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Mixing in brackish lakes due to surface ice : a physical model Bluteau, Cynthia Evelyn 2006

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Mixing in Brackish Lakes due to Surface Ice A Physical Model by C y n t h i a E v e l y n B lu teau B . E n g . , M c G i l l Universi ty, 2004 A T H E S I S S U B M I T T E D I N P A R T I A L 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 Master of A p p l i e d Science i n T h e Facul ty of Graduate Studies ( C i v i l Engineering) T h e Univers i ty of B r i t i s h C o l u m b i a October 2006 © C y n t h i a E v e l y n Blu teau , 2006 Abstract T h e effects of salt expelled by surface ice upon formation are investigated i n the laboratory to determine whether i t promotes meromixis i n lakes. T h e experiments consist of creating surface ice in an insulated container and le t t ing i t melt, while taking a t ime series of temperature measurements at different depths. T h e model lake has dimensions 0.34m x 0.18m x 0.3m depth and is sufficiently well insulated to allow the formation of an reverse temperature stratification i n the water column. T h e experiments start w i t h wel l -mixed saline solution at room temperature. In i t ia l sal ini ty ranges from O g L - 1 to 15 g L - 1 of potassium chloride. In a l l experiments, significant mix ing occurred beneath the ice dur ing its formation. T h e ice expels salt creating colder, more saline and hence denser water below the ice, which then mixes w i t h warmer water located at depth. A n unstable temperature stratification, supported by the accumulat ion of saline waters near the bo t tom of the lake, is present after the ice is completely melted. T h e propor t ion of salt expelled from the ice is a function of the in i t i a l lake salinity, as are the details of the c i rcula t ion under the ice. i i Contents A b s t r a c t i i Contents i i i L i s t of Tables v L i s t of F igures v i L i s t of A b b r e v i a t i o n s i x Acknowledgements x Co-au thorsh ip statement x i 1 I n t roduc t ion 1 1.1 General Int roduct ion 1 1.2 Theoret ical Background 2 1.2.1 Temperate freshwater lakes 3 1.2.2 Properties of Saline Solutions 6 1.2.3 Salt exclusion from ice 8 1.3 Li terature Review 10 1.3.1 M i x i n g caused by salt exclusion from ice: field studies 10 1.3.2 Double-Diffusive Convect ion 13 B i b l i o g r a p h y 17 2 M i x i n g i n b rack i sh lakes due to surface ice 21 2.1 Introduct ion 21 2.2 Methods 22 2.2.1 Exper imenta l apparatus 22 2.2.2 Temperature t ime series 23 2.2.3 T i m e of ice formation 24 2.2.4 General details of experiments 24 2.2.5 Discrete sal ini ty measurements 26 2.2.6 Ice sal ini ty and salt-balance 26 2.2.7 Heat flux computat ions 26 2.3 Results 27 2.3.1 Salt-balance 27 2.3.2 Temperature t ime series 28 2.3.3 Sal in i ty profiles 38 2.4 Discussion 38 2.4.1 M i x i n g processes 38 2.5 Conclusions 45 i i i Bibliography 46 3 Conclusions and Recommendations 48 Bibliography 50 A Equation of State 51 A . l Determining Sal in i ty 51 A . l . l T w a n d T / 53 A . 2 Determining Densi ty 54 B Experimental Results 59 B . l T r i a l , T , Exper iments 61 B . l . l 2D Nature 61 B . l . 2 Slower Coo l ing 61 B.1.3 Ex tend ing Coo l ing 63 B . 1.4 Insulat ion Test 65 B .2 Pre l iminary , P, Results 66 B . 3 F i n a l , F , Results • • • • 66 C CT vertical profiles 82 C . l M S C T I Ca l ib ra t i on 82 C . 2 Challenges 83 C . 2.1 Temperature Sensor 83 C . 2.2 Conduc t iv i ty Sensor 85 D Heat Fluxes 88 D . l Theoret ical Heat Fluxes 88 D . l . l Governing Equat ions 88 D.2 Heat F l u x Computa t ions 92 D.2.1 Es t ima t ing wal l heat resistance, Rw 92 D.2.2 Es t ima t ing experimental qtot 96 D.2.3 Con t r ibu t ion of ind iv idua l heat fluxes terms 98 iv List o f Tables 1.1 Densi ty difference between water at the Tmd and water at Tf for various salin-ities. T h e th i rd co lumn shows the corresponding sal ini ty increase required to overcome the s tabi l iz ing reverse temperature stratification. Values were computed w i t h the equation of state for seawater at atmospheric pressure {UNESCO, 1981) 8 2.1 Exper iments undertaken w i t h temperature t ime series measurements, along w i t h corresponding salt balance results. *Salinity measurements were taken i n experiments conducted at this salinity. ^ A n experiment was conducted w i t h two moorings at this sal inity 28 2.2 Average heat fluxes dur ing each phase. A negative sign represents heat lost. *Rough estimate since water temperatures i n phase III in i t i a l ly cool before warming 33 2.3 Densi ty difference between water at the Tmd and water at Tf for various salinities. The th i rd co lumn shows the corresponding sal ini ty increase re-quired to overcome the s tabi l iz ing reverse temperature stratification. T h e last co lumn shows the tota l mass of salt expelled from the ice dur ing phase II. Values were computed w i t h the equation of state for potassium chloride at atmospheric pressure 42 A . l Conduc t iv i t y of pure water and potass ium chloride aqueous solutions i n m s c m - 1 as a function of temperature (Lide, 2006) 52 A . 2 Tmd and Tf da ta for potassium chloride aqueous solutions (Lide, 2006; Wash-burn, 2003) 52 A . 3 Densities for potassium chloride solutions at various temperatures and con-centrations (Perry and Green, 1997; Lide, 2006) 57 B . l Exper iments done w i t h t ime series temperature measurements 60 D . l Exper imenta l heat losses dur ing au tumn cool ing for various experiments. . 98 v List of Figures 1.1 Equa t ion of state for fresh water at atmospheric pressure. T h e dashed line represents the Tm<j. T h e density of ice at 0 ° C is « 917 k g m - 3 4 1.2 T y p i c a l d imic t ic lake behaviour 5 1.3 Equa t ion of state for sea water at atmospheric pressure (UNESCO, 1981). Contours represent densities i n at (kg m ~ 3 ) as a function of sal ini ty and temperature. T h e dashed lines show the dependency of Tmd and the 7 / on salinity 7 1.4 Schematic of a meromict ic lake 8 1.5 Schematic of double-diffusive instabili t ies for brackish waters. Schematic of a) fingering regime, b) diffusive regime. Note: Twater < Tmd- F igure adapted from Ruddick and Gargett (2003). T h e green and red arrows show respectively the density fluxes associated to the transport of heat and salt. 15 2.1 Schematic of the model lake used to conduct the experiments 23 2.2 Tmd and Tf for potassium chloride aqueous solutions at atmospheric pres-sure. The markers represent the original da ta obtained from Lide (2006); Washburn (2003) 25 2.3 Temperature t ime series for an experiment conducted at 4 g L _ 1 . (a) A i r temperatures; (b) M o o r i n g water temperatures; (c) M o o r i n g water temper-ature when water temperatures are below 5 ° C . A and B represents a per iod of slower cooling preceded and followed by a sudden drop i n T . C is a typica l temperature fluctuation, suggesting heat exchange w i t h water above and at depth. The ice cover per iod is represented by the black rectangle 29 2.4 Z o o m on freezing regions of a l l salinities investigated. M represents the t ime when complete convective m i x i n g of the water co lumn occurred. A and B represents a per iod of slower cooling preceded and followed by a sudden drop i n temperature 31 2.5 Compar i son between recorded water temperatures and expected water tem-peratures when assuming that there is no convective movement i n the lake. The thicker smooth lines represent the expected water temperatures. T h e Tmd is represented by the solid black line 34 2.6 Z o o m on phase I V , thawing, for a l l salinities investigated. Event A represents the t ime when the fresh surface layer was deep enough to permit surface water temperatures to increase at a faster rate 37 2.7 Sal in i ty profile obtained from water sampl ing after ice melt-out for an ex-periment conducted at a) 1 g L - 1 and b) 2 g L _ 1 . T h e dashed line represents the sal ini ty profile before commencing experiments. T h e markers show the depth where the samples were taken. T h e error bars, which are smaller than the markers, represent the measurement error of 1% 38 2.8 Schematic of vert ical salt and heat d is t r ibut ion after (a) ice melt-out, (b) as surface water approach Tmd in i t ia t ing convective m i x i n g in surface and intermediate water, (c) when the surface halocline deepens and is eroded due to surface heating, and (d) when convective m i x i n g ceases i n surface and in-termediate water (phase V ) . T h e red and green arrows represent respectively heat and salt fluxes. T h e dashed lines show the previous profiles. Note that the increase i n sal ini ty at depth may be gradual, and not a sudden step as suggested by the salt profile 44 A . l Potass ium chloride concentration as a function of temperature and conduc-tivi ty. Contours represent salinities i n g L - 1 53 A . 2 Tmd and T ) for potassium chloride aqueous solutions at atmospheric pres-sure. T h e markers represent the or iginal da ta obtained from Lide (2006); Washburn (2003) 55 A . 3 Equa t ion of state for potassium chloride aqueous solutions at atmospheric pressure. The dashed line represents the Tmd 58 B . l Slower Coo l ing and spat ial var iabi l i ty (March 6, 2006 at 2 g L - 1 ) 62 B . 2 Slower C o o l i n g ( M a r c h 8, 2006 at 2 g L " 1 ) 64 B . 3 Ex tend ing Coo l ing ( A p r i l 11, 2006 at 4 g L - 1 ) . T h e l i d was opened but the freezer was not turned off un t i l 1 day after the beginning of the experiment. 65 B . 4 Insulat ion Test ( A u g 21, 2006 at 0 g L " 1 ) 67 B .5 October 24 at O g L " 1 68 B.6 December 7 at 1 g L " 1 69 B .7 November 16 at 1 g L ' 1 70 B.8 November 9 at 2 g L - 1 71 B . 9 November 2 at 4 g L " 1 72 B.10 November 8 at 8 g L " 1 73 B . 11 November 24 at 15 g L - 1 74 B.12 J u l y 19 at O g L - 1 75 B.13 M a y 23 at 1 g L - 1 76 B.14 M a y 29 at 1 g L - 1 . M i x e d the water co lumn to test the MSCTI from P M E 77 B.15 A p r i l 6 at 2 g L ~ 1 78 B . 16 A p r i l 19 at 4 g L " 1 79 B.17 J u l y 11 at 8 g L - J 80 B . 18 Augus t 30 at 15 g L " 1 81 C . l Temperature cal ibra t ion curve. In to ta l , 17 da ta points were used to obta in this cal ibrat ion curve 84 C.2 Compar i son of temperatures measured w i t h the MSCTI to temperatures obtained from the mooring. T h e left hand figures represent results from CT casts performed after ice melt-out, while the right hand side shows results from casts performed after spring mix ing 86 v i i D . l Theoret ical temperature dis t r ibut ion for freshwater, assuming heat losses only through the surface at Tf. Exper imenta l temperatures are represented by the thinner lines. T h e dashed line represents the Tmfi, while the solid line delimits phase I and II 94 D.2 Theoret ical temperature d is t r ibut ion assuming heat losses through the sur-face at Tf and boundaries. Exper imenta l temperatures are represented by the thinner lines. The dashed line represents the Tmd, while the solid line delimits phase I and II 96 D.3 qexp is the tota l heat fluxes according the recorded temperature readings dur ing phase I. qtotmin is the to ta l calculated heat fluxes assuming no latent heat losses (qc + qs + qr)- qtot'max is the calculated to ta l heat losses assuming the air is d ry (i.e. qiat is at its maximum) 100 D.4 Heat fluxes comparison between 2 experiments w i t h different insulat ing lay-ers. The dotted line represents an experiment conducted wi thout the addi-t ional fiberglass and styrofoam insulat ing layers. T h e solid line represents an experiment conducted w i t h the addi t ional insulat ion 101 v i i i List of Abbreviations ACS American Chemical Society CT Conductivity-Temperature CTD Conductivity-Temperature-Depth LED Light emitting diodes MSCTI MicroScale Conductivity and Temperature Instrument Tf Freezing Temperature Tm<i Temperature of Maximum Density THC Thermohaline circulation cell Tw Water Temperature Acknowledgements I would like to thank my supervisor, D r . Greg Lawrence, as well as Roger Pieters for their guidance and ideas through the complet ion of this thesis. I would also l ike to thank them for the encouragement i n the nai l -b i t t ing stages of wr i t ing this thesis. M y fellow students also provided helpful discussions related to p lanning m y experimental set-up and analysing experimental data. I would also like to thanks V i o l e t a M a r t i n , who was a great help i n and out the laboratory. Thanks to my family and friends for their support and encouragement through the pursuit of this degree. I a m grateful to have been supported through a P G S - M award from N S E R C . F ina l ly , thanks to Chr i s , for your encouragement and patience dur ing the final stages of this thesis. Co-authorship statement A l l the work presented i n this thesis was carried out by the author under the supervision of G r e g Lawrence and w i t h the guidance of Roger Pieters. T h i s work is or iginal , and references are made to existing literature. T h e ma in chapter of this thesis consists of a manuscript that w i l l be submit ted for publ ica t ion in the Journal of Limnology and Oceanography. Greg Lawrence and Roger Pieters provided suggestions dur ing a l l stages of this work, inc lud ing the preparation of this manuscript . x i Chapter 1 Introduction 1.1 General Introduction Most lakes i n the wor ld are much less saline than the oceans, which have a sal ini ty of approximately 34 g L - 1 . For example, Lake Ontar io i n the Great lakes system at U S -Canad i an border has a salinity of 0.21 g k g - 1 . Nevertheless other lakes can be saltier than the Ocean, notably Great Salt Lake (90 to 280 g L - 1 ) in the U n i t e d States and Lake E y r e i n Aus t r a l i a . Water-fi l led mine pits also tend to be more saline than lakes but less than the Ocean. Several mine-pits i n Canada are located i n northern regions where ice forms at their surface. They tend to be highly contaminated due to acid rock drainage and other contaminants result ing from min ing processes (Stevens and Lawrence, 1998). Water qual i ty of these lakes evolves continuously and it is important to understand the various physical processes that govern m i x i n g and redis tr ibut ion of contaminants, i n order to p lan remediation and manage these sites. A n important aspect of ice formation, which is the ma in topic of this research, is the rejection of brine to water under lying the ice. Br ine rejected dur ing ice formation increases sal ini ty below the ice, which can destabilize the water co lumn. Salt exclusion can cause transport of salt and heat from the upper layers to the lower layers of the lake; par t ia l ly or completely mix ing the water co lumn (Ferris et al, 1991; Gibson, 1999a,b; Willemse et al, 2004). T h e downwards transport of salt may also enhance meromixis i n water bodies by increasing sal ini ty at lower layers of the lake over time; increasing the overall s tabi l i ty of the water co lumn (Gallagher and Burton, 1988; Ferris et al, 1991; Miller and Aiken, 1996; Gibson, 1999a). T h e mel t ing of ice creates a fresh layer of water at the surface that increases 1 Chapter 1 the s tabi l i ty of the lake, promot ing meromixis . A wide variety of m i x i n g mechanisms have been postulated as a result of salt exclusion i n brackish and saline lakes. These m i x i n g mechanisms are explained later i n this chapter. T h e following chapters describe laboratory experiments, conducted to observe brackish ' lake' c i rcula t ion caused by salt exclusion from surface ice. A physical model was chosen for this purpose i n order to control the effects of bathymetry, weather conditions, ice product ion period, a l l of which can differ greatly from lake to lake. Chapter 2 describes the influence of sal ini ty on lake c i rcula t ion in i t ia ted dur ing ice product ion, and was wr i t ten as a draft for publ ica t ion i n a journal . T h e final chapter contains conclusions, which gives details for future work that s t i l l needs to be carried out to understand c i rcula t ion i n these lakes. 1.2 T h e o r e t i c a l B a c k g r o u n d T h e following sections w i l l describe the differences in seasonal behaviour of lakes having different concentrations of salt. In the following work, the effects of pressure on lake behaviour w i l l not be considered, i n order to focus on the m i x i n g caused by salt exclusion from surface ice. Pressure effects are important i n lakes deeper than « 100 meters. For this thesis, lakes were classified according to their salt content. Freshwater lakes are those that have salinities less than 0.5 g L - 1 , saline lakes have salinities greater than 24 g L - 1 , and brackish lakes are those w i t h salt concentrations between 0.5 g L - 1 and 24 g L - 1 . T h i s classification was used to differentiate between lakes where c i rcula t ion is affected by the temperature of m a x i m u m density ( T m d ) , and those where the Tmci has no influence (i.e. saline lakes). T h e l imi t between brackish and saline would depend on lake water specific ionic composi t ion, but for dilute seawater, the Tm<i is lower than the freezing temperature, Tf, at a sal ini ty of ~ 24 g L - 1 (see § 1.2.2). 