The effects of rigid ditch bank vegetation on velocity distribution and water surface profile in trapezoidal open channels were investigated. Forty-eight tests were used to study the impacts of different vegetation densities. Tests were run for three vegetation densities (1,600, 400, and 178 stems/m2) along a fixed, 4.00 m reach, against four different discharges, each with three different depths. The measured water levels and velocities were analyzed and it was found that increasing the vegetation density increased the water depth upstream of the vegetated reach. while lowering it within it, when compared to the unvegetated case. The water's velocity profile as a ratio to the unvegetated case (V/u) is sigmoid, i.e., the maximum velocity (V/u) max occurs in the lower half of the water column, increasing shear stress near the bed, and, in turn, the likelihood of bed erosion along the vegetated channel's centerline. V/u increased with increasing vegetation density and Fro. A multiple regression analysis was done to assess the impact of ditch bank vegetation density on flow parameters.

  • The study examines the hydraulic issues that may arise in trapezoid open channels due to the presence of vegetation on its sides slopes.

  • The presence of vegetation changes water levels and increases velocity near the bed which increases the possibility of bed erosion.

Graphical Abstract

Graphical Abstract
Graphical Abstract
     
  • Y

    Water depth (m);

  •  
  • Yo

    Water depth in the unvegetated case (m);

  •  
  • Yin

    Average water depth in the vegetated reach (m);

  •  
  • h

    Vertical height of the measured velocity point above the bed (m);

  •  
  • V

    Water velocity in the vegetated case (m/s);

  •  
  • u

    Water velocity in the unvegetated case (m/s);

  •  
  • Vin

    Water velocity in the middle of the vegetated reach (m/s);

  •  
  • Average flow velocity in the unvegetated case (m/s);

  •  
  • Fro

    Froude number in the unvegetated case.

  •  
  • g

    Gravitational acceleration (m/s2);

  •  
  • λ

    Vegetation density (λ=П N0 d2/4, where N0 is the number of stems per unit bank area and d the stem diameter (m), and

  •  
  • Q

    Discharge (l/s).

Ditch bank vegetation grows on an open channel̀s side slopes. It has both positive and negative effects, depending on the purpose of the hydraulic conduit. For example, it lowers conveyance capacity by obstructing flow – reducing the flow cross-section area and increasing resistance to flow. On the other hand, it increases bank stability, reduces erosion, provides habitat for aquatic and terrestrial wildlife, and filters pollutants (Nepf et al. 1997; Kemp et al. 2000; Tang et al. 2008).

The impact of ditch bank vegetation on the hydraulic parameters of an open channel (velocity distribution, water surface profile, friction coefficient, etc.) changes in relation to the flow discharge, bank slope, vegetation density, etc.

Several laboratory studies (Afzalimehr & Dey 2009; Hirschowitz & James 2009; Hopkinson & Wynn 2009; Afzalimehr et al. 2010; Bledsoe et al. 2011; Czarnomski et al. 2012; Masouminia 2015; Mohammadzade et al. 2016; Liu et al. 2017) on the effect of ditch bank vegetation, evaluating and analyzing vegetation effects on velocity distribution, turbulence intensity and kinetic energy, and Reynold's shear stresses. Table 1 is a review summary of the impact of ditch bank vegetation on flow characteristics.

Table 1

Summary literature review on the impact of ditch bank vegetation on flow characteristics

