{"@context":{"@language":"en","Affiliation":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","AggregatedSourceRepository":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","Campus":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","Creator":"http:\/\/purl.org\/dc\/terms\/creator","DateAvailable":"http:\/\/purl.org\/dc\/terms\/issued","DateIssued":"http:\/\/purl.org\/dc\/terms\/issued","Degree":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","DegreeGrantor":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","Description":"http:\/\/purl.org\/dc\/terms\/description","DigitalResourceOriginalRecord":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","Extent":"http:\/\/purl.org\/dc\/terms\/extent","FileFormat":"http:\/\/purl.org\/dc\/elements\/1.1\/format","FullText":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","Genre":"http:\/\/www.europeana.eu\/schemas\/edm\/hasType","GraduationDate":"http:\/\/vivoweb.org\/ontology\/core#dateIssued","IsShownAt":"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt","Language":"http:\/\/purl.org\/dc\/terms\/language","Program":"https:\/\/open.library.ubc.ca\/terms#degreeDiscipline","Provider":"http:\/\/www.europeana.eu\/schemas\/edm\/provider","Publisher":"http:\/\/purl.org\/dc\/terms\/publisher","Rights":"http:\/\/purl.org\/dc\/terms\/rights","ScholarlyLevel":"https:\/\/open.library.ubc.ca\/terms#scholarLevel","Title":"http:\/\/purl.org\/dc\/terms\/title","Type":"http:\/\/purl.org\/dc\/terms\/type","URI":"https:\/\/open.library.ubc.ca\/terms#identifierURI","SortDate":"http:\/\/purl.org\/dc\/terms\/date"},"Affiliation":[{"@value":"Applied Science, Faculty of","@language":"en"},{"@value":"Civil Engineering, Department of","@language":"en"}],"AggregatedSourceRepository":[{"@value":"DSpace","@language":"en"}],"Campus":[{"@value":"UBCV","@language":"en"}],"Creator":[{"@value":"James, Christina","@language":"en"}],"DateAvailable":[{"@value":"2009-12-03T20:58:06Z","@language":"en"}],"DateIssued":[{"@value":"2004","@language":"en"}],"Degree":[{"@value":"Master of Applied Science - MASc","@language":"en"}],"DegreeGrantor":[{"@value":"University of British Columbia","@language":"en"}],"Description":[{"@value":"Quesnel Lake, is a deep (511m maximum depth) fjord-type lake in northeast\r\nBritish Columbia, Canada. Mixing processes in the lake exchange deep-water\r\nwith surface water and contribute to the renewal of surface-water nutrients and\r\noxygenated deep-water. These processes are of great consequence to the lake's\r\ntrophic dynamics and understanding them will enable better management of\r\nthe large salmon resources in Quesnel Lake.\r\nTo better understand large-scale convective processes, a lake-specific equation\r\nof state was developed. Water samples were collected at locations around\r\nQuesnel Lake and analysed for ionic and non-ionic composition as well as other\r\nquantities that are integral to determining the lake's equation of state including\r\npH, alkalinity and specific conductance. A relationship was developed to\r\nfind lake water salinity from CTD data. Salinity was in turn related to density\r\nusing a modified form of a general limnological equation of state. The equation\r\nof state developed for Quesnel Lake gives densities accurate to \u00b1 0.0018kg\/m\u00b3\r\nwhereas the general equation of state (based on seawater composition) is only\r\naccurate to \u00b1 0.0158kg\/m\u00b3 for Quesnel Lake water samples.\r\nThe lake-specific equation of state was used to identify gravitational instability\r\nin density profiles estimated from CTD data. In order to compare water\r\nparcel density within a profile, the hydrostatic pressure effect must be removed.\r\nThe three quantities that are used for this purpose, potential density, quasi-density\r\nand standard density, were compared. Quasi-density was found to be\r\nmost appropriate for Quesnel Lake's deep water which is near the temperature\r\nof maximum density. Quesnel lake water column stability was quantified using\r\nthe Brunt-Vaisala frequency calculated using quasi-density.","@language":"en"}],"DigitalResourceOriginalRecord":[{"@value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/16247?expand=metadata","@language":"en"}],"Extent":[{"@value":"4965283 bytes","@language":"en"}],"FileFormat":[{"@value":"application\/pdf","@language":"en"}],"FullText":[{"@value":"MIXING PROCESSES FROM CTD PROFILES USING A LAKE-SPECIFIC EQUATION OF STATE: QUESNEL L A K E by CHRISTINA J A M E S B.Sc , University of British Columbia, 2001 A THESIS' S U B M I T T E D IN PARTIAL F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D SCIENCE in T H E F A C U L T Y O F G R A D U A T E STUDIES (Department of Civil- Engineering; Environmental Fluid Mechanics) UNIVERSITY OF BRITISH C O L U M B I A November 2004 \u00a9Chris t ina James, 2004 Abstract Quesnel Lake, is a deep (511m maximum depth) fjord-type lake in northeast Bri t ish Columbia, Canada. Mix ing processes in the lake exchange deep-water with surface water and contribute to the renewal of surface-water nutrients and oxygenated deep-water. These processes are of great consequence to the lake's trophic dynamics and understanding them wil l enable better management of the large salmon resources in Quesnel Lake. To better understand large-scale convective processes, a lake-specific equa-tion of state was developed. Water samples were collected at locations around Quesnel Lake and analysed for ionic and non-ionic composition as well as other quantities that are integral to determining the lake's equation of state includ-ing p H , alkalinity and specific conductance. A relationship was developed to find lake water salinity from C T D data. Salinity was in turn related to density using a modified form of a general limnological equation of state. The equation of state developed for Quesnel Lake gives densities accurate to \u00b1 0.0018 k g \/ m 3 whereas the general equation of state (based on seawater composition) is only accurate to \u00b1 0.0158kg\/m 3 for Quesnel Lake water samples. The lake-specific equation of state was used to identify gravitational insta-bility in density profiles estimated from C T D data. In order to compare water parcel density within a profile, the hydrostatic pressure effect must be removed. The three quantities that are used for this purpose, potential density, quasi-density and standard density, were compared. Quasi-density was found to be most appropriate for Quesnel Lake's deep water which is near the temperature of maximum density. Quesnel lake water column stability was quantified using the Brunt-Vaisala frequency calculated using quasi-density. i i Contents Abstract ii Table of Contents .'til, List of Figures v i i List of Tables viii List of Notations ix Acknowledgements xi 1 Introduction 1 2 Literature Review 4 2.1 Other Works related to Equations of State 4 2.2 State Variables 5 2.2.1 Temperature 5 2.2.2 Salinity 9 2.2.3 Pressure 12 2.3 Relationships 13 2.3.1 Relating Conductivity to Specific Conductance 13 2.3.2 Relating Specific Conductance to Salinity 15 2.3.3 Relating Salinity to Density 16 2.4 Profile Stability 17 2.4.1 Potential Density 18 2.4.2 Quasi-Density 18 2.4.3 Standard Density 20 2.4.4 Brunt-Vaisala Frequency 21 3 Methods 23 3.1 Water Samples 23 3.2 Calculating Conductivity 26 3.3 Finding Salinity 30 3.4 Determining the Coefficient of Haline Contraction 31 3.5 Measuring Density 33 3.6 CTD Profiles 34 3.7 Applying Quesnel Lake's Equation of State 34 3.7.1 Quasi-Density 34 iii 3.7.2 Standard Density 36 3.7.3 Brunt Vaisala Frequency 36 4 Quesnel Lake's Equation of State 38 4.1 Equation for fT \u2022 ; . . 38 4.2 Equation for Salinity . . . 41 4.2.1 Finding the Constant of Proportionality, A 41 4.2.2 Salinity Equation 42 4.3 Equation of State for Quesnel Lake 43 4.3.1 Coefficient of Haline Contraction 43 4.3.2 Quesnel Lake's Equation of State 45 4.3.3 Error 45 5 Local Stability 50 5.1 Quasi-Density 50 5.2 Standard Density 55 5.3 Instability Identification , 57 5.4 Density Currents 66 6 Conclusion 70 7 Future Work 73 7.1 Thorpe Scale 73 7.2 M9 Thermistor Chain 74 7.3 Further Investigation of Density Currents 75 References 76 A Polynomial Coefficients 81 A',1 Limiting Equivalent Conductivity 81 A.2 Reduction Factor 82 B The Carbonate System 83 C Matlab Equation of State Toolbox 86 C.l densitycalc.m 88 C.2 relationships.m 89 C.3 C25.m 91 C.4 carbonates.m '. 93 C.5 equivalents.m 94 C.6 LEC.m 95 iv C.7 reductioncoeff.m \u2022\u2022 96 C.8 keff.m . . 