F.M. Boyce

Influence of Lake Surface Area and Depth Upon Thermal Stratification and the Depth of the Summer Thermocline

Among the important physical characteristics of a lake are whether it stratifies seasonally, and if so, the depth to which wind-mixing is limited by the stratification. It is generally known that sufficiently shallow lakes tend to remain isothermal throughout the year and that the depth of the thermocline in stratified lakes correlates positively with the surface area of the lake. Observations from lakes in several different regions of the temperate zone of the northern hemisphere show that whether a lake stratifies depends on both the maximum depth and the surface area of the lake, whereas the depth of the thermocline depends primarily on the surface area. A modification of previously published scaling arguments provides a plausible theoretical basis for some of this behavior. These arguments account for additional shear-induced mixing associated with the fundamental internal seiche in small lakes and with near-inertial motion in big lakes. For lakes of cross-basin diameter less than 5,000 m (surface area less than 25 km2), an estimate of the depth of the thermocline, h, at the time of maximum heat content is given by: h≅2.0(τgΔρ)1/2L1/2 where τ is the wind stress associated with late summer storms, Δp is the density contrast between epilimnion and hypolimnion typical for lakes in that region near the time of maximum heat content, g is the gravitational acceleration, and L is the square root of the surface area of the lake. A consistent set of units must be employed.

Seasonal Thermal Cycle of Lake Erie

A summary of the seasonal water temperature characteristics of Lake Erie and the 1979 and 1980 thermal structure in the central basin is described. Ice cover extends over 90% of Lake Erie most winters. Minimum surface temperature usually occurs in February (0.1° C) but fully mixed conditions at 1°C or less occur in January with isothermal conditions at (1°C) occurring from mid-February to mid-March. The thermal bar advance lasts about 5 to 6 weeks from April to mid-May and permanent stratification usually begins in mid-June with maximum heat storage in mid-August and overturn in mid-September. The central basin thermocline position varies significantly from year to year, the variability of the upper and lower mesolimnion boundaries being as large as 10 m. Thermocline position shows some dependence on prevailing meteorological conditions and has implications to the development of central basin anoxia. Temperature increases and decreases depicted on isotherm plots for stations in the central basin show correspondence with peak wind stress events. During fragile stability conditions, even moderate wind stresses of less than 0.5 dynes/cm2 are capable of producing upper layer deepening. Episodes of complete vertical mixing in response to high wind stresses of 3 dynes/cm2 during storm periods are observed. Double thermoclines are evident at several locations within the basin and temperature changes resulting from an influx of hypolimnetic water from the Pennsylvania Ridge is documented. Periods of hypolimnetic entrainment are clearly observed along with thermocline tilting of 1 to 2 meters toward the south.

Response of the Thermal Structure of Lake Ontario to Deep Cooling Water Withdrawals and to Global Warming

It has been proposed to cool buildings in downtown Toronto using cold, deep water withdrawn from Lake Ontario. 50 m3 s−1 of sub-thermocline water would be withdrawn from a depth of 80 m at a temperature close to 4°C, distributed to chillers throughout the city, and discharged on the surface in the nearshore zone at a temperature of 12°C. Compared with electrically-powered chillers, the Deep Lake Water Cooling (DLWC) scheme is thermodynamically elegant and environmentally beneficial in many ways. Using a one-dimensional thermodynamic model of Lake Ontario, this paper assesses the physical impact of the DLWC scheme on the whole lake under present and future conditions. We conclude that the lake could presently absorb the heat from the proposed Toronto installation and 20 others like it without major lake-wide physical changes. At a conservative estimate of 1000 m3 s−1 with an 8°C temperature differential, the DLWC scheme would reject approximately 33.5 GW of “waste heat” to Lake Ontario. Under our best estimate of a 2 x CO2 climate scenario, the deep waters could be 2–3°C warmer than they are now. The DLWC system would be less efficient, but the lake would retain a similar overall cooling capacity. Neither biological consequences nor the local physical impact of the discharge of heated subsurface water from the DLWC system are addressed in this study.

Lake Erie Research: Recent Results, Remaining Gaps

Abstract Evidence that oxygen depletion rates in the central basin hypolimnion were increasing and would lead to increasingly severe late summer anoxia resulted in a large public investment in both the U.S. and Canada to construct sewage treatment plants in order to reduce the phosphorus load to Lake Erie. Improvements in the water quality indicators, phosphorus and chlorophyll, have been achieved in the decade since these measures went into effect. There is no clear evidence, however, for a corresponding “recovery” in hypolimnetic oxygen depletion. It is now recognized that physical processes, driven by winds and solar heating with strong interannual fluctuations, influence the timing and severity of late-summer anoxia, and make it difficult to detect long-term trends. As a result of the 1979 and 1980 intensive field experiments, many of the physical processes are better understood, better documented, and new possibilities exist for improved numerical hydrodynamical modeling. Systems modelers have exploited the voluminous Lake Erie data to generate convincing water quality models that account for the physical variability as well as simulating biochemical parameters. In some respects the modelers have pushed beyond the frontiers of established knowledge of biochemical processes and thus challenge process-oriented researchers to confirm or reject their findings. A consensus is forming among Lake Erie researchers that the key to understanding the lakes response to changing external loading lies in a detailed understanding of the sediment/water interaction. Study of sediment-water interactions calls for interdisciplinary efforts that will involve physicists, biologists, chemists, and modelers. An appendix to this paper lists specific research recommendations.