AuthorsResearch typeSimulated channel typeVegetation model
Main Result
Type Rigid/ FlexibleStem simulation
Diameter (mm)DensityDistribution
Liu et al. (2017)  Experimental Semi-trapezoidal Rigid 10–308 stems/m2 Both linear and staggered Increasing the river bank vegetation density increased the velocity in the main channel more than at the riverbank. 
Mohammadzade et al. (2016Experimental Rectangular Flexible 4.2 (rice stems) 290 stems/m Linear Ditch bank vegetation increased shear stress near the channel bed where the vertical shear stress profile is sigmoid (S- shaped). 
Masouminia (2015)  Numerical (3D modeling in FLUENT/ ANSYS) Semi-trapezoidal Rigid 20–308 stems/m2 Both linear and staggered The flow velocity over the side slope becomes less than that over the main channel, initiating a momentum transfer from higher to lower velocity. 
Czarnomski et al. (2012)  Experimental Semi-trapezoidal Rigid 4.54 202 and 615 stems/m2 Linear Leaf simulations were an important influence on near-bank turbulence intensities and Reynolds stresses, whereas the side slope's influence was small relative to that of vegetation density. 
Bledsoe et al. (2011)  Numerical (3D modeling in FLUENT/ ANSYS) Trapezoidal Rigid Simulated as high and low density Linear Ditch bank vegetation concentrates flows in the channel center, causing a reduction in shear stresses near the bank zone and increasing them in the channel center. 
Afzalimehr et al. (2010)  Experimental Rectangular Flexible Rice stems 400 stems/m Linear The maximum Reynolds stress occurs near the bed at the flume centerline but, due to the strong effect of the vegetation, it occurs at y/h=0.5 near vegetated banks. 
Hopkinson & Wynn (2009)  Experimental Rectangular Both rigid and flexible Various configurations Downstream velocity decreased near the bank for all vegetation treatments, but the reduction did not cause a reduction in total shear stress for all vegetation types. 
Afzalimehr et al. (2009)  Experimental Rectangular Flexible Wheat stems Linear along the channel wall Reynolds stress distribution is non-linear, where there is vegetation along channel side slopes; and depends on the distance from the wall. 
Hirschowitz & James (2009)  Experimental Rectangular Rigid 200 stems/m Both linear and staggered An empirical equation was developed to determine channel discharge, using a composite resistance coefficient, which combined the effects of the channel bed and vegetation interfaces. 
AuthorsResearch typeSimulated channel typeVegetation model
Main Result
Type Rigid/ FlexibleStem simulation
Diameter (mm)DensityDistribution
Liu et al. (2017)  Experimental Semi-trapezoidal Rigid 10–308 stems/m2 Both linear and staggered Increasing the river bank vegetation density increased the velocity in the main channel more than at the riverbank. 
Mohammadzade et al. (2016Experimental Rectangular Flexible 4.2 (rice stems) 290 stems/m Linear Ditch bank vegetation increased shear stress near the channel bed where the vertical shear stress profile is sigmoid (S- shaped). 
Masouminia (2015)  Numerical (3D modeling in FLUENT/ ANSYS) Semi-trapezoidal Rigid 20–308 stems/m2 Both linear and staggered The flow velocity over the side slope becomes less than that over the main channel, initiating a momentum transfer from higher to lower velocity. 
Czarnomski et al. (2012)  Experimental Semi-trapezoidal Rigid 4.54 202 and 615 stems/m2 Linear Leaf simulations were an important influence on near-bank turbulence intensities and Reynolds stresses, whereas the side slope's influence was small relative to that of vegetation density. 
Bledsoe et al. (2011)  Numerical (3D modeling in FLUENT/ ANSYS) Trapezoidal Rigid Simulated as high and low density Linear Ditch bank vegetation concentrates flows in the channel center, causing a reduction in shear stresses near the bank zone and increasing them in the channel center. 
Afzalimehr et al. (2010)  Experimental Rectangular Flexible Rice stems 400 stems/m Linear The maximum Reynolds stress occurs near the bed at the flume centerline but, due to the strong effect of the vegetation, it occurs at y/h=0.5 near vegetated banks. 
Hopkinson & Wynn (2009)  Experimental Rectangular Both rigid and flexible Various configurations Downstream velocity decreased near the bank for all vegetation treatments, but the reduction did not cause a reduction in total shear stress for all vegetation types. 
Afzalimehr et al. (2009)  Experimental Rectangular Flexible Wheat stems Linear along the channel wall Reynolds stress distribution is non-linear, where there is vegetation along channel side slopes; and depends on the distance from the wall. 
Hirschowitz & James (2009)  Experimental Rectangular Rigid 200 stems/m Both linear and staggered An empirical equation was developed to determine channel discharge, using a composite resistance coefficient, which combined the effects of the channel bed and vegetation interfaces. 

In fact, the impact of ditch bank vegetation depends on many complex, interacting factors, including flow conditions, distance between the ditch bank vegetation and the measurement point, and vegetation spacing.

This study's primary aim was to investigate the effects of rigid ditch bank vegetation on water's surface profile and velocity under subcritical flow, at different discharge rates and vegetation densities in a trapezoidal open channel.

