A nested-grid hydrodynamic modeling system is used to study circulation and temperature distributions in Lake Huron and adjacent areas. This nested system is based on a three-dimensional, primitive-equation z-level ocean model. The nested system consists of two sub-components: a coarse-resolution outer model covering Lake Huron and Georgian Bay with a horizontal resolution of roughly 2.5 km, and a fine-resolution inner model covering eastern Lake Huron and northwestern Georgian Bay with a horizontal resolution of roughly 900 m. The inner model produced reasonably well the three-dimensional flow and thermal structure over the coastal boundary layer close to the eastern shore of the lake.
Bordered by the province of Ontario and the state of Michigan, Lake Huron (LH) is the second largest Laurentian Great Lake and the fifth largest freshwater lake in the world. LH contains 3,540 km3 of water at low water datum and has a horizontal dimension of about 330 km east to west and 295 km north to south, with a maximum water depth of about 230 m and an average water depth of about 60 m. The most dominant topographic feature in LH is a ridge of Niagara Dolomite that extends from Thunder Bay, Michigan on the west side, across the lake to Point Clark, Ontario on the east side (Fig. 1), separating the lake into the southwestern and eastern basins. LH comprises four interconnected water bodies: the Main Lake, Saginaw Bay, the North Channel and Georgian Bay, and the lake is connected to Lake Michigan via the Straits of Mackinac (SM) to the northwest, Lake Superior via St. Mary's River (SMR) to the north, and Lake St. Clair via the St. Clair River (SCR) to the south. Major inflows to LH come from Lake Superior via SMR (about 2,100 m3 s− 1) and Lake Michigan via SM (about 1,400 m3s− 1). Lake Huron discharges at its southern end through the SCR into Lake St. Clair, which in turn discharges through the Detroit River into Lake Erie.
Accurate numerical simulation of water movements and thermal structure in LH is crucial for development of water quality models in the lake and for small embayments of the North Channel and Georgian Bay. Sheng and Rao (2006) presented a nested-grid modelling system to reconstruct the large-scale circulation and temperature distributions in 1974-75. The nested-grid modelling system used in this study is based on the 3D primitive equation z-level ocean circulation model known as CANDIE (Canadian version of DieCAST, Sheng et al., 1998). An earlier version of the DIECAST model has been applied to various modelling problems on the continental shelf seas. The nested-grid modelling system of LH has two sub-components: a coarse-resolution outer model covering Lake Huron (LH) and Georgian Bay (GB) between 79.4°W and 84.7°W and between 43°N and 46.3°N; and a fine-resolution inner model covering eastern Lake Huron and western Georgian Bay between 81°W and 82.2°W and between 44.1°N and 46.1°N (Fig. 1). The main reason for setting up the inner model over this region was to resolve the detailed 3D currents and temperature distributions through the Main Channel and within the coastal boundary layer close to the eastern shore of the lake. The nested system uses the bathymetry of Schwab and Sellers (1996), with model horizontal resolutions of about 2.5 km and 900 m respectively for the outer and inner models. Both the outer and inner models have the same 30 unevenly spaced z-levels in the vertical. The nested system uses the sub-grid scale mixing parameterization scheme of Smagorinsky (1963) for the horizontal eddy viscosity, and the scheme proposed by Large et al. (1994) for the vertical mixing coefficient.
The outer model of the nested system has three open boundaries (i.e., northern, western and southern open boundaries), with specifications of steady inflows to LH from Lake Superior via SMR (∼ 2,100 m3s− 1) and Michigan via SM (∼ 1,400 m3s− 1) and outflows from LH into Lake St. Clair via SCR (∼ 3,500 m3s− 1). Gradient boundary conditions are used for temperature fields along the outer model open boundaries. As a result, the river runoff specified at the outer model open boundaries plays only a minor role in driving the general circulation in the lake. The currents and temperatures produced by the outer model are used to specify current and temperature distributions at the open boundaries of the inner model. In addition, the outer and inner models of the nested-grid system use the quadratic bottom friction parameterization with the drag coefficient set to 2.5 × 10− 3, and the no-slip condition at the model lateral closed boundaries, at which the normal and tangential flows and horizontal fluxes of temperature are set to zero. These boundary conditions appear to produce reasonable simulations in the coastal waters of the Great Lakes.
