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Streamflow response during the rapid retreat of a lake-calving mountain glacier Moyer, Alexis 2015

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Streamflow response during the rapidretreat of a lake-calving mountainglacierbyAlexis MoyerB.Sc., Gettysburg College, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Geography)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2015c© Alexis Moyer 2015AbstractThere has been increasing attention over the last decade to the potential effects of glacierretreat on downstream discharge and aquatic habitat. Of particular interest is the timingof "peak water," when the reduction in ice area associated with retreat begins to offset theincreased rate of climatic warming-induced melt. This study examines streamflow vari-ability downstream of Bridge Glacier, in the southern Coast Mountains of BC. The glaciercurrently calves into a proglacial lake, and has been retreating rapidly since 1991, when theterminus retreated into an over-deepened basin. Despite the glacier’s areal decrease from92 km2 in the early 1990s to 81 km2 in 2014, interannual climatic variability has obscuredany resulting reductions in late-summer streamflow.The objective of this study was to diagnose trends in streamflow, as associated with theaccelerating retreat of a lake-calving glacier, examining the role of calving and retreat onthe magnitude and timing of summer streamflow, as well as the persistence of icebergs inthe basin. Snow melt, ice melt, and rainfall-runoff were estimated using a semi-distributedhydrological model, with glacier area determined from Landsat imagery. Two seasonaldischarge trends were observed, an increase in winter flow attributed to ice discharge intothe lake, and a decrease in late-summer flow attributed to decreasing glacier area behindthe grounding line. Decreasing streamflow trends suggested that the glacier has passedpeak water, and that streamflow will continue declining with reducing glacier area.Surface and subaqueous iceberg melt were computed using an energy-balance approach,assuming that net radiation received by the ice-proximal basin was consumed by subaque-ous melt and heating of 0◦C melt water. Fractional iceberg cover in the proximal basin wasdetermined by spectral unmixing of Landsat imagery. Estimated melt volumes suggestedthat in the absence of large calving events, icebergs persist for roughly a year, with highfractional iceberg cover allowing for persistence into a second year. The results from thisstudy contribute to our understanding of streamflow response for retreating valley glaciers,many of which will likely experience a transient lake-terminating phase as the terminusretreats into over-deepened basins.iiPrefaceThis thesis is original work completed by the author. Guidance was given by the supervi-sory committee (Dan Moore, Michele Koppes, and Brett Eaton) and field assistance wasprovided by Lawrence Bird, Julia Newton, and Mark Richardson.A version of this work has been published as a poster (Moyer, A., Moore, RD. andKoppes, M. Streamflow response during the rapid retreat of a lake-calving mountain glacier)on which the author acted as lead investigator, composing and presenting the poster atthe 2015 Canadian Geophysical Union (CGU)/American Geophysical Union (AGU) JointAssembly.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation for the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.1 The peak water concept . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Proglacial lake formation and thermal regime . . . . . . . . . . . . . 51.3 A conceptual model of streamflow response to lake-calving . . . . . . . . . 71.4 Research questions and thesis structure . . . . . . . . . . . . . . . . . . . . 102 Study area and methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1 Study area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Meteorological data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Hydrological data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3.1 South Creek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3.2 West Creek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4 Statistical analysis of Bridge River streamflow data . . . . . . . . . . . . . 202.4.1 Trend analysis for monthly hydroclimatic data . . . . . . . . . . . . 202.4.2 Summer trends in discharge with climatic variability . . . . . . . . 202.5 Deterministic analysis and modelling . . . . . . . . . . . . . . . . . . . . . 212.5.1 First-order approximation of calving flux . . . . . . . . . . . . . . . 212.5.2 Glacio-hydrologic modelling . . . . . . . . . . . . . . . . . . . . . . 22ivTable of Contents2.6 Iceberg mixing dynamics and melt rates . . . . . . . . . . . . . . . . . . . . 242.6.1 Linear spectral mixture analysis of Landsat imagery . . . . . . . . . 242.6.2 Time lapse camera imagery . . . . . . . . . . . . . . . . . . . . . . . 272.6.3 First-order approximation of iceberg melt rates . . . . . . . . . . . 272.6.4 An energy balance approach to iceberg melt . . . . . . . . . . . . . 293 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.1 Overview of study period . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2 Statistical analysis of Bridge River streamflow . . . . . . . . . . . . . . . . 383.3 Deterministic analysis and modelling . . . . . . . . . . . . . . . . . . . . . 423.3.1 Estimated calving flux . . . . . . . . . . . . . . . . . . . . . . . . . 423.3.2 Glacio-hydrologic modelling . . . . . . . . . . . . . . . . . . . . . . 433.4 Iceberg variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.4.1 Iceberg mixing dynamics . . . . . . . . . . . . . . . . . . . . . . . . 453.4.2 Iceberg melt rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.1 Seasonal trends in discharge . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Lake-terminating glaciers and peak water . . . . . . . . . . . . . . . . . . . 504.3 Iceberg persistence and lake thermal regime . . . . . . . . . . . . . . . . . 504.4 A dual-method approach to trend analysis . . . . . . . . . . . . . . . . . . 525 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.1 Key findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.2 Future research directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55A Linear spectral mixture analysis extended methodology . . . . . . . . . 62vList of Tables1.1 Summary of previous observational studies on the effects of retreating glacierson streamflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Summary of previous projectional studies on the effects of retreating glacierson streamflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Instrument specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Most responsive HBV-EC parameters, with calibrated values from Stahlet al. (2008). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3 Wavelengths and spatial resolution of Landsat imagery used in analysis. . . 263.1 Mann-Kendall τ -values for monthly trends in streamflow, air temperature,number of melt days, and rain (n = 36). . . . . . . . . . . . . . . . . . . . . 383.2 Medians of monthly mean Bridge River streamflow, air temperature, andrainfall for pre- and post-1991 periods for December, January, and February(n = 36). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3 Adjusted R2 and associated p-values (in brackets) for multiple regressionsfor predicting monthly streamflow as a function of monthly air temperatureand rainfall (n = 29). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.4 Estimated coefficients, standard error of estimate, adjusted R2 and p-valuefor regression fits to Eqs. (2.10, 2.11, and 2.12), along with Kruskal-Wallischi-squared values for the residuals (n = 36). . . . . . . . . . . . . . . . . . 403.5 Changes in median discharge from late-summer and melt season multipleregression models and hydrological model over three periods of time (n = 31). 413.6 Estimated ice-proximal basin-wide iceberg melt rates and volumes for studyperiod (May 1 to September 23, 2014). . . . . . . . . . . . . . . . . . . . . . 46A.1 Dates of Landsat 4-5 MSS/TM and 7 ETM+ acquisitions. . . . . . . . . . . 68viList of Figures1.1 Graphic representation of the long-term effect of shrinking glacier volume(a) on streamflow (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Phases of a lake-calving glacier (a-d). . . . . . . . . . . . . . . . . . . . . . . 92.1 Map of study area, including Bridge Glacier, Bridge Lake, and the locationsof the time lapse camera, automatic weather stations (ridge top (RT) andlake-side (LS)), and the Water Survey of Canada gauging station. . . . . . . 122.2 Map showing locations of weather stations across the study region. . . . . . 132.3 Lake side (LS) weather station. . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Linear model used to predict daily precipitation (RLS) at the lake side (LS)station from daily precipitation at the Upper La Joie (ULJ) station. . . . . 152.5 Linear models used to predict air temperature, atmospheric vapor pressure,and incident shortwave radiation at the lake side (LS) station. . . . . . . . . 162.6 Rating curve for South Creek. . . . . . . . . . . . . . . . . . . . . . . . . . . 192.7 Linear models used to predict mean monthly air temperature (a) and totalmonthly precipitation (b) at the ULJ station based on values from Cli-mateWNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.8 Reflectance for fresh snow, glacier ice, and debris-covered glacier ice in thevisible, near-infrared, and mid-infrared parts of the electromagnetic spectrum. 252.9 Photographs of time lapse camera set-up. . . . . . . . . . . . . . . . . . . . 282.10 Photographs of painted rocks used to mark icebergs (a) and an example ofpainted rocks on sample iceberg (b). . . . . . . . . . . . . . . . . . . . . . . 292.11 Division of sample iceberg into triangles for surface area and volume esti-mations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1 Maximum, mean and minimum mean monthly air temperatures from theULJ weather station from the 1984 to 2014 melt seasons. . . . . . . . . . . 353.2 Maximum, mean and minimum mean daily discharge from the WSC gaugingstation for the 1979 to 2014 melt seasons. . . . . . . . . . . . . . . . . . . . 353.3 Meteorological variables monitored at the lake side (LS) station during thestudy period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.4 Hydrological and related variables measured during the study period. . . . 37viiList of Figures3.5 Trends in Bridge River discharge (QBR), air temperature (Ta), number ofmelt days (Ta > 0◦C), and precipitation as rain for December, January, andFebruary from 1979 to 2014. . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.6 Bridge River streamflow (QBR), mean monthly air temperature (Ta), andtotal monthly precipitation as rain for August, September, and the meltseason (May to October) from 1979 to 2014. . . . . . . . . . . . . . . . . . . 413.7 Time series of regression residuals for mean August (a), September (b), andmelt season (c) discharge from 1979 to 2014. . . . . . . . . . . . . . . . . . . 423.8 Observed and modelled dynamic discharge for the Bridge watershed for thepost-calibration period (1996 to 2014). . . . . . . . . . . . . . . . . . . . . . 433.9 Modelled mean discharge for August (a), September (b), and the melt season(May-October)(c) for the entire study period using the 1984, 2014, andchanging glacier extents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.10 Difference between modelled monthly and seasonal mean discharge withchanging glacier extent, compared to discharge modelled using the 1984glacier extent as baseline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.11 Fractional iceberg cover in the proximal basin derived from the linear spec-tral mixture analysis from 1984 to 2014. . . . . . . . . . . . . . . . . . . . . 463.12 Volumes of surface, subaqueous, and total iceberg melt as a function offractional ice cover for the 2014 (solid lines) and 2013 (dashed lines) studyperiods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47A.1 Brightness map from pixel purity index (PPI) performed on Landsat imageacquired for July 28, 2014. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63A.2 Landsat image (bands 1-4) acquired for July 28, 2014. . . . . . . . . . . . . 63A.3 Digital number and corresponding Landsat band for end-member spectraused in the LSMA of Landsat image acquired for July 28, 2014. . . . . . . . 64A.4 Spectrally unmixed image from Landsat scene acquired for July 28, 2014. . 64A.5 A comparison of spectral unmixing results of iceberg surface area in theproximal basin performed using two and three end-members. . . . . . . . . 65A.6 Photographs of icebergs in the proximal basin of Bridge Lake demonstrat-ing the spectral variability of icebergs during the melt season (a) and thepresence of blue ice on the now-exposed undersides of flipped icebergs (b). . 