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Hydrology and thermal regime of a proglacial lake fed by a calving glacier Bird, Lawrence 2014

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Hydrology and thermal regime of a proglaciallake fed by a calving glacierbyLawrence BirdB.Sc. Geography, University of Birmingham, UK, 2012a thesis submitted in partial fulfillmentof the requirements for the degree ofMaster of Scienceinthe faculty of graduate and postdoctoral studies(Geography)The University Of British Columbia(Vancouver)August 2014© Lawrence Bird, 2014AbstractThis study was motivated by an interest in understanding the physical processes drivingthe thermal regime of an ice-contact proglacial lake, in the context of its influence ondownstream water temperatures in the southern Coast Mountains of British Columbia,Canada.Field work was carried out at Bridge Glacier during the 2013 summer melt period, fromJune – September, focusing on quantifying the heat and water budgets and the thermalstructure of the lake. The proglacial lake extending from the terminus of Bridge Glacier,informally referred to as ‘Bridge Lake’, was approximately 5.9 km2 and discharged via asingle outlet. A barrier of icebergs caused the ice-proximal and distal portions of BridgeLake to behave as individual basins, although not separated by a sill.The mean net warming in summer 2013 between the glacier terminus and lake outletwas 2.7 ◦C. Net radiation provided the dominant energy input and net lateral advectionwas the dominant energy sink. The presence of icebergs provided a significant energy sinkand source of 0 ◦C melt water. Iceberg melt was equivalent to 6 – 7% of the mean dischargemeasured at the lake outlet. As icebergs are lost from Bridge Lake with continued glacierretreat, lake discharge is expected to decrease, having detrimental impacts on downstreamwater supplies for use in hydropower.The vertical thermal structure of the water column was monitored at 8 locations withinthe distal basin, with varying degrees of stratification observed with increasing distancefrom icebergs. Suspended sediment concentrations were inferred to dominate density vari-ations, inhibiting vertical mixing of the water column induced by temperature differences.A modelling exercise provided predictions of changes to the thermal behaviour ofBridge Lake with the removal of icebergs once Bridge Glacier becomes land-terminatingand ceases to calve icebergs. With the loss of icebergs, Bridge Lake is predicted to exhibithigher water temperatures and elevated advective energy transfer associated with outflow.Drawing upon previous studies and findings from the current study, a conceptual modelfor the effect of valley glacier retreat on downstream water temperatures is proposed.iiPrefaceThis thesis is original work completed by the author. Guidance was given by the super-visory committee and field assistance was provided by Alistair Davis, David West, JustinKnudson and Matt Chernos.A version of work in Sections 3.2.2 and 3.3 has been published as a poster [Bird, L.,Moore, RD. and Koppes, M. Thermal regime of a large proglacial lake fed by a calvingglacier]. The author acted as lead investigator, composing and presenting the poster at theCanadian Geophysical Union (CGU) 2014 meeting, as well as the Water and EnvironmentStudent Talks (WEST) 2014 conference. The author received the ‘Best Poster’ prize atWEST 2014.iiiContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation for the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Formation and characteristics of proglacial lakes . . . . . . . . . . . 21.2.2 Thermal characteristics of proglacial lakes . . . . . . . . . . . . . . . 41.3 Research objectives and thesis structure . . . . . . . . . . . . . . . . . . . . 72 Study area and methodology . . . . . . . . . . . . . . . . . . . . . . . . . 82.1 Study area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Data collection and processing . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.1 Meteorological data . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.2 Water temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.3 Lake stage and discharge . . . . . . . . . . . . . . . . . . . . . . . . 142.2.4 Calculation of inflows to the ice-proximal and distal basins . . . . . 162.2.5 Lake bed bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Non-advective surface energy fluxes . . . . . . . . . . . . . . . . . . . . . . . 162.3.1 Modelled shortwave radiation . . . . . . . . . . . . . . . . . . . . . . 17iv2.3.2 Modelled longwave radiation . . . . . . . . . . . . . . . . . . . . . . 182.3.3 Convective heat fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4 Advective energy fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4.1 Ice-proximal basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4.2 Distal basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5 Changes in heat storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5.1 Energy budget approach . . . . . . . . . . . . . . . . . . . . . . . . . 212.5.2 Spatial interpolation approach . . . . . . . . . . . . . . . . . . . . . 212.6 Heat budget analysis of the ice-proximal basin . . . . . . . . . . . . . . . . 232.7 Modelling temperatures in the ice-proximal basin for a no-iceberg scenario . 243 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.1 Overview of study period . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Observed temperature patterns . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 Outflow temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.2 Distal basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.3 Ice-proximal basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3 Distal basin heat budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3.1 Non-advective surface energy fluxes . . . . . . . . . . . . . . . . . . 403.3.2 Heat content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.4 Ice-proximal basin heat and water budgets . . . . . . . . . . . . . . . . . . . 443.5 Modelled temperatures in the ice-proximal basin for a no-iceberg scenario . 454 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.1 Thermal processes and regime of the ice-proximal basin . . . . . . . . . . . 484.2 Thermal processes and regime of the distal basin . . . . . . . . . . . . . . . 494.3 Comparison with other alpine lakes . . . . . . . . . . . . . . . . . . . . . . . 514.4 A conceptual model for the effect of valley glacier retreat on downstreamwater temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.1 Key findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.2 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59vA Comparison of interpolation techniques . . . . . . . . . . . . . . . . . . 64A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64A.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65A.2.1 Overview of interpolation schemes . . . . . . . . . . . . . . . . . . . 66A.2.2 Interpolation scheme testing . . . . . . . . . . . . . . . . . . . . . . . 67A.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68A.3.1 Heat content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68A.3.2 Surface water temperatures . . . . . . . . . . . . . . . . . . . . . . . 68A.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74A.4.1 Heat content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74A.4.2 Surface water temperatures . . . . . . . . . . . . . . . . . . . . . . . 75A.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75viList of TablesTable 1.1 Summary of previous limnological studies in proglacial lakes. . . . . . . . . . . 5Table 2.1 Instrument specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Table 2.2 Depths of water temperature measurements across vertical profiles in the distalbasin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Table 3.1 Total energy added to the distal basin of Bridge Lake by each heat flux through-out the study period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Table 4.1 Comparison of studies documenting the thermal influence of proglaciallakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52viiList of FiguresFigure 1.1 Classification of proglacial lakes . . . . . . . . . . . . . . . . . . . . . . . 3Figure 2.1 Map showing the study area, including Bridge Glacier, Bridge Lake andBridge River . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 2.2 Map showing the locations of monitoring equipment within the distalbasin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 2.3 Meteorological stations at Bridge Lake . . . . . . . . . . . . . . . . . . . 11Figure 2.4 Linear models used to predict (a) air temperature, (b) wind speed, and(c) atmospheric vapour pressure at AWS2 . . . . . . . . . . . . . . . . . 13Figure 2.5 Bridge Lake stage-discharge rating curve . . . . . . . . . . . . . . . . . . 15Figure 2.6 Schematic representation of adjustments in layer thickness with stagechanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 3.1 Long term record of mean monthly SWE from the ‘Green Mountain’River Forecast Centre automated snow pillow (Station ID: 1C12P) . . . 28Figure 3.2 Long term record of mean monthly air temperatures from the ‘Whistler’meteorological station (Station ID: 1048898) . . . . . . . . . . . . . . . 29Figure 3.3 Long term record of daily discharge taken from the Water Survey Canada(WSC) ‘Bridge River (South Branch) below Bridge Glacier’ gaugingstation (Station ID: 08MEO23) . . . . . . . . . . . . . . . . . . . . . . . 30Figure 3.4 Time series of meteorological variables monitored at AWS1 throughoutthe study period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 3.5 Time series of outflow water temperatures, lake temperatures, air tem-perature, precipitation, discharge and lake stage recorded throughoutthe study period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 3.6 Contour plots showing variations in water temperatures over time . . . 35viiiFigure 3.7 Vertical temperature profiles of monthly mean water temperatures at 3profiles, with increasing distance from mid-lake icebergs . . . . . . . . . 36Figure 3.8 Time series plots of water temperatures measured at 4 depths across 3vertical profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 3.9 Map showing bathymetry of Bridge Lake . . . . . . . . . . . . . . . . . 38Figure 3.10 Vertical temperature profiles measured in the ice-proximal basin . . . . 39Figure 3.11 Vertical temperature profiles measured amongst mid-lake icebergs . . . 40Figure 3.12 Scatterplots comparing measured vs. modelled shortwave and longwaveradiation across the distal basin . . . . . . . . . . . . . . . . . . . . . . . 41Figure 3.13 Surface energy fluxes over the distal basin . . . . . . . . . . . . . . . . . 42Figure 3.14 Heat fluxes calculated for the distal basin of Bridge Lake . . . . . . . . 43Figure 3.15 Computed changes in heat content of the ice-proximal basin with vary-ing percentage ice cover . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 3.16 Percentage contribution of surface, sub-aqueous and total iceberg melt to meanlake discharge over the study period. . . . . . . . . . . . . . . . . . . . . . . 46Figure 3.17 Results from the ‘continuously stirred tank reactor’ model used to modelthe ice-proximal basin for a no-iceberg scenario . . . . . . . . . . . . . . 47Figure 4.1 Conceptual diagram showing the effects of sustained valley glacier re-treat on downstream water temperatures . . . . . . . . . . . . . . . . . 55Figure A.1 Schematic diagram displaying the process used to remove grid pointsfrom interpolated layers across the distal basin . . . . . . . . . . . . . . 66Figure A.2 Scatter plot of both ‘control’ heat contents calculated using InverseDistance Weighting (IDW) and Nearest Neighbour (NN) interpolationschemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure A.3 Scatter plots showing the relationship between the ‘control’ heat con-tent calculated using IDW interpolation and results calculated omittingindividual profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure A.4 Scatter plots showing the relationship between the ‘control’ heat con-tent calculated using NN interpolation and results calculated omittingindividual profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Figure A.5 Differences in surface water temperature predictions between the ‘con-trol’, calculated using IDW interpolation, and results calculated omit-ting individual profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72ixFigure A.6 Differences in surface water temperature predictions between the ‘con-trol’, calculated using NN interpolation, and results calculated omittingindividual profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73xAcknowledgementsThe culmination of this work has been influenced by so many people. First and foremost,thanks go to my supervisor Dan Moore, without whom this work would not have beenpossible. Dan’s enthusiasm was never-ending, as was his encouragement throughout. Iam grateful to Michele Koppes for her guidance in generating ideas, as well as preparingand carrying out the field campaign. Michele’s comments throughout the writing of thethesis were also appreciated.Funding was provided by operating grants to Professor Dan Moore and Michele Koppesfrom Natural Sciences and Engineering Research Council (NSERC). The author was sup-ported by a Graduate Award from the UBC Faculty of Arts.Special thanks go to Alistair Davis for his endured assistance in the field (along withhis renditions of ‘DMX’ and the ‘Vengaboys’). David West and Justin Knudson arealso thanked for their great efforts during a (somewhat soggy) field visit. Matt Chernosprovided useful comments and suggestions during the early stages of this study, as well asassistance in the field.I would like to extend thanks to the School of Geography, Earth and EnvironmentalSciences at the University of Birmingham, in particular to Professor David Hannah, forinitially introducing me to hydrology, and supporting me in my decision to pursue theopportunity at the University of British Columbia.Particular thanks go to my family. My parents have been nothing but supportive andencouraging since I flew the nest and moved to Vancouver. For this, I could not be moregrateful. An unmentionable number of people across Vancouver, as well as the UK, havemade this journey an unforgettable one, and I am truly thankful to them all.xiChapter 1Introduction1.1 Motivation for the studyLakes and reservoirs play a vital role in the transport and distribution of chemicals, sedi-ment and micro-organisms throughout fluvial environments (Ward and Robinson, 2000).Lentic water bodies have the potential to increase downstream water temperatures duringsummer months (Mellina et al., 2002; Webb et al., 2008). Changes to the thermal sig-nature of lentic-influenced fluvial systems can persist for extended distances downstream,affecting the solubility of oxygen and biological processes, and thus influencing aquaticecosystems (Beschta et al., 1987).Changes to the global climate have been the dominant driver for significant glacierretreat since the Little Ice Age of the 19th Century (Milner et al., 2009; Gilbert andButler, 2004), with accelerated retreat observed over the last 2 – 3 decades (Barry, 2006).With glacier retreat projected to continue throughout the current century (Carey, 2007),glacier-fed hydrologic systems have received significant attention within the literature overthe last decade.Many studies have focused on stream temperature dynamics within proglacial envi-ronments (e.g. Milner et al., 2001; Brown et al., 2006; Moore, 2006; Cadbury et al.,2008) due to the importance of stream temperatures for aquatic ecology. Moore (2006)found glaciers and snowfields decrease water temperatures in July, August and September,whilst providing little or no influence during colder months when melt water discharge de-creases. Moore (2006) suggested that continued glacier retreat within British Columbiamay lead to progressive warming of glacier-fed streams in summer and early autumn. In-creased stream temperatures could have detrimental impacts for the survival of cold-waterspecies, including salmonids, which are of high economic importance in the waterways of1British Columbia (Beschta et al., 1987; Fleming, 2005). However, it is important to notethat for streams which currently have initial water temperatures below the thermal optimafor aquatic organisms, some warming could be beneficial.High elevation proglacial lakes are another component of proglacial hydrologic systemsthat can act as thermal regulators to through-flowing glacier melt water (Weirich, 1986a;Uehlinger et al., 2003). The influence of proglacial lakes on water temperatures has re-ceived comparatively little attention within scientific literature, despite their increasingprevalence associated with glacier retreat (Warren and Kirkbride, 1998; Masetti et al.,2010).A significant body of literature has focused on thermal processes acting within la-custrine environments (e.g. Salenc¸on, 1997; Gerten and Adrian, 2002; Garrett et al.,2010; Mishra et al., 2011), although the majority of studies have focused on lakes in non-glacierized basins. Thermal stratification is found to exist in many (but not all) lenticenvironments at some point throughout the year. During summer months, heating ofthe epilimnion (surface layer) commonly results in warmer, less dense water overlying ahypolimnion layer of colder, more dense water (Ullyott and Holmes, 1936). The two lay-ers are separated by a steep vertical temperature gradient (thermocline). Temperatureinversions commonly occur in winter months if the lake surface freezes, resulting in coldwater overlying warmer water. Typically, the water column becomes isothermal duringspring and autumn months following vertical mixing induced by density variations