Effects of vegetation on flow through free water surface wetlands

ECOLOGICAL ENGINEERING

ELSEVIER

Ecological Engineering 5 (1995) 481-496

Effects of vegetation on flow through free water surface wetlands Ranjit S. Jadhav, Steven G. Buchberger

*

Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati, OH 45221-0071, USA Received 23 September 1994; accepted 6 April 1995

Abstract The one-dimensional Saint-Venant equations are modified to account for stem drag and volumetric displacement effects of dense emergent plants on free surface flow. The modified equations are solved with an implicit finite difference method to give velocities and depths for shallow flows through a vegetated wetland channel. Estimated flow profiles are used to investigate how vegetation density, downstream boundaries and aspect ratio affect detention time, an important parameter in determining nutrient and pollutant removal efficiencies of wetlands constructed to treat wastewater. Results show that free water surface wetlands may exhibit static, neutral or dynamic behavior. Under static conditions, the wetland behaves like a pond in which displacement effects caused by submerged plant mass invariably decrease detention times. Under dynamic conditions, stem drag induced by aquatic plants predominates and wetland detention times increase with vegetation density. These opposing responses are separated by a narrow neutral condition where the presence of vegetation has virtually no net effect on detention time. For a given flow rate and surface area, detention times and hence treatment efficiencies in vegetated free water surface wetlands can be managed to some degree by adjusting the downstream control or by changing the aspect ratio. Keywords: Saint-Venant equations; Constructed wetlands; Detention time ; Vegetated channels; Wetland hydrodynamics

1. Introduction C o n s t r u c t e d w e t l a n d s h o l d p r o m i s e as cost-effective passive a l t e r n a t i v e s to t r e a t s o m e t y p e s o f w a s t e w a t e r ( U S E n v i r o n m e n t a l P r o t e c t i o n A g e n c y , 1988). W e t l a n d

* Corresponding author. Elsevier Science B.V. SSDI 0925-8574(95)00039-9

482

R.S. Jadhav, S.G. Buchberger /Ecological Engineering 5 (1995) 481-496

systems improve water quality through natural biogeochemical mechanisms which are mediated, in part, by local climate and hydrologic processes. Presently, about 300 constructed wetland systems in North America treat waste from municipal, industrial and agricultural point and nonpoint sources (Knight et al., 1994). Constructed wetlands are classified as either free water surface (FWS) or subsurface flow (SF) systems. FWS systems transport wastewater at shallow depths and low velocities through lined prismatic open channels; SF systems convey wastewater through gravel filled trenches. Wetland treatment systems contain dense stands of emergent aquatic vegetation intentionally introduced to promote pollutant degradation. These plants provide a substrate for microbial activity, translocate oxygen to roots and rhizomes and to some extent assimilate nutrients and other constituents present in the wastewater (Brix, 1993). In addition, aquatic macrophytes provide shading to suppress algae growth, add aesthetic appeal to wetland treatment systems and may offer food and habitat to native wildlife (Hammer, 1992). Besides playing an important indirect role in pollutant removal, aquatic plants influence the flow of water through the wetland. Vegetative stem drag increases flow resistance beyond the friction offered by the wetland channel bed. Stem drag effects are especially pronounced in shallow channels and marshland areas (Shih and Rahi, 1982). Conversely, during precipitation events, vegetation may decrease flow resistance by shielding the water surface from direct rainfall impact which otherwise would augment flow resistance at shallow depths (Yoon and Wenzel, 1971). Aquatic plants occupy space. Hence, wetland vegetation obstructs the cross-sectional area and reduces the bottom wetted perimeter available for flow (Pitlo and Dawson, 1990). Porosities ranging from 86 to 98% have been measured at vegetated wetlands operated by TVA (Watson and Hobson, 1989). Finally, aquatic plants may reduce free water surface evaporation by intercepting solar radiation and suppressing wind speeds near the air-water interface (Eisenlohr, 1966) though this effect may be offset by transpiration losses. One issue that has not been addressed concerns the effect of emergent vegetation on wetland detention time. Detention time is an important parameter in predicting nutrient and pollutant removal efficiencies of constructed wetlands (Reed et al., 1995). In this paper, we present and solve a one-dimensional model for unsteady, nonuniform flow through dense vegetation in a FWS constructed wetland. The proposed model is a modified version of the classic Saint-Venant equations and accounts for the volume occupied by plant mass and the drag induced by vegetation stems. These effects are parameterized using measurable vegetation characteristics. With the aid of this model, we examine how vegetation density, downstream boundaries, and the wetland aspect ratio affect hydraulic detention times in FWS wetlands constructed for wastewater treatment. 2. Present methods

