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Suspended sediment in Quesnel Lake following the Mount Polley Mine tailings spill Granger, Brody 2020

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Suspended sediment in Quesnel Lake followingthe Mount Polley Mine tailings spillbyBrody GrangerB.A.Sc., The University of British Columbia, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Civil Engineering)The University of British Columbia(Vancouver)June 2020© Brody Granger, 2020The following individuals certify that they have read, and recommend to the Faculty of Graduateand Postdoctoral Studies for acceptance, the thesis entitled:Suspended sediment in Quesnel Lake following the Mount Polley Mine tailings spillsubmitted by Brody Granger in partial fulfillment of the requirements for the degree of Master ofApplied Science in Civil Engineering.Examining Committee:Bernard Laval, Civil Engineering EngineeringSupervisorSvein Vagle, Institute of Ocean Sciences, Fisheries and Oceans CanadaSupervisory Committee MemberiiAbstractIn the four years that followed the 4 August 2014 tailings dam failure at Mount Polley Mine, BritishColumbia, Canada, water quality data indicated an ongoing sediment loading to Quesnel Lake andthe Quesnel River. Within one day of the tailings dam failure, a flood of slurry entered the smaller,downstream basin of Quesnel Lake, called the West Basin. Previous studies had shown highlyelevated turbidity in the West Basin through the first autumn and winter after the spill, and abovebackground turbidity each autumn and spring from 2015 onwards. It remained unclear how long thisseasonally elevated turbidity would last. In this thesis, we evalutate sediment transport in QuesnelLake following the rapid inflow of a vast quantity of material. This thesis applies conservation ofmass in two ways: first, using data collected between 10 September 2014 and 21 December 2018 toestimate suspended sediment mass and mass flows into and out of the West Basin; and second, usingan analytical model. On 10 September, 37 days post-spill, an estimated 38000± 11000 Mg of solidsremained suspended in the West Basin; this decreased to within background levels (<300 Mg) byearly June 2015. Between 10 September 2014 and 3 June 2015, 4000 ± 1200 Mg of sedimentflowed from the West Basin into the Quesnel River, and ∼ 31000 Mg entered the main basin ofQuesnel Lake. A gradually decaying, seasonal cycle emerged thereafter: near background eachsummer, somewhat elevated during winter and spring, and above background each autumn, withan interannual decrease in magnitude. Remobilization of a turbid, bottom layer by internal wavemotions during each autumn of 2015-2018 contributed to an increased mass of suspended sedimentin the West Basin. Together with the observed mass trend, an analyticial mass balance model ofa simplified, two basin system suggests a return to background suspended sediment levels by onedecade post-spill.iiiLay SummaryThe largest accidental spill of mining waste that has occurred to date in Canada began in the earlymorning on 4 August 2014, at Mount Polley Mine, a copper and gold mine located in central BritishColumbia. Within the day, nearby Quesnel Lake received a volume of waste roughly equivalentto 2% of the volume of its smaller, downstream basin, the West Basin, where the spill entered thelake. In this study, we evalutated the movements of fine sediment in Quesnel Lake and the QuesnelRiver using water quality data collected between 10 September 2014, 37 days post-spill, and 21December 2018. We then developed a simplified, two basin model based on mathematical theorywhich broadly decribes the response of Quesnel Lake’s two basins, and used this to estimate thatsuspended sediment will have returned to background levels ten years after the spill.ivPrefaceFor consistency, I have used the pronoun we throughout the text. In many cases, my use of weacknowledges that there are individuals whose contributions made this study possible, especiallyin regard to the enormous undertaking of data collection that continues in the Quesnel Lake andRiver system. I developed this thesis under the guidance of my supervisor and mentor in physicallimnology, Dr. Bernard Laval, who is the first coauthor listed on the manuscript-in-preparation thathas come out of this work. Dr. Svein Vagle, the second coauthor listed as well as my second thesiscommittee member, has been a key contributor to the design and servicing of the moorings andhas provided useful feedback at many stages of this work’s development. As well, I have receivedhelpful comments and suggestions on the text from two further coauthors: Dr. Philip N. Owens,and Dr. Ellen L. Petticrew. They oversaw and participated in collection of the CTD data used inthis study, along with staff at the University of Northern British Columbia’s Quesnel River ResearchCentre in Likely, BC. Dr. Andrew K. Hamilton offered me a valuable opportunity to collaborate asa coauthor of a companion study to this thesis which has recently been accepted for publication inthe journal Water Resources Research, and gave me a leg up in processing CTD data.In other cases, the use of we is misleading. The data analysis, reasoning, and writing containedherein are my own.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Study site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Lake sedimentation processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.1 Rivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.2 Bottom dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.3 Currents between basins . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Prior accounts of the Mount Polley spill . . . . . . . . . . . . . . . . . . . . . . . 102.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11vi3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1 Field data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Mass concentration from turbidity . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3 Conceptual model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1 Initial regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Seasonal regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45viiList of TablesTable 3.1 Four suspensions used in laboratory testing: settling time (tsettle); median particlediameter (d50); mass concentration (c, 0.45 µm filter); and turbidity (Tu). Notethat suspension D was too dilute to be measured by the particle size analyser. . . 20Table 4.1 Suspended sediment mass in the West Basin by date. Error estimates are onlygiven for mass based on EDF CTD data, as transects capture spatial variation insuspended sediment concentration. Mass data are also presented in Figure 4.2b. 26Table 4.2 Cumulative mass flows by period within the initial regime for each of three WestBasin suspended sediment mass sinks: the Quesnel River, equation (3.5) inte-grated through time; settling, equation (3.7) integrated through time; and ex-change with the main basin, estimated from the West Basin’s sediment massbalance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28viiiList of FiguresFigure 1.1 Map of West Basin with 20 m depth contours. Inset (i) shows the location ofQuesnel Lake in British Columbia, inset (ii) shows the location of the WestBasin in Quesnel Lake, and inset (iii) is an along-thalweg depth plot for theWest Basin indicating locations of CTD stations and moorings (also indicatedin main panel). Note that ST11 and ST7 have shallow cast depths indicated bydotted lines in (iii), as these two are located near shore. . . . . . . . . . . . . . 4Figure 3.1 Moored (JFE) sensor turbidity data processing. Two example time series aredepicted from the 23 September 2015 to 22 September 2016 deployment period.Raw turbidity is shown in (a); spikes and drift were removed to give the turbiditydata shown in (b). Panel (c) shows the JFE and SBE (CTD) turbidity data thatwe used to determine slope and offset; with the resulting formazin-standardizedturbidity time series appearing in (d). . . . . . . . . . . . . . . . . . . . . . . 15Figure 3.2 Turbidity estimates from ADCP echo. The multicolored lines in (a) representecho power (four beams) in the bin corresponding to a depth of 102 m; after av-eraging the four echo powers, losses from beam spreading and sound absorptionhave been added to give relative backscatter (RB, dB). In (b), the dotted line in-dicates best fit from the log-linear regression of RB to CTD turbidity (Tu, FTU)measured at station ST10; the the dotted line’s slope and offset correspond tothe constants A and B, respectively, in equation (3.1). The resulting echo-basedturbidity time series estimates are shown for three depths in (c). . . . . . . . . 17ixFigure 3.3 c-Tu laboratory results: (a) Seapoint (two CTDs, y-axis) compared to benchtop(Hach, x-axis) Tu (FTU), the latter calibrated to formazin standard. Markerswith errorbars indicate the mean and one standard deviation of CTD data fromeach dilution (≈ 240 samples). (b) Hach turbidity for varying c, with error-bars indicating one standard deviaton (3 samples). Dashed lines show linearfit (least-squares regression) of each suspension’s c-Tu correlation (Pearson’sr ≥ 0.99). (c) upper, expected, and lower values of kc that we use in equation(3.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 4.1 Vertical profiles of suspended sediment concentration at CTD station ST9 in theWest Basin (a-c) and ST8 near the Junction (d-f). Note the change in scale forthe x-axes of (b) and (e), and the differing y-axes for the West Basin and theJunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 4.2 Suspended sediment timeline, 10 September 2014 to 21 December 2018: (a)West Basin concentration at three depths (note: 4 and 38 m depth c are basedon turbidity, while 95 m depth c is based on acoustic echo intensity (ADCP)data; and, to improve readability, processed JFE data (Figure 3.1d) and ADCPdata (Figure 3.2c) are smoothed with a 1 week moving average); (b) West Basinmass (upper and lower bounds given by errorbars); Quesnel River (c) dailyaveraged flow; (d) concentration; and (e) mass flow (upper and lower boundsgiven by grey shaded region). In (a), (b), and (d), grey shading indicates periodsof mixis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 4.3 Seasonal stratification and sediment distribution during 2016 in the West Basin.(a) Temperature through depth at CTD station ST9 (note: the 11 November tem-perature profile uses thermistor data from mooring M3). (b-e) Contour plots ofc through depth along the thalweg, with triangles showing where CTD stationsare located. Red triangles (b-d) or dotted line (e) indicate where temperatureprofles shown in (a) were measured. . . . . . . . . . . . . . . . . . . . . . . . 31xFigure 4.4 Autumn temperature (a,c) and suspended sediment (b,d) contour plots. Reddots to the left of (a) and (c) indicate thermistor depths on mooring M3, andblue triangles along the top of (b) and (d) indicate the timing of CTD transects.The last three CTD transects in (d) are shown in greater detail in Figure 4.5. . . 32Figure 4.5 Autumn 2016 CTD (a,b,c) and ADCP (d) data, (a)-(c) compare c profiles atneighbouring stations ST9 and ST10, and (d) shows the along-thalweg horizon-tal current velocity measured 5 m above bottom at TuADCP. . . . . . . . . . . 