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The hydraulic efficiency of fringing versus banded vegetation in constructed wetlands Graham A. Jenkins ∗ , Margaret Greenway School of Environmental Engineering, Grifﬁth University, Cooperative Research Centre for Catchment Hydrology, Nathan, Qld 4111, Australia Received 30 January 2004; received in revised form 28 January 2005; accepted 10 March 2005

Abstract This paper describes a numerical model study that has been undertaken to investigate the effects of emergent fringing and banded vegetation on the hydraulic characteristics of constructed wetlands. The model study demonstrates that poorly designed wetlands with inappropriate layout of wetland vegetation can result in a significant reduction in the hydraulic efficiency of the wetland system. An empirical relationship is developed between the vegetation characteristics, the wetland shape and the hydraulic efficiency of the system. The relationship developed allows wetland designers and managers to combine computationally simple continuously stirred tank reactor models of the wetland system with long-term hydrologic analysis to determine the impacts of different design strategies. This relationship also indicates that the hydraulic efficiency will not be significantly influenced by the length-to-width ratio for heavily vegetated wetlands where short-circuiting occurs. The aim of the study has been to aid designers of constructed wetlands by developing a qualitative understanding of the hydraulic effects of wetland vegetation and wetland shape on the hydraulic efficiency of the system. © 2005 Elsevier B.V. All rights reserved. Keywords: Constructed wetlands; Water quality; Urban stormwater; Two-dimensional modeling; Contaminant transport; Vegetation; Hydraulic retention time distribution

1. Introduction Constructed wetlands incorporated into the urban landscape can assist in improving stormwater quality. The treatment of stormwater as it flows through a wetland is the result of a complex interaction ∗ Corresponding author. Tel.: +61 7 3875 7961; fax: +61 7 3875 7459. E-mail address: [email protected] (G.A. Jenkins).

0925-8574/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ecoleng.2005.03.001

between the physical, chemical and biological processes (Greenway, 2004). Vegetation is a dominant feature of wetland systems and plays an important role in these treatment processes, including the filtration of particles, reduction in turbulence, stabilization of sediments and provision of increased surface area for biofilm growth (Greenway, 2004; Greenway and Jenkins, 2004). These processes are controlled by the hydraulic interaction between the vegetation and the water as it flows through the system.

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The spatial variation in the type and density of wetland vegetation means that the hydraulic characteristics also vary spatially throughout the system. This spatial variation produces two-dimensional flow characteristics with more water flowing through the less vegetated regions. The result is that the water flowing through a wetland system will not stay as a discrete plug, but will tend to form short-circuiting paths. Each plug of water will spend a different amount of time in the wetland, depending on the path taken as it flows through the system. Therefore, there is no single hydraulic retention time, and in fact the hydraulic characteristics produce a hydraulic retention time distribution. The concept of hydraulic retention time is an important one in the design of artificial wetland systems, as it describes the amount of time that a plug of stormwater spends within the wetland system. The amount of treatment taking place depends on the amount of time the plug of water spends within the wetland system. Therefore, good engineering design demands a detailed understanding of the hydraulic characteristics within a wetland system. As the vegetation plays such an important role in these hydraulic characteristics, it is important to understand the relationship between the vegetation and the hydraulic characteristics. This paper describes a study to investigate the interaction between the vegetation characteristics, wetland shape and the hydraulic efficiency of constructed surface water wetland systems. The aim of the study has been to aid designers of constructed wetlands by developing a qualitative understanding of the hydraulic effects of wetland vegetation and wetland shape on the hydraulic efficiency of the system. The paper uses a two-dimensional hydraulic model to develop an empirical relationship between the hydraulic efficiency of a constructed wetland, the spatial arrangement and density of vegetation within the system and the wetland shape.

hydraulic characteristics within the system have a significant influence on the efficiency of the wetland as a treatment device. As noted by Persson et al. (1999), many wetland management problems can be attributed to poor hydrodynamic characteristics within the wetland system. The hydrodynamic characteristics within a wetland system are affected by features such as: • the shape of the wetland; • the hydraulic characteristics of the inlet and outlet structures; • the wetland bathymetry; • the vegetation type, density and spatial distribution; • mixing. Under ideal plug flow conditions, all of the water that enters the wetland stays together as a single plug as it flows through and exits the system. The time that this plug of water stays in the system is referred to as the hydraulic retention time. A longer hydraulic retention time allows for more of the treatment processes to be completed. The hydraulic retention time under ideal plug flow conditions can be defined by Equation (1). Tn =

