discussion and Recommendations

#### 4.1. Discussion

_{7:18}) close to 0, we adopt a pragmatic approach of using the classification metamodel (Y

_{1}) outputs and combining them with the GP-based metamodel outputs. However, from a theoretical point of view, this is not fully satisfactory. One way to improve the indicators relying on the GP-based metamodels close to 0 is to increase the number of learning scenarios providing Y = 0 values. We tested this strategy by adding 40 non-flood event scenarios to the existing 174 scenarios used in the learning dataset; no significant improvement was found. A more promising perspective of improvement is to use refinements of GP models that are tailored for modelling positive functions and may provide more accurate metamodel predictions of output values close to zero. Two main examples of these refinements are truncated GP models [57] and constrained GP models [61,62]. If metamodels other than GPs are considered, then it would also be possible to have an interaction between the classification problem of zero outputs and the regression problem of non-zero outputs. Possibilities that would warrant investigation are to tailor the loss function for metamodels relying on empirical risk minimisation (see [40]) or to use nearest-neighbour methods. In the latter case, the rationale is that the averages of the observed outputs are non-negative and are exactly zero when all outputs are zero.

#### 4.2. Recommendations

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Acronyms and Abbreviations

ACO-Gp | Ant colony-based algorithm for the structural optimisation of Gaussian process models with scalar and/or functional inputs |

CRAN | Comprehensive R Archive Network |

DDTM56 | Direction Départementale des Territoires et de la Mer (translation: Departmental Directorate of Territories and the Sea) of French department 56 (Morbihan) |

DEM | Digital elevation model |

DGPS | Differential Global Positioning System |

DHI | Danish Hydraulic Institute |

FEWS | Forecast and early warning system |

GP | Gaussian process |

HT | High tide |

HPC | High-performance computing |

IGN | Institut National de l’Information Géographique et Forestière (translation: National Institute of Geographic and Forestry Information) |

LOO | Leave one out |

LOPS | Laboratoire d’Océanographie Physique et Spatiale (translation: Physical and Space Oceanography Laboratory) |

MARC | Modélisation et Analyse pour la Recherche Côtière (translation: Modelling and Analysis for Coastal Research) |

MEDDTL | Ministère de l’Écologie, du Développement Durable des Transports et du Logement (translation: Ministry of Ecology, Sustainable Development, Transport and Housing) |

MIKE21 | software package for the 2D modelling of hydrodynamics, waves, sediment dynamics, water quality and ecology; for more details, see https://www.mikepoweredbydhi.com/products/mike-21-3, accessed on 25 July 2021 |

PCA | Principal component analysis |

RF | Random forest |

RGE | Référentiel à grande echelle (translation: large-scale reference system) |

TELEMAC2D | module of the TELEMAC system for solving the Saint-Venant equations using The finite-element or finite-volume method and a computational mesh of triangular elements; for more details, see http://www.opentelemac.org, accessed on 25 July 2021 |

SDIS56 | Service Départemental d’Incendie et de Secours (translation: Departmental Fire and Rescue Service) of French department 56 (Morbihan) |

SHOM | Service Hydrographique et Océanographique de la Marine (translation: French Navy Hydrographic and Oceanographic Service) |

SWASH | Simulating Waves till Shore. SWASH is a general-purpose numerical tool for simulating unsteady, non-hydrostatic, free-surface, rotational flow and transport phenomena in coastal waters driven by waves, tides, buoyancy and wind forces. It provides a general basis for describing wave transformations from deep water to a beach, port, or harbour, complex changes to rapidly varied flows, and density-driven flows in coastal seas, estuaries, lakes and rivers. For more details, see https://swash.sourceforge.io/, accessed on 25 July 2021 |

VISOV | Volontaires Internationaux et Soutien Opérationnel Virtuel (translation: International Volunteers and Virtual Operational Support) |

VOST | Virtual Operations Support Team |

VVS | Vigilance Vague Submersion (translation: wave-flood warning) |

WW3 | WAVEWATCH III^{®}, a community wave modelling framework that includes the latest scientific advancements in the field of wind-wave modelling and dynamics |

## Appendix A. The Flood Event on 10 March 2008 (Observations and Model Results)

**Figure A1.**Model validation: maximal simulated water depth and observed flooded houses during the Johanna event. Source: [6].

## Appendix B. Cross-Validation Plots for Metamodels Y_{8} to Y_{13}

^{2}values for the continuous outputs and a high percentage of hits for the categorical outputs.

**Figure A2.**Cross-validation of the Y

_{8}–Y

_{11}metamodels: comparison between the observations (the numerically calculated Y values) and the predictions of the GP-based metamodels. The colour scales correspond to the colour scales of the indicators using these metamodels (see Figure 3 and Table 1).

**Figure A3.**Cross-validation of the Y

_{12}–Y

_{17}metamodels: comparison between the observations (the numerically calculated Y values) and the predictions of the GP-based metamodels. The colour scales correspond to the colour scales of the indicators using these metamodels (see Figure 3 and Table 1).

