Model Insights into the Role of Bed Topography on Wetland Performance

Abstract

Free water surface constructed wetlands can be effective systems for contaminant removal, but their performance is sensitive to interactions among flow dynamics, vegetation, and bed topography. This study presents a numerical investigation into how heterogeneous bed topographies influence hydraulic and contaminant transport behavior in a rectangular wetland. Topographies were generated using a correlated pseudo-random pattern generator, and flow and solute transport were simulated with a two-dimensional, depth-averaged model. Residence time distributions and contaminant removal efficiencies were analyzed as functions of the variance and correlation length of the bed elevation. Results indicate that increasing the variability of bed elevation leads to greater dispersion in residence times, reducing hydraulic efficiency. Moreover, as the variability of bed elevation increases, so does the spread in hydraulic performance among wetlands with the same statistical topographic parameters, indicating a growing sensitivity of flow behavior to the specific spatial configurations of bed features. Larger spatial correlation lengths were found to reduce the residence time variance, as shorter correlation lengths promoted complex flow structures with lateral dead zones and internal islands. Contaminant removal efficiency, evaluated under the assumption of uniform vegetation, was influenced by bed topography, with variations becoming more pronounced under conditions of lower vegetation density. The results underscore the significant impact of bed topography on hydraulic behavior and contaminant removal performance, highlighting the importance of careful topographic design to ensure high wetland efficiency.

1. Introduction

Free-water surface (FWS) wetlands can be effective solutions for treating wastewater from urban and industrial sources. The ability of constructed wetlands to significantly reduce various contaminants is well established [1,2], with studies highlighting their efficiency in eliminating biological oxygen demand [3], chemical oxygen demand [4], total suspended solids [5,6], total nitrogen, and nitrate nitrogen [7,8], as well as ortho-phosphate and total phosphorus [9], alongside fecal coliforms and Escherichia coli [10].

The removal of contaminants in wetland systems is not only reliant on natural biochemical processes, but is also fundamentally influenced by flow hydrodynamics and mixing processes [11,12], where bed topography plays a critical role alongside vegetation [13]. The intricate relationship between wetland hydrodynamics and biochemical processes is not fully understood [14,15], and therefore, predicting wetland performance remains challenging.

Ideally, effective treatment performance in wetlands is achieved when flow distribution approximates plug flow, a condition in which all water parcels remain in the system for the same duration, equal to the nominal residence time [1,16]. However, perfect plug flow is never achieved in practical applications, and water depth variations can result in heterogeneous velocity fields that lead to residence time distributions with a large variance, ultimately diminishing treatment efficiency. The hydraulic performance of a wetland refers to the extent to which actual flow conditions approach this ideal plug flow behavior, and is strongly influenced by both vegetation characteristics and topographical features. In general, increased flow resistance due to vegetation and bed topography leads to lower mean velocities and longer retention times, which are critical for supporting biochemical reactions [7,17]. However, spatial variability in stem density and topography can significantly alter internal flow patterns and cause deviations from ideal plug flow.

The heterogeneity of bed topography and vegetation density can create preferential paths of low hydraulic resistance, facilitating rapid water discharge and potentially leading to reduced treatment efficiency—a phenomenon known as short-circuiting [17,18,19,20]. Several studies have investigated the role of vegetation density and spatial distribution on wetland performance [21,22,23,24,25], and have shown that vegetation type, density, and spatial arrangement are the key determinants of a wetland’s hydraulic behavior. Indeed, vegetation plays a vital role in controlling the residence time distribution [26,27] and the degree of mixing and recirculation within a wetland [28,29]. This interplay between hydrodynamics and vegetation influences the contact time between contaminants and biota [30], which in turn determines the treatment efficiency of the wetland.

Relatively less understood is the role of bed topography and wetland behavior. Wetland topographic heterogeneity plays a critical role in enhancing biodiversity by creating a mosaic of microhabitats that support a wide range of species with diverse ecological requirements [31]. Variations in elevation, such as hummocks, depressions, and ridges, influence hydrology, soil moisture, and nutrient availability, fostering distinct environmental conditions within a single wetland system. For instance, higher areas may support vegetation that thrives under drier conditions, while lower, waterlogged areas provide habitats for aquatic plants, invertebrates, amphibians, and fish. This spatial diversity enables coexistence among species with contrasting habitat preferences, increasing overall biodiversity.

