MEASURING AND MODELING LARGE-SCALE POLLUTANT DISPERSION

IN SURFACE WATERS

Ferdi L. Hellweger

Civil and Environmental Engineering Department 400 Snell Engineering Center

Northeastern University Boston, MA 02115

(617) 373-3992 ferdi@coe.neu.edu

www.coe.neu.edu/~ferdi

ABSTRACT Dispersion is an important process affecting the transport of pollutants from wet-weather discharges, like storm sewer outfalls and combined sewer overflows (CSOs). This paper briefly reviews the technology available for measuring and modeling large-scale dispersion in surface waters. Then, several case studies of instantaneous inputs of tracers and pollutants are discussed, including deliberate releases of tracers to the Hudson, Wind-Bighorn and Missouri Rivers and accidental releases of pollutants to the Rhine, Somes (Romania) and Sacramento Rivers. For each case, measurements and model simulations are presented and discussed. Future research opportunities to investigate the dead-zone storage mechanism using high-resolution geographic data (National Hydrography Dataset, NHD) and high-resolution three-dimensional hydrodynamic models are discussed. The HUSKY1 modeling framework is presented, which is an MS Excel-based one-dimensional modeling framework incorporating the dead zone storage mechanism. KEYWORDS Dispersion, Surface Water, Spill, Tracer, Model, HUSKY1

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1. INTRODUCTION Traditionally, large-scale dispersion of instantaneous inputs has been mostly important for accidental pollutant spills, like the pesticide spill into the Rhine River in 1986 (Capel et al., 1988), the aluminum spill into the Rivers Camel and Allen, UK in 1988 (Bielby, 1988), the pesticide spill into the Sacramento River in 1991 (Saviz et al., 2000) and the cyanide spill into the Somes River in Romania in 2000 (Koncsos and Fonyo, 2004). Non-accidental inputs of pollutants, like those resulting from municipal wastewater treatment plants, did not fall into this category, because they are more or less continuous. However, today the focus has shifted away from continuous point sources to event-driven intermittent point and non-point sources, like direct rainfall runoff, storm sewer outfalls and combined sewer overflows (CSOs). For those discharges, the input is (or can often be approximated as) instantaneous. This paper reviews some of the technology used to measure and model large-scale dispersion of instantaneous inputs of pollutants into surface water systems. More complete reviews of dispersion in surface waters are provided by Fischer et al. (1979), Rutherford (1994) and Martin and McCutcheon (1999). 2. MEASURING TECHNOLOGY Tracers are used to measure dispersion. A number of tracers are available and several factors should be considered when choosing a tracer, including:

• Detectability • Level of background concentration • Toxicity • Aesthetics (i.e. public reaction to coloring a waterbody) • Cost • Fate and transport properties (see next list)

An important factor to consider is the fate and transport properties that subject the tracer to removal processes from the water column, including:

• Adsorption to and settling with particles (e.g. Rhodamine B) • Diffusion to the sediment bed porewater • Absorbtion by vegetation • Volatilization (e.g. SF6) • Decay

o Biodegradation o Photolysis (e.g. Fluorescein)

A number of tracers and the scale at which they have been applied are summarized in Table 1. More complete reviews of tracers for surface waters are provided by Smart and Laidlaw (1976), Wilson et al. (1986) and Martin and McCutcheon (1999).

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Table 1. Some Tracers for Spills

Application(s)

Max. Scale

Name

River

Reference Space (km)

Time (d)

deliberate

sulfur hexafluoride (SF6) Hudson(1)

Caplow et al. (2004) 50 7

Ho et al. (2002) 100 13 rhodamine B

Mississippi(2) Stewart (1967) 205 3.9

rhodamine BA

Antietam(2) Taylor and Solley (1971) 67 2.0

rhodamine WT Wind-Bighorn(1)(2)

Lowham and Wilson (1971) 181 2.4

Missouri(1)(2)

Yotsukura et al. (1970) 227 1.7

Red(2)

Nordin and Sabol (1974) 200 5.2

Sabine(2)

Nordin and Sabol (1974) 209 4.6

Mississippi(2)

Nordin and Sabol (1974) 295 3.2

Chattahoochee(2)

Nordin and Sabol (1974) 105 1.6

accidental various chemicals Rhine(3)

See text 706 14

metam sodium Sacramento(4)

