Impact of Wind on Stormwater Pond Particulate Removal

Spherical particles with diameter, $d$, and specific density, $s$, are generally assumed to settle according to Stokes law (Andral et al. 1999), with a speed ofHere, $g$ = gravitational acceleration and $\nu$ = kinematic viscosity of water. The characteristic timescale for settling is the time to travel over the water depth, $H$, i.e.

The settling term, $S$, in Eq. (1) depends on the vertical Peclet number, which describes the strength of particle deposition relative to vertical mixing, i.e.

The depth-averaged vertical diffusion coefficient in the water column scales on a representative vertical shear velocity, $u_{*}$, as

In a wind-dominated system, momentum transfer is driven by the surface shear velocity:Here, ${\tau }_s$ = fully developed wind shear stress; $W_{10}$ = measured wind speed at a 10-m elevation over the ground; and $\rho$ = density of water. Eq. (6) represents a theoretical maximum. The wind response in small systems may be lower due to fetch limitations and sheltering. To account for this, the representative shear stress may be taken as the average of surface and bed shear velocity produced by wind-driven currents, or

The coefficient $k_1$ is affected by land slope and vegetation cover around the pond. It can be assessed from velocity measurements in the pond, as discussed later in this paper [Eq. (35)]. Eq. (4) may be rewritten as

If $P{e}_z\ge 20$, then particles are unaffected by vertical mixing. The settling term is a constant, resulting in a linear deposition of particles with time (Dhamotharan et al. 1981). Alternatively, if $P{e}_z\le 0.2$, then particles are continuously redistributed over depth and the settling term is represented as a first order decay.

The key parameter governing the removal in a stormwater pond is the particle fall number (Li et al. 2007). Defined as the ratio between the nominal residence time, $t_n$, and particle settling time, i.e.it compares the strength of advective transport [left hand side, Eq. (1)] to settling, $S$. The nominal residence time represents the average time particles stay in the system and is the ratio between the pond volume, $V$, and throughflow rate, $Q$, i.e.

In transient storage systems, $Q$ may be taken as the average of inflow rate, $Q_{\text{in}}$, and outflow rate, $Q_{\text{out}}$.

The particle fall number may be written as

The governing hydraulic parameter determining the removal of particles of different diameters is the residence time to water depth, $t_n/H$, which will be referred to hereafter as the inverse overflow rate, defined as the ratio of surface area and throughflows, $A/Q$, which is not affected by water depth.

The parameter governing the hydraulic regime in Eq. (1) is the longitudinal Peclet number, which compares the strength of transport by advection to diffusion ($U_{x}L/D_x$). In the context of particulate removal, the advective speed is that of throughflows across width and depth ($U_x=Q/BH$). Incorporating longitudinal dispersion associated with vertical shear, a conservative estimate of the Peclet number can be taken as (see Andradóttir and Mortamet 2016)

If $P{e}_x<2$, then dispersion dominates throughflows, and the pond mimics a continuously stirred reactor more than plug flow (Tsai and Chen 2013). The Peclet number can be rewritten in terms of shear bed velocity and inverse overflow rate as

${Pe}_x$ is therefore sensitive to the pond length-to-depth aspect ratio, $L/H$.

Sediments from the bed may be resuspended into the water column if the wind-induced bed shear stress, ${\tau }_b$, exceeds the critical shear stress for erosion, ${\tau }_{cr}$, i.e.

The critical shear stress can be estimated based on empirical relationships, such as the Fischenich (2001) formula for silt

A friction angle, $\varphi =35°$, is representative of fine sediments in tailing ponds (Kachhwal et al. 2012). The nondimensional grain size diameter is

The erosion rate of suspended sediments from the bottom may be represented as (Bengtsson and Hellström 1992)

The erosion coefficient, $C_e$ ($\mathrm{g}/{\mathrm{m}}^2/\mathrm{h}$), and exponent, $n=1–2$, depend on site characteristics, such as bed sediments, grain size, and consolidation time. A coupled 3D sediment transport-hydrodynamic model accounting for spatial variability in water depth and wind driven waves may be needed to assess erosion accurately in small, fetch-limited systems (e.g., Bentzen et al. 2009; Bentzen 2010).

An analytical steady state particulate removal model that accounts sequentially for various wind effects in a stormwater pond was derived from Eq. (1). The three key model input parameters were (1) particle diameter $d$; (2) inverse overflow rate; $t_n/H$; and (3) wind shear bed velocity $u_{*b}$. These parameters, along with a selection of others, allow assessing the nondimensional parameters presented in the theoretical background section (Table 1).