Resistance to flow in vegetated wetlands can be attributed to bed friction and stem drag. Often both effects are lumped together and characterized with a single

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483

bulk roughness term. For instance, Manning's equation with a high n value has been suggested to compute the flow rate through vegetated FWS wetlands (US Department of Agriculture, 1992). Petryk and Bosmajian (1975) give guidance to estimate Manning's n for steady uniform flow through a vegetated channel. Shih and Rahi (1982) report composite n values as high as 0.60 for shallow flow through subtropical marshes. Owing to nonuniform water surface profiles, very slow velocities and the presence of emergent aquatic plants, serious questions arise about the validity of applying Manning's equation to shallow flows over vegetated surfaces (Turner et al., 1978). While Manning's equation with an inflated roughness coefficient is expedient, this approach does not properly represent the effects of emergent vegetation nor the influence of downstream boundaries on the wetland flow profile. To overcome these inadequacies, alternative empirical friction laws have been proposed (Hammer and Kadlec, 1986; Maheshwari and McMahon, 1992). These empirical relations, however, need site specific calibration and hence may have limited utility in models to simulate and optimize constructed wetlands for wastewater treatment (Buchberger and Shaw, 1995). 3. Model development

As shown in Fig. 1, the FWS wetland is visualized as a prismatic open channel partially filled with emergent vegetation. The vegetation is represented by a

Z~ ~

÷ ~--~--Qxdx -

d

x

~

y-~--t~y dx x

Datum

(a) Elevation View

(b) Cross Section Fig. I. Blow through a wetland with emergentvegetation.

484

R.S.

Jadhav, S.G. Buchberger / Ecological Engineering 5 (1995) 481-496

random array of unbranched rigid vertical cylinders rooted in the channel floor and protruding above the water surface. Since most FWS constructed wetlands have simple linear geometries, channel flow is assumed to be one-dimensional along a straight longitudinal axis. Due to the presence of vegetation, velocity profiles tend to be uniform in the vertical direction (Strelkoff and Fangrneier, 1974). 3.1. Governing equations

A modified form of the classic Saint-Venant equations is presented to more accurately reflect flow conditions expected in a densely vegetated FWS wetland. The modified one-dimensional continuity equation can be written (Jadhav, 1994) OQ --

Ox

o + --(7/A)

= 0

~x

(1)

while the modified momentum equation is

oo (o )

m+__ at Ox ~

+flAg

~ ox

-So+

- + g(,r/A) 3

2g(nA) 3

=0

(2)

where Q A x y t SO Sf g

= = = = = = = = = = = = =

flow (m3/s) channel cross-sectional area (m 2) longitudinal distance along the channel (m) water depth (m) time (s) longitudinal slope of the channel bottom friction slope gravitational acceleration ( m / s 2) porosity effective wetted perimeter (m) bottom width of the wetland channel (m) average stem diameter (m) vegetation density, number of stems per unit area (m-Z) drag coefficient associated with bed friction = drag coefficient associated with stem friction

Pe B D m

Cdb

=

Cds

Porosity represents the percentage of the total volume below the free water surface that is occupied by water. For a wide rectangular channel, porosity can be written 7/"

~7 = 1 - ~ r n D 2

(3)

