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Wave attenuation in coastal mangroves in the Red River Delta, Vietnam
Journal of Asian Earth Sciences 29 (2007) 576–584 www.elsevier.com/locate/jaes
Wave attenuation in coastal mangroves in the Red River Delta, Vietnam S. Quartel a
a,*
, A. Kroon b, P.G.E.F. Augustinus a, P. Van Santen a, N.H. Tri
c
Department of Physical Geography, Faculty of Geosciences, Institute for Marine and Atmospheric Research, Utrecht University, P.O. Box 80.115, 3508 TC Utrecht, The Netherlands b University of Copenhagen, Institute of Geography, Øster Voldgade 10, 1350 Copenhagen, Denmark c Vietnam National University, Mangrove Ecosystem Research Division, Hanoi, Viet Nam Received 16 November 2004; received in revised form 19 September 2005; accepted 26 May 2006
Abstract Wave attenuation was studied in a coastal mangrove system in the Red River Delta, Vietnam on the coast north of Do Son. From sea towards land the study area consisted of a bare mudflat, covered by a sandy layer with embryonic cheniers, abruptly changing into a muddy tidal flat overgrown with mangroves. Three instrumented tripods (A–C) placed in a cross-shore profile, were used to measure current velocity and water level, at the open tidal flat, at the beginning of the mangrove vegetation, and in the mangrove vegetation, respectively. Measurements were conducted in the wet season in July and August 2000. The elevation of the area was surveyed using a levelling instrument. Over the bare sandy surface of the mudflat, the incoming waves are reduced in height (and energy density) due to bottom friction. This reduction decreases with increasing water depth. In the mangrove vegetation, the bottom friction exerted by the clay particles is very low. However, the dense network of trunks, branches and above ground roots of the mangrove vegetation causes a much higher drag force. For the mangrove vegetation which mainly consists of Kandelia candel, the drag force can be approached by the function CD = 0.6e0.15A (with A being the projected cross-sectional area of the under water obstacles at a certain water depth). For the same muddy surface without mangroves the function would be CD = 0.6. 2006 Elsevier Ltd. All rights reserved. Keywords: Mangrove forest; Wave height reduction; Coastal defence
1. Introduction Mangroves are tidal forest ecosystems on muddy soils in sheltered saline to brackish environments. They are considered as the low-latitude equivalent of salt marshes and mainly grow in tropical regimes. Mangrove forests are composed of bushes and trees with special root systems for both water and air supply. Because of these root systems, the trees are adapted to grow in anaerobic and unstable conditions of waterlogged muddy soils (Augustinus, 2004). The trunks and roots above the ground have a considerable influence on the hydrodynamics and sediment transport within the forests.
*
Corresponding author. Tel.: +31 30 2535735; fax: +31 30 2531145. E-mail address: [email protected] (S. Quartel).
1367-9120/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jseaes.2006.05.008
Mangrove forests play an important role in flood defense by dissipating incoming wave energy and reducing the erosion rates. Besides, the wave-driven, wind-driven, and tidal currents also reduce due to the dense network of trunks, branches and aboveground roots of the mangroves. This latter can be seen as an increased bed roughness. Physical processes of wave dissipation across an intertidal surface with mangroves are not widely studied. Wu et al. (2001) described and modelled the tidal currents in the mangroves, focusing on the current velocity predictions in channels and tidal creeks. Mazda et al. (1997a) and Massel et al. (1999) measured and described the surface wave propagation in mangrove forests. Both studies focused on the wave energy dissipation by bottom friction and vegetation density, where the vegetation impact was incorporated by an extra component of the drag force (see also Mazda
S. Quartel et al. / Journal of Asian Earth Sciences 29 (2007) 576–584
et al., 1997b). Wave dissipation across an intertidal flat with salt marshes has recently gained more attention (e.g. Brampton, 1992; Kobayashi et al., 1993; Mo¨ller et al., 1999; Mo¨ller and Spencer, 2002; Cooper, 2005). This paper describes the wave reduction over a tidal flat and within a contiguous mangrove area in the Red River Delta, Vietnam. Field experiments are used to reach the main purpose: to quantify the wave reduction and wave energy dissipation in these two areas, incorporating the vegetation as an extra drag force. 2. Study area The Red River Delta is one of the largest deltas in Vietnam and lies in the northern part of Vietnam where the Red River flows into the Bay of Tonkin (Fig. 1). The northern part of the Red River Delta is a tide-dominated system where waves are less important, due to the sheltering effect of Hainan Island and the Chinese mainland. The tides in the Bay of Tonkin are diurnal with a range of 2.6–3.2 m (mesotidal). Active intertidal mudflats, mangrove swamps and supratidal marshes in estuaries and along open coastlines characterize the coastal areas (Mathers and Zalasiewicz, 1999). The study was conducted on a tidal flat and adjacent mangrove forest situated near Do Son on the Red River Delta (Fig. 1). The mudflat was characterized by sediments of <2 lm diameter (Fig. 2). The eastern part of the mudflat faced the open sea and was covered by a sandy layer with a mean grain size ranging between 100 and 250 lm. This sandy layer was between 2 and 40 cm thick. The western part of the mudflat was overgrown with mangroves and the westward located inland area was separated from the mangrove forest by a sea dyke. Three instrumented tripods (A–C) were placed along a cross-shore profile (Fig. 2). The average slope of the profile
577
between tripod A and B was 0.19%, which was typical for the whole sand-covered mudflat. The sandy surface on the mudflat extended further seaward of tripod A for several hundreds of meters. Ridges and runnels were observed on the beach plain and the ridges consisted of sand lying on top of the mudflat. These ridges were cheniers in an embryonic stage. The sand was probably derived by winnowing. The cheniers were 10–40 cm high and their crest were aligned north-south. The chenier surfaces were covered with two dimensional wave ripples (10 cm in length). Current ripples were sometimes present in the troughs. Chenier ridges were best developed at the landward site of the beach plain. The mangrove forest was situated between the sand-covered part of the mudflat and the sea dyke (between tripod B and C in Fig. 2). The variation in bed level in the mangrove area was very small and there were no ripples present. Tripod C was positioned at a slightly lower elevation than tripod B. On the north-east side, the mangrove swamp was drained by a tidal channel, just outside the study area. The muddy soil was very soft and at least 3 m thick. The vegetation between tripod B and C consisted for 88.9% of Kandelia candel, 7.4% of Sonneratia spec. and 3.7% of Avicennia marina. The Kandelia candel occurred in bushes and small trees, and had hardly any roots above the ground. The soil between the mangrove trees was full of invertebrates. 3. Methods 3.1. Field methods Hydrodynamic measurements were conducted using pressure sensors and electromagnetic flow devices. These instruments were attached to the three tripods. The three
Fig. 1. Topographical map of Vietnam and the Red River Delta with Do Son south east of Haiphong.
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1 relative height [m]
W
E mangrove forest on a
0
muddy soil
1
2
unvegetated beach plain consisting of a mudflat covered by a sandy layer
↑
↑
C
B
↑ A
0
100
200
300 400 crossshore distance [m]
500
600
700
Fig. 2. Placed tripods A, B and C, on a cross-shore transect of the field site Do Son.
legs of a tripod were 1.20 m apart and the height of the legs was 0.80 m. The three tripods were placed along a crossshore profile (Fig. 2). Tripod A was placed at the seaward side of the tidal flat and collected the boundary conditions for this research. Tripod B was placed on the border of the bare mudflat, covered by sand, and the area where mangrove vegetation began. Tripod C had its position in the mangrove forest, 31.8 m landward from the tripod B. Each tripod was equipped with one pressure sensor at 0.2 m above the bed and one electro-magnetic flow device (EMF) at 0.14 m above the bed. The pressure sensor measured the pressure of the water column above the instrument. This pressure was corrected for atmospheric pressure and then converted to the water depth by linear wave theory. The dynamic pressure component of the measured pressure signal was depth-adjusted, since the maximum water height above the pressure sensor was about 1.9 m. The alongshore and cross-shore velocities were measured with the EMF. The burst interval between measurements was 1 h and the burst length was 1024 s (17 0 0400 ). The sampling frequency was 2 Hz. A traditional levelling instrument was used to measure the bed level heights along the transect where the tripods were positioned. The data were also used to determine the slope of the tidal flat and the morphometry of the ridges. The accuracy of the heights derived with this instrument was in the order of 0.01 m. The height of the profile was measured against mean sea level.
ment heights on the tripod (Fig. 3). The wave height (Hrms) during the measurement period was related to the average water depth (h), with higher waves during higher water levels. The wave conditions were mainly low energy. Wave driven processes like longshore currents, undertow, and low frequency waves could be neglected in these low energy wave conditions. The burst-averaged measured flow velocity at 14 cm above the bed was about 0.02–0.20 ms1.
