Using Turbulence Model Results to Quantify Oxygen ...

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Using Turbulence Model Results to Quantify Oxygen Reaeration in an Estuary Dissolved Oxygen Model Benoit R. Duclaud1 and James D. Bowen2 Abstract An alternate means of quantifying oxygen reaeration was investigated in a model of dissolved oxygen in an estuary. The three-dimensional hydrodynamic and water quality model EFDC was used to simulate dissolved oxygen (DO) conditions in North Carolina’s Lower Cape Fear River Estuary. A review of DO monitoring data showed that the upper portion of the water column was frequently undersaturated with respect to dissolved oxygen even though hypoxia was not usually observed in the bottom waters. In the impaired area of the estuary, surface reaeration was expected to be a significant source of DO to the water column. Even though reaeration has been shown to be dependent on the local energy dissipation rate near the water surface, water quality models typically use macroscale measurements of wind and water velocity to establish the reaeration rate coefficient. In this study we investigated the use of results from the turbulence closure submodel of a hydrodynamic model to quantify the local energy dissipation rate and, in turn, the dissolved oxygen mass transfer coefficient. Significant differences were seen in the statistical distribution of reaeration rates. The existing formulation showed a lognormal distribution, with a relatively small number of high reaeration rates. The new formulation showed a higher abundance of relatively high reaeration rates, and these high rates were seen more often during the summer period when DO was lowest in the estuary. Although the differences in predicted DO between the two methods were not dramatic, minimum DO in the estuary was as much as 1.0 mg/L higher using the new formulation. Based upon these results, it does seem that further investigation of the method for quantifying reaeration rate in estuarine water quality models is justified.

1

Graduate Research Assistant and 2Associate Professor, Department of Civil and Environmental Engineering, University of North Carolina at Charlotte, Charlotte NC 28223, (704) 687-2304.

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Introduction When a surface water body is unpolluted and a relatively low amount of naturally occurring degradable organic matter is present, dissolved oxygen concentrations are close to the saturation concentration. Wastewater inputs will often result in an increase of dissolved and particulate organic matter in the receiving water body. This organic matter provides food to aerobic, heterotrophic organisms such as bacteria. This biological activity leads to a drop in dissolved oxygen levels. When oxygen drops in the stream below the saturation concentration, oxygen from the atmosphere enters the water to reach a new gas-liquid equilibrium, a process that is known as reaeration. A conceptual model to describe gas transfer across the air/water interface is known as the two-film model (Whitman 1923, Lewis et al. 1924). According to this theory, mass transfer between the two phases occurs via serial molecular diffusion across thin motionless air and water films at the interface. Because oxygen has a relatively low solubility in water, processes occurring within the water phase typically control the transfer of oxygen between the liquid and gas interface in natural water bodies (Chapra 1997). With this assumption, the flux of dissolved oxygen, J (g/m2/s), across the interface can be written as: J = K l (os − o)

(1)

where os and o are the saturation and water bulk phase dissolved oxygen concentrations (g/m3), respectively and Kl is the oxygen mass-transfer coefficient (m/s). Quantitative models of dissolved oxygen depletion and reaeration have a long history (e.g. Streeter and Phelps 1925). Today a wide variety of unsteady, multidimensional water quality models (e.g. WASP, CE-QUAL-W2, HEM3D) are available for analyzing dissolved oxygen depletion (Ambrose et al. 1993, Cole and Buchak 1995, Park et al. 1995). In each of these models it is necessary to quantify the oxygen mass transfer coefficient. In estuary water quality models, the oxygen mass transfer coefficient is typically assumed to be the sum of two coefficients describing current and wind effects. For example, both Thomann and Fitzpatrick (1982) and Park et al. (1995) calculate the estuarine oxygen mass transfer coefficient as:

K l = K lQ + K lW

(2)

where KlQ is the mass transfer coefficient due to tidal motions, and KlW is the mass transfer coefficient due to wind effects. The tidal motion and wind components of the mass transfer coefficient are calculated as:

