Arts, Faculty of
Geography, Department of
DSpace
UBCV
Browning, Billy
Master of Science - MSc
University of British Columbia
Glacially fed streams face increasing threats due to changes in stream temperature and flow from continued glacier recession and climate change. These systems support unique ecological communities, often highly sensitive to thermal changes. However, understanding the governing processes of stream temperature in large glacially fed stream reaches remains limited, with a lack of literature focused on larger rivers with tributaries. The objective of this study was to quantify the drivers of stream temperature dynamics in a 24 km long reach of the glacially fed Lillooet River in the southern Coast Mountains, BC. To support the application of HydroCouple, a reach-scale process-based stream temperature model, a new stream shading model was developed that used a LiDAR digital surface model to simulate shade from riparian vegetation and a conventional DEM to simulate topographic shade. Based on a comparison with shade interpreted from high-resolution PlanetScope imagery, the model simulated shade accurately both at individual points and for reach-scale averages. The model was used to simulate incident shortwave and longwave radiation at the stream surface. Air temperature, vapour pressure and wind speed were monitored at both landbased and above- stream meteorological stations. While the differences between land-based and above-stream observations were broadly similar to those found in previous studies, there were some distinct patterns that were attributed to the timing of daily maximum water temperature, which occurred near midnight rather than early afternoon, as is more typical for non-glacier-fed streams.HydroCouple was applied without calibration under the assumption that bed heat conduction and hyporheic heat exchange were negligible. The model showed good performance (RMSE = 0.30 oC, ME = 0.03 oC) compared to previous literature. Longitudinal advection of the upstream boundary condition had an overwhelming impact on downstream temperatures, leading to low sensitivity to streamflow or energy exchange variations. Tributaries muted main channel stream temperature variations, typically reducing temperatures by 0.5 oC around midnight (daily maxima) and increasing them by 0.2 oC during the afternoon (daily minima). Net radiation at the stream surface increased stream temperatures by 0.3-0.4 oC during peak solar hours and shifted daytime daily minimum stream temperatures on average 40 minutes later.
Process-based modelling of streamtemperature dynamics in a glacially fed riversystembyBilly BrowningB.Sc. Geography, University of Birmingham, UK, 2020A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Geography)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2023© Billy Browning, 2023The following individuals certify that they have read, and recommend to the Faculty ofGraduate and Postdoctoral Studies for acceptance, the thesis entitled:Process-based modelling of stream temperature dynamics in a glacially fed river systemsubmitted by Billy Browning in partial fulfillment of the requirements forthe degree of Master of Sciencein GeographyExamining committee:Dan R. Moore, Professor, Geography, UBCSupervisorIan McKendry, Professor, Geography, UBCSupervisory Committee MemberAndre Zimmermann, Principal Geomorphologist, Northwest Hydraulics ConsultantsAdditional ExamineriiAbstractGlacially fed streams face increasing threats due to changes in stream temperature andflow from continued glacier recession and climate change. These systems support uniqueecological communities, often highly sensitive to thermal changes. However, understandingthe governing processes of stream temperature in large glacially fed stream reaches remainslimited, with a lack of literature focused on larger rivers with tributaries. The objective ofthis study was to quantify the drivers of stream temperature dynamics in a 24 km long reachof the glacially fed Lillooet River in the southern Coast Mountains, BC.To support the application of HydroCouple, a reach-scale process-based stream tem-perature model, a new stream shading model was developed that used a LiDAR digitalsurface model to simulate shade from riparian vegetation and a conventional DEM to simu-late topographic shade. Based on a comparison with shade interpreted from high-resolutionPlanetScope imagery, the model simulated shade accurately both at individual points andfor reach-scale averages. The model was used to simulate incident shortwave and longwaveradiation at the stream surface.Air temperature, vapour pressure and wind speed were monitored at both land-based and above-stream meteorological stations. While the differences between land-basedand above-stream observations were broadly similar to those found in previous studies, therewere some distinct patterns that were attributed to the timing of daily maximum watertemperature, which occurred near midnight rather than early afternoon, as is more typicalfor non-glacier-fed streams.HydroCouple was applied without calibration under the assumption that bed heatconduction and hyporheic heat exchange were negligible. The model showed good perfor-mance (RMSE = 0.30 oC, ME = 0.03 oC) compared to previous literature. Longitudinaladvection of the upstream boundary condition had an overwhelming impact on downstreamtemperatures, leading to low sensitivity to streamflow or energy exchange variations. Trib-utaries muted main channel stream temperature variations, typically reducing temperaturesby 0.5 oC around midnight (daily maxima) and increasing them by 0.2 oC during the after-noon (daily minima). Net radiation at the stream surface increased stream temperatures by0.3-0.4 oC during peak solar hours and shifted daytime daily minimum stream temperatureson average 40 minutes later.iiiLay SummaryGlacially fed streams are facing increased threats due to the effects of melting glaciers, whichalter stream temperature and flow. These streams have unique temperature patterns thatsupport thermally sensitive ecosystems. However, the relative controls on stream tempera-ture are not well understood in large glacially fed streams. This study focused on modellingstream temperatures at the reach-scale for a 24 km stretch of the Lillooet River in theCoast Mountains of British Columbia during the summer. A novel contribution of thisstudy was to accurately characterize relations between above-stream and land-based me-teorological observations and to develop a new model that simulates stream-surface shadefrom nearby vegetation and surrounding topography. The aforementioned methods enabledstream temperatures to be accurately modelled without the need for calibration. The studyfound that upstream heat flow significantly impacted downstream temperatures, overshad-owing the effects from tributary inputs and energy exchanges between the stream surfaceand atmosphere.ivPrefaceThis thesis is original work completed by the author. Guidance was given by the supervisorycommittee (Dan Moore and Ian McKendry) and field assistance was provided by SierraCollins, Zijie Chai, Lilianne Callahan, Amy McIntyre and Emma Lowe.A version of this work was given as a presentation titled: ‘Modelling contributionsof riparian vegetation and topography to stream shade and view factors using LiDAR andconventional elevation data’ (Browning and Moore, 2023). The the author acted as leadinvestigator, composing and presenting the work at the 2023 Canadian Geophysical Union(CGU) meeting.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation for study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 Processes influencing stream temperature . . . . . . . . . . . . . . . . . 31.2.2 Process-based stream temperature models in glacially fed streams . . . 71.3 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1 Study area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Data collection and field methods . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.1 Overview of stream monitoring sites . . . . . . . . . . . . . . . . . . . . 152.2.2 Meteorological data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 Stream temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.4 Streamflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3 Modelling and analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.1 Stream shade model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.2 Stream temperature model . . . . . . . . . . . . . . . . . . . . . . . . . 283 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.1 Overview of the study period . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Stream boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.1 Observed stream temperatures . . . . . . . . . . . . . . . . . . . . . . . 383.2.2 Observed streamflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.3 Diel variations in stream temperature and flow . . . . . . . . . . . . . . . . . 443.4 Above-stream meteorological conditions . . . . . . . . . . . . . . . . . . . . . 45vi3.4.1 Air temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.4.2 Atmospheric vapour pressure . . . . . . . . . . . . . . . . . . . . . . . . 503.4.3 Wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.5 Shade and view factor modelling . . . . . . . . . . . . . . . . . . . . . . . . . 553.5.1 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.5.2 Stream shade and shade fraction . . . . . . . . . . . . . . . . . . . . . . 563.5.3 Sky view factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.6 Stream temperature model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.6.1 Surface-atmosphere energy exchanges . . . . . . . . . . . . . . . . . . . 643.6.2 Model performance for the full period of record . . . . . . . . . . . . . . 653.6.3 Streamflow simulations for Jul. 29 to Aug. 5 . . . . . . . . . . . . . . . 684 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.1 Above-stream meteorology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.2 Assessment of stream shade model . . . . . . . . . . . . . . . . . . . . . . . . 834.3 Consistency of streamflow data . . . . . . . . . . . . . . . . . . . . . . . . . . 844.4 Observed stream temperature dynamics . . . . . . . . . . . . . . . . . . . . . 854.5 Model performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.6 Model sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.7 Implications for understanding the scale-dependence of stream temperaturedynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.1 Summary of key findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.2 Future recommendations and research . . . . . . . . . . . . . . . . . . . . . . 90References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Appendix A - Pyrgeometer internal temperatures . . . . . . . . . . . . . . . . . . 102viiList of Tables1.1 Summary of process-based stream temperature modelling studies regardingglacially-fed streams. RMSE = Root mean square error. . . . . . . . . . . . . 102.1 Meteorological instrument specifications. OSMS and ASMS represent the opensite meteorlogical station and above stream meteorlogical station, respectively. 192.2 Summary of the stream temperature model scenarios. . . . . . . . . . . . . . . 353.1 Mean daily stream temperature statistics for the monitoring period at each sub-reach. Only the data points that correspond with the observational timings atall four sub-reaches are included for comparisons. . . . . . . . . . . . . . . . . 403.2 ASMS deployment times, deployment length (hours) and summary statisticsfor above-stream air temperatures (𝑇𝑎∶𝐴𝑆) during ASMS deployment. All timesare relative to PDT (UTC-7) . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.3 Results of regression model fits for predicting above-stream atmospheric vapourpressure (𝑒𝑎∶𝐴𝑆) using vapour pressure measured at the open-site met stationOSMS (𝑒𝑎∶𝑂𝑆)and Pemberton Airport atmospheric vapour pressures (𝑒𝑎∶𝑂𝑆) aspredictors. Results include corrected Akaike’s information criterion (𝐴𝐼𝐶𝑐),residual standard error (RSE), intercept (𝑏0) and the coefficients for the pre-dictor variables for all coefficients with 𝑝 < 0.01. Bold indicates the model thatwas selected to predict above-stream vapour pressure over the entire study pe-riod. Only the 89 data points where all observations overlap between all threesites were included to allow direct comparison of 𝐴𝐼𝐶𝑐 values. . . . . . . . . . 533.4 Above-stream wind speed statistics (ms−1). Note that wind speeds of 0 ms-1were replaced with values of 0.15 (half the stall speed). . . . . . . . . . . . . . 543.5 Summary of Planet Scope satellite imagery (Planet Team, 2017) used for modeltesting including the calendar date, time and solar elevation (𝑆𝜃) and azimuthangles (𝑎𝜃) (𝑜) during image acquisition. Ground truthing results include theobserved and predicted shaded area (km2) as 𝑠𝑎 and ̂𝑠𝑎, respectively and thecalculated observed and predicted shade fractions as 𝑠𝑜𝑏𝑠 and ̂𝑠𝑝𝑟𝑒𝑑, respec-tively. Δ𝑠𝑡 is the difference in shade fraction between observed and predicted. 