3.2. Measuring period
r¼
The hydrodynamic measurements started on July 19th 2000 at 13:00 (burst 4814) and ended on August 13th 2000 at 22:00 (burst 5423). Only bursts with a wave height over 5 cm were used for further analysis. A total of 94 bursts were analyzed and most of these were measured during high water spring tide. The root-mean-square wave height (Hrms) and the significant wave period (T1/3) of the incident waves with frequencies over 0.05 Hz and of the infragravity waves with frequencies below 0.05 Hz were computed for each recorded burst. This resulted in time-series of Hrms and T1/3 for successive high-tide periods in the field period, when the water level was well above the instru-
where H x1 is the wave height at the seaward point x1 and H x2 is the wave height at a position 100 m inshore (x2). The measured conditions at tripod A matched the computed water levels and wave heights at this location (calibration procedure) and the wave height reduction to tripod B was computed. The application of the wave energy decay model was not justified in the mangrove area between tripod B and C, since two criteria were not valid: the mangrove area consisted of muddy sediments and the friction of the vegetation had a major influence on the wave height reduction. Mazda et al. (1997a) found a wave reduction increase with an increase in density and height of the
3.3. Analysis methods Normally, wave attenuation appeared to be non-linear over ’rough’ intertidal surfaces (e.g. Brampton, 1992; Kobayashi et al., 1993; Mo¨ller et al., 1999) and over the boundary between bare mudflat and mangroves. This implied that the rate of wave reduction over a flat sloping area was non-linear with the distance travelled by the wave and detailed wave transformation models had to be used to study this aspect. The wave attenuation over the unvegetated sand covered beach plain between tripods A and B (Fig. 2) was computed with a wave energy decay model over the measured cross-shore profile. This wave energy decay model was based on Battjes and Janssen (1979) and included wave shoaling, refraction and dissipation by bottom friction, breaking and rollers. The wave energy reduction was computed and the wave height reduction between the tripods was estimated by the ratio (see also Mazda et al., 1997a): H x1 H x2 ; H x1
ð1Þ
0.3
7
0.225
6
0.15
5
0.075
4
0
3
b 2.4
0.24
→onshore
2.1
1.8
1.5
1.2 4800
0.12
0 offshore←
water depth [m]
1
flow velocity vector [m.s ]
wave height [m]
a
579
wave period [s]
S. Quartel et al. / Journal of Asian Earth Sciences 29 (2007) 576–584
4900
5000
5100 5200 time [burst]
5300
0.12
0.24 5500
5400
Fig. 3. Time series of (a) wave height, Hrms (solid line), and the wave period, T1/3 (points), and (b) average water depth, h (solid line), and flow velocity vector (points) at tripod A.
mangrove vegetation. The resistance of the vegetation and the bottom friction generate a drag force that causes this reduction of wave height (Mazda et al., 1997b). They measured a maximum ratio of 0.2 in mangroves of about 2.5 m height. The drag force, exhibited upon the water motion by the mangrove trees, occurred throughout the whole water depth. Mazda et al. (1997a) estimated the effect of the flow resistance due to mangroves as a bottom friction. This drag coefficient, CD, was approximated by: pffiffiffi 32 2 h2 H x1 CD ¼ 1; ð2Þ p H x1 Dx H x2 where h is the water depth and Dx distance x2 x1. Eq. (2) is only valid when shoaling by bottom friction of the incoming waves is neglected in the mangrove area. The CD is also influenced by the vegetation density. The amount of submerged branches and leaves depend on the age and species of the mangroves and significantly increases with increasing water depth. The bottom friction on a tidal flat without mangroves was exerted only by propagating waves. The size of the sediment particles of the bed and, when present, the bed forms determined the bed roughness and affected the bottom friction. The wave height reduction on a tidal flat without mangroves was computed by (Van Rijn, 1994): 1 1 ¼ þ aðx1 x2 Þ; H x2 H x1
ð3Þ
4f w x3 ; 6p g n c sinh3 ðkhÞ
ð4Þ
a¼
where fw is a friction factor, x the angular frequency, g the acceleration of gravity, n the ratio of group and phase velocity, c the phase velocity and k the wave number. Note that Eqs. (3) and (4) are only valid for a non-sloping bed. ˆ d/ ˆ dA The fw differed with the flow conditions. Laminar (U 4 4 5 ˆ ˆ t < 10 ), hydraulic smooth (10 < UdAd/t < 10 ) or ˆ d/t > 105) was computed by using ˆ dA hydraulic rough (U ˆ d (peak amplitude ˆ Ud (peak orbital velocity near the bed), A of the horizontal displacement at the bed), and t (kinematic viscosity 1 · 106 m2 s1). In general, the mud is hydraulic smooth (Soulsby, 1997) and the friction coefficient near the bed was calculated by (Van Rijn, 1994): ^ d =tÞ0:5 for U ^ d =t < 104 ; ^ dA ^ dA fw ¼ 2ðU ^ d =tÞ ^ dA fw ¼ 0:09ðU
0:2
for 10
4
ð5Þ
^ d =t < 10 : ^ dA < U 5
ð6Þ
The bed shear stresses for currents, sb,c, and waves, sb,w, were both calculated with Eqs. (7) and (8) to get an estimation about the importance of the friction caused by currents (Van Rijn, 1994): 1 2; sb;c ¼ qfw;c U ð7Þ 8 1 ^ d Þ2 ; ð8Þ sb;w ¼ qfw;w ðU 4 where fw,c (fw,w) is the friction factor induced by currents (waves) and U is the depth-averaged flow velocity. The bed shear stress due to currents in proportion to the total bed shear stress showed the contribution of the currents in the bottom friction: s b,c/sb,w + sb, c, which was negligible. Therefore in this paper, only the fw was taken into account.
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are presented in Fig. 4. The burst numbers point at rising tide (5127–5129), high water (5130–5131) and falling tide (5132–5134). The peak frequencies of the spectra were similar for all locations and the spectral density clearly showed a reduction over the cross-shore profile for all tidal stages. This means that the wave heights were reduced along the cross-shore transect from tripod A to C. Most of the waves were shoaling and rarely broke on the beach plain between tripod A and B. There were no breaking waves observed in the mangrove forest between tripod B and C. The relative wave heights, defined as the ratio between the local wave
4. Results 4.1. Measured changes of the wave field The measured wave height (Hrms), wave period (T1/3), water depth (h) and flow velocity at tripod A over 15 measured tides are presented in Fig. 3. The spring-tide at burst numbers 5127–5134 was studied in more detail. The wave heights were depth limited and increased from about 0.15–0.25 m during rising tide. The spectral densities of the measured wave records of all tripods (A, B and C)
burst 5128
2
energy [m .s]
burst 5127
0.14
0.14
0.12
0.12
0.12
0.12
0.1
0.1
0.1
0.1
0.08
0.08
0.08
0.08
0.06
0.06
0.06
0.06
0.04
0.04
0.04
0.04
0.02
0.02
0.02
0.02
0
0.5
1
0
0
frequency [Hz]
0.5
1
0
0
frequency [Hz]
0.5
1
0
burst 5133
0.14
0.14
0.12
0.12
0.1
0.1
0.1
0.1
0.08
0.08
0.08
0.08
0.06
0.06
0.06
0.06
0.04
0.04
0.04
0.04
0.02
0.02
0.02
0.02
0.5 frequency [Hz]
1
0
0
0.5 frequency [Hz]
1
0
1
burst 5134
0.14
0.12
0
0.5 frequency [Hz]
0.12
0
0
frequency [Hz]
burst 5132
burst 5131
0.14
2
burst 5130
0.14
0
energy [m .s]
burst 5129
0.14
0
0.5 frequency [Hz]
1
0
tripod A tripod B tripod C
0
0.5 frequency [Hz]
Fig. 4. Energy density spectrum from bursts 5127–5134 for tripod A, B and C.