2 Chapter 1 1.2.1 Temperate freshwater lakes T h e behaviour of freshwater lakes is controlled by the d is t r ibut ion of heat w i t h i n the water body. Pure water behaves differently than most l iquids i n that the temperature of m a x i m u m density (3.98 °C) does not coincide w i t h the freezing temperature ( 0 ° C ) . T h e equation of state for pure water at sea level, plotted i n Figure 1.1 using the equation developed by Chen and Millero (1986), shows that water at the temperature of m a x i m u m density, Tmd, becomes lighter when it cools or warms. T h i s behaviour facilitates ice formation on freshwater lakes, and inhibi ts freshwater lakes from freezing completely from top to bot tom. U p o n freezing, pure water also becomes less dense. T h e density of ice is ss 917 kg m - 3 compared to 999.868 k g m " 3 for pure water at Tf (Fischer et al, 1979). T h e Tmd has a large influence on annual c i rcula t ion i n freshwater lakes. In temper-ate regions, most freshwater lakes are dimic t ic . D i m i c t i c lakes are those that completely turn-over twice a year, i n au tumn and i n spring (Hutchinson, 1957). A schematic of the behaviour of a typica l d imic t ic freshwater lake is given i n Figure 1.2. D u r i n g the summer months, freshwater lakes usually have warm and well oxygenated surface water (epil imnion) separated from nutrient r ich bo t tom water (hypolimnion) that can be low i n oxygen due to degradation of organic matter. The stratification i n these lakes is due to solar heating of surface water, which causes the surface layer to become lighter. T h e warm surface waters are separated from the cold bo t tom waters by a thermocline. Since temperature is the pr i -mary stratifying agent i n freshwater lakes, the locat ion of the thermocline coincides w i t h the density gradient (pycnocline). A s the summer progresses, the ep i l imnion warms and deepens due to wind m i x i n g and entrainment of deep water. T h e bo t tom waters typ ica l ly remain close to the Tmd-W h e n au tumn cooling begins, surface waters become heavier, which erodes the thermo-cline and deepens the epi l imnion. Once the surface layer has cooled to the Tmd, the kinet ic energy provided by wind is capable of mix ing the entire lake. Lake turn-over permits redistr ibut ion of oxygen and nutrients at a l l depths of the lake. After au tumn turn-over, subsequent cool ing permits surface waters to stratify as the 3 Chapter 1 1000 E Water Temperature ( C ) Figure 1.1: Equa t ion of state for fresh water at atmospheric pressure. T h e dashed line represents the T m ( j . T h e density of ice at 0 ° C is sa 917 k g m ~ 3 . surface becomes colder than the Tmd. T h i s is called reverse temperature strat if ication to dist inguish it from summer stratification (Figure 1.2). S t rong winds can weaken or destroy the inverse stratif ication by making cold surface water m i x w i t h warmer water at depth. In some cases, this mix ing may permit bo t tom waters to become colder than Tmd. Nonetheless, continued surface cool ing w i l l cause surface waters to eventually reach the Tf and ice w i l l start to form. Ice usually forms first along the shallower edges of the lake and then progresses toward the center of the lake. Complete ice cover creates a barrier to w ind mix ing , inh ib i t ing mix ing beneath the ice dur ing the winter months. M a n y other processes such as strong river inflows (Carrnack et ai, 1986) and groundwater inflow can cause m i x i n g 4 Chapter 1 Summer stratification Autumn turn-over T I Epilimnion Winter reverse stratification Spring turn-over Figure 1.2: T y p i c a l d imic t ic lake behaviour in lakes dur ing winter, but w i l l not be considered here. T h e barrier to w ind m i x i n g caused by surface ice combined w i t h high oxygen demand can result in oxygen depletion and cause winter fish ki l ls (Rogers, 1992). Increasing i n solar radia t ion and warmer air temperatures at the beginning of spring melt the ice cover. Once completely melted, subsequent heating warms the surface waters making them heavier as they approach the Tmd. T h e s tabi l i ty of the water co lumn decreases unt i l enough kinetic w i n d energy is provided to m i x completely the lake. Then , the water co lumn has a uniform temperature approximately equal to the Tmti. Subsequent heating w i l l stratify the water co lumn dur ing the summer months as explained previously, unless w i n d energy is sufficient to destratify the water column. 5 Chapter 1 1.2.2 Properties of Saline Solutions A description of the seasonal behaviour of saline lakes requires an explanat ion of the effects of sal ini ty on the equation of state for lake water. A s sal ini ty increases, the Tmd decreases from the pure water value of 3.98 °C . The Tmd drops l inearly w i t h increasing sal ini ty and the slope of the linear relationship depends on the specific ionic composi t ion of lake water (Wuest et al., 1996). For d i lu ted sea water, the relationship between sal ini ty and Tmd is i l lustrated i n Figure 1.3. T h e equation of state for solutions containing potass ium chloride, KCL, is shown in A p p e n d i x A . For potassium chloride, the shape of the equation of state is s imi lar to Figure 1.3, except the contr ibut ion of KCl is equivalent to « 0.82 the sa l ini ty of di luted seawater. W i t h increasing salinity, the freezing temperature, Tf, of water also decreases. T h e relationship of Tf w i t h sal ini ty is approximately linear and again depends on the specific ionic composi t ion. T h e relationship is shown for d i lu ted seawater in F igure 1.3. T h e freezing temperature crosses the Tmd at a sal ini ty of approximately 24 g L _ 1 ( F i g u r e 1.3). T h i s means that water freezes before the Tmd is reached and reverse temperature strat-ification is no longer possible above this salinity. For saline water bodies devoid of any salt-stratification, the entire water co lumn needs to cool to Tf before ice can form, which explains why it is difficult for ice to form i n the oceans. In contrast, ice forms rapid ly i n freshwater lakes after reverse temperature-stratification is established, as only a shallow surface layer has to cool to Tf before ice can form. For the case of saline lakes that are salt-stratified, the behaviour is quite different. A stable salt-stratification can inhibi t lake turn-over. Lakes that don't tu rn over completely are classified as meromict ic (Hutchinson, 1957). M e r o m i x i s is usually a state that results from chemical stratification and is more common i n deep lakes. In meromict ic lakes the stagnant bo t tom waters or monol imnion is often oxygen depleted (Figure 1.4). T h e upper layers of the water co lumn or mixo l imn ion are well mixed at some point of the year and oxygenated due to w ind energy. In some instances meromixis is desirable, especially i n lakes where bo t tom waters and sediments are heavily contaminated. T h e contaminants become 6 Chapter 1 Salinity (g kg 1) Figure 1.3: Equa t ion of state for sea water at atmospheric pressure (UNESCO, 1981). Contours represent densities i n at (kg m - 3 ) as a function of sal ini ty and temperature. T h e dashed lines show the dependency of Tmd and the Tf on salinity. isolated from the lake surface and can be stored wi thout posing risks to b io ta l i v ing around and near the lake surface. T h i s is often the case of open mine pits that are filled w i t h water. The equation of state for sea water i n Figure 1.3 shows the dependency of density on sal ini ty and temperature. A t cold temperatures near the Tmd, density varies most ly w i t h sal ini ty (J^ —• 0). For example, the difference i n density between freshwater at the Tmd and freshwater at Tf is 0.133 k g m - 3 and has the equivalent effect on density as increasing sal ini ty from 0 to 0.163 g k g - 1 . For di lute seawater at 15 g k g - 1 , the difference i n density between freshwater at the Tmd and freshwater at Tf is 0.013 k g m - 3 , and has the equivalent effect on density as increasing sal ini ty by 0.015 g k g - 1 . T h i s smaller density difference 7 Chapter 1 P, s M i x o h m n i o n (mixed layer) Figure 1.4: Schematic of a meromict ic lake between water at Tf and Tmd at higher salinities is due to the more rapid decrease of the Tmd w i t h sal inity (Figure 1.3). Thus , lakes w i t h higher sal ini ty water have a weaker reverse temperature stratification, and are consequently less l ikely to support an unstable salt stratif ication (see Table 1.1). Sal in i ty ( g L " 1 ) A p ( T m d _ T / ) ( k g m " 3 ) A S ( g k g - 1 ) 0 0.133 0.163 1 0.122 0.149 2 0.111 0.137 4 0.091 0.112 8 0.056 0.069 15 0.013 0.015 24 0 0 Table 1.1: Densi ty difference between water at the Tmd and water at Tf for various sal ini-ties. T h e th i rd co lumn shows the corresponding sal ini ty increase required to overcome the s tabi l iz ing reverse temperature stratification. Values were computed w i t h the equation of state for seawater at atmospheric pressure (UNESCO, 1981). 1.2.3 Salt exclusion from ice A general description w i l l be given of the ma in factors that influence salt-exclusion upon ice formation i n brackish waters. T h i s is by no means a complete description of a l l en-8 Chapter 1 vironmental parameters (e.g. cooling rate, w i n d and water currents) that can affect ice structure, composi t ion and thickness. U p o n freezing, water becomes less dense by forming a crystal structure. The crystal latt ice makes it difficult for dissolved salts to remain in the ice upon freezing, unlike l iqu id saline solutions where salts can easily dissolve between polar water molecules (Eicken, 2003). T h e size and charge of typ ica l ions make them poor substitutes for water molecules i n the crysta l lattice, though there are exceptions such as sulphates. Hence, the crys ta l structure of ice forces dissolved salts to be excluded upon freezing. However, a smal l fraction can remain t rapped i n l iqu id inclusions w i t h i n the ice (Eicken, 2003). T h e propor t ion of salt present i n ice dur ing the freezing process depends main ly on the rate of freezing (i.e. air temperature), the in i t i a l sal inity of the freezing water, and the age of the ice (i.e. new ice versus multi-year ice). Higher freezing rates increase the amount of salt t rapped i n the ice. New sea ice created from seawater at 35 g k g - 1 w i l l have a sal ini ty between 7 g k g - 1 and 14 g k g - 1 , depending on the freezing rate (Gross, 1993). Older ice w i l l typica l ly contains less salt due to drainage of brines over t ime (Gross, 1993). Water at higher sal inity w i l l t rap a higher propor t ion of salt dur ing ice formation. In fact, this property explains the differences i n appearance between sea and lake ice (Eicken, 2003). New sea ice is generally whiter due to higher concentration of salts present i n the ice (~40% of the in i t i a l sal ini ty) . In contrast, lake ice formed from fresh water is transparent (black ice) since a large propor t ion of salt (>97%) is expelled dur ing its formation (Eicken, 2003). In this research, water sal ini ty was the pr inc ipa l variable affecting the propor t ion of salt expelled from the ice. T h e air temperature, and the age of the ice are constant due to the nature of the experiments performed (see § 2.2). 9 Chapter 1 1.3 Literature Review 1.3.1 Mixing caused by salt exclusion from ice: field studies Brackish lakes located at high latitudes are often ice-covered during part of the year. When ice forms at their surface, salts are excluded from the ice to the underlying water, which increases water salinity. Salt exclusion from surface ice has been reported to promote meromixis as well as mix the water column (Gallagher and Burton, 1988; Ferris et ai, 1991; Miller and Aiken, 1996; Gibson, 1999a,b; Willemse et ai, 2004). The field observations can be summarised as follows and will be explained in subsequent sections: • Density brine formed near shore can sink; increasing salinity at depth, which can in turn, promote meromixis • Creation of a isohaline and isothermal convection cell beneath the ice, initiating partial or complete mixing Stewart and Platford (1986) concluded that descending salt-fingers (see § 1.3.2) during ice formation were the main cause for hypersaline monolimnetic water found in Garrow Lake as well as Lake Sophia in the Canadian arctic. This conclusion was supported by high oxygen concentrations found below the chemocline in Lake Sophia, but has been I contested by Ouellet and Page (1987) who believe hypersaline groundwater is responsible for the presence of hypersaline brines (S~90 gkg -1) in Lake Garrow as first proposed by Page et al. (1984). These hypersaline groundwater are considered to result from freezing of seawater trapped by isostatic rebound (Ouellet et ai, 1989; Page et ai, 1984). This hypothesis is supported by previous work on Alaskan and Western Canadian Lakes done by Howard and Prescott (1973), which observed salt concentrations 10 to 20 times higher in pore water of adjacent soils than in lake water. In their study, they also found that pore water in adjacent soils had a ionic composition similar to the unfrozen lake waters (Howard and Prescott, 1973). In the present study however we will focus on the effects of salt exclusion on circulation. 10 Chapter 1 Dens i ty B r i n e F lows Gallagher and Burton (1988) proposed the creation of brine flows near the shallower edges of E l l i s F jo rd , Anta rc t i ca , as a mechanism to increase its stabil i ty. T h e dense brine flows travel along the basin walls un t i l reaching water of the same density; t ranspor t ing saline water to depth. T h i s phenomenon has been observed i n a smal l arctic lake using dye and conductivi ty-temperature-depth (CTD) profiles to trace water movements w i t h i n the lake (Welch and Bergmann, 1985). Evidence of these density currents were also found near the edges of Organic Lake, A n t a r c t i c a (Ferris et al, 1991). T h i s process was proposed to explain meromict ic conditions i n E l l i s F jo rd , A n t a r c t i c a (Gallagher and Burton, 1988) and ini t ia ted vert ical m i x i n g i n the water co lumn (Gallagher and Burton, 1988; Gibson, 1999a). Willemse et al. (2004) have found conduct iv i ty and temperature anomalies occur-r ing at deeper locations i n Store Salts0, Greenland, as the winter progressed; ind ica t ing that colder, more saline water was transported downward through the water co lumn by haline convection. Furthermore, Miller and Aiken (1996) have proposed density currents as a mechanism that introduced t r i t i u m into bo t tom water of Lake F ryxe l l , An ta rc t i ca . T h e presence of t r i t i u m suggests that a por t ion of the bo t tom water was i n contact w i t h the atmosphere because t r i t i u m results from anthropogenic emissions, which peaked in the 1950s and 1960s as a result of nuclear testing (Miller and Aiken, 1996). T r i t i u m was deemed to be a good tracer for water movement due to its short half life of 12.3 years (Miller and Aiken, 1996). Thermohaline Circulation Cells Researchers have suggested that salt excluded from surface ice creates thermohaline con-vection (THC) under the ice i n lakes, notably lakes i n the Vestfold H i l l s i n East A n t a r c t i c a (Ferris et ai, 1991; Miller and Aiken, 1996; Gibson, 1999b) and Store Salts0 i n Greenland (Willemse et ai, 2004). Thermohal ine convective is established when saline (and denser) water created below the ice mixes downward creating an isothermal and isohaline convec-t ion cell (Gibson, 1999b). Thermohal ine c i rcula t ion extends downwards as ice product ion 11 Chapter 1 persists dur ing the winter months, decreasing lake s tabi l i ty (Gibson, 1999b; Willemse et ai, 2004). The abi l i ty to m i x the entire body depends on the salt-stratification already present i n the lake; weaker salt-stratification permits THC to penetrate to deeper depths. There has been evidence suggesting that winters w i t h more ice product ion enhance vert ical m i x i n g i n saline water bodies like E l l i s F j o r d in the Vestfold Hi l l s of A n t a r c t i c a (Gibson, 1999b). Ferris et al. (1991) have also st ipulated that saltier surface water w i l l induce a m i x o l i m n i o n that penetrates to deeper depths than fresher surface water, preventing meromixis i n cases where a weak density gradient exists between the mixo l imn ion and the monol imnion . In brackish lakes the behaviour is sl ightly different. A layer of more saline and colder (T < Tm(i) water can remain stat ical ly stable over warmer and fresher bo t t om water. A n example of this would be Pav i l i on Lake, B r i t i s h C o l u m b i a . T h e lake has an average specific conduct iv i ty of 400 fiScm-1 (Lim et ai, 2006). C T D casts conducted i n M a r c h 2006 showed a slight decrease i n specific conduct iv i ty ( l O ^ S c m - 1 ) accompanied by an increase i n temperature from 2 ° C to 4 ° C from the surface to 35 meters (Lim et ai, 2006). Another example is Tai l ings Lake, a brackish lake ( S « 1 g L - 1 ) i n Nor the rn Canada . After fall turn-over, the lake became unstratified bo th i n temperature and salinity. However, periodic C T D profiles throughout the remainder of the year suggest that the water co lumn convectively mixed prior to the end of the winter due to exclusion of 99% of salt from the ice (Pieters and Lawrence, 2006). In fact, the overall sal ini ty i n Tai l ings Lake had increased dur ing the winter due to ice formation, and the salt d i s t r ibu t ion i n the water co lumn was uniform in M a r c h 2006, when CTD casts were performed (Pieters and Lawrence, 2006). A t that t ime, a slight reverse temperature strat if ication was present i n the water co lumn. T h i s reverse temperature stratif ication and uniform salt d i s t r ibut ion suggest that the water co lumn convectively mixed pr ior to M a r c h 2006 and that reverse temperature strat if icat ion established itself afterward due to surface heat losses. Ferris et al. (1991) have postulated that freeze-out of salt du r ing ice formation can m i x the water co lumn to a greater extent than w i n d induced mix ing . T h i s phenomena has been 12 Chapter 1 observed i n B u r t o n Lake, A n t a r c t i c a ; the mixed layer due to salt exclusion from the ice reached a depth of 11 meters near the end of the winter of 1987 i n contrast to a wind-induced m i x i n g layer of 5 meters i n the summer (Ferris et al, 1991). Ano the r example would be Store Salts0 i n southwestern Greenland, w i t h a m a x i m u m depth of 14 meters. T h i s lake had a mixo l imn ion 9.5 meters deep at the end of winter 2001, compared to 5.75 meters i n the summer (Willemse et al, 2004). These observations can be also be a t t r ibuted to the fresh surface layer created by ice melt-out, which stabilises the water co lumn dur ing spring and summer. In the study of Anta rc t i c lakes conducted by Gibson (1999b), mult iple steps i n sal ini ty and temperature were observed i n the vert ical profiles. T h e steps were reported to be ther-mohaline convective cells separated by unmixed sharp interfaces that are usual ly sharper closer to the surface (Gibson, 1999b). Gibson and Burton (1996) suggested that these steps resulted from THC that extended to deeper depths dur ing previous years. S imi lar THC cells were also observed i n Lake Vanda , located i n the M c M u r d o D r y Val leys i n A n t a r c t i c a (Spigel and Prison, 1998) as well as i n Nor thern C a n a d a (Ludlam, 1996). F ina l ly , some authors have reported both the presence of density currents along the shallow edges of water bodies, and the presence of an isothermal, isohaline convection cells beneath the ice to explain salt d is t r ibut ion i n northern saline lakes (Ferris et al., 1991; Miller and Aiken, 1996; Willemse et al, 2004). 