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The heat budget of Quesnel Lake, British Columbia Potts, Daniel John 2004

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T H E H E A T B U D G E T O F Q U E S N E L L A K E , B R I T I S H C O L U M B I A by Daniel John Potts B. A. Sc., University of British Columbia, 2002 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M A S T E R OF APPLIED SCIENCE in T H E FACULTY OF GRADUATE STUDIES Department of Civil Engineering We accept this thesis as conforming to the required standard The University of British Columbia August 2004 © Daniel John Potts, 2004 FACULTY OF GRADUATE STUDIES THE UNIVERSITY OF BRITISH COLUMBIA L i b r a r y A u t h o r i z a t i o n In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Name of Author (please print) Date (dd/mm/yyyy) Title of Thesis: (W ^oAot^ cJr CXjpjiy\e) i^£Q-! E n y i s ^ (olvr^d<A The University of British Columbia Vancouver, B C C a n a d a / t l L ^ O . Year: 2 C O f Degree: Department of ;grad.ubc.ca/forms/?formlD=THS page 1 of 1 last updated: 20-Jul-04 A B S T R A C T Quesnel Lake, a long, narrow fjord lake in the Interior Plateau, is the deepest lake in British Columbia (506 m). This pristine, oligotrophic lake and its watershed are a cornerstone of the province's salmon fishery, and were historically home to up to 30% of the Fraser River sockeye run. The transport processes and spatial distribution of oxygen and nutrients in the lake are controlled by temperature stratification; therefore, a solid understanding of the lake's thermal structure and of the dynamics controlling that structure is vital to ecological management decisions. Water temperatures in the lake were measured with two thermistor moorings, one of » which reached a depth of 283 m. Weather data recorded at Williams Lake airport were used to estimate heat and mass fluxes at the lake surface. The temperatures of the three largest inflowing rivers were measured, and river flow rates were measured or estimated. Inflows estimated from historic flow data balanced the water budget well except during the summer of 2003, which was unseasonably dry. In fall as the surface waters cooled towards 4°C, the mixed layer deepened until the entire water column briefly became isothermal. Because of pressure effects on water's temperature of maximum density, 1-D transport processes cannot explain this isothermal condition. Episodic cooling of the deep water during winter was likewise inexplicable by 1-D principles. During spring warming, the mixed layer deepened only to 153 m, and complete turnover did not occur. The heat content of the lake reached a maximum on 23 August 2003 and a minimum on 11 March 2004. The heat budget, or difference between 9 9 minimum and maximum heat content was 1.72 GJm" (41.1 kcal cm" ). Heat flux estimates overpredicted the lake's heat budget by 3.5%, and indicated that shortwave and longwave radiation and evaporation were dominant. Flows across a sill into the lake's West Basin were estimated by two methods, using conservation of volume and conservation of heat energy. The estimated flow rates were comparable to the limits imposed by 2-layer inviscid hydraulic control. Temperature fluctuations in Quesnel River were due to basin- and lake-scale internal motions. ii T A B L E OF CONTENTS Abstract » Table of Contents i" List of Tables v List of Figures vi List of Symbols ix Acknowledgments xii 1.0 Introduction 1 2.0 Literature Review 4 2.1 Previous Studies at Quesnel Lake 4 2.2 Heat Budgets of Other Lakes 5 2.3 The Density of Water 8 2.4 Seasonal Turnover in Temperate Lakes 9 3.0 Data Collection 12 3.1 Quesnel Lake Surface Level 12 3.2 Bathymetry of Quesnel Lake 13 3.3 Inflows and Outflow of Quesnel Lake 14 3.3.1 Measurement of Inflow Temperatures 14 3.3.2 Estimation of River Flow Volumes 16 3.4 Weather near Quesnel Lake 20 3.4.1 Lakeshore Weather Stations 20 3.4.2 BC Ministry of Forests Stations 21 3.4.3 Williams Lake Airport 22 3.5 Temperatures in Quesnel Lake 22 iii 4.0 Calculations 25 4.1 Selection and Modification of Meteorological Data 25 4.1.1 Temperature Data Comparison : 25 4.1.2 Wind Speed Data Comparison 26 4.1.3 Solar Radiation Data Comparison 26 4.1.4 Presentation of Meteorological Data 27 4.2 Heat Budget Calculations 29 4.2.1 Heat Content 29 4.2.2 Surface Heat Flux 30 4.2.3 Water Budget 33 4.2.4 Advective Heat Fluxes 34 5.0 Results and Discussion 37 5.1 Lake Temperature Observations 37 5.2 Heat Budget 41 5.3 Estimation of Flow Rates Over A Sill 47 5.3.1 Background 47 5.3.2 Thermocline Method 50 5.3.3 Heat Content Method 51 5.3.4 Estimated Flows Across the Sill 53 6.0 Conclusions and Recommendations 56 References 59 Appendix A: Modeling Quesnel Lake using DYRESM 63 iv LIST OF TABLES Table 1 Water Survey of Canada gauging stations near Quesnel Lake. Years of operation, historic mean flow (Qg), catchment area (Ag) and catchment label (for Figure 9) are listed 17 Table 2 Sensor specifications on the Vantage Pro weather stations: sampling interval, accuracy and resolution 21 Table 3 Temperature comparison between YWL and lake stations. See text for details of the calculations. ...\ 25 Table 4 Comparison of RMS wind speeds (ms"1) between YWL and lake stations. The RMS wind speed from YWL is different for each comparison because the comparison period changes 26 Table 5 Summary of sine curves fit to measured heat content (M8) and integrated fluxes, using least squares. The sine curves both fit quite tightly, with RMS error less than 5% 42 Table 6 Total energy added to Quesnel Lake by each heat flux over the 327-day period.43 Table 7 Criteria for determining the signs of QE and Qn. TL is compared to temperatures at M8 only. The last two columns indicate the appropriate mooring from which to take epilimnetic and hypolimnetic temperatures for further calculations 53 v L I S T O F F I G U R E S Figure 1 Map of Quesnel Lake with inset showing its location relative to the province of BC. The lake's North and East Arms, junction and West Basin are labelled; major rivers are marked with arrows, and a dot locates the town of Likely 1 Figure 2 The dependence of fresh water density on temperature and pressure (depth). Contours of density are given in kgm"3. The temperature of maximum density, TMD, is indicated by the dotted line 8 Figure 3 Schematic illustrations of temperature profiles leading to deep penetrative convection by the thermobaric instability. Temperature profile, solid line; previous profile, dashed line; TMD, dotted line, (a) Hypothetical initial stable profile, (b) Thermocline displaced downward by wind or internal wave action, (c) Unstable water mass mixes downward until meeting colder water 11 Figure 4 Quesnel Lake level during the study period. Water level is given relative to the WSC gauge, with z increasing downwards 12 Figure 5 Hypsometric curve for Quesnel Lake, showing horizontal area as a function of depth. Breakpoints in the curve approximately match key depths in the lake. The hypsometric curve for the West Basin is indicated by the bold line 13 Figure 6 Map of Quesnel Lake showing contours of depth every 100 m. The deepest point is in the East Arm, whose sides are steeper than 45° in places 14 Figure 7 Map of Quesnel Lake, showing the locations of the three river thermistors, the three major inflowing rivers, and the outflowing Quesnel River 15 Figure 8 Temperature records from thermistors in the major inflowing streams to Quesnel Lake: (a) Horsefly River, (b) Mitchell River and (c) Niagara Creek. Horsefly River reached zero degrees, and for two months, reportedly froze over. Niagara Creek's thermistor appears to have been exposed to air from 20 August 2003 to 1 May 2004. 16 Figure 9 Catchments within Quesnel Lake's watershed, numbered according to Table 1. The grouping of catchments is indicated by shading (see text). Gauge locations are indicated by '+' signs. Numbers in gauged catchments (G) represent annual runoff depths in mm yr"1. Runoff depths in ungauged regions were taken from nearby catchments as indicated by arrows. Where multiple arrows enter a single catchment, runoff depths in the source catchments were averaged 18 Figure 10 (a) Estimated monthly flows entering Quesnel Lake from the three catchment groups, (b) Historic monthly flows in Quesnel River and measured flows (2003/2004) from the WSC gauge 20 Figure 11 Map of Quesnel Lake area showing the locations of weather stations and of the thermistor moorings in the West Basin (M2) and at the junction (M8) 21 Figure 12 Structural details of the thermistor chain at the junction of Quesnel Lake (M8). 23 vi Figure 13 Temperatures recorded by the thermistor mooring at the junction of Quesnel Lake. The depth in metres of each thermistor is indicated on the left 24 Figure 14 Comparison of daily solar radiation measured at Elysia Resort and estimated from YWL cloud cover data. The totals for the 51-day period differ by 11% 27 Figure 15 Meteorological data from YWL used in surface heat flux calculations. Wind speeds were scaled from 10 m to 2 m measurement level by a logarithmic law 28 Figure 16 Total inflows to Quesnel Lake estimated from monthly historic flows (section 3.3.2) and from the water budget (Equation 9). The historic flows clearly overestimate inflows in summer 2003 34 Figure 17 Air and river temperatures between 25 July and 26 October 2003. Air and river temperatures approximately match each other during the summer and early fall. 35 Figure 18 Temperature records from selected thermistors on M8. Thermistor depths in metres are indicated near each trace. The lake was isothermal to 283 m at about 3.98°C on 31 December 2003, and isothermal to 153 m at 3.5 to 3.75°C between 19 April and 5 May 2004 37 Figure 19 Isotherms in Quesnel Lake, interpolated from daily average temperatures on M8. Bold contours are every degree; fine contours, every 0.2 degree 38 Figure 20 Profiles of temperature versus depth, measured by M8 during (a) fall "turnover" and (b) spring "turnover." 39 Figure 21 (a) Temperatures measured at 283 m during the winter. Major cooling events occurred on 30-31 January and 15-16 March 2004. (b) Vertical temperature profiles immediately after each cooling event. On each profile a temperature maximum occurs at 153 m. The dotted line in each plot indicates TMD 41 Figure 22 The average daily heat content of Quesnel Lake as measured by M8, and the integrated heat fluxes estimated from meteorological data. The peak-to-trough difference in measured heat content is 1.72 GJm"2 or 41.1 kcal cm"2 42 Figure 23 Principal components and total of the heat flux into Quesnel Lake 44 Figure 24 Contours of depth (m) in Quesnel Lake. The West Basin is separated from the main lake body by a shallow sill, indicated by the broken line 48 Figure 25 Isotherms (°C) in the upper 40 m of (a) the West Basin and (b) the main lake body. Thermistor data have been smoothed by a low pass Fourier filter with 24-hr cutoff. The 11 °C isotherm is bold in each plot. Ticks on the vertical axes indicate instrument depths. Temperature data in the West Basin are courtesy of John Morrison (Morrison, 2004) 48 Figure 26 Schematic of thermocline displacement in Quesnel Lake. Here, wind stress causes downwelling in the West Basin by pushing in epilimnetic water (QE), which displaces the hypolimnetic water below (QH) 49 vii Figure 27 Flows into the West Basin epilimnion, predicted by the thermocline and heat content methods. Dashed lines indicate the approximate limits imposed by hydraulic control 54 Figure 28 (a) Sample temperature profde (15 April 2004) from the DYRESM simulation of Quesnel Lake using in-situ density to evaluate stability. The dotted line is TMD. The profile is clearly unstable, (b) In-situ density profile corresponding to (a). The pressure effects on density mask the instability 63 Figure 29 (a) When DYRESM is modified to use potential density to compute stability, the initial profde (1 August 2003) gets mixed from 76 m to the bottom in the first timestep. (b) Potential density profiles corresponding to the initial condition and mixed condition in (a). The stable initial condition appears to be unstable, judging from potential density, and is therefore mixed immediately 64 Figure 30 A comparison of DYRESM simulation results against field data from Quesnel Lake. Heavy isotherms are integer temperatures between 1 and 12°C; fine isotherms are every 0.2°C between 2 and 5°C. Only the top 80 m of the lake is shown. The M8 temperature data were averaged in 72-hour bins to remove the higher-frequency waves 66 viii L I S T O F S Y M B O L S The following is a list of the symbols used in this thesis. Symbols from the Latin and Greek alphabets are listed separately. Latin Characters A area, m2. A o surface area, m2. Ag area of gauged catchment, m2. Au area of ungauged catchment, m2. cP specific heat of water, 4184 Jkg"loC"'. cPa specific heat of air, 1000 Jkg"loC"'. cPi specific heat of ice, 2090 Jkg'^ C'1. C fraction of the sky covered by cloud, dimensionless. E evaporation rate, ms"1. fcs clear sky attenuation factor, dimensionless. g acceleration due to gravity, 9.81 ms"2. h water level, m. h\ thermocline depth, m. H heat content, GJm"2. L latent heat of vaporisation of water, calculated, Jkg"1. LQ lake length, m. L S latent heat of melting ice, 3.35-105 Jkg"1. n number of days in data comparison. N evaporation coefficient, dimensionless. p pressure, mb. Po standard air pressure, 1013 mb. P rate of precipitation, ms"1. qo solar radiation reaching the upper atmosphere, Wm"2. <?A EVAP heat carried away by mass of evaporated water, Wm"2. qA, ppT heat added to the lake through precipitation, Wm"2. qINFLOW heat added to the lake by inflowing water, Wm"2. ix qui latent heat of evaporated water, Wm"2. quNA longwave radiation absorbed by the water surface, Wm"2. qLWE longwave radiation emitted by the water surface, Wm"2. qouTFLOw--- heat carried away by outflow, Wm"2. qsENs sensible heat flux, Wm"2. qsuRF total surface heat flux, Wm"2. qsw shortwave radiation penetrating the lake surface, Wm"2. qror total heat flux, Wm"2. Q volume flow rate, mV. QE flow into West Basin epilimnion, m3s"'. QG flow from a gauged catchment, mV1. QH flow into West Basin hypolimnion, mV. QINFLOW calculated total inflow to Quesnel Lake, m3s"'. QQR flow rate in the Quesnel River, mV1. QU flow from an ungauged catchment, m3s"'. R rain rate, ms"1. Ri shortwave reflectivity of the water surface, dimensionless. S rate of solid precipitation, in ms"1 of water. t time, s. T temperature, °C. To water surface temperature, °C. T2 air temperature at 2 m above ground, °C. TL effective temperature of net flow into West Basin, °C. TMD temperature of maximum density of water, °C. TQR temperature of Quesnel River, °C. TR rain temperature, °C. TREF reference temperature, °C. Ts temperature of solid precipitation, °C. «io wind speed at 10 m above ground, ms"1. «2 wind speed at 2 m above ground, ms"1. URMS root-mean-square wind speed, ms"1. V volume, m . VWBE volume of the West Basin's epilimnion, m3. x W Wedderburn