66viiiList of SymbolsSymbol Descriptionαi Albedo of ice surfaceαw Albedo of water surfaceA Area under curve of salt concentration (g s m−3)Alake Lake basin surface area (m2)Aprox 2014 proximal basin surface area (m2)cpa Specific heat capacity of air (J kg−1 K−1)cpw Specific heat capacity of water (J kg−1 K−1)ct Concentration of injected salt (g m−3)CF Salt dilution concentration factor (g m−3 µS−1 cm−1)D Turbulent transfer coefficientea Atmospheric vapor pressure (kPa)esat Saturation vapor pressure (kPa)ew Water surface vapor pressure (kPa)ε Clear sky emissivityεi Emissivity of water and ice surfacesεw Emissivity of water and ice surfacesE Evapotranspiration (m s−1)EC Electrical conductivity (µS cm−1)fice 2014 fractional ice coverg Gravitational acceleration (m s−2)h Ice thickness at the calving front (m)HF Critical flotation thicknessHC Lake heat content (W m−2)k von Karman constantK ↓ Incident shortwave radiation (W m−2)Lf Latent heat of fusion (J kg−1)Lv Latent heat of vaporization (J kg−1)L ↓ Incident longwave radiation (W m−2)m Number of Landsat bandsM Mass of salt (kg)Msub Subaqueous iceberg melt volume (m3)ixList of SymbolsMsurf Surface iceberg melt volume (m3)Mtot Total iceberg melt volume (m3)P Barometric pressure (kPa)Qe(i) Latent heat flux over ice surface (W m−2)Qe(w) Latent heat flux over water surface (W m−2)Qgf Ice discharge into lake (m3 s−1)Qh(i) Sensible heat flux over ice surface (W m−2)Qh(w) Sensible heat flux over water surface (W m−2)Qout Streamflow exiting basin outlet (m3 s−1)Qm Runoff from surface snow and ice melt (m3 s−1)Qn(i) Net energy flux over ice surface (W m−2)Qng Runoff from non-glacier sources (m3 s−1)Qp(i) Precipitation energy flux over ice surface (W m−2)Qp(w) Precipitation energy flux over water surface (W m−2)Qr(i) Net radiation flux over ice surface (W m−2)Qr(w) Net radiation flux over water surface (W m−2)ρa Air density (kg m−3)ρi Ice density (kg m−3)ρw Water density (kg m−3)R Precipitation (m s−1)Rb Pixel reflectanceRB Bulk Richardson numberRH Relative humidity (%)σ Stefan-Boltzmann constant (W m−2 K−4)S Stage (m)Θ Stability correction factorTa Air temperature (◦C)Ti Ice surface temperature (◦C)Tmelt Melt water temperature (◦C)Tref Reference temperature (◦C)Tw Mean surface water temperature (◦C)TK Mean temperature of air layer (K)u Wind speed (m s−1)v Mean glacier velocity (m s−1)V Ice-proximal basin volume (m3)w Width of glacier calving front (m)Za Height at which Ta and u are measured (m)Z0 Roughness length for momentum (m)Zx Roughness length for vapor pressure and air temperature (m)xAcknowledgementsMany people have been influential throughout the process of completing this research.First and foremost, my sincere thanks goes to my two supervisors, Dan Moore and MicheleKoppes, without whom this work would never have come to fruition. Dan’s endless energyand encouragement both in the field and in the office was an inspiration, as was his assis-tance making sure my first camping trip at the glacier ran smoothly. Michele’s guidance inthe field and in thinking creatively about methodology was invaluable, encouraging me tothink outside the box and become a more independent researcher. I am grateful to both ofmy supervisors, as well as my third reader, Brett Eaton, for their constructive commentsduring the thesis writing process.Funding was provided by operating grants to Professor Dan Moore and Michele Koppesfrom the Natural Sciences and Engineering Research Council (NSERC) of Canada. Theauthor was supported by a Graduate Award from the UBC Faculty of Arts as well as aGraduate Student Research Grant from the Geological Society of America (GSA).Special thanks go to Lawrence Bird for always being willing to listen to and provideadvice for solving many of my technical issues, both in the office and in the field. Thanksalso goes to Matt Chernos for his assistance with time lapse camera programming and toJoel Trubilowicz for patiently providing hours of modelling suggestions. Julia Newtown isthanked for spectacular field and camping assistance, as is Mark Richardson, for teachingme everything I’d possibly need to know about dilution salt gauging and for being the bestfirst mate while boating around enormous icebergs.I would also like to thank the Environmental Studies Department at Gettysburg College,and in particular Professor Sarah Principato, for instilling in me a passion for glaciologyresearch and for being a wonderful academic mentor and friend. Additionally, I would notbe where I am today without the experience of traveling to Kangerlussuaq, Greenland withthe Danish Institute for Study Abroad, where my interest in climate and ice studies wasfurther ignited.Additional thanks to my long-distance friend Trisha Gabbert for being a great soundingboard for all my ideas and for keeping me sane these past two years. Finally, I’d like tothank my family for their loving support and patience over the years, and for alwaysencouraging me to pursue my interests, even if it means moving across the country.xiChapter 1Introduction1.1 Motivation for the studyMountain glaciers play an important role in moderating the inter-annual variability ofstreamflow, in particular by maintaining flow during warm, dry weather in late summerand early autumn. In addition, glaciers moderate stream temperatures, providing a coolinginfluence during warm, dry weather (Fleming and Clarke, 2003; Jansson et al., 2003; Stahlet al., 2008). The prolonged retreat of mountain glaciers worldwide since the Little IceAge and continued retreat into the 21st century will undoubtedly affect the timing andextent of late-summer streamflow (Hock et al., 2005; Oerlemans, 2005; Marshall et al.,2011). Predicted reductions and increased annual variability in glacier-fed streamflowhas important implications for water resource management and the protection of aquatichabitat (Jansson et al., 2003; Stahl et al., 2008; Milner et al., 2009). In addition, reducedstreamflow from sustained glacier retreat could have serious effects on human populationsthat depend on glaciers as a fresh water source (Mark and McKenzie, 2007).Many studies have focused on the response of annual and late-summer streamflow toreduced alpine glacier areas worldwide, resulting in the development of the "peak water"concept, the time at which the reduction in ice area associated with retreat begins to offsetthe increased rate of ice melt associated with climatic warming (Tables 1.1 and 1.2). Thesestudies have focused on the hydrologic consequences of the retreat of land-terminatingglaciers. However, the retreat of valley glaciers will sometimes result in the formation ofproglacial lakes as over-deepened bedrock basins are exposed. Glaciers that terminate inlakes typically retreat at an accelerated rate due to the calving of floating termini, whichleads to instability of the ice margin and subsequent rapid mass loss (Warren and Kirkbride,2003; Post et al., 2011). Therefore, streamflow from lake-calving glaciers is expected torespond differently to shrinking glacier volume, reaching peak water at different times, andwith different rates, than from land-terminating glaciers.The objective of this study is to diagnose streamflow variability at a proglacial stream11.1.MotivationforthestudyTable 1.1: Summary of previous observational studies on the effects of retreating glaciers on streamflow, where LT and LCindicates land-terminating and lake-calving glaciers, respectively, and NS indicates not-specified. An observation of ↑ Q and ↓ Qindicate increasing and decreasing discharge, respectively. The combination of the two indicate an increase in discharge followedby a decrease. Current phase indicates response phase of peak water.Study Location Basin area Glacier Glacier Time Observation Current(river(s)) (km2) cover (%) type phaseFleming Wann, BC CA 269 NS LT 1964-1993 ↑ Q 1and Clarke White, YK CA 6240 NS LT 1975-1999 ↑ Q 1(2003) Kluane, YK CA 4950 NS LT 1953-1995 ↑ Q 1Takhini, YK CA 4070 NS LT 1965-1986 ↑ Q 1Alsek, YK CA 16200 NS LT 1975-1999 ↑ Q 1Collins Lonza, CH 77.8 36.5 LT 1966-2004 ↑ Q, ↓ Q 3(2006) Rhone, CH 38.9 52.2 LT 1966-2004 ↑ Q, ↓ Q 3Massa, CH 195 65.9 LT 1931-2004 ↑ Q 1Stahl and BC, CA NS 0.015 - 61.7 LT 1976-1996 ↓ Q 3Moore (2006)Brabets et al. Tanana, AK US 66,300 6 LT 1962-2005 ↑ Q 1(2009) Yukon, AK US 831,000 1 LT 1956-2005 ↑ Q 1Baraer et al. Marcara, PE 221 19.5 LT 1953-1996 ↑ Q, ↓ Q 3(2012) Colcas, PE 237 17.4 LT 1954-1996 ↑ Q, ↓ Q 3Rio Santa, PE 4768 7.2 LT 1954-2008 ↑ Q, ↓ Q 3Los Cedros, PE 114 18.5 LT 1954-1999 ↑ Q, ↓ Q 3Pachacoto, PE 194 6.9 LT 1953-1996 ↑ Q, ↓ Q 3Paron, PE 49 38.7 LT 1953-1983 ↑ Q 1Querococha, PE 62 2 LT 1953-1995 ↑ Q, ↓ Q 3Engelhardt Alfotbreen, NO 8.3 51 LT 1961-2012 ↑ Q 1et al. (2014) Nigardsbreen, NO 66 72 LT 1961-2012 ↑ Q 1Storbreen, NO 8.0 65 LT 1961-2012 ↑ Q 1Duethmann Kakshaal, CN 18,410 4.4 LT 1957-2004 ↑ Q 1et al. (2015) Sari-Djaz, CN 12,950 21 LT 1957-2004 ↑ Q 121.1.MotivationforthestudyTable 1.2: Summary of previous projectional studies on the effects of retreating glaciers on streamflow, where LT and LCindicates land-terminating and lake-calving glaciers, respectively, and NS indicates not-specified. An observation of ↑ Q and ↓ Qindicate increasing and decreasing discharge, respectively. The combination of the two indicate an increase in discharge followedby a decrease.Study Location Basin area Glacier Glacier Time Observation(river(s)) (km2) cover (%) typeSingh and Spiti, IN 10071 2.5 LT 1987-1990 ↑ QKumar (1997)Braun et al. Vernagtbach, AT 11.4 79 LT 1974-1995 ↑ Q(2000) Rofenache, AT 98.2 41 LT 1982-1995 ↑ Q, ↓ QVenter Ache, AT 164.7 38 LT 1982-1992 ↑ QHuss et al. Zinal, CH 17.5 65 LT 2007-2100 ↑ Q, ↓ Q(2008) Moming, CH 9.5 63 LT 2007-2100 ↑ Q, ↓ QWeisshorn, CH 6.9 39 LT 2007-2100 ↑ Q, ↓ QPrasch et al. Lhasa, CN 26339 2 LT 1970-2080 ↑ Q(2013)Stahl et al. Bridge, BC CA 152.4 61.8 LC 2004-2095 ↓ Q(2008)31.2. Backgroundprior to and during a period of accelerated retreat following formation of a proglacial lakeand associated mass loss by calving. The role of calving and retreat on the magnitude andtiming of summer flow is also examined, as is the persistence of icebergs in the lake basin.1.2 Background1.2.1 The peak water conceptMany studies of highly glacierized basins have focused on the response of streamflow tothe reduction of land-terminating glaciers (Tables 1.1 and 1.2). Through the use of bothhistorical and modelled data scenarios, four main phases of response have been identified(Figure 1.1). The first phase is marked by initially enhanced streamflow with decreasingglacier volume. As snow melts from lower elevations, the transient snowline of the glacierrises to higher elevation, exposing bare ice for melting and offsetting the areal ice lossexperienced at lower elevations (Collins, 2006). In the second response phase, streamflowcontinues to increase until a maximum is reached, known as peak water, at which timethe loss of surface area by terminal retreat compensates for the effect of higher snowlines(Braun et al., 2000; Jansson et al., 2003; Mark and McKenzie, 2007). It is unclear whenexactly this state of maximum streamflow occurs. However, studies in Europe and SouthAmerica demonstrated increasing streamflow for several decades before reaching a maxi-mum, followed by a decline (Braun et al., 2000; Collins, 2006; Huss et al., 2008; Baraeret al., 2012). In the third phase, the decrease in surface area caused by terminal retreatresults in a reduction in meltwater generation and consequently a declining trend in stream-flow (Collins, 2006). Finally, in phase four, streamflow continues a slow decrease until anew equilibrium is reached (Braun et al., 2000).Several observational studies of historical streamflow data suggest that many of theworld’s mountain glaciers are currently in the first phase, experiencing anywhere from threeto five decades of increased streamflow despite significant reduction in glacier area (Flemingand Clarke, 2003; Brabets and Walvoord, 2009; Engelhardt et al., 2014; Duethmann et al.,2015). Studies by Singh and Kumar (1997), Braun et al. (2000), and Prasch et al. (2013)suggest that streamflow from glaciated catchments will continue to increase for severaldecades under future climatic scenarios with increased air temperature and further reducedglacier area. In addition, it is suggested that basins in the Alps will reach peak waterstreamflow within the next three to four decades, followed by significant decreases in flow41.2. Background(Braun et al., 2000; Huss et al., 2008).In contrast, observational studies in western Canada and Peru indicate that manymountainous drainage basins have already passed peak water and are currently in phase3, experiencing reduced streamflow (Stahl and Moore, 2006; Baraer et al., 2012). A fu-ture climate scenario study by Stahl et al. (2008) supports this observation, modellingdecreased streamflow for the Bridge River basin in British Columbia, Canada, from 2004to 2095. However, no significant decreases in late-summer streamflow have been recordeddownstream to date. TIME B A STREAMFLOW GLACIER VOLUME PHASE 1 PHASE 2 PHASE 3 PHASE 4 V (m3 ) t Q (m3  yr-1) Figure 1.1: Graphic representation of the long-term effect of shrinking glacier volume (a) on stream-flow (b). See text for description of phases. Adapted from Jansson et al. (2003).1.2.2 Proglacial lake formation and thermal regimeProglacial lakes form when retreating glaciers expose over-deepened valleys, where meltwater draining from the glacier is bound by ice, sediment, or bedrock and begins to collect(Masetti et al., 2009; Benn and Evans, 2010; Carrivick and Tweed, 2013). Many proglaciallakes form where the glacier terminus is not in contact with the lake, and no calving willoccur. Other proglacial lakes are ice-contact lakes, where the ice front terminates in thelake, if the produced meltwater is sufficient to fill the basin. The position of the terminus51.2. Backgroundwithin an ice-contact lake is dependent upon three main factors: the water depth, theice thickness, and the rates of ice flow and calving (Holdsworth, 1973; Benn and Evans,2010). Crevasse development, glacier thinning, and rising lake levels due to increased meltbehind the grounding line result in episodic calving from the terminus (Masetti et al., 2009;Trussel et al., 2013). A glacier terminus will transition from grounded to floating if surfacemelt thins the ice thickness at the terminus below a critical flotation thickness, HF , basedon the densities of ice and water. For fresh water lakes, HF is approximately 1.1 timesthe water depth at the terminus location (Benn and Evans, 2010). Studies of ice-contactlakes with floating termini in New Zealand found that calving events primarily consist offrequently occurring low magnitude events (10 - 102 m3 of ice) from the subaerial part ofthe terminus, as well as periodically occurring high magnitude events (103-104 m3) fromboth the subaerial and subaqueous parts of the terminus (Warren and Kirkbride, 1998).The direct surface and subaqueous melting of the ice front accounts for most lake inflow.Glacier-fed lakes tend to remain colder than non-glacier-fed lakes, and thus maintaincooler water in their outlet streams (Uehlinger et al., 2003; Robinson and Matthaei, 2007).This cooling effect, similar to that of a shady stream reach, is necessary for the survival ofmany organisms, such as salmonids and small invertebrates (Fleming, 2005; Milner et al.,2009). Water temperature has many impacts on lake and stream characteristics, includingdissolved oxygen levels, species distribution and growth rates, and various chemical andbiological processes (Webb et al., 2008).The thermal regime of proglacial lakes depends on many factors, including basin sizeand structure, seasonal variations in meteorological conditions, and lake inflow and outflowrates (Chikita et al., 2010). Two common regimes have been identified, with some lakesdemonstrating thermal stratification and others appearing well mixed (Warren and Kirk-bride, 1998; Carrivick and Tweed, 2013). Well-mixed lakes demonstrate a thick, nearlyisothermal layer below a surface-warmed layer, with a sharp decrease in water temperatureoften observed at lower depths, resulting from sediment-rich, dense meltwater plumes exit-ing beneath the glacier (Weirich, 1984; Richards et al., 2012; Carrivick and