98 C.9 salinity.m 99 v List of Figures 1 Map of Quesnel Lake 2 2 Density Dependence on Temperature 6 3 Illustration of a Stable Profile that crosses TMD 8 4 TMD a n d Tfreezing for seawater 9 5 Density dependence on Salinity 11 6 TMD dependence on Pressure 13 7 Quasi-Density Illustration 19 8 Schematic of Brunt Vaisala Frequency 22 9 Map of water sample stations, July 2003 23 10 Composition of Quesnel Lake water samples 26 11 Map of water sample stations, June 2004. 27 12 Sample fits for Aj and f 29 13 Concentrations of Si vs. Ca 38 14 Temperature factor fx function for Quesnel Lake 39 15 Measured and Calculated specific conductance for Quesnel Lake . . . 40 16 Measured and Calculated Specific Conductance for several B C lakes. . 41 17 C25 vs Salinity for determining A 42 18 Comparing density with and without Quesnel Lake salinity contribution 44 19 Measured and calculated densities for Quesnel Lake 48 20 Measured and calculated densities for Quesnel Lake Compared with E O S C M \u2022 \u2022 \u2022 49 21 Comparison of Potential and Quasi-Density Profiles 50 22 Quasi-Density found using E O S C M and E O S Q L 52 23 Quasi-Density Profiles for 2001, 2002, and 2003 53 24 Quasi-Density Profiles for for 2003 throughout Quesnel Lake 54 25 Standard density calculated varying TQ : 55 26 Density as a function of Temperature and Pressure (2D) 56 27 Bin Average Quasi-Density 58 28 Power spectrum for 2002 Quasi-density profile 59 29 Brunt Vaisala Frequency found using Various B i n Sizes 60 30 Brunt Vaisala Frequency found using E O S C M and EOSQL 61 31 Brunt Vaisala Frequency found using Potential Density and Quasi-Density 62 32 Profiles of the Brunt-Vaisala Frequency for 2001, 2002, and 2003 . . . 64 33 Profiles of the Brunt-Vaisala Frequency for 2003 throughout Quesnel Lake 65 34 Illustration of density current 69 35 Map showing location of Mooring 9 \u2022. 74 vi 36 The Carbonate System 83 37 Matlab Toolbox Flowchart 87 v i i List of Tables 1 Depth of Water Samples, July 2003 24 2 Summary of Tests on Quesnel Lake water samples 25 3 Depths of Water Samples, June, 2004 27 4 Stoichiometric combination of ions. 32 5 Anton Paar Densitometer calibration values 46 6 Depths at which thermisors are attached to Mooring 9 in Quesnel Lake's East Arm 75 viii List of Notations L i s t of Symbols A the coefficient of proportionality between specific conductance and salinity B percentage offset of Quesnel Lake coefficient of haline contraction to coefficient of haline contraction in equation of state developed by Chen and Millero (1986) Ci measured concentration of ion i C conductivity CT.... conductivity measured at temperature T and pressure P D standard density fi reduction coefficient of ion i fp.... pressure factor fx . . . . temperature factor m . . . . concentration of a dissolved solid in Quesnel Lake N . . . . Brunt Vaisala frequency or stability frequency p pressure r conductivity ratio R2 . . . . coefficient of determination S salinity S0 . . . . reference salinity used in standard density T temperature T0 . . . . reference temperature used in standard density TMD \u2022 \u2022 temperature of maximum density x square root of concentration of all dissolved solids in Quesnel Lake z depth z' integration variable for depth used in quasi^density zr reference depth used in quasi-density and potential density a coefficient of thermal expansion 3 coefficient of haline contraction 7 temperature-dependent coefficient for compressibility Aj . . . . equivalent conductivity of ion i ' A \u00b0 \u00b0 . . . . limiting equivalent conductivity of ion i A equivalent conductivity of a salt ^ adiabatic lapse rate of density p . . . . . density ix p0 .... mean density PCM \u2022 \u2022 density calculated with the equation of state developed by Chen and Millero (Chen and Millero, 1986) Pp0t . . . potential density Pquasi \u2022 \u2022 quasi-density PQuesnei density calculated with the equation of state developed specifically for Quesnel Lake cr p-1000, [kg\/m3] 6 potential temperature List of Abbreviations E O S C M Equation Of State developed by Chen and Millero (Chen and Millero, 1986) ' CTD .. Conductivity - Temperature - Depth probe DDW . De-ionised Distilled Water PESC . Pacific Environmental Sciences Centre PVT . . Pressure Volume Temperature properties E O S Q X Equation Of State developed specifically for Quesnel Lake x Acknowledgements I would like to express my gratitude to the following people for their assistance in the completion of this thesis. I would like to thank Dr. Bernard Laval, my supervisor, who has been a great source of ideas and guidance through this process. I am very grateful to the researchers from the Institute of Ocean-Sciences, Fisheries and Oceans Canada including Dr: Eddy Carmack, John Morrison and Dr. Svein Vagle who have helped me carry out my field work and develop some of the ideas presented here. Fellow students including Daniel Potts and Ryan North also helped with field work. Roger Pieters from the Department of Earth and Ocean Sciences, University of British Columbia spent much time discussing the finer points of this project with me. Thank you also to Dr. Svein Vagle of the Institute of Ocean Sciences, the Provincial Ministry of Water Land and Ai r Protection and Fisheries and Oceans Canada's Cultus Lake Laboratory for providing ship time. I was supported by Fisheries and Oceans Canada under the Science Subvention Research grant. Dr. Greg Lawrence from the Department of C iv i l Engineering, University of British Columbia also provided generous assistance in this project. I am also very thankful to Brock Wilson and Sabina and Douglas James, for their love through this process. xi 1 Introduction Quesnel Lake is a part of the Fraser River system and is an important habitat for salmon. Historically, Quesnel Lake received up to one third of the entire Fraser River run of salmon as they spawn in the lake or pass through it on their way to their natal streams. This makes Quesnel Lake a gateway to the catchment which contributes the largest salmon population to the Fraser River watershed (Royal, 1966). After the rock slide at Hell's Gate in 1913, the salmon population in Quesnel Lake was reduced to the point where there were too few salmon to make observations (Thompson, 1945). In recent years, salmon escapement has returned to near record numbers increasing to 3.5 million in 2001 (Fisheries and Oceans Canada, 2001). Thus, a critical management issue concerns the lake's primary productivity, and the role lake mixing and convection plays in returning nutrients to the surface (euphotic) layer of the lake. The deep water of Quesnel Lake has oxygen levels near or at saturation suggesting that deep water is being ventilated by oxygenated surface water. Also, nutrients from bottom waters are, in some way, being recycled to the surface where these nutrients then support primary production. Therefore, a motivation for studying Quesnel Lake is to determine what mechanisms contribute to vertical mixing and deep water renewal and how these mechanisms affect the Quesnel Lake salmon resource. Quesnel Lake, located on the western edge of the Cariboo mountains in British Columbia (BC), Canada, is a steep-sided fjord-type lake consisting of three long, narrow arms (Fig 1). With a maximum depth of 511 m, it is the deepest lake in B C and one of the deepest lakes in the world. It has a volume of approximately 41.5 km 3 and a surface area of 266.3 km 2 . Quesnel Lake has three major in-flowing rivers, the Horsefly River, Mitchell River and Niagara Creek and one major outflow, the Quesnel River. Conductivity - temperature - depth (CTD) profilers are routinely used for oceano-graphic and limnological research. These instruments measure the conductivity, tem-perature and pressure as they descend through the water column. In order to study 1 Figure 1: Map of Quesnel Lake. Data from Campbell (2001). Place names are used in text. vertical mixing in Quesnel Lake, density profiles, calculated from in-situ C T D mea-surements, were used. To find density profiles from C T D data, a lake specific equation of state must be employed. The equation of state relates a fluid's density, p, to its temperature, T , salinity, S, and pressure, p: p = p(T,S,p) (1) While T and p are both directly measured by a C T D , lake-specific relations are required to estimate salinity from in-situ measurements. Once a salinity relation has been established, a modified general equation of state (e.g. Chen and Millero, 1986) can be used to determine water column density. Regions of mixing can often be identified from density profiles by isolating sections where density inversions, and therefore instabilities, occur (Hohmann