1
S. Quartel et al. / Journal of Asian Earth Sciences 29 (2007) 576–584
height and local water depth were also small (<0.2; waves of 0.2 m over 1.8 m water depth in Fig. 3) and in the range of non-breaking waves under all tidal stages. 4.2. Wave field attenuation over the bare sandy surface of the mudflat The rate of the measured wave height reduction over the sandy surface was computed with Eq. (1) and expressed per meter cross-shore. The measured distance between tripod A and tripod B was 314.5 m and between tripod B and C 31.8 m. This measured wave height reduction over the sand-covered mudflat per meter cross-shore is plotted against the local water depth at tripod A in Fig. 5a and showed a decrease with an increase of the water depth. A linear expression between the wave height reduction per meter cross-shore and the water depth had a gain of 12 · 104 (R2 = 0.61). The drag coefficient, CD, was computed with Eq. (2). Its value varied between 0.11 and 0.86. The resistance coefficient of the sandy surface lowered with a larger water depth (Fig. 5b). This trend corresponded with the tendency of wave height reduction. The wave height reduction between tripod A and tripod B was also computed with a wave energy decay model. This model included shoaling and refraction and dissipation due to bottom friction. The wave height
wave height reduction
a
581
decay of the Hrms over the cross-shore profile for the selected spring-tide (bursts 5127–5134) are shown in Fig. 6. The wave heights and water levels at the offshore boundary were almost similar to those at tripod A and the optimal setting was reached when the measured values at tripod A matched the computed ones. The patterns in Fig. 6 clearly showed shoaling waves and wave decay was mainly the result of bottom friction. Rapid decreases of wave height were only observed in the first and last bursts (Hrms profiles) and were the result of dissipation of wave energy by wave rollers and bottom friction at shallow water depths. The measured and computed wave height reductions (Eq. 1) between tripod A and B are presented in Fig. 7. Most of the computed wave height reduction data are within 10% of the measured ones with a roughness factor for bed friction of 0.02. This result even improved when the roughness factor for bed friction increased to 0.04 for cases with high values of wave height reductions. 4.3. Wave field attenuation in the mangrove forest The measured wave height reduction per meter crossshore in the mangrove was higher than the measured wave height reduction per meter cross-shore over the sandy surface (Fig. 5a). The wave height reduction per
0.012
beach plain mangrove mud bed
0.008
0.004
0
resistance coefficient
b
4.5 beach plain mangrove mud bed 3
1.5
0
0
0.5
1 1.5 water depth [m]
2
2.5
Fig. 5. (a) Variation of wave reduction, r, and (b) resistance coefficient, CD, with water depth. The mud bed values are computed. The smooth lines are trend lines.
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Hrms [m]
0.3
0.2
0.1
Hrms [m]
0.3
0.2
0.1
relative height [m]
0
0. 5 C
B
1 A
1.5 100
200 300 cross shore distance [m]
400
Fig. 6. Computed wave height (Hrms) decrease over the cross-shore transect using a wave energy decay model. Upper panel: burst 5127 (solid), 5128 (dashes), 5129 (dash-dot) and 5130 (dotted). Middle panel: burst 5131 (dotted), 5132 (dash-dot), 5133 (dashed) and 5134 (solid). Lower panel shows the cross-shore profile again. The position of the tripods are indicated with the vertical lines (A–C).
meter cross-shore in the mangrove forest was small at lower water levels and increased towards high tide. However, the variation of the wave height reduction per meter cross-shore with the water depth was larger than on the sand-covered mudflat, and the explained variance was less (R2 = 0.26). The wave height reduction between tripod B and C was also computed with the wave energy decay model. The pattern of wave height reduction in Fig. 6 clearly shows an underestimation of the wave height reduction between B and C (see also Fig. 7). The contribution of the mangrove vegetation as a friction factor was clear. The network of trunks, branches and above ground roots of the mangrove trees were seen as an increased bed roughness for incoming waves. This increased bed roughness caused more friction and dissipated more wave energy which resulted in higher rates for the wave height reduction. The resistance coefficient, CD, increased with an increasing water depth in the mangrove forest (Fig. 5b), as expected from the relation between the water depth and the wave height reduction per meter cross-shore. The trend line for the variation of CD with the water depth was similar to the trend found by Mazda et al. (1997a), with the same direction and exponential shape.
The wave reduction per meter cross-shore over a muddy soil without vegetation was computed with Eqs. (3)–(8) (Fig. 5a). The friction, caused by currents acting upon the bed particles, was computed with the use of measured flow velocities (friction on average 0.012). The friction, caused by waves was computed with the measured ˆ d) and the measured amplitude of the orbital velocity (U ˆ d) (friction on average 0.049). The bed bottom orbital (A shear stress due to currents (0.008 Nm2) was a small part of the total bottom friction (sb,c/sb,w + sb,c). The bed shear stress due to waves (0.34 Nm2) was most of the time over 95% of the total friction factor. Therefore, reduction in wave height outside the mangroves was computed with only the friction factor due to wave activity. Wave reduction per meter cross-shore over the muddy surface was very small with maximum wave reduction values of 6 · 104. The contribution of the sediment size of clay to the computed bottom friction was negligible and the computed resistance coefficient, CD, on an uncovered mud bed did not significantly vary with water depth and had a mean value of 0.005 (Fig. 5b). The vegetation between tripods B and C over 5 m width consisted of Kandelia candel (88.9%), Sonneratia spec. (7.4%) and Avicennia marina (3.7%). The trees between
S. Quartel et al. / Journal of Asian Earth Sciences 29 (2007) 576–584
increase of CD with an increase of A. The exponential function of
0.8
C D ¼ 0:601e0:1548A ;
computed reduction ratio
0.75
0.65
5. Discussion
0.6
0.55
0.55
0.6 0.65 0.7 0.75 measured reduction ratio
0.8
Fig. 7. Measured and computed wave height reduction ratios for Hrms (Eq. 1). The stars refer to the spring-tide bursts between tripod A and B (314.5 m apart) and the crosses between tripod B and C (31.8 m apart). The solid line is the perfect match and the dotted lines are the 10% difference lines. Note: the ratio between B and C (mangrove area) is not so good, despite its shorter distance. An increase of the bottom roughness (to values of 0.04) for the higher measured ratios will even make a better match with the computations between A and B.
the tripods were measured for their trunk height, trunk width, foliage height and foliage width. These parameters were used to estimate a certain area that was projected towards the incident waves. These projected areas of different mangrove trees are averaged over one meter width and resulted in the total projected area of mangrove trees (A) between tripod B and C. The total projected area of the mangrove trees varied for different water levels. The projected area increased considerably by the surface of the foliage when the water level exceeded the trunk height. The drag force was caused by the vegetation and depended on the density of the vegetation Mazda et al. (1997a). The relation between the projected area of obstacles and the resistance coefficient is presented in Fig. 8 and showed an
resistance coefficient
4.5
3
1.5
0
0
ð9Þ
described this relation over the 31.77-m distance between tripod B and C with a correlation of 0.53. Thus, the resistance coefficient would be 0.601 over 31.77-m, and 0.019 per cross-shore meter, assuming there is no mangrove vegetation.