Tweed, 2013).The presence of floating icebergs, as well as strong katabatic winds in the valley, promotea uniform temperature distribution throughout the lake (Warren and Kirkbride, 1998).Richards et al. (2012) showed that proglacial lakes tend to experience condensation ratherthan evaporation, with lake surface temperatures falling below air temperatures. Reduc-tion in glacier area, and consequently runoff into the lake basin, will lead to an increasedresidence time of water in the basin, resulting in higher streamflow temperatures (Richards61.3. A conceptual model of streamflow response to lake-calvinget al., 2012).Bird (2014) presented a conceptual model for temperatures in ice-contact lakes onceglacier calving ceases. For the 2013 melt season, Bird (2014) used a heat-budget modelto demonstrate that the temperatures of the ice-proximal basin of Bridge Lake wouldincrease by 0.7 to 1.9 ◦C in a no-iceberg scenario. Increased lake water temperatures wouldincrease lake outflow temperatures, influencing aquatic habitat downstream of the lake. Ofparticular concern are salmonids, which are sensitive to thermal changes (Fleming, 2005).Therefore, it is important to determine the residence time of icebergs within a proglaciallake as a basis for understanding how long they will persist–and influence the lake’s thermalregime–once the glacier becomes land-terminating.Ice-contact lakes have a significant impact on glacial characteristics and behavior, mod-ifying terminus position through flotation and calving, increasing both ice flow and the rateof grounding line retreat. This change in glacier behavior, particularly in discharge frommelt, dampens diurnal variations in downstream flow and has substantial effects on themagnitude of streamflow. Yet data on characteristics (i.e. calving flux, ice flow, and in-fluence on streamflow) of lake-calving glaciers are practically non-existent (Warren andKirkbride, 1998; Trussel et al., 2013). Based on our current understanding of basic hydro-logic processes, a conceptual model is proposed in the following section to provide a basisfor generating specific hypotheses regarding the effect of iceberg calving on downstreamdischarge.1.3 A conceptual model of streamflow response tolake-calvingStreamflow response (m3 s−1) to lake-calving can be interpreted using a water balanceapproach:Qout = Qm +Qgf +Qng +Alake(R− E)−dVdt(1.1)where Qout (m3 s−1) is streamflow at the lake outlet, Qm (m3 s−1) is the addition of waterfrom surface snow and ice melt from behind the grounding line, Qgf (m3 s−1 w.e.) is thedischarge of ice into the lake across the grounding line, Qng (m3 s−1) is the addition ofwater from sources other than the glacier, Alake (m2) is the surface area of the lake basin,R (m s−1) and E (m s−1) are precipitation and evaporation, respectively, and dV/dt (m371.3. A conceptual model of streamflow response to lake-calvings−1) is the change in lake volume with time.Lake-terminating glaciers progress through four stages, with distinct implications forstreamflow generation (Figure 1.2). The first stage is pre-calving, when the glacier isgrounded along its entire length (Figure 1.2a). In this stage, surface snow and ice melt(Qm) runs off the glacier and into an ice-contact proglacial lake basin. The second stagebegins when the glacier retreats enough that it exposes an over-deepened basin, allowingmeltwater to collect and form an ice-proximal lake basin (Figure 1.2b). At this stage, if theice thickness is less than HF , the terminus begins to float and the volume of ice in front ofthe grounding line (e.g. the volume of ice floating) raises the lake level, having an immediateimpact on streamflow exiting the lake basin (Qout). In the third stage, the glacier continuesto thin and retreats into deeper water, where the inverse relation between water depth andbasal effective pressure promotes more rapid calving and retreat (Benn et al., 2007) (Figure1.2c). As water depth increases, the effective pressure at the base of the glacier decreases,leading to increased sliding and flow velocity, which delivers ice to the calving front atan increased rate. Since the icebergs were originally part of the floating terminus, theirvolume has already been accounted for in the lake’s water balance, and their melting, bothsurface and subglacial, has no additional impact on lake water level or streamflow. Inboth the second and third stages only surface snow and ice melt (Qm) behind the glaciergrounding line and additional glacier flow (Qgf ) are contributing additional volume to thelake and increasing streamflow (Qout). Finally, in the fourth stage, the glacier has thinnedand retreated enough that the base of the ice front is completely emerged from the lakeand calving ceases (Figure 1.2d). Eventually all the icebergs currently in the lake will meltwithout being replenished. As in the first stage, surface snow and ice melt (Qm) run offinto the basin.Once the glacier reaches terminus flotation (i.e. stage 2), there should be a seasonalchange in streamflow patterns. During the summer months, there should be a reductionin snow and glacier surface melt (Qm), and therefore streamflow (Qout), as the area ofglacier behind the grounding line diminishes. During the winter months, there should bean increase in streamflow, as the discharge of ice into the lake via normal glacier flow(Qgf ) effectively displaces an equivalent volume of water. It is assumed that surface melt(Qm), non-glacial discharge (Qng), and precipitation (P ) and evapotranspiration (E) areunaffected by glacier flotation and calving during during the winter, and thus not associatedwith a trend in discharge. Therefore, any trends seen in discharge are assumed to be relatedto glacier flow and the resulting change in lake level.81.3. A conceptual model of streamflow response to lake-calving  (a) Stage 1: Glacier fully grounded along entire length.  (b) Stage 2: Glacier retreats past over-deepened basin and terminus begins to float.  (c) Stage 3: Glacier continues to retreat and calving begins.  (d) Stage 4: Glacier once again fully grounded and calving ceases.Figure 1.2: Phases of a lake-calving glacier (a-d). Dashed line indicates the location of the groundingline.91.4. Research questions and thesis structure1.4 Research questions and thesis structureA review of existing studies on the hydrology and dynamics of ice-contact lakes, as outlinedin Section 1.2, sheds light on current gaps in our understanding of how streamflow respondsto the accelerating retreat of a lake-calving glacier. The current study was designed toaddress these gaps, using the conceptual lake-calving model presented in Section 1.3 togenerate the following key research questions:1. Are there any seasonal trends in Bridge River streamflow that can be associatedwith decreasing glacier area and the onset of calving losses? The following specifichypotheses, based on the conceptual model, are tested:(a) Late-summer streamflow should decrease due to the decreased area for surfacemelt behind the grounding line, and(b) Winter discharge should increase due to the addition of the ice discharge term,Qgf , to the lake’s water balance2. How rapidly are the icebergs in the proglacial lake melting and what implicationsdoes this have for the lake thermal regime?3. How long are the icebergs likely to persist in the lake once the glacier retreats up-valley of the over-deepened, lake-filled basin (i.e. stage four of the conceptual model)?This thesis is structured in the following manner: Chapter 2 presents the study areaand a detailed description of data collection and analysis; Chapter 3 presents the resultsof the study and Chapter 4 links these results back to the research questions mentionedabove; and finally, Chapter 5 summarizes the key findings and provides areas for futureresearch.10Chapter 2Study area and methodology2.1 Study areaThe study area encompasses the Bridge River catchment, located in the southern CoastMountains in British Columbia, Canada (Figure 2.1). Bridge glacier, a lake-terminatingglacier at the head of Bridge River, originates in the highly maritime environment along thecoastal divide of the Pacific Ranges and terminates in the drier, more interior environmentlying in their rainshadow. At the location of a Water Survey of Canada (WSC) gaugingstation, the river basin drains an area of approximately 139 km2, of which Bridge Glacierin 2014 covered approximately 73.1 km2 (52.7%). Elevation within the catchment rangesfrom approximately 1400 to 2800 m a.s.l.Bridge Glacier has retreated significantly in the past few decades, experiencing a re-duction in total area (including extent outside the watershed) from approximately 91 km2in the early 1990s to its current area of approximately 82 km2. The portion of the glacierwithin the Bridge River watershed decreased in area from 81.5 km2 to 73.1 km2 duringthe same time period. The glacier terminates in a proglacial lake, hereafter referred to asBridge Lake. Bridge Lake is divided into ice-proximal and distal basins separated by abarrier of icebergs pinned against a submerged terminal moraine. The distal basin area isapproximately 1.35 km2, varying slightly with lake level, which varies through the summerin response to changes in glacier runoff. The ice-proximal basin area ranged from approx-imately 0.56 km2 in 1984 to approximately 4.90 km2 in 2014, depending on the retreat ofthe glacier terminus.Two creeks drain into Bridge Lake, one referred to as South Creek, a glacier fed streamflowing into the southwest portion of the lake, and the other referred to as West Creek,which includes melt from a secondary land-terminating tongue of Bridge Glacier. BridgeLake then drains into Bridge River at the northeast end of the distal basin. A WSC gaugingstation is located approximately 3 km downstream of the lake outlet, where discharge iscontinuously estimated. Bridge River then flows approximately 50 km downstream, where112.1. Study area Figure 2.1: Map of study area, including Bridge Glacier, Bridge Lake, and the locations of thetime lapse camera, automatic weather stations (ridge top (RT) and lake-side (LS)), and the WaterSurvey of Canada gauging station.it feeds Lajoie Dam, one of the power plants in a complex operated by BC Hydro. Thiscomplex is the third largest development operated by BC Hydro, consisting of three damsthat store water for four generating stations, providing 6 to 8% of British Columbia’selectrical supply (BC Hydro, 2013). Any future decreases in Bridge River streamflow willtherefore result in less power production, with associated losses of revenue to BC Hydro.The Bridge Glacier watershed was chosen for this analysis due to the abundance oflong-term data available at the site, including: Landsat and MODIS satellite imagery from1984 and 2001 to present, respectively; continuous discharge records downstream from 1979to present (WSC gauging station); and meteorological data nearby from 1984 to presentat the Upper La Joie (ULJ) weather station.122.2. Meteorological data2.2 Meteorological dataMeteorological data were collected from three automatic weather stations (AWS) acrossthe study region, one located at the side of Bridge Lake (LS), one located on a ridge topoverlooking the lake (RT), and the third located approximately 27 km east-northeast ofthe glacier, the BC Hydro ULJ station (Figure 2.2). The RT station was established andhas been running since 2006 (Shea and Moore, 2010), and was used to extend the LSair temperature and incident shortwave radiation to the length of the entire 2014 meltseason. Air temperature, relative humidity, barometric pressure, wind speed and direction,and incident shortwave and longwave radiation were scanned at the LS station every 10seconds and averaged over 10–minute intervals. Total rainfall was measured every 10minutes. Measurements were collected from July 8, 2014, to September 23, 2014. Allinstruments (Table 2.1) were mounted approximately 1.5 m above the ground on a tripodand connected to a Campbell Scientific CR10X data logger housed in a waterproof case(Figure 2.3). The rain gauge was inoperable between July 8 and August 12. Therefore,daily precipitation totals for this period were estimated by regressing daily precipitationat the LS station against daily precipitation at the ULJ station (Figure 2.4). Figure 2.2: Map showing locations of weather stations across the study region (ULJ = Upper LaJoie, LS = lake side, and RT = ridge top). The black outline is the watershed boundary for theWSC gauging station located approximately 3 km downstream of Bridge Glacier.132.2. Meteorological dataTable 2.1: Instrument specificationsVariable Sensor Range AccuracyAir temp. (Ta) Rotronic HC-S3 -30 to +60◦C ±0.2◦CRel. humidity (RH) Rotronic HC-S3 0-100% ±1.5% (23◦C)Baro pressure (P ) Vaisala PTB110 500-1100 hPa ±0.3 hPa (20◦C)Wind speed (u) R.M. Young 05108 0-100 m s−1 ± 0.3 m s−1Wind direction R.M. Young 05108 360◦ ±3◦Incident SW (K ↓) Kipp & Zonen SPLite2 0.4-1.1 µm ±4.6%Incident LW (L ↓) Kipp & Zonen CGR3 4.5-42 µm ±4.0%Precipitation (R) TX Electronics TR-525M - ±1.0%Stage (S) Onset U20 Level Logger 0-4 m ±0.15%Water temp. (Tw) Onset Tidbit v2 -20 to +70◦C ±0.2◦CElectrical WTW TetraCon 325 1 - 106 µS cm−1 -conductivity (EC) WTW Cond 340i 0 - 1999 µS cm−1 ±0.5%(probe and meter)Water depth (m) Lowrance HDS-7 ∼ 915 m -Figure 2.3: Lake side (LS) weather station. Note: photograph was taken during period of high lakelevel - station was normally approximately 5 m inland from the shore.Mean monthly air temperature and total monthly precipitation from 1985 to 2011were extracted from ClimateWNA v4.72 for the purpose of predicting these variables inearlier years using a regression with measured variables. ClimateWNA v4.72 is a softwareprogram developed by the Center for Forest Conservation Genetics at the University ofBritish Columbia that uses PRISM and ANUSPLINE monthly normal data (1961-1990),142.2. Meteorological dataas well as gridded anomalies based on the University of East Anglia Climatic ResearchUnit data product, to calculate seasonal climate variables based on elevation and specificlatitude and longitude coordinates (Wang et al., 2012). The latitude and longitude (50.85◦,-123.23◦) and the elevation (1829 m a.s.l.) of the ULJ station were used to extract thetemperature and precipitation values.0 5 10 15 20 250246810ULJ Precipitation ( mm day−1 )LS Precipitation ( mm day−1  )RLS^  = 0.310 RULJ + 0.148Figure 2.4: Linear model used to predict daily precipitation (RLS) at the lake side (LS) station fromdaily precipitation at the Upper La Joie (ULJ) station. The solid line indicates linear regressionand the dashed line