number, dimensionless. z depth, increasing downward, m. z mean depth, m. ZMAX maximum depth, m. Greek Characters GCe free convective evaporation coefficient, ms"1. Oh sensible heat transfer coefficient, Wm"2oC"1. ea atmospheric emissivity, dimensionless. £w water surface emissivity, dimensionless. p water density, kgm"3. a Stefan-Boltzmann constant, 5.67-10"8 Wm"2. T. shear stress, Pa. Q.0 saturation water vapour concentration at the water surface, kg kg D.2 water vapour concentration at 2 m, kg kg"1. xi A C K N O W L E D G M E N T S This thesis and the research it presents could not have been completed without the assistance of many. My supervisor, Dr. Bernard Laval, gave much time, encouragement, guidance and critical feedback. The Institute of Ocean Sciences, and John Morrison in particular, shared field expertise, manpower and data. The insights of Dr. Eddy Carmack were much appreciated. Dr. Roger Pieters was a great help in preparing and calibrating the field instruments. Fellow-students Christina James, Ryan North and Gabe Sentlinger assisted with field work. The Department of Fisheries and Oceans Cultus Lake Laboratory and the Provincial Ministry of Water, Air and Land Protection provided ship time. The BC Forest Service Protection Program and Environment Canada provided weather data. The author was supported by a PGS-A award from NSERC. xii 1.0 I N T R O D U C T I O N Quesnel Lake, the deepest in British Columbia (BC), rests mostly in the Interior Plateau, about 70 km southeast of Quesnel. The northern and eastern arms of this narrow, fjord-type lake extend into the Cariboo Mountains, giving it an east-west span of 81 km and a north-south span of 36 km. The shores of the lake are' in the interior western hemlock biogeoclimatic zone, while the upper reaches of its catchments are in the subalpine Engelmann spruce zone (Farley, 1979). Quesnel Lake is shaped a bit like a 'w' (Figure 1) and its surface area is only 266 km2 despite its horizontal extent. Its mean depth is 157 m, and the deepest survey point is 506 m (Campbell, 2001). The average residence time of the lake's 41.8 km of water is 10.1 years, based on a mean annual outflow of 131 m s" . Horsefly River, the lake's most significant inflow, drains .2750 km2 in the Interior Plateau, where annual rainfall averages 500-1500 mm yr"1. Two other major inflows, the Mitchell and Niagara, each drain less than 600 km2 but flow down from the Cariboo Mountains, where annual rainfall is typically 1500-2500 mm yr"1 (Farley, 1979). Figure 1 Map of Quesnel Lake with inset showing its location relative to the province of BC. The lake's North and East Arms, junction and West Basin are labelled; major rivers are marked with arrows, and a dot locates the town of Likely. 1 Although there is logging in the lake's watershed, Quesnel Lake is essentially pristine and oligotrophic, with a total phosphorus concentration of 2.0 pg L"1 (Stockner and Shortreed, 1983). Reported levels of total dissolved solids range from 62 mg L"1 (Stockner and Shortreed, 1983) to 90 mg L"1 (James, 2004); the latter value was adopted for calculations involving salinity in this thesis. Quesnel Lake lies in the watershed of the Fraser River, which drains a total of 217 000 km (Morrison et al., 2002). This watershed is home to most of BC's sockeye salmon, which are the cornerstone of the province's fishing industry. Although it is only 5930 km2 (Environment Canada, 2002), the Quesnel Lake watershed has historically been home to as much as 30% of the Fraser River sockeye salmon run (Royal, 1966). After hatching in streams or along lake shores, juvenile sockeye rear in fresh water for a year or two before journeying downstream to the ocean. They spend their adult lives at sea, and finally migrate back to their natal streams where they spawn and die, usually in their fourth year of life. Unfortunately, early in the twentieth century the Quesnel sockeye population was nearly wiped out by obstructions on the Quesnel and Fraser Rivers. To facilitate gold mining activities a dam was built on the Quesnel River near Likely in 1897 (Thompson, 1945). It severely reduced the passage of spawning sockeye until an adequate fishway was constructed in 1904. Less than ten years later, railway construction in the Fraser Canyon constricted the Fraser River at Hell's Gate to such an extent that migrating adult salmon were blocked or delayed, and failed to spawn (Thompson, 1945). Fishways were constructed at Hell's Gate in 1945, and the Fraser salmon population began to revive. Although the recovery of the Quesnel sockeye population has been slow, the number of returning spawners is now nearing its historic level. There were over four million in 1909 (Thompson, 1945); in 2001 there were 3.5 million, and in 2002, 3.7 million (Shortreed and Grout, 2003). The success of spawning salmon is closely related to water temperature. River temperatures above about 18°C cause stress to salmon and are also associated with disease in the fish (Royal, 1966). Consequently, the Canadian Department of Fisheries and Oceans (DFO) monitors temperatures in the Fraser River and its tributaries, and during spawning season also forecasts river temperatures to assist management decisions (Foreman et al., 1997). As part of the above monitoring program, the temperature of Quesnel River is recorded. The river's temperature shows unusually large swings of temperature over short periods of time during the summers; for example, in 2002 the temperature rose by more than 7°C in a single day (Morrison, 2004). Hoping to determine the cause of these temperature fluctuations, DFO moored instruments in the West Basin of Quesnel Lake. From the data collected at these moorings was bom further interest in the physical limnology the lake. As one of the world's ten deepest lakes, Quesnel Lake is interesting from a purely scientific perspective; however, there are further reasons to investigate the annual thermal structure of Quesnel Lake. Firstly, the lake is the rearing habitat for millions of juvenile salmon. The lake's ecology is governed by the distribution and transport of nutrients and oxygen throughout the water column; these in turn are governed by thermal stratification. Therefore, knowledge of the lake's thermal structure is critical for ecological management. Secondly, the lake has been proposed as a candidate for fertilization to increase its productivity (MacLellan et al., 1993). Although this proposal is not presently being pursued, it may be in the future, in which case it will be doubly important to understand the transport and dispersion processes in the lake. Thirdly, there is hope that temperature measurements in Quesnel Lake will continue long-term (decades) for the purpose of detecting, monitoring and predicting the effects of climate change. The material presented in this thesis would provide a foundation for such a study. The primary objective of the research described in this thesis is to establish the heat budget of Quesnel Lake. When related to lakes, the term 'heat budget' is used commonly to mean "the amount of heat energy that would be released if the lake were cooled from its maximum (summer) to minimum (winter) heat content." This thesis not only addresses this precise quantity, but also explores the nature of Quesnel Lake's thermal structure over the course of a year. 3 2.0 L I T E R A T U R E R E V I E W 2.1 P R E V I O U S S T U D I E S A T Q U E S N E L L A K E This section reviews the various limnological studies that have been carried out at Quesnel Lake, or have included the lake. None, however, looked closely at its internal thermal dynamics. In the late 1970's and 1980's several surveys and assessments were carried out in BC lakes to identify candidates for production enhancement by lake fertilization. Stockner and Shortreed (1983), for example, surveyed 19 lakes in three broad geoclimatic zones, and named Quesnel Lake as the most promising candidate for fertilization in its zone. Shortly prior to this, Stockner and Costella (1980) took short sediment cores from eight sockeye nursery lakes, aiming to determine whether the lakes' trophic statuses had changed in the past few centuries. The cores from Quesnel Lake showed a dramatic drop in productivity at the beginning of the twentieth century, corresponding to mining activities in the Quesnel and Horsefly Rivers, and showed increased productivity again after 1945. The increased productivity was coincident with the start of the sockeye population's recovery, implying that adult salmon carcasses contribute substantially to the lake's nutrient budget. In 1986 limnological investigations were done in five BC lakes, with monthly sampling from May to October (Nidle et al., 1990). Of particular interest are the reported surface and epilimnion temperatures, which varied considerably between stations at Quesnel Lake. During a given survey in June and July, surface temperatures differed by as much as 4.6°C between stations. Similarly, mean epilimnetic temperatures differed between stations by over 4°C during surveys in June and October, though only by 1.3°C in August. Stations of minimum and maximum temperature were not always the same. Nidle et al. (1990) did not sample in the East Arm, but earlier measurements by Stockner and Shortreed (1983) suggest it is often the coldest. In the fall of 1981, they observed that the surface of the lake's East Arm was 4.5°C colder than the West Basin. Furthermore, in 1982 Morton and Williams (1990) observed that the East Arm's surface temperature was colder than the junction by 8.5°C in June and by 4.5°C in August. 4 From 1985 to 1990 there was a substantial limnological study of Quesnel Lake, from which data were published by Nidle et al. (1994) and MacLellan et al. (1993). Conductivity-temperature-depth (CTD) profiles of the lake from those and subsequent years (Nidle et al., 1994; DFO, unpublished data) reveal that the water column at the junction of the lake, where temperatures were measured for this thesis, is representative of the whole lake at most times. However, in May the Horsefly and Mitchell Rivers warm the surface water near their mouths. Also, in October the East Arm's epilimnion is always colder than the other arms or the junction. In other summer months the East Arm is not always colder; in 1995, CTD casts were made every two weeks, and the East Arm was alternately colder and warmer than the West Arm. Several studies have made connections between the lake's thermal structure and the behaviour and vitality of its fish. Hume et al. (1994) observed that Quesnel Lake fry tended to be larger than Shuswap Lake fry; the size difference was attributed to the warmer mean temperature of Quesnel Lake's "hypolimnion" over the fry's growing period (9.2 versus 7.6°C). Hume et al. do not define "hypolimnion," but seem to mean the fry's preferred habitat depth. The 1982 investigations of Morton and Williams (1990) showed that 75% of the sockeye's zooplankton forage was in the epilimnion; however, the sockeye tended to remain in the hypolimnion, so the thermocline acted as an apparent barrier between the sockeye and their food. An investigation in 1987 made by Levy et al. (1991) confirmed their hypothesis that juvenile sockeye congregate at the thermocline at night. The concentration of fish at the thermocline was so distinct that, after a storm, a tilt in the thermocline could be identified by locating the fish on an echo sounder transect. 2.2 H E A T B U D G E T S O F O T H E R L A K E S As mentioned previously, the heat budget of a lake is the difference between the maximum and minimum heat content of a lake over an annual cycle. Heat content is generally measured in units of energy normalized by the surface area of the lake (GJm"2 or kcal cm" ). Many authors have published heat budgets or related studies of lakes throughout the world. For example, Frempong (1983) published a study of Esthwaite Water, England. 5 Using thermistor chains and meteorological measurements, he addressed the diel aspects of the thermal structure and heat fluxes over seven days at various times of the year. Frempong observed clear diel periodicity in the wind, which mixed warm surface waters downward during the daytime; however, during the night when the air was still, vertical circulation in the top 3 m was driven convectively by cooling at the surface. Frempong demonstrated the importance of considering sub-daily meteorological data when predicting the water column's thermal structure near the surface. In this thesis, hourly meteorological data were used for computations. DeHoyos et al. (1998) studied Lake Sanabria, a medium-sized lake in northwest Spain, for four annual cycles (mean depth, z = 27 m; surface area, A0 = 3.46 km"). The interannual variability in the lake's heat budget was around 10%, and was dominated by rainfall variability from year to year. Rainfall was important because of the throughflow of River Tera; the lake's average residence time is 1.4 yr. Variations in rainfall in Quesnel Lake's watershed should have a much smaller impact on its heat budget because its residence time is over ten years. In Lough Neagh (z =8.6 m, Ao = 383 km ), Northern Ireland, Gibson (1973) was unable to detect a thermocline and observed that lake temperature closely mimicked air temperature, with a seven-day lag. Apparently, the small depth and large surface area enabled the wind to keep Lough Neagh well mixed, and the heat content was controlled by sensible heat transfer. Its heat budget was 0.58 GJm"2. Water temperature, and therefore heat content, exhibited a clear sinusoidal pattern with a period of 365 days. This thesis follows Gibson's example by fitting sine curves to the measured and predicted heat content of Quesnel Lake. Between 1991 and 1995 water temperature and meteorological measurements were made at Crater Lake, Oregon (Crawford et al., 2000). The heat content of this caldera lake (zMAX = 589 m, Ao = 53.2 km2) was computed from thermistor chain data and compared against integrated heat flux estimates based on the weather station measurements. (This thesis presents the same comparison, for Quesnel Lake.) In four separate comparison periods, from 2.5 to 9.5 months long, the integrated heat fluxes agreed with the observed heat 6 content of Crater Lake to within 5%. The only exceptions to this agreement were due to cold inflows which caused horizontal temperature gradients in the epilimnion. A one-dimensional turbulence model predicted the evolution of the lake's thermal structure well, apart from the deep water renewal, which they assert is a three-dimensional process. Schertzer (1978) reported the heat budget and monthly evaporation estimates for Lake Superior. Evaporation was computed as a residual of the heat budget and compared to estimates from meteorological parameters and from the water budget. Energy budget and water budget estimates of evaporation agreed fairly well, and revealed that the empirical mass transfer method overestimated condensation rates when the boundary layer was stable. Partial ice cover during February and March 1973 also contributed to discrepancies between evaporation estimates. At Quesnel Lake, condensation is very infrequent (see section 5.2), and the empirical mass transfer method of estimating evaporation was considered adequate. Lake Ontario (z = 84 m, Ao = 19 000 km2) was the subject of a joint Canadian-American study (Robertson and Jenkins, 1978). The dominant terms in its heat budget were shortwave and longwave radiation, and latent heat transfer. Sensible heat transfer became important only in winter months, and advected heat was insignificant because of the lake's long hydraulic residence time (7.7 yr). Gorham (1964) and Timms (1975) each compiled heat budgets and other key characteristics for large numbers of lakes. Gorham correlated the heat budgets of 71 temperate lakes with area, mean depth and volume. The strongest correlation was with lake volume; this correlation predicts a heat budget for Quesnel Lake of 1.54 GJm"2. Correlations with area and mean depth predict 1.43 and 1.59 GJm"2, respectively. Timms (1975) observed that the annual variation in lake heat budgets was controlled not only by geographic location but also by lake morphometry. Mean depth had the greatest influence, with deeper lakes generally having a higher coefficient of variation for their annual heat budgets. The four lakes in his study with mean depths over 100 m ranged from 7.8% to 25.3% in their coefficients of annual variation. 