Coastal flooding event definition based on damages: Case study of Biarritz Grande Plage on the French Basque coast

TL;DR: In this paper, a statistical analysis was carried out to find the best combination of source variables explaining the reported damages for the identified storms, considering source and aggregated variables based on the empirical run-up formula or the wave energy flux.

About: This article is published in Coastal Engineering.The article was published on 2021-06-01 and is currently open access. It has received 6 citations till now. The article focuses on the topics: Return period.

Summary

1. Introduction

• Mitigating coastal flooding is a common concern of countries with maritime borders.
• Nations cope with this problem by developing coastal flood management plans, for which, one important task is the identification of coastal zones at flooding risk [3] .
• At this stage an important distinction has to be made between source, response variables and impacts.
• A multivariate threshold can also drive the declustering procedure. [9] used a bivariate threshold in which an event is defined when both the significant wave height and the meteorological surge exceed given values.
• In section 3, the different rules are tested against the damage historical data and the best ones are retained.

2.1 Site description

• The Basque coast (Fig. 1 ) is a 200 km rocky coast facing the Atlantic Ocean and stretching from the north of Spain to the south west of France.
• The authors specifically focused on one site : the so-called Biarritz "Grande Plage" (Fig. 2 ), a touristic seaside resort where hotels, casino, infrastructures are often damaged by storms. [17] .
• Finally, the water front is composed of a waterfront boardwalk located at 7.65m CD.

2.2.1 Damage database

• A database reporting flooding events and associated damages was collected at the French Basque coast scale by a research in archives for the period 1950-2014 [18, 19, 20] .
• The main source of data comes from systematic investigations in the national and local press, and in particular in the regional newspaper Sud-Ouest, as well as in the public archives kept by the government representatives, public bodies and local authorities.
• A confidence index (1: reliable, 0: low reliability) has been added to this information for more relevant statistical processing.
• With regard to damages, 5 events generated a level damage 2 with good reliability and 4 caused moderate damage with only one assessment considered unreliable in this category.
• Indeed, the additional information on the occurrence of flooding and the associated confidence level, is rather scarce due to the low confidence level associated to this information (only 5 new events are associated to good confidence : 3 flooding and 2 no flooding events).

2.2.2 Wave and water level data

• In addition to the former damage database, a corresponding hazard database composed of wave and water level data and covering the same period was also established [21] .
• Unfortunately, these mea-surements cover a too short period to be used for the statistical study.
• WWMII data were compared with the directional wave buoy measurements located 6 km off Biarritz in [21] .

2.3 Source and structural variables

• Several variables can be used to build the damage function.
• Structural or response variables can also be computed to explain damages.
• They are generally made up of a combination of source variables and potentially some site-specific characteristics such as the beach slope for instance.
• These structural variables are computed for a given sea state represented by the time t (i.e., one t for one sea state) in the following.
• For the run-up computation, the authors relied on the empirical formulation proposed by [26] : EQUATION in which : the tangent of the angle) of the considered beach which is obviously not constant in the present study.

2.4 Data processing

• Data processing is performed using R, the free software environment for statistical computing and graphics [28] .
• Tests were also performed with the 3H time step (i.e., considering water level only when wave data are known) and the results were very similar.
• The second one is to select the maximum for one variable and take the value of the other variable at the same time .
• In the second hypothesis, damages are rather explained by a cumulative effect of several successive destructive high tide events.
• In CART, the procedure starts with a learning phase where the best way to classify storms is determined using hazard variables according to the target variable (here the damages indices from the Table 1 ).

2.5 Validation

• After determining damage rules according to Table 1 , the authors need to test these on the whole wave and water level data set.
• A good damage rule is supposed to detect a high percentage of the historical events while avoiding false positives.
• The authors propose two methods for the validation of the rules.

2. the damage rule requires a calculation over the storm duration

• In the first case, the authors will only need to test every date in the dataset and verify if the corresponding threshold(s) is/are exceeded by the values of the considered variables at that date.
• This time window, depending on the value of τ, includes variable number of dates (i.e. tide cycles).
• Since, after applying a rule (step 1 : rule application), it is possible for an event to contain more than one date meeting a rule criterion, consecutive dates are grouped into a cluster counting as only one event for the validation (step 2 : cleansing).
• The time lapse fixed to consider clusters as independent is equal to three tidal cycles (i.e., 36H).
• The final step is the distinction between historical events from the data (i.e., damage level 1 and 2 from Table 1 ) with false positives (0 from Table 1 and non identified dates).