duringsummer and winter. However, whilst the influence of cold glacier melt water and thepotential presence of a calving icefront and sediment-laden underflows are known to alterthe mixing and warming regimes of proglacial lakes, the dominant processes are not wellunderstood.The objective of this study was to contribute to an understanding of the physicalprocesses driving the thermal regime of an ice-contact proglacial lake, in the context of itsinfluence on downstream water temperatures. The remainder of this chapter will provide(1) a literature review highlighting existing knowledge gaps surrounding proglacial lakesand (2) specific research objectives to be addressed within this study.1.2 Literature review1.2.1 Formation and characteristics of proglacial lakesWith continued retreat of large valley glaciers, the formation of proglacial lakes is expectedto become more prevalent with the exposure of over-deepened valleys (Warren and Kirk-2bride, 1998; Masetti et al., 2010). As glaciers retreat, melt water drains into over-deepenedvalleys bounded by ice, sediment or rock restrictions (Warren and Kirkbride, 1998; Bennet al., 2007). Terminal moraines frequently dam cirque lakes, whilst glacial outwash canbe responsible for damming valley-floor lakes (Gage, 1975).Proglacial lakes can take two forms: (1) distal proglacial lakes, fed by a proglacialstream reach from the glacier terminus, and (2) ice-contact proglacial lakes (Figure 1.1),typically supplied by direct surface and basal melting, or mass loss, from the termi-nus of a calving glacier (Masetti et al., 2010), in addition to supra-glacial runoff fromthe non-lacustrine portion of the glacier. Ice-contact lakes generally exist for a limitedduration, appearing when the glacier terminus retreats into a sufficiently over-deepenedbasin and disappearing via either (1) evaporation and sub-terrain seepage, (2) infilling byglacio-fluvial sediments or (3) continued glacier retreat resulting in conversion to a distalproglacial lake (Masetti et al., 2010).Glacier melt water drains into aproglacial stream reach from the glacier terminus. Typically, rockor sediment restrictions down-stream dam glacier melt water,resulting in the formation of distal proglacial lakes.Glacier melt waterdrains into an over-deepened basin andis bounded by ice,sediment or rockrestrictions. Theglacier terminusremains in contactwith the lake and maycalve icebergs.2112Glacier       Ice-contact lake:       Distal lake:GlacierFigure 1.1: Schematic representation of two forms of proglacial lakes: 1) Ice-contact proglacial lakes associated with calving glaciers and 2) Distalproglacial lakes associated with land-terminating glaciers.Lacustrine calving glaciers, associated with ice-contact proglacial lakes, generate dif-ferent physical, morphological, thermal and hydrological properties compared to land-terminating glaciers (Warren and Kirkbride, 1998; Benn et al., 2007). The influence ofthe presence of a calving icefront on the thermal regime of ice-contact lakes has received3minimal attention. Carrivick and Tweed (2013) outlined a number of studies focusing onhydrological and sedimentological properties of ice-contact lakes. However, the author isaware of only two studies (Warren and Kirkbride, 1998; Masetti et al., 2010) that haveconsidered the thermal characteristics of these environments (Table 1.1).1.2.2 Thermal characteristics of proglacial lakesCold glacier melt water generally warms as it flows through proglacial lakes (Weirich,1986a; Uehlinger et al., 2003). For example, Richards et al. (2012) found a mean warmingof 1.8 ◦C between the inlet and outlet of Place Lake, which exceeded the mean warming inthe stream channel between the lake outlet and treeline. Thermal patterns in low altitudetemperate lakes are controlled by meteorological conditions, basin morphology and scale,hydrologic residence times, seasonal variations, water clarity, the presence of groundwaterinputs and basin location (Escobar et al., 2009; Chikita et al., 2010). However, under-standing glacier-fed lakes is even more complex due to the presence of strong katabaticwinds and cold, sediment-laden inflows.In non-glacial lakes, changes in the heat content are normally driven by surface ex-changes (Chapra, 1997). In proglacial lakes, however, advective heat transfers associatedwith inflow and outflow may also play an important role due to the high inflows that occurduring summer melt (Richards et al., 2012).In non-glacial lakes and reservoirs, temperature is usually the main control on waterdensity and hence on stability and vertical mixing (Ullyott and Holmes, 1936). Withinproglacial lakes, density is also influenced by high suspended sediment concentrationswhich can outweigh the effect of temperature (Matthews, 1956; Harris, 1976; Richardset al., 2012). It is difficult to identify a common rule of thermal stability within proglaciallakes. Some lakes appear consistently well mixed (holomictic), such as Exception Lakein southern British Columbia (Weirich, 1986b). Other lakes, such as Maude and Godleylakes in the southern New Zealand Alps (Warren and Kirkbride, 1998), experience varyingdegrees of stratification, completely mixing annually or bi-annually (monomictic or dim-ictic). Proglacial lakes have also been found to experience changes in stratification on ashorter timescale. Richards et al. (2012) observed a distinct regime shift in vertical tem-perature profiles from colder water temperatures towards the bottom of the water columnearly in the summer, to a near isothermal water column throughout one summer. Theyattributed this shift to cessation of cold, highly turbid pulses of glacier discharge sinkingto the lake bed.4Table 1.1: Summary of previous limnological studies in proglacial lakes.Author Location Main focus Elevation Catchment Relation Lake Area Max(m.a.s.l) Area (km2) to glacier (km2) depth (m)Hood et al. Lake O’Hara, Groundwater importance 2010-3490 14 DS 0.26 42(2006) BC, Can within an alpine headwater lakeRoy and Hayashi Lake O’Hara Groundwater exchanges 2010-3490 14 DS both 2 m *1; 10 m *2(2008) watershed, within two small alpine lakes 0.026BC, CanRichards et al. Place Lake, Thermal regime of small 1830 - 200 m 0.072 12(2012) BC, Can proglacial lakeUehlinger et al. Bermina Massif, Thermal patterns in 1766 – 4049 66.5 DS 0.22 -(2003) Swiss Alps river corridorsMasetti et al. Miage Lake, Hydrological characterisation 2069 11 Calving - -(2010) Italian Alps of an ice-contact lakeChikita et al. Peyto Lake, Sediment-laden underflows - - DS approx. 48(1996) AB, Can 1.2Gilbert and Butler Meziadin Lake, Limnology and sedimentation 244 530 DS 34 133(2004) BC, CanMatthews Garibaldi Lake, Limnology and sedimentation 1484 - DS 10 119(1956) BC, CanGilbert and Shaw Sunwapta Lake, Sedimentation - - DS 0.24 10(1981) AB, CanWeirich Purcell Mtns, Density-induced underflows - 6.5 DS approx. 5(1986a) BC, Can (sub-basin) 0.4Warren and Kirkbride Mount Cook NP, Temperature and bathymetry 870 – 1095 - Calving 0.12 – 1.95 55 – 136(1998) New Zealand*1 Lake Hungabee*2 Lake Opabin5Although the heat content and mixing and stratification within proglacial lakes in-fluence outflow temperatures, few studies have considered these simultaneously. Streamtemperature studies within proglacial environments (e.g. Uehlinger et al., 2003; Robinsonand Matthaei, 2007) have documented inflow and outflow temperatures from proglaciallakes without considering the physical processes contributing to the observed warming.Understanding the physical controls on mixing and warming within proglacial lakes willenable better informed predictions regarding the influence of sustained glacier retreat onlacustrine, and downstream fluvial environments.Heat content can be computed from water temperatures measured throughout thewater column and a knowledge of the lake bathymetry. Surface energy exchanges, coupledwith advective exchanges at the lake inflow and outflow, can be used to model the heatcontent of a lake. These techniques have been used by many researchers to understand thethermal behaviour of lakes and reservoirs at a variety of time scales (e.g. Schertzer, 1978;Frempong, 1983; Potts, 2004). However, to the knowledge of the author, only 1 study haspreviously conducted heat budget analyses for a proglacial lake (Richards et al., 2012) –this work was carried out within Place Lake, a distal proglacial lake in the southern CoastMountains of British Columbia.Previous studies within proglacial lakes (Table 1.1) have focused predominantly onmixing processes and stratification from the perspective of sedimentation, but did notaddress the implications for the downstream thermal regime (e.g. Matthews, 1956; Gilbertand Shaw, 1981; Gilbert and Butler, 2004). There has been no consideration of lateralvariations in water temperature or the effect of icebergs on the heat content of proglaciallakes. When associated with tidewater glaciers, icebergs reduce ocean water temperaturesthrough latent and sensible heat exchanges (Warren and Aniya, 1999; Benn et al., 2007).Therefore, it is hypothesised that a similar behaviour would be observed in lacustrineenvironments.Modelling the thermal behaviour of lakes and reservoirs can provide useful insightto the processes responsible for driving thermal change, enabling predictions of futurechanges associated with climate change and glacier retreat. However, due to the complex-ity of lacustrine environments, lakes and reservoirs are commonly assumed to be laterallyisothermal, as in the 1-dimensional model ‘DYnamic REservoir Model (DYRESM)’ (e.g.(Tanentzap et al., 2007)). It is unclear whether this assumption would be valid for anice-contact lake, and it requires testing with field observations to evaluate the validity of1-dimensional systems for these systems.With proglacial lakes expected to become more prevalent as glacier retreat continues,there is an increasing need to understand the influence of these systems on downstream6fluvial environments. There is a clear need for studies in proglacial lakes that incorporateenergy budget analysis, along with observations of controls on mixing and stratificationin the context of the lake heat content and its influence on downstream water temper-atures. In addition, the influence of a calving icefront and iceberg generation on watertemperatures requires investigation.1.3 Research objectives and thesis structureThe review in Section 1.2 has identified a number of knowledge gaps in the understandingof the thermal regime of ice-contact proglacial lakes, and these form the context for thestudy presented here. The specific research objectives to be addressed are outlined below.1. To characterise the heat budget of an ice-contact proglacial lake, considering therelative influence of (a) advective transfers from inflow and outflow and (b) surfaceenergy exchanges.2. To determine how the vertical thermal structure of an ice-contact lake varies withdistance from a calving icefront. How does the presence of icebergs within the waterbody alter the vertical distribution of heat? What processes drive stratificationand/or mixing within ice-contact proglacial lakes?3. To use knowledge generated by objectives 1 and 2, coupled with results from previousstudies, to generate a conceptual model for the modification of downstream watertemperatures with continued valley glacier retreat, particularly during the period ofactive calving into an ice-contact proglacial lake.The remainder of this thesis is organised as follows. Chapter 2 describes the studysite and provides details of field and data analysis methods. Chapter 3 presents results ofthe field campaign and data analysis. Chapter 4 discusses how findings from this studyhelp to address the research objectives outlined above. Chapter 5 summarizes the mainconclusions of this study and identifies areas where further research is required.7Chapter 2Study area and methodology2.1 Study areaThis study focused on an ice-contact proglacial lake extending from the terminus of BridgeGlacier (hereafter referred to as ‘Bridge Lake’). Bridge Glacier is an outlet glacier of theLillooet Icefield, located 180 km northwest of Vancouver (Figure 2.1), in the southernCoast Mountains of British Columbia, Canada. Bridge Glacier has diminished in areafrom approximately 88 km2 in 2002 (Allen and Smith, 2007) to 64 km2 in 2010. Thecalving terminus of Bridge Glacier is known to have been floating in Bridge Lake since theearly 1990s (Ryder, 1991), resulting in periodic calving events of large tabular icebergsinto Bridge Lake. The hydrologic regime is characterised by low winter flows due to wintersnowfall and high spring/summer flows as a result of snow and glacier melt. The meanannual peak daily discharge leaving Bridge Lake between 1978 – 2011 was approximately48 m3 s-1.Bridge Lake is approximately 1400 m.a.s.l and 5.9 km2 in area, with two distinctbasins (Figure 2.1). Although the basins are not separated by a sill, a barrier of ice andsubmerged moraine separate the ice-proximal and distal basins, causing them to behaveindependently. The ice-proximal basin covers an area of 4.48 km2 with depths extendingto over 180 m. The distal basin extends from the submerged moraine at mid-lake to thelake outlet, with an average depth of 3.4 m. The submerged moraine traps icebergs in theice-proximal basin, with few remnant icebergs entering the distal basin. Two proglacialstreams enter Bridge Lake. One enters at the western end of the ice-proximal basin justnorth of the calving glacier front. The other enters close to mid-lake, just upstream ofthe submerged moraine, and is sourced from a small mountain glacier on White CrossMountain, on the south side of Bridge Lake. Bridge Lake contains 3 islands (each < 0.068150020002500             Elevation          (m a.s.l)Bridge GlacierBridge LakeBridge Riverl0 m 5 kmNll VancouverPembertonBridge GlacierBritish  Columbia11lDistal BasinIce−proximal BasinWSC Gauging StationFigure 2.1: Map showing the study area, including Bridge Glacier, Bridge Lakeand Bridge River. Contour intervals are 100 m. The glacier polygon repre-sents the extent of Bridge Glacier in September 2013. The orange dashed linerepresents the shallower, distal basin and the red dashed line represents thedeeper, ice-proximal basin within Bridge Lake. WSC gauge: ‘Bridge River(South Branch) below Bridge Glacier’ (Station ID: 08MEO23).km2) within the distal basin.Bridge Lake drains through one outlet at the northeast end of the distal basin. Wa-ter Survey of Canada (WSC) have operated a stream gauging station (ID: 08MEO23)approximately 3 km downstream of the Bridge Lake outlet since 1978 (Figure 2.1). BCHydro operates a hydro-electric facility on Bridge River, which generates 6 – 8% of BritishColumbia’s electricity (BC Hydro, 2013).2.2 Data collection and processingThe field campaign for this study spanned the 2013 summer melt season, with first accessfollowing ice break-up in late June. Meteorological variables and water temperatures weremonitored continuously throughout the season, while bathymetric data were collectedmanually during all field campaigns. Figure 2.2 shows locations of monitoring equipment.All in-situ monitoring equipment was restricted to the distal basin due to large, dynamicicebergs resulting in early-season equipment loss in the ice-proximal basin.90 m 500 mllllllllAAABDEFGHAWS1AWS2lTwWater level measured approximately  3 km away, in the ice−proximal basinllDistal BasinIce−proximal BasinBridge RiverVertical Temperature ProfileAutomated Weather StationOutflow Water TemperatureFigure 2.2: Map showing the location of monitoring equipment within the distalbasin.2.2.1 Meteorological dataAir temperature, relative humidity, wind speed, incident shortwave and longwave radiationand barometric pressure were measured on the shore at mid-lake (AWS1) every 10 sand averaged every 10 min (Figure 2.3a). Total precipitation was recorded every 10min. Instruments (Table 2.1) were mounted on a tripod at 1.5 m above the surfaceand connected to a Campbell Scientific CR10X data logger within a waterproof housing.Barometric pressure was recorded by a stand-alone Onset U20 Logger. A Kestrel 4500Pocket Weather Tracker was deployed on a floating platform within the distal basin (Figure2.3b), measuring air temperature, relative humidity and wind speed 1.5 m above the watersurface (AWS2). The Kestrel was deployed during three of the field campaigns (15th –21st June; 11th – 21st July and 11th – 16th August 2013).Atmospheric vapour pressure (ea) was calculated for both meteorological stations as:ea = esat(Ta)×RH100(2.1)where ea is atmospheric vapour pressure (kPa), esat is saturation vapour pressure (kPa) at10(a) On-shore AWS (b) Floating AWSFigure 2.3: Meteorological stations at Bridge Lake: (a) on-shore AWS set-up atmid lake (AWS1); (b) floating AWS set-up within the distal basin (AWS2).air temperature (Ta) (◦C) and RH is relative humidity (%). Saturation vapour pressurewas calculated following Tetens (1930):esat(Ta) = 0.611 exp[aTT + b](2.2)where esat is saturation vapour pressure (kPa) and a and b are 17.27 and 237.26, respec-tively, when T > 0 ◦C, and 21.87 and 265.5 when T < 0 ◦C.Data loss at AWS1 on 17-08-2013 resulted in 12 missing data records between 10:20 and12:10. Missing values of air temperature, vapour pressure and wind speed were estimatedby linear interpolation between the records at 10:10 and 12:20.Missing values of incident longwave radiation were estimated from the interpolatedvalues of air temperature using the Stefan-Boltzmann law:L ↓= εaσT4a (2.3)where εa is atmospheric emissivity, σ is the Stefan-Boltzman constant (5.67 × 10−8 Wm−2 K−4) and Ta is interpolated air temperature (K). Emissivity values were linearlyinterpolated between those calculated using measured values of L ↓ and Ta at 10:10 and12:20:11Table 2.1: Instrument specificationsVariable Notation Sensor Range AccuracyAir