7 2.3 T H E D E N S I T Y O F W A T E R The density of water is a function of temperature, pressure and salinity. The dependence of density on temperature and pressure is illustrated in Figure 2. Density increases approximately linearly with pressure, but varies quadratically with temperature. At any given pressure, fresh water has a density maximum, as indicated by the dotted line in Figure 2. At atmospheric pressure, water achieves a maximum density of 999.972 kgm"3 at 3.9839°C (Chen and Millero, 1986). However, it has been widely known since the late 1800's that the temperature of maximum density, TMD, decreases with increasing pressure. Wright (1931) notes that temperatures in many deep lakes are less than 4°C throughout the year, precisely as a result of this phenomenon. Eklund (1965) derived from water's equation of state an equation giving the temperature of maximum density: TMD - 4.00 - 0.021p, with temperature in °C and pressure in bars. Chen and Millero (1986) provide a much more precise equation for TMD which includes the effects of salinity, and which was used for calculations in this thesis. Quesnel Lake's salinity of 90 mg L"1 depresses TMD by about 0.02°C. o -50 -100 -150 -E 200 -Q. 250 -CD Q 300 -350 : 400 -450 : 500 -idoe-^000.5 -• -4 6 Temperature, °C 10 Figure 2 The dependence of fresh water density on temperature and pressure (depth). Contours of density are given in kgm' 3 . The temperature of maximum density, TMD, is indicated by the dotted line. 8 2.4 S E A S O N A L T U R N O V E R IN T E M P E R A T E L A K E S Temperate lakes are those in which the surface temperature passes through 4°C twice yearly (Carmack and Farmer, 1982). In shallow (<100 m) temperate lakes the water column becomes isothermal and "overturns" at those two times each year, according to a well-understood cycle. In summers, warm air temperatures and abundant solar heating create a warm epilimnion, or surface layer. Since the water temperatures throughout the lake are at or above the temperature of maximum density (~4°C), the warmer epilimnion floats stably upon the cooler hypolimnion (deeper layer). When the surface water cools in the fall, convective mixing deepens and cools the epilimnion. The density differential across the thermocline therefore decreases, weakening the buoyancy stratification. Once the stratification is weak enough, wind stress on the water can mix the entire water column; this is the so-called "fall turnover." Wind mixing and convection continue to cool the lake until the water column reaches 4°C, at which temperature the thermal expansion coefficient changes sign. Further cooling creates a cold, buoyant epilimnion which is stable throughout the winter, and upon which ice forms in some lakes. In spring when the epilimnion warms, the stratification weakens again until wind and convective mixing can bring about "spring turnover" and the water column is again isothermal at 4°C. Continued warming will then act to stabilize the epilimnion, completing the annual cycle. If the ratio between surface heat fluxes and wind mixing energy is high enough, the isothermal mixing period will be brief, and the hypolimnion will remain near 4°C throughout the year, protected by strong stratification. In deep (>100 m) temperate lakes the annual cycle of turnover is complicated by pressure effects on the temperature of maximum density, TMD (section 2.3). For example, consider the cooling of lakes in fall, in the absence of wind. When epilimnetic water is cooled it will sink until it reaches either the bottom or a layer of water denser than itself. Thus in a shallow lake, epilimnetic water cooled to 4°C will sink to the bottom because there can be no denser water, and lake overturn will occur. However, in a deeper lake a descending plume of 4°C water may encounter 3.5°C water which lies closer to TMD, and it will not continue to sink, nor will overturn occur without some form of mechanical forcing. The 9 implications of this complexity for renewal of bottom water in deep temperate lakes have been described thoroughly (Farmer and Carmack, 1981, Killworth et al., 1991, and Weiss et al., 1991), and are summarized below. Temperature profiles below 100 to 200 m are typically intermediate, between the TMD line and 4°C, with temperatures gradually decreasing with depth; for example, Quesnel Lake, Crater Lake (Crawford et al., 2000) and Lake Baikal (Killworth et al., 1991). Although epilimnetic water cannot sink to the bottom by free convection, deep water can be renewed through the thermobaric instability (Weiss et al., 1991). This renewal process is illustrated by the series of temperature profiles in Figure 3, and is described by Farmer and Carmack (1981), Weiss et al. (1991) and Killworth et al. (1991). In panel (a) a hypothetical temperature profile is shown, with a "knee" in the profile where it crosses TMD (dotted line). This profile is stable (Eklund, 1965): the water warmer than TMD decreases in temperature with depth, and the water colder than TMD increases in temperature with depth. Stability of a water column means that if a given parcel of water is displaced upward or downward, a restoring (buoyancy) force will oppose the displacement. The stability in panel (a) is only conditional, however (Weiss et al., 1991). If wind mixing or an internal wave displaces the whole thermocline downward, as shown in panel (b), part of the profile becomes gravitationally unstable, being warmer than TMD and yet increasing in temperature with depth. In panel (c) the unstable portion of the profile has mixed downward under free convection until encountering colder water. As well, the' water displaced by the sinking plume rises and warms the thermocline, thus conserving heat. Clearly, bottom water in deep lakes cannot be renewed by the common cycle of seasonal turnover. Instead, it must be episodically displaced by plumes of cold water destabilized by the thermobaric effect, through cabbeling (Shimaraev, 1993), wind mixing, internal waves or other mechanisms. Geothermal heat gradually warms this bottom water, preparing it to be displaced by future cold plumes (Crawford et al., 2000). 10 Temperature, °C Figure 3 Schematic illustrations of temperature profiles leading to deep penetrative convection by the thermobaric instability. Temperature profile, solid line; previous profile, dashed line; TMD, dotted line, (a) Hypothetical initial stable profile, (b) Thermocline displaced downward by wind or internal wave action, (c) Unstable water mass mixes downward until meeting colder water. 11 3 . 0 D A T A C O L L E C T I O N Quite a variety of data were collected for the analysis of Quesnel Lake's heat budget. The lake's water level and bathymetry were required to determine the lake volume. Heat was carried in and out of the lake by rivers, whose flow rates and temperatures were required. ' To estimate heat and mass fluxes at the water surface a suite of empirical equations were used, as detailed in section 4.2.2. These equations required measurements of wind speed, air temperature, water surface temperature, humidity, precipitation, cloud cover and air pressure. Finally, the heat content of the lake was calculated from temperatures measured at various depths in the water column. 3.1 Q U E S N E L L A K E S U R F A C E L E V E L The Water Survey of Canada (WSC) operates a gauge at Likely to record the surface level of the lake (WSC, 2004). Quality-controlled lake level data were available up to the end of 2003, and WSC provided raw data up to the middle of July 2004. The lake level is plotted in Figure 4. For consistency with depth measurements, water level is defined with z increasing downwards. The lake surface is approximately 727 m above mean sea level (Canada Centre for Mapping, 1989). 01—i i i i i i i —i—~» 1 i i 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, D D / M M Figure 4 Quesnel Lake level during the study period. Water level is given relative to the WSC gauge, with z increasing downwards. 12 3.2 B A T H Y M E T R Y O F Q U E S N E L L A K E In October 2001 a bathymetric survey of Quesnel Lake was done by Coast Pilot, Ltd. (Campbell, 2001). The survey's datum was the record low water level; for this work, all depths were adjusted to a new datum, the zero of the WSC gauge at Likely. At the time of the survey, the lake level was -0.8 m on the WSC gauge (with z increasing downwards); therefore the survey's shoreline points were assigned a depth of -0.8 m. Coast Pilot's 2081 depth points and 1037 shore points were interpolated to a grid with mesh size 100 m. From this mesh, the horizontal area of the lake was computed at intervals of 1 m from the surface to the deepest point. The surface area of the lake was computed directly from the positions of the shoreline points. With a water level of -0.8 m as measured by the gauge at Likely, the lake has surface area 266.3 km2, volume 41.81 km3 and mean depth 157 m. The hypsometric curve is shown in Figure 5. When the lake level rises, the lake surface area increases by about 0.6% m"1. Since the lake level fluctuated less than 2 m, the surface area is assumed constant. For convenience in calculating distances, etc., all maps and locations in the rest of this thesis are presented in Universal Transverse Mercator (UTM) coordinates. Northings are distances north of the equator, and Eastings are distances east of a standard meridian, which for Quesnel Lake (UTM Zone 10) is 123°W. Both are expressed in metres. The central meridian (123°W) is given a false Easting of 500 000 m. Figure 6 shows a map of Quesnel Lake with bathymetric contours every 100 m. Figure 5 Hypsometric curve for Quesnel Lake, showing horizontal area as a function of depth. Breakpoints in the curve approximately match key depths in the lake. The hypsometric curve for the West Basin is indicated by the bold line. 13 Figure 6 Map of Quesnel Lake showing contours of depth every 100 ni. The deepest point is in the East Arm, whose sides are steeper than 45° in places. 3.3 I N F L O W S A N D O U T F L O W O F Q U E S N E L L A K E 3.3.1 Measurement of Inflow Temperatures One term in a lake's heat budget represents advected heat from inflowing water. Quesnel Lake has dozens of inflowing streams, but 64% of the inflow comes from three main ones (section 3.3.2): Horsefly River, Mitchell River and Niagara Creek (Figure 7). Thermistors were placed in the mouths of these three rivers, as described below. The thermistor placed in the Horsefly River operated from 29 July 2003 to 25 May 2004. The Onset Stowaway thermistor was inside a plastic waterproof case which gave it a time constant of roughly 15 minutes. The plastic case was housed in a stainless steel cylinder open at both ends, which was chained to a tree on the bank. The point of deployment was at a broad S-bend in the river (Figure 7), at E 607448, N 5812878. The river bed was rocky. On recovery in May the cylinder had corroded significantly, although not enough to prevent water from flowing past the thermistor's plastic case. Local resident Ian Norquay said that Horsefly River was frozen over for about two months during the winter. 14 The thermistor placed in Mitchell River operated from 31 July 2003 to 25 May 2004, and was encased and secured in the same way as the Horsefly thermistor, at E 648029, N 5849049 (Figure 7). Mitchell River is slow, meandering and subcritical where it enters Quesnel Lake's North Arm. It has a small secondary channel, and its bed is of fine sediment. On recovery in May the cylinder had corroded significantly, and was choked with sediment which was easily rinsed out. The thermistor placed in Niagara Creek operated from 30 July 2003 to 22 June 2004, and was encased and secured in the same way as the Horsefly thermistor. The glacially fed Niagara Creek enters Quesnel Lake over an impressive waterfall. The cliffs at the shore prevented GPS reception at the point of deployment but a reading was taken slightly offshore at E 674152, N 5831345. A brown, turbid plume extends from the foot of the falls some distance into the lake before plunging below the surface. This plume follows the shore to the right (southwest) and on 23 June 2004 extended about 420 m. Niagara Creek was colder than the other two rivers during summer 2003 and spring 2004. 5.8051 1 1 1 1 1 1 1 1 L 1 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 East ings (m) x 1 Q 5 Figure 7 Map of Quesnel Lake, showing the locations of the three river thermistors, the three major inflowing rivers, and the outflowing Quesnel River. 15 The temperatures recorded by these three thermistors are shown in Figure 8. They were all calibrated before deployment in July 2003, and their post-calibration accuracy is ±0.2°C; sensor resolution is also 0.2°C. 20 i i i i i i i -jV%ii/r\ jj. (a) Horsefly River i i i i 10 0 i i i i i i i i i i i u i L _ mm T m v M : i i i i 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, DD/MM Figure 8 Temperature records from thermistors in the major inflowing streams to Quesnel Lake: (a) Horsefly River, (b) Mitchell River and (c) Niagara Creek. Horsefly River reached zero degrees, and for two months, reportedly froze over. Niagara Creek's thermistor appears to have been exposed to air from 20 August 2003 to 1 May 2004. In July 2003 a local fisherman said that the Niagara falls were already at low level, but apparently the water level at the foot of the falls dropped still further, as did the lake level (Figure 4). The thermistor record from Niagara shows the sharp diumal fluctuations indicative of exposure to air, between 20 August 2003 and 1 May 2004. These data were therefore discarded. The Horsefly and Mitchell thermistors were both re-deployed in May 2004. However, due to a problem with the computer used to set them up, they recorded no data. The treatment of these gaps in the data will be discussed in section 4.2.4. 