KlQ =

DlU H

KlW = 0.728Uw0.5 − 0.317Uw + 0.0372Uw2 2

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where Dl is oxygen’s molecular diffusivity (m2/s), U is the depth-averaged water velocity (m/s), H is the water depth (m), and Uw is the wind speed measured 10 m above the water surface (m/s). The two equations for KlQ and KlW can be recognized as the O’Connor-Dobbins equation (1958) that was originally developed for rivers and the Banks-Herrera equation (1977) that was developed for lakes. Recent advances in monitoring technology have allowed researchers to simultaneously measure the fine-scale turbulence structure and the rate of oxygen reaeration in both the laboratory (e.g. Moog and Jirka 1999, McKenna and McGillis 2003, Tsumori and Sugihara 2006) and in the field (e.g. Zappa et al. 2003). These studies have shown that reaeration rates are dependent on the local turbulence dissipation rate at the water surface. In natural systems, surface energy dissipation can be affected by both tidal and wind mixing, but not necessarily in the manner assumed in the formulations used to quantify the oxygen mass transfer coefficient. Fortunately, hydrodynamic models such as EFDC (Hamrick 1992, 1996) use the Mellor-Yamada (1982) turbulence closure submodel, which calculates turbulence parameters that can be used to calculate surface energy dissipation. Utilizing this information from the turbulence closure model, it is possible to develop an alternate means of estimating surface reaeration that may more appropriately combine the effects of circulation and wind forcings. The purpose of this research was to develop an EFDC application that could be used to test an alternate formulation of the oxygen mass transfer coefficient, utilizing results from EFDC’s turbulence closure submodel. The following section describes the turbulence-based formulation that was used in this study. The modified EFDC model was applied to simulate dissolved oxygen concentrations in North Carolina’s Lower Cape Fear River Estuary. Because surface DO concentrations are frequently below saturation values, this system provides an ideal test for the alternate oxygen mass transfer coefficient equation. A series of model runs were used to analyze differences in predicted reaeration rates and model predicted dissolved oxygen concentrations. Turbulence-based Reaeration Prediction Equations A second conceptual model of mass transport across the air/water interface describes the water not as a stagnant film, but one in which eddy motions bring parcels of water to the surface for a period of time. Then, while the parcel of water is at the surface, dissolved gas enters across the interface. Finally eddy motions move the parcel of water away from the surface where it mixes into the bulk water. This conceptual model is known as the penetration theory (Higbie 1935). The penetration theory was then improved and generalized by assuming that parcels of water are brought and leave the surface randomly (Danckwerts 1951) by integral scale eddies that do most of the transport of momentum and contaminants. As flows become more turbulent, small scale eddies play an important role in surface

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renewal and thus reaeration. Lamont and Scott (1970) took in consideration the small scale eddies and obtained the following equation:

K l ∝ Sc −1 2 (εν )

14

(4)

where ε is the near surface turbulent energy dissipation rate (m2/s3), νis the kinematic viscosity of water (m2/s), and Sc is the Schmidt number (Sc = ν/Dl), the ratio of the kinematic viscosity to the molecular diffusivity of oxygen. The near surface turbulent energy dissipation rate can be expressed as (Tennekes and Lumley 1973):

ε=

u3 l

(5)

where u is the velocity scale for the energy containing eddies (m/s), and l is the turbulence lengthscale (m). Combining these two equations gives the following equation for the oxygen mass transfer coefficient: ⎛ u 3 ⎞1 4 K l ∝ Sc −1 2ν 1 4 ⎜ ⎟ ⎝ l ⎠

(6)

