Introduction

Coastal areas are prone to an increasing number of natural disasters due to the impacts of climate change (Weisse et al. 2012). Among these impacts, rising sea levels and extreme storms are considered major threats to coastal regions. The mean sea level has risen about 1–2 mm per year throughout the past century, most of which has occurred over the past few decades (Jevrejeva et al. 2006). Coastline waves, flooding, and destructive storms have resulted in human and economic losses in nearshore zones. Therefore, it is important to decrease these harmful effects using available coastline protection methods. Both artificial methods (i.e., rigid structures such as dikes, walls, and embankments and wave-breaking structures) and natural methods (i.e., flexible structures such as coastal vegetation cover, dunes, and coral reefs) can be implemented to decrease the wave height. However, artificial methods require major investments and can be expensive in developing countries (Tanaka 2009). In many coastal regions, vegetation cover is considered an implicit component of the flood defense system (Koch et al. 2009; Borsje et al. 2011).

Vegetation cover protects the coastal area by preventing wave-induced soil erosion. Soil erosion is a process of separation and transport of soil materials (Ellison 1947). It is a global problem because of adverse economic and environmental effects. Soil erosion rate depends mainly on the separation of soil particles and the transport yield of the land runoff (Borrelli 2013).

Vegetation cover effectively reduces the wave energy, runoff, and flow velocity and increases the surface roughness (Fathi-Maghadam and Kouwen 1997; Zhang et al. 2018). The coastal vegetation cover at the tidal surface has the potential for stabilizing, trapping, and accumulating the sediments. The presence of plants on the coast directly increases the erosion threshold of bed sediments (Chen et al. 2012) and, therefore, controls the process of erosion and sediment transport (Gurnell 2014). Moreover, coastal vegetation cover significantly directs the seasonal currents and water levels (Vastila and Jarvela 2017). In coastal lagoons, the vegetation cover can effectively reduce the wave energy (Harada and Imamura 2005), wave velocity (Granata et al. 2001; Turker et al. 2006), sediment transport rate (Jalil-Masir et al. 2021 and 2022), and the destructive effects of the storm (Chang et al. 2017) and tsunami (Noarayanan et al. 2012). Nepf et al. (2007) demonstrated that dense vegetation cover could prevent turbulence from penetrating the coast and control the wave energy. Similarly, turbulence was low in coastal beds with vegetation cover compared with those without that, as shown by Granata et al. (2001) and Pujol et al. (2013). Also, increased cover density and consequently reduced flow velocity inside the vegetation cover was found to significantly increase the sediment deposition in a study by Vastila and Jarvela (2017). According to Mu et al. (2019), sediment transport rate showed higher sensitivity to base stem cover and vegetation density than did to other factors; therefore, the base stem surface can be used as an effective factor for reducing the soil erosion and sediment transport rate.

The interaction between vegetation cover and flow dynamics is complex. Some field studies (Bradley and Houser 2009) and laboratory experiments (Tschirky et al. 2000; Mirzakhani et al. 2023) have evaluated the effectiveness of vegetation cover in reducing the wave energy by reducing the wave height or changing the surface tension. Some field studies, on the other hand, have examined the influence of vegetation cover on sediment transport in beaches and canals (Fan et al. 2006, Mazda et al. 2002, Montakhab et al. 2012, Escobar and Montoya 2018, Rozynski 2020, Zhang et al. 2020). Their results indicated the importance of vegetation cover in coastal management and the effect of cover density and arrangements on the flow and sediment transport rate. Some laboratory and numerical studies also evaluated the role of different patterns of vegetation cover in lowering the sediment transport rate. Kuegler et al. (2021) and Jalil-Masir et al. (2022) showed that rectangular and triangular patterns outperformed the random layout in decreasing sediment transport rate. Vastila and Jarvela (2017) presented a model for flow and sediment transport and showed that when the vegetation cover density increased, the flow velocity and sediment transport rate decreased. Tuan Vu et al. (2017) studied the numerical simulation of the presence of Posidonia on hydrodynamic behavior and sediment transport rate in Almanarre beach. The results of their developed model indicated that the presence of Posidonia resulted in significant changes in the hydrodynamic parameters of sediment and increased coastal erosion in Almanarre beach. Moreover, Nardin et al. (2018) concluded that vegetation cover could stabilize the bed, increase the resistance to storms, and trap the sediments. They also showed that vegetation cover could decrease the shear stress and increase sedimentation by up to 10% in swamps. Jin and Romkens (2001) proved that the vegetation cover density, flume slope, and sediment grain size were the primary factors for estimating the sediment trapping efficiency. Turker et al. (2006) indicated a direct relationship between the erosion level and wave height and an inverse relationship between the erosion level and vegetation cover density.

