SHORELINE EVOLUTION DUE TO HIGHLY OBLIQUE INCIDENT WAVES AT
WALVIS BAY, NAMIBIA
1
3
Berry Elfrink, Gordon Prestedge2, Cesar B.M. Rocha , and Jørgen Juhl
4
Abstract: This paper describes the development of a large-scale spit formation at the city of Walvis
Bay, Namibia. The observed acceleration of shoreline evolution was found related to a shift in the
mean wind direction that occurred in the late seventies and continues until today. The study included
mathematical modeling of coastal processes and was supported by an extensive field data collection
program.
INTRODUCTION
The coastline of Southwest Africa is characterized by the presence of several large-scale sand
spit formations. The Namibian coastline between Sandwich Bay, located S of Walvis Bay and
Swakopmund is oriented almost North-South. Further to the north the coastline is oriented from SSE
to NNW. The location of the project site is shown in Fig. 1.
Fig. 1: Location of the project site
The predominant waves come from a narrow directional band between S and SSW. The wave
conditions are quite stable throughout the year and are dominated by swell from S to SW. The
1) DHI Water and Environment, Agern allé 11, DK-2970 Hørsholm, Denmark. bre@dhi.dk
2) Prestedge Retief Dresner Wijnberg, Marina Centre,West Quay Road,Victoria & Alfred Waterfront, Cape Town,
South Africa. Gprestedge@prdw.co.za
3) Univ. of Itajaí (UNIVALI)CTTMAR. Rua Uruguai 458, Itajaí-SC, 88302-202. Brazil. centro@cttmar.univali.br
4) COWI Consulting Engineers and Planners A.S. Parallelvej 15, DK-2800 Lyngby, Denmark. jju@cowi.
average significant wave height is of the order of 2m. The tidal range is approximately 1 m. Tidal
currents in the near shore zone are weak, of the order of 0.1 m/s.
At Sandwich Bay and Walvis Bay large coastal features have developed which change the local
orientation of the coastline to SSE-NNW. The formation of the coastal spits has lead to the
development of coastal marshes and mud flats that are flooded during high tide. The tranquil
environment behind the spit is of great importance for bird life in SW Africa. The Pelican Point
Peninsula, a sand spit of approximately 10 km, provides shelter for wave action for the city of
Walvis Bay. The spit was estimated to grow (at Pelican Point) with a rate of approximately 15 m/yr.
towards N. The Port of Walvis Bay has since several centuries been the main Port of Namibia.
During recent years beach erosion was observed at Donkey Bay, located along the spit. The possible
breaching of the spit might lead to increased exposure to wave action. This was a major concern for
the community of Walvis Bay. The objective of the project was to analyze the morphological
evolution of the spit and to evaluate the risk of breaching due to wave induced erosion.
PROBLEM ASSESSMENT
The formation of the Pelican Point Peninsula is the result of an instability of the shoreline due
to the large angles of wave incidence. It is expected that climatological variations have given rise
to variations in offshore wave conditions. Such variations in wave conditions, especially with regard
to wave direction, may have provoked the formation of new spits that developed on the “back” of
the existing one. While the new spit developed, the former was partially eroded. The present
Peninsula has thus been formed during a number of stages. The initial spit was located closer to the
shore than the present Peninsula. During following stages, the Peninsula developed further towards
W. Aerial photographs of the Pelican Point Peninsula clearly show large-scale sedimentary structures
that support this hypothesis. It is possible that the initiation of a new spit was associated with an
exceptionally high discharge of the Kuiseb River, that had caused a temporary opening to the sea.
However, it is expected that the development of a new spit could also occur without such an event.
The large angle of wave incidence gives rise to unstable shoreline configurations e.g. initial
shoreline perturbations may not be smoothened out by the wave action but can develop to large-scale
spit formations. The littoral drift along a sandy beach reaches a maximum if the angle between the
shore normal and the incoming waves in deep water is approximately 45°, Fredsøe and Deigaard
(1992). Along a stable shoreline, a perturbation will decrease in size and a straight shoreline will
tend to develop. In cases where this angle is larger the shoreline is unstable and any perturbation can
be amplified in size until the shoreline attains the orientation where the littoral transport is maximal.