35Figure 5.1 Two basin system: (a) compares the analytical solution, given by equations(5.10)-(5.12), to the volumetric average of West Basin suspended sediment con-centration; and (b) depicts the transport terms for the upstream and downstreambasin mass balances. The y-axis intercept is at 0.1 g/m3, which is slightly higherthan the approximate median pre-spill c =0.08 g/m3. . . . . . . . . . . . . . . 40xiAcknowledgementsThank you to the staff at the Quesnel River Research Centre: Sam Albers, Michael Allchin, LaszloEnyedy, Todd French, Caitlin Langford, Ido and Jordan Lindgren for providing technical assistancein the field, and especially for collecting CTD data; to all those who helped service the moorings:Kelly Graves, Sam Brenner, Lydia Smith, Sarah Chang, and Je´re´mie Bonneau; to fellow researchersIdo Hatam and Susan Baldwin for helping to bring the slocores ashore; to Mount Polley MiningCorporation for CTD data from the first post-spill fall, winter, and spring; and to Environment andClimate Change Canada, both for making environmental data available online, and for providingfinancial support through the Environmental Damages Fund.To my parents, Cheryl and Clive, thanks for giving me a place to stay and home cooked mealson my way to and from field work (as well as through my whole upbringing).xiiChapter 1IntroductionThe presence of suspended sediment in lakes is often apparent in the color and clarity of the water(Bloesch, 1995). Oligotrophic lakes contain predominantly minerogenic particles, such as silts andclays (Ha˚kanson and Jansson, 1983); with less abundant organic (i.e., low loss on iginition) andinorganic, biogenic particles (Wetzel, 2001a). Higher suspended sediment concentration leads tomore light scattering and absorption, which alters primary productivity by limiting the depth of thephotic zone, and modifies the distribution of heat from incoming solar radiation (Valipour et al.,2017; Wetzel, 2001b). Where nutrients or pollutants are associated with sediment, changes in con-centration can have ecological effects (Ha˚kanson and Jansson, 1983). Riverine inflows are typicallythe main source of allochthonous (from the drainage basin, carried into the lake) sediment (Scheuet al., 2015), as is the case with the glacial flour that gives many mountain lakes their turquoisecolor. Lake Winnipeg provides two examples of autochthonous (from within the lake) sediment:decaying organic matter produced by vast, green algal blooms; and brown silt and clay resuspendedfrom the bottom in shallow regions during strong winds (Schindler and Vallentyne, 2008).In deeper regions, below the oscillatory motions of surface waves, currents resulting from basin-scale internal waves (seiche) can resuspend sediment (Bloesch, 1995; Gloor et al., 1994, 2000;Valipour et al., 2017). Internal seiching occurs during stratified periods when sustained wind-forcingtilts the density interface. Gravity acts to restore this tilt, and the lake becomes a mechanical oscil-lator damped mainly by bottom shear stress (Wu¨est et al., 2000), which in turn creates a turbulently1mixed benthic boundary layer (Marti and Imberger, 2006). Most seiche damping (and its asso-ciated turbulence) occurs where lake bathymetry interacts with the density interface, for exampleconstrictions between basins, or the sloping bottom region around a basin (Chowdhury et al., 2016;Lawrence et al., 1997). Benthic matter that is entrained by these flows is mixed along with heatto form uniform, localized parcels of fluid. Depending on the density of this fluid, it may flow tothe bottom as a turbidity current, or sink to a level of neutral buoyancy within the background den-sity gradient. From there, it will collapse radially into the lake’s interior as a lens-like, horizontalintrusion (Wain and Rehmann, 2010).On 4 August 2014, a breach in the perimeter embankment dam surrounding the tailings storagefacility at Mount Polley Mine, a copper and gold producer in central British Columbia, Canada,released 25 million m3 of waste solids and water into the surrounding environment (MPMC, 2015).Within one day of the breach, ~20 M m3 of tailings, scoured surficial material, and water (bothinterstitial and supernatant) entered the West Basin of Quesnel Lake (Figure 1.1). While most of thesolids settled quickly to the bottom where they formed a several meter thick deposit, an appreciablemass of fine sediment remained in suspension (on the order of 10 Gg in early October 2014, nearlyall of it below 35 m depth, roughly the depth of the density interface; Petticrew et al., 2015).To date, no peer-reviewed report has provided a detailed account of the fate of this sediment inQuesnel Lake and the Quesnel River, in British Columbia’s Fraser River catchment. Attempts tonumerically model Quesnel Lake following the spill have produced estimates of how much spill-related sediment flowed into the Quesnel River and the main basin of Quesnel Lake (Tetra TechEBA, 2015). Given the limited data used to verify the model, the relability of these estimates isquestionable.The Mount Polley spill was a unique case: a slug injection of mine waste into a comparitivelysmall, downstream basin in a two basin lake (the term slug injection describes a single, effectivelyinstantaneous release of substance.) Theory suggests that in a two basin system, the response toa slug injection of sediment will be two-phased: initial, fast decay of mass giving way to long-term, slow decay (Chapra, 1997). Earlier work by Hamilton et al. (2020), described in Chapter2, has similarily shown that the amount of sediment in the West Basin through most of the first2year post-spill was significantly larger than in the second and third years post-spill. Our sedimenttransport observations (Chapter 4) are presented in two sections which correspond to the two phasespredicted by theory and observed in the West Basin: section 4.1, where we have paid particularattention to the relative importance of three sinks (river, lake bottom, and main basin) in removingsuspended sediment mass from the West Basin; and section 4.2, where we assess these three sinksas well as sediment sources, notably the influence that seiche-driven bottom dynamics had on theapparent sediment loading to the hypolimnion of the West Basin each autumn of 2015-2018. Lastly,in Chapter 5, we assess the long-term recovery trend using an analytical mass balance model, anddiscuss the implications for suspended sediment, as well as other pollutants, discharged into QuesnelLake.1.1 Study siteQuesnel Lake (volume: 41.8 km3, surface area: 266 km2), shown in Figure 1.1, inset (ii), extendsfrom the foothills of the Cariboo Plateau into the Cariboo Mountains of central British Columbia,Canada. Viewed on a map oriented east-up, the lake’s three arms resemble a lowercase “y”. At amaximum depth of 512 m (Gilbert and Desloges, 2012), it is the deepest fjord lake in Canada andthe third deepest lake in North America. Like most fjord lakes, it is long (east-west thalweg length:95 km), narrow (mean width: 2.7 km), and has multiple basins (two). The West Basin (volume: 1km3, surface area: 22 km2) is the hook at the bottom of the lowercase “y” (Figure 1.1, main panel).It curves from a westerly to a northerly orientation over 20 km, broadening and deepening froma 35 m sill near Cariboo Island to its deepest section offshore of Hazeltine Creek, then becomingshallow and narrow towards the outflow. Its maximum depth prior to the spill was 121 m (Gilbertand Desloges, 2012); the spill decreased this to 108 m (MPMC, 2015). Near the town of Likely inthe northernmost reach of the West Basin, Quesnel Lake drains into the Quesnel River (mean annualflow = 131 m3/s; Laval et al., 2012).The 4 August 2014 spill entered the West Basin via Hazeltine Creek (Figure 1.1, main panel).Mount Polley Mine’s location to the west of the West Basin is shown in Figure 1.1, inset (ii). Themine’s tailings storage facility is located about 9 km upstream and 200 m above the small delta3Figure 1.1: Map of West Basin with 20 m depth contours. Inset (i) shows the location ofQuesnel Lake in British Columbia, inset (ii) shows the location of the West Basin inQuesnel Lake, and inset (iii) is an along-thalweg depth plot for the West Basin indicatinglocations of CTD stations and moorings (also indicated in main panel). Note that ST11and ST7 have shallow cast depths indicated by dotted lines in (iii), as these two arelocated near shore.4where Hazeltine Creek drains into the West Basin. By 1 December 2015, Mount Polley Mine haddiverted the flow of Hazeltine Creek into two settling ponds which discharged runoff, along withmine effluent, through diffusers at 40 m depth in the West Basin until 30 September 2017 (MPMC,2018). From that date onward, the mine piped effluent directly to the diffusers and reestablished theHazeltine Creek inflow at the shoreline.5Chapter 2Literature ReviewBy the 1950s, limnologists and sedimentologists had begun to apply conceptual and mathematicalmodels to describe sediment transport in lakes (Ha˚kanson and Jansson, 1983). Increasing attentionhas since been given to the science of lake sediment transport, largely due to an increasing awarenessof the harm that contaminated sediment can cause to lake ecosystems and human water use (Chapra,1997). Our knowledge of the physical processes that control sedimentation has continued to growas a wider variety of lakes have been studied; still, studies of lake sediment transport are conductedon a case-by-case basis, as the complexity of the problem negates the use of a universal formula ormethod (Mehta, 2014).The first section of this chapter provides a three-part conceptual overview of the physical pro-cesses that dominate sediment transport in Quesnel Lake: rivers bring in sediment, and take outless than they bring in (section 2.1.1); the sediment that stays in the lake either sinks to the bottom(where it may come back up, section 2.1.2); or remains in suspension (to be transported by currentswithin the lake, section 2.1.3).The second section is a summary of two studies that described the physical and chemicalchanges in Quesnel Lake resulting from the 4 August 2014 spill. The first, by Petticrew et al.(2015), gave an account of these changes between 4 August and 2 October 2014. The second, byHamilton et al. (2020), extended the study period until November 2017.62.1 Lake sedimentation processes2.1.1 RiversMost lakes eventually become filled with sediment, transformed on geological timescales into me-andering river landscapes (Ha˚kanson and Jansson, 1983). An interesting case in point is KamloopsLake, a deep, intermontane lake located about 200 km to the south of Quesnel Lake in the Thomp-son River system. Kamloops Lake is expected to be 98% filled with sediment by 5750 CE (Pharoand Carmack, 1979). This inevitable fate makes sense in light of an observation by Carmack et al.