According to Rafael and Giovanni (2016), although the flow velocity significantly decreases in dense vegetation cover, the suspended sediment capacity increases because each tree barrier results in raised turbulence near that barrier.

Termini (2015) used laboratory data to study the influence of stem density, submerged flow, average flow, and flow transfer specifications in vegetation cover on the flow transfer. Their results suggested that the stem density affected both the flow profile and flow transfer and that the submerged flow affected the momentary exchange between the vegetation cover layers. Ding and Fu (2021) evaluated the quantitative relationship between substrate morphology and sediment transport capacity in a flume with vegetation cover. Their results indicated that flow regimen, hydraulic variables, and sediment transport capacity were influenced by the bed shape.

The literature review shows that less attention has been paid to the effect of terrestrial coastal forest on the sediment transport rate and trapping. In this study, the effect of terrestrial coastal forest on sediment trapping efficiency was examined by laboratory experiments. A new direct measurement method was applied to measure the wave-driven force on the modeling area based on the momentum principle using a separate movable flume and an attached load cell. A formula was also proposed for determining the sediment transport rate on the coast in the presence of forest cover.

Materials and method

Dimensional analysis

To determine the sediment trapping efficiency in the forest cover under the stable flow conditions and the fluid properties, first, the essential dimensionless parameters were extracted using the dimensional analysis (Table 1 and Eq. 1).

Table 1 Parameters involved in the sediment trapping efficiency of coastal forest cover
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$$f\left(F,{\tau }_{v},H,d,V,{\mu }_{w},{\rho }_{w},w,g{L}_{g},L,S,{D}_{50},{M}_{i},{M}_{o}\right)=0$$
(1)

The dimensionless parameters were obtained using Buckingham π theorem (Eq. 2):

$$\mathrm{f}(\frac{gd}{{V}^{2}}, \frac{H}{y}, \frac{\mu }{{\mathrm{p}}_{w }V H} ,\frac{W}{d}, \frac{gd}{{V}^{2}}, \frac{L}{d}, \frac{{D}_{50}}{d},\frac{H}{{D}_{50}}, S,\frac{{L}_{g}}{d}, \frac{{M}_{0}}{{M}_{i}}, \frac{{\varvec{F}}\boldsymbol{ }}{{\rho }_{{\varvec{w}}}Hd{{\varvec{V}}}^{2}}, \frac{{\tau }_{v}}{{{\rho }_{w}V}^{2}})=0$$
(2)

As the coastline slope (S), forest cover length (Lg), forest cover width (d), and sediment grain size remained constant (D50), the dimensionless proportions of \(\frac{{L}_{g}}{d}\), \(S\), and \(\frac{{D}_{50}}{d}\) were omitted. Then, \(\frac{L}{d}\) and \(\frac{W}{d}\) were combined to define and replace the density number (λ). In the following section, a method is described for determination of this parameter. Also, dimensionless numbers of \(\frac{gd}{{V}^{2}}\) and \(\frac{\mu }{{\mathrm{p}}_{w }V H}\) , named Froude and Reynolds numbers, respectively, were omitted because of the nature of the studied flow and generated turbulence from waves in the coastline zone. Then, \(\frac{{M}_{0}}{{M}_{i}}\) was converted to \(\frac{{M}_{i}-{M}_{0}}{{M}_{0}},\) which is the rate of sediment trapped by the forest cover (Te). Drag coefficient (\({C}_{D}\)) represented by \(\frac{F }{{\rho }_{w}Hd{V}^{2}}\) , was converted to \(\frac{F }{{\rho }_{w}{V}^{2}\sum nHd}\) to account for total surface against the flow. Considering the height (H) of the traveling wave when hitting the forest cover (before each row of the forest), the number (n) of forest cover in each row, and the tree diameter (d), the important dimensionless parameters were finally represented as follows:

\(\mathrm{f }(\frac{{M}_{i}-{M}_{0}}{{M}_{0}},\frac{H}{y} , \frac{H}{{D}_{50}},{C}_{D}, \frac{{\tau }_{v}}{{{\rho }_{w}V}^{2}},\uplambda ) = 0\) (3) The sediment trapping efficiency was studied using the proportion of \(Te=\frac{{M}_{i}-{M}_{o}}{{M}_{o}}\) in this study. Consequently, Eq. 4 was used to extract a mathematical relationship for calculating sediment transport rate in different cover arrangements based on the trapping efficiency.

$${Q}_{s}=1-Te= f (\frac{H}{y} , \frac{H}{{D}_{50}},{C}_{D}, \frac{{\tau }_{v}}{{{\rho }_{w}V}^{2}},\uplambda )=0$$
(4)

Where Qs is the rate of sediment transport to the next area of the forest cover zone, and Te is the proportion of the sediment trapping yield to the initial sediment yield (%). The equation presented by Nardin et al. (2016) was used to estimate τv (Eq. 5).

$${\tau }_{v}=\frac{1}{2}p{C}_{D}\lambda d{h}_{v}{V}^{2}$$
(5)

Where CD is the drag coefficient, \(\lambda\) is the stem density number (stem counts per unit area), and hv is the tree height.

Laboratory settings and experimental stages

To evaluate the sediment trapping efficiency of the forest cover, the experiments were performed in a flume of 8.3 m length and 0.6 m width and height. Experiments were performed in two groups of forest cover and without forest cover (control), each having the following setting: 3 input wave heights (6, 9, and 12 cm), a series of distances (5 × 5, 10 × 10, 15 × 15, and 20 × 20 cm), 4 cover widths (perpendicular to wave direction; 45, 30, 15, and 60 cm), and 15 density values resulting from parallel and staggered patterns (Table 2 and Fig. 1). The density number, used to differentiate between the patterns, was calculated as follows:

$$\lambda =\frac{Q\times G}{T},$$

where \(\lambda\) is the density number (stems/m2), \(Q\) is the number of stems per m2 in each arrangement, \(G\) is the number of stems in each experiment (for the width and distance between the trees in each arrangement), and \(T\) is the number of stems per unit width along the forest cover in each arrangement.

Table 2 Forest cover configuration
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Fig. 1
figure 1

Forest cover placement in parallel and staggered patterns

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The tree cover was simulated using rigid plastic cylinders of 0.9 cm diameter and 32 cm height. The waves in this study were generated based on the solitary wave simulation. The important reasons for this simulation were the transitional nature of the solitary wave (i.e., the movement of water particles beneath the wave surface) and the side view of the wave, which remains almost unchanged when moving in the uniform medium of the sea (Chang and Hwung 2006). Accordingly, the solitary wave was generated by sudden opening of the water reservoir gate in the laboratory, based on the method by Jalil-Masir et al. (2021).

A 2-m length of the flume was designated as the wave reservoir. Plexiglass walls were fixed at one end, and a metal sliding gate was installed at the other end of the reservoir. A cable pulley system, including tow ropes and weights, was applied for opening the sliding the gate (Fig. 2a). A scale of 1:50 was used based on the Froude number (1:30 to 1:60) to simulate the wave height (Heller 2011). According to the methods by Mu et al. (2019) and Jalil-Masir et al. (2021), the flume floor before the coastal plate was covered with sand grains with an average size of 0.35 mm (Fig. 2b). Sediments were collected from the coast with a fixed horizontal slope of 1.84 m lenght, 0.6 m width, and 0.1 m height and inserted in the flume.

Fig. 2
figure 2

The laboratory equipment: a) sliding gate, b) coast and sediments, c) ADV

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Sediments removed by each generated wave were collected from the output valve and stored in some mesh bags. Then, they were placed in the laboratory for 36 h to dry and weighed using a scale with 0.01 g sensitivity.

In each experiment, the sediment transported to the adjacent area to the forest cover (M0) was measured and compared with the sediment transported to a similar area in a forest cover-free zone (Mi) to calculate the trapped sediment percentage using the Te equation. This procedure could reduce the influence of other experimental conditions and estimate the sediment trapping function of the forest cover more accurately.

An acoustic Doppler velocimeter (ADV) was used to measure the wave velocity in each experiment (Fig. 2c). A video camera was installed in front of the flume to record the wave movements. The recordings were then converted to the relevant screenshots, based on which the wave height of each point was calculated using some scales on the flume wall. The extracted data were used to analyze the forest cover-wave interactions. The details of each run are presented in the attachment.