1.3.2 Double-Diffusive Convection T h i s section w i l l give a short descript ion of double-diffusive instabil i t ies that occur i n waters that have more than one stratifying agent. M a n y papers examine the impact of double-diffusive instabili t ies i n the oceans (Merryfield, 2000; Kunze, 2003; Ruddick and Gargett, 2003). Very l i t t le information can be found concerning the possibi l i ty of double-diffusive convection i n brackish waters, where the effects of the Tmd on density are important . T h e conditions under which double-diffusive instabili t ies can occur i n reverse temperature strat-ified water bodies w i l l be given along w i t h a short summary of double-diffusive theory. A 13 Chapter 1 thorough explanat ion of double-diffusive ins tabi l i ty theory can be found i n Turner (1973). Double-Diffusive Theory T h e general conditions required to ini t iate double-diffusive instabili t ies are as follows: • T w o species w i t h different diffusivities are present i n the water co lumn (e.g. heat and salt) • One of the species has a destabil ising effect on density while the other has a s tabi l is ing effect • T h e water-column is s tat ical ly stable (i.e. l ight fluid over heavier fluid) These instabili t ies are a result of heat diffusing approximately 100 times faster than salt. W h e n temperature stabilises the water column and sal ini ty destabilises it , fingering insta-bili t ies can occur. For the opposite case of a stable salt-gradient and a unstable temperature gradient, diffusive ins tabi l i ty can take place i n the water co lumn (Turner, 1973). These two double-diffusive instabili t ies, salt-fingering and diffusive, w i l l be explained below i n greater detail . Fingers Reg ime In the finger regime, long narrow convecting cells t ranspor t ing salt and heat are called salt-fingers. In the oceans, they can be found when salty and warm water is above colder and fresher water. W h e n these instabilit ies are ini t ia ted, heat diffuses from the salt-fingers faster than salt, mak ing the salt-fingers denser as they progress downwards. In brackish waters influenced by the Tm<i, salt-fingers can also occur when salty and cold (Tw < Tm(i) water overlays fresher and warmer water (see Figure 1.5a). Diffusive R e g i m e T h i s type of double-diffusive ins tabi l i ty initiates convective m i x i n g i n ind iv idua l layers that are separated by a sharp interface. In seawater, cold freshwater must overly warmer and 14 Chapter 1 a) b) Figure 1.5: Schematic of double-diffusive instabili t ies for brackish waters. Schematic of a) fingering regime, b) diffusive regime. Note: Twater < Tmd- F igure adapted from Ruddick and Gargett (2003). The green and red arrows show respectively the density fluxes associated to the transport of heat and salt. saltier water for this type of instabili t ies to occur. Faster diffusion of heat than salt through the interface makes water above the pycnocline warmer and convect upwards. W h i l e , water below the sharp interface becomes colder and denser, in i t ia t ing convection downwards. T h e same behaviour would be expected for brackish waters below the Tmd where wa rm and fresh water overlies colder and more saline water; the only difference being the direct ion of heat fluxes (see Figure 1.5b). Density Ratio Rp Various methods are used to determine if double-diffusive instabili t ies can occur i n the water column. The density ratio Rp, also called the s tabi l i ty rat io, is used by oceanographers to determine the l ikel ihood of double-diffusive instabil i t ies occurr ing i n the oceans. T h e s tabi l i ty ratio is calculated w i t h the following equation (Ruddick and Gargett, 2003): 7? - — t t p ~ (3AS' (1.1) where a is the thermal expansion coefficient ( ° C _ 1 ) , (3 the haline contract ion coefficient ( g k g " 1 ) " 1 , A S 1 the difference i n sal ini ty over a given depth, and A T the difference i n tem-15 Chapter 1 perature over the same depth. T h e numerator i n Equa t ion 1.1 represents the cont r ibut ion of temperature to the density of water and the denominator represents the contr ibut ion of salinity. W h e n the temperature gradient is s tabi l is ing and the density ratio, Rp > 1, the finger regime is possible (Ruddick and Gargett, 2003). W h i l e the diffusive regime is possible when the salinity gradient is s tabil ising and Rp < 1, provided that the density gradient is stable (Ruddick and Gargett, 2003). A n upper bound for the possibi l i ty of double-diffusive instabili t ies is the diffusivity ratio where KT is the molecular diffusivity of heat and Ks the molecular diffusivity of salt (Ruddick and Gargett, 2003). Salt and heat fluxes due to f ingering Schmitt (1979) developed equations to calculate the flux of salt and heat in i t ia ted by fingering through an interface. The flux of salt, F S , is calculated using the following equation Schmitt (1979): f3Fs = C(gKT)1/3(PAS)4/\ (1.2) where C=0.051 when Rp > 3.5 and C= 0.1 when Rp —>1. T h e variable KT represents the molecular diffusivity of heat i n water i n m 2 s - 1 . T h e flux of heat, FT is related to the flux of salt by the density flux ratio,7 (Schmitt, 1979): ^ W s ( L 3 ) Schmitt (1979) found 7 to be smaller than 1, indicat ing that there is a larger density flux associated to the downward transport of salt t han to the upward flux of heat. 7 is equal to 0.7 when Rp < 2.5, 7 is ss 0.58 when 2.5< Rp <4 and 7 ss 0.3 for Rp >6 (Schmitt, 1979). 16 Bibliography Carmack , E . , R . Wiegand , R . Daley, C . Gray, S. Jasper, and C . Pharo , Mechanisms influencing the c i rcula t ion and dis t r ibut ion of water mass i n a med ium residence-time lake, Limnol. Oceanogr., 31, 249-265, 1986. Chen , C . T . , and F . J . Mi l l e ro , Precise thermodynamic properties for na tura l waters covering only the l imnological range, Limnol. Oceanogr., 31, 657-662, 1986. Eicken , H . , Sea Ice: An Introduction to its physics, biology chemistry and geology, chap. 2, pp. 22-81, Ist ed., B lackwel l Scientific, London , U K , 2003. Ferris, J . M . , J . A . E . G ibson , and H . R . B u r t o n , Evidence of density currents w i t h the potential to promote meromixis in ice-covered saline lakes, Palaeogeogr., Palaeoclima-teol, Palaeoecoi, 84, 99-245, 1991. Fischer, H . , E . L i s t , R . K o h , J . Imberger, and N . Brooks (Eds.) , Mixing in Inland and Coastal Waters, Academic Press, San Diego, U S A , 1979. Gallagher, J . B . , and H . R . B u r t o n , Seasonal m i x i n g of E l l i s F jo rd , Vestfold Hi l l s , Eas t Anta rc t i ca , Estuarine, Coastal and Shelf Sc., 27, 363-380, 1988. Gibson , J . A . E . , T h e role of ice in determining m i x i n g intensity in E l l i s F jo rd , Vestfold Hi l l s , Eas t Anta rc t i ca , Antarct. Sci., 11, 419-426, 1999a. Gibson , J . A . E . , T h e meromict ic lakes and stratified marine basins of the Vestfold H i l l s , Eas t Anta rc t i ca , Antarct. Sci, 11, 175-192, 1999b. Gibson , J . A . E . , and H . R . B u r t o n , Meromic t i c antarctic lakes as recorders of c l i -mate change: T h e structures of A c e and Organic lakes, Vestfold Hi l l s , An ta rc t i ca , i n Pap. Proc. R. Soc. Tasman., pp. 73-78, Hobar t Tasmania , 1996. 17 Chapter 1 Gross, M . , Oceanography, a view of the earth, 6 ed., Prent ice H a l l , Englewood Cliffs, New Jersey, U S A , 1993. Howard , H . H . , and G . W . Prescott , Seasonal var ia t ion of chemical parameters i n A l a s k a n tundra lakes, Am. Midi. Nat., 90, 154-164, 1973. Hutchinson, G . , A treatise on limnology. Volume 1: Geography, physics, and chemistry, John W i l e y & Sons, Cambridge, U K , 1957. Kunze , E . , A review of oceanic salt-fingering theory, Prog. Oceanogr., 56, 399-417, 2003. L i m , D . , B . Lava l , R . Pieters, D . R e i d , D . Anderson, M . M a c r i , and C . M c K a y , L imno log -ica l characterization of P a v i l i o n Lake, B C , 2006, In preparat ion for submission to A q u a t i c Sciences. L u d l a m , S. D . , The comparative l imnology of high arctic, coastal, meromict ic lakes, J. Pa-leolimnol., 16, 111-131, 1996. Merryf ie ld , W . , Or ig in of thermohaline staircases, J. Phys. Oceanogr., SO, 1046-1068, 2000. M i l l e r , L . G . , and G . R . A i k e n , Effects of glacial meltwater inflows and moat freezing on m i x i n g in an ice-covered An ta rc t i c lake as interpreted from stable isotope and t r i t i u m distr ibutions, Limnol. Oceanogr., 41, 966-976, 1996. Ouellet , M . , and P . Page, Comments on "hypersaline gradients in two Canad ian H i g h A r c t i c Lakes" by k. m . stewart and r. f. platford, Can. J. Fish. Aquat. Sci., 44, 1676-1678, 1987. Ouellet, M . , M . D ickman , M . Bisson, and P. Page, Physical-chemical characteristics and origin of hypersaline meromict ic Lake Gar row in the Canad ian high A r c t i c , Hydrobiologia, 172, 215-234, 1989. 18 Chapter 1 Page, P., M. Ouellet, C. Hillaire-Marcel, and M. Dickman, Isotopic analyses (180,13 C, 1 4 C) of two meromictic lakes in the Canadian Arctic Archipelago, Limnol. Oceanogr., 29, 564-573, 1984. Pieters, R., and G. A. Lawrence, Impact of salinity and ice-cover on a subarctic lake, 2006, draft for Minsitry of Indian and Northern Affairs, Government of Canada. Rogers, C. K., Impact of an artificial circulation device on the heat budget of an ice-covered mid-latitude lake, Master's thesis, University of British Columbia, Vancouver, 1992. Ruddick, B., and A. E. Gargett, Oceanic double-diffusion: introduction, Prog. Oceanogr., 57, 381-393, 2003. Schmitt, R., Flux measurements on salt fingers at an interface, J. Mar. Res., 37, 419-436, 1979. Spigel, R. H., and J. Priscu, Physical limnology of the McMurdo Dry Valleys lakes, Antarct. Res. Ser., 72, 153-187, 1998. Stevens, C. L., and G. A. Lawrence, Stability and meromixis in a water-filled mine pit, Limnol. Oceanogr., 43, 946-954, 1998. Stewart, K. M., and R. F. Platford, Hypersaline gradients in two Canadian High Arctic Lakes, Can. J. Fish. Aquat. Sci., 43, 1795-1803, 1986. Turner, J., Buoyancy Effects in Fluids, Cambridge University Press, Cambridge, UK, 1973. UNESCO, Background papers and supporting data on the Iinternational Equation of State of Seawater 1980, Tech. rep., UNESCO, 1981. Welch, H. E., and M. A. Bergmann, Water circulation in small arctic lakes in winter, Can. J. Fish. Aquat. Sci., 42, 506-520, 1985. 19 Chapter 1 Wil lemse , N . W . , O . van D a m , P . - J . van Helvoort , R . Dankers, M . Brommer , J . Schokker, T . E . Vals tar , and Ft. de Wolf, Phys ica l and chemical l imnology of a subsaline athalassic lake i n West Greenland, Hydrobiologia, 524, 167-192, 2004. Wuest, A . , G . Piepke, and J . D . Halfman, Combined effects of dissolved solids and tem-perature on the density stratification of Lake M a l a w i , Limnol. Climatol. Paleoclimatol. of the East African Lakes, 338, 325-357, 1996. 20 Chapter 2 Mixing in brackish lakes due to surface ice 2 . 1 I n t r o d u c t i o n Lakes that don't tu rn over completely dur ing the year, are classified as meromict ic (Hutchin-son, 1957). Meromix i s is usually a state that results from chemical stratif ication and is more common i n deep lakes. In meromict ic lakes the stagnant bo t t om water or mono-l imnion is often oxygen depleted. W h i l e , the upper layer or mixo l imn ion is typica l ly wel l mixed at some point of the year and oxygenated due to wind energy. Saline lakes can be found a l l over the world , notable examples include Great Salt Lake i n the U n i t e d States and Lake Eyre i n Aus t r a l i a . In addi t ion, a large proport ion of na tura l lakes are saline. In fact, there is 85 400 k m 3 of water stored i n saline lakes compared to 91 000 k m 3 i n freshwater lakes (Shiklomanov and Rodda, 2003). A large number of saline lakes are found i n glaciated regions (Shiklomanov and Rodda, 2003), and meromict ic lakes tend to be more common i n these regions (Walker and Likens, 1975). Man-made lakes such as water filled open mine pits are also usually saline, meromictic and present at h igh latitudes. These lakes tend to be h ighly contaminated due to acid rock drainage and other contaminants result-ing from min ing processes (Stevens and Lawrence, 1998). T h e water qual i ty of these lakes continuously evolves due to physical and biogeochemical processes, and is often affected by remediat ion efforts. C i rcu la t ion of saline water bodies i n cold climates is influenced by surface ice formation. A version of this chapter will be submitted for publication in the Limnology and Oceanography. Bluteau, C.E. , Pieters, R., and G.A. Lawrence. 2006. Mixing in brackish lakes due to surface ice. 21 Chapter 2 Salt exclusion from ice has been reported to ini t iate m i x i n g i n lakes dur ing the winter months, as well as promote meromixis (Gibson, 1999b,a; Miller and Aiken, 1996; Ferris et ai, 1991; Willemse et al, 2004). In some cases, ice forming near the shallower edges of a basin has been reported to create dense brine flows, which transport salt to depth and increase lake s tabi l i ty (Gallagher and Burton, 1988; Ferris et ai, 1991; Miller and Aiken, 1996; Gibson, 1999a). Others have suggested that salt exclusion from ice creates an isothermal and isohaline convective cell (THC) beneath the ice, which extends further down as ice product ion persists dur ing winter, decreasing lake s tabi l i ty over t ime (Ferris et al, 1991; Ludlam, 1996; Spigel and Priscu, 1998; Gibson, 1999b; Willemse et ai, 2004). Past field studies have generally addressed the influence of salt i n the c i rcula t ion of lakes i n cold cl imate, disregarding the effects of temperature, which are significant i n freshwater lakes. In brackish lakes that are less saline than 24 g L - 1 , the freezing temperature, Tf, is lower than the temperature of m a x i m u m density, Tmd- Hence, temperature and sal ini ty play a role i n lake c i rcula t ion throughout the year. T h i s definit ion for the te rm brackish was used to differentiate between lakes where c i rcula t ion is affected by the temperature of m a x i m u m density (Tmd), and those where the Tmd has no influence (i.e. saline lakes). T h i s chapter examines laboratory experiments conducted to examine the c i rcula t ion caused by salt exclusion from surface ice. T h e mass of salt expelled from the ice is a function of the in i t i a l salinity, as are the details of lake circulat ion. T h e influence of the Tmd on ci rcula t ion i n ice covered lakes w i l l also be discussed. 2.2 Methods 2.2.1 Experimental apparatus T h e experiments were conducted i n a 0.34m x 0.18m x 0.3m deep 'lake' that was sufficiently well insulated to allow the formation of an reverse temperature strat if ication i n the water column. T h e container had 3 ma in insulat ing layers: the outer wal l consisting of 50 m m of 22 Chapter 2 Freezer wall Styrofoam insulation Fiberglass insulation 65 cm Elevation view of apparatus Compressor 40 cm Plan view of apparatus Figure 2.1: Schematic of the model lake used to conduct the experiments. styrofoam, an intermediate layer of fiberglass insulat ion and an inner layer of styrofoam. A schematic of the apparatus can be found in Figure 2.1. The tank walls were made of plastic and the to ta l depth of water for a l l experiments was 245 m m . 2.2.2 Temperature time series Temperature sensors and a 12 bit H O B O data logger, obtained from Onset, were used to obtain a t ime series of temperature measurements at 4 different depths: 1, 8, 17, and 21.5 c m from the bo t tom of the container. The mooring of temperature sensors was placed at equal distance from each sidewall of the container (Figure 2.1). Temperatures were recorded every 30 seconds for the entire durat ion of the experiment, though the sensor response 2:\ Chapter 2 time is longer (90% after 1 min in stirred water). After calibration, the accuracy of the temperature sensors was ±0.035 °C and their resolution 0.03 °C over the range of water temperatures encountered during experiments. Air temperature was measured at 0.15 m above the water surface with a HOBO U10 data logger. This logger had an accuracy of ±0.4 °C, a resolution of 0.10°C, and recorded air temperatures at the same frequency as the sensors located in the water column. The response time for the air temperature logger was approximately 10 minutes. 2.2.3 Time of ice formation A web cam was placed overnight inside the freezer in order to determine when surface ice formed. Light emitting diodes (LED) were used to light the inside of the freezer while photographs were taken every 15 minutes with the web cam. The LEDs were uniformly distributed on a plate that had the same dimensions as the surface area of the model lake. They were placed 0.25 m above the water surface and produced insignificant heat. Trial experiments conducted with and without LEDs showed no differences in water tempera-tures. 