indicates a 1:1 line.Air temperature, relative humidity, and incident shortwave radiation at the RT stationwere averaged over ten minute intervals and collected from May 1, 2014, to August 13, 2014,for use in a regression with variables at the LS station. Air temperature, incident shortwaveradiation, and atmospheric vapor pressure calculated from the RT station variables wereregressed with LS variables from July 7 to August 13 and the resulting equations used topredict LS variables from May 1 to July 6 (Figure 2.5). Predicted variables were combinedwith measured LS variables to create a complete dataset from May 1 to September 23 foruse in energy balance estimates of iceberg melt (see Section 2.6.4).Incident longwave radiation at the RT station was calculated from May 1 to September23 as follows (Sicart et al., 2006):L ↓= εσT 4a (2.1)152.2. Meteorological data5 10 15 20 255101520ridgetop2014$Ta[9966:14862]Ta[230:5126]RT Ta (°C)LS T a (°C)LS Ta^  = 0.45 RT Ta + 2.790.2 0.4 0.6 0.8 1.00.50.60.70.80.91.01.1ea.RT[9966:14862]ea[230:5126]T ea (kPa)LS e a (kPa)LS ea^ = 0.49 RT ea + 0.410 200 600 100002004006008001200Kdown.W[9966:14862]Kdown[230:5126]RT K ↓ (W m−2)LS K↓(W m−2 )LS K^ ↓  = 0.92 RT K ↓  + 8.94Figure 2.5: Linear models used to predict air temperature, atmospheric vapor pressure, and incidentshortwave radiation at the lake side (LS) station. The solid line indicates linear regression and thedashed line indicates a 1:1 line.where Ta is the predicted air temperature in Kelvin, σ is the Stefan-Boltzmann constant(5.67 x 10−8 W m−2 K−4), and ε is the clear-sky emissivity, estimated as (Sicart et al.,2006):ε = 1.24×[eaTa] 17(2.2)where ea (kPa) is atmospheric vapor pressure, calculated for both the regressed data set andthe measured LS station data set (using the corresponding air temperatures and relativehumidities) as:ea = esat(Ta)×RH100(2.3)where esat is the saturation vapor pressure (kPa) and RH is the relative humidity (%).The saturation vapor pressure (esat) was calculated as follows (Tetens, 1930):esat(Ta) = 0.611 exp[aTaTa + b](2.4)where a and b are constants equal to 17.27 and 237.26 or 21.87 and 265.6 when Ta ≥ 0◦Cor when Ta is < 0◦C, respectively.Evaporation rate (E, m s−1) was calculated from the 10-minute-resolution meteorolog-162.3. Hydrological dataical data as:E =Qe(w)ρwLv(2.5)where ρw is the density of water (1000 kg m−3), Lv is the latent heat of vaporization (2.48x 106 J kg−1), and Qe(w) is the latent heat flux over the lake surface (W m−2). The latentheat flux was calculated using the following form (Moore et al., 2005) of the Dalton-typeequation from Webb and Zhang (1997):Qe(w) = 285.9(0.132 + 0.143u)(ea − ew) (2.6)where u is the wind speed averaged every 10 minutes (m s−1) recorded approximately1.5 m above the lake surface and ew is the water surface vapor pressure (kPa). The watersurface vapor pressure was calculated as the saturation vapor pressure for the water surfacetemperature (Tw). A mean proximal basin Tw of 1.1◦C was approximated from lake surfacetemperatures from a previous thermal regime analysis of the lake performed by Bird (2014).2.3 Hydrological dataStage and water temperature measurements were taken in two locations: in the streamnear the outlet of South Creek and in the outlet of West Creek into the ice-proximal basin.Water temperature was also recorded in Bridge River about 100 m downstream of thelake outlet. At each location, an Onset U20 level logger and Tidbit temperature logger(Table 2.1) were deployed, secured to shore and weighed down to the lake or stream bedusing a rock gabion. For protection, all instruments were housed in 15 to 20 cm longPVC piping with 1 cm diameter holes drilled approximately 5 cm apart to accommodateflow. Measurements were recorded at 10 minute intervals. The level logger located at theoutlet of West Creek was found no longer submerged upon removal in late September andtherefore all measurements recorded after its exposure were discarded. In addition, therewas a large build up of sediment in the PVC piping of the logger located at the outlet ofSouth Creek, which may have an effect on recorded levels.Bridge River daily discharge from 1979 to 2014 were obtained from the WSC gaugingstation located approximately 3 km downstream of the lake outlet in the river. Dischargewas sub-sampled in 10 minute intervals to match other measured meteorological and hy-172.3. Hydrological datadrological variables. Due to the fact that there is only an 8% difference in watershed areabetween the lake outlet and the WSC gauging station, and that there are no tributariesflowing into Bridge River between the two, discharge measured at the station is assumedrepresentative of lake outlet discharge.2.3.1 South CreekDischarge was measured at South Creek a total of 25 times throughout the field seasonusing dilution gauging by dry salt injection. A known mass, typically about 1 kg, of tablesalt was dumped into a turbulent section of the creek and the electrical conductivity (EC)of the water was measured downstream, at a point where the salt was considered well mixedwithin the creek. EC was measured in a calm part of the stream using a WTW TetraCon325 standard conductivity cell (Table 2.1). Discharge (QSC , m3 s−1) was calculated usingthe following equations from Hudson and Fraser (2005):QSC =MA(2.7)where M is the mass of salt (g) and A (g s m−3) is the area under the graph of saltconcentration through time and can be calculated as:A = Σ(ct × tint) (2.8)where ct (g m−3) is the concentration of injected salt at time t and tint (s) is the timebetween recorded measurements. The concentration of salt (ct) is calculated using thebackground electrical conductivity (EC0, µS cm−1) and the conductivity at time t (ECt):ct = (ECt − EC0)× CF (2.9)where CF (g m−3 µS−1 cm−1) is a calibration factor based on the relationship betweenEC and ct. The calibration factor changes based on the probe used for EC measurement,the stream temperature, and the background conductivity. Values for CF were determinedby calibration in the laboratory using samples of creek water.A rating curve was created to predict discharge for the entire field season, using the first22 measured discharges and stages (Figure 2.6). The final three discharge measurementswere taken after the South Creek level logger was removed, and were therefore excluded.182.3. Hydrological dataThe following relation was fitted to the data using nonlinear regression:log(Qˆ) = a+ b× log(Q− c) (2.10)where Qˆ is the predicted discharge and a, b and c are coefficients. After fitting the coeffi-cients, the relation was back-transformed to predict Q.0.35 0.40 0.45 0.501.01.52.02.53.03.5Stage (m)Q (m3 s−1 )model fit10% error bandsFigure 2.6: Rating curve for South Creek. See text for description of fitting procedure.2.3.2 West CreekDischarge was measured at West Creek a total of 12 times throughout the field seasonusing the same methods found in Section 2.3.2. A rating curve was produced to predictdischarge for the entire field season. However, the discharge measurements did not display aclear relation with stage, likely due to incomplete mixing at the point of EC measurement.Therefore, given that West Creek emanates from a second, land-terminating tongue ofBridge Glacier approximately 1 km upstream and consists entirely of meltwater from thattongue, the contribution of West Creek to lake inflow is lumped in with the contributionsfrom other glacier sources (Qm and Qgf ).192.4. Statistical analysis of Bridge River streamflow data2.4 Statistical analysis of Bridge River streamflow data2.4.1 Trend analysis for monthly hydroclimatic dataMean monthly discharge, air temperature, and precipitation as rain were analyzed in orderto detect any trends with glacier calving phase. The air temperature and precipitation datafrom 1985 to 2014 were directly measured at the ULJ station. Data from 1979 to 1984 werepredicted using measured values from the ULJ station and modelled ClimateWNA v4.72data from 1985 to 2011 (Figure 2.7). All data were split into two groups, pre-1991 and 1991to present, to represent pre- and post-calving periods. Mann-Kendall tests were performedto detect monotonic trends in discharge, air temperature, or rainfall. This trend test waschosen because it can accommodate non-normal distributions and nonlinear trends, as wellas being robust to outliers (Helsel and Hirsch, 2002).−10 −5 0 5 10−15−10−50510ClimWNA Ta (°C)ULJ T a (°C)ULJ Ta^ = 0.93 ClimWNA Ta + 0.28(a)0 100 200 300 4000100200300ClimWNA Total Precip (mm)ULJ Total Precip (mm)RULJ^  = 0.65 RClimWNA + 13.16(b)Figure 2.7: Linear models used to predict mean monthly air temperature (a) and total monthlyprecipitation (b) at the ULJ station based on values from ClimateWNA. The solid line indicatesthe linear regression and the dashed line indicates a 1:1 line.2.4.2 Summer trends in discharge with climatic variabilityInterannual variability in monthly mean discharge for August and September and for theentire melt season (May to October) from 1979 to 2014 were analyzed following the ap-proach of Stahl and Moore (2006). The first step involved fitting the following regression202.5. Deterministic analysis and modellingmodels for August and September to account statistically for the effects of melt intensity(represented by monthly mean air temperature), precipitation, and discharge of carry-overstorage from the preceding month:QAug(t) = b0 + b1Ta(t) + b2R(t) + b3QJuly(t) + e(t) (2.11)QSept(t) = b0 + b1Ta(t) + b2R(t) + b3QAug(t) + e(t) (2.12)where QJuly, QAug, and QSept are the mean monthly July, August, and September dis-charges (m3 s−1) in year t, respectively; Ta(t) (◦C) and R(t) (mm) are the mean monthlyair temperature and total monthly precipitation in year t at the ULJ weather station, biare coefficients to be determined by regression, and e(t) represents the regression residuals.A simplified regression model was fit for the melt season from May to October, ac-counting statistically for the effects of melt intensity (represented by mean melt season airtemperature) and total precipitation:QMay−Oct(t) = b0 + b1Ta(t) + b2R(t) + e(t) (2.13)where QMay−Oct is the mean melt season discharge (m3 s−1) in year t and Ta(t) (◦C) andR(t) (mm) are the mean melt season air temperature and total melt season precipitationin year t.The second step involved applying the Mann-Kendall test for trends to the residuals.In addition, the residuals were classed into three periods of roughly equal length: onepre-calving period from 1979 to 1991, one post-calving period from 1992 to 2003, and asecond post-calving period from 2004 to 2014. Loess curves were also fit to each set ofresiduals to aid in trend visualization, using a degree of 1 to reduce sensitivity to outlyingend residuals.2.5 Deterministic analysis and modelling2.5.1 First-order approximation of calving fluxIn order to approximate the winter ice flux of Bridge Glacier for use in a water balanceapproach (Equation 1.1), it was assumed that surface melt (Qm), non-glacial discharge212.5. Deterministic analysis and modelling(Qng), and precipitation (R) and evapotranspiration (E) are unaffected by glacier flotationand calving during the winter, and thus not associated with a trend in discharge. Therefore,all glacier flow into the lake (Qgf ) during winter has an immediate effect on lake volume,effectively displacing an equal mass of water, and thus increasing discharge. A first-orderapproximation of glacier calving flux (Qgf , m3 s−1 w.e.) was calculated as follows:Qgf = (v × w × h)×ρwρi(2.14)where v is the mean glacier velocity at the calving front in 2013 (m s−1), w is the width ofthe calving front (m), h is the ice thickness at the calving front (m), and ρi is the densityof ice (917 kg m−3).The mean glacier velocity at the calving front was estimated by Chernos (2014) for thesummer of 2013 using monoscopic time lapse camera images and manual feature tracking.Images were taken every 30 minutes, both parallel and perpendicular to the glacier termi-nus, and features were tracked over the course of the summer. Pixel displacements wereconverted to distance displacements to estimate annual glacier velocity with an estimateduncertainty of ±43 m a−1.2.5.2 Glacio-hydrologic modellingThe HBV-EC hydrological model, a conceptual parametric model based on the SwedishHBV model (Lindstrom et al., 1997), was used to predict watershed streamflow responseto glacier retreat for the study period. This model was previously calibrated for the BridgeGlacier watershed by Stahl et al. (2008), who used both daily streamflow and seasonalmass balance as calibration targets to ensure that snow and glacier melt contributionswere properly estimated (Table 2.2). A brief description of the model is provided below;see Stahl et al. (2008) for more details.The model uses a grouped response unit (GRU) approach, with GRUs defined based onelevation, land cover (open, forest, water, and glacier), slope, and aspect. The model runsat a daily time step, using daily main air temperature and total precipitation as input.Air temperature and precipitation are extrapolated above and below the elevation of theweather station using vertical gradients determined as part of the calibration procedure.Daily snowmelt is computed using a modified temperature index, with the melt factor afunction of day of year, slope, aspect, and forest cover (Hamilton et al., 2000). Ice melt is222.5. Deterministic analysis and modellingthen computed once the accumulated snow has melted by multiplying the open snow meltfactor by a multiplier, MRG, to account for the lower albedo of glacier ice compared tosnow. Total runoff for each glacier GRU is then routed through a linear reservoir with anoutflow coefficient dependent upon snow depth. Runoff for each non-glacier GRU is routedthrough a soil moisture routine, followed by two lumped reservoirs representing both rapid,shallow and slower, deeper flow paths.Landsat imagery from 1984 to 2014 was used to map glacier area (km2) within theBridge River watershed for each year with a significant change in glacier terminus position.Daily mean air temperature (◦C) and total precipitation (mm) were acquired from theULJ weather station, and potential evapotranspiration (mm) was calculated based on thePriestley-Taylor equation (Priestley and Taylor, 1972), using the ‘EcoHydRology’ packagein R (R CoreTeam, 2002).Table 2.2: Most responsive HBV-EC parameters, with calibrated values from Stahl et al. (2008).Model Component Parameter Description ValueAtmosphere PGRADL Fractional precipitation increase 0.0016with elevation below EMID (m−1)PGRADH Fractional precipitation increase 0.0001above EMID (m−1)EMID