Waves of 6, 9, and 12 cm height were generated in front of the coast with forest cover. Measured from the flume floor, the corresponding water depth behind the gate was 25.6, 39.5, and 47 cm for each wave (Fig. 3). A still water depth of 10 cm was considered for the flat coast in front of the cover zone.

Fig. 3
figure 3

Generating wave under the forest cover density of 273 stem counts per unit area (parallel)

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Results and discussion

Forest cover effect on sediment trapping efficiency

The results showed that forest cover could trap 84% of the total sediment that was transported to the cover-free case. The forest cover, as a resisting factor, decreases the wave power and results in higher sediment trapping efficiency. The forest cover can also block the flow and decrease the wave height and energy, especially in placement patterns with higher densities, and lead to less sediment transportation.

Effects of configuration, inter-tree distance, wave height, and row count

The effects of these characteristics can be seen in Figs. 4 and 5. The calculation of sediment trapping efficiency (using the equation \(Te=\frac{{M}_{i}-{M}_{o}}{{M}_{o}}\), as explained in section 2-1) for different cover arrangements indicates that the forest cover could increase the sediment trapping efficiency in both the parallel and staggered patterns.

Fig. 4
figure 4

Sediment trapping efficiency (T0) in different ratios of wave height to still water height (H/y) for different forest cover rows in parallel patterns

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Fig. 5
figure 5

Sediment trapping efficiency (T0) in different ratios of wave height to still water height (H/y) for different forest cover rows in staggered patterns

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As can be seen in the figures, the staggered pattern was found to have higher efficiency in sediment trapping than the parallel pattern. In fact, the alternate rows in the staggered pattern result in more wave energy loss, more absorbed wave power, and higher sediment trapping efficiency than the rows in the parallel pattern. However, the difference was not significant when density increased as shown in the next section (3-1-2).

According to the figures, when the distance between the trees increased, the curve slope became steeper, i.e., the function of trees was more influenced by changes in the wave height.

Also, when the wave height increased, the sediment trapping efficiency decreased. For example, the 6-cm height wave showed higher sediment trapping efficiency than 9- and 12-cm height waves. When the water depth and, therefore, the pressure of the reservoir water increased, the velocity of the wave, upon hitting the cover, increased, resulting in increased sediment yield in downstream and decreased trapping efficiency.

When the row count of the forest cover increased, the trapping efficiency increased, too. Jalil Masir et al. (2021) found that reducing the row count in a coastal forest consisting of flexible trees (with branches and leaves) decreased the sediment transport rate. The results of the rigid cover in this study confirm their results.

In addition, when the row count decreased, the sediment trapping efficiency decreased, too. For example, in the fixed distance of 15 × 15 cm and wave height of 9 cm, the sediment trapping efficiency decreased by 46% and 47% in the parallel and staggered pattern, respectively, when the number of rows decreased from 5 to 2. In fact, less wave power is absorbed by the fewer numbers of rows.

Effect of density

The effect of density on the sediment trapping was examined through the graphs presented in Fig. 6.

Fig. 6
figure 6

Sediment trapping efficiency based on forest cover density: a) staggered , b) parallel pattern

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As can be seen, in both parallel and staggered patterns, when the forest density increased, the sediment trapping efficiency increased, too. The trapping efficiency reached from 20% in the lowest density to 84% in the highest density (273 m2/stem). Therefore, forest cover density is an important factor in controlling the sediment transport.

According to the Figure, when the forest cover density doubled from 33 to 66, the sediment trapping efficiency increased by 38.77%. This percentage was found to be lower for densities from 12 to 24 because the distance between the trees changed, and the distance showed more effect than the row count. In higher densities, the number of forest rows increases, and the distance decreases. So, more sediment is trapped between the trees, and the sediment trapping efficiency increases. Moreover, a smoother slope is seen in the parallel pattern than in the staggered pattern, indicating higher trapping efficiency in the staggered pattern. (3.79% and 14.28% increase in trapping efficiency in the maximum and minimum density, respectively). The staggered pattern covers a wider area than the parallel pattern ,which leads to a greater dissipation rate of wave energy and higher cover efficiency. However, as the density increased, the difference in reducing the sediment trapping rate between the two patterns became less significant. The differences in sediment trapping efficiency in the highest and lowest densities in two patterns can be implied in Table 3.

