NONIDEAL AND PULSED FLOW: APPLYING RESIDENCE TIME DISTRIBUTIONS TO STORMWATER TREATMENT WETLANDS

A Thesis

Presented in Partial Fulfillment of the Requirements for

the Degree Master of Science in the Graduate

School of The Ohio State University

By

JeffF. Holland, B.S., B.A.

The Ohio State University 2003

Master's Examination Committee:

Dr. Jay Martin, Adviser

Dr. Timothy Granata Approved by

Dr. Noel Cressie

Department of Food, Agricultural, and Biological Engineering ABSTRACT

The residence time distribution (RTD) representing the hydraulics of a wetland is an important tool for modeling and designing treatment wetlands for optimal constituent removal. To correctly use RTD results, it is necessary to understand the conditions under which this distribution remains stable. Dye tracer experiments were conducted on a stormwater treatment wetland to investigate hydrologic factors affecting RTD characteristics. Dye was introduced into the inflow under normal flow conditions and during simulated storm flows, providing a range of flow rates and water levels. Dye distribution in the outlet was measured using an in-situ fluorometer. Results indicate that flow rates did not have a significant effect on the RTD. RTDs normalized for volume and flow showed a significantly shorter minimum travel time at higher water levels.

Conversely, the centroids of dye distributions were reduced at lower water levels. Both these results demonstrate that water level can have a direct impact on the RTD of a wetland. For the wetland in this study, hydraulic efficiency decreased with deeper water.

These results further the understanding of RTD dynamics during pulsed conditions, and will aid in the design and management of wetlands. Tools for modeling pulsed flows and constituent fluxes in wetlands, although well developed in theory, have not been well tested in practice. High-frequency monitoring of suspended solids and flows in a stormwater treatment wetland enabled application and analysis of these tools. A dynamic flow- and volume-weighted time variable, analogous to the retention time in steady-flow systems, is one important tool tested in this study.

Cross correlations with time lags demonstrated that the dynamic time variable was a better predictive variable of pulsed events than was the standard time variable. This study also demonstrated that RTD modeling with reaction kinetics of suspended solids during storm events produces a better explanation of outflow data than possible with steady, plug-flow models. Using only input and output data, an RTD model explained sedimentation rates with less unexplained variance than the standard, plug-flow model.

The results of this study underscore the utility and importance of RTD modeling for complex flows. In memory of my dad who taught me how to find answers to my own questions

IV ACKNOWLEDGMENTS

I wish to thank my adviser, Jay Martin, and co-adviser, Tim Granata for giving me support, and encouragement and for putting their trust in me during this study. I also wish to thank committee member Noel Cressie for all his help and valuable time.

I am very thankful for the design and construction work done by Dan Gill, Tim

Salzman, and Alex Daughtery. For the technical assistance of Chris Gecik, Kevin

Duemmel, and Carl Cooper, I am greatly indebted.

Many thanks also go to Mark Schmittgen, for his assistance on the farm, to Chris

Keller for his advice on using dye tracers, to Mark Benjamin, for supplying a draft of his publication in press, to Tim Lippman for help with statistical methods, and to James

Carleton for providing suggestions on investigating reaction rates.

This study would not have been possible without funding from the Ohio

Agricultural and Research Development Center and generous donations from Agri Drain

Corporation.

v VITA

October 23, 1976 ...... Born - San Pedro, CA, USA

1999-2000 ...... Research Assistant, Western Washington University

2000 ...... B.S. Biology/Mathematics Combined, Western Washington University

2000 ...... B.A. German Language, Western Washington University

2002-present ...... Graduate Research Assistant, The Ohio State University

PUBLICATIONS Research Publication 1. Peterson, M.A., S. Dobler, J. Holland, L. Tantalo, and S. Locke, 2001. Behavioral, molecular, and morphological evidence for a hybrid zone between Chrysochus auratus and C-cobaltinus (Coleoptera: Chrysomelidae). Ann. Entomol. Soc. Am. 94, 1-9.

FIELDS OF STUDY Major Field: Food, Agricultural, and Biological Engineering

VI TABLE OF CONTENTS

Page Abstract ...... ii Dedication ...... iv Acknowledgments ...... v Vita ...... vi List of Tables ...... ix List of Figures ...... x Chapters:

1. Effects of wetland depth and flow rate on residence time distribution characteristics ...... 1 1.1. Introduction ...... 1 1.1.1. Tracer Studies ...... 1 1.1.2. Residence Time Distributions ...... 2 1.1.3. Factors influencing hydraulic characteristics ...... 4 1.1.4. Purpose of study ...... 6 1.2. Methods ...... 6 1.2.1. Site description ...... 6 1.2.2. Materials ...... 7 1.2.3. Experimental Protocol ...... 8 1.2.4. Data analysis ...... 9 1.2.5. Natural events ...... 12 1.3. Results ...... 13 1.4. Discussion ...... 14 1.4.1. RTD sensitivity to hydrologic influences ...... 14 1.4.2. Design and management implications ...... 15 1.4.3. Assessment of hydraulic efficiency metrics ...... 16

Vll 1.4.4. Limitations of this study ...... 17 1.5. Conclusion ...... 18 ') Analysis and modeling of suspended solids from high-frequency monitoring of a storm water treatment wetland ...... 28 2.1. Introduction ...... 28 2.1.1. Stormwater treatment wetlands ...... 28 2.1.2. The case study ...... 30 2.2. Materials and Methods ...... 31 2.2.1. Site description ...... 31 2.2.2. Field and Laboratory methods ...... 31 2.2.3. Residence time distributions ...... 33 2.2.4. Dye tracer residence time distribution ...... 34 2.2.5. Modeling outflow with residence time distributions ...... 35 2.2.6. Reaction kinetics ...... 36 2.2.7. Models for determining sedimentation rates ...... 39 2.2.8. Investigating storm events ...... 40 2.2.9. Cross correlations ...... 42 2.3. Results and Discussion ...... 43 2.3.1. Cross correlations ...... 43 2.3.2. Sedimentation kinetic models ...... 46 2.3.3. Limitations of this study ...... 50 2.4. Conclusions ...... 52 References ...... 66

Vlll LIST OF TABLES

Table 1.1 Experimental settings for the 2003 dye tracer experiments, showing the average flow rates applied by irrigation water and the wetland water level settings for each tracer experiment...... 20

lX LIST OF FIGURES

Figure Page

1.1 Conceptual diagram of the effects of mixing scale (A) and short circuiting (B) on residence time distribution characteristics ...... 21

1.2 Diagram of the setup for the dye tracer experiments at the Waterman Farm wetlands...... 22

1.3 Bathymetric map of wetland basin. Contours every 1Ocm, with depths labeled at 30cm intervals. Depths are relative to survey station ...... 23

1.4 Volume versus stage relationship of the experimental wetland based on survey data. This relationship is used to find the volume of the wetland when the elevation of the water at the outlet (stage) is known ...... 24

1.5 Statistics of the residence time distribution (RTD) characteristics unde~ differing flow rates and depths. Comparisons are made between flow rates (averaged two water levels) and water levels (averaged over two flow rates) (mean± standard error) for (A) Peak concentration time; (B) minimum dye travel time, (C) RTD centroid (first moment); and (D) variance ofRTD (second moment) ...... 25

1.6 Comparison of two representative residence time distribution (RTD) curves run at different water levels ...... 26

x 1. 7 Residence time distribution of a dye tracer during natural, pulsed flow for low water level (A) and high water level (B), each shown with associated statistics ...... 2 7

2.1 Diagram of the stormwater treatment wetland at the Waterman Farm in Columbus, OH ...... 54

2.2 Bathymetric map of wetland basin. Contours every lOcm, with depths labeled at 30cm intervals. Depths are relative to survey station ...... 55

2.3 Stage (water depth from base of outlet device) versus volume relationship of wetland based on survey data ...... 56

2.4 Comparison of a dye tracer run under natural conditions and the RTD function used to model suspended sediments flowing through wetland based on a theoretical system of 2 continually stirred tank reactors (CSTR). Difference in area between the two curves represents the dye lost during the natural RTD experiment; the modeled RTD corrects for this error in the measured RTD ...... 57

2.5 Cross correlation for all water levels with 95% confidence intervals with time lags (A) in days and (B) in detention time (unitless). Vertical scale is preserved between the two plots for comparison ...... 58

2.6 Cross correlations at separated high and low water levels with time lags and 95% confidence intervals (Cl) in (A) days and (B) detention times. Vertical scale is preserved between the two plots for comparison ...... 59

2.7 Comparison of wetland outlet concentration as a function of time (A) and as a function of volume and flow-normalized time, ¢ (B). Corresponding

XI events are connected with arrows to demonstrate the nonlinear relationship between t and ¢ . The uneven spacing of ¢ is also evident in this comparison ...... 60

2.8 Fractional sediment retention of each storm event as a function of the peak outlet flow of the corresponding storm (a metric of hydraulic loading), modeled by linear regression (R2=0.47 and p=.002 by ANOVA) ...... 61

2.9 Comparison of sedimentation rate constants compared by different models, plotted versus peak flow rate of associated storm event with trends shown by linear regression and associated statistics ...... 62

2.10 Input mass flux of suspended solids to stormwater treatment wetland during adjacent rain events (A). Predicted outflow suspended solids concentration from RTD model 4with and without sedimentation dynamics compared with actual outflow (B) ...... 63

2.11 Relationship between the R2 fit of the RTD by flux model (Model 4) with the peak wetland outlet flow (a measure of hydraulic loading), shown with linear regression to determine if model accuracy changes with flow (R2 =0.15; p=.11 from ANOVA) ...... 64

2.12 Example of a bad fit of the RTD model. Input mass flux of suspended solids to stormwater treatment wetland during a single rain event (Top). RTD model outflow concentration prediction of suspended solids with and without sedimentation dynamics compared with actual outflow ...... 65

XII CHAPTER 1

EFFECTS OF WETLAND DEPTH AND FLOW RA TE ON RESIDENCE TIME

DISTRIBUTION CHARACTERISTICS

1.1. Introduction

I. I. I. Tracer Studies

Tracer studies are valuable tools for investigating flow conditions in wetlands.

By definition, a tracer is a passive substance that follows the flow path through a wetland in an unbiased manner. A tracer can be used to track the physical flow paths through a system (Thackston et al., 1987; Walker, 1998) or to investigate the cumulative effect of these flow paths on the system outflow (Levenspiel, 1972). Tracer studies are important for studying wetlands that are susceptible to nonideal and pulsed flow. Wetlands are traditionally modeled with plug flow, which assumes that water and its dissolved constituents run uniformly and without dispersion from inlet to outlet. When flow is nonideal, there is some amount of dispersion and uneven distribution that occurs to the elements passing through a wetland. The models that were developed for the ideal wetland often yield incorrect results for real wetlands subject to nonideal flow (Kadlec,

2000), or flow that is pulsed (Werner and Kadlec, 2000), such as during storm events.

1 Because wetlands do not always behave as the ideal models predict, quantitative studies are needed to understand the effects of pulsed flow (Wong and Geiger, 1997) and to reveal the behavior of nonideal flow in treatment wetlands (Kadlec, 2000).

1.1.2. Residence Time Distributions

A powerful application of a tracer study is its ability to measure the residence time distribution (RTD) of water and dissolved constituents flowing through a system. If a pulse of tracer is introduced into the system inflow, the outflow tracer concentration as a function of time will be a distribution reflecting the dispersive nature of the system. In the ideal case of plug flow, all of the tracer will exit at the same time, the residence time.