This equation will be referred to as the “turbulence-based equation” for the oxygen mass transfer coefficient. Description of the Model Application An EFDC model application was developed for the tidally affected region of the Cape Fear River watershed (Figure 1). The Cape Fear River flows for 200 miles through the North Carolina piedmont, crosses the coastal plain, and empties into the Atlantic Ocean near Southport. The river begins near Greensboro and WinstonSalem as two rivers, the Deep River and the Haw River. These two rivers converge near Moncure to form the Cape Fear River. The Black River joins the Cape Fear 15 miles above Wilmington, and the Northeast Cape Fear River enters the system at Wilmington. The Lower Cape Fear River Estuary occupies the southernmost 60 kilometers of the watershed, between Wilmington and the Atlantic Ocean The estuary includes not only the tidally affected portion of the Cape Fear River, but also the lowermost portions of the Black and Northeast Cape Fear Rivers (Figure 2). This area of the river basin is extremely important for saltwater animals because of its function as a nursery for juvenile fish, crabs, and shrimp. The hydrology of the Cape Fear Estuary is similar to that of most of the middle to large estuaries located along the US Atlantic Coast. During the summer and the beginning of the fall, the estuary has relatively low flows, whereas it has high flows from the end of the fall to the beginning of the spring. From a hydrodynamic perspective, the Cape Fear has a two-meter tide range and strong tidal currents (> 0.5 4

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m/s) in the navigational channel of the open estuary and in the narrow tidal river channels of the three tributaries (Ensign et al. 2004).

Model Region Figure 1. The Cape Fear River Basin, North Carolina A region of the estuary near the junction of the Cape Fear, Black, and Northeast Cape Fear Rivers is prone to low dissolved oxygen concentrations during the warm summer and early fall seasons (Mallin et al. 2003) as a result of natural and anthropogenic (both point and nonpoint source) organic matter loadings. Dissolved oxygen concentrations are frequently below saturation concentrations, and typically exhibit an unusual vertical distribution in which surface concentrations are consistently lower than bottom concentrations (Lin et al. 2006). Previous modeling studies of the estuary have replicated this behavior, and have shown reaeration to be an important component of the dissolved oxygen budget for this region (Tetra Tech 2001). To test the alternate equations for the oxygen mass transfer coefficient in an actual model application, an EFDC application for the Lower Cape Fear River estuary was developed for the calendar year 2003 (Duclaud 2007). An existing EFDC grid used earlier for a simulation of DO dynamics (Tetra Tech 2001) was used for this study. For this investigation, no attempt was made to perform a quantitative calibration of the DO model; instead water quality kinetic constants (e.g. organic

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Black River

Cape Fear River

Northeast Cape Fear River

60 North - South Distance (km)

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Station NCF117

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20 30 40 50 60 East - West Distance (km) Figure 2. Model Region Showing Model Cells Shaded by Water Depth and Monitoring Station Locations matter degradation rates, SOD values, etc.) from the previously calibrated model were used as is. A qualitative comparison to monitoring data from previous years was performed to ensure the model was giving reasonable results. The curvilinear orthogonal grid had 954 cells, with cell widths and lengths that ranged from approximately 0.3 to 0.8 km. The sigma vertical grid had eight vertical layers, with total water depths that ranged from a minimum of 1.5 m in the shallow fringing wetlands to 13 m in the dredged navigation channel. Upstream flow boundary conditions for the Cape Fear, Black, and Northeast Cape Fear Rivers were based upon continuous gauging stations operated by the United States Geological Survey at the Cape Fear River Lock & Dam #1 (USGS Station 02105769), the Black River near Tomahawk (USGS Station 02106500) and the Northeast Cape Fear River near Chinquapin (USGS Station 02108000). The Cape Fear station was located at the model boundary while the other two stations were located approximately 40 km upstream of the model boundary. For these stations, drainage area ratios were used to scale the flow data from the two monitoring stations. In order to specify the downstream open boundary condition, tidal harmonic constituents were calculated using data from NOAA’s Wilmington monitoring station. Twenty additional freshwater wastewater point source inputs were quantified using information obtained from the North Carolina Division of

