Cheng He, Paul F. Hamblin and Murray N. Charlton

Environment Canada, National Water Research Institute

867 Lakeshore Rd., Burlington, ON, Canada L7R 4A6

Tel: (905) 336-4921 Fax: (905) 336-4989, Paul.Hamblin@cciw.ca

Abstract: Exchange between harbours and embayments with the open coastal zone of large lakes can be a controlling factor for the water quality of these water bodies. In order to quantify the transport of water quality constituents in a harbour connected to a large lake, two-dimensional hydrodynamic and transport models have been extended to three dimensions and an extensive set of field observations collected. The models’ performance is assessed by comparison of output with field observations. Use is made of a naturally occurring gradient in the salinity or total dissolved solids (TDS) distributions for testing the ability of the model to simulate such contaminants as dissolved phosphorus. In particular, we examine in some detail the salinity distribution in an arm of the harbour where its concentration ranges from 0.3 to 0.6 g/kg. It is found that the model replicates the distribution along the arm and also in the channel connecting the harbour to the lake, supporting its application to water quality problems.

The need to quantify the impacts of such municipal developments as sewage treatment plant outfalls, sewage outfall diversions and drinking water supply in coastal zones as has led the development of mathematical models, for example, Signell et al. (2000) and Johnson et al. (1993).While there is a rich diversity of coastal models reported in the literature such as the Proceedings of the biannual Estuarine and Coastal Modelling Conferences, from 1987 to 1999, almost all of these coastal models have been applied to the marine setting rather than to lakes. In the past several issues of these Proceeedings more studies are devoted to three-dimensional (3-D) models as computational resources have greatly improved. Despite these improvements, in large lakes it is still not feasible to run whole-lake simulations with 3-D hydrodynamic and transport models with the resolution required for resolving the details necessary to assess the impacts of shoreline development. Studies dealing with the application of 3-D models to the coastal areas of large lakes are scarce and have tended to concentrate on the flow and thermal fields, for example, He and Hamblin (2000) and Hamblin et al. (2000). As thermal exchanges predominantly occur across the water surface, evaluation of modelled thermal distributions as a means of studying contaminant transport in the nearshore zone applies only to those substances that enter the aquatic environment via the surface in a widely distributed fashion. Heat is not a good surrogate for those chemical substances entering the water from point sources such as rivers and sewage treatment plant discharges. What is needed in this case is a tracer that also issues from the same sources. The problem with added tracers such as dye is their cost and that they breakdown in the natural environment. Ideally, the best tracers are conservative. Measuring noxious substances directly is often not feasible as they are not chemically inert, are costly to measure and can not be recorded automatically.

Total dissolved solids (TDS) is a tracer that is considered to be highly conservative in lakes. Moreover, it can be measured in place inexpensively with standard field instrumentation and either in an unattended mode with self-recording instrumentation or in an attended fashion from a survey vessel. Conductivity, salinity and TDS are related to one another. Rodgers (1998) provides formulae for correcting conductivity for temperature and relating it to salinity. Unlike estuaries where there is often a wide dynamic range of salinity along the length of the water body, lakes do not possess, in general, a sufficiently broad range in salinity concentration to test models. Herein, we report on an unusual situation of a contaminated water body in which there is well established natural fourfold gradient in conductivity or TDS over the water body. The area of interest, Hamilton Harbour, is located at the western extremity of one of the North American Great Lakes, Lake Ontario (Figure 1).

Hamilton Harbour has been designated as an area of concern by the International Joint Commission, that is, an area where pollution guidelines and standards are routinely exceeded. For this reason it has received much attention by aquatic researchers in the past. One of the principal concerns is eutrophication. Dillon and Rigler (1974) showed that the water quality of lakes in the Province of Ontario is sensitive to the total phosporus concentration. Charlton and Le Sage (1996) pointed out that despite attempts at eutrophication control excessive total phosphorus and ammonia concentrations continue to persist in Hamilton Harbour. Poulton et al. (1986) plotted profiles of ammonia and total phosphorus in the Burlington Ship Canal and compared them to profiles of conductivity. They found a close correspondence between conductivity and these pollutants and established that conductivity is a good tracer for these substances. Extensive measurements of the distributions of temperature and conductivity were made in 1988 by Spigel (1989) on cross and along harbour transects. While Klapwijk and Snodgrass (1985) were the first to exploit salinity to infer exchange from a box model approach, to our knowledge this is the first attempt to model conductivity distributions with 3-D models in the study area. One of the objectives of the study is to calibrate and evaluate models which can be applied to the assessment of impacts from proposed expansions or diversions of sewage treatment plants in Hamilton Harbour (Charlton 1996). The principal focus and goal of this paper is to provide a critical assessment of the model’s ability to determine the transport of contaminants in the coastal zones of large lakes.

