A STORM CLASSIFICATION BASED ON THE BEACH EROSION POTENTIAL IN THE CATALONIAN COAST. E. Tonatiuh Mendoza & José A. Jiménez

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1 A STORM CLASSIFICATION BASED ON THE BEACH EROSION POTENTIAL IN THE CATALONIAN COAST E. Tonatiuh Mendoza & José A. Jiménez Laboratori d Enginyeria Marítima, ETSECCPB, Universitat Politècnica de Catalunya, c/jordi Girona 1-3, Campus Nord, D Barcelona, Spain. tonatiuh.mendoza@upc.edu, jose.jimenez@upc.edu Abstract: Storms along the Catalonian coast previously classified in terms of their energy content are re-analyzed to take into account their erosion potential effects on the coast. This was done in two-step procedure. The first step consists in modeling their effects on two representative beach profiles by using SBEACH. The coastal response was characterized through two bulk erosion parameters, beach retreat and eroded volume. In the second step, the effort was devoted to look for a parametric way to estimate the storm erosion potential in such a way that by simply using synthetic information on storm characteristics, similar bulk erosion values to the obtained by using SBEACH be obtained. To do this, several beach profile change dimensionless predictors were tested. Although the use of some of these predictors gave reasonable predictions, it was found that the inclusion of the storm duration was a key variable to reduce the scatter in the response. Moreover, to properly reproduce reflective and dissipative beach profile erosion, predictors explicitly including beach slope have to be used. Here we propose to use the JA parameter multiplied by the storm duration. Using the JA t parameter a final 5-classes scale based on the erosion potential and beach retreat ranging from I (lowest erosion potential) to V (highest erosion potential) was obtained. INTRODUCTION The impact of storms on coastal areas induce a range of potential hazards such as beach and dune erosion, overwash and/or inundation in natural undeveloped- areas and infrastructure damages in developed urbanized- coasts. Although, in principle, it seems reasonably to argue that storms with larger energy content will induce larger beach erosion, this is not necessarily true. This is because other parameters will modulate the induced morphodynamic response, some of them related to storm characteristics such as storm duration, wave period and water level and, other related to the coast subjected to the impact such as beach profile and relative orientation.

2 Within this context, the main aim of this paper is to re-analyze storms along the Catalonian coast - previously classified in terms of their energy content by Mendoza and Jiménez (2004) in terms of their erosion potential effects on the coast. In addition of this, the second objective was to develop a methodology in which in a simple way the erosion potential of a storm could be calculated from their synthetic characteristics such as wave height, wave period and duration. This was done in two-step procedure. The first step consists in estimating the potential erosion induced by the storm by modeling their effects on beach profiles representative of the Catalonian coast by using SBEACH. The coastal response was characterized through two bulk parameters, the maximum shoreline retreat and the beach eroded volume. In both cases, it is considered that no boundary conditions such as seawalls and waterfront restricting the beach erosion do exist and, in consequence the estimated response should be some kind of worst scenario. In the second step, obtained erosion values were related to a set of dimensionless beach profile change predictors. The objective was to look for the best dimensionless parameter giving a right order of magnitude of the induced response. Once this parameter is selected, it is used to estimate the erosion induced by all the storms included in a wave time series of 14 years to obtain a final 5-category erosion potential storm classification. BEACH EROSION POTENTIAL VALUES In order to estimate the potential eroded volume and shoreline recession after the impact of a given storm, the numerical model for simulating storm-induced beach change (SBEACH) was used. The SBEACH is an empirically based model that calculates the net cross-shore sand transport rate in four zones from the dune or beach face, through the surf zone, and into the offshore past the deepest break-point bar produced by short period incident waves (Larson and Kraus 1989; Wise et al. 1996). Input Data Storms recorded in the Catalonian coast obtained from a 14 years long directional wave time series were classified by Mendoza and Jiménez (2004) in a five categories classification based on their energetic content (Table 1). From all the recorded storms, NW storm events were neglected because although they were recorded by the buoy at 50 m depth they are generated by seaward blowing intense NW winds (Mestral in vernacular) that are not relevant for coastal impacts since they are waves propagating offshore (see general configuration of the Catalonian coast in Figure 1). Table 1. Storm categories based on wave energy content (after Mendoza and Jiménez, 2004) Storm class Duration (h) Hs (m) Tp (s) Energy (m² h) I Weak II Moderate III Significant IV Severe V Extreme From each storm class, the most energetic storms were selected to simulate their erosion potential. This resulted in 15 weak storms (category I), 20 moderate and significant events (categories II and III), the whole set of severe storms, 8 (category IV) and the unique storm categorized as extreme (category V). 2