Temp. TaRotronic HC-S3-30 to +60 ◦C ±0.2 ◦CRel. Humidity RH 0 - 100% ±1.5% at 23 ◦CWind Speed u Met One 014a 0 - 45 m s-1 ±0.11 m s-1[stall speed: 0.45 m s-1]Incident short K ↓ Kipp & Zonen CM6B 0.3 - 2.8 µm -1%/m s-1Incident long L ↓ Kipp & Zonen CGR3 0.3 - 2.8 µm -1%/m s-1Precipitation Precip Texas Electronics TR-525M ±1.0% up to 2”/hr(50 mm/hr)Baro Pressure P Onset U20 0 - 207 kPa ±0.30%Air Temp. TaKestrel 4500 PocketWeather Tracker-10 to +55 ◦C ±0.5 ◦CRel. Humidity RH 0 - 100% ±3%Wind Speed u 0.6 - 60 m s-1 ±3%Water Temp. Tw Onset Tidbit v2 -20 to +70 ◦C ±0.2 ◦CStage Stage Onset U20 0 - 4 m Max. error: ±0.15%εa =L ↓σT 4a(2.4)Simple linear regressions of air temperature, wind speed and atmospheric vapour pres-sure between AWS2 and AWS1 were used to predict a continuous time series of thesevariables that were representative of conditions above the water surface (Figure 2.4).2.2.2 Water temperatureDue to the large number of dynamic icebergs in the ice-proximal basin, it was not possibleto maintain temperature logger profiles for continuous monitoring of lake temperature.Vertical profiles of lake water temperature were monitored at eight locations within thedistal basin using Tidbit temperature loggers (Table 2.1), programmed to record at 10min intervals. At each profile location, loggers were fixed at a range of depths (Table 2.2)to a rope secured between a surface buoy and a weight on the lake bed. Early seasonequipment loss close to mid-lake required a replacement profile to be installed during thesecond field campaign. As a result, the length of data record differs between profiles (Table2.2). All water temperature records end on 13-09-2013.Water temperature loggers were deployed just downstream of the lake outlet (Figure2.2) and near the mouth of a tributary stream on the north side of Bridge Lake. Eachlogger was housed in white PVC pipe and attached to a rock gabion positioned in thestream, and a secondary anchor on the stream bank. This ensured that the loggers didnot move during high flows and measurements were not influenced by shortwave radiation12lllllll llllll llll llllllllllllllllllllll lll llllllllllllllllllllllllllllllllllllll llllll lll llllllllllllllllllllllll llllllllllllllllll l llllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllll lllllllllll lll lllllllll lllllllllllll lllllllll ll ll l lllll llllllllllllllllllllll llllllllllllllll llllllllllllllllllll llll llll l lll lll lllllllllllllllll llllllllllllllllllllllllll lllllllll lllll llllllllllllll ll llllllllllll llllllllllllll l lllll llllllllllll l ll lllll lllllllllllllllllllll l lllllllllllllll llllllllllllll lllllllll lll lllll llllllll l lllllllllllllll lllllllll lllllll lllllllllllll llllllllllllllllllllllllllllll llllllllllllll llllllllllllllllllllllllll lllllllllllllllllll lllllllllllllllllll lllllllllllll llllllllllllllllllll lllllllllllll llll llll lllll lll lllllllllll lllllllll l lll ll ll lll lllllllllllllllllllllllllllllll llll llllllllllllllll llllllllllllllllllllllllllllll ll llllllll lllllllllllllllllll lll llllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ll llllll lllllll lllll lllllllllllllll lllllllllllllllllllllllllllllllll llll llllllllllllll llllllll llllllllllllllllllllllllllllllllllll lll llllllllllll lllllllll lll lllllllllllllllllllllllllll lll llllllll lllllllllll ll lllllll l l llllllllllll llllllllllllllllllllll lllllll llllllll llllllll lllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllll lll lllll ll llllllllllllllllll lllll llll lllllllllll lllllllllllllllllllllll llllllllllllllllllllllllll llll lllllllllllllll lllllllll llllllllllll lllllllllllll llllllllllllllllllllllllllllllllllll llllllllllll llllllllllllllll llllllllllll lllll5 10 15 20051015AWS1 − Ta (°C)AWS2 − T a (°C)(a)R2 = 0.66Ta^AWS2 = 1.237TaAWS1 + 0.767lllllll l llllllllllll lllllllll llll llllll llll llllllllllll lll llllllllll l llllllll llllllllllll ll llllll ll lllllll llll llllll lll lll lll llllllllllllllll ll llllll lll llllllllllll lllllllll lllllllll lllllllllllll l lllll lllllllllllll lllll lll llll ll ll llll lllllllllllllllllllllllllllllllllllllllll lllllllll lllll lllllllllllllllllllllllll llllll llllllll l llll lllllll lll llllllllllllllllll lllllllllllllllllllllllllllll llll llllllllllllllllllllllllll lll lllllll lllllll lllll lll l llllllllll llllllllllllllllll llll llll l lllll lllllllllllllll lllllllll lllllllllllllll lllllllllllllllllllllllll llllllllllllllllllllllllll lllllllllllllllllllllll llll llll lllll ll llllll lllllll llllllllllllllllllll lllllllllll lllllll lllllll llllllllllllll llllllllllllllllll llllllllllllllllllllllllllll ll llllll llllllll lll lllllllllllllllll llllllllll llllllll lllllllllllllllllllllllllllllllll llllllllll llllllllllllllllllllllllllll llllllllllllll llll lllllllllllllllllllll l llllllll llllllllllllll llll lllllllllllllll l lll lllllll l lllllllllllllllllllllllll llllllllll llllllllllllllllllllllllll lllllllllll lllll llllll lllll lllllllllllllllllllll llllllllll lllllllll llllll llll llllll ll llllllllllllllllll llllllllllllll llllll lll lllllll l ll lllllllllllllllllllllllll llllll l lllllllllllllllllll llllllllllllll l llllllll ll lll lllllllllllllllllllllllllllllllllllllllllll ll lllllllllllllll lllll llllll lllll lll lllllllllll lll llllllllllllllllllllllll l llllll lllllll llllllllllll lllllllllllllll llllllllll ll llllllll lllllllllllllllllllllllllllllllllllllllllll llllllllllllllll lll lllllll lll lllllllllllllll2 4 6 8024681012AWS1 − u (m s−1)AWS2 − u (m s−1 )(b)R2 = 0.66u^AWS2 = −0.052uAWS1 + 1.127ll lll llllllllllllllll lllllllllllllllllllll llllllllllll lllllllll lllllllllllll lllllllllllll llllllll llllllllllllllllllllllllll ll llll lll lllllllllllllllllll lllllll llllllll lllllllllllllllllllllllllllllllll ll llllll lll lllll ll lllllllllllll ll l lll lllllllllllllllll ll lllllll lllllllllllll llllllll llllllllll ll llllllllllllllllllllll lllllll lllll lllllllll llll l lllll l ll llllll l lllll llllllllllll lll lllll lllllllllllllllllllllllllllllllllllllllll llll lll llllllllllllll llll llllll ll llllllllllllllllllllllllllllll llllllllllllllll ll llll llll lllllllll llllllllllllll lll llllllllll llll llllll llllllllllll l lllll llllllllllllllllllllllll llllllllllllllllllllllllll llllll lllllllllll l l lllll lllllllllll llllllll lllllll llllllll lllll lllllllll lllll lllllllll llllll llllllllll lllll lll llllllll ll llllllll l llllllllllll lllll lllllllllll llll llllll llllllllllllllllllllllllllllll ll llllllllllllllllllll llllllll llll llllllllllllll lllllllllllllllllll ll llllllll llllllllllllll llllll llll llllllll lll llll lllllllll lllll lllllllllllll lllll lllllllllll llll lllllllllllllllll llllllllllllllllllllll llllll ll llll lll ll llllllllllll lllllll lllll llll lll llllllllll l0.5 0.6 0.7 0.8 0.9 1.0 1.10.60.81.01.2AWS1 − ea (kPa)AWS2 − e a (kPa)(c)R2 = 0.82ea^AWS2 = 0.011eaAWS1 + 1.1051:1 lineLinear fit lineFigure 2.4: Linear models used to predict (a) air temperature, (b) wind speed, and(c) atmospheric vapour pressure at AWS2. Each value represents an averageover a 10 min interval.13Table 2.2: Depths of water temperature measurements across vertical profiles inthe distal basinProfile Depths of temperature measurements (m) Date deployedA 0, 0.5, 1, 2, 3.5, 5 16-06-2013AA 0, 1 16-06-2013B 0, 0.5, 1, 2, 3.5, 5.5 14-07-2013D 0, 0.5, 1, 2, 3, 4 20-06-2013E 0, 0.5, 1, 2, 3, 4 20-06-2013F 0, 0.75, 1.75, 3.75 19-07-2013G 0, 0.75, 1.75, 3.75 19-07-2013H 0, 0.25, 0.5, 1, 2, 3, 3.5 17-08-2013or the stream bed temperature.Manual measurements of water temperature were taken at various depths over 26locations within the ice-proximal basin. A weight connected to a rope spool marked at 1m intervals was used to deploy Tidbit temperature loggers to selected depths throughoutthe water column to a maximum depth determined by bathymetric data. Loggers wereprogrammed to record water temperatures every 30 s and were deployed for 15 min ateach location. The modal water temperature measurement at each depth was chosento represent the point at which each logger reached equilibrium. These data provideda ‘snapshot’ in time of water temperature variability with depth across the ice-proximalbasin.2.2.3 Lake stage and dischargeLake stage was measured in both basins to observe for the presence of seiching withinBridge Lake. Onset U20 water level loggers (Table 2.1) were attached to rock gabions onthe lake bed and secured to the lake shore to prevent movement. Loggers were programmedto record at 10 min intervals. Data from the distal basin stage logger showed a substantialincrease in depth in early August, persisting until the logger was removed. This increaseis likely due to the logger slipping to a greater depth, or becoming buried in the lakebed. Cross-correlation analysis between stage data from the ice-proximal basin and thedistal basin revealed that seiching did not occur within Bridge Lake. Therefore, stagedata obtained from the ice-proximal basin was used to represent stage for the entire lake.Small step changes were observed within the data due to small movements of the loggerposition across the season. Shift corrections were applied to the data to remove thesesteps. Stage data were smoothed using a 3-point binomial filter to remove small scale14variability associated with surface waves and calving events.Lake discharge data were taken from the WSC gauging station downstream of thelake outlet. Discharge was recorded at 5 min intervals, but data were sub-sampled at 10min intervals to match meteorological and water temperature data sets. Adjustments tothe water level logger at the WSC gauging station were responsible for substantial stepchanges within discharge data. In order to account for these, a stage-discharge ratingcurve was developed using stage data collected in the ice-proximal basin. Early seasondata, prior to the first observed step change in discharge, were used to generate the ratingcurve. The following relationship was fitted using the nls() function in R (R Core Team,2012):̂logQ = 0.025 + 4.374 · log(S − 1.174) (2.5)where ̂logQ is the predicted log discharge (m3 s-1) and S is stage (m). The rating curvewith early season data is shown in Figure 2.5.lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllll ll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll1.0 1.1 1.2 1.3 1.4304050607080Stage (m)Q (m3  s−1 )Best fit line10% error bandsFigure 2.5: Bridge Lake stage-discharge curve. Error bands represent ±10% of thecalculated discharge.152.2.4 Calculation of inflows to the ice-proximal and distal basinsInflow to the ice-proximal basin (qin) was calculated as:qin =∆Vpt∆t+ qmid − (R ·Ap) + (E ·Ap) (2.6)where ∆Vpt is the change in ice-proximal basin volume (m3) over the time interval ∆t,qmid is outflow to the distal basin (m3 s-1), R is the precipitation rate (m s-1), Ap is thesurface area of the ice-proximal basin (m2) and E is the evaporation rate (m s-1). Thechange in ice-proximal basin volume, ∆Vpt , can be calculated as:∆Vpt = ∆S ·Ap (2.7)where ∆S is the change in lake stage (m). The discharge out of the ice-proximal, andinflow to the distal basin, qmid, was calculated as:qmid =∆Vdt∆t+ qout − (R ·Ad) + (E ·Ad) (2.8)where ∆Vdt is the change in distal basin volume (m3) over the time interval ∆t, qout is thelake outflow discharge (m3 s-1), assumed to equal discharge measured at the WSC gaugingstation 3 km downstream, and Ad is the surface area of the distal basin (m2). The changein distal basin volume, ∆Vdt was calculated using an analogous form of Equation 2.7.2.2.5 Lake bed bathymetryBathymetric data were obtained for both basins of Bridge Lake using a Lowrance HDS-7 Generation 2 Touch and DownScan Imaging Transducer. Although every effort wasmade to minimize errors, the accuracy of the device was affected by a number of factors,including changes in the angle of the transducer head and rapid changes in direction. Anembedded GPS unit provided spatial coordinates associated with depth measurementsacross the lake. Over 800 measurements of lake depth were taken during the season.Large and dynamic icebergs prevented access to large areas within the ice-proximal basin,resulting in a higher density of depth measurements within the distal basin, where accesswas easier.2.3 Non-advective surface energy fluxesThe net non-advective energy exchange at the water surface, Qn, was calculated as:16Qn = Qr +Qh +Qe (2.9)where Qr is the surface averaged heat flux due to net radiation, Qh is the sensible heatflux and Qe is the latent heat flux. All components have units of W m-2. The energyinput by net radiation, Qr, was calculated as:Qr = K ↓ (1− α) + εwL ↓ −εwσT4w (2.10)where K ↓ is incident shortwave radiation (W m-2), α is the albedo of the water surface,εw is the emissivity of the water, L ↓ is the incident longwave radiation (W m-2) andTw is the mean temperature of the water surface (K). The albedo of the water surfacewas assumed constant at 0.1 throughout the study period. Commonly, α is assumed con-stant at 0.05 for water surfaces (Oke, 1987); however, due to the presence of fine glacialsuspended sediment in proglacial lakes, a higher α value has been found more represen-tative (Sakai et al., 2000). The emissivity of the water was assumed to be 0.97 (Oke, 1987).2.3.1 Modelled shortwave radiationMeasured solar radiation was adjusted to account for the spatial variability of topographicshading over the lake surface. A 25 m resolution gridded Digital Elevation Model (DEM)was used to provide surrounding topographic features. A regular grid at 20 m resolutionwas generated across the distal basin surface, generating X and Y coordinates for 3529locations. A 40 m resolution regular grid was generated across the ice-proximal basin,generating X and Y coordinates for 2795 locations. The lake surface was assumed hori-zontal, giving a slope and aspect of 0 for all grid points. Incident shortwave radiation foreach grid point across the lake was then calculated as:K ↓= K ↓dir δ(t) +K ↓diff fv (2.11)where K ↓dir is the direct and K ↓diff is the diffuse component of incident shortwaveradiation, fv is the sky-view factor and δ(t) is 1 when the sun is above the horizon and 0when the sun is below the horizon. Sky-view factors were calculated for all grid points as:fv =1pi2pi∫0Ha∫0cos(θ) sin(θ)dθda (2.12)17where θ is the zenith angle, a is the azimuth angle andHa is the horizon angle for a specifiedazimuth (Richards et al., 2012). Horizon angles were computed for 36 directions, at 10◦intervals of ground azimuths. The integral over azimuth angles was thus approximated asa summation over the 36 directions.The local solar positions (azimuth and zenith angles) were calculated using equationsfrom Iqbal (1983). The diffuse fraction of incident solar radiation was calculated using thefollowing equations (Erbs et al., 1982):kd =1.0− 0.09τ for τ ≤ 0.220.951− 0.1604τ + 4.388τ2−16.638τ3 + 12.336τ4 for 0.22 < τ ≤ 0.800.165 for τ > 0.80(2.13)where τ is the ratio of the global-to-extraterrestrial shortwave radiation, where the com-puted potential extraterrestrial shortwave radiation (K ↓pot) was calculated as:K ↓pot= S cos(θ) (2.14)where S is the solar constant (1367 W m-2). The diffuse component of the incidentshortwave radiation was then calculated as:K ↓diff= kdK ↓AWS1 (2.15)where K ↓AWS1 was the incident shortwave radiation measured at AWS1 (W m-2). Thedirect component of incident shortwave radiation was then calculated as the differencebetween incident shortwave radiation measured at AWS1, and the computed diffuse short-wave radiation (Richards et al., 2012):K ↓dir= K ↓AWS1 −K ↓diff (2.16)2.3.2 Modelled longwave radiationIncident longwave radiation was measured at AWS1 and distributed across the lake surfaceusing the same regular grid as for modelling shortwave radiation. Incident longwaveradiation was calculated at each grid cell following Richards et al. (2012):L ↓= L ↓AWS1 fv + (1− fv)εtσT4t (2.17)18where L ↓AWS1 is the incident longwave radiation (W m-2) measured at AWS1, εt is theemissivity of the surrounding terrain, assumed to equal 0.95 (Oke, 1987) and Tt is thetemperature of the surrounding terrain (K), assumed to equal air temperature.2.3.3 Convective heat fluxesThe latent heat flux was calculated for each grid cell on the lake surface using an adaptedform of the Dalton-type equation from Webb and Zhang (1997), used extensively in pre-vious studies (e.g. Moore et al., 2005; Hannah et al., 2008; Chikita et al., 2010; Leach andMoore, 2011):Qe = 285.9(0.132 + 0.143u)(ea − ew) (2.18)where u is wind speed (m s-1) measured 1.5 m above the water surface and assumedconstant across the lake surface, ew and ea are water surface and air vapour pressures re-spectively (kPa). Atmospheric vapour pressure was calculated using equation 2.1. Vapourpressure at the water surface, ew, is assumed to equal esat(Tw). Surface water temperatureswere spatially interpolated to each cell using an Inverse-Distance Weighting (IDW) inter-polation scheme, with the power value (p) of 2. The mean lake surface water temperature(Tw) was taken for each time step.The sensible heat flux was calculated as:Qh = [(cpaP )/(0.622Lv)][(Ta − Tw)/(ea − ew)]Qe (2.19)where cpa is the specific heat of air at constant pressure (J kg-1 ◦C-1), P is atmosphericpressure (kPa), Lv is the latent heat of vaporization (2.48 × 106 J kg-1) and Ta is airtemperature (◦C).2.4 Advective energy fluxes2.4.1 Ice-proximal basinThe advective energy transfer associated with inflow to the ice-proximal basin was calcu-lated as:Hi = ρwcpw · qin · (Tin − Tref )/Ap (2.20)where ρw is the density of water (1000 kg m-3), cpw is the specific heat of water (4.18 ×103 J kg-1 K-1), Tin is the temperature of inflowing water (◦C), assumed to be 0 ◦C melt19water and Tref is a reference temperature (◦C), set to 0 ◦C. The advective energy transferout of the ice-proximal basin was calculated as:Hmid = ρwcpw · qmid · (Tmid − Tref )/Ap (2.21)where Tmid is the