See text 75 16

cyanide Somes-Tisza-Danube See text 2,000 28 (1)See case study in text. (2)Time scale based on time to centroid at most downstream station. (3)Time scale based on time of spill to last measurement (DKR, 1986). (4)Time scale based on time of spill to last detectable MITC measurement (CVRWQCB, 1991). 3. MODELING TECHNOLOGY 3.1. Simple One-Dimensional Modeling The fate and transport of a dissolved substance in a one-dimensional surface water system is governed by the advection-dispersion-decay equation:

cKxcE

xcU

tc

−∂∂

+∂∂

−=∂∂

2

2

[1]

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Where c [g m-3] is the concentration, t [s] is the time, x [m] is the distance, U [m s-1] is velocity, E [m2 s-1] is the longitudinal dispersion coefficient and K [s-1] is the first-order decay rate constant. For the idealized case (i.e. straight uniform channel, constant flow) and an instantaneous input the equation can be solved analytically (e.g. Chapra, 1997):

( ) tKtEtUx

etEA

Mtxc−

−−

= 4

2

2),(

π

[2] Where M [g] is the mass input and A [m2] is the cross sectional area. The equation is useful, but often the assumption of constant geometry and flow introduces an unacceptable error. For that reason numerical solutions to Equation 1 are often utilized:

( ) ( )i

tii

ti

ti

ii

iiiiti

ti

ii

iiiitiii

tiii

ti

tti V

tcVKccL

AEcc

LAE

cQcQcc ∆

−−−−−−+= +

+

++−

−

−−+−−

∆+1

1,

1,1,1

,1

,1,11,1,1

[3] Where i denotes the segment number, Q [m3 s-1] is the flow rate, L [m] is the mixing length (i.e. ∆x) and V [m3] is the volume. Alternative approaches for handling the advection term (i.e. centered difference), various solution methods (e.g. Crank-Nicolson), numerical dispersion and stability are discussed by Chapra (1997). For this idealized case the model predicts that the concentration plume from an instantaneous input of a substance will have a Gaussian shape (a.k.a. bell curve, normal distribution) in space, but from the viewpoint of a fixed observer, the passing tracer plume will have an asymmetric shape, because it continues to spread out as it passes the observer (Chapra, 1997). 3.2. Transient Storage Modeling in One-Dimensional Models Transient storage of a tracer or pollutant mass in stagnant pools of water (a.k.a. dead zones), fundamentally a two- or three-dimensional process, is often found to be important to the transport of instantaneous inputs. For that reasons the one-dimensional model discussed in the previous sub-section is often modified to include transient storage, as was done by Nordin and Troutman (1980) and Reichert and Wanner (1987). The equation for the concentration in the main channel is (after Nordin and Troutman, 1980):

( )mdmmmm cc

TcK

xcE

xcU

tc

−+−∂∂

+∂

∂−=

∂∂ ε

2

2

[4]

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The equation for the concentration in the dead zone is:

( )dmdd cc

TcK

tc

−+−=∂

∂ 1

[5] where the subscripts m and d refer to main channel and dead zone, respectively. The size of the dead zones is defined by ε , the ratio of dead zone cross sectional area (or volume) to main channel area (or volume). The exchange between the main channel and the dead zones is defined by T [s], the residence time in the dead zone. As with the advection-dispersion-decay equation described in the previous section, the equations for transient storage can be solved numerically:

( ) ( )

( ) imtim

tidim

i

itimim

tim

tim

ii

iimiitim

tim

ii

iimiitimii

timii

tim

ttim V

t

ccVT

cVK

ccL

AEcc

LAE

cQcQcc

,,,,,,

1,,1,

1,,1,1,,

,1

,1,,1,1,1,,1

,,∆

−+−

−−−−−

+=+

+

++−

−

−−+−−

∆+

ε

[6]

( )id

tid

timid

i

tidid

tid

ttid V

tccVT

cVKcc,

,,,,,,,1 ∆

−+−+=∆+

[7] These are the equations used by the HUSKY1 model presented in more detail in Appendix A of this paper. 3.3. Available Modeling Frameworks Many modeling frameworks (i.e. computer codes) are available that solve the simple one-dimensional equations described in the previous sections or the more complicated three-dimensional equations. Some modeling frameworks for spills including references to documentation and applications are summarized in Table 2. Other, more complete reviews of water quality models are provided by Wurbs (1995), Shoemaker et al. (1997) and Fitzpatrick et al. (2001). 3.4. Model Inputs – Dispersion Coefficient The number of input parameters varies by model and ranges from the hand-full needed for the one-dimensional models to many more for the more complicated two- and three-dimensional models. Some parameters are relatively easy to estimate, like the channel depth or flow rate. The dispersion coefficient, on the other hand, is more difficult to