## Appendix C. Cross-Validation Plots for Metamodel Y_{I8}

**Figure A4.**Cross-validation of the maximal water heights predicted by metamodel Y

_{18}and provided by the numerical model for scenarios 50, 42, and 10 among the 174 learning scenarios. X

_{i}is the index of the spatial points (from 1 to 889, sorted in increasing order using the numerical results for each scenario). The panels show the RMSE, Q

^{2}, and CA (coverage accuracy) indicators. The CA indicator quantifies how many test points are contained in the two standard-deviation (denoted σ) confidence interval.

## Appendix D. Screen Captures of the FEWS User Interface

**Figure A5.**Screen capture of the FEWS webpage synthesising predictions for the six next high tides. The left panel shows the results of the I

_{1}indicator (shown in green here, as no flood is predicted).

**Figure A6.**Screen capture of the FEWS webpage showing indicators I

_{1}to I

_{6}and I

_{9}to I

_{13}. The other indicators are shown only when C(I

_{1}) > 2, which is not the case for the present prediction.

**Figure A7.**Screen capture of the FEWS webpage showing the forcing conditions X (here, X = X

_{MARC}). The forcing conditions in orange correspond to the last major flooding event (10 March 2008, Windstorm Johanna).

## References

- McGranahan, G.; Balk, D.; Anderson, B. The rising tide: Assessing the risks of climate change and human settlements in low elevation coastal zones. Environ. Urban.
**2007**, 19, 17–37. [Google Scholar] [CrossRef] - Oppenheimer, M.; Glavovic, B.C.; Hinkel, J.; van de Wal, R.; Magnan, A.K.; Abd-Elgawad, A.; Cai, R.; Cifuentes-Jara, M.; DeConto, R.M.; Ghosh, T.; et al. Sea Level Rise and Implications for Low-Lying Islands, Coasts and Communities. In IPCC Special Report on the Ocean and Cryosphere in a Changing Climate; Pörtner, H.-O., Roberts, D.C., Masson-Delmotte, V., Zhai, P., Tignor, M., Poloczanska, E., Mintenbeck, K., Alegría, A., Nicolai, M., Okem, A., et al., Eds.; IPCC: Geneva, Switzerland, 2019. [Google Scholar]
- Jongman, B. Effective adaptation to rising flood risk. Nat. Commun.
**2018**, 9, 1–3. [Google Scholar] [CrossRef] [Green Version] - Zijlema, M.; Stelling, G.; Smit, P. SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters. Coast Eng.
**2011**, 58, 992–1012. [Google Scholar] [CrossRef] - Le Roy, S.; Pedreros, R.; André, C.; Paris, F.; Lecacheux, S.; Marche, F.; Vinchon, C. Coastal flooding of urban areas by overtopping: Dynamic modelling application to the Johanna storm (2008) in Gâvres (France). Nat. Hazards Earth Syst. Sci.
**2015**, 15, 2497–2510. [Google Scholar] [CrossRef] [Green Version] - Idier, D.; Pedreros, R.; Rohmer, J.; Le Cozannet, G. The Effect of Stochasticity of Waves on Coastal Flood and Its Variations with Sea-level Rise. J. Mar. Sci. Eng.
**2020**, 8, 798. [Google Scholar] [CrossRef] - Idier, D.; Rohmer, J.; Pedreros, R.; Le Roy, S.; Lambert, J.; Louisor, J.; Le Cozannet, G.; Le Cornec, E. Coastal flood: A composite method for past events characterisation providing insights in past, present and future hazards—joining historical, statistical and modelling approaches. Nat. Hazards
**2020**, 101, 465–501. [Google Scholar] [CrossRef] [Green Version] - Doong, D.-J.; Chuang, L.Z.-H.; Wu, L.-C.; Fan, Y.-M.; Kao, C.C.; Wang, J.-H. Development of an operational coastal flooding early warning system. Nat. Hazards Earth Syst. Sci.
**2012**, 12, 379–390. [Google Scholar] [CrossRef] - Tromble, E.; Kolar, R.; Dresback, K.; Hong, Y.; Vieux, B.; Luettich, R.; Gourley, J.; Kelleher, K.; Van Cooten, S. Aspects of Coupled Hydrologic-Hydrodynamic Modeling for Coastal Flood Inundation. In Proceedings of the Eleventh International Conference on Estuarine and Coastal Modeling, Seattle, WA, USA, 4–6 November 2009; pp. 724–743. [Google Scholar]
- Stansby, P.; Chini, N.; Apsley, D.; Borthwick, A.G.L.; Bricheno, L.M.; Horrillo-Caraballo, J.M.; McCabe, M.; Reeve, D.E.; Rogers, B.; Saulter, A.; et al. An integrated model system for coastal flood prediction with a case history for Walcott, UK, on 9 November 2007. J. Flood Risk Manag.