Experiments were conducted in a 0.6 m wide, 0.42 m deep, 16 m long, horizontal bed, recirculating trapezoidal flume, at the Channel Maintenance Research Institute's hydraulics laboratory. The water level was controlled with a tail-gate at the end of the flume. For all tests, with and without vegetation, a fixed set of 4 discharge rates each with 3 water depths was used.

Simulation of rigid vegetation is common – e.g., in Stone & Shen 2002; James et al. 2004; Meftah et al. 2006; Kothyari et al. 2009; Cheng & Nguyen 2011; Panigrahi 2015; Ahmed & Hady 2017; Chakraborty & Sarkar 2018; Wang et al. 2018; and Tong et al. 2019. (See Table 2).

Table 2

Summary review of rigid vegetation simulations

AuthorsFlume properties
Vegetation model
TypeLengthWidthBed condition/materialSubmergenceStem simulation
mmShapedMaterialDiameter (mm)Spacing (Δx) /Density*Distribution
Tong et al. (2019)  Rectangular 0.4 Covered with PVC sheets Not submerged Cylindrical PVC 10 cm Linear 
Wang et al. (2018)  12.5 0.3 PVC sheets Not submerged PVC 10 Density (1, 2 and 4%) Staggered 
Chakraborty & Sarkar (2018)  10 0.4 Plexiglas's Submerged PVC Random Distribution 
Ahmed & Hady (2017)  12 0.4 Sand (d50=0.62) Submerged PVC 10 22.72, 11.9, and 9.61 cm Linear 
Panigrahi (2015)  12 0.6 Water-resistant plywood sheet Both submerged and not submerged Iron 6.5 10 cm Both linear and staggered 
Cheng & Nguyen (2011)  12 0.3 Steel Not submerged Steel 3.2, 6.6 and 8.3 3 and 6 cm Staggered 
Kothyari et al. (2009)  16 0.5 Stainless steel Not submerged Stainless steel 10 3.2–20.3 cm Staggered 
Meftah et al. (2006)  0.3 Water-resistant plywood sheet Submerged Metallic 10 cm Linear 
James et al. (2004)  0.1 Sand (d50=0.48) Not submerged Steel 2.5, 5, and 7.5 cm Staggered 
Stone & Shen (2002)  12 0.45 Water-resistant plywood sheet Both submerged and not submerged Wood 3.18, 6.35 and 12.7 3.8, 4.6 and 7.6 cm Staggered 
This study Trapezoidal 16 0.6 concrete Not submerged Cylindrical Steel 2.5, 5, and 7.5 cm Staggered 
AuthorsFlume properties
Vegetation model
TypeLengthWidthBed condition/materialSubmergenceStem simulation
mmShapedMaterialDiameter (mm)Spacing (Δx) /Density*Distribution
Tong et al. (2019)  Rectangular 0.4 Covered with PVC sheets Not submerged Cylindrical PVC 10 cm Linear 
Wang et al. (2018)  12.5 0.3 PVC sheets Not submerged PVC 10 Density (1, 2 and 4%) Staggered 
Chakraborty & Sarkar (2018)  10 0.4 Plexiglas's Submerged PVC Random Distribution 
Ahmed & Hady (2017)  12 0.4 Sand (d50=0.62) Submerged PVC 10 22.72, 11.9, and 9.61 cm Linear 
Panigrahi (2015)  12 0.6 Water-resistant plywood sheet Both submerged and not submerged Iron 6.5 10 cm Both linear and staggered 
Cheng & Nguyen (2011)  12 0.3 Steel Not submerged Steel 3.2, 6.6 and 8.3 3 and 6 cm Staggered 
Kothyari et al. (2009)  16 0.5 Stainless steel Not submerged Stainless steel 10 3.2–20.3 cm Staggered 
Meftah et al. (2006)  0.3 Water-resistant plywood sheet Submerged Metallic 10 cm Linear 
James et al. (2004)  0.1 Sand (d50=0.48) Not submerged Steel 2.5, 5, and 7.5 cm Staggered 
Stone & Shen (2002)  12 0.45 Water-resistant plywood sheet Both submerged and not submerged Wood 3.18, 6.35 and 12.7 3.8, 4.6 and 7.6 cm Staggered 
This study Trapezoidal 16 0.6 concrete Not submerged Cylindrical Steel 2.5, 5, and 7.5 cm Staggered 

Density*: the ratio of the bottom areas of all stems to that of the flume area for the vegetated section.