3 The beaches along the Catalonian coast have been schematized by means of two representative profiles -reflective to dissipative ones- covering the range of existing ones. The reflective profile is composed by coarse sand (d mm) with a relatively high berm and a steep slope (tan β 0.1) and it can be considered as representative of coastal areas such as the Costa Brava and Maresme. The dissipative beach profile is composed by fine sand (d mm), with low berms and of very mild slope (tan β 0.01). They are easily overtopped during storms and are mainly present in the Costa Dorada and the Ebro delta regions. CATALUNYA Fig. 1. Study area. Results Table 2 shows main parameters defining the erosion of reflective beaches (eroded volume and beach retreat) for each storm class. Due to the relative high berm of these profiles, beach retreat was characterized at three different heights above the mean sea level (+3 m, +2 m and 0 m). Regarding the eroded volume, results clearly shown that beach erosion increases as the storm class increases, with mean values (averaged over the number of storms used for each category) ranging from -3 m 3 /m up to -92 m 3 /m for classes I and V respectively. For this type of profiles, weak storms (class I) do not induce a significant beach retreat. From the three controlled heights, the uppermost one (+3 m) was the one showing systematically the largest retreat resulting in a post-storm profile flattened in comparison with the initial one. The retreat starts to be significant for class II storms with a mean retreat of 2.5 m, which was progressively increasing up to a maximum value of about 21 m for class V storm (Table 2). It has to be considered that although in these calculations reflection is not included, some authors consider to be relevant in controlling a significant part of the beach response for these profiles (e.g. Baquerizo et al. 1998). 3

4 Table 2. Reflective beach storms induced erosion potential Storm Class Reflective beach V (m 3 /m) * X (m) +3 ** X (m) +2 ** X (m) 0 ** II III IV V * V: eroded mean volume from the inner beach, ** X: mean beach retreat at z = +3.0, +2.0 and 0 m. Table 3 shows the corresponding erosion potential values obtained for dissipative beaches. As in the previous case, eroded volumes increase with the storm class. Thus, in general, dissipative beaches erode with volume losses between -8 m 3 /m and -13 m 3 /m in the full range of storm classes which is approximately the 27% of volume changes obtained for the reflective beaches. As in the previous case, class I storm did not generate a significant beach retreat. For these very flat profiles (tan β = 0.01) retreat starts to be significant for class IV storms. In any case, it has to be considered that these profiles are usually overtopped during the storm (the real measured berm height was +1 m above the MSL) and, in some of the cases, the obtained (simulated) results try to reproduce overwash processes that for the employed version of the model have to be considered only as indicative. This is actually being improved by separately considering those cases in which overwash will be relevant. Table 3. Dissipative beach erosion potential for each storm class Storm Class Dissipative beach V (m 3 /m) * X (m) +1 ** X (m) +0.5 ** X (m) 0 ** II III IV V * V: eroded mean volume from the inner beach, ** X: mean beach retreat at z = +1, +0.5 and 0 m. BEACH EROSION POTENTIAL BY USING SIMPLE PREDICTORS Once the erosion potential of each storm was characterized by using a morphodynamic numerical model fed by detailed storm characteristics (a detailed recorded- time series of wave height and period during the storm was used as input data in the simulations), the next step was to look for a simple method able to capture the most significant part of the profile response but using simpler information. The final goal is to have a simple predictive method in such a way that the potential erosion to be experienced by a profile could be obtained by using synthetic wave characteristics during the storm (maximum or mean significant wave height, period and duration). 4