553.6 Confusion matrix of model validation results. Numbers represent the numberof gridded 20-m cell centroids (POIs) that were classified as true positive (TP),true negative (TN), false positive (FP) and false negative (FN) when comparingmodelled shade to all nine satellite scenes. . . . . . . . . . . . . . . . . . . . . 563.7 Classification performance statistics from confusion matrix including the accu-racy, 𝐹1−𝑠𝑐𝑜𝑟𝑒 and Matthews correlation coefficient (MCC) and the maximumrange of possible values for each statistic. . . . . . . . . . . . . . . . . . . . . 57viiiList of Figures2.1 Study area of the Lillooet River catchment and highlighted monitoring area.Lillooet River catchment delineated from the above stream meteorological sta-tion (ASMS) at the BC Highway 99 bridge. Map projected in NAD83 / UTMzone 10N. Lillooet catchment contains DEM with draped multi-directional hill-shade. Glacier boundaries (permanent snow and ice) retrieved from GLIMS andNSIDC (2019). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Monitoring area including field sites and established gauge stations. Map pro-jected in NAD83 / UTM zone 10N. PVDD gauge station located at Upper Lil-looet (UL) monitors stream temperature and flow (ID: 08MG00A), WSC gaugestation at Lower Lillooet (LL) monitors streamflow (station ID: 08MG005) andWSC gauge station at Ryan River (RR) monitors stream temperature and flow(station ID: 08MG028). Blue stream segment highlights the Lillooet studyreach for which stream temperature were modelled and red stream segmenthighlights the ground truthing stream reach, the methods of which are de-scribed in Section 2.3.1.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Open site meteorlogical station (OSMS) situated in an open field in PembertonMeadows at Miller’s Farm Beer Farmers. . . . . . . . . . . . . . . . . . . . . . 182.4 Pictures of the above stream meteorological station (ASMS) deployed over BCHighway 99 bridge over the Lillooet River. Red circle denotes the locations ofASMS. Pictures taken from right bank and river flows from left to right. . . . 192.5 The relationship between water temperatures measured at the PVDD gaugestation and the UL tidbit, with a fitted regression line and a 1:1 line. . . . . . 202.6 The difference in streamflows between the Lower Lillooet gauge station andthe sum of the boundary and tributary flow conditions as a function of time.Segmented regression model in red. 𝑄𝐿𝐿, 𝑄𝑈𝐿, 𝑄𝑅𝑅 and 𝑄𝑀𝐶 represent thestreamflows at Lower Lillooet, Upper Lillooet, Ryan River and Miller Creekrespectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.7 Schematic diagram of finding the horizon angle 𝐻𝜃 from a point of interest toa grid cell of an elevation raster. 𝑎𝜃 is the azimuth angle measured clockwisefrom north. The 𝑧 value is the elevation (m) at grid cell 𝑥𝑦. This diagram rep-resents a planar cartesian system for visualization purposes, whereas a geodesicgeographic system was used to calculate 𝐻𝜃 and 𝑎𝜃. . . . . . . . . . . . . . . . 252.8 Schematic diagram of the cells (𝑐) and junctions (𝑗) used to longitudinallydiscretize the stream reach for the stream temperature model. Light blue boundby dark blue curved lines represent the stream surface and the bounding streambanks. Red dots represent the location of each junction that creates each cell(green rectangles). Grey line represents the stream centerline. . . . . . . . . . 29ix3.1 Maximum, mean and minimum mean monthly air temperatures (𝑜C) at Pem-berton Airport meteorological station (PAMS) (Station ID: 1086082, elevation:204 m a.s.l) for the period 1985-2021. Monthly air temperatures for 2022 areshown in blue. Air temperatures during the field season at the open site me-teorological stations (OSMS) are shown in red (elevation: 227 m a.s.l). Onlycomplete months of data were included for OSMS. Grey polygon represents themonitoring period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2 Monthly mean total precipitation (mm) for the period 1985-2021 (grey) and2022 (blue) at Pemberton Airport meteorological station (PAMS). Monthlytotal precipitation at the open site meteorological station (OSMS) during themonitoring period (red). Only complete months of data were included for OSMS. 373.3 Maximum, mean and minimum mean daily discharge (m3s−1) at the Lower Lil-looet WSC Gauge station (Station ID: 08MG005). 2022 mean daily dischargedisplayed in blue. Grey polygon represents monitoring period. . . . . . . . . . 383.4 Meteorological variables monitored at the open site meteorological station(OSMS) throughout the monitoring period, recorded every 10 minutes. (a) in-cident shortwave radiation (𝐾 ↓𝑂𝑆), (b) incident longwave radiation (𝐿 ↓𝑂 𝑆),(c) air temperature (𝑇𝑎∶𝑂𝑆), (d) atmospheric vapour pressure (𝑒𝑎∶𝑂𝑆), (e) windspeed (𝑢), (f) barometric pressure (𝑃𝑏) and (f) rainfall. . . . . . . . . . . . . . 393.5 Meteorological variables observed at Pemberton Airport Meteorological sta-tions (PAMS). (a) air temperature (𝑇𝑎∶𝑃𝐴), (b) atmospheric vapour pressure(𝑒𝑎∶𝑃𝐴), and (c) wind speed (𝑢𝑃𝐴). . . . . . . . . . . . . . . . . . . . . . . . . 403.6 Water temperatures (𝑇𝑤) for Upper Lillooet (a), Ryan River (b), Miller Creek(c) and Lower Lillooet (d) (oC). Upper Lillooet and Ryan River 𝑇𝑤 are fromgauging stations operated by WSC, whereas Miller Creek and Lower Lillooet𝑇𝑤 are from tidbit water temperature loggers. Red lines for UL are values thatwere interpolated using the linear regression between 𝑇𝑤 at the UL PVDDgauge station as a function of 𝑇𝑤 at the UL tidbit temperature logger. Bluelines represent linear interpolation between coinciding periods of no data at theUL tidbit temperature logger and the UL PVDD gauge station. Gaps in thetime series represent data removed due to suspected dewatering. . . . . . . . . 413.7 (a) Maximum, mean and minimum mean daily air temperatures at OSMS(𝑇𝑎∶𝑂𝑆). (b) Mean daily water temperatures at UL, RR, MC and LL (𝑇𝑤). . . 423.8 Stream discharge (𝑄) for Upper Lillooet (a), Ryan River (b), Miller Creek (c)and Lower Lillooet (d) (m3s-1). Upper Lillooet streamflow from PVDD gaugestation, Ryan River and Lower Lillooet streamflow from WSC gauge stationand Miller Creek streamflow derived from from the model fitting of the stagerating curve produced from the velocity-area streamflow measurements. Greyline represents the uncorrected Upper Lillooet streamflows compared to thebias corrected streamflows in black. . . . . . . . . . . . . . . . . . . . . . . . . 433.9 Stream temperature (𝑇𝑤) at Upper Lillooet (UL), Ryan River (RR), MillerCreek (MC) and Lower Lillooet (LL) between 29 July and 5 August. Timezonein PDT (UTC-7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44x3.10 (a) Timing of daily maximum water temperature (𝑇𝑤) at Upper Lillooet (UL),Ryan River (RR), Miller Creek (MC) and Lower Lillooet (LL) as red, blue,green and orange, respectively. (b) Timing of daily minimum 𝑇𝑤 at UL, RR,MC and LL. Horizontal colored lines represent the mean timing of maximumand minimum water temperatures between 29th July and 5th August. Horizon-tal dotted grey lines represent 1-hour intervals. Note that RR water tempera-ture is recorded hourly. Timezone in PDT (UTC-7). . . . . . . . . . . . . . . 463.11Observed stream temperatures (𝑇𝑤) as a function of streamflow (𝑄) colored bydate for Upper Lillooet (UL), Ryan River (RR), Miller Creek (MC) and LowerLillooet (LL). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.12 Pairwise relations between air temperatures measured at three weather sta-tions: ASMS versus OSMS (a), ASMS versus Pemberton Airport (b), andOSMS versus Pemberton Airport (c). Dashed line represents a 1:1 relation.Note that 𝑇𝑎∶𝑂𝑆 was recorded every 10 minutes throughout the entire field sea-son, 𝑇𝑎∶𝐴𝑆 was recorded every 10 minutes throughout field deployment visitsand 𝑇𝑎∶𝑃𝐴 was recorded every hour throughout the entire field season. . . . . . 483.13Time series of air temperatures during ASMS deployment comparing air tem-peratures at ASMS (𝑇𝑎∶𝐴𝑆) in blue and OSMS (𝑇𝑎∶𝑂𝑆) in red. Grey lines repre-sent incident longwave radiation at OSMS (𝐿 ↓𝑂𝑆) and grey polygons representperiods of shade, modelled using the shade model methods in Section 2.3.1).Timezone in PDT (UTC-7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.14Relations between above-stream air temperature and air temperature at OSMS.All data are shown in panel (a), with symbol colour indicating sky condition.Panels (b) to (d) present data separately by subset, with the fitted regressionsshown as red lines. In panel (d), the solid line is the segmented regression usedin further analysis and the dashed red line represents a simple linear regressionfor comparison. Equations for the regressions are shown in Equation (3.1),Equation (3.2) and Equation (3.3). . . . . . . . . . . . . . . . . . . . . . . . . 513.15Time series of predicted above-stream air temperature throughout the entirefield season as used as input for the stream temperature model. . . . . . . . . 523.16 Pairwise relations between vapour pressures measured at three weather sta-tions: ASMS versus OSMS (a), ASMS versus Pemberton Airport (b), andOSMS versus Pemberton Airport (c). Dashed line represents a 1:1 relation.The solid red line in panel (b) is the regression relation used in later analysis;the dashed red line in panel (a) is a regression fit for those data. Dashed linerepresents a 1:1 relation. Note that 𝑒𝑎∶𝑂𝑆 is recorded every 10 minutes through-out the entire field season, 𝑒𝑎∶𝐴𝑆 is recorded every 10 minutes throughout fielddeployment visits and 𝑒𝑎∶𝑃𝐴 is recorded every hour throughout the entire fieldseason. Only the 89 data points where all observations overlap between allthree sites were included in a) and b). All pair-wise data points correspondingwith OSMS and PAMS are included in d). . . . . . . . . . . . . . . . . . . . . 523.17Time series of predicted above-stream atmospheric vapour pressure over theentire field season. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.18Histograms of wind speed (𝑢) at (a) ASMS, (b) OSMS and (c) PAMS. . . . . 54xi3.19Relationships between observed wind speeds at ASMS (𝑢𝐴𝑆) and OSMS (𝑢𝑂𝑆)(a), ASMS and Pemberton Airport (𝑢𝑃𝐴) (b), and OSMS and Pemberton Air-port (c). Dashed black line represents the 1:1 relationship. All available obser-vations on a pairwise basis are plotted. . . . . . . . . . . . . . . . . . . . . . . 543.20 Example satellite scene used for model validation with modelled shade in black(shaded) and white (unshaded) and manually delineated observed shading fromsatellite imagery as transparent red polygon. Grey lines represent 100 m ele-vation contours. Delineated stream boundary is in blue. . . . . . . . . . . . . 553.21Comparison between predicted and observed shade fractions ( ̂𝑠𝑡). . . . . . . . 563.22Variation of shade patterns through time on August 16, 2022. Modelled shadefrom LiDAR is shown in dark green (Riparian shade), topographic shade fromthe CDEM is in red, shade cast by both features is in black, and cells with noshade are in white. Also shown is canopy height (m) calculated by differencingthe LiDAR DSM and DTM for a 200-m buffer along the delineated LillooetRiver water surface polygon. Inset map shows the Lillooet monitoring reach inlight blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.23Variation of modelled shade patterns for three sections of Lillooet River at19:00 on August 16, 2022. Riparian shade from LiDAR is shown in dark green,topographic shade from the CDEM is in red, shading cast by both features isin black, and cells with no shade are in white. Locations of stream sectionsare shown on the inset map. Also shown is canopy height (m) calculated bydifferencing the LiDAR DSM and DTM for a 200-m buffer along the delineatedLillooet River water surface polygon. Inset map shows the Lillooet monitoringreach in light blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.24Diurnal variation of mean reach-wide shade fraction (𝑆𝑡). Total shade is shownas a black line, while the separate contributions of riparian shade from LiDARand topographic shading from the Canadian DEM (CDEM) are shown as greenand red lines, respectively. Vertical grey lines represent 2-hour intervals. Time-zone in PDT (UTC-7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.25Amount of daily modelled sunlight hours for each stream cell in grey, meannumber of sunlight hours for the entire stream reach in black and the dailynumber of sunlight hours at the open site meteorological station (OSMS) inred. Timezone in PDT (UTC-7). . . . . . . . . . . . . . . . . . . . . . . . . . 613.26Modelled sky view factor (𝑓𝑣) at each 20-m-grid POI. Delineated stream bound-ary as blue lines. Inset map provides reference extents for stream reach seg-ments and highlights the large scale topographic features using the CDEMshaded from black (low elevations) to white (high elevations). . . . . . . . . . 623.27 Longitudinal variation in the mean sky view factor (𝑓𝑣) for each 100-m cellused in the stream temperature model. . . . . . . . . . . . . . . . . . . . . . . 