Studies have shown that wetland microtopography significantly influences ecosystem functioning, vegetation composition, and biogeochemical processes, as it affects water table dynamics and soil saturation [32]. In particular, hummocks are associated with greater species richness and higher nutrient concentrations, while hollows show elevated nitrate and sulfate levels. This impact is more pronounced in wetter conditions, suggesting that water table proximity is a key determinant of wetland biogeochemistry [32,33]. In tidal wetlands, complex zonation patterns are observed, with elevation and hydroperiods explaining only part of the variability in wetland cover distribution [34]. In coastal peatlands, elevation correlates strongly with soil organic matter content and carbon-to-nitrogen ratios [35]. Microtopography and flow regime also influence plant species assemblages and carbon stock in floodplain wetlands [36]. It has also been shown that microtopography in peat-accumulating wetlands affects microbial function and carbon and nitrogen cycling, with hummocks and hollows exhibiting different patterns of microbial activity [37]. Moreover, increasing microtopographic heterogeneity may serve as an early indicator of ecosystem transition in salt marshes [38], whilst microtopographic modifications can alter soil characteristics and promote vegetation restoration in coastal mudflats [39]. Ref. [40] have also shown that, in the Everglades, changes in vegetation and microtopography have altered historical flow patterns, affecting ecosystem resilience. Understanding the complex interplay between microtopography, transport, and biochemical processes is therefore crucial for effective wetland management, restoration, and conservation efforts.

Despite increasing recognition of the importance of wetland microtopography, its influence on hydraulic performance and solute transport remains poorly quantified, particularly from a modeling perspective. In this study, a two-dimensional depth-averaged hydrodynamic and solute transport model was used to investigate the effect of bed topography on the hydraulic performance of a wetland. The objective is to gain a deeper understanding of how spatial variations in bed elevation, and the resulting variations in water depth, influence residence time distributions and solute concentration reduction efficiency. To this end, heterogeneous bed elevation fields were generated using a 2D Gaussian random field generator, with topographic variability statistically characterized by standard deviation and correlation lengths in the horizontal plane. The resulting hydraulic and concentration reduction efficiencies were evaluated as a function of the statistical parameters of bed topography. The effect of anisotropic topographies was also investigated by considering the different correlation lengths of bed elevation in the longitudinal and transverse directions. The results provide useful insights into the factors affecting wetland performance, thereby informing the development of more effective design criteria.

2. Model

2.1. Wetland Model

The two-dimensional, depth-averaged numerical model of a wetland was used to simulate the velocity field and the transport of a dissolved tracer under steady flow conditions. The hydrodynamic model is based on the shallow-water equations whereas the solute transport model is based on the depth-averaged advection–diffusion equation. The use of a shallow water model coupled with a depth-averaged solute transport model is justified by the dominance of horizontal over vertical transport in the simulated wetlands, and by the fact that vertical stratification is not considered in this study. The hydrostatic pressure assumption remains valid under laminar flow conditions. Additionally, the solute is assumed to be uniformly distributed at the inlet, while density and thermal stratification are neglected, and vegetation is assumed to be emergent and uniformly distributed. Under these assumptions, the depth-averaged solute transport model is expected to provide a reasonable approximation of system behavior. This modeling approach offers a computationally efficient and physically sound means of assessing the hydraulic and treatment performance of the wetland.

It should be noted, however, that neglecting vertical variations in flow and solute concentration may reduce accuracy in systems with strong stratification, spatially variable vegetation, or significant vertical gradients at the inlet. Additionally, the assumption of uniformly distributed vegetation does not capture the potential correlation between water depth and vegetation density, but allows the study to isolate the effects of bed topography on flow hydrodynamics. The interaction between water depth and vegetation distribution is beyond the scope of this work and is left for future investigation.

2.2. Hydrodynamic Model

Under the assumption of hydrostatic pressure, stationary flow, and negligible wind and Coriolis forces, the depth-integrated velocity field and water depth can be described by the following equations (e.g., [41]):

$$\begin{array}{cc}\hfill {\displaystyle \frac{\partial \left(h{U}_x\right)}{\partial x}}+{\displaystyle \frac{\partial \left(h{U}_y\right)}{\partial y}}& =0\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill {\displaystyle \frac{\partial \left(h{U}_x^2\right)}{\partial x}}+{\displaystyle \frac{\partial \left(h{U}_x{U}_y\right)}{\partial y}}& =-gh{\displaystyle \frac{\partial z_s}{\partial x}}-{\displaystyle \frac{{\tau }_{bx}}{\rho }}-{\displaystyle \frac{{\tau }_{vx}}{\rho }}\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill {\displaystyle \frac{\partial \left(h{U}_x{U}_y\right)}{\partial x}}+{\displaystyle \frac{\partial \left(h{U}_y^2\right)}{\partial y}}& =-gh{\displaystyle \frac{\partial z_s}{\partial y}}-{\displaystyle \frac{{\tau }_{by}}{\rho }}-{\displaystyle \frac{{\tau }_{vy}}{\rho }}\hfill \end{array}$$