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estimate. It has to be realized that the dispersion coefficient (E) varies in space and time, and is a function of the model type or model complexity:

E = f (space, time, model) [8]

Table 2. Some Spill Modeling Frameworks

Name(1)

Properties(2)

Documentation

Application(s)

Analytical Solution

1D, K

This paper (Section 3.1), Thomann and Mueller (1987), Chapra (1997)

HUSKY1 1D, DZ, K This paper (Section 3.2)

This paper, see text

DAFLOW /BLTM

1D, L, K Jobson and Schoellhamer (1987), Jobson (1997)

Graf (1995), Nishikawa, et al. (1999)

ECOMSED 3D, K Blumberg et al. (1999), HydroQual (2001)

Hellweger et al. (2004)

OTIS 1D, DZ, K Runkel (1998, 2000) Laenen and Bencala (2001), Fernald, et al. (2001)

RMA-2/4Q 2D, K Norton et al. (1973), King (1993, 1990), King and DeGeorge (1994)

Saviz et al. (2000)

MARS 2D, K Hellweger et al. (2003)

Hellweger and Cheney (2004)

(1)Model Acronyms: BLTM = Branched Lagrangian Transport Model, DAFLOW = Diffusion Analogy FLOW, ECOM = Estuarine and Coastal Ocean Model, MARS = Model for the Assessment and Remediation of Sediments, OTIS = One-dimensional Transport with Inflow and Storage, RMA = Resource Management Associates. (2)Properties: 1D = one dimensional, 2D = two dimensional, 3D = three dimensional, DZ = dead zone, stagnant zone, transient storage, K = reaction kinetics, L = lagrangian. The dependence of the dispersion coefficient on the model complexity is illustrated in Figure 1. In the simple one-dimensional model (Section 3.1), the dispersion coefficient accounts for all mechanisms responsible for the spreading of the concentration plume, including molecular diffusion, turbulent diffusion and transverse and vertical shear dispersion, as well as the effect of dead zones. However, if the effect of the dead zones is explicitly accounted for (Section 3.2), then the dispersion coefficient only accounts for molecular diffusion, turbulent diffusion and transverse and vertical shear dispersion. Finally, when using high-resolution, three-dimensional models, the process of shear dispersion is explicitly accounted for and the dispersion coefficient only accounts for molecular and turbulent diffusion. Therefore, if two models, a simple one-dimensional model and a high-resolution three-dimensional model, are calibrated to the same data, the

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dispersion coefficient will be lower in the three-dimensional model. In fact, the model dispersion coefficient decreases with model complexity, as shown in Figure 1. Care should therefore be taken when characterizing the dispersion in a given water body using a dispersion coefficient without reference to a model.

Model Complexity

Mod

el D

ispe

rsio

n C

oeffi

cien

t 1D 1DDZ

2DV

3D

MolecularDiffusion

TurbulentDiffusion

TransientStorage

LateralShearDispersion

VerticalShearDispersion

Mechanism accounted for with other parts of model

Mechanism accounted for with dispersion coefficient

Model Complexity

Mod

el D

ispe

rsio

n C

oeffi

cien

t 1D 1DDZ

2DV

3D

MolecularDiffusion

TurbulentDiffusion

TransientStorage

LateralShearDispersion

VerticalShearDispersion

Mechanism accounted for with other parts of model

Mechanism accounted for with dispersion coefficient

Figure 1. Model Dispersion Coefficient vs. Model Complexity. Note that “Model Dispersion Coefficient” is the sum of the assigned and numerical dispersion in the model. Model types: 1D = one-dimensional, 1D DZ = one-dimensional with dead zones, 2D V = two-dimensional vertically integrated, 3D = three-dimensional.