VOL Q

(1)

where Tn is the nominal hydraulic retention time, VOL the wetland volume and Q is the flow rate through wetland. However, in real wetland systems, the water does not stay together as a single plug as it flows through the system. All of the features listed above play a role in the distribution of water as it flows through the wetland system and therefore affect the hydraulic retention time of any one plug of water within the system. Furthermore, the spatial variability of these features within a wetland system means that the hydraulic retention time of water flowing through the system is described by a distribution, rather than a single value. 2.2. The hydraulic efﬁciency of wetlands

2. Hydraulics of wetlands 2.1. Hydraulic retention time The physical, chemical, and biological treatment processes that occur within a constructed wetland system rely on the flow of the water through the system to facilitate these treatment processes. Therefore, the

Thackston et al. (1987) have undertaken a study of the effect of basin shape on the retention time distributions for shallow sedimentation basins. In this study, published data on conservative tracer studies from a number of sedimentation basins were investigated to identify the shape characteristics that are dominant in affecting the retention time distributions. Thackston et

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al. (1987) noted that the effective volume ratio indicates the volume of the basin that is effective in the treatment processes taking place in the basin. The effective volume ratio was defined as the ratio of the mean retention time to the nominal retention time, given by: η=

Tm Tn

(2)

where Tm is the mean hydraulic retention time. It was also found by Thackston et al. (1987) that the basin length-to-width ratio, L/W, had the most significant influence on the effective volume ratio, η. An equation was derived to predict the effective volume ratio, based on the length-to-width ratio of the basin, given by: L η = 0.85 1 − exp −0.59 (3) W where η is the effective volume ratio and L/W is the basin length-to-width ratio. Persson et al. (1999) have shown that many measures of the hydrodynamics of flow in ponds and wetlands, such as the effective volume ratio, inadequately describe the efficiency of the flow characteristics within the system. They defined the hydraulic efficiency of a wetland, λ, as the ratio of the time taken for a conservative tracer to reach a peak at the wetland outlet to the nominal hydraulic retention time, given by: λ=

Tp Tn

(4)

where λ is the hydraulic efficiency of the wetland and Tp is the time taken for a conservative tracer to reach a peak at the wetland outlet. Persson et al. (1999) state that the hydraulic efficiency provides a good measure of the effective volume within the system, as well as the pollutant residence time distribution. The hydraulic efficiency can be determined directly from a conservative tracer response curve, overcoming the problems associated with defining the mean residence time from tracer response curves with long receding limbs. However, the most significant advantage of the hydraulic efficiency as shown by Wong et al. (2002) is that it can be related to the number of continuously stirred tank reactors (CSTR’s) used to model the behaviour of wetlands and other treatment devices.

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CSTR models allow a relatively simple modeling approach for the design and assessment of wetlands in the treatment of pollutants. Although more complex models have been applied in the design of wetland systems, such as those described by Walker (1998), they are generally much more computationally intensive and require significant expertise on the part of the operator. The advantage of the CSTR modeling approach adopted by Wong et al. (2002) is that the treatment of pollutants within the wetland can be accurately and quickly modeled over long hydrologic periods. This gives the designer or manager more freedom to assess more complex management strategies using a range of treatment devices. Persson (2000) also investigated the effect of wetland shape on the hydraulic efficiency λ and found that wetlands with large values of L/W produced higher values of λ. The study undertaken by Persson (2000) used a two-dimensional flow model to investigate a range of wetland shapes and configurations. As the wetland length-to-width ratio L/W increased, the flow conditions more closely approached plug flow. Thackston et al. (1987) and Persson (2000) demonstrated that the recirculation zones at the inlet and mixing zones within the basin have a significant effect on the flow characteristics. Water entering the basin or wetland has limited ability to mix with water within the recirculation zones. Also, zones of limited mixing within the basin reduce the volume of water that is effective in the treatment of the water flowing through the system. The resulting short-circuiting causes the flow characteristics to depart from those described by ideal plug flow conditions. 2.3. The effect of vegetation Although the bed material and the cross-section shape affect the hydraulic roughness within a wetland, it is often the vegetation characteristics that have the most significant influence on the flow characteristics. Typically, wetlands include a variety of vegetation types including those that are emergent, floating leaved attached, free floating and submerged (Greenway, 2003, 2004). The complex hydraulic characteristics produced by the different types of vegetation found in a wetland are due in part to the “flexible nature” of the vegetation. This flexibility means that during high flows, the vegetation will tend to bend and