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Water Quality. Meteorological forcings used data collected at the Wilmington Airport by the National Weather Service. The turbulence-based equation for the oxygen mass transfer coefficient was implemented in EFDC by taking advantage of information available from its turbulence closure model. EFDC’s turbulence closure model calculates at every time step and every cell the integral length scale, l (m) and turbulent kinetic energy, qq (m2/, which can be substituted into the turbulence-based equation for oxygen mass transfer, as: ⎛ (qq1/ 2 ) 3 ⎞1 4 ⎛ 38⎞ −1 2 1 4 qq K l ∝ Sc −1 2ν 1 4 ⎜ (7) ⎟ ⇔ K l ∝ Sc ν ⎜ 1 4 ⎟ ⎝ l ⎠ ⎝ l ⎠ The kinematic viscosity and the Schmidt number depends on the water temperature. It is expected that the water temperature will vary from 0 to 30 degrees Celsius. Within that temperature range, the factor Sc −1 2ν 1 4 is expected to vary by 17 percent (Lide 2004). For this initial investigative study, however, it was assumed that this factor would be constant. Furthermore, a proportionality constant was empirically set to a value that forced the time-averaged mass transfer coefficient using the turbulence based equation to be equal to that when the O’Connor-Dobbins + Banks-Herrera formula is used. Using this constant, KRO, set empirically to 10.08 (m0.5 s-0.25), the turbulence-based equation for the oxygen mass transfer coefficient becomes:

⎛ qq 3 8 ⎞ K l = KRO × ⎜ 1 4 ⎟ ⎝ l ⎠

(8)

The equation was implemented in EFDC as a new option, thus retaining all of the existing means of computing reaeration. Results The 2003 simulation year was characterized by several high flow events in the spring and summer and one high wind event associated with Hurricane Isabel in late September (Figure 3). In the Wilmington area this hurricane was primarily a wind event, as Cape Fear River inflows did not rise significantly above normal. In general, 2003 was considered a very wet year in the watershed. Daily snapshot values of the model calculated instantaneous oxygen mass transfer coefficients were obtained from the model at 24 stations uniformly distributed throughout the estuary. As mentioned earlier, the scaling constant used in the turbulence-based equation for oxygen mass transfer coefficient, KRO, was set to a value (KRO = 10.08) such that the mean oxygen mass transfer coefficients were identical for the traditional O’Connor-Dobbins + Banks-Herrera formula and the turbulence-based equation. Despite having identical means, the distribution of values was quite different (Figure 4). Mass transfer coefficients using the traditional

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Cape Fear Inflow (m /s)

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Figure 3. Cape Fear River flows at NC 11 (panel a) and wind speeds (panel b) in the Lower Cape Fear River Estuary during 2003. 1600

a)

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0 0

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Figure 4. Histograms of oxygen mass transfer coefficients for the 2003 model run with the traditional equation (a) and the turbulence based equation (b). 8

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approach were only slightly skewed, and were skewed towards the lower values. Many more high reaeration values were observed for the turbulence-based equation case. As a result, the median value for the oxygen mass transfer coefficient using the traditional approach (0.82 m/d) was nearly 50% higher than the turbulence-based equation median value (0.57 m/d, Figure 4). Time history scatter plots of daily snapshot values at the 24 sites plotted together with the daily spatial average also clearly show the difference in the distribution of values. The O’Connor-Dobbins + Banks-Herrera equation is much more tightly clumped around the daily spatial average (Figure 5, panel a) as compared with the predicted values using turbulence-based equation (Figure 5, panel b). The skewness in the mass transfer coefficients using the turbulence-based

Oxygen Mass Transfer Coefficient (m/d)

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Oxygen Mass Transfer Coefficient (m/d)

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Figure 5. Time histories of oxygen mass transfer coefficients for the year 2003 model run using the traditional equation (panel a) and turbulence based equation (panel b).