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4. CASE STUDIES 4.1. Hudson River (New York) On July 25, 2001 about 4.3 mol of SF6 was deliberately released in a short period of time in Newburgh Bay on the Lower Hudson River by Ho et al. (2001). Following the release the spatial extent of the concentration plume was sampled from a boat on a daily basis for about two weeks. The release was simulated by Hellweger et al. (2004) using an existing ECOMSED model developed by Blumberg et al. (2004). The measured and simulated spatial concentration profiles (plumes), presented for two days in Figure 2, differ from the ideal Gaussian shape in two ways. First, there are smaller scale “secondary” peaks at the upstream and downstream ends of the plume (e.g. km 90, Figure 2a). Second, there is a large-scale asymmetry. Downstream of about km 80 the tracer plume seems to spread out faster.

0

500

1,000

1,500

60 80 100 120

Distance from Battery (km)

(b) 4 August 2001(a) 27 July 2001

0

5,000

10,000

60 80 100 120

Distance from Battery (km)

SF6

Con

c. (f

mol

/L)

Figure 2. Measured (points) and simulated (line) SF6 concentration in the Hudson River Estuary (from Hellweger et al. 2004). The heavy and thin lines in panel (b) correspond to models with and without salt, respectively. Using a model sensitivity analysis, Hellweger et al. (2004) demonstrated that the secondary peaks are a result of a process called tidal trapping (Okubo, 1973). As the “main plume” moves up and down the river with the tide, a mass of tracer can get temporarily trapped in an embayment. This is illustrated in Figure 3, which shows a “pocket” of water with high tracer concentration trapped near Wappinger Creek. If the plume is traversed and sampled from a boat on a one-dimensional transect, the pocket of high-concentration water will appear as a secondary peak.

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WappingerCreekWappingerCreek

Figure 3. Map of simulated SF6 concentration in Newburgh Bay on the Hudson River Estuary (from Hellweger et al. 2004).

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The large-scale asymmetry evident in Figure 2b is due to a spatial gradient in dispersion characteristics. The point where the asymmetry starts (km 80) is about the limit of salinity intrusion (at that time). The estuarine circulation downstream of that point enhances dispersion by a process called shear dispersion (Pritchard, 1954; Fischer, 1972), which leads to the higher dispersion and the large-scale asymmetry. 4.2. Wind-Bighorn River (Wyoming) On March 21 and June 29, 1971 about 3.8 kg (8.4 pounds) of Rhodamine WT was released in the Wind-Bighorn River below Boysen Reservoir and measured at several locations downstream to Greybull, Wyoming by Lowham and Wilson (1971). The two dates were characterized by different flow conditions, termed here low and high flow. This and the Missouri River data (discussed subsequently) were simulated by Nordin and Troutman (1980) using regular and dead zone models. However, they don’t present profiles of the concentration plumes and for that reason, the model simulations were repeated using the HUSKY1 model framework and are presented here. Nordin and Troutman (1980) also present data and model application to Bear Creek (Colorado), but that study is not large-scale (max. distance scale 11 km) and therefore not included here. Parameters for this and subsequent model applications are presented in Table 3. Note that the focus of the model applications was on the shape of the concentration profile. For that reasons other parameters (e.g. area, decay rate constant, mass input) were adjusted with considerable liberty.

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Table 3. Model Input Summary(1)

Wind-Bighorn(2)

Parameter Low Flow High Flow

Missouri(2)

Somes(6) M [kg]

3.1 (3.9)(4)

3.1 (3.7)(4)

54 (54)

120k (105-110)(4)

A [m2] 55-83(3)(4) 120-180(3)(4) 560-660(3)(4) 230-260(3)(4) E [m2 s-1] N: 51 (92)

DZ: 20 (13)(4)(5) N: 130 (160) DZ: 35 (7)(4)(5)

N: 600 (1950) DZ: 400 (490)(4)(5)

N: 65 (60-70)

DZ: 30(4)(5) U [m s-1] 0.68-0.99

(0.88-0.91)(3) 1.29-2.00 (1.47-1.56)(3)

1.34-1.69 (1.59-1.66)(3)

0.53-0.60 (0.58-0.66)(3)(7)

