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Under-ice circulation in an Arctic lake : observations from two field seasons in Lake Kilpisjärvi, Finland Graves, Kelly Elise 2015

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Under-ice circulation in an Arcticlake: observations from two fieldseasons in Lake Kilpisja¨rvi, FinlandbyKelly Elise GravesB.A.Sc., The University of British Columbia, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Civil Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)April 2015c© Kelly Elise Graves 2015AbstractHigh spatial resolution CTD profiles and Acoustic Doppler Current Profilervelocity measurements show significant rotational basin-wide circulation un-der ice in May of 2013 and 2014 at Lake Kilpisja¨rvi, Finland (69◦01’N,20◦49’E), a seasonally ice-covered, Arctic lake with negligible through-flow.In 2013, a high-pressure horizontal density anomaly with vertically pairedrotating circulations was observed. The estimated maximum cyclonic andanti-cyclonic azimuthal velocities magnitudes were 0.03 and 0.02 m s-1. TheRossby radius (Rri), the horizontal length scale at which rotational effectsbecome as important as pressure effects, was estimated to be ∼ 160 m andthe Rossby number (R0), the ratio of the centripetal acceleration to the Cori-olis acceleration, ∼ 0.2. It is hypothesized that this circulation was drivenby heat flux at the shorelines from warm incoming streams causing a densityflow down the slopes to the centre of the lake where the flow converged. Thisflow was balanced with a shoreward flow beneath the ice. These flows weremodified by the earth’s rotation which resulted in the rotational circulationobserved.In 2014, a cyclonic, low-pressure horizontal density anomaly was ob-served near the centre of the lake and was vertically paired with a weakanti-cyclonic anomaly in the top 10 m (mean depth of the lake is 19.5 m).iiAbstractThe estimated azimuthal velocities had maximum cyclonic and anti-cyclonicmagnitudes of 0.006 and 0.003 m s-1. The anomaly was estimated to haveRri ∼ 240 m, with R0 ∼ 0.12. It is hypothesized that this circulation wasdriven by sediment release of heat to the overlying water causing a tilt inthe isopycnals near the shores of the lake that caused an inward pressureforce that was balanced by the Coriolis force and, to a lesser extent, thecentripetal acceleration force.The 2013 observations were made immediately prior to ice-off, and the2014 observations were 12 days prior to ice-off. This time difference allowedfor significantly different ice and snow conditions, and the addition of warminflows which forced the circulation closer to the ice-off date. These observa-tions add to the growing understanding of the relationship between thermaldistribution and circulation under ice.iiiPrefaceI, Kelly Graves, am the author of this thesis. All work contained in thisdocument is original. I assisted in the design, execution and data collectionfor both the 2013 and 2014 field seasons at Lake Kilpisja¨rvi. All analysis ismy original work with guidance and supervision from Dr. Bernard Laval.The 2013 observations at Lake Kilpisja¨rvi for project CONCUR, pre-sented in chapter 2, and the initial analysis, presented in chapter 3 arepartially presented in Axisymmetric circulation driven by marginal heatingin ice-covered lakes by G.B. Kirillin, A.L. Forrest, K. Graves, A. Fischer,C. Engelhardt, and B.E. Laval which has been accepted for publication inGeophysical Research Letters.Partial observations, presented in chapter 2, and results, presented inchapter 3, from the 2013 field season have been published in Under-ice,basin-scale circulation in an Arctic Lake by K. Graves, A.L. Forrest, B.E.Laval, and G. Kirillin which was presented at the Proceedings of the 17thInternational Workshop on Physical Processes in Natural Waters (Trento,Italy). As well as, Under-ice circulation, modified by the Earth’s rota-tion, in an Arctic lake by K. Graves, B. E. Laval, A.L. Forrest, and G.Kirillin which was presented at 22nd International Association of Hydro-Environmental Engineering and Research International Symposium on IceivPreface(Singapore). Both of these were original works by me.The 2013 observations that I assisted in collecting have also been pre-sented in Standing waves during ice breakup in an arctic lake by G. Kirillin,C. Engelhardt, A. Forrest, K. Graves, B. Laval, M. Leppa¨rant, and W. Rizkwhich was presented at the Proceedings of the 17th International Work-shop on Physical Processes in Natural Waters (Trento, Italy). As well as,Standing Waves during Ice Breakup in a Polar Lake by G. Kirillin, C. Engel-hardt, A. Forrest, K. Graves, B. Laval, M. Leppa¨rant, and W. Rizk whichwas presented at 22nd International Association of Hydro-EnvironmentalEngineering and Research International Symposium on Ice (Singapore). Aposter, Polar lake circulation during ice break-up by G. Kirillin, A. Forrest,K. Graves, and B. Laval was also presented at the European GeoscienceUnion General Assembly 2014 (Vienna, Austria).vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Winter Limnology . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Observations of Rotational Circulation Patterns in Lakes . . 41.3 Rotational Effects on Motion . . . . . . . . . . . . . . . . . . 61.3.1 Ekman Number and Thicknesss . . . . . . . . . . . . 81.3.2 Rossby Number . . . . . . . . . . . . . . . . . . . . . 91.3.3 Geostrophic Flow . . . . . . . . . . . . . . . . . . . . 101.3.4 Cyclogeostrophic Flow . . . . . . . . . . . . . . . . . 111.3.5 Cyclostrophic Flow . . . . . . . . . . . . . . . . . . . 131.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13viTable of Contents2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1 Field Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Field Seasons . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.1 2013 Field Season . . . . . . . . . . . . . . . . . . . . 162.2.2 2014 Field Season . . . . . . . . . . . . . . . . . . . . 202.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1 2013 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 2014 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.1 2013 Data Discussion . . . . . . . . . . . . . . . . . . . . . . 514.2 2014 Data Discussion . . . . . . . . . . . . . . . . . . . . . . 554.3 2013 and 2014 Comparison . . . . . . . . . . . . . . . . . . . 585 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64AppendicesA Water Sample Results . . . . . . . . . . . . . . . . . . . . . . . 69viiList of Figures2.1 Map of location of Lake Kilpisja¨rvi . . . . . . . . . . . . . . . 152.2 2013 CTD and ADCP locations . . . . . . . . . . . . . . . . . 182.3 2014 CTD locations . . . . . . . . . . . . . . . . . . . . . . . 213.1 Across and along-lake temperature distributions 26 May 2013 273.2 Extents of the 2013 horizontal density anomaly . . . . . . . . 283.3 Direction of the mean ADCP velocities . . . . . . . . . . . . . 303.4 Across-lake ∂P ∂r−1, vθg, and vθcg for 26 May 2013 . . . . . . 333.5 Percent difference for vθcg and vθg . . . . . . . . . . . . . . . 353.6 Contours of the components in the cyclogeostrophic force bal-ance 26 May 2013 . . . . . . . . . . . . . . . . . . . . . . . . . 363.7 Percentage of each component in the cyclogeostrophic forcebalance 26 May 2013 . . . . . . . . . . . . . . . . . . . . . . . 373.8 Contours of patched vθcg and percent difference for 26 May2013 across-lake transect . . . . . . . . . . . . . . . . . . . . . 403.9 Along-lake estimates of vθg and vθcg for 26 May 2013 . . . . . 413.10 Comparison of vθA to vθcg and vθg at comparable radial dis-tances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42viiiList of Figures3.11 Corrected estimates for vθcg with level of no-motion at thebottom for 26 May 2013 . . . . . . . . . . . . . . . . . . . . . 443.12 Across and along lake temperature distributions 26 May 2014 453.13 ∂P ∂r−1, vθg, vθcg, and the percent difference in vθg and vθcg 483.14 Contours of the components in the cyclogeostrophic force bal-ance 26 May 2014 . . . . . . . . . . . . . . . . . . . . . . . . . 50ixAcknowledgementsA few words on a page can not effectively convey the extent of my gratitudefor the help and support of many people over the course of my research;however, I will try.To begin, I must thank the members of the two field teams that I joinedat Lake Kilpisja¨rvi: Georgiy Kirillin, Christof Engelhardt, Alex Forrest, JeffWilliams, Larry Kost, Elisa Lindgren, Tom Kokkonen, Will Rizk, CeciliaA¨ija¨la¨, and Franzi Po¨schke. I will be ever grateful for showing me the ropes(both literally and figuratively). “Kiitos.”I need to thank both the Environmental Fluid Mechanics and the Physi-cal Oceanography groups at UBC for their input. Also, I greatly appreciatethe discussions I had with Greg Lawrence, Roger Pieters, Ted Tedford, RichPawlowicz, Stephanie Waterman and Susan Allen.I also owe great thanks to Andrew Hamilton for his mentorship and dailyinput.Also, Bernard Laval, thank you for all of this.Thanks to my family and friends for putting up with my rambling ad-ventures in the Arctic.xChapter 1IntroductionFreshwater lakes cover an estimated 125 000 km2 (Wetzel , 1975) of theearth’s surface, and many of these lakes experience ice-cover for some of ora significant portion of their annual lake cycle. However, relatively little isknown about their physical dynamics during the ice-cover period. The clas-sic view is there is insignificant circulation (Welch, 1952); however, recentobservations have shown that ice-covered lakes can experience considerablecirculation forced by sediment heat flow, solar radiation, differential heating,seiches caused by the oscillation of the ice-cover, as well as ground and sur-face water inflows (Bengtsson, 1996; Bengtsson et al., 1996; Kirillin et al.,2012). When circulation occurs over large distances or is slow it can bemodified by the Coriolis force resulting in rotating density anomalies.Circulation in ice-covered lakes is important because it transports dis-solved and suspended solids, nutrients, and heat throughout a lake body.When circulation patterns persist over time, this has implications for themicro-organisms that live in the lake (Huttula et al., 2010). However, beforethe effect of under-ice circulation can be understood, the circulation patternsthemselves need to be understood (Rizk et al., 2012). This work presents ob-servations made during two winter field seasons at Lake Kilpisja¨rvi, Finland.11.1. Winter LimnologyThe two field seasons present two markedly different circulation patternscaused by horizontal rotating density anomalies. Before presenting theseobservations, a review of thermal structure and dynamics of ice-coveredlakes is presented.1.1 Winter LimnologyThe thermal structure and dynamics of ice-covered lakes are related, andare markedly different than those that occur during the ice-free period.The ice-cover period can be broken up into winter 1 and winter 2 (Kir-illin et al., 2012). Winter 1 is the the beginning portion of winter whenthe lake is ice and snow covered. During this time, ice-cover insulates thelake and the heat content of the lake changes very little (Bengtsson, 1996)because solar radiation penetration is negligible and has little effect on theheat content of the water column (Bengtsson et al., 1996). This is becausemost of the incoming solar radiation is reflected off the snow surface andthe portion that is not reflected is almost completely absorbed into thesnow (Bengtsson and Svensson, 1996). Therefore, the thermal structure ofthe water column is largely determined by atmospheric conditions prior tofreeze-up (Bengtsson and Svensson, 1996). For example, if wind events werestrong prior to ice on, it would take longer for ice to form which would al-low the water temperature to cool more (Wetzel , 1975). Conversely, weakwinds could lead to rapid ice formation and the water would be warmer.Also, the heat content of the lake changes very little because of the lowheat conductivity of snow which reduces the transfer heat from the warmer,21.1. Winter Limnologyunder-lying water column to the ice and then from the ice through the snowto the atmosphere (Kirillin et al., 2012). The thermal structure beneaththe ice-cover is inversely stratified with colder water (0◦C at the ice-waterinterface) overlying warmer water (2◦C - 4◦C) (Ellis et al., 1991). This oc-curs in fresh water lakes, where salinity has little to no effect on the density,because density decreases as water temperature decreases below 4◦C (thetemperature of maximum density).The main forcing of circulation and mixing in winter 1 is the release ofheat from the sediment that accumulated during the summer (Bengtsson,1996; Zdorovennova, 2009). This forcing dominates because the ice-coverprevents wind, the predominant driver of circulation during ice-free periods,from transferring momentum to the water surface (Bengtsson, 1996). Afterwind, the next most dominant forcing, through-flow, is reduced during win-ter because the main precipitation received in the catchments of mid andhigh latitude lakes is in the form of snow which reduces surface inflows andthrough-flows.As winter progresses, the transfer