Mid-point elevation (m) 2100TLAPSE Temperature lapse rate (◦C m−1) 0.006Snow AM Aspect/slope influence on melt factor 0.25TM Threshold temperature for -0.69snowmelt (◦C)CMIN Melt factor for winter solstice 1.01(mm◦C−1 d−1)DC Increase in melt factor between winter 2.08and summer solstice (mm◦C−1 d−1)Glacier MRG Ratio of melt of glacier ice to melt 1.52of seasonal snowThe model was run in the GreenKenue modelling environment developed by Environ-ment Canada (http://www.nrc-cnrc.gc.ca/eng/solutions/advisory/green_kenue_index.html), using the aforementioned air temperature, precipitation, and potential evapotran-spiration. The watershed was split into 96 GRUs, based on 8 elevation classes (each232.6. Iceberg mixing dynamics and melt ratesapproximately 200 m), 3 slope classes (0-28◦, 29-58◦, or >58◦), 2 aspect classes (north orsouth), and 2 landcover classes (glacier or open non-glacier). For simplicity, the distinc-tion between open and forested areas was not made. However, because only 3.2% of theopen non-glacier land cover was classified as forest, this simplification should not have asignificant influence on simulated streamflow. Total watershed discharge was calculated asa sum of the discharge estimated for each GRU.In order to account for the effect of changing glacier area on discharge, the model wasrun 31 times for the period 1984 to 2014, each run using the glacier extent from a differentyear. The final time series of predicted discharge was then generated by extracting fromeach run the discharge for the year corresponding to the glacier extent, and then combiningthese. This approach facilitated the prediction of a continuous discharge time series thatincorporated the effects of ongoing glacier retreat. In addition, predicted streamflow usingthe 1984 and 2014 extents were plotted for comparison.2.6 Iceberg mixing dynamics and melt rates2.6.1 Linear spectral mixture analysis of Landsat imageryFresh snow, glacier ice, and debris-covered glacier ice have unique wavelength-dependentspectral reflectance and can be differentiated from each other as well as from other back-ground materials in an image as long as the spectral resolution is sufficiently narrow (Figure2.8) (Gao and Liu, 2001). Icebergs can be identified within a body of water as both recentlycalved debris-covered ice and the flipped clean undersides of glacier ice. Icebergs are oftensmaller than the spatial resolution of the imagery used for identification, creating pixelsthat are a mixture of glacier ice, dirty glacier ice, and water. For mixed pixels, traditionalsupervised pixel classifications cannot be used to identify materials, as the signature of eachpixel does not match one unique class. Instead, linear spectral mixture analysis (LSMA),a sub-pixel classification technique, is used to unmix the signature, separating each pixelinto fractions of each landcover class identified in the image.Landsat imagery acquisition and preprocessingLandsat Thematic Mapper (TM 4-5) and Enhanced Thematic Mapper (ETM+ 7) sceneswere acquired from the start of the melt season in May to the end of the melt season in242.6. Iceberg mixing dynamics and melt ratesOctober from 1984 to 2014, with the exception of the years 1987, 1991, and 1996, whichhad high cloud cover over the study area in all available scenes. Of the scenes acquired,images with snow or light cloud cover obscuring the ice-proximal lake basin were discarded(refer to Table A.1 in Appendix A for complete list of images analyzed). Both LandsatTM 4-5 and ETM+ 7 have a temporal resolution of 16 days, allowing for multiple scenesover the course of the melt season. Given that glacier ice and dirty glacier ice have thelargest spectral separation in the visible and near-infrared parts of the electromagneticspectrum, only the first four bands were used in the analysis (Table 2.3). Scan-line gaps(image striping) were not corrected for due to the fact that none were overlapping with thestudy area. A visual inspection of images layered with mapped glacier shapefiles providedevidence for a good fit, and therefore the scenes were not geometrically rectified. A 2%linear stretch was applied to improve contrast before beginning the LSMA.Figure 2.8: Reflectance for fresh snow, glacier ice, and debris-covered glacier ice in the visible,near-infrared, and mid-infrared parts of the electromagnetic spectrum. Modified from Hall andMartinec (1985).252.6. Iceberg mixing dynamics and melt ratesTable 2.3: Wavelengths and spatial resolution of Landsat imagery used in analysis.Landsat 4-5 TM Landsat 7 ETM+Band λ (µm) Resolution (m) λ (µm) Resolution (m)1 0.45-0.52 60 0.45-0.52 302 0.52-0.60 60 0.52-0.60 303 0.63-0.69 60 0.63-0.69 304 0.76-0.90 60 0.77-0.90 30Linear spectral unmixingLSMA is based on the assumption that each pixel contains a linear combination of afew spectrally distinct components, including shade from topographical relief (Adams andSmith, 1986; Elmore et al., 2000; Wang et al., 2014). The fractions of these components,called end-member spectra, are estimated by modelling the relationship between each end-member spectra and each mixed pixel. It is also assumed that the end-member spectra arenot themselves mixtures of other components (Elmore et al., 2000). The primary modelused to unmix the images was (Elmore et al., 2000; Wang et al., 2014):Rb =n∑i=1fiRi,b + Eb (2.15)where Rb is the reflectance of a given pixel in band (b), fi is the fractional abundance ofeach end-member (i), Ri,b is the reflectance of each end-member (i) in band (b), and Ebis the error of the fit for each band (b). For this analysis, there are four equations perimage, one for each Landsat band used in the linear spectral unmixing. While the sum ofall fi values must be equal to 1, they are not individually constrained in value between 0and 1. However, values outside this range should not be physically possible, and are takento indicate error in the analysis (Adams et al., 1995; Elmore et al., 2000). The fractionalabundance (fi) is estimated by minimizing the root mean square error (RMSE) as follows(Wang et al., 2014):RMSE =√√√√m∑b=1(Eb)2m(2.16)where m is the total number of bands considered.262.6. Iceberg mixing dynamics and melt ratesLinear spectral unmixing was applied to each image in the study period using ENVI5.1, unmixing only the ice-proximal basin of Bridge Lake where icebergs are present. Totaliceberg surface area (km2) and percent ice cover were then calculated based on the numberof pixels categorized as clean or dirty glacier ice. A detailed description of the end-memberselection process can be found in Appendix A.Calving period identificationPeriods of increased calving were manually identified by making visual comparisons ofglacier terminus shape and position in subsequently timed Landsat images. These periodsare compared to LSMA estimated changes in total ice cover in order to correlate calvingperiods with subsequent changes in lake ice cover.2.6.2 Time lapse camera imageryImages from a time lapse camera previously installed by M. Chernos and A. Davis onJuly 17, 2013, were used to track iceberg movement in the ice-proximal basin during the2014 field season. The Canon EOS Rebel T3i camera with a 10-20 mm wide-angle lenssits facing the glacier terminus, capturing one photograph an hour during daylight hours(Figure 2.9). The camera is powered by two lithium batteries charged by a solar panel anduses command line script to control a DigiSnap 2000 intervalometer. The time lapse cameraset-up was left at Bridge Glacier at the end of the field season, with images currently beingtaken to capture the freeze-over and break-up of the lake ice and any calving events. Moreinformation on exact camera location and significance can be found in Chernos (2014).2.6.3 First-order approximation of iceberg melt ratesIn order to calculate a first-order approximation of iceberg melt rates, icebergs were trackedby boat and time lapse imagery throughout the field season in the ice-proximal basin. ALowrance HDS-7 Gen2 fish finder (Table 2.1) was attached to an inflatable Zodiac Zoomboat via a wooden plank and used to record GPS position and water depth encircling 10selected icebergs. Each iceberg was marked with a combination of red, blue, or orangerocks in July (Figure 2.10) and distance of the boat from the iceberg and height above thewaterline were visually estimated. Each iceberg was also categorized as either groundedor floating based on lateral melt notches from contact with surface lake water. Icebergswere considered grounded when consecutive melt notches were visible, with notch position272.6. Iceberg mixing dynamics and melt rates(a) front view of camera (b) back view (including glacier)Figure 2.9: Photographs of time lapse camera set-up.indicating lake level changes over time. Floating icebergs do not have visible melt notches,as they rise and fall with changing lake level. In August, only one of the original tenicebergs was relocated in the lake for size comparison mapping. Five more icebergs weremarked and mapped, including the original iceberg from July. In September, one of theicebergs tagged in July was found and one tagged in August was found and mapped forsize comparison.For each iceberg, surface area was calculated by connecting the GPS coordinates inESRI ArcMap and dividing each polygon into triangles based on height above the waterlineand accounting for the distance of the boat from the iceberg (Figure 2.11). Total volumeof each individual iceberg was calculated by summing the volume of ice above and undereach triangle, using the water depth where the iceberg was grounded and using the 9/10thrule where the iceberg was floating for ice thickness below the waterline, based on therelative densities of ice and water. Individual melt rates (m3 d−1) were calculated for eachiceberg by taking the volume difference between positively identified icebergs over the timebetween identifications. These melt rates where then scaled to the entire ice-proximal basinby dividing each rate by the fraction of 2014 average iceberg surface area that each icebergrepresented (i.e. fraction of each iceberg out of average 2014 iceberg surface area of 1.02km2). Basin-wide iceberg melt volume (m3) was then estimated by multiplying basin-wide282.6. Iceberg mixing dynamics and melt rates(a) (b)Figure 2.10: Photographs of painted rocks used to mark icebergs (a) and an example of paintedrocks on sample iceberg (b).melt rates by the number of days in the study period between May 1 and September 23,and used to constrain an energy-balance model of iceberg melting in the lake, as describedin the following section.Figure 2.11: Division of sample iceberg into triangles for surface area and volume estimations.2.6.4 An energy balance approach to iceberg meltAn energy balance for the ice-proximal basin was calculated to estimate surface and sub-aqueous iceberg melt volumes. Subaqueous melt was calculated by assuming that the net292.6. Iceberg mixing dynamics and melt ratesenergy absorbed at the water surface is consumed both by warming the glacier dischargewater from 0 to 1.1◦C, the temperature at which water discharges from the proximal basin,as estimated by Bird (2014), and by iceberg melt below the water line (Funk and Roth-lisberger, 1989). This approach is justified by the fact that Bird (2014) did not observemarked changes in temperature profiles in the proximal basin over a summer field season.The total iceberg melt volume (Mtot, m3) was calculated by summing the surface andsubaqueous melt volumes:Mtot = Msurf +Msub (2.17)whereMsurf andMsub (m3) are the energy-balance estimated surface and subaqueous meltvolumes, respectively. The iceberg surface melt volume was calculated for the length ofthe field season (July 7 - September 23, 2014) as follows:Msurf =fice ×Aprox ×Qn(i)ρwLf(2.18)where fice is the fractional lake ice cover based on the LSMA results (0.1 to 0.8), Aproxis the 2014 surface area of the ice-proximal basin (4.87 x 106 m2), Qn(i) is the net energyexchange over the ice surface (W m−2), and Lf is the latent heat of fusion (3.34 x 105 Jkg−1).The net energy exchange over the ice surface Qn(i) was calculated as follows:Qn(i) = Qr(i) +Qe(i) +Qh(i) +Qp(i) (2.19)where Qr(i), Qe(i), Qh(i), Qp(i) (all W m−2) are the energy fluxes from radiation, latentheat, sensible heat, and precipitation falling on the lake, respectively. The energy fluxassociated with radiation over ice was calculated as follows:Qr(i) = K ↓ (1− αi) + εiL ↓ −εiσT4i (2.20)where K ↓ and L ↓ (W m−2) are incident short- and longwave radiation, respectively, αiis the albedo of the ice surface (0.3), εi is the emissivity of ice from Oke (1987) (0.97), andTi is the ice surface temperature (273.15 K).The latent and sensible heat fluxes over the ice surface are calculated using the Hock302.6. Iceberg mixing dynamics and melt rates(1998) bulk aerodynamic approach with stability corrections:Qe(i) = ρaLv ×D × (0.622/P )× (ea − ei) (2.21)Qh(i) = ρacpa ×D × (Ta − Ti) (2.22)where ρa is the air density (kg m−3) estimated using barometric pressure and air temper-ature as per the ideal gas law, P is the barometric pressure (kPa), ei is the ice surfacevapor pressure (kPa), and cpa is the specific heat capacity of air (1010 J kg−1 K−1). Theturbulent transfer coefficient for latent and sensible heat (D) is calculated as follows:D =(k2u)×Θlog(Za/Z0)log(Za/Zx)(2.23)where k is the von Karman constant (0.4), Θ is a stability correction, Za is the height atwhich u and Ta are measured (1.5 m), Z0 is the roughness length for momentum (0.002 m),and Zx is the roughness length for vapor pressure and air temperature (m), scaled using themomentum roughness, giving Zx = Z0/300 (Hock, 1998). The stability correction factor(Θ) is calculated as follows (Price and Dunne, 1976; Shea, 2009):Θ =11 + 10RBRB ≥ 0(1− 16.0RB)0.75 RB < 0(2.24)where RB is the bulk Richardson number, calculated following Sicart et al. (2005):RB =g × (Ta − Ti)× (Za − Z0)TK ∗ u2(2.25)where g is the gravitational acceleration (9.81 m s−2) and TK is the mean temperature ofthe air layer in Kelvin.The advective energy flux associated with precipitation falling onto the iceberg surfacewas calculated as:Qp(i) = ρwcpw ×R× (Ta − Tref ) (2.26)where cpw is the specific heat capacity of water (4180 J kg−1 K−1), R is the precipita-312.6. Iceberg mixing dynamics and melt ratestion rate recorded at the LS and ULJ weather stations (m s−1), and Tref is a referencetemperature (0◦C).The iceberg subaqueous melt volume (Msub, m3) was calculated using the average netradiation flux over the water surface (Q¯r(w)) from May 1 to September 23, the period duringthe year when lake surface water is exposed