K [day-1] 0.0 0.35(4) 0.2(4) 0.0 ε [%] (3.43) (5.62) (4.21) 5%(4) T [hr] 0.426 (0.852)(4) (0.368) 2.00 (3.99)(4) 2.5(4) (1)N = normal/regular model, DZ = dead zone model. (2)Based Nordin and Troutman (1980) and Nordin and Sabol (1974). Where applicable literature values are provided in parentheses. (3)Varies by reach. (4)Calibrated to data. (5)Numerical simulation subject to numerical dispersion. Value reported is Ep = Em + En, see Chapra (1997). (6) Based Koncsos and Fonyo (2004), UNEP (2000), WWF (2002). Where applicable literature values are provided in parentheses. Release time is 1/30/00 22:00 based on time of first report by site worker (UNEP, 2000). (7)From UNEP (2000). U = 2.1-2.4 km h-1 upstream of Yugoslavia. For the low flow case (Figure 4) both the regular and dead zone models can reproduce the observed temporal concentration profiles. However, for the high flow case (Figure 5), the observed concentration profiles exhibit a significant “tail”, which can not be explained by the simple one-dimensional model. The dead zone model can reproduce the observed concentration profile.

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0

5

10

15

20

25

30

0 10 20 30 40 50 60 70

Time (hr)

Con

cent

ratio

n (

g/L)

Wind River Canyon(km 9)

Thermopolis(km 33)

Lucerne(km 50)

Winchester(km 75) Worland

(km 100) Manderson(km 142)

Greybull(km 181)

0

1

2

3

4

5

6

28 30 32 34 36 38 40

Figure 4. Measured (points) and simulated (line) Rhodamine WT concentration in the Wind-Bighorn River at various locations (data from Lowham and Wilson, 1971). Thin and heavy lines correspond to regular and dead zone models, respectively. Low Flow Case.

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0

5

10

0 10 20 30 40

Time (hr)

Con

cent

ratio

n (

g/L)

Wind River Canyon(km 9)

Thermopolis(km 33)

Lucerne(km 50)

Winchester(km 75) Worland

(km 100) Manderson(km 142) Greybull

(km 181)

0

1

2

16 18 20 22 24

Figure 5. Measured (points) and simulated (line) Rhodamine WT concentration in the Wind-Bighorn River at various locations (data from Lowham and Wilson, 1971). Thin and heavy lines correspond to regular and dead zone models, respectively. High Flow Case.

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4.3. Missouri River (US) On November 13, 1967, 54 kg (120 lb) of Rhodamine WT was released near Sioux City, Iowa on the Missouri River and the concentration was measured at several locations downstream up to Plattsmouth, Nebraska by Yotsukura et al. (1970). The concentration profiles exhibit a significant tail and only the deadzone model can reproduce them adequately.

0

1

2

3

4

5

0 10 20 30 40 50 60

Time (hr)

Con

cent

ratio

n (

g/L)

Decatur Bridge(km 66)

Blair Bridge(km 134) Ak-sar-ben Bridge

(km 187) Plattsmouth Bridge(km 227)

Figure 6. Measured (points) and simulated (line) Rhodamine WT concentration in the Missouri River at various locations (data from Yotsukura et al., 1970). Thin and heavy lines correspond to regular and dead zone models, respectively. 4.4. Rhine River (Europe) On November 1, 1986 a fire occurred at a chemical storehouse in Schweizerhalle, Switzerland. The water from the firefighting operation, along with a large number and quantity of chemicals was washed into the Rhine River and became completely mixed over the cross section after passing through a hydroelectric power plant 5 km downstream from the spill (Capel et al., 1988). Various models were used to simulate the spill (Reichert and Wanner, 1987; Mossman et al., 1988; Wanner et al., 1989). The model of Reichert and Wanner (1987) accounts for stagnant zones, the effect of which is illustrated using simulations with and without stagnant zones. The results, shown in Figure 7 (top panel), demonstrate the importance of accounting for the dead-zone storage process.

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0

10

20

30

40

11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12 11/13

Dis

ulfo

ton

Con

c. (

g/L) Dead Zones

No Dead Zones

Maximiliansau(km 362)

Mainz-Wiesbaden(km 498)

Bad Honnef(km 640)

Lobith(km 865)

Reichert and Wanner (1987)

0

10

20

30

40

11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12 11/13

Dis

ulfo

ton

Con

c. (

g/L)

Wanner et al. 1988Mossman et al. 1988

Figure 7. Measured (points) and simulated (lines) disulfoton concentration in the Rhine River at various locations. Data are from DKR (1986) and model results were digitized from from Reichert and Wanner (1987), Mossman et al. (1988) and Wanner et al. (1989). Note that model simulations were “ungraphed” off published papers, which causes them to appear “weavy” here. Original references should be consulted for more accurate representation of the model results.