et al., 1997). Identifying where Quesnel Lake's 2 water columns become unstable is an integral part of understanding how this deep (> 250m) lake mixes vertically. This paper will describe the processes by which water samples were taken from Quesnel Lake and analysed in order to determine the lake-specific equation of state for Quesnel Lake, hereafter referred to as EOSQZ,. Chapter 2 will outline work done by previous researchers on this topic. Chapter 3 will give detail about the field work that was carried out at Quesnel Lake along with the method by which the data was analysed. Chapter 4 will show the results of this analysis, namely the developed E O S Q L . Chapter 5 will investigate local stability using the E O S Q L and the Brunt-Vaisala Frequency in conjuction with C T D profiles and describe a proposed mechanism that is contributing to the deep water ventilation of Quesnel Lake. 3 2 Literature Review This section presents a summary of other works that have addressed equations of state and local stability. In doing so, proceedures that are applied to Quesnel Lake water samples and C T D profiles are identified. Specifically, this section addresses other works related to equations of state (Section 2.1), the introduction of state variables (Section 2.2) and the specific issues related to each one, the developement of the relationships required to determine an equation of state (Section 2.3), and the strategies other researchers have used to investigate profile stability (Section 2.4). 2.1 Other Works related to Equations of State In the ocean, the relative proportions of dissolved salts are nearly constant through-out the world (Lewis, 1980). Therefore, only one equation of state is required to characterise stability throughout the world's oceans. In contrast, the salinity in lakes may vary from lake to lake or even between different water masses within a lake (i.e., differences in salt content between the hypo-, meta- and epilimnion) (Wuest et al., 1996). Varying local geology and river inflow can contribute to differing ion ratios (Millero, 2000a; Gray et al., 1979) which can affect the relationship between mea-sured salinity and calculated salinity. For this reason, there is no analogous universal equation of state for all lakes. Compared to other deep lakes in the world, mixing processes in Quesnel Lake have received little scientific attention to date. With the similar motivation of under-standing mixing processes, lake-specific salinity and density relationships have been developed by numerous researchers studying other deep lakes: \u2022 Lake Baikal in Siberia (Hohmann et al., 1997), at 1632m, which is the deepest lake in the world and is located in the Baikal Rift Zone. \u2022 Lake Malawi (Wuest et al., 1996), which is 700m deep and lies on the borders of Zambia, Tanzania Mozambique and Malawi, is also a rift lake and is the third deepest lake in the world. \u2022 Lake Issyk-kul (Vollmer et a l , 2002b), which is 668m deep and is located in the T ien Shan mountains of Kyrgyzs tan is the fifth deepest lake in the world. \u2022 Crater Lake (McManus et al . , 1992) in Oregon, which is 590m deep and is in the collapsed caldera of Mount Mazama. It has hydrothermal vents that introduce thermally and chemically enriched water. It is the deepest lake in the Uni ted States and the seventh deepest lake in the world. \u2022 Island Copper Mine P i t (Fisher, 2002) on Vancouver Island, B C , Canada, which is 340m deep. It was ini t ia l ly filled wi th salt water but, due to the inflow of acid rock drainage and disassociation of ions from the pit walls, the water's chemical composition changed wi th time such that the practical salinity scale, developed for seawater, no longer applies. A time dependent salinity correction was developed to be used wi th the equation of state for seawater. A l though the situation for this lake is fundamentally different from Quesnel Lake, Island Copper M i n e P i t is mentioned here because similar principles were employed i n developing its equation of state. In these examples, the lake-specific equations are pr imari ly determined from chem-ical analysis of water samples taken from the given lakes. 2.2 State Variables A s described by E q . 1, the equation of state depends on three variables: T, S and p. This section w i l l outline how density is affected by each, as well as describe some of the complications associated wi th them. 2.2.1 Temperature F i g . 2 shows the dependence of density on temperature. Above 4\u00b0C, density generally increases wi th decreasing temperature. A t zero salinity and at atmospheric pressure, 5 Temperature fC) Figure 2: Dependence of density on temperature at atmospheric pressure and zero salinity. The vertical dashed line marks TMD- This plot is based on the seawater equation of state given in Millero et aL (1980). density reaches a maximum of 999.972 kg-m~3 at a temperature of 3.98\u00b0C. This is known as the temperature of maximum density, TMD, and plays an important role in turnover in shallow (< 150 m) lakes. In shallow lakes, vertical mixing occurs when the stratification within the lake deteriorates due to temperature changes resulting from downward mixing of cooler surface water in spring and autumn. When the entire water column approaches 4\u00b0C, the stratification is reduced to the point of near uniform density. This loss of the water column stability results in seasonal turnover. The temperature of maximum density, TMD, has been a point of interest for other researchers in lake studies. In the early 1960s there was a short debate in Science between Eklund (1963, 1965) and Johnson (1964) relating to this subject. The focus was the Strom line (identified by Strom, 1945) which was incorrectly identified as TMD- Eklund showed that TMD is actually approximately 4 \u00b0 C at the surface and has 6 a temperature gradient of \u2014 0.021\u00b0C\/bar (Eklund, 1963) whereas the Strom line is the temperature gradient at which a profile has maximum stability (Eklund, 1965). Another point of contention was whether or not temperature profiles could cross over the temperature of maximum density. Imboden and Wuest (1995) address this topic and show that profiles may pass over the temperature of maximum density if they have a positive slope when profile temperatures are greater than TMD and a negative slope when profile temperature are equal or less than TMD, as illustrated in Fig. 3. Fig. 3 shows the change in TMD with depth along with a theoretical winter temperature profile when reverse stratification occurs. Although the temperature profile crosses TMD, it is stable. If, at any place in the profile, a water parcel was moved upwards, it would be heavier than the surrounding water (i.e. closer to TMD) and would fall back to its original position. Conversely, if a water parcel was pushed downwards, it would be less dense as it would be further away from the TMD line, and would return to its original position due to buoyancy forces. This is the condition for stability. Other researchers have investigated the effects OITMD o n lake stability problems as it plays an integral role in several interesting mixing mechanisms. For example, TMD plays a large role in the dynamics of thermobaric instabilities which have been studied by Sherstyankin and Kuimova (2002); Killworth et al. (1996) and Weiss et al. (1991). Thermobaric instabilities take place when wind or other external forcing pushes the cold water in the upper part of a reversely stratified water column down to where it is warmer than the local TMD- If this occurs, the overlying water becomes denser than the underlying water, resulting in episodic, local mixing. See Weiss et al. (1991) for a detailed explanation. Cabelling, another phenomena that relies on the anomaly of TMD, occurs when two water masses, one cooler than TMD and one warmer, mix together to make heavier water with a temperature closer to TMD- This heavier water then sinks and creates a plume of down-welling surface water called a thermal bar. Thermal bars occur when incoming river water or water near a lake's shore heats up while the bulk of the lake remains cold. A thermal bar can- move across a lake 7 Temperature Figure 3: Illustration of a stable profile that crosses TMD- Based on the seawater equation of state in Millero et al. (1980). as the season changes. This phenomenon has been studied by researchers including Shimaraev et al. (1993), Carmack (1979b) and McDougall (1987). TMD effects do not cause complications in oceanic waters. Fig. 4, which shows how seawater TMD (calculated using the equation of state for seawater extended to T = \u2014 5.5\u00b0C for illustration purposes only) and seawater Tjreezing change with pressure. At the surface, the extrapolated TMD is cooler than Tfreezing. As pressure is increased, these values diverge. In waters with high (> 24.7 \u00b0 \/ 0 0 ) salinity content (like in the bulk of the ocean) water will always freeze before it reaches its TMD-For this reason, TMD effects need not be considered. However, in fresh water like in Quesnel Lake, TMD > Tfreezing making TMD effects relevant. 