In the nonideal case, however, there is not one single residence time of the system, as is assumed in simplified wetland models (Mitsch and Gosselink, 2000); rather, there is a distribution ofresidence times, an RTD. RTD analysis was originally developed for steady-flow reactors in chemical engineering. The RTD can be used to assess reactor efficiency and to predict outflow concentrations (Levenspiel, 1972). The relationship of the RTD and chemical reactions also enable modeling of nutrient dynamics in wetlands under pulsed conditions (Werner and Kadlec, 2000).

Wetland engineers use RTD analysis to identify wetland design characteristics that affect treatment efficiency. Under nonideal flow conditions, such as uneven mixing and flow distribution, treatment efficiency is often diminished. An RTD can be used to identify inefficiencies, such as zones of diminished mixing, where the area of a detention basin is not being optimally utilized for pollutant treatment (Thackston et al., 1987;

Kadlec, 1994). RTD analysis can even be applied to a hypothetical wetland using fluid

2 dynamic models to investigate effects of wetland shape or aspect ratio on the flow efficiency (Walker, 1998; Persson et al., 1999). Such analyses have been used to redesign wetlands for optimal performance (Koskiaho, 2003). RTD analysis has also been used to optimize inlet (Shilton and Prasad, 1996) and outlet structures (Konyha et al., 1995) or both (Ta and Brignal, 1998) for maximum treatment efficiency.

In consideration of these important applications of RTD analysis, it is useful to reduce an RTD to a single number, the hydraulic efficiency. The hydraulic efficiency represents the ability of a wetland to distribute its flow evenly throughout its area, maximizing contact time of pollutants in the system and the efficiency to break down these pollutants. Thackston (1987) introduced the concept of hydraulic efficiency by quantifying the relative position of the RTD's centroid. The centroid of an RTD shifts to a lower value with increased short-circuiting due to the effective loss ofretention volume

(Fig. 1.1 ). Complex systems, such as vegetated wetlands, are often described in equivalent number to continually stirred tank reactors, or CSTRs (Levenspiel, 1972;

Kadlec and Knight, 1996). In this manner, a system can be compared to an equivalent volume of many small CSTRs, or a few large CSTRs. Many small CSTRs in series represent a system with a small mixing scale, which has a small RTD spread and resembles plug flow (Fig. 1.1 ). As the number of equivalent CSTRs decreases, the mixing scale and the spread of the RTD increase (Fig. 1.1 ). A large R TD spread is considered inefficient for a chemical reaction system (Levenspiel, 1972). Persson et al.

(1999) synthesized these effects of mixing and short circuiting by defining the hydraulic efficiency as the product of a measure of the R TD shift and spread.

3 1.1.3. Factors influencing hydraulic characteristics

While many wetland studies have focused on the applicability of RTD analysis to wetland modeling and design (Walker, 1998; Persson et al., 1999; Werner and Kadlec,

2000), fewer studies have investigated factors affecting stability of the RTD in a wetland

(Kadlec and Knight, 1996). The RTD's sensitivity to external factors is important if a single or even limited number of RTDs are used to characterize the hydrology of a wetland. In conventional waste treatment facilities, it is common to run tracer tests at various flow rates and water levels to assess the system performance under varying conditions (AWW ARF, 1996). Because the morphology of a wetland basin and its associated vegetation is typically more complex than that of a municipal treatment system, similar studies are needed to determine under which conditions a measured R TD is applicable.

Many factors can affect flow dynamics of a wetland. Aquatic macrophytes, for example, can greatly affect flow patterns. Emergent vegetation has been shown to enhance lateral diffusion in a wetland (Nepf et al., 1997; Nepf, 1999) as well as vertical benthic secondary flows (Nepf and Koch, 1999). Enhancement oflateral and vertical diffusion in a wetland could potentially improve its hydraulic efficiency. If patchy vegetation creates stagnant zones of diminished mixing, however, this can decrease the effective volume and thus the hydraulic efficiency of a wetland (Thackston et al., 1987).

The strong role of vegetation indicates that seasons or ecological succession may influence the characteristics of wetland flow. Basin morphology also affects flow rates and therefore the RTD (Koskiaho, 2003). Convective circulation (Oldham and Sturman,

2001) and diffusion driven by wind or molecular movement (Kadlec and Knight, 1996;

4 Keller and Bays, 2000) can also affect the RTD of a wetland. Changes in hydro logic conditions, such as flooding in riparian wetlands, have been shown to greatly affect RTD characteristics (Stern et al., 2001 ).

It is logical that hydrologic factors, such as water depth and flow rate, affect the

RTD of a wetland. Increases in system volume at a given flow rate increase the retention time, thus extending the RTD in time. The equivalent effect can be seen by decreasing the flow rate for a given volume. For this reason, it is common to normalize the RTD's

abscissa by retention time (Levenspiel, 1972; A WWARF, 1996). This normalization procedure, essential for comparing RTDs of systems under different hydro logic

conditions, i3 complicated by pulsed flow, where there may not be one single system

volume or flow rate. Werner and Kadlec (1996) developed a dynamic normalization

procedure for RTD analysis of such pulsed systems. While hydrologic changes can

stretch or compress the raw RTD, this procedure assumes that each condition will have

the same intrinsic normalized RTD. However, it remains to be demonstrated under

which circumstances the RTD results of this normalization method (Werner and Kadlec

1996) can be applied to different conditions. Certain extremes would be expected to

break the concept of an intrinsically stable RTD. Effects of wind and diffusion may

dominate at extremely long retention times. Turbulent diffusion from vegetation and

other obstructions would be expected to be related to the Reynolds number, and thus flow

velocity (Nepf et al., 1997). Basin morphology and vegetation would also be expected to

have different effects relative to different water depths. Studies are needed to investigate

the stability of the RTD under varying hydro logic conditions to assess the efficacy of

hydraulic characterization using tracers during pulsed flow.

5 1.1.4. Purpose ofstudy

The purpose of this study was twofold. The major goal was to investigate the sensitivity of the normalized RTD under different depths and flow rates. The results will help determine under which conditions nonideal flow models and hydraulic characterizations can be based on a single RTD. Second, this study investigated whether depth management should take hydraulic efficiency into account. While water depth can be designed for and managed in constructed wetlands, engineers often disagree as to what the optimal depth of a wetland should be (Wong and Somes, 1995; Mitsch and Gosselink,

2000). To accomplish these goals, a series of dye tracer experiments was run on a small constructed wetland under controlled flow rates and water levels. Water level and flow rate were regulated with adjustable-depth control structures and agricultural irrigation water.

1.2. Methods

1.2.1. Site description

This study was performed in the spring and summer of 2003 on a 250m2 wetland constructed on the Waterman Research Farm at the Ohio State University in Columbus,

Ohio (Fig. 1.2). The wetland had three adjacent inlet structures (Agri Drain Corp.) that discharged water from storm flow, overland flow, and nursery pad irrigation runoff, and one outlet that discharged to another wetland cell. To simulate storm flow, water was added to the overland inflow structure using a vinyl hose connected to a 2 inch, high­ discharge irrigation riser. Flow rates were controlled by valves on the hose and riser.

Although all three inlets conducted flow during real storm events, simulated storm events

6 were only conducted through the overland flow entrance. An adjustable weir was used to control the depth (i.e. water level) in the wetlands. To do this, boards with watertight seals were slid into a track, raising or lowering the weir to a predetermined level (Fig.

1.2).

To determine the volume and depth of the wetland for different flow conditions, wetland topography and weir positions were surveyed using a total station in the summer of 2002 (Fig. 1.3). The survey results were processed by computer to define a relationship between water level and wetland volume, using the assumption that the water level at the outlet is uniform across the wetland (Fig. 1.4).

I.2.2. Materials

Each inlet and outlet to the wetland was monitored by a YSI 6-series sonde (YSI,

Inc.), set upstream of the V-notch weir (Fig. 1.2). Capable ofresolving depth to± 1 mm, the YSI devices monitored flow based on the measured weir head (ASTM, 2002). The outlet YSI device had an in-situ probe specifically designed to detect the fluorescence of the dye tracer Rhodamine WT.

Rhodamine WT was chosen, not only because of the fluorometer's compatibility with existing instrumentation, but because Rhodamine WT is a commonly-used dye tracer in wetland studies (Stem et al., 2001 ). Rhodamine WT has a low natural background interference (Wilson et al., 1986) and acceptably low adsorption and degradation rates in small systems with residence times less than one week (Lin et al.,

2003).

7 1.2.3. Experimental Protocol

To concurrently test the effects of high and low water levels and high and low flows on the RTD, 12 experiments were performed over a period of 13 weeks. The flow rates were difficult to maintain precisely during the experiments and, therefore, were quantified by their averages of 1.2L/s for low flow and 3.2L/s for high flow. The average depth settings were 17cm for low water level and 40cm for high water level (Table 1.1 ).

Experiment sets were performed in monthly blocks to balance the seasonal

influences on each controlled condition (Table 1.1 ). For the relatively small sample size of this experiment, it would have been possible under fully randomized settings to have

one set of experimental prescriptions become climatologically biased by grouping at the beginning or the end of the study. A prescription of weekly-changing water levels was

randomized over each monthly block. Two flow rates were assigned to each week, and

their order was chosen randomly. Each flow pair was performed on one of each water

level per month. A protocol was developed for the paired tracer experiments to run at the

first occurrence of each water level each month or to postpone the experiments until the

next similar water level in the case of inclement weather or technical constraints (Table

1.1 ).

Preceding each dye tracer experiment, the irrigation flow was set to a

predetermined level (Table 1.1) and allowed to flush the wetland for at least one

detention time to allow for thermal equalization. Rhodamine WT dye was added in

approximate proportion to wetland volume: approximately 4 grams pure Rhodamine WT

for the low water level and 10 grams for high water level. Dye was added to the inlet by

slowly pouring four gallons of a mixture of dye and wetland water into the overland flow

8 structure (Fig. 1.2). At the outlet, the YSI sensor equipped with the Rhodamine probe

(Fig. 1.2) monitored the dye concentration and weir head every five minutes.

1.2.4. Data analysis

Although each dye tracer experiment was run under relatively steady conditions, each RTD had to be normalized in order to compare between conditions of different flow rates and system volumes. Werner and Kadlec ( 1996) proposed normalizing the RTD by

flow rate and by system volume, where time on the abscissa is replaced by dimensionless

flow-weighted time, ¢ :

¢ = ff Q(t') dt' (I. I) 1" V(t')

where t0 is the time of dye delivery, Q(t) is the outflow rate, V(t) is the wetland volume,

and t' is a dummy variable of integration. Because the theoretical residence time for a

system with steady flow occurs at ¢=1, the parameter ¢ can be thought of as the number

of theoretical retention times. Werner and Kadlec ( 1996) defined ¢ under the special

case where V(t) is assumed to be a constant: Vsys· In the present study, the volume-to-

stage (i.e. water level) relationship (Fig. 1.4) enabled the calculation of volume as a

function of time, V(t), providing a more accurate description of the system volume. The

dimensionless RTD function, based on a tracer of mass M, is defined as:

C'( ¢) = C(¢)V(¢) (1.2) M

9 where C( ¢)is the outflow concentration, and V( ¢)the system volume, both functions of flow-weighted time (Werner and Kadlec, 1996). For consistency in this study, each RTD was analyzed over the interval 0<¢<2.