(3)

in which $U_x$ and $U_y$ are the depth-averaged velocity components along the x and y directions; h is the mean water depth; $z_s$ is the water surface elevation; $\rho$ is water density; ${\tau }_{bx}$ and ${\tau }_{by}$ are the bed shear stresses in the x and y directions, respectively; and ${\tau }_{vx}$ and ${\tau }_{vy}$ are the flow resistances due to vegetation in the x and y directions, respectively.

Bed shear stresses depend on bed roughness, represented by Manning’s friction coefficient M, whereas vegetation-induced stresses depend vegetation density, n, and stem diameter, d. Details of how these stresses are parameterized in the model can be found in [24]. In this work, we assumed bed roughness to be uniform and used a Manning’s friction coefficient $M=0.025\mathrm{s}{\mathrm{m}}^{-1/3}$, which is within the typical range for bare soil. The simulations were carried out considering two different vegetation scenarios with the uniform stem density and diameter. A first scenario with a density of $n=500\mathrm{stems}{\mathrm{m}}^{-2}$ and a diameter of $d=3$ mm, and a second scenario with density $n=250\mathrm{stems}{\mathrm{m}}^{-2}$ and diameter $d=6$ mm. These values are within the ranges reported by [42] for the salt marsh grass Spartina alterniflora.

Previous studies have shown that vegetation biomass and diversity are controlled by water depth [31,43]. In particular, [43] found a negative correlation between water depth and vegetation biomass in the St. Lawrence River wetland in North America. However, more general empirical correlations between vegetation density and water depth are not available in the existing literature; therefore, in this study, we chose to isolate the effect of bed topography and assumed a uniform vegetation density. A numerical study on the effect of the heterogeneity of vegetation density in synthetic free-water surface wetlands with uniform bed topography was presented by [24].

2.3. Solute Transport Model

The depth-integrated concentration, $C(x,y,t)$, of a reactive tracer passing through the wetland was simulated using the 2-D, depth-integrated, advection-diffusion equation with a first-order reaction term,

$$\begin{array}{cc}\hfill {\displaystyle \frac{\partial \left(hC\right)}{\partial t}}+{\displaystyle \frac{\partial \left(h{U}_{x}C\right)}{\partial x}}+{\displaystyle \frac{\partial \left(h{U}_{y}C\right)}{\partial y}}=& \\ & {\displaystyle \frac{\partial }{\partial x}}\left(h{E}_{xx}{\displaystyle \frac{\partial C}{\partial x}}+h{E}_{xy}{\displaystyle \frac{\partial C}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(h{E}_{yx}{\displaystyle \frac{\partial C}{\partial x}}+h{E}_{yy}{\displaystyle \frac{\partial C}{\partial y}}\right)-kC\hfill \end{array}$$

(4)

where k is the areal removal rate ($\mathrm{m}{\mathrm{yr}}^{-1}$). In this study, we assumed $k=11.5\mathrm{m}{\mathrm{yr}}^{-1}$, which is the average value of the removal rate of ammonia reported by [17] for a set of 131 wetlands. The coefficients $E_{ij}$ account for both turbulent diffusion and shear dispersion due to vertical velocity gradients, and is expressed as a function of vegetation drag, stem diameter, flow velocity, and water depth, as described in [24].

In the simulations, transformation processes are limited to wet areas, as flow and solute transport occur only where water depth is non-zero. Transformations that may take place in dry or intermittently waterlogged zones are not considered.

2.4. Numerical Simulations

Simulations were performed for an approximately $L_x=100\mathsf{m}$ long and $L_y=50\mathsf{m}$ wide rectangular wetland, with a centrally aligned inlet–outlet configuration and inlet–outlet widths of 5 m (Figure 1). In the simulations, we imposed the flow rate $Q=4.8\ell /\mathrm{s}$ and set the water depth at the outlet so that the mean residence time was 6 days in all simulations, which is reasonable for an FWS wetland [17,44]. Since the plan area of the wetland is the same for all simulations, the average water depth is the same, namely $H=0.5$ m. The additional resistance due to vegetation is explicitly taken into account by the vegetation drag model mentioned in Section 2.2.