This phenomenon is known from several locations around the world, Mangor (2001). The mechanics
of shoreline development for stable and unstable beaches is illustrated in Fig. 2. For large wave
angles, the littoral transport decreases for increasing wave angles. For the present site, the dominant
angle of offshore wave incidence is significantly larger than 45 degrees. The offshore wave rose is
shown in Fig. 3. If small variations in the wave conditions occur, the shoreline orientation will tend
to change accordingly. The bypass of sand from the Southern part of the peninsula through Donkey
Bay towards the northern part is determined by these variations in wave conditions.
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Elfrink et al
Fig 2: Illustration of shoreline instability for large angles of wave incidence. The solid line represents
an initial perturbation of the shoreline, the dashed line indicates the shoreline position after some time.
The arrows indicate the direction and relative magnitude of the littoral drift.
Fig. 4 shows an aerial photograph of the area around Donkey Bay. The shoreline evolution here
is characterized by periods of relatively strong beach accretions, interrupted by periods of stagnation.
During the accretion phase, the protuberance at Donkey Bay is amplified and migrates towards N,
whereas shoreline erosion occurs along the shoreline N of Donkey Bay. During periods of stagnation,
the shoreline is partly recovered and the bypass of sediment towards Pelican Point continues. The
photo shows the location and orientation of former shorelines
HISTORICAL SHORELINE CHANGES
Available aerial photographs were analyzed to perform a qualitative assessment of historical
shoreline changes along the Pelican Point Peninsula. Fig.5 shows the shoreline configurations of
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Elfrink et al
1976, 1993 and 2002. The figure shows northward shoreline migration at Donkey Bay and shoreline
erosion N of it. Fig 6 shows the shoreline development at Donkey Bay between 1958 and 2002.
Fig 3 (left): Annual offshore wave rose, depth 132m, based on data from June 1997 – June 2002.
Fig 4 (right): Aerial photo of Donkey Bay showing a new spit on the back of an ancient formation.
Fig. 5: Historical shoreline evolution between 1976 and 2002
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Elfrink et al
Fig.6: Shoreline development at Donkey Bay between 1958 and 2002
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Elfrink et al
The figure shows that the Peninsula N of Donkey Bay was considerably wider in 1958 than it is
today. Furthermore, the northward shoreline migration since 1958 is seen clearly. The shoreline
changes between 1958 and 1969 and between 1969 and 1976 are relatively small compared to the
changes after 1976. This accelerated shoreline evolution around Donkey Bay was expected to be due
to changes in the wave conditions. If the dominant wave direction would change then the equilibrium
shoreline orientation would change accordingly. Under the present wave conditions, the shoreline
will tend to develop towards a orientation with maximal littoral transport. A rotation of the dominant
wave conditions towards South would thus lead to an anti clockwise rotation of the equilibrium
shoreline orientation along the main part of the Peninsula. Similarly, a rotation of the wave directions
towards W would lead to a clockwise rotation. In order to verify whether such changes in wave
conditions had occurred, an analysis of long term offshore wave data must be performed. However,
long-term wave records with sufficient degree of accuracy with regard to wave directions were not
available. Therefore, an analysis of long-term wind data, collected at the Airport of Cape Town,
South Africa, was performed. It is clear that wind conditions in this location do not necessary
resemble wind conditions at Walvis Bay. Especially winds from land, e.g. from northern and eastern
directions may differ considerably between the two locations. However, the dominant wave direction
at Walvis Bay is S to SW. Therefore it was assumed that changes in wind conditions at Cape Town
were similar to changes at Walvis Bay for this direction interval.
Fig. 7 shows the annual mean wind speed for the period between 1941 and 2000. The analysis
was made on the basis of hourly wind records collected at an elevation of 17m at the Airport of Cape
Town. Fig. 8 shows the annual mean wind direction for the same period. Mean values were
calculated separately for two periods : October – March and April – September.
The mean wind speed during October-March is approximately 4 m/s whereas it is approximately
1 m/s during April-September. Time variations are seen to be quite small. Wind speeds were slightly
higher around 1950 and slightly lower around 1965, but generally not much variation is observed.