633.28 Boxplot of modelled sky view factor (𝑓𝑣) values for each POI for the normalmodel (grey) and when only taking into account the CDEM (red) and LiDAR(green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.29 a) Predicted albedo (𝛼) using the FWa-3 categorical SSC model derived byMcMahon and Moore (2017). b) Atmospheric emissivity (𝜖𝑎). . . . . . . . . . 64xii3.30Reach-averaged radiative exchanges for the Lillooet stream reach including in-cident long and shortwave radiation (𝐿 ↓𝐴𝑆 and 𝐾 ↓𝐴𝑆, respectively), outgoinglong and shortwave radiation (𝐿 ↑𝐴𝑆 and 𝐾 ↑𝐴𝑆, respectively) and net all-waveradiation (𝑄∗). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.31 (a) Reach-averaged radiative exchanges for the Lillooet stream reach includingincident long and shortwave radiation (𝐿 ↓𝐴𝑆 and 𝐾 ↓𝐴𝑆, respectively), out-going long and shortwave radiation (𝐿 ↑𝐴𝑆 and 𝐾 ↑𝐴𝑆, respectively) and netall-wave radiation (𝑄∗). (b) Radiative exchanges at the cell that experiencedthe highest average sunlight hours (Cell 265). (C) Radiative exchanges at thecell that experienced the lowest average sunlight hours (Cell 165). Timezonein PDT (UTC-7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.32Above-stream air temperature ( ̂𝑇𝑎∶𝐴𝑆) (a), reach-averaged sensible (𝑄ℎ) andlatent (𝑄𝑒) heat fluxes estimated by the stream temperature model (b) andthe difference between above stream atmospheric vapour pressure ( ̂𝑒𝑎∶𝐴𝑆 ) andreach-averaged above-stream atmospheric vapour pressure ( ̂𝑒𝑤) (c). Baselinemodel scenario used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.33Modelled streamflow (?̂?) at Lower Lillooet (LL) using the baseline model sce-nario (a), which includes the bias-corrected UL (Upper Lillooet) streamflows,and the UL uncorrected model scenario (b). . . . . . . . . . . . . . . . . . . . 683.34Modelled (red) and observed (black) stream temperatures for the seven mod-elling scenarios at the model cell corresponding to the Lower Lillooet (LL)field. Upper Lillooet (UL) stream temperatures are shown in grey. Root-mean-square errors (RMSE) only include the period up to Sept. 21 (grey poly-gons) and also exclude the first 12 hr to minimize the effect of incorrectly setinitial conditions. UL = Upper Lillooet, LL = Lower Lillooet, WS = windspeeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.35Modelled (red) and observed (black) streamflows (𝑄𝐿𝐿) at LL (top-panel) fromJul. 29 to Aug. 5. Modelled and observed stream temperatures (𝑇𝑤) at LL(remaining panels). Observed 𝑇𝑤 at UL in grey. Timezone in PDT (UTC-7). . 713.36Observed and modelled stream temperature for Jul. 29 to Aug. 5. Top panelrepresents observed Lower Lillooet (LL) streamflow (𝑄𝐿𝐿) and remaining pan-els show the differences between each model scenario and the baseline modelstream temperatures at LL (Δ𝑇𝑤). Positive values mean that the scenario pro-duces higher stream temperatures than the baseline model. Timezone in PDT(UTC-7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.37Modelled stream temperatures (𝑇𝑤) for each cell as distance downstream fromthe Upper Lillooet (UL) using the baseline scenario. . . . . . . . . . . . . . . 733.38The timing of daily maximum (a) and minimum (b) modelled stream temper-atures for the baseline (red circle), advection-only (green triangle), no-RyanRiver (blue plus) and no-Miller Creek (orange cross) scenarios at LL as a func-tion of date. Dashed colored lines represent the corresponding mean times andsolid black line represents the mean of observed timings. Note that the streamtemperature model calculated stream temperature every 30 minutes. Timezonein PDT (UTC-7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74xiii3.39Modelled stream temperature (a) (𝑇𝑤) and discharge (b) (𝑄) above Ryan River(RR) at cell 199 (green), between RR and Miller Creek (MC) at cell 201 (blue)and below MC at cell 204 (red), with observed Upper Lillooet (UL). Observed𝑇𝑤 and 𝑄 at Upper Lillooet (UL) in grey. Timezone in PDT (UTC-7). . . . . 753.40Differences in modelled stream temperatures ( ̂𝑇 [𝑤]) between cells downstreamand upstream of Ryan River (a) and cells downstream and upstream of MillerCreek (MC). Cell numbers increase from upstream to downstream. The base-line model scenario was used for calculations. Positive values represent down-stream cell conditions that are warmer than the upstream cell conditions. Time-zone in PDT (UTC-7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.41Modelled stream temperatures at LL during the period 29th July to 5th August(red) compared to the observed stream temperatures (𝑇𝑤) at LL (black) andUL (grey). Timezone in PDT (UTC-7). . . . . . . . . . . . . . . . . . . . . . 783.42 Streamflow at Lower Lillooet (top panel) and the differences between eachmodel scenario and the baseline model stream temperatures at LL (Δ𝑇𝑤).Positive values indicate that the scenario produces higher stream temperaturesthan the baseline scenario. Timezone in PDT (UTC-7). . . . . . . . . . . . . 793.43The difference in modelled stream temperatures (𝑇𝑤) between the energy ex-change scenarios and baseline scenario as distance downstream from UpperLillooet (UL). Positive values represent where modelled stream temperatureare greater than baseline scenario values. Timezone in PDT (UTC-7). . . . . 80A.1 Stage as a function of width using the stream geometry measurements pro-vided by Hutchinson (2023) at the two monitoring locations. Regression linepresented in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103A.2 Stream cross-section observed during 2023 high flows using ADCP measure-ments near the Upper Lillooet FSR Bridge and provided by Zimmermann(2023). Red line represents the bottom width, blue line represents streamwater surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103xivList of AbbreviationsAbbreviation DescriptionASMS Above-stream meteorological stationCDEM Canadian digital elevation modelCSHComponent Channel solute and heat transport componentDEM Digital elevation modelDSM Digital surface modelDTM Digital terrain modelFN False negative classificationFP False positive classificationFSR Forest service roadHTSComponent Hyporheic and transient storage zone heat transport componentLiDAR Light detecting and rangingLL Lower LillooetMC Miller CreekMCC Matthews correlation coefficientME Mean errorNHC Northwest Hydraulic ConsultantsOSMS Open-site meteorological stationPAMS Pemberton Airport Meteorological stationPOI Point of interestPVDD Pemberton Valley Dyking DistrictRHEComponent Radiative heat exchange heat exchange componentRMSE Root mean square errorRR Ryan RiverRSE Residual standard errorSfM Structure from motionSSC Suspended sediment concentrationTN True negative classificationTP True positive classificationUL Upper LillooetWSC Water Survey of CanadaxvAcknowledgementsI am deeply grateful to the countless number of people who have been influential throughoutthe research process. First and foremost, I would like to express my sincere appreciation tomy supervisor, Dan Moore. Dan’s passion, dedication and unparalleled guidance throughoutthe entire research process made this thesis possible. Especially during unexpected circum-stances, his patience, invaluable advice and attention to detail during such a pivotal timemade a huge difference. I consider myself fortunate to have had him as a supervisor. IanMcKendry’s comments and guidance throughout the final writing stages were also appreci-ated.Funding for this research was provided by operating grants to Professor Dan Moorefrom Natural Sciences and Engineering Research Council (NSERC). The author was sup-ported by a Graduate Award from the UBC Faculty of Arts.I extend special thanks to my dedicated field team, whose enthusiasm and commit-ment made spending extended periods surrounding Pemberton Valley even more enjoyable.Their support in carrying equipment during intense heat and through swarms of mosquitoesgreatly contributed to the success of the data collection processes.An extended thanks goes Professor Nicholas Barrand and other professors in theSchool of Geography, Earth and Environmental Sciences at the University of Birmingham,for igniting my passion for hydrology and glacially influenced systems. I am deeply thankfulto Archipelagos Institute of Marine Conservation for providing me with unparalleled fieldexperience, cherished memories and the opportunity to work alongside exceptional colleaguesand friends. Their belief in my ideas and research remains a constant source of motivation.Finally, my heartfelt thanks go to my family for their consistent support and encour-agement in pursuing my interests. Without them, I would not have had the opportunity tomove abroad and progress as far as I have today. I am also grateful to my friends, both inCanada and back at home in the UK, for keeping me relatively sane throughout the yearsand always encouraging me. Their constant presence, enthusiasm and humour have mademy undergraduate and graduate experiences unforgettable, and I am incredibly blessed tocall them my friends.xviChapter 1Introduction1.1 Motivation for studyA stream’s thermal regime is one of the most important factors influencing its ecological andbiogeochemical processes (Mellina et al., 2002; Caissie, 2006; Moore, 2006; Woolway andMerchant, 2019; Leach et al., 2021), with specific influences on ecosystem productivity andnutrient cycling (Jankowski and Schindler, 2019) and the distribution and spawning rate ofaquatic organisms (Caissie, 2006; Isaak et al., 2010). The significance of stream temperatureregimes on hydroecological systems varies on a range of spatio-temporal scales. For example,the timing of fish migration and spawning represents an adaptation to seasonal patterns ofboth stream discharge and temperature, while localized thermal heterogeneity can providerefuge for cool-water adapted species during short periods of elevated stream temperatures(Ebersole et al., 2003; Frechette et al., 2018). Elevated stream temperatures can result inmorbidity and mortality of cold- and cool-water species (Coutant, 1977, 1999), and can in-fluence inter-species competition and thus fish species assemblages (e.g., Parkinson et al.,2016). Given the potentially negative impacts of elevated stream temperature, there hasbeen growing concern in recent decades regarding stream temperature response to projectedclimate warming and the resulting increased risk of wildfire, as well as anthropogenic pres-sures such as forest harvesting and urbanization (Moore et al., 2005a, 2009; Nelson andPalmer, 2007; Leach and Moore, 2010).Glacier melt in mountain catchments plays a key role in determining streamflow andtemperature from diel to interannual time scales (Fountain and Tangborn, 1985; Stahl etal., 2008; Milner et al., 2017). In particular, glacier melt moderates stream temperaturesand maintains streamflow during the summer dry season when non-glacierized catchmentstypically experience low flows and high stream temperatures (Hannah et al., 2005; Moore,2006; Stahl and Moore, 2006). These distinctively controlled stream temperature and flowregimes, controlled by the magnitude and timing of glacier melt, create unique habitat and1thermal refuge for many fish and endemic macroinvertebrate species (Castella et al., 2001;Snook and Milner, 2001; Stahl et al., 2008; Muñoz et al., 2015). The regulatory effect ofhighly glacially influenced systems often supports highly adapted, low taxonomically diversecommunities that are especially sensitive to change (Milner et al., 2017).Global glacier mass loss outside ice sheets has accelerated since the turn of the cen-tury (Meier et al., 2007; Radić and Hock, 2011; Zemp et al., 2015; IPCC, 2019), contributingto one-third of the total projected 21st century sea-level rise (Gardner et al., 2013; Zemp etal., 2019). Despite only making up approximately 12 % of global glacierized regions outsideice sheets, glaciers of western North America account for one-third of all glacier inducedsea-level rise (Arendt et al., 2009; Zemp et al., 2019). This extensive climate-induced glacierrecession not only has significant effects on sea-level but can cause a cascade of impacts ondownstream hydrological regimes, water supplies and marine environments (Jacobsen et al.,2012; Milner et al., 2017).As glaciers retreat, their ability to moderate flow and temperature during extendeddrought conditions will decline (Stahl and Moore, 2006; Moore et al., 2009; Rood et al., 2016;Do et al., 2017). Based on empirical analysis, the resulting reductions in summer meltwaterinputs and diminished thermal capacity of glacially fed rivers, coupled with projected in-creases in air temperature, could cause significantly elevated summer stream temperatures(Moore et al., 2013). Recent and projected climate change in glacially fed hydrological en-vironments includes earlier snowmelt onset, further contributing to these hydrological shifts(Nijssen et al., 2001; Stahl et al., 2008; Arismendi et al., 2012). Rising water temperatureshave already been linked to the mortality of some Pacific Salmon populations (Muñoz et al.,2015), and decreased flows can