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equations can clearly be seen. Also of interest is how the daily spatial average for the turbulence-based equation follows the pattern seen in the river inflow, while the traditional equation seems more affected by the high wind events. For instance, the traditional equation exhibits peaks in early July and mid-September, which corresponds to times of high wind events (Figure 3, panel a), while the turbulence equation shows three peaks in March and April and another in mid July at times which correspond to high flow events (Figure 3, panel b). Several runs were made to investigate the sensitivity of the turbulence-based estimates of oxygen reaeration to changes in flow and/or wind. To do this, a fixed ratio was applied to all freshwater inflows, and to the wind velocity. Three full-year model runs were made with the ratio set to 0.75, 1.0, and 1.25. As expected, increasing either the wind speed or the freshwater inflow increased the predicted oxygen mass transfer coefficients using the turbulence-based formulation (Figure 6), but in both cases the changes in mean values were subtle. The flow increase had a more pronounced effect, as the mean value increased by 15% as the ratio was varied from 0.75 to 1.25, whereas changing the wind ratio from 0.75 to 1.25 increased the mean value by only 5%. The flow effect seemed more important on the high end of the distribution of mass transfer coefficients, as the relative increase in 75th and 95th percentile values was larger than that for the median. 2.5 Oxygen Mass Transfer Coefficient (m/d)

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2 1.5 1 0.5 0

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Figure 6. Percentile plots of oxygen mass transfer coefficients for various levels of flow or wind speed ratios. Each box boundary shows the 5th and 95th percentile values. Dashed lines show the 25th and 75th percentiles, while the center solid line shows the median value. Time history comparisons of the predicted oxygen mass transfer coefficients were also examined at individual stations in different regions of the estuary (see Figure 2 for site locations). Here we show comparisons at one site in the upper oligohaline portion of the estuary (station NC 11), one site in the middle mesohaline portion of

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the estuary (station Navassa, Nav) and one station in the lower saline portion of the estuary (station M23). At station NC11 (Figure 7, panel a), the turbulence-based equation produces generally higher oxygen mass transfer coefficients as compared with traditional O’Connor-Dobbins + Banks-Herrera equation. The temporal pattern

Oxygen Mass Transfer Coefficient (m/d)

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Figure 7. Time histories of oxygen mass transfer coefficients for the year 2003 model runs using the traditional and turbulence based equations at an upper (panel a), middle (panel b), and lower (panel c) estuary station.

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for the turbulence-based equation follows closely the flow time history (Figure 3), with three peaks seen in March and April, another peak seen near the end of June, and a large peak seen in mid-August. The traditional equation does not produce these flow related peaks, although there are peaks associated with high wind events in July and September. Computed oxygen mass transfer coefficients at station Navassa (Figure 7, panel b), show a very similar temporal pattern, although in this case the mean values produced by the two methods (approx. 1.0 m/d) are much closer to one another. At this station there are periods of time between the high flow events where the O’Connor-Dobbins + Banks-Herrera equation produces higher predicted oxygen mass transfer coefficients (e.g. Figure 7, panel b, June and July), which appear to be times of relatively higher winds. The lower estuary station (Figure 7, panel c) looks significantly different than the other two stations. In this case the turbulence-based equation produces generally lower predicted oxygen mass transfer coefficients, and shows relatively little temporal variation. The high flow peaks are not seen here as they are at the other two stations. One peak is seen in late October that does seem to be a high wind event, but this event does not produce high values for the oxygen mass coefficient using the traditional equation. As at the other sites, the O’Connor-Dobbins + Banks-Herrera equation does produce peaks that coincide with the high wind events associated with Hurricane Isabel in late September and another event in early July (Figure 7, panel c). To investigate whether differences in the model predicted oxygen mass transfer coefficient would produce different predicted dissolved oxygen concentrations, we ran a three-year simulation (January 2003 – December 2005) of the Lower Cape Fear Estuary model. The only difference between the two runs was the method used to calculate reaeration. Here we show results of the two runs at the Navassa station (Figure 8). Only surface DO concentrations are shown, as this is where the system would likely be most sensitive to changes in reaeration and in this system bottom water hypoxia is not an issue. The Navassa station is in the region where oxygen depletion is most severe and occurs most frequently. As expected, dissolved oxygen concentrations varied significantly from winter to summer, with the lowest dissolved oxygen concentrations occurring in the early fall (Figure 8, panel a). The relatively wet summer of 2003 had generally higher model predicted dissolved oxygen concentrations as compared with 2004 and 2005. Dissolved oxygen concentrations were usually higher using the turbulencebased equation as compared with the O’Connor-Dobbins + Banks-Herrera formulation. A seasonal pattern was observed in the difference in predicted dissolved oxygen concentrations. Not surprisingly, the largest difference in dissolved oxygen concentrations occurred during times when the predicted dissolved oxygen concentration was lowest. During the late summer/ early fall periods of 2003, 2004, and 2005, the difference in predictions was as high as 1.0 mg/L. In 2003, the difference stayed above zero for several months late in the year, and stayed above 0.5