In addition to the open-boundary forcing (i.e. currents and temperature along the model open boundaries) described above, two additional model forcings were used to simulate the 3D circulation and thermal structure in the lake in 1974-75. We forced the model with wind stress calculated from the wind speeds extracted from the coarse-resolution National Centres for Environmental Prediction (NCEP) reanalysis data with amplitudes modified based on the observed wind in the lake. The first additional model forcing is wind stress applied at the lake surface. The wind stress was obtained from the observed wind speeds at three meteorological stations M2, M3 and M4 in LH based on the bulk formula suggested by Large and Pond (1981). The second additional model forcing is the net heat flux (NHF). Since there were no NHF observations made in Lake Huron during the study period, it is assumed to be horizontally uniform and equal to the climatological monthly mean NHF calculated from results produced by the Great Lakes Net Basin Supply Forecast (GLNBSF) Model (http: mcc.sws.uiuc.edu/glakes/hur/nhu.html) for simplicity. Lake surface temperatures were measured at four meteorological stations M1, M2, M3 and M4 in LH but only for the period from year day 130 to 320 in 1974. As a result, the input lake surface temperature (LST) used in model simulation is also assumed to be horizontally uniform and equal to the linear combination of observed LST and the climatological monthly mean LST (LSTclim) calculated from the GLNBSF model results during the above LST observation period and equal to LSTclim at other times (Sheng and Rao, 2006). The assumption that the heat flux is evenly distributed over the surface of the lake must be considered approximate only.
We initialized the nested-grid hydrodynamic modelling system with a spatially uniform temperature of 4°C and salinity of 0.2 ppm at every model grid point, and force the model with the time-varying and spatially uniform wind stress and net surface heat fluxes described above. We integrated the nested-grid system for two years from January 1, 1974 to the end of 1975. The typical spin-up time of the lake circulation is relatively short, due mainly to the strong wind-driven character of the lake hydrodynamics. Therefore, the effect of the initial condition on the long-term model simulation should be negligible after a few weeks.
Results and Discussion
Sheng and Rao (2006) showed that the outer model performs reasonably well in reproducing the observed currents and temperature in the Lake (Saylor and Miller, 1979; Sloss and Saylor, 1975). The model results generate a cyclonic coastal jet in both Lake Huron and Georgian Bay, which is relatively stronger in summer and fall than those in other seasons. The outer model also generates reasonably well the seasonal evolution of thermal stratifications in the upper 30 m in the lake. It was also shown that fine-resolution inner model reproduces reasonably well the circulation features produced by the outer model, and much better the detailed circulation features over the coastal boundary layer (CBL) close to the eastern shoreline of LH, due mainly to a better representation of bottom topography and dynamics within the CBL by the inner model using a finer horizontal resolution than the outer model. The CBL comprises a frictional boundary layer (FBL) near the coast and an inertial boundary layer (IBL) offshore. The main difference between the FBL and IBL is that the momentum imparted by the wind stress is balanced by bottom and shore friction within the FBL and balanced by the Coriolis term, bottom friction and pressure gradients within the IBL (Rao and Murthy, 2001). Based on the current meter studies made in summer of 1974 over the coastal region near Point Clark of Lake Huron (Fig. 2), Murthy and Dunbar (1981) suggested that the FBL and IBL widths are respectively about 2 km and 7 km in summer months in LH.
Figure 3a presents vertical distributions of monthly mean along-shore currents at transect A in February 1974 produced by the inner model with a fine horizontal resolution of 900 m. The February mean along-shore currents at the transect are characterized by relatively weak currents at the coast and sea bottom due to the shore and bottom friction, and a surface-intensified strong velocity core of about 9 cm s− 1 at about 4 km from shore. The center of this high velocity core varies from about 3 km from shore at the surface to 5 km at 30 m depth. The along-shore currents are more vertically uniform in the top 40 m beyond 5 km from shore and decrease to 2∼ 3 cm s− 1 at 10 km. By choosing the position at which the alongshore currents reach a maximum as the boundary between the FBL and IBL, the FBL width produced by the inner model is about 4 km in February 1994 along transect A.