0.7
0.5 0.5
583
2
4
6
8
10
12
projected area of the obstacles [m2] Fig. 8. Variation of projected area of obstacles per meter width with the drag coefficient in the mangrove forest. The smooth line is the exponential trend line.
The studied site consisted of two different sections: the sandy surface with the cheniers in an embryonic stage, and the muddy mangrove swamp. The sandy surface layer covering the clay subsoil over a length of at least 500–600 meters was almost flat (Fig. 2). The wave height data from tripod A showed that the waves were depth-limited. Small water depths corresponded with small wave heights and large water depths correspond with higher incident waves. The wave energy decay over the sandy surface could be well described with a wave energy decay model, originally based on Battjes and Janssen (1979). The measured wave height reductions as expressed by Eq. (1) were almost similar to the computed wave height reductions under these cases with shoaling waves. However, the measured wave energy decay in the mangrove area was clearly much higher than the computed ones. The bottom friction in the latter area was clearly underestimated and the cohesive forces of the muddy sediments and its depth-varying bed strength were not incorporated in the wave energy decay model. Energy losses in the mangroves (wave height reduction) were mainly assigned to friction from the trees on the waves. The influence of local currents on wave-current interactions and wave energy dissipation was neglected. The cross-shore current velocity at very shallow water depths only reached its maximum values at the start and end of the selected spring-tide (current velocities in the order of 0.02–0.20 ms1). The contribution of the sediment size of the clay to the bottom friction was marginal, although muddy sediments appear to undergo an elastic response to the pressure of the progressive waves that could cause energy losses. The motion of the soft bottom has a wavelike appearance of oscillations (Suhayda, 1978). The vertical displacement of the bottom is 180 out of phase with the wave pressure. The wave crest corresponds with a depression in the bottom. The phase shift results from the effect of the internal viscosity of mud. This loss of energy by a surface wave due to bottom forcing is significant larger than the energy loss due to bottom friction (Suhayda, 1978). The effect of the interaction of waves with soft bottom sediments at the study site was not measured and could not be included in the current analysis of the collected data. However, the muddy surface under mangroves was subjected to relatively fast consolidation as a result of the water extraction and growth of the underground roots of the mangroves. It
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was therefore less sensitive for movement, but the effect could still be significant. The drag force due to the dense network of trunks, branches and above ground roots was the main cause of the high rate of wave reduction in the mangrove forest. At higher water levels there was more vegetation flooded and the drag coefficient increased. The drag coefficient was related to the area of flooded vegetation, but could well differ with changes in the structure of the vegetation. Different species have different sizes and kind of trunks and leaves, creating a rough or smooth surface. Besides, the leaves may be flexible, variable in shape and change over the seasons. The function for the correlation between the projected area and the drag force is therefore probably not linear. The exponential function Eq. (9) gave a good estimation of the drag force for this field site (see Fig. 8). The friction due to wave–fluid mud interaction could be an explanation for the difference in the drag coefficient values per meter cross-shore: 0.005 and 0.019 (Section 4.3). The value of 0.005 was computed for a muddy soil with Eqs. (3)–(8) and was only valid when the energy losses were due to the sediment particle size of the bed. The drag coefficient 0.019 was distracted from the variation in the exposed cross-area of mangrove obstacles with the drag coefficient and was computed based on Eq. (9) assuming A = 0. The process described by Suhayda (1978) could cause the significant difference between those two values. 6. Conclusions The following conclusions were based on the field measurements on wave attenuation over a bare mudflat with a sandy cover and within a mangrove forest. The wave height reduction over the sandy surface layer on the mudflat is mainly caused by bottom friction of shoaling waves and can be well computed with a wave energy decay model based on Battjes and Janssen (1979). This model can not be used in mangroves where the wave reduction is significant higher. Here, the resistance of the vegetation, expressed by friction caused by the size and structure of the vegetation exposed to the waves, mainly determines the wave energy dissipation. The wave height reduction of shoaling waves over the sandy surface layer on the mudflat decreases with an increase in water depth, due to decreasing relative wave heights. For the mangroves, the wave height reduction increases with an increase in water depth due to an increase in the vegetation exposed to the waves. The drag force exerted by mangroves depends on the species and the density of the vegetation, and for a vegetation consisting of Kandelia candel (88.9%), Sonneratia spec. (7.4%) and Avicennia marina (3.7%), the drag force can be approached by the function CD = 0.601e0.1548A (with A being the projected area of the under water obstacles at a certain water depth). The measured wave height reduction r through mangroves was obviously larger than over the beach plain
(Fig. 5a). Comparing the wave height reduction for similar water depths (h = 1.25–1.55 m), the wave height reduction by mangroves was 5–7.5 times larger then by bottom friction only. This indicates clearly the importance of the mangrove vegetation for coastal defence. Acknowledgments The authors thank the students and staff members of Vietnam National University for their logistic assistance. We also thank Hans de Boois for his active support and enthusiasm during the field work. The constructive comments of two anonymous reviewers on an earlier version of this manuscript were gratefully appreciated. References Augustinus, P.G.E.F., 2004. Geomorphology and sedimentology of mangroves. In: Geomorphology and Sedimentology of Estuaries. Developments in Sedimentology 53. Elsevier Scientific Publishers, Amsterdam, The Netherlands. Battjes, J.A., Janssen, J.P.F.M., 1979. Energy loss and set-up due to breaking of random waves. In: Proceedings ICCE, ASCE, pp. 569– 587. Brampton, A.H., 1992. Engineering significance of british saltmarshes. In: Allen, J.R.L., Pye, K. (Eds.), Saltmarshes: morphodynamics, conservation and engineering significance. Cambridge University Press, London, pp. 115–122. Cooper, N.J., 2005. Wave dissipation across intertidal surfaces in the Wash Tidal Inlet, Eastern England. Journal of Coastal Research 21-1, 28–40. Kobayashi, N., Raichle, A.W., Asano, T., 1993. Wave attenuation by vegetation. Journal of Waterway, Port, Coastal and Ocean engineering 199-1, 30–48. Massel, S.R., Furukawa, K., Brinkman, R., 1999. Surface wave propagation in mangrove forests. Fluid Dynamics Research 24, 219–249. Mathers, S., Zalasiewicz, J., 1999. Holocene sedimentary architecture of the Red River Delta, Vietnam. Journal of Coastal Research 15 (2), 314–325. Mazda, Y., Magi, M., Kogo, M., Hong, P., 1997a. Mangroves as a coastal protection from waves in the Tong King delta, Vietnam. Mangroves and Salt Marshes 1, 127–135. Mazda, Y., Wolanski, E., King, B., Sase, A., Ohtsuka, D., Magi, M., 1997b. Drag force due to vegetation in mangrove swamps. Mangroves and Salt Marshes 1, 193–199. Mo¨ller, I., Spencer, T., 2002. Wave dissipation over macro-tidal saltmarshes: effects of marsh edge typology and vegetation change. Journal of Coastal Research SI36, 506–521. Mo¨ller, I., Spencer, T., French, J.R., Legget, D.J., Dixon, M., 1999. Wave transformation over salt marshes: a field and numerical modelling study from North Norfolk, England. Estuarine, Coastal and Shelf Science 49, 411–426. Soulsby, R.L., 1997. Dynamics of Marine Sands: A Manual for Practical Applications. Thomas Telford Publications, London. Suhayda, J.N., 1978. Surface waves and bottom sediment response. Marine Geotechnology 2, 135–146. Van Rijn, L.C., 1994. Principles of Fluid Flow and Surface Waves in Rivers, Estuaries, Seas, and Oceans, 2nd Ed. Aqua Publications, Amsterdam, The Netherlands. Wu, Y., Falconer, R., Struve, J., 2001. Mathematical modelling of tidal currents in mangrove forests. Environmental Modelling and Software 16, 19–29.