Moments of the dimensionless RTD functions were used to calculate the hydraulic efficiency. The moments of the normalized RTD functions are defined as: . Mo = JC'(¢)d¢ (1.3) 0 . M1 = J¢C'(¢)d¢ (1.4) 0

ro 2 • M 2 = fC¢-M1.) C'(¢)d¢ (1.5) 0

The zeroth moment of the normalized RTD, Mo·, is equivalent to the fraction of the mass of the dye recovered. The first moment, M 1 *, is the centroid of the RTD. The second moment, M2 *, is the variance of the RTD, which accounts for the spread of the dye over time. In theory, Mo*= M 1*=1 for a normalized RTD of a conservative tracer in a system with no dead zones (Werner and Kadlec, 1996). Consequently, the deviation of these moments from the ideal case can be used to quantify the hydraulic efficiency.

Different metrics of hydraulic efficiency were calculated and compared in this

study. In order to quantify short circuiting, Thackston (1987) defined hydraulic

efficiency as the ratio of the actual and theoretical residence time:

t • A-=-=M (1.6) f T I

Where A-,is the hydraulic efficiency proposed by Thackston (1987), tis the mean

residence time, equivalent to M 1 •• and Tis the theoretical residence time determined by 10 the surveyed volume and measured flow. For a normalized RTD, T=l, and -11 = M 1 •.

When flow or volume vary during the tracer experiment, i and Tare difficult to calculate

and M 1 • should be used. Tracer spread was also used as a measurement of hydraulic efficiency. While there are many ways of measuring tracer spread (Persson et al., 1999),

M2 •was used in this study. A synthesized version of hydraulic efficiency was also calculated:

(1.7) where Ar is the hydraulic efficiency proposed by Persson et al. ( 1999), N is the equivalent number of continuously stirred tank reactors (CSTRs) in series, tp is the time of peak concentration, and tp * is the normalized time of peak concentration. This concept of hydraulic efficiency is simplified algebraically by the assumption that the RTD spread can be modeled by series of CSTRs.

Minimum travel time was also calculated as a characteristic of the RTD that identifies short-circuiting and mixing. The minimum travel time, t,,,, was defined as the shortest time of travel from the inlet to outlet. Theoretically, this is the time elapsed between the introduction of dye at the inlet and the detection of dye at the outlet.

However, background fluctuations in fluorescence made the initial signal in the outlet difficult to determine. Therefore, a minimum travel time was defined arbitrarily as the time of the last measurement before the measured concentration reached 3% of the peak concentration. The time identified with this method matched the first rise of the RTD curve.

11 Because experiments were conducted in paired combinations of flow rates, two­ sided, paired t-tests were used to statistically compare how flow rates affected the RTD characteristics. This yielded five degrees of freedom from the twelve tracer experiments.

Two-sided, pooled t-tests were used to compare the effects of water level on RTD statistics, yielding 11 degrees of freedom for this test. All tests were used to determine

, with a 95% confidence level whether the differences of the mean RTD characteristics, A-1

Ar, tm, and M1 *,were nonzero.

1.2.5. Natural events

Dye tracers were also used to measure natural, pulsed-flow events in the wetland.

Using similar methods to the experiments with artificially simulated flow, dye was added to the storm-flow wetland inlet (Fig. 1.2) immediately preceding a large storm event and outflow measurements and data analysis were made as before. Because the storm-flow tracer experiments relied on multiple storm events to complete the RTD curve, their long and unpredictable time frame excluded the possibility ofreplication. Technical constraints also limited the quality of data. The Rhodamine probe introduced spiked noise under high-turbidity conditions. The extreme spikes (i.e. outliers) were problematic in the high water level experiment and were replaced by the surrounding mean values, degrading the signal and thus the data quality. As a result, natural events were not statistically compared to flows created using irrigation water, but are presented only for a subjective comparison.

12 1.3. Results

Dye recovery (Mo*. 100%) for all experiments ranged from 75%-95% with an average of 84%. There were no consistent differences between the RTD plots at different flow rates. None of the parameters for hydraulic efficiency differed significantly • between high and low flow rates: At (p=0.4 7), AP (p=0.81 ), tm (p=0.98), and M 2 (p=0.27),

(Fig. 1.5).

The RTD plots for high and low water levels appeared distinctively different (Fig.

1.6). While the RTD of the low water level was unimodal, the RTD for the high water level was usually bimodal, with the first peak typically higher and narrower than the main peak of the low water level RTD (Fig. 1.6). These differences were reflected in the RTD statistics (Fig. 1.5). The minimum travel time, tm. was significantly shorter for the higher water level (p= .00012) and the centroid, At was significantly lower for the higher water level (p=.016). The spread, or M2 *, however, did not show a significant effect due to water level (p=.54 ). The mean hydraulic efficiency of Persson et al. ( 1999), AP , was significantly larger at the lower water level, although this difference was only marginally significant (p=.041) (Fig. 1.5).

Two natural dye tracers were successfully run during natural storm flow, one at high water level, and one at low water level. The RTDs of the natural dye tracers appeared different from those of the simulated storm flows (Fig. 1. 7), though they showed similar, general trends. For natural flow events, the RTD for the high water level

, had lower values of ,1,1 AP, tm, and M2 *compared to the RTD of the low water level (Fig.

1.7).

13 1.4. Discussion

1.4.1. RTD sensitivi~v to hydrologic influences

The results of this study indicate that the RTD of a wetland is sensitive to changes in water depth, but not as proportionally sensitive to changes in flow rate. If this result is characteristic of wetlands in general, then it indicates that the normalization proposed by

Werner and Kadlec ( 1996) should work appropriately for moderately varying flow rates, during which the wetland's water level does not change appreciably. Care should be taken in interpreting an RID during periods of large fluctuations in system volume, since the hydraulic efficiency is affected by volume fluctuations. Werner and Kadlec ( 1996)

acknowledged that determining wetland volume, a step necessary for normalization, is not straightforward under large volumetric fluctuations. This problem was avoided in

this study by defining volume as a function of time, V(t), a procedure not feasible for

many wetlands. It should be noted that, in the present study, the flow rates differed by a

factor of 2. 7 and depth varied by a similar magnitude of 2.4. Natural flow rates may vary

by magnitudes greater than those tested in this experiment, whereas depth fluctuations are

more likely to remain within the range tested in this study. It is therefore expected that

flow effects on the RTD may be greater under naturally pulsed conditions. In this study,

not enough tracers were run under naturally pulsed condition to test this conjecture.

Under extremely low to zero flow rates that may occur between pulsed events, other

dispersive mechanisms will most likely affect RTD characteristics by dominating

hydraulic mixing. These dominating mechanisms, which include convective, molecular,

14 and wind-driven diffusion, are difficult to isolate and measure with RTD analysis because of the long retention times involved at low flow rates.

1.4.2. Design and management implications

The depth effect on hydraulic efficiency observed in this study may be important when wetland design and management are considered. The reduced normalized mean detention time, A-,, observed at higher water levels is a clear indication of short circuiting.

Additionally, reductions in the normalized minimum travel time, lm, and peak concentration time, A,P, could be effects of short circuiting or reduced plug flow efficiency. Thus, all the parameters expressing hydraulic efficiency, except for the RTD spread, M 2 *, show lower efficiency for the higher water levels. This indicates that less efficient flow patterns may be more prevalent at greater water depths. Although water level is taken into consideration during wetland design and management, the depth effect on hydraulic efficiency is not commonly considered. Aside from physical or technical constraints, factors deciding design depth are typically ecology (Batzer and Resh, 1992;

Mitsch and Gosselink, 2000) and hydro logic effectiveness, a measure of compliance with the minimum prescribed retention time in a stormwater treatment wetland (Wong and

Geiger, 1997). Long-term changes in wetland depth affect vegetation distributions

(Mitsch and Gosselink, 2000), which would be expected to have an impact on hydraulic efficiency, but depth settings in this study were too transient to have an effect on vegetation. Although vegetation undoubtedly had an effect on this study, it was not a controlled part of the experimental setup. If the results of this study are representative of

15 other wetlands, the effect of depth on hydraulic efficiency should be a factor considered during wetland design and management.

1.4.3. Assessment of hydraulic efficiency metrics

In general, short circuiting is never desirable in a treatment wetland because treatment area is effectively lost (Thackston et al., 1987; Kadlec, 1994). This may not be of concern in wetland ecology, but it is of practical concern regarding the performance of

, a treatment wetland. Short circuiting, quantified by A,1 is therefore an unquestionably important factor to be resolved from RTD analysis. Plug-flow efficiency (Ta and

Brignal, 1998), based on the RTD spread, or M 2 • in this study, is not as clear to interpret.

It can be shown for all reaction rates of first order kinetics or greater that the treatment efficiency is maximized with plug flow. Any type of mixing reduces the treatment efficiency unless the reaction follows zero-order kinetics, in which case plug flow and mixed flow have equivalent reaction completions (Levenspiel, 1972; Lawler and

Benjamin, 2003). There are other benefits to mixed flow, however, that may negate the advantages of plug flow on treatment efficiency. Mixed flow can stabilize and equalize pulsed inputs by diluting potentially dangerous pollutant inputs (Lawler and Benjamin,

2003). Therefore, in some circumstances, mixing is at most desirable, or at least neutral, even though some concepts of hydraulic efficiency undervalue this effect.

In conclusion, both aspects of hydraulic efficiency, the measurement of plug flow efficiency and the measurement of short circuiting, are important for hydraulic characterization. Because of the different implications of each of these aspects of hydraulic efficiency, future researchers may want to consider these effects separately, as

16 this and other studies (Ta and Brignal, 1998) have done. The synthesis of these two concepts proposed by Persson et al. ( 1999), though convenient to calculate, is not universally applicable. Not only is some important information lost, but reducing the calculation to one small aspect of the RTD, the peak concentration time, may make this procedure susceptible to error, especially when the RTD is not smooth (Fig. 1.7). The hydraulic efficiency metric Ar is therefore only ideal under certain circumstances.

Similarly, the minimum travel time, t 111 , which is a function of both mixing scale and short

circuiting, is a measurement that should not stand alone.

1.4.4. Limitations of this study

Although the number of repetitions in this experiment is large compared to many

RTD studies of wetlands, sample size for this experiment was nonetheless small in a

statistical sense. The possibility cannot be rejected that the differences in flow rate in this

experiment do have some effect on the RTD. The different dispersal effects discussed

earlier may not have been evident under the flow rates used in this experiment.

The irrigation water, with an average temperature of 14°C, was cooler than the

ambient wetland water temperature which had an average summer temperature of 20°C,

and the average summer storm flow temperature of 23°C. Although the initial flushing of

the wetland minimized this temperature difference between the irrigation water and

previous water in the wetland, the conditions may not have been representative of what

would occur during a natural storm. This effect was subjectively confirmed by thermal

stratification made visible by the dye tracer. The same stratification was not visible when

dye was added during natural storm events with comparatively warmer runoff The

17 centroids for all tracer tests using irrigation water were less than unity, indicating short circuiting was occurring under all conditions (Fig. 1.5). Thermal stratification probably accounted for some of this short circuiting. The remaining short circuiting is likely a result of the proximity of the inlet to the outlet (Fig. 1.2). Because of these temperature effects, these results cannot necessarily be extrapolated to natural flow conditions.

Ideally, an experiment comparing different water levels should be run under fully natural flow conditions. However, such conditions are difficult to control and replicate.

Data from the natural dye tracer studies appear to support the findings of the controlled study, but there are many factors that complicate this interpretation. For example, the three inlets (Fig. 1.2) conveyed runoff in different proportions during storm events. The tracer added during low water level to the storm flow inlet may have been initially circumvented by flow from the nursery inlet, which was flowing strongly before the storm event. This likely decreased the centroid and increased minimum travel time, and in doing so could have artificially inflated other measurements of hydraulic efficiency. It was also clear from the noise in the high water level natural event that there may have been some instrumentation problems (Fig. 1. 7) since the time series was extremely noisy.