3.3.2 Estimation of River Flow Volumes Together, the Horsefly, Mitchell and Niagara contribute over half of the inflow to the lake. For the purpose of computing the lake's heat budget, temperatures must be assigned to every inflow; therefore, the remainder of the lake's catchment has been divided, and 16 grouped with the watersheds of these three streams (Figure 9). This section describes the catchment grouping and flow volume estimation. None of the three above streams is gauged at the point of discharge into the lake, so regional analysis was necessary to estimate flow volumes. Fortunately, several streams in or near the lake's catchment area are or have been gauged. These historic data are available from HYDAT 2000 (Environment Canada, 2002) and are summarized in Table 1. The table lists each gauging station's name and its years of operation, mean historic flow, and reported watershed area. The last column of the table gives label numbers corresponding to Figure 9. Records from several stations in the region were not used because their period of operation was short, the data were old, and they conflicted with more recent records. Table 1 Water Survey of Canada gauging stations near Quesnel Lake. Years of operation, historic mean flow (Qg), catchment area (Ag) and catchment label (for Figure 9) are listed. Station Name Years Qg, mV T-Ag, km Figure 9 Cariboo River below Kangaroo Creek 26-95 95.5 3260 (13) Clearwater River at outlet of Hobson Lake 59-83 45.2 904 (15) Hobson Creek below Bois Grenier Creek 71-84 7.8 162 (14) Horsefly River above McKinley Creek 55-00 19.7 785 (9) Little Horsefly River near Horsefly 49-58 4.3 422 (8) McKinley Creek below outlet of McKinley Lake 64-00 5.1 430 (12) Mitchell River at outlet of Mitchell Lake 61-82 12.6 245 (1) Moffat Creek near Horsefly 64-00 3.5 539 (11) Quesnel River at Likely 24-00 131 5930 (D-(12) Regional similarity was assumed in estimating the stream flows throughout the catchment. The historic annual and monthly flows, Qg, for the gauged streams in or near Quesnel Lake's catchment were compiled from HYDAT 2000 (Environment Canada, 2002). Annual and monthly flows from ungauged catchments, Qu, were then estimated from a ratio of catchment areas with nearby gauged catchments: QJAU = Qg/Ag. This 17 calculation assumes that nearby catchments receive the same rainfall and have the same runoff characteristics, so that the monthly or yearly "runoff depth," QIA, in mm yr"1, is constant. In the absence of better data this assumption must be tolerated; however, the range of runoff depths among gauged catchments was 205-1622 mm yr"1, so care was taken to match up catchments with similar topography and elevation. x 10" 5.881—i-5.86 5.84 CO f 5.82 C o 2 5.8 5.78 5.76 Horsefly Group ] Mitchell Group BB Niagara Group (13) G: 924 (14) G: 1577 + H (15) G: + 1516 5.9 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 Eastings (m) x 10 Figure 9 Catchments within Quesnel Lake's watershed, numbered according to Table 1. The grouping of catchments is indicated by shading (see text). Gauge locations are indicated by '+' signs. Numbers in gauged catchments (G) represent annual runoff depths in mm yr' 1. Runoff depths in ungauged regions were taken from nearby catchments as indicated by arrows. Where multiple arrows enter a single catchment, runoff depths in the source catchments were averaged. Catchment boundaries were delineated manually, by the author, on a 1:250 000 scale map of the area (Canada Centre for Mapping, 1989), dividing the lake's watershed into twelve 18 catchments (Figure 9). Five of these are gauged, or have a gauge within them; the other seven are not. For the five, runoff depths were calculated from the areas and historic flows reported in HYDAT 2000 (Environment Canada, 2002). Gauged catchments are marked in the figure with "G: number", where "number" is the runoff depth in mm yr"1. For the seven, runoff depths were transferred from one or more nearby catchments, as indicated by arrows in Figure 9. Where several arrows enter a single catchment, the runoff depths of the neighbouring catchments were averaged. The grouping of the twelve catchments into regions represented by the three stream temperature measurements is indicated by shading in the figure. As a check of the manual delineation of catchment boundaries, the areas of the gauged catchments were compared to those reported in HYDAT 2000 (Environment Canada, 2002). They agree within 3% except for the Moffat and Little Horsefly catchments. The total catchment area is calculated as 5949 km2, which is a mere 0.3% above the 5930 km2 reported in HYDAT 2000. The mean flow summed from all the catchments, neglecting precipitation and evaporation at the lake's surface, is estimated at 139 mV1. The mean historic outflow in Quesnel River is given as 131 mV by HYDAT 2000 (Table 1). Monthly runoff volumes from each catchment in a group were summed to give an estimate of the monthly flows from the whole group. Temperatures recorded by the three river thermistors were associated with the respective group's monthly flows for the purpose of heat budget computations. The estimated monthly flows for each group are displayed in Figure 10a. The Horsefly, Mitchell and Niagara streams themselves contribute about 64% of the total inflow from the three catchment groups. Quesnel River is gauged at Likely (WSC, 2004). In Figure 10b, the measured flows during the study period are plotted against historic monthly flows from HYDAT 2000 (Environment Canada, 2002). The flows during summer 2003 were unseasonably low, as was the lake level (Figure 4). It is very likely that the inflows in summer 2003 were also less than the estimated volumes; therefore, the inflows were adjusted to balance the water budget before heat fluxes were calculated. This inflow adjustment is described in section 4.2.3. 19 r- 400 I Ui ™E 300 £ 200 f 100 o Inflows I ' I Horsefly Group I I Mitchell Group Niagara Group r- 400 E 300 5 200 ^ 100 o (b) Quesnel River WSC Gauge 2003/2004 [ I Historic Monthly Average Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Figure 10 (a) Estimated monthly flows entering Quesnel Lake from the three catchment groups, (b) Historic monthly flows in Quesnel River and measured flows (2003/2004) from the WSC gauge. 3.4 W E A T H E R N E A R Q U E S N E L L A K E 3.4.1 Lakeshore Weather Stations To record weather conditions on Quesnel Lake a weather station was erected in the North Arm at Goose Spit, E 646059, N 5847200 (Figure 11). The station was a Davis Instruments Vantage Pro (VP), equipped with sensors measuring wind speed and direction, temperature, humidity, air pressure, and rainfall. It operated from 31 July to 25 September 2003, when it was dismantled for the winter. John Morrison (Morrison, 2004) operated two identical VP stations on the docks at Elysia Resort (E 633130, N 5820096) and Nielsen's Lakeshore Cabins (E 598921, N 5827512). Morrison's station at Elysia Resort operated between 27 June and 22 September 2003, and was also equipped with a solar radiation sensor between 1 August and 22 September 2003. The station at Nielsen's operated between 24 June and 20 September 2003. The VP stations logged average hourly values from each sensor. The sampling interval, accuracy and resolution of each sensor is listed in Table 2. 20 Table 2 Sensor specifications on the Vantage Pro weather stations: sampling interval, accuracy and resolution. Sensor Sampling Interval Accuracy Resolution Wind speed 2.5 s ±1 ms"1 0.5 ms"1 Wind direction 2.5 s ±11° 22.5° Rainfall 10 s 4% or 0.25 mm 0.25 mm Temperature 10 s ±0.5°C 0.1 °C Humidity 60s 4% 1% Solar Radiation 60s ±90 Wm"2 1 Wm"2 x 10 5.85 5.84 5.83 f 5.82 C £ 5.81 o Z 5.8 5.79 5.78 Elysia Resort h o YWL * Vantage Pro Weather Station A BC Forests Weather Station O Airport, Environment Canada + Thermistor Mooring 5.6 5.8 6.2 6.4 Eastings (m) 6.6 6.8 x 105 Figure 11 Map of Quesnel Lake area showing the locations of weather stations and of the thermistor moorings in the West Basin (M2) and at the junction (M8). 3.4.2 BC Ministry of Forests Stations The BC Ministry of Forests operates a network of weather stations across the province, through the BC Forest Service Protection Program. Data from the stations closest to Quesnel Lake (labelled "LIKELY RS" and "NIAGRA" in Figure 11) were generously made available, for the period between January 2002 and April 2004 (BC Forest Service Protection Program, 2004). These stations recorded hourly wind speed and direction, 21 temperature, humidity and precipitation. Presumably due to station maintenance work, there are irregular gaps in the data from these stations. 3.4.3 Williams Lake Airport v Weather data from Williams Lake Airport (YWL, Figure 11) were purchased from Environment Canada for the period from January 2003 to June 2004 (Environment Canada, 2004). The hourly data include measurements of wind speed and direction, temperature, humidity, air pressure and cloud fraction. In addition, daily records were made of solid and liquid precipitation. 3.5 T E M P E R A T U R E S IN Q U E S N E L L A K E To date, nine thermistor moorings have been deployed in Quesnel Lake, most of which are owned and serviced by DFO. The first seven moorings were placed in the West Basin to explore reasons for the rapid rise and fall of temperatures in Quesnel River. To compute the heat content of the lake, and to better understand the lake's internal dynamics, an eighth mooring (M8) was placed at the junction of Quesnel Lake (Figure 11). This section deals with M8, while section 5.3 presents and discusses measurements at Mooring 2 (M2) in the summer of 2003. A full discussion of the West Basin moorings and Mooring 9 will be published elsewhere. Structurally, the mooring consisted of a steel spar buoy at the surface, connected to an anchor at the bottom by a 1-cm Kevlar line. The details of the connections are illustrated in Figure 12. All ten thermistors were attached to the Kevlar line, which was 310 m long. The top of the Kevlar was about 3 m below the water surface, and the 2.5-cm polypropylene rope at the bottom was about 2 m long. Since the mooring was deployed in a water depth of about 293 m, the radius of motion of the buoy should have been less than 120 m. 22 x z t Spar Buoy Anchor Chain, 25 kg Thermistors Kevlar Line Figure 12 Structural details of the thermistor chain at the junction of Quesnel Lake (M8). Measurements at M8 were taken steadily from 30 July 2003 to 22 June 2004, with a 2-hour break for servicing on 23 September 2003. The buoy's original position was E 632015, N 5822817. On 23 September 2003 it was recovered at E 632131, N 5822539, a distance of 301 m south-southeast of its initial deployment, and then redeployed at E 632056, N 5822181. On 22 June 2004 it was recovered at E 631950, N 5822475, a distance of 313 m north-northwest of its previous deployment, and then redeployed at E 632079, N 5822808. Since the observed buoy motions are greater than the anchor should allow, it appears that strong winds and waves on the lake can drag the anchor a few hundred meters. Fortunately the lake bottom is relatively flat in this vicinity and the mooring did not move out of its design depth. The depths of the mooring's ten thermistors were 3, 8, 13, 23, 33, 43, 53, 78, 153 and 283 m. From July to September 2003 the six uppermost thermistors were Onsets (accuracy: ±0.2°C, resolution: 0.2°C) and the deepest four were Brancker TR-1000's (accuracy: +0.002°C, resolution: 0.001°C). In September 2003 all ten thermistors were replaced with Brancker TR-1000's, though the calibrated accuracy of that set of Branckers was only +0.003°C. The Onsets each took readings every 15 minutes, and the Branckers, every 2 23 minutes. The calibrated thermistor records from the mooring are plotted in Figure 13; these data will be discussed in section 5.1. Since the length of the Kevlar line allows the buoy some motion, the depths of the thermistors are not quite constant. Under windy conditions the mooring should make an angle of not more than 21.5° to the vertical; therefore, the depth of each thermistor may be reduced by as much as 7.5% under those conditions. No corrections were made to the thermistor depths, for two reasons. Firstly, temperature is only a strong function of depth in the epilimnion, where the errors in depth will be smallest. Secondly, measurements of wind speed on the lake are not available for most of the period under consideration. 22 i 1 1 1 1 1 1 1 1 1 1 r 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, DD/MM Figure 13 Temperatures recorded by the thermistor mooring at the junction of Quesnel Lake. The depth in metres of each thermistor is indicated on the left. 24 4.0 C A L C U L A T I O N S 4.1 SELECTION AND MODDJICATION OF METEOROLOGICAL D A T A For calculation of heat fluxes at the lake's surface, a continuous set of meteorological data are required from August 2003 to June 2004. Since neither the Vantage Pro stations (VP) nor the BC Forests stations (BCF) provided a complete record for this period, the Williams Lake airport (YWL) data were selected. However, the airport is roughly sixty kilometres from the lake, and weather there could be significantly different. Therefore, a comparison of key variables between YWL and the stations near the lake was necessary. The only variable meriting adjustment was wind speed; all other YWL data were used directly. 4.1.1 Temperature Data Comparison Average daily temperatures were compared between YWL and each weather station at the lake. The "error" in the YWL temperatures was computed as AT = TUke Stalion - TmL. Table 3 lists the mean and root-mean-square (RMS) of AT for each lake station, as well as the number of days, n, in the comparison. Since the mean difference between YWL temperatures and lake station temperatures was substantially less than 1°C for four out of five stations, and the RMS difference was less than 2°C, the airport temperatures were used directly as temperatures at the lake. Table 3 Temperature comparison between YWL and lake stations. See text for details of the calculations. Lake Station Name Mean AT, °C RMS AT, °C n Goose Spit 0.60 1.40 55 Elysia Resort 0.40 1.29 86 Nielsen's -1.01 1.62 85 LIKELY RS -0.35 1.60 439 NIAGRA -0.24 1.72 197 25 4.1.2 Wind Speed Data Comparison The RMS wind speeds measured at each lake station were compared to those from YWL. Table 4 lists RMS wind speeds in ms"1 for each lake station over its deployment period, together with the RMS wind speed from YWL for the same period. Wind speeds were generally higher at YWL than at the lake stations, particularly when the comparison period included winter months. Table 4 Comparison of RMS wind speeds (ms1) between YWL and lake stations. The RMS wind speed from YWL is different for each comparison because the comparison period changes. Lake Station Name Station URMS YWL URMS Comparison Period, DD/MM/YY Goose Spit 2.94 2.80 01/08/03 to 24/09/03 Elysia Resort 1.48 2.82 28/06/03 to 21/09/03 Nielsen's 1.05 2.83 25/06/03 to 18/09/03 LIKELY RS 1.51 3.73 01/01/03 to 19/05/04 NIAGRA 2.26 3.59 01/01/03 to 22/05/04 Quesnel Lake is too large an area to be realistically characterised by a uniform wind field. In fact, the author has observed winds on Quesnel Lake to vary from calm to moderate over the space of 10 km or less, judging from wave heights. Nevertheless, there are insufficient data to warrant any complex processing of wind speeds and directions. The YWL wind speeds have therefore been used with only a single correction factor applied. Since airports report wind speeds at 10 m above ground, and the calculations and model to be discussed below require winds speeds at 2 m, the YWL winds were scaled according to the logarithmic law (Tennessee Valley Authority, 1972): u2 -w10(2/10)0'36 =0.56u10. 