temperature of water leaving the ice-proximal basin and entering the dis-tal basin (◦C). The advective energy exchange associated with rainfall falling directly ontothe water surface was calculated by assuming that precipitation was at air temperature,as follows:Hp = ρwcpw ·R · (Ta − Tref ) (2.22)2.4.2 Distal basinThe advective energy transfer associated with inflow to the distal basin was calculated as:Hmid = ρwcpw · qmid · (Tmid − Tref )/Ad (2.23)where Tmid is the temperature of water entering the distal basin from the ice-proximalbasin (◦C). The advective energy associated with outflow was calculated as:Ho = ρwcpw · qout · (Tout − Tref )/Ad (2.24)where Tout is the outflow water temperature (◦C). The advective transfer associated withevaporation/condensation was calculated as:He = ρwcpw · E · (Tw − Tref ) (2.25)where Tw is the mean surface water temperature (◦C) of the distal basin and E is theevaporation rate (m s-1), calculated as:E =QeρwLv(2.26)The advective energy exchange associated with precipitation, Hp, was calculated usingEquation 2.22.202.5 Changes in heat storageChanges in heat storage in the distal basin of Bridge Lake were calculated using an energybudget approach, and by utilising water temperature measurements and spatial interpo-lation to calculate the heat content of individual layers and subsequently the whole basin.These approaches are described below.2.5.1 Energy budget approachThe heat budget of the distal basin of Bridge Lake, assuming negligible groundwaterexchanges, was calculated as follows (Richards et al., 2012):∆HC∆t= Hmid +Qn +Hp −Ho −He (2.27)where all units are in W m-2.2.5.2 Spatial interpolation approachThe total heat content of the distal basin can be determined using known water temper-atures as follows (Richards et al., 2012):HC =ρwcpwAd∑jVj(T¯j − Tref ) (2.28)where HC is the heat content (J m-2), Vj is the volume of the layer j (m3) and T¯j is themean water temperature measured at layer j (◦C). The heat content of the distal basinwas calculated at hourly time steps. Water temperatures measured at each vertical profileacross the distal basin were linearly interpolated, using the reglin() function in R (R CoreTeam, 2012), to provide predictions of water temperatures (T̂w) at 0.5 m depth incrementsbetween the water surface and lake bed. At each 0.5 m interval, water temperatures werespatially interpolated onto a 20 m regular grid across the basin. IDW interpolation (p= 2) was used for this analysis, following the results outlined in Appendix A. Nearestneighbour interpolation was used to assign lake depths to each grid cell, utilising detailedbathymetric data collected across the distal basin.The volume of layer j was calculated as:Vj = nj ·Ag ·Dj (2.29)where nj is the number of grid cells which exist at depth j, Ag is the area represented by21hmind0hmaxh(t)+++d0h(t)DjFigure 2.6: Schematic representation of changes in layer thickness given changesin lake stage.each grid cell (m2) and Dj is the depth of layer j (m). The depth of layer j at any giventime step was calculated as:Dj = 0.5 ·h+ d¯0hmax + d¯0(2.30)where 0.5 is the maximum depth of layer j (m), h is lake stage (m), d¯0 is the mean depthof the distal basin (m) and hmax is the maximum lake stage (m). The depth adjustmentfor each layer is shown schematically in Figure 2.6. Note that the vertical distribution oftemperature loggers changed with lake stage; however, the altered depth placements couldnot be accounted for and were assumed negligible.The change in heat content over time was then calculated as:∆HC∆t=HC(t+1) −HC(t)∆t(2.31)where HC(t) represents the total heat content at time t (J m-2) and ∆t is the change intime (s).222.6 Heat budget analysis of the ice-proximal basinThe heat and water budgets for the ice-proximal basin were calculated to provide a first-order approximation of surface iceberg melt contribution to lake discharge and excessenergy consumption in sub-aqueous iceberg melt. The methods used are laid out below.The change in heat content over time, ∆HC/∆t, was calculated as:∆HC∆t= Hi +Qnw +Hp +Hni −Hmid (2.32)where Qnw is the net surface energy exchange over the water surface (W m-2), Hp is theadvective energy transfer from precipitation falling directly onto the water surface (Wm-2) and Hni is the advective energy exchange from surface iceberg melt (W m-2). Netsurface energy exchange over the water surface was calculated as:Qnw = (1− fi) ·Ap · (Qrw +Qew +Qhw) (2.33)where fi is the fraction of the basin’s surface area occupied by icebergs and Qrw , Qew andQhw are calculated using Equations 2.10, 2.18 and 2.19 respectively.Advective energy exchange from surface iceberg melt was calculated as:Hni = fi ·Ap(Qri +Qhi +Qei +QpiρwLf)· ρwcpw · Tm (2.34)where Lf is the latent heat of fusion (3.34 × 105 J kg-1) and Tm is the temperature of themelt water (◦C), assumed to equal 0 ◦C. The energy input associated with radiation, Qri ,was calculated as:Qri = K ↓ (1− α) + εiL ↓ −εiσT4s (2.35)where α = 0.3, εi is the emissivity of the ice, assumed to equal 0.97 (Oke, 1987) and Ts isthe surface temperature of the ice (K) set to 0 ◦C. The energy exchange associated withprecipitation falling directly onto the iceberg surface (Qpi) was calculated as:Qpi = ρwcpw ·R · (Ta − Tref ) (2.36)Latent and sensible heat exchanges over the iceberg surfaces were calculated using thebulk aerodynamic approach using stability corrections described by Hock (1998):Qh = ρacpa ·DH · (Ta − Ts) (2.37)23Qe = ρaLv ·DE · (0.622/P )(ea − ei) (2.38)where ρa is air density (kg m-3) calculated using air temperature and barometric pressuremeasured at AWS1, following the ideal gas law and Ts and ei are surface temperature (0◦C) and vapour pressure (kPa), respectively. Turbulent transfer coefficients DH and DEare calculated as:DH = DE =(k2u) ·Θ[log(Za/Z0)log(Za/Zx)](2.39)where k is the von Karman constant (0.4), Za is the height at which Ta and u are measured(1.5 m), Z0 is the roughness length for momentum, assumed to equal 2 mm (Sverdrup,1936; Shea, 2009), Zx is the roughness length for temperature and vapour pressure, scaledto the momentum roughness following Hock (1998), giving Zx = Z0/300. The stabilitycorrection, Θ, is estimated using the bulk Richardson number, Rb:Rb =g(Ta − Ts)(Za − Z0)TK · u2(2.40)where g is gravitational acceleration (m s-2) and TK is the mean temperature of the airlayer (K). The sign of Rb influences the magnitude of the stability correction, with positiveRb for stable cases and negative Rb for unstable cases:Θ =(1− 5.2Rb)2, Rb > 0(1− 16.0Rb)0.75, Rb < 0(2.41)The contribution of surface iceberg melt (Sm) to lake discharge was calculated as:Sm = fi ·Ap(Qri +Qhi +Qei +QRiρwLf)(2.42)2.7 Modelling temperatures in the ice-proximal basin for ano-iceberg scenarioGiven the lack of strong vertical variation in water temperatures, the ice-proximal basinwas assumed to behave like a ‘continuously stirred tank reactor’ (CSTR). Modelling theice-proximal basin in this way allowed a prediction to be made about how water temper-atures may change once Bridge Glacier ceases to calve icebergs.24Water balanceThe water balance for the ice-proximal basin was calculated as:∆V∆t= qin − qmid + (R− E) ·Ap (2.43)The initial volume was calculated as:V0 = A¯p ·Dmean (2.44)where A¯p is the average basin surface area (m2), assuming that area changes are negligibleas stage changes and Dmean is the average depth of the ice-proximal basin (m). Thevolume of the ice-proximal basin was then calculated as:V(t) = V(t−∆t) + ∆t ·∆V∆t(2.45)Heat balanceThe heat balance for the ice-proximal basin was calculated as:∆HC∆t= Hi −Hmid +Hp −He +Qn (2.46)where Hi and Hmid are advective fluxes associated with inflow and outflow respectively(W m-2), He is the advective flux associated with evaporation/condensation (W m-2), Hpis the advective flux associated with precipitation (W m-2) and Qn is the net exchange atthe water surface (W m-2). Surface energy exchanges were calculated for the ice-proximalbasin, assuming that the albedo remained constant (0.1) across the surface and there wasno influence of ice-cover on reflected radiation. Water temperatures were set at the meanwater temperature of all vertical profiles measured throughout the ice-proximal basinand around icebergs at mid-lake. Advective energy transfer associated with inflow wascalculated as:Hi = ρwcpw · qin · (Tin − Tref ) (2.47)where Tin is the water temperature of the inflow, set as the mean water temperature ofthe ice-proximal basin (◦C). The advective energy transfer associated with outflow fromthe ice-proximal basin, Hmid, was calculated using an analogous equation. The advectiveflux associated with evaporation/condensation was calculated as:25He = ρwcpw · E ·Ap · (T¯w − Tref ) (2.48)where T¯w is the mean water temperature of the ice-proximal basin (◦C). Advective energyassociated with precipitation was calculated as:Hp = ρwcpw ·R ·Ap · (Ta − Tref ) (2.49)The net surface energy exchanges (Qn) were calculated using equations shown in Sec-tion 2.3. The initial heat content of the ice-proximal basin was calculated as:HC0 = V0 · (T¯w − Tref ) · ρwcpw (2.50)The temporal variation in heat content was then calculated as:HC(t) = HC(t−∆t) + ∆t ·∆HC∆t(2.51)The mean water temperature of the ice-proximal basin (T¯w) was calculated from themodelled heat content and volume as:T¯w(t) =HC(t)ρwcpw · V(t)(2.52)26Chapter 3ResultsThis chapter begins with an overview of the study period (Section 3.1) to set the 2013study period into a longer term context. The temperature dynamics within Bridge Lakeare then described (Section 3.2). Heat budget modelling of the distal and ice-proximalbasins is presented in Sections 3.3 and 3.4, respectively. Section 3.5 presents results ofmodelled temperature changes associated with the absence of icebergs in Bridge Lake.3.1 Overview of study periodThe winter preceding the 2013 study period was characterized by lower than average snowaccumulation (Figure 3.1). Mean monthly air temperatures during 2013 were consistentlyabove the long-term average measured at Whistler, approximately 95 km southeast ofBridge Glacier (Figure 3.2). During 2013, the months June – September experiencedmean air temperatures that were 0.6, 2.4, 1.2 and 1.7 ◦C higher, respectively, than thelong-term average at Whistler. Mean monthly air temperatures peaked in July at 18.6◦C. Streamflow measured approximately 3 km downstream of Bridge Lake was generallynear average to above average for most of the 2013 melt season (Figure 3.3). Peak annualdischarge for 2013 (69.5 m3 s-1) occurred on August 18th, a little later than the mean dateof annual peak discharge, which occurs on July 27th. Note that the streamflow data for2013 are provisional and subject to change prior to final approval by WSC.Continuous records of meteorological variables measured throughout the study periodare shown in Figure 3.4. Three large rain events occurred during the study period, in lateJuly and mid- and late-August. These coincided with periods of low incident shortwaveradiation, high incident longwave radiation and suppressed air temperatures.Outflow water temperatures exhibited diurnal variations superimposed on a seasonal27050010001500Mean monthly SWE (mm water equivalent)Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Declllllll l llMaximumMeanMinimum2013Figure 3.1: Maximum, mean and minimum mean monthly snowpack water equiv-alent (SWE) from 1993 - 2012. Mean monthly SWE for 2013 is shown in red.Data are taken from the ‘Green Mountain’ River Forecast Centre automatedsnow pillow (Station ID: 1C12P) located 40 km east of Bridge Lake at anelevation of 1,766 m.a.s.l.cooling trend (Figure 3.5). Seasonal discharge ranged between 28.5 – 73.3 m3 s-1 (mean= 49 m3 s-1). Diurnal variations of discharge coincided with daytime snow and ice melt,with rapid increases in discharge from Bridge Lake following precipitation events. A largestep change in recorded stage for the distal basin occurred in early August (Figure 3.5f),caused by movement of the pressure transducer rather than a true change in stage. Asa result, data collected in the ice-proximal basin were used to represent lake stage acrossthe lake following cross-correlation analysis verifying that seiching did not occur.3.2 Observed temperature patterns3.2.1 Outflow temperaturesWater temperatures measured at the outlet of Bridge Lake ranged from 1.2 – 5.1 ◦C (mean= 2.7 ◦C) during the study period, peaking on June 22nd (Figure 3.5a). Two periods ofreduced water temperatures around the 24th – 28th June and the 16th – 18th August28−100102030Mean monthly air temperature (°C)Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Declllllll llllllMaximumMeanMinimum2013Figure 3.2: Maximum, mean and minimum mean monthly air temperatures fromthe ‘Whistler’ meteorological station (Station ID: 1048898; Elevation: 658m.a.s.l) for the period of 1977 to 2011. Mean monthly air temperatures for2013 are shown in red.coincided with reduced air temperature and incident solar radiation. Typical diurnalranges varied from over 2 ◦C during the first half of the study period, to 1.5 ◦C duringthe second half. Precipitation events coincided with reduced water temperatures duringthe second half of the study period, coupled with typically lower air temperatures.3.2.2 Distal basinWithin this section, references to thermal stability and instability refer to densities inferredfrom water temperature and do not consider vertical variations in suspended sedimentconcentration, which were not measured. However, the effects of suspended sedimentconcentration on density will be addressed in the discussion (Chapter 4).Throughout the study period, mean lake temperatures ranged from 0.5 – 4.6 ◦C, whilstmean surface water temperatures peaked at 3.9 ◦C, below the temperature of maximumdensity, 4 ◦C. Mean surface water temperatures showed greater diurnal variability thanthose measured at 1 m and 3 m depths (Figure 3.5b). Mean water temperatures at 1 mand 3 m depths were typically lower than surface temperatures during the day, but higher29050100150Mean daily discharge (m3  s−1 )Jan Mar May Jul Sep Nov JanMaximumMeanMinimum2013 Raw WSC data2013 Seasonal fitted fataFigure 3.3: Maximum, mean and minimum mean daily discharges from 1978 to2011. Mean daily discharges for 2013 are shown in red. Data are taken fromthe WSC ‘Bridge River (South Branch) below Bridge Glacier’ (Station ID:08MEO23) gauging station. The blue line represents discharge data calcu-lated using Equation 2.5.at night. Furthermore, temperatures measured at 3 m tended to remain higher than thoseat 1 m.Contour plots of water temperature variations with depth and time are shown inFigure 3.6. Profile B (Figure 3.6a), located closest to icebergs at mid-lake, exhibited awell mixed water column, with warming of the upper 0.5 m attributed to surface energyexchanges. The period of warmer, denser water between 23rd – 27th July follows a peakin air temperatures.Water temperature dynamics measured at Profile AA (Figure 3.6b) were similar tothose at Profile B, with a well mixed water column and a diurnal warming/cooling trend.A distinct change in the thermal structure of the water column occurred on 6th August,with warmer, denser water underlying cooler water. This switch coincided with the largestep change observed in stage data collected in the distal basin (Figure 3.5f), suggestingthat it may be an artefact of the profile moving, rather than a true change in thermalbehaviour.Profiles A and D (Figures 3.6c and 3.6e) displayed similar characteristics, with localised300400800K↓(W m−2 ) (a)240300360tisoL↓(W m−2 ) (b)051015T a (°C)(c)0.00.40.81.2e a (kPa)(d)02468u (m s−1 )(e)Jul Aug Sep0.01.02.0Precipitation  (mm / 10 min) (f)Figure 3.4: Meteorological variables monitored at AWS1 during the study period,recorded every 10 mins: (a) incident shortwave radiation at AWS1; (b) in-cident longwave radiation at AWS1; (c) air temperature; (d) atmosphericvapour pressure; (e) wind speed; (f) precipitation.310123456tisoT w (°C)(a)0123456tisoT w (°C)(b) 0 m1 m3 m051015T a (°C)(c)0.01.02.0Precipitation  (mm / 10 min) (d)0204060Q (m3  s−1 )(e)Jul Aug Sep0.01.02.0Stage (m)(f)Distal basinIce−proximal basinFigure 3.5: Outflow water temperatures, lake temperatures, air temperature, pre-cipitation, discharge and lake stage recorded at 10 min intervals during thestudy period: (a) outflow water temperatures; (b) average lake temperaturesat 3 depths; (c) air temperature; (d) precipitation; (e) lake discharge and(f) lake stage. In panel (f), the red line denotes the stage record from thedistal basin, with a large step change in early August. Data from the ice-proximal basin were used for all analysis. Note: discharge and stage datawere smoothed using a 3-point binomial filter.32periods of warming and cooling throughout the study period. The water column at ProfileA tended to remain well mixed with depth, with temperatures ranging between 0 – 4 ◦C.The water column at Profile D remained well mixed throughout the study period, withtemperatures decreasing throughout August.Profile E (Figure 3.6d) showed greater vertical variation than other profiles throughoutthe study period. Days of elevated water temperatures observed in mid-July coincidedwith mid-July air temperature highs. Towards the end of the study period, there was ashift in the thermal structure of the water column in this area, with stratification occurringas cooler water consistently overlaid warmer, denser water.Water temperature variations at Profiles G and F (Figures 3.6f and 3.6g) were similar.Surface heating was evident at both profiles, although effects penetrated deeper into thewater column at Profile F. Water temperatures showed a cooling trend throughout theseason. The water column remained relatively well mixed, likely caused by the presenceof turbulence associated with currents as water leaves Bridge Lake.Profile H (Figure 3.6h) was installed on the 