For the solute transport equation, the boundary conditions are given by a constant normalized concentration at the inlet, $C/C_0=1$, an open boundary condition at the outlet, and a no-flux condition on the remaining boundaries of the flow domain. The equations were solved via a custom-made finite volume code that solves the Saint-Venant equations and the depth-averaged scalar transport equation in 2D. The shallow water model uses a second-order accurate time integration scheme combined with a van Leer flux-limited TVD method [45] for the spatial discretization of advection. Solute transport is modeled using the explicit wave propagation algorithm implemented in the CLAWPACK software (version 3.0) for the advection term, as described in [46,47], and the implicit Crank–Nicolson method for diffusion. The computational domain is discretized using a uniform grid of square cells with a resolution of 0.5 m. A time step of 1 min was used in the simulations and was found to ensure time-step convergence.

2.5. Bed Topography

The two-dimensional Gaussian random fields of bed elevation, $z_b(x,y)$, were generated using a spectral method [48], with a given variance ${\sigma }_h^2$ and correlation lengths ${\lambda }_x$ and ${\lambda }_y$ in the streamwise (x) and lateral (y) directions, respectively. Note that, in the simulations performed in this study, the variations in the free surface elevation are extremely small relative to the mean water depth, and therefore, the variance of the bed elevation is, for all practical purposes, the same as the variance of the water depth.

In the simulations, the standard deviation of the bed elevation, ${\sigma }_h$, was varied from 0 to 0.4 m, whereas the correlation length, $\lambda$, was varied from 5 m to 20 m, i.e., from 0.05 to 0.2 times the longitudinal size of the wetland, L, and from 0.1 to 0.4 times the width of the wetland, W. In order to generalize the results of the analysis, it may be preferable to refer to the non-dimensional standard deviation ${\sigma }_h/H$ and the correlation length $\lambda /H$, obtained by normalizing the dimensional parameters with the average water depth, $H=0.5$ m. The normalized ranges of the variation of ${\sigma }_h/H$ and $\lambda /H$ are therefore from 0 to 0.8 and from 10 to 40, respectively. We considered both the isotropic fields of bed elevation, for which $\lambda ={\lambda }_x={\lambda }_y$, and anisotropic fields, for which ${\lambda }_x\ne {\lambda }_y$.

The ranges of standard deviation and correlation length considered in this study were selected to represent wetland beds ranging from flat to strongly heterogeneous, while ensuring that the assumptions underlying the shallow water, depth-averaged framework remain valid. The range of variation in ${\sigma }_h$ encompasses the variability observed in natural wetlands, e.g., [49], where localized features such as ridges, depressions, and channels can produce significant deviations in bed elevation. By exploring this range, we aim to capture a broad spectrum of realistic wetland configurations and offer insights that are broadly applicable to wetland design and assessment.

For each set of parameter values, we generated 300 random topographies and simulated flow and mass transport through the wetland. Based on several tests, this was more than sufficient to obtain accurate statistics of the chosen performance metrics that are independent from the number of generated random fields.

2.6. Efficiency Metrics

In this work, we imposed the discharge and the average flow depth so that the mean residence time was the same for all simulated wetlands. We then analyzed the hydraulic performance based on the residence time distributions (RTDs), looking in particular at the standard deviation of the residence time. The residence time distribution, $R\left(t\right)$, was calculated by simulating the transport of a passive tracer ($k=0\mathrm{m}{\mathrm{yr}}^{-1}$ in Equation (4)) with a constant concentration, $C_0$, at the inlet, and a concentration of zero in the wetland. The cumulative RTD, $R\left(t\right)$, was then calculated as the normalized output concentration, $C_{\mathrm{out}}\left(t\right)/C_0$.

The first moment of the RTD is the mean residence time, $t_m$, i.e., the average time that a water parcel remains in the wetland. This is calculated from the complementary cumulative distribution function, $R_c\left(t\right)=1-R\left(t\right)$, as

$$t_m={\int }_0^{\infty }{R}_c\left(t\right)dt$$

(5)

The second central moment of the residence time, i.e., its variance, is calculated as

$${\sigma }_t^2={\int }_0^{\infty }2t{R}_c\left(t\right)dt-t_m^2$$

(6)

which provides a measure of the spreading around the mean value, $t_m$.