1.5. Conclusion

The strength in this study is the demonstration that water level can significantly affect the flow characteristics through a wetland. The study also indicates that the flow distributions at higher water levels may be less efficient than at lower water levels. All other factors being equal, this effect could potentially negate the constituent removal

18 advantage that the longer detention time of a deeper wetland may impart. Future experiments should test if this effect is consistent under different conditions and in different wetlands. This study also indicates that minor fluctuations in flow rate do not significantly affect the RTD. This supports hydraulic characterization using Werner and

Kadlec's (1996) RTD normalization procedure, given that the system depth does not undergo a large relative change. Because controlled RTD comparisons are difficult but needed for wetland studies, the concerns caused by using irrigation water were outweighed by the control advantage of the experimental design.

19 Week water level First applied Second applied

begin prescription flow (Lis) flow (Lis)

Monthly block 1

19-May low 2.27 0.29

26-May high 2.08 1.08

Monthly block 2

16-Jun high 1.56 3.33

23-Jun low 1.51 3.36

Monthly block 3

14-Jul low 3.36 1.19

2-Aug high 1.52 5.03

Table 1.1. Experimental settings for the 2003 dye tracer experiments, showing the average flow rates applied by irrigation water and the wetland water level settings for each tracer experiment.

20 • 3 O A .·. - 1 CSTR §2.5 +; Fully mixed system l_. Hl,,-As mixing scale ~.~.- ;ocg~~~s ~ 2 has largest spread c = \ decreases, the system approaches cu \ plug flow and spread decreases g 1.5 0 0 1 J Centroid remains at unity -g ...... -----~·---- ... - ~~ for all mixing scales

\\I ..~ ...... ____ _ ~E0.5t~:::::.:~~....i..~~=:'=:::::~~-=-~-=~=~::=::::::::'.~::."::=:'.:=::::~~~i!!!l:j.... 0 ..... " ...... , g 0 0.5 1 1.5 2 2.5 Theoretical retention times, +

,--

Short circuiting shifts RTD toward origin, and centroid below unity.

0.5 1 1.5 2 2.5 Theoretical retention times, +

Figure 1.1. Conceptual diagram of the effects of mixing scale (A) and short circuiting (B) on residence time distribution characteristics.

21 IRRIGATION RISER

NURSERY PAD 4700m"2 NURSERY RUNOFF l NORTH 2" HOSE

EXPERIMENT Al WETLAND

OVERLAND KEY STORMFLOW, OUTFLOW SIMULATED t7;\ YSI OC:OO WATER QUALITY STORMFLOW, AND co / \.V AND FLOW PROBE DYE TRACER INPUT •i V·NOTCH WEIR

STORM FLOW AGRI DRAIN WATER FROM FARM LEVEL CONTROL BOX DJ CONTROL BOX

Figure 1.2. Diagram of the setup for the dye tracer experiments at the Waterman Farm wetlands.

22 North

4

2 '--~.J...-~~...... _~~---L-~~__..J'---~~-'-~~-'-....-::'-----'-~~~.L--~..L-J -20 -15 -10 -5 0 5 10 15 distance in meters

Figure 1.3. Bathymetric map of wetland basin. Contours every lOcm, with depths labeled at 30cm intervals. Depths are relative to survey station.

23 x 104 1s.--~~-,-~~~~~~~~~~~~~~~~~~~~~~~~~~

16

14

4

2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 wetland stage - meters from outlet base

Figure 1.4. Volume versus stage relationship of the experimental wetland based on survey data. This relationship is used to find the volume of the wetland when the elevation of the water at the outlet (stage) is known.

24 A B 0 . 4 ~------~ 0 . 2 ~------~

0.3 0.15

0.2 0.1

0.1 0.05

c D

0.4 ~------~

0.3

-11 N ~ 0.2

0.1

Figure 1. 5. Statistics of the residence time distribution (RTD) characteristics under differing flow rates and depths. Comparisons are made between flow rates (averaged two water levels) and water levels (averaged over two flow rates) (mean ± standard error) for (A) Peak concentration time; (B) minimum dye travel time, (C) RTD centroid (first moment); and (D) variance ofRTD (second moment).

25 I I I I low water level high water level

.-2.5 - ..._...-e- 0 c: 0 :;::; 2 ~ ~ c: -Q) (.) c: 8 1.5 Q) :::s -0 ~ 1-- - cu.~ .....E 0 Zo.s-.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Theoretical retention times,

Figure 1.6. Comparison of two representative residence time distribution (RTD) curves run at different water levels.

26 ~ --.---- c)~ 1.2 I\ c: water level = low 0 I\ +:l 1 I \ (';) A. =0.44 ... p t: 0.8 \ C1J u \ = A.t =0.84 t =0.41 g 0.6 • M~ m u ~ ~ 0.4 •,, I :g 0.2 . '"--.._._. j E ~---...... --.... -~ ... o------dL_ __ _L___ _J__ __ _l_ __ _L.. __ __j__ __ ...:::i~'":...~"':'_'.""'"."':··~r~~~·~l g 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Theoretical retention times, +

.. ------r--- -c) c: 4 water level = high 0 +:l (';) 1.. =0.083 ... 3 p c: -C1J u c: M~ = "-t =0.31 t =0.026 0 2 m u "'O (I) N 1 co ...E 0 0 c 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Theoretical retention times, +

Figure 1. 7. Residence time distribution of a dye tracer during natural, pulsed flow for low water level (A) and high water level (B), each shown with associated statistics.

27 CHAPTER2

ANALYSIS AND MODELING OF SUSPENDED SOLIDS FROM HIGH­

FREQUENCY MONITORING OF A STORMWATER TREATMENT WETLAND

2.1. Introduction

2.1.1. Stormwater treatment wetlands

Stormwater treatment wetlands can be engineered as efficient solutions for stabilizing and treating polluted stormwater runoff (Kadlec and Knight, 1996). In addition to being able to detain and dampen storm-flow pulses, wetlands can also retain excess nutrients and solids that may pollute downstream waters (Raisin and Mitchell,

1995; Wong and Geiger, 1997). Although wetlands constructed for treating polluted water are well studied (Kadlec and Knight, 1996), stormwater treatment wetlands still present a particular challenge to wetland scientists. Short-lived storm events are difficult to sample at appropriate frequencies, leading to false representations of pulsed events

(Braskerud, 2002b ). Many studies have been conducted on wetlands over long time periods, but more research is needed to follow dynamics that occur during individual

storm events (Wong and Geiger, 1997).

28 A wetland is typically modeled as an ideal chemical reactor. Water is assumed to travel in steady, plug flow. Under plug flow, water travels at a spatially uniform velocity without dispersion or mixing, from inlet to outlet (Levenspiel, 1972). A single reaction rate is then usually assigned to each pollutant or constituent of interest (Kadlec and

Knight, 1996). Research has shown, however, that reaction rates can vary. Kadlec

(2000) demonstrated that under nonideal flow, meaning when the plug-flow assumption is violated, standard wetland models predict reaction rates that are incorrect. Nonideal flow occurs regularly in wetlands in the form of flow dispersion. Wetland processes can also proceed at different rates under different conditions. Reaction rates for biochemical processes, for example, are affected by temperature (Kadlec, 1999; Braskerud, 2002b) and sedimentation rates are influenced by temperature and particle size, which can change under different hydraulic loads (Braskerud, 2002c ). Long-term monitoring has shown that ideal wetland models can, nonetheless, be adequate tools to represent wetlands subjected to pulsed flow (Carleton et al., 2001). Models for stochastically pulsed wetlands under nonideal flow predict, however, that wetland performance criteria may be incorrectly assessed with plug-flow models (Werner and Kadlec, 2000).

Residence time distribution analysis has become an important aspect of modeling nonideal and pulsed flows in wetlands. A residence time distribution, or RTD, is a probability distribution of the amount of time a non-reacting particle will spend in a system (Levenspiel, 1972). When plug flow conditions are not met, RTDs can be used with reaction kinetics to accurately model the flux of constituents through a system.

RTD analysis also lends itself to pulsed flows (Werner and Kadlec, 1996). RTD modeling has been regularly applied to industrial chemical reactors (Levenspiel, 1972;

29 Nauman and Buffham, 1983) as well as to a limited extent in wetlands (Werner and

Kadlec, 2000). More studies are needed to test the effectiveness of RTD modeling in wetlands. It will be particularly important to apply RTD modeling to wetland events of extremely short and pulsed nature where the assumptions of steady, plug-flow models do not apply.

2.1.2. The case study

A study was performed on a stormwater treatment wetland with high-frequency monitoring equipment. The concentration and flux of suspended solids during pulsed events were monitored at inlets and outlets of the wetland. Suspended solids was chosen as the water quality parameter to monitor because concentrations can be measured using a turbidimeter, with minimal laboratory confirmation (Lewis, 1996), a procedure that would preclude high-frequency monitoring. Although pollutants such as phosphorus and nitrogen are typically used as indicators of wetland water quality (Craft, 1997; Reddy et al., 1999), suspended solids also play an important role in water quality (Koskiaho,

2003). Wetlands are often designed to capture suspended solids by sedimentation in order to reduce biochemical oxygen demand (Bolton and Greenway, 1999) and to retain adsorbed phosphorus (Jordan-Meille et al., 1998). The high-frequency sampling in this study enabled applications, such as cross correlations with time lags and RTD modeling, which have not been practical in other studies dependant on laboratory samples.

30 2.2. Materials and Methods

2.2.1. Site description

This study was performed from April to September of 2003 on a 500m2 wetland constructed on the Waterman Agricultural and Natural Resource Laboratory at the Ohio

State University in Columbus, Ohio, USA (Fig. 2.1 ). The wetland had two adjacent inlet structures that discharged water from an upstream wetland and from storm runoff. Storm runoff was conducted via pipe from parking lots, buildings, and fields around the farm.

An adjustable weir was used to control the water level (i.e. depth) in the wetlands. A nearby weather station maintained by the Ohio Agricultural Research and Development

Committee (OARDC) collected hourly weather data.

2.2.2. Field and Laboratory methods

To determine the volume and depth of the system, wetland topography and weir positions were surveyed in the summer of 2002 (Fig. 2.2). Using survey results, a relationship between water level and wetland volume was defined, assuming that the water level at the outlet is uniform across the wetland (Fig. 2.3)

Each inlet and outlet to the wetland was monitored by a YSI 6-series sonde (YSI,

Inc.), set upstream of the V-notch weir (Fig. 2.1). Capable ofresolving depth to± 1 mm, the YSI devices monitored flow based on the measured height of the water behind the V­ notch weir (ASTM, 2002). The YSI sondes were equipped with self-cleaning nephelometric turbidimeters, which measured turbidity in nephelometric turbidity units

(NTU) by quantifying infrared backscatter. The outlet YSI device was also outfitted with an in-situ probe specifically designed to detect the fluorescence of the dye tracer

31 Rhodamine WT. The sondes were set to automatically log data at IO-minute intervals.

They measured turbidity and weir head during the study, and were recalibrated each month. Occasional cleaning was necessary to clear debris from the optical sensors.

One of two water level settings was assigned randomly during each week of the study. Over a total of 21 weeks, the shallow setting occurred for 12 weeks and the deep setting for 9 weeks. As calculated from the volume divided by the surface area, the shallow water level had an average depth of 15cm, and the deeper water level had an average depth of 24cm. Because many of the analyses required evenly-spaced data, missing data caused problems. This was resolved by replacing data gaps (from when sondes were removed for servicing) in the dataset with interpolated data for gaps less than 1 hour and with zeros for gaps greater than 1 hour. All data analysis was processed with programs written using Matlab software (MathWorks, Inc.).