2.5.2 Method 2 : preliminary event detection

• U e must be high enough to create independent clusters but low enough to include the important events.
• The subset obtained is then formed of clusters, each including several values for the parameters corresponding to the rule tested.
• The next step is to select one value (or set of values) by cluster directly based on the rule considered.
• This is performed by applying the function of the corresponding rule on the specified time information.

3. the damage threshold

• Max(η)) over each cluster time window.the authors.
• Finally, the damages threshold (i.e., (5., 3.) in the example) is used to count the events and assign them to their respective categories.

2.6 Return period

• The best rule functions will be used to compute the return period (RP) of the extreme events found in the historical investigations.
• The three steps for validating damage rules with method 1 : 1) apply the rule to the entire dataset, 2) cleanse the dates identified in order to count only one per event, 3) sort the non identified dates between dates arguably attachable to events (close in time) and totally unknown ones.

Clusters

• Complete wave and water level dataset Event detection (threshold u e + separation window of 36H).
• One value by cluster (applying the rule function without threshold) i.i.d. event subset (see Sections 2.6 and 3.3).

Damage threshold

• The two steps for validating damage rules with method 2 : 1) apply a threshold u e to the dataset to detect events at least separated by 36H (separation/merging procedure), 2) select one value by cluster by applying the rule function, 3) apply the rule damage threshold and count events.
• May for instance expect storm events showing the highest RP values to be associated to the most severe damages.
• The EVT distribution of the events subset is estimated using the Generalized Pareto Distribution (GPD) (see, e.g., [31] ).
• The literature provides several solutions to optimize the choice of u based on either graphical, parametric or mixed methods.
• Here the authors needed preferably a single value for the reason explained hereafter.

3.1 Calibration of rules with the historical database

• In order to build rules consistent with damages observed during storm events, the first step is to investigate how the combinations of variables defined in Figure 3 are distributed when considering the 30 historical storms previously collected.
• In each Figure, the maximum, mean and cumulative values are calculated over each storm duration.
• It may also be possible to discriminate damage level from damage level 1 by increasing these two values.
• Considering mean wave energy flux and water level is not as accurate as considering the maximum values as storms of different damages starts to be mixed in the 2D plot while cumulative variables still appear inappropriate.
• Figure 9 shows results from simultaneous values for the energy flux P and the water level η.

3.2.1 Method 1 : direct rule application

• Since, the rules R5, R6, R7 and R8 do not use two non simultaneous maxima they can be written :.
• To fill columns "0", "1", "2" and "Non identified dates", the authors compare these binary values with the events presented in Table 1 .
• This optimum result is not obtained with any rule.
• Nevertheless, except for rules R2 and R8 which lead to a lot of false positives, every rule shows relatively good performance in detecting events, the best ones being R1, R3 (the best rule) and R4, therefore the rules using a time window but not only wave period as wave parameter.
• The authors also note that the results depends moderately on the time window value.

3.2.2 Method 2 : preliminary event detection

• The authors tested the most efficient rules (i.e. rules R1, R3 and R4) of the previous section along with rules R5 and R6, which will be used in the return period computation.
• The following event thresholds have been found to give satisfactory results in the rules validation :.
• They are consistent with the results of the previous method, the rule R3 still being the most efficient rule.
• The authors note that the choice of the first threshold(s) used to create the clusters depends on the rule function considered and possibly on the site studied.
• Conversely, a too high threshold (8.5 m here) will reduce the average size of clusters and finally lead to more false positives.

3.3 Estimation of storm return periods

• R3 is one of the two best rules, based on the same variables as R6, but authorizing based on non simultaneous maxima.
• This last rule is also retained to illustrate the importance of this calculation choice in the RP final result.
• This operation reduced the time series to 924 clusters.
• This threshold is then used to estimate the parameters of the GPD.
• The mathematical thresholds are slightly higher than the damage thresholds (i.e., respectively 400 J.m −1 .s −1 and 4.00 m) illustrating a situation where a few damaging events RP may not be properly modeled.

Rules Events Rule

• The number of false positives is obtained by adding up the numbers in column "0" and the column "Non identified dates".
• This raises the question of precision in the historical data, especially regarding the dates of the events.
• When comparing the three tables, it is obvious that the RP of a particular event strongly depends on the rule applied to define the event subset.