The total removal efficiency was assessed by solving Eq. (1) for the steady state outflow concentration, $C_{\text{out}}$, and assess how much it deviated from that of the inflow, $C_{\text{in}}$, i.e.

Fig. 1 plots the hydraulic removal efficiency ($C_{*}\ll C_{\text{in}}$) as a function of the particle fall number for four different flow regimes. In the ideal case of no wind [NW, Eq. (19)], all particles are removed within $N_f=1$. Wind stirring (WS) [Eq. (20)] reduces the particle treatment by 37% for $N_f=1$. To achieve an 80 and 95% particle removal requires $N_f=1.6$ and 3, respectively. As $N_f$ is linearly correlated with a pond surface area [Eq. (11)], a 1.6- to 3-times-larger surface area is required to achieve high treatment levels when WS is present, as compared to when it is not. Wind-induced basin-scale mixing [BSM, Eq. (21)] further impairs treatment performance, reducing the removal efficiency by an additional 10–20% from that of the WS model for $N_f=1–10$. An 80 and 95% removal of particles is attained at $N_f=4$ and 19. Accounting for the effective volume [EV, Eq. (23)], using $e=0.6$ from Bentzen et al. (2008) numerical tracer experiments of a wind-dominated stormwater pond reduces the treatment efficiency more moderately, or by an additional 13 and 5% from the BSM model for $N_f=1$ and 10, respectively. $N_f=5.6$ and 30 are required to achieve 80 and 95% removal, respectively.

Fig. 2 explores the effect of wind driven shear bed velocity on the hydraulic removal of different particle sizes for a range of hydraulic loading conditions. At low winds ($SCI\ge 1$), removal efficiency is simulated with the NW model [Eq. (19)]. Once wind is strong enough to promote short circuiting ($SCI<1$), the SC model for exponentially depositing particles [$P{e}_z\le 0.2$, Eq. (27)], or its weighted average with the model for linearly depositing particles [$P{e}_z\approx 20$, Eq. (24)], is used. When wind is strong enough to promote longitudinal mixing ($P{e}_x<2$), the EV model [Eq. (23)] applies. For simplicity, $e$ is assumed independent of wind strength [Eq. (28)]. Fig. 2(a) shows that limited wind is required to fully mix clay particles ($d\le 2\mathrm{\mu m}$) in the vertical ($P{e}_z\le 0.2$ at $u_{*b}\approx 0$). The removal efficiency drops from 10–80% to 6–33% during wind for $t_n/H=0.5–4\mathrm{day}/\mathrm{m}$. Once the shear bed velocity exceeds the critical value of $0.6\mathrm{cm}/\mathrm{s}$, wind driven currents and waves may resuspend fine materials collected in the shallow sections, further impairing the particulate treatment [not shown, referring to Eqs. (17), (29), and (30). Fig. 2(b) suggests that wind could also severely constrain the removal of fine silt from 90–100% (NW) to 35–81% (EV). A higher shear bed stress is required to remobilize these particles from the bed. Figs. 2(c and d) suggest that a considerable wind may be needed to vertically mix medium ($u_{*b}>0.2\mathrm{cm}/\mathrm{s}$) and coarse silt ($u_{*b}>0.5\mathrm{cm}/\mathrm{s}$). Winds lower the removal efficiency moderately to 72% for medium silt, and 86% for coarse silt according to the EV model for $t_n/H=0.5\mathrm{day}/\mathrm{m}$. To summarize, wind mixing most severely affects the removal of small silt and clay particles ($<6\mathrm{\mu m}$). Such particles may require weeks to settle. Consequently, fine solids may be only partially removed during a runoff event that lasts hours or one day, contributing to so-called wash loads (or background concentration), both during wet and dry periods. Removal of small particles is important because of their higher toxicity and higher pollutant concentrations (Sansalone and Buchberger 1997). In a structurally well designed pond, wind may constrain up to 30% of the removal of medium silt particles, which are representative of medium grain diameter in runoff. Alternatively, in a pond with high width-to-length ratio or short separation between inlet and outlet, wind mixing may improve the removal efficiency by reducing the pond’s inherent structural short-circuiting.