4.1.3 Solar Radiation Data Comparison Solar radiation was measured by the VP station at Elysia Resort during the summer of 2003 (section 3.4.1). Using the empirical relations discussed below (section 4.2.2), solar radiation can be estimated from geographical parameters and cloud cover data. In Figure 14, measured solar radiation from Elysia Resort is compared with solar radiation 26 estimated from YWL cloud cover data and Quesnel Lake's geographical parameters. The total solar radiation measured at Elysia Resort over the 51-day period was 11% less than the total estimated using YWL cloud cover data. This difference is equivalent to average daily radiation of only 22 Wm"2, which less than the nominal accuracy of the VP sensor (+90 Wm" ), but the difference may be due to shading of the sensor. 350 r 0 u 1 I I I , I I I 02/08 09/08 16/08 23/08 30/08 06/09 13/09 20/09 Date in 2003, DD/MM Figure 14 Comparison of daily solar radiation measured at Elysia Resort and estimated from YWL cloud cover data. The totals for the 51-day period differ by 11%. 4.1.4 Presentation of Meteorological Data Apart from wind speed, which was scaled according to the logarithmic law, all meteorological data were taken directly from YWL. This section presents the meteorological data in daily-averaged form (Figure 15); however, hourly data were used in the actual calculations described in the following section. Rain and snow measurements at YWL are recorded only as daily totals, and thus were not averaged. Daily temperatures varied between -30°C and 24°C. There were two significant "cold snaps" in January 2004; the first was under clear skies, but the second was accompanied by heavy snowfall (Figure 15a and d). Generally, higher wind speeds were recorded between October and March than in the rest of the year, with daily RMS speeds sometimes exceeding 4 ms"1 (Figure 15b). The total precipitation over the 327 days was 416 mm. 27 i r E 900 850 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, DD/MM Figure 15 Meteorological data from YWL used in surface heat flux calculations. Wind speeds were scaled from 10 m to 2 m measurement level by a logarithmic law. 28 4.2 H E A T B U D G E T C A L C U L A T I O N S The heat budget of Quesnel Lake is an expression of the first law of thermodynamics, which says that the change in energy stored in a system is equal to the net energy entering the system. For Quesnel Lake the most significant form of energy is heat. The heat stored in the lake, and the net heat entering the lake, are defined and computed as described in the following sections. 4.2.1 Heat Content Following the first law of thermodynamics, the heat content of a lake would be measured in units of energy. However, to facilitate comparisons between lakes, it is standard to normalize the heat content by surface area. Typically lake heat budgets are reported in units of kcal cm"2; this thesis will use the SI, GJm"2, but the key results will also be converted to kcal cm"2 for comparison purposes (1 GJm"2 = 23.90 kcal cm"2). The heat content, H, of Quesnel Lake is defined by the following equation: H = ±-[pcP{T-TREF)dV (1) A) Where: p = density of water, 1000 kgm"3. cP = specific heat of water, 4184 Jkg'^ C"1. Ao = surface area of the lake, 266 km . V = volume of the lake, 41.8 km3. T = water temperature, °C. TREF = reference temperature (see below), °C. The key terms in this equation are the temperatures, T and TREF- T was found by interpolating between thermistors on M8. This calculation assumes that temperature varies only with depth, which is not strictly true. In fact, internal waves create horizontal temperature gradients (more in sections 5.1 and 5.3); nevertheless, average values of H over time will be correct despite the passage of such waves. M8 was located approximately at the node of the first vertical mode longitudinal seiche to minimize noise 29 in the temperature record due to seiching. Water below the deepest thermistor was assumed to be at its temperature of maximum density. Farmer (1975) discusses the usefulness of potential temperature as opposed to in-situ temperature in studies of deep lakes. Deep water in Quesnel Lake is infallibly between 3.0 and 4.0°C. For temperatures in this range, the adiabatic correction to be added to in-situ temperature is no larger than +0.0025°C in depths up to 500 m. Since the correction would be as small as the instrument accuracy in Quesnel Lake, potential temperatures were not computed for this thesis. Heat content is defined with respect to a reference temperature, such that when T = TREF, H - 0. The most common choices for T R E F are 0°C, for simplicity, and 4°C, the temperature of water's maximum density at atmospheric pressure. In a shallow temperate lake the water column is isothermal at 4°C during spring and fall turnover; therefore, if TREF = 4°C, then H > 0 implies summer stratification while H < 0 implies reverse (winter) stratification. In deep temperate lakes (>200 m) the temperature of maximum density varies appreciably with depth, and deep temperatures can remain < 4°C year round; this is the case in Quesnel Lake. For this reason, the reference temperature has been defined as the temperature of maximum density, which is a function of depth (section 2.3): T R E F = TMD(z). 4.2.2 Surface Heat Flux Using meteorological data, it was possible to estimate each component of the heat flux into the lake. The total heat flux, qTOj, is broken into components as follows: QTOT = Qsw QLWA QLWE ILAT QSENS ~*~ QADV (2) The first five terms of the right hand side represent solar shortwave radiation, absorbed longwave radiation, emitted longwave radiation, latent heat of evaporated water and sensible heat transfer, all in Wm"2. These will each be described, in turn; the sixth term, advective heat flux, will be dealt with in section 4.2.4. The Tennessee Valley Authority (TVA) has published a comprehensive report describing the estimation of heat and mass fluxes at an air-water interface (TVA, 1972). The empirical formulas provided in TVA 30 have been adopted, and are presented below. All meteorological data were taken from YWL, as described in section 4.1. Water surface temperature was taken from the uppermost thermistor of M8. Solar shortwave radiation is estimated from date, time, cloud cover, dewpoint temperature and geographic parameters. Cloud cover can decrease solar radiation at the ground by up to 65%. ^=(1-JR,)(1-0.65C2)/C^0 (3) Where: qsw = solar radiation penetrating the lake surface, Wm" . R, = shortwave reflectivity of the water surface, dimensionless. This is a function of cloud cover and solar altitude. C = fraction of the sky covered by cloud, dimensionless. fcs = clear sky attenuation factor, dimensionless. This is a function of dewpoint temperature, solar altitude, ground reflectivity and seasonal dust coefficients. Ground reflectivity in the surrounding area was taken as 0.09, representing leaf and needle forest. Dust coefficients were taken from TVA's Madison, Wisconsin, data (TVA, 1972). qo = solar radiation reaching the upper atmosphere, Wm"2. This is a function of date, time and geographic position. Absorbed longwave radiation is estimated from air temperature and cloud cover. Because atmospheric emissivity, £a, depends quadratically on air temperature, absorbed longwave radiation is effectively proportional to air temperature to the sixth power. Cloud cover can increase downwelling longwave radiation by up to 17%. ^=0.97£ ao-(7; 2 + 273)4(l + 0.17C2) (4) Where: qLWA = longwave radiation absorbed by the water surface, Wm" . Ea = atmospheric emissivity, dimensionless. eo = 0.937 • 10~5 (r2 + 273)2. a = Stefan-Boltzmann constant, 5.67-10"8 Wm"2. T-i = air temperature at 2 m above ground, °C. 31 Emitted longwave radiation is estimated from the water surface temperature: W=-^(7o+273) 4 (5) Where: OLWE = longwave radiation emitted by the water surface, Wm"2 ew = water surface emissivity, 0.96. T0 = water surface temperature, °C. Latent heat of evaporated water is given by: ILAT = ~P L E (6) Where: qiAT = latent heat of evaporated water, Wm" . L = latent heat of vaporisation of water, Jkg"1. L = 2.50-106 - 2.39 To. E = rate of evaporation of water, ms"1, estimated by: EJN^U2{S10-S12\ u2>0 ( ? ) 1 a,{a0-a2), « 2=o «2 = wind speed at 2 m above ground, ms"1. £lo = saturation water vapour concentration at the water surface, kg kg"1. This is calculated from water surface temperature and air pressure. Q.2 = water vapour concentration at 2 m above ground, kg kg"1. This is calculated from relative humidity, and air temperature and pressure. p = air pressure, mb. po = standard air pressure, 1013 mb. N = evaporation coefficient, dimensionless, discussed below. (Xe = free convective evaporation coefficient, ms"1. This is a function of T2, To, p and humidity. A plethora of empirical equations for estimating evaporation are presented by TVA (1972). Once their units have been converted, all the equations have the same form and differ only in the evaporation coefficient, N. (The same coefficient also appears in the sensible heat transfer equation.) For lake data, TVA recommends the Marciano-Harbeck value, N = 2.48-10"6. TVA proposed a correction to Abased on the stability of the air near 32 the water surface; however, the correction was tentative and unverified, and was not adopted for calculations in this thesis. Sensible heat transfer to the water is estimated by: _JNpcPau2{T2-T0), u2>0 { o:h(T2-T0), M2=0 Where: qsENS = sensible heat flux, Wm"2. cPa = specific heat of air, 1000 Jkg"loC"'. (Xh = sensible heat transfer coefficient, Wm"2oC"1. This is a function of T2, T0, p and humidity. 4.2.3 Water Budget As mentioned in section 3.3.2, the summer of 2003 was unseasonably dry. Since evaporation was estimated, sufficient data were available to calculate the total inflow to the lake using conservation of volume: QINFLOW ~ QQR + AD Where: + E-P dt (9) QINFLOW = calculated total inflow to Quesnel Lake, mV1. Q Q R = measured flow rate in the Quesnel River, m s" (Figure 10). h = water level in Quesnel Lake, m. (Recall that height was defined with z increasing downward.) P = rate of precipitation into Quesnel Lake, ms'1. In Figure 16 the total inflows to Quesnel Lake estimated from historic flows in the watershed (Figure 10a) are compared against flows calculated by conservation of volume (Equation 9). Clearly, the water budget must be balanced for the heat budget to balance. Therefore, the inflow volumes estimated in section 3.3.2 were scaled, forcing the combined inflow from the three catchment groups to equal the inflow calculated from the water budget, and keeping the relative proportion of inflows from each group unchanged. These adjusted inflows were then used to calculate the advective heat flux. 33 500 Estimate! from Historic Flows Calculated from Water Budget 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, DD/MM Figure 16 Total inflows to Quesnel Lake estimated from monthly historic flows (section 3.3.2) and from the water budget (Equation 9). The historic flows clearly overestimate inflows in summer 2003. 4.2.4 Advective Heat Fluxes The final component of heat flux is associated with mass fluxes into and out of the lake. Water enters the lake through rivers, and by precipitation, and leaves through Quesnel River, and by evaporation. The advective heat flux term is broken down accordingly: QADV ~ QINFLOW ^~1A,EVAP "^Q OUTFLOW ~*~QA,PPT Heat added to the lake through inflows is computed from: (10) w ^ Z a ^ - U (ID A) i Where: i = index corresponding to the Horsefly, Mitchell and Niagara catchment groups. Qi = rate of inflow from catchment group i, mV1 (Figure 10). Ti = temperature of inflowing water from group i, °C. The temperature of inflowing water from each group, T,, was taken as the daily-averaged temperature recorded by the corresponding thermistor. As mentioned in section 3.3.1, the thermistor records have a few gaps: the Niagara thermistor was intermittently out of the water between 20 August 2003 and 1 May 2004, and the Horsefly and Mitchell thermistor records only extend to 25 May 2004 (Figure 8). During the gap in the Niagara 34 data, flows from that group were assigned the same temperature as the Horsefly group. After 24 May 2004, the Horsefly and Mitchell temperatures were set equal to the mean daily air temperature. This is justified by a comparison of air and river temperatures during the summer of 2003 (Figure 17). i i i 01/08 01/09 01/10 Date in 2003, DD/MM Figure 17 Air and river temperatures between 25 July and 26 October 2003. Air and river temperatures approximately match each other during the summer and early fall. Heat transported from the lake by the mass of evaporated water is given by: 1A,EVAP= PCPETO (12) Heat carried out of the lake by the Quesnel River is given by: ^OUTFLOW = 7 QQRTQR (13) A) Where: TQR = temperature of Quesnel River, °C, assumed equal to the lake's surface temperature, 7b, as measured by the uppermost thermistor of M8. Heat added to the lake through precipitation is given incorrectly by Equation 4.85 in TVA (1972), which fails to subtract the heat lost during the change of state when solid precipitation enters the lake. Adams and Lasenby (1978) emphasize the importance of the latent heat term, Ls, which has been included in this calculation: 35 QA, PPT = PR[cP(TR-TREF)]-pS[cPi{0-Ts) + Ls+cP{TREF-0)} (14) Where: R = rain rate, ms"1. TR = rain temperature, °C. TR is taken as T2 and forced >0 when necessary. Strictly, TR should be the wet bulb temperature, which was not measured. However, since Tweibuib ~) T2 as humidity -> 100%, this approximation is acceptable during precipitation events. S = rate of solid precipitation, in ms"1 of water. Ts = temperature of solid precipitation, °C. Ts is taken as T2 and forced <0 when necessary. cPi = specific heat of ice, 2090 Jkg"1 °C"1. L S = latent heat of melting ice, 3.35-105 Jkg"1. Groundwater seepage and direct surface runoff into the lake are effectively combined with the river inflows, since the inflows have been back-calculated from the water budget. This assumption will introduce error into the advective heat flux term only to the extent that the temperatures of these smaller flows differ from the river temperatures. 