restrict the migration and spawning of Salmon species thatheavily rely on the thermally regulated summer stream temperatures and heightened flows(Dorava and Milner, 2000).Given the thermal sensitivity of glacier-fed streams, it is imperative to develop ac-curate models for predicting stream temperature response to climate change, glacier retreat,and their interactions. Empirical models based on spatial comparisons, such as that de-veloped by Moore et al. (2013), can provide first-order estimates of stream temperatureresponse to glacier change. However, such models are based on historical climate and land-cover conditions, and may not remain valid under future conditions (Moore et al., 2009).The next section provides a review of stream temperature processes and process-based modelling, with a particular focus on glacier fed catchments. The review is intendedto highlight specific knowledge gaps that form the basis for the study objectives, which areoutlined in the last section of this chapter.21.2 Literature review1.2.1 Processes influencing stream temperatureStream temperature patterns in time and space reflect the interacting effects of a range ofhydrological and micrometeorological processes (Caissie, 2006; Leach et al., 2023). Theseenergy exchanges include vertical energy exchanges at the water surface and stream bed,lateral advective heat transfers associated with water inputs by overland flow, groundwaterand tributaries, and longitudinal advection and dispersion. The following sections reviewthese processes, with a specific focus on knowledge gaps related to glacier-fed streams.1.2.1.1 Net radiationEnergy exchanges at the water surface include net radiation and the sensible and latent heatfluxes. Of these fluxes, net radiation is usually the dominant control on diel and seasonalvariations in stream temperature (Sinokrot and Stefan, 1994; Moore et al., 2005a). Netradiation includes the combined exchanges of short- and longwave radiation.Incident solar radiation at a given time and location is a function of time-varyingfactors including year, time of day and weather conditions, and also site characteristicsincluding latitude, slope, aspect and elevation of the point of interest. The direct componentof solar radiation can be influenced by shading by surrounding topography and riparianvegetation, while the diffuse component depends on the sky view factor, which representsthe fraction of isotropic radiation from the celestial dome that is not blocked by surroundingtopography or vegetation canopy. The sky view factor is a function of the amount anddistribution of visible sky when looking vertically upward from the stream surface (Mooreet al., 2005b).In steep alpine proglacial streams, shading by riparian vegetation would be minimaldue to the lack of trees (Cowie et al., 2014). However, shading by surrounding topographymay be important (Richards et al., 2012). In addition to the effects of topographic shading,incident solar radiation would also be influenced by the aspect and slope of the channel, whichinfluences incidence angles. In downstream reaches, where glacier-fed streams flow throughforested valleys, both topographic shade and that associated with riparian vegetation couldbe significant.Calculation of topographic shading and view factors based on a digital elevationmodel is relatively straightforward (Richards et al., 2012). An alternative approach is tomake field measurements of the vertical angles to the topographic horizon for a range ofazimuth angles for each point of interest (Rutherford et al., 1997). Calculation of shadingby riparian vegetation and the stream banks requires additional information. For example,3Rutherford et al. (1997) used field measurements of vertical angles to the top of the canopyfor a range of azimuths for each point of interest. Another field-based approach involves theuse of hemispherical photographs, which can be used to model shading from topography,stream banks and riparian vegetation (Moore et al., 2005b). A limitation to field-basedmethods is that they are only feasible for smaller streams or lower flows due to the needto make measurements within the stream channel. A common alternative approach is toapply geometric models, which treat the stream reach as being straight and use a simplifiedgeometric representation of the stream banks and riparian vegetation to compute shadowpatterns over the stream (Li et al., 2012; Moore et al., 2014). Over the last decade, the in-creasing availability of LiDAR data has provided opportunities for modelling shade patternsand view factors without extensive field work (Loicq et al., 2018; Hyatt, 2022). However,the approaches used to date only account for the effects of the stream banks and riparianvegetation, and do not incorporate topographic influences on shading and view factors.The albedo of a stream surface varies as a function of solar incidence angle, theratio of diffuse to global radiation, suspended sediment concentration (SSC), and wateraeration (McMahon and Moore, 2017). The latter two influences are particularly relevantfor proglacial streams. For example, Richards and Moore (2011) found that the albedo ofa steep, bouldery proglacial stream ranged from about 0.1 at lower streamflow to about 0.4at higher flows. This positive relation was attributed to increased aeration at higher flows.McMahon and Moore (2017) found that, for flatwater streams, albedo ranged from about0.05 for low values of SSC to about 0.14 for highly turbid streams.Incident longwave radiation includes that emitted from the atmosphere, terrain andvegetation canopy. It is a function of the temperatures, emissivities and view factors associ-ated with visible sky, terrain and canopy (Moore et al., 2005b; Leach et al., 2023). The viewfactors for computing diffuse solar radiation are the same as those for longwave radiation,so that all of the preceding considerations are applicable.1.2.1.2 Sensible and latent heat fluxesSensible and latent heat fluxes tend to be of secondary magnitude relative to net radiation,except possibly for streams that lack wind sheltering and that experience high water temper-atures (Moore and Leach, 2021). These fluxes are typically modelled using empirical windfunctions of the form:𝑄𝑒 = (𝑎 + 𝑏𝑢)(𝑒𝑎–𝑒𝑤) (1.1)and4𝑄ℎ = 𝑄𝑒𝛾𝑇𝑎 − 𝑇𝑤𝑒𝑎 − 𝑒𝑤(1.2)where 𝑄𝑒 and 𝑄ℎ are the latent and sensible heat fluxes (W m-2), respectively, 𝑢 is windspeed above the stream surface (m s-1), 𝑒 is vapour pressure (kPa), 𝑇 is temperature (oC), thesubscript 𝑎 refers to the atmosphere overlying the stream surface, the subscript 𝑤 refers tothe water surface and 𝛾 is the psychrometric constant (kPa oC-1), and 𝑎 and 𝑏 are empiricalcoefficients.Many studies use values for 𝑎 and 𝑏 derived by Penman (1956), which Szeitz andMoore (2020) found to provide reasonable results for flatwater conditions for a range of smallto medium mountain streams in the southern Coast Mountains of British Columbia. Someresearch has suggested that the Penman coefficients underestimate the sensible and latentheat fluxes for steep cascading streams with significant aeration (John, 2008; Dufficy, 2019),but that work has not been formally published.A challenge for modelling the sensible and latent heat fluxes is in specifying above-stream meteorological data. Many studies use measurements made at nearby land-basedweather stations (Brown et al., 2010; e.g. Chikita et al., 2010; Magnusson et al., 2012;Somers et al., 2016). However, a limited number of studies have found that above-streamconditions during summer days tend to have lower air temperatures, higher humidities andlower wind speeds than recorded at land-based sites (Benyahya et al., 2010; Leach and Moore,2010; Guenther et al., 2012). However, no studies appear to have examined above-streammeteorological conditions for a glacier-fed stream.1.2.1.3 Surface-subsurface interactionsHyporheic exchange involves the infiltration of stream water through the bed or banks intothe sediments surrounding the stream channel and its subsequent discharge into the streamafter flowing through the subsurface. Where there is a difference in temperature between thestream water and that discharging back into the stream, there will be a net advective energyflux (Boano et al., 2014; Leach and Moore, 2014). Factors affecting this process can be theinfluence of groundwater, temperature differences in bedrock and geology or temperaturechanges of the main channel water column during the hyporheic flow path process (Arrigoniet al., 2008; Boano et al., 2014). Hyporheic heat exchange is most important for smallerstreams, in which the rate of water flow through the hyporheic zone is a large proportion oftotal streamflow (Leach et al., 2023), and is not expected to be a major component of thestream energy budget for a glacier-fed river during summer.Groundwater inflow typically plays an important role in muting diel and annualstream temperature variations, particularly by causing a cooling effect in summer months and5a warming effect in winter months, even in high mountain environments (Constantz, 1998;Malard et al., 2002; Somers and McKenzie, 2020). Similarly to the effect of hyporheic flows,groundwater inflow generally influences stream temperature more significantly in smallerstreams (Leach et al., 2023).1.2.1.4 Bed heat conductionBed heat conduction is associated with vertical temperature gradients in the stream bed.It tends to be associated with downward heat transfer during the warming phase of theday and upward transfer during the cooling phase. The magnitude of conduction can bestrongly influenced by hyporheic exchange and groundwater discharge through the bed. Bedconduction is most important for smaller streams, and becomes overwhelmed by other fluxesfurther downstream in larger-order rivers (Sinokrot and Stefan, 1993; Hebert et al., 2011;Leach et al., 2023).1.2.1.5 Longitudinal advection and dispersionLongitudinal advection refers to the downstream transfer of heat associated with the meanflow velocity of the stream. Longitudinal dispersion refers to the transfer of heat associatedwith velocity variations both vertically and across the channel. The latter process can playa large role in influencing stream temperatures in headwater streams with complex flow pat-terns that create a wider range of flow velocities (Leach et al., 2023). However, studies showthat in larger or faster-moving streams where flow velocities are more consistent, the rela-tive influence of longitudinal dispersion compared with advection is minimal (Sinokrot andStefan, 1993; Carrivick et al., 2012). The significance of longitudinal advection is directly re-lated to the longitudinal temperature gradient (Sinokrot and Stefan, 1993; Leach and Moore,2011), which can be affected by abrupt longitudinal changes in surface energy exchanges,such as can be associated with shifts in vegetation patterns (Moore et al., 2005a), or tempo-ral changes in upstream boundary conditions. Glacier-fed streams tend to exhibit high flowsduring periods of high surface energy inputs, suggesting that longitudinal advection may beparticularly important for these systems.1.2.1.6 Tributary mixingThe effect that tributary inflows have on stream temperature at the reach scale dependson the contrast in temperature between the inflow and main channel and the proportionalcontribution to overall discharge (Moore et al., 2005a). Especially in glaciated catchments,when the timing, magnitude and temperature of tributary inputs can vary substantially, theireffect on the main channel temperature could be significant. These temperature changes canincrease the thermal gradient just below the tributary junction (Leach et al., 2023). Even6if tributary inflows are small relative to the main channel, the lateral mixing process cancreate localized temperature differences that provide thermal refuge for aquatic species suchas fish (Kaya et al., 1977; Ebersole et al., 2001; Wang et al., 2020).The distance downstream at which the input becomes completely mixed can varysignificantly. Attempts to characterize the mixing length as a multiple of channel width showthat while mixing lengths are typically between 100 and 300 multiples of the channel width,values between studies can vary notably (Rutherford, 1994; Gaudet and Roy, 1995) and val-ues at the same site can still show significant temporal variation (Lane et al., 2008; Knudson,2012). When recording observational data for modelling stream temperature, it is thereforeimportant to consider lateral mixing distances to ensure that measured temperatures arerepresentative of the stream cross-section.1.2.2 Process-based stream temperature models in glacially fedstreamsModels used to predict stream temperatures span a continuum from empirical to process-based. Empirical models relate observed stream temperature to predictor variables suchas air temperature, solar radiation, streamflow and catchment area (Moore et al., 2013).Process-based models, on the other hand, simulate the driving physical processes that governstream temperature.Empirical models are