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flatten, thus reducing the apparent roughness. Experiments by Kouwen and Unny (1973) have shown that the Manning n of grass lined channels reduces as the product of the velocity and the depth of flow increases. Kouwen and Li (1980) and Kouwen (1988) derived a set of equations to describe the effect of flexible vegetation on the bed roughness in open channels. The equations have been derived to describe the effect of vegetation on Manning n for flood drainage channels, during high flow conditions that are typical of a flood. However, in a constructed wetland system, the flow conditions during small frequent runoff events will have a greater impact on the treatment of stormwater within the system than those that occur during flood events. Under low flow conditions where the vegetation undergoes relatively little flexibility, Kadlec (1990) has shown that the drag on an individual stem of emergent vegetation can be used to describe the shear stress produced by the vegetation in the wetland. It is difficult to derive an empirical relationship between the hydraulic efficiency λ and the L/W ratio for wetlands from the studies described by Persson et al. (1999) and Persson (2000). Also, there has been no such relationship derived for wetlands with fringing littoral vegetation. An empirical relationship similar to that derived for the effective volume ratio by Thackston et al. (1987), between λ, the length-to-width ratio of the wetland and the density and distribution of fringing vegetation within the wetland, would allow designers and managers to accurately model these wetland systems using the relatively simple CSTR modeling approach.

3. Effect of vegetation density and distribution on hydraulic efﬁciency

The model TDFLOW, developed by the first author, solves the two-dimensional depth averaged shallow water flow equations using an iterative Alternating Direction Implicit (ADI) scheme. The model uses a rectangular coordinate system, and is based on the model described by Jenkins and Keller (1990). The equations solved include: Momentum in the X-direction: ∂U ∂U ∂U ∂h τbx +U +V +g + ∂t ∂X ∂Y ∂X ρH 2 2 ∂ U ∂ U =ν + ∂X2 ∂Y 2 Momentum in the Y-direction: τby ∂V ∂V ∂h ∂V +U +V +g + ∂t ∂X ∂Y ∂Y ρH 2 2 ∂ V ∂ V =ν + 2 ∂X ∂Y 2

One of the problems with studying the flow characteristics of natural and constructed wetlands is that they are highly two-dimensional in nature. Therefore, numerical models provide a useful tool to study these flow characteristics, and to investigate the relationships between the various physical characteristics of the wetland. The MS Windows based two-dimensional flow model TDFLOW was used to study the impact of vegetation cover on a number of hypothetical model wetlands.

(6)

Continuity of mass: ∂h ∂(HU) ∂(HV ) + + =0 (7) ∂t ∂X ∂Y where U is the depth average velocity in the Xdirection, V the depth averaged velocity in the Ydirection, h the water surface elevation, τ bx and τ by the bed shear stress in the X- and Y-directions, H the water depth (=h − z), z the bed elevation, ν the eddy viscosity coefficient (=Ev∗ H), E the dimensionless eddy viscosity coefficient and v∗ is the shear velocity. The effect of the emergent vegetation on the bed roughness in the wetland was modeled using the drag force applied to each stem, described by Kadlec (1990): 2

3.1. Two-dimensional model study

(5)

V (8) 2 where FD is the drag force on vegetation stem, CD the stem drag coefficient, which is a function of the stem Reynolds number, D the stem diameter and V is the depth averaged water velocity. The stem drag coefficient CD in Equation (8) is a function of the stem Reynolds number, and is relatively constant at a value of CD = 1 for stem Reynolds numbers approximately greater than 100. However, for smaller stem Reynolds numbers, there will be a significant increase in CD applied to the vegetation stems. It FD = CD HDρ

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has been assumed in this study that CD remains constant throughout all of the computations. By combining the stem drag force with the average bed shear stress produced by the non-vegetated part of the bed, Equation (9) can be derived to describe the equivalent Manning n for a section of wetland crosssection that includes emergent vegetation. MCD D 2/3 n = no + (9) R 2g where no is the equivalent Manning n for the nonvegetated part of the bed and M is the stem spacing/m2 . The TDFLOW model was used to calculate steady flow conditions through each of the model wetland configurations. A pulse of a conservative contaminant tracer was then injected into the steady flow at the inlet, and the model was used to simulate a tracer test for each wetland. TDFLOW was used to solve the mass balance equation for the two-dimensional transport of a conservative contaminant. The model uses an ADI scheme based on that described by Leendertse and Gritton (1971), to solve the following contaminant transport equation: ∂C ∂C ∂C ∂ ∂C +V − Kx H +U ∂X ∂Y ∂X ∂X ∂t ∂ ∂C − Ky H =0 (10) ∂Y ∂Y where C is the concentration of the conservative contaminant tracer being transported and Kx and Ky are the dispersion coefficients in the X- and Y-directions. 3.2. Model conﬁgurations The numerical model study was undertaken to investigate the effects of vegetation on the distribution of flow through rectangular wetlands with a range of length-to-width ratios, L/W. Nine different wetland configurations were modeled, each of which had a surface area of 7000 m2 with the depth at the outlet fixed at 500 mm. A summary of the wetland configurations modeled is shown in Table 1. A steady flow rate of 200 L/s was applied to each wetland, producing a nominal hydraulic retention time of Tn = 4.90 h. In all of the cases studied, the inflow was modeled as a point source and both the inflow and outflow were centrally located.