The May mean along-shore currents at transect A have similar distributions as those in February, except that the along-shore currents are relatively stronger over the FBL in May than in February (Fig. 3b). The along-shore currents in May reach a maximum value of about 11 cm s− 1 at about 3 km from shore, and decrease to about 1 cm s− 1 at 10 km from shore. The FBL width in May produced by the inner model is about 3 km, which is slightly narrower than in February. Vertical distributions at transect A of monthly mean currents and temperature in August (Fig. 3c) differ significantly from those in February and May, due mainly to strong thermal stratifications in summer months in the lake. The August mean thermal structure at the transect is characterized by a strong thermal stratification in the top 40 m and weak stratification below 60 m, with warmest waters of greater than 22°C over the inshore region (figures not shown). The overall distributions of temperatures within the CBL in August produced by the inner model agree reasonably well to the observed thermal structures in the Great Lakes determined by Rao and Murthy (2001). The August mean along-shore currents at transect A are characterized by a near-surface high velocity core of about 8 cm s− 1 centered at about 3 km from shore and broad, surface-intensified along-shore currents over the offshore region between 10 km and 30 km from shore, The along-shore currents decrease with depth and are very weak below 40 m (Fig. 3c). Dynamically, the along-shore currents at the transect are driven primarily by horizontal gradients of baroclinic pressures associated with the summer thermal stratification. The November mean along-shore currents within the FBL at transect A are very similar to those in August, with a near-surface high velocity core of about 9 cm s− 1 centered at about 3 km from shore (Fig. 3d). Different from the model results in other three months, the November along-shore currents have a sub-surface high velocity core centered at about 30 m from the lake surface at about 4 km from shore. Beyond 10 km from shore, the November along-shore currents at the transect are about 4 to 6 cm s− 1 in the top 60 m, with many small-scale circulation features.
We next assessed the model performance in simulating hydrodynamics in LH in the inner grid. Figure 4 shows a comparison of the observed monthly mean currents with the monthly mean currents produced by the fine-resolution inner model at the three different depths in the months of December, February and April. Although there were only a small number of observed currents available over the inner model domain, the inner model results reproduced the observed monthly mean currents reasonably well, particularly the currents through the Main Channel and coastal currents over the coastal region near Point Clark.
Summary and Conclusions
A nested-grid modelling system was developed for Lake Huron and Georgian Bay based on the primitive equation z-level ocean circulation model known as CANDIE. The nested-grid modelling system was used to reconstruct the large-scale circulation and temperature distributions in 1974–75. During this period an extensive field program was conducted in Lake Huron. The model was forced with monthly mean net heat flux and wind stress calculated from the wind speeds extracted from the coarse-resolution National Centres for Environmental Prediction (NCEP) reanalysis data with amplitudes modified based on the observed wind in the lake. The observed lake surface temperature was also used in forcing the model. The model results generate a cyclonic coastal jet in both Lake Huron and Georgian Bay, which is relatively stronger in summer and fall than those in other seasons. The model also generates the seasonal evolution of thermal stratifications in the upper 30 m in the lake reasonably well. The fine-resolution inner model simulates reasonably well the three dimensional circulation and thermal structures over the coastal boundary layer close to the eastern shore of LH. A comparison of model results with the observed currents and temperature fields demonstrates significant skills of the z-level CANDIE model in simulating the large-scale hydrodynamics in LH and GB and fine-scale circulation over the coastal region. One of the principal reason for developing hydrodynamic model for Lake Huron is to use the circulation patterns predicted by the circulation model to better estimate the transport of suspended and dissolved chemical and biological material that can affect the water quality. Some studies in this direction are already in progress.