relatively simple to generate and typically have lower datarequirements than process-based models (Benyahya et al., 2007; Dugdale et al., 2017). Whileempirical models can be valuable for hind-casting historic stream temperatures or predictingstream temperature under current conditions, they may not remain valid under conditionsof changing environmental conditions, including climate changes, glacier retreat, changesin channel morphology, and changes in riparian vegetation. Process-based models can, inprinciple, account for these environmental changes and are thus more appropriate in thecontext of understanding the effects of climate change and glacier retreat on stream thermalregimes.Process-based models can be developed using either a Eulerian or Lagrangian frame-work. Eulerian models simulate the variation of temperature through time for fixed pointsalong the stream. Lagrangian models, in contrast, compute the changes in temperature ofa discrete parcel of water as it flows downstream (Leach et al., 2023). In addition, hybridframeworks have been used in stream temperature models (Yearsley, 2009).Process-based models can be further distinguished by the spatial scale at which theyoperate. Many models operate purely at reach or stream network scales. Application of thesemodels requires specification of upstream boundary conditions (i.e., stream temperature7and discharge at the stream heads) and lateral boundary conditions (i.e., temperature anddischarge of lateral inflows as a function of space and time). Other models simulate thecoupled influence of hydrologic and thermal processes over an entire catchment, includingthe stream network; boundary conditions along the channel are computed as part of thesimulation process.Two studies have applied catchment-scale models with a specific focus on glacier-fedsystems. In the study of Du et al. (2022), the influence of glaciers was estimated by run-ning the model with glacier-melt contributions to streamflow turned on and off. Michel etal. (2022) applied a series of process-based catchment-scale models to analyze the potentialimpact of climate change on stream temperatures in 12 catchments within the Swiss Alpsthat ranged in drainage area from 3.4 to 973 km2 (Michel et al., 2022). The authors reportedthat the coarse resolution of the DEM used to calculate shading provided an underestima-tion of riparian vegetation and topographic shading, which collectively contributed to theoverestimation of stream temperature.While catchment-scale models can be useful for generating a holistic understandingof the coupled influences of hydrology and thermal processes, a limitation is that errors insimulated runoff generation or the temperatures of lateral inflow will propagate into thesimulation of stream temperatures along the reach. Hence, these models may not provide arobust basis for understanding reach-scale influences such as shading by riparian vegetation.As seen in Table 1.1, previous studies using reach-scale process-based stream tem-perature models in glacially fed streams focused predominantly on small stream reaches withmaximum lengths of 6 km and widths of 25 m. Within these studies, process-based mod-els accurately simulated stream temperature. For example, Chikita et al. (2010) modelledstream temperatures with an RMSE of 0.24 oC for a 2-km-long proglacial stream reach withno vegetation. In that study, shortwave radiation and bed friction accounted for 32 and 38% of the stream’s thermal input. However, shortwave radiation, temperature and relativehumidity and wind speed were measured at three different locations.All studies presented in Table 1.1 used meteorological and radiative observationsmeasured at open-site locations to represent above-stream surface energy fluxes. As far asthe author is aware, there are no reach-scale process-based modelling studies that monitoredabove-stream micro-meteorology. Of the studies that had riparian vegetation, aerial imagerywas used to calculate a static index of percentage shade from overhang (Somers et al.,2016; Baker et al., 2018). This approach may provide inaccurate estimates of incident solarradiation because it does not account for diel and seasonal variations in shading that areassociated with changing solar angles.Limiting research to small stream reaches decreases the size of potential tributaryinput influences. Some study reaches contained no tributaries (Carrivick et al., 2012; Baker8et al., 2018), one study assumed any flow input throughout the reach length was due todistributed flow (Cardenas et al., 2014), and another study reported small lateral inputsmostly from small springs (Somers et al., 2016). In contrast, only two studies monitored theinputs at a confluence of relatively significant flow contribution (Chikita et al., 2010; Mag-nusson et al., 2012). Especially in glacially fed systems, quantifying the effect of tributarieson stream temperature dynamics can improve our understanding of how large catchmentswith multiple glacially fed inputs might respond to changes in glacier retreat and catchmenthydrology.Based on this review, there appears to be a paucity of research investigating thereach-scale stream temperature processes in larger glacially fed streams that flow in valleyswith significant riparian forest cover. In particular, there appears to be a lack of attentionto accounting for the effects of both topography and riparian forest on radiative exchangesand in accounting for differences in meteorological conditions between the above-streamenvironment and the weather stations used to provide input data. Finally, no studies appearto have investigated how the diel cycles of discharge and meteorological conditions interactto drive diel variations in stream temperature.9Table 1.1: Summary of process-based stream temperature modelling studies regarding glacially-fedstreams. RMSE = Root mean square error.Author Location SolutionschemeRMSE(𝑜C)Catchmentsize(km2)Reachlength(km)Streamwidth(m)TributariesBaker et al.(2018)QuilcayhuancaValley, PeruEulerian 0.26 - 1.2 3.0-14.0 NoneSomers et al.(2016)QuilcayhuancaValley, PeruEulerian 0.38 - 4 2.2-14.0 33 ( 80% smallsprings)Magnussonet al. (2012)Damma glacierstream,SwitzerlandLagrangian - 12 1.5 7.5-25.0 1Cardenas etal. (2014)Urbach River,SwitzerlandEulerian 0.4 - 1 7.0-15.0 No, distributedinflowsChikita etal. (2010)Phelan Creek,AlaskaLagrangian 0.24 31.1 2 - 1 confluenceCarrivick etal. (2012)KarsajokkRiver, ArcticSweedenEulerian 0.3-2.4 - 6 4 NoneCatchmentswithin thisstudyUpper Lillooet,BC, Canada- - 1516 - - 2 majortributaries 3Catchmentswithin thisstudyLower Lillooet,BC, CanadaEulerian 0.3 2100 24 75.1 1 4 majortributaries 4Catchmentswithin thisstudyRyan River,BC, Canada- - 417 - 46 2 NoneCatchmentswithin thisstudyMiller Creek,BC, Canada- - 78 - 41 2 None1 Stream width calculated as mean model cell stream width2 Stream width calculated at confluence to Lillooet River3 Tributaries include: Meager Crk. and Rail Road Crk.4 Tributaries include: Meager Crk., Rail Road Crk., Ryan R. and Miller Crk.101.3 Research objectivesThe literature review in the preceding section has highlighted a number of knowledge gapsrelated to the mechanisms that control stream temperature dynamics in glacially fed streamsusing reach-scale process-based stream temperature models. Based on these gaps, this studywas designed to achieve the following five objectives:1. To develop a robust approach to account for the combined effects of stream banks,riparian vegetation and topography on incident radiation at a stream surface.2. To quantify the differences in meteorological conditions above the stream relative tothose measured at a land-based weather station.3. To evaluate the ability of a process-based reach-scale model to simulate downstreamchanges in stream temperature and discharge with no calibration.4. To use the model to evaluate the relative importance of surface energy exchange andlongitudinal advection.5. To use the model to evaluate the sensitivity of stream temperature to (a) uncertaintyin the input data and (b) tributary inflow.The remainder of this thesis comprises four chapters: Methods, Results, Discussionand Conclusions.11Chapter 2Methods2.1 Study areaLillooet River is located in the Pacific Ranges of the southern Coast Mountains of BritishColumbia, where the lower course flows through the town of Pemberton, approximately 160km north of Vancouver, BC. The Lillooet River flows in a U-shaped valley that was carved bythe Cordilleran Ice Sheet in the Pleistocene Epoch. Mountain peaks reach elevations up to3000 m a.s.l. (Prent and Hickin, 2001; Friele et al., 2005; Slaymaker et al., 2017). Mesozoicgranitic and metamorphic rocks dominate the bedrock of the river catchment (Slaymaker etal., 2017; Martins et al., 2023). Steep bedrock valley slopes containing a thin colluvial ormoraine veneer meet the flood plain at a steep angle, typical of old fjord valleys developedin resistant rock in this region of the Coast Mountains (Jordan and Slaymaker, 2007). Thevalley floodplain was made from postglacial infilling of a fjord lake that once submerged theriver valley (Friele et al., 2005). Based on glacier outlines from 2019 (GLIMS and NSIDC,2019), approximately 16 % of the entire Lillooet catchment drainage area is glacierized.The river’s main stem originates at the outlet of Silt Lake, which is fed by the LillooetIcefield (Figure 2.1). The upper course of the Lillooet River, extending down valley fromSilt Lake to Railroad Creek, is mostly braided with a cobble bed, with colluvial gravel fansfrom tributary valleys regularly encroaching the 1 km wide flood plain (Friele et al., 2005;Martins et al., 2023). The lower reach, from Railroad Creek to Ryan River, has a wanderingto meandering morphology with a pebble-cobble bed and an active floodplain of 1.5 to 2 kmin width that is bounded by steep bedrock slopes on the west and east sides (Weatherly andJakob, 2014). Below Ryan River, the Lillooet River transitions to a more gravel-sand bed,with reduced sinuosity decreasing as the bed becomes confined by an extensive dyke networkas it flows through Pemberton and eventually into Lillooet Lake 15 km downstream (Nenerand Wernick, 1997; Weatherly and Jakob, 2014; Martins et al., 2023).The orientation and location of the Coast Mountains provide a dominant rain shadow12on the Lillooet catchment from the precipitation sourced by the atmospheric circulation ofthe North Pacific to the southwest (Slaymaker et al., 2017). Cool wet winters contributeto annual precipitation that ranges from 1,100 to 2,000 mm (Nener and Wernick, 1997).During late winter, streamflow is often at its lowest due to most of the precipitation fallingas snow and the effect of seasonal streamflow recession that begins in late autumn (Nenerand Wernick, 1997; Martins et al., 2023). Hot dry summers promote the onset of snow andglacier melt, making July the month that experiences peak mean monthly flows (Martins etal., 2023). During the melt season, substantial glacial silt from considerable meltwater flowsthrough the catchment, until most of it eventually settles in Lillooet Lake (Martins et al.,2023).The hydrologic regime is dominated by seasonal snowmelt, which peaks in June, withsubstantial contributions of glacier melt in July through September. The increased ice andsnow melt during these months creates significant diel discharge variability with a typicalrange from 7 to 35 % of the daily mean discharge. In contrast, late autumn and winterare dominated by baseflow, with diel streamflow variations of less than 10 % during wintermonths (Prent and Hickin, 2001). Occasional rain-on-snow events during autumn and wintercan cause abrupt increases in flow for several days, and can produce the highest peak flows.Large debris flows originating within the Meager Creek catchment dominate sedimentsupply throughout the Lillooet River by providing high volumes of coarse clastic sediment,despite only covering 2 % of the Lillooet River drainage area (Jordan, 1994; Friele et al.,2005; Slaymaker et al., 2017). The largest recorded landslide in the Lillooet River watershedoccurred in August 2010, originating from the collapse of the southwest edge of Mount Meager(Roberti et al., 2017). The resulting flow entered Meager Creek and then spread out acrossthe Lillooet River valley. The resulting deposits formed a 10 to 15 m thick debris barrier(Roberti et al., 2017), temporarily damming the Lillooet River and eventually causing floodsurges that increased downstream sediment deposition along the river length (Slaymaker etal., 2017).Two other main tributaries to the Lillooet River are Ryan River (RR) and MillerCreek (MC). Ryan River joins the Lillooet River approximately 4 km upstream of Pembertontownship, has a drainage area of 417 km2 and was 16 % glacierized in 2019 (GLIMS andNSIDC, 2019). Miller Creek joins the Lillooet River approximately 300 m downstream ofthe RR confluence, has a drainage area of 78 km2 and was 22 % glacierized in 2019 (GLIMSand NSIDC, 2019).Dense riparian vegetation dominates both banks of the upper to middle