(1979) that Thompson River water is three to four times more turbid at the inflow than at the outflow.Sediment is not only less abundant at the outflow, it is also comprised of smaller particles than at theinflow (Pharo and Carmack, 1979). This illustrates the process of selective settling: large particlessettle faster than small particles do, so fewer large particles remain in suspension at the outflow.For a given particle size, a fraction of inflowing sediment will escape via an outflowing river, andthe remainder will be buried in the lake bottom. In a study of Lake Laitaure in Lapland, Sweden,Axelsson (1967) showed the relationship between particle size and outflowing/deposited fractionsfor varying river flow. Under widely varying flow rates (25 to 400 m3/s), 90-100% of inflowing sed-iment with a diameter of less than 2 µm remained in suspension at the outflow. In contrast, 0-10%of sediment with a diameter of greater than 20 µm remained in suspension.At an inflow, the density of river water relative to lake water will control where fine sedimentgoes within a lake. In Kamloops Lake, coarse sediment (sand) settles on the face of the delta atthe inflow of the Thompson River during every season; while fine sediment is carried in a plume ofriver water which enters the lake differently from season to season, depending on the lake’s state ofthermal stratification (Carmack et al., 1979). If river water is less dense than surface water in thelake, the plume of river water will form an overflow. Otherwise, a plunge point will form where theinertia of the incoming water is met by the buoyancy of lake surface water. The river plume willthen either sink to a level of neutral buoyancy and insert itself into the water column as an interflow,or sink all the way to the bottom and become an underflow. In the case of interflows, plume velocitycan also affect sediment deposition, as shown by Scheu et al. (2015) in Lake Maggiore, Italy. The7authors described an increased rate of bottom sediment accumulation occurring under patches ofturbulence which arose from shear forces exerted by ambient lake water on the interflowing riverplume. Turbulent eddies carry fine sediment particles downward (and upward, and sideways) fasterthan they can settle; in Lake Maggiore, this can lead to as much as a tenfold increase in sedimentdeposition over settling alone (Scheu et al., 2015). The chaotic, every-directional transport of tur-bulence is analogous to diffusion, with the net movement of sediment occurring down-gradient (inthe direction of decreasing concentration). Because the river plume has a higher concentration ofsediment than the water between the interflow and the lake bottom has, the net transport is down.In Quesnel Lake, three inflows make up most of the hydrological and natural sediment input:the Horsefly River, the Mitchell River, and the Niagara River (also known as Niagra Creek, Figure1.1). Gilbert and Desloges (2012) showed that since the last ice age, the highest rate of sedimentaccumulation has occurred on the lake bottom near the inflow of the Horsefly River in the West Arm.At the inflow of the glacier-fed Niagara River in the East Arm, a bifurcating plume forms whilethe lake is stratified each summer, with one turbid layer transporting sediment along the seasonalthermocline, and another along the lake bottom (Hamilton et al., 2020). The Mitchell River flowsinto the North Arm; its sediment contribution is small compared to the other two, because of settlingin upstream Mitchell Lake.2.1.2 Bottom dynamicsSettling naturally leads to an accumulation of particles at the lake bottom. Two outcomes are pos-sible for sediment that has reached the bottom: it may remain on the bottom, to be buried undermore sediment, or it may be resuspended (Chapra, 1997). Fine sediment burial is rare on slopesinclining more than 4-5% (Ha˚kanson and Jansson, 1983). The sedimentological record of QuesnelLake backs this out: across-lake acoustic surveys done by Gilbert and Desloges (2012) show nearlyno sedimentation on the sloping sides of the lake, and several tens of meters of sediment in flatlayers overlying the bottom bedrock. Seiching is one reason for why so little sediment remains onthe sloping sides of a lake long enough to be buried. Some of the fastest, most turbulent currentsin lakes occur along slopes, especially during upward motion of the thermocline (Chowdhury et al.,82016; Marti and Imberger, 2006). When the shear stress caused by bottom friction exceeds a criticalvalue for a given type of sediment, that sediment is resuspended (Bloesch, 1995). For poorly con-solidated fine sediment, critical shear stress can be very low, such that even the comparitively gentleshear exerted by seiche currents along the flat bottom can cause resuspension (Gloor et al., 1994).In this case, sediment concentration is higher toward the lake bottom, and shear-driven turbulencewill result in the upward transport of sediment.Sediment resuspension over a sloping bottom is a different matter. In the second paragraphof Chapter 1, we briefly described how seiche-driven resuspension along slopes and subsequentturbulent mixing can lead to either an intrusion that transports sediment horizontally into the lake’sinterior, like a riverine interflow; or a turbidity current that takes sediment to the bottom, like ariverine underflow (Marti and Imberger, 2006; Wain and Rehmann, 2010). The main differencebetween river and resuspension sediment input is that the former is continual, while the latter isepisodic (Chapra, 1997). In Aya Hayden Lake, Iowa, USA, seiche-induced mixing along a slopingbottom was shown to cause the horizontal transport of material via radially propogating intrusions(Wain and Rehmann, 2010). The intrusions observed in Aya Hayden Lake had a propogation speedon the order of 1 cm/s based on arrival times between CTD stations. Seiche amplitudes of ∼0.5m were associated with this transport, in a basin much smaller than those of Quesnel Lake, whereamplitudes of tens of meters are common in the autumn.2.1.3 Currents between basinsSediment will remain suspended so long as water movements within the lake carry it upward morethan it settles downward. But while settling is decidedly downward, water movements are threedimensional, which can greatly affect the spatial distribution of sediment in a lake. A generaldiscussion of lake dynamics as they relate to sediment transport is beyond the scope of this chapter;for readers wanting to familiarize themselves with the topic, many good introductions have beenwritten on mixing and transport in seasonally stratified lakes (cf. Fischer et al., 1979; Chapra, 1997;Wetzel, 2001c).There is a particular type of current that is not covered in any introductory texts that we are aware9of; that occurs between basins of lakes with multiple basins (like Quesnel Lake), as well as betweenoceanic basins (e.g. a fjord connected to the ocean by a shallow constriction); and that plays acentral, dynamic role in Quesnel Lake following periods of sustained wind forcing when the lake isthermally stratified. This phenomenon, called seiche pumping, was found by Lawrence et al. (1997)to significantly increase the exchange of oxygen between the north and south basins of Amisk Lake,Alberta. Seiche pumping is the net result of oscillatory, layered flows that exchange water betweenbasins; each cycle is accompanied by some mixing, which over time tends to move suspended anddissolved matter from areas of higher concentration to areas of lower concentration. Gilbert andDesloges (2012) have hypothesized that Quesnel Lake’s lowest rate of sediment deposition occursin the West Basin (0.22 mm annually) not only because the latter lacks major inflows, but alsobecause its hypolimnetic water is flushed by internal seiching (Laval et al., 2008).What is missing from the observational science of lake sedimentation is a description of whathappens to a lot of sediment that is introduced all at once, as can happen in a landslide, a flood,or a tailings dam failure. To that end, our aim is to evaluate the short and long term sedimentaryeffects of the Mount Polley spill in Quesnel Lake using a mass balance (Chapter 3). Our approachis two-pronged: data and an analytical model, presented in Chapters 4 and 5, respectively.2.2 Prior accounts of the Mount Polley spillMost of the sediment that entered Quesnel Lake during the Mount Polley spill settled rapidly tothe bottom of the West Basin, as we mentioned in Chapter 1, while a comparatively small fractionremained in suspension. During the spill, the mixture of mine process water, tailings, and erodedsurficial material from Hazeltine Creek (together called slurry) sank as it entered the warm, clearsurface water and then dispersed laterally throughout the deep, cold water of the lower layer, calledthe hypolimnion. Although warm, the slurry was laden with suspended and dissolved material andso was more dense than the lake’s water. Through late summer and early autumn 2014 in the WestBasin, nearly all of the suspended sediment mass was confined below 30 m depth in a highly turbid,hypolimnetic plume (> 100 nephelometric turbidity units, NTU). The addition of slurry increasedhypolimnetic water temperature by ~2.5°C; overlying this 7.5°C hypolimnetic water was a layer10of colder (5°C) water with lower turbidity (~10 NTU). Because fresh water is most dense at veryslightly less than 4°C, for 5°C water to be on floating on top of 7.5°C water, dissolved or suspendedmatter must be present in the lower water mass to increase its density. Petticrew et al. (2015)used this fact to estimate that a minimum of ~30 Gg of sediment was needed to maintain stablestratification in the West Basin through September 2014. Sediments sampled from the hypolimneticplume during this time exceeded provincial freshwater sediment quality guidelines for total arsenic,copper, iron, and manganese (Golder Associates Ltd., 2015; Petticrew et al., 2015).Petticrew et al. (2015) reported on three paths through which suspended sediment exited thehypolimnetic plume in the West Basin. On 20 August 2014, the authors showed turbidity exceeding1000 NTU near the bottom of the West Basin. By 10 September 2014 (the start of our study),turbidity at the same location and depth was around 200 NTU. This decrease was mainly the resultof the first path: sediment settling out of suspension and depositing on the bottom. The second pathwas the Quesnel River, in which the authors observed periods of cool temperature combined withelevated turbidity which they attributed to upwelling in the lake. During upwelling, internal seichedisplaces hypolimnetic water to the surface; this tends to occur at the far ends of long, narrow lakes,as is the case with the northern reach of the West Basin where Quesnel Lake flows into the QuesnelRiver. Upwelling after the spill raised turbid, 7.5°C hypolimnetic water to the surface where it couldbe drawn into the river. The third path by which suspended sediment left the West Basin, over theCariboo Island sill, was detected as a layer of turbid water spreading eastward into the main basinof Quesnel Lake, a direction opposed to that of the mean hydraulic flow. The authors suggested thisupstream transport could have been due to episodic, seiche-driven flushing of hypolimnetic water.In Chapter 4, we provide evidence of another mechanism for the observed upstream transport: thatof a horizontally propagating intrusion, similar to the river interflows that we have discussed above.2.3 ObjectivesOne objective of our study is to evaluate the relative importance of the three paths (also called sinks)identified by Petticrew et al. (2015) for sediment to leave the West Basin (settling to the bottom,flowing out the Quesnel River, or moving east into the main basin of Quesnel Lake). Another11objective is to evaluate sources of sediment to the West Basin. A follow-up study to Petticrew et al.