5 This was done comparing the results obtained by using SBEACH with a set of beach profile change predictors and following the previous works of Jiménez et al. (1997) to compare the variables characterizing beach profile erosion with the corresponding values of such predictors. In all the cases maximum and mean significant wave heights and periods during the storm have been tested. There exist numerous studies on the use of beach profile predictors to delineate beach profile changes, but most of them mainly deal with the qualitative part of the problem, i.e. the type of change (e.g. Larson and Kraus, 1989; Kraus et al., 1991). In this work we continue previous findings of Jiménez et al. (1993, 1997) about the use of such predictors in quantitative terms, i.e. to estimate the volume of sediment eroded from the beach. These authors found that the D and P parameters (see description below) showed the best predictive behaviour in qualitative terms, but to use them as quantitative ones, it was necessary to include the beach slope (tan β) as an additional variable. These both two observations were used to empirically derive a parameter taking profit of the goodness of D to predict the type of change and including the slope to improve its quantitative capability, the JApredictor. D predictor This parameter was originally developed by Gourlay (1968), although it was proposed to be used as a beach profile change predictor by Dean (1973). It assumes that the offshore sediment transport is mainly done in suspension. It is based on the idea that the breaking waves put the sediment on suspension and, after arriving to its maximum height above the bottom, the net transport is determined by a relation between the time the particle takes to fall and the semi-period of the incident waves. It is given by Ho Do = ( WsT ) where H o is the wave height, W s is the fall velocity of the sediment and T is the wave period. P predictor Although this predictor was proposed by Dalrymple (1992) is equivalent to the one originally proposed by Kraus et al. (1991) although in a bulk manner (grouping all the terms into a single numebr) and it is given by: P o = 2 ( gh ) o 3 ( wt) o The original form of the predictor was empirically derived by Kraus et al. (1991) by looking the best line for separating accretion and erosion profiles following the works of Dean (1973) but allowing changing the exponent in the used parameters. JA Predictor This predictor was developed by Jiménez et al. (1993, 1997) that includes the D-parameter and the beach slope. This is also an empirically based parameter that calculates the excess of the actual D- values for the corresponding above its equilibrium value and that includes the beach slope to 5

6 improve its quantitative predictability (the score to predict the type of beach profile change is given by the D-parameter). It is given by o o, e o 0.5 JA = D D m where D o,e is the D-parameter at equilibrium (2.7 for deep water), D o indicates that it evaluated in deep water. The type of the beach profile change is given by the sign of (D o,e - D o ) with positive values indicate accretion and negative ones erosion. Evaluation of the predictors performance All the runs performed for the different storm classes were used in the analysis. For each one, the erosion measurements eroded volume and beach retreat- were compared to the corresponding value of the selected predictors. As a first approximation and following the results of Jiménez et al. (1993, 1997), it is assumed that a linear function will be enough to describe the relation between them if any. The analysis was done by means of a linear regression analysis by least squares in which the determination coefficient, R 2, can be interpreted as indicative of the goodness of the linear model to describe the dat. Table 4 shows the results obtained for each of the tested predictors, where it can be seen that, in general, predictors seems to do a much better predictive work for the case of reflective beaches than for dissipative ones. From the set of tested parameters, P is the best one whereas D and JA give almost the same predictability. On the other hand, none of the tested predictors could be considered as of any quantitative predictive parameter of the storm induced erosion in dissipative beaches. Table 4. Regression analysis results between SBEACH and predictors Predictor R 2 reflective beach R 2 dissipative beach D * P * JA * * Predictor s values using maximum Hs and T values. The apparent lack of predictability observed in the previous results could be explained due to the fact that the definition of the predictors does not include any information on storm duration. In fact, since they have been mostly derived from laboratory experiments in which wave conditions are constant during each run and they are acting on the profile until reaching equilibrium. In prototype conditions, wave conditions vary during the storm and, depending on the storm duration, beach profiles will be subjected to a varying impact and, in consequence, its response will also vary. Thus, it should be expected that two storms with the same wave height and period but with different storm durations will induce an erosive response of different magnitude. This implies that for properly considering the erosive response under storms with a simple beach profile predictor, the storm duration has to be included as a key parameter. This need has been also considered for estimating simple indexes of beach erosion under storms by Kriebel and Dalrymple (1995), Balsillie (1999) and Zhang et al. (2001) among others. 6