16th August to observe the penetrationof surface warming at a higher spatial resolution than other profiles. Surface heating hada negligible influence on water temperatures at this location. Warmer water remainedtowards the bottom of the lake.Figure 3.7 shows mean monthly water temperatures with depth at profiles B, E andG. These profiles were chosen to illustrate the change in stratification with increasingdistance from the icebergs. The thermal structure at Profile B varied through the studyperiod, as surface warming influenced the upper 0.5 m between 10:00 – 18:00 in July andAugust, but influences only extended until 14:00 during September. Daytime warming ofthe entire water column occurred during July, but did not exist in August and September.Profile E exhibited stratification throughout the study period, with warmer waterunderlying colder water. Daytime warming and evening cooling trends were sustainedthroughout the study period at Profile E, with the largest degree of daytime warming inJuly. The average warming of the water column between 06:00 and 18:00 in July was 1.7◦C, decreasing to 1.1 ◦C in September.Profile G displayed similar degrees of daytime warming and night time cooling, butdid not stratify. The water column remained thermally well mixed throughout, except forsurface warming influences to a depth of approximately 0.5 m. The intensity of surfacewarming increased throughout the day. Both profiles E and G experienced the majorityof warming between 10:00 and 14:00 throughout the season, with the rate of warmingdecreasing after 14:00.Water temperatures measured at 4 depths at profiles B, E and G are shown in Figure33−5−4−3−2−10 (a)−10 (b)−5−4−3−2−10 (c)Depth (m)−4−3−2−10Jul Aug Sep(d)01234567Tw (°C)Figure continues on next page.34−4−3−2−10 (e)−3.5−3−2.5−2−1.5−1−0.50 (f)−3.5−3−2.5−2−1.5−1−0.50 (g)Depth (m)−3.5−3−2.5−2−1.5−1−0.50Jul Aug Sep(h)01234567Tw (°C)Figure 3.6: Contour plots showing variations in water temperature with depth overtime: (a) Profile B; (b) Profile AA; (c) Profile A; (d) Profile E; (e) Profile D;(f) Profile G; (g) Profile F; (h) Profile H. Note that plots (a) – (g) progresswith distance from mid-lake icebergs. Profile H (plot (h)) is located on thewestern side of the distal basin.35−5−4−3−2−1006:0010:0014:0018:0022:00July July July−5−4−3−2−10Depth (m)August August August0 1 2 3 4 5−5−4−3−2−10 September0 1 2 3 4 5Tw (°C)September0 1 2 3 4 5SeptemberTw (°C)Depth (m)Profile B Profile E Profile GFigure 3.7: Vertical temperature profiles, showing monthly mean water tempera-tures with depth. Horizontal grey dashed line denotes the lake bed. Distancefrom mid-lake icebergs increases from Profile B – G (left – right).3.8. The distance of profiles B, E and G from icebergs increases sequentially. Surface waterat Profile B (Figure 3.8a) remained consistently warmer than deeper layers. Temperaturesmeasured at 0.5, 2 and 5 m depths were similar, suggesting a well mixed water column.In contrast to Profile B, water temperatures at Profile E (Figure 3.8b) measured atthe surface and 0.5 m were lower than those deeper within the water column. Nighttime cooling influenced the upper portion of the water column more strongly than deeperportions, resulting in an unstable water column. Throughout the day, a similar thermalstructure developed, with sporadic periods of stability when surface temperatures exceededthose measured within the lower portion of the water column.Surface warming variations at Profile G (Figure 3.8c) were less intense than thoseobserved at Profile B. The water column remained well mixed throughout the period,360123456 (a) 0 m0.5 m2 m5 m0123456T w (°C)(b) 0 m0.5 m2 m4 mAug 03 Aug 08 Aug 13 Aug 18 Aug 23 Aug 28 Sep 020123456 (c) 0 m0.75 m1.75 m3.75 mFigure 3.8: Time series plots of (a) Profile B; (b) Profile E and (c) Profile G,displaying water temperatures at 4 depths between August 1st and August31st. Distance from mid-lake icebergs increases from Profile B – G (top –bottom).with large diurnal temperature variations measured throughout the water column. Thesurface layers at Profile G exhibited higher temperatures than the lower portion of thewater column during the afternoon. Throughout the 31-day period, water temperaturesat profiles B and E remained below the temperature of maximum density, 4 ◦C, while onlysurface temperatures at Profile G exceeded 4 ◦C on days in early August.3.2.3 Ice-proximal basinWater temperatures were measured at 26 locations across the ice-proximal basin (Figure3.9) at various times throughout the study period. The vertical profiles can be grouped intothose measured within the ice-proximal basin and those measured at mid-lake, amongst3750100150          Depth (m)0 m 1 kmlll ll llllllllllllll llll3692224 252612324 58217101112 15 16 1819201314 17No Datall Ice−proximal profilesMid−lake profilesFigure 3.9: Bathymetry across Bridge Lake. White area denotes high density oficebergs, resulting in an absence of bathymetric data. This area is excludedfrom interpolation. Coloured points represent the locations of vertical tem-perature profiles taken within the ice-proximal basin and around mid-lake.Numbers denote profile identification numbers, corresponding to vertical tem-perature profiles displayed in Figures 3.10 and 3.11.icebergs. Figure 3.10 shows vertical profiles of water temperatures within the ice-proximalbasin. In general, the water column remained well mixed with depth throughout thestudy period. Figure 3.10(n) shows a marked decrease in temperature at a depth of 110m. Steep temperature gradients observed at the surface of the water column in Figures3.10(b, e, k and l) are expected to be an artefact of the time of day that measurementswere taken, and meteorological conditions (particularly incident shortwave radiation). Themean temperature measured within the ice-proximal basin was 1.2 ◦C.At mid-lake, water temperatures remained more consistently isothermal throughoutthe water column (Figure 3.11). Once again, the extent of surface warming varied be-tween profiles, as a result of meteorological conditions and time of day. The mean watertemperature measured at mid-lake, amongst icebergs, was 0.9 ◦C.38lllll l12080400Depth (m)(a)13−08−13 12:11Profile: 1lllll l(b)13−08−13 12:43Profile: 2lllllll(c)13−08−13 13:15Profile: 3lllllll(d)13−08−13 13:50Profile: 4lllllll12080400Depth (m)(e)13−08−13 14:33Profile: 5llllll l(f)13−08−13 15:13Profile: 6lllllll(g)13−08−13 15:55Profile: 7 llllll l(h)13−08−13 16:31Profile: 8lllllll12080400Depth (m)(i)15−08−13 10:39Profile: 9l lllllllll(j)16−07−13 12:52Profile: 21llllllllllTw (°C)(k)16−07−13 13:36Profile: 22lll llll l l0.0 1.0 2.0Tw (°C)(l)16−07−13 15:34Profile: 23lllll0.0 1.0 2.012080400Tw (°C)Depth (m)(m)14−07−13 11:49Profile: 24 l lllllllll0.0 1.0 2.0Tw (°C)(n)14−07−13 12:54Profile: 25lll0.0 1.0 2.0(o)15−07−13 12:42Profile: 26Tw (°C)Tw (°C)Depth (m)Figure 3.10: Vertical temperature profiles across the ice-proximal basin. Profilenumbers correspond to location numbers shown in Figure 3.9. Date andtime of measurements beginning are marked on plots.3.3 Distal basin heat budgetIn this section, results from the radiation modelling are first presented, followed by surfaceenergy fluxes across the distal basin. The heat content calculated using IDW interpolationis displayed, along with advective and non-advective fluxes used to model the heat content.39lllllll151050Depth (m)(a)15−08−13 11:57Profile: 10 llllll l(b)15−08−13 12:28Profile: 11ll l(c)15−08−13 14:09Profile: 12 lllllll(d)15−08−13 14:41Profile: 13lllll l151050Depth (m)(e)15−08−13 15:11Profile: 14lllll l(f)15−08−13 15:43Profile: 15lllll l(g)15−08−13 16:35Profile: 16llllll0.0 1.0 2.0(h)16−08−13 10:31Profile: 17llllll0.0 1.0 2.0151050Depth (m)(i)16−08−13 10:54Profile: 18llllll0.0 1.0 2.0(j)16−08−13 11:20Profile: 19lllll0.0 1.0 2.0Tw (°C)(k)16−08−13 11:45Profile: 20Tw (°C)Tw (°C)Depth (m)Figure 3.11: Vertical temperature profiles amongst mid-lake icebergs. Profilenumbers correspond to location numbers shown in Figure 3.9. Date andtime of measurements beginning are marked on plots.3.3.1 Non-advective surface energy fluxesModelled effects of topography were minor, except during the morning and evening whentopographic shading reduced incident shortwave radiation to the lake surface, relative towhat was measured at AWS1 (Figure 3.12). The sky-view factor for all grid points acrossthe distal basin ranged between 0.93 and 0.97, compared to a sky-view factor of 0.96 atAWS1. Modelled incident longwave radiation was higher than that measured at AWS1during the morning and evening.Surface energy fluxes across the distal basin are shown in Figure 3.13. Energy input bynet radiation dominated surface energy exchanges, with a seasonal peak of 1015 W m-2.The latent heat flux was dominantly positive throughout the study period, indicating thatcondensation prevailed over evaporation. The sensible heat flux was dominantly positivethroughout the study period, ranging from -1.9 W m-2 to 326.7 W m-2. Sensible heatflux values were often almost twice the magnitude of the latent heat flux, but both were40llllllllllllllllll llllllllllllllll llllllllllllllllllllllllllllllllllllll ll llllllll lllllll lllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllll llllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllll lll lllllll lllll l lllllllllllllllllll llllllll lllllll0 200 400 600 800 100002004006008001000Modelled  K ↓ (W m−2)Measured  K↓(W m−2 )(a)1:1 linelllllll llllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ll llll llllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllll llllllllll llllllllll llllllllllllllll lllllllllllllllllllllllllllllll lll lllllllllllllllllll llllllll llllllll lllllllllll240 260 280 300 320 340 360240260280300320340360Modelled  L ↓ (W m−2)Measured  L↓(W m−2 )(b)1:1 lineFigure 3.12: Measured (AWS1) vs. modelled average incident (a) shortwave; (b)longwave radiation across the distal basin.minimal terms compared to the energy input from net radiation.3.3.2 Heat contentFigure 3.14 shows hourly (some averaged from 10 min data) fluxes used to calculate theheat content of the distal basin throughout the study period. The dominant source ofheat to the distal basin was the net surface energy exchange, Qn (Figure 3.13). Advectiveenergy loss from the lake outflow was the dominant sink of heat from the basin. Advec-tive energy transfer from evaporation/condensation and precipitation were both negligibleterms (Figures 3.14d and 3.14e).Sensitivity analysis was used to determine an appropriate temperature for water flow-ing into the distal basin. Heat added to the basin via inflow was sensitive to the assumedwater temperature of the inflow (Figure 3.14b). Sensitivity analysis suggested that totalenergy added to the distal basin via inflow ranged from 0 – 1042 MJ m-2 with inflow watertemperatures of 0 – 1 ◦C. Subsequently, the sum of all fluxes for the study period variedfrom -861.8 to 180.2 MJ m-2 with varying inflow temperatures.The heat content of the distal basin calculated using IDW interpolation (Figure 3.14f)showed diurnal variability that closely followed that observed in outflow temperatures(Figure 3.5a). Over the season, the distal basin of Bridge Lake lost 0.5 MJ m-2 of energy.A summary of all fluxes is given in Table 3.1. Based on heat content calculations410400800Q e (W m−2 )(a) CondensationEvaporation0400800Q h (W m−2 )(b)Jul Aug Sep0400800Q r (W m−2 )(c)Figure 3.13: Surface energy fluxes over the distal basin: (a) Latent heat flux; (b)Sensible heat flux and (c) Net radiation. Albedo was set at 0.1.using observed water temperatures (Figure 3.14f), it was possible to constrain inflowtemperatures to a narrower range. Given that the distal basin of Bridge Lake lost heatover the study period, inflow water temperatures were capped at 0.82 ◦C as the sum ofall fluxes becomes positive at higher temperatures. Considering the uncertainty of theheat flux calculation, the uncertainty of inflow water temperatures can be constrained.For example, using an uncertainty of ±5% for incident shortwave radiation results in anuncertainty of ±80 MJ m-2 within Qr alone. As a result, inflow temperatures yielding anegative sum of fluxes (representing a loss of heat from the distal basin) within ±80 MJm-2 of ∆HC are considered reasonable estimations.Table 3.1 displays results for inflow temperatures ranging from 0.76 – 0.82 ◦C. Energybudget estimates of heat content calculated using inflow temperatures within the rangeof 0.76 – 0.82 ◦C agree reasonably with those calculated using temperature profiles across4204008001200Q n (W m−2 )(a)050150250H i (W m−2) (b)200400600800H o (W m−2 )(c)−0.20.20.6H e (W m−2 )(d)010203040H p (W m−2 )(e)Jul Aug Sep152535HC (MJ m−2) (f)Figure 3.14: Bridge Lake distal basin heat fluxes: (a) net energy exchange at thewater surface; (b) advective energy transfer associated with inflow (greylines denote 0.1 ◦C Tw increments from 0 – 1 ◦C and blue lines are Tw= 0.76 – 0.82 ◦C); (c) advective energy transfer associated with outflow;(d) advective energy transfer associated with evaporation/condensation; (e)advective energy transfer associated with precipitation and (f) heat contentof the distal basin, calculated using IDW interpolation.43the distal basin. Heat budget results suggest that the distal basin had a mean warmingeffect of 1.85 – 1.9 ◦C between the ice barrier and the lake outlet.Table 3.1: Total energy added to the distal basin of Bridge Lake by each heat fluxthroughout the study period.Heat Flux Total (MJ m-2)Net radiation 1440.2Latent heat flux 103Sensible heat flux 361.2Advective: Inflow 791.9 – 854.5Advective: Outflow -2768.1Advective: Evaporation -0.3Advective: Precipitation 2.3Sum of fluxes -69.9 to -7.3∆HC from IDW -0.53.4 Ice-proximal basin heat and water budgetsSince water temperatures in the ice-proximal basin were not observed to increase through-out the study period, it is hypothesised that a substantial portion of the energy added tothe ice-proximal basin across the water surface was consumed in iceberg melt. Figure 3.15illustrates the calculated change in heat content of the ice-proximal basin over the studyperiod. The heat budget was calculated for a range of fractional ice cover (fi) to addressuncertainty in this value.The net addition of energy associated with 0 – 50% surface ice coverage decreased from1693 to 847 MJ m2, respectively, for the study period. Surplus energy was sufficient tomelt between 2.2 × 107 and 1.2 × 107 m3 of ice, respectively, with 10 – 50% of the basin’ssurface area covered by ice.The estimated volume of ice melted can be converted to a seasonally averaged icebergmelt rate (Figure 3.16). It is assumed that surplus energy was consumed in sub-aqueousiceberg melt since this term cannot be quantified in equations outlined in Section 2.6.Figure 3.16 shows the percentage contribution of surface, sub-aqueous and total icebergmelt to the mean lake discharge over the study period for values of fi ranging 0 – 0.5.Surface ice melt increases whilst sub-aqueous and total iceberg melt rates decrease withincreased ice cover. With decreasing surface ice cover, from 50 – 10%, total iceberg melt44Jul Aug Sep500100015002000Heat Content (MJ m−2)fi = 0fi = 0.1fi = 0.2fi = 0.3fi = 0.4fi = 0.5Figure 3.15: Computed changes in heat content of the ice-proximal basin withvarying percentage ice cover. fi = fraction of basin surface area occupiedby icebergs.can account for 6 – 7% of the mean discharge out of Bridge Lake.3.5 Modelled temperatures in the ice-proximal basin for ano-iceberg scenarioFigure 3.17 shows hourly (averaged from 10 min data) results of the CSTR model used topredict changes in the heat content and water temperatures of the ice-proximal basin inthe absence of icebergs. Temperature changes within the ice-proximal basin were modelledincorporating their effect on advective energy loss via outflow (Figure 3.17b).If no icebergs were present within Bridge Lake over the study period, water tempera-tures are predicted to have increased from 1.1 – 3 ◦C over the first half of the study periodbefore decreasing to 1.7 ◦C at the end of the season. The modelled total heat content ofthe ice-proximal basin showed the same trend as predicted water temperatures, increasing450.0 0.1 0.2 0.3 0.4 0.501234567Fraction of lake occupied by icebergsPercent contribution to lake discharge (%)Surface meltSub−aqueous meltTotal meltFigure 3.16: Percentage contribution of surface, sub-aqueous and total icebergmelt to mean lake discharge over the study period.from 308 – 834 MJ m-2 during the first half of the study period before decreasing to 489MJ m-2 at the end of the season (Figure 3.17d). Advective energy transfer associatedwith outflow is predicted to have increased throughout the season, explaining the decreasein heat content and water temperatures during the later half of the season. Advectiveenergy exchange associated with evaporation/condensation remains negligible throughoutthe study period.46Basin volume (m3 ×108)33.013.02 (a)H o(W m−2 ×108)2814 (b)0.00.40.8H e(W m−2 )(c)300500700HC (MJ m−2)(d)Jul Aug Sep0.01.02.03.0T w (°C)(e)Figure 3.17: Results from the CSTR model used to model the ice-proximal basinfor a no-iceberg scenario, showing (a) the volume of the basin; (b) theadvective energy loss from outflow; (c) the advective energy transfer as-sociated with evaporation/condensation; (d) the modelled heat content ofthe ice-proximal basin and (e) the modelled water temperatures of the ice-proximal basin. Water temperatures in (e) are calculated from the heatcontent results in (d).47Chapter 4DiscussionThis chapter is separated into four sections: (1) major controls on the thermal regimeof the ice-proximal basin; (2) major controls on the thermal structure and regime of thedistal basin; (3) a comparison of results from this study to those from previous studiesand (4) a tentative conceptual model of proglacial stream temperature response to retreatof valley glaciers.4.1 Thermal processes and regime of the ice-proximal basinWithin the ice-proximal basin, surface energy exchanges provided the dominant heat in-put. Surface energy exchanges were dominated by net radiation, which is consistent withfindings by Richards et al. (2012) at Place Lake. The vapour flux was dominated by con-densation, adding energy to the ice-proximal basin. The addition of energy to the lake viathe latent heat flux (as condensation) is not characteristic of lentic water bodies duringsummer (Webb and Zhang, 1997; Webb et al., 2003). However, a previous study on aproglacial lake (Richards et al., 2012) found similar results to those at Bridge Lake, as aresult of low water temperatures that limit the surface vapour pressure. The dominantheat sink was advective outflow.The water column was dominantly isothermal throughout the entire depth (Figure3.10), indicating a well mixed water body. The processes driving vertical mixing arelikely wind-induced mixing and mechanical stirring from the movement of icebergs drivenby strong katabatic flows. The effects of wind-induced mixing were found to extend todepths of 70 m in Lake Jo¨kulsa´rlo´n in south-east Iceland by Harris (1976). Colder water atlower layers is likely due to sediment-laden underflows exiting the base of Bridge Glacier.Weirich (1984, 1986b) observed frequent density-driven underflows in Exception Lake in48British Columbia, frequently reaching a thickness of 1.5 m. At Place Lake, Richards et al.