Mean residence time of lagoons in shallow vegetated floodplains

Lagoons interspersed within wetlands are expected to increase the residence time of the flow in the system which, in turn, will lead to enhanced pollutant removal thus ensuring a good ecological status of the ecosystem. In this study, lagoons interspersed in vegetated wetlands have been mimicked in the laboratory to develop a theoretical model to establish the impact three major driving parameters (the vegetation density surrounding a lagoon, the depth aspect ratio [length vs. depth] of the lagoon and the circulating flow – through the Reynolds number) have on determining the residence time of the flow in the lagoon. The results indicate that, according to the maximum free available area of the flow, the presence of vegetation (Juncus maritimus) decreases the residence time. In addition, an increase in the Reynolds number of the circulating flow in the wetlands also resulted in a decrease in the lagoon residence time. Nevertheless, lagoon residence times were found to depend on the depth of the lagoon, with deeper lagoons having higher residence times. The length of the lagoon, however, was found not to affect the residence time. High lagoon residence times in either natural or constructed wetlands are desirable because they enhance pollutant removal from the water. Although, if the residence times are too long, this may lead to anoxic water conditions that could in fact threaten the wetland's ecosystem.


| INTRODUCTION
Constructed wetlands (CW) are nature-based, eco-friendly technologies that provide sustainable solutions to unique environmental problems such as removing sludge particles and organics resulting from microbial degradation (Vymazal, 2010;Vymazal, 2020;Yang et al., 2020). They have also been efficient in removing emerging contaminants such as antibiotics and antibiotic resistance gens (Chen et al., 2019;Ma et al., 2020), ibuprofen and caffeine (de Oliveira et al., 2019) and pesticides and nutrients from plant nursery runoff (McMaine et al., 2020) among others (Ilyas & van Hullebusch, 2020).
CW can be integrated into conventional treatment plants to treat potable, waste or even industrial waters (Šereš et al., 2020;Vymazal, 2010). CW facilitate the removal of chemicals from wastewater and also homogenize the physical and chemical characteristics of the flow (Schaafsma et al., 2000). As such, they offer low-cost and low-maintenance processes of removing wastewater N and P through precipitation into the soil bottom, soil adsorption of chemicals, plant uptake with organic matter accumulation, and microbial immobilization (Margalef-Martí et al., 2019). In addition, they provide new habitats for aquatic organisms, refuges for wildlife, and can be used as recreational or educational facilities . In other words, CW are eco-friendly water treatment solutions with added ecological values. CW mimic natural wetland areas, are rich in biodiversity and capable of improving the ecological status of the ecosystem via an optimal reuse of water. Although they usually require large areas of land, multilayer CW can provide a compact version that allows them to be integrated into urban areas (Nakamura et al., 2017).
Most CW present large shallow vegetated areas interspersed with deeper lagoons lower in vegetation density than the nearby shallow vegetated areas (Min & Wise, 2009). Lagoons provide physical and biochemical transformation processes that differ from other parts of the system, thus providing a more complete water treatment. The main function of a lagoon is to increase the permanence time of the water in the treatment process (Ruffino, 2015). Within lagoons, wastewater is treated following a series of physical, biological and biogeochemical natural processes, characterized by a high retention rate of algae, pH buffering and a further reduction of general sewage parameters (Steinmann et al., 2003). In ponds and wetlands, the length/width (length-to-width, L:W) aspect ratio of lagoons has been found to be critical for sediment and pollutant removal. While a high length/width aspect ratio will increase the flow path in the system and its effective retention flow time, it can also lead to overflow problems resulting from an accumulation of vegetation litter in time (Kadlec & Wallace, 2009). The U.S. Environmental Protection Agency (EPA) manual (1999) states that, in general, CW are built with width aspect ratios L:W ≤ 4:1 to avoid hydraulic problems. Persson et al. (1999) showed that for lagoons to perform efficiently, the width aspect ratio should be greater than 1.88 but less than 5. Although the width aspect ratio has been well studied, the depth of the systemdespite being recognized as a principal design factor for efficient wastewater treatmentis still much of an unknown (Ioannidou & Pearson, 2018). Most of the research has been concentrated on determining the effect depth has on flooding in wetlands, which affects plant physiology because of soil oxygen concentration, soil pH, nutrients and toxic chemical concentrations (Tsihrintzis, 2004). However, as an increase in the depth (from 0.4 to 0.6 m) of CW has been demonstrated to increase nutrient removal (Song et al., 2019), the vertical length scale of the system therefore plays an important role in determining the retention time of the flow and should be studied to optimize the performance of the CW.