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mg/L for all of October. In 2004 and 2005 the difference in predicted dissolved oxygen concentrations was much more dynamic. In the summer of 2004, from May through August, the difference seemed to be periodic, with monthly peaks of about 0.75 mg/L and a monthly minimum of about 0.0 mg/L (Figure 8, panel b). In September 2005 there was a period when the turbulence-based estimate of the oxygen mass transfer coefficient produced lower predicted dissolved oxygen concentration. The maximum difference for that month was slightly less than 0.75 mg/L. 14

Top DO, ODBH Top DO, TBE

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Dissolved Oxygen (mg/L) DO Difference, TBE - ODBH (mg/L)

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Figure 8. Model predicted surface DO concentrations at station Navassa (Nav) from 2003 to 2005 using traditional and turbulence based estimates of the oxygen mass transfer coefficient (panel a) and the time history of the difference in the DO predictions (panel b).

Discussion and Conclusions In this model simulation of the lower Cape Fear River Estuary, where surface dissolved oxygen concentrations are frequently below saturation, accurate prediction of the reaeration rate would seem to be an important factor in an accurate prediction of dissolved oxygen. Indeed, in this study, significant differences were seen between the results of the two methods of computing the oxygen mass transfer coefficient, and this did result in a measurable difference in the model predicted dissolved oxygen concentration.

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Interesting differences were seen in the distribution of predicted oxygen mass transfer coefficients. The turbulence-based predictions seemed to be more variable in both time and space. This lead to a significant difference in the calculated median values between the two methods, with the O’Connor-Dobbins+Banks-Herrera equation producing a median predicted oxygen mass transfer coefficient that was more than twice as high as that produced by the turbulence-based equation. In part this was an artifact of the methodology that forced the means of the two distributions to be equal. We believe that it is possible to calculate the dissolved oxygen concentrations without this assumption. In this study we used the laboratory and field-based measurements of dissipation and reaeration merely to determine the proportionality of our relationship. We believe that we could also use these data to quantify the constant needed to calculate the mass transfer coefficient directly. In future work we plan to investigate this possibility. Model predictions of mass transfer coefficients from the turbulence-based equation varied more from upper to lower estuary than did estimates arising from the O’Connor-Dobbins + Banks-Herrera equation. This seemed to be a function of the turbulence-based equation’s higher sensitivity to differences in flow. Both sensitivity testing (Figure 6) and the time history plots at various stations (Figure 7) showed that increasing the flow did increase the predicted oxygen mass transfer coefficient. On the other hand, the traditional formulation seemed relatively more sensitive to changes in wind forcings and seemed relatively insensitive to changes in flow. Comparisons of predicted mass transfer coefficients using the two formulations varied significantly from site to site. Of the three sites shown, the relatively shallow river dominated site (site NC11, Figure 8, panel a) had higher predictions using the turbulence-based equation; the deeper, wider, more wind exposed, and tidally dominated site (site M23, Figure 8, panel c) had higher predictions using the traditional approach; and the intermediate site (site Navassa, Figure 8, panel b) had predictions that were roughly similar. This preliminary analysis suggests that the correspondence between the two methods might depend on physical factors that differ from site to site. To further investigate the factors behind the differences between the estimates at a particular site, we looked at the predicted time averaged mass transfer coefficients at the three sites mentioned, and at three additional sites in the estuary (NCF117, M61, and M18, see Figure 2 for locations). Two of these six sites are in the upper estuary (NC11, NCF117), two are in the middle estuary (Navassa, M61) and two are in the lower estuary (M23, M18). For each of these six sites, we calculated the time averaged predicted mass transfer coefficient, and plotted it against the (cell depth)-0.5. This scaling was used because it is used in the O’Connor-Dobbins equation (Equation 3), and varies significantly from site to site. While velocity differences are also expected, results from the hydrodynamic model show that the upper and lower sites have similar maximum current velocities (approx. 0.5 m/s), with the middle estuary sites having similar, but generally lower velocities. Thus we expected there to be relatively less variation in water velocity than in cell depth.