However, the mean wind directions indicate a clear shift that started in the late seventies and
continues until present. For October – March, where the strongest winds occur, this shift is in the
order of 20 degrees in anti clockwise direction. For April-September this shift seems somewhat
higher, approximately 40 degrees, but considerably more scatter is observed. Similar analyses for
higher moments of wind speed showed the same pattern as the one shown here. The above analysis
of wind data lead to the conclusion that the observed variations in wind conditions are in agreement
with the observed change in shoreline behavior at Donkey Bay.
In order to quantify the expected future shoreline evolution and to develop and verify possible
schemes of human interventions the coastal sediment balance must be known. The sediment balance
was obtained through mathematical modeling of waves, near shore hydrodynamics and sediment
transport.
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Elfrink et al
Fig. 7: Mean wind speed collected at Cape Town, South Africa between 1941 and 2000
Fig.8: Mean wind direction collected at Cape Town, South Africa between 1941 and 2000
MATHEMATICAL MODELING OF WAVES
In order to calculate the littoral sediment balance, near shore wave characteristics must be
calculated along the entire project site. Therefore, a wave study was performed to analyze the
transformation of waves propagating from deep water into the near shore zone.
The offshore wave data were derived from a global wave model as operated by the UK
Meteorological Office. The location of the model grid point was 23.1º S, 13.8º E at a water depth
of 132 m. The offshore data covered the time period between June 1997 and June 2002 and included
significant wave height, peak period and mean wave direction at 6-hourly intervals. From the
offshore data, annual offshore wave statistics were derived and a discrete number of wave events e.g.
combinations of wave height, period and mean wave direction, were transformed to the near shore
zone. The offshore wave statistics are presented in tables 1 – 2.
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Elfrink et al
Table 1:
Calculated Offshore Wave Statistics based on UKMO data between June 1997 and
June 2002 Significant Wave Height Hs vs. Peak Period Tp
Tp (s)
Hs(m)
4
6
0.75
0.05
0.09
1.00
0.28
2.01
0.14
1.25
0.39
4.13
0.87
1.50
0.21
15.30
2.84
0.09
10
12
Acc.
-
-
-
0.14
-
-
2.44
-
-
5.39
-
18.45
1.75
-
11.93
3.34
0.14
0.02
15.42
2.00
-
17.77
6.01
0.28
0.09
24.15
2.25
-
7.69
2.92
0.21
0.02
10.83
2.50
-
7.99
3.71
0.19
0.02
11.91
2.75
-
3.14
1.64
0.18
-
4.96
3.00
-
1.96
1.80
0.14
-
3.90
3.25
-
0.46
0.51
0.07
-
1.04
3.50
-
0.12
0.55
0.04
-
0.71
3.75
-
-
0.19
0.02
-
0.21
4.00
-
-
0.19
0.04
-
0.23
4.25
-
-
0.07
0.02
-
0.09
4.50
-
-
0.07
-
-
0.07
4.75
-
-
0.04
-
-
0.04
5.00
-
-
0.02
-
-
Acc.
Table 2:
8
0.94
72.60
24.91
1.41
0.02
0.14
100. 00
Calculated Offshore Wave Statistics based on UKMO data between June 1997 and
June 2002 Significant Wave height Hs vs. Mean Wave Direction MWD.
MWD(deg)
Hs (m) ≤ 150
0.75
-
1.00
-
165
0.04
-
180
-
195
210
225
240
255
-
270
-
285
Acc
0.07
0.04
0.02
0.02
0.48
0.92
0.41
0.32
0.21
0.05
1.11
2.14
0.95
0.49
0.35
0.19
0.02
0.05
0.05
5.39
-
-
≥ 300
0.02
-
0.14
-
2.44
1.25
0.02
1.50
0.04
0.05
4.91
8.02
2.81
1.01
0.69
0.32
0.16
0.12
0.32
18.45
1.75
0.04
0.02
3.87
7.53
2.17
0.64
0.55
0.12
0.09
0.04
0.39
15.42
2.00
0.02
0.14
5.85
12.33
3.73
1.06
0.57
0.14
0.18
0.05
0.09
24.15
2.25
-
0.05
2.56
5.69
1.78
0.44
0.14
0.05
-
0.02
0.09
10.83
2.50
-
0.05
3.13
6.38
1.55
0.51
0.12
0.04
-
0.04
0.09
11.91
2.75
-
0.07
1.31
2.67
0.67
0.19
0.02
0.02
-
-
0.02
4.96
3.00
-
0.04
0.83
2.17
0.69
0.14
-
0.04
-
-
-
3.90
3.25
-
0.42
0.48
0.11
0.04
-
-
-
-
1.04
3.50
-
0.28
0.21
0.14
3.75
-
0.16
0.05
4.00
-
0.04
0.12
4.25
-
-
0.05
0.02
4.50
-
-
0.07
4.75
-
-
5.00
-
-
Acc.