Hypolimnion Flow Between the Central and Eastern Basins of Lake Erie During 1977 (Interbasin Hypolimnion Flows)

Abstract The shallow central basin of Lake Erie (mean depth 19 m) is separated from the deeper eastern basin (mean depth 28.5 m) by the Pennsylvania Ridge which extends southward from the base of Long Point to Erie, Pennsylvania. The crest of the ridge lies at a depth of 15 m except for a narrow notch near Erie, Pennsylvania, where communication between the two basins extends to 24 m depth. Both basins are stratified in summer, and the thin (2 m) hypolimnion of the central basin becomes depleted of oxygen by late summer. Flows to the hypolimnion of the central basin from the mid thermocline water of the eastern basin have been thought to be important sources of dissolved oxygen to the central basin. Data from ship cruises and current meter moorings made in 1977 have been used to form an estimate of the hypolimnion flux across the sill area. A strong correlation between winds and mean flux is observed and the dynamic balance appears to be one where surface pressure gradient created by wind stress is opposed by internal pressure gradients and by bottom friction. While the total quantity of oxygen transported by the subsurface flow is significant in terms of the later summer oxygen consumption of the central basin hypolimnion, its effects are confined to the eastern half of that basin due to the relatively weak horizontal diffusion in the mid-basin hypolimnion.

Inertial Frequency Current Oscillations in the Central Basin of Lake Erie

Abstract Circularly polarized currents at or near the local inertial frequency are a common occurrence in the offshore regions of the Great Lakes during the stratified season. Spectra of horizontal currents from Lake Eries central basin are dominated by an inertial frequency peak during the summer months. A review of theory concludes that, in addition to the conventional view that these motions are inertial-gravitational standing waves of the Poincare type, we must also consider the possibility of pure inertial motions forced by the wind in the surface layer and by the opposing surface pressure gradient or setup in the subsurface layers. Stratification controls the vertical distribution of turbulent stress in the water column. Current meter and thermistor array data from 1979 are reviewed in detail, confirming the observation of Boyce and Chiocchio (1987) that the largest inertial motions occur above the seasonal thermocline, and relating occurrences of large, mid-water column, inertial motion in the details of the thermal stratification. The hypothesis that the principal response of the water column to a changing wind field is the direct result of surface stress and pressure gradient is tested with simple diagnostic models that explain the subsurface maximum of the inertial-period motion in terms of a water column alternating between three and two moving layers.

Water Movements at a Mid-Central Basin Site: Time and Space Scales, Relation to Wind, and Internal Pressure Gradients

Abstract Current meter and thermistor string records made at a mid-basin site from May, 1979, through February, 1980, and during August, 1980, are used to determine the time and space scales of horizontal motion in mid lake and to relate these to the major forcing variables. Motions at frequencies larger than 0.125 cycles per hour are horizontally coherent over a few km only, whereas lower frequency motions may cohere significantly over tens of km in the stratified season. Of the four depths sampled, 10 m, 15 m, 20 m, and 21 m, highest current speeds are associated with circularly polarized clockwise rotating motion at the inertial period at 15-m depth. Surveillance cruise data show the mid central basin array to be located in a zone of relatively flat thermocline topography but suggested that internal pressure gradients might at times be large enough to influence bottom flow. Limited small-scale sampling in the vicinity of the mid-basin array reveals the existence of intense but short scale (5 km) internal pressure gradients that are undersampled by the array of thermistor strings (separated by 10 km). Multivariate statistical techniques in the frequency domain indicate that the internal pressure gradients estimated by means of the array of thermistor strings are of marginal dynamical significance (although the smaller scale gradients may in fact contribute substantially to the observed variance). A simple model of locally driven currents appropriate to a region of constant depth is proposed. This model and the statistical analyses together help to interpret the effects of wind stress and Coriolis forces. Many of the observed features of circulation, including seasonal evolution, can be related to the role of stratification in governing the vertical distribution of turbulent mixing.

A Comparison of Drogues, Current Meters, Winds, and a Vertical Profiler in Lake Erie

Abstract As part of an extensive survey of the temperature and currents of the central basin, Lake Erie, a vertical automatic profiling system (EVAPS) was deployed at an offshore location for 3 days in August 1980. This system, which is considered to be new to Great Lakes studies, consisted of acoustic current meters, temperature sensors, and a pressure gauge which by the use of a bottom mounted winch could be made to ascend and descend through the water column. The profiler permitted the collection of continuous vertical temperature and velocity profiles. From these profiles, temperatures and the horizontal components of the flow were extracted at several depths and compared to standard measurements from current meters, drogues, and a meterological buoy. Such a comparison demonstrated satisfactory agreement of the conventional data with the profile measurements and thus establishes the validity of this novel approach to measurement of flow in a large lake.

Evaluation of Sediment Traps in Lake St. Clair, Lake Ontario, and Hamilton Harbour

Abstract Sediment traps are simple, inexpensive devices that yield time-integrated samples of material suspended in the water column. Although many different designs have been proposed, there seems to be general agreement that the cylindrical settling tube is a design capable of yielding quantitative results in relatively calm waters. The reliability of these or any other trap in shallow water with significant wave orbital motions is unknown. This paper describes our attempts to assess the field performance of conventional settling tubes and two versions of horizontally-ported chambers in shallow, wave-dominated water. We find that catch rates of the horizontally-ported chambers correlate strongly and positively with the root mean square horizontal flow velocity over the trapping interval. We suspect a similar dependence exists for the settling tubes. With present levels of understanding, results from sediment traps of these designs deployed in shallow, wave-dominated water should be given qualitative status only.