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Plotting the time-averaged model predicted oxygen mass transfer coefficient against (cell depth)-0.5 showed some interesting trends. First, it does seem that some of the variation in the value of the average mass transfer coefficient is related to local water depth (Figure 9). This trend seemed stronger for the turbulence-based estimates (Figure 9, open symbols) as compared with the O’Connor-Dobbins+BanksHerrera formulation (Figure 9, filled symbols). Secondly, the middle estuary stations (Figure 9, squares) are generally lower than the other locations, although this not universally true. Also, significantly more site-to-site variation is seen in the predictions from the turbulence-based estimate. The fact that this scaling was only partially successful in explaining site-to-site variation was not surprising, as the scaling completely ignores wind effects. It does suggest that differences from site to site do depend on physical characteristics.

TBE, upper ODBH, upper

2 Time Average Oxygen Mass Transfer Coefficient (m/s)

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TBE, middle ODBH, middle

TBE, lower ODBH, lower

1.5

1

0.5 0.2

0.3

0.4

0.5 -0.5

(Cell Depth)

0.6

0.7

0.8

-0.5

(m )

Figure 9. Time average oxygen mass transfer coefficients at two upper estuary (NC11, NCF 117), two middle estuary (Nav, M61) and two lower estuary (M18, M23) stations using the O’Connor-Dobbins+BanksHerrera equation (ODBH) and the turbulence based equation (TBE). The solid line is not a best-fit line, but represents y = 2.5 * x.

An unresolved question at this point is whether the new equation will improve the calibration performance of the dissolved oxygen model. Based on the magnitude of the differences in predicted dissolved oxygen, we expect there to be a significant difference in calibration performance between the traditional and turbulence based formulations of the oxygen mass transfer coefficient. It is hoped that the use of Mellor-Yamada turbulence closure model will improve the dissolved oxygen model

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just as it improves the hydrodynamic model, by providing a better description of the temporally and spatially varying turbulent structure. We plan to calibrate the DO model with both the traditional and turbulence-based formulations for reaeration. Once this is accomplished, we will be able to better assess the advantage of our turbulence-based estimates of oxygen mass transfer coefficients. Acknowledgement This material is based upon work supported by the National Science Foundation under Grant No. 0326811 and from an additional grant from the North Carolina Department of Environment and Natural Resources. References Ambrose, R.B., Wool, T.A., and Martin, J. L. (1993), “The Water Quality Analysis Simulation Program WASP5, Part A: Model Documentation,” Environmental Research Laboratory, Office of Research and Development, U.S. Environmental Protection Agency, Athens, GA, September 1993. Banks, R. B., and Herrera, F. F. (1977). “Effect of wind and rain on surface reaeration.” J. Environ. Engr. Div. ASCE, 103(EE3): 489-504. Chapra, S. C. (1997). “Surface Water Quality Modeling.” WCB McGraw-Hill, Boston, MA, 844 pp. Cole, T., and Buchack, E. (1995). “CE-QUAL-W2: A two-dimensional, laterally averaged, hydrodynamic and water quality model, version 2.0.” Technical Report E1-95-1. U.S. Army Engineer Waterways Experiment Station. Vicksburg, MS. Danckwerts, P. V. (1951). “Significance of liquid-film coefficients in gas absorption.” Indus. & Eng. Chem., 43(6), 1460-1467. Duclaud, B. R. (2007). “Improved reaeration prediction for the Lower Cape Fear River Estuary, North Carolina.” MS Thesis, University of North Carolina at Charlotte, Charlotte, NC. Ensign, S. H., Halls, J. N., and Mallin, M. A. (2004). “Application of digital bathymetry data in an analysis of flushing times of two large estuaries.” Computers & Geosciences, 30, 501-511. Hamrick, J. M. (1992). “A three-dimensional environmental fluid dynamics computer code: Theoretical and computational aspects.” The College of William and Mary, Virginia Institute of Marine Science, Special Report 317, 63 pp.