The numerical simulation of the transport of a passive scalar is protracted for a sufficiently long time so that $C_{\mathrm{out}}/C_0\approx 1$ at the end of the simulation, and $t_m\approx t_n=V/Q$, where V is the water volume in the wetland.

In general, a wetland can be modeled as a number (N) of continuous stirred tank reactors (CSTRs) in series [17]. In the case of a single tank ($N=1$), the wetland behaves as a well-mixed reactor, resulting in an exponential RTD with $\sigma =t_n$. Conversely, a model with a large number of tanks produces a system approaching plug flow, which corresponds to a variance of the residence time approaching zero. According to [50], the number of tanks in series, N, can be determined from the inverse of the dimensionless variance (${\sigma }_{\theta }=\sigma /t_n$):

$$N={\sigma }_{\theta }^{-2}={\left({\displaystyle \frac{\sigma }{t_n}}\right)}^{-2}$$

(7)

and can be used to compute the dispersion efficiency of the wetland [29]:

$$e_d=1-{\sigma }_{\theta }^2=1-{\displaystyle \frac{1}{N}}$$

(8)

which is equal to 1 in the ideal limit of plug flow, as ${\sigma }_{\theta }$ approaches zero.

An alternative metric of wetland efficiency is the volumetric efficiency, $e_v$, which according to [29] represents the effective volume of a wetland system and is defined as

$$e_v={\displaystyle \frac{t_m}{t_n}}$$

(9)

where $t_m$ is the mean residence time measured in a field tracer test. It is noted that, for a completely passive tracer, the mean residence time should equal the nominal residence time in the limit case where the distribution of the residence time is sampled for an infinitely long time and the tail of the distribution is accurately represented. In the present study, all simulated wetlands have the same water volume and flow rate, resulting in identical nominal residence times across all cases. Since the residence time distributions are reconstructed over a sufficiently long duration to allow for full mixing, we have $t_m\approx t_n$. Therefore, according to the definition above, $e_v\approx 1$ for all wetlands.

For the same reason, the hydraulic efficiency index, $e_h$, defined by [29] as the product of volumetric efficiency and dispersion efficiency,

$$e_h=e_v·e_d={\displaystyle \frac{t_m}{t_n}}\left(1-{\displaystyle \frac{1}{N}}\right)$$

(10)

is approximately equal to $e_d$ in all simulations.

An alternative metric for the degree of mixing is based on the time taken for 90% of the injected tracer to leave the system, $t_{90}$, and is defined as follows:

$${\theta }_{90}={\displaystyle \frac{t_{90}}{t_n}}$$

(11)

Generally, higher values of ${\theta }_{90}$ indicate poor mixing, with ${\theta }_{90}\approx 1$ in the ideal case of complete mixing. Again, this parameter is correlated to the variance of the residence time, ${\sigma }_t^2$, as for the same $t_n$, higher values of ${\sigma }_t$ imply higher values of ${\theta }_{90}$ and therefore lower degrees of mixing.

For the simulations with a reactive tracer, we also evaluated the concentration reduction efficiency:

$$E_c={\displaystyle \frac{C_i-C_o}{C_i}}=1-{\displaystyle \frac{C_o}{C_i}}$$

(12)

In this study, the input flow rate is imposed, and steady-state conditions are assumed. Although evapotranspiration can be significant in some wetland systems, it is neglected here to focus on the dominant advective–dispersive transport processes; as a result, inflow equals outflow. Therefore, the ratio of the output mass rate to the input mass rate equals the ratio of the output concentration to the input concentration, and the concentration reduction efficiency also represents the mass removal efficiency.

3. Results and Discussion

3.1. Flow Patterns

Examples of simulated wetlands with isotropic bathymetry fields are shown in Figure 1. Specifically, Figure 1a shows a wetland with a uniform water depth. The wetlands in Figure 1b–d, have a non-uniform random bed elevation with correlation length $\lambda =5$ m and a standard deviation ${\sigma }_h/H=0.2$, $0.4$, and $0.6$, respectively. As previously mentioned, in all cases, the mean water depth is the same, i.e., $H=0.5$ m. It can be seen that, for this value of the correlation length, if the standard deviation of bed elevation is sufficiently high, there can be a formation of internal dry zones, i.e., islands. For higher values of the correlation length, the occurrence of internal dry zones becomes less likely.