4. Discussion

• Impact is included at the initial stage of coastal flooding events definition by intercomparing rules based on waves and water level parameters to a damage dataset obtained from recent historical records in the Biarritz Grande Plage, French Basque coast.
• In the present paper, elaborated rules based on maximal, mean, integral values of source and aggregated variables over storm duration, combining waves and water level, were used and confronted to the damage database.
• Indeed, good results for the explanation of damages are consistently obtained when combining the maximal values of a wave related variable with the maximal value of a water level related one (e.g.,max(H s ) and max(η), max(P) and max(η), etc.) compared to the mean parameters and the integral or accumulated parameters.
• This is an interesting information, showing that a proper automatic event definition may require more than one date to be accurate and account for the complexity and variability of the events.
• Nevertheless, one striking conclusion of the paper is that, if the rules are good to predict damages, their application to calculate RP leads to very different results.

5. Conclusions

• The authors compared a database of source variables gathering waves and water level hindcast and observation data and a storm impact database obtained by investigations in archives and local newspapers, a site dominated by waves and tides on the French Basque coast over a period of 65 years to find statistical rules explaining damages.
• The rules were then verified by applying them on the wave and water level dataset.
• The following conclusions can be drawn from this work : .
• The method presented in this study was therefore able to establish a link between damages and RP.

Figures

Figure 1. Location of the study site on the France map (left panel) with a zoom on the Basque coast (right panel - red rectangle) with buoys (Anglet and Saint-Jean-de-Luz) and tide gauges (Socoa) used on this study.

Figure 2. Photographs of the Grande Plage of Biarritz showing a few of the assets frequently flooded (left panel - ©Google Maps), the Grande Plage waterfront and the the casino building (right panel - ©FranceBallade)

Figure 11. Extrapolation plot for the GPD computed with the time series η +R2% (rule R5) for a threshold of 7.26 m. The lines correspond to the model and its 95% confidence interval, the black dots correspond to the empirical values from the time series.

Figure 12. Maxima of the Run-up R2% versus maxima of water level η during historical events. The left plots corresponds to values computed with a constant beach slope β = 0.09 (similar to Figure 7 without applying distribution correction). The right plots are obtained by computing the Run-up maximum run-up R2% by sampling one random beach slope for each event from a uniform distribution (with parameters min = 0.06 and max = 0.12). Each line corresponds to a different set of random slopes used to compute the run-up on the right panel.

Figure 4. The three steps for validating damage rules with method 1 : 1) apply the rule to the entire dataset, 2) cleanse the dates identified in order to count only one per event, 3) sort the non identified dates between dates arguably attachable to events (close in time) and totally unknown ones. The result can take the form of a count of events based on the damages index (0,1 or 2) if the event is existing or NI for ”Not identified”.

Figure 5. The two steps for validating damage rules with method 2 : 1) apply a threshold ue to the dataset to detect events at least separated by 36H (separation/merging procedure), 2) select one value by cluster by applying the rule function, 3) apply the rule damage threshold and count events. The result can take the form of a count of events based on the damages index (0,1 or 2) if the event is existing or NI for ”Not identified”.

Figure 8. Total water level (a) / Hs +η (b) versus mean wave direction over storm duration. (1) maximum value of total water level / Hs +η over storm duration, (2) mean value of total water level / Hs +η , (3) cumulative value of total water level / Hs +η .

Figure 10. (a) storms as a function of the maximum I (in x-axis) and the average of θm (y-axis). (b) storms as a function of water level η at maximum of I (x-axis) and wave power P at maximum of I (y-axis)

Figure 9. Wave energy flux versus water level (a) values of P taken when η is maximum (b) values η taken when P is maximum

Table 4. List of storms ranked by decreasing RP based on rule R5. In pink, events not reported in the damage database (Table 1).

Figure 6. Significant wave height Hs (a) / peak period Tp (b) / energetic period Tm10 (c) versus water level, (1) maximum values calculated for both variables over storm duration, (2) mean values for both variables over storm duration, (3) cumulative values for both variables over storm duration. Damage level : 0 (black), 1 (blue), 2 (red) (points represented by a cross ”+” are data of low confidence see Table 1).

Figure 7. Energy flux P (a) / wave run-up R2% as calculated by Stockdon’s formula (b) versus water level, (1) maximum values calculated for both variables over storm duration, (2) mean values for both variables over storm duration, (3) cumulative values for both variables over storm duration. Damage level : 0 (black), 1 (blue), 2 (red) (points represented by a cross ”+” are data of low confidence see Table 1).

Table 5. List of storms ranked by decreasing RP based on rule R6. In pink, events not reported in the damage database (Table 1)

Figure 3. Diagram summarizing the different possibilities of event definition based on data taken from the ”Andrea” storm (between 26/02/2014 and 03/03/2014 as symbolized by pink lines).