8 Temperature CC) Figure 4: TMD and Tfreezing for seawater at S=35 as a function of pressure. 2.2.2 Salinity Often fresh water lakes are assumed to have zero salinity. Making this assumption can lead to errors when calculating the physical and chemical properties of lakes. This was first pointed out by Chen and Millero (1977a) in relation to mistakes made in estimating Lake Ontario properties under the assumption that the water had zero salinity. The average salinity in Lake Ontario is 0.209 \u00b0 \/ 0 0 which, according to the equation of state developed by Chen and Millero (1976), is enough to depress TMD by more than 0.04\u00b0C Chen and Millero (1977a). Lake water salinity, the composition of dissolved solids, cannot be found by making one measurement alone. Only a fully detailed chemical analysis on a water sample can determine its salinity (Lewis, 1980). This process is too time consuming for routine use and consequently a simpler method must be developed in order to measure salinity throughout a water column. This is done by relating salinity to easily measured C T D 9 parameters. For ocean water, C T D parameters are related to salinity using the practical salin-ity scale of 1978 (PSS78) (Dauphinee, 1980; Lewis, 1980; Hill et a l , 1986). This relationship is based on extensive measurements conducted at five seperate labora-tories (Dauphinee, 1980) and is the standard equation used to determine salinity in seawater. PSS78 determines a \"practical salinity\" based on measurements of the con-ductivity ratio, r, defined in Eq. 2 as the ratio of the conductivity of the sample to the conductivity of a standard potassium chloride solution (KCI) at S=35 and T=15 \u00b0C at atmospheric pressure (Lewis, 1980): (7(35,15,0) V ' PSS78 assumes that all waters with the same conductivity ratio, r, have the same salinity. The original PSS78 equation is only valid for salinities in the range of 2 to 42. Hill et al. (1986) extended the validity of PSS78 to salinities between 0 and 2 by adding a correction term. However, this extended equation still only applies to waters with the same compositions as seawater. Fig. 5 shows isopycnals of seawater with temperature and salinity changes to help illustrate density's dependence on salinity. At most temperatures the density of a lake's water is heavily dependent on the temperature of the water. However, in the temperature range near TMD, f r approaches 0. In this range, changes in density are less sensitive to changes in temperature, and salinity effects may become important. The salt content of freshwater lakes must be considered when calculating density in deep lakes such as Quesnel Lake where much of the water has temperature near TMD throughout the year (Fig. .6 a). Millero (2000b) proposes that using the equation of state for seawater at low salinities for lake water with the same salinity is adequate. He argues that the changes in the properties of low salinity solutions are independent of the specific salt added because, when diluted, the ion-ion interactions of salts in solution are reduced. He compares relative density (pin-suu \u2014 pmean) calculated based on the composition of 10 Salinity (\u00b0\/ ) Figure 5: Plot showing the dependence of density on temperature and salinity using seawater at low salinities for illustration. The horizontal dashed line marks TMD-Contour interval is lkg\/m?. This plot is based on the equation of state.developed for the limnological range in Chen and Millero (1986) at atmospheric pressure. Lakes Baikal (S=0.0963 % 0 ) , Malawi (S=0.205 \u00b0 \/ 0 0 ) , and Tanganyika (S=0.568 \u00b0 \/ 0 0 ) with the relative density for seawater diluted to the same total salinity and finds that the values agree to within the error inherent in the seawater equations. He concludes that lake salinity can be taken to have the same composition as seawater diluted to the same concentration of total dissolved solids as the lake water being studied. This approach for brackish Lake Issyk-kul ( S = 6 . 0 6 \u00b0 \/ o o ) was disputed by Vollmer (2002) who showed that, at this concentration, the proportion of the ions dissolved is important and so the composition of the lake must be considered. In order to use any equation of state, a water body, ocean or lake, must have a composition with a constant proportion of concentrations. As the total concentration 11 of ions change, the individual ions dissolved in the water must change at the same rate in order to maintain constant proportionality of ions and apply an equation of state. Changes in conductivity must reflect changes in both ionic and non-ionic constituent concentrations. McManus et al. (1992) discuss the issue of constant relative compo-sition in their study of Crater Lake. The concentration of silicic acid, a non-ionic constituent introduced to Crater Lake via submerged thermal vents, was compared to the concentration of a strong electrolyte (Na +) meant to represent the lake's ionic salinity. McManus et al. (1992) showed that in Crater Lake silicic acid varies directly with ionic constituents and, therefore, variations in specific conductance will reflect the variations in overall concentration of dissolved solids. The proportional varia-tion of ionic and non-ionic constituents is assumed in studies of other lakes (Vollmer et a l , 2002b; Hohmann et al., 1997; Wuest et al., 1996). If this were not the case, the non-ionic contributors to salinity could not be parameterised in terms of easily measured quantities such as those measured by a C T D . The only alternative would be to measure non-ionic constituent concentrations directly. 2.2.3 Pressure Pressure plays a role by mechanically increasing density due to compression. Because cold water is more compressible than warm water, TMD decreases with increasing pressure. Fig. 6b shows the relationship between pressure and TMD- In deep lakes, renewal processes may take longer than in shallow lakes because bottom water is constrained by the pressure dependence of TMD- For example, as surface water cools below 4 \u00b0C, it will not mix downwards because it is less dense than water at TMD below. Cool bottom water (i.e. T < 4\u00b0C) will not mix upwards because it is closer to TMD when under pressure. In this way, interaction between surface and bottom waters can be suppressed. Small variations in the temperature profiles of Fig. 6b may or may not represent instabilities. The fluctuation in temperature may be compensated by a fluctuation in salinity resulting in a stable profile. Only with the use of an accurate equation of state 12 Figure 6: (a) Temperature profiles in East Arm of Quesnel Lake from 2001 to 2003. (b) Blow up of temperature profiles over temperature range of 3 to 4 \u00b0C. can instabilities be identified. Once density profiles are established, quasi-density and the Brunt-Vaisala Frequency will be used to locate instabilities. In this way, mixing in Quesnel Lake can be analysed. 