Figure 1 also shows the streamlines obtained by considering 100 source points at the inlet, which are seen to become more irregular as the variance of bed elevation is increased. Figure 1a shows the case of a wetland with uniform bed topography, and therefore almost uniform flow depth. Figure 1b shows a wetland with ${\sigma }_h/H=0.2$, in which the pattern of streamlines is very similar to that of a uniform wetland, but we make an exception for a higher variance of flow velocities due to the differences in water depth. A similar flow pattern is also found for ${\sigma }_h/H=0.4$, but in this case, we can also observe small internal islands and lateral bars which act as breakwaters and significantly deflect the streamlines. For the wetland in Figure 1d, it can be seen that there is an island which causes a flow contraction and a partition of the flow into two main pathways. In this case, there is an additional obstruction induced by two large lateral bars, which create a wetland with the two main detention basins. A further partition of the flow is induced by small internal wetlands inside the second basin. This case well illustrates the complex flow patterns that can arise in the wetland with a large variance in bed elevation. In general, as the variance of bed elevation ${\sigma }_h$ increases, larger lateral dead zones appear where lower velocities are found, and even internal dead zones can appear when internal dry zones are present.

3.2. Isotropic Bed Topography

We first investigated the hydraulic performance of a wetland with isotropic topography, i.e., wetlands with bed elevation fields in which the correlation lengths in the x and y directions are the same, ${\lambda }_x={\lambda }_y$. Figure 2 shows the behavior of the standard deviation of the residence time, ${\sigma }_t$ as a function of the standard deviation of bed elevation, ${\sigma }_h$. It can be seen that the average standard deviation of the residence time seems to follow a sigmoid function, which increases with the standard deviation of bed elevation, but reaches a horizontal asymptote for ${\sigma }_h/H\approx 0.6$. This implies that the hydraulic efficiency decreases on average for a higher ${\sigma }_h/H$. If we consider the definition of $e_h$ expressed by Equation (10), the highest hydraulic efficiency among the simulated wetlands is obtained for ${\sigma }_h/H=0$ and is equal to 0.96, whereas the minimum efficiency is obtained for ${\sigma }_h/H=0.8$ and is equal to 0.64. Hence, the variation of the average hydraulic efficiency across the tested topographies is around 30%.

In addition to the median value of ${\sigma }_t/t_n$, the graph in Figure 2 shows the range corresponding to the 16th and 84th percentiles, which is representative of the standard deviation of a normal distribution, and the range corresponding to the 5th and 95th percentiles, which is representative of the extreme values. It is observed that the spreading around the mean of ${\sigma }_t/t_n$ also increases for increasing ${\sigma }_h/H$, which is consistent with the formation of more complex flow structures with lateral dead zones and internal dry zones as the topographical complexity increases. The range of variation of ${\sigma }_t/t_n$ for ${\sigma }_h/H=0.8$ is quite large, as the 5th percentile corresponds to ${\sigma }_t/t_n\approx 0.4$ and the 95th percentile corresponds ${\sigma }_t/t_n\approx 0.8$.

This variation indicates that, for heterogeneous bed topographies with the same statistical parameters, the particular topography can make a significant difference on the hydraulic performance of a wetland. Considerable differences in hydraulic performance were also found by [22] for a channelized wetland where the channelization is induced by differences in vegetation density. Although their study is limited to uniform bed topographies, their results show that the level of channelization—as produced by the difference in vegetation density in the channel and the surrounding, more highly vegetated zones—and the shape of the channel can significantly affect the hydraulic performance of a wetland. Similarly, for non-uniform bed topographies, we can expect that, for the same variance in bed elevation, the shape of the preferential flow pathways induced by bed forms are key to determining the performance of the wetland.

We then investigated the effect of the correlation length, $\lambda$, assuming a constant vegetation density in the wetland, so as to isolate the effect of bed topography. In all simulations, the normalized variance of the bed elevation ${\sigma }_h/H$ is set to $0.8$. The results are shown in Figure 3. It can be observed that ${\sigma }_t/t_n$ decreases as the correlation length increases, and hence the hydraulic efficiency, $e_h$, is higher for larger correlation lengths. This is due to the formation of more complex flow patterns for smaller correlation lengths, characterized by the presence of lateral dead zones and internal dry zones. Note that, while the variance of ${\sigma }_t/t_n$ is almost constant for the range of correlation lengths $\lambda$ considered in the simulations, the range of variation of the most extreme values appears to decrease for increasing $\lambda$. This is likely due to the lower flow complexity, particularly the reduced likelihood of solute trapping in dead zones, which not only decreases the variance of the residence time but also narrows its range of variation.