2.2.4 General details of experiments Each experiment started with a well-mixed saline solution at room temperature, the initial salinities investigated being 0, 1, 2, 4, 8 and 15 g L - 1 of potassium chloride. For every experiment, 14 liters of saline solution was created from distilled water and ACS certified potassium chloride obtained from Fisher Scientific at 99-100.5% purity. Potassium chloride solutions were used since the equation of state, and the Tmd and Tf as a function of salinity are known (Lide, 2006; Washburn, 2003). The linear relationships between salinity and Tf and Tm<i for aqueous potassium chloride solutions are shown in Figure 2.2. The freezer lid was left open for a period of 20 minutes when placing the 'lake' into the freezer. After 19 hours of cooling at -12.8 ± 0.2 °C, the freezer was shut off and the lid was opened to let the ice thaw. Air temperatures during the warming period differed slightly 24 Chapter 2 Figure 2.2: Tmd and Tf for potassium chloride aqueous solutions at atmospheric pressure. The markers represent the original da ta obtained from hide (2006); Washburn (2003). from one experiment to another. T h e y were always between 20 °C to 22 ° C , depending on air temperatures i n the laboratory. Indiv idual experiments were terminated after 2 days. B y that t ime, the ice had completely melted and the entire water co lumn was warmer than the Tmd. Exper iments were replicated three to four times for each sal ini ty investigated. T h e results presented throughout this chapter are representative of a l l replicates conducted at a given salinity. A n experiment was also conducted to determine the var iabi l i ty of vert ical heat d is t r ibut ion from one horizontal locat ion to another w i t h i n the container. T h e temperature t ime series for this experiment can be found i n A p p e n d i x B , i n addi t ion to temperature t ime series for a l l experiments performed for this thesis. 25 Chapter 2 2.2.5 Discrete salinity measurements In certain experiments, 40-mL aliquots were taken w i t h a syringe at 6 different depths i n the water co lumn to establish the vert ical salt d is t r ibut ion after ice formation (melt-out). Conduc t i v i t y and temperature of the aliquots were measured w i t h a W T W - 3 3 0 hand held conduct iv i ty meter, i n order to evaluate their salt concentrations. T h e conduct iv i ty meter measurements were accurate w i th in ± 0 . 5 % of the reading, and the temperature readings were accurate w i th in ± 0 . 1 ° C . After t ak ing aliquots from the water co lumn, the experiments were terminated due to the volume of water removed. A n at tempt was made to use a microscale conduct iv i ty and temperature instrument (MSCTI) to obta in vert ical sal ini ty profiles at h igh spat ia l resolution. However, difficulties were encountered when measuring temperature and conduct iv i ty w i t h the MSCTI (see A p p e n d i x C ) . A s a result, only the data obtained from discrete sal ini ty measurements were used to draw conclusions on vert ical salt d is t r ibut ion . 2.2.6 Ice salinity and salt—balance A set of experiments was performed to measure the degree of salt exclusion from the ice and to obta in a salt-balance for the system. T h e experiments commenced i n the same fashion as described i n § 2.2.4, but after 19 hours of cooling, the surface ice was removed and left to melt. The volume of bo th melted ice water and the remaining water were measured before measuring conductivi ty. Volumes and salinities were used to find the mass of salt expelled from the ice for each sal ini ty investigated. 2.2.7 Heat flux computations Heat fluxes i n the water co lumn were approximated from temperature readings obtained w i t h the 4 H O B O temperature sensors, assuming that each sensor represented the water temperature for one fourth of the to ta l water depth. T h e equation used for est imating 26 Chapter 2 experimental heat fluxes was the following: qexp = pCph^, (2.1) where p represents water density, Cp is the specific heat of water, and h is the water depth represented by an ind iv idua l sensor equivalent to 25% of the to ta l water depth. T h e var ia t ion of temperature w i t h t ime ( ^ ) was obtained from the measured temperature t ime series for each sensor. To ta l heat fluxes were obtained by summing heat fluxes of the 4 ind iv idua l sensors. G i v e n the number of sensors, these heat fluxes estimations are considered approximate for periods when a temperature gradient is present in the water column. However, comparisons amongst heat fluxes calculated for ind iv idua l experiments can s t i l l be made, since the sensors were always located at the same depths. 2.3 Results 2.3.1 Salt-balance A summary of the percentage of salt excluded from the ice upon its formation, along w i t h salinity of the ice, and volume of ice produced can be found i n Table 2.1. W i t h the freezing rates encountered dur ing the experiments, approximately 5% of salts remained i n the ice dur ing the freezing process. Past studies have shown that new sea ice created from seawater at 35 g L - 1 w i l l retain from 20% to 40% of the in i t i a l mass of salts (Gross, 1993). W h i l e lake ice formed from freshwater (S < 0.5 g L - 1 ) w i l l retain approximately 3% of salt (Eicken, 2003). V i s u a l observations of the surface ice showed that experiments conducted above 4 g L _ 1 created whiter ice, while lower salinity experiments had a clear ice sheet (black ice). T h i s is consistent w i t h ice t rapping a higher concentrat ion of salt at higher sal ini ty (Eicken, 2003). For freshwater, the thickness of surface ice formed was approximately 8 m m . It was thinner for experiments conducted at higher salinities due to lowering of the Tm(i (Table 2.1), 27 Chapter 2 which increased the amount of t ime taken before the ice could form. In most experiments, the ice sheet was generally thicker along the edges of the container. For experiments conducted at 15 g L - 1 , the lowering of the Tmd reduced the ice product ion per iod to 2.5 hours compared to 5 hours for freshwater experiments. A s a result, for this experiment complete ice cover was not at tained and there were s t i l l visible patches of water at the surface when the freezer l i d was opened. 2.3.2 Temperature time series T h e temperature t ime series has been subdivided into 5 different phases representing the various seasons of a temperate year. Spr ing was subdivided into two phases to differentiate between when ice cover was present or not at the surface. Phases I through V represent respectively: au tumn cooling, ice formation (winter), ice thaw, spring warming and sum-mer. These five phases w i l l be explained i n the following sections, along w i t h information per ta ining to heat fluxes. Freshwater experiments were used as controls to determine the influence of sal inity on heat dis t r ibut ion, which was used as a tracer for water movement. The complete temperature t ime series for a l l sensors is shown i n Figure 2.3 for an experi-ment conducted at 4 g L - 1 of potassium chloride, which is representative of those conducted between 1 and 4 g L - 1 . Exper iment sal ini ty ( g L - 1 ) Salt expelled (%) Ice sal ini ty ( g L - 1 ) 0 1* 95.0 0.05 2 f * 94.0 0.12 4 94.1 0.24 8 94.7 0.43 15 94.2 0.87 Table 2.1: Exper iments undertaken w i t h temperature t ime series measurements, along w i t h corresponding salt balance results. *Salinity measurements were taken i n experiments conducted at this salinity, t A n experiment was conducted w i t h two moorings at this salinity. 28 Chapter 2 Time in hours Figure 2.3: Temperature time series for an experiment conducted at 4gL _ 1 . (a) Air temperatures; (b) Mooring water temperatures; (c) Mooring water temperature when water temperatures are below 5°C. A and B represents a period of slower cooling preceded and followed by a sudden drop in T. C is a typical temperature fluctuation, suggesting heat exchange with water above and at depth. The ice cover period is represented by the black rectangle. 29 Chapter 2 Phase I: Autumn cooling T h i s phase is dominated by cooling that creates denser water at the surface that is capable of mix ing the entire water co lumn (Figure 2.3b). There is no salt or temperature strat if ication to inhibi t over-turning i n this phase. T h e average to ta l heat losses through the surface and sidewalls were estimated to be 280 W m - 2 . Heat fluxes through sidewalls account for approximately 21% of to ta l heat fluxes (see A p p e n d i x D ) . Phase II: Ice formation (winter) In this phase, reverse temperature stratification established itself i n the water co lumn and ice formation began. Acco rd ing to pictures taken every 15 minutes w i t h the web cam, from the t ime ice was observed on the water surface on one picture, complete ice cover was present on the following picture. Ice formed on average w i t h i n 10 minutes from the t ime the temperature sensor closest to the surface reached the Tmd. Figure 2.4 shows the recorded temperatures dur ing phase II for a l l salinities investi-gated, inc luding those for freshwater. Temperature readings for a l l sensors dropped non-monotonical ly in t ime, w i th the exception of sensors i n freshwater experiments (Figure 2.4). T h e amplitudes of temperature fluctuations were smaller for sensors located at depth, and became smaller as ice product ion persisted. T h e y ceased when warming began at the end of phase II (Figure 2.4b-f), indicat ing that m i x i n g ceased. Water temperatures i n freshwater experiments cooled monotonical ly and d id not show evidence of m i x i n g (Figure 2.4a). 1 g L - 1 to 4 g L - 1 In experiments conducted between 1 g L - 1 and 4 g L - 1 , the temper-ature t ime series of the surface sensor show periods when water is cooling at a slower rate, which are followed and preceded by sudden drops i n temperatures (event A , B i n Figure 2.3c). In some cases, these periods of slower cooling lasted for as long as an hour (Figure 2.3c). T h e y usually became shorter as ice formation progressed, and were shorter for experiments conducted at lower salinities (Figure 2.4b-d). Comple te turn-over was not observed nor was par t ia l turn-over i n the top th i rd of the water co lumn dur ing phase 30 Chapter 2 S = 0 gL-1 S = 1 gL 12 14 16 18 20 12 14 16 18 20 S = 2 gL 1 S = 4 gL 12 14 16 18 20 12 14 16 18 20 S = 8gL"1 S = 15gL Time in hours Time in hours Figure 2.4: Z o o m on freezing regions of a l l salinities investigated. M represents the t ime when complete convective m i x i n g of the water co lumn occurred. A and B represents a period of slower cooling preceded and followed by a sudden drop i n temperature. 31 Chapter 2 II. In fact, a temperature gradient always existed between the two top-most temperature sensors (Figure 2.4a-d). T h i s temperature gradient became stronger over t ime and was stronger for experiments conducted at lower salinities (Figure 2.4a-d). In general, at higher salinities the temperature strat if ication amongst the three bo t tom sensors was weaker than i n experiments conducted at lower salinities (Figure 2.4b-d). In some instances, the deepest sensor even displayed colder temperatures than the sensor located above i t (Figure 2.4b-e). Hence, creating an unstable temperature gradient that was most noticeable for the 4 g L - 1 experiment. T h i s unstable temperature gradient between the two deepest sensors was at most 0.24 °C (Figure 2.3d), which was larger than the accuracy of the temperature sensors ( ± 0 . 0 3 5 ° C ) . T h e unstable temperature gradient was present at the onset of ice formation, and d id not ini t iate over-turn. It suggests saline water was transported at depth, possibly due to ice forming in i t i a l ly near the walls. 8 g L _ 1 and 15 g L - 1 For experiments conducted at higher salinities, only weak tem-perature gradients were established (Figure 2.4e, f). These gradients were per iodica l ly removed presumably because of mix ing caused by descending salty plumes (events M , F i g -ure 2.4e, f). These events happened short ly after ice formation and reoccurred several t imes dur ing phase II (events M , Figure 2.4e, f). In the 15 g L - 1 experiment, the sudden drops i n temperature recorded at the 2 n d sensor from the surface occurred simultaneously w i t h recorded drops at the surface sensor (Figure 2.4f). A s for the 8 g L _ 1 experiment, there was generally a lag between cooling at the two top sensors (Figure 2.4f). T h e 2 n d sensor from the surface usually cooled simultaneously w i t h the recorded warming at the surface sensor (Figure 2.4f). Heat fluxes Heat losses dur ing ice formation were computed using Equa t ion 2.1, using the measured temperatures i n phase II. T h e average computed heat fluxes are shown i n Table 2.2, and were greater for experiments conducted at higher salinities. A s a result, bo t tom water temperatures were colder i n those experiments. Pred ic t ion of water temperatures were also calculated and compared against measured 32 Chapter 2 water temperatures (Figure 2.5). T h e predictions were obtained by assuming the surface is at Tf, heat is diffusing through the water co lumn and lost through the container walls, and the water co lumn is s tat ical ly stable (see A p p e n d i x D.2) . T h e y were val idated beforehand against the temperature t ime series of a freshwater experiment. F igure 2.5 shows that measured temperatures i n brackish experiments are colder than expected. These discrep-ancies are more obvious for the 3 deepest sensors, and for experiments conducted at higher salinities (Figure 2.5). T h e y are a result of convective motions i n the ' lake' , which was not taken into account when predict ing water temperatures. Exper iment sal ini ty I II III* I V V ( g L " 1 ) ( W m ~ 2 ) ( W i n " 2 ) ( W m ~ 2 ) ( W m - 2 ) ( W m ~ 2 ) 0 - 2 8 6 - 9 1 - 1 0 154 131 1 - 2 7 7 - 1 0 0 - 1 5 133 113 2 - 2 7 2 - 1 1 4 - 7 124 107 4 - 2 8 9 - 1 2 4 - 1 2 111 100 8 - 2 7 6 - 1 4 5 - 2 3 117 124 15 - 2 8 6 - 1 4 5 - 1 8 90 128 Table 2.2: Average heat fluxes dur ing each phase. A negative sign represents heat lost. *Rough estimate since water temperatures i n phase III in i t i a l ly cool before warming. Phase III: Ice thaw (early spring) T h i s phase begins when the freezer l i d is opened and ends when the ice is completely melted. D u r i n g this phase, the water co lumn temperature is below the Tm(i and is reversely stratified (Figure 2.6a-e). Due to the high latent heat of fusion of water, the incoming surface heat fluxes are used to melt the ice sheet rather than to increase water temperature. In fact, for the case of freshwater, water temperatures continued to drop for another hour before gaining heat at a rate of 5 W m - 2 . T h i s behaviour was observed for a l l experiments, expla ining the relatively smal l heat losses for phase III (Table 2.2). T h e heat was gained most ly at the surface as shown by faster r is ing water temperatures near the surface (Figure 2.6a-f). In brackish experiments, ice melt-out created a fresh surface layer (see § 2.3.1). 33 Chapter 2 S = 0 gL 1 S = 1 gL 15 20 25 15 20 25 15 20 25 15 20 25 Time in hours Time in hours Figure 2.5: Compar i son between recorded water temperatures and expected water tem-peratures when assuming that there is no convective movement i n the lake. T h e thicker smooth lines represent the expected water temperatures. The Tmd is represented by the solid black line. 34 Chapter 2 Phase IV: Spring warming (after ice-off) T h i s phase begins when the ice layer is completely melted, and ends when density stratifi-cat ion is stable throughout the water column. Figure 2.6 shows the recorded temperatures dur ing phase I V for a l l salinities investigated, inc luding those for freshwater. T h i s phase is dominated by surface heating, which made water at the surface warmer, and denser than water at depth (Figure 2.6). In freshwater experiments, shallower water mixed immediate ly w i t h water at depth, un t i l the temperature stratif ication became stable at the end phase I V (Figure 2.6a). 1 g L - 1 to 4 gL_1experiments In brackish experiments, the fresh layer created from ice melt compensated for the unstable temperature gradient (Figure 2.6b-d). The surface sensor recorded water temperatures that increased at a faster rate than deeper sensors (Figure 2.6b-d). These recorded temperatures also warmed non-monotonical ly throughout most of phase I V , indica t ing that mix ing was occur W h e n the temperature of the 2nd sensor from the sensor reached the same tempera-ture as the sensor below i t , their temperature readings continued to rise at the same rate (Figure 2.6b-d). T h i s suggests this intermediate layer of water was convectively mix ing , as shown by the non-monotonic water temperatures, which persisted un t i l reaching the Tmd (Figure 2.6b-d). In these experiments, an unstable temperature gradient was present between the two deepest sensors (Figure 2.6b-d). The destabil ising temperature gradient was smaller i n experiments conducted at higher salinities (Figure 2.6b-d). T h i s destabil ising temperature gradient at depth d i d not ini t iate convective mix ing , as shown by monotonic warming recorded at the deepest sensor (Figure 2.6). T h i s implies that bo t tom waters were more saline than intermediate waters. 8 g L - 1 and 15 g L~ Experiments In the 8 g L _ 1 experiment, the appearance of an unstable temperature gradient near the surface was delayed due to lower ice product ion i n 3 5 Chapter 2 phase II (Figure 2.6). Because the fresh layer was in i t i a l ly very t h in i t lay above the surface sensor. A s a result of surface heating, this fresh layer eventually deepened enough for the surface sensor to record its warmer temperatures (Event A , F igure 2.6e). T h e absence of an unstable temperature gradient for the 15 g L - 1 experiment is also a t t r ibuted to lower ice product ion i n phase II (Figure 2.6f). A t 8 g L - 1 , there was no unstable temperature gradient between the two deepest sen-sors. The fluctuating temperatures recorded at the deepest sensor indicate that m i x i n g i n intermediate water was reaching the depth of this sensor (Figure 2.6e). However, i n exper-iments conducted at 15 g L - 1 , an unstable temperature gradient was observed between the two deepest sensors (Figure 2.6f). T h e absence of significant deep m i x i n g i n this experiment suggest that bo t tom waters were more saline than intermediate waters. Heat fluxes B o t t o m water warmed faster i n experiments that had evidence of m i x i n g at depth; such as the freshwater and the 8 g L - 1 experiments (Table 2.2). Heat fluxes for al l experiments conducted w i t h salt were between 90 and 133 W m - 2 . W h i l e , heat fluxes i n freshwater experiments were highest at 154 W m - 2 . T h i s higher value is caused by the lack of salt stratification, permi t t ing heat to be transported throughout the water co lumn by convective mix ing . In phase I V , to ta l heat fluxes were much larger than dur ing phase III due to the absence of ice cover. Phase V : Summer T h i s phase is characterised by a stable temperature strat if ication (Figure 2.3). Surface heating permits shallow water to wa rm faster and to become lighter than water at depth, fn general, heat fluxes were smaller than in phase I V due to the absence of convective m i x i n g i n the water column. For freshwater experiments, average heat fluxes were approximately 130 W m " 2 . 