It is generally agreed that the hydraulic residence time (HRT) dictates the removal efficacy of deep wetland zones and is principally connected to hydrological conditions (Dierberg et al., 2002). HRT depends on the hydrology, (i.e., water depth and flow rate through the wetland system), and also on the hydraulics characterized by the vegetation and the shape of the wetland (Johannesson et al., 2015).
The flow past a lagoon (deep zone) creates a shear layer at the interface between the flow and the deep zone which is characterized by the highest transport of momentum. In low aspect depth ratios, a main vortex dominates the flow (Jackson et al., 2013;Ouro et al., 2020;Sandoval & Mignot, 2019), while in high aspect depth ratios other secondary rotating structures can be formed. The secondary vortex is reported to increase the residence time of the flow within the deep zone (Jackson et al., 2013). Although shallow operational depths in CW lead to a flow-through regime, deep operational depths result in dissipated flow detention or ponding velocities (Ioannidou & Pearson, 2018). Consequently, it is worthwhile determining lagoon residence time in terms of flow velocity, as well as the lagoon length to depth ratio at the interface.
High nutrient loadings and their accumulation in ponds or deep zones of CW are expected to result in an increase in the pond phytoplankton stock (Aizaki et al., 1986), resulting in eutrophication. However, the role of vegetation in CW is to reduce the nutrient load not only via the direct uptake by plant roots and rhizomes, but also through microorganism action (Agudelo et al., 2012;McMaine et al., 2020). The flow through emergent vegetation in wetlands is determined by the Reynolds number for plants (Re p = ud/ν, where d is the plant diameter, u is the flow velocity and ν is the kinematic flow viscosity). For Re p < 200, two eddies are generated behind the plants, thus increasing the retention time of any contaminant in the system. However, for Re p > 200, eddies detach from the plants, producing a transport of momentum and mass downstream (Nepf et al., 1997). In addition, vegetation produces a lateral diffusion of contaminants in wetlands, consequently increasing the length of the paths that particles or contaminants will travel (i.e., increasing their residence time in the system) (Serra et al., 2004). The increase in the retention time of the contaminants around plant roots and rhizomes is expected to enhance the uptake of pollutants and the sedimentation of particles (Soler et al., 2017) and, therefore, increase the effectiveness of the treatment. The presence of macrophytes in the littoral areas of lagoons modifies the quality of the lagoon water, as well as the sedimentary rates observed (Pawlikowski & Kornijów, 2019). In contrast, and as shown in the case of the Vistula Lagoon in Russia, the low impact the littoral vegetation had was attributed to the low canopy density and also to the presence of bare soil areas interspersed within the vegetation (Viaroli et al., 2008). Vegetated areas in CW have been found to produce short-circuiting. This is due to fast flowpaths experiencing longitudinal dispersion but not producing flow exchange with dense surrounding vegetation (Lightbody, Nepf & Bays, 2009).
Most of the research to date has concentrated on the type of vegetation that best optimizes the uptake of nutrients and the reduction of contaminants (Ghosh & Gopal, 2010) in CW. Deep zones situated transversally to vegetated marsh areas can offset short-circuiting by reducing flow velocity and producing lateral mixing, and by reducing the probability that certain flowpaths prevail along the whole wetland (Lightbody et al., 2009). Despite these studies, there is still a gap in the knowledge about the effects vegetation density has on modifying hydrodynamics and water quality in the different sized lagoons interspersed within the wetlands.