36 5 . 0 R E S U L T S A N D D I S C U S S I O N 5.1 L A K E T E M P E R A T U R E O B S E R V A T I O N S The temperatures recorded by M8 were first plotted in Figure 13, and selected thermistor records are reproduced in Figure 18. Beginning in August the surface temperature (3 m) falls, passing through 4°C on 31 December and reaching an instantaneous minimum of 1.64°C on 5 February. The surface cools fastest in late September, at 0.34°C day"1, but with mixed layer deepening the cooling slows to 0.02°C day"1 by December. Cooling rates in two other deep BC lakes, Babine and Kamloops, were 0.2°C day"1 (October) and 0.15°Cday"' (October and November), respectively, which agree with the cooling in Quesnel Lake before December (Carmack and Farmer, 1982). As in Quesnel Lake, the cooling in Kamloops Lake decelerated significantly in December with mixed layer deepening. 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, DD/MM Figure 18 Temperature records from selected thermistors on M8. Thermistor depths in metres are indicated near each trace. The lake was isothermal to 283 m at about 3.98°C on 31 December 2003, and isothermal to 153 m at 3.5 to 3.75°C between 19 April and 5 May 2004. 37 The surface warms steadily at 0.03°C day"1 from 6 March to 17 April, at which time the mixed layer reaches 153 m. From 17 April the water column down to 153 m warms isothermally at 0.018°C day"1 until 5 May, when the mixed layer becomes shallower than 153 m. In contrast to the fall "turnover," the water column in spring is never isothermal to the deepest thermistor (Figure 19). During fall cooling, as the mixed layer deepens past each thermistor, the thermistor's temperature at first rises, indicating the entrainment of water at the bottom of the mixed layer (Figure 18). Quesnel's mixed layer deepens at about 0.3 m day"1 in September and October, but accelerates and finally plunges to the bottom in the last half of December (Figure 19). As the mixed layer deepens and cools, the density difference between epilimnion and hypolimnion shrinks, increasing the internal seiche period and amplitude. By November and December isotherms rise and fall over 50 m due to internal wave motions. Parallel observations were also made in Babine and Kamloops lakes (Carmack and Farmer, 1982). u I I I I _ 1 I I I I I 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, DD/MM Figure 19 Isotherms in Quesnel Lake, interpolated from daily average temperatures on M8. Bold contours are every degree; fine contours, every 0.2 degree. After the surface temperature passes through 4°C, stratification near the surface reappears within two days, with the formation of a cold, buoyant layer. A well-mixed layer does not appear until about 6 March, when the surface temperature begins to rise, causing 38 convective mixing. The mixed layer gradually deepens to include the 78-m thermistor on 5 April, and finally the 153-m thermistor on 20 April. To facilitate discussion of the fall cooling and spring warming processes, two series of temperature profiles are plotted in Figure 20. The temperatures have been averaged over daily intervals to remove noise from high-frequency internal waves and diumal heating and cooling at the water surface. As the mixed layer cools in the fall (Figure 20a), the average surface temperature is slightly colder than the water beneath it, showing that heat loss at the surface is driving convective mixing. Once the surface cools below the temperature of maximum density, heat loss causes immediate restratification and the mixed layer becomes shallower than M8 can measure. The temperature gradient within the epilimnion lasts until the surface begins to warm in March (Figure 18). While the surface layer is warming up towards TMD, the surface temperature is slightly warmer than the underlying water (Figure 20b); therefore heating at the surface drives convective mixing in spring just as cooling did in fall. MD ^ ~ . 0 1 - D e c - 2 0 0 3 15-Dec-2003 - * - 01-Jan-2004 - e - 05-Jan-2004 - * - 15-Jan-2004 MD 05-Apr-2004 20-Apr-2004 - * - 28-Apr-2004 05-May-2004 20-May-2004 Temperature, °C Figure 20 Profiles of temperature versus depth, measured by M8 during (a) fall "turnover" and (b) spring "turnover." Although the fall cooling and spring warming have similarities near the surface, the processes are not symmetric in the deep water. On 30 and 31 December 2003, the temperature at 283 m rose above 3.95°C for 31 hours (Figure 19 and Figure 21a). It is 39 impossible for such warm water to have descended by free (1-D) convection, because at that depth it is less dense than the original colder (3.75°C) water. Since the water column in preceding days was isothermal to within 1°C and was near TMD, the periods of various internal wave motions were approaching infinity. It seems quite likely that a slow, large-amplitude internal wave temporarily displaced the 3.95°C water down to 283 m, because internal waves of increasing amplitude were observed in the preceding weeks (Figure 19) and also because the temperature at 283 m rebounded to 3.75°C by 10 January (Figure 21b). Daily average wind speeds at YWL reached 5 ms"1 in late December (Figure 15b), thus lending credibility to this hypothesis. Between 19 April and 5 May 2004, however, when the upper 153 m was isothermal, no parallel warming event occurred at the bottom (20 April, 28 April and 5 May in Figure 20b). This seasonal asymmetry seems to support the conclusion of Carmack and Weiss (1991) that spring turnover is less efficient at mixing deep lakes than fall turnover. Two significant cooling events occurred at 283 m during the winter (Figure 21a), and they are also unexplainable by 1-D processes. On 30-31 January 2004 the temperature at 283 m dropped suddenly from 3.7 to 3.5°C, and on 15-16 March, from 3.5 to 3.35°C. Vertical temperature profiles immediately after both cooling events show clear temperature maxima at 153 m (Figure 21b), ruling out the possibility that down-gradient diffusion (turbulent or eddy diffusion) cooled the deep water. It is tempting to call on the thermobaric instability to explain these cooling events, but the temperature profiles at the end of each event do not support that hypothesis either. The reader may recall that after convection initiated by a thermobaric instability, the temperature profile will have a broad maximum extending down to the greatest depth reached by the descending plume (Figure 3c). Since the temperature maximum in the 31 January and 16 March profiles appears at 153 m but not at 283 m, the deep water cannot have been cooled by such a descending plume. Possible explanations for the cooling include internal waves and gravity currents flowing down the lake's thalweg. Many deep temperature profiles in March and April appear to be unstable. On 16 March (Figure 21b) and 5, 20 and 28 April (Figure 20b), for example, the temperature decreases 40 with depth between 153 and 283 m despite being colder than TMD- Such profdes are unstable (Eklund, 1965): water displaced downward from 153 m would be closer to TMD, and therefore denser, than the in-situ water encountered. Nevertheless, it does not appear to convect downward. Since the temperatures are so close to TMD, weak salinity stratification may be stabilizing the profile. Alternately, linear interpolation between 153 and 283 m may not adequately describe the temperature profile and its stability. 01/12 01/01 01/02 01/03 01/04 01/052.5 Date in 2003/2004, DD/MM 3 3.5 Temperature, °C Figure 21 (a) Temperatures measured at 283 m during the winter. Major cooling events occurred on 30-31 January and 15-16 March 2004. (b) Vertical temperature profiles immediately after each cooling event. On each profile a temperature maximum occurs at 153 m. The dotted line in each plot indicates TMD. 5.2 H E A T B U D G E T The heat content of Quesnel Lake was calculated from temperatures measured at M8 (Figure 22). Following the methods described in section 4.2, each component of the heat flux into Quesnel Lake was calculated. The total heat flux was integrated over time and compared against the measured heat content. For plotting, the heat content on 31 July 2003 was added to the integrated heat flux as an initial condition. The two lines overlie one another quite closely. 41 1.5r _•] Ii i i i i i i i i i i 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, DD/MM Figure 22 The average daily heat content of Quesnel Lake as measured by M8, and the integrated heat fluxes estimated from meteorological data. The peak-to-trough difference in measured heat content is 1.72 GJm'J or 41.1 kcal cm"2. The measured heat budget of the lake, or difference between maximum and minimum heat content, was 1.72 GJm" 2 or 41.1 kcal cm"2. The maximum measured heat content was on 23 August 2003, and the minimum, on 11 March 2004. The heat budget estimated by the integrated fluxes was slightly larger, at 1.78 GJm"2. Possible reasons for this difference are discussed below. The RMS difference between the curves was 0.15 GJm"2. For further quantitative comparison, a sine curve with 365-day period was fit to each line using least squares. Table 5 compares the two fitted sine curves. The difference in heat budget (amplitude) between the measured heat content and integrated fluxes is more pronounced in the fitted curves. Table 5 Summary of sine curves fit to measured heat content (M8) and integrated fluxes, using least squares. The sine curves both fit quite tightly, with RMS error less than 5%. Parameter Fit to Heat Content (M8) Fit to Integrated Fluxes 2 x Amplitude, GJm'2 1.44 1.77 RMS error in fit, % 4.5% 2.1% Origin, t 6 June 10 June Origin, H, GJm"2 0.34 0.30 42 The zeros of the measured heat content were on 5 January and 7 May 2004. Ideally the zeros would occur at "turnover", or by definition, when the water column was all at TMD (Equation 1). The fall zero is 5 days late because at turnover the deep water was nearly 4°C, well above its TMD- The spring zero occurs as the mixed layer recedes above 100 m; it comes at the end of the isothermal period because isothermal conditions persisted in the epilimnion only while it was below its TMD- Had 4°C been selected as the reference temperature instead of TMD, the fall zero would have been closer to the date of turnover, but the spring zero would have been even later. Figure 23 presents each component of the net heat flux (Equation 2). Advective heat fluxes due to precipitation and evaporation (section 4.2.4) are included in the total but not plotted individually, because their RMS values were only 7 and 1 Wm" , respectively. The heat fluxes are summarized in Table 6, which lists the total energy transfer for each flux over the 327-day period. Table 6 Total energy added to Quesnel Lake by each heat flux over the 327-day period. Heat Flux Total, GJm'2 Absorbed shortwave 3.18 Absorbed longwave 7.31 Emitted longwave -9.54 Latent heat -0.97 Sensible heat -0.33 Advected: inflow 0.18 Advected: outflow -0.19 Advected: evaporation -0.009 Advected: precipitation -0.054 Total -0.41 43 400 -100" 1 1 1 1 1 1 L 500 p 1 1 1 1 1 1 r 30 li I I . I I I L i I I I I 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, DD/MM Figure 23 Principal components and total of the heat flux into Quesnel Lake . Solar radiation was a major source of heat, supplying a total of 3.18 GJm"2 over the 327-day calculation period, as estimated from cloud cover at Williams Lake airport (YWL). During the summer of 2003, these estimates were 11% higher than the measured radiation at Elysia Resort (section 4.1.3). 44 Net longwave radiation consistently removed heat from the lake, for a total loss of 2.23 GJm"2. Emitted longwave radiation was fairly steady, staying between 300 and 400 Wm"2 all year. Longwave is emitted from the very surface of the water, so error may be introduced by using temperature at 3 m depth for this computation. An error of 1°C in surface temperature would result in an approximate error of 5 Wm" in emitted radiation, or a total error of 0.14 GJm" over the 327 days. Absorbed longwave radiation is effectively proportional to absolute air temperature to the sixth power (Equation 4), and varied between 100 and 400 Wm" . Not surprisingly, its minima coincided with cold snaps in early and late January (Figure 15a). Evaporation peaked in the hot, dry summer of 2003, and was responsible for a large heat loss, totalling 0.97 GJm"2 through latent heat plus 0.009 GJm"2 through the associated mass flux. The total height of evaporated water was 390 mm over 327 days. Condensation was predicted only on 25 May 2004. Evaporation is the most difficult surface flux to estimate because it depends on so many parameters; these include wind speed, and temperature and humidity gradients near the lake surface. Schertzer (1978) concluded that non-neutral conditions above the water surface were important to consider when condensation played a large role in the heat budget. As this was not the case at Quesnel Lake, a simpler empirical formulation (Equation 7) is considered sufficient. Although sensible heat occasionally warmed the lake, it caused a net heat loss of 0.33 GJm" . Sensible heat transfer is proportional to wind speed as well as to the air-water temperature differential (Equation 8). The negative peaks occurred during the January cold-snaps, and the positive peak at the end of March corresponds to warm temperatures and high winds (Figure 15). The inflows to Quesnel Lake, as well as its outflow, were unseasonably low during the summer of 2003, and played small roles in the heat budget. Cold temperatures and reduced flows made the advective heat flux practically disappear during the winter. Only in June 2004 were the flows and temperatures high enough to significantly influence the heat budget. During that month the temperatures in the two largest inflows were not measured due to instrument failure, and they were assumed to be at air temperature 45 (section 4.2.4). The total heat fluxes from inflow and outflow were 0.18 and -0.19 GJm"2, respectively. Precipitation contributed both positive and negative heat fluxes, depending whether snow or warm rain was falling. The negative heat flux due to snowfall dominated because the latent heat of melting ice is so large. The net heat loss due to precipitation was 0.054 GJm"2. In computing the lake's heat content from thermistor data two assumptions were made, neither of which impacts the computed heat budget significantly. Firstly, the water surface temperature was assumed to be the same as at 3 m. In the absence of wind, the surface temperature should be slightly warmer than at 3 m in summer, and slightly colder in winter. However, even if the top 3 m of the lake were a whole degree warmer or colder, the heat content would differ by a mere 0.01 GJm"2. Secondly, the water below 283 m was assumed to be constant at TMD- Judging by the thermistor record at 283 m the deep water likely fluctuated in temperature slightly. However, since the lake volume below 283 m is only 3.82 km3, even if the deep temperatures change by a full degree the heat content changes by only 0.06 GJm"2. It is clear from Figure 22 and from the best fit sine curves that the integrated heat fluxes slightly overpredicted the lake's heat budget. From the fitted sine curves the maximum rates of winter cooling and summer heating were 144 Wm"2 according to heat content, and 176 Wm"2 according to the integrated heat fluxes. Solar and longwave radiation rates are relatively well-established in comparison to evaporation and sensible heating, which sensitively depend on temperature and humidity gradients. Since the weather data used in calculations were actually from a land station, it is quite possible that temperature and humidity gradients near the water surface are being overestimated, thus increasing both the rate of cooling in winter and the rate of heating in summer. Nevertheless, at the end of eleven months, the curves of heat content and integrated heat flux converge to within 1% of their amplitudes, implying that the errors in the heat flux estimation are seasonally symmetric. 