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Table 1 Summary of wetland configurations modeled Wetland configuration

Length (m)

Width (m)

L/W

A B Ca D Ea F Ga Ha J Kb

50 70 100 125 140 40 250 350 500 500

140 100 70 56 50 175 28 20 14 14

0.357 0.700 1.43 2.23 2.80 4.38 8.93 17.5 35.7 35.7

a

Wetland configurations modeled with vegetation cover. A model grid spacing of 1.0 m was adopted in wetland configuration J, whilst a model grid spacing of 0.5 m was adopted in wetland configuration K to test the effect of grid size on the numerical solution. b

The dimensions of the hypothetical model wetlands were chosen so that the range of length-to-width ratios studied matched those described by Thackston et al. (1987) and Persson (2000). In all of the cases studied, the numerical grid size was fixed at 1.0 m in both the Xand Y-directions. Wetland model K had the same configuration as that for model J, except that the grid spacing was set to 0.5 m as a test of the numerical solution. To investigate the effect of fringing vegetation cover on hydraulic efficiency in the model wetlands, the vegetation cover in the transverse direction was varied for model configurations C, E, G and H. For each of these configurations, vegetation densities of M = 10, 100 and 1000 stems/m2 were modeled for three different areas of fringing vegetation coverage. The Manning n for the wetland vegetation was determined using Equation (9), and it was assumed that all of the vegetation had a diameter of D = 10 mm, which is typical of Schoenoplectus validus vegetation. The drag coefficient for the vegetation was adopted as CD = 1. The non-vegetated part of the wetland was assumed to have a Manning n = 0.035. For all of the cases studied, the fringing vegetation was symmetrically distributed along the outer longitudinal sides of the wetland, as shown in Fig. 1. 3.3. Model results 3.3.1. Non-vegetated wetland models The flow characteristics produced by the twodimensional model for each of the model wetland con-

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Fig. 1. Conceptual configuration for wetland models.

figurations are similar to those displayed for wetland model E, as shown in Fig. 2. As the flow enters the wetland, there is a recirculation zone on either side of the influent jet. There are also zones of relatively low velocity on either side of the outlet in the far right-hand corners. These zones are relatively ineffective in treating pollutants flowing through the wetland as relatively small amounts of influent enter these zones. When comparing wetlands with different L/W ratios, the most significant difference in the flow characteristics is the size of the recirculation zones located adjacent to the inlet jet. For small ratios of L/W, the recirculation zones are large enough to intersect the wall at the far end of the wetland. This results in only a very small volume of the wetland being effective in the treatment processes. As the L/W ratio increases, the size of these recirculation zones decreases, with a resulting increase in the volume of water that is effective in the treatment processes. The conservative tracer was injected at the inlet to each wetland as a plug over a 1 min period, and the tracer concentration was recorded at the model wetland outlet. A typical tracer response is shown in Fig. 3. In all of the wetland models, the tracer response curve is

Fig. 2. Unscaled velocity vectors for non-vegetated wetland model E.

Fig. 3. Outlet tracer concentration for non-vegetated wetland model E.

characterised by a relatively steep rising limb, followed by a flatter receding limb. All of the model simulations were run for durations of 10 h to ensure that a significant percentage of the tracer was recovered at the wetland outlet. More than 91% of the tracer was recovered for the non-vegetated wetland models. Table 2 shows the data derived from the tracer response curves for each of the non-vegetated wetland models. Persson (2000), Persson et al. (1999) and Kadlec and Knight (1996) show that the dimensionless variance of the tracer response curve, (σ/Tm )2 , provides information on the amount of dispersion and mixing present within the system. Fig. 4 demonstrates that, for the non-vegetated wetland models, the dimensionless

Fig. 4. Dispersion for the non-vegetated wetland model results.

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Table 2 Results for non-vegetated wetland models Wetland configuration

L/W

Tm (h)

(σ/Tm )2

Tp (h)

Tracer recovered at outlet (%)