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487

increase in wetland detention time because the governing factor is the volume rather than the depth of water in the channel. Two opposing outcomes must be considered: (1) a "static" effect that is independent of velocity and (2) a "dynamic" effect that occurs only when water is moving. The static effect reduces the volume of water in the channel because plant mass occupies space. Conversely, the dynamic effect increases the volume of water because flow depths rise in response to resistance induced by stem drag. Vegetation, therefore, can either increase or decrease detention time depending on whether the static or dynamic effect predominates. The behavior depends on interactions among flow rate, vegetation density and downstream boundary controls. To illustrate, we compare the effect of vegetation density on the average depth and detention time for two examples: (1) flow in a simple open channel reach free of boundary effects and (2) flow through a FWS wetland controlled by a downstream weir spanning the full width of the channel. Both cases are identical in dimensions and frictional properties. Based on a recent inventory of constructed wetlands (Knight et al., 1994), the following parameters are assumed: length, L -- 500 m; width, B = 50 m; longitudinal slope, S O= 0.1%; Manning's n for bed friction, n = 0.10; coefficient of drag for the stems, Cds = 1.0; average stem diameter, D--0.02 m; and vegetation densities ranging from rn = 0 to 500 stems/m 2. This combination of D and m yields channel porosities between r / = 85 to 100%, typical of values observed in the field. A known constant inflow is introduced at the upstream boundary. The depth of water varies in each case depending upon the vegetation parameters and downstream boundary. E x a m p l e 1: Simple Open C h a n n e l R e a c h : For steady uniform flow, Eq. (2) simplifies to, q=

J

Cdb n + 2

(6) + ½CdsmDy

where q = Q / B is the discharge per unit width. When rn = 0 Eq. (6) reduces to a Manning-Chezy type rating equation, q = a y t3 where ot and /3 are rating curve parameters. From this expression, water depths can be calculated for a given discharge and vegetation density. Using Eq. (5) with V = BLy, the corresponding detention times for steady uniform flow are ~yL 0 = - -

(7)

yo 0 q=V

(8)

q Results, plotted in Fig. 3, lead to three general observations. First, for a given discharge, the detention time O increases with increasing vegetation density, m. From Eq. (7), this implies ~TY> Yo where Y0 is the water depth supported by bed friction only under steady uniform flow in a channel without vegetation. To see this, note that for a wide open channel free of vegetation (m = 0 and rt = 1), Eq. (6) becomes

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0.25

"O

0,15-0' ...................................................................................................... 2

O

0.1 ~

....................................................................................................................................................

t~

0.05t ............................................................................ 0

0

50

160 l g0 260 250 360 ago 460 4~0 500 Vegetation density(stems/m2)

Fig. 3. Detentiontimefor uniformflowin a simpleopen channel.

Eqs. (6) and (8) can be equated and rearranged to give Yo

Yo

rl

1 - --mD 2 4

(9)

The left-hand side of the inequality represents the actual depth attained by water moving through the vegetated channel. The expressions on the right hand side can be viewed as the standing level that results when a water column of height yo is placed in a control volume of porosity r/. Eq. (9) shows that the actual water depth supported by bed friction and stem drag always exceeds the displaced water depth in a vegetated channel subject to steady uniform flow. Hence dynamic effects prevail over static effects in this example and, by virtue of Eq. (7), detention times must increase with an increase in vegetation density as seen in Fig. 3. Second, for a given vegetation density, the detention time O decreases as the discharge increases. From Eq. (7) this implies that the discharge per unit width q grows faster than the depth y. Jadhav (1994) shows that the elasticity of discharge with respect to depth, fl, exceeds unity

dq/q

5

A(y) + 2 K ( y )

fl=-dy/y

3

1 +K(y)

(lo)

where A(y)=Y/Pe is the ratio of flow depth to the effective wetted perimeter (defined in Eq. 4) and K ( y ) is a dimensionless function that measures the relative

R.S. Jadhav, S.G. Buchberger / Ecological Engineering 5 (1995) 481-496

485

with m and D defined in Eq. (2). It is assumed that porosity is independent of water depth. The effective wetted perimeter Pe for a wide rectangular channel is ee ~" ~ B + 2y

(4)

The model separates the bed friction from the stem drag. This distinction has already been considered by Einstein and Banks (1950), Weltz et al. (1992) and Kao and Barfield (1978) for shallow overland flow and by Kadlec (1990) for a wetland situation. Additional details on the representation of resistance to flow are given by Jadhav (1994).

4. Model verification

No closed-form solution is available for the governing equations. Therefore, a weighted four-point implicit finite difference method (Fread, 1973) is employed to solve Eqs. (1) and (2) with boundary conditions specified depending on the problem. Two examples from the literature are used to verify the model. One is based on the conventional Saint-Venant formulation (m = 0) and the other uses the modified equations (rn > 0) incorporating stem drag.