(2015), authored by Hamilton et al. (2020), has shown seasonal sediment loading to be an ongoingissue for the West Basin. Each autumn of 2015 to 2017, Hamilton et al. (2020) observed a slightturbidity increase (1 to 2.5 NTU) in the West Basin hypolimnion. The authors attribute this yearlyincrease to bottom currents, driven by seiche, which remobilize an unconsolidated bottom sedimentlayer. In Chapter 4, we show further evidence that seiching leads to sediment loading each autumn.12Chapter 3Methods3.1 Field data collectionIn the wake of the August 2014 spill, several organizations either initiated or increased water qualitymonitoring in Quesnel Lake and the Quesnel River. This study used data collected by provincialand federal government, industry, and public research institutions; the authors are affiliated witha collaboration that we herein refer to as the Environmental Damages Fund (EDF), named for thegroup which provided financial support through Environment and Climate Change Canada (ECCC).EDF data include vertical profiles collected in Quesnel Lake using two Seabird Electronicsconductivity, temperature, depth (CTD) profilers, both equipped with Seapoint Turbidity Sensors.CTD data from each downcast were depth averaged into 1 m bins. Our West Basin pre-spill CTDdataset consisted of 16 profiles from 12 dates between 2006 and 2012, with data from spring throughearly autumn, and no data from late autumn or winter. From 10 September 2014 onwards, the 10CTD stations shown in Figure 1.1 were profiled on a bi-weekly basis during the late April to earlyDecember field seasons (71 transects collected during this study period). The pre-spill data and theearly years (2014-2017) of post-spill data were collected using an SBE19plus we refer to as theDFO CTD (SN 4057). The 2018 CTD data were collected using the UBC CTD (SBE19plusV2, SN7035). Turbidity (Tu, formazin turbidity units, FTU) data from each CTD have been corrected toformazin standard.13Continuous, in-lake suspended sediment concentration data came from four moored turbiditysensors (JFE Avanatech Co., model ACLW-USB) and a moored acoustic Doppler current profiler(ADCP; Teledyne RD Instruments, 1200 kHz WH-ADCP). Between November 2014 and October2018, we deployed three turbidity sensors in the West Basin (4 m and 38 m depth at mooring M3,10 m depth at mooring ADCP1) and a fourth just east of the Cariboo Island sill (10 m depth atmooring ADCP2, Figure 1.1). Especially with shallower sensors during the warm, late summerand early fall periods, raw turbidity data were often noisy or spiky, indicative of biological fouling(Figure 3.1a). For unknown reasons, negative turbidity values were sometimes recorded; thesewere removed in the first step of data processing. In the second step, we removed those periodsof each turbidity time series for which standard deviation calculated over a 6 hour sliding window(25 samples) exceeded 12%. We chose a 6 hour interval to allow for diurnal fluctuation and found,through trial and error, that a standard deviation threshold of 12% was effective for removing large,random spikes. In the third step, we corrected each time series for sensor drift, which may havebeen the result of mechanical wearing on the sensor by the wiper, leading to gradually increasingturbidity. As an example, during the third deployment period (2 October 2015 to 27 September2016), SBE turbidity data from both 4 and 38 m at station ST9 (Figure 1.1) showed a decreasing,overall trend, while JFE data from these depths on mooring M3, especially the 38 m sensor, showedan increasing trend (Figure 3.1a). For each turbidity time series, we matched the trend of the JFEdata to that of the SBE data by rotating the former to conform to the slope of the latter. Figure 3.1bshows JFE turbidity data which have been corrected for drift (and, prior to that, noise), along withthe turbidity values used for the fourth and final step: determining a scale and offset for correctionto formazin standard. Here we computed the slope and offset for each JFE turbidity time seriesusing linear, least squares regression of JFE to SBE turbidity data (Figure 3.1c).Echo intensity recorded by the downward-facing, 1200 kHz ADCP on mooring TuADCP servedas a proxy for turbidity, based on the relation:Tu(est) = 10A∗RB+B, (3.1)14Figure 3.1: Moored (JFE) sensor turbidity data processing. Two example time series are de-picted from the 23 September 2015 to 22 September 2016 deployment period. Rawturbidity is shown in (a); spikes and drift were removed to give the turbidity data shownin (b). Panel (c) shows the JFE and SBE (CTD) turbidity data that we used to determineslope and offset; with the resulting formazin-standardized turbidity time series appearingin (d).15where RB is relative backscatter, in decibels (dB), and A and B are constants determined by linearregression to CTD turbidity measured at station ST10. Following Gartner (2004), we calculated RBby converting echo intensity (E, counts) to echo power (decibels, dB) and adding losses for beamspreading and sound absorption, as:RB = kE(E−Er)+2αR+20log10R, (3.2)where α is the sound absorption coefficient (dB/m) for water (we used the formula of Francois andGarrison, 1982); R is the distance (m) along the beam to the depth bin being measured; Er is thesystem noise floor, taken as the lowest recorded E for each of the four transducer beams; and kEis a beam-specific calibration constant. For a 1200 kHz RDI ADCP, kE ranges from 0.35 to 0.55dB/count (Deines, 1999). In his San Francisco Bay study, Gartner (2004) had neither manufacturer-supplied nor laboratory-calibrated kE values, and lacking these or physically-based alternatives,used kE = 0.45 dB/count. Like Gartner, we did not have predetermined kE values for our ADCP.But unlike San Francisco Bay, suspended sediment concentration in Quesnel Lake was rarely above1 g/m3 during the ADCP’s deployment (Chapter 4), and an accurate kE was needed to resolveturbidity through depth in these low-sediment conditions. During servicing and redeployment on3-4 October 2017, the ADCP was repositioned from 8 m to 12 m above bottom. This allowed us tocompare time series of RB from the first deployment to corresponding depths from the second. Weaveraged the four echo powers of each 0.5 m bin before adding losses from spreading and absorptionto get RB from equation (3.2) (Figure 3.2a). The multicolored line in Figure 3.2a represents fourecho power time series (kE(E−Er)), one from each transducer, from the 0.5 m bin closest to 102 mdepth, or 6 m above bottom. During the first deployment (30 September 2016 to 3 October 2017),this was the fourth bin; and during the second (4 October 2017 to 26 September 2018), the twelfth.Starting at 0.45 dB/count, we adjusted kE iteratively until RB was aligned between deployments forbins at 102, 104, and 106 m depth, and in this way arrived at kE = 0.37 dB/count. A time seriesof ADCP echo-based turbidity estimates at these three depths is given in Figure 3.2c, along withthe linear regression of RB to Tu measured at CTD station ST10 (Figure 3.2b) that was used to16Figure 3.2: Turbidity estimates from ADCP echo. The multicolored lines in (a) represent echopower (four beams) in the bin corresponding to a depth of 102 m; after averaging the fourecho powers, losses from beam spreading and sound absorption have been added to giverelative backscatter (RB, dB). In (b), the dotted line indicates best fit from the log-linearregression of RB to CTD turbidity (Tu, FTU) measured at station ST10; the the dottedline’s slope and offset correspond to the constants A and B, respectively, in equation (3.1).The resulting echo-based turbidity time series estimates are shown for three depths in (c).determine the constants A and B used in equation (3.1).In addition to its two turbidity sensors, mooring M3 had 15 thermistors (RBR duoTD, duoCT,and soloT; depths: 4, 8, 13, 18, 23, 28, 33, 38, 43, 53, 63, 73, 78, 83, 93, and 103 m). In section 4,we have used their temperature data along with velocity data from the 1200 kHz ADCP at mooringTuADCP to show how thermal stratification and internal wave-driven currents relate to sedimenttransport.Through the first winter post-spill, Mount Polley Mining Corporation (MPMC) used a CTD17profiler (YSI EXO2 Sonde) to measure physical data in Quesnel Lake. As far as we are aware, theseprofiles were the only high vertical resolution turbidity data collected during this period. Herein weinclude turbidity data from 14 profiles collected between 1 November 2014 and 30 May 2015; thesecompare well to EDF turbidity profiles (DFO CTD, formazin-standardized values) taken within afew days from the nearest station (ST9, Figure 1.1) in November 2014 and May 2015.ECCC monitors turbidity in the Quesnel River through the Federal-Provincial Freshwater Qual-ity Monitoring and Surveillance Network (FWQMS), and flow (Q, m3/s) through the Water Surveyof Canada. We used these data to estimate suspended sediment concentration and mass flow inthe Quesnel River (described in section 3.3). We have assumed the river to be completely mixed,such that a point sample of turbidity collected at mid-span from Likely Bridge (Figure 1.1) is rep-resentative of the cross section. In the year following the spill, sampling occurred weekly, and thenbi-weekly or monthly thereafter. Between sample dates, we estimated turbidity by linear interpo-lation. For comparison, we have also included continuous in-river turbidity measurements madeby MPMC at a location 1.5 km downstream of Likely Bridge (MPMC, 2015), as well as in-laketurbidity near the outflow recorded by a moored EDF sensor (10 m depth on mooring ADCP1) andthe EDF CTDs (3 m depth at station ST11, Figure 1.1).3.2 Mass concentration from turbidityHerein we have estimated suspended sediment mass concentration (c≡ m/V , where m is mass andV is volume) from turbidity. The relationship of turbidity to mass concentration varies greatly fordifferent sediment types, so we developed a site-specific correlation in the laboratory. Using linear,least-squares regression, we calculated slope (kc) and offset (Tu /0):c = kcTu+Tu /0, (3.3)for a suspension of a given particle size distribution. The sediment we used was collected as a coresample, using a slocore device, from the deep part of the West Basin offshore of Hazeltine Creekon 17 June 2016 (Hatam et al., 2019). The core’s uppermost sediment had been removed by an18earlier experiment, and our dry sample had a coarser size distribution (D50 ≈ 10µm) than Petticrewet al. (2015) found below 35 m depth, six weeks post spill (D50 ≈ 1µm). By mass, large particlescontribute less to turbidity than do finer particles, making the correlation of c to Tu sensitive to theparticle size distribution of the suspension. To remove large particles, we mixed sample sedimentinto distilled water in a 70 cm high, 10 cm diameter tube and left the suspension to settle for periodsvarying from one day to two weeks (Table 3.1). We then used a 2 mm diameter hose to siphon offthe supernatant suspension. In this way we obtained four suspensions of varying median