2.3 Relationships 2.3.1 Relating Conductivity to Specific Conductance Conductivity, the ability of an aqueous solution to carry an electric charge, is de-pendent on the concentration of ions present, and on the temperature and pressure of the solution. Often, measured conductivity is converted to specific conductance at a reference temperature and pressure. Doing this removes the temperature and pressure signals and leaves only a conductivity signal that reflects the concentration 13 of ionic constituents. In North America, the reference temperature and pressure for specific conductance are T = 25\u00b0C and p = 0 bar, respectively (Physical and Aggre-gate Properties, 2000). A conversion between the measured in-situ conductivity, C\u00a3, to the specific conductivity, C ^ , can be approximated by: Cr \u2014 fp \u2022 fr \u2022 C\u00b05 (3) where fp is the temperature-dependent pressure correction, which accounts for the increase in conductivity due to compression of water, and fr is the temperature cor-rection, which accounts for the dependence of conductivity on temperature for a given composition (Wuest et al., 1996). This conversion is analogous to the conductivity ratio, r, used by oceanographers (Perkin and Lewis, 1980) (See Eq. 2). Bradshaw and Schleicher (1965) experimentally determined an empirical relation-ship between pressure and the electrical conductance of seawater. Other researchers (e.g. Wuest et al., 1996; Hohmann et al., 1997) who have studied deep lakes have extended Bradshaw and Schleicher's formula to low salinities through linear extrap-olation and applied it to their respective lake waters. In addition, Hohmann et al. (1997) experimentally verified the extrapolated values. The temperature and pres-sure sensors of a C T D were wrapped in plastic before it was lowered to keep the same water parcel throughout the depth of the profile. The change in electrical conductiv-ity with pressure was measured directly. The experiment yielded pressure correction values that are remarkably close to the extrapolated values for the same parameter (Hohmann et a l , 1997). In his study of Lake Issyk-Kul, Vollmer (2002) uses a pres-sure dependence that is developed specifically for this lake in order to eliminate small errors that are introduced by using equations developed for seawater. In the present study, for lack of a study that is more appropriate for describing pressure effects in lakes, the formula developed by Bradshaw and Schleicher (1965) extrapolated to low salinities was used to determine the pressure correction factor fp, in the equation of state for Quesnel Lake. The temperature correction depends on a lake's composition and so must be found 14 specifically for each lake. The temperature correction is determined by finding the ratio of conductivity at zero pressure, Cj. , to C$5 over a range of temperatures, at a fixed pressure (P = PatmosPheric = Odbar) and then fitting this data to a function. Researchers have found the temperature correction both experimentally and analyti-cally. Gray et al. (1979) and Johnson (1989) did this experimentally by measuring the conductivity of a sample of lake water over a range of temperatures in a laboratory and then fitting the collected data to a function to find the form of fT. Analytically, the temperature correction is determined by analysing a water sample for ionic com-position, pH and alkalinity and using the collected data to calculate conductivity over a range of temperatures. This procedure was outlined in detail by Wuest et al. (1996) and used by Hohmann et al. (1997). There are a variety of functions that can be used to fit the conductivity and temperature data. Standard methods suggest the following form for this relationship: fT = % = \\+.*{T-2S) (4) \u00b0 2 5 where a is a temperature coefficient, calculated for individual water samples. Other forms that can be used are an exponential function (Gray, 1979) or, more commonly, a polynomial form (Wuest et al., 1996). The analytical method will be applied to Quesnel Lake water samples overO to 25 \u00b0C, the natural temperature range found in Quesnel Lake and will be described in more detail in Section 3. 2.3.2 R e l a t i n g S p e c i f i c C o n d u c t a n c e t o S a l i n i t y Rather than convert conductivity data to specific conductance, McManus et al. (1992) directly related salinity to temperature and in-situ conductivity using a least squares regression. A more common method is to relate salinity to specific conductance through one of two ways. For a dilute solution, a relationship between specific con-ductance and salinity is approximated to be linear (Sorensen and Glass, 1987) as was done for Arrow Lakes by Wuest (1999). Alternatively, if more precision is required, 15 a temperature dependent third order polynomial can be used as was done by Wuest et al. (1996) for Lake Malawi and Hohmann et al. (1997) for Lake Baikal. Quesnel Lake, which is ultra-oligotrophic, has ion concentrations that are low enough to make ion-ion interactions negligible and for this reason, salinity is assumed to be linearly related to conductivity. 2.3.3 Relating Salinity to Density To calculate density in seawater, U N E S C O (1981) recommends using the equation of state developed in 1980 (EOS80) for temperatures between -4 and 40 \u00b0C, pressures between 0 to 1000 bar and salinities between 0 to 40 \u00b0 \/ 0 0 . Developed separately, Chen and Millero (1977b) initially presented an equation of state suitable for limnological systems based on temperature and pressure effects of fresh water combined with seawater effects on salinity. This limnological equation of state assumes that a lake's salt composition is identical to that of seawater, but diluted to the same concentration (Chen and Millero, 1977b). This equation was modified to have a claimed accuracy better than 2 x 10 _ 6g- c m - 3 and re-presented, along with relationships for other P V T properties such as thermal expansibility, isothermal compressibility and temperature of maximum density by Chen and Millero (1986). The equation of state presented by Chen and Millero (1986) specifically for the limnological range will hereafter be referred to as E O S C M - E O S C M , which was used by McManus et al. (1992) for Crater Lake, is valid for limnological ranges of temperatures between 0 and 30 \u00b0C, pressures between 0 and 1700 bars and salinities between 0 and 0.6 \u00b0 \/ 0 0 . E O S C M does not consider the unique composition of lakes. Millero (2000a) later suggested that one possible way to deal with the differing composition of water is to use an existing equation of state for seawater composition with a correction in density for added solutes. Reseachers including Wuest et al. (1996) and Hohmann et al. (1997) have found corrections for their respective lakes by determining an adjusted coefficient of haline contraction and using it in E O S C M - The coefficient of haline contraction, 16 8, defined by: describes the influence of salinity on density, i.e.: (5) p = Po(l + p-S) (6) where p0 is the average density. Wuest et al. (1996) found the coefficient of haline contraction for Lake Malawi at p=0 bar and T = 2 5 \u00b0 C was 1.028 times greater than that found by E O S C M due to the stability, Wuest et al. (1996) use E O S C M with B M a l a w i = 1.028 \u2022 pChen+Muiero i n p l a c e of pChen+Muiero_ Hohmann et al. (1997) use the same method. The method outlined by Wuest et al. (1996) will also be applied to Quesnel Lake. Density can also be measured directly. Fisher (2002) used density, measured with a densitometer, to back calculate the salinity of Island Copper Mine pit water samples. Grafe et al. (2002) showed that density can also be measured in-situ to an accuracy of pm 1 kg\/m 3 with an ultrasonic pulse transmitted through a quartz glass cylinder and received by a piezo ceramic. Direct density measurements of Quesnel Lake water were done with a densitometer to verify the lake-specific relationships for salinity and density developed in this paper. Local vertical stability is described by Imboden and Wuest (1995) as a condition in which, if a water parcel is displaced isentropically by a small vertical distance, it re-turns to its original depth due to buoyancy forces. Because pressure plays a large role in determining in-situ density, profiles of density often increase monotonically simply because of the compressibility of water. In situ-density is not a good representation of stability because, if a water parcel experiences forcing (i.e. internal waves), it could be displaced vertically and its density would change due to pressure.. This change in density in the displaced parcel could result in a non-monotonically increasing, or differing composition from dilute seawater. In calculations for density structure and 2.4 Profile Stability 17 unstable, density profile. In order to address water column stability, in-situ density is often converted into a quantity that allows for easy comparison of densities of water parcels experiencing different pressures. Three such quantities are described below. 