of heat from the sediment to the bot-tom water decreases (Bengtsson, 1996; Rizk et al., 2014). The lake transi-tions from winter 1 to winter 2 when the water column and the sedimentreach the same temperature and no heat is transferred between them (Kir-illin et al., 2012). During this time, snow cover begins to disappear andsolar radiation is able to penetrate the ice and warm the water column(Bengtsson, 1996; Zdorovennova, 2009). The amount of solar radiation thatreaches the water column is controlled by the amount of remaining snowand the type of ice; more solar radiation penetrates through black ice than31.2. Observations of Rotational Circulation Patterns in Lakeswhite ice which has many air bubbles and scatters more light (Wetzel , 1975;Bengtsson, 1996). With penetration, the upper water column warms andbecomes denser, because the water is below the temperature of maximumdensity. This causes gravitational instability that drives convection: themain circulation forcing in winter 2.Near the end of winter 2, the shallower regions around the shores ofthe lake warm faster than the deeper parts of the lake (Bengtsson, 1996)and moats, ice-free regions around the lake (Vincent and Laybourn-Parry ,2008), may form. The way in which the ice-surface degrades can affect howthe water column warms. If ice degrades evenly, then the water column iswarmed consistently over the surface area of the lake. This leads to verti-cal convection, even mixing of the water column and no horizontal densityvariability. If the ice surface degrades unevenly, the amount of solar radi-ation that reaching the water surface varies causing differential heating ofthe water column. This leads to horizontal density variations across thelake. Horizontal density differences beneath ice-cover have been observedand have, at times, been associated with rotational circulation.1.2 Observations of Rotational CirculationPatterns in LakesBasin-wide rotational circulation patterns, referred to as gyres, eddies orvortices, have been observed in lakes under ice (Likens and Ragotzkie, 1966;Rizk et al., 2012; Forrest et al., 2013) and have been predicted by computersimulations (Huttula et al., 2010). Similar circulation patterns have been41.2. Observations of Rotational Circulation Patterns in Lakesobserved in open-water conditions in lakes; however, open-water horizontaldensity anomalies are typically forced by wind (Emery and Csanady , 1973),seiches interacting with bathymetry (Kirillin et al., 2008), or heat releasefrom bottom sediments (Akitomo et al., 2004). Unlike open-water anoma-lies, under-ice anomalies are not a result of wind forcings and their smallerdifferences in density can exist longer because they are not broken up by thewind (Rizk et al., 2012). Radially symmetric, horizontally unstable densityanomalies have been observed to persist for a minimum of 6 days (Forrestet al., 2013) to most of the winter (Rizk et al., 2014). Their symmetryimplies rotation and the persistence implies that the horizontally unstabledensity anomalies were held in place by a balance of forces.Similar rotational circulations have be found under ice in the ocean (Tim-mermans et al., 2008) and in the atmosphere (Gill , 1982). These types offlow are common in dynamic meteorology; therefore, most dynamic meteo-rology texts include sections on these flows that detail their characteristicsand the methods used to analyze them. There does not exist a physicallimnology reference that summarizes rotational circulations in lakes usingsimilar methods. This work makes an attempt to fill that gap. To be able todo that, first a summary of relevant geophysical fluid flows and characteri-zations methods are presented. These methods are then used to analyze theunder-ice observations made at Lake Kilpisja¨rvi, Finland in 2013 and 2014.Finally, results are compared to previous observations of rotating horizontaldensity anomalies.51.3. Rotational Effects on Motion1.3 Rotational Effects on MotionRotating circulation under ice is often associated with density differences.It is not always clear whether the circulation is caused by the density dif-ferences, or if the density differences are caused by the rotating circulation.The density stratification in these flows results in barotropic pressure forcesand maintains circulation (Holton, 2004). Most often, these flows occur overlarge length scales, such as oceanic and atmospheric currents; however, thereare similar small scale flows in the environment, such as those observed insome lakes. These flows are affected by the earth’s rotation because of theirlong time scale.For flows that are not affected by the earth’s rotation, the coordinatesystem used for analysis is fixed with reference to the distance stars, and arotating coordinate system that rotates with the earth is used. To a station-ary observer of these flows on Earth, the flow is deflected by an “apparentforce”, (i.e. that does no work), referred to as the Coriolis force, which is aresult of the earth’s rotation (Stommel and Moore, 1989; Kundu and Cohen,2004). For these types of flows, positions and motions are referenced to afixed point on the earth which rotates at a constant rate about the poles(Ω = 2pi rad day-1 where Ω is angular velocity) with respect to the inertialframe. The intensity of the rotation varies with latitude (θ) and is given byf = 2Ωsinθ where f is the Coriolis parameter.To determine whether a motion is significantly affected by the Coriolisforce, the horizontal length scale of the motion is compared to the Rossby61.3. Rotational Effects on Motionradius of deformation given byRr =cf(1.1)where c is the wave speed. Rr is the horizontal length scale at which rota-tional effects become as important as pressure effects. When the length scaleof the motion of interest is much less than Rr, the motion is not affectedby the earth’s rotation. When the horizontal length scale is comparable toor greater than Rr, then the earth’s rotation is important. Rr can eitherbe external (Rre) or internal (Rri). Rre is a comparison of the barotropicpressure to the Coriolis forces, and uses the shallow water, non-dispersivewave speed given by c =√gh where g is gravitational acceleration, and his the depth of the fluid of interest. Rri is a comparison of the baroclinicpressure to the Coriolis forces. It is an approximation of a two-layer system,with c =√g′heq where g′ = g∆ρρ0is the reduced gravity (ρ0 is the referencedensity of 1000 kg m-3) and heq is an adjusted layer thickness.For lake circulation to be influenced by the Coriolis force, the laterallake dimensions must be equal to or greater than Rr (Gill , 1982; Rizk et al.,2014). Rri is smaller than Rre, and for ice-covered lakes, is typically arounda few hundred meters, which is generally smaller than the lateral dimensionsof the lake; therefore, the Coriolis force can play an important role in lakemotions under ice-cover (Rizk et al., 2014).These rotational circulations can be idealized to be steady state (inde-pendent of time) and purely horizontal (vertical motion is negligible com-pared to horizontal motion); therefore, the residual accelerations (du dt−1,71.3. Rotational Effects on Motiondv dt−1, dw dt−1) are equal to zero (Gordon et al., 1998). To simplify theanalysis of these flows, the frictional effects, away from the boundaries, needto be estimated and found to be negligible.1.3.1 Ekman Number and ThicknesssFrictional effects are estimated with the Ekman number, the ratio of theviscous force to the Coriolis force (per unit volume) (Kundu and Cohen,2004), which is given byE =viscous forceCoriolis force=νfL2(1.2)where ν is the kinematic viscosity which has a molecular value of 10-6 m2s-1 and has been observed under ice to be 10-4 m2 s-1 (Bengtsson, 1996),and L is the horizontal length scale of the flow. When E <<1, frictionaleffects are negligible. This is the case for most flows away from boundaries(Greenspan, 1968). The distance from the boundary where friction becomesimportant is given by the Ekman boundary layer thickness given byδEk =√2Avf(1.3)(Kundu and Cohen, 2004) where Av is the vertical turbulent viscosity coef-ficient which has been estimated to have a maximum value under ice of ∼10-4 m2 s-1 (Bengtsson, 1986). Varying f from 0 to 1.45 x 10-4 s-1 (maximumoccurs at the poles), and using the maximum value for the turbulent eddyviscosity, δEk ranges from 0 to 1.4 m. Above this distance from the bottom,81.3. Rotational Effects on Motionfrictional effects can be neglected.The viscosities in (1.2) and (1.3) are different, and their values varydepending on the reference. (Pedlosky , 1987) (1987) replaced Av by ν forlaminar flow. For conservative estimates, values that give the largest E andδEk can be used. Or, a range of viscosities from molecular to the maximumturbulent eddy viscosity can be used.Once frictional effects are estimated to be negligible, common steady, ro-tational circulations can be analyzed. These types of circulations are definedby the forces that contribute to their balances. They are: (1) geostrophic(i.e. between Coriolis and pressure forces), (2) cyclogeostrophic (i.e. be-tween Coriolis, centripetal acceleration, and pressure forces), and (3) cy-clostrophic (i.e. between pressure and centripetal acceleration forces).1.3.2 Rossby NumberOne way to estimate whether a system is in geostrophic or cyclogeostrophicbalance is to calculate the Rossby number (Ro). This is the ratio of thecentripetal acceleration to the Coriolis acceleration, and is an estimate ofthe importance of non-linear terms (convective acceleration) (Greenspan,1968). Ro is given byRo =non-linear accelerationCoriolis acceleration≈U2/LfU=UfL≈√g′Hf2L2=RriL(1.4)where U and L are the horizontal velocity and length scales. For geostrophicflow, the Coriolis force is much more important, so Ro <<1, for cyclo-geostrophic flow Ro is O(1), and for cyclostrophic flow Ro >>1.91.3. Rotational Effects on Motion1.3.3 Geostrophic FlowGeostrophic flow occurs when a pressure gradient force is balanced by theCoriolis force (Ro <<1). This type of balance is not valid near the equator(because f becomes small), near boundaries (so, E <<1) or for unsteadyflows (Kundu and Cohen, 2004). The flow from high to low pressure ismodified, or deflected by the earth’s rotation. In the northern hemisphere,the deflection is to the right of the pressure force and to the left in thesouthern hemisphere. This causes the flow to be along lines of constantpressure or density (isobars) (Cushman-Roisin, 1994). The horizontal forcebalances per unit mass are given byfug = −1ρ0∂P∂y(1.5)fvg = +1ρ0∂P∂x(1.6)where ug and vg are the geostrophically balanced velocities in the x andy directions respectively, and P is pressure. If the pressure distribution isknown, the horizontal velocities are given byug = −1ρ0f∂P∂y(1.7)vg =1ρ0f∂P∂x(1.8)and referred to as the geostrophic wind (Gill , 1982). Since geostrophic cir-culation is rotational, cylindrical co-ordinates (r, θ, z ) can be more usefulthan Cartesian co-ordinates. The equivalent horizontal velocity in cylin-101.3. Rotational Effects on Motiondrical coordinates is the azimuthal geostrophic velocity (vθg) and is givenbyvθg =1ρ0f∂P∂r(1.9)where r is the radial distance from the centre of the rotation.If the hydrostatic assumption is made, given by∂P∂z= −ρg (1.10)(Kundu and Cohen, 2004), and is combined with (1.7) and (1.8), the ver-tical shear of the horizontal velocity is related to the horizontal densitygradients. This shows that the Coriolis force allows a horizontally unstablesystem, where pressure/density varies horizontally, to be maintained with-out any input of additional energy (Cushman-Roisin, 1994). This is knownas thermal wind in atmospheric science.1.3.4 Cyclogeostrophic FlowCyclogeostrophic flow, away from boundaries (E <<1), occurs when thereis a balance between pressure gradient, Coriolis, and centripetal accelerationforces. Since the centripetal acceleration and Coriolis forces are of compa-rable magnitude, Ro O(1). In the force balance, which is also referred toas a gradient wind balance, the centripetal acceleration force is always di-rected outwards from the centre of the horizontal pressure anomaly. Thedirection of the pressure force depends on whether the system is high or lowpressure; the resultant pressure force from a high-pressure anomaly pointsoutwards, and vice versa for a low-pressure anomaly. The direction of the111.3. Rotational Effects on MotionCoriolis force then balances the pressure and centripetal acceleration forces.The resulting velocity is directed is to the right of the pressure force (in thenorthern hemisphere).The cyclogeostrophic force balance per unit mass is given by−v2θcgr− fvθgc = −1ρ0∂P∂r(1.11)where, from left to right, the terms are the centripetal acceleration, Coriolisand pressure forces per unit mass, and vθcg is the cyclogeostrophic azimuthalvelocity. (1.11) can be solved for vθcg using the quadratic formula. This givestwo solutions for vθcg fromvθcg = −fr2±√(fr)24+rρ0∂P∂r. (1.12)To determine which solution is correct, it is important to remember thatcyclogeostrophic flow is a result of the pressure gradient, and, if there is nopressure gradient, there is no