**2013**, 6, 229–252. [Google Scholar] [CrossRef] [Green Version] - Stokes, K.; Poate, T.; Masselink, G.; King, E.; Saulter, A.; Ely, N. Forecasting coastal overtopping at engineered and naturally defended coastlines. Coast. Eng.
**2020**, 164, 103827. [Google Scholar] [CrossRef] - Merrifield, M.A.; Johnson, M.; Guza, R.T.; Fiedler, J.W.; Young, A.P.; Henderson, C.S.; Lange, A.M.Z.; O’Reilly, W.C.; Ludka, B.C.; Okihiro, M.; et al. An early warning system for wave-driven coastal flooding at Imperial Beach, CA. Nat. Hazards
**2021**, 108, 2591–2612. [Google Scholar] [CrossRef] - Mosavi, A.; Ozturk, P.; Chau, K.-W. Flood Prediction Using Machine Learning Models: Literature Review. Water
**2018**, 10, 1536. [Google Scholar] [CrossRef] [Green Version] - Fotovatikhah, F.; Herrera, M.; Shamshirband, S.; Chau, K.-W.; Ardabili, S.F.; Piran, J. Survey of computational intelligence as basis to big flood management: Challenges, research directions and future work. Eng. Appl. Comput. Fluid Mech.
**2018**, 12, 411–437. [Google Scholar] [CrossRef] [Green Version] - Kaya, C.M.; Tayfur, G.; Gungor, O. Predicting flood plain inundation for natural channels having no upstream gauged stations. J. Water Clim. Chang.
**2017**, 10, 360–372. [Google Scholar] [CrossRef] - Dong, S.; Yu, T.; Farahmand, H.; Mostafavi, A. A hybrid deep learning model for predictive flood warning and situation awareness using channel network sensors data. Comput. Civ. Infrastruct. Eng.
**2020**, 36, 402–420. [Google Scholar] [CrossRef] - Dai, W.; Tang, Y.; Zhang, Z.; Cai, Z. Ensemble Learning Technology for Coastal Flood Forecasting in Internet-of-Things-Enabled Smart City. Int. J. Comput. Intell Syst
**2021**, 14, 166. [Google Scholar] [CrossRef] - Rohmer, J.; Idier, D. A meta-modelling strategy to identify the critical offshore conditions for coastal flooding. Nat. Hazards Earth Syst. Sci.
**2012**, 12, 2943–2955. [Google Scholar] [CrossRef] - Jia, G.; Taflanidis, A.A. Kriging metamodeling for approximation of high-dimensional wave and surge responses in real-time storm/hurricane risk assessment. Comput. Methods Appl. Mech. Eng.
**2013**, 261–262, 24–38. [Google Scholar] [CrossRef] - Simpson, T.; Poplinski, J.; Koch, P.N.; Allen, J. Metamodels for Computer-based Engineering Design: Survey and recommendations. Eng. Comput.
**2001**, 17, 129–150. [Google Scholar] [CrossRef] [Green Version] - Basher, R. Global early warning systems for natural hazards: Systematic and people centred. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.
**2006**, 364, 2167–2182. [Google Scholar] [CrossRef] - Rohmer, J.; Idier, D.; Pedreros, R. A nuanced quantile random forest approach for fast prediction of a stochastic marine flooding simulator applied to a macrotidal coastal site. Stoch. Environ. Res. Risk Assess.
**2020**, 34, 867–890. [Google Scholar] [CrossRef] - Betancourt, J.; Bachoc, F.; Klein, T.; Idier, D.; Pedreros, R.; Rohmer, J. Gaussian process metamodeling of functional-input code for coastal flood hazard assessment. Reliab. Eng. Syst. Saf.
**2020**, 198, 106870. [Google Scholar] [CrossRef] [Green Version] - López-Lopera, A.F.; Idier, D.; Rohmer, J.; Bachoc, F. Multioutput Gaussian processes with functional data: A study on coastal flood hazard assessment. arXiv. 2020. Available online: https://arxiv.org/abs/2007.14052 (accessed on 25 July 2021).
- Idier, D.; Aurouet, A.; Bachoc, F.; Baills, A.; Betancourt, J.; Durand, J.; Mouche, R.; Rohmer, J.; Gamboa, F.; Klein, T.; et al. Toward a User-Based, Robust and Fast Running Method for Coastal Flooding Forecast, Early Warning, and Risk Prevention. J. Coast. Res.
**2020**, 95, 1111–1116. [Google Scholar] [CrossRef] - Cariolet, J.M. Inondation des Côtes Basses et Risques Associés en Bretagne: Vers une Redéfinition des Processus Hydrodynamiques Liés aux Conditions Météo-Océaniques et des Paramètres Morphosédimentaires. Océan, Atmosphère. Ph.D. Thesis, Université de Bretagne Occidentale, Brest, France, 2011. [Google Scholar]
- Pedreros, R.; Idier, D.; Le Roy, S.; David, A.; Schaeffer, C.; Durand, J.; Desmazes, F. Infragravity Waves in a Complex Macro-tidal Environment: High Frequency Hydrodynamic Measurements and Modelling. J. Coast. Res.
**2020**, 95, 1235–1239. [Google Scholar] [CrossRef] - Haiden, T.; Janousek, M.; Vitart, F.; Ben-Bouallegue, Z.; Ferranti, L.; Prates, F. Evaluation of ECMWF Forecasts, Including the 2021 Upgrade. Available online: https://www.ecmwf.int/en/elibrary/20142-evaluation-ecmwf-forecasts-including-2021-upgrade (accessed on 8 October 2021).
- Kramer, M.; Terheiden, K.; Wieprecht, S. Safety criteria for the trafficability of inundated roads in urban floodings. Int. J. Disaster Risk Reduct.
**2016**, 17, 77–84. [Google Scholar] [CrossRef] [Green Version] - Jonkman, S.; Penningrowsell, E.C. Human Instability in Flood Flows1. JAWRA J. Am. Water Resour. Assoc.
**2008**, 44, 1208–1218. [Google Scholar] [CrossRef] - MEDDTL. Guide Méthodologique Plans de Prévention des Risques Littoraux, 2014. Available online: https://www.ecologie.gouv.fr/sites/default/files/Guide%20PPRL%20-%20version%20finale%20mai%202014.pdf (accessed on 25 July 2021).
- Gallien, T.W.; Kalligeris, N.; Delisle, M.-P.C.; Tang, B.-X.; Lucey, J.T.D.; Winters, M.A. Coastal Flood Modeling Challenges in Defended Urban Backshores. Geosciences