2.4.1 Potential Density Often, potential density, ppotentiai, the density a water parcel would have it if were moved isentropically from its original pressure to a reference pressure, is used to remove the compression effect on density and allow comparison of water parcels within a C T D profile (Stansfield et al., 2001; Wuest et a l , 1996; McManus et a l , 1996). For potential density, the integrated adiabatic lapse rate of the parcel between the original position and reference pressure is subtracted from the in-situ density. Ppotential(z, Zr) = p(z) - J <&(z,z')dz' (7) where z is the depth (positive upwards), zr is a reference depth, and \\& is the adiabatic lapse rate for density of a water parcel undergoing isentropic transport, defined by: . T \/ \/ R , N rdp[d(zuz2),S(z1),p(z2)} *\\.zliz2) \u2014 \u2014\\ 1 jisentropic- {\u00b0J az2 where 6 is potential temperature, the temperature a water parcel would have it if were moved isentropically from its original pressure to a reference pressure. However, because potential density is a path-independent quantity, the second term reduces to two simple terms and the expression for ppotentiai simplifies to: Ppotentializ, ZT) = P(z) + (P(S, 0, 0) - P(z)) = P(S, 6, 0) (9) 2.4.2 Quasi-Density Quasi-density, pquasi, introduce by Peeters et al. (1996), also removes the compression effect on density. Peeters et al. (1996) define quasi-density as: Pquasi(z, Zr) = P{z) - J \" z')dz' (10) 18 Temperature Figure 7: (a) Illustration of important variables for potential and quasi densities, (b) Illustration of water parcel-being moved through TMD when calculating potential density. Quasi-density differs from potential density by comparing in-situ density with the integrated adiabatic lapse rate of the background water through which the parcel would pass if moved between the original pressure and a reference pressure. Fig. 7a illustrates the difference between potential density (i.e. if parcel 1 was moved to the surface without interacting with its environment) and quasi-density (i.e. if parcel 1 was moved to the surface while interacting with its environment such as parcel 2 at Z=Z'). Considering a parcel's interaction with its environment makes quasi-density path-dependent. A vertical path is assumed in its calculation. Quasi-density has no physical representation making it more difficult to conceptualise than potential density. 19 The reference depth often used in limnology and oceanography is the surface (i.e. zr = 0). For potential density, a water parcel's density is determined at the surface which is equivalent to calculating the parcel's thermal expansion coefficient, a = y^f, at the surface: p = p0(l + BS-aT) (11) However, because a changes sign at TMD, calculating a deep water parcel's a at the surface can cause sign errors to occur (Fig. 7b). Quasi-density takes into account the water surrounding the water parcel, and it's stability is determined locally so the sign errors, introduced in potential density, are avoided. Near TMD, potential density is not adequate for determining stability (Ekman, 1934), whereas quasi-density gives accurate vertical structure in the water column (Peeters et al., 1996). Peeters et al. (1996) argues that quasi-density, is the quantity most appropriate for the comparison of density from various depths in deep lakes that reach temperatures near TMD-Quasi-density was used by Hohmann et al. (1997) for Baikal and will be applied to Quesnel Lake C T D profiles in the present work. 2.4.3 Standard Density Foster (1995) also introduced a quantity that removes the compressibility signal from in-situ density. Standard density, D, defined in Eq. 12, assumes that the measured water parcel's density's pressure dependence is linearly related to the pressure de-pendence of a reference water parcel. This is described by Foster's Eq. 1 replicated here: D(S, T, P) = p(S, T, P) \u2022 4 | ^ 4 (12) p{S0,T0,P) where D is the depressurised standard density, S0 and T0 are the salinity and tem-perature of the reference water parcel respectively. Foster (1995) chose SQ \u2014 35 and T0 = 0\u00b0C which are close to the measured temperature and salinity of the water in his study. He also suggests that standard density should be used only for small ranges of temperature and uses standard density to investigate deep water formation in the Antarctic in the temperature range of -2 to +2 \u00b0C. 20 2.4.4 Briint-Vaisala Frequency The Briint-Vaisala frequency, N, also known as the stability frequency, is the fre-quency at which a parcel will naturally oscillate if displaced from a position of neutral buoyancy. The stability, E, is proportional to N 2 and so is important in identifying where instabilities occur in the water column (Millard et al., 1990). N 2 is defined according to Eq. 13 (Imboden and Wuest, 1995). N> = - 9 - . 9 \/ . (13) p oz When N2 > 0, the water column is stable, when N2 < 0 the water column is unstable (Gill, 1982). Millard et al. (1990) describes various common ways of calculating N 2 from C T D measurements and compares the results. Peeters et al. (1996) calculated the Briint-Vaisala frequency according to its definition (Imboden and Wuest, 1995) using quasi-density in the place of potential density (Eq. 14). = r L _ . d y n a s t ^ Pquasi 9z Because quasi-density provides only local stability information, the Briint Vaisala frequency calculated with quasi-density also only provides information on local sta-bility. By taking the derivative of pquasi with z, the following expression is found (Eq. 24 from Peeters et al. (1996)): dpquasi _ ,dp _ dp . . dz ~{dz)isen dz 1 ' Term 1 on the right hand side is the change in density with depth, or adiabatic lapse rate of density, of a parcel of water moved a finite distance isentropically through the water column. It is compared with term 2 on the right hand side which is the adiabatic lapse rate of density of the surrounding water moved the same distance. Fig. 8 helps to illustrate the stability criteria. If the change in density of the water parcel (term 1 in Eq. 15) over the distance Az due to a change in pressure is smaller than the change in density of the surrounding water (term 2 in Eq. 15), the parcel 21 p 3 (PJ) p 3
Density (Kg\/mJ 100 200 300 400 500 P S - P S = o -(c) 0.069 0.07 Density difference (Kg\/m3) Figure 18: Comparing density with and without Quesnel Lake salinity contribution: (a) T and S profiles from the deep basin of Quesnel Lake, 2001. (b) Profiles of density, with and without the contribution from S. (c) Difference betwen density estimated using S calculated using Eq. 35 and density estimated with S=0. Fig. 18a shows T and S profiles from the deep basin of Quesnel Lake. Below approximately 100m, the temperature roughly follows TMD- At temperatures near TMD, the thermal expansion coefficient is near-zero, and so small salinity effects play an important role in determining water column stability. To illustrate this, Fig. 18b shows the corresponding profiles of density, both with and without the contribution from salinity and Fig. 18c shows the difference between these two curves. This differ-ence highlights the importance of salinity's contribution to density in understanding' vertical mixing processes in the deep waters of Quesnel Lake. 44 4.3.2 Quesnel Lake's Equation of State E O S C M is modified for Quesnel Lake salinity according to Eq. 29 to produce EOSQ\/ , : PQuesnel = 0.9998395 + 6.7914 \u2022 10~ 5 \u2022 T - 9.0894 \u2022 10\" 6 \u2022 T2 \u2022, \u2022 +1.0171 \u2022 10~ 7 \u2022 T 3 - 1.2846 \u2022 10~ 9 \u2022 T 4 \u2022 \u2022 \u2022 +1.592 \u2022 10~ U \u2022 Tb - 5.0125 \u2022 10\" 1 4 \u2022 T 6 \u2022 \u2022 \u2022 +1.096 \u2022 (8.181 \u2022 10~ 4 - 3.85 \u2022 10~ 6 \u2022 T + 4.96 \u2022 10~ 8 \u2022 T2) \u2022 S. (41) where S is determined from C T D data using a lake-specific equation (eq. 35). 4.3.3 Error Fifteen samples taken throughout Quesnel Lake have been analysed to find fr. Since this function is dependent on composition and since they have been taken from differ-ent parts of the lake, the question remains: to what accuracy can density be estimated from C T D data using a single equation of state? Error is introduced into .the developed E O S Q L by many avenues. They include the following: \u2022 Error in the original measurements by PESC of concentrations of the major ions dissolved in Quesnel Lake; \u2022 Error is introduced by using marine equations to find concentrations of compo-nents of the carbonate system for Quesnel Lake water; \u2022 Error is introduced in the fitting process of polynomials to limiting equivalent conductivity and reduction coefficients data; \u2022 E O S Q X has been found based on the composition of 15 samples taken from various places around Quesnel Lake, because some variability exists between these samples, E O S Q L , which is based on the average, will not be specific to different lake regions; 45 \u2022 Variability exists in the plot of Si vs. Ca (Fig. 13) showing that the assumption that they are regularly proportional is inaccurate, and; \u2022 The charge balance for the average composition of the 15 samples is not zero, which