36 Chapter 2 Figure 2.6: Zoom on phase I V , thawing, for a l l salinities investigated. Event A represents the t ime when the fresh surface layer was deep enough to permit surface water temperatures to increase at a faster rate. 37 Chapter 2 2.25 Figure 2.7: Sal in i ty profile obtained from water sampling after ice melt-out for an experi-ment conducted at a) 1 g L - 1 and b) 2 g L - 1 . The dashed line represents the sal ini ty profile before commencing experiments. T h e markers show the depth where the samples were taken. T h e error bars, which are smaller than the markers, represent the measurement error of 1%. 2.3.3 Salinity profiles Discrete conduct iv i ty and temperature measurements throughout the water co lumn after ice melt-out show that ice formation created a stable salt gradient below the fresh sur-face layer (Figure 2.7). For experiments conducted at 1 g L - 1 , this gradient was less than 0.03 g L - 1 from the sample taken below the fresh layer to the bo t tom of the ' lake' . For the case of experiments conducted at 2 g L - 1 , the increase in sal ini ty at depth was greater. It was approximately 0.07 g L - 1 from below the fresh layer to the bo t tom of the container (Figure 2.7b). These sal ini ty increase are greater than the accuracy of sal ini ty measure-ments equal to 1% of the sal ini ty measurement. 2.4 Discussion 2.4.1 Mixing processes T h i s section w i l l concentrate on the experimental results obtained for brackish water dur ing phase II and I V . E i the r the temperature or sal inity i n these phases had a destabil ising effect 38 Chapter 2 on density. Phase II: Ice formation (winter) Various m i x i n g processes are involved i n t ranspor t ing excluded salt throughout the water column. T h e following is a list of these m i x i n g processes, which can be supported by the temperature t ime series of the four sensors (see Figure 2.4b-f): • Sudden release of cold and saline water from beneath the ice, in i t i a t ing convection • Densi ty currents t ransport ing salt at depth, which are more prominent at the onset of ice formation • Exchange of heat upwards and salt downwards throughout the water co lumn by salt-fingers and /or normal convection The reverse temperature stratification below the ice can support some salt while keeping a stable density stratification. However, i t could not support the to ta l mass of salt that is excluded from the ice dur ing any of the experiments (Table 2.3). A t the onset of ice formation, salt exclusion rates are greater because the ice has not yet provided insula t ion to the water column. A s a result, the cold and saline water beneath the ice is destabilized, and mixes down w i t h warmer water at depth. T h i s sudden m i x i n g translates into sudden drops i n temperature at the surface sensor, which were more drastic at the onset of ice formation (e.g. Event A , Figure 2.4c,d). A reduction i n salt exclusion over t ime would permit the water co lumn to establish a stronger temperature stratification. T h i s feature was observed i n the 1, 2 and 4 g L - 1 experiments (Figure 2.4b-d). In most experiments, the ice was thicker along the edges of the container than in the center. T h i s would permit salt to be carried down along the edges by means of dense brine flows as proposed by Gallagher and Burton (1988); Ferris et al. (1991); Miller and Aiken (1996); Gibson (1999a). These dense brine flows would expla in the unstable temperature gradients observed between the two deepest sensor at the onset of ice formation. T h e y would transport salt at depth, and explain why the unstable temperature gradients d id 39 Chapter 2 not ini t iate over-turn (Figure 2.4b-e). In fact, a sal inity increase w i t h depth was confirmed by discrete CT measurements done after ice melt-out (see § 2.3.3). T h e dissapearance i n some instances of the observed unstable temperature gradients over t ime (Figure 2.4b, c), may be a result of heat exchange from water i n the v ic in i ty of the 2nd sensor from the bo t tom toward colder water above. Hence, pe rmi t t ing it to cool below the temperature of the deepest sensor (Figure 2.4b, c). It is necessary to stress that these features were never observed i n freshwater experiments. T h e water co lumn was always reverse temperature stratified (Figure 2.4a). Heat exchange throughout the water co lumn was observed at a l l depths. It cannot be explained solely by heat losses through the surface and boundaries (see Figure 2.5). For instance, the second sensor from the top i n the 2 g L - 1 experiment often displays cool ing periods followed by warming periods, as shown between event A and B on Figure 2.4c. The water i n the v ic in i ty of this sensor cools rapidly as i t loses heat to water above, and i n the process i t gains salt. T h i s increase i n salt facilitates subsequent exchange w i t h water below it , permi t t ing it to warm. In fact, while this sensor is warming, the two sensors below it suddenly cool (Figure 2.4c). T h i s process or exchange could also explain why the temperature at the surface dropped more slowly between event A and B on Figure 2.4c, d. It is unclear how the heat is exchanged. It could be due to m i x i n g of heavy surface water (salty and cold) w i t h l ighter water below (warm and fresh) between sensors. It may also be a result of salt fingering i n which case heat would be transported upwards, while salt is t ransported downwards. T h e heat and salt fluxes that would be generated by salt fingering were calculated based on the work of Schmitt (1979) (see § 1.3.2). For the calculations, it was assumed the reverse temperature strat if ication was support ing an unstable salt gradient. A salt gradient equivalent to the m a x i m u m amount of salt that can be sustained by the reverse temperature gradient, while keeping a stable density gradient ( i ip —1). Equat ions 1.2 and 1.3 were applied to the temperature measurements of the 2 g L - 1 experiment, when the surface sensor was cooling more slowly between event A and B on 40 Chapter 2 Figure 2.4c. A t event A , when the 2nd sensor from the surface is just about to warm, the estimated upward heat fluxes and downward salt fluxes are respectively 33 W m " 2 and 0.088 g h - 1 between the two sensors closest to the surface. T h e same calculations were done between the bo t tom sensors and the 2nd sensor from the surface, and yielded an upward heat flux of 38 W m - 2 and a downward salt flux of 0.068 g h - 1 . These estimations suggest the 2nd sensor should be warming at f» 5 W m " 2 , since it gains more heat from below (38 W m " 2 ) than it is gives to water below (33 W m " 2 ) . T h e calculated salt fluxes are greater than the average salt exclusion rate observed dur ing experiments (0.077 g h " 1 ) . T h e heat and salt fluxes calculations were repeated w i t h the temperatures recorded five minutes after event A , when the 2nd from the surface is just about to start cool ing again (Figure 2.4c). The estimated upward heat fluxes and downward salt fluxes are respectively 51 W m " 2 and 0.12 g h " 1 between the two sensors closest to the surface. W h i l e those calculated between the bo t tom sensors and the 2 n d sensor from the surface, yielded an upward heat fluxes of 12 W m " 2 and a downward salt flux of 0.002 g h " 1 . The balance between these heat fluxes, suggest that the 2 n d sensor from the surface should be cool ing at a rate of 39 W m " 2 due to salt fingering. Hence, the results from the salt fingering calculations could explain some of the features i n the temperature record. However, addi t ional measurements such as temperature and sal ini ty profiles, as well as visual is ing the flow beneath the ice would be required to establish the actual presence of salt fingers. Influence of salinity A t higher salinities, the salt gradient required to overcome the stabi l i ty provided by a reverse temperature strat if ication is much less (Table 2.3). In addi t ion, the amount of salt expelled from the ice is higher in experiments conducted at higher sal ini ty (Table 2.3). These characteristics influence the transport of salt and hence the heat d is t r ibut ion i n the water column. For instance, it enables the destruction of the temperature gradient between the 2 n d sensor from the surface and the sensor below it (Figure 2.4d). A temperature gradient should have normal ly existed between these two 41 Chapter 2 sensors, if it had not been for salt exclusion (see Figure 2.5). A t salinities of 8 g L - 1 and 15 g L - 1 , complete m i x i n g of the water co lumn occurred for s imilar reasons, a weak s tabi l i ty provided by the reverse temperature stratification, accentuated by larger amount of expelled salt (Table 2.3). These characteristics can also explain the longer dura t ion and higher frequency of observed m i x i n g events i n experiments conducted at higher sal ini ty (Figure 2.4b-f). Exper iment sal ini ty ( g L - 1 ) Ap(Tmd^Tf) ( k g m - 3 ) A S ( g k g - 1 ) Salt expelled (g) 1 0.126 0.187 0.17 2 0.120 0.177 0.34 4 0.107 0.157 0.68 8 0.082 0.121 1.14 15 0.046 0.068 1.55 Table 2.3: Densi ty difference between water at the Tmd and water at Tf for various sal ini-ties. T h e th i rd co lumn shows the corresponding salinity increase required to overcome the s tabi l iz ing reverse temperature stratification. T h e last co lumn shows the to ta l mass of salt expelled from the ice dur ing phase II. Values were computed w i t h the equation of state for potassium chloride at atmospheric pressure. Phase I V : S p r i n g w a r m i n g The temperature record dur ing phase I V and the ice sal ini ty suggest that the water co lumn is comprised of three dist inct layers. T h e surface layer is fresh due to ice melt-out, its temperature is represented by the sensor closest to the surface. The intermediate layer is unstratified, bo th in sal ini ty and temperature, as shown by the temperature record of the two middle sensors (Figure 2.6). The bo t tom layer is stagnant i n experiments conducted between 1 and 4 g L - 1 and at 15 g L - 1 , and its temperature is represented by the deepest sensor (Figure 2.6b-d,f). A schematic of ' lake' m i x i n g along wi th the proposed d is t r ibut ion of salt and heat dur ing phase I V is shown in F igure 2.8. Ini t ial ly, a reverse temperature strat if ication is present, making the water co lumn stable i n temperature and sal ini ty (Figure 2.8a). W i t h the continuous input of heat, convective m i x i n g is in i t ia ted at the surface. Denser fluid w i l l convect downwards un t i l reaching the halocline, separating the fresh cap from intermediate 42 Chapter 2 water (Figure 2.8b). Faster diffusion of heat than salt through the halocline would permit intermediate water to convect downwards, as a result of double-diffusive convection (F ig -ure 2.8b). T h i s slower exchange of salt, along w i t h continuous surface heating, permits a deepening of the fresh surface layer and erosion of the halocline (Figure 2.8c). T h e sur-face and intermediate layer continue to convectively m i x un t i l becoming 'doubly ' stable i n temperature and salinity (Figure 2.8d). Temperatures measured by the surface sensor of the 8 g L - 1 experiment, support the hypothesis that the fresh layer deepened, as a result of surface heating (Figure 2.6e). F r o m the temperature record (Figure 2.6) and conduct iv i ty measurements (Figure 2.7a, b), it seems l ikely that salt accumulated at depth. In experiments conducted between 1 g L - 1 and 4 g L - 1 , the bo t tom layer remained stagnant throughout phase I V (Figure 2.8). Significant mix ing d id not occur at depth, even though an unstable temperature gradient was present (Figure 2.6b-d). In order to inhib i t over-turn, bo t tom waters would have to be more saline than intermediate waters. T h e required sal ini ty increase from intermediate to bo t tom waters is approximately 0.007 g L - 1 according to the temperature record of experiments conducted at 1 g L - 1 . It typ ica l ly becomes smaller as t ime progresses i n phase I V , suggesting that convection i n the intermediate layer is reaching deeper depths, slowly eroding the salt gradient. Discrete CT measurements pr ior to phase I V show an increase of 0.005 g L - 1 between the intermediate and bo t tom layer for an experiment conducted at 1 g L - 1 (Figure 2.7). T h i s measured increase i n sal ini ty is smaller than the accuracy of the instruments used to measure conduct iv i ty and temperature. However, for an experiment at 2 g L - 1 , the measured increase i n salinity is approximately 0.03 g L - 1 , and is more than the required sal ini ty of 0.009 g L - 1 needed to stabilise the recorded unstable temperature gradient (Figure 2.4c). A t an in i t i a l sal ini ty of 8 g L _ 1 , there is no unstable temperature gradient at depth, where mix ing is t ak ing place (Figure 2.6e). Comple te m i x i n g observed i n these experi-ments dur ing phase II would have destroyed any salt gradient (Figure 2.4e). However, a different behaviour was observed for a l l replicates done at 15 g L - 1 . A n unstable tempera-43 Chapter 2 c) T < T m d d) T > T m d Figure 2.8: Schematic of vert ical salt and heat d is t r ibut ion after (a) ice melt-out, (b) as surface water approach Tmd in i t i a t ing convective m i x i n g i n surface and intermediate water, (c) when the surface halocline deepens and is eroded due to surface heating, and (d) when convective m i x i n g ceases i n surface and intermediate water (phase V ) . T h e red and green arrows represent respectively heat and salt fluxes. T h e dashed lines show the previous profiles. Note that the increase i n salinity at depth may be gradual, and not a sudden step as suggested by the salt profile. ture gradient was present at depth and requires a s tabil is ing sal ini ty increase of f» 0.02 g L - 1 to inhib i t over-turning. T h i s value is greater than those calculated from the temperature measurements of experiments conducted between 1 g L - 1 and 4 g L - 1 . Interpretation of the 15 g L - 1 experiments is difficult because complete ice cover was not a t ta ined (§ 2.3.1). In future experiments, it would be useful to extend the cooling per iod to ensure complete ice 44 Chapter 2 cover. 2.5 Conclusions T h i s research is a first step i n understanding m i x i n g processes that are in i t ia ted i n brackish lakes due to salt exclusion. T h e results indicate that the Tmd can influence lake s tabi l i ty and m i x i n g behaviour. Other important parameters would include salt exclusion rates, and the spat ial and temporal var iabi l i ty of ice cover formation i.e. rap id m i x i n g at the onset of ice formation versus slower mix ing dur ing the rest of the winter. T h e lowering of the Tm(i at higher salinities affects lake c i rcula t ion by reducing the s tabi l i ty provided by a reverse temperature stratification. T h e reverse stratif ication becomes to weak to support saline water beneath the ice, enabling m i x i n g at greater depths and even complete over-turn . In this research, salt exclusion enabled sudden m i x i n g at the onset of ice formation, and in i t ia ted transport of saline water at depth. It is unclear by which means salt was transported to depth, al though it generally created a stable sal ini ty stratif ication in the subsequent ' spring ' . Further experiments would be required to determine the exact m i x i n g mechanisms oc-curr ing beneath the ice. Notable examples include, flow visual isat ion beneath the ice and salt fingering experiments for cases where reverse temperature stratif ication is s tabi l is ing the water column. Past laboratory experiments having dealt generally w i t h seawater, where wa rm and salty water must overlay colder and fresher water to ini t iate fingering. Fur ther experiments should include more detailed measurements i n a larger, better insulated tank to reduce heat losses through the bo t tom and sidewalls. Current ly, comparisons between this laboratory da ta and field observations i n brackish lakes is underway. The thickness of ice and the s tabi l i ty provided by the fresh water created by mel t ing ice were not investigated i n this research. However, this should not be ignored as i t would have major effects on m i x i n g i n subsequent years, and consequently affecting the long-term evolution of brackish lakes i n cold climates. 45 Bibliography Eicken, H . , Sea Ice: An Introduction to its physics, biology chemistry and geology, chap. 2, pp. 22-81, 1 s t ed., B lackwel l Scientific, London , U K , 2003. Ferris, J . M . , J . A . E . G ibson , and H . R . B u r t o n , Evidence of density currents w i t h the potential to promote meromixis i n ice-covered saline lakes, Palaeogeogr., Palaeoclima-teol, PalaeoecoL, 84, 99-245, 1991. Gallagher, J . B . , and H . R . B u r t o n , Seasonal m i x i n g of E l l i s F jo rd , Vestfold Hi l l s , Eas t Anta rc t i ca , Estuarine, Coastal and Shelf Sc., 27, 363-380, 1988. Gibson , J . A . E . , T h e role of ice i n determining m i x i n g intensity in E l l i s F jo rd , Vestfold Hi l l s , East Anta rc t i ca , Antarct. Sci., 11, 419-426, 1999a. Gibson , J . A . E . , T h e meromict ic lakes and stratified marine basins of the Vestfold H i l l s , East Anta rc t i ca , Antarct. Sci., 11, 175-192, 1999b. Gross, M . , Oceanography, a view of the earth, 6 ed., Prentice H a l l , Englewood Cliffs, New Jersey, U S A , 1993. Hutchinson, G . , A treatise on limnology. Volume 1: Geography, physics, and chemistry, John W i l e y & Sons, Cambridge, U K , 1957. Lide , D . R . (Ed.) , CRC Handbook of Chemistry and Physics, pp. 5-71, 5-73, 8-66, 86th ed., C R C Press, 2006. L u d l a m , S. D . , The comparative l imnology of high arctic, coastal, meromict ic lakes, J. Pa-leolimnol., 16, 111-131, 1996. 