η

λ

A B C D E F G H J K

0.357 0.700 1.43 2.23 2.80 4.38 8.93 17.5 35.7 35.7

0.285 0.579 1.54 2.62 3.00 3.57 4.35 4.70 4.89 4.88

0.168 0.196 0.423 0.232 0.130 0.0457 0.0547 0.0326 0.0190 0.0196

0.216 0.430 1.02 1.83 2.32 1.236 3.96 4.41 4.68 4.67

92.9 92.3 91.2 92.0 92.0 92.4 95.6 97.8 99.6 99.4

0.0581 0.118 0.313 0.535 0.612 0.728 0.889 0.960 0.997 0.997

0.0440 0.0878 0.208 0.374 0.474 0.639 0.808 0.900 0.956 0.955

variance reaches a maximum of 0.42 for L/W = 1.43. For wetlands with relatively small L/W ratios, the recirculation zones adjacent to the inlet jet are so large that conditions close to plug flow occur between the inlet and outlet with only a small amount of dispersion taking place. However, as indicated in Table 2, the recirculation zones are so large that flow through the wetland is confined to only a small volume, so that the effective volume ratio η is also very small. As the L/W ratio increases, the dispersion gradually reduces, as the flow characteristics begin to approach plug flow. Also, for larger values of L/W, Table 2 indicates that the effective volume ratio increases. It is under these conditions that a wetland will be most effective at treating influent. Not only do the flow conditions begin to approach plug flow, but also most of the wetland volume is effective in the treatment process. Fig. 5 presents a comparison of the effective volume ratio η derived from the non-vegetated wetland model results with the data presented by Thackston et al. (1987). It can be seen from this figure that the design curve derived by Thackston et al. (1987) for the prediction of η based on the basin L/W ratio tends to under-predict the results for the non-vegetated wetland models. However, the non-vegetated wetland model results fit well within the data presented by Thackston et al. (1987). Wetland model configuration K was undertaken as a test of the numerical model adopted for simulating the flow conditions. The model grid size will have the biggest effect for model configuration J, as it produces the smallest recirculation zones for all of the wetlands tested. A grid size of 0.5 m was adopted for model con-

figuration K, which increased the computational effort to approximately eight times that of the other model configurations. Comparison between the model results for model configurations J and K indicates that halving the grid size has made minor differences to the predicted flow characteristics. Therefore, it can be concluded that the grid size adopted in the two-dimensional model has minor impact on the hydraulic characteristics predicted for the hypothetical wetlands. 3.3.2. Fringing vegetation in the wetland models As demonstrated by Thackston et al. (1987), the practical design of wetlands is best achieved by the adoption of a design relationship that includes the most

Fig. 5. Effective volume ratio for non-vegetated wetland model compared with Thackston et al. (1987).

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Table 3 Results for vegetated wetland models for wetland configuration C Vegetation cover (%)

Vegetation density M (stems/m2 )

Tm (h)

(σ/Tm )2

Tp (h)

Tracer recovered at outlet (%)

λ

λp

22.9 51.4 74.3 22.9 51.4 74.3 22.9 51.4 74.3

10 10 10 100 100 100 1000 1000 1000

1.54 1.55 1.80 1.56 1.51 1.84 1.58 1.50 1.34

0.427 0.517 0.732 0.434 0.585 1.038 0.440 0.645 1.207

1.02 1.02 1.01 1.02 1.02 0.944 1.03 1.01 0.856

91.4 90.7 90.4 91.5 89.5 88.0 91.6 91.3 87.4

0.208 0.208 0.206 0.209 0.208 0.193 0.210 0.206 0.175

0.871 0.711 0.582 0.817 0.587 0.404 0.788 0.523 0.311

significant measurable characteristics of the system. For a constructed wetland, these characteristics include not only the length-to-width ratio L/W, but also the density and spatial distribution of vegetation within the system. The model runs undertaken with fringing vegetation were designed to provide information to derive a design relationship for hydraulic efficiency λ, that is similar to that presented by Thackston et al. (1987) for the effective volume ratio η. As with the non-vegetated wetland models, the model was run until steady flow conditions were achieved, a plug of conservative tracer was injected at the inlet and the tracer concentration was measured at the wetland outlet. The retention time for flow that enters the fringing vegetation will be significantly longer than that for the flow through the non-vegetated section, due to the increased drag created by the vegetation. The tracer response curves for the fringing vegetation models have longer and flatter receding limbs than those for the nonvegetated wetland models. Tables 3–6 indicate that the

tracer recovery for the vegetated wetland models is generally less than that observed in the non-vegetated wetland models. Aside from the differences expected from pure advection, more mixing and dispersion take place in the fringing vegetation cases modeled, as indicated by the increased values of (σ/Tm )2 . Inspection of Tables 3–6 indicates that the length-towidth ratio L/W has a significant effect on the hydraulic efficiency λ of the wetlands with fringing vegetation. As with the non-vegetated wetlands, the hydraulic efficiency λ is greater for wetlands with larger L/W ratios. However, it can also be noted that the hydraulic efficiency λ reduces as the amount and density of fringing vegetation increase in the wetland. This indicates that even relatively long and narrow wetlands will have relatively low values of hydraulic efficiency when there is a significant amount of dense fringing vegetation. This effect can be explained by inspection of the flow characteristics produced within the wetland models. The most significant effect of the L/W ratio is the size of the recirculation zones adjacent to the inlet and