By demonstrating how the increased variance in water depth due to bed topography leads to greater variance in residence time and reduced hydraulic efficiency, the research aligns with previous findings on the crucial role of microtopography in influencing water flow and storage in wetlands [32,40]. The observation that more heterogeneous bed topographies result in a wider range of hydraulic performances further supports the notion that microtopographic variability significantly impacts ecosystem functioning, as seen in studies by [37,38].

3.3. Anisotropic Bed Topography

We evaluated the effect of anisotropic topography by considering different correlation lengths in the x- and y-directions, thus creating bed forms elongated in the two directions. In the simulations, we first set ${\lambda }_y=5\mathrm{m}$, which is to 0.1 times the width of the wetland, W, and varied ${\lambda }_x$ from 5 to 20 m, i.e., from 10 to 40 times the average depth H, which corresponds to between 0.05 and 0.2 times the longitudinal length of the wetland, $L_x$. We then set ${\lambda }_x=5\mathrm{m}$ and varied ${\lambda }_y$ from 5 to 20 m, i.e., from 0.05 to 0.1 the longitudinal size of the wetland. For all the topographies considered here, ${\sigma }_h/H=0.8$.

Example bathymetric maps and streamlines for wetlands with anisotropic bed topography are shown in Figure 4. In particular, Figure 4a,b show two wetlands with bed forms elongated in the x direction, with ${\lambda }_x=10$ m and ${\lambda }_x=20$ m, respectively, whereas Figure 4c,d show wetlands with bed forms that are more elongated in the y direction, with ${\lambda }_y=10$ m and ${\lambda }_y=20$ m, respectively. It can be observed that increasing the longitudinal correlation length, ${\lambda }_x$, reduces the number of bed forms within the wetland, while increasing their size. This can lead to the formation of narrow preferential flow channels. In contrast, increasing the transverse correlation length, ${\lambda }_y$, results in bed forms that resemble baffles, creating larger lateral dead zones.

Figure 5a,b show the effect of the variation of the longitudinal and lateral correlation lengths, respectively. It can be seen that the standard deviation of the residence time decreases on average from ${\sigma }_t/t_n\approx 0.6$ to ${\sigma }_t/t_n\approx 0.4$ as ${\lambda }_x$ is increased from $10H$ to $40H$, i.e., from 5 to 20 m, whereas the spreading around the mean does not differ substantially. Conversely, for an increasing ${\lambda }_y$, we do not observe a monotonic decrease in the standard deviation of the residence time. Instead, the maximum mean value of ${\sigma }_t$ is found for ${\lambda }_y/L_y=0.2$, i.e., ${\lambda }_y=10$ m. The observed trends are likely to be due to a reduction in flow complexity as the correlation length of bed elevation becomes large relative to the size of the wetland.

Ref. [24] investigated the effect of anisotropic vegetation patterns and found better concentration reduction efficiencies for wetlands with elongated patches of vegetation perpendicular to the flow direction compared to those obtained with patches parallel to the flow direction. This is likely due to the smaller fluxes of contaminant through the densely vegetated zones, where the removal rate is higher. Instead, the results in Figure 5 suggest better hydraulic efficiencies, i.e., a lower ${\sigma }_t/t_n$ for an elongated bed forms parallel to the flow direction. These results are not in contradiction with each other, because contaminant removal ultimately depends on how the vegetation is distributed relative to the bed topography.

3.4. Impact on Contaminant Removal Efficiency

The relationship between the variability of water depth and the concentration reduction efficiency was investigated by considering a non-zero reaction rate in the mass transport model, as explained in Section 2.3. Figure 6 shows the results obtained for wetlands with a normalized correlation length of bed elevation $\lambda /H=10$ and two different settings for vegetation: (a) $n=500\mathrm{stems}{\mathrm{m}}^{-2}$ and $d=3$ mm; and (b) $n=250\mathrm{stems}{\mathrm{m}}^{-2}$ and $d=6$ mm. In both cases, the areal removal rate, k, was set to $11.5\mathrm{m}{\mathrm{yr}}^{-1}$.