**2018**, 8, 450. [Google Scholar] [CrossRef] [Green Version] - Van der Meer, J.W.; Allsop, N.W.H.; Bruce, T.; De Rouck, J.; Kortenhaus, A.; Pullen, T.; Schüttrumpf, H.; Troch, P.; Zanuttigh, B. Manual on Wave Overtopping of Sea Defences and Related Structures. An Overtopping Manual Largely Based on European Research, but for Worldwide Application. EurOtop. 2018. Available online: www.overtopping-manual.com (accessed on 12 October 2020).
- Grilli, A.R.; Westcott, G.; Grilli, S.T.; Spaulding, M.L.; Shi, F.; Kirby, J.T. Assessing Coastal Hazard from Extreme Storms with a Phase Resolving Wave Model: Case Study of Narragansett, RI, USA. Coast. Eng.
**2020**, 160, 103735. [Google Scholar] [CrossRef] - Nicolae-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] [Green Version] - SWASH Team. Swash User Manual, Swash Version 6.01, TU Delft. 2019. Available online: http://www.tudelft.nl/swash (accessed on 25 July 2021).
- Ardhuin, F.; Rogers, W.E.; Babanin, A.V.; Filipot, J.; Magne, R.; Roland, A.; Van der Westhuysen, A.; Queffeulou, P.; Lefevre, J.; Aouf, L.; et al. Semiempirical dissipation source functions for ocean waves. Part I: Definition, calibration, and validation. J. Phys. Oceanogr.
**2010**, 40, 917–941. [Google Scholar] [CrossRef] [Green Version] - Le Maître, O.P.; Knio, O.M. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics; Springer: Berlin/Heidelberg, Germany, 2010; ISBN 978-90-481-3520-2. [Google Scholar]
- Rasmussen, C.E.; Williams, C.K.I. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning); The MIT Press: Cambridge, MA, USA, 2005. [Google Scholar]
- Hastie, T.; Tibshirani, R.; Friedman, J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction; Springer: Berlin/Heidelberg, Germany, 2009; ISBN 978-0-387-84858-7. [Google Scholar]
- Wasserman, L. All of Nonparametric Statistics; Springer: Berlin/Heidelberg, Germany, 2006; ISBN 10 0387251456. [Google Scholar]
- Gouldby, B.; Méndez, F.J.; Guanche, Y.; Rueda, A.; Mínguez, R. A methodology for deriving extreme nearshore sea conditions for structural design and flood risk analysis. Coast Eng.
**2014**, 88, 15–26. [Google Scholar] [CrossRef] [Green Version] - Tharwat, A. Linear vs. quadratic discriminant analysis classifier: A tutorial. Int. J. Appl. Pattern Recognit.
**2016**, 3, 145–180. [Google Scholar] [CrossRef] - Perrin, T.; Roustant, O.; Rohmer, J.; Alata, O.; Naulin, J.; Idier, D.; Pedreros, R.; Moncoulon, D.; Tinard, P. Functional principal component analysis for global sensitivity analysis of model with spatial output. Reliab. Eng. Syst. Saf.
**2021**, 211, 107522. [Google Scholar] [CrossRef] - Rohmer, J.; Lecacheux, S.; Pedreros, R.; Quetelard, H.; Bonnardot, F.; Idier, D. Dynamic parameter sensitivity in numerical modelling of cyclone-induced waves: A multi-look approach using advanced meta-modelling techniques. Nat. Hazards
**2016**, 84, 1765–1792. [Google Scholar] [CrossRef] - Li, M.; Wang, R.-Q.; Jia, G. Efficient dimension reduction and surrogate-based sensitivity analysis for expensive models with high-dimensional outputs. Reliab. Eng. Syst. Saf.
**2020**, 195, 106725. [Google Scholar] [CrossRef] - Al Kajbaf, A.; Bensi, M. Application of surrogate models in estimation of storm surge:A comparative assessment. Appl. Soft Comput.
**2020**, 91, 106184. [Google Scholar] [CrossRef] - Breiman, L. Random forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef] [Green Version] - De Boor, C. A Practical Guide to Splines. Applied Mathematical Sciences; Springer: New York, NY, USA, 1978; p. 348. [Google Scholar]
- Jolliffe, I. Principal Component Analysis; Springer: Berlin/Heidelberg, Germany, 2011. [Google Scholar]
- Antoniadis, A.; Helbert, C.; Prieur, C.; Viry, L. Spatio-temporal metamodeling for West African monsoon. Environmetrics
**2012**, 23, 24–36. [Google Scholar] [CrossRef] [Green Version] - Muehlenstaedt, T.; Fruth, J.; Roustant, O. Computer experiments with functional inputs and scalar outputs by a norm-based approach. Stat. Comput.
**2016**, 27, 1083–1097. [Google Scholar] [CrossRef] [Green Version] - Nanty, S.; Helbert, C.; Marrel, A.; Pérot, N.; Prieur, C. Sampling, Metamodeling, and Sensitivity Analysis of Numerical Simulators with Functional Stochastic Inputs. SIAM/ASA J. Uncertain. Quantif.
**2016**, 4, 636–659. [Google Scholar] [CrossRef] - Betancourt, J.; Bachoc, F.; Klein, T.; Gamboa, F. Ant Colony Based Model Selection for Functional-Input Gaussian Process Regression. 2020. Available online: https://hal.archives-ouvertes.fr/hal-02532713v2 (accessed on 25 July 2021).
- R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria. Available online: https://www.R-project.org/ (accessed on 25 July 2021).
- Betancourt, J.; Bachoc, F.; Klein, T.R. Package Manual: Gaussian Process Regression for Scalar and Functional Inputs with funGp-The In-Depth Tour. RISCOPE Project. 2020. Available online: https://hal.archives-ouvertes.fr/hal-02536624 (accessed on 25 July 2021).
- Stein, M.L. Prediction and inference for truncated spatial data. J. Comput. Graph. Stat.