courses ofthe Lillooet River, containing mostly Douglas fir, Sitka Spruce and western hemlock amongothers (Martins et al., 2023). As the river flows through the middle to lower course, ripariancanopy cover is punctuated by agricultural fields that generally dominate the eastern banks.13Figure 2.1: Study area of the Lillooet River catchment and highlighted monitoring area. Lillooet Rivercatchment delineated from the above stream meteorological station (ASMS) at the BC Highway99 bridge. Map projected in NAD83 / UTM zone 10N. Lillooet catchment contains DEM withdraped multi-directional hillshade. Glacier boundaries (permanent snow and ice) retrievedfrom GLIMS and NSIDC (2019).142.2 Data collection and field methods2.2.1 Overview of stream monitoring sitesThe field campaign for this study was carried out between July and October 2022. Themonitoring reach extended from the Lillooet Forest Service Road (Lillooet FSR) bridgecrossing (Upper Lillooet site) down to the location of the Water Survey of Canada (WSC)water level recorder (Lower Lillooet site), a total length of 24 km (Figure 2.2). The drainagearea at the Upper Lillooet (UL) site is 1516 km2, of which 19 % was glacierized in 2019(GLIMS and NSIDC, 2019). The Lower Lillooet (LL) site has a drainage area of 2100 km2and was 18 % glacierized in 2019 (GLIMS and NSIDC, 2019). Monitoring also focused onMiller Creek (MC) and Ryan River (RR).2.2.2 Meteorological dataAn open site meteorological station (OSMS) was deployed throughout the entire field season,while an above stream meteorological station (ASMS) was deployed for six periods of up to26 hours during field campaigns. All data collected and presented throughout this studywere standardized relative to PDT (UTC-7).2.2.2.1 Open-site conditionsData representing open-site conditions were acquired from an Open Site Meteorological Sta-tion (OSMS), which was located in the middle of a barley field at Millers Farm (Figure 2.2).This site was selected to minimize the influence from shading by topography or vegetationand was deployed from July 28 to October 4. Open-site meteorological data were also ac-quired from the Pemberton Airport Meteorological Station (PAMS) (Climate ID: 1086081and 1086081). PAMS was located approximately 2.3 km southeast of the ASMS site. Thosedata included air temperature, relative humidity and wind speed, recorded at an hourlyinterval.Variables monitored at OSMS included air temperature, relative humidity, windspeed, barometric pressure and incident shortwave and longwave radiation; see Table 2.1 forinstruments and specifications. Measurements were sampled every 10 seconds and averagedevery 10 minutes. Instruments were mounted on a tripod 1.5 m above the ground andconnected to a Campbell Scientific CR10x data logger, as seen in Figure 2.3. Total rainfallwas recorded every 10 minutes using a tipping bucket rain gauge installed on the ground andconnected to the Campbell Scientific CR10x data logger. Barometric pressure was recordedby an independent Onset U20 Logger connected to the OSMS tripod frame.Measurements for incident shortwave and longwave radiation were recorded using a15Figure 2.2: Monitoring area including field sites and established gauge stations. Map projected in NAD83 /UTM zone 10N. PVDD gauge station located at Upper Lillooet (UL) monitors stream tempera-ture and flow (ID: 08MG00A), WSC gauge station at Lower Lillooet (LL) monitors streamflow(station ID: 08MG005) and WSC gauge station at Ryan River (RR) monitors stream tempera-ture and flow (station ID: 08MG028). Blue stream segment highlights the Lillooet study reachfor which stream temperature were modelled and red stream segment highlights the groundtruthing stream reach, the methods of which are described in Section 2.3.1.4.16Kipp and Zonen CM3 pyranometer and a CGR3 pyrgeometer, respectively (Table 2.1). TheCM3 pyranometer recorded voltages (mV) that were converted to irradiance (Wm-2) usingthe specific sensitivity of the device (mV/Wm-2). Incident longwave radiation (Wm-2) wascalculated as follows:𝐿 ↓𝑂𝑆= 𝐿𝑛𝑒𝑡 + 𝜎 ⋅ (273.15 + 𝑇𝑏4) (2.1)where 𝐿 ↓𝑂𝑆 is incident longwave radiation measured at OSMS, 𝐿𝑛𝑒𝑡 is net radiation atthe pyrgeometer’s surface (Wm-2) as computed from the output voltage, 𝜎 is the Stefan-Boltzmann constant (5.67 × 10−8 𝑊𝑚−2𝐾−4) and 𝑇𝑏 is the CGR3’s built in temperaturesensor’s temperature (oC) (Kipp & Zonen, 2018).During times of the day when the sun was at its strongest, the internal pyrgeometertemperature sensor would record extreme negative values. This was presumed to be due tothe daytime heat affecting either the wiring or the housing of the sensor. Therefore, 𝑇𝑎 mea-sured by the externally mounted Rotronic HC-S3 sensor was assumed to be an appropriateproxy for 𝑇𝑏 in Equation (2.1).Atmospheric vapour pressure (𝑒𝑎) (kPa) at OSMS, ASMS and PAMS was calculatedas:𝑒𝑎 = 𝑒𝑠𝑎𝑡(𝑇𝑎) ⋅𝑅𝐻100 (2.2)where 𝑒𝑎 is atmospheric vapor pressure (kPa), 𝑒𝑠𝑎𝑡 is saturation vapour pressure (kPa) at airtemperature (𝑇𝑎) (𝑜C) and 𝑅𝐻 is the relative humidity (%) of the specific meteorologicalstation. Saturation vapour pressure at each meteorological station was calculated as follows:𝑒𝑠𝑎𝑡(𝑇𝑎) = 0.611 ⋅ 𝑒𝑥𝑝(17.27 ⋅ 𝑇𝑎𝑇𝑎 + 237.26) (2.3)where 𝑒𝑠𝑎𝑡 is saturation vapour pressure (kPa) (Tetens, 1930).A faulty cable caused missing values of wind speed at OSMS between July 28 andSeptember 2. Observed wind speeds of zero (below the sensor stall speed) were replacedwith values that represented half the stall speed, which were 0.25 and 0.30 ms-1 for OSMSand ASMS, respectively.2.2.2.2 Above-stream conditionsTo observe meteorological conditions over the stream surface, a Kestrel 4500 Pocket WeatherTracker (ASMS) was deployed from the pedestrian section of the BC Highway 99 bridge(Figure 2.4) during field visits. The Kestrel recorded air temperature, relative humidity andwind speed approximately 1-1.5 m above the stream surface. As the ASMS was deployed17Figure 2.3: Open site meteorlogical station (OSMS) situated in an open field in Pemberton Meadows atMiller’s Farm Beer Farmers.from a pedestrian section of a highway bridge, the risk of theft or alteration by a member ofthe public meant that it was only deployed during field visits and not continuously deployedthroughout the entire field season.Air temperature, wind speed and atmospheric vapour pressure were compared be-tween the three meteorological stations (OSMS, PAMS and ASMS) to provide an overviewof the monitoring regions meteorological conditions. The most robust relationships betweenthe above stream (ASMS) and open site (OSMS and PAMS) observations were chosen andused to predict continuous above stream meteorological conditions throughout the entiremonitoring period.2.2.3 Stream temperatureWater temperature (𝑇𝑤) was monitored at 10-minute intervals at the UL, LL, MC and RRsites (Figure 2.2) using Onset TidbiT v2 temperature loggers. The loggers have a range of-20 to 70 oC and a stated accuracy of ± 0.2oC. The loggers were each encased in a whitePVC pipe with holes drilled along the length to act as a radiation shield. Loggers in theirshields were anchored to the stream bed by a concrete weight that was connected by a lengthof clothesline to a tree on the river bank.Water temperature data for the UL site were also provided by Pemberton ValleyDyking District (PVDD) with an OTT PLS sensor that recorded temperature at a 5-minuteinterval with an accuracy of ± 0.5 oC between the range of -25 to 70oC. The OTT-PLS is18Figure 2.4: Pictures of the above stream meteorological station (ASMS) deployed over BC Highway 99bridge over the Lillooet River. Red circle denotes the locations of ASMS. Pictures taken fromright bank and river flows from left to right.Table 2.1: Meteorological instrument specifications. OSMS and ASMS represent the open site meteorlogicalstation and above stream meteorlogical station, respectively.Variable Notation Sensor Range AccuracyOSMS:Air temp. 𝑇𝑎 Rotronic HC-S3 -30 - 60 oC ± 0.2 oCRel. humidity 𝑅𝐻 Rotronic HC-S3 0 - 100% ± 1.5% (23 oC)Wind speed 𝜇 Met One 014a 0.5 - 45 ms-1 ± 0.11 ms-1Incident SW 𝐾 ↓ Kipp and Zonen CM3 0.3 - 2.8 𝜇m -1%/ms-1Incident LW 𝐿 ↓ Kipp and Zonen CGR3 0.3 - 2.8 𝜇m -1%/ms-1Precipitation 𝑅 Texas Electronics TR-525M - ± 1%Barometric pressure 𝑃 Onset U20 0 - 207 kPa ± 0.3%ASMS:Air temp. 𝑇𝑎 Kestrel 4500 Pocket -10 - 55 oC ± 0.5 oCRel. humidity 𝑅𝐻 Kestrel 4500 Pocket 0 - 100% ± 3%Wind speed 𝑢 Kestrel 4500 Pocket 0.6 - 60 ms-1 ± 3%operated by Northwest Hydraulic Consultants Ltd (NHC) and installed on the left side ofLillooet River, across from the tidbit logger installed for this study.Onset U20 water level loggers were installed alongside the temperature loggers at RRand MC (Figure 2.2) to record stream temperature and stage at 5-minute intervals. Theseloggers have an accuracy for stage of ± 0.03 m and water temperature of ± 0.44oC.The PVDD UL stream temperature logger experienced periods of missing satellitecommunications while UL tidbit logger occasionally experienced dewatering periods, espe-cially toward the end of the monitoring period. The PVDD logger had a more completerecord, so those data were used as the upstream boundary conditions for the stream tem-perature modelling. Periods when both sensors were dewatered typically only lasted 2 to 5hours or less and did not include daily maxima and minima. For those periods, missing data19were infilled by linear interpolation. For periods when the PVDD logger was experiencingmissing communications but the tidbit was not experiencing dewatering, missing data wereinfilled using a regression model (see Figure 2.5). Hysteresis loops in the relation are believedto be the result of lateral thermal heterogeneity caused by shallow flow over gravel bars justupstream of the two sensors during certain flow conditions.Figure 2.5: The relationship between water temperatures measured at the PVDD gauge station and theUL tidbit, with a fitted regression line and a 1:1 line.2.2.4 StreamflowStreamflow data for LL and RR were acquired from WSC as provisional data (i.e., subjectto change following further review) and are maintained to WSC standards. They measurestage using a Tavis pressure transducer with a precision of 0.1 % FS at LL and an OTTPLS pressure transducer with a precision of 0.05 % FS at RR. Streamflow data for UL wereprovided by PVDD where they also measure stage using an OTT PLS pressure transducer.The sensors sample multiple stage values that are averaged, and the average is stored every5 minutes.Stage was recorded at MC every 5 minutes using an Onset U20 water level loggerand a barometric Onset U20 logger at OSMS for barometric reference. Streamflow wascalculated using the velocity-area method based on measurements using a velocity meter20mounted on a wading rod. Calculations were performed using the mid-section method.Wading measurements were only feasible at lower flows. To measure higher flows, saltdilution gauging was attempted. However, despite using a mixing reach of more than 30times the wetted width, mixing was incomplete, and it was not possible to use a longermixing length. Therefore, for the benefit of the PVDD and this project, NHC constructed arating curve for the period using flow data collected by a private client and the stage recordcollected as part of this study. The resulting flow series was used for this research.However,the high flow streamflow measurements and resulting curve were not provided in this thesisdue to data sharing agreements between NHC and their client.Since the MC gauge was located within 100 m of the confluence with Lillooet River,lag time between these locations was assumed negligible. In contrast, the WSC gauge onRyan River is located approximately 5.4 km upstream of the confluence of the Lillooet River.Therefore, onsite water level logger stage observations at RR were compared with the WSCgauge stage observations using two approaches to determine a lag time between the twosensor locations. The first approach involved computing the time difference between dailypeaks and troughs at both sensors and plotting them against the discharge at the WSC gaugestation. The result of this analysis indicated no clear relationship between the two variables;therefore, the lag time was assumed to be constant and equal to the mean lag time of 65minutes. The second approach involved a cross-correlation analysis of the stage observationsusing Spearman’s rank correlation coefficient, which also yielded a lag time of 65 minutes.This lag between the WSC gauge station and RR water level logger was then extrapolatedto the location of the confluence with the Lillooet River to give a lag time of 95 minutes(rounded to the nearest 5 minutes). The RR streamflow and stream temperature time serieswere lagged by this value to act as a proxy for these variables at the timing of input intothe Lillooet River compared to the measurement conception at the upstream WSC gaugestation.To check the overall consistency of the streamflow measurements, the observed LLstreamflow was compared to the sum of the streamflows recorded at UL, RR and MC. Whileone would expect disagreement on a sub-daily time scale, the discrepancy should not exhibitlonger-term trends if the observations were accurate. Figure 2.6 highlights multiple shiftsin the discrepancy between the sum of upstream flows and observed flows at LL. Due tothe magnitude of the differences in flows at the beginning of August, it was assumed thatthe erroneous streamflow measurements were sourced from the UL gauge station. The ULstreamflows were bias-corrected by fitting a segmented regression model over the streamflowdifferences as a function of time (Figure 2.6). The regression model provided the magnitudeof correction to add to the UL streamflows at each time step to account for the ‘missing’streamflows between UL and LL.21Figure 2.6: The difference in streamflows between the Lower Lillooet gauge station and the sum of theboundary and tributary flow conditions as a function of time. Segmented regression model inred. 