Wave attenuation in coastal mangroves in the Red River Delta, Vietnam S. Quartel a
a,*
, A. Kroon b, P.G.E.F. Augustinus a, P. Van Santen a, N.H. Tri
c
Department of Physical Geography, Faculty of Geosciences, Institute for Marine and Atmospheric Research, Utrecht University, P.O. Box 80.115, 3508 TC Utrecht, The Netherlands b University of Copenhagen, Institute of Geography, Øster Voldgade 10, 1350 Copenhagen, Denmark c Vietnam National University, Mangrove Ecosystem Research Division, Hanoi, Viet Nam Received 16 November 2004; received in revised form 19 September 2005; accepted 26 May 2006
Abstract Wave attenuation was studied in a coastal mangrove system in the Red River Delta, Vietnam on the coast north of Do Son. From sea towards land the study area consisted of a bare mudflat, covered by a sandy layer with embryonic cheniers, abruptly changing into a muddy tidal flat overgrown with mangroves. Three instrumented tripods (A–C) placed in a cross-shore profile, were used to measure current velocity and water level, at the open tidal flat, at the beginning of the mangrove vegetation, and in the mangrove vegetation, respectively. Measurements were conducted in the wet season in July and August 2000. The elevation of the area was surveyed using a levelling instrument. Over the bare sandy surface of the mudflat, the incoming waves are reduced in height (and energy density) due to bottom friction. This reduction decreases with increasing water depth. In the mangrove vegetation, the bottom friction exerted by the clay particles is very low. However, the dense network of trunks, branches and above ground roots of the mangrove vegetation causes a much higher drag force. For the mangrove vegetation which mainly consists of Kandelia candel, the drag force can be approached by the function CD = 0.6e0.15A (with A being the projected cross-sectional area of the under water obstacles at a certain water depth). For the same muddy surface without mangroves the function would be CD = 0.6. 2006 Elsevier Ltd. All rights reserved. Keywords: Mangrove forest; Wave height reduction; Coastal defence
1. Introduction Mangroves are tidal forest ecosystems on muddy soils in sheltered saline to brackish environments. They are considered as the low-latitude equivalent of salt marshes and mainly grow in tropical regimes. Mangrove forests are composed of bushes and trees with special root systems for both water and air supply. Because of these root systems, the trees are adapted to grow in anaerobic and unstable conditions of waterlogged muddy soils (Augustinus, 2004). The trunks and roots above the ground have a considerable influence on the hydrodynamics and sediment transport within the forests.
*
Corresponding author. Tel.: +31 30 2535735; fax: +31 30 2531145. E-mail address: [email protected] (S. Quartel).
1367-9120/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jseaes.2006.05.008
Mangrove forests play an important role in flood defense by dissipating incoming wave energy and reducing the erosion rates. Besides, the wave-driven, wind-driven, and tidal currents also reduce due to the dense network of trunks, branches and aboveground roots of the mangroves. This latter can be seen as an increased bed roughness. Physical processes of wave dissipation across an intertidal surface with mangroves are not widely studied. Wu et al. (2001) described and modelled the tidal currents in the mangroves, focusing on the current velocity predictions in channels and tidal creeks. Mazda et al. (1997a) and Massel et al. (1999) measured and described the surface wave propagation in mangrove forests. Both studies focused on the wave energy dissipation by bottom friction and vegetation density, where the vegetation impact was incorporated by an extra component of the drag force (see also Mazda
S. Quartel et al. / Journal of Asian Earth Sciences 29 (2007) 576–584
et al., 1997b). Wave dissipation across an intertidal flat with salt marshes has recently gained more attention (e.g. Brampton, 1992; Kobayashi et al., 1993; Mo¨ller et al., 1999; Mo¨ller and Spencer, 2002; Cooper, 2005). This paper describes the wave reduction over a tidal flat and within a contiguous mangrove area in the Red River Delta, Vietnam. Field experiments are used to reach the main purpose: to quantify the wave reduction and wave energy dissipation in these two areas, incorporating the vegetation as an extra drag force. 2. Study area The Red River Delta is one of the largest deltas in Vietnam and lies in the northern part of Vietnam where the Red River flows into the Bay of Tonkin (Fig. 1). The northern part of the Red River Delta is a tide-dominated system where waves are less important, due to the sheltering effect of Hainan Island and the Chinese mainland. The tides in the Bay of Tonkin are diurnal with a range of 2.6–3.2 m (mesotidal). Active intertidal mudflats, mangrove swamps and supratidal marshes in estuaries and along open coastlines characterize the coastal areas (Mathers and Zalasiewicz, 1999). The study was conducted on a tidal flat and adjacent mangrove forest situated near Do Son on the Red River Delta (Fig. 1). The mudflat was characterized by sediments of <2 lm diameter (Fig. 2). The eastern part of the mudflat faced the open sea and was covered by a sandy layer with a mean grain size ranging between 100 and 250 lm. This sandy layer was between 2 and 40 cm thick. The western part of the mudflat was overgrown with mangroves and the westward located inland area was separated from the mangrove forest by a sea dyke. Three instrumented tripods (A–C) were placed along a cross-shore profile (Fig. 2). The average slope of the profile
577
between tripod A and B was 0.19%, which was typical for the whole sand-covered mudflat. The sandy surface on the mudflat extended further seaward of tripod A for several hundreds of meters. Ridges and runnels were observed on the beach plain and the ridges consisted of sand lying on top of the mudflat. These ridges were cheniers in an embryonic stage. The sand was probably derived by winnowing. The cheniers were 10–40 cm high and their crest were aligned north-south. The chenier surfaces were covered with two dimensional wave ripples (10 cm in length). Current ripples were sometimes present in the troughs. Chenier ridges were best developed at the landward site of the beach plain. The mangrove forest was situated between the sand-covered part of the mudflat and the sea dyke (between tripod B and C in Fig. 2). The variation in bed level in the mangrove area was very small and there were no ripples present. Tripod C was positioned at a slightly lower elevation than tripod B. On the north-east side, the mangrove swamp was drained by a tidal channel, just outside the study area. The muddy soil was very soft and at least 3 m thick. The vegetation between tripod B and C consisted for 88.9% of Kandelia candel, 7.4% of Sonneratia spec. and 3.7% of Avicennia marina. The Kandelia candel occurred in bushes and small trees, and had hardly any roots above the ground. The soil between the mangrove trees was full of invertebrates. 3. Methods 3.1. Field methods Hydrodynamic measurements were conducted using pressure sensors and electromagnetic flow devices. These instruments were attached to the three tripods. The three
Fig. 1. Topographical map of Vietnam and the Red River Delta with Do Son south east of Haiphong.
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1 relative height [m]
W
E mangrove forest on a
0
muddy soil
1
2
unvegetated beach plain consisting of a mudflat covered by a sandy layer
↑
↑
C
B
↑ A
0
100
200
300 400 crossshore distance [m]
500
600
700
Fig. 2. Placed tripods A, B and C, on a cross-shore transect of the field site Do Son.
legs of a tripod were 1.20 m apart and the height of the legs was 0.80 m. The three tripods were placed along a crossshore profile (Fig. 2). Tripod A was placed at the seaward side of the tidal flat and collected the boundary conditions for this research. Tripod B was placed on the border of the bare mudflat, covered by sand, and the area where mangrove vegetation began. Tripod C had its position in the mangrove forest, 31.8 m landward from the tripod B. Each tripod was equipped with one pressure sensor at 0.2 m above the bed and one electro-magnetic flow device (EMF) at 0.14 m above the bed. The pressure sensor measured the pressure of the water column above the instrument. This pressure was corrected for atmospheric pressure and then converted to the water depth by linear wave theory. The dynamic pressure component of the measured pressure signal was depth-adjusted, since the maximum water height above the pressure sensor was about 1.9 m. The alongshore and cross-shore velocities were measured with the EMF. The burst interval between measurements was 1 h and the burst length was 1024 s (17 0 0400 ). The sampling frequency was 2 Hz. A traditional levelling instrument was used to measure the bed level heights along the transect where the tripods were positioned. The data were also used to determine the slope of the tidal flat and the morphometry of the ridges. The accuracy of the heights derived with this instrument was in the order of 0.01 m. The height of the profile was measured against mean sea level.
ment heights on the tripod (Fig. 3). The wave height (Hrms) during the measurement period was related to the average water depth (h), with higher waves during higher water levels. The wave conditions were mainly low energy. Wave driven processes like longshore currents, undertow, and low frequency waves could be neglected in these low energy wave conditions. The burst-averaged measured flow velocity at 14 cm above the bed was about 0.02–0.20 ms1.