**1992**, 1, 91–110. [Google Scholar] - Gormley, C.; Tong, Z. Elasticsearch: The Definitive Guide: A Distributed Real-Time Search and Analytics Engine; O’Reilly Media: Sebastopol, CA, USA, 2015; ISBN 9781449358525. [Google Scholar]
- Chang, W.; Cheng, J.; Allaire, J.; Xie, Y.; McPherson, J. Shiny: Web Application Framework for R. R Package Version 1.5.0. 2020. Available online: https://CRAN.R-project.org/package=shiny (accessed on 25 July 2021).
- Le Cornec, E.; Le Bris, E.; Van Lierde, M. Atlas des Risques Littoraux sur le Département du Morbihan. Phase 1: Recensement et Conséquences des Tempêtes et Coups de Vent Majeurs; Rapport d’étude GEOS-DHI; Direction Départementales des Territoires et de la Mer du Morbihan: Vannes, France, 2012. [Google Scholar]
- Vanhatalo, J.; Vehtari, A. Sparse log Gaussian processes via MCMC for spatial epidemiology. Proc. Mach. Learn. Res.
**2007**, 1, 73–89. [Google Scholar] - López-Lopera, A.F.; Bachoc, F.; Durrande, N.; Roustant, O. Finite-dimensional Gaussian approximation with linear inequality constraints. SIAM/ASA J. Uncertain. Quantif.
**2018**, 6, 1224–1255. [Google Scholar] [CrossRef] - Bachoc, F.; Suvorikova, A.; Ginsbourger, D.; Loubes, J.-M.; Spokoiny, V. Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding. Electron. J. Stat.
**2020**, 14, 2742–2772. [Google Scholar] [CrossRef] - Liu, X.; Guillas, S. Dimension reduction for Gaussian process emulation: An application to the influence of bathymetry on tsunami heights. SIAM/ASA J. Uncertain. Quantif.
**2017**, 5, 787–812. [Google Scholar] [CrossRef] - Jonkman, S.N.; Kok, M.; Vrijling, J.K. Flood Risk Assessment in the Netherlands: A Case Study for Dike Ring South Holland. Risk Anal.
**2008**, 28, 1357–1374. [Google Scholar] [CrossRef] - Kwadijk, J.C.J.; Haasnoot, M.; Mulder, J.P.M.; Hoogvliet, M.M.C.; Jeuken, A.B.M.; van der Krogt, R.A.A.; van Oostrom, N.G.C.; Schelfhout, H.A.; van Velzen, E.H.; van Waveren, H.; et al. Using adaptation tipping points to prepare for climate change and sea level rise: A case study in the Netherlands. Wiley Interdiscip. Rev. Clim. Chang.
**2010**, 1, 729–740. [Google Scholar] [CrossRef] - Mel, R.A.; Viero, D.P.; Carniello, L.; D’Alpaos, L. Optimal floodgate operation for river flood management: The case study of Padova (Italy). J. Hydrol. Reg. Stud.
**2020**, 30, 100702. [Google Scholar] [CrossRef] - Harley, M.D.; Kinsela, M.A.; Sánchez-García, E.; Vos, K. Shoreline change mapping using crowd-sourced smartphone images. Coast. Eng.
**2019**, 150, 175–189. [Google Scholar] [CrossRef] - Silvertown, J. A new dawn for citizen science. Trends Ecol. Evol.
**2009**, 24, 467–471. [Google Scholar] [CrossRef] - Roger, E.; Tegart, P.; Dowsett, R.; Kinsela, M.A.; Harley, M.D.; Ortac, G. Maximising the potential for citizen science in New South Wales. Aust. Zoöl.
**2020**, 40, 449–461. [Google Scholar] [CrossRef] - Liu, S.B. Crisis Crowdsourcing Framework: Designing Strategic Configurations of Crowdsourcing for the Emergency Management Domain. Comput. Support. Cooperative Work. (CSCW)
**2014**, 23, 389–443. [Google Scholar] [CrossRef] - Kankanamge, N.; Yigitcanlar, T.; Goonetilleke, A. Kamruzzaman Can volunteer crowdsourcing reduce disaster risk? A systematic review of the literature. Int. J. Disaster Risk Reduct.
**2019**, 35, 101097. [Google Scholar] [CrossRef] - Bates, P.D.; Dawson, R.J.; Hall, J.W.; Horritt, M.S.; Nicholls, R.J.; Wicks, J.; Hassan, M.A.A.M. Simplified two-dimensional numerical modelling of coastal flooding and example applications. Coast. Eng.
**2005**, 52, 793–810. [Google Scholar] [CrossRef] - 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] - Haigh, I.D.; Ozsoy, O.; Wadey, M.P.; Nicholls, R.; Gallop, S.L.; Wahl, T.; Brown, J. An improved database of coastal flooding in the United Kingdom from 1915 to 2016. Sci. Data
**2017**, 4, 170100. [Google Scholar] [CrossRef] [Green Version] - Tavares, A.O.; Barros, J.L.; Freire, P.; Santos, P.P.; Perdiz, L.; Fortunato, A.B. A coastal flooding database from 1980 to 2018 for the continental Portuguese coastal zone. Appl. Geogr.
**2021**, 135, 102534. [Google Scholar] [CrossRef] - Azzimonti, D.; Ginsbourger, D.; Chevalier, C.; Bect, J.; Richet, Y. Adaptive design of experiments for conservative estimation of excursion sets. Technometrics
**2021**, 63, 13–26. [Google Scholar] [CrossRef] [Green Version] - Boudière, E.; Maisondieu, C.; Ardhuin, F.; Accensi, M.; Pineau-Guillou, L.; Lepesqueur, J. A suitable metocean hindcast database for the design of Marine energy converters. Int. J. Mar. Energy
**2013**, 3–4, e40–e52. [Google Scholar] [CrossRef] [Green Version] - Dee, D.P.; Balmaseda, M.; Balsamo, G.; Engelen, R.; Simmons, A.J.; Thépaut, J.-N. Toward a consistent reanalysis of the climate system. Bull. Am. Meteor. Soc.
**2014**, 95, 1235–1248. [Google Scholar] [CrossRef]