(2012) also inferred the presence of turbidity currents, responsible for abrupt decreases inwater temperatures towards the bottom of the water column. It is difficult to comment onthe thickness of turbidity currents within the ice-proximal basin, although their presenceis likely, given observed temperatures and results from previous studies.The absence of seasonal warming within the ice-proximal basin suggests that surfaceenergy inputs were consumed by net advection and iceberg melt. Results from energybalance modelling (Figure 3.16) suggest that iceberg melt consumed 847 – 1524 MJ m-2of energy for fractional ice cover ranging from 0.5 – 0.1 over the study period.Higher percentage cover of icebergs results in a lower heat content of the ice-proximalbasin (Figure 3.15) and a decrease in the computed surplus energy as energy inputs occurover a reduced water surface area. Surface energy exchanges at the ice surface are con-sumed by ice melt and do not contribute to the heat content of the ice-proximal basin,except via the advective flux associated with the melt water.Estimated iceberg melt was equivalent to 6 – 7% of the mean discharge leaving BridgeLake, regardless of the assumed fractional ice cover, which is not an insubstantial amount.When Bridge Glacier retreats to the point that it is land-terminating and icebergs nolonger occur, mean discharge measured at the lake outlet is likely to decrease by 2.9 –3.4 m3 s-1, resulting in reduced water availability for power generation and thus reducedrevenue to BC Hydro.In addition, results from the CSTR model (Figure 3.17) suggest that the loss of ice-bergs from Bridge Lake will result in higher water temperatures and elevated advectiveenergy transfer associated with outflow. Higher outflow temperatures will influence down-stream aquatic ecosystems, especially salmonids which are particularly sensitive to thermalchanges (Fleming, 2005). Warming could have beneficial or detrimental impacts depend-ing on whether downstream water temperatures were above or below the thermal optima.Elevated water temperatures will also alter the thermal stability of Bridge Lake, resultingin changes in physical processes driving mixing and altering the dominant energy ex-changes. For example, evaporation is likely to prevail over condensation as surface watertemperatures increase, changing the micro-climate above the water surface and reducingthe outflow from the lake.4.2 Thermal processes and regime of the distal basinWithin the distal basin, surface energy exchanges were dominated by net radiation (Figure3.13), as in the ice-proximal basin. Condensation dominated the vapour flux, adding49energy to the distal basin (Figure 3.13a). The dominant heat sink from the distal basinwas net advection – similar results were found by Richards et al. (2012) at Place Lake.It is important to note a source of uncertainty within the calculated heat content.Since the deepest vertical temperature profiles (profiles A and B) extended to a depth of5 m, no temperature data existed for the volume of water existing below 5 m (note that amaximum depth of 19.3 m was measured in the distal basin). The absence of temperaturedata at depths greater than 5 m resulted in an approximate water volume of 1.9 × 105m3 omitted from heat content calculations. This may account for some of the differencesbetween calculated and modelled heat content results (Table 3.1).Seasonal cooling observed throughout the distal basin is a result of a decrease in solarradiation following the summer solstice, altering the magnitude of surface energy fluxes.Assumed inflow temperatures (0.76 – 0.82 ◦C) were lower than those measured amongstmid-lake icebergs (Figure 3.11), suggesting that water is cooled further as it flows throughthe barrier of ice at mid-lake. High concentrations of icebergs have been found to reducewater temperatures in Antarctic waters (Budd et al., 1980; Benn et al., 2007). In addition,Budd et al. (1980) found melt rates to increase following iceberg breakage and rollover.Icebergs found at mid-lake comprise ice debris from larger iceberg breakages, suggestingthat melt rates may be higher at mid-lake than within the ice-proximal basin, furthercontributing to colder inflowing water.Variations in the thermal structure of the water column at profiles B, E and G can beexplained by considering diurnal surface heating and suspended sediment concentrations.Profile B exhibits diurnal warming (Figure 3.8a), which would typically promote verti-cal mixing. However, surface layers became warmer than deeper layers, suggesting thatvertical mixing did not occur. The inhibition of vertical mixing is likely due to highersediment concentrations found within the deeper portion of the water column having astronger effect on density than temperature (Warren and Kirkbride, 1998). The sourceof sediment is expected to be entrainment of bed sediment from wind turbulence and thetransfer of suspended sediment from the ice-proximal to the distal basin, since no externalsediment source existed within the distal basin.Profile E (Figure 3.8b) was dominantly thermally stable with the lower portion ofthe water column generally warmer than the upper portion, except during the afternoon.Surface heating was responsible for driving vertical mixing during the afternoon, whilesurface cooling over night produced less dense water in the upper layers, resulting in astratified water column. The water column at Profile G (Figure 3.8c) remained well mixedwith depth over night and during the morning. Afternoon surface heating lead to warmerwater overlying cooler water in the lower portion of the water column. The extent of50surface warming generated water temperatures indicative of vertical mixing, although thiswas not observed. The absence of vertical mixing was likely a result of higher sedimentconcentrations within the lower portion of the water column, as at Profile B (Figure 3.8a).The energy balance analysis used within this study does not consider groundwaterinfluences, despite their importance highlighted by Roy and Hayashi (2008). However, nowarm water inputs, indicative of groundwater influences (Carrivick and Tweed, 2013), wereobserved within Bridge Lake, suggesting that groundwater does not contribute directly tothe heat content of Bridge Lake. It is also likely that the volume of groundwater dischargeis much smaller than the volume of melt water input.Lateral warming was observed with distance from icebergs (Figure 3.7) suggestingcomplex circulation cells are present within the distal basin. As a result, it would not beappropriate to model the distal basin as laterally uniform using a 1-dimensional mixingmodel (e.g. DYRESM). Modelling circulation within the distal basin would require a morecomplex, 3-dimensional model.4.3 Comparison with other alpine lakesTo the knowledge of the author, only one previous study (Richards et al., 2012) quantifiedthe energy budget of a proglacial lake (Table 1.1). However, several studies have docu-mented inflow and outflow temperatures for alpine lakes (Table 4.1), providing a limitedbasis for contextualizing the findings at Bridge Lake.The two basins of Bridge Lake exhibited different degrees of warming, controlled by thepresence (absence) of icebergs, as well as their relative sizes and depths. Assuming thatoutflow from Bridge Glacier was at 0 ◦C, energy exchanges within the ice-proximal basinwere responsible for a mean net warming effect of 0.76 – 0.82 ◦C. It is important to notethat thermal influences from the two proglacial streams entering Bridge Lake have beenignored. Inflows from these streams would have temperatures greater than 0 ◦C providingadditional warming influences. In addition, ignoring the influences of these inflows meansthat the sub-aqueous melt estimate should be an underestimate. The degree of warmingobserved within the ice-proximal basin is the lowest seen within any study considered(Table 4.1) and is likely due to the basin having a significantly larger volume than anyof the other lakes, as well as the cooling effect of the icebergs. Energy exchanges withinthe distal basin resulted in stronger warming, ranging from 0.4 – 4.3 ◦C (mean = 1.9 ◦C),which is likely a result of the short residence time (1.3 days) due to the shallow depthsand smaller volume.The mean net warming from the glacier terminus to the lake outlet was 2.7 ◦C. Similar51warming was observed by both Weirich (1986b) and Uehlinger et al. (2003). However,both of those lakes were distally fed and significantly smaller than Bridge Lake (Table4.1), suggesting that the presence of icebergs and a calving icefront are responsible forbuffering warming influences of surface energy exchanges. In addition, Robinson andMatthaei (2007) observed warming up to 8 ◦C in a non-glacially influenced lake, whichsuggests that lentic environments are vulnerable to more warming without the influenceof glacier melt.Table 4.1: Comparison of studies documenting the thermal influence of proglacial lakes. Thistable is based on a table presentation (Richards et al., 2012), with the addition of thisstudy.Study Location GF SA V Elev MRT MWBridge Lake Coast Mtns, Yes - 1.4 4.7×106 *1 1400 1.3 1.9(Distal basin) BC, Can CalvingUehlinger et al. Bermina Massif, Yes - 0.22 1.5×106 2159 2-3 2-4(2003) Swiss Alps DistalRichards et al. Coast Mtns, Yes - 0.072 4.3×105 *2 1830 4 1.8(2012) BC, Can DistalWeirich Purcell Mtns, Yes - 0.24 1.19×106 2195 9-13 1.6/1.9(1986b) BC, Can DistalBridge Lake Coast Mtns, Yes - 4.48 300×106 *3 1400 73.8 0.79(Ice-proximal basin) BC, Can CalvingRobinson and Matthaei Macun, Swiss No 0.12 - 2631 - 6-8(2007) AlpsGF - Glacier-fed; SA - Surface area (km2); V - Volume (m3); Elev - Elevation (m.a.s.l); MRT - Meanresidence time (days); MW - Mean warming between inflow and outflow (◦C).*1 Estimated using a mean depth of 3.37 m, calculated from bathymetric data.*2 Estimated from assumed bathymetry.*3 Estimated using a mean depth of 66.9 m, calculated from bathymetric data.4.4 A conceptual model for the effect of valley glacier re-treat on downstream water temperatureAs Bridge Glacier continues to retreat, calving will cease and the glacier will becomeland-terminating, resulting in the eventual loss of icebergs from Bridge Lake. The lossof icebergs will result in an increased heat content (and subsequent downstream watertemperatures) due to a reduction in the surface area for which surface energy exchangeswere previously consumed by iceberg melt. Discharge from Bridge Lake should decrease52with further glacier retreat (Hock et al., 2005), resulting in an increased residence timeand greater warming of the water body. In addition to greater warming, decreased dis-charge will have detrimental impacts on downstream water supplies for use in hydropowerproduction. If water temperatures exceed 4 ◦C, lake stability will increase with surfaceheating, causing stratification (Warren and Kirkbride, 1998; Warren and Aniya, 1999).Drawing upon previous studies and findings from the current study, a conceptual modelfor the effect of continued retreat of large valley glaciers on water temperatures is proposed(Figure 4.1). As large valley glaciers continue to retreat, the formation of proglacial lakes inover-deepened basins is expected to become more prevalent (Warren and Kirkbride, 1998;Benn et al., 2007; Masetti et al., 2010). Figure 4.1 displays four distinct phases throughwhich glaciers may transition as retreat continues. As glaciers retreat, the upstreamextension of proglacial streams exposes glacial melt water to increased energy inputs,increasing water temperatures downstream (Figure 4.1(2)). As proglacial lakes begin toform, downstream water temperatures increase due to stratification and heating of theepilimnion (Mellina et al., 2002). As lakes increase in size, their residence time increases,resulting in more warming and further elevated downstream water temperatures.If glaciers experience a transient calving phase following the formation of a proglaciallake (as is occurring at Bridge Glacier), the rate of warming is expected to reduce asa result of the consumption of energy by the melting of icebergs (Figure 4.1(3)). Asthe glacier continues to retreat and ultimately becomes land-terminating, the formationof icebergs will cease and icebergs will eventually become absent from the lake (Figure4.1(4)). Within Bridge Lake, the loss of icebergs is likely to cause the lake to behaveas a single basin, with the disappearance of the ice barrier. At this point, there will begreater opportunity for the lake to warm, as more of the surface energy exchange willbe available to heat the water. As the glacier continues to retreat, the increase in thelength of proglacial stream between the glacier snout and the lake will promote streamwarming and thus higher inflow temperatures (Figure 4.1(4)). Warmer inflows result in agreater warming of the lake. In addition, higher inflow temperatures will alter the densitystructure of the lake, as inflowing water could become less dense than the lake water,resulting in surface plumes of warmer water, rather than inflows plunging to the lakebed. However, turbidity currents could still exist, at least transiently, as was observed atPlace Glacier by Richards et al. (2012). The density of inflowing water will be alteredfurther by the reduction in sediment load as proglacial streams increase in length andproglacial sediment stability increases. Reduced suspended sediment concentrations willresult in sediment-laden underflows becoming less frequent and temperature controlledstratification prevailing.53An increase in water temperatures is likely to alter the magnitude and intensity ofsurface energy exchanges. Higher water temperatures may reverse the latent heat flux,with evaporation dominating, removing energy and water from the system.Over time, changes in channel morphology and riparian forest development will alterthe thermal response of proglacial streams (Cowie et al., 2014). Changes in proglacialfluvial environments will influence inflow temperatures and the downstream modificationof outflow temperatures. Milner and Petts (1994) summarised geomorphic, thermal andecological impacts of sustained glacier retreat in downstream proglacial channels (Figure 3in Milner and Petts (1994)). A reduction in in-stream sediment loads over time will reducescouring of algal communities, enhancing their abundance and persistence in downstreamenvironments (Milner et al., 2009).5412341 2 3 412 3 4       Glacier is in a stable state. Watertemperatures remainconstant at 0 °C asglacier outflow exitsdirectly from the glacier snout.        Glacier terminates at an over-deepenedbasin and begins tocalve, producingicebergs. Water temperatures continueto increase, but at aslower rate due toiceberg melt bufferingatmospheric warming.       Glacier begins toretreat, forming a pro-glacial stream. Watertemperatures increase non-linearlyas the glacier retreatsand the streamincreases in length.       