𝑄𝐿𝐿, 𝑄𝑈𝐿, 𝑄𝑅𝑅 and 𝑄𝑀𝐶 represent the streamflows at Lower Lillooet, Upper Lillooet,Ryan River and Miller Creek respectively.2.3 Modelling and analyses2.3.1 Stream shade model2.3.1.1 Digital elevation data sources and processingA model was developed to compute the spatial and temporal variability of shade over theLillooet River study reach. Shading associated with the surrounding topography was de-termined using the Canadian Digital Elevation Model (CDEM) (Geogratis, 2016) with a0.75 arc second resolution (~15 m in the X direction and ~20 m in the Y direction and atthe Pemberton latitude of 50.3220o N). Shading cast by riparian vegetation and the streambanks was determined using open-source point cloud LiDAR data provided by Lidar BC(2016a), which was used to create a digital surface model (DSM) using the ‘grid_canopy’function in the ‘lidR’ package (Roussel and Auty, 2022) in R (R Core Team, 2022) with aresolution of 1 m.The boundary of the Lillooet stream surface was delineated using LiDAR data toprovide an accurate and more up to date representation of the stream surface than availablevia other data sources. A 1-m-resolution slope layer was created using a digital terrainmodel (DTM) provided by Lidar BC (2016b) using the ‘terrain’ function in the rasterpackage (Hijmans, 2023). The slope layer was reclassified by reassigning all slopes above1.6o to ‘NULL’. The reclassified raster layer was then converted to produce vector polygons.22The polygon feature with the largest area corresponded to the continuous delineation of theLillooet River water surface. Manual editing of the delineated river boundary was carriedout in QGIS (QGIS Development Team, 2021) to eliminate river confluences and erase asmall 350 m stretch of the channel that was cut off due to the incomplete extent of the DTMand LiDAR point cloud data.A regular 20-m grid was created that spanned the river reach, which was then maskedto the boundary of the delineated stream surface. The elevation value (𝑧) at each point wasextracted from the DTM. Horizon angles and resulting stream shading and view factors werecalculated at each of the 20-m grid points for a set of azimuth angles. The grid resolutionof 20 m was chosen as a compromise between maximizing spatial resolution while keepingcomputational processing time to a manageable length. The river-surface grid points arehereafter referred to as points of interest (POI).2.3.1.2 Calculation of horizon angles for each POIA 250-m buffer of the resulting stream surface delineation was created and used to maskthe LiDAR-derived DSM to represent the riparian zone vegetation and reduce processingtime when calculating horizon angles. The maximum horizon angle between each POI andeach gridded elevation raster pixel from the CDEM and LiDAR DSM was calculated for 10oazimuth bands (𝐻𝑚𝑎𝑥) as follows:𝐻𝑚𝑎𝑥 = max(𝐻𝑎𝑏) (2.4)where 𝐻𝑎𝑏 is the horizon angle between a POI and each raster pixel for a specific 10o azimuthband 𝑎𝑏. 𝐻𝑎𝑏 was calculated as follows:𝐻𝑎𝑏 = 𝑟 ⋅ arctan(Δ𝑧𝑑 ) (2.5)where 𝑟 is a constant conversion factor from radians to degrees (57.2958), Δ𝑧 is the differencein elevation a POI and the raster pixel (m) and 𝑑 is the distance between each raster pixel andthe POI (m). To allow accurate distance and angle calculations over distances larger thanthe stream reach for CDEM topographic shading, the geodesic Haversine formula (Sinnott,1984) to calculate distance between two points on the Earth’s surface was used to calculate𝑑 as follows:𝑑 = 2𝑅 ⋅ arctan(√𝑏√1 − 𝑏) (2.6)where 𝑅 is the radius of the Earth (6.371 × 106 m) and 𝑏 is an intermediate step calculatedas follows:23𝑏 = sin2 (Δ𝜙2 ) + cos𝜙1 ⋅ cos𝜙2 ⋅ sin2 (Δ𝜆2 ) (2.7)where 𝜙1 and 𝜙2 are the latitudes for each POI and each elevation raster pixel, respectively,Δ𝜙 is the difference between 𝜙1 and 𝜙2 and Δ𝜆 is the difference between the longitudes ofa POI (𝜆1) and each elevation raster pixel (𝜆2).To determine 𝐻𝑚𝑎𝑥, the 10o azimuth band (𝑎𝑏) for each value of 𝐻𝑎𝑏 was determinedas follows:𝑎𝑏 = ⌈𝑎𝜃Δ𝑎⌉ (2.8)where 𝑎𝜃 is the azimuth angle from a POI to an elevation raster pixel, ⌈𝑥⌉ represents 𝑥rounded up to the next integer value, andΔ𝑎 is the azimuth interval (10 o). 𝑎𝜃 was calculatedusing the Haversine bearing formula (Sinnott, 1984) as follows:𝑎𝜃 = 𝑟 ⋅ arctan(sinΔ𝜆 ⋅ cos𝜙2cos𝜙1 ⋅ sin𝜙2 − sin𝜙1 ⋅ cos𝜙2 ⋅ Δ𝜆) (2.9)which generates 𝑎𝜃 values in the range ± 180o; the values were converted to provide a rangebetween 0o and 360o bearing clockwise from north. 𝐻𝑚𝑎𝑥 was calculated individually for theCDEM and LiDAR DSM to enable later analysis of the separate contributions of riparianvegetation and large scale topography to stream shading and view factors. A schematicdiagram outlining an example of calculating the horizon angle from a POI on the streamsurface to a raster elevation pixel is presented in Figure 2.7.The LiDAR DSM elevation interpolation between the overhanging canopy edge andwater surface was irregular and inconsistent. Therefore, the shade model did not take intoconsideration shade from any features that overhung the delineated stream surface boundary.However, due to the width and size of the Lillooet stream reach, the effect of overhangingvegetation on the overall radiation received at the stream surface was considered negligible.2.3.1.3 Calculation of shadingSolar elevation (𝑆𝜃) and azimuth angles (𝑎𝜃) relative to each POI throughout the entiremonitoring period at time 𝑡 were calculated using the ‘solarpos’ function in the maptoolspackage (Bivand and Lewin-Koh, 2022). The solar calculations in the ‘solarpos’ functionare based on equations presented by Meeus (1991), are used by the National Oceanic andAtmospheric Administration (NOAA), provide an accuracy of within one minute for latitudesbetween ± 72o, and include corrections for atmospheric refraction effects (Bivand and Lewin-Koh, 2023). A given POI was considered to be shaded at a given time 𝑡 if the solar elevationangle was lower than the maximum horizon angle for the corresponding azimuth band (𝑎𝑏)24(i.e., 𝑆𝜃 < 𝐻𝑚𝑎𝑥). When shading occurred only from CDEM pixels, the POI was assumed tobe experiencing ‘topographic shade’; when shading occurred only from LiDAR DSM pixels,the POI was assumed to be experiencing ‘riparian vegetation shade’. It was also noted if aPOI was experiencing shading from both CDEM pixels and LiDAR DSM pixels at the sametime. Shading at ASMS was also calculated to fit regression models with air temperature inSection 3.4.1.Figure 2.7: Schematic diagram of finding the horizon angle 𝐻𝜃 from a point of interest to a grid cell ofan elevation raster. 𝑎𝜃 is the azimuth angle measured clockwise from north. The 𝑧 valueis the elevation (m) at grid cell 𝑥𝑦. This diagram represents a planar cartesian system forvisualization purposes, whereas a geodesic geographic system was used to calculate 𝐻𝜃 and 𝑎𝜃.2.3.1.4 Satellite validationPlanetScope satellite imagery, produced by the PlanetScope satellite constellation, is ac-quired by approximately 130 satellites that are able to image the entire land surface of theEarth every day with a maximum resolution of about 3 m (Planet Team, 2023). This reso-lution is adequate to visualize and map shade patterns over Lillooet River, and the productwas thus used to act as a ‘ground truth’ to quantify the accuracy of the stream shade model.The low sinuosity and north-south facing orientation of the Lillooet study stream reachmeant that there was little to no shading in any of the available summer season PlanetScopeimagery. However, the mostly west-east orientated section of Lillooet River approximately4 km downstream of BC Highway 99 Bridge provided abundant shading. This downstreamsection was therefore chosen as the location for satellite ground truthing of the stream shademodel and is highlighted in red in Figure 2.2.Satellite imagery was selected based on the highest shading proportions of availablesummer season imagery along the ground truthing reach. This stream reach was delineatedand shading was modelled along the reach at the satellite image acquisition time and date25and regular gridded points were created at the centroids of each 20-m raster pixel fromthe shade model output. Observed shading was manually delineated using satellite imageryas polygon vector data using QGIS (QGIS Development Team, 2021). POIs that weremodelled as shaded were given a predicted value of 1 and POIs that were modelled asunshaded were given a predicted value of 0. Similarly, POIs that overlapped manuallydelineated shade polygons were given observed value of 1 and those that did not overlapany manually delineated shade polygons were given an observed value of 0. The resultingobserved and predicted shade values (𝑠𝑜𝑏𝑠 and 𝑠𝑝𝑟𝑒𝑑 respectively) were calculated. Thesevalues were averaged over the reach of interest for each satellite scene to compute observedand predicted shade fractions. A confusion matrix of all classified POIs was created to enablea count of the true positive (TP), true negative (TN), false positive (FP) and false negative(FN) classifications and provide a performance summary of the entire shade modelling resultsacross all satellite scenes. The accuracy of the model was computed as follows:𝑎𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = 𝑇𝑃 + 𝑇𝑁𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁 (2.10)where accuracy ranges between 0 to 1 and represents the ratio between the count of correctlypredicted classes and the total count of predictions in the confusion matrix. While theaccuracy is often a widely excepted measure used to summarize model performance, the 𝐹1-score is usually preferred when the class distribution is imbalanced due to the considerationof negative results, for example if there is considerably more shade than no-shade. The𝐹1-score was calculated as follows:𝐹1 =2 ⋅ 𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 ⋅ 𝑟𝑒𝑐𝑎𝑙𝑙𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 + 𝑟𝑒𝑐𝑎𝑙𝑙 (2.11)where the precision was calculated as𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 = 𝑇𝑃𝑇𝑃 + 𝐹𝑃 (2.12)and recall was calculated as𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 = 𝑇𝑃𝑇𝑃 + 𝐹𝑁 (2.13)While accuracy computed on confusion matrices is among one of the most popularlyadopted metrics for binary classification, the measure can show overoptimistic inflated re-sults, especially when expected classes are imbalanced. The 𝐹1 score can also still presentinflated results despite taking negative classifications into consideration (Chicco and Jurman,2020). The Matthews correlation coefficient (MCC) is generally considered more reliable asa high score is only produced if the prediction obtained sufficient results in all of the ground26confusion matrix categories (TP, FN TN and FP) in proportion to both the size of positiveand negative elements in the data (Chicco and Jurman, 2020). This metric is thereforeparticularly useful in the case of shade modelling due to the likelihood of a high proportionof shaded classes during dusk and dawn and a low proportion of shaded classes during peaksun elevation times. The MCC was calculated as follows:𝑀𝐶𝐶 = (𝑇𝑃 ⋅ 𝑇𝑁) − (𝐹𝑃 ⋅ 𝐹𝑁)√(𝑇𝑃 + 𝐹𝑃) ⋅ (𝑇𝑃 + 𝐹𝑁) ⋅ (𝑇𝑁 + 𝐹𝑃) ⋅ (𝑇𝑁 + 𝐹𝑁)(2.14)where MCC ranges from -1 to 1 (Chicco and Jurman, 2020). Values of -1 indicate totaldisagreement between predicted and observed classes, values of 0 represent completely ran-dom classification between predicted and observed and values of 1 indicate total agreementbetween predicted and observed classes.2.3.1.5 Sky view factorThe sky view factor (𝑓𝑣) is a function of the geometry and spatial distribution of shadeelements across the sky dome. It ranges from a value of 0 (no sky visible when lookingupward from the stream surface) to 1 (no blockage of the sky). The Lillooet stream reachwas assumed to be horizontal for the purpose of modelling 𝑓𝑣 due to its low longitudinalgradients. Values of 𝑓𝑣 for each POI were assumed to be constant throughout the entirestudy period due to consistent leaf coverage of riparian vegetation given that the monitoringperiod lay entirely between leaf-out in spring and leaf-fall in autumn. 