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Hamrick, J. M. (1996). “Users manual for the Environmental Fluid Dynamic Code.” The College of William and Mary, Virginia Institute of Marine Science, Special Report 328, 224 pp. Higbie, R. (1935). “The rate of absorption of a pure gas into a still liquid during short periods of exposure.” Trans. Amer. Inst. Chem. Engin. 31, 65-389. Lamont, J. C., and Scott, D. S. (1970). An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChE. J. 16(4): 513-519. Lewis, W.K., and Whitman W. G. (1924). “Principles of gas absorption.” Ind. Eng. Chem., 16(12), 1215-1220. Lide, D. R. (2004). “CRC Handbook of Chemistry and Physics.” 85 ed. CRC. 2656 pp. Lin, J., Xie, L., Pietrafesa, L. J., Shen, J., Mallin, M. A, and Durako M. J. (2006). “Dissolved oxygen stratification in two micro-tidal partially-mixed estuaries.” Estuarine, Coastal and Shelf Science, 70, 423-437. Mallin, M. A., McIver, M. R., Wells, H. A., Williams, M. S., Lankford, T. E., and Merrit, J.F. (2003). “Environmental assessment of the lower Cape Fear River system, 2002-2003.” CMS Report Number 03, Center for Marine Science, University of North Carolina at Wilmington, Wilmington, NC. McKenna, S. P. and McGillis, W. R. (2003). “The role of free-surface turbulence and surfactants in air–water gas transfer.” International Journal of Heat and Mass Transfer, 47, 539–553. Mellor, G. L., and Yamada, T. (1982) “Development of a turbulence closure model for geophysical fluid problems.” Rev. Geophys. Space Phys., 20, 851-875. Moog, D. B. and Jirka, G. H. (1999). “Air-water gas transfer in uniform channel flow.” Journal of Hydraulic Engineering, 125(1), 3-10. O'Connor, D. J., and Dobbins, W.E. (1958). “Mechanism of Reaeration in Natural Streams." Transactions of the American Society of Civil Engineers, 123, 641666. Park, K., Kuo, A.Y, Shen, J., and Hamrick, J.M. (1995). “A three-dimensional hydrodynamic-eutrophication model (HEM3D): description of water quality and sediment processes submodels.” The College of William and Mary, Virginia Institute of Marine Science. Special Report 327, 113 pp.

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Streeter, H. W., and Phelps. E. B. (1925). “A study of the pollution and natural purification of the Ohio River.” Public Health Bulletin No. 146. Public Health Service. Washington, D.C. Tennekes H., and Lumley J. L. (1972). “A First Course in Turbulence.” The MIT Press. Cambridge, MA. 300pp Tetra Tech, Inc. (2001). “A water quality model of the Lower Cape Fear River Estuary.” Technical Report to the City of Wilmington, Wilmington, NC. 159 pp. Thomann R. V., and Fitzpatrick JF. (1982). “Calibration and verification of a mathematical model of the eutrophication of the Potomac Estuary.” Report by Hydroqual, Inc. Mahwah, NJ, to DES, Dist. Col. Tsumori, H., and G Sugihara. (2006). “Lengthscales of motions that control air– water gas transfer in grid-stirred turbulence.” Journal of Marine Systems, doi: 10.1016/j.jmaryss2006.03.018. Whitman WG. (1923). “The two-film theory of gas absorption.” Chem. Metallurg. Eng., 29(4): 146-148. Zappa, C. J., P. A. Raymond, E. A. Terray, and W. R. McGillis. (2003). “Variation in surface turbulence and the gas transfer velocity over a tidal cycle in a macrotidal Estuary.” Estuaries. Vol. 26, No. 6, p. 1401–1415.

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