may have an impact on the coefficient of haline contraction, 3, determined in E O S Q L . To assess error in E O S Q L , calculated densities were compared to densities mea-sured directly with an Antor Paar densitometer. To calibrate the densitometer, the density of D D W was measured. Table 5 shows the expected and measured results of these measurements. Based on the root mean square of the differences between the expected and measured values, an offset of 2.6 x 1 0 - 6 g\/cm 3 was assumed in subsequent density measurements. Table 5: Measured Density values of distilled, deionized water (DDW) used to cali-brate the Anton Paar Densitometer , Density of D D W Expected g\/cm3 Measured g\/cm3 0.998203 0.998204 0.998205 0.998205 0.998206 0.998207 The results of density measurements of all Quesnel Lake water samples collected in July 2003 and June 2004 are shown in Figures 19 and 20. Fig. 19 shows measured densities and densities calculated with E O S Q L along with a 1:1 line. The outlier in the upper right hand corner of the plot was taken at the Niagara Creek inflow to Quesnel Lake's East Arm. This water had high silt content at the time of collection which may account for its uncharacteristically high specific conductivity. The linear correlation coefficient of the data in Fig. 19, excluding 46 the outlier, is B? = 0.929 indicating that 93% of the variation in density can be explained with the 1:1 line. This correlation coefficient is close to 1 suggesting a linear relationship between measured and calculated densities. Also, to assess the need of developing a lake specific equation of state, densities calculated E O S C M were compared to densities calculated with E O S Q L and densities measured with the densitometer (Fig. 20). Although the densities calculated using E O S Q L are often on the low end of the measured values, they are within the esti-mated error of the measured values. Also, the density values calculated with E O S Q \u00a3 are closer to the measured valued than those calculated with E O S C M - The standard deviation between measured values of density and those calculated with EOSQZ, is 0.0018 kg\/m 3 . The standard deviation between measured values of density and those calculated with E O S C M is 0.0157 kg\/m 3 which is signficantly larger than that cal-culated with EOS<2\u00a3. E O S C M describes Quesnel Lake water density less accurately than reported by Chen and Millero (1986). The outlier samples (samples 7 and 8 in Fig. 20) are again apparent. Neither E O S Q L nor E O S C M accurately predict density for water in that area of the lake. 47 -1.65 -1.66 -1,67 -1.68 -1.69 n) - 1 7 -1.71 -1.72 -1.73 x measured vs. calculated - - 1:1 line R2=0.929 (ommitting outlier) X X -1.73 -1.725 -1.72 -1.715 Calculated o (kg\/m3 -1.71 -1.705 Figure 19: Measured and calculated densities for water samples collected from Ques-nel Lake in July 2003 and June 2004. The outlier in the upper right hand corner of the plot was taken at the Niagara Creek inflow to Quesnel Lake's East Arm. 48 -1.65 -1.66 -1.67 -1.68 \\ -1.69 ~ -1.7 -1.71 -1.72 -1.73 -1.74 I T * Chen and Millero EOS o Quesnel Lake EOS x Measured o o * * * * 1 1 * * * *\u2022 5 J 5 ? * * * * 8 10 12 14 16 18 Sample Number 20 22 Figure 20: Comparison of densities at T=20 \u00b0C and P=0 bar in Quesnel Lake: density measured directly with the Anton Paar densitometer; density calculated with E O S Q L , and density calculated with E O S C M - The outlier samples (samples 7 and 8) were taken at Niagara Creek inflow to Quesnel Lake's East Arm. Neither EOSQI, nor E O S C M accurately predict density for water in that area of the lake. 49 5 Local Stability Developing EOSQL was done in the interest of investigating the deep water ventilation in Quesnel Lake. A preliminary look at vertical mixing gives an indication of where and how this ventilation is taking place. For this reason, profiles of quasi-density and the Briint-Vaisala frequency have been found based on C T D profiles. Figure 21: A comparison of potential and quasi densities for C T D profile taken in 2001: a) plot of in-situ density, b) potential and quasi-density, c) zoom-in of potential and quasi-density. 5.1 Q u a s i - D e n s i t y Quasi-density profiles were found according the procedure explained in Section 3.7.1. Fig. 21 illustrates the importance of using quasi-density for investigating local stabil-ity. Fig. 21a shows a plot of in-situ density. The hydrostatic pressure is the dominant 50 signal in this density plot. In order to get a plot of a quantity that can be used to as-sess column stability and compare densities from within a profile, this pressure signal must be removed. Both potential and quasi-density serve this purpose and plots of both for a C T D cast taken in the East Arm in 2001 are shown in Fig. 21b. Both of these return a virtually vertical profile - one with no hydrostatic pressure signal. Once zoomed in (Fig. 21c), one can see that the potential and quasi-density plots are not perfectly vertical. The potential density plot shows that below the thermocline, den-sity gradually decreases thereby predicting a mostly unstable profile. Quasi-density predicts a profile which contains some instability but has nearly monotonically in-creasing densities and is stable. Quasi-density was shown to be more appropriate than potential density by arguments made in Section 2.4.2 and is supported by the validity of the pressure-free profiles predicted by each. In Quesnel Lake, quasi-density should be used to study local stability rather than potential density. Quasi-density was found from a C T D profile using E O S Q L and E O S C M to calculate in-situ density. Fig.22 shows this comparison. Quasi-density calculated with EOSQL is different than that calculated with E O S C M - However, the difference is primarily a simple offset in values; the structure of the profiles are still very similar. This will be explored further in Section 5.3 where the Briint Vaisala Frequency is discussed. Fig. 23 displays quasi-density profiles from the C T D data collected in the East Arm over three years (2001, 2002 and 2003) in order to gain insight into how the vertical structure in the water column varies over a period of time. Quasi-density profiles in the East Arm over the three year period all demonstrate very similar characteristics. Profiles have generally increasing slopes with density flucturations of simlar magnitude. Fig. 24 displays quasi-density profiles from the C T D data collected in July 2003 at each of the stations presented in Fig. 9 as well at the junction in order to gain insight on how vertical structure varies spatially throughout the lake. Quasi-density profiles from 2003, taken around Quesnel Lake, show different characteristics. The profile taken at the junction echoes characteristics of profiles taken in the North and 51 Figure 22: E O S C M and E O S Q L for C T D profile taken in 2001. Although density values are different, the water column stability is roughly the same in each profile. West Arms. For example, three small spikes in the West Arm profile at 65, 145 and 200 dbar are also present in the Junction profile at the same depths. A small step in quasi-density at 105 dbar in the North Arm is also present in the Junction profile at the same depth. 52 53 400' ' : 1 1 1 1 1 1 ' 0.044 0.046 0.048 0.05 0.052 0.054 0.056 Standard Density, D (kg\/m3) Figure 25: Standard density calculated by varying the temperature, T0, of the refer-ence parcel to temperatures bracketing TMD in Quesnel Lake (3\u00b0C to 4\u00b0C). 5.2 Standard Density The value calculated for standard density is very sensitive to which temperature is chosen as the temperature of the reference parcel and less sensitive to the reference parcel's salinity. Fig. 25 shows the standard density profiles calculated for the C T D cast collected at Quesnel Lake in 2001 with varying temperatures which bracket the variation in deep temepratures in Quesnel Lake chosen as the reference. Fig. 25 illustrates that the choice of reference temperature is critical to calculating a quantity that is meaningful for finding local stability in the water column. Standard density calculated from the 2001 Quesnel Lake C T D casts with T 0 = 3\u00b0C shows an almost entirely unstable profile while the same C T D cast calculated with TA = 4\u00b0C shows an almost entirely stable profile. 