4.1. Verification of conventional Saint-Venant formulation In the absence of vegetation (m = 0, r / = 1), Eqs. (1) and (2) simplify to the conventional Saint-Venant formulation. Solution of these equations was verified using the example cited in Fread and Harbaugh (1971) involving estimation of the water surface profile in a trapezoidal channel of bed slope S O= 0.0016, bottom width B = 6.1 m and Manning's n = 0.025 subject to a steady inflow of 11.3 ma/s and a small dam at the downstream boundary. Based on these conditions and taking m---0, the modified Saint-Venant formulation produced a water surface profile identical to the result reported by Fread and Harbaugh (1971).

4.2. Verification of modified Saint-Venant formulation Fenzl (1962) measured flow resistance in a rectangular flume (21.34 × 0.24 m) sloped at 0.225% containing metal stems. Water surface elevations, controlled with a tail gate, were recorded along the length of the flume for a known discharge. Artificial roughness was created using vertical segments of #13 gauge (D = 0.00238 m) galvanized steel wire having densities of 113.0, 200.2, 452.1 and 1808.3 stems/m 2 of bed surface. Fenzl found that a dimensionless Chezy-type flow resistance parameter (ratio of mean velocity to shear velocity) decreased with increasing hydraulic radius in the obstructed channel. Some of his laboratory results, reproduced in Fig. 2, are compared against predictions from the modified Saint-Venant equations. Eqs. (1) and (2) were solved simultaneously to obtain steady state depths and velocities along the length of the flume. The upstream boundary was a known

R.S. Jadhav, S.G. Buchberger ~Ecological Engineering 5 (1995) 481-496

486

100

t_

E o.

~---~

Ixg~a:

1----~

i,-=0 = "2

[]

"

t

L .... i

i m = 2 0 0 . 2 m "2 ! m = 1 8 0 8 . 3 m "2

~

=

I

0

O

[

7--

J

i

I

[---I •

D z~

8 --

"

J

- F -

t

I !

J

-~

.--+

t

--r~

-F

bd=i

F 1

i i/

I

i

l I

"[Y] , i|

I

i

J

J i

~

,

I-,, 7 , - 7 -

! --h---P-q--+--

j ~L: d---k-~oi i i

%

! 1

= i ~ I

i

e-

n,."

j

= !

I~

10

f

Prea~ted F e ~

!

I

I

I

i

i

i

i i

0.01

d

0.1

Hydraulic radius of bed and wires (m) Fig. 2. Observed and predicted flow resistance parameters.

inflow. At the downstream boundary, a single valued rating curve was imposed to generate the same average depth as reported by Fenzl. As shown in Fig. 2, these numerical predictions agree quite well with Fenzl's lab measurements. Slight discrepancies are due to the approximations in simulated average depths (which are not exactly the same as given by Fenzl) and in the simulation of downstream boundary. These results show that the proposed model successfully captures the resistance effects of rigid, emergent roughness elements in open channel flow.

5. Model

application

In this section, the modified Saint-Venant equations are used to investigate how vegetation density, downstream control, and aspect ratio affect wetland detention times.

5.1. Effect of vegetation on detention time For a given discharge Q, the detention time for nonuniform one-dimensional flow along a prismatic channel of length L, width B and average vegetation density m is given by

~B /orLy(m'x )dx = ~l

°=V

7e

(s)

where V is the total volume of water and submerged plant mass while the product ~V is the volume of water in the channel. Emergent vegetation will raise the water level above the depth that exists without vegetation. However, this rise in water level does not necessarily lead to an

R.S. Jadhav, S.G. Buchberger/ Ecological Engineering5 (1995) 481-496

489

influence of flow resistance due to stem drag and bed drag at a depth y in a wide channel, K(y) =

C dsDmBy 2CdbPe

(11)