Table 4 Results for vegetated wetland models for wetland configuration E Vegetation cover (%)

Vegetation density M (stems/m2 )

Tm (h)

(σ/Tm )2

Tp (h)

Tracer recovered at outlet (%)

λ

λp

24.0 48.0 72.0 24.0 48.0 72.0 24.0 48.0 72.0

10 10 10 100 100 100 1000 1000 1000

2.96 2.98 3.10 2.64 2.59 2.93 2.58 2.12 1.68

0.192 0.217 0.223 0.171 0.435 0.619 0.178 0.277 0.751

2.25 2.15 1.95 2.14 1.88 1.49 2.08 1.73 1.21

91.9 91.7 92.0 89.7 88.3 88.9 91.0 89.7 83.9

0.459 0.438 0.398 0.436 0.383 0.305 0.424 0.353 0.248

0.865 0.730 0.595 0.807 0.615 0.422 0.777 0.555 0.332

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Table 5 Results for vegetated wetland models for wetland configuration G Vegetation cover (%)

Vegetation density M (stems/m2 )

Tm (h)

(σ/Tm )2

Tp (h)

Tracer recovered at outlet (%)

λ

λp

28.6 50.0 71.4 28.6 50.0 71.4 28.6 50.0 71.4

10 10 10 100 100 100 1000 1000 1000

4.19 4.15 4.26 3.67 3.37 3.97 3.40 2.75 2.34

0.0825 0.0944 0.0964 0.125 0.272 0.436 0.118 0.236 0.585

3.58 3.28 2.99 3.17 2.59 1.99 2.98 2.25 1.49

93.5 93.0 93.5 89.4 86.0 90.7 90.8 88.2 82.8

0.730 0.670 0.611 0.647 0.528 0.405 0.607 0.460 0.304

0.839 0.719 0.598 0.771 0.599 0.427 0.735 0.536 0.337

the limited mixing zones adjacent to the outlet. These zones are predominantly within the fringing vegetation sections of the wetlands. Where there is dense vegetation covering a large portion of the outer section of the wetland, short-circuiting through the central non-vegetated section is taking place. In this case, the recirculation zones and limited mixing zones have less impact on the flow characteristics. Therefore, it is expected that changes to the length-to-width ratio L/W will have less impact than in wetlands with sparse fringing vegetation. 3.3.3. Banded vegetation in the wetland models The previous wetland models demonstrate that fringing vegetation reduces the hydraulic efficiency of a wetland by producing short-circuiting flow through the central non-vegetated region. This short-circuiting is due to the different hydraulic characteristics of the various flow paths through the system. Therefore, the hydraulic efficiency of the wetland should not be affected by vegetation that is placed in bands across

the wetland. This is because all of the flow paths through the wetland will pass through the banded vegetation, and each will have the same hydraulic characteristics. Therefore, three wetland models were set-up to investigate the effect of banded vegetation on the flow characteristics through a wetland. The wetland model configuration G was adopted for each of the banded vegetation models tested. In each case, the wetland comprised a central band of vegetation that was 62 m long and spanned completely across the wetland. The remaining sections of the wetland contained no vegetation. Steady flow was modeled through each of the wetland models, and a conservative tracer was injected as a plug at the inlet. The tracer response was then measured at the outlet to the wetland. The results for each of the banded vegetation models are given in Table 7. Comparison with the results given in Table 2 for the nonvegetated wetland model configuration G indicates that the banded vegetation has only made minor changes to

Table 6 Results for vegetated wetland models for wetland configuration H Vegetation cover (%)

Vegetation density M (stems/m2 )

Tm (h)

(σ/Tm )2

Tp (h)

Tracer recovered at outlet (%)

λ

λp

20.0 50.0 70.0 20.0 50.0 70.0 20.0 50.0 70.0

10 10 10 100 100 100 1000 1000 1000

4.64 4.62 4.68 4.35 3.87 4.40 4.08 3.17 3.03

0.0609 0.0877 0.0810 0.104 0.244 0.330 0.105 0.271 0.496

4.06 3.61 3.35 3.70 2.78 2.19 3.52 2.38 1.63

96.8 96.4 97.0 93.5 87.8 93.4 92.2 87.1 84.2

0.829 0.737 0.684 0.755 0.567 0.447 0.718 0.486 0.332

0.888 0.679 0.606 0.840 0.599 0.438 0.814 0.536 0.351

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Table 7 Results for banded vegetation in wetland model configuration G Vegetation cover (%)

Vegetation density M (stems/m2 )

Tm (h)

(σ/Tm )2

Tp (h)

Tracer recovered at outlet (%)