In earlier modelling work in the area of interest Dick and Marsalek (1973) were the first to apply internal hydraulic theory to the exchange flow between the harbour and lake. Hamblin and Lawrence (1990) showed how this exchange was reduced by bottom and interfacial friction and that accounting for these processes brought the observations of stratified exchange in the Burlington Ship Canal of Spigel (1989) into closer agreement. Hamblin (1998) discussed two-dimensional plan hydrodynamic and transport models of Hamilton Harbour and the Burlington Ship Canal which are applicable to the unstratified period.

The shoreline configuration, bathymetry and locations of the measurement points of the study area are shown from a 3-D perspective view in Figure 2. The observations consist of area-wide surveys of temperature, conductivity and current profiles to provide the initial conditions for the model and moored meteorological stations, tide gauges and thermistor chains to provide the model forcing over the domain and along the outer lake boundary. Estimates of loading of TDS were made from flow, conductivity and temperature measurements on the main tributaries on a weekly basis over the experimental period. The salinity at the outer boundary of the computational domain was set to that of Lake Ontario of 0.15 g/Kg. A detailed plot of the instrument locations in the vicinity of the connecting channel where exchange flows occur is given in Figure 3 This plot also shows the location of the points of highly graded finite element mesh used in LACOM3D, the three dimensional lake and coastal model used in this study. The reader is referred to He and Hamblin (2000) for a description of the mathematical model. As was the case in their study 16 bottom conforming levels were used in the vertical. It is noted that similarly to the model of Johnson et al. (1993) lateral diffusion of momentum, heat and salt was not accounted for in the model equations. Additional conductivity data logged by a self-recording profiler (Figure 3) and detailed transects of conductivity taken aboard a small survey vessel (Figure 1) are the main subjects of the present study. The attended conductivity data were measured by a profiler of Hydrolabs manufacture while the moored data were based on 10-min readings of conductivity by string of eight Campbell Scientific conductivity sensors recorded on a logger at the surface.

First, the results of the simulations for temperature and flow are reviewed since without reasonable agreement between modelled and observed flow and temperature fields it would not be possible to successfully model a tracer. A three-day period was selected for a detailed analysis of the model performance after 18 days from the model startup on July 5, 1996, a time thought to be sufficient that the lack of specification of the initial flow field ought to be negligible. It is noted that the initial salinity distribution in the Windermere Channel was measured on July 8.

Modelled and observed three-day averaged temperature profiles at three locations in the Burlington Ship Canal were shown to be in reasonable agreement by Hamblin et al. (2000) and that the mean curves differed by less than the rms errors between the individual observations and modelled temperatures averaged over the period. The three profiles showed a general upward slope of the isotherms from harbour to lake in agreement with hydraulic theory. As might be expected from prior studies in the area during the stratified season (Hamblin 1998), both model and observations indicated bidirectional exchange; that is, an outflow of warm harbour water underlain by cooler Lake Ontario inflow. Differences between modelled and observed temperatures at the centre of the harbour out of the direct influence of the exchange were seen (Hamblin et al., 2000) to be somewhat larger than those in the ship canal (Figure 1) but sufficiently small that the density of the inner water body was adequately simulated over long periods of time. This is important as the density contrast between the harbour and lake drives the stratified exchange flow.

As well as the comparison of the mean structure, Hamblin et al. (2000) also examined the detailed model response, again, over the same three-day period. While the model time step was of the order of 10s and current profiles were measured every minute, 30-min averages of both were used in an analysis of the exchange flow data. In order to simplify the analysis the model results and observations for flow were decomposed into a number of modes. Greco (1998) fitted a constant plus a hyperbolic tangent function to observed temperature and current profiles in the ship canal. Similarly, Hamblin et al. (2000) fitted the expression, a +btanh((z-c)/d), to both observed and the modelled currents at each depth, z.