46 The observed heat budget of 1.72 GJm"2 is slightly higher than the predictions from Gorham's (1964) correlations, which range from 1.43 to 1.59 GJm"2, based on area, volume and depth. 5.3 ESTIMATION O F F L O W R A T E S O V E R A S ILL Temperature data from Mooring 2 (M2) in the West Basin were made available by John Morrison (Morrison, 2004). These data revealed that wind-forced internal motions were causing two-way flow across the sill which separates the West Basin from the main body of Quesnel Lake (Figure 24). Based on mass and energy conservation, two methods were devised to estimate the magnitude of this two-way flow. The following work was presented in a slightly different form at a recent conference (Potts et al, 2004). 5.3.1 Background Figure 25 shows the temperatures measured at two different locations in the lake. Temperatures at Mooring 2 (M2) are representative of the West Basin, while those at Mooring 8 (M8) represent the main lake body (Figure 11). Clearly, far greater swings in temperature are observed at M2 than at M8. The fluctuations in the temperature of the West Basin are attributable to two-way advection, surface heat fluxes and hydraulic throughflow. This section shows that two-way advection dominates, and focuses on quantifying this advection of water masses between the West Basin and the main lake body, using two methods. To illustrate the mechanism of two-way advection, consider the following conceptual model (Figure 26). A wind, causing a shear stress r, blowing across a lake of length LQ, with thermocline depth h\ and density differential Sp, will result in downwelling at the upwind end of the lake. The balance between stratification and wind is represented by the Wedderburn number, W = gSph? / T L 0 . If W<1, the thermocline will surface at the downwind end of the lake under strong wind events (Thompson and Imberger, 1980). In Figure 26, wind blowing westward is pushing epilimnetic water into the West Basin at a rate QE. The thermocline in the West Basin is therefore pushed down, and hypolimnetic water is displaced out of the West Basin, across the sill, at a rate QH. 47 Figure 24 Contours of depth (m) in Quesnel Lake. The West Basin is separated from the main lake body by a shallow sill, indicated by the broken line. T 1 i • — — 1 1 r 01/08 11/08 21/08 01/09 11/09 21/09 Date in 2003, D D / M M Figure 25 Isotherms (°C) in the upper 40 m of (a) the West Basin and (b) the main lake body. Thermistor data have been smoothed by a low pass Fourier filter with 24-hr cutoff. The IPC isotherm is bold in each plot. Ticks on the vertical axes indicate instrument depths. Temperature data in the West Basin are courtesy of John Morrison (Morrison, 2004). 48 Two-way adveclion > -QH Wind stress T Main lake body Figure 26 Schematic of thermocline displacement in Quesnel Lake. Here, wind stress causes downwelling in the West Basin by pushing in epilimnetic water (QE), which displaces the hypolimnetic water below (Qn). For this discussion, the West Basin is defined as the portion of Quesnel Lake west of the broken line in Figure 24. The West Basin, separated from the main lake body by a shallow (35 m) sill, has a maximum depth of 113 m, and represents 8.6% and 2.3% of the lake's surface area and volume, respectively. At the sill, the lake is divided into two channels which flow around a small island (Figure 24). Ten times between 2 August and 20 September 2003, the heat content of the West Basin changed at a rate over 5000 Wm'2 The net surface heat flux peaked at 830 Wm"2 on clear days, and averaged 70 Wm"2. The Quesnel River could have removed a maximum of 320 Wm"2 (per unit of Basin surface area), assuming an outflow temperature of 18°C. Clearly, surface heat flux and throughflow alone were too small to account for the observed changes in heat content. Two methods were used to estimate the magnitude of a two-way advective exchange that could make up the difference (Figure 26). The first, called the 'thermocline method', is based on conservation of volume. The second, called the 'heat content method', is based on conservation of heat energy in the West Basin. With limited data, these simple methods provide, at best, possible upper and lower bounds to the rates of flow across the sill. The most important data for each method are the temperatures at M2, which has a subsurface float and thermistors at depths of 5, 10, 20, 30, 50 and 98 m. Internal wave activity in the West Basin causes local, high-frequency, temperature variations at M2. Within the West Basin, the longitudinal internal seiche period is approximately one day; 49 therefore, M2 data were treated with a low pass Fourier filter with 24-hr cutoff. M8 data were treated with the same filter. 5.3.2 Thermocline Method Flows across the sill can be estimated from the conservation of volumes of the epilimnion and hypolimnion of the West Basin. Here, the thermocline is considered to be impermeable over the period of interest. Typical surface and deep temperatures were 18 and 4°C, and their mean, 11°C, was chosen to define the boundary between epilimnion and hypolimnion (Figure 25a, bold line). The depth of this isotherm was determined by linear interpolation from the filtered M2 temperature record. From the hypsometric curve for the West Basin (Figure 5), the volume above the thermocline was then calculated. Lake level changes, precipitation and evaporation are assumed to be negligible (see below), so conservation of volume reduces to the following equations, from which the flows across the sill, QE and QH, were computed: dVWBE/dt = QE-QQR_ (15) QE + Q H = Q Q R (16) Where: VWBE = volume of the West Basin epilimnion (above 11°C isotherm), m3. QQR = discharge from the West Basin by Quesnel River, m s" . QE = flow of epilimnetic water into the West Basin across the sill, mV1. QH = flow of hypolimnetic water into the West Basin across the sill, mY1. For the three periods when the 11°C isotherm rose above the 5-m thermistor (Figure 25a), flows could not be estimated by this method. Between 1 August and 22 September 2003, the water level of Quesnel Lake dropped 0.45 m (Figure 4), which is equivalent to a mean flow of 2.3 mV1. Computed exchange flows were on the order of thousands of mV1 (Figure 27), so the omission of lake level changes from volume conservation is justified. By the same argument, the depths of precipitation (+0.045 m) and evaporation (-0.075 m) were also negligible. 50 5.3.3 Heat Content Method Flows across the sill can also be estimated from the conservation of heat energy in the West Basin; for instance, an increase in the basin's heat content represents an exchange of inflowing warm water and outflowing cold water. The heat content, H, of the West Basin was calculated according to Equation 1, using the West Basin's surface area (22.6 2 3 km ) and volume (0.985 km ) for Ao and V. For the heat content method, only the rate of change of H is important, and not its magnitude. Since the temperature measured at 98 m was constant at 4.7 + 0.2°C, heat content was calculated for only the top 98 m of the water column. Measured meteorological data were used to estimate surface heat fluxes into the West Basin, using the same empirical relations described in section 4.2.2. Data were recorded at the Nielsen's weather station throughout the period of interest (Figure 11). Since Nielsen's is on the West Basin, these data were chosen for surface heat flux calculations. Solar radiation was measured only at Elysia Resort, and those data were assumed to be representative of the West Basin as well. Average daily cloud cover was back-calculated from the measured solar radiation at Elysia and theoretical clear-sky radiation (fcsqo in Equation 3). The surface heat flux into the basin was broken the following components, as described in section 4.2.2: QsURF = Qs\V + QLWA iLWE + QLAT + IsENS (17) Heat advected by precipitation and evaporative mass transfer was almost negligible in the lake's annual heat budget (section 5.2). Since precipitation and evaporative mass transfer were neglected in the water budget for the West Basin (section 5.3.2) it was consistent to omit them from this surface heat flux estimation as well. Heat flux through the lake bottom was also assumed negligible. With these assumptions, conservation of heat is given by: = W +£^-\QE(TE-TKEF)+QH{Th-TREF)-QQR(TQR-TREF)) (18) Where: Tg = temperature of epilimnetic water crossing the sill, °C. 51 TH = temperature of hypolimnetic water crossing the sill, °C. TQR = temperature of Quesnel River, assumed equal to West Basin surface, °C. The advective heat flux terms are left explicit in Equation 18 because the objective is to solve for QE and QH. Combining Equations 16 and 18 allows cancellation of the TREF terms from 18, leaving ^ = <1SURF + ETL(QETE + QHTH-QQRTQR) (19) dt The temperatures of epilimnetic and hypolimnetic water crossing the sill (TE and TH) were taken from M2 and M8 depending on which direction the flow was going. For example, when epilimnetic water was entering the West Basin, its temperature was taken from M8; when it was leaving the West Basin, its temperature was taken from M2. This dependence of TE and TH on the signs of QE and QH made the direct solution of Equations 16 and 19 impossible. Therefore, to predetermine the signs of QE and QH, an intermediate quantity, TL, was introduced. Because of Equation 16, the net flow across the sill is equal to QQR, which is always positive. This net flow from the lake into the West Basin has an effective temperature, TL, defined by: QQRTL=QETE+QHTH (20) After substituting Equation 20 into 19, TL can be found immediately. The net flow rate across the sill is always positive, so there are only three possible regimes of flow. Since epilimnetic temperatures are always higher than hypolimnetic temperatures in summer, the signs of QE and QH can be deduced from Equation 20, given that QQR > 0. Table 7 lists the signs of QE and QH, together with the TL criterion, for each regime. Fortunately, for the TL criteria, TE and TH are taken from the same mooring: M8. 52 Table 7 Criteria for determining the signs of QE and QH. TL is compared to temperatures at M 8 only. The last two columns indicate the appropriate mooring from which to take epilimnetic and hypolimnetic temperatures for further calculations. Regime Criterion QE QH TE TH 1 TL > T~E(M8) >0 <0 M8 M2 2 TH(M8) <TL< TE(M8) >0 >0 M8 M8 3 TL < Tn(M8> <0 >0 M2 M8 To best represent the actual flows, TE and TH should be taken at intermediate depths. For simplicity, however, the temperatures were taken at the extremes of the sill's depth range: 0 and 35 m, respectively. This simplification partially explains why this method generally predicts lesser exchange volumes than the thermocline method. The surface water temperature at each mooring was assumed to be equal to the top thermistor's temperature. Once TE and TH are determined from the criteria in Table 7, Equations 16 and 20 are solved simultaneously for QE and QH. 5.3.4 Estimated Flows Across the Sill Compared to the isotherms in the main lake body, those in the West Basin rise and fall dramatically (Figure 25). While the heat content of the whole lake remains relatively constant, two-way advection across the sill can cause the West Basin's heat content to vary by more than 5000 Wm"2. Since the West Basin has only 2.3% of the lake's volume, lake-scale internal motions can greatly modify the West Basin's thermal structure without much change to isotherms outside the basin. The exchange of warm and cold water across the sill was predicted by both the thermocline method and the heat content method. Epilimnetic flows predicted by both methods are shown in Figure 27; the root-mean-square flows were 1990 and 1530 m s" for the thermocline and heat content methods, respectively. In contrast, Quesnel River's maximum flow for the period was only 126 m3s"'. Since the river flow was comparatively small, from Equation 16 we observe that QH ~ -QE, therefore, only Qg is plotted. The flow estimates from the two methods are qualitatively similar. Figure 27 indicates that 53 peaks coincide, though there is disagreement in their magnitudes. In general, the thermocline method predicts flows of greater magnitude and with sharper peaks. o LL 20000 15000 '</, 10000 £ 5000 CO Or -5000 -10000^ Thermocline Method Heat Content Method 01/08 11/08 21/08 01/09 Date in 2003, MM/DD 11/09 21/09 Figure 27 Flows into the West Basin epilimnion, predicted by the thermocline and heat content methods. Dashed lines indicate the approximate limits imposed by hydraulic control. The isotherms in the West Basin (Figure 25a) reveal at least two modes of internal wave activity. A vertical mode one internal seiche is observed at one end of a lake when isotherms rise and fall together, as they did in the West Basin on 27 August, for example. The second vertical mode of motion occurs when isotherms diverge and converge, alternately expanding and shrinking the metalimnion, as seen between 22 and 24 August. The thermocline and heat content methods both capture the first vertical mode motion, but neither can accommodate the second vertical mode because they do not represent flows within the metalimnion. In pure second-mode vertical motion, the isotherm at the center of the metalimnion will neither rise nor fall, and the total heat content will remain constant. Therefore, the thermocline and heat content methods should predict zero flow when second-mode motions occur. The maximum flow predicted by the thermocline method exceeds 15 000 mV1. However, the magnitude of flows across a sill is limited by hydraulic control (Farmer and Armi, 1986). The sill was approximated by a rectangular cross-section having the same maximum depth (35 m) and total area (23 300 m2). For this simplified geometry, Farmer and Armi's analytical result predicts a maximal, in viscid, steady state exchange flow of 54 3 1 3330 m s" in each direction. Clearly, several peak flows predicted by each method lie outside this bound (Figure 27). Both methods assume that isotherms in the West Basin are horizontal. In reality, however, the thermocline may tilt, and horizontal temperature gradients may appear. Such horizontal variations in temperature cannot be inferred from the M2 record, and likely account for the large peaks in both estimates. Unsteady barotropic forcing, for which the methods used here do not account, may also play a role in modifying the exchange flow. Water velocities can be estimated using the same simplified sill geometry. By Farmer and Armi's (1986) result, maximum epilimnetic and hypolimnetic velocities should be 0.23 and 0.38 ms"1, respectively; two-way flows greater than 3330 mV1 imply even higher velocities. Using current meters, Farmer (1978) measured water velocities as an internal surge passed over a 65-m sill in Babine Lake, a lake with geometry similar to Quesnel Lake. He measured velocities as high as 0.25 ms"1; therefore, estimated velocities in Quesnel Lake near or higher than 0.25 ms"1 should be plausible over its 35-m sill. 55 6 . 