particlediameter with which we developed c(Tu) correlations through laboratory tests.We determined the c of each suspension by filtering 100 mL (suspensions A, B, and C) or 250mL (suspension D) through 0.45 µm pore diameter papers (in triplicate) and weighing the dry massof sediment retained. Over four trials (one for each suspension), we immersed the CTD turbiditysensors in a continually stirred bucket of distilled water (V = 6 L), covering the bucket to limitambient light interference as we ran each CTD (i.e., DFO and UBC) in turn for 1 minute. Wethen uncovered the bucket, measured turbidity using a benchtop turbidimeter (Hach), and added anincrement (10 or 20 mL pipette) of suspension, repeating until turbidity reached 7 FTU (typically10 increments). This turbidity is roughly double the highest recorded in situ between 2015 and2017 (Hamilton et al., 2020). The benchtop turbidimeter served as our reference instrument, as wecalibrated it to formazin standard during each trial (two point calibration at <0.1 and 20 FTU). Forboth the dry sample and the finer suspensions, we measured effective particle size distribution (nopre-treatment) with a laser particle size analyser (Malvern Mastersizer Hydro 2000).We found the c(Tu) correlation in the 0 to 7 FTU range to be effectively linear for each ofthe twelve combinations we tested (three instruments with four suspensions). Offset (Tu /0, distilledwater turbidity) varied most for the DFO CTD (minimum: 0.52 FTU, maximum: 0.93 FTU, Figure3.3a), less for the UBC CTD (0.22 to 0.25 FTU), and least for the benchtop turbidimeter (0.10 to0.11 FTU, Figure 3.3b). Slope (kc, sensor response) was lowest for the DFO CTD (0.50 to 0.62g/m3/FTU, not shown), slightly higher for the UBC CTD (0.54 to 0.68 g/m3/FTU, not shown), andhighest for the benchtop turbidimeter (0.66 to 0.93 g/m3/FTU, Figure 3.3b).To assess CTD offset (Tu /0), we looked to data collected during the latter half of our study at19Table 3.1: Four suspensions used in laboratory testing: settling time (tsettle); median particlediameter (d50); mass concentration (c, 0.45 µm filter); and turbidity (Tu). Note that sus-pension D was too dilute to be measured by the particle size analyser.suspension A B C Dtsettle (h) 21.5 43 72 307d50 (µm) 5.8 2.1 1.6 -c (g/m3) 114±1 165±2 142±9 54±3Tu (FTU) 184±4 319±6 257±5 90±2Figure 3.3: c-Tu laboratory results: (a) Seapoint (two CTDs, y-axis) compared to benchtop(Hach, x-axis) Tu (FTU), the latter calibrated to formazin standard. Markers with error-bars indicate the mean and one standard deviation of CTD data from each dilution (≈240 samples). (b) Hach turbidity for varying c, with errorbars indicating one standarddeviaton (3 samples). Dashed lines show linear fit (least-squares regression) of each sus-pension’s c-Tu correlation (Pearson’s r≥ 0.99). (c) upper, expected, and lower values ofkc that we use in equation (3.3).the station furthest from the West Basin (ST8, Figure 1.1). Here, the lowest turbidities measuredwere 0.14 FTU for the DFO CTD, and 0.10 FTU for the UBC CTD, both in the range of Tu /0 for thebenchtop turbidimeter. The Tu /0 variation seen with the CTDs in the laboratory could have resultedfrom sensor interference (ambient light and/or reflections of the incident beam off the bottom/sidesof the bucket and the water surface). The design of the benchtop turbidimeter limits interference,and CTD turbidity data collected at station ST8 indicated that interference is also limited in situ.Herein we scale CTD turbidity to the benchtop reference, using the average ratio of CTD kc tobenchtop kc from four suspension trials (0.7 for the DFO CTD and 0.75 for the UBC CTD). We takedistilled water turbidity to be Tu /0 = 0.1 FTU.20The nominal accuracy of a Seapoint Turbidity sensor is ± 2% of measured values (Seapoint,2013). Figure 3.3 (a) shows standard deviations of the UBC CTD that are greater than we wouldexpect for a nominal accuracy of 2%, while DFO CTD standard deviations are within the expectedrange. We swapped the two sensors in the laboratory and found that random fluctuations in the UBCCTD turbidity data were originating in the sensor. As mentioned, we depth average CTD turbidityinto 1 m bins. A nominal profiling velocity of 1 m/s (actual profiling velocity is typically slightlyless) and a 4 Hz sample rate gives four samples per bin. Averaging CTD laboratory data into foursample bins caused standard deviation to decrease slightly for the DFO CTD, and by about halffor the UBC CTD. For upper and lower bound c estimates in Quesnel Lake, we have included aninstrument error of ± 2% for the DFO CTD, and ± 10% for the UBC CTD.Australian Laboratory Services (ALS) processed the FWQMS water samples collected from theQuesnel River. For these turbidity data, we have assumed the ALS turbidimeter performs similarilyto our benchtop (Hach) unit. Such instruments have a nominal accuracy of ± 2%. In our laboratorytests, the standard deviation from three measurements of a given sample was typically between 1and 3% of the mean. For upper and lower bound c estimates in the Quesnel River, we have used aninstrument error of ± 6% (two standard deviations about the mean).3.3 Conceptual modelConservation of mass gives that, provided suspended sediment m does not undergo chemical trans-formation over the time scale of interest, its rate of change in a basin is equal to the sum of massflows across the basin’s boundaries (dm/dt = Σm˙). For the West Basin, we have considered massflows associated with four boundaries: to the north, the Quesnel River (m˙r); along the bottom (m˙b);the shoreline (i.e. inflowing streams, m˙s); and to the east, the main basin of Quesnel Lake (m˙l).For the river, m˙r is always negative, while for stream inflows, m˙s is always positive. The sign ofm˙b depends on whether settling (m˙b < 0) or resuspension (m˙b > 0) dominates; and the sign of m˙ldepends on whether the net flow of sediment mass over the Cariboo Island sill is eastward (m˙l < 0)or westward (m˙l > 0).We calculated upper and lower bounds of West Basin suspended sediment m from vertical tur-21bidity profiles collected at five CTD stations (ST6, ST7, ST9, ST10, and ST11, Figure 1.1) asfollows: from each set of five profiles, make an upper bound vertical Tu profile comprised of themaximum observed values across all profiles for each 1 m depth bin, and likewise use minimum Tuto make a lower bound vertical profile; add/subtract sensor error to upper/lower bound Tu profiles;convert these to vertical c profiles using equation (3.3) with upper/lower kc estimates; and integrateeach through the West Basin’s volume-depth curve (V (z), z positive downwards, zb = 108 m):m =∫ zb0c(z)V (z)dz. (3.4)Our best estimate (expected m value) is based on the median turbidity across all profiles for eachbin, with c(z) from equation (3.3) using the average kc of the four suspensions given in Table 3.1,and the same V (z) curve as we use for upper and lower m bounds.For the Quesnel River, we used daily-average flow (Q) to estimate sediment mass flow (m˙r,Mg/day) as:m˙r = Q · c ·0.0864 s ·Mgday ·g , (3.5)with upper bound, expected, and lower bound c from equation (3.3) using FWQMS turbidity data.We estimated turbidity between bottle sample dates by linear interpolation. Section 4 gives cumu-lative mass flow (Mg) by solar season, which we calculate by multiplying m˙r from equation (3.5)by ∆t = 1 day and summing over the number of days between equinox and solstice. Throughoutthe text, the terms summer, autumn, winter, and spring correspond to the solar year, except whenfollowed by a state of stratification (e.g. spring mixis or winter inverse stratification).Suspended sediment collected in bottle samples from 30, 60, and 90 m depth in the West Basinon 18 September 2014 had a median particle diameter slightly smaller than 1 µm (Petticrew et al.,2015). For a particle with a diameter d = 10−6 m and density ρp = 2500 kg/m3, the Stokes’ settlingvelocity (ws, m/s) is:ws =g18(ρp−ρ f )µd2 = 5.6 ·10−7m/s≈ 5cm/day. (3.6)22where g = 9.8 m/s2 is the gravitational constant, ρ f = 1000 kg/m3 is fluid density, and µ = 0.0015kg/ms is the dynamic viscosity of the fluid (cf. Ha˚kanson and Jansson, 1983, Chapter 6). Using thisvelocity, we calculated an approximate settling mass flow rate (m˙b) for the date of each West Basinc(z) profile as:m˙b =−∫ zb0c(z)wsA(z)dz, (3.7)where A(z) is the bottom area at depth z. For dates between c(z) profiles, we estimated m˙b usinglogarithmic interpolation; i.e., linearly interpolating ln(m˙b). We do not give upper and lower boundsfor m˙b; rather, we treat these as order-of-magnitude estimates, reflecting their uncertainty (the exactconditions affecting settling are complex, as the vertical velocity component of currents may en-hance or negate a particle’s downward motion through the water; cf. Gloor et al., 1994; Scheu et al.,2015).23Chapter 4ResultsPrior to the 4 August 2014 spill, turbidity in the West Basin was typically low (< 0.4 FTU), withsome instances of higher turbidity near the surface during spring (Hamilton et al., 2020). Sinceour c(Tu) correlations are based on sediment from the spill, they may not be accurate for naturalsediment. Still, we need a point of reference to be able to say what normal sedimentary conditionsare in Quesnel Lake. Lacking a better alternative with which to estimate pre-spill c from turbidity(such as a bulk sample of natural sediment to use in laboratory calibrations), we apply equation(3.3) with the same linear coefficients used for post-spill turbidity data (Figure 3.3). Doing so, wefind a maximum c≈ 1.1 g/m3 observed between 1 and 3 m depth in the West Basin on 3 June 2008(Figure 4.1a); this would have most likely been associated with a riverine overflow. Hypolimneticsediment c in the West basin was typically < 0.2 g/m3. Using the median and maximum c observedin the pre-spill data at each depth in the West Basin, based on equation (3.4), the approximate pre-spill median and maximum m were 75 and 280 Mg, respectively (Table 4.1). Note: from here on, toavoid switching between metric prefixes, we will describe mass in units of Mg (1 Mg = 1000 kg =1 ton).Quesnel Lake’s response to the Mount Polley spill has unfolded in two phases (Hamilton et al.,2020). Here we mark the end of the first phase (referred to as the initial regime, section 4.1) as theapproximate date when the total mass of sediment in the West Basin first fell below the historicalmaximum value; as we shall see, this occurred around early June 2015, ten months following the24Figure 4.1: Vertical profiles of suspended sediment concentration at CTD station ST9 in theWest Basin (a-c) and ST8 near the Junction (d-f). Note the change in scale for the x-axesof (b) and (e), and the differing y-axes for the West Basin and the Junction.spill. The subsequent, seasonal regime (section 4.2) appears to be ongoing; we will use the pre-spillmedian suspended sediment m in Chapter 5 as a benchmark to define when the seasonal regime willhave ended (i.e., how long Quesnel Lake will take to recover from the sedimentary effects of thespill.)4.1 Initial regimeLet’s return to the ∼30000 Mg of suspended sediment that Petticrew et al. (2015) estimated tobe in suspension below 30 m depth in the West Basin hypolimnion in early summer/late autumn2014, based on water column stability (described in section 2.2). On 10 September 2014, WestBasin hypolimnion concentrations measured at CTD station ST9 ranged from 20 g/m3 at 30 mdepth to over 100 g/m3 near the bottom (Figure 4.2a). Applying equation (3.4) to the 10 Sept 2014,25Table 4.1: Suspended sediment mass in the West Basin by date. Error estimates are only givenfor mass based on EDF CTD data, as transects capture spatial variation in suspendedsediment concentration. Mass data are also presented in Figure 4.2b.date event m (Mg)- pre-spill median 75- pre-spill maximum 28003 June 2008 CTD cast (Figure 4.1a) 23004 Aug 2014 Mount Polley spill -10 Sept 2014 CTD transect (Figure 4.1b) 38000±1100022 Sept 2014 autumnal equinox 2500009 Oct 2014 CTD transect (Figure 4.1b) 17000±500005 Nov 2014 CTD transect (Figure 4.1b) 9200±190022 Nov 2014 onset of autumnal mixis 760010 Dec 2014 CTD cast (Figure 4.1b) 760021 Dec 2014 winter solstice 600020 Mar 2015 spring equinox 130024 Mar 2015 onset of spring mixis 130003 June 2015 end of initial regime (approx.) 