flow. The solution of interest from (1.12) isthe positive root (as the negative root will give a value for vθcg even if thereis no pressure gradient). The direction of the flow depends on the type ofpressure system. In the northern hemisphere, flow is cyclonic (in the samedirection as the earth’s rotation) for a low-pressure centre (low-density) andanti-cyclonic for a high-pressure centre (high-density) (Gill , 1982).It is possible for the radicand (the terms under the square root) in (1.12)to be less than zero. This results in a complex solution for the azimuthalvelocity, which indicates the system is no longer in cyclogeostrophic balance121.4. Summarydue to two possibilities. (1) There is acceleration across isobars and thesystem is unsteady or affected by friction. (2) The radius of curvature is toosmall to balance the horizontal pressure difference.1.3.5 Cyclostrophic FlowCyclostrophic flow occurs when the Coriolis force can be neglected; therefore,there is a force balance between the centripetal and pressure gradient forces,given byv2r=1ρ0∂P∂r(1.13)which results in cyclostrophic motion. This occurs when the horizontalscales are small, or f is small. This type of system only exists for a low-pressure anomaly because it balances the outward oriented centripetal force(Cushman-Roisin, 1994). This is the type of balance that allows dust devilsand waterspouts to exist (Renno and Bluestein, 2001). The flow is nor-mal to the direction of the balance. Cyclostrophic flow can be cyclonicor anti-cyclonic. For cyclostrophic flow, Ro >>1 because the centripetalacceleration is much more important than the Coriolis acceleration.1.4 SummaryFor ice-covered lakes in winter 2, the increased solar radiation penetratingthrough the degrading snow and ice cover can lead to horizontal densitydifferences. These density difference cause horizontal pressure gradients thatcan exist in geostrophic, cyclogeostrophic or cyclostrophic balance. For thesebalances to exist, there must be rotational circulation.13Chapter 2MethodsThis chapter first presents geographical, environmental and weather infor-mation on the field site studied, Lake Kilpisja¨rvi, Finland. Then the datacollected and the collection methods used during the two field seasons arepresented. Finally, the methods used to analyze the data are described.2.1 Field SiteLake Kilpisja¨rvi is a seasonally ice-covered lake located in northwestern Fin-land at 69◦01N, 20◦49E (Figure 2.1). Since it is above the Arctic Circle, itis referred to as an arctic or polar lake. It is below the tundra line, the 10◦CJuly isotherm, and the Arctic marine boundary (Vincent and Laybourn-Parry , 2008). The shores of the lake are bordered by Finland (east, north-east and south), Sweden (west), and Norway (north-west). Lake Kilpisja¨rvihas two basins: the north basin and the south basin. This study focuses onthe north basin, which has a mean depth of 19.5 meters (m) (Leppa¨rantaet al., 2012), a maximum depth of 57 m, a surface area of 37.2 square kilo-metres (km2) and is located 473 m above sea level (Yang et al., 2013). Themajor inflow is from Lake Siilasja¨rvi in the north. There are numeroussmaller surface inflows from streams from the low-lying mountains that sur-142.1. Field SiteFinlandSwedenNorway3 kmFigure 2.1: Map of Finland, Sweden and Norway. The yellow star is the locationof Lake Kilpisja¨rvi which is shown in the inset.round the shore of Lake Kilpisja¨rvi. During spring, snowmelt flows overlandinto the lake. The north basin of Lake Kilpisja¨rvi flows into the south basinwhich then flows into the River Ko¨nka¨ma¨eno and then eventually into theBaltic Sea.The climate can be characterized as sub-arctic. Records from the Kilpisja¨rviBiological Station (run by the Faculty of Biological and Environmental sci-ences at the University of Helsinki) located on the east shore of the lakeshow the annual mean average air temperature is -2.3◦C, with a mean an-nual wind-speed of 2.52 m s-1 and a total annual precipitation is 447 mm152.2. Field Seasonsin the form of snow and rain. The mean date of ice break-up/ice-off is 18June, the latest break-up was 1 July 1997 and the earliest was 2 June 1963.In this case, ice break-up and ice-off both refer to when the majority of thelake is free of ice.2.2 Field SeasonsTwo field campaigns were conducted at Lake Kilpisja¨rvi from 25 May to 3June 2013 and 19 May to 26 May 2014.2.2.1 2013 Field SeasonThe first field campaign was for the project named Solar convection andlateral currents under lake ice cover (CONCUR), which took place at LakeKilpisja¨rvi from 25 May to 3 June 2013. This field campaign was part of aninternational collaboration with Germany, Finland, and Canada. Fundingfor the project was provided by the International Network for TerrestrialResearch and Monitoring in the Arctic (INTERACT) and Natural Sciencesand Engineering Research Council of Canada (NSERC).At the beginning of the field campaign, the lake was covered with 0.6m of ice with the exception of the shallow areas around the shores of thelake (littoral areas) that were free of ice cover and became larger with time.These areas shall be referred to as moats (Vincent and Laybourn-Parry ,2008). The ice itself was made up of regions of solid ice, and regions ofcandlestick ice (vertical columns of ice that are tightly packed together).There was no snow on the ice-surface and very little snow on the shores.162.2. Field SeasonsDuring this period of time, there was 24 hours of daylight.From 26 May onwards, Lake Kilpisja¨rvi was subject to rapidly warmingtemperatures. After 27 May, the ice surface was unsafe to work on be-cause it began to degrade and break-up. On 6 June 2013 Lake Kilpisja¨rviexperienced the earliest ice-off since 1963.Data CollectedConductivity-temperature-depth (CTD) loggers, made by Richard BranckerResearch Ltd. (RBR) XR-620, were used to collect measurements of tem-perature and conductivity vertically through the water column (profiles).The RBR CTD was set to start collecting measurements when it reached acertain pressure value (pressure thresholding). The RBR CTD recorded 6samples per second (i.e. 6 Hz) and the CTD was lowered at approximately0.5 m s-1. The RBR CTD has a conductivity range of 0 to 2 mS cm-1, aresolution <0.00002 mS cm-1 and an accuracy of ± 0.003 mS cm-1. Thetemperature ranges from -5 to 35◦C, has a resolution of <0.002◦C and anaccuracy of ± 0.002◦C. The pressure has a resolution of <0.001 %, and anaccuracy of ± 0.05 %.To collect measurements under the ice-surface, holes were drilled throughthe ice with a hand-auger. Ice chunks and slush were removed from the holesand the CTD was lowered down through the water column by hand untilit reached the bottom then it was raised. When the holes were initiallydrilled, ice thickness and snow depth measurements were collected at eachCTD profile location. To measure the thickness of the ice, a fishing gaff (apole with a hook on the end) was lowered through the hole in the ice until172.2. Field Seasonsit caught on the under side of the ice and the location of the water surfacewas noted on the fishing gaff. Snow depth was measured with a ruler in theice hole where it was easier to note the transition from ice to snow.The CTD profiles were used to construct transects which are a seriesof vertical profiles that are evenly spaced along a straight line. Two CTDtransects were establish during this field campaign: across-lake, and along-lake transects. These are shown on Figure 2.2.NWAcross-lake transectAlong-lake transectADCP location 1 kmFigure 2.2: 2013 CTD profile locations for the across-lake transect (blue circles)and along-lake transect (green circles), and the ADCP location (red dot). Thismap only shows the north basin of Lake Kilpisja¨rvi.The across-lake transect consisted of profiles spaced approximately 50 mapart starting 50 m from the eastern shore and reaching to approximately100 m from the western shore. On the morning of 25 May, the first 16profiles of the across-lake transect were collected. In the evening of 25 May,182.2. Field Seasonsthe same 16 CTD profiles were repeated and 9 more profiles were added tothe western most profile for a total of 25 profiles. On 26 May, the 25 profileswere repeated and 31 new profiles were added across the width of the lakestarting at the western most profile for a total of 56 profiles.The along-lake transect consisted of 20 profiles spaced approximately 100m apart starting from approximately 100 m from the northern shore. Thistransect was collected at the same time as the full across-lake transect on 26May. The two transects intersected at profile 14 of the along-lake transectand profile 23 of the across-lake transect. These transects were collectedover a period of three hours and can be considered synoptic.After the CTD transects were collected, a 600 kHz Teledyne RD Instru-ments Acoustic Doppler Current Profiler (ADCP) was used to collect veloc-ity measurement profiles in the water column at one location that can beseen in Figure 2.2. The ADCP collected measurements every 5 seconds from23:07:39 30 May 2013 to 15:07:39 4 June 2013. The ADCP was mountedon the bottom of the lake at 18.65 m with the beams looking upwards. Itrecorded northern and eastern velocities in 65 vertical bins that are 0.3 mtall. The measurements begin 1.72 m from the bottom and reach 20.92 mabove the bottom (the bins near the surface were removed as they partiallyextended above surface).Air temperature, snow depth and rain data was provided by the Kilpisja¨rviBiological Station for April, May, June and July of 2013. Hourly averagesof wind speed and direction for May and June 2013 were provided by theFinnish Meteorological Institute.Three water samples were collected on 2 June 2013 and a laboratory192.2. Field Seasonsanalysis was conducted to determine the chemical composition of the lakewater. The results of the chemical analysis can be found in Appendix A.The chemical composition was used to determine the water density.2.2.2 2014 Field SeasonThe second field campaign was for the project named (LACUNA) whichtook place at Lake Kilpisja¨rvi from 19 May to 26 May 2014. The project waspartially funded by INTERACT, NSERC and Northern Scientific TrainingProgram (NSTP). It was an international collaboration between Germany,Finland, Australia, and Canada. The objective of this project was to inves-tigate, through another intensive field campaign, how under-ice circulationobserved in spring forms and collapses.During the winter leading up to the campaign, Lake Kilpisja¨rvi wassubject to record snowfall. Some of this snow and slush was still present onthe ice throughout the campaign. At the beginning of the campaign, theice was 1 m thick. No additional snow accumulated and no moats formedaround the exterior of the lake during the campaign. There was 24 hoursof sunlight for the duration of the field campaign. Some icy rain fell duringthe field campaign; however, not significant amounts.Data CollectedTwo JFE Advantech CO., Ltd. RINKO CTD profilers collected measure-ments of temperature and conductivity through the water column. TheRINKO CTD profilers were set to start collecting data when the externalswitch was turned on prior to being lowered through the auger hole in the202.2. Field Seasonsice at approximately 0.5 m s-1. The RINKO CTD profiler has a conductivityrange of 2 to 70 µS cm-1, a resolution of 0.001 µS cm-1 and an accuracy of ±0.01 µS cm-1. The temperature sensor has a range of -3 to 45◦C, resolutionof 0.001◦C, and an accuracy of ± 0.001◦C. The depth range is 0 to 600 m,resolution of 0.01 m, and an accuracy of ± 0.3 %.The locations of the CTD profiles were chosen to repeat some of the CTDprofiles from the previous field season. The across-lake transect consisted of29 profiles spaced at 100 m intervals (instead of intervals of 50 m from the2013 field season). The along-lake transect was shifted to the approximatecentre of across-lake transect and consisted of 10 profiles spaced at 100 mintervals. The across and along-lake profile locations can be seen on Figure2.3.Across-lake transectAlong-lake transectNW1 kmFigure 2.3: 2014 CTD profile locations for the across-lake transect (blue circles)and along-lake transect (green circles). This map only shows the north basin ofLake Kilpisja¨rvi.212.3. Data AnalysisOn 19 May 2014, 9 CTD profiles were collected with a RINKO CTDlogger on the across-lake transect. On 20 May 2014, CTD profiles werecollected at the previous 9 CTD locations and 20 more profiles were collected(total transect of 29 profiles). The same 29 profiles were repeated on 21May, in reverse order. The along-lake transect also collected on 21 May.This transect started between profile 14 and 15 on the across-lake transect.Both across and along-lake transects were repeated on 22 May. On 23 and24 May, the across-lake transect was repeated. On 26 May, both the acrossand along lake transects were repeated.Air temperature, snow depth, and rain data was provided by the Kilpisja¨rviBiological Station for April, May, June, and July of 2014. Hourly averagesof wind speed and direction for May and June 2014 were provided by theFinnish Meteorological Institute.2.3 Data AnalysisThe purpose of the analysis