0.11
0.02
0.02
0.49
-
-
-
-
-
-
-
-
0.21
-
-
-
-
-
-
0.23
-
-
-
-
-
-
-
-
-
-
-
-
-
0.02
-
-
-
-
-
-
-
0.02
-
-
-
-
-
-
-
25.11
48.80
-
0.05
15.11
8
4.86
0.02
-
2.69
0.02
0.99
0.44
0.34
0.02
0.02
0.02
1.10
0.71
0.09
0.07
0.04
0.02
100.00
Elfrink et al
The wave transformation was performed by DHI’s wave model MIKE 21 NSW. This is a
stationary, directionally decoupled parametric wave model, which describes the propagation, growth
and decay of wind waves in near shore areas. The model simulates fields of spectrally averaged wave
conditions that are constant in time. The mechanisms of wave refraction, shoaling, directional
spreading, wave-current interaction, growth due to wind, and dissipation due to breaking and bed
friction are all included in the model. Wave diffraction and reflections are not included. Wave
current interaction was neglected as the tidal currents are weak. The simulations were performed on
a model grid with spatial resolution of ∆x = 50m, ∆y = 200m. The water level was taken constant
as MSL in all simulations.
Model calibration was performed by comparing the simulated wave conditions with near shore
wave data that was collected off Pelican Point in a water depth of 32 m. The wave model is
calibrated by tuning the assumed shape of the wave energy spectrum and by adjusting a number of
wave propagation parameters that determine directional spreading and energy loss due to breaking.
Fig 9 shows a simulated wave field along the project site. At the offshore boundary the
significant wave height was taken as 1.5m, the mean wave direction was 185 degrees and the peak
period was 8 s. The figure shows that the large angle of incidence creates a shadow zone at Donkey
Bay. Further N towards Pelican Point the wave height is seen to increase slightly. At the edge of the
spit, the wave height becomes virtually zero.
Fig.9: Simulated wave field around Pelican Point Peninsula
Offshore input data: Hs=1.5m, Tp=8s, MWD=185 deg.
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Elfrink et al
After the model calibration had been concluded approximately 120 discrete wave events were
simulated that represent the annual wave statistics.
Fig. 10: Simulated near shore wave climates along the project site.
Inshore wave data were extracted in a number of locations at the 10m-depth contour along the
project site. The calculated inshore wave climates are shown graphically in Fig. 10. The simulated
inshore wave climates were used as input in the calculation of the littoral sediment balance.
ANNUAL SEDIMENT BALANCE
Annual longshore sediment transport rates were calculated along the project shoreline. The
simulations were performed with LITDRIFT, which is the littoral drift module of DHI’s coastal
sediment transport modeling system LITPACK. The model includes important sediment transport
mechanisms such as non-linear wave motion, turbulent bottom boundary layer, wave breaking and
sediment grading. LITDRIFT is essentially a combination of a 1D-wave model, a 1D-surf zone
hydrodynamic model, and an intra-wave sediment transport model (STP). The model will shoal,
refract and break the input wave from the toe of the profile to the shoreline. A longshore current will
be generated based upon the radiation stresses from the wave transformation. The effect of shoreparallel currents due to forcing other than wave breaking may also be input to the model. The
simultaneous wave and current conditions are thus determined at every point along the given profile.