The data from the turbidimeters was transformed into suspended solids units by calibration with laboratory samples. Grab samples were taken adjacent to the sondes three times per week at each active inflow and outflow. Upon filtration, each sample was shaken well to resuspend particulate solids. Subsamples of 60mL were vacuum-filtered through pre-weighed, 4µL polymer filters. Filters were dried and reweighed, and the difference yielded total filtered solids (TFS) in mg/L, which was assumed to be equivalent to total suspended solids (TSS). Data from the turbidimeters were taken within

20 minutes before and after each grab sample and averaged together to determine a calibration relationship with the sonde' s nephelometric turbidity units (NTU). Because this relationship is typically linear (Gippel, 1989; Lewis, 1996), a linear regression model was used to explain the variance in TSS based on the turbidity reading. Measurements

32 were not used when the turbidimeters gave uncharacteristically high readings, attributed to fouling or interference from debris on the wipers. The regression equation was

1 1 2 determined to be TSS = turbidity-0.487mg·L- -NTU- , with R = 0.84, which was used to

1 convert all turbidity readings (NTU) to TSS concentrations (mgL- ).

2.2.3. Residence time distributions

The exit age distribution function, one form of the residence time distribution

(RTD), is

E(t) = C(t). Q(t) (2.1) M where M is the tracer mass input, C(t) is the outlet concentration as a function of time, and Q(t) is the outlet volumetric flow rate. E(t) has units of inverse time. An analogous representation of the RTD is a dimensionless description of the concentration versus time function:

C'( t) = C(t)V(t) (2.2) M

1 where C(t) is the outflow concentration (mg·L- ), and V(t) the system volume (L), both functions of time. Traditionally, volume is considered a constant (Werner and Kadlec,

1996), but in this study, the volume can fluctuate significantly during storm events and changes in prescribed depth settings, making a single, averaged volume unrepresentative of any situation. Therefore, volume in the present study is described as a function of time. The C'(t) function is typically normalized by replacing the argument with a dimensionless measure of time, as seen in Chapter 1 (Equation 1.2). Werner and Kadlec

(1996) demonstrated that under pulsed flow time can be normalized continuously by flow

33 rate and system volume. This yields a dimensionless unit, representative of effective retention times:

r fQ(t')dt' ¢l\' =-'"--­ (2.3) vsvs

where ¢ w is the flow weighted time variable (dimensionless), tis standard time, t0 is an arbitrary beginning time, Q(t) is flow as a function of time, and t' is a dummy variable for integration. Because Werner and Kadlec (1996) were working on systems with small volumetric fluctuations, they defined volume as an average system volume, Vsys· Because of the changing volumes in this study, flow and volume normalized time was defined based on Equation 2.3, but with volume as a function of time, rather than as a constant:

¢ = If Q(t') dt' (2.4) V(t') 10 where ¢ is the flow and volume weighted time variable (dimensionless) and V(t) is the wetland volume as a function of time, with t' as a dummy variable of integration. In the special case that V(t) is a constant, Vsys, Equation 2.4 reduces to Werner and Kadlec's

(1996) version (Equation 2.3).

2.2.4. Dye tracer residence time distribution

One successful dye tracer was run on the wetland to determine the residence time distribution. A pulse of 14g of Rhodamine WT dye was diluted with 4 gallons of wetland water and mixed in the storm flow inlet (Fig. 2.1) before a forecasted storm event. The outflow concentration was measured by the fluorometer at the outlet. The outlet concentration curve was normalized by Equations 2.2 and 2.4 to yield an RTD expressed 34 by C'(¢) (Fig. 2.4). Only 50% of the dye was recovered at the outlet. Incomplete dye recovery occurred because of chemical degradation and adsorption of the dye tracer

(AWW ARF, 1996; Lin et al., 2003), due to the long period of time needed to wash through the entire tracer (from two storms spaced at 6 days). An artificial RTD curve was used to fit the minimum dye travel time ( ¢ =. l) and centroid ( ¢ =.66), while maintaining a 100% recovery of an ideal tracer (Fig. 2.4 ). This curve was based on the theoretical RTD from two continually stirred tank reactors in series (CSTR) with a minimum travel time delay (Kadlec and Knight, 1996). This artificial RTD was used for modeling flow through the wetland because it maintained the approximate shape but did not exhibit the random noise and degradation of the real tracer.

2.2.5. Modeling outflow with residence time distributions

If the RTD of a system is known, it can be used to predict what happens to mass inputs, even when inputs and flow rates are pulsed. Equation 2.2 can be rearranged to show the output concentration resulting from a pulsed mass input at time ti:

C(t)= C'(t-t;)·M(t;) (2.5) V(t) where C(t) is the output concentration, M(ti) is the pulse of mass input at the input time ti, and t- ti is the time elapsed from mass input (residence time). In the case that mass input flux is a continuous function of time, a differential mass input can be approximated by

!JM(ti)=Cin(ti) · Qin(ti) · !Jti, where !Jti is one time step, and Qin (ti) is the input flow at the time of mass input, and C(t) from Equation 2.5 can be considered the fractional concentration from that mass input. The output concentration is then the sum of all fractional concentrations due to each mass input: 35 (2.6)

This equation is only valid for an initially relaxed system, meaning that Cn ( t

(Nauman and Buffham, 1983); otherwise, there could be unknown constituents already in the system that are not accounted for.

2.2.6. Reaction kinetics.

Most wetland reactions, including the sedimentation of suspended solids, are

assumed to follow first-order reaction kinetics (Kadlec and Knight, 1996). If the

background concentration is assumed to be zero, a common assumption with suspended

solids (Braskerud, 2002c ), the removal is defined by:

(2.7)

wheref(y) is the fractional removal at the fractional distance y (unitless) between the

1 wetland inlet and outlet, ka is the areal rate constant (m ·yr- ), and q is the hydraulic

1 loading rate (m·yr- ). In this study, where measurements are only taken at the inflow and

outflow locations, y will always be unity. An equivalent form to this equation is

C(t) f(t) = --= exp(-kv ·t) (2.8) cin (t)

where f(t) is the fractional removal after a detention time oft in the wetland and kv is the

1 volumetric rate constant (day- ). Wetland scientists typically use Equation 2.7 with the

areal rate constant, ka, which is related to the volumetric constant by ka=kv·h ·E:, with a

conversion from days to years, where h is the wetland depth and E: is the wetland void

fraction (Kadlec, 2000). Equation 2.8 with the volumetric rate constant was chosen for

36 use in this study because the time dependency makes it ideal for modeling rate reactions during pulsed flow. For this reason, Equation 2.8 is also the standard representation of first-order reactions in chemical engineering (Levenspiel, 1972).

The fractional removal of Equation 2.8 can be combined with the initially relaxed system of Equation 2.6 to incorporate reaction kinetics into the output concentration

(Levenspiel, 1972):

C(f)= C'(t-f;)·J(t-f;)·C;n(f;)·Q;n(f;) /1(. f (2.9) i=O V(t) I where tin Equation 2.8 becomes t-t;, the residence time. Note that C;n(tJ·Q;n (t;) is the input mass flux rate, a factor that will be revisited in the following sections. In the discrete case with evenly-spaced time steps, LJt, Equation 2.9 can be described by the matrix operation:

C(t) = X · f (t) (2.10) wheref(t) is the column vector of length N of the fraction remaining after time t for each time interval LJt, and C(t) is the corresponding output concentration vector of the same size. Xis an N by N matrix with entries defined as:

X C'(tn-l -ln-m)·C111(tn-m)·Q111(tn-m) /1t = (2.11) nm v(tn-1) where n is the row, m is the column, for 1

37 is a lower triangular matrix for an initially relaxed system, because n-m in the upper triangular portion is less than zero. When flow is unsteady, C'(tn-rln-m) is a unique RTD

function at time t11 _1 of a constituent added at time t11 _111 , which can be defined by denormalizing the general RTD function C'( ¢ n-1-¢ n-nJ- Werner and Kadlec (1996) demonstrated that, in theory, normalizing the RTD by ¢ w yields a consistent shape for

C'(¢ w ), even when the denormalized RTDs have very different characteristics. This observation was used in reverse to denormalize the model RTD (Fig. 2.4) to fit each unique flow and volume condition. Time denormalization was accomplished by interpolating C'(¢ n-rr/J n-nJ onto the corresponding standard time, ln-1-tn-m, using the relationship between t and¢ (Equation 2.4).

Although the discrete outlet concentration equation (Equation 2.10) is important for predicting outflow concentrations, it can also be employed for determining the fractional removal function,f(t). It would appear that there is a unique solution for the vector f(t) in Equation 2.10, as there are exactly as many unknowns in the indeterminate f(t) as there are columns of the matrix X; however, two factors prevent this solution: (1) the first columns of X are normally zero due to the initial RTD values; and (2) in a real system with noise, a least-square solution is desired, in which there are more columns in the matrix Xthan unknowns in the vectorf(t). If first-order kinetics (Equation 2.8) are used forf(t), however, there is only one unknown, kv. Unfortunately, Equation 2.8 is nonlinear and its product with X (Equation 2.10) cannot be linearized using logarithms when Xhas more than 1 nonzero entry per row (this would occur only under plug flow or with a pulsed input flux). Therefore, the least squares solution cannot be solved using the normal equations. A numeric solution, however, is possible for f(t). Since applying 38 Equation 2.10 is only practical with the help of a computer, solving the least squares

solution for kv by iteration is not unreasonable. One possible way a least square solution

for an indeterminate f(t) could be found using the normal equations would be to define X

over a very large interval and remove columns from the right side (corresponding to very

smallf(t), which is not of interest), or to vertically stack independent X matrices and C(t)

outputs on top of each other, so as to create significantly more rows than columns.

Because short events were isolated in this study, kv was solved numerically by iteration.

2.2. 7. Models for determining sedimentation rates

Four models were used to investigate the sediment retention rate during storm

events. The first two models employ the fractional change from inflow to outflow of

Equation 2.8, without considering the time-variable nature of the flow. Model 1 utilized

the ratio of mean inflow concentration to mean outflow concentration as the fractional

removal,f(t). Model 2 utilized the relationship of mean inflow mass flux to mean

outflow mass flux, which effectively weights concentrations by flow rate to give

preference to high flow events. Retention time was calculated by a flow-weighted

1 average of0.66· V(t)-Q(tl , where 0.66· V(t) is the effective volume of the system, since

0.66 is the RTD centroid. So that these models could be compared with the RTD model,

flow weighting of the retention time avoided lowering the retention time with low-flow

periods surrounding the storm event. In other words, the length of the time interval

selected around a storm event biases the measure of mean detention time; using the flow­

weighted mean is intended to reduce this bias.

39 Models 3 and 4 employed the RTD relationship of inflow to outflow as described by Equation 2.10. In both of these models, the reaction constant was solved for iteratively, by choosing the kv value that yielded the least square solution between the output predicted by the model and the observed output. In model 3, the solution kv value was found by minimizing the squared error in output concentration, similar to model 1.

Analogous to Model 2, Model 4 used the least square solution based on minimizing error in output mass flux. Thus, Model 4 also gives preference to the events that happened during elevated flow, but was mechanistically identical to Model 3.

The output of the RTD model (Model 3 or 4) that exhibited the least unexplained variance in reaction rates was compared against a mean-value output. The goodness-of­

2 fit parameter, R , was calculated to quantify the variance of the data explained by the model. ANOVA statistics were calculated to test how significantly the model explained the variance of the mean output values more closely than one single mean. In essence, this compared whether the RTD model (based on the output time series) was more appropriate than the plug flow model (based on a single mean for the entire event), an important question for understanding the applicability of the more complex RTD model.