Eqs. (23) and (30) represent a physically based analytical model that may be used to predict removal efficiencies on an event basis in a small wind-dominated stormwater pond where basin-scale mixing and vertical stirring are effective ($P{e}_x<2$, $P{e}_z\le 0.2$). The key input data are (1) particle size distribution (PSD) of entering runoff; (2) hydraulic flow rates entering the pond ($Q_{\text{in},t}$), and preferably also out of the pond ($Q_{\text{in},t}$); and (3) effective volume, $e$, and background concentration, $C_{*}$, summarizing wind-effects at bulk level. As a first order approximation, $e$ may be taken as 60% based on Bentzen et al. (2008) numerical tracer experiments. The background concentration, however, varies with inflowing TSS and biochemical factors (Kadlec 2000; Barrett 2008), as well as wind [Eqs. (29) and (17)]. Therefore, the model should preferably be tested against field measurements.

The forward difference solution for concentration at the outlet for a given time step, $t$, associated with particle size classes, $j$, representing a ratio of total mass, $PSDj$, is

The parameters $e$ and $C_{*}$ are assumed to be time invariant, which is not necessarily the case (see, e.g., Wong et al. 2006). By fitting the numerical solutions to measured TSS in the outflow, the model can be calibrated for $e$ and $C_{*}$ (and initial concentration $C_0$) based on the mean diameter $d_{50}$, for which the PSD of the entering runoff as well as background concentrations is equal to one. Alternatively, particle size classes can be simulated separately and summed up as

The Víkurvegur wet retention pond treats the surface runoff from the 9-ha mixed residential and light commercial suburb Grafarholt [Reykjavík, Iceland; Fig. 3(a)]. Accounting for an average runoff coefficient of 0.5, the catchment is 4.5 reduced hectares (rha). The oval pond is 112 m long, 26 m wide, and with a design depth of 2 m. A length-to-width ratio, $L/B\approx 4:1$, ensures high effective volume (Thackston et al. 1987), i.e.

The water inlet situated on the southern end of the pond consists of a submerged 600-mm diameter concrete pipe intruding about 10 m into the pond. The outlet of the pond, situated on the northern end to reduce short-circuiting, consists of a stone trap, 500-mm PEH pipe, and V-shaped overflow structure. The slanted ($1:3$) side walls are lined with large stones for wave and scour protection. The pond is in a traditional sense overdesigned with a surface area of $650{\mathrm{m}}^2$ per reduced hectare, a result of a flow diversion made after the pond was built.

The water depth was measured manually with a pole with an accuracy of $\pm 2\mathrm{cm}$ on April 23, 2009 (reference water level: 52.14 m a.s.l., 0.09 m higher than the design water level), at thirteen stations at 5 m intervals across three transects [dots, Fig. 3(b)]. A thick layer of loose bottom sediments was detected along the transect closest to the inlet. The average water depth there was $1.61\pm 0.11\mathrm{m}$, with a maximum depth of 1.72 m, indicative of a 38-cm thick sediment layer. In comparison, the measurement probe hit solid ground at the center of the pond near its outlet, indicative of limited sediment accumulation. The average water depth of the pond was assessed as 1.7 m.

Removal of TSS during four runoff events (Fig. 4), representing varying wind and hydraulic loadings, is summarized in Table 3. The start of a throughflow event was taken when hourly inflow exceeded $2.5\mathrm{L}/\mathrm{s}$, and the end when $Q$ dropped below 2 and $1\mathrm{L}/\mathrm{s}$ for the winter and spring storms, respectively. The outflows represent 15–94% of the inflowing volume, the lower bound reflecting the difficulties of sampling water during the long tails of the outflows. Event mean metrics were calculated as weighted averages with throughflows.

Table 3 shows that wind-induced short-circuiting was predicted to occur within 2–6 h, corresponding to $SCI<0.04$, which is an order of magnitude lower than documented in stormwater ponds driven solely by throughflows (Persson 2000). The median size particles were vertically mixed during all events as $P{e}_z\le 0.2$. While entering pollution may be initially transported like plug flow with circulatory currents, it is well mixed within the time it resides within the pond reflected in $P{e}_x<2$. Resuspension of small clay size particles ($d_{10}=2.2\mathrm{\mu m}$) was not likely in the center of the pond as ${\chi }_{10}<1$. These wind metrics support the use of the EV model with no background concentration ($C_{*}=0$) as a starting point.

The three columns to the right consider the pond’s treatment performance. The event mean particle fall number ranged from 11 to 70, for which the analytical EV model [Eq. (23)] with 60% effective volume based on Bentzen et al. (2008) predicts over 87% hydraulic removal efficiency. The measured event mean removal efficiency, based on the ratio of event mean TSS concentrations in the in- and outflow ranged, however, from 88% during the February event to negative values during the low-intensity, long-duration May 10 storm, suggesting that the pond was a source of solids during that event. Background concentrations are, therefore, important in this pond.