For shallow flow in a wide open channel free of vegetation, A(y)<< 1 and K(y) = 0, in which case Eq. (10) gives/3 = 1.67, a result expected from a Manning's type rating curve. Third, as vegetation density increases, detention time becomes less sensitive to discharge. This behavior can also be explained with Eqs. (10) and (11) which reveal that the elasticity coefficient /3 decreases as m increases. For large m values, /3 approaches unity, the discharge-depth rating curve becomes nearly linear, and hence, detention times are practically constant as seen in Eq. (7). Under this condition, an increase in discharge produces a proportional rise in the water depth so that their ratio remains fixed. In fact, this behavior has been observed in field situations. Maheshwari and McMahon (1992) report/3 values ranging from 0.85 to 2.00 (with many points clustered near unity) for shallow flows in irrigation ditches having dense emergent vegetation. Example 2: FWS Constructed Wetland with Downstream Control: Here it is assumed that a sharp crested rectangular weir of height 0.5 m spans the full width of the FWS wetland at the downstream boundary. All other aspects of this problem are identical to conditions assumed in Example 1. Water surface profiles were obtained from the modified Saint-Venant formulation given in Eqs. (1) and (2). Detention times were estimated from the resulting nonuniform flow profile using Eq. (5). In contrast to the first case, Fig. 4 shows that the detention times may decrease ( Q - - 1 0 0 0 0 m3/s) or increase (Q---35000 m3/s) with increasing vegetation density depending on the discharge. Although hypothetical, this example nonetheless illustrates the relationship between detention time and vegetation density may not be obvious and depends on the interplay between hydraulic conditions and vegetation parameters. The outcomes for both examples (uniform and nonuniform flow) can be summarized according to three cases given in Table 1 where Vo is the volume of water in the channel in the absence of vegetation. Case 1: When V > Vo/~, dynamic effects control and detention time increases with increasing vegetation density. This condition occurs for all steady uniform flows (see Eq. 9) and is predicted for steady nonuniform "high" flows. Case 2: When V = Vo/~, static and dynamic effects balance each other and vegetation density has no net effect on detention time. The volume of water displaced by submerged plant mass is compensated by the volume of water gained from the increase in flow depths due to stem drag. This neutral result corresponds to the condition d O / d m = 0 (Jadhav, 1994). Case 3: When V < Vo/,1, static effects control and detention time decreases with increasing vegetation density. This outcome is predicted for steady nonuniform "low" flows in a prismatic open channel with downstream control, provided reasonable porosities exist.

R.S. Jadhav, S.G. Buchberger ~Ecological Engineering 5 (1995) 481-496

490 0.7

O= 10,000 rn3/d 0,6 ...................................................................................

0.5 ............................................................................................ Q= 15,000 m3/d

. .

•~

0.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Q= 20,000 m3/d Q=25 000 m3/d

0.3

o t3

Q= 30,000 m3/d O. 2 ................................................... ~.:':~5,000" hi~/d .........................................................

0.1 ........................................................................................................

0

o

sb

l do

l go

2~

2go

a6o

ago 460 4go soo

Vegetation density (stems/m 2) Fig. 4. Detention time for nonuniform flow in a free water surface (FWS) wetland.

There are limits to Cases 2 and 3 since detention times can neither stay fixed nor decrease indefinitely. Continued increases in vegetation density eventually will reduce porosities to a point where the wetland behaves more like a porous medium than an open channel. Under these conditions, Eq. (2) becomes equiva-

Table 1 Summary of vegetation effects on wetland detention times Case

Water volume in channel

1

V>--

Vo "~

Vegetation effect on detention

dO -->0 dm

Comments

Uniform and nonuniform flow Dynamic effects control Vegetation increases detention times

v = Vo ~1

dO dm

Nonuniform flow only Static and dynamic effects are balanced Vegetation does not affect detention times

v < vo --

dO

--<0 dm

Nonuniform flow only Static effects control Vegetation decreases detention times

ILS. Jadhav, S.G. Buchberger/ Ecological Engineering 5 (1995) 481-496

491

0.7

0.6

........................................................................

m=

....

,-, 0.5-

~ 0.40

~ o.a-

0.1 . . . . . . . . . . . . . . .I . . . . . . . . . . . . . . . . . 0

0.2

o. ,s

ola

o.gs

o'.4

o. ,s

o.s

Weir height (m) Fig. 5. Variation in detention time with weir height, Q = 10000 m3/day.

lent to expressions used to describe porous media flow (Jadhav, 1994). In the transition to this case, dynamic stem drag effects would overtake static displacement effects and lead to Case 1 behavior where detention times increase with vegetation density. Numerical results for Example 2 indicate this transition begins at a porosity of about 71 = 50% (D = 2 cm and m = 1600 stems/m 2) which is much lower than values observed in existing wetlands.