3.2. Measuring period
r¼
The hydrodynamic measurements started on July 19th 2000 at 13:00 (burst 4814) and ended on August 13th 2000 at 22:00 (burst 5423). Only bursts with a wave height over 5 cm were used for further analysis. A total of 94 bursts were analyzed and most of these were measured during high water spring tide. The root-mean-square wave height (Hrms) and the significant wave period (T1/3) of the incident waves with frequencies over 0.05 Hz and of the infragravity waves with frequencies below 0.05 Hz were computed for each recorded burst. This resulted in time-series of Hrms and T1/3 for successive high-tide periods in the field period, when the water level was well above the instru-
where H x1 is the wave height at the seaward point x1 and H x2 is the wave height at a position 100 m inshore (x2). The measured conditions at tripod A matched the computed water levels and wave heights at this location (calibration procedure) and the wave height reduction to tripod B was computed. The application of the wave energy decay model was not justified in the mangrove area between tripod B and C, since two criteria were not valid: the mangrove area consisted of muddy sediments and the friction of the vegetation had a major influence on the wave height reduction. Mazda et al. (1997a) found a wave reduction increase with an increase in density and height of the
3.3. Analysis methods Normally, wave attenuation appeared to be non-linear over ’rough’ intertidal surfaces (e.g. Brampton, 1992; Kobayashi et al., 1993; Mo¨ller et al., 1999) and over the boundary between bare mudflat and mangroves. This implied that the rate of wave reduction over a flat sloping area was non-linear with the distance travelled by the wave and detailed wave transformation models had to be used to study this aspect. The wave attenuation over the unvegetated sand covered beach plain between tripods A and B (Fig. 2) was computed with a wave energy decay model over the measured cross-shore profile. This wave energy decay model was based on Battjes and Janssen (1979) and included wave shoaling, refraction and dissipation by bottom friction, breaking and rollers. The wave energy reduction was computed and the wave height reduction between the tripods was estimated by the ratio (see also Mazda et al., 1997a): H x1 H x2 ; H x1
ð1Þ
0.3
7
0.225
6
0.15
5
0.075
4
0
3
b 2.4
0.24
→onshore
2.1
1.8
1.5
1.2 4800
0.12
0 offshore←
water depth [m]
1
flow velocity vector [m.s ]
wave height [m]
a
579
wave period [s]
S. Quartel et al. / Journal of Asian Earth Sciences 29 (2007) 576–584
4900
5000
5100 5200 time [burst]
5300
0.12
0.24 5500
5400
Fig. 3. Time series of (a) wave height, Hrms (solid line), and the wave period, T1/3 (points), and (b) average water depth, h (solid line), and flow velocity vector (points) at tripod A.
mangrove vegetation. The resistance of the vegetation and the bottom friction generate a drag force that causes this reduction of wave height (Mazda et al., 1997b). They measured a maximum ratio of 0.2 in mangroves of about 2.5 m height. The drag force, exhibited upon the water motion by the mangrove trees, occurred throughout the whole water depth. Mazda et al. (1997a) estimated the effect of the flow resistance due to mangroves as a bottom friction. This drag coefficient, CD, was approximated by: pffiffiffi 32 2 h2 H x1 CD ¼ 1; ð2Þ p H x1 Dx H x2 where h is the water depth and Dx distance x2 x1. Eq. (2) is only valid when shoaling by bottom friction of the incoming waves is neglected in the mangrove area. The CD is also influenced by the vegetation density. The amount of submerged branches and leaves depend on the age and species of the mangroves and significantly increases with increasing water depth. The bottom friction on a tidal flat without mangroves was exerted only by propagating waves. The size of the sediment particles of the bed and, when present, the bed forms determined the bed roughness and affected the bottom friction. The wave height reduction on a tidal flat without mangroves was computed by (Van Rijn, 1994): 1 1 ¼ þ aðx1 x2 Þ; H x2 H x1
ð3Þ
4f w x3 ; 6p g n c sinh3 ðkhÞ
ð4Þ
a¼
where fw is a friction factor, x the angular frequency, g the acceleration of gravity, n the ratio of group and phase velocity, c the phase velocity and k the wave number. Note that Eqs. (3) and (4) are only valid for a non-sloping bed. ˆ d/ ˆ dA The fw differed with the flow conditions. Laminar (U 4 4 5 ˆ ˆ t < 10 ), hydraulic smooth (10 < UdAd/t < 10 ) or ˆ d/t > 105) was computed by using ˆ dA hydraulic rough (U ˆ d (peak amplitude ˆ Ud (peak orbital velocity near the bed), A of the horizontal displacement at the bed), and t (kinematic viscosity 1 · 106 m2 s1). In general, the mud is hydraulic smooth (Soulsby, 1997) and the friction coefficient near the bed was calculated by (Van Rijn, 1994): ^ d =tÞ0:5 for U ^ d =t < 104 ; ^ dA ^ dA fw ¼ 2ðU ^ d =tÞ ^ dA fw ¼ 0:09ðU
0:2
for 10
4
ð5Þ
^ d =t < 10 : ^ dA < U 5
ð6Þ
The bed shear stresses for currents, sb,c, and waves, sb,w, were both calculated with Eqs. (7) and (8) to get an estimation about the importance of the friction caused by currents (Van Rijn, 1994): 1 2; sb;c ¼ qfw;c U ð7Þ 8 1 ^ d Þ2 ; ð8Þ sb;w ¼ qfw;w ðU 4 where fw,c (fw,w) is the friction factor induced by currents (waves) and U is the depth-averaged flow velocity. The bed shear stress due to currents in proportion to the total bed shear stress showed the contribution of the currents in the bottom friction: s b,c/sb,w + sb, c, which was negligible. Therefore in this paper, only the fw was taken into account.
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are presented in Fig. 4. The burst numbers point at rising tide (5127–5129), high water (5130–5131) and falling tide (5132–5134). The peak frequencies of the spectra were similar for all locations and the spectral density clearly showed a reduction over the cross-shore profile for all tidal stages. This means that the wave heights were reduced along the cross-shore transect from tripod A to C. Most of the waves were shoaling and rarely broke on the beach plain between tripod A and B. There were no breaking waves observed in the mangrove forest between tripod B and C. The relative wave heights, defined as the ratio between the local wave
4. Results 4.1. Measured changes of the wave field The measured wave height (Hrms), wave period (T1/3), water depth (h) and flow velocity at tripod A over 15 measured tides are presented in Fig. 3. The spring-tide at burst numbers 5127–5134 was studied in more detail. The wave heights were depth limited and increased from about 0.15–0.25 m during rising tide. The spectral densities of the measured wave records of all tripods (A, B and C)
burst 5128
2
energy [m .s]
burst 5127
0.14
0.14
0.12
0.12
0.12
0.12
0.1
0.1
0.1
0.1
0.08
0.08
0.08
0.08
0.06
0.06
0.06
0.06
0.04
0.04
0.04
0.04
0.02
0.02
0.02
0.02
0
0.5
1
0
0
frequency [Hz]
0.5
1
0
0
frequency [Hz]
0.5
1
0
burst 5133
0.14
0.14
0.12
0.12
0.1
0.1
0.1
0.1
0.08
0.08
0.08
0.08
0.06
0.06
0.06
0.06
0.04
0.04
0.04
0.04
0.02
0.02
0.02
0.02
0.5 frequency [Hz]
1
0
0
0.5 frequency [Hz]
1
0
1
burst 5134
0.14
0.12
0
0.5 frequency [Hz]
0.12
0
0
frequency [Hz]
burst 5132
burst 5131
0.14
2
burst 5130
0.14
0
energy [m .s]
burst 5129
0.14
0
0.5 frequency [Hz]
1
0
tripod A tripod B tripod C
0
0.5 frequency [Hz]
Fig. 4. Energy density spectrum from bursts 5127–5134 for tripod A, B and C.