to radiation (no seasonal lake ice cover). Thisestimation represents the volume of ice that incoming energy is sufficient to melt:Msub =(1− fice)×Aprox × Q¯r(w) ×∆t−Qoutρwcpw × (Tw − Tmelt)−∆HCρwLf(2.27)where ∆t (s) is the length of the time interval considered (the length of the open waterseason for radiation), Qout is the annual discharge volume into Bridge River (m3), Tmeltis the temperature of glacier melt water, assumed to equal 0◦C, and ∆HC is the changein internal heat content, which is assumed negligible due to near constant lake watertemperatures on an annual basis.The radiative exchange over the open water was computed as:Qr(w) = K ↓ (1− αw) + εwL ↓ −εwσT4w (2.28)where αw is the albedo of water, set to 0.1 (Sakai et al., 2000), εw is the emissivity ofwater, set to 0.97, and Tw is the water surface temperature, set to 274.15 K (1.1◦C), basedon results from Bird (2014).Energy fluxes from latent and sensible heat, and precipitation over the lake wherecalculated from the 2014 field season, from July 7 to September 23. During this timeperiod, all three combined only accounted for approximately 23% of the total energy fluxfrom radiation over the lake surface, which dominates the net energy budget. As bothlatent and sensible heat energy fluxes require wind velocity near the surface for estimation,it was not possible to calculate the fluxes for the entire melt season (May to October), andtherefore only the net radiation flux was used for calculating annual subaqueous icebergmelt. The equations for calculating latent and sensible heat, and precipitation energy fluxesduring the summer study period are shown below.The energy flux associated with latent heat over the water (Qe(w)) was calculated as inEquation 2.4, and the flux associated with sensible heat was calculated as:Qh(w) = [(cpaP )/(0.622Lv)]× [(Ta − Tw)/(ea − ew)]×Qe(w) (2.29)322.6. Iceberg mixing dynamics and melt rateswhere Ta is the measured LS station air temperature (◦C). The energy exchange associatedwith precipitation falling onto the water surface is calculated as:Qp(w) = ρwcpw ×R× (Ta − Tref ) (2.30)33Chapter 3ResultsChapter 3 starts with comparison of the 2014 study period to historical meteorological andhydrological data (Section 3.1). The statistical analyses of Bridge River streamflow as wellas the water balance and glacio-hydrologic modelling analyses are then detailed (Section 3.2though 3.4, respectively). Finally, Section 3.5 presents iceberg variation results, includinglake iceberg dynamics and energy balance-produced melt rates.3.1 Overview of study periodMean monthly air temperature recorded at the ULJ weather station for the 2014 meltseason was near or above the historical mean monthly air temperature from 1984 to 2013(Figure 3.1). July and August were significantly warmer than average, with temperatures2.15◦C and 2.82◦C above the historical means, respectively. Mean daily discharge recordeddownstream at Bridge River for the 2014 melt season was consistently near or above thehistorical mean discharge from 1979 to 2013 on a daily basis (Figure 3.2). Mean dailydischarge for 2014 peaked at approximately 69.5 m3 s−1 on July 19th, slightly earlier thanthe date of the peak of the mean discharge over the period (July 27th). However, 2014summer discharge also had a second peak flow of approximately 68.8 m3 s−1 on August16th.Meteorological variables recorded during the 2014 melt season at the LS weather stationare shown in Figure 3.3. Three large precipitation events occurred during the study period,one in mid-July, one in mid-August, and one in mid-September. Precipitation events coin-cided with reduced wind speeds and incoming shortwave radiation and increased longwaveradiation. Hydrological variables recorded during the 2014 melt season are shown in Figure3.4. Peaks in South Creek discharge mirror those seen in Bridge River discharge, whichpeaked at 69.5 m3 s−1 on July 19th. Bridge River and South Creek outflow temperaturesdemonstrated diurnal variations as well as gradual decreases over the course of the fieldseason.343.1. Overview of study period051015T a (°C)May Jun Jul Aug Sep OctMax and Min (1979−2013)Mean (1979−2013)2014Figure 3.1: Maximum, mean and minimum mean monthly air temperatures from the ULJ weatherstation from the 1984 to 2014 melt seasons. Mean monthly temperatures for 2014 are shown in red.050100150Mean daily Q (m3 s−1 )May Jun Jul Aug Sep Oct NovMax and Min (1979−2013)Mean (1979−2013)2014Figure 3.2: Maximum, mean and minimum mean daily discharge from the WSC gauging stationfor the 1979 to 2014 melt seasons. Mean daily discharge for 2014 is shown in red.353.1. Overview of study period04008001200 (a)K↓(W m−2 )200250300350(b)L↓(W m−2 )05101520 (c)T a (°C)0.00.40.81.2(d)e a (kPa)012345 (e)u (m s−1 )0246(f)Precipitation(mm/day)July 10 July 21 Aug 2 Aug 14 Aug 25 Sept 6 Sept 18Figure 3.3: Meteorological variables monitored at the lake side (LS) station during the studyperiod, including incident shortwave radiation (a), incident longwave radiation (b), air temperature(c), atmospheric vapor pressure (d), wind speed (e), and precipitation (f).363.1. Overview of study period05101520 (a)T a (°C)05101520 South CreekBridge River(b)T w (°C)0246(c)Precipitation(mm/day)020406080 (d)Q BR (m3s−1)012345 (e)Q SC (m3s−1)July 10 July 21 Aug 2 Aug 14 Aug 25 Sept 6 Sept 18Figure 3.4: Hydrological and related variables measured during the study period, including airtemperature (a), Bridge River and South Creek outlet water temperature (b), precipitation (c),mean daily Bridge River discharge (d), and South Creek discharge (e). Note: South Creek dischargewas truncated at 0.80 m3 s−1 due to the limited range of the rating curve.373.2. Statistical analysis of Bridge River streamflow3.2 Statistical analysis of Bridge River streamflowThere are significant increases in winter discharge between the pre- and post-calving glacierphases (pre- and post-1991) from 1979 to 2014 for the months of December, January, Febru-ary, and March (Figure 3.5; Table 3.1). Increases in median winter streamflow averagedapproximately 0.20 m3 s−1 (Table 3.2). There were no significant increases in mean airtemperature or precipitation as rain during these months, nor did the number of melt daysincrease significantly (Table 3.1). In addition, regressions between discharge, mean airtemperature, and total precipitation were not significant for the months of December orJanuary (Table 3.3).Table 3.1: Mann-Kendall τ -values for monthly trends in streamflow, air temperature, number ofmelt days, and rain (n = 36). Note: bold values indicate significance at p < 0.01 and * or **indicates significance at p < 0.001 or p < 0.0001, respectively.Month QBR Ta Melt days RainJanuary *0.36 0.20 0.27 0.22February 0.30 0.20 0.15 0.01March **0.41 -0.08 -0.04 -0.03April 0.20 -0.03 0.08 0.01May 0.09 0.02 0.28 0.07June 0.01 0.02 *0.43 0.13July 0.13 0.28 0.25 -0.12August 0.04 *0.36 0.25 -0.03September 0.03 0.19 0.14 0.31October -0.02 -0.02 0.15 -0.07November 0.12 0.08 0.09 -0.03December *0.31 0.06 -0.18 -0.01Table 3.2: Medians of monthly mean Bridge River streamflow, air temperature, and rainfall forpre- and post-1991 periods for December, January, and February (n = 36).Month Median QBR (m3 s−1) Median Ta (◦C) Median Rain (mm)pre-1991 post-1991 pre-1991 post-1991 pre-1991 post-1991December 0.986 1.238 -7.01 -6.75 0.00 0.00January 0.601 0.800 -6.52 -5.79 0.00 0.00February 0.533 0.697 -6.88 - 4.46 0.00 0.00383.2. Statistical analysis of Bridge River streamflow1980 1990 2000 20100.51.02.05.0Q BR (m3s−1)December1980 1990 2000 20100.51.01.5Q BR (m3s−1)January1980 1990 2000 20100.40.61.01.4Q BR (m3s−1)February1980 1990 2000 2010−14−10−8−6−4T a (°C)1980 1990 2000 2010−12−8−6−4−2T a (°C)1980 1990 2000 2010−10−8−6−4−2T a (°C)1980 1990 2000 201002468Number of melt days1980 1990 2000 201002468Number of melt days1980 1990 2000 201002468Number of melt days1980 1990 2000 20100102030Rain (mm)1980 1990 2000 20100103050Rain (mm)1980 1990 2000 20100510152025Rain (mm)Figure 3.5: Trends in Bridge River discharge (QBR), air temperature (Ta), number of melt days (Ta> 0◦C), and precipitation as rain for December, January, and February from 1979 to 2014. Dashedblue lines indicate medians before and after 1991 and red lines indicate loess curves.393.2. Statistical analysis of Bridge River streamflowTable 3.3: Adjusted R2 and associated p-values (in brackets) for multiple regressions for predictingmonthly streamflow as a function of monthly air temperature and rainfall (n = 29). Note: boldvalues indicate significance at p < 0.05.Month QBR with Ta QBR with Rain QBR with Ta & RainDecember -0.017 (0.4770) 0.015 (0.2435) -0.019 (0.4851)January -0.027 (0.6330) 0.019 (0.2217) 0.002 (0.3710)February 0.224 (0.0018) -0.019 (0.5022) 0.316 (0.0023)The multiple regression models using monthly mean air temperature and total precipi-tation, and monthly, lagged Bridge River discharge to predict mean August and Septemberdischarge account for 44 and 55% of the variance in streamflow, respectively (Figure 3.6;Table 3.4). The regression model using mean melt season air temperature and total pre-cipitation to predict melt season discharge accounts for 61% of the variance in streamflow.All three regression p-values were significant at p < 10−3. Evaluated using α = 0.10,Mann-Kendall test results indicate weak but statistically significant negative association ofAugust and September residuals with time (p = 0.05 and 0.08, respectively). Melt seasonresiduals also demonstrate a negative association with time, but the trend is not consid-ered significant (p = 0.22). For August, September, and the melt season, median residualssuggest a decrease in summer discharge from 1984 to 2014 of approximately 4.5, 4.0, and1.1 m3 s−1, respectively, after climatic variation is accounted for by the regression model(Figure 3.7; Table 3.5).Table 3.4: Estimated coefficients, standard error of estimate, adjusted R2 and p-value for regressionfits to Eqs. (2.10, 2.11, and 2.12), along with Mann-Kendall tau values for the residuals (n = 36).Note: bold values indicate significance at p < 0.01 and * or ** indicates significance at p < 0.001or p < 0.0001, respectively.Period b0 b1 b2 b3 se R2 τAugust -0.447 **2.996 *0.080 0.189 4.83 0.44 -0.23September -0.677 **1.670 *0.062 0.225 3.32 0.55 -0.20Melt season 2.270 **2.696 0.007 - 1.79 0.61 -0.15403.2. Statistical analysis of Bridge River streamflow1980 1995 2010304050Q BR (m3s−1 )August1980 1995 201015202530Q BR (m3s−1 )September1980 1995 2010202428Q BR (m3s−1 )Melt season1980 1995 20107891113T a (°C)1980 1995 201046810T a (°C)1980 1995 20107891011T a (°C)1980 1995 2010050100150Rain (mm)1980 1995 20102060100Rain (mm)1980 1995 2010200400Rain (mm)Figure 3.6: Bridge River streamflow (QBR), air temperature (Ta), and precipitation as rain forAugust, September, and the melt season (May to October) from 1979 to 2014.Table 3.5: Changes in median discharge from late-summer and melt season multiple regressionmodels and hydrological model over three periods of time (n = 31). Period 1 is from 1984 to 1990,period 2 is from 1991 to 2003, and period 3 is from 2004 to 2014.Month ∆Q1−2 (m3 s−1) ∆Q1−3 (m3 s−1)regressed modelled regressed modelledAugust -4.1 -0.76 -4.5 -3.7September -2.2 -0.55 -4.0 -2.5Melt season -1.5 -0.52 -1.1 -2.4413.3. Deterministic analysis and modelling−50510 (a)Residuals Aug ( m3 s−1  )−6−2246 (b)Residuals Sept ( m3 s−1  )1980 1985 1990 1995 2000 2005 2010 2015−3−11234 (c)Residuals May−Oct ( m3 s−1  )Figure 3.7: Time series of regression residuals for mean August (a), September (b), and melt season(c) discharge from 1979 to 2014. Dashed blue lines indicate medians before 1991, between 1992 and2003, and after 2003, and red lines indicate loess curves.3.3 Deterministic analysis and modelling3.3.1 Estimated calving fluxChernos (2014) estimated that Bridge Glacier exhibited periods of rapid retreat (up to400 m a−1) from 2009 to 2012 and periods of little to no calving activity, with an overallmean flow velocity of 139 m a−1. Glacier width (w) and ice thickness (h) at the calving423.3. Deterministic analysis and modellingfront are approximately 1055 and 110 m, respectively (Chernos, 2014). The first-orderapproximation of average calving flux of Bridge Glacier is 0.51 m3 s−1. The averagecalving flux represents approximately 62 and 76% of the mean winter discharge recordedat the Bridge River WSC gauging station for the historical record and for the 2014 season,respectively.3.3.2 Glacio-hydrologic modellingModelling of total streamflow during the period from 1996 to 2014 yielded a Nash-Sutcliffemodel efficiency of 0.91 (Figure 3.8), matching the 1986 to 1995 calibration period efficiencyof 0.91 (Stahl et al., 2008). Summer peak flows and winter low flows are reproduced wellby model parameters, but large rainfall events were not matched well.020406080Q (m3s−1 )ObservedModelled1996 1998 2000 2002 2004 2006 2008 2010 2012 2014Figure 3.8: Observed and modelled dynamic discharge for the Bridge watershed for the post-calibration period (1996 to 2014).Reducing glacier area has a significant impact on seasonal discharge (Figure 3.9). Thereduction of glacier area within the watershed from 81.5 km2 in 1984 to 73.1 km2 in 2014is associated with a decrease in median streamflow of approximately 3.7, 2.5, and 2.4 m3s−1 for August, September, and the melt season, respectively (Figure 3.10; Table 3.5).433.3. Deterministic analysis and modelling253035404550Mean Q Aug (m3s−1 ) (a)101520253035Mean Q Sept (m3s−1 ) (b)1985 1990 1995 2000 2005 2010 201515202530Mean Q May−Oct (m3 s−1 ) (c) 1984 extent2014 extentchanging extentFigure 3.9: Modelled mean discharge for August (a), September (b), and the melt season (May-October)(c) for the entire study period using the 1984, 2014, and changing glacier extents.1985 1990 1995 2000 2005 2010 2015−6−4−20Difference in Mean Q (m3s−1AugustSeptemberMelt season (May−October)Difference in Mean Q (m3s−1 )Figure 3.10: Difference between modelled monthly and seasonal mean discharge with changingglacier extent, compared to discharge modelled using the 1984 glacier extent as baseline.443.4. Iceberg variations3.4 Iceberg variations3.4.1 Iceberg mixing dynamicsBoth the Landsat imagery and time lapse photo analyses demonstrate the dynamic envi-ronment of the ice-proximal lake basin. Time lapse photos showed much iceberg movementthroughout the day, with icebergs shifting towards the glacier terminus in the morning,before shifting away from the terminus in the afternoon. Total iceberg surface area esti-mated by the spectral unmixing of Bridge Lake varies both within and among melt seasons,showing a marked overall increase in