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, D1 08034 Barcelona, Spain. [email protected], [email protected]
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.
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
I Weak
II Moderate
III Significant
IV Severe
V Extreme
Duration (h)
12
29
49
85
192
Hs (m)
2
2.4
2.8
3.9
5.9
Tp (s)
6.5
6.8
7.7
8.9
11.1
Energy (m² h)
32.1
90.5
205.2
543.4
1455.5
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
C
A
TA
LU
N
YA
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 (d50 ≥ 0.6 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 (d50 ≈ 0.25 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.
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
m3/m up to -92 m3/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
Table 2. Reflective beach storms induced erosion potential
Storm Class
Reflective beach
II
III
IV
V
∆ V (m3/m) *
-11.7
-29.5
-44.5
-92.1
∆ X (m) +3 **
2.5
7.4
10.3
21.6
∆ X (m) +2 **
1.6
5.6
9.1
19.4
∆ X (m) 0 **
1
3.3
6.2
15.8
*∆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 m3/m and -13 m3/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
II
III
IV
V
∆ V (m3/m) *
-8.1
-9.5
-10.2
-12.9
∆ X (m) +1 **
0.2
0.4
5.8
24.6
∆ X (m) +0.5 **
1.2
1.3
2.9
6.5
∆ X (m) 0 **
0.3
0.9
1.1
1.6
*∆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
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
Do =
Ho
(WsT )
where Ho is the wave height, Ws 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:
Po =
( gH o2 )
( w3o T )
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 Dvalues for the corresponding above its equilibrium value and that includes the beach slope to
5
improve its quantitative predictability (the score to predict the type of beach profile change is given
by the D-parameter). It is given by
JAo = Do,e − Do
0.5
m
where Do,e is the D-parameter at equilibrium (2.7 for deep water), Do indicates that it evaluated in
deep water. The type of the beach profile change is given by the sign of (Do,e - Do ) 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, R2, 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
*
D
*
P
*
JA
R2 reflective beach
0.60
0.79
0.59
R2 dissipative beach
0.11
0.19
0.085
* 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
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, R2 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 R2 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.
14
100
Dissipative Beach
Reflective Beach
80
SBEACH (∆Vol m3 /m)
12
60
40
10
Y = 9.35E-008 X + 7.98
R-squared = 0.50
8
Class I
Class II
Class III
Class IV
Class V
20
Class I
Class II
Class III
Class IV
Class V
6
0
0
1000000
2000000
P * dt
3000000
0
4000000
20000000
40000000
P * dt
60000000
80000000
Fig. 2. Linear regression results between P dt and SBEACH for reflective (left)
and dissipative (right) beaches.
100
14
Dissipative Beach
Reflective Beach
80
Y = 4.39 X + 2.15
R-squared = 0.865
12
SBEACH (∆Vol m3 /m)
SBEACH (∆Vol m3 /m)
SBEACH (∆Vol m3 /m)
Y = 3.07E-005* X + 1.90
R-squared = 0.880
60
40
Y = 1.07 X + 7.61
R-squared = 0.64
8
Class I
Class II
Class III
Class IV
Class V
20
10
Class I
Class II
Class III
Class IV
Class V
0
6
0
5
10
15
20
25
0
JA * dt
2
4
JA * dt
6
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
R2 reflective beach
0.79
0.88
0.86
Predictor
*
D dt
*
P dt
*
JA dt
R2 dissipative beach
0.61
0.5
0.64
* 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.
100
100
Dissipative
Reflective
80
Y = -2.801E-007 X + 16.433
R-squared = 0.030
60
Sbeach ∆V (m3/m)
Sbeach ∆V (m3/m)
80
40
60
40
20
20
0
0
0
20000000
40000000
P dt
60000000
Dissipative
Reflective
Y =4.14 X + 3.40
R-squared = 0.862
0
80000000
5
10
15
20
25
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
Table 6. Regression analysis results using both beach types
R2
0.01
0.03
0.86
Predictor
D dt *
P dt *
JA dt *
* 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,
EP = 4.14( JA dt ) + 3.40
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 m3/m (class I) up to –100 m3/m (class V) for reflective beaches and from -5
m3/m up to -29 m3/m for dissipative ones.
Table 7. Reflective beach erosion potential for each storm class
Reflective beach
Dissipative Beach
3
Erosion Class
∆ V (m /m) *
*∆ V (m3/m) *
I
-7.0
-4.7
II
-11.5
-6.4
III
-21.5
-9.1
IV
-39.3
-13.9
V
-102.5
-28.8
* 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
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 (REN2003-09029-C03-01/MAR) and the EU (GOCE-CT2004-505420) 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.
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