of the CTD measurements is to investigatebasin-scale temperature and density patterns. To remove small-scale vari-ability, the CTD profiles were vertically averaged every 1 m, the top 1 mof data was removed to reduce variability, and the profiles were horizon-tally averaged every 100 m. The location of the data points is recorded inlatitudes, longitudes, and depths below the water surface.The measured temperatures, conductivities and water composition givethe density of the water at each data point calculated using the InternationalThermodynamic Equation of Seawater (TEOS-10) (McDougall and Barker ,222.3. Data Analysis2011). The density distribution was analyzed to characterize horizontaldensity anomalies.The internal Rossby radius of deformation (Rri) and the Rossby number(Ro) were calculated to determine whether the system was in geostrophicor cyclogeostrophic balance. For this calculation, the difference in densitybetween the horizontal density anomaly core, and the surrounding water wasdetermined. The mean density of the core was calculated for the region ofwater encapsulated within the horizontal and vertical extents of the anomaly.The mean density was calculated for the surrounding regions. The densitydifference, the height of the horizontal density anomaly, and the Coriolisparameter (f ) were used to calculate Rri. When this radius is the same orderof magnitude as the observed radius of the horizontal density anomaly, thewater (away from boundaries) is assumed to be in cyclogeostrophic balance.To confirm that the friction effects were minimal, the Ekman number (E )(1.2) and the Ekman thickness (δEk) ( 1.3) were calculated, both assumingthat the vertical turbulent viscosity coefficient is ∼ 10-4 m2 s-1 (Bengts-son, 1986) and the kinematic viscosity is ∼ 10-6 m2 s-1. These values werechosen because they will give the maximum values of E and δEk which isconservative.Making the hydrostatic assumption (1.10), and assuming that the hor-izontal pressure difference is zero at the surface (equivalent to assuming alevel of no-motion at the surface), the azimuthal cyclogeostrophic velocities(vθcg) were estimated from (1.12). The hydrostatic pressure field was deter-mined by P =∫ 0z ρgdz ∼∑n1 ρng∂z where ρn is the density of a given waterparcel, g is the gravitational acceleration (9.81 m s-2) and z is the height of232.3. Data Analysisthe water parcel. The horizontal pressure gradient (∂P ∂r-1) is approximatedbetween neighbouring profiles (∂P ) over the distance separating them (∂r)when the core of the density anomaly lies along the current transect. If thetransect that is being analyzed does not cross through the centre of hori-zontal density anomaly, then the horizontal pressure differences are calcu-lated between the transect profiles and the assumed centre of the horizontaldensity anomaly. The calculated horizontal pressure gradient is evaluatedhalfway between the profiles for which the difference is calculated. For adense-core (high-pressure) horizontal density anomaly, the positive root so-lution (1.12) is used to calculate vθcg. For dense-core anomalies, certainvalues of ∂P ∂r-1 and r near the centre have no real and physical solution(section 1.3.4). To find a solution for this region, the azimuthal geostrophicvelocities (vθg) from (1.9) are used if they are found to be of the same orderas vθcg.The magnitudes of the ADCP velocities in the azimuthal direction (vθA)were compared to the estimated azimuthal velocities (vθcg and vθg) obtainedfrom the CTD measurements.24Chapter 3ResultsThis chapter presents the results of the analysis of the data collected in the2013 and 2014 field campaigns at Lake Kilpisja¨rvi.3.1 2013 ResultsThe ice had a mean thickness of 0.6 m at the beginning of the field campaign(25 May 2013) and 0.4 m immediately prior to break-up on 3 June 2013.There was no snow on the ice for the duration of the campaign. The dailymean air temperature increased from 5.9◦C on 25 May 2013 to 10.4◦C on 3June 2013, and the mean air temperature for the period of study was 11.7◦C(calculated using the daily mean air temperatures). The wind had a meanspeed of 10 km hr-1 and a mean direction of 184◦. For Lake Kilpisja¨rvi,the water temperatures ranged between 0 and 3.1◦C, and the specific con-ductance ranged from 15.7 to 20.2 µS cm-1. For a lake with this range ofwater temperatures and specific conductance, the temperature has a greatereffect on the density than the specific conductance; therefore, the tempera-ture and density distributions follow the same pattern, and density increaseswith increasing temperature.From the distributions of water temperature on the across and along-253.1. 2013 Resultslake CTD transects on 26 May 2013 (Figure 3.1), it can be seen that thewater temperature increases with depth which is expected for an ice-coveredlake (the water is inversely stratified). Horizontally, the water temperatureis not uniform. For most of the water column, the temperature decreaseshorizontally away from the shore, and then increases again near the centreof the lake. This horizontal temperature variation indicates that the wa-ter is horizontally unstable. It is considered horizontally unstable becausethere is colder, less dense water beside warmer, denser water, which impliesa horizontal pressure gradient. The temperature transects also show thatwithin 10 m of the bottom boundary, isotherms run parallel to the slope ofthe boundary. This indicates a flow parallel to the bottom slope directedtowards the centre of the lake. The across-lake CTD transect shows thatthere is a region of warmer, denser water near the centre of the lake thatis nearly cylindrical and is surrounded by cooler, less dense water. Thiscreates a horizontal density difference between the inner, dense core and thesurrounding less dense water. In atmospheric and oceanic sciences, this isreferred to as a dense-core/high-pressure horizontal temperature (or den-sity) anomaly. The across-lake CTD transect is a vertical slice through thisstructure.From visual inspection, the cylindrical core of the anomaly is locatedon the across-lake transect approximately 1600 m from the east shore withan approximate radius of 350 m and a height of 22 m. The along-laketransect did not intersect the across-lake transect near the core of the densityanomaly, which is why the core of denser water does not appear on the along-lake transect.263.1. 2013 ResultsDepth [m]Distance from East shore [m] 5001000150020002500010203040Depth [m]Distance from North shore [m] 200400600800100012001400160018002000010203040      1.3                             1.4                             1.5                             1.6                             1.7                             1.8                             1.9                             2.0Temperature [°C]a) AC 26 May 2013 b) AL 26 May 2013 Figure 3.1: Contour plots of temperature with contours every 0.025◦C rangingfrom 1.3 to 2.0◦C. The across and along-lake transects are shown in panel a) andb) respectively. The data has been vertically averaged every 1 m. The distancealong the x-axis is the distance from the eastern and northern shores for panels a)and b) respectively. The black vertical lines represent the location where the twotransects intersect at 90◦.The density distribution, which has the same pattern as the temperaturedistribution, is used to investigate the force balance of the horizontal densityanomaly and the surrounding water. The centre of the horizontal densityanomaly was determined to be 1600 m from the east shore by calculating thelocation about which the anomaly is symmetric and the location of the leasthorizontal density variability. Since the anomaly is not perfectly symmetric,both the eastern and western anomaly radii on the across-lake transect wereestimated to determine the width of the anomaly. The anomaly radii are thelocations where the horizontal density difference is the greatest (i.e. wherethe anomaly transitions to the surrounding water) in Figure 3.2. The easternand western maximum radial distances are estimated to be approximately273.1. 2013 Results370 m and 320 m. The radius is taken to be 350 m. The height of theanomaly was taken as the vertical distance in the water column that has thegreatest density difference, which is 22 m.5001000150020002500−5−4−3−2−1012Distance from East shore [m]Horizontal density difference [kg m− 3  ]  2.5 m3.5 m4.5 m5.5 m6.5 m7.5 m8.5 m9.5 m10.5 m11.5 m12.5 m13.5 m14.5 m15.5 m16.5 m17.5 m18.5 m19.5 m20.5 m21.5 m22.5 m23.5 m24.5 mx 10 - 3Figure 3.2: Horizontal density differences [kg m-3] for depths ranging from 2.5 to24.5 m. The distance along the x-axis is the distance from the eastern shore. Theregion of interest falls between 1000 and 2000 m. The left and right-most verticallines represent the western and eastern horizontal extents of the density anomaly.The centre vertical line represents the vertical axis about which the horizontaldensity anomaly is symmetric (the centre).Considering that the horizontal density anomaly is approximately radi-ally symmetric about the centre, a cylindrical coordinate system (r, θ andz ) is used for the analysis where r is the radial distance from the centre ofthe horizontal density anomaly, θ is taken to be positive counter-clockwise,283.1. 2013 Results0◦ to the east and 180◦ to the west on the across-lake, and z is the verticaldistance taken as positive downwards.Since the inner core is assumed to be steady and is denser than thesurrounding water, the core is applying an outward pressure force on the lessdense water; therefore, there must be a force directed towards the centre ofthe anomaly that is balancing the outward pressure force. If the anomalywas not affected by the Coriolis force, the inner water would flow radiallyoutwards and the outer water would flow inward over top of the denser wateruntil the system reached equilibrium. However, this was not observed whichsuggests a balance that includes Coriolis force.To estimate whether the balance was affected by the earth’s rotation, theinternal Rossby radius, Rri, was estimated by first determining the densitydifference between the dense core of the horizontal density anomaly (meandensity of 999.9603 kg m-3) and the surrounding less dense water (meandensity of 999.9579 kg m-3). The mean density difference between the coreand surrounding water was 0.0024 kg m-3 which gives an effective gravity of2.2 x 10-5 m s-2. When the estimated height of the anomaly, 22 m, and f of1.36 x 10-4 s-1 (for a latitude of 69◦) are used, Rri ∼ 160 m. This is less thanthe observed radius of 350 m, indicating the anomaly was modified by theearth’s rotation and was in either geostrophic or cyclogeostrophic balance.Cyclostrophic balances do not exist for dense core anomalies (section 1.3.5);therefore, it is not in cyclostrophic balance. Because this is a dense-coreanomaly in the northern hemisphere, with a level of no-motion assumed atthe surface, the circulation is anti-cyclonic (clockwise) about the centre ofthe anomaly. The direction of the measured ADCP velocities support the293.1. 2013 Resultsprediction of anti-cyclonic circulation. The direction of the mean ADCPvelocities can be seen in Figure 3.3.5 .6 m5.8 m6.1 m6.4 m6.7 m7.0 m7.3 m7.6 m7.9 m8.2 m8.5 m8.8 m9.1 m9.4 m9.7 m10.0 m10.3 m10.6 m10.9 m11.2 m11.5 m11.8 m12.1 m12.4 m12.7 m13.0 m13.3 m13.6 m13.9 m14.2 m14.5 m14.8 m15.1 m15.4 m15.7 m16.0 m16.3 m16.6 m16.9 m17.2 m17.5 m17.8 m18.1 m18.4 mEastSouthNorthWest Depths below surfaceNWAcross-lake Along-lake ADCP 1 kmFigure 3.3: Direction of the mean ADCP velocities over the depth of the watercolumn (shown with varying colours and the line lengths are proportional to themean velocity). The dashed line is the azimuthal direction. The inset map is of theADCP location (red cross) with respect to the CTD transects.The high density core, the direction of the ADCP velocities, and Rrisupport a rotational circulation in a balance modified by the earth’s ro-tation. This balance is either geostrophic or cyclogeostrophic. Using Rriand L ∼ 350 m, Ro (1.4) ∼ 0.2. This indicates magnitude of the centripetalacceleration force is approximately 20 % of the magnitude of the Coriolis ac-celeration force. This does not automatically indicate whether the anomalyis in geostrophic (Ro <<1) or cyclogeostropic (Ro O(1)) balance; there-fore, further analysis is needed of both balances to determine which is most303.1. 2013 Resultsappropriate.To investigate the geostrophic and cyclogeostrophic balances using themethods discussed in section 2.3, friction needs to be neglected. To confirmthat this is reasonable, the Ekman number (1.2) was estimated for a rangeof eddy viscosities 10-6 m2 s-1 (molecular) (Bengtsson et al., 1996) to 10-4m2 s-1 (turbulent) (Bengtsson, 1996) with L ∼ Rri. E ranged from ∼ 10-10to 10-8 which are both <<1; therefore, frictional effects can be neglected.The Ekman boundary layer thickness (1.3) was found to range from 0.1 to1.2 m (for molecular and turbulent viscosity). To be conservative, δEk ∼ 1.2m and the balances are valid above this distance from the bottom boundary.To estimate the azimuthal velocity distribution for both the geostrophicand cyclogeostrophic balances, the horizontal pressure gradient distribution(∂P ∂r−1) is needed. It is determined by assuming that the ice surfacehas zero horizontal pressure variability which is equivalent to assuming thatthere is no motion at the surface. This assumption has been used by Forrestet al. (2013) and is a good first estimate for use in ice-covered lakes. Thehorizontal pressure difference is calculated outwards from the centre of thehorizontal density anomaly; therefore, a negative horizontal pressure dif-ference corresponds to decreasing pressure with increasing radial distance,and a positive value has increasing pressure with increasing radial distance.