The results show that mean removal efficiency is lower in wetlands with a non-uniform topography compared to those with uniform beds. This reduction is more pronounced under sparser vegetation conditions, with a difference of approximately 10% between the case of ${\sigma }_h/H=0.5$ and the case of a flat bed. Moreover, substantial variability in removal efficiency is observed among the wetlands with the same standard deviation of bed elevation, with differences exceeding 30% for more heterogeneous topographies. This suggests that, although the statistical properties of the bed topography are identical, the relative positioning of the bed features can significantly influence flow patterns and short-circuiting, leading to divergent treatment outcomes. It is also apparent that variations in the removal efficiency are more pronounced for the second vegetation scenario, which is characterized by a smaller vegetation density but a larger stem diameter compared to the first scenario.

It must be stressed that these results are based on the assumption of a uniform vegetation density all over the wetland. In actuality, there is often a correlation between bed elevation and vegetation density [31], with studies showing higher vegetation biomass in lower depth regions [43]. Numerical simulations conducted by [24] for rectangular wetlands with spatially random vegetation distributions have shown that the concentration reduction efficiency is primarily dependent on the average vegetation density, with relatively minor variations due to the spatial variability of vegetation density. In particular, [24] found that the ensemble average of the total mass removal decreases for larger variances and correlation lengths of the vegetated field, which finds a physical explanation in the existence of preferential flow paths induced by variations in flow resistance as a result of the spatially varying vegetation density. It must be pointed out, however, that their study considered diversion wetlands in which the difference between the water surface elevation at the inlet and the outlet is imposed, or in other words, the average head gradient is imposed, while the flow rate through the wetland varies accordingly. Conversely, in the present study, we imposed the same flow rate in all simulations and let the water surface gradient vary accordingly. Under these conditions, the mass removal rate depends only on the concentration reduction efficiency, i.e., on the ratio of the outlet concentration to the inlet concentration, whereas in the work of [24], the difference in the mass removal rate for wetlands with the same average vegetation density is due to differences in the flow rate through the wetland. Therefore, the presence of a variable vegetation density in a wetland with a non-uniform bed topography is unlikely to produce significant differences from the results found in this study for a uniform vegetation density.

The lack of correlation between bed topography and vegetation growth in our simulations stands in contrast to studies such as those by [36,39], which showed that microtopographic variation strongly influenced vegetation composition and growth, either through altered flow regimes [36] or through changes in soil moisture and salinity [39]. In our analysis, we isolated the effect of bed topography by assuming a uniform vegetation distribution. This allowed us to focus specifically on the hydraulic implications of topographic heterogeneity, independently of the feedback from spatially variable vegetation. The differences in the treatment performance observed despite this simplification suggest that even in the absence of vegetation-topography correlations, the spatial arrangement of topographic features can significantly impact wetland function. These findings align with previous work that emphasized the role of vegetation patterns in shaping wetland performance, e.g., [24,33,34].

4. Conclusions

This study highlights the crucial role of bed topography in influencing the hydraulic performance of free water surface wetlands. Through Monte Carlo simulations, we demonstrated that greater topographic heterogeneity affects flow patterns and contaminant transport, increasing residence time variability and thereby reducing hydraulic performance. The reduction in performance was more pronounced in wetlands with smaller spatial correlation lengths, as they exhibited more complex flow patterns.

Contaminant transport analysis revealed that, while the average removal efficiency across wetlands with the same mean residence time does not vary significantly, greater topographic variability results in a higher variability of the removal efficiency, which is more pronounced under the conditions of lower vegetation density. This suggests that while bulk performance may be predictable based on the mean residence time and the average areal removal rate, the particular spatial configuration of bed features can significantly impact treatment reliability.

It is important to note that the results presented here were obtained under the assumption of uniform vegetation stem density and diameter across the wetland. The interaction between vegetation density and water depth, which was not explored in this study, offers a valuable direction for future research. Additionally, while the shallow water and depth-averaged solute transport models provide a computationally efficient framework for simulating wetland hydraulics and treatment performance, they are based on a few simplifying assumptions. Vertical variations in flow and solute concentration are neglected, which may reduce accuracy in systems with strong stratification, non-uniform vegetation, or vertical gradients at the inlet. These limitations should be considered when interpreting the results, particularly for more complex or heterogeneous wetland systems.

Despite these limitations, the findings underscore the importance of considering bathymetric variability in wetland design. Strategically incorporating topographic diversity can enhance residence time distribution and improve contaminant removal, contributing to more effective and sustainable water treatment strategies.