**Figure 1.**Location and topo-bathymetry of the study site (

**a**,

**b**) and computational domains of the models (WW3 and SWASH) in the modelling chain (

**a**). The star indicates the location of the offshore wave forcing. Panel (

**b**) is adapted from Idier et al. (2020c) and updated (the local DEM, DEM2008, was replaced by DEM2015–2018, see Section 2.4).

**Figure 3.**Colour scale for each indicator I

_{j}. For each indicator, the number of classes differs, ranging from 1 to 4, 1 to 5, or 1 to 6, depending on the indicator.

**Figure 4.**Three main steps in the construction of a metamodel. Here, the “true” model is a function $f$ of the input vector X = (x

_{1},x

_{2}). First, a design of experiments is created, consisting of 12 pairs of input values (left plot). Second, the corresponding 12 computations of the “true” model are carried out (centre plot), providing the 12 input/output pairs constituting the data points needed to construct the metamodel (third plot from the left). Third, the metamodel is a function of the full input domain (here, a square) that interpolates (or approximates) the 12 input/output pairs (right plot).

**Figure 5.**Logic tree to combine the different metamodel outputs Z

_{k}and construct the indicators I

_{j}, with C corresponding to the classification shown in Figure 3. The star symbol (*) indicates that a post-processing based on logical quantitative relations (see the box bottom left) is applied.

**Figure 6.**Simplified backend architecture of the FEWS. The MARC (https://marc.ifremer.fr/, accessed on 15 July 2021) and DATASHOM (https://data.shom.fr/, accessed on 15 July 2021) platforms provide the X forecasted data.

**Figure 7.**X dataset: (

**a**) learning dataset used for the scalar input metamodels (i is the scenario index from 1 to 144), (

**b**) learning dataset used for the functional input metamodels (174 curves for the 174 scenarios), and (

**c**) distribution of the data from the historical hydro-meteorological database (1900–2016, data from [7]). ξ IGN69 (

**top**panel) is the water level resulting from the mean sea level, tide, and atmospheric storm surge referenced to the IGN69 vertical datum. The horizontal dotted red line (

**top**panel) indicates the threshold for which land is flooded only under the action of the mean sea level, tide, and atmospheric storm surge.

**Figure 8.**Ratio of the number of scenarios where the pixel is flooded to the total number of scenarios for the functional input grid experiment.

**Figure 9.**Cross-validation of the Y

_{1}to Y

_{6}metamodels: comparison between the observations (the numerically calculated Y

_{num}values) and the predictions of the GP-based metamodels. The predictive capability is measured by the coefficient of determination Q

^{2}(the closer Q

^{2}is to one, the higher the prediction quality) and the accuracy (ACC) for the classifier associated with Y

_{1}(see Section 2.5.3 for details) The colour scales in panels (

**a**,

**b**) correspond to the colour scales of indicators I

_{1}(classes 1 and 2) and indicators I

_{2}through I

_{6}, respectively.