∂P ∂r−1 for the 26 May 2013 across-lake transect is shown in Figure 3.4 a.Near the centre of the transect, within a radial distance of 750 m from thecentre of the horizontal density anomaly, the horizontal pressure differenceis negative. This corresponds to the high-density region that has higherpressure than the surrounding, less dense water. The magnitude of the hor-313.1. 2013 Resultsizontal pressure difference increases with depth. From a radial distance of750 m outwards, the horizontal pressure difference is positive. This is be-cause horizontally the density is increasing as the distance approaches theshore where the isopycnals run parallel to the bottom slope.The estimated azimuthal geostrophic velocities (vθg) from (1.9) can beseen in Figure 3.4 b. The negative vθg are anti-cyclonic and correspond tothe region of negative ∂P ∂r−1 from panel a and the high-pressure core ofthe anomaly. Figure 3.4 b shows that from the centre of the anomaly toa radial distance of 750 m, vθg is anti-cyclonic. The anti-cyclonic valuesalso increase with depth. The maximum anti-cyclonic vθg is estimated to be-0.02 m s-1 and occurs 250 m to the west and 330 m to the east of the centreof the horizontal density anomaly at a depth of 28.5 m. At this velocity, itwould take a particle 25 or 33 hours to make one complete circuit at theseradii. Using these values, Ro ∼ 0.5 and 0.4. Beyond the radial distance of750 m, vθg is cyclonic and increases with depth. The maximum cyclonic vθgis 0.029 m s-1 at a radial distance of 1030 m. This gives Ro ∼ 0.2.The estimated azimuthal cyclogeostrophic velocities (vθcg) from (1.12)can be seen in Figure 3.4 c. Positive and negative azimuthal velocitiesindicate cyclonic and anti-cyclonic flow about the centre of the horizontaldensity anomaly. The distribution of vθcg is similar to that of vθg with oneexception; there is a region near the centre that has no real or physicalsolution (the white region). Neglecting the white region for now, from thecentre of the anomaly to a radial distance of approximately 750 m, vθcg isanti-cyclonic and increases in magnitude with depth. The maximum anti-cyclonic vθcg of -0.021 m s-1 occurs at a radius of 528 m which gives Ro ∼323.1. 2013 ResultsDepth [m]−1000 −500 0 500 1000 15000510152025303540Depth [m]−1000 −500 0 500 1000 15000510152025303540Distance from anomaly centre [m]Depth [m]−1000 −500 0 500 1000 15000510152025303540  −0.020                          −0.016                          −0.012                          −0.008                          −0.004                           0.000                           0.004   −0.03                           −0.02                           −0.01                            0.01                            0.02                            0.03   −0.02           −0.01            0.00            0.01            0.02∂ P ∂ r - 1 [Pa m-1] vΘg [m s -1]  vΘcg [m s -1] a)b)c)Figure 3.4: Contours of the horizontal pressure difference (∂P ∂r−1) [Pa m-1] (panela), vθg [m s-1] (panel b), and vθcg (panel c) for the across-lake transect on 26 May2013. The contour intervals for panel a) are 0.001 Pa m-1, 0.005 m s-1 for panel b),and 0.0025 m s-1 for panel c). The distance along the x-axis is the radial distancefrom the centre of the density anomaly (0 m). Positive distances are to the eastand negative distances are to the west. The solid black contour line represents inpanels a), b) and c) represent ∂P ∂r-1 = 0, vθg = 0, and vθcg = 0. Positive andnegative azimuthal velocities are cyclonic and anti-cyclonic.333.1. 2013 Results0.3 and it would take a particle 45 hours to make one complete revolutionat this speed and radius. Beyond 750 m, vθcg is cyclonic and increases inmagnitude with depth. The maximum cyclonic vθcg of 0.021 m s-1 occurs ata radial distance of 1030 m and a depth of 29.5 m which gives Ro ∼ 0.15.The region with no real and physical solution occurs, mathematically, whenthe radicand (the terms under the square root in 1.12) is less than zero.This occurs because the horizontal pressure force is more negative than thecentripetal acceleration force is positive at that location (as discussed insection 1.3.4). While there may not be a solution in this region from thecyclogeostrophic balance, there are ways to estimate the azimuthal velocitiesin this region.Before the azimuthal velocities can be estimated for white region in Fig-ure 3.4 c, the estimates of vθg and vθcg are compared by non-dimensionalizingthe difference between them (vθcg − vθg) by the mean of the velocities((vθcg + vθg)/2). This is shown in Figure 3.5 where the greatest difference(53 %) occurs at a radial distance of 130 m, and a depth of 14.5 m. Thisfollows since the difference in the two balances is the inclusion of the cen-tripetal acceleration force which has the greatest impact near the centre ofthe anomaly. The minimum difference (-16 %) occurs at a radial distanceof 1030 m, and a depth of 29.5 m. The mean percent difference is 0.53 %.The mean value indicates that over the transect the difference in the twobalances are negligible; however, there is a significant difference near thecentre of the transect, which is of interest to this analysis.To further investigate the importance of the centripetal acceleration force(Fc) in the cyclogeostrophic force balance, the values of Fc, Coriolis (Fcor)343.1. 2013 ResultsDistance from density anomaly centre [m ]Depth [m]−1000 −500 0 500 1000 15000510152025303540  −20       −10         0        10        20        30        40        50Percent DifferenceFigure 3.5: Contours of the percent difference in vθcg and vθg given by (vθcg −vθg)/((vθcg + vθg)/2)100). Contour intervals of 5%.and pressure difference (Fp) forces per unit mass were calculated and canbe seen in panels a, b, and c) respectively in Figure 3.6. The maximumvalue of Fc is one order of magnitude smaller than Fcor and Fp. However,the greatest value occurs near the centre of the horizontal anomaly. Theabsolute value of each force per unit mass was also compared to the sumof the absolute values of all of the forces per unit mass and is presented asa percentage in Figure 3.7. Panel c shows that Fc has a range of 21 % (ata radial distance of 125 m) to 0.003 % (virtually no impact). This followsfrom Ro ∼ 0.2. Fc was greatest near estimated Rri of the horizontal densityanomaly, and decreased radially outward. Panel b shows that Fcor has arange of 50 % to 42 %. Panel c shows that Fp has a range of 50% to 29353.1. 2013 Results%. From this analysis, it can be seen that Fc has an impact on the forcebalance for radial distances less than 750 m; therefore, the horizontal densityanomaly is in cyclogeostrophic balance.Depth [m]  −1000 −500 0 500 1000 1500010203040Depth [m]  −1000 −500 0 500 1000 1500010203040Distance from density anomaly centre [m]Depth [m]  −1000 −500 0 500 1000 150001020304012345678−2−10123−3−2−1012x 10 - ⁷x 10 - 6[m s⁻²][m s⁻²]a) Centripetal acceleration force/unit massb) Coriolis force/unit massc) Pressure force/unit mass[m s⁻²]x 10 - 6Figure 3.6: Contours of a) centripetal acceleration force per unit mass, b) Coriolisforce per unit mass, and c) pressure force per unit mass for the across-lake transectcollected on 26 May 2013. The contour intervals for panels a, b, and c are 1 x 10-7,0.5 x 10-6, and 0.5 x 10-6 m s-2. The distance along the x-axis is the radial distancefrom the centre of the density anomaly (0 m). Positive distances are to the eastand negative distances are to the west.An estimate of azimuthal velocity distribution for the entire transectis desired including the region where there is no real, physical solution forthe cyclogeostrophic balance. As a first estimate, the values of vθg areapplied to this region which can be seen in Figure 3.8 a. Similar to previousestimates, horizontally from 0 to an approximate radial distance of 750 m,363.1. 2013 Results−1000 −500 0 500 1000 15000102030405060Input [%]−1000 −500 0 500 1000 15000102030405060Input [%]−1000 −500 0 500 1000 15000102030405060Input [%]Distance from density anomaly centre [m]a) Centripetal acceleration force b) Coriolis force c) Pressure force Figure 3.7: Percent of the absolute value of the a) centripetal acceleration forceper unit mass, b) Coriolis force per unit mass, and c) pressure force per unit massover the sum of the absolute value of the three forces for the across-lake transectcollected on 26 May 2013. The distance along the x-axis is the radial distance fromthe centre of the density anomaly (0 m). Positive distances are to the east andnegative distances are to the west.the azimuthal velocity is anti-cyclonic and reaches a maximum anti-cyclonicvelocity at 520 m. After this distance, the velocity magnitude decreases,until 750 m, where it transitions from anti-cyclonic to cyclonic. Verticallyin the anti-cyclonic region, the magnitude of the azimuthal velocity increaseswith depth until 23.5 m, and then decreases to the bottom.Another estimate for the distribution of vθcg is using one of the com-ponents of the cyclogeostrophic solution. When regions have no real andphysical solution, a solution still exists; however, it is a complex solution373.1. 2013 Results(vcomp = vreal + ivimag) where vreal is the real component in the azimuthaldirection and vimag is the imaginary component in the radial direction. Thecomplete distribution of vθcg can be estimated using vreal which is the sameas solving the cyclogeostrophic equation using the minimum allowable pres-sure difference. This is shown in Figure 3.8 b. This estimate results in asimilar pattern as the previous estimate with the maximum anti-cyclonicazimuthal velocity occurring at 380 m and a depth of 29.5 m. For this esti-mate, the azimuthal velocity inside the horizontal density anomaly increaseswith depth until it reaches the maximum magnitude, and then is uniformto the bottom.The difference between the two estimates is shown in Figure 3.8 c whichshows the difference in the first and second estimate non-dimensionalized bythe mean of the two estimates. The greatest percent difference occurs nearthe centre of the horizontal density anomaly at 40 m near the bottom.The existence of complex solutions near the centre of the horizontaldensity anomaly indicates that there is a radial component to the velocityand that the initial assumption that the density anomaly has no radialvelocity is not entirely accurate. The radial velocity component is equivalentto vimag of the complex solution and is shown in Figure 3.8 d. This showsthat vimag only exists where there is no real and physical solution to vθcg, andthat it increases away from the centre of the anomaly to a radial distance of250 m, and increases vertically with depth. vimag ranges from 0 to 0.0175 ms-1, and has a mean of 0.001 m s-1. This indicates that the horizontal densityanomaly was not steady; however, since these transects are a snapshot intime and the full transects were not repeated, the data collected cannot be383.1. 2013 Resultsused to determine whether or not the horizontal density anomaly is steady,spinning-up or spinning-down. To investigate motion at one time, the steadyassumption is an appropriate first estimate.The same methods of estimating vθg and vθcg were used for the along-lake transect with similar results shown in Figure 3.9 where panels a throughf correspond to depths of 5, 10, 15, 20, 25, and 30 m. The azimuthalvelocity estimates start at a radial distance of 200 m because the along-laketransect did not cross through the centre of the horizontal density anomaly.From Figure 3.9, the velocity magnitudes decrease with radial distance andtransition from anti-cyclonic to cyclonic. The velocities also increase inmagnitude with depth. The greatest difference between vθg and vθcg occurswithin 250 m of the centre of the horizontal density anomaly. This is similarto the results from the across-lake transect and this is expected due tothe inclusion of the centripetal acceleration force in the cyclogeostrophicbalance.To determine whether the estimates of vθcg are reasonable, they arecompared to the measured ADCP velocities. Since the ADCP was locatedat a radial distance of 1330 m, which is outside the region where there is noreal and physical solution, the patched estimates can not be compared tothese measured velocities. The azimuthal component of the ADCP velocities(vθA) are compared to vθg and vθcg at similar radial distances and are shownin Figure 3.10 a. vθA is anti-cyclonic and decreases in magnitude with depth.vθg and vθcg are cyclonic and increase in magnitude with depth. vθA, vθg,and vθcg have a similar slope in panel a. However, vθA approaches 0 m s-1near the bottom, and vθg, and vθcg approach 0 m s-1 near the surface. vθg393.1. 