7 Due to this, the storm duration was added to all the above presented predictors by simply multiplying its value by the duration in hours. Table 5 shows the obtained results in the regression analysis with the new definition of each parameter. As it can be seen, R 2 values increase for all the cases, but this increase in predictability is much higher in the case of dissipative beaches, in such a way that under this new scenario, we can consider that these predictors can be also used to quantitative indicate the erosion in dissipative profiles. Figure 2 and 3 show the obtained relations for the two predictors presenting the largest R 2 values for both two profile types. In both figures, but especially in that obtained for P, a large scatter in the data is observed for the dissipative beach. 100 Reflective Beach 14 Dissipative Beach 80 Y = 3.07E-005* X R-squared = SBEACH ( Vol m 3 /m) SBEACH ( Vol m 3 /m) Class I Class II Class III Class IV Class V 8 Y = 9.35E-008 X R-squared = 0.50 Class I Class II Class III Class IV Class V P * dt P*dt Fig. 2. Linear regression results between P dt and SBEACH for reflective (left) and dissipative (right) beaches. 100 Reflective Beach 14 Dissipative Beach 80 Y = 4.39 X R-squared = SBEACH ( Vol m 3 /m) SBEACH ( Vol m 3 /m) 10 Y = 1.07 X R-squared = Class I Class II Class III Class IV Class V 8 Class I Class II Class III Class IV Class V JA * dt JA * dt Fig. 3. Linear regression results between JA dt and SBEACH for reflective (left) and dissipative (right) beaches. 7

8 Table 5. Regression analysis results between SBEACH and predictors adding storm duration Predictor R 2 reflective beach R 2 dissipative beach D dt * P dt * JA dt * * Predictor s results using mean Hs and mean T values. If we consider all the cases together, i.e. a joint analysis of reflective and dissipative profiles, results obtained for both two predictors P dt and JA dt are shown in figure 4. As it can seen, in the case of the P predictor (figure 4 left) the two data sets appear clustered, showing that although the erosion can be reasonable well reproduced by this parameter when they are separately considered, when they are analysed in an integrated manner, its predictability clearly drops out (see Table 6). Results showed in figure 4 should indicate that a storm with characteristics determining a given P value impacting on two beaches with different beach slopes would produce a much larger erosion in the steeper profile (as expected), but as P does not include information about the beach slope, it is not able to properly include this source of variability in the response. On the other hand, when this analysis is done with the JA dt function (figure 4 right), a very different behaviour is observed. Thus, when reflective and dissipative beaches are treated as a unique data set, the obtained relation reproduce well the overall data set with a R2 value of 0.86 (Table 6). This difference in the predictability is due to the fact that this parameter was the only one of the tested that included the initial beach slope as a variable Dissipative Reflective 80 Sbeach V (m 3 /m) Y = E-007 X R-squared = Sbeach V (m 3 /m) Dissipative Reflective Y =4.14 X R-squared = P dt JA dt Fig. 4. Joint comparison using reflective (dots) and dissipative (triangles) beaches as the same data-set between P dt (left) and JA dt (right) functions vs SBEACH volume change. 8