5.2. Effect of downstream boundary on detention time If the discharge is held constant while the height of the downstream weir is raised, then the increased volume of water in the channel leads to longer detention times. Several runs were made to assess the effect of the downstream boundary on detention time in a vegetated wetland. The parameters used are identical to those in Example 2, except that weir height, Hw, varies from 0.2 to 0.5 m. Results, plotted in Fig. 5, show that for a given discharge there are three outcomes corresponding to the cases listed in Table 1. At low weir heights, Case 1 prevails. Dynamic stem drag effects predominate and detention time increases with vegetation density. At high weir heights, Case 3 occurs. Static displacement effects control and detention time decreases with vegetation density. For a fixed vegetation density, these opposing outcomes are separated by a critical weir height, Hwc--0.30 m, delineating the neutral condition for Case 2. Here static effects balance dynamic effects and vegetation has no net influence on detention time. For a given discharge, Hw¢ increases slightly with vegetation density; for a given vegetation density, H~c increases appreciably with discharge.

R.S. Jadhav, S.G. Buchberger ~Ecological Engineering 5 (1995) 481-496

492

0,9

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

"~ 0.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,o

"--" o

0.6 .

=

0.5 .

.

0.4 .

.

0

Q= 10,000 m3/d . . . . .

. .

. .

. .

. .

. .

. .

.

.

.

.

.

.

.

.

.

. . .

.

. .

.

. .

.

.

m=O

. .

~ .

.

.

r

.

.

.

.

.

.

.

.

n

-

.

.

.

.

..........

_ m = 500 t000

. .

.

I~I

_ m = I000 0.3-

Q=35,000

m3/d

~

m=500

. . . . . . . . . . . . .

r.=O

/ 0.1

o

.

o

.

g

.

.

.

.

.

.

1'o

.

.

2b

.

.

.

25

.

3o

Aspect ratio Fig. 6. Variation in detention time with aspect ratio for Q = 10000 and 35000 m3/day.

5.3. Effect of aspect ratio on detention time FWS wetlands are often sized on the basis of areal loading rates for various contaminants. While many length and width combinations can be used to achieve any desired wetland surface area, high aspect ratios are generally preferred to encourage plug flow and minimize short-circuiting (Steiner and Freeman, 1989). Runs were made to determine how detention times varied among nine wetlands each having a common surface area of 2.5 ha but different floor configurations with aspect ratios ranging from 0.1 to 25. The height of the downstream weir was selected such that, in the absence of vegetation, each wetland had a common nominal detention time for a given inflow. Results, shown in Fig. 6, lead to two conclusions: (1) when all other factors (e.g. flow rate, vegetation density and surface area) are held constant, detention times in vegetated wetlands increase with aspect ratio and (2) the sensitivity of the detention time to the aspect ratio increases with vegetation density. These results are readily explained by first considering the base case where all configurations have a common detention time without vegetation. As the aspect ratio increases with surface area fixed, travel distances grow and, hence, water velocities must increase to maintain a constant detention time. When vegetation is introduced, the resulting stem drag is greater and more extensive in long slender wetlands with high velocities than in short wide wetlands with low velocities. Flow resistance induced by this stem drag raises water levels and hence increases detention times.

I~ S. Jadhav, S.G. Buchberger / Ecological Engineering 5 (1995) 481-496

493

As illustrated by the slope of the responses shown in Fig. 6, the incremental effects of stem drag become more pronounced as vegetation density increases. For Q -- 10 000 m3/day, the wetland behaves as a static (Case 3) system for all aspect ratios shown. However, for Q -- 35 000 ma/day, the wetland switches from a static (Case 3) to dynamic (Case 1) system when the aspect ratio exceeds 6. In conjunction with observations from the previous section, this behavior suggests that a neutral condition (i.e. one where wetland vegetation has no net effect on detention times) can be achieved either by adjusting the wetland aspect ratio during design or by manipulating the downstream weir height during operation.