iceberg surface area starting in early 2005 (Figure3.11), when the terminus broke apart and the glacier retreated approximately 0.47 km(Chernos, 2014). The largest increase in total iceberg surface area in the lake occurredin 2010, when another large calving event resulted in the glacier retreating substantiallytoward its current position.Fractional iceberg cover in the proximal lake basin varied from 1984 to 2014, changingwith proximal basin area, dependent upon terminus position and lake level. The fractionaltotal iceberg cover peaked in late 2007, 2010 and 2011, covering approximately 0.71, 0.75,and 0.71 of the proximal basin, respectively (Figure 3.11). These increases in fractional ice-berg cover, particularly in the fractional iceberg cover considered debris-covered or "dirty,"follow periods of increased calving. Increases in fractional clean glacier ice cover followingcalving periods can be attributed to increased iceberg movement (i.e. rolling and splitting)in the wake of large waves created by the calving event, which increase the total surfacearea of iceberg available for melt.The mean RMS error for the Landsat LSMA is 1.16 ± 1.01 DN (or digital number),with the highest (8.09 ± 4.42 DN) and lowest (0.313 ± 0.356 DN) errors occurring in 2007and 1986, respectively. Ideally, the RMS error for each pixel of each image should be lessthan 1 DN, within the instrument error (Adams and Smith, 1986). Fifty-eight percent ofthe images in the study period have RMS errors within 1 DN, suggesting evidence of asuccessful linear spectral unmixing analysis in those years.3.4.2 Iceberg melt ratesFractional ice cover (fice) in the proximal basin during the 2014 study period ranged from0.16 to 0.25, averaging 0.21. The mean first order approximation of basin-wide icebergmelt rate under the average fractional coverage was 4.30 x 104 m3d−1 (Table 3.6). Scaling453.4. Iceberg variations1985 1990 1995 2000 2005 2010 20150.20.30.40.50.60.7Fractional iceberg coverFigure 3.11: Fractional iceberg cover in the proximal basin derived from the linear spectral mixtureanalysis from 1984 to 2014. Vertical grey panels indicate periods of increased calving as identifiedby visually inspecting subsequent Landsat imagery.up this rate to include the entire study period from May 1 to September 23, mean icebergmelt volume was 6.28 x 106 m3.Table 3.6: Estimated ice-proximal basin-wide iceberg melt rates and volumes for study period (May1 to September 23, 2014).Iceberg 6 Iceberg 10 Iceberg 11 MeanMelt rate (m3d−1) 5.69 x 104 6.09 x 104 1.12 x 104 4.30 x 104Melt volume (m3) 8.31 x 106 8.89 x 106 1.63 x 106 6.28 x 106For a similar fraction of lake ice cover (fice = 0.20), the 2014 iceberg melt rate andtotal melt volume using an energy-balance modelling approach were 6.00 x 104 m3d−1 and2.19 x 107 m3, respectively (Figure 3.12). Melt volumes decrease with increasing fractionalice cover, with a minimum melt volume of 1.30 x 107 m3 when fice = 0.80.463.4. Iceberg variations0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8051015202530Fraction of lake covered by icebergsVolume of ice melt ( 106 m3 )MsurfMsubMtotFigure 3.12: Volumes of surface, subaqueous, and total iceberg melt as a function of fractional icecover for the 2014 (solid lines) and 2013 (dashed lines) study periods, as estimated from the energybalance approach.47Chapter 4Discussion4.1 Seasonal trends in dischargeOverall, the hydrological model fit to discharge is good, yielding a Nash-Sutcliffe modelefficiency of 0.91 both in the calibration period (1986 to 1995) and in the post-calibrationperiod (1996 to 2014). The model tended to under-predict streamflow during rain events,which are known to be predicted more poorly than meltwater runoff (Jost et al., 2012).During heavy rainfall events, the rapid flow path reservoir is unable to represent bothglacier melt and rainfall runoff, due to their non-linearity and difference in spatial patterns(Jost et al., 2012). In addition, although there are calibrated model parameters to correctthe measured precipitation, the ULJ station is located 27 km inland from the glacier andmay not represent rainfall in portions of the catchment closer to the glacier and lake basin.Interestingly, model results in this study demonstrated similar results to those fromStahl et al. (2008), which predicted a decrease in August streamflow by approximately 6.0m3 s−1 from 2004 to 2014, compared to median decrease by 3.7 m3 s−1 estimated in thisstudy. Their model also projected a reduction in glacier area of 4.0 km2 by 2014, consistentwith the reduction of 3.9 km2 determined from satellite imagery.Seasonal trends observed in Bridge River streamflow support the hypotheses presentedin Section 1.4, that late-summer streamflow should decrease with reduced glacier areabehind the grounding line and that winter flow should increase with the addition of icedischarge to the lake. First, late-summer streamflow decreased in association with shrinkingglacier area behind the glacier grounding line. The decrease in median streamflow residualsby approximately 4.5, 4.0, and 1.1 m3 s−1 in August, September, and during the meltseason, respectively, is consistent with the decrease in glacier area behind the grounding linefrom 1984 to present. These streamflow reductions are in reasonable agreement with thoseproduced by hydrological modelling, which suggested a reduction in August, September,and melt season median streamflow by 3.7, 2.5, and 2.4 m3 s−1, respectively. The slightlysmaller changes predicted by the HBV-EC for August and September are consistent with484.1. Seasonal trends in dischargethe fact that the model used total glacier area within the watershed to estimate discharge,including the floating terminus where melt does not actively contribute to discharge. Thetrends in the residuals from the August and September regression models had p-valuesin the range 0.05 to 0.10. Although it is common to test hypotheses at p < 0.05 orsmaller, using a higher threshold of p < 0.10 can be justified considering the relativelyshort period of record and the relatively high inter-annual variability (Bawden et al., 2014;Frost, 2015). Importantly, the directions of the trends are consistent with those indicatedby the deterministic modelling.The second seasonal trend evident in discharge is increased winter flow from Januarythrough March, when median flow increased significantly following the 1991 flotation of theglacier terminus (i.e. when the glacier entered stage two of the conceptual model). Thereare three main hypotheses that could explain the observed increase, including (1) theworking hypothesis of ice discharge into the lake (Qgf ), (2) an increase in mid-winter meltand rainfall, and (3) a shifting bias in the methods used for estimating winter streamflow.Ice discharge into the lake is estimated using mean glacier flow velocity. Many studies reportthat winter glacier flow velocities are typically less than late-spring and early-summervelocities (O’Neel et al., 2001; Bingham et al., 2003; Burgess et al., 2013; Abe and Furuya,2015). Sundal et al. (2011) suggested an average summer speed-up of 50 to 125% of winterglacier flows. Due to the fact that the mean glacier velocity used in this analysis was basedupon late-spring and summer speeds, the estimated mean glacier velocity in the winter isassumed to decrease by at least 50%, from 139 to 69.5 m a−1. The resulting estimatedwinter ice discharge into the lake, 0.26 m3 s−1, is larger than, but of the same order ofmagnitude as, the observed increase in median discharge (0.20 m3 s−1), suggesting that icedischarge during the winter is a highly plausible explanation for increased streamflow.An increase in mid-winter melt and rainfall, as suggested by the second hypothesis,would indicate an increase in air temperatures from the pre- to post-flotation periods. Re-gression between streamflow and air temperature was only significant for February, whenair temperature increased by approximately 2.42◦C post-1991 flotation. However, mediantemperatures following 1991 were still well below 0◦C, and there was no significant increasein the number of melt days. In addition, there were no significant relationships observedbetween streamflow and precipitation during the winter, which suggests that neither in-creased mid-winter melt nor rainfall are likely explanations for the observed increase instreamflow.The third hypothesis relates to the fact that, when the stream channel contains ice494.2. Lake-terminating glaciers and peak watercover, the rating curve is no longer valid, and streamflow is estimated by methods that ofteninvolve subjective judgement (Hamilton and Moore, 2012). Therefore, it is impossible todiscount that at least some of the observed increase in winter streamflow could be spurious,merely a result of a shift in the method used for estimating flow.4.2 Lake-terminating glaciers and peak waterBoth the hydrological modelling and statistical analyses support the hypothesis that BridgeGlacier has already passed the point of peak water, and that the onset of calving and asso-ciated increase in retreat rate resulted in a decline of late-summer streamflow by about 10%of the pre-calving mean discharge for August and 14% for September. Bridge River stream-flow can be expected to continue to decline with future climatic warming-induced glacierretreat, consistent with the projections of Stahl et al. (2008), with associated consequencesfor water resources and aquatic habitat.As far as we can determine, this is the first study that tracked streamflow variationswith the retreat of a lake-terminating glacier (Tables 1.1 and 1.2). The results of this studysuggest that once calving begins, there is a reduction of the time spent in the first twophases of peak water, or an acceleration of progress through phase three. This observationis particularly relevant for valley glaciers, many of which will experience a transient lake-terminating and calving phase with continued retreat.4.3 Iceberg persistence and lake thermal regimeResults from the linear spectral mixture analysis and images from the time-lapse cameraprovide evidence for the dynamic nature of iceberg cover in the proximal basin. Fluctuatingfractional ice cover demonstrates that icebergs in the basin are constantly shifting andbreaking apart, exposing more surface area for increased surface and subaqueous melt. Inparticular, fractional cover of clean glacier ice is quite variable through the years, likelyrepresenting periods with widespread turnover and break-up of icebergs. The shifting oficebergs in the basin towards the glacier terminus in the morning and then away from theterminus in the afternoon makes tracking individual icebergs throughout the melt seasonnearly impossible.The estimated total annual melt volumes for the mean fractional ice cover in 2014 arean order of magnitude larger than those approximated using field measurements. This504.3. Iceberg persistence and lake thermal regimeis expected, as energy-balance estimated melt volumes are annual estimates, includingsurface and subaqueous melt during the summer, as well as subaqueous melt during thewinter, which are not accounted for by the field-estimated melt rates, which only relate tothe melt season. The field-estimated melt rates were also scaled up based on the surfacearea of iceberg cover, not by the iceberg volume, which was not possible due to lack ofinformation. Additionally, field-estimated melt rates and volumes are rife with uncertainty,with error introduced through visual estimation of distance from icebergs and heights abovethe waterline. The GPS unit used for coordinate location also introduced error, with ahorizontal accuracy of ± 7 m affecting surface area estimates.For the full range of fractional ice cover in 2014 (0.16 to 0.25), energy-balance estimatedtotal annual melt volumes are comparable to those estimated for 2013 by Bird (2014).Under the assumptions of the energy-balance model, which assumes that all energy enteringthe system is used either to melt icebergs or to heat melt water, the slightly larger estimatesfor 2013 can be attributed to a lower annual lake outlet discharge. A lower discharge meansthat more of the radiation flux absorbed by the water surface from May to Septemberwas able to contribute to iceberg melt, rather than heating glacier meltwater to reachaverage lake temperatures. Total net radiation over the lake ice-proximal basin from Mayto September, the largest contributing factor to estimated annual melt, is larger for 2014(2.18 x 109 W m−2), as compared with 2013 (2.09 x 109 W m−2), eliminating increasedradiation as a contributing factor for the higher melt estimated in 2013.The annual volume of ice flowing into the proximal basin (Qgf ) under average flowvelocity, 1.61 x 107 m3, is less than the estimated annual melt volume (Mtot), suggestingthat for years without large calving events, all icebergs calved into the lake would likelymelt within a year. This is particularly true for years with low fractional iceberg cover(between 0.10 and 0.30), when annual melt volume peaked at 2.34 x 107 m3. For yearswith fractional ice cover between 0.70 and 0.80, annual melt volume peaked at 1.45 x 107m3, suggesting that icebergs could persist into the start of a second year when fractionaliceberg cover is high.Once Bridge Glacier transitions into stage four of the conceptual model, where theglacier has retreated up-valley of the lake-filled basin and ceases calving, icebergs alreadypresent in the lake will likely persist for only one year, after which the basin will becomefree of icebergs. Once iceberg-free, there will be substantial impacts on the structure andthermal regime of the lake, as well as on temperatures downstream in Bridge River. Bird(2014) suggested that the current two lake basins split by a submerged terminal moraine514.4. A dual-method approach to trend analysiswill behave as a single basin post-calving, as the icebergs will no longer create a barrierbetween the two. Increased surface energy exchange over the lake will allow for higher watertemperatures both in the lake and downstream in Bridge River, as energy will no longerbe consumed by melting icebergs. In addition, the retreat and grounding of the glacierwill result in a decrease in discharge exiting the lake basin, which will warm outgoingwater even more, as water will have a longer residence time in the basin, increasing watertemperatures by at least 0.7◦C, before exiting at the outlet (Bird, 2014). The decreasingtrend in discharge currently seen in streamflow will become even more apparent once calvingceases, having an impact on hydropower plant operations downstream.4.4 A dual-method approach to trend analysisThis study utilized a dual-method approach to detecting and attributing trends in stream-flow, a promising approach that can increase confidence in results. The first method, adata-based method of statistical streamflow trend analysis, is direct and fully data-based,and is not subject to parameter and structural uncertainties inherent in all hydrologicmodels (Finger et al., 2015). However, it is difficult to determine whether any identifiedrelationships between streamflow and other variables are due to physical cause and effectrelationships or are simply noise in the data (Duethmann et al., 2015). The second method,a modelling-based method to streamflow trend analysis, allows the attribution of trendsthrough process-based modelling. The modelling-based approach is further strengthenedby other data, such as the mass balance estimates used for parameter calibration. However,this approach is time consuming and introduces more uncertainty into the results, a func-tion of model parameters and structure (Duethmann et al., 2015). Using a combination ofthese two independent methods is helpful in diagnosing what is actually responsible for theobserved trends in streamflow data. As the results from both analyses are in reasonableagreement with each other, the confidence in the presented results is increased.52Chapter 5Conclusions5.1 Key findingsThe main findings from this study are summarized below:• Seasonal trends observed in Bridge River streamflow support the conceptual responsemodel and trend hypotheses, with streamflow increasing in the winter months due tocontinued flow of glacier ice into the lake, and streamflow decreasing in the summermonths due to reducing glacier area behind the grounding line.