In this study, the mean residence time of a lagoon interspersed within a wetland has been evaluated in terms of the lagoon's structure (depth aspect ratio) and the flow regime (Reynolds number), along with the effect the emergent vegetation has on the residence time in the lagoon. The study has been performed using a laboratory-scale model that mimics scales and flow conditions found in actual wetlandpond systems. The results from the study provide a quantitative understanding of residence time in wetland lagoons in relation to wetland vegetation, flow, and shape which, in turn, may help engineers to design more efficient and cost-effective water systems.

| The experimental conditions tested
Experiments were carried out in a laboratory straight flume measuring 500 cm × 40 cm × 50 cm (Table 1). At the entrance to the flume, a honeycomb was used to straighten the flow produced at the inlet (Nepf et al., 1997), while at the outlet of the flume, an 18 cm high gate ensured a constant flow level. Two platforms measuring 120 cm long at the base, 100 cm long at the top and 10 cm high, were constructed and placed in the flume to create a deep zone between them that would represent a V-shaped lagoon (Figure 1(a)-(c)). Next, 100 cm × 40 cm × 1 cm perforated bases covered with 0.6 cm diameter holes, where the plant stems would be distributed, were placed on each platform. The height of the lagoon was considered to be from the top of the perforated platforms down to the bed of the flume.
Two water heights were considered: H = 5 and 11 cm. To study the shallow lagoon with H = 5 cm, a new base was positioned inside the lagoon at a height of 6 cm from the bed of the flume. To study different lagoon lengths, the second platform was moved longitudinally along the flume to different positions along its main axis. The vegetation in the shallow areas consisted of stems of real Juncus maritimus vegetation (Figures 1(b),(c)), typical of river floodplain zones and saltmarshes, which was collected near the Ter river (Catalonia, North-East Spain). Seven canopy densities were considered (n = 0, 354, 707, 884, 1061, 1415, and 1768 plants m −2 ) in accordance with the range in the canopy densities found in saltmarshes (Leonard & Luther, 1995;Leonard, Wren, Beavers, Lane, & Service NP, 2002). From the canopy density (n) and the value of the stem diameter, d, the percentage of the area covered by the vegetation in the shallow vegetated areas, (i.e., the solid plant fraction [SPF = nπd 2 /4]), can be calculated . These canopy densities corresponded to solid plant fractions SPF = 0, 1, 2, 2.5, 3, 4 and 5, respectively. Next, the vegetation was randomly distributed using a computer function Ros et al., 2014;Serra et al., 2001) and stems were cut to 20 cm long to ensure that the vegetation was emergent. Three to four stems were attached and tied with tape to build a 0.6 cm thick plant that fitted into the holes that had been previously drilled into the platforms. The frontal area of the vegetation can be calculated as (h w − H)dN (where N is the total number of stems, Note: SPF is the solid plant fraction of the shallow vegetated areas, ad is the frontal area of the vegetation per unit volume, H is the depth of the lagoon, L is the length of the base of the lagoon, u 0 is the velocity at the inlet of the flume and H/(L + 2L s ) is the aspect ratio of the lagoon, where L s is the length of the slopes (Figure 1). h w is the water depth from the flume base, H is the lagoon depth and d is the stem diameter). The total volume in the vegetated region is The volume of the vegetation opposing the flow can be considered as ad (Nepf et al., 1997) (Table 1). Therefore, 1 − ad represents the porosity of the vegetated area, that is, the volume of the free void space available for the fluid. To cover a wide range of canopy densities, lagoon water lengths and depths and flow velocities at the inlet of the flume, a total of 40experiments (Table 1) were carried out.

| Residence time in the lagoon
The residence time in the lagoon (τ) was calculated from the vertical velocity components at the interface (z int , Figure 1) following the method described by Weitbrecht and Jirka (2001), where τ could be determined from: where Q int is the exchange volume per unit time through the interface and V is the volume of the lagoon. The exchange volume per unit time through the interface can be calculated by: where W is the width of the lagoon (equal to the width of the flume W = 40 cm), L is the length of the lagoon at the base, L s is the length of the lagoon slopes (i.e., the length of the lagoon at the interface is L + 2L s ) and the volume of the cavity V can be determined by: where H is the depth of the lagoon (Figure 1). E is the flux of water from the lagoon to the main stream through the interface and can be calculated as: where n is the number of measuring points along the lagoon interface and w is the mean vertical velocity measured at each interface position. By putting Equations (2) and (3) into (1), we obtain the residence time in the lagoon τ as: The residence time τ in the lagoon was calculated from Equation (5).