λ

24.8 24.8 24.8

10 100 1000

4.36 4.36 4.37

0.0549 0.0560 0.0612

3.97 3.97 3.91

95.3 95.4 95.1

0.810 0.810 0.799

the flow characteristics. As expected, the hydraulic efficiency for the banded vegetation is the same as that for the non-vegetated wetland, regardless of the density of vegetation adopted. This indicates that the adoption of banded vegetation within a wetland is preferable to fringing vegetation, as it does not produce shortcircuiting or reduce the hydraulic efficiency of the system. Therefore, the wetland will be able to take full advantage of the treatment processes facilitated by the vegetation. 3.4. An empirical design relationship for hydraulic efﬁciency in wetlands with fringing vegetation The numerical model study has indicated that the flow characteristics within the wetlands are primarily influenced by the advection between the inlet and outlet. However, it is also clear that mixing and dispersion within the wetland play a significant role as well. This mixing and dispersion occur: • between the water flowing through the wetland and the recirculation zones and limited mixing zones; • between the water flowing through the vegetated and non-vegetated sections. Therefore, to derive an empirical design relationship between the hydraulic efficiency λ, and the wetland shape and vegetation characteristics, it is best to first focus on the advective processes taking place from the inlet to the outlet. The flow path of the water through a wetland system can be characterised as a set of parallel streamtubes, which distribute the flow depending on the spatial distribution of the hydraulic characteristics within the system. The hydraulic retention time of the water as it flows along each streamtube will be given by Equation (11). Ti =

Li Ai Qi

(11)

where Ti is the hydraulic retention time in streamtube i, Li the length of flow path along streamtube i, Ai the cross-sectional area of streamtube i and Qi is the flow rate through streamtube i. The flow through an individual streamtube will be controlled by the conveyance of the streamtube and the hydraulic gradient from the inlet to the outlet by: Ki 1/2 1/2 (12) Qi = Ki Si = √ hL Li where Ki is the conveyance in streamtube i, Si the hydraulic gradient in streamtube i (=hL /Li ) and hL is the head loss from the inlet to the outlet. The conveyance Ki is a measure of the carrying capacity of the streamtube i (Chow, 1973) and can be defined by any suitable equation that describes the hydraulic roughness of the streamtube. The hydraulic gradient within a wetland system is generally small in comparison with the depth, and the head loss from the inlet to the outlet hL will be equal for flow along all streamtubes. Therefore, the total flow through the wetland can be found by summing Equation (12) for all of the streamtubes: Ki 1/2 √ hL Q= Qi = (13) Li Furthermore, by dividing Equation (12) by Equation (13), and noting that the head loss hL is the same in both equations, the amount of flow through an individual streamtube can be given as: √Ki Li √Ki Li

Qi =

Q

(14)

An important implication of Equation (14) is that the flow through a streamtube is significantly affected by the ratio of the streamtube conveyance to the total conveyance through the wetland. The streamtube conveyance is a function of both the geometric properties

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and the hydraulic roughness of the streamtube crosssection. Assuming plug flow through each streamtube, a tracer response at the wetland outlet would be composed of a set of discrete plugs of conservative tracer, each occurring at time Ti , defined by Equation (11). The peak concentration will occur for the streamtube carrying the largest flow rate, so that the hydraulic efficiency under ideal plug flow conditions λp is found by dividing Equation (11) by Equation (1) and substituting in Equation (14): 3/2 Tp L A 1 Ki √ λp = = (15) Tn K Li max VOL where the subscript ‘max’ denotes the streamtube that carries the maximum flow rate, √ which will be defined by the streamtube where K/ L is a maximum. Equation (15) represents the hydraulic efficiency that would occur in an infinitely long wetland, where advective processes dominate, the effects of recirculation and limited mixing zones are negligible and mixing and dispersion can be ignored. The results of the numerical model study indicate that these effects cannot be ignored in constructed wetlands. However, as the advective processes play such a significant role in the flow characteristics, it is also clear that λp will have a strong influence on the hydraulic efficiency λ for the wetland. Equation (16) was fitted to the data from the vegetated and non-vegetated model results by using a least squares analysis. The correlation coefficient for the curve is R2 = 0.973. L λ = 0.96λp 1 − exp −(0.58 − 0.36λp ) (16) W The equation produces a series of curves, each of which depends on the value of λp for the wetland, as shown in Fig. 6. As with the equation derived by Thackston et al. (1987) for the effective volume ratio η, Equation (16) suggests that the hydraulic efficiency will never reach the value expected for ideal flow conditions, even for wetlands with very large values of L/W. Equation (16) can be used to estimate the number of CSTR’s that are required to model the wetland system, where a wetland designer or manager knows the wetland shape and fringing vegetation characteristics. As the density and coverage of fringing vegetation increase in a wetland, the value of λp will decrease. Inspection of Equation (16) and Fig. 6 indicates that the

Fig. 6. Hydraulic efficiency λ vs. length-to-width ratio for vegetated and non-vegetated wetlands.

influence of the length-to-width ratio L/W decreases as the value of λp decreases. This implies that the length-to-width ratio L/W will have very little effect on the hydraulic efficiency of wetlands with extremely dense fringing vegetation. Kadlec and Knight (1996) and Kadlec (2000) also concluded from wetland tracer tests that the length-to-width ratio L/W had little influence on the hydraulic retention time distribution of constructed wetlands with vegetation.