46 Chapter 2 Mi l l e r , L . G . , and G . R . A i k e n , Effects of glacial meltwater inflows and moat freezing on mix ing i n an ice-covered An ta rc t i c lake as interpreted from stable isotope and t r i t i u m distr ibutions, Limnol. Oceanogr., 4.1, 966-976, 1996. Schmit t , R . , F l u x measurements on salt fingers at an interface, J. Mar. Res., 37, 419-436, 1979. Shiklomanov, I., and J . R o d d a (Eds.) , World Water Resources at the Beginning of the Twenty-First Century, International Hydrology Series, Cambr idge Univers i ty Press, C a m -bridge, U K , 2003. Spigel, R . H . , and J . Pr i scu , Phys ica l l imnology of the M c M u r d o D r y Val leys lakes, Antarct. Res. Ser., 72, 153-187, 1998. Stevens, C . L . , and G . A . Lawrence, S tabi l i ty and meromixis i n a water-filled mine pi t , Limnol. Oceanogr., 43, 946-954, 1998. Walker , K . , and G . Likens, Meromix i s and a reconsidered typology of lake c i rcula t ion pat-terns, Verhandlungen, Internationale Verinigung fur Theoretische und Angewandte Lim-nologie, 19, 442-458, 1975. Washburn , E . W . (Ed.) , International Critical Tables of Numerical Data, Physics, Chem-istry and Technology, vol . I l l , pp. 107-108, 1 s t ed., K n o v e l , 2003. Wil lemse, N . W . , O . van D a m , P . - J . van Helvoort , R . Dankers, M . Brommer , J . Schokker, T . E . Vals tar , and H . de Wolf, Phys ica l and chemical l imnology of a subsaline athalassic lake i n West Greenland, Hydrobiologia, 524, 167-192, 2004. 47 Chapter 3 Conclusions and Recommendations Labora tory experiments were conducted to investigate m i x i n g i n brackish lakes due to salt exclusion from ice. A physical model was chosen for this purpose i n order to control the effects of lake bathymetry, weather conditions, ice product ion per iod, a l l of which can differ greatly from lake to lake. T h e experiments isolated the influence of salinity. T h e y demonstrate that salt exclusion enables sudden m i x i n g at the onset of ice formation, and initiates vert ical t ransport of saline water. T h i s t ransport of saline water, or iginat ing from beneath the ice, creates a stable density strat if ication the subsequent spring. D u r i n g the experiments, a layer of saline water formed beneath the ice and is supported by a stable reverse temperature stratif ication. Salt accumulates i n this layer un t i l becoming too heavy. T h i s causes the water co lumn to become unstable and initiates sudden m i x i n g w i t h warmer water below. A t higher salinities, the lowering of the Tmd affects lake ci rcu-la t ion by reducing the s tabi l i ty provided by the reverse temperature strat if ication. T h e reverse stratification becomes too weak to support saline water beneath the ice, enabling mix ing at greater depths and even complete over-turn. T h i s behaviour is accentuated by larger amounts of salt expelled by the ice at higher salinities. In the experiments conducted, downward transport of salt accompanied by significant upward heat fluxes were observed throughout the dura t ion of ice formation. T h i s transport played a role i n increasing water sal ini ty beneath the ice and acted at a l l depths. T h e temperature t ime series show that this transport was a slow vert ical process, exchanging heat and salt amongst adjacent layers of water. T h e temperature t ime series of intermediate waters (i.e. 2nd sensor from the surface) demonstrates the exchange of heat more clearly. A t this location, cooling and warming occurs depending on the balance between heat fluxes 48 Chapter 3 given to colder water above and heat received from warm water below. The heat exchange is dr iven by an increase i n sal ini ty of shallower waters, which initiates downward salt fluxes. T h e results in Chapter 2 suggest that brackish lakes could be subdivided into two groups based on their sal inity: a high sal ini ty (S > 8 g L - 1 ) group where the Tmd is smal l and the amount of salt expelled from the ice is high, permi t t ing complete over-turn; and a lower sal ini ty group (1 g L - 1 < S < 4 g L - 1 ) where a reverse strat if ication is always present. Further investigations and experiments are required to determine the detailed nature of m i x i n g beneath the ice. It would be informative to conduct flow visual isat ion beneath the ice to investigate the possible presence of salt fingers. It may be that an unknown m i x i n g mechanism is applicable to brackish lakes, where the effects of the Tmd are significant. It would be desired to compare the laboratory data to field observations. Temperature t ime series from lakes i n the Northwest Terr i tory (S ra 1 g L - 1 ) show similar features as lab-oratory experiments, but more thorough analysis is s t i l l underway (Pieters and Lawrence, 2006). Further attention should be given to salt exclusion rates, as there is an indica t ion that slower processes are occurr ing throughout the freezing processes along w i t h rap id mix-ing at the onset of ice formation. T h e thickness of ice and the s tabi l i ty provided by the fresh cap were not investigated i n this research. However, this should not be ignored as it would have major effects on m i x i n g i n subsequent years, and consequently affecting the long-term evolution of brackish lakes i n cold climates. 49 Bibliography Pieters, R . , and G . A . Lawrence, Impact of sal ini ty and ice-cover on a subarctic lake, 2006, draft for M i n s i t r y of Indian and Nor thern Affairs, Government of Canada . 50 Appendix A Equation of State A . l D e t e r m i n i n g S a l i n i t y Potass ium chloride concentrations (salinity) were determined from conduct iv i ty and tem-perature measurements. T h e conduct iv i ty of pure water is only 0.005 / / S c r n - 1 at 25 ° C while the conduct ivi ty of saline solutions is much higher due to salts dissociat ing into its charged ions. A t the concentrations investigated dur ing this research, the relationship be-tween potassium chloride concentration and conduct iv i ty is linear for a given temperature. However, the linear equation relat ing these two parameters differs from one temperature to another. For a given salinity, conduct iv i ty also varies l inearly w i th temperature; the relationship changing from one concentration to another. Often conduct ivi ty measurements are corrected to a reference temperature to yie ld spe-cific conductance, the reference temperature being usual ly 20 or 25 ° C . Then , a relation-ship specific to the ionic composi t ion and chosen reference temperature is used to calculate salinity. A widely used relationship to calculate specific conductance from conduct iv i ty and temperature measurements is as follows: c ' r ° > = u . ( T - r . ) ^ where C(T0) represents the corrected conduct iv i ty at the reference temperature T0, and C(T) the measured conduct iv i ty at temperature T. A n average value for a of 0.02 is often used for potassium chloride aqueous solutions. In reality, a varies w i t h temperature and salinity. Thus , Equa t ion A . l was not applied for this research since wide ranges of temperatures ( 0 ° C to 2 5 ° C ) and salinities (0 g L - 1 to 15 g L - 1 ) were investigated. Instead, 51 A p p e n d i x A Temperature °C Pure Water 0.01 m o l L " 1 0.1 m o l L " 1 1 m o l L - 1 0 1 .55x l0" 5 0.77292 7.11685 63.488 5 2 . 3 4 x l 0 " 5 0.89096 8.1837 72.03 10 3 . 1 3 x l 0 ~ 5 1.01395 9.29172 80.844 15 3 . 9 2 x l 0 - 5 1.14145 10.4371 89.9 18 4 . 3 9 x l 0 ~ 5 1.21993 11.1406 -20 4 . 7 1 x l 0 - 5 1.27303 11.6159 99.17 25 5 . 5 0 x l 0 - 5 1.40823 12.8246 108.62 30 6 . 2 9 x l 0 " 5 1.54663 14.0592 118.240 35 7 . 0 8 x l 0 - 5 1.68779 15.316 127.970 Table A . l : Conduc t iv i t y of pure water and potassium chloride aqueous solutions i n m s c m - 1 as a function of temperature (Lide, 2006). Sal in i ty ( g k g - 1 ) Tf ( ° C ) Tmd ( ° C ) 5 -0.23 -10 -0.46 2.39 20 -0.92 0.82 30 -1.38 -0.75 40 -1.85 -Table A . 2 : Tmd and Tf da ta for potassium chloride aqueous solutions (Lide, 2006; Wash-burn, 2003) a table w i t h 0.04 m s c m - 1 and 0.1 °C increments was created i n M a t l a b using conduct ivi ty, temperature data for three different concentrations of K C 1 and for pure water. T h e da ta for potassium chloride solutions was obtained at the following concentrations: 0.01 m o l L - 1 , 0.1 m o l L - 1 , 1 m o l L - 1 and can be found in Table A . l along w i t h da ta for pure water (Lide, 2006). T h i s table was used to evaluate sal ini ty from conduct iv i ty and temperature using the interp2 function available in M a t l a b . The errors i n est imating sal ini ty using this interpolat ion method were less than 1% of the calculated salinity. A contour plot of the interpolat ion table is given i n Figure A . l . 52 A p p e n d i x A Water Temperature ( ° C ) Figure A . l : Potass ium chloride concentration as a function of temperature and conduct iv-ity. Contours represent salinities i n g L - 1 . A.1.1 Tmd and T , The Tmd and Tf vary l inearly w i t h sal inity as i l lustrated in Figure A . 2 . T h e equation relating the Tmd i n °C to potassium chloride concentrations was obtained from a linear regression of the data i n Table A . 2 . T h i s equation at atmospheric pressure: Tmd = 3.9839 - 0.1580-5, (A.2) where S is potassium chloride concentrations in g k g - 1 . T h e value of 3 . 9 8 3 9 ° C for the Tmd of pure water was taken from the equation developed by Chen and Millero (1986) at 53 A p p e n d i x A atmospheric pressure: Tmd = 3.9839 - 0 .2219-S^ , (A.3) where Ssw is the sal ini ty of di luted seawater. T h e equation relat ing the Tf i n °C to potassium chloride concentrations at atmospheric pressure: Tf = -0 .0137 - 0.0460-5, (A.4) which was obtained from linear regression of the da ta i n Table A . 2 . T h e value for the Tf of pure water was also taken from the equation developed by Chen and Millero (1986) for di luted seawater at atmospheric pressure: Tf = - 0 .0137 - 0.0520-S™ (A.5) Equat ions A . 2 and A . 4 are represented graphical ly i n Figure A . 2 along w i t h the or iginal da ta used to derive these equations. A t a salinity of 35.7 g k g - 1 the effects of the Tmd on density are inexistent for potassium chloride solutions. In contrast to seawater, where the Tmd becomes lower than the Tf at a sal ini ty of approximately 24 g k g - 1 . A.2 Determining Density The equation of state for potassium chloride was obtained by modifying the equation of state for di luted sea water developed by Chen and Millero (1986). T h e general form of the formula developed by Chen and Millero (1986) neglecting pressure terms: p(T,S) = Po(T)+g{T)-S, (A.6) where g(T) is equivalent to 8(T)-p0(T). T h e haline contract ion coefficient, 3, varies w i t h temperature and is specific to the solution ionic composi t ion. T h e density of pure water, 54 A p p e n d i x A Figure A.2: Tma and Tf for potassium chloride aqueous solutions at atmospheric pressure. T h e markers represent the original da ta obtained from Lide (2006); Washburn (2003). Po(T), as a function of temperature, T,.developed by Chen and Millero (1986): p0(T) = 0.9998395 + 6.7914 • 10~5T - 9.0894 • 10 _ 6T 2 +1.0171 • 10-7T3 - 1.2846 • 10" 9r 4 (A.7) +1.1592 • 10~ ur 5 - 5.0125 • 10" 1 4T 6 where T is in °C , and p[T) is i n units of g e m - 3 . T h e function g(T) in E q u a t i o n A.6 was reduced by Chen and Millero (1986) to a quadrat ic formula of the following form: g(T) = a-bT + cT2, (A.8) 55 A p p e n d i x A where a, b and c are positive constants that depend on the salts present i n solution. In the equation of state developed by Chen and Millero (1986), the constants acm, bcm and ccm are respectively 8 .181-10 - 4 , 3 .85-10 - 6 and 4 .96 -10 - 8 . These constants yie ld densities, Pcm(T, S), that are i n units of g e m - 3 when salinities are expressed in g k g - 1 . For potassium chloride, the constants a ^ , bkd and Ckd were determined using density da ta obtained from Perry and Green (1997); Lide (2006), and da ta concerning the var ia t ion of the Tmd w i t h sa l in i ty (Washburn, 2003). Others have appl ied a rat io of the lake water haline contraction coefficient to the haline contract ion coefficient of di lu ted seawater to these three constants; i n order to yie ld the equation of state for water that have a different ionic composi t ion than seawater (Wuest et al., 1996). However, using the same rat io for constants, akci, bkd and Ckd, overestimated the Tmd, especially at h igh salinities. T h i s discrepancy may be i n part due to the fact that the equation of state developed by Chen and Millero (1986) is for di lu ted seawater, which contains a mixture of different salts. W h i l e , the current research uses a saline solut ion containing only potassium chloride. In addi t ion, the equation of state from Chen and Millero (1986) is va l id for salinities ranging from 0 to 0.6 g k g - 1 , when salinities i n the current research range from 0 to 20 g k g - 1 . Thus , each constant, a^d, bkd and Ckd, was determined ind iv idua l ly ; their ratios w i t h their counterpart i n pcm(T, S) being a l l different. The constant akd was found using handbook data for densities of potassium chloride at 0 ° C (Table A . 3 ) . A t this temperature, Equa t ion A . 6 is reduced to: Pkd(0,S) = po(0) + akdS, (A.9) _3 where a was found to be equal to 6 .764-10 - 4 g^™-l • D i v i d i n g a by p o (0) yields the haline contract ion coefficient at T= 0 ° C , which is equal to 6 .765-10 - 4 ( g k g - 1 ) - 1 . A n approximate value for the constant bkd was found using the Tmd da ta for potassium chloride and comparing w i t h the equation developed by Chen and Millero (1986). T h e Tmd is sensitive to the value of the constant b. Hence, an in i t i a l estimate for bkd was found 56 A p p e n d i x A Sal in i ty ( g k g " 1 ) 0 ° C 20 °C 25 °C 5 - 1.0014 -10 1.00661 1.00462 1.00342 15 - 1.0078 -20 1.01335 1.01103 1.00977 25 - 1.0142 -30 - 1.0174 -35 - 1.0207 -40 1.0269 1.02391 1.02255 Table A . 3 : Densities for potassium chloride solutions at various temperatures and concen-trations (Perry and Green, 1997; Lide, 2006). by comparing the slopes of the equations relat ing sal ini ty to Tmd for d i lu ted seawater and potassium chloride solutions (Equations A . 2 and A . 3 ) . T h e ratio of the slopes for bo th of these equations (02219)1 was equal to 0.712. T h e in i t i a l estimate for bkd was deemed to be 2 .74-10 - 6 k g c m _ 3 o C _ 1 (bkci= 0 .7126 c r n ) . A n in i t i a l guess for ckd was obtained by calculat ing the ratio of the haline contraction coefficient, Bkci, equal to (or f ^ ) - T h e n , mul t ip ly ing the ratio Bkd w i t h ccm to yie ld Ckd- The constants bkd and Ckd were then modified to minimize errors between calculated and theoretical Tmd, and between calculated and theoretical densities for potassium chloride. T h e final equation of state used for est imating densities for potassium chloride, wh ich is va l id for salinities between 0 and 20 g k g - 1 and temperatures ranging from 0 to 25 °C : Pkd(T, S) = Po(T) + (akd - bkdT + ckdT2)S ( A . 10) where p0(T) is calculated from Equa t ion A . 7 . S is the concentration of potassium chloride i n g k g - 1 , and constants akd, bkd, and ckci are 6 .764-10 - 4 , 2 .71-10 - 6 , 4 . 49 -10 - 8 respectively. The density, pkd (77, S), is i n units of g c m - 3 . Discrepancies between density computed w i t h E q u a t i o n A . 10 and theoretical values i n Table A . 3 was less than 2 . 5 - I O - 5 g e m - 3 . The Tmd obtained from differentiating E q u a -t ion A . 10 w i t h respect to temperature was w i t h i n 0.05 °C of the theoretical Tmd i n Table A . 2 . 57 A p p e n d i x A Figure A . 3 : Equa t ion of state for potassium chloride aqueous solutions at atmospheric pressure. T h e dashed line represents the Tmd-58 Appendix B Experimental Results Table B . l summarizes experiments i n which temperature measurements were made. A t the in i t i a l stages of this research, t r i a l experiments, denoted by the letter T i n Table B . l , were done w i t h dis t i l led water to validate the physical model . These t r i a l experiments, TI through T 3 , served to ensure that enough insulat ion was provided for a reverse strat if ication to establish itself i n the water column. T h e y had variable sensor depths, water volume, and even variable insulat ion to determine appropriate experimental conditions to be used i n the experiments depicted i n Chapter 2. Exper iments T 4 and T 5 were effectuated to test lights, which were required to take pictures of the water surface w i t h the web cam. The addi t ional purpose of Exper iment T 4 was to determine how water temperatures differed from the sidewalls and the middle of the ' lake' , when salt was present i n the ' lake' . Exper iment T 6 was done to verify the assumption that colder temperatures found at the end of the cool ing per iod i n prel iminary, P, experiments, were due par t ly because of the extended cooling per iod (Append ix B.1 .3) . Exper iment T7 is an insulat ion test that was performed wi thout any addi t ional fiberglass and styrofoam insulat ion. It was performed w i t h the same sensor depths, volumes, and cooling periods as the final, F, experiments. A l l pre l iminary experiments, P, used a volume of potassium chloride solut ion equal to 13 liters. T h e sensors i n these experiments were located at 2, 9, 15 and 20 c m from the bo t tom of the ' lake' , which was placed direct ly on the bo t tom of the freezer. T h e cool ing period varied slightly from one experiment to another but were a l l w i t h i n 17 to 18 hours. The experiments denoted w i t h the letter F in Table B . l are the final results used to draw conclusions on the effects of sal inity on under ice c i rcula t ion (see Chapter 2). These 59 A p p e n d i x B Exper iment name Date Sal in i ty ( g L " 1 ) Comments T I Oc t 5/05 0 N o insulat ion, V = 1 0 L T 2 O c t 24/05 0 V = 1 2 L T 3 Oc t 28/05 0 Ex tended cooling, V = 1 0 L T 4 M a r 6/06 2 lamp, 2 moorings T 5 M a r 8/06 2 lamp, C T T 6 A p r 11/06 4 Extended cooling, C T T 7 A u g 19/06 0 Insulat ion test P I N o v 2/05 4 -P 2 N o v 7/05 8 -P 3 N o v 9/05 2 -P 4 N o v 16/05 1 -P 5 N o v 2 4 / 0 5 15 -P 6 Dec 7/05 1 -F I A p r 6/06 2 C T F 2 A p r 19/06 4 C T F 3 M a y 29/06 1 C T , syringe F 4 M a y 23/06 1 C T , syringe F 5 J u l y 11/06 8 -F 6 J u l y 19/06 0 • -F 7 A u g 30/06 15 -Table B . l : Exper iments done w i t h t ime series temperature measurements experiments were a l l conducted w i t h 14 liters of solut ion, and w i t h a constant cool ing per iod of 19 hours. T h e temperature sensor tips in those experiments were placed at 1, 8, 17, and 21.5 c m from the bo t tom of the container. T h e to ta l water depth i n the ' lake' was 24.5 cm. In the final experiments, the ' lake' was raised by 2.5 c m from the bo t tom of the freezer to permit CT measurements at deeper depths w i t h the MSCTI. Phys ica l constraints due to the traverse height, sensor length and freezer depth, made i t impossible to cast a deeper depths without raising completely the ' lake'. Th i s raising permit ted air to circulate freely under the ' lake' bo t tom. A web cam and LEDs were inside the freezer i n these experiments, i n order to determine when surface ice formed. In the 'Comments ' co lumn of Table B . l , it is indicated whether or not CT casts were done w i t h the MSCTI instrument. T h e 'Comments ' i n Table B . l also mention if aliquots were taken w i t h a syringe from the ' lake' to establish the ver t ical d i s t r ibut ion of salinity. 