To obtain a model that describes the dependence of τ with the main variables of the system, the Buckingham pi-theorem was applied. This theorem is based on the assumption that physical laws should be independent of the dimensions used to express the variables (Evans, 1972). The model is based on finding the relationship between the non-dimensional parameters of the problem, which can be expressed from the number k of dependent variables with m physical dimensions.
According to the definition, in the present study there are six independent variables (τ, ad, u 0 , H and L + 2L s , W) and two physical dimensions (length and time). Therefore, four (k-m) non-dimensional parameters can be written The first non-dimensional parameter represents the balance between the mean residence time and the time for a parcel of fluid flowing at the velocity of the main channel to travel a distance equivalent to the length of the interface (L + 2L s ). The second nondimensional parameter is the porosity of the vegetated area, that is, the free area available for the flow. The third parameter corresponds to the aspect ratio of the lagoon and the fourth parameter to the Reynolds number that characterizes the regime of the fluid.

| Reynolds stress
The turbulent velocity components were obtained by subtracting the mean of the velocity from each instantaneous velocity as: where u 0 is the turbulent velocity for the x velocity component, u i is the instantaneous velocity and u is the mean velocity in the x-axis.
The same expression can be applied to the y and z velocity components and the turbulent velocities in the y and z axis can be calculated as v 0 and w 0 , respectively. The root mean square value of the turbulent velocities has been considered as the turbulent components of the velocity (u 0 , v 0 , w 0 ). Therefore, the Reynolds stress can be calculated as -u 0 w 0 . In the plots, the temporal mean Reynolds stress − u 0 w 0 will be represented and named hereafter as -u 0 w 0 . The Reynolds stress averaged along different points of measurement will be named as <−u 0 w 0 > .

| Scaling of the model wetland
Therefore, where λ L is the ratio between the length scale of the CW and the model. The ratio between the flow rates can be also calculated as: Considering the total length of the model formed by two shallow veg- The aspect ratio of the lagoons studied ranged between 0.09 and .44 (Table 1). In the CW case considered, deep zones with different sizes can be found with aspect ratios in the range of 0.03 to 0.27, therefore, partially in the range of aspect ratios studied in the model.

| RESULTS
Within the lagoon, velocity profiles indicate that flow velocity decreased downwards, with its highest value being in the upper part of the water column and its lowest value at the base of the lagoon.
Positive   Above the lagoon, and from the profiles taken at the centre of the cavity, the flow velocity was greater as the lagoon length decreased. This is because as the lagoon becomes smaller, its centre is situated closer to the shallow region where the velocity is greater than u 0 (measured at x 0 , flume inlet), since the vegetated zone is shallower. In addition, plants produced an additional reduction in the free area available for the fluid through the vegetation and, in turn, an increase in the velocity of the flow in the lagoon, that is, short-circuiting. The increased flow effect due to the adjacent plants was also observed by Nepf et al. (1997)  found from low to high discharges following through a submerged patch of flexible vegetation (Folkard, 2005). This has also been observed in flow through lateral surface storage zones (Sandoval & Mignot, 2019). The increase in the Reynolds stress after a patch of emergent vegetation with the canopy density was also observed by Montakhab et al. (2015). In their work, the Reynolds stress after the vegetated patch decreased with distance which aligns with the findings of the present study. In contrast, Maji et al. (2017) found a decrease in the Reynolds stress after a patch of emergent vegetation.