**Figure 10.**Cross-validation of the Y

_{7}metamodel: comparison between the observations (numerically calculated Y

_{num}values) and the predictions of the GP-based metamodels. The predictive capability is measured by Q

^{2}(the closer Q

^{2}is to one, the higher the prediction quality). The colour scale corresponds to the colour scale of indicator I

_{1}(except that there is no “blue” class here). White dots indicate a correct class prediction; the remaining points are coloured according to the predicted class.

**Figure 11.**Cross-validation of the Y

_{18}metamodel. (

**a**) RMSE over the 174 scenarios of the learning dataset computed by LOO cross-validation. (

**b**) Y

_{18}“predictions” obtained with the metamodel for three of the 174 scenarios by LOO cross-validation compared with the “observations” Y

_{num}obtained directly from the numerical model outputs. The colour scale in panel (

**b**) corresponds to the colour scale of indicator I

_{14}.

**Figure 12.**Prediction of Z

_{1}over the period 1900–2010 (

**a**) and the numbers of true and false alarms over the 48 damage database events versus the V1 threshold on Z

_{1}(b). In (

**a**,

**b**), the dashed line indicates the selected threshold after optimisation (V1 = 62 m

^{3}). In (

**a**), the bolded dates correspond to highly confident information in the damage event database, while italicised dates correspond to moderately confident information in the damage event database, i.e., meaning that there is damage but that we are not fully certain of our classification. In (

**b**), a true (false) alarm corresponds to case where Z

_{1}≥ V1 (Z

_{1}< V1) and a (no) historical flood has been reported.

**Figure 13.**Hindcasts of indicators I

_{1}to I

_{13}for cases where (

**a**) there are at least a few instances of overtopping (i.e., C(I

_{1}) ≥ 2) and (

**b**) the flood is at least of minor intensity (i.e., C(I

_{1}) ≥ 3). The colour bars correspond to the colour code defined for each indicator (see Figure 3). The dates corresponding to events 1 through 9 in panel (

**b**) are (in order) 2 February 1904, 9 January 1924, 18 December 1945, 19 December 1945, 27 January 1948, 29 January 1948, 15 February 1957, 10 March 2008, and 28 February 2010.

**Figure 14.**Results from the numerical simulations of the nine events identified in Figure 13b (such that C(I

_{1}) ≥ 3 based on the meta-models and post-processing outputs). (

**a**) Indicators directly computed from the numerical hydrodynamic simulations without any post-processing; (

**b**) maximal water height (m) computed from the numerical output over 6 h with a time step of 1 min. The respective flood surface areas (m

^{2}) in panel (

**b**) are 5589, 12,006, 13,860, 3465, 8208, 2070, 2088, 4167, and 1215.

Needs | Indicator I_{j} | j |
---|---|---|

- •
- Flood event or not
- •
- Flood intensity, e.g., whether a flood is larger than the one induced by Johanna
| Flood intensity | 1 |

- •
- Ensure the safety of Gâvres municipality and emergency service employees during flood survey operations
- •
- Trigger surveys by Gâvres municipality and emergency services
| Human risk at survey point GP1 | 2 |

Human risk at survey point GP2 | 3 | |

Human risk at survey point GP3 | 4 | |

Human risk at survey point GP4 | 5 | |

Human risk at survey point G1 | 6 | |

- •
- Knowing how many and which type of relevant pumping engines to bring to the territory
| Mean water discharge | 7 |

Maximal water discharge | 8 | |

- •
- Accessibility and functioning of crisis management buildings
| Water height in front of the town hall | 9 |

Water height in front of the gymnasium | 10 | |

- •
- Practicability of roads (yes or no) for passenger car and rescue vehicles
- •
- Emergency operation triggering
| Practicability of road portion 1 | 11 |

Practicability of road portion 2 | 12 | |

Practicability of road portion 3 | 13 | |

- •
- Rescue operation triggering (e.g., as soon as the water depth exceeds 0.1 m in residential areas, emergency services must intervene)
- •
- Houses whose inhabitants should be evacuated
| Water height in hundreds of pre-selected locations | 14 |

**Table 2.**Computed quantities Yi, intermediate variables Z

_{k}, and correspondence with the indicators I

_{j}. The input column indicates that the inputs of the metamodels are either scalar (S), i.e., steady, or functional (F), i.e., unsteady.