4. Conclusions Surface water wetlands rely on vegetation to facilitate the treatment of stormwater as it flows through the system. Some of the most important functions of the vegetation are the result of physical processes such as filtration, stabilization of sediments and provision of increased surface are for biofilm growth. However, the spatial distribution of the vegetation within the wetland can have a significant effect on the hydraulic characteristics of the system. A two-dimensional numerical model study has been described which investigates the impact of fringing vegetation on the hydraulic characteristics of a surface water wetland. The two-dimensional model study has shown that the wetland shape as well as the vegetation density and spatial distribution has a significant impact on the hydraulic characteristics of the wetland. An empirical design relationship has been developed as part of this study to provide surface water wetland

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designers with a tool to predict the hydraulic efficiency for wetlands with fringing vegetation. The study also demonstrates that placing vegetation in bands across the wetland does not produce the reduction in the hydraulic efficiency that is observed for wetlands with fringing vegetation. However, it is noted that the effect of the wetland shape on the hydraulic efficiency has a reduced impact as the density and spatial distribution of fringing vegetation increases. Acknowledgements The authors are grateful to the Cooperative Research Centre for Catchment Hydrology and the School of Environmental Engineering at Griffith University for their funding of this research project. The authors would also like to thank the reviewers of the original paper for their constructive advise regarding the paper. References Chow, V.T., 1973. Open Channel Hydraulics, International ed. McGraw Hill, Singapore. Greenway, M., 2003. Suitability of macrophytes for nutrient removal from surface flow constructed wetlands receiving secondary treated effluent in Queensland, Australia. Water Sci. Technol. 48 (2), 249–256. Greenway, M., 2004. Constructed wetlands for water pollution control—processes, parameters and performance. Dev. Chem. Eng. Miner. Processes 12 (5/6), 491–504. Greenway, M., Jenkins, G.A., 2004. A comparative study of the effectiveness of wetlands and ponds in the treatment of stormwater

in subtropical Australia. In: Proceedings of the 9th International Conference on Wetland Systems for Water Pollution Control, Avignon, France, pp. 65–72. Jenkins, G.A., Keller, R.J., 1990. Numerical Modelling of Flows in Natural Rivers, Conference on Hydraulics in Civil Engineering, Sydney, pp. 22–27. Kadlec, R.H., 1990. Overland flow in wetlands: vegetation resistance. J. Hydraulic Eng., ASCE 116 (5), 691–706. Kadlec, R.H., 2000. The inadequacy of first-order treatment wetland models. Ecol. Eng. 15, 105–119. Kadlec, R.H., Knight, R.L., 1996. Treatment Wetlands. CRC Press, Boca Raton, 893 pp. Kouwen, N., 1988. Field estimation of the biomechanical properties of grass. J. Hydraulics Res. 26 (5), 559–568. Kouwen, N., Li, R.M., 1980. Biomechanics of vegetative channel linings. J. Hydraulics Div., ASCE 106 (HY6), 1085– 1103. Kouwen, N., Unny, T.E., 1973. Flexible roughness in open channels. J. Hydraulics Div., ASCE 99 (HY5), 713–728. Leendertse, J.J., Gritton, E.C., 1971. A Water Quality Simulation Model for Well Mixed Estuaries and Coastal Seas, vol. II. Computation Procedures. Rand Corp, R-708-NYC. Persson, J., 2000. The hydraulic performance of ponds of various layouts. Urban Water 2, 243–250. Persson, J., Somes, N.L.G., Wong, T.H.F., 1999. Hydraulics efficiency of constructed wetlands and ponds. Water Sci. Technol. 40 (3), 291–300. Thackston, E.L., Shields Jr., F.D., Schroeder, P.R., 1987. Residence time distributions of shallow basins. ASCE J. Environ. Eng. 113 (6), 1319–1332. Walker, D., 1998. Modelling residence time in stormwater ponds. Ecol. Eng. 10, 247–262. Wong, T.H.F., Fletcher, T.D., Duncan, H.P., Coleman, J.R., Jenkins, G.A., 2002. A model for urban stormwater improvement conceptualisation. In: Proceedings of the Ninth International Conference on Urban Drainage, Portland, OR, p. 598.