300±11021 June 2015 summer solstice 24026 August 2015 yearly minimum 140±3023 Nov 2015 seasonal regime maximum 600±140horizontally averaged West Basin c(z) profile (not shown, but similar to the station ST9 c(z) profile)gives a mass of 38000±11000 (Table 4.1), putting Petticrew et al. (2015)’s stability-based estimatewithin range of our turbidity-based estimate.Through autumn 2014, West Basin surface c gradually increased (Figure 4.2), until the initiallyclear surface water had become visibly green. Hamilton et al. (2020) gave an account of surfacemixed layer deepening and entrainment of the turbid, hypolimnetic water that led to this “greening.”This surface color change had occurred by mid-November 2014. By 10 December, c was near 7g/m3 through depth near CTD station ST9 (Figure 4.1). Temperature data presented in Hamiltonet al. (2020) likewise indicate that the West Basin was fully mixed at this time, which is also con-sistent with sediment c near 7 g/m3 in the Quesnel River (Figure 4.2d). Based on the c(z) profileshown in Figure 4.1b, approximately 7600 Mg of sediment was suspended in the West Basin on10 December 2014 (Table 4.1). By 3 June 2015, m had decreased to 300± 110, approaching thepre-spill maximum m. Thus, over nine months between 10 September 2014 and 3 June 2015, WestBasin suspended sediment m had decreased by two orders of magnitude. With this in mind, we will26Figure 4.2: Suspended sediment timeline, 10 September 2014 to 21 December 2018: (a) WestBasin concentration at three depths (note: 4 and 38 m depth c are based on turbidity,while 95 m depth c is based on acoustic echo intensity (ADCP) data; and, to improvereadability, processed JFE data (Figure 3.1d) and ADCP data (Figure 3.2c) are smoothedwith a 1 week moving average); (b) West Basin mass (upper and lower bounds given byerrorbars); Quesnel River (c) daily averaged flow; (d) concentration; and (e) mass flow(upper and lower bounds given by grey shaded region). In (a), (b), and (d), grey shadingindicates periods of mixis.now turn to the sinks responsible for this decrease in West Basin sediment m: the Quesnel River,settling, and exchange flows.The Quesnel River had its part in removing sediment during the inital regime, accounting for4000± 1000 Mg, or just over 10% of the total decrease in West Basin m between 10 September2014 and 3 June 2015 (Table 4.2). Sediment c in the river at the sampling location is controlled bysurface c in the West Basin, as that part of the channel has no inflowing tributaries or eroding banks,and until October 2014 the surface mixed layer (epilimnion) had not entrained enough sedimentfrom the hypolimnion to cause an appreciable increase in river mass flow, m˙r, based on equation(3.5). Through October and November, the surface mixed layer deepened in Quesnel Lake, and m˙rincreased as lake surface c increased (Figure 4.2e). On 11 December 2014, with the West Basin in27Table 4.2: Cumulative mass flows by period within the initial regime for each of three WestBasin suspended sediment mass sinks: the Quesnel River, equation (3.5) integratedthrough time; settling, equation (3.7) integrated through time; and exchange with the mainbasin, estimated from the West Basin’s sediment mass balance.period Ques. R. (Mg) settling (Mg) exchange (Mg)10-22 Sept 2014 70±15 700 12000autumn 2014 2200±600 2000 15000winter 2015 1200±250 250 3200spring 2015 600±150 80 400total 4000±1000 3000 31000autumnal mixis, river c and m˙r peaked at 7 g/m3 and 58±14 Mg/day, respectively. The 4000±1000Mg of sediment that flowed into the Quesnel River during the initial regime represents nearly two-thirds of the cumulative river mass flow observed over our study period (6900±1500 Mg between10 September 2014 and 21 December 2018).Similarily, a small fraction of the initial West Basin m decrease can be attributed to settling (Ta-ble 4.2). Equation (3.7) states that settling mass flow (m˙b) will decrease as concentration decreases:the West Basin c(z) profile for 10 September 2014 gives m˙b = 62 Mg/day; for 10 December 2014, 8Mg/day; and for 13 April 2015, 1.4 Mg/day. In total, settling during the initial regime (between 10September 2014 and 3 June 2015) accounts for about 8% of the decrease in West Basin suspendedsediment m for that regime.Thus, during the initial regime, river outflow and settling combined account for only about20% of the observed decrease in West Basin sediment mass. The mass balance for the West Basintherefore suggests that most (∼80%) of the sediment mass in suspension on 10 September 2014flowed east out of the West Basin, over the Cariboo Island sill, and into the main basin of QuesnelLake (Table 4.2). The elevated c found on 12 December 2014 near the Junction (Figure 4.1e)supports this conclusion. CTD data presented by Petticrew et al. (2015) showed that sediment massflow east over the sill (m˙l) had begun by early August. They observed a continuous, turbid layer thatpropagated east along the density interface (i.e. thermocline at z ≈ 20m). Based on relative arrivaltimes at CTD stations, the authors estimated a propogation speed of ∼1 cm/s. By 18 September2014, this layer had passed CTD station ST0 in the West Arm (Figure 1.1). Four kilometers west at28station ST2, the layer was found between 15 and 40 m depth with c up to 6 g/m3.To find an approximate scale of the m˙l associated with this layer, we first consider the physicalmechanism for its propagation. In the Sea of Galilee (also called Lake Kinneret or Tiberius), second-vertical-mode seiche motions have been shown to constrict the metalimnion, forcing its horizontaldisplacement as a “metalimnetic jet.” Horizontal current velocities of 25 cm/s transport suspendedmaterial from the periphery to the interior of Lake Kinneret (Marti and Imberger, 2006). Anotherplausible mechanism for the turbid layer observed in Quesnel Lake is that of a buoyancy-drivenhorizontal intrusion (Manins, 1976). We assume the intrusion (turbid layer) crosses the lake’s fullwidth and is propagating along its long axis, a reasonable assumption considering the West Armis around 2 km wide and a distance of some 20 km separates station ST2 from Cariboo Island.A laterally bounded intrusion of height h will propagate at up ≈ 0.2Nh, where N =√g∆ρ/ρ0his the average buoyancy frequency across the intrusion of height h, with reference density ρ0 =1000 kg/m3 (Scheu et al., 2015). In the case of station ST2 on 18 September 2014, up = 4 cm/s.Comparing the scales of second-vertical-mode seiche velocity and theoretical intrusion propogationspeed, we find the latter to be closer to the observed 1 cm/s. Multiplying this observed velocity bythe cross-sectional area of the West Arm between 15 and 40 m depth at station ST2 (∼63000 m2),and an average c of 3.5 g/m3, gives m˙l ≈ 190 Mg/day, roughly three times that of m˙b (settling) formid-September 2014.We have shown that between 10 September 2014 and 21 December 2018, suspended sediment min the West Basin underwent a two order of magnitude decrease, which the mass balance attributesmainly to sediment carried into the main basin of Quesnel Lake by exchange flows. We gave anestimated scale for eastward mass flow for 18 Sept 2014, but our limited information did not allowus to integrate eastward mass flow through time as we do for mass flow in the Quesnel River.Nonetheless, we were able to infer the cumulative mass flow associated with eastward mass flux fora given period using a mass balance for the West Basin.294.2 Seasonal regimeSuspended sediment m in the West Basin continued decreasing through summer 2015, the firstsummer of the seasonal regime (Figure 4.2b), eventually reaching a minimum of 140± 30 Mg(Table 4.1). On 19 August 2015, the c(z) profile measured at CTD station ST9 showed West Basinc in the range of pre-spill levels through depth (Figure 4.1c). As was the case for the initial regime,this decline in West Basin sediment c and m over the first summer of the seasonal regime was due tosediment being flushed either down the Quesnel River or into the main basin of Quesnel Lake, or,to a lesser extent, settling to the bottom of the West Basin (settling mass flow was m˙b ≈ 1.4 Mg/dayon 13 April 2015, compared to river m˙r ≈ 5 Mg/day). But whereas suspended sediment m onlydecreased during the initial regime, m underwent periods of increase during the seasonal regime,most notably through the breakdown of stratification each year as the lake approached autumnalmixis (Figure 4.2b). Later in this section, we will describe the conditions associated with increasingsuspended sediment m in the West Basin.But first: an overview of the West Basin’s seasonal suspended sediment cycle (first describedby Hamilton et al., 2020), for which we shall use the year 2016 as our central example (mainlybecause this was the first autumn period for which we have bottom velocity data from mooringTuADCP; Figure 1.1). At the onset of stratification in April, c increased slightly through depth(Figure 4.1c), and also increased westward toward the outflow (Figure 4.3b). Summer stratificationwas always the longest period of a given yearly cycle (Figure 4.2), leading to the lowest overallsuspended sediment c in the West Basin. Through spring into summer, c decreased first in theupper water column (Figure 4.3c), and by September approached yearly minimum levels throughall depths (Figure 4.3d).Part way through the autumn breakdown of stratification, on 11 November 2016, a marked cincrease appeared in the lower half of the West Basin water column (Figure 4.3e; Figure 4.4d;Figure 4.5a-c), similar to the previous year, where elevated c was found below 40 m depth at CTDstation ST9 on 23 November 2015 (Figure 4.1c). Upper water column c increased as the lakeapproached autumnal mixis in 2016, with c slightly lower in the surface mixed layer (4 m and 38m depth) than c measured at the bottom (100 m depth, Figure 4.2a). Surface mixed layer c stopped30Figure 4.3: Seasonal stratification and sediment distribution during 2016 in the West Basin.