• Bridge Glacier has most likely passed the point of peak water, and can be expected toshow continued decreases in discharge with future climatic warming-induced glaciershrinkage, as suggested by the projections by Stahl et al. (2008). If a valley glacierreaches the lake-calving stage, an acceleration though the phases of peak water intodeclining streamflow is anticipated.• The ice-proximal basin of Bridge Lake is a highly dynamic environment, showingfluctuating iceberg cover due to calving and strong katabatic winds in the valley,increasing the amount of surface area available for melt.• Once calving of the glacier ceases, icebergs currently in the lake basin will meltquickly, persisting for a maximum of two years under fractional iceberg cover of 0.70or more. An iceberg-free lake basin will be subject to greater summer warming,leading to higher downstream temperatures in Bridge River.• It is beneficial to use a dual-method approach when attributing trends in streamflow,as confidence in the results are increased by the use of two independent methods.Furthermore, the additional application of a process-based model provides a strongerbasis for attributing the cause of trends than purely data-based trend analysis.535.2. Future research directions5.2 Future research directionsThis study has explored the response of streamflow to a rapidly retreating lake-terminatingglacier in both pre- and post-calving stages, bringing to light the impacts of calving stageon streamflow trends and also identifying areas where future work is necessary to gain abetter understanding of the complex nature of these environments.Future work should focus on identifying and studying similar scenarios, where the pres-ence of lake-terminating glaciers is coupled with long-term streamflow records and glacierarea data. As this is the only study known to the author that examines the relationshipbetween glacier retreat and streamflow in a lake-calving environment, more studies arerequired to support and verify both the conceptual response model and the demonstratedseasonal trends in discharge.To better constrain estimated iceberg melt rates and volumes using an energy-balanceapproach and to reduce uncertainty, further work is needed to calculate iceberg melt ratesfrom field data. As evident in this study, tracking iceberg changes in a high-energy ice-proximal lake basin proved difficult. Future studies should focus on finding better ways totrack and identify marked icebergs. Additionally, knowing the underwater configurationof selected icebergs would be helpful in estimating their volume, and could potentially beshown using side-scanning sonar. The use of LiDAR to determine changes in volume abovethe water line would also be useful.As only 58% of the Landsat scenes from the linear spectral mixture analysis had errorslow enough to be considered successfully unmixed, future studies involving separating ice-bergs from water using remotely sensed images should make further efforts in identifyingend-members. Measuring the spectral reflectance of silty lake water and debris-covered ice-bergs in the field would be the ideal way to identify these end-members for classification.Additionally, comparing measured end-remembers to those identified in other studies andadding them to spectral libraries for future reference would be beneficial.As in this study, future studies of streamflow trends should employ a dual-methodapproach, using both data-based statistical analyses and deterministic modelling-basedmethods for increased confidence in the results.54ReferencesAbe, T. and Furuya, M. 2015. 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Science, 224(4647):384–387.61Appendix ALinear spectral mixture analysisextended methodologyEnd-member spectra selectionThe most critical step in performing a significant linear spectral unmixing is the selection ofend-members (Tompkins et al., 1997). Endmember spectra can be derived from two mainsources, end-member libraries or the images themselves (Bateson and Curtiss, 1996; Wanget al., 2014). Endmember library spectra are measured in a laboratory under ideal settingsand therefore might provide a more pure spectra for unmixing (Dawelbait and Morari,2012). However, image end-members spectra are easy to obtain and produce the samescaling as the image from which they are derived, allowing for easy detection of changeover time (Wang et al., 2014).In this study, end-member spectra were derived from each Landsat scene through thecompletion of a pixel purity index (PPI). The purest pixels in an image are likely thebest options for image end-members, assuming that pure pixels are unmixed. The PPIrepeatedly projects pixels into a set of randomly generated unit vectors to identify pixelsprojected at the extremes and give those pixels more weight as they are considered purerthan other pixels (Boardman et al., 1995). In this analysis, a PPI was performed for eachimage in ENVI 5.1, repeating each 10,000 times in blocks of 250 iterations. A thresholdfactor of 3 was used to flag all pixels that were 3 digital numbers (DN) away from theidentified extreme pixels, which was chosen based on the noise level of the data. The finaloutput image of each PPI is a brightness map, with more extreme (or pure) pixels shown inlighter colors than those pixels which are heavily mixed (Figure A.1). Pure pixels were thenoverlain with the original Landsat scene for interactive selection of end-member spectra(Figure A.2). A plot of reflectance values of the selected end-members shows the expectedreflectances for ice and water (Figure A.3).62End-member spectra selectionFigure A.1: Brightness map from pixel purity index (PPI) performed on Landsat image acquired forJuly 28, 2014. Dashed red line indicates location of ice-proximal basin and yellow circles indicatelocations of end-member spectra.Figure A.2: Landsat image (bands 1-4) acquired for July 28, 2014. Dashed red line indicateslocation of ice-proximal basin and yellow circles indicate locations of end-member spectra.In order to check the validity of the interactively selected end-member spectra, 4-dimensional scatter plots of all pixels per band were created for every tenth image. Theselected end-members should fall within the vertices of the plotted points. A visual checkwas also completed, comparing the spectrally unmixed image to the original and visuallyinspecting the distribution of end-members in the lake (Figure A.4).63End-member spectra selectionFigure A.3: Digital number and corresponding Landsat band for end-member spectra used in theLSMA of Landsat image acquired for July 28, 2014.Figure A.4: Spectrally unmixed image from Landsat scene acquired for July 28, 2014. Dashed redline indicates location of ice-proximal basin and yellow circles indicate locations of end-memberspectra. Red, green, and blue pixels represent water, dirty, and clean glacier ice, respectively.Combinations of those colors represent mixed pixels (e.g., pink pixels represent a mixture of waterand clean ice).Two versus three end-membersInitially, only two end-members were selected, one for ice and one for water. However, afterunmixing each Landsat scene in the study period and visually comparing the estimated64End-member spectra selectionpercent total ice coverage to the scene and to personal accounts of lake ice content, a thirdend-member for dirty glacier ice was added. In the event that a pure dirty glacier iceend-member spectra was not present in the lake basin, the spectra was selected from thetongue of the glacier.There is a significant difference for most years between the total ice area and percentcover estimated using two and three end-member spectra (Figure A.5). For the sampleLandsat scene acquired for July 28, 2014, two end-member unmixing (glacier ice and water)resulted in 0.35 km2 of total ice and 7.2% ice cover in the proximal basin. When visuallycompared to the Landsat scene, these values seemed far too low, an indication that theLSMA was not accurately unmixing the lake pixels. When performed using three end-memebers, including one for dirty glacier ice, the unmixing resulted in 1.21 km2 of totalice and 24.7% cover, which seems more reasonable when compared to the Landsat scene.1985 1990 1995 2000 2005 2010 20150.01.02.03.0Ice area (km2 )3 Endmembers2 EndmembersFigure A.5: A comparison of spectral unmixing results of iceberg surface area in the proximal basinperformed using two and three end-members.65LSMA errors, assumptions, and limitationsLSMA errors, assumptions, and limitationsMany factors may have contributed to pixels and images with mean RMS errors largerthan 1 DN, including shade in the landscape due to surface roughness and topography(Adams et al., 1995) or the presence of melt ponds and supraglacial streams on top ofthe large, tabular icebergs during the melt season (Gao and Liu, 2001), both of whichchange the spectral reflectance of the Landsat scene and are not accounted for within theend-members. However, it is necessary to use imagery during the melt season in order tocapture the spectral reflectance of icebergs in the lake without the influence of winter lakeice cover. Additionally, the presence of blue ice brought to the surface post-iceberg rollingand breaking is not accounted for within the end-members and will confuse the unmixingprocess (Figure A.6).(a) (b)Figure A.6: Photographs of icebergs in the proximal basin of Bridge Lake demonstrating the spectralvariability of icebergs during the melt season (a) and the presence of blue ice on the now-exposedundersides of flipped icebergs (b).In addition to the above mentioned sources of error, the selection of end-membershas a large influence on the unmixing results. Selecting image end-members is a verysubjective process, depending highly upon user intervention to judge the resemblance ofspectra to actual ground end-member reflectance. Due to the spatial resolution of theLandsat imagery, it is likely that each end-member contains some contamination (Elmoreet al., 2000). As a result, there are many fractions of end-members that are less than zeroor greater than one in any given year of the study period. These fractions should not be66LSMA errors, assumptions, and limitationspossible, indicating spectral variability in the scene not accounted for by the linear model(Adams et al., 1995), and were thus removed from the unmixing analysis. This suggests thatthree end-members are insufficient to accurately model the natural variability of surfacematerials in the lake basin.The general assumption made with LSMA is that a linear relationship between imageend-members and mixed pixels exists in the first place. However, it is possible that anon-linear relationship exists, produced when photons interact with more than one surfacematerial and are thus scattered before returning to the sensor (Ray and Murray, 1996).Non-linear spectral mixing is more common between vegetation and soil (Roberts et al.,1993; Ray and Murray, 1996), but could be a factor when unmixing the closely associatediceberg types and silty water in the lake basin.The main limitation of this LSMA is that it has poor repeatability. Due to the subjectivenature of end-member selection, different users will collect different end-member spectraand thus the LSMA could produce vastly different results (Bateson and Curtiss, 1996).The PPI process used to ensure the selection of pure end-member spectra is a randomizedprocess, meaning that different vectors are projected each time the PPI is performed (Wanget al., 2014). Therefore the same pixels may not be classified as pure every time the sameimage is indexed and the same pixels may not even be selected by the same user for anindividual image.Despite the numerous errors, assumptions, and limitations of the LSMA performedin this study, the results can still be used to diagnose potential relationships betweenhydrological factors and their relative contributions to discharge within the study area.67Landsat image acquisitionLandsat image acquisitionTable A.1: Dates of Landsat 4-5 MSS/TM and 7 ETM+ acquisitions.Year Julian Day(s) Landsat Sensor1984 199/263/271 5 TM/5 MSS/4 MSS1985 201/209, 225/265 5 TM/4 MSS/5 MSS1986 181, 213, 220, 229, 268, 293 5 TM1988 258, 274 5 TM1989 157, 205, 276 5 TM1990 199, 247/263 5 MSS/5 TM1992 198, 214, 237 5 TM1993 223, 271/255 5 MSS/5 TM1994 171, 194, 267 5 TM1995 197, 254 5 TM1997 266 5 TM1998 269 5 TM1999 200, 264 7 ETM+2000 203, 267 7 ETM+2001 205 7 ETM+2002 177, 193, 225, 257, 264 5 TM2003 211, 243,275 7 ETM+2004 182, 214, 278 7 ETM+2005 208/216 5 TM/7 ETM+2006 243/203, 267, 283 5 TM/7 ETM+2007 262/190, 206, 254 5 TM/7 ETM+2008 217, 258, 274/193, 257, 273 5 TM/7 ETM+2009 267/211, 243 5 TM/7 ETM+2010 206/230 5 TM/7 ETM+2011 177/249 5 TM/7 ETM+2012 188, 220 7 ETM+2013 206, 254 7 ETM+2014 193, 209, 257 7 ETM+68

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