In recent research, the rigid vegetation stems have been represented by 3 mm diameter steel rods set in a staggered grid pattern with 25, 50, and 75 mm center spacings, both longitudinally and transversely, and secured above a drilled-hole steel panel. Three vegetation densities – 1,600, 400, and 178 stems/m2 – were used, with a fixed reach length of 4.00 m at the flume center. Figure 1 shows the experimental channel with vegetation on its sides and Table 3 summarizes the flow conditions of the experiment.

Table 3

Experimental conditions

Vegetation properties
Flow conditionDischarge (l/s)Tailwater depth**No of runs
Vegetation densityArrangementSpacing cmStems/m2
Unvegetated n/a n/a n/a Subcritical flow 40, 35, 30, 25 Three different depths for each discharge 12 
High (λ>0.0113) Staggered 2.5 1,600 40, 35, 30, 25 12 
Medium (λ>0.0028) 5.0 400 40, 35, 30, 25 12 
Low (λ>0.0013) 7.5 178 40, 35, 30, 25 12 
Runs (total) 48 
Vegetation properties
Flow conditionDischarge (l/s)Tailwater depth**No of runs
Vegetation densityArrangementSpacing cmStems/m2
Unvegetated n/a n/a n/a Subcritical flow 40, 35, 30, 25 Three different depths for each discharge 12 
High (λ>0.0113) Staggered 2.5 1,600 40, 35, 30, 25 12 
Medium (λ>0.0028) 5.0 400 40, 35, 30, 25 12 
Low (λ>0.0013) 7.5 178 40, 35, 30, 25 12 
Runs (total) 48 

**The tailwater depths are related to three Froude number ranges for the unvegetated case (Fro); 1. Fro=0.11–0.15; 2. Fro=0.15–0.20 and 3. Fro=0.21–0.30.

Figure 1

Artificial canal, with rigid vegetation on the channel side slopes.

Figure 1

Artificial canal, with rigid vegetation on the channel side slopes.

Close modal

Water depths were measured every 0.50 m along the canal centerline using an ultrasonic level meter (Sondar) in all runs – Figure 2(a). Three velocity profiles were measured – upstream and downstream of, and within the vegetated reach – using a Vectrino (3-D water velocity sensor Lab Probe) – Figures 2(b) and 3.

Figure 2

Experimental tools. (a) ultrasonic level meter (Sondar) and (b) Vectrino 3D water velocity sensor.

Figure 2

Experimental tools. (a) ultrasonic level meter (Sondar) and (b) Vectrino 3D water velocity sensor.

Close modal
Figure 3

Velocity measuring points upstream, within, and downstream of the vegetated reach.

Figure 3

Velocity measuring points upstream, within, and downstream of the vegetated reach.

Close modal
Buckingham's Pi-theorem was used for dimensional analysis to determine the relationship between vegetation density, and the changes in water depth and velocity within the vegetated reach. The relationships obtained can be written in the form of Equation (1). Figure 4 is a definition sketch of the ditch bank vegetation channel and shows the measurement locations.
formula
(1)
where, Yin is the average water depth along the centerline of the vegetated reach (m), Yo the water depth in the unvegetated case (m), Vin the flow velocity in the middle of the vegetated reach (m/s), the corresponding velocity in the unvegetated case (m/s), the vegetation density (the cross-sectional area of the cylinders (stems) per unit bank area, λ=П N0 d2/4, where N0 is the number of stems per unit side area and (d) the stem diameter (m), and Fro is the Froude number in the unvegetated case.
formula
(2)
where ū is the average velocity in the unvegetated case (m/s) and is the gravitational acceleration (m/s2).
Figure 4

Cross-section of the vegetated reach.

Figure 4

Cross-section of the vegetated reach.

Close modal

Effect of ditch bank vegetation on flow parameters

Water surface profile through the vegetated reach

The water surface profile along the flume centerline was surveyed with an ultrasonic level meter, to understand the influence of vegetation density on it. The water profiles arising at different vegetation densities are shown in Figure 5.

Figure 5

Canal water surface profile at Q=40 l/s with different vegetation densities, for (a) Fro=0.15, (b) Fro=0.20, and (c) Fro=0.30.