5.4. Example 3: comparison of detention time estimates A third example illustrates how estimates of detention time vary among three different approaches. The hydraulic and geometric conditions for the wetland are the same as those given in Example 2. Differences arise from the way in which the depth of flow is estimated. As summarized below, two approaches (Cases a and b) assume a uniform depth in the direction of flow, an assumption often invoked in practice; the third approach (Case c) is based on a more realistic nonuniform depth profile. 1. Case a: O from Eq. (7) with y taken as normal depth from Manning's equation. 2. Case b: O from Eq. (7) with y taken as downstream weir height (prism approach).

2.0

u

:

Q

1.0-

0.5-

0.0

o

so'oo

Ioooo is6oo

20600 2s6oo 30600 asooo

Discharge (m3/day) Fig. 7. Detention times computed by 3 methods with vegatation density, m = 500 stems/m 2.

494

R.S. Jadhav, S.G. Buchberger ~Ecological Engineering 5 (1995) 481-496

3. Case c: ® from Eq. (5) with y computed from the modified St. Venant equation. Results, plotted in Fig. 7, show a dimensionless detention time ratio as a function of discharge for a vegetation stem density of m = 500 stems/m 2. Detention times from Manning's equation (Case a) are consistently less than those estimated from the modified St. Venant (Case c). Conversely, detention times from the prism approach (Case b) are consistently greater than estimates from the modified St. Venant equation. These discrepancies occur because neither approach based on uniform flow depths properly accounts for the backwater effects caused by the downstream boundary. Manning's equation (Case a) gives normal flow depths that are too shallow while the prism approach (Case b) assumes a depth that is too deep. The magnitude of the detention time discrepancies decreases as the discharge increases since the effect of the downstream boundary becomes less pronounced for higher flows. This example underscores the importance of accurately defining the depth profile for estimating detention times and predicting treatment performance of free water surface wetlands constructed for water quality improvement.

6. Summary and conclusions A modified form of the one-dimensional Saint-Venant equations was presented to describe shallow flow through a FWS constructed wetland. This model incorporates reductions in the cross-sectional area and additional drag due to emergent vegetation through use of directly measurable vegetation parameters. Numerical experiments were performed to investigate how emergent vegetation, downstream boundary and aspect ratio impact wetland detention time. Depending on the interaction between geometric and hydraulic parameters, a wetland may exhibit static, neutral, or dynamic behavior. If the downstream weir is high or the aspect ratio is small, then flow velocities are low and the wetland tends to behave as a static pond system. Displacement effects caused by submerged plant mass predominate and detention time invariably decreases with vegetation density. On the other hand, when the downstream weir is low or the aspect ratio is large then flow velocities are high and the wetland tends to behave as a dynamic system. Stem drag controls and detention time increases with vegetation density. These opposing responses are separated by a neutral condition where the presence of vegetation has virtually no net effect on detention time. Detention time is a crucial link between hydraulic and ecologic aspects of wetland behavior. Findings of this study have direct implications for ecological engineering of natural treatment systems since detention time is an important design parameter of wetlands constructed for water quality improvement. Estimates of wetland detention time based on an expedient Mannings-Chezy equation may lead to unrealistic expectations of actual treatment performance.

R.S. Jadhav, S.G. Buchberger /Ecological Engineering 5 (1995) 481--496

495

7. List of notations

Symbol

Meaning

A B Cab Cas D g

cross-sectional area of the flow bottom-width of the wetland drag coefficient associated with the bed friction only drag coefficient associated with the stem friction only average diameter of the vegetation stems acceleration due to gravity weir height ratio of stem to bed drag effects length of the wetland vegetation density Manning's roughness coefficient associated with bed friction only effective perimeter flow flow per unit width time volume of water and vegetation volume of water in the absence of vegetation longitudinal distance along the wetland length depth of the water depth of water in the absence of vegetation coefficient of the rating curve exponent of the rating curve or elasticity of discharge with respect to depth porosity detention time ratio of depth to effective wetted perimeter

K L m n

Q q t V

Vo x

Y Yo

/3 O

Acknowledgements This work was supported in part by a grant under contract DE-AC05-76OR00033 from the US Department of Energy E R / W M Young Faculty Award Program and by grant 14-08-0001-G2039 from the State of Ohio Water Resources Center.

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