60 A p p e n d i x B B . l Trial, T , Experiments B . l . l 2 D Nature The results from experiment T 4 i n Figure B . l shows the var iabi l i ty of water temperatures, depending i n the distance away from the imperfectly insulated sidewalls. T w o moorings, which bo th had two sensors, were placed i n the ' lake' . M o o r i n g A was located beside the sidewall and the other, moor ing B, was placed i n the center of the container (see Legend i n F igure B . l ) . A n attempt was made to place the sensors of moor ing A at the same depths as those on moor ing B. However, the recorded temperatures seem to indicate that the surface sensor on mooring A was placed closer to the ice-water interface than the equivalent sensor on mooring B. T h e slight difference i n height and the non-linear relationship between distance from the ice-water interface and water temperature, could explain why the surface sensor on moor ing A displayed colder temperatures (Figure B . l ) . Furthermore, recorded temperatures from moor ing A show smaller temperature fluctuations than those recorded near the middle of the ' lake' . It may be that water located closest to the sidewalls is less sensitive to the effects of brine exclusion from the ice (Figure B . l ) . In deed, heat losses through the sidewalls dur ing phase II would create lighter water, mak ing i t more difficult for saline, denser water near the ice-water interface to travel down near the edges than i n the middle of the ' lake'. It must be noted that experiment T 4 had as secondary goal to test the effects of a 25 watt lamp placed wi th in the freezer to take pictures w i t h the web cam. Thus , water temperatures obtained i n experiment T 4 cannot be compared to results from any of the preliminary, P, or final, F, experiments. B . 1 . 2 Slower Cooling Exper iment T 5 was conducted w i t h a 25 watts l amp w i t h i n the freezer to provide light for tak ing pictures w i t h the web cam (Figure B.1 .2) . T h e lamp provided too much heat and heat fluxes through the boundaries were compet ing w i t h those at the surface. In deed, the 61 A p p e n d i x B - 0 . 5 -_ ^ I i I i i i i 1 1 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Time in days Figure B . l : Slower C o o l i n g and spat ial var iabi l i ty (March 6, 2006 at 2 g L - 1 ) bo t tom sensor displayed colder water temperatures than the remaining of the water co lumn dur ing phase I and at the onset of phase I I . The ice product ion per iod was reduced w i t h 62 A p p e n d i x B the presence of the lamp; it took 2.5 hours more before ice started to form at the surface, than it took for an equivalent experiment done without the lamp. T h e freezing period also had to be extended i n order to obtain complete ice cover on the surface. Water temperatures dur ing the warming per iod (phase I V ) showed no evidence that salt-stratification was present i n the water-column, possibly because the formed ice was too th in to create a substantial fresh layer upon mel t ing (Figure B.1.2) . In fact, when a very th in layer of ice is formed, the fresh surface layer and its warmer temperatures cannot reach the surface sensor. T h e previous results made it necessary to use L E D s as a light source w i t h i n the freezer, to ensure insignificant heat product ion dur ing subsequent F experiments. T h e use of LEDs was also required to ensure that bo t tom water remained warmer (and denser) than the rest of the water co lumn dur ing phase II. B . 1 . 3 Extending Cooling Exper iment T 6 was performed i n the same fashion as F experiments (§ 2.2), at the exception that the ' lake' was left to cool for 23 hours instead of 19 hours. The results of experiment T 6 demonstrate that extending the freezing per iod permits water temperatures, at the end of phase II, to become colder than they would have been w i t h a shorter cooling per iod (Figure B .3 ) . These colder temperatures are probably a result of the imperfect insula t ion around the experimental apparatus. In fact, heat losses do occur through the sidewalls but to a lesser extent than at the surface (see A p p e n d i x D ) . T h e effects of variable cool ing periods on water temperatures were removed i n subsequent (F) experiments by ensuring they were a l l left to cool for the same per iod of 19 hours. Unfortunately, the stratif ication i n the ' lake' was dis turbed at 1.3 days from the in i t i a l start of the experiment due to testing of the MSCTI profiler after ice melt-out (F ig -ure B .3 ) . Results obtained from the warming per iod of experiment T 6 were not used to draw conclusions on the effects of extending the ice product ion per iod on ' spr ing ' water temperatures. 63 A p p e n d i x B (ii A p p e n d i x B n r Thawing j i_ 0.6 0.8 1 1.2 1.4 1.6 o o CD 3 -<—' TO 15 CD Q_ E Te 10 i— 5 5 Zoom on region where T < T 0.7 0.8 0.9 Time in days 1.2 Figure B . 3 : Ex tend ing C o o l i n g ( A p r i l 11, 2006 at 4 g L 1 ) . The l i d was opened but the freezer was not turned off un t i l 1 day after the beginning of the experiment. B.1.4 Insulation Test Exper iment T 7 was conducted to verify the effect of removing layers insulat ion used i n experiments discussed i n Chapter 2. It was effectuated w i t h the same experimental con-65 A p p e n d i x B dit ions as the final, F, experiments at 0 g L - 1 . Exper iment T 7 was used to establish the reduction of heat losses that can be achieved w i t h addi t ional insulat ion (see § D.2.3) . B.2 Preliminary, P , Results T h i s section contains plots for a l l prel iminary experiments i n Table B . l , wh ich were a l l conducted prior to January 2006. T h e shallower water depths used i n P experiments resulted i n weaker temperature gradients between sensors, especially between the two top-most sensors. T h e dura t ion of freezing differed s l ight ly from one experiment to another. These variations i n freezing periods explains why the boundary between phase II and III occurs at different times for each experiment. T h e web cam was not present dur ing these experiments. Thus , the t ime period when ice cover is present at the surface is not indicated on the plots i n Figures B .5 through B . l l . B.3 Final,F, Results Figures B.12 through B.17 show the final temperature moor ing results presented i n Chap-ter 2. A l l dashed vert ical magenta i n these plots indicate the t ime when CT casts w i t h the MSCTI were done. There are some instances where the water co lumn was dis turbed due to the CT casts. Temperature readings after these disturbances were ignored i n any analysis done w i t h the data. The following figures have been placed i n ascending order of their in i t i a l salinity. 66 Appendix B 67 68 69 A p p e n d i x B Figure B . 7 : November 16 at 1 g L 1 70 Appendix B Appendix B 72 A p p e n d i x B i 1 1 1 r—i 1 - 1 r i I i i I i i I i 1 1—1 1 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Time in days Figure B.10: November 8 at 8 g L 1 73 A p p e n d i x B O o _ 20 -4—' CC & 0 E CD -20 < 0 0.2 0.4 0.6 0.8 1.2 1.4 i i i i i Freezing Thawing i i i i i i i i 1.6 1.8 O o CD i_ zs "cc 1_ CD C L E CD CD -t—' cc 0.4 0.5 Zoom on region where T w < T_ d 0.6 0.7 0.8 0.9 Time in days 1.1 Figure B . l l : November 24 at 15 g L 1 71 75 A p p e n d i x B 0.2 0.4 0.6 0.8 1 1.2 Zoom on region where T w < T"m d 1.4 0.5 0.6 0.7 0.8 0.9 Time in days 1.6 Figure B.13: M a y 23 at 1 g L " 1 76 Appendix B 77 Appendix B 0.2 0.4 0.6 0.8 1 1.2 Zoom on region where T w < T"md 0.5 0.6 0.7 0.8 0.9 Time in days Figure B.15: Apr i l 6 at 2 g L 7 8 Appendix B Zoom on region where T < T a w md 0.5 0.6 0.7 0.8 0.9 1 Time in days 1.1 1.2 Figure B.16: Apr i l 19 at 4 g L - i 7!) Appendix B 8 0 Appendix B 81 Appendix C CT vertical profiles A set of experiments was performed to determine the ver t ical salt d i s t r ibu t ion i n the ' lake' after ice melt-out and the subsequent ' spr ing ' . A microscale conduct iv i ty and temperature instrument (MSCTI) obtained from P M E was used w i t h a ver t ical traverse to obta in CT profiles i n the water column. T h e following section discusses the ca l ibra t ion procedure and difficulties encountered when measuring temperature and conduct iv i ty w i t h the MSCTI. The purpose of this A p p e n d i x is to give details for future users about the challenges and appl icabi l i ty of using the MSCTI i n the laboratory for this type of research. C . l M S C T I Calibration The instrument was cal ibrated for temperature and conduct iv i ty prior to each cast following instructions given i n the operator's manual (PME, 2005). In general, 3 aqueous solutions of potassium chloride were created to calibrate the sensor for conduct iv i ty and 2 samples of cold tap water were used to calibrate for temperature. T h e aqueous solutions bracketed the expected salinities for each experiment; a solut ion was as concentrated as the in i t i a l solution of the experiment, the other was di lu ted to half that concentration and the most di luted was at 0.5 g L - 1 to respect the conduct iv i ty range that can be measured w i t h the MSCTI. The conduct iv i ty and temperature of the saline solutions were measured using a W T W - 3 3 0 hand held conduct ivi ty meter prior to ca l ibra t ing the MSCTI. T h e two tap water samples were poured i n 50-ml vials and placed i n an ice bath. One sample was cooled at the lowest expected temperature 1 °C) and the other was cooled to « 7 ° C . The temperatures of these solutions were measured w i t h a 0.1 °C thermometer pr ior 82 A p p e n d i x C to t ak ing measurements w i t h the MSCTI. For each solut ion, 10 scans were taken w i t h the MSCTI, which measures voltage at a frequency of 4 H z . A n addi t ional temperature cal ibrat ion was obtained from the 3 saline solutions that were left at room temperature. Thus, 3 data points were obtained to bracket the range of expected temperatures and another 3 were obtained to bracket the expected conductivi t ies. C.2 Challenges C . 2 . 1 Temperature Sensor T h e exponential relationship relating temperature T i n kelvins to voltage V(T): VT = GTexp(A + | ) + V O F F T ( C . l ) where A , B, gain GT are cal ibra t ion constants. VaffT was determined w i t h the method described i n the user manual (PME, 2005). It was found to be equal to -4.986 volts for the MSCTI used. Equa t ion C . l can be modified to have only two constants: VT = exp(A' + ^) +VoffT, (C.2) where A' is a cal ibrat ion constant equal to A+lnGr- A c c o r d i n g to the manufacturer F A Q s website (PME), temperature sensor w i l l main ta in its ca l ibra t ion for months. Thus , a l l temperature calibrations effectuated prior to each experiment, were used to establish the temperature cal ibrat ion curve (see Figure C . l ) since a l l of them were performed between M a r c h and M a y 2006. Constants A' and B were found by rearranging Equa t ion C .2 : H V T - V O F F T ) = A' + ^ , (C.3) 83 A p p e n d i x C 2 0 gl i i i i i i 3.35 3.4 3.45 3.5 3.55 3.6 3.65 1/T, where T is in Kelv ins x 10 3 Figure C . l : Temperature cal ibra t ion curve. In total , 17 da ta points were used to obta in this cal ibrat ion curve. which yields a linear equation of the form: y = d + mx) ( C 4 ) where y represents l n ( V r — K Z / T ) and x is equivalent to ^ . T h e slope m is equal to the cal ibrat ion constant B i n Equa t ion C .2 , while the intercept d represents A'. These cal ibrat ion constants, A' and B, are equal to respectively -10.5967 and 3431.9 Ke lv in s w i t h the set gain and the MSCTI used dur ing experiments. Difficulties were encountered when determining the vert ical d is t r ibut ion of temperature w i t h i n the water-column. T h i s was most noticeable for casts done at colder temperatures 84 A p p e n d i x C after ice melt-out. T h e conversion of voltages to temperature d id not y ie ld temperatures wi th in those obtained w i t h the mooring of H O B O U12 temperature sensors (Figure C.2) . T h i s may be par t ly due to the difficulty i n ca l ibra t ing the sensor at cold temperatures, worsened by the exponential relationship between temperature and voltages (Equa t ion C.2) . In deed, differentiating Equa t ion C.2 w i t h respect to temperature shows how voltages are more sensitive to temperature changes at lower temperatures: 8Vr AVT = ^ A T , (C.S) which equals to: AVT = - ^ f exp U' + | ) A T (C.6) Ca l ib ra t ing properly the solutions at cold temperatures was difficult w i t h the MSCTI. Notably, keeping the cold solutions at a constant temperature when a large temperature gradient is present between the cal ibrat ion solut ion and the surrounding air i n the labo-ratory. Us ing a larger ca l ibra t ion solut ion volume and a larger ice ba th may help i n this regard but was imprac t ica l w i t h the current experimental set-up. T h e MSCTI had to be calibrated above the model lake w i t h the traverse s i t t ing on the edges of the freezer walls, l im i t i ng the size of the cal ibrat ion apparatus. T h i s chosen set-up was required since cal ibra t ion drifts are significant for the conduct iv i ty sensor, especially i f the sensor t ip gets i n contact w i t h air (PME, 2005). C.2.2 Conductivity Sensor To relate conductivi ty, C, to the measured voltages of the MSCTI, VQ, a linear relation-ship is used: Vc — Gc • C + V0ffc (C.7) where Gc is the gain specific to the conduct iv i ty sensor, and V0ffc the voltage of a solut ion w i t h conduct iv i ty equal to zero. Dis t i l l ed water and tap water have low enough conduct iv-85 A p p e n d i x C s •c • Initial S 1.8 1.9 2.1 2.2 2.3 2.4 Conductivity (mscm 1), Salinity (gkg 1) 250 200 150 100 50 1.8 1. 2.1 2.2 2.3 2.4 Conductivity (mscm 1), Salinity (gkg 1) Figure C.2 : Compar i son of temperatures measured w i t h the MSCTI to temperatures obtained from the mooring. T h e left hand figures represent results from CT casts performed after ice melt-out, while the right hand side shows results from casts performed after spring mix ing . 86 Appendix C ities for the determination of K / / C , since the minimum conductivity that the MSCTI can measure is 0.5 mscm -1. The term V0ffc w a s found to be -5.000 volts for the sensor used. The value for Gc, for the set gain was typically around 0.210 ms - 1 cm, and differs for each experiment. The MSCTI was used to determine the general shape of the vertical salt-structure in the water column rather than the absolute salinity. In deed, the conductivity (and hence salinity) structure obtained is very sensitive to the calibration constants used. Amongst the three solutions used to calibrate for conductivity prior to an experiment, the calibra-tion constant, Gc, varied by ± 3%. This variation can explain the discrepancies bewteen conductivities computed with the MSCTI measurements and those measured from the aliquots removed with the syringe (see Figure 2.7). When performing a downcast with the MSCTI through the water column, conductivity measurements suddenly spiked, creating a step in conductivity (Figure C.2). This step occurred at the same depth for each downcast and upcast performed. The distance from the water surface to the location where the step occurred was equivalent to the length of the MSCTI sensor tip. Its length was larger than resolution of the vertical profiles, which was 4 m m with the chosen traverse speed of 1 mm sec-1 and the measurement frequency of 4 Hz. To remove these conductivity steps (i.e. voltage hikes), submerging completely the sen-sors prior to taking measurements with the MSCTI might be beneficial. However, sub-merging completely the sensors was not possible for the current research. It would have resulted in missing data near the surface that were important for establishing the depth of the fresh surface layer after ice melt-out. 87 Appendix D Heat Fluxes D . l Theoretical Heat Fluxes D. l . l Governing Equations T h e following equations describe the possible heat transfer mechanisms that can occur dur ing experiments. Surface Heat Fluxes Tota l heat fluxes, qtot can be calculated as follows: where qr is radiat ion heat losses, qs represents sensible (or free convection) at the water surface, qiat are latent heat losses due to evaporation and qc are losses due to conduct ion through the ' lake' boundaries. E a c h of these terms w i l l be explained ind iv idua l ly i n the following sections. Radiat ion heat fluxes (qr) T h e tota l radia t ion heat fluxes, qr, are equal to qri + qro- L o n g wave radiat ion emit ted by the water surface, qro, is calculated using the following formula: qtot = qr + qs + Qiat + <7< ( D . l ) (D.2) 8 8 A p p e n d i x D where a represents the Stefan-Bol tzman constant equal to 5 . 