1
S. Quartel et al. / Journal of Asian Earth Sciences 29 (2007) 576–584
height and local water depth were also small (<0.2; waves of 0.2 m over 1.8 m water depth in Fig. 3) and in the range of non-breaking waves under all tidal stages. 4.2. Wave field attenuation over the bare sandy surface of the mudflat The rate of the measured wave height reduction over the sandy surface was computed with Eq. (1) and expressed per meter cross-shore. The measured distance between tripod A and tripod B was 314.5 m and between tripod B and C 31.8 m. This measured wave height reduction over the sand-covered mudflat per meter cross-shore is plotted against the local water depth at tripod A in Fig. 5a and showed a decrease with an increase of the water depth. A linear expression between the wave height reduction per meter cross-shore and the water depth had a gain of 12 · 104 (R2 = 0.61). The drag coefficient, CD, was computed with Eq. (2). Its value varied between 0.11 and 0.86. The resistance coefficient of the sandy surface lowered with a larger water depth (Fig. 5b). This trend corresponded with the tendency of wave height reduction. The wave height reduction between tripod A and tripod B was also computed with a wave energy decay model. This model included shoaling and refraction and dissipation due to bottom friction. The wave height
wave height reduction
a
581
decay of the Hrms over the cross-shore profile for the selected spring-tide (bursts 5127–5134) are shown in Fig. 6. The wave heights and water levels at the offshore boundary were almost similar to those at tripod A and the optimal setting was reached when the measured values at tripod A matched the computed ones. The patterns in Fig. 6 clearly showed shoaling waves and wave decay was mainly the result of bottom friction. Rapid decreases of wave height were only observed in the first and last bursts (Hrms profiles) and were the result of dissipation of wave energy by wave rollers and bottom friction at shallow water depths. The measured and computed wave height reductions (Eq. 1) between tripod A and B are presented in Fig. 7. Most of the computed wave height reduction data are within 10% of the measured ones with a roughness factor for bed friction of 0.02. This result even improved when the roughness factor for bed friction increased to 0.04 for cases with high values of wave height reductions. 4.3. Wave field attenuation in the mangrove forest The measured wave height reduction per meter crossshore in the mangrove was higher than the measured wave height reduction per meter cross-shore over the sandy surface (Fig. 5a). The wave height reduction per
0.012
beach plain mangrove mud bed
0.008
0.004
0
resistance coefficient
b
4.5 beach plain mangrove mud bed 3
1.5
0
0
0.5
1 1.5 water depth [m]
2
2.5
Fig. 5. (a) Variation of wave reduction, r, and (b) resistance coefficient, CD, with water depth. The mud bed values are computed. The smooth lines are trend lines.
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Hrms [m]
0.3
0.2
0.1
Hrms [m]
0.3
0.2
0.1
relative height [m]
0
0. 5 C
B
1 A
1.5 100
200 300 cross shore distance [m]
400
Fig. 6. Computed wave height (Hrms) decrease over the cross-shore transect using a wave energy decay model. Upper panel: burst 5127 (solid), 5128 (dashes), 5129 (dash-dot) and 5130 (dotted). Middle panel: burst 5131 (dotted), 5132 (dash-dot), 5133 (dashed) and 5134 (solid). Lower panel shows the cross-shore profile again. The position of the tripods are indicated with the vertical lines (A–C).
meter cross-shore in the mangrove forest was small at lower water levels and increased towards high tide. However, the variation of the wave height reduction per meter cross-shore with the water depth was larger than on the sand-covered mudflat, and the explained variance was less (R2 = 0.26). The wave height reduction between tripod B and C was also computed with the wave energy decay model. The pattern of wave height reduction in Fig. 6 clearly shows an underestimation of the wave height reduction between B and C (see also Fig. 7). The contribution of the mangrove vegetation as a friction factor was clear. The network of trunks, branches and above ground roots of the mangrove trees were seen as an increased bed roughness for incoming waves. This increased bed roughness caused more friction and dissipated more wave energy which resulted in higher rates for the wave height reduction. The resistance coefficient, CD, increased with an increasing water depth in the mangrove forest (Fig. 5b), as expected from the relation between the water depth and the wave height reduction per meter cross-shore. The trend line for the variation of CD with the water depth was similar to the trend found by Mazda et al. (1997a), with the same direction and exponential shape.
The wave reduction per meter cross-shore over a muddy soil without vegetation was computed with Eqs. (3)–(8) (Fig. 5a). The friction, caused by currents acting upon the bed particles, was computed with the use of measured flow velocities (friction on average 0.012). The friction, caused by waves was computed with the measured ˆ d) and the measured amplitude of the orbital velocity (U ˆ d) (friction on average 0.049). The bed bottom orbital (A shear stress due to currents (0.008 Nm2) was a small part of the total bottom friction (sb,c/sb,w + sb,c). The bed shear stress due to waves (0.34 Nm2) was most of the time over 95% of the total friction factor. Therefore, reduction in wave height outside the mangroves was computed with only the friction factor due to wave activity. Wave reduction per meter cross-shore over the muddy surface was very small with maximum wave reduction values of 6 · 104. The contribution of the sediment size of clay to the computed bottom friction was negligible and the computed resistance coefficient, CD, on an uncovered mud bed did not significantly vary with water depth and had a mean value of 0.005 (Fig. 5b). The vegetation between tripods B and C over 5 m width consisted of Kandelia candel (88.9%), Sonneratia spec. (7.4%) and Avicennia marina (3.7%). The trees between
S. Quartel et al. / Journal of Asian Earth Sciences 29 (2007) 576–584
increase of CD with an increase of A. The exponential function of
0.8
C D ¼ 0:601e0:1548A ;
computed reduction ratio
0.75
0.65
5. Discussion
0.6
0.55
0.55
0.6 0.65 0.7 0.75 measured reduction ratio
0.8
Fig. 7. Measured and computed wave height reduction ratios for Hrms (Eq. 1). The stars refer to the spring-tide bursts between tripod A and B (314.5 m apart) and the crosses between tripod B and C (31.8 m apart). The solid line is the perfect match and the dotted lines are the 10% difference lines. Note: the ratio between B and C (mangrove area) is not so good, despite its shorter distance. An increase of the bottom roughness (to values of 0.04) for the higher measured ratios will even make a better match with the computations between A and B.
the tripods were measured for their trunk height, trunk width, foliage height and foliage width. These parameters were used to estimate a certain area that was projected towards the incident waves. These projected areas of different mangrove trees are averaged over one meter width and resulted in the total projected area of mangrove trees (A) between tripod B and C. The total projected area of the mangrove trees varied for different water levels. The projected area increased considerably by the surface of the foliage when the water level exceeded the trunk height. The drag force was caused by the vegetation and depended on the density of the vegetation Mazda et al. (1997a). The relation between the projected area of obstacles and the resistance coefficient is presented in Fig. 8 and showed an
resistance coefficient
4.5
3
1.5
0
0
ð9Þ
described this relation over the 31.77-m distance between tripod B and C with a correlation of 0.53. Thus, the resistance coefficient would be 0.601 over 31.77-m, and 0.019 per cross-shore meter, assuming there is no mangrove vegetation.