Table 6. List of storms ranked by decreasing RP based on rules R3. In pink, events not reported in the damage database (Table 1)

Table 1. Database of damages related to coastal flooding in the Biarritz Grande Plage. When the events correspond to known storms, their name is used if not their number. The dates and durations are either extracted or inferred from the press and archives. The Confidence indices are coded as 1 (confident) or 0 (not confident). Damage is coded in intensity 0 (weak/absent), 1 (moderate) or 2 (strong) and flooding occurrence is coded by 1 (presence) and 0 (absence). The last column indicates the storms recognized as CATNAT and the corresponding dates. The state of natural disaster (natural catastrophe = CATNAT) is a situation whose recognition in France by the Ministry of the Interior allows for the systematic compensation of victims of damage caused by various natural agents. This procedure was established in 1982.

Table 2. Method 1 rules validation results for τ = 4 and τ = 6. For each rule, the number of identified category 0, 1 or 2 events is given along with the number of unrecorded events in the historical dataset. It should be remembered that, during the latter, of the 30 events listed, 21 (respectively 4, 5) were Category 0 (1, 2, respectively). The number of false positives is obtained by adding up the numbers in column ”0” and the column ”Non identified dates”.

Table 3. Method 2 rules validation results. For each rule, the number of identified category 0, 1 or 2 events is given along with the number of unrecorded events in the historical dataset. It should be remembered that, during the latter, of the 30 events listed, 21 (respectively 4, 5) were Category 0 (1, 2, respectively). The number of false positives is obtained by adding up the numbers in column ”0” and the column ”Non identified dates”.

Frequently asked questions

Q1. What have the authors contributed in "Coastal flooding event definition based on damages: case study of biarritz grande plage on the french basque coast" ?

This paper presents a method to include damage at the initial stage of coastal flooding events definition and in return periods computation. The methodology is illustrated within a local study carried out in Biarritz Grande Plage, a meso-tidal, wave dominated beach located on the french basque coast in the south west of France. A statistical analysis was first carried out to find the best combination of source variables explaining the reported damages for the identified storms. Most of the rules formerly studied, except the ones using wave period only as wave parameter, were able to correctly perform this task. Nevertheless, the discrepancy still observed among the different rules calls for further work in this direction. 

Q2. What have the authors stated for future works in "Coastal flooding event definition based on damages: case study of biarritz grande plage on the french basque coast" ?

Then, the rules skill was retrospectively tested over the total time span, showing the existence of efficient rules, which could be potentially used for damage prediction for future events. Nevertheless, from the results of the paper, it seems that there is still significant work to be done to ensure that each individual storm potential impact is assessed accurately on an appropriate metric respecting the point of view defended in this paper. 

Q3. What is the test based on Kendall’s coefficient?

The test based on Kendall’s τ coefficient does not reject independence between the two variables composing the event dataset, allowing the use of equation (8) to estimate the joint probability. 

Q4. How many storms were observed at the Grande Plage?

The number of storms, for which only Biarritz was mentioned is 30 and the number of flood events at the Grande Plage is 13, which represents one third of the storms observed over the period 1950-2014. 

Q5. What is the main reason for the increasing population on the coast?

Whereas the problem is more and more acute due to the growing coastal population and associated infrastructures [1], climate change also increases pressure on the coast by sea level rise which allows the ocean to reach usually protected areas [2]. 

Q6. What is the main limitation of the paper?

another limitation of this study is the unknownbeach profile variability over time during the studied period and its effect on the damages induced by coastal flooding. 

Q7. What is the rule for a storm?

The best rule was the one based on wave energy flux (or equivalently the significant wave height) and water level maxima over the event.• 

Q8. What is the main reason why RP should be used in applied studies?

Stakeholders being mostly concerned by the impacts to the coast and population, RP should reflect this aspect in applied studies. 

Q9. What is the effect of the analysis of quantile graphs on the sea state?

The analysis of quantile/quantile graphs shows an underestimation by the model for extreme sea states, detrimental to this type of study precisely focused on these events. 

Q10. What is the return period of the event x > x,y > y?

The return period of the event {x > x,y > y} is thennaturally computed asRP(x,y) = µP̂r(x > x,y > y)= µP̂r(x > x)P̂r(y > y)= µ{1− Ĝx(x)}{1− Ĝy(y)} ,(8)whereµ = 2015−1949+1∑t∈T 1{x(t)> ux,y(t)> uy} .