Glacier becomesland terminating. Watertemperatures increasemore rapidly due to thelack of energyconsumption by icebergmelt, suppressing the warming of water. TimeTw (°C)Figure 4.1: Conceptual diagram showing the effects of sustained valley glacier re-treat on downstream water temperatures. Suggested water temperatures aretaken from the red dot in all panels of this figure.55Chapter 5ConclusionsThe first section of this chapter outlines the key findings from this study, which addressthe research objectives outlined in Section 1.3. The final section provides areas wherefurther study is required to aid understanding of proglacial systems.5.1 Key findingsBridge Lake had a net warming effect in summer 2013 of 1.1 – 5.1 ◦C (mean = 2.7 ◦C)assuming inflow to the ice-proximal basin was 0 ◦C glacier melt water. Energy exchangeswithin the ice-proximal basin accounted for 0.76 – 0.82 ◦C of the total warming, whilstenergy exchanges within the distal basin dominated the net warming.Within both basins, surface energy exchanges provided the main heat source to BridgeLake, dominated by solar radiation. The latent and sensible heat fluxes were both minimalinfluences, relative to net radiation. The latent heat flux was dominated by condensation,as water temperatures were sufficiently low that the water surface had a lower vapour pres-sure than the atmosphere. As a result, vapour pressure gradients were typically low anddirected towards the lake surface. Advective energy exchanges associated with evapora-tion/condensation and precipitation were negligible throughout the study period. Withinthe distal basin, advective energy gained from inflow provided a secondary significant heatinput. Advective energy loss via outflow provided the largest heat sink from the distalbasin, with a total loss of 2768.1 MJ m-2 over the study period. In total, the distal basinof Bridge Lake experienced a net loss of 0.5 MJ m-2 of heat over the summer. This agreesreasonably with the net loss of -69.9 to -7.3 MJ m-2 calculated using an energy budgetmodel, considering the uncertainties associated with components of the energy budget.Sensitivity analysis of inflow temperatures suggested that the modelled heat content56of the distal basin was particularly influenced by advective energy inputs from the inflow.Assumed inflow temperatures were lower than those observed around mid-lake icebergs,suggesting that water was cooled further as it flowed through the barrier of ice betweenthe ice-proximal and distal basins.Since no seasonal warming was observed within the ice-proximal basin, it is hypothe-sised that surface energy inputs were consumed by net advection and iceberg melt. Energybalance modelling of the ice-proximal basin suggests that iceberg melt is an importantcomponent of lake discharge, equivalent to 6 – 7% of the mean discharge leaving BridgeLake, with decreasing surface ice cover from 50 – 10%. Results from the CSTR modelwithin the ice-proximal basin suggest that the loss of icebergs from Bridge Lake will resultin increased advective energy loss via the outflow of Bridge Lake, impacting downstreamaquatic ecosystems.Observed water temperatures within the ice-proximal basin were consistently isother-mal to depths of approximately 80 m, with surface heating penetrating to a depth ofapproximately 0.5 m. Occasional steep temperature gradients observed at the bottom ofthe water column are hypothesised to be due to cold, sediment-laden underflows exitingBridge Glacier and sinking to the lake bed.Vertical temperature profiles showed differing degrees of stratification throughout thedistal basin. Lateral warming was observed with distance from icebergs as the influenceof 0 ◦C melt water weakened. Variations in the thermal structure of the water columnwere controlled by diurnal surface heating and suspended sediment concentrations, nottemperature as would be expected in most non-glacial lakes. It is possible that verticalconvective currents, generated by 0 ◦C melt water at the ice-water interface, were in partresponsible for the well mixed water column close to mid-lake icebergs.The presence of a submerged terminal moraine, coupled with the barrier of ice presentat mid-lake, causes the two halves of Bridge Lake to behave as individual basins, despitethe lack of topographic separation by a sill. However, as icebergs are lost from BridgeLake, it is expected to function as a single basin.5.2 Future researchThis study has provided key insights into the thermal behaviour of ice-contact proglaciallakes, although it has also highlighted a number of areas where further research is requiredto better understand the dynamic nature of these environments.One key finding from this study is the absence of lateral uniformity within differentlayers of the water column. As a result, applying a standard 1-dimensional model (such as57DYRESM) to a proglacial lake would not produce an accurate representation of the naturalsystem. Therefore, there is a need for consideration of complex circulation cells whenmodelling these systems, suggesting that the implementation of 3-dimensional mixingmodels would be more appropriate.Findings within this study, along with work done by others (e.g. Matthews, 1956;Weirich, 1986a,b), suggest that suspended sediment is a crucial determinant of waterdensity, and thus vertical temperature variations. As a result, further studies are neededto investigate the influence of suspended sediment on density variations. Spatially sampledsuspended sediment concentrations would enable inferences to be made about sedimentdynamics and their influence on density variations throughout the water column. Studyingsediment dynamics would also allow the presence of sediment-driven underflows to beidentified.Within this study, the importance of iceberg melt on (1) the buffering of water tem-peratures and (2) the contribution to outflow discharge has been identified. Further con-sideration of iceberg melt rates will enable more informed predictions of (1) changes to thethermal regime and (2) changes to the water balance as glacier retreat continues. BridgeLake provides an ideal site for this research due to the large number of icebergs cur-rently present, in addition to the glacier nearing a transition to being a land-terminatingglacier. The impact on lake discharge holds particular economic importance with regardsto downstream hydropower generation.Although no groundwater interactions were evident within Bridge Lake, these requireconsideration within future studies as their importance has been noted by Roy and Hayashi(2008). The role of groundwater discharge could increase as glaciers retreat and melt waterinputs decline.Expanding the study domain to include the downstream reach will provide valuableinsight into the distance downstream that the glacial thermal signature extends. Thedownstream extent of thermal influence is expected to change as glacier retreat continuesand Bridge Lake becomes distally fed. Processes controlling downstream water tempera-tures require understanding as valley-bottom reaches provide important habitat for aquaticecological communities, including salmonids.58ReferencesAllen, S. M. and Smith, D. J. 2007. Late Holocene glacial activity of Bridge Glacier,British Columbia Coast Mountains. Canadian Journal of Earth Sciences,44:1753–1773.ASTM 1996 (2010). D5922-96(2010) ‘Standard guide for analysis of spatial variation ingeostatistical site investigations’. ASTM International, West Conshohocken, PA.Barry, R. G. 2006. The status of research on glaciers and global glacier recession: areview. Progress in Physical Geography, 30(3):285–306.BC Hydro 2013. Bridge River.https://www.bchydro.com/community/recreation_areas/bridge_river.html.Accessed: August 4th, 2014.Benn, D. I., Warren, C. R., and Mottram, R. H. 2007. 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Annals of the Association of American Geographers,76(3):396–413.63Appendix AComparison of interpolationtechniquesA.1 IntroductionIn order to determine the most appropriate interpolation technique to utilise within thisstudy, preliminary analysis compared popular interpolation schemes to assess which ismost robust when predicting water temperatures and subsequently calculating the heatcontent for the distal basin of Bridge Lake over the 2013 melt season.A modified ‘leave-one-out’ cross-validation was used to assess the results of interpo-lation techniques. Due to the spatial distribution of observed water temperatures withinthis study, along with the limited number of observed points, it was possible to excludea number of interpolation schemes immediately. Triangulated Irregular Network (TIN)interpolation was not considered since all observed points were well within the distal basinboundary, causing a significant portion of the basin to be excluded from interpolation. Inaddition, predicted water temperatures were required across a regular grid in order tocalculate the heat content of uniform grid cells – TIN results would produce irregularlysized grid cells across the basin.Kriging techniques require a semivariogram to be generated for every interpolated sur-face – due to the limited number of observed points within this dataset, semivariogramsvaried substantially between each interpolation. Kriging results were, therefore, very un-reliable and difficult to interpret. In addition, due to the number of interpolated surfacesthat were required (for multiple depths and multiple time steps), it was necessary to usean automated kriging procedure, fitting a semivariogram model to each interpolation.Preliminary tests of this method, using the ‘autoKrige’ function within the ‘automap’64package in R (R Core Team, 2012), were disappointing. A large percentage of semivari-ogram models did not fit the data due to the package selecting an inappropriate model.In particular, the small number of data points did not allow for robust identification ofthe most appropriate semivariogram model. Kriging is commonly considered appropriateon datasets with a minimum of 30 data points in order to eliminate this variation betweensemivariograms (ASTM, 2010).Preliminary analysis compared Inverse Distance Weighting (IDW) and Nearest Neigh-bour (NN) interpolation schemes used to predict water temperatures (and subsequentlycalculate heat content) within the distal basin of Bridge Lake by removing individual lo-cations of observed water temperatures and re-running interpolations. Results were thencompared to a control heat content calculation and surface water temperature predictionscalculated using all locations of observed water temperatures.A.2 MethodologyThe distal basin was split into 20 × 20 m grid cells, providing 3529 ‘points of interest’(POI’s) across the basin surface for interpolation. NN interpolation was used to assigneach POI a depth, using the DEM of the lake bed generated from bathymetric data.NN interpolation was deemed the most appropriate, since lake depths were not expectedto express a smooth trend at the spatial resolution at which measurements were taken.Assigned depths allow POI’s to be excluded from interpolated surfaces which exist belowtheir depth (Figure A.1). This accounts for volume differences between interpolated layers.65A B C D E F G H I J K L M N O P Q R S T U V W X Y Z−7−6−5−4−3−2−10Depth (m)Point of interestLake bedFigure A.1: Schematic diagram displaying how POI’s are removed from interpo-lated surfaces exceeding their depth. All POI’s are included in the surface (0m) interpolated surface; Only POI’s coloured red are included in the inter-polated surface at 5 m depth. The grey area represents the non-uniformityof the lake bed.A.2.1 Overview of interpolation schemesIDW interpolation estimates water temperatures at each POI using values from all ob-served points, weighted by an inverse function of the distance of each observed point fromthe POI. Weights can be expressed as:λi =1/dpin∑i=11/dpi(A.1)where di is the distance between a POI (x0) and an observed point (xi), p is an exponentthat controls the distance-decay of influence and n is the number of sampled points usedwithin this interpolation (Li and Heap, 2014). Within this study, p was set to 2, giving‘inverse distance squared’ interpolation.NN interpolation estimates water temperatures at each POI by assigning the value ofthe nearest observed point. Perpendicular bisectors were drawn between sampled points(n) to produce ‘Voronoi polygons’ (Vi, i =1,2,. . . , n), used to assign observed values to66POI’s (Li and Heap, 2014). Resultant polygons contained an observed point (xi) in thecentre, and POI’s within each polygon are closer to xi than any other observed point.Weights assigned to POI’s are expressed as:λi =1 if xi ∈Vi,0 otherwise.(A.2)where Vi is a given polygon and xi is the nearest observed point within Vi. All POI’swithin Vi are assigned the water temperature measured at xi, giving T̂w(x0) = Tw(xi) (Liand Heap, 2014).A.2.2 Interpolation scheme testingIn order to compare interpolation schemes, a modified ‘leave-one-out’ cross-validation wasused. Water temperatures were initially estimated using data from all 8 observed points,giving a ‘control’ heat content calculation for both IDW and NN interpolations. Forsubsequent predictions (8) of water temperatures, one observed point was removed inturn, giving water temperature predictions using just 7 observed points. Each resultingheat content calculation was compared to the ‘control’.This cross-validation technique differs from the traditional ‘leave-one-out’ techniquesince the objective is not to test the ability of an interpolation to predict water tem-peratures at the location of the removed observed point, but to compare the impact ofremoving individual observed points on heat content calculations.In addition, spatial differences associated with removing different observed points wereidentified, by assessing differences in surface water temperature predictions at 12:00 onSeptember 12th 2013. Differences between surface water temperature predictions werecalculated and plotted to visualise the sensitivity of each interpolation scheme to hav-ing observed points removed. Tests were conducted on results from both IDW and NNinterpolation techniques.In addition to testing individual interpolation schemes, both ‘control’ heat contentswere compared to assess how differently IDW and NN interpolations affect heat contentestimates.67A.3 ResultsA.3.1 Heat contentFigure A.2 shows the relationship between both ‘control’ heat contents. An R2 of 0.998shows that there is little difference between the two results, with the largest differencesseen at the extremes.Heat content was calculated np times, where np is the number of profiles (np = 8).In each iteration, one profile was removed. These results were then compared to the‘control’ heat content for each interpolation scheme (IDW - Figure A.3; NN - Figure A.4).The results of each heat content calculation were compared to the ‘control’ by simplyconsidering the coefficient of determination (R2). IDW results produced a range of R2values from 0.983 - 0.999, whilst NN results produced R2 values ranging from 0.966 - 0.999.Results from both interpolation schemes show that removing profiles A – E produce themost variation, while profiles F – H had less of an impact on the heat content calculations.A.3.2 Surface water temperaturesSurface water temperature predictions were compared for a single time (12:00 on Septem-ber 12th). The purpose of this analysis was to assess whether differences in surface watertemperature predictions could be attributed to influences from removing specific profiles,different interpolation schemes, or whether they were within the error of the temperatureloggers (±0.2 ◦C).Figure A.5 shows the difference between surface water temperatures predicted usingall 8 profiles (‘control’) and removing each profile in turn using IDW interpolation. Re-sults from removing profiles AA, D, E and G show localised areas where differences aregreater than the ±0.2 ◦C accuracy of the temperature loggers. All other results show thatpredicted surface water temperatures are within the accuracy of the temperature loggers.Figure A.6 shows results using the NN interpolation scheme. Removing profiles A, AA,B, D, E and G introduced differences outside the accuracy of the temperature loggers. Itis also important to note that, typically, the area and magnitude of these differences tendsto be larger than those seen when using IDW interpolation.Differences in excess of the error of the temperature loggers are introduced on feweroccasions using the IDW interpolation scheme than NN, generating more consistent results.Large differences are observed between IDW and NN results, with respect to the area ofthe basin affected by differences in surface water temperature predictions. Despite large(small) areas of differences in surface water temperatures seen when using the NN (IDW)68lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllll llllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllll llllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllll llllllllllllllllllllllllllllllllllll llllllllllllllllllllllllll lllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll−500 0 500−5000500IDW ∆HC/∆tNN ∆HC/∆tR2 = 0.998Linear fit line1:1 lineFigure A.2: Scatter plot of both ‘control’ heat contents calculated using IDW andNN interpolation schemes. All units are in W m-2. All data were smoothedthrough time using a 3-point binomial filter.interpolation method, the average difference associated with removing a sampled pointfrom each interpolation is within the accuracy of the temperature loggers (±0.2 ◦C) acrossthe entire basin surface.69llllllll lllllllllll ll llllllllllll lllllll ll llllllllllllll lllll ll l lllllllllllll l ll lllll ll l lllllllll lll ll ll l l lllllllllllllll lllllllll l l lllllll llllllllllllllllllllll lllllllllllllllllllll lllllllll llllllllll l llllllllllllllllllll lllllllllllllllllll llllllllllllll lllllllll llllllllll llllllllllllll lllllllllll ll llllll ll llllllllllll lllllllll llllllllll llllllllllllllllllllll ll lllllllllllllllll llllllll lllllllllllllllll lllllllll llllllll ll llllllllllllllll l llllllllllllll lllllllll llll lllllll lllllllllllllllll l llllllllllll lllllllllllll ll lllllllllllllllll lllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllll lllllll llllllllllllll llllllllllllllllllllllllllllllllll lll llllllllllll llllllllll lllllllll llllllllll llllllll lllllllllllll lllllllllllllll lllll llll llllllllllllll lllllllllll llll llllllllllll llll llllllllllll llll llllllllll llllllllll lllllllll lllllllllllllll−500 0 500−5000500'A' removed (a)R2 = 0.9833llllllll lllllllllllll llllllllllll llllllll llllllllllllllll lllll ll ll lllllllllll l ll llllllll lllllllllll ll lll ll llllllllllllll lll llllllllll l ll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllll lllllll llllllllllllllllllllllll llllllll lllllllllllllllllll llllllllllll lllllllllllllllllllllllllllllllll llllllllllllll llllllll llllllllllllllllllll lllllllll llllllll lllllllll llllllll lllllllllllll llllllllllllllllllllll lllllll ll llllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllll lllllllllll l ll lllllllll llllll lllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllll lllllllllllllllllll llllll llllllll lllllllll