0 CONCLUSIONS AND RECOMMENDATIONS The watershed of Quesnel Lake is one of the most important spawning grounds for BC's sockeye salmon. After hatching, juvenile salmon swim downstream into the lake, where they feed and grow before finally migrating to the Pacific Ocean. The distribution of oxygen and nutrients throughout the lake is governed primarily by thermal stratification. Clearly, to wisely manage the ecological resources in Quesnel Lake a good understanding of the lake's thermal regime is essential. The research described above has provided an outline of the seasonal variations in lake temperature, and reveals which heating and cooling processes dominate. Temperatures at depths between 3 and 283 m were measured for 327 days by a mooring of ten thermistors at the approximate midpoint of the lake. The shallowest thermistor reached a maximum daily temperature of 19.7°C three times in August 2003, and a minimum daily temperature of 1.9°C on 7 February 2004. During fall cooling and spring warming, as the surface temperature approached 4°C, convection deepened and mixed the surface layer. Once the surface temperature passed 4°C the water near the surface immediately stratified again due to the sign reversal in water's thermal expansion coefficient at 4°C. On 31 December 2003 the lake was isothermal near 4°C, but in spring when the surface temperature passed through 4°C the water column had already restratified, never having become completely isothermal. The asymmetry of fall and spring turnover is partly caused by pressure effects on TMD- The temperatures observed at 283 m rose from 3.5°C to over 3.95°C and then fell to 3.35°C, indicating that the deep water was being renewed. The processes causing these temperature fluctuations cannot be fully explained by 1-D principles. The heat content of Quesnel Lake was computed based on the thermistor temperature records and the lake's bathymetry. The heat budget, or difference between maximum and minimum heat content, was 1.72 GJm"2 or 41.1 kcal cm'2. Based on weather data from Williams Lake airport (YWL) and hydrometric data from the Water Survey of Canada, heat fluxes into and out of the lake were estimated for the 327-day study period. Integration of these heat fluxes gave an estimated heat budget of 1.78 GJm"2, only 3.5% larger than the observed heat budget. Rates of winter cooling and summer heating were 56 both overestimated by about 32 Wm"2 or 22%, but surprisingly, the cumulative error was less than 1% (0.012 GJm"2) at the end of 327 days. Dominant terms in the heat budget were solar radiation (+3.18 GJm"2), longwave radiation (-2.23 GJm"2) and evaporation (-0.97 GJm"). Weather data from YWL agreed reasonably with data from near-lake stations, except for wind speeds which were adjusted for height above ground. Inflows computed from conservation of volume agreed well with monthly averages estimated from regional hydrologic analysis, except in summer 2003 which was unseasonably dry. The net impact on the heat budget of inflow and outflow was less than 1%. Heat fluxes at the water surface due to evaporation and sensible heat transfer are strongly dependent on temperature and humidity gradients near the water surface. Since the weather data for the above calculations were taken from YWL, better estimates of evaporative and sensible heat fluxes could certainly be obtained if weather data were measured on or beside the lake itself. Furthermore, during field work at the lake, the wind was observed to vary spatially over relatively short distances. To properly characterize the wind field, a network of a dozen or more anemometers would be required. CTD transects of the lake between 1985 and 1995 (Nidle et al., 1994; DFO, unpublished data) revealed substantial horizontal temperature gradients, particularly during fall cooling. However, the available data made it necessary in this thesis to assume a 1-D temperature structure. To determine internal wave motions and to describe mixing processes in the deeper water it will be necessary either to operate more thermistor chains or to carry out numerous CTD transects. Whether by thermistor mooring or CTD, it will be necessary also to measure temperatures to the very bottom of the lake before deep water renewal can be observed, described and quantified. Fluctuations in the heat content of Quesnel Lake's West Basin were chiefly due to two-way advection across the sill. The two methods of estimating two-way flows across the sill gave similar results. The root-mean-square flows, 1990 and 1530 m3s"', were smaller than hydraulic limits (3330 mY1), although many peaks were not, due to limitations in the data and methods. The implied water velocities (-0.23 ms"' at the surface) should be noticeable to water craft. Descriptions of the two-way flow could be refined if current 57 velocities were measured and if temperatures were measured at higher spatial resolution. Fluctuations in the temperature of Quesnel River are apparently due to basin- or lake-scale internal motions. Modeling Quesnel Lake would be a logical continuation of the work presented in this thesis. Some very preliminary results from a 1-D model, DYRESM (Imberger and Patterson, 1981), are presented in Appendix A. However, the mixing scheme of DYRESM does not handle the subtle effects that control mixing and stability near TMD, and modification of the model was beyond the scope of this thesis. Further comments and recommendations appear in Appendix A. 58 REFERENCES BC Forest Service Protection Program, 2004. PO Box 9502, Stn Prov Govt, Victoria, BC, V8W 9C1. Campbell, Ian J., 2001. CP Drawing No. CP01247. Coast Pilot, Ltd., Hydrographic Surveys, Sidney, BC, 250-656-2109. Canada Centre for Mapping, 1989. Quesnel Lake. Series A502, Map 93A, Edition 3 MCE. Department of Energy, Mines and Resources Canada. Carmack, E. C. and D. M. Farmer, 1982. 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Science 74: 413. 62 APPENDIX A : MODELING QUESNEL L A K E USING D Y R E S M DYRESM (Dynamic Reservoir Simulation Model) is a 1-D model developed for water quality simulations of lakes and reservoirs, and is more fully described elsewhere (Imberger and Patterson, 1981). In short, DYRESM uses a Langrangian scheme to represent water quality parameters in horizontal layers of variable thickness. This appendix presents preliminary results from DYRESM simulations of Quesnel Lake, and gives recommendations for the continuation and refinement of this effort. For all simulations, the initial temperature profiles were taken from M8 data and the meteorological inputs were as described in section 4.1. The current version of DYRESM (v. 3.0.0-bl) uses in-situ density for calculations of stability and mixing. Unfortunately, with this mixing scheme, unstable temperature profiles near 4°C can remain unmixed, because density depends more strongly on pressure than on temperature. Figure 28 shows an example of an unstable profile from a DYRESM simulation which appears to be stable when judged by in-situ density. Clearly the pressure effects on density must be removed before stability is evaluated. Temperature, °C l n _ S i t u D e n s i t y ! k g m -3 Figure 28 (a) Sample temperature profile (15 April 2004) from the DYRESM simulation of Quesnel Lake using in-situ density to evaluate stability. The dotted line is TMD. The profile is clearly unstable, (b) In-situ density profile corresponding to (a). The pressure effects on density mask the instability. 63 The most common method of removing pressure effects from density is to calculate potential density. Potential density is the density a water parcel would have were it lifted adiabatically to a reference depth (typically the water surface). In Quesnel Lake, where the adjustment for potential temperature is so small (section 4.2.1), this is effectively the same as setting pressure equal to zero in the equation of state when density is calculated. In an attempt to obtain more meaningful (and believable) results from the DYRESM simulation of Quesnel Lake, pressure was set to zero in DYRESM's density calculation. Indeed, the simulation results were more realistic; however, the use of potential density eliminates the effects of pressure on TMD- Unfortunately, the (stable) initial profile (1 August 2003) is immediately mixed by DYRESM because the potential density profile appears to be unstable (Figure 29). 0 50 100 150 200 f 250 CD O 300 350 400 450 500 (a) Initial condition t = tQ + At 3.5 4 4.5 Temperature, °C 0 50 100 150 E 200 .g Q . 250 CD Q 300 350 400 450 500 1 1 • i • (b) i -1000.046 1000.047 Potential Density, kg m -3 Figure 29 (a) When DYRESM is modified to use potential density to compute stability, the initial profile (1 August 2003) gets mixed from 76 m to the bottom in the first timestep. (b) Potential density profiles corresponding to the initial condition and mixed condition in (a). The stable initial condition appears to be unstable, judging from potential density, and is therefore mixed immediately. Even when the DYRESM code is modified to use potential density, the results are still clearly unsatisfactory. The next level of possible refinement is quasi-density, which accurately assesses stability even in deep lakes near TMD- James (2004) provides a full discussion of the use of various density modifications in stability calculations for lakes. 64 Figure 30a shows the results from the DYRESM simulation of Quesnel Lake, using in-situ density to evaluate stability. The lake cools in agreement with the field data (Figure 30c) until the end of November, but in December it cools far too quickly, developing a shallow cold layer at the surface that approaches 0°C on about 26 December. DYRESM's equation of state does not handle subzero water temperatures or ice, so the simulation had to be terminated at that point and restarted in mid-February. (If the simulation was restarted before mid-February, the model threatened to crash again due to subzero temperatures at the surface.) In February the surface temperatures cool too quickly, but by April the surface warms through 4°C. Because in-situ density is used to evaluate stability, the water column does not become isothermal at or near 4°G (recall Figure 28). Rates of heating and cooling at the surface in winter and spring appear to be too high. Figure 30b shows the results from a parallel simulation using potential density to evaluate stability. Although the dynamics below 76 m were completely unrealistic (recall Figure 29), the upper 76 m matched the field data more closely than Figure 30a did. The water column becomes briefly isothermal at the beginning of December, but quickly develops inverse stratification and tends to 0°C at the surface by about 26 December. After restarting the simulation in February, the upper 80 m matches the field data much better, including the deepening and warming of the well-mixed layer in March and April. However, in May and June the surface restratifies too strongly. Clearly, the use of potential density in stability calculations greatly improved DYRESM's predictions for the top 76 m, particularly in near-isothermal conditions. However, the behaviour of deep water is incorrectly predicted by this method. Furthermore, restratification in both winter and spring appears to be too strong, suggesting that either heat fluxes or heat redistribution are improperly captured in these simulations of Quesnel Lake. Modification of the DYRESM code to use quasi-density in stability calculations was beyond the scope of this thesis, but is strongly recommended for any further modeling work on deep temperate lakes. 65 (a) DYRESM, Using In-Situ Density to Calculate Stability 0 n i i i i i i i i i r 80 u (b) DYRESM, Using Potential Density to Calculate Stability 1 1 1 1 1 - ' ^ ^ = = = 5 ^ | > 5 j 1 J 1 V 4 i 3-1 i i i i (c) Field Data, from Mooring 8 0 U . i i ) i n un i i i i_i \\i \ iii/\ i i r v . \ \ m , 01/08 01/09 01/10 01/11 01/12 01/01 01/02 01/03 01/04 01/05 01/06 Date in 2003/2004, DD/MM Figure 30 A comparison of DYRESM simulation results against field data from Quesnel Lake. Heavy isotherms are integer temperatures between 1 and 12°C; fine isotherms are every 0.2°C between 2 and 5°C. Only the top 80 m of the lake is shown. The M8 temperature data were averaged in 72-hour bins to remove the higher-frequency waves. 66 THE UNIVERSITY OF BRITISH COLUMBIA FACULTY OF GRADUATE STUDIES > B I B L I O G R A P H Y O F T H E S E S R E L A T E D T O B R I T I S H C O L U M B I A The University of British Columbia Library maintains The Bibliography of Theses on British Columbia History and Related Subjects. This important online reference source is available on the Internet through the UBC Library online catalogue. The Bibliography is used by students and researchers at UBC and other libraries and research institutions in British Columbia, Canada, and other countries. If your thesis topic is related to British Columbia (e.g., history, geography, literature, science, special topics, etc.), please complete in the following: Name: PcDTTS* bAWEL (Last) (First) Degree:- f J \ . /\, Sc. Graduating Year: 2 - 0 0 ^ Department C i Ui j RA^ i r~&^ Tit le of t hes i s : TK ,^ rfg^ *f kudo &T «^4~ CW-SrygJ Lake. Qr'lTi^k Co\or^U Accompanying Materials: • Yes K No If yes, indicate type: List keywords that describe your thesis topic (be specific and use as many as possible: Un^ i i M P f l s . ) ^ ^ V ' T ^ Solar fvA4~iof\lr)irsayJo\V£- rodlofrioA evaftowdiort ,/Jafer-o 7 - - > - , , , — P - — — — = — — ^ "Tl/\gr/v\r)r>Qri(S i / i^a t r xUv j TflwipertxTv;r-& Thank you for your assistance. grad.ubc.ca/forms/?formlD= page 1 of 1 last updated: 20-M-04 

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