7.3 Results
7.3.3 Cross-shore Transport
Both cross-shore beach response models described in § 7.2.5 were applied to the syn- thetic wave dataset. The time convolution approach was used to estimate erosion return periods, whereas the shoreline evolution model was used to evaluate short and long term shoreline positions and the statistics thereof.
Erosion Return Periods
Fig. 7.7 shows the erosion return periods associated with both simulated and observed wave records. Independent events were delineated with a two week window as used by Corbella & Stretch (2012b). The erosion volumes estimated using the simulated waves are similar to the observed. This demonstrates two key results of the simula- tion technique. Firstly the simulated storms have similar durations to those of the observed sequence. Furthermore the simulated storms have comparable wave energy to the observed storms. The eroded volumes for return periods less than 40 years are significantly different from those estimated in Corbella & Stretch (2012a). However erosion volumes associated with return periods greater than 40 years are both simi- lar in value and in the slope of the plots. The erosion volumes for associated return periods in Corbella & Stretch (2012a) were estimated using a process based model.
Fig. 7.7 does not show an upper limit as proposed in literature and has a similar shape to the results found in (Callaghan et al., 2008; Ranasinghe et al., 2013). The eroded volumes for different return periods are similar in magnitude to those estimated in Callaghan et al. (2008).
The results are tightly distributed for volumes associated with return period<20 years. However the larger spread of values for return periods > 20 years is expected as the synthetic wave records are only 100 years long.
Shoreline Positions
The DEM was calibrated using beach profile data from a site situated south of Durban (refer Fig. 7.1). The site was chosen because data was not affected by the sand bypass scheme at the port entrance. Furthermore the site is situated on a relatively straight section of coastline. Therefore any divergence in longshore transport rates is negligible.
The EBP parameters were estimated using Eq. 7.10 with the following assumptions:
• The critical angle of repose (ϕ) was assumed as 15◦.
10
-210
-110
010
110
2Return Period (yrs)
0 50 100 150 200 250
Volume m 3/m
Fig. 7.7 The erosion return periods based on the convolution method after Kriebel
& Dean (1993) showing the median (red line) and 80% confidence limits (shaded).
Scatter points show erosion volumes and return periods for the observed dataset.
Erosion volumes previously estimated by Corbella & Stretch (2012a) are shown by the grey crosses.
• The median grain size D50 was estimated as 0.25 mm.
• ht was assumed equal to the closure depth of 15 m (Mather & Stretch, 2012).
According to beach profile dataht =15 m occurs at a distancext ≈1200 m from the reference datum.
• The shoreline position was chosen relative to the 0 MSL contour.
• The maximum shoreline position on record was assumed to be Smax =75 m from which Vs was estimated.
The accretion/erosion rate parametersC±were estimated using a simple least squares technique. Although Jara et al. (2015) set C+ = C−, for the present study we esti- matedC+= 5×10−7 s−1 and C−= 5×10−4 s−1. The calibration suggests that beach
erosion occurs significantly faster than accretion i.e. erosion occurs at a time scale of approximately 3 hours whereas accretion takes approximately 4 months. Fig. 7.8 shows that for the observation period the DEM is able to capture the general trends of erosion and accretion, but does not accurately describe the extreme shoreline posi- tions. This is attributed both to model limitations as well as missing data. Between 1993 – 2002 there are large periods of missing wave and shoreline data increasing the modelling difficulty. However the model performs significantly better between 2002 – 2009 and appears to capture the beach response to the largest wave event on record (March 2007) well.
1993 1995 1997 1999 2001 2003 2005 2007 2009 20
30 40 50 60 70 80
S (m)
0.0 3.5 8.0
Hs (m)
Fig. 7.8 The 0 MSL contour shoreline position for the beach profile used herein for the period 1993–2009. The observed shoreline positions are shown as scatter points connected with dashed lines. Modelled shoreline positions are shown with the solid black line. The wave height data for the period is also shown.
The DEM was applied to the synthetic wave dataset. Fig. 7.9 shows an example of a 100–year shoreline position simulation using the simulated waves. It is interesting to note the effect of storm clustering on shoreline position as well as the effect of single large storm events. For example there are a number of storm events that appear to cluster during the period 2070 – 2079 which result in similar erosion quantities as single events in 2016 and 2029.
Figs. 7.10(a) & (b) show the probability distribution function (PDF) and cumula-
tive distribution function (CDF) for the simulated shoreline positions with the 5thand 95th% confidence limits. The mean shoreline position for the 0 MSL contour is ap- proximately 50 m from the reference datum and the distributions reveal a heavy lower tail. This is expected since the erosion rate parameter obtained from the calibration is larger than the accretion rate parameter. Coupled with the high energy wave climate this implies that the shoreline often does not fully recover to its equilibrium position between storm events.
7.3Results
1999 2009 2019 2029 2039 2049 2059 2069 2079 2089
0 20 40 60 80
S (m)
3.5 Hs (m)
Fig. 7.9 Example of simulated 0 MSL contour shoreline positions using the synthetic wave dataset for the period 1990–2090.
Wave height data are shown in the top panel
151
0 20 40 60 80 100 Shoreline Position (m)
0.00 0.02 0.04 0.06 0.08 0.10 0.12
0 10 20 30 40 50 60 70 80
Shoreline Position (m) 0.0
0.2 0.4 0.6 0.8 1.0
Cummulative Probability
(a) (b)
Fig. 7.10 Shoreline position PDF (a) and CDF (b) for the 0 MSL contour as calculated using the simulated waves. The median (red line) and the 5th and 95th% confidence limits (shaded) are also shown in the plot.