9 Table 6. Regression analysis results using both beach types Predictor R 2 D dt * 0.01 P dt * 0.03 JA dt * 0.86 * Predictor s results using mean Hs and T values. Final Erosion Classification According to the obtained results, JA dt can be considered as good quantitative predictor for beach profile changes under storm impacts (when cross-shore transport is the dominant mechanism, so overwash and inundation regimes are not being considered, see Sallenger, 2000). Thus, the final erosion potential classification of the recorded storms in the Catalonian coast was obtained by using the fitted JA dt function, ( JA ) EP = 4.14 dt + It has to be stressed that the use of this relationship is only to obtain in situ calibrated eroded volumes but to obtain a relative classification of storms in term of the erosion potential, the use of JA dt should be enough since the obtained relationship is linear. This equation was used for the entire data set of storms from which the final 5-classes erosion potential classification was derived (Table 7). In general terms, erosion potential increases with storm class, defined in terms of their energetic content (Mendoza and Jiménez, 2004), with eroded volumes ranging from -7 m 3 /m (class I) up to 100 m 3 /m (class V) for reflective beaches and from -5 m 3 /m up to -29 m 3 /m for dissipative ones. Table 7. Reflective beach erosion potential for each storm class Reflective beach Dissipative Beach Erosion Class V (m 3 /m) * * V (m 3 /m) * I II III IV V * Eroded mean volume from the inner beach for each erosion potential class SUMMARY AND CONCLUSIONS In this work, storms along the Catalonian coast have been analyzed to characterize their erosion potential. Firstly, the erosion induced by a representative data set of storms characteristic of the wave climate of the Catalonian coast already classified in terms of their energetic content by Mendoza and Jiménez (2004) was calculated by using the SBEACH for two representative profiles 9

10 of the Catalonian coast (reflective and dissipative). With this analysis, eroded volumes and beach retreat for each storm were obtained. Secondly, a parametric way to estimate the storm erosion potential measured in the same terms that as it was with the case of SBEACH- was derived. The idea behind this was to look for a simple erosion parameter in such a way that by simply using synthetic information on storm characteristics, similar bulk erosion values to the obtained by using SBEACH be obtained. This was done by analyzing the quantitative predictive behavior of a set of beach profile predictors. Obtained results showed that it is necessary to include the storm duration to properly reproduce the calculated storm induced erosion. Moreover, to properly reproduce the behavior of reflective and dissipative beaches in a consistent manner it is mandatory to include the beach slope as a main variable in the predictor. From all the tested predictors, the JA parameter multiplied by the storm duration, JA dt, was found to have the best quantitative predictability for the tested data set. The JA dt function was used to produce the final five classes erosion potential classification of storms in the Catalonian coast. Using the entire data set of storms, results gave a range of erosion potential from 7 m³/m (class I) to 100 m³/m (class V) for reflective beaches and from 5 m³/m (class I) to 30 m³/m (class V) for dissipative ones. This means that erosion produced by these storms in dissipative beaches will be about a 30% of the eroded volume in reflective ones. In any case, it has to be also considered that overwash transport could be important for dissipative and flat beach profiles and that here it has not be properly considered.. ACKNOWLEDGEMENTS This work has been done in the framework of MeVaPlaya and FLOODsite research projects, funded by the Spanish Ministry of Education (REN C03-01/MAR) and the EU (GOCE-CT ) respectively. The authors thank DPTOP (Generalitat de Catalunya) for supplying the data used in this study. The first author was supported by doctoral studies grant of the National Science and Technology Council of México (CONACyT). The second author was supported by a University Research Promotion Award for Young Researchers of the Government of Catalonia. REFERENCES Balsillie, J.H. (1999) Volumetric beach and coast erosion due to storm and hurricane impact. Open File Report No. 78, Florida Geological Survey, Tallahassee. Baquerizo, A., Losada, M.A., and Smith. J.M. (1998) Wave reflection from beaches: a predictive model. Journal of Coastal Research 14, Dalrymple, R.A. (1992). "Prediction of Storm Normal Beach Profiles". Journal of Waterway Port Coastal and Ocean Engineering, 118, Dean, R.G. (1973). "Heuristic Models of Sand Transport in the Surf Zone". First Australian Conference on Coastal Engineering, Sydney, Australia, Jiménez, J.A., Sánchez-Arcilla, A., and Stive, M.J.F. (1993). "Discussion on prediction of storm/normal beach profiles". Journal of Waterway Port Coastal and Ocean Engineering, 119, Jiménez, J. A., Sánchez-Arcilla, A., and Valdemoro, H. I. (1997). "Predicción de los cambios en el perfil de playa utilizando parámetros adimensionales sencillos". Revista de Obras Públicas, 3362,

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