(a) Temperature through depth at CTD station ST9 (note: the 11 November temperatureprofile uses thermistor data from mooring M3). (b-e) Contour plots of c through depthalong the thalweg, with triangles showing where CTD stations are located. Red triangles(b-d) or dotted line (e) indicate where temperature profles shown in (a) were measured.increasing each year at the onset of autumnal mixis.The subsequent period of inverse stratification each winter brought a decrease in c and m (Hamil-ton et al., 2020; note that near the surface, this decrease is more pronounced under ice cover). Then,through each spring mixis, c and m increased to similar peak values as those observed during thepreceeding autumnal mixis (Figure 4.2a,b). The long term trend in peak m through the seasonalregime saw lower maxima during autumn and spring mixis with each passing year. This study’sfinal CTD transect, collected on 4 December 2018, showed m still above the historical maximum(Figure 4.2b). The trend indicates that this would also have been the case in spring 2019, but that intime seasonal fluctations in m will occur within the range of naturally occurring sediment mass.The decaying trend we see in West Basin suspended sediment m during the seasonal regime tellsus that sinks of suspended sediment were overcoming sources on an inter-annual basis, while thecyclical pattern in m tells us that sources were overcoming sinks during certain parts of the year. Wenow consider the role of each sink during the seasonal regime, starting with river flushing.31Figure 4.4: Autumn temperature (a,c) and suspended sediment (b,d) contour plots. Red dotsto the left of (a) and (c) indicate thermistor depths on mooring M3, and blue trianglesalong the top of (b) and (d) indicate the timing of CTD transects. The last three CTDtransects in (d) are shown in greater detail in Figure 4.5.In the Quesnel River, sediment c followed the cyclical pattern of West Basin surface c throughthe seasonal regime (Figure 4.2d), ranging from lows of c ≈ 0.1 g/m3 during summer and winterstratified periods to highs of c≈ 0.4 g/m3 at autumn and spring mixis. Both Q and m˙r were highestduring spring freshet (although still an order of magnitude smaller than peak levels seen in Decem-ber 2014, during the initial regime), and peaked in either late May or early June of each year (thestudy period maximum Q = 471 m3/s was recorded on 26 May 2018, which coincided with theseasonal cycle maximum m˙r = 11±2 Mg/day; Figure 4.2c). High river c also followed heavy pre-cipitation early in autumn 2015 and 2016; these periods are indicated by increased river flow (Q),and result in elevated mass flow (m˙r = 4.5± 1 Mg/day on 29 September 2016, Figure 4.2e). Theleast outflow of sediment through the river occurred during winter. This may seem unremarkablegiven that flow rates (Q, Figure 4.2c) reach their yearly minima, but there is another reason for whywinter sediment flushing is so insubstantial.Especially under ice cover, winter inverse stratification leads to a quiescent surface layer, and32these waters become exceptionally clear as sediment settles out. The surface turbidity sensor onmooring M3 has a nominal depth of 4 m, based on a yearly average. In midwinter, when the waterlevel is at its lowest, this sensor can come to within 2 m of the surface. From mid-February untilmid-March 2017, c was below its level of detection (Figure 4.2a), and bottle samples taken from theriver had similarily low c (Figure 4.2d). Based on a particle settling velocity of ws = 5 cm/day, near-total stillness under the ice could cause complete clarification to 2 m depth within 40 days. As wediscuss next, seiche-driven resuspension and surface mixed layer deepening raised bottom sedimentto the surface prior to each winter of 2015 to 2018. Much more of this sediment would have beenflushed out of the basin by the river were it not for the settling that winter inverse stratificationallowed for.Flushing of suspended sediment by exchange flows between the West Basin and the main basinof Quesnel Lake is the other sink we must consider (we need not consider settling on an inter-annual basis, for reasons we will explain shortly). The strong concentration gradient found betweenthe West Basin and the main basin of Quesnel Lake during the initial regime meant that the flow ofsediment into the West Basin was negligible compared to the flow out. During the seasonal regime,however, this one-way assumption no longer holds. Because of the slow settling velocity of fineparticles, a substantial mass of spill-related sediment would have remained in suspension in themain basin. Additionally, the main basin receives sediment from three large rivers (the Horsefly,Mitchell, and Niagara, described in Chapter 2), meaning that under natural conditions, the sedimentc gradient would lead to a net flow of sediment into the West Basin (also the direction of the hy-draulic gradient). Nonetheless, because river m˙r decreases once the lake is stratified, the processof West Basin hypolimnetic flushing by exchange flow must account for most of the decrease insediment m that we observe during stratified periods (Figure 4.2b). Having considered these sinks,we will finally consider sources of sediment.Hamilton et al. (2020) showed that increased hypolimnetic suspended sediment c was associ-ated with baroclinic seiching, something we will now explore in further detail as we discuss thebottom as a source of sediment. Previously, we considered mass flow across the bottom boundary(m˙b) in terms of settling to assess how much of the decrease in West Basin sediment m could be33attributed to m˙b over the initial regime. During autumn of each year in the seasonal regime, m˙b ismore important as a source of sediment, through resuspension, than it is as a sink, through settling.Seiche motion has been shown to generate currents in lakes that can transport suspended sedimentinto the water column in two ways: from the bottom up, through turbulent mixing in the benthicboundary layer; and from the sides in, through intrusions (Gloor et al., 1994; Marti and Imberger,2006; Wain and Rehmann, 2010). In summer 2016, a several centimeter-thick, cloudy, mobile layerwas observed overlaying more consolidated material in cores taken from the spill-affected bottomregion of the West Basin (Hamilton et al., 2020); this has been hypothesized to be the source ofelevated hypolimnetic turbidity each autumn of 2015-2018. Strictly speaking, sediment in this layeris already in suspension; here the term “resuspension” is used to describe the movement of sedi-ment out of this layer into the water column where it may be detected using a profiling or mooredinstrument.To demonstrate the effect of seiche on West Basin c during the seasonal regime, Figure 4.4shows temperature and c through depth and across time in the autumns of 2015 and 2016, whileFigure 4.5 shows c(z) profiles together with bottom current velocity from autumn 2016. As thesurface mixed layer deepens and seiche amplitude increases, distinct layers of increased c appearin the lower half of the water column (Figure 4.4). CTD transects each autumn record these layers,often at multiple depths, and occasionally at coherent depths in neighbouring CTD stations ST9 andST10. We show an example of these layers in profiles collected on 17 November 2016, at depthsof around 55 and 62 m (Figure 4.5b). These spikes in suspended sediment c could indicate thehorizontal transport of sediment by intrusions (cf. Wain and Rehmann, 2010), and they are strongertoward ST10, meaning that these two particular examples would have originated from the slopingbottom toward the northern (downstream) end of the West Basin.As discussed in Chapters 1 and 2, sediment resuspension and bottom boundary mixing aredifferent for sloping and flat bottom regions. In Lake Alpnach, Switzerland, Gloor et al. (1994)observed sediment resuspension over a flat bottom during bursts of current with velocities of upto 7 cm/s. Velocity data collected below 100 m depth at mooring TuADCP (Figure 1.1) duringautumn 2016 showed horizontal velocities of up to 8.6 cm/s (recorded 5 m above bottom at 01:1234Figure 4.5: Autumn 2016 CTD (a,b,c) and ADCP (d) data, (a)-(c) compare c profiles at neigh-bouring stations ST9 and ST10, and (d) shows the along-thalweg horizontal current ve-locity measured 5 m above bottom at TuADCP.on 25 November 2016; Figure 4.5d). The peak velocity for the period shown occurred betweenCTD transects on 17 November and 1 December 2016. What is interesting to note is that suspendedsediment m does not appreciably increase between these two dates (Figure 4.2b). This could indicatethat earlier in autumn 2016, the critical shear stress needed to remobilize unconsolidated bottomsediment had already been exceeded for a sufficient duration to raise sediment into the water column.Even higher horizontal current velocities were recorded in autumn 2017 (not shown), yet the WestBasin’s maximum observed sediment m that year was slightly lower than was observed in autumn2016 (Figure 4.2b). It appears that seiche currents in the West Basin have been strong enough35to resuspend bottom sediment during each autumn of the seasonal regime, and that the decayinginterannual trend we observe in sediment m could result from there being less sediment available toresuspend.Aside from the periods of increasing m that we observed each fall, we also saw a slight increasein West Basin m toward the end of each period of winter inverse stratification as the lake approachedspring mixis (typically around March of each year; Figure 4.2b). We attribute this increase partly toriverine sediment input: the c(z) profile collected at CTD station ST9 on 6 June 2016 shows slightlyelevated c between the surface and 20 m depth, indicative of a riverine overflow. Another poten-tial source of sediment m during the breakdown of winter inverse stratification is remobilizationof bottom sediment. Unfortunately, with limited spatial coverage of c during the winter months,we are unable to resolve this process to the same degree as we have done for the seiche-drivenremobilization during the autumn.A last, and lesser source of sediment is the pair of multi-port diffusers located around 50 mdepth, 250 m offshore of Hazeltine Creek (described in section 1.1). Denoting their associatedsediment mass flow as m˙d , we calculate an upper-range estimate using their permitted annual meanflow rate (Q = 29000 m3/day) and maximum concentration (c = 7 g/m3, actual c varies, and istypically below the permitted level; MPMC, 2018) to give m˙d ≈ 0.2 Mg/day. This upper boundestimate is one to two orders of magintude smaller than the loading required to explain the increasein West Basin m during each autumn of 2015-2018.36Chapter 5DiscussionQuesnel Lake is gradually returning toward its background level of naturally occurring suspendedsediment. One aspect that is central to how the lake is recovering was that the 4 August 2014flood entered the lake’s smaller, downstream basin. Here we draw on theory for insight into howinter-basin flows, relative basin size, particle settling, and river flow broadly shaped the system’sresponse. We begin with the case of one completely mixed basin; examining what would havehappened if the spill had occurred during autumnal mixis into a lake the size and shape of the WestBasin, with an outflow comparable to the Quesnel River, and an equally sized inflow.The mathematical theory for such a problem is well formulated for continuously stirred tankreactors (CSTRs, cf. Chapra, 1997). If the flow (Q) that enters a CSTR