55 1.002 Density using QL-EOS, S=0 (g\/cm3) Figure 26: Density as a function of Temperature and Pressure (2D). The inset shows a blow up of the indicated region with bolded line illustrating the difference in slope between density gradients at 0\u00b0C and 7\u00b0C. The reason for this difference lies in the assumption that the change in density due to pressure at one temperature is equal to the change in density due to pressure at another temperature. Figures 26 helps to illustrate this point. Fig. 26 is a plot of density as a function of pressure with multiple lines showing this dependence for varying temperatures. The bold lines highlight the density gradients at two tempera-tures, one higher than TMD at 7\u00b0C, and one lower at 0\u00b0C. These lines are not parallel. The gradients of density with pressure are different at adjacent temperatures. This make it inappropriate to try to predict the change in density with pressure based on a parcel at a reference temperature different than the in-situ temperature with water neat TMD-Significant error would be introduced if standard density were calculated for a profile near 0\u00b0C with a reference parcel assumed to be at 7\u00b0C. This example illus-56 trates an extreme case and gradients do become more similar at closer temperatures. However, this difference in gradients is large enough near TMD to cause errors when using standard density to assess stability. Standard density performed well for the work Foster (1995) did in the Antarctic. He suggests that standard density is only valid for small temperature ranges. More accurately, standard density is only valid for small ranges of temperature away from TMD where the changes of density with pressure are more uniform for neighbouring temperatures. Because Foster (1995) is applying the standard density concept in salt water, water that will freeze before approaching its temperature of maximum density, the anomalies which occur near TMD in fresh water are inconsequential to his work. However, standard density cannot be applied to the investigation of deep water ventilation of Quesnel Lake water, whose water temperature mostly lies near TMD-5.3 I n s t a b i l i t y I den t i f i ca t i on Quasi-density is used to calculate the Briint Vaisala frequency in order to identify where density inversions occur. Quasi-density is noisy when calculated directly from C T D profiler data. Consequently, the Briint Vaisala frequency calculated from quasi-density is also noisy \u2014 too noisy to identify instabilities. To filter out noise and to gain a meaningful signal, the quasi-density profile is smoothed through bin averaging. The total change in density over the instability is less than the fluctuations in unfiltered quasi-density, illustrating the need to bin average. By identifying the trends in the quasi-density data over a resolution of interest, instabilities of that resolution size are identified. Fig. 27 shows a blown up section of the quasi-density profile with an inset of the entire profile. The blown up section of the profile also features the profile after bin averaging has been performed with various bin sizes. A power spectrum for this quasi-density profile is shown in Fig. 28 on a log-log scale. Because so many frequencies are present in the quasi-density profile in Fig. 27, the power spectrum plot was generated in order to determine if there is some obvious 57 250 0.056 0.058 0.06 no bin averaging -- binsize=2 dbar \u2014 binsize=8 dbar binsize=20 dbar J i 0.058 0.0585 0.059 0.0595 0.06 0.0605 Quasi Density, p ' \"quasi Figure 27: Quasi-density of C T D profile taken in 2003 in Quesnel Lake's Junction bin averaged to remove noise from signal into bin of sizes 2 dbar, 8 dbar and 20 dbar. The insert shows the entire profile. feature that could impartially help select a cutoff frequency for which signals with greater frequency could be considered noise. Fig. 28 displays frequency power data with a relatively constant negative slope and no such feature is present. Briint Vaisala frequency plots are examined with various frequencies filtered out using bin averaging. The Briint Vaisala frequency, N 2 , and its error have been found for three bin sizes: 2, 8 and 20 dbar (Fig. 29). The N 2 profiles where found using E O S Q L - For progressively smaller bin sizes N 2 becomes less noisy and its error also becomes smaller. The mean error in N 2 for profiles found with bin sizes 2 dbar, 8 dbar and 20 dbar are 5.5 x 10 - 7 s - 2 , 1.6 x 10 - 7 s~2, and 7.4 x 1 0 - 8 s - 2 respectively (see Section 3.7.3) . However, vertical resolution is lost in this process. It is crucial to know what size instability is of interest to know what size bin to choose. Choosing 58 io- 3 Wave Number, k (m') Figure 28: Power Spectrum for the unfiltered quasi-density profile taken in 2003 at the Junction in Quesnel Lake. too large a bin may reduce resolution to a point where instabilities of interest are no longer visible as was done for this profile with a bin size of 20 dbar. For the purpose of this study, a bin size of 8 dbar was used to compare N 2 profiles calculated from C T D profiles taken in Quesnel Lake's East Arm in 2001, 2002, and 2003. Also, N 2 profiles taken in 2003 from Quesnel Lake's three Arms, Junction and West Basin are also compared. From this series of profiles, one is able to deduce the resolution at which water column is completely stable. For example, the centre plot in Fig. 29 shows that when looking at a resolution of 8 dbar, there are some places in the profile that are slightly unstable. However, at a resolution of 20 dbar, the entire water column appears to be neutrally stable. 59 LO f o k< .Q T3 OJ o II d> N '(\/J C Figure 29: Briint Vaisala frequency of C T D profile taken in 2003 in Quesnel Lake's Junction found using Quasi-density averaged in to bins of sizes 2 dbar, 8 dbar and 20 dbar. The error in the Briint Vaisala frequency is also plotted for each of these bin sizes. 60 N2(p .(QL-EOS))-N2(p .(CM-EOS)) Figure 30: a)Briint Vaisala Frequency found using E O S C M and E O S Q \/ , for C T D profile taken in 2001, b) the difference between N 2 calculated with \/ ^ u a s j (EOSQ^) and Pquasi ( E O S C M ) . Fig. 30 shows N 2 calculated for the profile taken in 2001 (for comparison with profiles featured in Fig. 22) with quasi-density using both E O S Q X and E O S C M for comparison as well as the difference in the two quantities. The two equations of state predict very similar profiles. The difference indicates that E O S Q L shows greater stratification through the water column and so estimates that instabilities are more unstable and that stabilities are more stable than what E O S C M estimates. How-ever, the structure (i.e. gradient) predicted by the two equations of state are nearly indistinguishable. Fig. 31 shows N 2 calculated with both potential and quasi-density for comparison based on densities calculated with EOSQ\/_,. In Fig. 21, potential density portrays a profile with an unstable region (i.e. positive slope) below approximately 250 m. This is echoed in N 2 profile of the potential density profile. 61 0 50 100 150 bar) 200 CD 250 CO W CD 300 CL 350 400 450 500 5= * -5 N 2 (s- 2) 4 5 x 10~7 Figure 31: Briint Vaisala Frequency found using ppotentiai and.pquaSi- for C T D profile taken in 2001. \u2022 62 Fig. 32 displays N 2 profiles from the C T D data collected in the East Arm over three years (2001, 2002 and 2003) in order to gain some perspective how the vertical structure in the water column varies over a period of time. Fig. 33 displays N 2 profiles from the C T D data collected at each of the stations presented in Fig. 9 as well at the junction in order to gain some perspective on how vertical structure varies spatially throughout the lake. Again, N 2 profiles in the East Arm.over the three year period all demonstrate very similar characteristics. Profiles indicate that the majority of the water column below approximately 50 m is close to being neutrally stable, save some locations in 2001 and 2002 where the profile becomes slightly unstable. N 2 profiles from 2001 and 2002 both exhibit these unstable regions near 400m depth. Quasi-density profiles taken in 2003, from the different areas around Quesnel Lake, show differing characteristics. The East Arm profile has N2 ~ 0 s - 2 below 50 m. Compared to other areas in Quesnel Lake, the East Arm is relatively neutrally stable. This may be an indicator as to how deep water ventilation is taking place in this region of the lake. 63 to hrj O O CTQ H - 1 Pi l-S t o \u00ab O CO o t o t o \u2022 \u2022 O B CO 0 O-to o o 00 5' i CD >-i P= 00 CD CL o CD Cd < P; 00 P-CD CD O CD ex o O H O o B C D \" CO 2001 N 2 ( \u00b0 s - 2 ) X 1 0 - 7 2002 \\ J fj '> \u2022-* > r* V 0 50 100 150 200 250 300 350 400 450 2 \u00b0 5 N