llllllllllll lllllllll lll llllllllllll−500 0 500−5000500'AA' removed(b)R2 = 0.9939lllllllllllllllllllll llllllllllllllll llllllllllll lllllll lllllll llllll lll llllll lllll lllll lllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllll llllll lllllllllllll llllll lllllllllllll lllllllllllllllll llllllllllllllllllllll lllllllll lllllllllllllllllllllllllll llllllllllllllllllll lllllllllllllll lllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllll lllllllllllllll llllllllllllllllllllllllllllllllll llllllll ll llllll lllllllll l llllllll lllllll llllllllll llllllllllllllllllllll lllllllllllllllllllllll llllllllll lllllllllllllllllllllllllllllllllllllll ll llllllllllllllll lllll llllllllll llllllllllllllllllllllllllllllllllllllllllll llllllllllllll lll llllllllllllllllllllllll lllllllllllllllllllllllllllllllllllll−500 0 500−5000500'B' removed(c)R2 = 0.9898lllllllllllllllllllll llllllllllllllllllll llllllllllllllllllllll llllllll lllllllll llllllll lllll ll llllllllllll ll ll lllllll ll l llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllll llllllllll llllllllllllllllllllll lllllllll llllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllll lllll lllllllllll lllll lllllllllllllllllll llllllll lllllll lllllllllll llllllll lllll llllllllllllll llllll llllllllllllllllllllllll llllllllllllllll llllllllllllllllllllllllllllllllll lllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllll−500 0 500−5000500'D' removed(d)R2 = 0.9973llllllllllllllllllll l lllllllllllllllllllll llllllllllllll l ll llll lllllllll llllllll llllllllllll ll lll lll ll llllllllllll llllllllll ll lllllll llllllllllllllllllllllll llllllllllllll llllllllllllllllllll llllllllllllllll lllllllllll llllllllll llllllllllllll lllllllll lll llllll lllllllllll llllllll llllllllllll lllllllll llllllllllllllllll lllllllll llllll llllllllll lllll lllllllllllllllll lllllllllll llllllllll llllllllllllllll llllllllllllllllll l llllllllll llllllllllllll llllll llllll ll llllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llll lllll lllllllllllllllllllllllllllll lllllllllll lllll lllllllll lllllllllllllllllllllllllllllll lllllllll lllllllllllllllllll lllll lllllll llllllllllll llll lll lllllllllllllllllllllllllllllllllllllll lllllllllll lllllll llllllllllllllllll llllllllllll−500 0 500−5000500'E' removed(e)R2 = 0.9913lllllllllllllllllllll llllllllllllllll llllllllllll lllllll lllllll llllll lll llllll lllll lllll lllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllll llllll llllllllllllllllllllllll llllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllll lllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllll ll lllllllllllllllllllllllllllllll−500 0 500−5000500'F' removed(f)R2 = 0.9991lllllllllllllllllllll llllllllllllllll llllllllllll lllllll lllllll llllll lll llllll lllll lllll lllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllll llllll lllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllll llll l lll lllllllllllllllllll lllllllllllllllll lllllllllllllllllllllllll ll lllllllllllllllllllllllllllllllllllll−500 0 500−5000500IDW Control'G' removed(g)R2 = 0.9992lllllllllllllllllllll llllllllllllllll llllllllllll lllllll lllllll llllll lll llllll lllll lllll lllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllll llllll llllllllllllllllllllllllll llllllllllllll llll l ll llllllllll lllllllll llllllllllll lll lllllll llllll ll llllllllll llllllllll lllllllll llllllllllllllllll−500 0 500−5000500IDW Control'H' removed(h)R2 = 0.9996Linear fit line 1:1 lineFigure A.3: Scatter plots showing the relationship between the IDW ‘control’ re-sults and results calculated omitting profile (a) A; (b) AA; (c) B; (d) D; (e)E; (f) F; (g) G; (h) H. Axes represent ∆HC/∆t and all units are in W m-2.All data were smoothed using a 3-point binomial filter.70llllllllllllllllll ll lllllllllllllllllll ll l llllllllllllllllllll ll l l l llllllllllll ll ll lll ll l l llllllllll lllll ll l l l llllllllllllll ll lll llllllllll l llllllll llllllllll lllllllllllllllllllllllllllllllllll lllllllllllllllllllll ll lllllllllll lllllllllllll llllllllllllllllllll llllllllllllllllll llllllllllllllllllllllllllllllllllllll lllllllllll l lllllll ll lllllllll l llllllll llllllll llllllllllllllllllllllll llllllll lllllllllll lllllllllllllllllllllllllllllllllllll llllllll lllllllllllllllllll llllllllllllllllllllllllllllll llllllllllllll llllllllll lllllll lllllllllllllll llllllll lllll llllllllllllllll l llllllllllllllllllllllllllllllllllllll lllllll lllllllllll lllllllllllllll llllllllllll lllll lllllllllllll lllllllll lll lllllllllll ll ll lllllllllll llllllll llllllllllllll lllllllllllllll lllllllllll llllllllllllllllllll ll llllllll lllllllll lllllllllllllll llllll lllllll llllll ll lll llllllllllllllllllllllllllllll lllllll lll llllllll ll lll lllll llllllll llll lllll lllllllllllllllllllll lllll lllllllll lll llllll llllllll lllllllllll lll llllll l llllllllllllllllllllllllllll−500 0 500−5000500'A' removed (a)R2 = 0.9655lllllllllllllllllllllllllllllllll lllllllll lllllllllllllll ll ll lll ll lllllllllll l lllllllllllllllllllll ll lll ll llllllllllllllllll lllll llllllllll llllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllll llllllll lllllllllll lllllllll lllllll llllllllllll lllllll llllllllll ll l ll llllllllllllll lllllllll lllllllllllll l l ll llllllllllllll lllllllllllllllll llllllllllllllllll lllllllllllllll llllllllllllllll llllllllllllllllll llllll lllllllllllllllllllllllllllllllllllll llll ll ll ll lllllll llllllllll lllllllllll llllllllllllll lllllllllllllllllllllllllll lllllllllllllllllllllllllllllllll lllllllllllllllllllllllllll lllllllllllllllll llllllll llllllllllllllllllllllllllllllllll lllll llllllllllllllllllllllllllllllllllll llll llll llllll llllllllllllll lllllllllllll lllllll lllllllllllllllllllllllllllll−500 0 500−5000500'AA' removed(b)R2 = 0.9904lllllllllllllllllll lllllllllllllllllll lllllllllllll ll lllll llllllllllllll lllll lll llll llllllll llllll llllllllll llllllllll llllllllllllllllllllllllllll lllllllll llllllllllll lllllllll llllllllllll llllllllll lllllllllll llllllllllllllllllll lllllllllll llllllllll llllllllllllllllllllllllllll lllllllllllllllllllllllllllll lllllllll llllllllll llllllll lllllllllllllll lllllllllllllll lllllllll llllllllllllllllll llllllllllllllllllllllllllllll llllllllll l lll llllllllllllllll lllllll llllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll l llllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllll ll−500 0 500−5000500'B' removed(c)R2 = 0.9915lllllllllllllllllllllllllllllllllllllllll ll lllllllllllllllll ll ll lllllll lllllllll ll llllllllllllllll ll ll lllllll ll llll lllllllll ll llllllll lllllllllll llllllllllllllllllllllllllllllllllllllllllllllllll llllllllll llllllllll lllllllll llllllllll lllllllllllllllll lllllllllll lllll llllllllllllllllllll lllllllll l ll llllllll lllllll llllllllllllllllll llllllllllllllllll llllllll llllllllll lllllllllllllllllllllllllllllllllll lllllll lllllllllllllllllllllllllll llllll lllllllll llllll llllllllllllllllllllllllllllllllllllllllllllllll lllllllllllll lllllllllllllllllllllllll llllllllllllllllll lll lllllllllll llllll lllllllllllllllllllllllllllllllll llllllllllllllllllllll lll llll l lll llllllllll ll llll lll lllllllllllllllll llllllllllll−500 0 500−5000500'D' removed(d)R2 = 0.9942llllllllllllllllllll lllllllllllllllllllllllllllllllll ll llll ll llllll ll llllllll lllllllllllll ll lll lllllllll llllllllllllllllllllllllllll llllllllll lllllllllllllllll lllllllllllllllllll llllllll llllllllll lllllllllll lllllllllll llllllllllll lllllll lll ll llllllllll lllll llllllll llllll llllllll lllllllllllllllll lllllll lll lllllllll llllllllllllllllllllllllllllll lllllll llllll llllllllllllll lllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllll llll llll lllllll llllll llllllllllllllllllllllllllllllllllllllllll llll llll lllllllllllllllll llllllllllll l l lll llllllllllllllllllllllllllllllll−500 0 500−5000500'E' removed(e)R2 = 0.997lllllllllllllllllll lllllllllllllllllll lllllllllllll ll lllll llllllllllllll lllll lll llll llllllll llllll llllllllll llllllllll llllllllllllllllllllllllllll lllllllll lllllllllllllllllll lllll llllll llllll llllllllllllllllll llllllllllllllllllllllllllllllllll lllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllll−500 0 500−5000500'F' removed(f)R2 = 0.9996lllllllllllllllllll lllllllllllllllllll lllllllllllll ll lllll llllllllllllll lllll lll llll llllllll llllll llllllllll llllllllll llllllllllllllllllllllllllll lllllllll lllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllll llllllllllllllllll lllllllllll llllllllllll lllllllllllllllllllllll lllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllll lllllllllllllllllllllllllllllllllllll−500 0 500−5000500NN Control'G' removed(g)R2 = 0.999lllllllllllllllllll lllllllllllllllllll lllllllllllll ll lllll llllllllllllll lllll lll llll llllllll llllll llllllllll llllllllll llllllllllllllllllllllllllll lllllllll lllllllllllllllllll lllllllllllll lllll ll l ll llllllllllllll llll lllll lllllllll ll llllll llllllllllllll lllllll lllllll lllllllll lllllllllllllllllll lllll−500 0 500−5000500NN Control'H' removed(h)R2 = 0.9997Linear fit line 1:1 lineFigure A.4: Scatter plots showing the relationship between the NN ‘control’ resultsand results calculated omitting profile (a) A; (b) AA; (c) B; (d) D; (e) E; (f)F; (g) G; (h) H. Axes represent ∆HC/∆t and all units are in W m-2. Alldata were smoothed using a 3-point binomial filter.71Easting (m)Northing (m)5632500563300056335005634000llllllll AAABDEFGHMissing A 465000 465500 466000llllllll AAABDEFGHMissing AAllllllll AAABDEFGHMissing B 465000 465500 466000llllllll AAABDEFGHMissing D465000 465500 466000llllllll AAABDEFGHMissing Ellllllll AAABDEFGHMissing F465000 465500 466000llllllll AAABDEFGHMissing G5632500563300056335005634000llllllll AAABDEFGH0 500 mMissing H−0.8−0.6−0.4−0.20.00.20.40.60.8Tw (°C)Figure A.5: Difference in surface water temperature predictions between the ‘control’ predictions and results from re-moving each profile, using the IDW interpolation scheme. Panel names identify which profile has been removedfrom each interpolation.72Easting (m)Northing (m)5632500563300056335005634000llllllll AAABDEFGHMissing A 465000 465500 466000llllllll AAABDEFGHMissing AAllllllll AAABDEFGHMissing B 465000 465500 466000llllllll AAABDEFGHMissing D465000 465500 466000llllllll AAABDEFGHMissing Ellllllll AAABDEFGHMissing F465000 465500 466000llllllll AAABDEFGHMissing G5632500563300056335005634000llllllll AAABDEFGH0 500 mMissing H−0.8−0.6−0.4−0.20.00.20.40.60.8Tw (°C)Figure A.6: Difference in surface water temperature predictions between the ‘control’ predictions and results from re-moving each profile, using the NN interpolation scheme. Panel names identify which profile has been removedfrom each interpolation.73A.4 DiscussionA.4.1 Heat contentDifferences between IDW and NN interpolation schemes have little importance when cal-culating the total heat content of the distal basin of Bridge Lake. When using all datacollected, both interpolation schemes performed similarly due to the scale at which theseare applied. Observed similarities are likely because of differences in the heat content ofindividual grid cells (≈ 200 m3), which result from differences in predicted water temper-atures, becoming insignificant when the heat content of the total basin (4.7 × 106 m3) iscalculated.When considering which interpolation scheme is more robust in terms of generatingreliable results repeatedly, it is difficult to chose between IDW and NN. Differences inheat content results when removing observed points, regardless of which interpolationscheme is used, are dependent on which sampled point is removed. This suggests thatsome points have a more significant influence over larger areas of the distal basin thanothers. Particularly, including data from profiles F and G appears to stabilize heat contentcalculations. This is likely due to the large number of POI’s that are heavily weighted infavour of water temperatures measured at these locations as a function of their proximityto other observed points. These results suggest that it is not the interpolation schemesthemselves which influence results, rather the number and location of observed pointsincluded in analysis.Greater differences between ‘control’ heat contents and results excluding profile B isexpected to be a result of its proximity to large icebergs and resultant cold water enteringthe study basin. Profile B is the only profile subjected to decreased water temperaturesfrom cold inflow, causing the removal of this profile likely to result in the over estimationof the total heat content. However, this is not the case, suggesting that POI’s heavilyinfluenced by data collected at profiles A and AA provide a buffer to cold water inflows.The greater difference and variation in heat content calculations returned by removingProfile A can be attributed to the vertical extent of this profile. At the beginning of theseason, Profile A was the only profile extending to a depth of 5 m. All other profiles had amaximum depth of up to 4 m. As a result, by excluding Profile A, no interpolated surfacecan be created at a depth of 4.5 or 5 m until the time when Profile B was deployed. Thisomits 4.2 × 105 m3 of the water volume within the distal basin – not an insignificantamount.At this scale, removing an observed point from analysis does not produce significantlydifferent results. However, this may not be the case if interpolations were used at different74spatial scales, particularly if the interest is on small-scale physical processes.A.4.2 Surface water temperaturesComparing surface water temperature predictions generated with individual observedpoints removed provides evidence of clear differences between IDW and NN interpolationschemes. Localized areas of difference beyond the accuracy of the temperature loggersare observed using the IDW interpolation scheme when profiles D, E and G are removed.Aside from these three results, removing other observed points generated differences whichcan be accounted for by the accuracy of the temperature loggers. IDW results contrastwith spatial differences associated with the NN interpolation scheme, which propagateacross larger areas of the distal basin. These results are likely because each sampled pointis ‘responsible’ for water temperature values assigned to a larger number of POI’s, and noadjustment is made to account for the relative distance to each sampled point. Regardlessof the interpolation scheme, all differences are a factor of the proximity of a given observedpoint to others and the relative area of the basin that is weighted heavily in favour of thatpoint.Surface water temperature predictions when profiles D and E are removed individuallyreturn the largest differences to the ‘control’ results regardless of the interpolation schemeused. This suggests that these profiles may exhibit different water temperatures thanother profiles, making them more important to produce a realistic prediction of surfacewater temperatures.It is interesting to note that removing observed points when using the NN interpolationscheme results in the majority of the surface water temperatures being under-predictedcompared to the ‘control’ result. However, IDW results are less consistent, with the resultdependent on the observed point being removed.Although differences are sensitive to which observed point is removed, the average dif-ference associated with removing observed points is within the accuracy of the temperatureloggers, across the entire basin surface. This is true for both IDW and NN interpolationschemes. This suggests that the removal of individual observed points is not a limitingfactor for successful interpolations.A.5 ConclusionsInterpolation schemes can generate different results and interpretations depending on thescale at which they are applied. Preliminary analysis has found that when considering75interpolations directly (surface water temperatures), IDW and NN produce different re-sults as a function of their inherently different mathematical basis. However, when theseresults are up-scaled to provide measures of heat content within the distal basin of BridgeLake, the results generated do not display significant differences.It is important to consider the influence of measurement error introduced when initiallycollecting data in the field. The average difference associated with removing individualobserved points is within the error of the temperature loggers. As a result, it is suggestedthat any differences introduced by the choice of interpolation are small enough (< ±0.2◦C) to not have a significant influence on results within this study.Surface water temperature predictions were more consistent using the IDW interpo-lation scheme, with only localised areas of differences outside the error of temperatureloggers. Clear differences between IDW and NN schemes were observed when predictingwater temperatures, but no significant differences existed between heat content results.Removing observed points close to the basin inflow generated larger differences in thecalculated heat content, likely due to increased uniformity of water temperatures closer tothe outflow. It is not conclusive whether these results are indicative of the interpolationschemes themselves, or simply the format of this particular study. However, for the pur-poses of analysing these data and comparing the measured heat content of the distal basinwith that modelled from surface energy fluxes and advective flows through the basin, theresults are informative enough. The observed behaviour of IDW interpolation is deemedto provide the most realistic prediction of how water temperatures change across a surface,thus, IDW interpolation is used to generate all results requiring interpolation within thisstudy.76

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