At a given location in the profile, this information is combined with local sediment characteristics
and is used as input to the generalized sediment transport model STP, resulting in the determination
of the sediment transport potential at the given location along the profile. Repeated calls to STP
result in the determination of the spatially varying sediment transport potential across the entire
profile for the given wave event. Repeated calls to LITDRIFT for all wave events, with subsequent
weighting of their transport rates by their respective annual occurrence frequencies, results in the
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Elfrink et al
determination of the annual littoral transport climate for the site. A good description of the physical
mechanics on which the sediment transport model is based is given in Fredsøe and Deigaard (1992).
At its offshore boundary the model uses the derived inshore wave statistics. As model input the
cross-shore bathymetry and the cross-shore variation of sediment characteristics (e.g. median grain
size and geometrical spreading) are specified. The model calculates the local wave fields assuming
locally parallel depth contours (locally uniform beach).
Due to the assumption of locally uniform conditions along the beach, this type of model can not
be expected to resolve the details of sediment transport along curvy beaches such as the area just N
of Donkey Bay and around Pelican Point. Along the beach just N of Donkey Bay the waves are
significantly lower due to the sheltering effect of the large-scale protuberance, i.e. the new spit
developing in this area. This creates longshore variations in wave set-up that cause a local inversion
of the longshore current pattern. This creates a large-scale clockwise circulation. Further N towards
Pelican point, the wave driven current becomes northward again and the sediment transport towards
Pelican Point continues. These characteristics of flow and sediment transport were verified by means
of 2D hydrodynamic simulations (Not shown here).
Fig. 11 shows the calculated annual transport rates in a number of locations along the project site.
The numbers in the figure correspond to a profile number as shown in the lower right corner of the
figure. It is seen that the transport rates at Donkey Bay decrease rapidly in northern direction. This
indicates a strong beach accretion in this area. North of Donkey Bay the littoral transport increases
towards Pelican Point, thus indicating net loss of sediment which is reflected in beach erosion. At
Pelican point the transport rates decrease due to the shoreline orientation at the spit. This is reflected
in beach accretion at Pelican Point.
Fig.11: Annual sediment transport along the Pelican Point Peninsula. (3D View from NW)
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Elfrink et al
An analysis of aerial photographs indicates that the averaged annual growth of the spit at Pelican
point corresponds to a net north going littoral transport of the order 1 million m3/year. It is seen that
this corresponds quite well with the simulated transport rates, despite the lack of good calibration
data.
Despite the shortcomings of the sediment transport model on the curvy stretches along the
shoreline, the overall picture of the simulated littoral transport is clear and corresponds with the
observed shoreline changes.
CONCLUSIONS
The littoral transport along the Pelican point Peninsula is dominated by the effect of highly
oblique incident waves. Model simulations indicate a maximal annual littoral drift along Pelican
Point Peninsula of the order 1 million m3/year
The offshore angles of wave incidence e.g. the angle between the offshore wave crests and the
shoreline is larger than 45 degrees. Under these circumstances small initial perturbations of the
shoreline are not smoothened out by the waves but may develop into large-scale coastal features.
This process is presently active at the Pelican Point peninsula. A new spit is presently being formed
at Donkey Bay. The formation of the spit causes shoreline erosion between Donkey Bay and Pelican
Point.
An analysis of aerial photographs has shown that the shoreline along the Peninsula was more
or less stable between 1958 and 1976. The observed erosion N of Donkey Bay started in the late
seventies and is related to a shift in the mean wind direction that continues until today.
ACKNOWLEDGEMENTS
The authors would like to express their gratitude to Timo Mufeti, Walvis Bay City Council for
his assistance in the field and to Geoff Smith, CSIR, Stellenbosch, South Africa for his assistance
in providing long-term wind data in the region.
REFERENCES
Fredsøe, J., and Deigaard, R,. 1992. Mechanics of Coastal Sediment Transport. Advanced Series
on Ocean Engineering – Vol. 3 World Scientific Prentice Hall, ISBN 981-02-0841-3 (pbk). 369
pp.
Mangor, K., 2001. Shoreline Management Guidelines. DHI- Water and Environment.
ISBN 87-981950-9-3. 232pp.
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Elfrink et al
KEY WORDS: Shoreline evolution, climate changes, sediment transport, coastal morphology,
SW Africa.
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Elfrink et al