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The models of Mossman et al. (1988) and Wanner et al. (1989) (Figure 7, bottom panel) do not contain stagnant zones and therefore do not capture this important feature in the data. The model by Mossman et al. (1988) does include storage in the sediment bed (porewater and sorbed), which theoretically can have the same transient storage effect as the dead zones. However, the effect of this mechanism is not evident in the simulated concentrations. Additional simulations to other chemicals (e.g. thiometon) are presented by Mossman et al. (1988) and Wanner et al. (1989). 4.5. Sacramento River (California) On July 14, 1991, a train of the Southern Pacific Railway derailed at the Cantara Loop and a tank car fell into the Sacramento River, raptured and spilled 19-27 metric tons of the pesticide metam sodium. Metam sodium decays by hydrolysis and photolysis into methyl isothiocyanate (MITC) and other products. MITC in turn volatilizes to the atmosphere. Saviz et al. (2000) developed a one-dimensional model of the Sacramento River using a modified version of the RMA-2/RMA-4Q modeling framework. As can be seen in Figure 8, “two data points near hour 60 [7/17/91 9-10 AM] indicate a long trailing edge of the plume which was not predicted by the model” (Saviz et al., 2000).

0

10

20

30

40

7/16/91 12:00 7/17/91 0:00 7/17/91 12:00 7/18/91 0:00 7/18/91 12:00

MIT

C C

onc.

(mg/

L)

Doney Creek(km 67)

Figure 8. Measured (points) and simulated (line) MITC concentration in the Sacramento River at Doney Creek (67 km from spill). Data are from CVRWQCB (1991) and model simulation were digitized from Saviz et al. (2000) (Run 5). Note that model simulations were “ungraphed” off published papers, which causes them to appear “weavy” here. Original references should be consulted for more accurate representation of the model results.

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4.6. Somes-Tisza-Danube River (Europe) On January 30, 2000, heavy precipitation and snowmelt lead to a breach of a dam of a wastewater pond in Baia Mare, Romania and ~100 tons of cyanide (as well as heavy metals) were spilled into the Somes-Tisza-Danube River system. The cyanide plume was detected at the Danube Delta on the Black Sea (2,000 km) four weeks after the spill (UNEP, 2000; Sotentino, 2000; WWF, 2002). The HUSKY1 model was used to simulate the concentration in the most upstream area of the spill, the Somes River. The results, shown in Figure 9, indicate that the plumes have significant tails, which can not be reproduced by the regular model. The dead zone model can reproduce the observed concentration profiles adequately. Koncsos and Fonyo (2004) used a one-dimensional, time-variable model parameterized using river geometry and flow data to simulate cyanide and copper concentrations over a larger spatial area.

0

10

20

30

40

50

2/1 2/2 2/3

Date

Cya

nide

Con

c. (m

g L-1

)

Tunyogmatolcs(~120 km)

Csenger(~90 km)

Figure 9. Measured (points) and simulated (line) cyanide concentration in the Somes River at two locations in Hungary. Thin and heavy lines correspond to regular and dead zone models, respectively. 5. DISCUSSION 5.1. Non-Gaussian Concentration Profiles Under ideal conditions an instantaneous input of a pollutant should result in a Gaussian spatial, and skewed temporal (fixed observer) concentration profile. However, the case studies presented in this paper show that in most cases the observed plumes deviate significantly from theory. Several reasons can be responsible for this, including:

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• Non-instantaneous spill • Transient storage in:

o Stagnant water (a.k.a. dead zones) o Sediment bed

Porewater Adsorbed to particles

• Incomplete mixing (convective period) • Change in flow rate or velocity • Change in dispersion • Decay process with non-linear kinetics • Significant dispersion during period of observation (see “fixed observer”

discussion by Chapra, 1997) [temporal plume] • Significant decay during period of observation [temporal plume]

From the previous case studies it appears the affects of transient storage is an important process affecting the large-scale dispersion in rivers. 5.2. Transient Storage The average of the coefficients of skewness (Gt) of the observed temporal concentration profiles calculated by Nordin and Sabol (1974) for the Wind-Bighorn and Missouri Rivers are 0.98 and 1.34, respectively. The geomorphology of the two rivers is significantly different, as illustrated in Figure 10. At the scale shown, the Wind-Bighorn has more large-scale meanders and medium-scale features, like islands. The Missouri is relatively straight, but has small-scale man-made shoreline features throughout a large part of the study reach. It is possible that dead zones formed by these features are responsible for the larger skewness in the concentration profile. In that case, differences in “shoreline turtuosity” should be able to explain differences in skewness coefficients (Gt) between different rivers or the change in skewness coefficients (∆Gt / ∆x) for different reaches of the same river. Model parameters for the dead zone process (ε and T) calibrated to the tracer data, also shown in Figure 10, are consistent with this. Although the relative size of the dead zone is about 5% for both models, the dead zone residence time is significantly longer in the Missouri River.