has zero suspended sedimentconcentration (cd), the sediment mass balance is given by:dmdt=Vddcddt=−Qcd−wsAdcd , (5.1)where Ad is lake surface area, Vd is volume (constant with inflow equal to outflow), and ws is particlesettling velocity. Here time is the independent variable, and concentration is the dependent variablefor which we solve an initial value problem to obtain an expression for cd(t). Grouping constant37terms (with Vd/Ad = Hd , average depth), we have:dcddt=−(QVd+wsHd)cd =−λcd , (5.2)which for an initial concentration cd(0) = ci has a solution:cd(t) = cie−λ t . (5.3)The exponential term λ is the decay constant; its inverse is the e-folding time, for 63% removal(1− e−1 ≈ 0.63) of mass. For dissolved matter, equation (5.2) retains the flushing term (Q/Vd) butnot the settling term (ws/Hd), and provided the substance is not removed by chemical reactions, itse-folding time will be the basin’s residence time (tr = Vd/Q = 1 km3/100 m3/s ≈ 100 days). Thisalso applies to 1 µm diameter particles that settle at 5 cm/day in a basin with an average depth ofHd = 42 m (that of the West Basin), as ws/H in this case is two orders of magnitude smaller thanQ/Vd .Compared to this one basin case, we see a much higher flushing rate in the West Basin throughautumnal mixis of 2014. Fitting an exponential decay curve to the mass time series over this periodgives an e-folding time of about 50 days, half that of the one basin case. By extension, half of theflushing may be attributed to the river; indeed, observed river mass flow (m˙r) in early December2014 is roughly half that of the observed rate of decrease in the West Basin. The settling m˙b weestimate for this period in section 4.1 is one order of magnitude smaller than m˙r. Although this alesser disparity than the two orders of magnitude given by equation (5.2), it still suggests that massflow eastward over the Cariboo Island sill was comparable to mass flow down the Quesnel River atthis time.Using this result, we will extend the CSTR theory to a two basin system with constant, bi-directional exchange flow (Qx) equal in magnitude to river flow (Qr = 131 m3/s). As with QuesnelLake, we will consider the case of an upstream basin (denoted with the subscript u) with greatervolume (Vu = 40.8 km3, Vd = 1 km3) and surface area (Au = 243 km2, Ad = 23 km2). The schematicin Figure 5.1b depicts the transport terms that apply to each basin, also given in equations (5.6)-38(5.9). The mass balance for each basin is affected by its own concentration as well as that of theother basin, yielding a system of two linear, homogeneous, ordinary differential equations:dcudt=−αuucu +αudcd , (5.4)dcddt= αducu−αddcd , (5.5)with coefficients (α) given by the transport terms:αuu =Qr +QxVu+wsHu, (5.6)αud =QxVu, (5.7)αdu =Qr +QxVd, and (5.8)αdd =Qr +QxVd+wsHd. (5.9)The general solution to this two basin system has the form:cu(t)cd(t)= c(t) = k f eλ f tη f + kseλstηs, (5.10)with two decay terms, denoted by the subscripts f and s, corresponding to fast and slow response. Aswith the two regimes observed in the West Basin following the spill, the solution predicts an initialperiod of rapidly decreasing c transitioning into a slow, sustained decrease. The decay constants forthese two regimes are the eigenvalues λ f and λs, given by:λ f ,s =−(αuu +αdd)±√(αuu +αdd)2−4(αuuαdd−αudαdu)2. (5.11)39Figure 5.1: Two basin system: (a) compares the analytical solution, given by equations (5.10)-(5.12), to the volumetric average of West Basin suspended sediment concentration; and(b) depicts the transport terms for the upstream and downstream basin mass balances.The y-axis intercept is at 0.1 g/m3, which is slightly higher than the approximate medianpre-spill c =0.08 g/m3.The relative weighting of each basin’s role in the fast and slow regimes is given by the fast andslow eigenvectors η f and ηs, as:η f ,s = αudαuu +λ f ,s=αdd +λ f ,sαdu . (5.12)Having calculated λ f ,s and η f ,s, one specifies the initial concentrations of the upstream and down-stream basins to determine the constants k f and ks in equation (5.10). For the present case, weinitilize the model at the onset of autumnal mixis 2014 in the West Basin (22 November= t(0)).We take cu(0) = 0.7 g/m3 (roughly, the decrease in West Basin m between 10 September and 22November 2014, which was 30000 Mg, less the cumulative river and settling mass flows, whichwere 800 and 2300 Mg, respectively, divided by Vu), and cd(0) = 8 g/m3 (the remaining mass sus-pended in the West Basin, which was 8000 Mg, divided by Vd). For this completely mixed, two40basin model, we also assume the sediment remaining in suspension had the Stokes’ velocity of 1µm particles (ws = 5 cm/day; section 3.3).The particular solution to this two basin, analytical model is plotted in Figure 5.1, along withWest Basin c from mass data (Figure 4.2b). To remove the oscillatory effect of seiche on West Basinc in Figure 5.1, we smooth m with a 21 day moving average before dividing by Vd . Because themodel uses constant transport terms, it cannot capture the seasonality of the real system. Nonethe-less, three key aspects of the real system are reflected in the model: the decay rate of the initialregime (given by the eigenvalue λ f ); the timing of the transition between regimes; and the decayrate of the seasonal regime (given by λs). All three of these are inherent to the modelled system (i.e.independent of initial concentrations). Initially, the fast term in equation (5.10) dominates decayof cd ; this results from the coefficient αdd being two orders of magnitude larger than αuu, αud , andαdu, meaning that cd is controlled by the combined flushing from river and exchange flows betweenthe two basins. Later, during slow decay, both cd and cu are controlled mainly by the upstreambasin due to its larger volume and surface area. Whereas the settling term in the coefficient αdd isinsignificant, for αuu it is on the same order as the flushing term, giving a slow decay e-folding timeof about 5 years (half the residence time of Quesnel Lake). The similarity between the two basinmodel’s slow decay and the observed inter-annual trend could suggest that the whole of QuesnelLake is recovering from the spill, rather than its effects having been confined to the West Basin. Byaltering cu(0) and/or cd(0), we can adjust the long term decay trend to match the peak c observedeach autumn in the West Basin. Our interest is in finding the time at which the modelled cd willbe equal to the pre-spill median (c ≈ 0.08 g/m3), so that we may assess how long it will take forQuesnel Lake to return to its naturally occurring sediment load. Doing so, we find this time to beapproximately one decade.A problem that arises in using a completely mixed model to describe a seasonally stratifiedsystem is that the model will overpredict river mass flow, because river c during stratified periodstends to be lower than surface c. The model’s completely mixed assumption holds during peri-ods of autumnal and vernal mixis (grey-shaded timespans indicated in Figure 4.2). At those times,which make up less than a quarter of a given year, river c is approximately the volumetric average41West Basin c. During stratified periods (most of the year), c near the surface of the West Basin,and consquently in the river, are lower than the volumetric average (most sediment mass is in thehypolimnion). In the particular solution shown in Figure 5.1, between 22 November 2014 and 21December 2018, the model gives cumulative river mass flow ≈ 10000 Mg, twice that observed inthe Quesnel River over this period (based on data shown in Figure 4.2e). Although the model pro-vides a broad description of Quesnel Lake’s two-phased response to the slug injection of suspendedsediment following the the Mount Polley spill, it is not a replacement for data when assessing theactual mass flows of suspended sediment out of the West Basin.Note that during each of the summer stratified periods of 2015-2018, the rate of West Basin cdecrease is similar to the fast decay predicted for cd in the model. The completely mixed model’sfast decay results from both river and inter-basin flushing, whereas in the real, stratified West Basin,the river draws water (and suspended sediment) only from the surface mixed layer. In their study oflate summer upwelling in Quesnel Lake, Laval et al. (2008) estimated a residence time of 6-8 weeksfor the West Basin hypolimnion based on observed changes in heat content. Upwelling occurs whenthe hypolimnion is brought to the surface by a tilted thermocline; it is associated with large seicheamplitudes, which the West Basin experiences because it is located at the extreme end of QuesnelLake’s long axis. Since c is typically higher in the hypolimnion (Figures 4.2a and 4.3b), the rateat which suspended sediment is flushed from the West Basin during the summer stratified perioddepends heavily on the exchange flows driven by seiche.42Chapter 6ConclusionsOf the 38000 ± 11000 Mg of sediment that was in suspension below 30 m depth in Quesnel Lake’sWest Basin on 10 September 2014, <200 Mg remained in the water column by August 2015, oneyear post-spill. Most (∼80%) of that mass exited east over the Cariboo Island sill during an initial,post-spill regime of sustained, rapid decay that lasted until early June of 2015. Of the ∼7000Mg of sediment that flowed down the Quesnel River during the four year study, one third did soduring the first autumn post-spill, and another sixth during the first winter. In the ensuing years, aseasonal pattern in West Basin sediment mass emerged: late summer yearly minima; loading fromremobilization of bottom sediments during the breakdown of stratification leading to autumnal mixismaxima; decrease to winter local minima during inverse stratification; increase due to riverine andbottom sediment input to spring mixis maxima; and decrease following the onset of stratification.The autumn and spring maxima of this seasonal regime show an overall decreasing trend.Consistent with the two regimes we observed in the West Basin, the analytical solution to a massbalance model for a system of two, completely mixed basins with constant exchange flow betweenbasins and constant river flow predicts an initial, fast decay and a long-term, slow decay. Thissolution overpredicts mass flow in the river, but nevertheless gives two decay rates which reflectthe observed decay rates of each regime and the timing of the transition from fast to slow decay ofsediment concentration. Fitting the slow decay curve of the model to the autumnal maxima of WestBasin sediment mass, and determining the point in time at which this curve crosses the pre-spill43median mass, we find that Quesnel Lake will return to pre-spill levels of suspended sediment withinapproximately one decade of the 4 August 2014 spill.44BibliographyV. Axelsson. The Laitaure Delta: A study of deltaic morphology and processes. GeografiskaAnnaler. Series A, Physical Geography, 49(1):1, 1967. doi:10.2307/520865. → page 7J. Bloesch. Mechanisms, measurement and importance of sediment resuspension in lakes. Marineand Freshwater Research, 46:295–304, 1995. doi:10.1071/MF9950295. URLhttp://www.publish.csiro.au/mf/MF9950295. → pages 1, 9E. C. Carmack, C. B. J. Gray, C. H. Pharo, and R. J. 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