2013 ResultsDepth [m]−1000 −500 0 500 1000 1500010203040Depth [m]−1000 −500 0 500 1000 1500010203040Depth [m]−1000 −500 0 500 1000 1500010203040Distance from density anomaly centre [m]Depth [m]−1000 −500 0 500 1000 1500010203040   −0.03                           −0.02                           −0.01                            0.01                            0.02                            0.03Azimuthal velocity [m s-1]a)b)c)d)   −0.03                                   −0.02                                   −0.00                                    0.01                                    0.02                Azimuthal velocity [m s-1] −70         −40         −10          20          50          80         110    PercentDifference 0.000                0.004                0.008                0.012                0.016               Radial velocit [m  s-1]Figure 3.8: Contours of a) vθcg patched with vθg, b) vθcg patched with vreal fromthe cyclogeostrophic balance solution, c) the percent difference of panels a and bnon-dimensionalized by the mean of the two solutions, and d) vimag component ofthe cyclogeostrophic velocity. Panel a and b have contour intervals of 0.0025 m s-1,panel c has intervals of 10 %, and panel d has intervals of 0.001 m s-1. Positive andnegative values of azimuthal velocity are cyclonic and anti-cyclonic. The distancealong the x-axis is the radial distance from the centre of the density anomaly (0 m)with positive distances to the east and negative distances to the west. The solidblack contour line represents values of 0 m s-1 for a, b and d, and 0 % for c.403.1. 2013 Results200 300 400 500 600 700−20−15−10−505200 300 400 500 600−20−15−10−505200 250 300 350 400 450 500−20−15−10−505200 250 300 350 400−20−15−10−505200 250 300 350 400−20−15−10−505200 250 300 350 400−20−15−10−505Radial distance [m] Radial distance [m]x 10 -3 x 10 -3x 10 -3x 10 -3x 10 -3x 10 -3a) 5 m b) 10 mc) 15 me) 25 md) 20 mf) 30 mAzimuthal velocity [m s-1 ]v g northv g southv cg northv cg southFigure 3.9: Panels a, b, c, d, e, and f show estimates of vθg and vθcg for depths of 5,10, 15, 20, 25, and 30 m. Xs marks vθg and the dots marks vθcg. Blue markers are tonorth of intersection of the across and along-lake transects and green markers are tothe south. Positive and negative azimuthal velocities are cyclonic and anti-cyclonic.and vθcg approach 0 m s-1 near the surface because the surface was initiallyassumed to be the level of no-motion. vθA (which comes from a directmeasurement of velocity) shows that the azimuthal velocity near the surfaceis not zero, and that the level of no-motion is approximately the bottom.When the magnitude of vθA near the surface (0.027 m s-1) is subtracted fromthe estimated vθg and vθcg (at similar radial distance) the adjusted vθg andvθcg have similar values and follow the same pattern as the measured vθAshown in Figure 3.10 b. This indicates that the assumption that the surfaceis the level of no-motion is incorrect, and that the level of no-motion is nearthe bottom.413.1. 2013 Results−0.025 −0.02 −0.015 −0.01 −0.005 0 0.005 0.01 0.015 0.0202468101214161820Azimuthal velocity [m s -1 ]Depth [m]−0.03 −0.025 −0.02 −0.015 −0.01 −0.005 002468101214161820Azimuthal velocity [m s -1 ]Depth [m]v g  1380 m ALv g  1280 m ALv g  1330 m ACv g  1230 m ACADCP 1330 mv cg  1380 m ALv cg  1280 m ALv cg  1330 m ACv cg  1230 m ACa)b)Figure 3.10: Panel a) comparison of vθA to vθcg and vθg [m s-1] at comparable radialdistances on the across (AC) and along-lake (AL) transects and panel b) correctedcomparison for level of no-motion at the bottom.The previously estimated patched distributions of vθcg were based on theassumption that the level of no-motion was at the surface and which wasachieved by integrating down from the surface. Since the measured ADCPazimuthal velocities indicate that the level of no-motion is at the bottom,these estimate may not be representative of the actual distribution. Toestimate vθcg with the level of no-motion at the bottom, the transect shouldbe integrated up from the bottom; however, since the lake bottom is not423.2. 2014 Resultsflat this is difficult to do; therefore, vθcg at the bottom of each profile wassubtracted over the entire depth of the profile for the entire distribution.This was done to both the estimated distributions of vθcg patched with vθgand with the real component of vθg which can be seen in panels a andb of Figure 3.11. The distributions are nearly vertical inversions of theoriginal estimated distributions; however, the circulations are in the oppositedirection. From beneath the ice surface downwards, the circulations arecyclonic for 0 to 750 m. There are small regions near the bottom at 100 mand 500 m in panel a, and 500 m in panel b where the flow is anti-cyclonic.From 750 m radially outwards, the flow is anti-cyclonic. Unlike the initialestimated distributions, the magnitudes of the azimuthal velocities decreasewith depth. Also, near the centre of the horizontal density anomaly, thereis a depth beneath which the circulation transitions from cyclonic to anti-cyclonic.3.2 2014 ResultsAt the beginning of the 2014 field campaign, the ice had a mean thicknessof 1.0 m with a layer of snow and slush that was 0.05 to 0.20 m thickon top. The ice thickness decreased by 0.15 to 0.35 m over the period ofstudy; however in contrast to 2013, no moats formed. The mean daily airtemperature over the period of study was 3.5◦C. The mean wind speed was13 km hr-1 from 19 to 26 May 2014 with a mean direction of 209◦.Ten CTD transects were collected during the period of study and allshow that the temperatures measured were below 4◦C. The across and along-433.2. 2014 ResultsDepth [m]−1000 −500 0 500 1000 15000510152025303540Distance from density anomaly centre [m]Depth [m]−1000 −500 0 500 1000 15000510152025303540   −0.03                           −0.02                           −0.01                            0.01                            0.02                            0.03   −0.03                                   −0.02                                   −0.00                                    0.01                                    0.02                Geostrophic patchedazimuthal velocity[m s-1]Real cyclogeostrophicazimuthal velocity[m s-1]a)b)Figure 3.11: Contours of distribution of vθcg patched with vθg (panel a) and vreal(panel b) corrected for level of no-motion at the bottom for across-lake transectcollected on 26 May 2013. Contour intervals of 0.0025 m s-1. Positive and negativeazimuthal velocities are cyclonic and anti-cyclonic.lake temperature distributions collected on 26 May 2014 (panels a and b ofFigure 3.12) are representative of the 10 transects. From the distributionsof water temperature, it can be seen that the water temperature increaseswith depth (inversely stratified) and is vertically stable. If the lake washorizontally stable, the isotherms would be horizontal; however, Figure 3.12a shows horizontal variation in temperature, though much less than observedin 2013. From the east to west, the temperature decreases horizontally untilapproximately 1500 m from the east shore. Here, it begins to increase withdistance. This causes a slight upward curve (concavity) in the isothermsover the width of the lake.Similar to the 2013 results, conductivities were low; therefore, the tem-443.2. 2014 ResultsDepth [m]Distance from East shore [m] 5001000150020002500010203040Depth [m]Distance from intersection with AC transect (black line) [m]100 200 300 400 500 600 700 800 900 1000010203040     0.5                                     1.0                                     1.5                                     2.0                                     2.5                                     3.0Temperature [ºC]a) AC 26 May 2014b) AL 26 May 2014Figure 3.12: Contours of temperature for the across (AC) and along-lake (AL)transects (panels a and b) 26 May 2014 with contour intervals of 0.05 ◦C. Thedata has been vertically averaged every 1 m. The distance along the x-axis is thedistance from the eastern shore (panel a) and distance from the intersection of thetwo transects (panel b). The black vertical line in panel a is where the two transectsintersected along the across-lake transect at ∼ 90◦.perature and density distributions follow similar patterns. Since there ishorizontal variation in temperature, there is also horizontal variation indensity. Horizontally, there is less dense water at the centre of the lake withdenser water on either side. This creates an upward concavity in the isopy-cnals. The denser water near the shores applies an inward directed pressureforce on the less dense water in the centre. This creates a low-pressure hor-izontal density anomaly in the centre of the lake. This isopycnal concavitywas present for the 7-day observation period; therefore, the anomaly is as-sumed to be steady. Since the denser water did not flow inward under the453.2. 2014 Resultsless dense water (which would have flowed outward and over), there musthave been a force opposing the inward pressure force from the denser fluid.This indicates that there was a balance of forces and since the concavity ofthe anomaly was over the entire width of the lake, it is possible that thebalance could be geostrophic, cyclogeostrophic, or cyclostrophic.The maximum horizontal variation in density, in the top 20 m of thewater column, is used to estimate the type of balance and was found tobe 0.0088 kg m-3 at a depth of 12.5 m. This gives g’ of 8.63 x 10-5 ms-2. Assuming a height of 12.5 m (the height over which the isopycnalsappear to be concave), Rri ∼ 240 m. This radius is less than the horizontallength of the concavity of the isopycnals ∼ 2000 m which indicates that thecirculation is modified by the earth’s rotation and is in either geostrophic orcyclogeostrophic balance. Using Rri and L ∼ 2000 m, Ro is 0.12 which doesnot immediately indicate which balance the circulation is subject to.Since Rri and Ro do not immediately indicate the type of balance, bothgeostrophic and cyclogeostrophic balances are investigated to determine thedifference between the two. Both balances depend on the presence of ahorizontal pressure difference; therefore, ∂P ∂r−1 was calculated movingaway from the centre of the anomaly, and assuming that the level of no-motion is directly beneath the ice surface. This can be seen in Figure 3.13 a.In the top 10 m of the water column, ∂P ∂r−1 increases laterally to the westuntil 250 m, then decreases until it reaches a minimum at approximately1000 m. ∂P ∂r−1 also increases in magnitude with depth in the top 10m. Below 10 m, ∂P ∂r−1 increases radially outward from the centre untilapproximately 500 m to the east and all the way to the sloping boundary463.2. 2014 Resultsto the west. This shows that the centre of the anomaly is a low-pressurecentre. ∂P ∂r−1 also increases with depth from 10 m until the bottom.Using the same methods as mentioned in the previous section (Sec-tion 3.1), vθg and vθcg are estimated for the transect and can be seen in panelsb and c in Figure 3.13. ∂P ∂r−1, vθg, and vθcg have similar patterns wherepositive ∂P ∂r−1 values correspond to cyclonic motion and negative valuescorrespond to anti-cyclonic motion. Since this is a low-pressure horizontaldensity anomaly, there is a solution everywhere for the cyclogeostrophic es-timated because ∂P ∂r−1 is positive in the core and the radicand is alwaysreal. The estimates of azimuthal velocity distribution show that there isa shallow (0 - 10 m) anti-cyclonic horizontal anomaly above a cyclonicallyrotating anomaly that reaches from 10 m to the bottom boundary. The twocirculations are not directly on top of one another, the upper anti-cyclonicanomaly is shifted to the east by approximately 100 m. Both maximumvθg and vθcg, 0.0063 and 0.0059 m s-1, occur 764 m to the west of the cen-tre of the anomaly. Using (1.4), this gives Ro ∼ 0.06. Minimum vθg andvθcg, -0.0030 and -0.0033 m s-1, occur 278 m to the east of the centre ofthe anomaly which gives Ro ∼ 0.08. The difference between vθcg and vθgis non-dimensionalized by the mean of the two values and is presented as apercentage in Figure 3.13 d. The greatest positive percent difference of 9 %occurs at 280 m and a depth of 8.5 m and is due to vθcg being greater thanvθgs. The greatest negative percent difference is due to vθg being greaterthan vθcg, -19 %, occurs at 75 m and 33.5 depth. Both these locations areinside the estimated Rri and are near the centre.To further investigate the importance of Fc in the cyclogeostrophic force473.2. 