2.2.8. Investigating storm events

Each model was used to solve for kv during each significant precipitation event that occurred over the period of study. A significant precipitation event was defined arbitrarily as >I cm of rain over any 16 hour period. Precipitation intervals for investigation were defined based on the OARDC weather station data. Data from the wetland database were then taken from 3 hours before the beginning of the significant

40 precipitation to 12 hours after each precipitation. By this protocol, the intervals were allowed to be different lengths. For example, two hourly precipitation events of 0.6cm each spaced 8 hours apart (9 hours from beginning to end) would register as a significant precipitation event, and the corresponding interval would be 24 hours (3 hours before, plus 9 hours during and between, plus 12 hours afterwards).

Sedimentation rate constants are known to be associated with hydraulic loading.

Higher hydraulic loading rates have more energy to suspend larger particles, which have higher settling velocities (Braskerud, 2002c ). Theoretically, it can be demonstrated that water depth has no influence on sedimentation rates, since the increased detention time associated with deeper water is offset by the longer distance required for a particle to

fully settle (Hazen, 1904; Braskerud, 2002a). A good model for determining sedimentation rates was therefore expected to have most of its variance explained by hydraulic loading. This was used as a criterion for assessing the efficacy of different

sedimentation rate models. The kv values of each storm were analyzed separately by each

model. A linear regression with ANOV A analysis was run on each set of kv values to

determine the amount of variance explained by the linear relationship with hydraulic

loading. Hydraulic loading is traditionally calculated in units ofm·year-1 to reflect the

mean hydrologic conditions of a wetland (Kadlec and Knight, 1996). Since this study

focuses on particular storms, the peak flow measured at the outlet was deemed a more

appropriate measure of the intensity of a storm event, and standard flow units, L·s- 1 were

maintained.

41 2.2.9. Cross correlations

Cross correlations run at a series of time lags can be used to determine the significance of lag effects (Lippmann and Holman, 1990), such as the time delay from inlet to outlet in a wetland due to detention time. Cross correlations with time lags were run on the entire time series data from April through September 2003. Just as an RTD curve relates output concentration to input mass, input suspended solids flux was correlated with output concentration, using an array of time lags. The cross correlations

with time lags were run to quantify the lag effect of detention time on solids transport.

The correlations were also used to determine whether the dynamic time variable ¢ is a

more appropriate explanatory variable of solids flux through the wetland than time.

Cross correlations with time lags require data measured over evenly spaced time

variables. Although the data of this experiment were measured over evenly-spaced 10

minute intervals, ¢ is a nonlinear function of time. In order to enable cross correlations

with time lags in phi, a non-traditional method was developed. An artificial variable, ¢ *,

was created by taking the minimum and maximum ¢ values and creating an evenly­

spaced array of values. The turbidity data were then linearly interpolated from the

original, heterogeneously spaced ¢ onto the artificial, homogeneously spaced ¢ *. Cross

correlations were run on the interpolated turbidity values with time lags in ¢ *. Cross

correlations with time lags were run under three conditions: 1) the entire data set, 2) the

high water level alone and 3) the low water level alone. On the datasets where only one

water level was considered, the time and ¢ * variables were preserved unchanged, and the

42 turbidity data were either preserved or redefined as zero, depending on which water level they corresponded to.

Confidence intervals for the cross correlations were determined by the number of theoretically independent observations, N*. The long time-lag artificial skill method, based on the assumption that any correlation at arbitrarily long time lags is artificial, was used to determine N* (Davis, 1976; Lippmann and Holman, 1990).

2.3. Results and Discussion

2.3.1. Cross correlations

All cross correlations showed a significant correlation with a peak occurring at a positive time lag between input and output data. The maximum correlation conducted relative to ¢•was 1.7 times larger than the maximum correlation relative to standard time, t (Fig. 2.5). When cross correlations were calculated on distinct water levels, the lower water levels corresponding to smaller volumes had shorter peak cross correlations in time (Fig. 2.6A). The cross correlations in ¢•showed the opposite trend, peaking at a lower value for the higher water levels (Fig. 2.6B).

The higher correlation values for the ¢ • variable (Fig. 2.5) indicate that the dynamic variable ¢ was indeed a better predictive variable of the flux of suspended solids than was the static variable of standard time. This can be explained in that the actual detention times are different for every event through the wetland. In other words, the peak correlation time of one event would be different than that of a different event.

When all events are combined together in one cross correlation, these different times will tend to cancel each other out, reducing the total correlation. The variable ¢, on the other 43 hand, should be a predictive variable of constituent travel through the wetland, indifferent to the flow rate (Werner and Kadlec, 1996); therefore, events should all have similar peak correlations, thus reinforcing each other when the entire dataset is considered. The smaller shift in maximum correlation values under ¢ * lags as compared to standard time

lags (Fig. 2.6) supports this conjecture.

Because the cross correlations were conducted on the same variables used to calculate RTDs, input mass and output concentration, it is not surprising that the cross

correlations in ¢ * retain some of the characteristics of the residence time distribution.

For example, the cross correlations (Fig. 2.5B and 2.6B) and the RTDs (Fig. 2.4) all

reach a peak between O< ¢ <1. No such generalization can be made about the

correlations in standard time (Fig. 2.5A and 2.6A) since this is dependent on transient

flow rates and system volumes. The ratio between the peak RTD concentration time and

the mean detention time has been shown to be a metric of hydraulic efficiency, or the

effectiveness of the wetland system to distribute its flow evenly throughout its area to

maximize treatment efficiency (Persson et al., 1999). Although the hydraulic efficiency

is typically measured by analysis of the RTD from a tracer experiment, results of the

present study indicate that the cross correlation with time lags measured in evenly spaced

¢ * intervals may also be used to assess hydraulic efficiency.

This observation leads to interesting implications of the cross correlations run at

different water levels. It is clear that a longer mean detention time is expected in a deeper

wetland setting with a larger volume (Kadlec and Knight, 1996). Thus, it is expected that

the cross correlations in standard time, t, will peak at a later time for the higher water

level setting (Fig. 2.6A). Cross correlations in ¢ *, however, are expected to peak at the 44 same value at any water level or flow rate, under the assumption that a normalized R TD remains unchanged under these conditions (Werner and Kadlec, 1996). Indeed, the correlations in time show a larger relative shift due to depth settings (65% difference) than do the cross correlations calculated in ¢ * (11 % difference) (Fig. 2.6). The relatively small change in peak correlation in ¢ * at different depth settings may result from chance, especially over the short time frame of this experiment; however, it is also possible that this shift may be a result of a change in the intrinsic R TD of the system at the different water levels. Although this observation cannot be statistically confirmed, the cross correlations in ¢ * at different water levels (Fig. 2.6) supports the findings from Chapter 1 that demonstrated an inverse relationship between peak R TD value and wetland depth setting.

The 95% confidence intervals on the cross correlations increased dramatically in width when the independent variable of the cross correlations was changed from t to ¢ *.

This observation is not surprising when the concentration data are compared in t and ¢ .

The storm events expressed int are randomly distributed with null spaces in between, yet when these same data are expressed in¢*, high-flow events appear regular (Fig.2.7).

Correlations at long lags in ¢ * will therefore tend to still be high, reflecting the regularity of the data. A longer experimental time frame may have minimized this artificial correlation. Since the confidence intervals were based on the measurement of artificial skill from long time lags (Davis, 1976), the phenomenon of inflated confidence intervals in ¢ * may be a limitation of the method used to calculate the confidence intervals and the length of the dataset, and not a limitation of the data quality.

45 2.3.2. Sedimentation kinetic models

A total of 19 independent storm events were evaluated, with peak flow rates ranging from 4.4L·s-1 to 122L·s-1 and maximum ¢ values ranging between 0.57 to 8.81.

Maximum ¢ value is the ratio of the cumulative outflow volume to the wetland volume,

or the effective number of retention times elapsed. Although fractional retention

decreased as a function of peak flow (Fig. 2.8), each of the four models showed an

increase in the sedimentation rate constant as the peak flow increased (Fig. 2.9).

Fractional retention is often reported as a performance criterion of treatment

wetlands (Carleton et al., 2001). The negative correlation between fractional retention

and hydraulic loading (Fig. 2.8), despite the positive relationship between sedimentation

rates and hydraulic loading (Fig. 2.9), indicates that fractional retention should be

reported together with hydraulic loading. Reporting only fractional retention may

undervalue the performance of a treatment wetland.

Of the four models investigated, only Model 4 had its variance in rate calculations

significantly explained by the peak flow (p=.006, ANOV A) (Fig. 2.9). The other models

(Models 1-3) demonstrate the same positive correlation between sedimentation rate and

hydraulic loading as Model 4, but each with unique slopes for this relationship (Fig. 2.9).

Upon closer inspection, it appears that Model 3 and 4 yield very similar reaction rates for

most events with one exception: one extreme outlier during a low-flow event in Model 3

greatly skews the regression coefficients (Fig. 2.9). Model 1 yields a similar slope

relationship to Model 4. The major difference between the rates calculated by Models 1

and 4 is that Model 1 has much greater variance not explained by hydraulic loading (Fig.

46 2.9). Model 2 does not have as much variance as model 1, but it also shows a lower slope

relationship between calculated rate and hydraulic load (Fig. 2.9).

Since Model 4 had the least unexplained variance, it was used to measure the

effectiveness of RTD modeling. Model 4 was able to fit a predicted outflow curve to the

actual outflow data with good precision, even with complicated inflow and outflow

relationships (Fig. 2.10). The goodness of fit between the model and the actual outflow,

2 R , appeared to increase slightly as the flow increased, but this increase was not

significant (p=0.11) (Fig. 2.11 ). With the exception of one event (Fig. 2.12), all storm

events yielded an outflow concentration prediction by Model 4 that significantly

explained the variance of the outflow concentration (ANOVA, p<.001 for all events).

Because ANOVA compares the time-series output of Model 4 with a single-mean output,

this test effectively compares Model 4 with Models 1 or 2. This demonstrates that for

most situations Model 4 yields a significantly better explanation of the observed data than

would a single average for the event that would have been predicted by Models 1 or 2

(Model 3 not tested). The one event analyzed by Model 4 whose RTD model did not

significantly explain the variance in the data (p=.66, ANOV A), appeared to have required

an RTD with a shorter minimum travel time (first rise of the RTD curve) to fit the

outflow data (Fig. 2.12). The occasional incorrect fit offers evidence that there is not

always a single, fixed RTD for the system. Although an unstable RTD would complicate

the modeling of pulsed flows, the simpler model of this study assuming a static RTD is

nonetheless acceptable, at least until factors determining the stability of RTDs are better

understood.

47 There is no definitive way from this study to verify which model gives the

"correct" answer for sedimentation rates. Only an independent measure of sedimentation rates, such as from sedimentation columns run on samples from each storm, would help to verify which model is most accurate. Model 4 seems most optimal because it explains the variance of the data by hydraulic loading, which is expected from past studies

(Braskerud, 2002c ). It is also possible, however, that Model 4 could be biased by hydraulic loading, as Kadlec (2000) indicates may occur with incorrect models. If this were the case, a model with lower variance and correlation with hydraulic loading, such as model 2, would fit the criterion for best model.