Figure 5

Canal water surface profile at Q=40 l/s with different vegetation densities, for (a) Fro=0.15, (b) Fro=0.20, and (c) Fro=0.30.

Close modal

As can be seen in Figure 5, the water depth increased upstream of the vegetated reach, but fell within the reach, compared to the unvegetated case. The relationship between water depth reduction in the vegetated reach, at different vegetation densities, and Fro (unvegetated), is illustrated in Figure 6 

Figure 6

Relationship between water depth reduction (Yin/Yo) within the vegetated reach and Fro in the unvegetated case.

Figure 6

Relationship between water depth reduction (Yin/Yo) within the vegetated reach and Fro in the unvegetated case.

Close modal

Figure 6 shows a positive relationship between Fro and the proportional water depth reduction (%). The proportional reduction within the vegetated reach increased with both increasing Fro and vegetation density.

Maintenance programs should be applied to manage ditch bank vegetation in open channels, because water level changes upstream of and within the vegetated reach which affects water distribution on branches as well as the calibration of opening gates. Drainage collectors will also be affected.

Impact of ditch bank vegetation on the velocity distribution

The water velocity sensor was mounted on a carriage to measure flow velocity in different vertical sections along the flume centerline. This was done upstream, within, and downstream of the vegetated reach. Figures 79 show the velocity profiles for different vegetation densities as ratios of the velocity in the unvegetated cases. In the figures, the term h/Y is the ratio between the vertical measuring distance (h) and the total water depth (Y).

Figure 7

Velocity profiles for different vegetation densities (λ) at Q=40 l/s and Fro=0.15, for (a) λ=0.0113, (b) λ=0.0028, and (c) For low λ=0.0013.

Figure 7

Velocity profiles for different vegetation densities (λ) at Q=40 l/s and Fro=0.15, for (a) λ=0.0113, (b) λ=0.0028, and (c) For low λ=0.0013.

Close modal
Figure 8

Velocity profiles for different vegetation densities (λ) at Q=40 l/s and Fro=0.20, for (a) λ=0.0113, (b) λ=0.0028, and (c) λ=0.0013.

Figure 8

Velocity profiles for different vegetation densities (λ) at Q=40 l/s and Fro=0.20, for (a) λ=0.0113, (b) λ=0.0028, and (c) λ=0.0013.

Close modal
Figure 9

Velocity profiles for different vegetation densities (λ) at Q=40 l/s and Fro=0.30, for (a) λ=0.0113, (b) λ=0.0028, and (c) λ=0.0013.

Figure 9

Velocity profiles for different vegetation densities (λ) at Q=40 l/s and Fro=0.30, for (a) λ=0.0113, (b) λ=0.0028, and (c) λ=0.0013.

Close modal

The velocity profile as a ratio of the unvegetated case (V/u) is sigmoid, i.e. the maximum velocity (V/umax) occurs in the lower half of the water column. The reason for increasing velocity near the channel bed may be the secondary current that occurs due to the presence of the side vegetation. This result accords with the work of (Afzalimehr & Dey 2009; Afzalimehr et al. 2010; Masouminia 2015; Mohammadzade et al. 2016; Liu et al. 2017), where it is concluded that the level of maximum velocity in the presence of vegetation on the channel walls is below the water surface and the maximum shear stress occurs near the channel bed.

Channel-side vegetation increases flow velocity near the bed – i.e., shear stress near the bed increases – which, in turn, increases the possibility of bed erosion on the vegetated channel's centerline. It is also noted that V/u increases with increasing vegetation density and correlates directly with the change in Fro in the unvegetated case at the same discharge – i.e., V/u is influenced by channel geometry. The maximum velocity occurred within the vegetated reach and is close to that measured just downstream of the vegetation. Figure 10 shows the relationship between V/u max within the vegetated reach and Fro at different vegetation densities.

Figure 10

Relationship between Vin/umax and Fro in the unvegetated case.

Figure 10

Relationship between Vin/umax and Fro in the unvegetated case.

Close modal

Empirical relationships

DataFit 9.0 statistical software packages were used for both statistical analysis and deriving empirical relationships (Oakdale Engineering 2008). A multiple regression analysis was performed at 95% confidence level. R2 was used as a measure of goodness of fit, where the predicted value indicates how well the model predicts responses for new observations.