2014 Results−1000 −500 0 500 1000010203040−1000 −500 0 500 1000010203040−1000 −500 0 500 1000010203040Distance from centre [m]−1000 −500 0 500 1000010203040!P !r-1 [Pa m-1]        −5                  −1                    3                    7     x 10 -7  −0.004                           0.000                           0.004                        vg [m s-1]  −0.030                          −0.022                          −0.014                          −0.006                           0.002                vcg [m s-1]  −20                                     −12                                     − 4                                       4                              Percent differencea)b)c)d)Depth [m]Depth [m]Depth [m]Depth [m]Figure 3.13: ∂P ∂r−1 for 26 May 2014 in panel a, vθg in panel b, vθcg in panel c,and the difference between vθcg and vθg non-dimensionalized by the mean of thetwo values (as a percentage). The contour interval for a is 1 x 10-7 Pa m-1 for panela, 0.001 m s-1 for panels b and c, and 1 % for panel d. Positive and negative valuesof azimuthal velocity are cyclonic and anti-cyclonic. The distance along the x-axisis the radial distance from the centre of the density anomaly (0 m) with positivedistances to the east and negative distances to the west. The solid black contourline represents values of 0 Pa m-1 for a, 0 m s-1 for b and c, and 0 % for d.balance, the values of Fc, Fcor, and Fp per unit mass were calculated andcan be seen in Figure 3.14. Below 10 m in panel a, Fc increases with radialdistance and depth until it reaches its maximum value at the bottom at aradial distance of 250 m. It then decreases with increasing radial distancefrom 0 m to 10 m, there is also an input from Fc at 5 m depth and 250483.2. 2014 Resultsm radius. For Fcor below 10 m in panel b, the input increases with radialdistance and depth, until it reaches the maximum value at the bottom ofthe 250 m radial distance. The values then decrease with increasing radius.From 0 to 10 m, Fc decreases with radial distance to 250 m, and depth to 5m. Then, the values increases with depth to 10 m and with radial distance.The distribution of Fpress follows that of Fcor except that where Fcor waspositive, Fpre is negative and vice versa. When comparing the magnitudes,it can be seen that the maximum value of Fc is one order of magnitudesmaller than Fcor and Fpress.As another method of comparison, the percent input from each of thethree terms was calculated (the absolute value of each term divided by thesum of all the absolute values of the terms). The percent input forFcor andFpress range from 40 to 50 % over the entire transect whereas Fc ranges from0 to 9 %, with a mean value of 2 %. The greatest value of Fc occurs at thecentre of the horizontal anomaly and decreases radially outward; therefore,Fc impacts the force balance within a radial distance 500 m.No ADCP measurements were available to compare to the estimates ofvθg and vθcg, so the estimates were left as is with no correction for differentlevels of no-motion.493.2. 2014 ResultsDepth [m]  −1000 −500 0 500 1000010203040246Depth [m]  −1000 −500 0 500 1000010203040−505Distance from density anomaly centre [m]  −1000 −500 0 500 1000010203040 −8−6−4−2  0  2  4x 10 -8x 10 -7x 10 -7[m s-1][m s-1][m s-1]a) Centripetal acceleration force/unit massb) Coriolis force/unit massc) Pressure force/unit massDepth [m]Figure 3.14: Contours of a) centripetal acceleration force per unit mass, b) Coriolisforce per unit mass, and c) pressure force per unit mass for the across-lake transectcollected on 26 May 2014. The contour interval for panel a is 1 x 10-8 m s-2, and 1x 10-7 m s-2 for panels b and c. The distance along the x-axis is the radial distancefrom the centre of the density anomaly (0 m). Positive distances are to the eastand negative distances are to the west.50Chapter 4DiscussionThis chapter will first separately discuss the results of the field campaigns,presented in chapter 3, and then will compare the results between years.4.1 2013 Data DiscussionIn 2013, the thermal and density structures were vertically stable; however,there was distinct horizontal temperature and density variation near thecentre of the lake where there was a cylindrical core of denser, warmer water.This denser water exerted an outward pressure force on the less dense watersurrounding it. When in steady state and modified by the earth’s rotation,an anti-cyclonic, rotating horizontal density anomaly extended from thesurface down paired with a weaker, less defined cyclonic circulation thatextends from near the bottom upwards.The observed anomaly had a radius ∼ 350 m, which is twice Rri ∼ 160m which indicated that the anomaly was affected by the earth’s rotation.Rri of 160 m is comparable to the estimate of Rri ∼ 200 m for the anomalyobserved in Pavilion Lake (Forrest et al., 2013), and Rri ∼ 220 m estimatedfor the anomaly observed in Lake Pa¨a¨ja¨rvi (Rizk et al., 2014). All of theseestimates are much smaller than the estimated Rri ∼ 10 km for anomalies514.1. 2013 Data Discussionunder sea-ice (Timmermans et al., 2008).Ro for the 2013 observations was estimated, using the observed den-sity differences, to be ∼ 0.2. This is less than the estimated Ro of 1.7for the Pavilion Lake cyclogeostrophic anomaly (Forrest et al., 2013) andthose estimated for the cyclogeostrophic anomalies under sea-ice (Ro ∼ 0.5to 0.99) (Timmermans et al., 2008). An Ro of 0.2 does not immediatelyindicate whether the anomaly is in geostrophic or cyclogeostrophic balance;therefore, both balances were investigated by estimating their associatedazimuthal velocities and comparing them.The distributions of vθg and vθcg were estimated; however, the horizontaldensity differences near the centre of the anomaly were unable to supporta purely azimuthal cyclogeostrophic balance. This resulted in radial veloc-ities and vθcg had a complex solution near the centre of the anomaly. Noother observation of horizontal anomalies in lakes have had this issue. Thiscould be because previous observations did not have high enough resolutionnear the centre of the anomaly. Two possible methods were investigated tocomplete the cyclogeostrophic solution: 1) using the geostrophic azimuthalvelocities, and 2) using the real component of the complex solution. Sincevery little is known about the region at the centre of high-pressure cyclo-geostrophic anomalies, and the two methods did not vary significantly, eithermethod is acceptable as a first estimate. When the complete distributionof vθcg was compared to vθg, they were found to be comparable, and onlyvary slightly near the centre (due to the difference in centripetal accelerationforce inclusion) and near the estimated Rri.To calculate the azimuthal velocities, the level of no-motion was taken at524.1. 2013 Data Discussionthe surface as a first estimation, this resulted in an anti-cyclonic anomaly inthe bottom region of the lake. However, comparing the azimuthal velocitiesto the measured azimuthal ADCP velocities, suggests the level of no-motionis actually near the bottom. To address this issue, the balances shouldhave been solved by integrating the force balance up from the bottom asopposed to down from the top when the level of no-motion is at the surface.However, since the lake’s bottom is not flat, it is difficult to do this withouta three dimensional model. Therefore, the estimated azimuthal velocity atthe bottom of each profile was subtracted from the entire profile so that thelevel of no-motion is at the bottom. This is a reasonable first estimate for thelevel of no-motion being at the bottom. This caused the horizontal densityanomaly to be contained in the upper portion of the lake and the directionof the circulation to switch direction. This is similar to the density anomalyobserved by Forrest et al. (2013) which was assumed to be contained inthe top layer; however, that level of no-motion was assumed at the surfacewhich reduced the interaction with the lake bottom.Prior to adjusting the estimates of azimuthal velocity for the level of no-motion at the bottom, the distributions did not show paired cyclonic andanti-cyclonic rotations; however, once adjusted, the cyclonic anomaly in thesurface layer is paired with a weak anti-cyclonic anomaly in the bottomlayer. This is similar to the anomalies observed in lakes by Forrest et al.(2013), and Rizk et al. (2014), in oceans by Timmermans et al. (2008), andpredicted in lake models by Huttula et al. (2010).The 2013 estimate of maximum anti-cyclonic vθg and vθcg are on theorder of 0.02 m s-1, and the maximum cyclonic velocities are on the order534.1. 2013 Data Discussionof 0.03 m s-1. These are comparable to observations made in Pavilion Lakewhere the the maximum cyclonic velocity was 0.021 m s-1 (Forrest et al.,2013). These estimated velocities are greater than the maximum 0.001 m s-1estimated in Lake Pa¨a¨ja¨rvi (Rizk et al., 2014), and the observed horizontalvelocities in Tub Lake of 3.047 x 10-4 m s-1 near the shore and 4.05 x 10-4m s-1 at the centre (Likens and Ragotzkie, 1966).It is hypothesized that the rotating circulation observed was driven byheat flux at the shorelines from incoming warm streams (Kirillin et al.,2015) and the heating of the water in the moats. The water entering themoats came from snow melt and was much warmer than the lake waterbecause it was subject to solar heating as it travelled over land and throughthe streams. This warmer, denser water created a dense underflow thatran down the slopes of the shore and converged towards the lake center,where it produced an upwelling of warmer denser water. From continuity,this upwelling needed to be balanced by a radial outward flow which was inthe form of return flow across the bulk water column. This flow was thendeflected to the right by the Coriolis force. This is similar to the pattern ofmid-winter circulation proposed by Welch and Bergmann which was drivenby heat release from the sediment and freeze out (1985). This density drivenflow was also observed by Rhines (1998) in experiments. However, the2013 circulation has a different hypothesized driving mechanism of the warmincoming streams which has also been proposed by Salonen et al. (2014)and compared to circulation forced by differential surface heating.There are two distinct regions in the 2013 observations: 1) the rotat-ing horizontal density anomaly in the centre of the lake, and 2) flow down544.2. 2014 Data Discussionthe slopes of the lake. As discussed previously, rotating horizontal densityanomalies have been inferred from previous observations and model predic-tions (Likens and Ragotzkie, 1966; Huttula et al., 2010; Forrest et al., 2013;Rizk et al., 2014); however, their formation and forcing mechanisms havenot been determined. Flow down slopes driven by heat release from thesediment has been suggested by Mortimer and Mackereth (1958) and sim-ilar flows have been observed by Likens and Ragotzkie (1966), Welch andBergmann (1985) and Malm (1998); however, it has not been observed, out-side the laboratory, to be forced by warm, dense inflow from streams duringthe end of winter.4.2 2014 Data DiscussionThe nearly horizontal isotherms and isopycnals observed near the centreof the lake in 2014 are expected in ice-covered lakes in winter when thelake is vertically stable and inversely stratified (Wetzel , 1975; Welch andBergmann, 1985). It is also expected that the lake be horizontally sta-ble with little horizontal temperature variability; however, when the entirelake transect is inspected, there are horizontal density differences that causeslight upward concavity in the isotherms and isopycnals over the width ofthe lake. This causes an inward directed pressure force which, when mod-ified by the earth’s rotation, caused vertically paired, rotating horizontaldensity anomalies. These horizontal density anomalies can be compared tosimilar observations and predictions with Rri, Ro, and azimuthal velocity.Rri for the observed cyclonic rotating anomaly was estimated, using the554.2. 2014 Data Discussionobserved horizontal density differences, to be 240 m which is less than theobserved length of the tilted isopycnals (∼ 1000 m). This Rri is comparableto the estimate for Rri ∼ 200 m from the anomaly observed by Forrestet al. in Pavilion Lake, British Columbia where the observed radius of theanomaly was 110 m (2013). Rizk et al. estimated that Rri ∼ 220 m whichwas one order of magnitude smaller than the observed length scale of theanomaly observed in Lake Pa¨a¨ja¨rvi. Since the observed radii were greaterthan or on the order of Rri, the observed anomalies were modified by theearth’s rotation which is further investigated by calculating Ro. Ro wasinitially estimated to be 0.12 for the observed system. This is less thanRo ∼ 1.7 estimated for Pavilion Lake where the system was assumed tobe in cyclogeostrophic balance (Forrest et al., 2013). The 2014 Ro is onthe order of the upper limit of the range of Ro ∼ 10-3 to 10-2 estimatedfor Lake Pa¨a¨ja¨rvi where the anomalies were assumed to be in geostrophicbalance (Rizk et al., 2014). Ro values of 0.5 to 0.99 have been estimated forthe rotating anomalies in cyclogeostrophic balance observed under sea-ice(Timmermans et al., 2008).Ro of 0.12 does not strongly indicate whether the observed system wasin geostrophic or cyclogeostrophic balance; therefore, both balances wereestimated and compared. The estimations of vθg and vθcg show the samepattern and the values do not vary significantly. They did vary near in thecentre which is expected because this is where the centripetal accelerationforce has the greatest impact and its inclusion is the difference between thetwo balances. Therefore, assuming one balance as opposed to the otherwould not result in significantly different azimuthal velocity distributions.564.2. 