6 7 x l 0 ~ 8 W m ~ 2 K ~ 4 , and e 0 the water (or ice) surface emissivity. T0 is the surface water temperature i n kelvins. T h e water emmis iv i ty was assumed to be equal to 0.96 (TVA, 1972; Incropera and DeWitt, 1996). T h e long wave radiat ion absorbed by the water surface, qri, is obtained from the fol-lowing relationship for lakes exposed to the atmosphere (TVA, 1972): qri = - 0 . 9 7 a e a i r T 4 r , (D.3) where eair is the air emissivity, which can be calculated w i t h the following relationship (TVA, 1972): eair = 0 .937-10- 5 ( l + 0 . 1 7 C 2 ) T 2 r , (D.4) where C is the percent c loud cover assumed to be equal to 1 due to the presence of the freezer walls. Tair is the air temperature i n kelvins, equal to 261K for the current experimental conditions. These conditions yielded a value of 0.747 for eair. Equat ions D .3 were applied to the experimental temperature data, though the experiments were not conducted outdoors (see A p p e n d i x D.2.1). N a t u r a l Convec t ive Hea t Transfer (qs) Heat losses due to natural convection at the water surface (or free convection) can be calculated using the following relationship: qs = ah(T0 - Tair), (D.5) where a/j is the convective heat transfer coefficient i n W m - 2 ° C _ 1 , T0 the water surface temperature i n Kelv ins , and Tair the surrounding air temperature i n Ke lv ins . T h e convec-tive heat transfer coefficient can be calculated using the following relationship for a w a r m 89 A p p e n d i x D horizontal surface being cooled from above (Incropera and DeWitt, 1996): Nu = 0 . 1 5 i ? a 1 / 3 , (D.6) which is va l id for 107<Ra < 1 0 n . T h e Rayle igh number, Ra is defined as (TVA, 1972; Incropera and DeWitt, 1996): Ra = — , (D,7) DapAV where g is the gravi tat ional constant, pa is the density of the surrounding air (1.348 k g m - 3 for dry air at -13 °C) and v is the kinemat ic viscosity of the surrounding air (12 .33-10 - 6 m 2 s _ 1 ) . Ap represents the density difference between the surrounding air and air at the water surface temperature. Da is the molecular diffusivity of air (17 .22-10 - 6 m 2 s - 1 at - 1 3 ° C ) , and the characteristic length, I, i n meters is (Incropera and DeWitt, 1996): l = y, (D.8) where As is the surface area of the water surface, and P its perimeter. Nu is the Nusselt number equal to (TVA, 1972; Incropera and DeWitt, 1996): N u = ^ , (D.9) T h e variable ka represents the molecular heat conduct iv i ty of air equal to 2 3 - 1 0 - 3 W m - 1 s _ 1 for dry air at -13 °C . Equa t ing Equa t ion D.6 to Equa t ion D.9 yields the final relationship used for est imating ah-ah = 0A5kair£(-^-) , (D.IO) where £ is a correction coefficient for the shape of the surface relative to a flat plate. It is assumed to be 0.5 for a lake surface and is equal to 1 for a perfectly flat surface (TVA, 1972). 90 A p p e n d i x D Latent heat of evaporation (qiat) The latent heat lost by evaporation is calculated w i t h Equa t ion D . l l : qiat = pLE, ( D . l l ) where p is the density of potassium chloride solut ion i n k g m - 3 , L the latent heat of evaporation in J k g - 1 (2.50-10 6 — 2390T o w i t h T0 i n ° C ) , and E is the evaporation rate of water in m s e c - 1 . T h e evaporation rate is calculated w i t h Equa t ion D.12: E = ae(no-ns), (D.12) where Q0 is the saturat ion vapor pressure of air at temperature T0 i n kg k g - 1 , which is also dependent on air pressure. Qs represents the vapour pressure of the air above the water i n kg k g - 1 , which depends on T0, the air relative humid i ty and air pressure. ae is the free convective evaporation coefficient i n m s e c - 1 and is a function of water temperature, humidity, air temperature and pressure. It can be approximated w i t h this relationship (TVA, 1972): ae = (D.13) Cpp where a/j is the sensible heat transfer coefficient calculated w i t h Equa t ion D.10, and Cp is the specific heat of water. Conduction (qc) T h e conduct ion term, qc, takes into account the remaining heat losses that occurs through the sidewalls of the container. It can be regarded i n some respect as the opposite of geothermal heating through the ' lake' boundaries. It can also be viewed as cool ing due to permafrost around the lake. The general form of the equation used to calculate heat losses due to conduction through layers of mater ial is the following (Incropera and DeWitt, 1996): 91 A p p e n d i x D (D.14) where kwau is the wal l conduct ion heat transfer coefficient i n W m - 2 ° C _ 1 , which is often reported by manufacturer i n units of W m - 1 ° C ~ 1 . D i v i d i n g this reported conduct iv i ty by the thickness of mater ia l w i l l y ie ld kwau i n W m - 2 ° C _ 1 . To take into account the possibil i ty of a large free convection heat coefficient at the wal l surface, E q u a t i o n D.14 was rewri t ten in a more general form: where Rw is the equivalent resistance to heat fluxes through the wal l i n W _ 1 m 2 ° C . T h e wal l resistance, Rw, was obtained from the experimental recorded temperatures obtained i n phase If (see A p p e n d i x D.2) . D.2 Heat Flux Computations D.2.1 Estimating wall heat resistance, Rw The resistance of the boundaries, R^, was obtained by t r i a l and error by compar ing ex-perimental and theoretical t ime series of water temperatures for each sensor dur ing phase II. The theoretical t ime series of temperature measurements were obtained by using the following boundary condit ion: which assumes that the surface is at the freezing temperature ( 0 ° C ) for a l l t ime t dur ing phase II. In reality, the locat ion where the water is at 0 °C varies w i t h t ime as ice product ion persists. However, the to ta l ice thickness of a few mill imeters made it reasonable to assume Qc = (D.15) Tw(0,t)=Ts = Tf (D.16) 92 Appendix D that the ice-water interface was located at depth z=0. The second boundary condition: Tw(z, 0) — Ti Tmd, (D.17) assumes that the initial temperature, T in the water column is at the Tmd- These two previous boundary conditions imply that the water column is at Tm<i and then a temperature of 0 °C (Tf) is suddenly applied to the surface. In reality, there is a delay between the time when the surface cools to Tf from Tmd- Taking into account this delay by applying a different boundary condition at the free surface is possible but has negligible effect on the final results. In addition, the experimental data of each sensor reach the Tmd at different times, and these delays between sensors are larger than the time it takes for the surface to cool from Tmd to the Tf. Hence, making it reasonable to assume that the surface cools instantaneously from Tmd to Tf. During phase II, faster cooling at the surface creates a stable water column with a reverse temperature stratification. Thus, it is possible to assume that limited water movement is occurring. The two previous boundary conditions yields the following general equation for unsteady temperature distribution in a semi-infinite body (Incropera and DeWitt, 1996): where Dw represents the molecular heat diffusivity of water. For distilled water, Equa-tion D.18 reduces to: and was applied using the 4 different depths, 2, where the temperature sensors were placed. The results of this equation, using a value for Dw equal to 1.36-10"7 m 2 s _ 1 for the tem-peratures encountered, is illustrated in Figure D.l along with the recorded experimental temperatures. The theoretical values computed with Equation D.19 were translated hori-zontally with time, to take into account the fact that experimental temperature readings (D.18) (D.19) 93 A p p e n d i x D 0.5 0.6 0.7 0.8 0.9 1 1.1 Time in days Figure D . l : Theoret ical temperature dis t r ibut ion for freshwater, assuming heat losses only through the surface at Tf. Exper imenta l temperatures are represented by the thinner lines. The dashed line represents the Tmd, while the solid line delimits phase 1 and II. reached the Tma> at different times. The two deepest sensors i n Figure D . l do not cool because of heat losses through the surface. In fact, cooling of deep water are a consequence of the imperfect insulat ion of the boundaries. The temperature drops for each sensor i, dTi, due to cooling though the sidewalls was discretized in t ime in the following way: dT AwkwaU(Tw - Tair) = pCpV—, (D.20) 94 A p p e n d i x D yielding: m = ^k^{Twi_Tairl ( D .2 i ) where dt has chosen to be same as the time span between temperature measurements (30 seconds). T h e value for Tw i is the value T(z,t) as calculated i n E q u a t i o n D.19 using the depth, z, below the surface where the sensors where located. Modif icat ions were made i n Equa t ion D.21 to take into account the fact that the two deepest sensors are affected by the bo t tom boundary, while the two surface sensors are not. These modifications involved changing the surface area and the affected volume i n E q u a t i o n D.21 . For the two surface sensors, the surface area affected by conduct ion heat losses is 0.5(AW — Ab), where Ab is surface area of the bo t tom boundary. T h e new equation for the two surface sensors ( i = l , 2) that represent half the to ta l water volume: d T i = (Aw-Ab)kwdt{Tw _ _ ( D 2 2 ) pCpv T h e modified equation for the two deepest sensors (i=3, 4): d T i = {Aw + Ab)kwdt{Tw _ _ ( D 2 3 ) pCpV T h e resulting temperature drop caused by heat losses through the sidewalls was calculated for each t ime step and sensor. T h e combined effect of boundaries and surface heat losses on water temperatures is shown in Figure D .2 . The value for Rw required to obta in these results was 1.75 W _ 1 m 2 ° C , and is comparable to published heat resistance data. T h e heat resistance provided by styrofoam is « 25 to 30 W " 1 m °C , and for fiberglass is « 2 4 W _ 1 m ° C (Incropera and DeWitt, 1996). M u l t i p l y i n g these values w i t h the thickness of mater ial used, and summing them w i l l y ie ld a theoretical Rw. In the present case, a 6 cm layer of styrofoam was used along w i t h a 1 to 1.5 c m thick fiberglass insulat ion layer, y ie ld ing a theoretical Rw « 1.75 to 2.18 W _ 1 m 2 °C . Us ing the calculated value for R^ i n Equa t ion D.15, along w i t h recorded water and air 95 A p p e n d i x D 0.5 0.6 0.7 0.8 0.9 1 1.1 Time in days Figure D.2: Theoret ical temperature d is t r ibut ion assuming heat losses through the surface at Tf and boundaries. Exper imenta l temperatures are represented by the thinner lines. The dashed line represents the T M ^ , while the solid line delimits phase I and II. temperatures from phase I, yields heat fluxes through the boundaries equivalent to ~ 21% of to ta l heat fluxes. T h e wal l resistance R^, would be less i f the thickness of the insulat ion was reduced or i f poorer qual i ty insulat ing materials were used. D . 2 . 2 Est imating experimental qtot Tota l experimental heat fluxes were estimated from readings obtained from the moor ing of temperature sensors dur ing ' au tumn cool ing ' (phase I). Es t ima t ion were also done w i t h readings obtained after the water co lumn reached Tma< and temperature gradient were 9 6 Appendix D present in the water column. These latter heat fluxes estimations are considered approx-imate due to the small number of sensors representing water temperatures for the entire water column. In addition, the vertical temperature distribution is non-linear and the sensor size (2 cm) is relatively large compared to the total depth of water. Thus, making it difficult to obtain an accurate estimate for total heat fluxes during phase II. However, comparisons amongst heat fluxes calculated for different experiments can be made since the sensors for all experiments were always located at the same depths. The results of these computations were previously given in § 2.3.2. Phase I-Uniform Temperature For the case with uniform temperature distribution in the water column, experimental heat fluxes per unit of surface area were calculated with this equation: where p represents the water density, Cp is the specific heat of water (4184 J kg 1 °C 1 at 20 °C), h is the average water depth obtained by dividing the 'lake' volume by its surface temperatures obtained during 'autumn cooling', the variations of specific heat and density were insignificant, ft was assumed that the main processes involved in cooling the water column during phase I, were sensible heat transfer (qs) at the surface and losses through the boundaries (qc). This implies that the temperature drops exponentially with time after placing the container within the freezer (Incropera and DeWitt, 1996): Qexp pCph (D.24) area (-j-), and ^  is the variation of temperature T with time t in seconds. For the range of (D.25) where R is equivalent to: (D.26) 97 A p p e n d i x D Exper iment Pure Water (Ju ly 1 9 / 0 6 ) To ta l heat losses ( W m 2 ) 1 g L " 1 (May23/06) 1 g L " 1 (May29/06) 2 g L - ^ A p t f / O e ) 4 g L - 1 ( A p r l 9 / 0 6 ) S g L - ^ J u l y l l / O O ) 286 277 272 289 276 286 mean standard deviat ion 281 6.8 Table D . l : Exper imenta l heat losses dur ing au tumn cooling for various experiments. Aw being the to ta l surface area of the lake boundaries. To ta l heat fluxes vary w i t h t ime and can be calculated using Equa t ion D.27: which yields heat fluxes in W m - 2 . Equa t ion D.27 was applied to water temperatures recorded dur ing phase I. T i m e averaged values of qexp are reported for phase I i n Table D . l . T h e mean experimental heat flux i n phase I is 281 W m - 2 w i t h a s tandard deviat ion of 6.9 W m - 2 (Table D . l ) . It must be noted that E q u a t i o n D.26 does not take into account convective m i x i n g i n the water column, nor evaporation and radiat ion. T h e consequence of these assumptions, is that the sensible heat transfer coefficient, ah, w i l l be overesti-mated wi th Equa t ion D.26 since i t includes the neglected radia t ion and evaporat ion terms. Nonetheless, the experimental temperature readings follow an exponential relationship and the R factor can be used to estimate heat fluxes w i t h equation D.27. T h e magnitude for each type of heat fluxes is given i n Figure D .3 . D.2.3 Contribution of individual heat fluxes terms T h e following plot shows the contr ibut ion of each type of heat fluxes along w i t h to ta l fluxes dur ing phase I. T h e latent heat of evaporation, qiat, i n F igure D .3 represents the m a x i m u m possible heat losses due to evaporation. In other words, it is assumed that the surrounding (D.27) -s 98 A p p e n d i x D air is completely dry, which is unl ikely but no measurements of relative humid i ty were obtained dur ing experiments. Latent heat fluxes due to evaporation can represent at most 5% of to ta l heat fluxes dur ing phase I. Heat fluxes due to long-wave radia t ion absorbed and emit ted by the water surface represent 50% of to ta l heat fluxes. Long-wave radia t ion heat fluxes absorbed by the water surface were estimated wi th E q u a t i o n D .3 , assuming that the freezer walls behaved s imi lar ly to a cloudy sky. Sensible heat transfer at the surface and conduct ion through the sidewalls are of s imilar magnitude dur ing phase I, even though the walls have a larger resistance to heat flux than the surface. T h e large conduct ion heat fluxes through the boundaries, is a consequence of the much larger surface area where conduct ion can take place. Influence of insulation T h e R value obta in for the experiments conducted w i t h complete insula t ion was equal to 0.88 W ° C _ 1 compared to a value of 1.12 W 0 C _ 1 for an experiment conducted wi thout the addi t ional fiberglass and s t ructural foam. These different values for R translates into to ta l heat losses reductions of ~ 25% w i t h the addi t ion of the s t ructural styrofoam and fiberglass insulat ion. Heat losses were approximately 370 W m - 2 when only one insulat ing layer of styrofoam was used, and were appproximately 281 W m ~ 2 w i t h the addi t ional insulat ion. T h e effect of increasing insulat ion on ' lake' water temperatures is i l lustrated i n Figure D.4 . The reduction i n heat losses through the boundaries (qc) w i t h the addi t ional insulat ion was also estimated. It was assumed that the difference i n heat fluxes between experiments done w i t h or without insulat ion, is a result of less conduct ion through the boundaries. Thus , boundary heat fluxes for the experiment conducted wi thout the ext ra fiberglass and styrofoam insulat ion, q'c, is equal to: Qc = (.Qexp - Qexp) + rqexp, (D.28) where r represents the heat lost through the boundaries for the experiment conducted w i t h 99 A p p e n d i x D 50 h QI I 1 I I I 1 1 0 2 4 6 8 10 12 14 Time in hours Figure D.3 : qexp is the to ta l heat fluxes according the recorded temperature readings dur ing phase I. qtotmin is the to ta l calculated heat fluxes assuming no latent heat losses (qc + qs + Qr)- qtot^ax is the calculated to ta l heat losses assuming the air is dry (i.e. qiat is at its maximum) . the complete insulat ion. It is equal to 0.21, as stated previously (see A p p e n d i x D.2.2). The variable qexp and q represent respectively the to ta l experimental heat fluxes w i t h and without the addi t ional layers of insulat ion. Thus, to ta l heat fluxes lost through the sidewalls wi thout the addi t ional layer of fiberglass and styrofoam is equal to: qc = [(370 - 281) + 0.21-281] W m " 2 = 148 W m " 2 , (D.29) which represents a propor t ion of to ta l heat fluxes lost through the walls equal to 40% of total heat fluxes. Thus , heat fluxes through the sidewalls and bo t tom were reduced by 100 A p p e n d i x D 201 1 1 1 1 1 1 r 4 -2 -n l I I I I I I I I 1 0 1 2 3 4 5 6 7 8 9 10 Time in hours Figure D.4: Heat fluxes comparison between 2 experiments w i t h different insulat ing layers. T h e dotted line represents an experiment conducted wi thout the addi t ional fiberglass and styrofoam insulat ing layers. The solid line represents an experiment conducted w i t h the addi t ional insulat ion. approximately 60% w i t h the addi t ional insulat ion. In order to reduce further the propor-t ion of heat lost through the boundaries, insulat ing materials w i t h lower heat conduct ion coefficient (kwau) would be required. T h e current freezer dimensions l imi ted the thickness of insulat ing materials used to insulate the ' lake' walls. 101 

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