The best-fit constant, a, in the above expression is an approximation to the surface pressure driven or barotropic flow which fluctuated with a several hour period, corresponding to the Helmholz period (Hamblin 1998). In general, the barotropic component of flow had an amplitude of around 10 cm/s. The modelled current corresponded poorly to it. However, at noon on July 24 an event occurred which was well above this background flow and appeared to have been modelled reasonably well.

The amplitude of the tanh function, b, may be interpreted as the densimetrically driven or baroclinic component of flow. The modelled component was found to closely agree with the observed of about 20 cm/s in magnitude especially in the latter half of the comparison period but the detailed fluctuations were not replicated by the model.

The height of the maximum shear above the bed, c, or interface between the oppositely flowing layers is an important consideration in exchange flow theory and may differ from the thermocline depth (Greco 1998) when barotropic flow is present. The comparison of the interfacial heights suggested that the model overestimated the thickness of the lower layer by 1 to 2 m.

Finally, the thickness of the interface between the two counterflowing layers, d, was slightly larger in the model although not as variable as the observations. It was mainly from 1 to 3m.

On account of the importance of the baroclinic component of flow for the summer water quality of Hamilton Harbour, the baroclinic flow as represented by the difference in current between the near surface and bottom levels was compared on a much longer term basis over almost the entire simulation period of 45 days. Modelled and observed currents were averaged over a 4-hr period, effectively filtering out high frequency fluctuations associated mainly with the barotropic component. Hamblin et al. (2000) obtained reasonable correspondence between the model and observations when the density contrast between the harbour and lake was strongest. Over the simulation period the first two-thirds had a strong thermal (density) contrast which was maintained by upwelling of colder water at the western end of Lake Ontario followed by a weaker or even reversed period. The sensitivity of the baroclinic exchange to the component of wind (stress) along the channel was notable. As the baroclinic exchange flow according to the simple decomposition procedure was suppressed by an adverse wind and enhanced by a wind in the same direction as the surface layer, it must also have included a wind drift component.

Turning to the main interest of this paper, similarly, the same three-day period well after model startup was chosen for comparison of salinity at the mid-point of the channel connecting the harbour to the lake in Figure 4. While the averaged profiles based on individual 10-min data agreed well with one another, it is unfortunate that there were no observations at the surface to evaluate the model results there.

The high salinity inflow about halfway through the simulation period is evident in Transect A in Figure 5. This more dense water entered the channel as an underflow but as the main channel deepened it separated from the bottom becoming an interflow at mid-depth as is apparent on the other transects. The model captured this intruding flow well. By the end of the channel (Transect E) both the model and observations showed that the salinity plume had been eliminated by vertical mixing.

Figure 6 shows a generally similar situation about two weeks later in the experiment. Although the modelled curves were not as detailed as the observations the main features along the length of the channel were well represented by the model suggesting that errors did not accumulate in the model over the computational period.

It cannot be claimed that the model accounted for the short term (30-min) fluctuations in the observed variables. On a longer term basis the model appeared to reasonably account for flow in the ship canal, temperature at various locations in the ship canal and harbour and salinity profiles in the ship canal and a tributary arm. It is encouraging that at least over a six-week simulation period, modelling errors did not appear to predominate. While the focus in the present study and that of Hamblin et al. (2000) is on the harbour and connecting ship canal, attention next needs to be directed to the evaluation of the model in the lake portion of the model domain.

In future coastal modelling experiments it is recommended that that profiles of flow along the outer boundary be measured along with water level and density structure and that data be collected over observation periods longer than six weeks in order to evaluate ability of the model to model seasonal trends in water quality variables.

The authors would like to acknowledge the assistance of J. Milne in the collection of field data in the Windermere Channel. R. Pieters and G.A. Lawrence are thanked for their participation in the study.

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Fig. 1 Geographic location of Hamilton Harbour. Note the location of conductivity transects stations in the Windermere Channel.

Fig. 2 Perspective view of the study area, bathymetry and location of observations in the model domain.

Fig. 3 Finite element mesh. Inset shows the Burlington Ship Canal and detailed locations of observation sites within the ship canal.

Fig. 4 Comparison of salinity profiles at station in the Burlington Ship Canal. Units are g/Kg.

 

Fig. 5 Comparison of salinity profiles at the transects in the Windermere Channel, July 23, 1996. Units are g/Kg.

 

Fig. 6 Comparison of salinity profiles at the transects in the Windermere Channel, August 6, 1996. Units are g/Kg.