2014 Data DiscussionFor the anomalies in 2014, the maximum magnitudes of the cyclonic andanti-cyclonic azimuthal velocities (for both geostrophic and cyclogeostrophicbalances) were 0.006 and 0.003 m s-1. These velocities are on the same orderof magnitude as those estimated in Lake Pa¨a¨ja¨rvi which were on the order of0.001 m s-1 (Rizk et al., 2014). The velocities are greater than observationsmade in Tub Lake of 3.047 x 10-4 m s-1 near the shores and 4.05 x 10-4 m s-1near the centre (Likens and Ragotzkie, 1966). However, the estimates areless than those from Pavilion Lake (0.021 m s-1) (Forrest et al., 2013) and0.01 m s-1 (Huttula et al., 2010) under lake-ice as well as under sea-ice (0.09to 0.26 m s-1) (Timmermans et al., 2008).From 0 to 10 m depth, there was a weak, anti-cyclonically rotating den-sity anomaly, and from 10 to the bottom, there was a slightly stronger,cyclonically rotating, horizontal density anomaly. The transition from anti-cyclonic to cyclonic represents a level of no-motion at 10 m. Vertically pairedrotating density anomalies have been observed under ice in lakes by Forrestet al. (2013), and Rizk et al. (2014), as well as in the ocean under sea-ice byTimmermans et al. (2008). Huttula et al. (2010) also predicted verticallypaired anti-cyclonic and cyclonic rotating density anomalies in the top andbottom of Lake Pa¨a¨ja¨rvi using the Princeton Ocean Model. These observa-tions typically refer to one rotating anomaly even though it is paired. Theanomaly that is referred to is considered the dominant anomaly, usually,because it has the greater thickness and sometimes a greater velocity.It is hypothesized that the horizontal density anomaly, which was evidentfrom the upward concavity in the isotherms and isopycnals, was formedwhen the ice-cover initially formed and heat was released from the sediment574.3. 2013 and 2014 Comparisoninto the overlying water causing an increase in water density just abovethe boundaries. This release of heat would have been greater closer to theshores which would account for the upward tilt in the isotherms. Therewas no other source of heat in 2014 because at the time of observationthe entire lake was covered in ice and snow which insulated and protectedthe water column from solar radiation (Arst et al., 2006). Since there wasno significant source or sink of heat, the slight horizontal density anomalywas able to persist and was balanced by the Coriolis force causing cyclonicflow about the low-pressure (lower-density) centre. This is similar to theobservations and model predictions for Lake Pa¨a¨ja¨rvi made by Rizk et al.(2014) where it was assumed that if the thermal regime of the lake was onlycontrolled by the input of heat from the sediment, water temperatures nearthe shores would increase and cause cyclonic rotation. Heat release from thesediment is also assumed to be the cause of convection that drove circulationin Tub Lake (Likens and Ragotzkie, 1966).4.3 2013 and 2014 ComparisonObservations from both field seasons measured water temperatures below4◦C, had vertically stable density profiles, and horizontal density variation.However, the horizontal density patterns observed in the two years weredifferent and caused basin-wide water circulations in opposing directions. In2013, there was a dominant, high-pressure horizontal density anomaly nearthe centre of the lake. If the level of no-motion is assumed to be directlybeneath the ice-surface, the anomaly is in the bottom of the lake and is anti-584.3. 2013 and 2014 Comparisoncyclonic. If the level of no-motion is assumed to be at the bottom, whichis supported by ACDP measurements, there is a strong cyclonic rotationin the upper region of the lake and an anti-cyclonic rotating anomaly inthe bottom layer of the lake. In 2014, there was a dominant low-pressurecyclonic density anomaly near the centre of the lake in the bottom region,and a weak anti-cyclonic anomaly in the upper region. The observationsbetween the two years have similarities as well as differences.The observed radii of the anomalies (1000 m for 2014 and 350 m for 2013)and the estimatedRri (∼ 240 m for 2014 and 160 m for 2013) are comparable.The estimates of Ro for the two years are also comparable with Ro ∼ 0.12for 2014 and 0.2 for 2013. In both years, it was not evident which forcebalance, geostrophic or cyclogeostrophic, was relevant. When the azimuthalvelocities (vθ) for both balances were estimated, it was found that theydid not vary significantly; therefore, the choice of either balance would notgreatly affect the results. However, the magnitudes of vθ were an order ofmagnitude different between years. In 2014, the maximum cyclonic andanti-cyclonic vθ were 0.006 and 0.003 m s-1, whereas in 2013, the maximumcyclonic and anti-cyclonic vθ 0.03 and 0.02 m s-1. Both years had pairedrotating anomalies.The differences in the observations is hypothesized to come from thedifference in the length of time from when the observations were made towhen ice-off occurred. In 2013, the observations were made at, during andafter ice-off. In 2014, ice-off did not occur until 18 June, 12 days after thelast day of study. This time difference allowed for variations in the ice andsnow-cover. In 2013, there were moats around the edges of the ice-cover594.3. 2013 and 2014 Comparisonthat were initially 1 m wide and continued to widen until ice-off. There wasalso no snow on the ice and the snow on the surrounding land had also beenmelting and running into lake overland and through streams. In 2014, therewere no moats around the ice which was completely covered in snow andslush. The surrounding area was also still covered in snow. This small differ-ence in duration before ice-off allowed for a significant change in the forcingmechanism of the anomalies. Similar findings were made by Salonen et al.(2014) where the small differences in water temperature near the end of theice cover period have great effects on lake hydrodynamics and the differencein snow and ice conditions can lead to interannual circulation differences.Rizk et al. (2014) also observed variation in the direction of rotating densityanomalies between years in Lake Pa¨a¨ja¨rvi which was attributed to the vari-ation in the initial winter stratification which was not measured in eitherthe 2013 or 2014 studies of Lake Kilpisja¨rvi.60Chapter 5ConclusionThis work presents analysis (chapter 2) and results (chapter 3) of observa-tions collected in two field seasons near the end of the ice-covered period atLake Kilpisja¨rvi. The two field seasons show two different and significantbasin-scale circulation patterns beneath the ice. These observations areimportant because significant basin-scale circulation during the ice-coveredperiod in lakes has not been extensively documented or analyzed. The 2013observations, presented in section 2.2.1, are also very unique because veryfew observations have been made directly prior to ice-off which was observedthat field campaign.In 2013, a high-pressure horizontal density anomaly was observed nearthe centre of the lake. This anomaly had vertically paired rotating circu-lations in the upper and lower regions of the lake. ADCP measurementsshow that the level of no-motion was near the bottom boundary of the lakeand not at the surface where it as initially assumed to occur. The densitydistribution was used to estimate the azimuthal velocities which were foundto have maximum cyclonic and anti-cyclonic values of 0.03 and 0.02 m s-1.The anomaly was estimated to have Rri ∼ 160 m, with Ro ∼ 0.2. It ishypothesized that this circulation is driven by heat flux at the shorelines61Chapter 5. Conclusionfrom incoming streams and, to a lesser extent, the warming of the moatssurrounding the ice-cover. This caused a density flow down the slopes to thecentre of the lake where the flow converges. From continuity, this flow wasbalanced with a shoreward flow beneath the ice surface. These flows weremodified by the earth’s rotation which results in the rotational circulation.In 2014, a low-pressure horizontal density anomaly was observed near thecentre of the lake. This anomaly had vertically paired rotating circulationsin the upper and lower regions of the lake. The level of no-motion wasestimated to be 10 m below the surface where the circulation transitionedfrom anti-cyclonic to cyclonic. The density distribution was used to estimatethe azimuthal velocities which were found to have maximum cyclonic andanti-cyclonic values of 0.006 and 0.003 m s-1. The anomaly was estimated tohave Rri ∼ 240 m, with Ro ∼ 0.12. It is hypothesized that this circulationwas driven by sediment release of heat to the overlying water causing a tiltin the isopycnals near the shores of the lake that caused an inward pressureforce that was balanced by the Coriolis force and, to a lesser extent, thecentripetal acceleration force. This is similar to expected results for under-ice circulation.It is hypothesized that the reason that the observations were differentbetween years was due to the duration between the observation period andice-off. The 2014 observations were collected 12 days prior to ice-off, andthe ice and snow conditions were similar to the conditions during the bulkof winter. The 2013 observations were made directly prior to ice-off, whichallowed the snow cover to melt (thus not insulating the lake) and warm in-flows to enter the lake. This short period of time allowed for large differences62Chapter 5. Conclusionthat created significantly different circulation patterns. It was found thatfor the small horizontal density differences measured under-ice during the2013 and 2014 studies, the choice of geostrophic or cyclogeostrophic balancedoes not greatly affect the resulting azimuthal velocities.Thermal and circulation patterns under-ice are related; however, this re-lation is not fully understood. These thermal distribution observations andtheir associated estimated circulation patterns, paired with the ADCP ob-servations of velocity will help to better understand the relationship betweenthermal patterns and water circulation under ice in lakes.63BibliographyAkitomo, K., M. Kurogi, and M. Kumagai (2004), Numerical study of athermally induced gyre system in Lake Biwa, Limnology, 5, 103–114.Arst, H., A. Erm, M. Leppa¨ranta, and A. Reinart (2006), Radiative charac-terists of ice-covered fresh- and brackish-water bodies, Proceedings of theEstonian Academy of Sciences, Geology, 55 (1), 3–23.Bengtsson, L. (1986), Dispersion in ice-covered lakes, Nordic Hydrology, 17,151–170.Bengtsson, L. (1996), Mixing in ice-covered lakes, Hydrobiologia, 322, 91–97.Bengtsson, L., and T. Svensson (1996), Thermal regime of ice coveredSwedish lakes, Nordic Hydrology, 27, 39–56.Bengtsson, L., J. Malm, A. Terzhevik, M. Petrov, P. Boyarinov, A. Glinsky,and N. 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Byron-Scott (1998), Dy-namic meteorology: a basic course, Arnold, London; New York.Greenspan, H. P. (1968), The theory of rotating fluids, Cambridge mono-graphs on mechanics and applied mathematics, Cambridge UniversityPress.Holton, J. R. (2004), An introduction to dynamic meteorology, InternationalGeophysics Series, vol. 88, fourth ed., Elsevier.Huttula, T., M. Pulkkanen, B. Arkhipov, M. Leppa¨ranta, V. Solbakov,S. Kunio, and K. Salonen (2010), Modelling circulation in an ice-coveredlake, Estonian Journal of Earth Sciences, 59 (4), 298–309.Kirillin, G., C. Engelhardt, and S. Golosov (2008), A mesoscale vortex in asmall stratified lake, Environmental Fluid Mechanics, 8 (4), 349–366.65BibliographyKirillin, G., M. Leppa¨ranta, A. Terzhevik, N. Granin, J. Bernhardt,C. Engelhardt, T. Efremova, S. Golosov, N. Palshin, P. Sherstyankin,G. Zdorovennova, and R. Zdorovennov (2012), Physics of seasonally ice-covered lakes: a review, Aquatic Sciences, 74, 659–682.Kirillin, G., A. L. Forrest, K. 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(1952), Limnology, McGraw-Hill, New York.Wetzel, R. G. (1975), Limnology, W. B. Saunders Company, Philadelphia,London, Toronto.Yang, Y., B. Cheng, E. Kourzeneva, T. Semmler, L. Rontu, M. Leppa¨ranta,K. Shirasawa, and Z. Li (2013), Modelling experiments on air-snow-iceinteractions over Kilpisja¨rvi, a lake in northern Finland, Boreal Environ-ment Research, 18, 341–358.Zdorovennova, G. E. (2009), Spatial and temporal variations of the water-sediment thermal structures in shallow ice-covered Lake Vendyurskoe(northwestern Russia), Aquatic Ecology, 43, 629–639.68Appendix AWater Sample ResultsWater samples were collected on 2 June 2013 and were analyzed at theUniversity of British Columbia Civil Engineering Department. These resultswere used for an equation of state to determine the water density from thetemperature and specific conductance.Table A.1: Water sample resultsConstituent Amount [mg L-1]Phosphate (P04) <0.02Calccium (Ca) 2.187Potassium (K) 0.305Magnesium (Mg) 0.443Sodium (Na) 0.955Strontium (Sr) 0.008Zinc (Zn) 0.054Sulfur (S) 1.021Silicon (Si) 0.552Silver (Ag) 0.004Aluminum (Al) 0.004Barium (Ba) 0.02269

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