Literature values of sedimentation rates vary greatly. A long-term study of seven stormwater treatment wetlands by Braskerud (2002a) determined ka rates ranging from

1 1 339m·yeaf to 727m·yeaf • A review of 35 studies by Carleton et al. (2001) found ka rates ranging 0.03m·yeaf1 to 135m·year-1 (calculated from reported fractional retention and hydraulic loading). Eight studies reviewed by Kadlec and Knight ( 1996) reported ka

1 1 1 values from 1000 m·year- to 9600 m·year- . When kv (daf ) used in this study is

converted to ka based on a mean wetland depth of 19cm and a fraction void (including

1 conversion factor) of 365day·year- , equivalent ka values of Model 4 range from

1 1 120m·year- to 1800m·year- , which is within the range ofliterature values. Some of the

low literature values for ka are likely deflated by using hydraulic loading averaged over

long time periods. Long-term hydraulic loading is much lower than instantaneous

hydraulic loading during a storm event, which is used in the RTD models 3 and 4, or the

flow-weighted mean detention time, which is used in plug-flow models 1 and 2. Aside

48 from true differences in settling rates and wetland efficiency, different methods for calculating sedimentation rates may account for some of the literature range.

This study experimentally demonstrates that the RTD model without (Equation

2.6) and with (Equation 2.9) reaction kinetics used in Models 3 and 4 can be used to model wetland treatment given complicated input forcing functions of flow and concentration. Although the continuous form of the RTD model is not used in this study, it is interesting to note how Equation 2.6 reduces to a form familiar in the literature. The continuous form of the outlet concentration can be expressed by taking the limit of equation:

C(t) = Lim (i: C' (t - ti)· Cin (ti)· Q;n (ti) t-.ti J /).ti ~ 0 i=O V(t)

= }C'(t -t;). cin (t;). Qin (ti) dt. (2.12) 0 V(t) I If the volumetric inflow and outflow are equivalent, i.e. Qin(tJ=Q(t), Equation 2.12 can be combined with Equations 2.1and2.2:

C(t) ="'IC' (t -ti). cin (t,). Q(t) dt Replacing Qin( tJ with Q( t) 0 V(t) I

"' ( C(t -~)V(t)) · Cin (ti)· Q(t) Applying Equation 2.2 = I V(t) t;

E(t-ti)·MJV(t)J·C (t )·Q(t) 00 (( Q(t) Ill I Applying Equation 2.1 =f V(t)·M t;

00 = fE(t- ti)· Cin (t;) · dti (2.13) 0

49 This is a convolution integral that can be equivalently expressed using convolution notation:

C(t) = E(t) * C;n (t) (2.14)

This relationship between the inflow concentration and the RTD is commonly used in chemical engineering to express output concentrations of complex input functions

(Levenspiel, 1972; Nauman and Buffham, 1983). The convolution integral (Equation

2.14) is the continuous representation of the matrix X (Equation 2.11 ).

2.3.3. Limitations ofthis study

RTD modeling is a "black box" approach to explaining complex flows (Carleton,

2002), one that utilizes a simple, phenomenological RTD to overstep the biological, fluid, and chemical mechanisms that actually occur in the spatial and temporal realm of the wetland. Many simplifying assumptions were therefore made about RTD and reaction modeling of pulsed constituents in this study. Reaction kinetics are not purely a function of time; for example, first-order reaction rates are functions of concentration, which changes as the flow disperses through the system (Levenspiel, 1972). Reaction rates are also related to a particular path though a wetland, which can be associated with a certain position on the RTD curve (Kadlec, 2000). Heterogeneous vegetation distributions and associated biofilms, as well as changes from aquatic to benthic habitats are major factors that cause pathway-specific reaction rates (Carleton, 2002). The reaction associated with a wetland is therefore better demonstrated as a damkohler number distribution, a derivative of the RTD that considers the connection between pathway-specific reaction rates and the RTD itself (Carleton, 2002). It must therefore be recognized that, even

50 under first-order reaction kinetics, the fractional removal,f(t), may not take its familiar form (Equation 2.8). Unfortunately, analysis of the RTD model with reaction kinetics

(Equation 2.9) revealed earlier that solving for f(t) is not straightforward.

This study also assumed that the normalized RTD function, C'( ¢)remained stable under all conditions. In doing so, some of the failure of the model to match the data (Fig.

2.12) demonstrated that the RTD may be unstable. Chapter 1 describes climactic, ecological, and hydrologic conditions that are known to affect RTD stability. Future studies on factors affecting RTD characteristics will therefore be useful. Additionally, empirical demonstration of how closely f(t) follows first-order kinetics will be of interest.

Although in need of some refinements itself, the R TD modeling used in this study is nonetheless a first and important step towards creating a more accurate depiction of pulsed and nonideal flows.

The need for knowing the exact RTD under a specific set of conditions together with earlier suggestions for findingf(t) suggest a novel experiment for investigating reaction rates. If a pollutant were artificially introduced as a pulse, solving for an indeterminatef(t) from the discrete RTD model with reaction kinetics (Equation 2.9) would be simplified. A pulsed input would also allow a tracer to be introduced simultaneously, eliminating the unknown nature of the exact RTD. In this manner, a simple solution for an indeterminate f(t) may be possible. This would be most effective with pollutants that can be detected in low concentrations and that have low background levels, such as a biodegradable pesticide (Anderson et al., 2002).

51 2.4. Conclusions

This study demonstrated the importance of using flow- and volume-weighed time,

¢,for describing pulsed flow in wetlands. The evenly spaced ¢*was shown to be an

important predictive variable of constituent flux through a wetland. When translated into

t, evenly spaced¢ *becomes variably spaced steps in standard time, closer together for

high flow and low volume, and farther apart for low volume and high flow.

Economically, this indicates for studies in stormwater treatment wetlands that flow-

weighted sampling (Braskerud, 2002c) should be utilized, when possible, to extract the

most information out of the least amount of samples. Expression of solids flux in ¢ also

demonstrated a novel method for evaluating hydraulic efficiency. Applying this

observation supported Chapter 1 that demonstrated changes in hydraulic efficiency

caused by wetland depth manipulation; in both cases, the relationship between depth and

hydraulic efficiency were inversely related. Dynamically normalized time variables, such

as¢, will continue to be important aspects of studying pulsed flows in wetlands.

RTD modeling also promises to be an important tool for investigating pulsed and

nonideal flows. RTD modeling of pulsed flows with first-order kinetics usually produced

remarkably accurate results (Fig. 2.10). The less common, but inaccurate results (Fig.

2.12), may be improved in the future with a more flexible or dynamic RTD

understanding. RTD modeling appears to offer the most effective method of describing

pulsed flows that does not require difficult spatial modeling of biological, chemical, and

fluid processes (Kadlec, 2000; Carleton, 2002). Applying the steady, plug-flow model to

inlet and outlet concentrations (Model 1) has yielded statistical results over the long term

that are similar to, though less consistent than the RTD model (Fig.2.9). This is a 52 powerful demonstration of a plug flow model working adequately over a long-term period (Carleton et al., 2001). These results also strongly support, however, the contention that extreme events considered individually may be incorrectly evaluated using steady, plug-flow models; thus, certain performance guidelines are overlooked

(Werner and Kadlec, 2000).

The use of automated data collection was instrumental in demonstrating that chemical engineering tools can be successfully applied to wetlands. Empirically confirming RTD models during short-lived events will be more challenging and not economical in many cases where laboratory samples are required. However, this is worth taking advantage of whenever possible. Cutting-edge tools for understanding pulsed and nonideal flow through wetlands, such as RTD modeling, once understood more fully, will lend important insight to setting guidelines for and aiding in the effective design of stormwater treatment wetlands.

53 FLOW FROM TREATMHIT WETLAND l STORMFLOW I 1 ometers I NORTH FROM FARM

STORMWATER TREATMENT WETLAND

0 YSl6000 WATER QUALITY AND FLOW PROBE

I• V-NOTCH WEIR • AGRI DRAIN WATER []] LEVEL CONTROL BOX CONTROL BOX

Figure 2.1. Diagram of the stormwater treatment wetland at the Waterman Farm in Columbus, OH.

54 Q) (.) ~ -25 !/) :.0- -30

0 10 20 30 40 50 distance in meters

Figure 2.2. Bathymetric map of wetland basin. Contours every 1Ocm, with depths labeled at 30cm intervals. Depths are relative to survey station.

55 5 x10 2. 5

2

~ Q) ==-;- 1.5 Q) E :J 0 > "'O c: 1 ell ~

0.5

oL.....--..... -===::...... ~~--.1.~~---L~~-L~~__._~~-'-~~....J 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 wetland stage - meters from outlet base

Figure 2.3. Stage (water depth from base of outlet device) versus volume relationship of wetland based on survey data.

56 /-,, natural dye tracer RTD I \ I \ modified 2 CSTR theoretical RTD I \ 1.2 I \ , \ I \ I \ c: IJ ' \ 0 1 :;:: ~ . \\ c: -

0 0.5 1 1.5 2 2.5

Figure 2.4. Comparison of a dye tracer run under natural conditions and the RTD function used to model suspended sediments flowing through wetland based on a theoretical system of 2 continually stirred tank reactors (CSTR). Difference in area between the two curves represents the dye lost during the natural RTD experiment; the modeled RTD corrects for this error in the measured RTD.

57 A ·----r--- B 0.8 - cross correlation 0.8 Peak occurs at 95% confidence interval ,..,-/ 4> = 0.46 0.7 0.7

0.6 0.6

Peak occurs at c: 0.5 c: 0.5 >"/ t = 0.030 days 0 .Q :;.:; ro ro Q5- i... 0.4 ~ 0.4 i... i... 0 0 (.) (.) en en en 0.3 (() 0.3 0 0 i... i... (.) (.) 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1 -0.5 0 0.5 1 -2 0 2 4 6 time lag - days cp lag - retention time

Figure 2.5. Cross correlation for all water levels with 95% confidence intervals with time lags (A) in days and (B) in detention time (unitless). Vertical scale is preserved between the two plots for comparison.

58 A B 0.8 low level correlation 0.8 low level 95% Cl ~.. high level 95% Cl - I '~ ' \, 0.7 high level correlation 0.7 low level peak J i 'l at =.468 J ' high level peak 0.6 ~·,~ low level peak 0.6 ' '- d i *t-- at =.418 ii at t=.029 days J I I ~ H j c: 0.5 II s::: 0.5 ~ ~ high level peak 0 I I \ .Q :;:::: I ~ ro ro I ~' 1(;at t=.057 days -a> ~ 0.4 i... 0.4 i... i... -f-\t_ .. ______0 0 (..) \-----i (..) I 1 \ (/) I ' \ \ .. . . ~ 0.3 ~ ~ \ (/) 0.3 0 \j ! ' \ i... I \ ~ e - - I (..) (..) ;I il. \' i -, \ I \• I-~ \ 0.2 0.2 \ \. \ •- -t ~ ; i\ ,,_ ; i ~ ' \ i ' j \ \/. /li \ 0.1 \,i) \ ·'··,, 0.1 )'V \ i \ ·.. -'. ! -,, '°"------\ If \ I\. i \ \. ------~------""·"-- ·; -· ·- ·- --.,._,,, -·--...... ! I \J \l \ \ 0 ·-· ". '·-·-··· 0 _; """\

-0.1 .______.______,______, -0.1 '-----'----'-----'----'------'---' -0.5 0 0.5 1 -2 0 2 4 6 time lag - days lag - retention time

Figure 2.6. Cross correlations at separated high and low water levels with time lags and 95% confidence intervals (CI) in (A) days and (B) detention times. Vertical scale is preserved between the two plots for comparison.

59 A

B 600r---f------;r------;r------;-----;r------;-----;#------;-----,r------;-----;rl------;-----,,,_-----;-----,r------;-----;-----;~

_J C) -E 400 cI .Q ~ 200 -c Q) g 0 0 ()

-200'--~~-'--~~--'-~~~~~---'---~~-'-~~----'--~~---'-~~--'~~~'---' 0 2 4 6 8 10 12 14 16 18 retention times - cf>

Figure 2.7. Comparison of wetland outlet concentration as a function of time (A) and as a function of volume and flow-normalized time, ¢ (B). Corresponding events are connected with arrows to demonstrate the nonlinear relationship between t and ¢. The uneven spacing of ¢ is also evident in this comparison.