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(b) Missouri RiverGt = 1.34

E = 400 m2/sε = 4%T = 2.0 hr

(a) Wind-Bighorn RiverGt = 0.98

E = 20-35 m2/sε = 3-6%T = 0.4 hr

(b) Missouri RiverGt = 1.34

E = 400 m2/sε = 4%T = 2.0 hr

(a) Wind-Bighorn RiverGt = 0.98

E = 20-35 m2/sε = 3-6%T = 0.4 hr

Figure 10. Representative sections of (a) Wind-Bighorn and (b) Missouri Rivers. Map data are USGS 1:24,000 Topo. Gt, ε and T values are from Nordin and Troutman (1980). Mile point is indicated for the Missouri River. The Wind-Bighorn section shown is between Winchester and Worland, Wyoming. With high-resolution digital data becoming available, like the National Hydrography Dataset (NHD), it would be useful to re-analyze the large database of past tracer experiments. Parameters derived from geographic data (e.g. a “shoreline turtuosity coefficient”) could be correlated to statistics of observed concentration profiles (i.e. coefficient of skewness, Gt) or to one-dimensional model parameters describing dead zone storage (i.e. ε and T of Nordin and Troutman, 1980; α and qd of Reichert and

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Wanner, 1987). The NHD data could also be useful in predicting dispersion coefficients (e.g. Sn of Seo and Cheong, 1998; Sf of Kashefipour and Falconer, 2002). In addition, high-resolution three-dimensional hydrodynamic models, which have been shown to be able to describe transient storage in a tidal environment (e.g. Hellweger et al., 2004) could be applied to further understand the physics of the dead-zone storage process. 6. SUPPLEMENTAL INFORMATION Appendix A is available from the author’s web page (www.coe.neu.edu/~ferdi). The appendix contains the HUSKY1 modeling framework in the form of an MS Excel spreadsheet and MS Word documentation. The program solves the one-dimensional advection-dispersion-decay equation (Equation 1) and the dead zone model (Nordin and Troutman, 1980). This is the program that was used for the Wind-Bighorn, Missouri and Somes simulations shown in this paper. 7. REFERENCES Bencala, K.; Cox, M. 2004. Rhodamine WT Reader. Surface-water quality and flow Modeling Interest Group (SMIG), U.S. Geological Survey, Washington, DC. Blumberg, A. F.; Khan, L. A.; St. John, J. P. 1999. Three-dimensional hydrodynamic model of New York harbor region. J. Hydr. Eng., 125:799-816. Blumberg, A. F.; Dunning, D. J.; Li, H.; Geyer, W. R.; Heimbuch, D. 2004. Use of a particle-tracking model for predicting entrainment at power plants on the Hudson River. Estuaries, 27:515–526. Bielby, G. H. 1988. The Lowermoor Environmental Report. South West Water Authority, Exeter, UK. Capel, P. D.; Giger, W.; Reichert, P.; Wanner, O. 1988. Accidental input of pesticides into the Rhine River. Environ. Sci. Technol., 22(9):992-997. Caplow, T.; Schlosser, P.; Ho, D. T. 2004. Tracer study of mixing and transport in the upper Hudson River with multiple dams. J. Environ. Eng., 130:1498-1506., Chapra, S. C. 1997. Surface water-quality modeling. McGraw-Hill, Boston, MA. CVRWQCB. 1991. Final Water Sampling Report, Southern Pacific – Cantara Spill. Central Valley Regional Water Quality Control Board (CVRQWCB), Redding, CA. DKR. 1986. Deutscher Bericht Zum Sandoz – Unfall, Mit Messprogram. Deutsche Kommission zur Reinhaltung thes Rheins (DKR), Mainz, Germany (in German).

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