Table 3 Sediment trapping efficiency in staggered and parallel patterns for each wave height in minimum and maximum densities
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Previous studies

In another study, Rose et al. (2014) discussed that in higher density and wave frequency, sediment suspension and sediment transport decreased.

In a similar study, Jalil-Masir et al. (2021) examined the effect of flexible coastal forest on the sediment transfer rate and showed that cover density (based on the inter-tree distance and the cover area) was more effective than cover alignment (parallel or staggered) in reducing the sediment transfer rate. According to their result, in the minimum density (inter-tree space of 20 × 20 cm and cover area of 60 × 30 cm2), the forest cove efficiency was 19%. In this study in the minimum density(inter-tree space of 20 × 20 cm and cover area of 45 × 15 cm2 ) the cover efficiency was 20%. Jalil-Masir et al. (2021) also reported that in the maximum density (inter-tree space of 15 × 15 cm and cover area of 60 × 75 cm2), the forest cove efficiency was 60%. In this study in the maximum density (inter-tree space of 5× 5 cm and cover area of 45 × 60 cm2 ) the cover efficiency was 84%.

Equation extraction for the estimation of sediment transport rate (\({Q}_{s}\))

Based on the dimensional analyses and obtained experimental data, the statistical methods were used to study the effect of the extracted effective dimensionless parameters on the sediment transport rate and to obtain a mathematical equation for predicting these values. Finally, Eq. 6 was extracted after collinearity and sensitivity analysis to determine the influence of each dimensionless proportion on the quantity of the phenomenon under stydy.

$$\mathrm{ln}\left(\frac{{Q}_{s}}{V{H}^{2}}\right)=3.25+0.617 ln\left(\frac{{D}_{50}}{H}\right)-0.647 ln\left(\lambda \right)$$
(6)

Where \({Q}_{s}\) (cm3/s) is sediment transport rate, V (cm/s) is cross-shore wave velocity, H (cm) is wave height at the beginning of forest zone, λ is density number (stem/m2), and \(\frac{{\mathrm{D}}_{50}}{\mathrm{H}}\) is a dimensionless proportion of the average size of sediment grains to the wave height. Eq. 6 was obtained based on the 70% of the experimental data. The remaining 30% was then used for validating this equation.

The proposed equation is applicable only to a certain sediment size. This study ignored examining different-sized particles due to experimental limitations, including difficulties in eroded coasts.

By inserting different cover densities in the formula, the sediment transport rate to the post-cover zone can be determined, and by comparing the different cover arrangements, the appropriate density can be decided for different coastal areas.

Using machine learning models for obtaining the appropriate equation is suggested for future research. These models have been applied in some recent studies for determining suspended sediment load (Ghanbari-Adivi et al. 2022; Darabi et al. 2021; Panahi et al. 2021; Ehteram et al. 2021; Banadkooki et al. 2020) and total sediment load (Jalil-Masir et al. 2022)

Statistical analysis shows a strong correlation between the data obtained from the equation and those from the experiments. The accuracy of the extracted equation is, therefore, acceptable (Table 4 and Fig. 7).

Table 4 Evaluation statistics of the equation for estimation of sediment transport rate
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Fig. 7
figure 7

Observed and calculated dimensionless sediment transport rate, (\(\frac{{Q}_{s}}{V{H}^{2}}\))

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Conclusion

Accurately predicting the sediment trapping efficiency of coastal forest cover is important in defining and implementing coastal stabilization and soil erosion plans. This work evaluated the effect of forest cover density along with arrangement patterns, inter-tree distances, cover width, and wave height on the sediment trapping efficiency.

The findings indicated that the forest cover with a higher density raised the sediment trapping by blocking the water flow and absorbing the wave energy. Increasing the density from 12 to 276 stem/m2 increased the trapping efficiency by four times. A 75% decrease in inter-tree distances increased the sediment trapping efficiency by 98%. Also, a four-times increase in the cover width increased the sediment trapping efficiency by 47%.

The sediment trapping efficiency was higher in the staggered pattern than in the parallel arrangement, but the difference was not significant, especially when density increased. The mean increase seen in trapping efficiency was 10%. It was 5% in the densities between 84–273stem/m2 and 21% in lower densities.

The sediment trapping efficiency of the forest cover decreased by 23% when the wave height increased by two times.

Also, by combining the experimental and statistical studies, an equation was presented for estimating the sediment transport rate in the post-cover zone based on forest cover density and wave height. Future studies are required to validate the proposed equation with the field data.