60 0.9 * * 0.8 * * 0.7 * c * 0 ~0.6 * (!.) * * (!.) * * .::- 0.5 Ctl c 0 * f5 0.4 * ....Ctl -0.3

0.2 *

0.1 *

0 0 20 40 60 80 100 120 140 peak flow - Lis

Figure 2.8. Fractional sediment retention of each storm event as a function of the peak outlet flow of the corresponding storm (a metric of hydraulic loading), modeled by linear regression (R2=0.47 and p=.002 by ANOVA).

61 PFR by cone. (Model 1) PFR by flux (Model 2) 40 slope=0.12 --;1 81 slope=0.016 2 2 30 R =017 R =0.11 p=0.093 sl p=0.17 * 20 + ------I 41 10 •r.* +. - ~ . 21~-- 0 * * 1t, + +. * -10~~~-~~~~~~~~~ o~~~~~~~~~--~~ 0 50 100 150 0 50 too 150 peak flow - Us peak flow - Us RTD by cone. (Model 3) RTD by flux (Model 4) so~~~~~~~~~~~--. 30~~~~~~~~~~~---, slope=0.035 slope=0.11 2 25 2 40 * R =0.020 R =0.40 p=0.58 ..- p=0.006 '> 20 ro 'O * 15 * * +* * * 10 * * 4* ** * * * * 0'--~~~,__~~~"--~~--' 0 50 100 150 50 100 150 peak flow - Us peak flow - Us

Figure 2.9. Comparison of sedimentation rate constants compared by different models, plotted versus peak flow rate of associated storm event with trends shown by linear regression and associated statistics.

62 0'---..l~__L""""~~...... ---~""""'"'-~~---'--~~-1.------'-~~~"'-~~---' 129.2 129.4 129.6 129.8 130 130.2 130.4 130.6 130.8 time - yearday B 800.-~~-,-~~~--.--~~~.-~~---.-~~-,-~~~--.--~~~.---~~___.,

...J """" model prediction without sedimentation -.. • actual outflow C) 600 E - model prediction with sedimentation c: 400 0 :;:::: 200 ~c: Q) g oi--.., 0 (.)

-200~~~~~~~-'--~~~-'--~~--'~~~~~~~-'--~~~-'--~~--' 129.2 129.4 129.6 129.8 130 130.2 130.4 130.6 130.8 time - yearday

Figure 2.10. Input mass flux of suspended solids to stormwater treatment wetland during adjacent rain events (A). Predicted outflow suspended solids concentration from RTD model 4with and without sedimentation dynamics compared with actual outflow (B).

63 * t 0.9 * * * ~* 0.8 *** if

0.7

N 0:: 0.6 lE Q5 "O 0.5 * 0 E 0.4

0.3 * * 0.2 *

0.1 0 20 40 60 80 100 120 140 peak flow - Us

Figure 2.11. Relationship between the R2 fit of the RTD by flux model (Model 4) with the peak wetland outlet flow (a measure of hydraulic loading), shown with linear regression to determine if model accuracy changes with flow (R2=0. l 5; p=.11 from ANOVA).

64 A 5000

~4000 E I ~ 3000 ~ c;:: I -5_2000 .5 1000 )l._ 0 146.8 146.9 147 . 147.1 147.2 147.3 147 4 time - yearday B

_J c, '"""" model prediction without sedimentation ·"'""""""" ...... ,...... ,,. E 30 actual outflow - model prediction with sedimentation c: .Q 20 -~ .. c: 10 .. .. ·... -Q) ...... ··· .. :· .. ···...•.. .. (.) ...... c: .. 0 0 (.) ········ -10 146.8 146.9 147 147.1 147.2 147.3 147.4 time - yearday

Figure 2.12. Example of a bad fit of the RTD model. Input mass flux of suspended solids to stormwater treatment wetland during a single rain event (Top). RTD model outflow concentration prediction of suspended solids with and without sedimentation dynamics compared with actual outflow.

65 REFERENCES

Anderson, K. L., K. A. Wheeler, J.B. Robinson, and 0. H. Tuovinen, 2002. Atrazine mineralization potential in two wetlands. Water Res. 36, 4785-4794.

ASTM, 2002. Standard test method for open-channel flow measurement of water with thin-plate weirs. Pages 590-597 in Annual book of ASTM standards. ASTM, Philadelphia.

AWWARF, 1996. Tracer Studies in Water Treatment Facilities: A Protocol and Case Studies. American Water Works Research Foundation, Denver, CO.

Batzer, D. P., and V. H. Resh, 1992. Wetland Management Strategies That Enhance Waterfowl Habitats Can Also Control Mosquitos. Journal of the American Mosquito Control Association 8, 117-125.

Bolton, K. G. E., and M. Greenway, 1999. Pollutant removal capability of a constructed Melaleuca wetland receiving primary settled sewage. Water Sci. Technol. 39, 199-206.

Braskerud, B. C., 2002a. Design considerations for increased sedimentation in small wetlands treating agricultural runoff. Water Sci. Technol. 45, 77-85.

Braskerud, B. C., 2002b. Factors affecting nitrogen retention in small constructed wetlands treating agricultural non-point source pollution. Ecol. Eng. 18, 351-3 70.

Braskerud, B. C., 2002c. Factors affecting phosphorus retention in small constructed wetlands treating agricultural non-point source pollution. Ecol. Eng. 19, 41-61.

Carleton, J. N., 2002. Damkohler number distributions and constituent removal in treatment wetlands. Ecol. Eng. 19, 233-248.

66 Carleton, J. N., T. J. Grizzard, A. N. Godrej, and H. E. Post, 2001. Factors affecting the performance of stormwater treatment wetlands. Water Res. 35, 1552-1562.

Craft, C. B., 1997. Dynamics of nitrogen and phosphorus retention during wetland ecosystem succession. Wetlands Ecology and Management 4, 177-187.

Davis, R. E., 1976. Predictability of sea surface temperature and sea level pressure anomalies over the North Pacific Ocean. J. Phys. Oceanogr. 6, 249-266.

Gippel, C. J., 1989. The Use ofTurbidimeters in Suspended Sediment Research. Hydrobiologia 176, 465-480.

Hazen, A., 1904. On Sedimentation. Transactions, American Society of Civil Engineers 53, 43-71.

Jordan-Meille, L., J.M. Dorioz, and N. Mathieu, 1998. An artificial flood to determine the hydrological network's contribution to phosphorus exports in a small rural watershed. Water Res. 32, 1801-1810.

Kadlec, R.H., 1994. Detention and Mixing in Free-Water Wetlands. Ecol. Eng. 3, 345- 380.

Kadlec, R.H., 1999. Chemical, physical and biological cycles in treatment wetlands. Water Sci. Technol. 40, 37-44.

Kadlec, R. H., 2000. The inadequacy of first-order treatment wetland models. Ecol. Eng. 15, 105-119.

Kadlec, R.H., and R. L. Knight, 1996. Treatment Wetlands. CRC Press, Boca Raton, FL.

Keller, C.H., and J. S. Bays, 2000. Tracer Studies for Treatment Wetlands, INTECOL Invited Papers Symposium 13 (Part 3); Constructed wetlands for wastewater and stormwater applications, 173-181.

Konyha, K. D., D. T. Shaw, and K. W. Weiler, 1995. Hydrologic Design ofa Wetland­ Advantages of Continuous Modeling. Ecol. Eng. 4, 99-116.

67 Koskiaho, J., 2003. Flow velocity retardation and sediment retention in two constructed wetland-ponds. Ecol. Eng. 19, 325-337.

Lawler, D. F., and M. M. Benjamin, 2003. Water Quality Engineering. McGraw Hill, in press.

Levenspiel, 0., 1972. Chemical reaction engineering, 2d edition. Wiley, New York.

Lewis, J ., 1996. Turbidity-controlled suspended sediment sampling for runoff- event load estimation. Water Resour. Res. 32, 2299-2310.

Lin, A. Y. C., J. F. Debroux, J. A. Cunningham, and M. Reinhard, 2003. Comparison of rhodamine WT and bromide in the determination of hydraulic characteristics of constructed wetlands. Ecol. Eng. 20, 75-88.

Lippmann, T. C., and R. A. Holman, 1990. The Spatial and Temporal Variability of Sand-Bar Morphology. J. Geophys. Res.-Oceans 95, 11575-11590.

Mitsch, W. J., and J. G. Gosselink, 2000. Wetlands, 3rd edition. John Wiley, New York.

Nauman, E. B., and B. A. Buffham, 1983. Mixing in Continuous Flow Systems. John Wiley & Sons, New York.

Nepf, H. M., 1999. Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resour. Res. 35, 479-489.

Nepf, H. M., and E.W. Koch, 1999. Vertical secondary flows in submersed plant-like arrays. Limnol. Oceanogr. 44, 1072-1080.

Nepf, H. M., J. A. Sullivan, and R. A. Zavistoski, 1997. A model for diffusion within emergent vegetation. Limnol. Oceanogr. 42, 1735-1745.

Oldham, C. E., and J. J. Sturman, 2001. The effect of emergent vegetation on convective flushing in shallow wetlands: Scaling and experiments. Limnol. Oceanogr. 46, 1486-1493.

68 Persson, J., N. L. G. Somes, and T. H.F. Wong, 1999. Hydraulics efficiency of constructed wetlands and ponds. Water Sci. Technol. 40, 291-300.

Raisin, G. W., and D. S. Mitchell, 1995. The use of wetlands for the control of non-point source pollution. Water Sci. Technol. 32, 177-186.

Reddy, K. R., R.H. Kadlec, E. Flaig, and P. M. Gale, 1999. Phosphorus retention in streams and wetlands: A review. Crit. Rev. Environ. Sci. Technol. 29, 83-146.

Shilton, A. N., and J. N. Prasad, 1996. Tracer studies ofa gravel bed wetland. Water Sci. Technol. 34, 421-425.

Stem, D. A., R. Khanbilvardi, J.C. Alair, and W. Richardson, 2001. Description of flow through a natural wetland using dye tracer tests. Ecol. Eng. 18, 173-184.

Ta, C. T., and W. J. Brignal, 1998. Application of computational fluid dynamics technique to storage reservoir studies. Water Sci. Technol. 37, 219-226.

Thackston, E. L., F. D. Shields, and P.R. Schroeder, 1987. Residence Time Distributions of Shallow Basins. J. Environ. Eng.-ASCE 113, 1319-1332.

Walker, D. J., 1998. Modelling residence time in stormwater ponds. Ecol. Eng. 10, 247- 262.

Werner, T. M., and R. H. Kadlec, 1996. Application of residence time distributions to stormwater treatment systems. Ecol. Eng. 7, 213-234.

Werner, T. M., and R.H. Kadlec, 2000. Stochastic simulation of partially-mixed, event­ driven treatment wetlands. Ecol. Eng. 14, 253-267.

Wilson, J. F., E. D. Cobb, and F. A. Kilpatrick, 1986. Fluorometric Procedures for Dye Tracing, U.S. Geological Survey, Denver, CO.

Wong, T. H.F., and W. F. Geiger, 1997. Adaptation of wastewater surface flow wetland formulae for application in constructed stormwater wetlands. Ecol. Eng. 9, 187- 202.

69 Wong, T. H.F., and N. L. G. Somes, 1995. A Stochastic Approach to Designing Wetlands for Stormwater Pollution-Control. Water Sci. Technol. 32, 145-151.

70