Relationship between λ and within the vegetated reach

An empirical equation was developed to assess the impact of ditch bank vegetation density on the decrease in water depth within the vegetated reach – Equation (3).
formula
(3)

All contributing factors were shown to be significant in prediction, i.e., all factors had p-values <0.0001. Tables 4 and 5 show the regression analysis results from Equation (3) and the significance of each variable. Figure 11 is a plot of the predicted and measured water depth decreases in the vegetated reach.

Table 4

Regression analysis results – Equation (3)

Variance Analysis
SourceDFSum of SquaresMean SquareF RatioProb (F)
Regression 0.002 0.001 129.269 0.000 
Error 33 0.000 0.000   
Total 35 0.002    
Variance Analysis
SourceDFSum of SquaresMean SquareF RatioProb (F)
Regression 0.002 0.001 129.269 0.000 
Error 33 0.000 0.000   
Total 35 0.002    
Table 5

Coefficient and significance of variables in Equation (3)

VariableValueLower LimitUpper LimitStandard Errort-ratioProb(t)
0.92 0.91 0.93 0.00 239.57 0.00 
−0.007 −0.008 −0.006 0.00 −12.95 0.00 
−0.015 −0.019 −0.012 0.00 −9.49 0.00 
VariableValueLower LimitUpper LimitStandard Errort-ratioProb(t)
0.92 0.91 0.93 0.00 239.57 0.00 
−0.007 −0.008 −0.006 0.00 −12.95 0.00 
−0.015 −0.019 −0.012 0.00 −9.49 0.00 
Figure 11

Comparison of measured and predicted .

Figure 11

Comparison of measured and predicted .

Close modal

Relationship between λ and the average velocity within the vegetated reach

An empirical equation – Equation (4) – was also developed to assess the impact of ditch bank vegetation density on velocity within the vegetated reach.
formula
(4)

All contributing factors were shown to be significant in prediction, i.e., all had p-values <0.0001. Tables 6 and 7 show the results of regression analysis of Equation (4) and the significance of each variable. Figure 12 is a plot of the predicted and measured velocity ratios within the vegetated reach.

Table 6

Regression analysis results – Equation (4)

Variance Analysis
SourceDFSum of SquaresMean SquareF RatioProb(F)
Regression 0.433 0.217 76.798 0.000 
Error 33 0.093 0.003   
Total 35 0.526    
Variance Analysis
SourceDFSum of SquaresMean SquareF RatioProb(F)
Regression 0.433 0.217 76.798 0.000 
Error 33 0.093 0.003   
Total 35 0.526    
Table 7

Coefficient and significance of variables in Equation (4)

VariableValueLower LimitUpper LimitStandard Errort-ratioProb(t)
1.74 1.56 1.92 0.09 19.85 0.00 
0.079 0.065 0.093 0.01 11.46 0.00 
0.048 0.028 0.068 0.01 4.81 0.00 
VariableValueLower LimitUpper LimitStandard Errort-ratioProb(t)
1.74 1.56 1.92 0.09 19.85 0.00 
0.079 0.065 0.093 0.01 11.46 0.00 
0.048 0.028 0.068 0.01 4.81 0.00 
Figure 12

Comparison between measured and predicted

Figure 12

Comparison between measured and predicted

Close modal

The effect of rigid ditch bank vegetation on water surface profile and velocity distribution under sub-critical flow conditions at different discharge rates and vegetation densities in a trapezoidal open channel was studied. It was noted that:

  • 1.

    Increasing the ditch bank vegetation density increases the water depth upstream of the vegetated reach significantly and reduces it within the vegetated reach.

  • 2.

    The decrease in water depth within the vegetated reach increased with increasing Fro.

  • 3.

    The velocity profile as a ratio of that of the unvegetated case (V/u) is sigmoid (S-shaped).

  • 4.

    V/u increased with increasing vegetation density and is also correlated directly with the change in Fro.

  • 5.

    V/u is influenced by channel geometry.

  • 6.

    The maximum velocity occurred within the vegetated reach and is close to that measured just downstream of the vegetated reach.

  • 7.

    V/umax occurs in the lower half of the water column, which increases shear stress near the bed and increases the possibility of bed erosion on the vegetation channel's centerline.

  • 8.

    Multiple regression analysis and the development of empirical equations were used to assess the impact of vegetation density on the reduction in water depth within the vegetated reach and its effect on flow velocity there.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

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