I | Significance of Y_{i} | Unit | Input | Z_{k} = f(Y_{i}) | No. j of the Indicator I_{j} for Which | |
---|---|---|---|---|---|---|

Z_{i} Is the Main Input | Z_{i} Is a Secondary Input | |||||

1 | Volume of water entering inland over 15 min | m^{3} | S | Z_{1} = Max_{t}(Y_{1}) | N.C. | 1 to 13 |

2 | Maximal water height over the cluster of points GP1, GP2, GP3, GP4, and G1 over 15 min | m | S | Z_{2} = Max_{t}(Y_{2}) | 2 | |

3 | Z_{3} = Max_{t}(Y_{3}) | 3 | ||||

4 | Z_{4} = Max_{t}(Y_{4}) | 4 | ||||

5 | Z_{5} = Max_{t}(Y_{5}) | 5 | ||||

6 | Z_{6} = Max_{t}(Y_{6}) | 6 | ||||

7 | Maximal flooded surface | m^{2} | F | Z_{7} = Y_{7} | 1 | 10, 11, 13 |

8 | Mean (Y_{8}) and maximal (Y_{9}) water discharge entering inland | m^{3}/h | F | Z_{8} = Y_{8} | 7 | |

9 | Z_{9} = Y_{9} | 8 | ||||

10 | Maximal water height over the event in front of the town hall (Y_{10}) and the gymnasium (Y_{10}) | m | F | Z_{10} = Y_{10} | 9 | |

11 | Z_{11} = Y_{11} | 10 | ||||

12 | For each road, Section 1, Section 2 and Section 3: total head (as defined in [29]) for the entire road (Y_{12},_{14},_{16}) and the highest track of the road (Y_{13},_{15},_{17}) | m | F | For k = 12,13,14Z_{k}(Y_{k} = 0) = 0, elseZ_{k}(Y_{k+1} < h_{E1}1) = 1Z_{k}(h_{E1} < Y_{k+1} &#; h_{E2}) = 2Z_{k} (h_{E2} < Y_{k+1}) = 3 | 11 | |

13 | ||||||

14 | 12 | |||||

15 | ||||||

16 | 13 | |||||

17 | ||||||

18 | Maximal water height in NP locations (NP = 989) | m | F | Z_{15} (n = 1:NP) = Y_{18} (n = 1:NP) | 14 |

**Table 3.**C(I

_{1}) values (the colour scale is in accordance with Figure 3: green for “nothing to report” and blue for “close to flood”) for the events where either the FEWS predicts C(I

_{1}) ≥ 2 or a regional official warning was emitted (VVS) from December 2018 to March 2021. NTR: Nothing to report. *: sources of photos: https://www.ouest-france.fr/bretagne/gavres-56680/gavres-avec-la-forte-houle-les-engins-ont-du-etre-deplaces-6544164 (accessed on 25 July 2021), https://observatoire-littoral-morbihan.fr/coastsnap-morbihan-2-2/ (accessed on 25 July 2021), https://hanslucas.com/vbelloni/photo/42304 (accessed on 25 July 2021).

Date | I_{1} Predictionwith X=, N Days in Advance (1 to 3) | I_{1} from the Numerical Modelling with X=, One Day in Advance | VVS Warnings | Observations [Town Hall Information; Photos] → Evaluation of I _{1} | ||||||
---|---|---|---|---|---|---|---|---|---|---|

X_{marc} | X_{datashom} | X_{marc} | X_{datashom} | |||||||

1 | 2 | 3 | 1 | 2 | 3 | 1 | 1 | |||

29 September 2019 | 2 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | NTR | [NTR; wave overtopping on the tombolo but outside the study area *] → 1 to 2 |

30 September 2019 | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 1 | NTR | |

14 January 2020 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | Orange | [NTR; water level close to the coastal defence crests at GP4 *] → 1 to 2 |

10 February 2020 | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 1 | Orange | |

11 March 2020 | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 1 | NTR | [NTR; No photo] → 1 to 2 |

9 April 2020 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | NTR | [NTR; No photo] → 1 to 2 |

17 October 2020 | 2 | 1 | 1 | 1 | 1 | 1 | NTR | [NTR; No photo] → 1 to 2 | ||

15 November 2020 | 2 | 2 | 1 | 1 | 2 | 1 | NTR | [NTR; No photo] → 1 to 2 | ||

16 December 2020 | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 2 | NTR | [NTR; No photo] → 1 to 2 |

30 January 2021 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | Orange | [small overtopping/overflow on the tombolo, but outside the study area; small overtopping *] → 2 |

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## Share and Cite

**MDPI and ACS Style**

Idier, D.; Aurouet, A.; Bachoc, F.; Baills, A.; Betancourt, J.; Gamboa, F.; Klein, T.; López-Lopera, A.F.; Pedreros, R.; Rohmer, J.;
et al. A User-Oriented Local Coastal Flooding Early Warning System Using Metamodelling Techniques. *J. Mar. Sci. Eng.* **2021**, *9*, 1191.
https://doi.org/10.3390/jmse9111191

**AMA Style**

Idier D, Aurouet A, Bachoc F, Baills A, Betancourt J, Gamboa F, Klein T, López-Lopera AF, Pedreros R, Rohmer J,
et al. A User-Oriented Local Coastal Flooding Early Warning System Using Metamodelling Techniques. *Journal of Marine Science and Engineering*. 2021; 9(11):1191.
https://doi.org/10.3390/jmse9111191

**Chicago/Turabian Style**

Idier, Déborah, Axel Aurouet, François Bachoc, Audrey Baills, José Betancourt, Fabrice Gamboa, Thierry Klein, Andrés F. López-Lopera, Rodrigo Pedreros, Jérémy Rohmer,
and et al. 2021. "A User-Oriented Local Coastal Flooding Early Warning System Using Metamodelling Techniques" *Journal of Marine Science and Engineering* 9, no. 11: 1191.
https://doi.org/10.3390/jmse9111191