In their case, however, the vegetated patch did not cover the whole width of the flume, thus producing an increase in the velocity and the Reynolds stress in the lateral area free of plants and a decrease behind the plants where the velocity of the flow was also reduced. In the present study, low canopy densities (ad ≤ 0.012) did not produce an increase in the Reynolds stress, whereas for ad ≥ 0.012, the Reynolds F I G U R E 6 Non-dimensional residence time of the lagoon (τu 0 / (L + 2L s )) versus (H/(L + 2L s ))Re 0.3 for the cases without plants (a) and versus (1 − ad)(H/(L + 2L s ))Re 0.3 for the cases with plants (b). The line represents the best fit linear trend to the data represented in each plot stress increased linearly with the canopy density. Therefore, density vegetation below 354 shoots m −2 (corresponding to ad = 0.012) produced similar behaviour to that of the non-vegetated case. In addition, the aspect ratio of the lagoon did not produce changes in the mean value of the Reynolds stress of the lagoon indicating, therefore, that a deeper lagoon did not affect the Reynolds stress at the interface compared to a shallower lagoon for the same lagoon depth. Hence, the main parameters determining the Reynolds stress were both the flow velocity and the canopy density.
The mean vertical flow velocity at the interface between the cavity and the water above increases from the leading edge of the cavity towards its centre, with negative velocities indicating that the flow enters the cavity zone in the first half of the lagoon. From x/ (L + 2L s ) = 0.55 to the trailing edge of the cavity, the vertical velocity decreased progressively and increased to positive velocities towards the trailing edge, indicating that the flow was directed upwards, out of the lagoon. The pattern of the circulation of the flow within a cavity has been found to depend on its shape (Jackson et al., 2015;Weitbrecht & Jirka, 2001). For example, in squared lateral cavities, Ouro et al. (2020) found mean flow velocities across the cavity and directed outwards from the cavity at the leading edge and towards the cavity at the trailing edge, i.e., following a clockwise circulation.
This is contrary to what has been found in the present study. This might be because the cavity studied here is vertical while in the other studies it was lateral. In a vertical cavity, it is expected that, due to gravity, the flow from the shallow region deepens as soon as it reaches the cavity, producing a counterclockwise circulation of the flow, that is, directed outwards at the trailing edge of the cavity and inwards at the leading edge of the cavity.
The non-dimensional mean residence time in the lagoon was found to depend on three parameters that characterize  (Drost et al., 2014;Jackson et al., 2012). However, the residence time did depend on the depth of the lagoon in such a way that deeper lagoons are expected to have higher residence times. Nevertheless, in some cases climatic conditions such as air temperature or wind might result in a thermal stratification of the lagoon (Kellner & Pires, 2002). The presence of stratification has been found to reduce the volume of the active zones from winter (without stratification) to summer (with stratification) from 70% to 20%, respectively (Torres et al., 1997). Moreover, the  (Jadhav & Buchberger, 1995). In such cases, considering the linear relationship found here, the reduction in the residence time in the lagoon would be up to 15% due to the presence of plants. A reduction in the mean residence time could prevent the accumulation of pollutants in lagoons, thus maintaining the biodiversity and richness of macroinvertebrates thriving in the water column (Sun et al., 2019).
The presence of vegetation has also been related to the increase in the biodiversity in ponds (Sun et al., 2019).
The results for the hydraulic residence time from the laboratory model mimicking field lagoons can be used to predict the experimental hydraulic residence times for the case of the Control and Baffled lagoons in the study from Ioannidou and Pearson (2018). and lagoon depth. These parameters must be considered crucial in order to provide efficient water treatment for pollutants. In the case where the reaction time of the pollutants is greater than the mean residence time of the water in the system, pollutants will be only partially retained by the system (Gajewska et al., 2020). However, in the case where the reaction time is lower than the mean residence time of the water in the system, the pollutants will be retained in the system. Therefore, at first glance, a very long residence time could be desirable to provide the best efficiency of the system. However, many biological processes that take place in a lagoon and in the shallow areas rely on the activity of numerous aquatic organisms (bacteria, algae, zooplankton, plants, plant roots) that, in turn, require oxygenated water. Long residence times could lead to anoxic conditions within the lagoon that might, therefore, threaten the organisms that inhabit the ecosystem (Kennish & Paerl, 2010). Taking into account all these previous considerations, an appropriate mean residence time of the flow in the system is needed. One that will not only guarantee efficient wastewater treatment but also provide a safe environment for all the organisms living in the habitat. ORCID Teresa Serra https://orcid.org/0000-0002-6075-5849