0.7
0.5 0.5
583
2
4
6
8
10
12
projected area of the obstacles [m2] Fig. 8. Variation of projected area of obstacles per meter width with the drag coefficient in the mangrove forest. The smooth line is the exponential trend line.
The studied site consisted of two different sections: the sandy surface with the cheniers in an embryonic stage, and the muddy mangrove swamp. The sandy surface layer covering the clay subsoil over a length of at least 500–600 meters was almost flat (Fig. 2). The wave height data from tripod A showed that the waves were depth-limited. Small water depths corresponded with small wave heights and large water depths correspond with higher incident waves. The wave energy decay over the sandy surface could be well described with a wave energy decay model, originally based on Battjes and Janssen (1979). The measured wave height reductions as expressed by Eq. (1) were almost similar to the computed wave height reductions under these cases with shoaling waves. However, the measured wave energy decay in the mangrove area was clearly much higher than the computed ones. The bottom friction in the latter area was clearly underestimated and the cohesive forces of the muddy sediments and its depth-varying bed strength were not incorporated in the wave energy decay model. Energy losses in the mangroves (wave height reduction) were mainly assigned to friction from the trees on the waves. The influence of local currents on wave-current interactions and wave energy dissipation was neglected. The cross-shore current velocity at very shallow water depths only reached its maximum values at the start and end of the selected spring-tide (current velocities in the order of 0.02–0.20 ms1). The contribution of the sediment size of the clay to the bottom friction was marginal, although muddy sediments appear to undergo an elastic response to the pressure of the progressive waves that could cause energy losses. The motion of the soft bottom has a wavelike appearance of oscillations (Suhayda, 1978). The vertical displacement of the bottom is 180 out of phase with the wave pressure. The wave crest corresponds with a depression in the bottom. The phase shift results from the effect of the internal viscosity of mud. This loss of energy by a surface wave due to bottom forcing is significant larger than the energy loss due to bottom friction (Suhayda, 1978). The effect of the interaction of waves with soft bottom sediments at the study site was not measured and could not be included in the current analysis of the collected data. However, the muddy surface under mangroves was subjected to relatively fast consolidation as a result of the water extraction and growth of the underground roots of the mangroves. It
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was therefore less sensitive for movement, but the effect could still be significant. The drag force due to the dense network of trunks, branches and above ground roots was the main cause of the high rate of wave reduction in the mangrove forest. At higher water levels there was more vegetation flooded and the drag coefficient increased. The drag coefficient was related to the area of flooded vegetation, but could well differ with changes in the structure of the vegetation. Different species have different sizes and kind of trunks and leaves, creating a rough or smooth surface. Besides, the leaves may be flexible, variable in shape and change over the seasons. The function for the correlation between the projected area and the drag force is therefore probably not linear. The exponential function Eq. (9) gave a good estimation of the drag force for this field site (see Fig. 8). The friction due to wave–fluid mud interaction could be an explanation for the difference in the drag coefficient values per meter cross-shore: 0.005 and 0.019 (Section 4.3). The value of 0.005 was computed for a muddy soil with Eqs. (3)–(8) and was only valid when the energy losses were due to the sediment particle size of the bed. The drag coefficient 0.019 was distracted from the variation in the exposed cross-area of mangrove obstacles with the drag coefficient and was computed based on Eq. (9) assuming A = 0. The process described by Suhayda (1978) could cause the significant difference between those two values. 6. Conclusions The following conclusions were based on the field measurements on wave attenuation over a bare mudflat with a sandy cover and within a mangrove forest. The wave height reduction over the sandy surface layer on the mudflat is mainly caused by bottom friction of shoaling waves and can be well computed with a wave energy decay model based on Battjes and Janssen (1979). This model can not be used in mangroves where the wave reduction is significant higher. Here, the resistance of the vegetation, expressed by friction caused by the size and structure of the vegetation exposed to the waves, mainly determines the wave energy dissipation. The wave height reduction of shoaling waves over the sandy surface layer on the mudflat decreases with an increase in water depth, due to decreasing relative wave heights. For the mangroves, the wave height reduction increases with an increase in water depth due to an increase in the vegetation exposed to the waves. The drag force exerted by mangroves depends on the species and the density of the vegetation, and for a vegetation consisting of Kandelia candel (88.9%), Sonneratia spec. (7.4%) and Avicennia marina (3.7%), the drag force can be approached by the function CD = 0.601e0.1548A (with A being the projected area of the under water obstacles at a certain water depth). The measured wave height reduction r through mangroves was obviously larger than over the beach plain
(Fig. 5a). Comparing the wave height reduction for similar water depths (h = 1.25–1.55 m), the wave height reduction by mangroves was 5–7.5 times larger then by bottom friction only. This indicates clearly the importance of the mangrove vegetation for coastal defence. Acknowledgments The authors thank the students and staff members of Vietnam National University for their logistic assistance. We also thank Hans de Boois for his active support and enthusiasm during the field work. The constructive comments of two anonymous reviewers on an earlier version of this manuscript were gratefully appreciated. References Augustinus, P.G.E.F., 2004. Geomorphology and sedimentology of mangroves. In: Geomorphology and Sedimentology of Estuaries. Developments in Sedimentology 53. Elsevier Scientific Publishers, Amsterdam, The Netherlands. Battjes, J.A., Janssen, J.P.F.M., 1979. Energy loss and set-up due to breaking of random waves. In: Proceedings ICCE, ASCE, pp. 569– 587. Brampton, A.H., 1992. Engineering significance of british saltmarshes. In: Allen, J.R.L., Pye, K. (Eds.), Saltmarshes: morphodynamics, conservation and engineering significance. Cambridge University Press, London, pp. 115–122. Cooper, N.J., 2005. Wave dissipation across intertidal surfaces in the Wash Tidal Inlet, Eastern England. Journal of Coastal Research 21-1, 28–40. Kobayashi, N., Raichle, A.W., Asano, T., 1993. Wave attenuation by vegetation. Journal of Waterway, Port, Coastal and Ocean engineering 199-1, 30–48. Massel, S.R., Furukawa, K., Brinkman, R., 1999. Surface wave propagation in mangrove forests. Fluid Dynamics Research 24, 219–249. Mathers, S., Zalasiewicz, J., 1999. Holocene sedimentary architecture of the Red River Delta, Vietnam. Journal of Coastal Research 15 (2), 314–325. Mazda, Y., Magi, M., Kogo, M., Hong, P., 1997a. Mangroves as a coastal protection from waves in the Tong King delta, Vietnam. Mangroves and Salt Marshes 1, 127–135. Mazda, Y., Wolanski, E., King, B., Sase, A., Ohtsuka, D., Magi, M., 1997b. Drag force due to vegetation in mangrove swamps. Mangroves and Salt Marshes 1, 193–199. Mo¨ller, I., Spencer, T., 2002. Wave dissipation over macro-tidal saltmarshes: effects of marsh edge typology and vegetation change. Journal of Coastal Research SI36, 506–521. Mo¨ller, I., Spencer, T., French, J.R., Legget, D.J., Dixon, M., 1999. Wave transformation over salt marshes: a field and numerical modelling study from North Norfolk, England. Estuarine, Coastal and Shelf Science 49, 411–426. Soulsby, R.L., 1997. Dynamics of Marine Sands: A Manual for Practical Applications. Thomas Telford Publications, London. Suhayda, J.N., 1978. Surface waves and bottom sediment response. Marine Geotechnology 2, 135–146. Van Rijn, L.C., 1994. Principles of Fluid Flow and Surface Waves in Rivers, Estuaries, Seas, and Oceans, 2nd Ed. Aqua Publications, Amsterdam, The Netherlands. Wu, Y., Falconer, R., Struve, J., 2001. Mathematical modelling of tidal currents in mangrove forests. Environmental Modelling and Software 16, 19–29.