𝑓𝑣 for each POI canbe expressed as follows:𝑓𝑣 =1𝜋 ∫2𝜋0∫𝐻𝑎0cos(𝜃) ⋅ sin(𝜃) 𝑑𝜃𝑑𝑎 (2.15)where 𝜃 is the zenith angle and 𝐻𝑎 is the horizon angle at azimuth angle 𝑎 (Richards et al.,2012). In practice, Equation (2.15) can be integrated over 𝜃 independently of the integrationover 𝑎, and re-expressed to enable the estimation of 𝑓𝑣 as follows:𝑓𝑣 ≈12𝜋 ⋅𝑛∑𝑖=1⋅ sin2(12𝜋 −𝐻𝑎𝑖) ⋅Δ𝑎𝑐𝑟 (2.16)where 𝑛 is the number of discrete azimuth angles, 𝐻𝑚𝑎𝑥 is the maximum horizon angle at aspecified azimuth band (as calculated in Section 2.3.1).272.3.2 Stream temperature model2.3.2.1 StructureThe HydroCouple modelling framework was chosen for application in this study (Buahin etal., 2019). This component-based model is based on the formulations presented by Neilsonet al. (2010). It operates at sub-hourly time steps and longitudinally partitions the streamreach into cells, which allows for the implementation of spatio-temporally dynamic streamtemperature fluxes such as solar radiation derived from stream shade modelling. The threemain components of the model that were used for this study were (1) the channel solute andheat transport component (CSHComponent), which includes the main channel advectionheat transport and routing, (2) the hyporheic transient storage (HTS) zone component(HTSComponent), in which heat exchange between the hyporheic transient zone and riverchannel is simulated, and (3) the radiative heat exchange component (RHEComponent), inwhich the net radiation at the stream surface and longwave radiation emitted by the streamare calculated.Stream components (cells) were created by calculating the stream reach centerlinebased on the delineated stream reach water surface (Section 2.3.1). Points were createdevery 100 m along the centerline using QGIS (QGIS Development Team, 2021) to representthe junctions of each longitudinally derived stream cell. Points were manually created ateach tributary location and at the upper and lower bounds of the Lillooet stream reach(corresponding to UL and LL monitoring sites). The central stream width was recorded foreach cell 𝑐, along with the coordinates and elevations at each junction 𝑗. A schematic diagramoutlining this process is displayed in Figure 2.8, where 𝑗𝑛 represents each junction and 𝑐𝑛represents each computational cell. The shade model POIs that fell within a computationalcell were used to create cell specific averages for 𝑆𝑡 and 𝑓𝑣.Hydraulic routing was solved internally using a kinematic wave approach similar toCardenas et al. (2014) and presented by Equation 1 in Leach et al. (2021). More detailedformulations of the energy balance equation to model the change in stream temperaturesover space and time are provided by Buahin et al. (2019).For the current application, it was assumed that, given the magnitude of the stream,bed heat conduction and hyporheic exchange would be relatively minor terms in the en-ergy budget. Accordingly, the hyporheic exchange and stream bed conduction componentrepresented in HTSComponent were switched off by ensuring that the advection coefficientbetween the main channel and the HTS zone and the coefficient of thermal diffusivity of thesediment in the HTS element were both set to zero. This process ensured that there was notransfer of energy between the ground, HTS and main channel, enabling the resulting streamtemperature model to represent only the stream surface-atmosphere energy exchanges within28the main channel and energy inputs of the tributaries.Figure 2.8: Schematic diagram of the cells (𝑐) and junctions (𝑗) used to longitudinally discretize the streamreach for the stream temperature model. Light blue bound by dark blue curved lines representthe stream surface and the bounding stream banks. Red dots represent the location of eachjunction that creates each cell (green rectangles). Grey line represents the stream centerline.2.3.2.2 Net radiationCell-specific net all-wave radiation, 𝐽 ∗𝑐 (Wm-2) can be expressed as follows:𝐽 ∗𝑐 = 𝐾∗𝑐 + 𝐿∗𝑐 (2.17)where 𝐾∗𝑐 is net shortwave radiation (Wm-2) and 𝐿∗𝑐 is net longwave radiation received atthe stream surface (Wm-2) for cell 𝑐. The calculation of 𝐾∗𝑐 and 𝐿∗𝑐 is described in thefollowing two sections.Net shortwave radiationEstimated cell average net short wave radiation at the stream surface was calculated asfollows:𝐾∗𝑐 = 𝐾 ↓𝐴𝑆𝑐 (1 − 𝛼) (2.18)where 𝐾 ↓𝐴𝑆𝑐 is the cell averaged incident short wave radiation (Wm-2) received at thestream reach surface and 𝛼 is the reach-averaged stream surface albedo at time t. 𝐾 ↓𝐴𝑆𝑐was calculated as:𝐾 ↓𝐴𝑆𝑐= 𝑔𝑡𝑐 ⋅ 𝐷(𝑡)𝑐 + 𝑓𝑣𝑐 ⋅ 𝑆(𝑡)𝑐 (2.19)where 𝑔𝑡𝑐 is the cell-averaged gap fraction, taken to be the complement of 𝑆𝑡 (calculated inSection 2.3.1), 𝐷(𝑡)𝑐 is the cell-averaged direct component of incident solar radiation (Wm-2)at time 𝑡, 𝑓𝑣𝑐 is the cell-averaged sky view factor (calculated in Section 2.3.1.5) and 𝑆(𝑡)𝑐is the diffuse component of incident solar radiation (Wm-2) at time 𝑡. Due to the fact thatonly total incident solar radiation was measured on site, solar radiation was partitioned into29diffuse and direct components using the method of Erbs et al. (1982) as used by Leach andMoore (2010). In this approach, the ratio of diffuse-to-global solar global radiation, 𝑘𝑑, iscomputed as follows:𝑘𝑑 =⎧{{⎨{{⎩1.0 − 0.09𝑘𝑡, for 𝑘𝑡 ≤ 0.220.951 − 0.1604𝑘𝑡 + 4.388𝑘2𝑡 − 16.638𝑘3𝑡 + 12.336𝑙4𝑡 , for 0.22 < 𝑘𝑡 ≤ 0.800.165, for 𝑘𝑡 > 0.80(2.20)where 𝑘𝑡 is the atmospheric clearness index, defined as the ratio of global-to-extraterrestrialsolar radiation, calculated as follows:𝑘𝑡 =𝐾 ↓𝑂𝑆𝐼𝑜(2.21)where 𝐾𝑂𝑆 ↓ is used as a proxy to represent the incident solar radiation above the riparianfoliage canopy and 𝐼𝑜 is the extraterrestrial radiation received outside of the Earth’s surface.𝐼𝑜 was calculated as follows:𝐼𝑜 = 𝐾0 ⋅ cos(90 − 𝑆𝜃) (2.22)where 𝐾0 is the solar constant, taken to be 1,367 Wm-2 and 𝑆𝜃 is the solar elevation angleat time 𝑡, as defined in Section 2.3.1.Although stream surface albedo measurements for low-gradient valley-bottomstreams have typically ranged between 0.05 and 0.13 (Leach and Moore, 2010; Knudson,2012; McMahon and Moore, 2017), the albedo of water is known to vary with incidenceangle of direct solar radiation, the ratio of diffuse to global radiation, suspended sedimentconcentration (SSC) and aeration (Han, 1997; Richards and Moore, 2011; McMahon andMoore, 2017). In this study, stream surface albedo was estimated using a flatwater albedomodel presented by McMahon and Moore (2017). The flatwater albedo model FWa-3 waschosen because it accounted for 60% of the variance in albedo measurements, which was thehighest of any of the models using categorical SSC measurements, with a root-mean-squareerror (RMSE) of 0.02 (McMahon and Moore, 2017). Albedo and SSC observations used asinputs for the regression models in McMahon and Moore (2017) were taken from streamswithin a similar region as this study, and included measurements over Lillooet River. Itwas therefore assumed that albedo model FWa-3 was reasonable for use in this study. Themodel is expressed as follows:𝛼 = 𝛽0 + 𝛽1 sin𝑆𝜃 + 𝛽2SSC+ 𝛽3𝜏 + 𝛽4(sin𝑆𝜃 ⋅ 𝜏) (2.23)30where 𝑆𝑆𝐶 is a categorical variable with a value of 0 for SSC < 30 mgL-1g and 1 otherwise,𝜏 is the atmospheric transmissivity, and the coefficients 𝛽0, 𝛽1, 𝛽2, 𝛽3 and 𝛽4 are 0.04, -0.01,0.03, 0.17 and -0.18, respectively. The value of 𝑆𝑆𝐶 was specified as 1 in this case becausethe summer season Lillooet SSC was always well above 30 mgL-1 for both Knudson (2012)and McMahon and Moore (2017).Atmospheric transmissivity was calculated as follows:𝜏 = 𝐾𝑂𝑆 ↓𝐾0 ⋅ cos 𝑖(2.24)where 𝑖 is the solar incidence angle, approximated here by 𝑆𝜃 due to the low slope of theLillooet stream reach.Net longwave radiationCell-averaged net longwave radiation at the stream surface can be represented as:𝐿∗𝑐 = 𝜀𝑤𝐿 ↓𝐴𝑆𝑐 −𝐿 ↑𝐴𝑆𝑐 (2.25)where 𝜀𝑤 is the emissivity of the stream, 𝐿 ↓𝐴𝑆𝑐 is the cell averaged longwave radiationthat is emitted by the atmosphere, terrain and vegetation and received at the stream surface(Wm-2) and 𝐿 ↑𝐴𝑆𝑐 is the cell averaged longwave radiation emitted by the stream surface(Wm-2). 𝜀𝑤 was assumed to be 0.95, which is the same value used by Knudson (2012) for thesame stream reach and is the mean of the water emissivity values provided by Oke (1987).The cell-averaged longwave radiation reaching the stream surface was calculated as:𝐿 ↓𝐴𝑆𝑐= [𝜀𝑎𝑓𝑣𝑐 + 𝜀𝑓(1 − 𝑓𝑣𝑐)] 𝜎 (𝑇𝑎∶𝐴𝑆 + 273.2)4 (2.26)where 𝜀𝑎 is the atmospheric emissivity, 𝜀𝑓 is the emissivity of foliage and 𝑇𝑎∶𝐴𝑆 is the esti-mated above stream air temperature interpolated from the relationship between measuredair temperatures at OSMS and ASMS. For this study, 𝜀𝑓 was assumed constant at 0.97 giventhe emissivity of deciduous trees between 0.97-0.98 (Oke, 1987), and the foliage temperaturewas assumed equal to air temperature. The atmospheric emissivity can be calculated byusing measured incident longwave radiation, air temperature and the calculated sky viewfactor at OSMS as follows:𝐿 ↓𝑂𝑆= [𝜀𝑎𝑓𝑂𝑆 + 𝜀𝑓(1 − 𝑓𝑂𝑆)] 𝜎 (𝑇𝑎∶𝑂𝑆 + 273.2)4 (2.27)where 𝐿 ↓𝑂𝑆 is the measured longwave radiation at OSMS (Wm-2), 𝑓𝑂𝑆 is the sky viewfactor at OSMS and 𝑇𝑎∶𝑂𝑆 is the air temperature at OSMS. 𝑓𝑂𝑆 was calculated using thesame methods as described in Section 2.3.1, though only CDEM shading was calculated due31to the limited extent of the LiDAR data. However, shading from vegetation was visuallyassessed to be negligible due to the location of OSMS within an open field. Equation (2.27)can then be rearranged to solve for 𝜀𝑎 as follows:𝜀𝑎 =1𝑓𝑂𝑆[ 𝐿 ↓𝑂𝑆𝜎(𝑇𝑎∶𝑂𝑆 + 273.2)4− 𝜀𝑓(1 − 𝑓𝑂𝑆)] (2.28)Cell-averaged longwave radiation emitted by the stream was calculated within the Hydro-Couple modelling framework using the modelled stream temperature as:𝐿 ↑𝐴𝑆𝑐= 𝜀𝑤( ̂𝑇𝑤𝑐 + 273.2)4 (2.29)where ̂𝑇𝑤𝑐 is the modelled stream temperature for cell 𝑐.2.3.2.3 Latent and sensible heat fluxesThe cell-specific latent heat flux is computed following Buahin et al. (2019) as:𝑄𝑒 = 𝜌𝑤 ⋅ 𝐿𝑣 ⋅ (𝑎 + 𝑏𝑢)(𝑒𝑎–𝑒𝑤) (2.30)where 𝑄𝑒 is the latent heat flux (Wm-2), 𝜌𝑤 is the density of water, taken to be 1000 kg m-3,𝐿𝑣 is the latent heat of vaporization (Jkg-1), 𝑎 and 𝑏 are empirical constants, 𝑢 is above-stream wind speed (m s-1), and 𝑒𝑎 and 𝑒𝑤 are the vapour pressures of the above-stream airand the water surface, respectively (kPa). 𝐿𝑣 is computed as a function of temperature andthe evaporative wind function coefficients 𝑎 and 𝑏 were 𝑎 = 5.505 × 10-8 ms-1kPa-1 and 𝑏 =1.600 × 10-8 kPa-1, respectively (Buahin et al., 2019; Moore and Leach, 2021).The cell-specific sensible heat flux is calculated using the Bowen ratio (𝐵𝑟) as follows:𝑄ℎ = 𝐵𝑟 ⋅ 𝑄𝑒 (2.31)where𝑄𝑐 is the sensible heat flux (Wm-2) and 𝐵𝑟 is the Bowen ratio (Bowen, 1926). Buahin etal. (2019) outlined the methods used for estimating the Bowen’s ratio, based on formulationspresented by Martin and McCutcheon (1998) and using a Bowen’s coefficient of 0.0651 (kPaoC-1).2.3.2.4 Lateral inflowsThe heat fluxes provided by lateral inflows represent the heat supplied by tributaries intothe channel and were calculated as follows:𝑆𝑙𝑎𝑡 = 𝜌𝑤 ⋅ 𝑐𝑝,𝑤 ⋅ 𝑞𝑙𝑎𝑡 ⋅ 𝑇𝑙𝑎𝑡 (2.32)where 𝑆𝑙𝑎𝑡 is the heat flux supplied by lateral inflows per unit length of the cell of input32(J m-1s-1), which varies over space and time, 𝑐𝑝,𝑤 is the specific heat capacity of water,taken to be 4184 J kg-1 oC-1, 𝑞𝑙𝑎𝑡 is the lateral inflow per unit length of the cell of input(m3s-1m-1), and 𝑇𝑙𝑎𝑡 is the temperature of the lateral inflows (oC). Lateral subsurface inflowswere not included in this analysis due to the time of year and the relatively low-permeabilityglaciolacustrine and alluvial deposits of the river valley, which would make subsurface inflowsnegligible relative to the main channel and tributary flows.2.3.2.5 Model set up and parametersThe HydroCouple model routes water downstream using a kinematic wave approach. Inthis application, a Manning’s roughness coefficient of 0.05 was assumed to be reasonableconsidering observed coefficients for a 450 m stretch of the Lillooet River just upstreamof the BC Highway 99 bridge (Prent and Hickin, 2001). A trapezoidal channel geometrywas assumed to allow stream width to vary with discharge. The reach-wide side slope andbottom width were estimated to be 0.09125 m/m and 12.5 m, respectively. These figureswere determined following the methods outlined in Appendix 5.2 using channel cross-sectiondata for the LL and UL site data provided by Hutchinson (2023) and Zimmermann (2023).The start and end time of the model runs were 2022-07-29 08:00:00 and 2022-10-04 12:00:00,respectively. All time-series data inputs to the model as well as the resulting outputs werestandardized to PDT (UTC-7).To evaluate model sensitivity and the relative importance of different controllingfactors, the stream temperature model was run under different scenarios and compared to a‘baseline’ model that included all of the best estimates for above stream meteorological andradiative exchanges.• The model was run using the uncorrected and corrected UL streamflow data to under-stand the sensitivity of stream temperatures to uncertainty in the upstream discharge.Model scenarios without any tributary inflow from RR or MC were run to understandthe influence of tributary inflows on the heat budget and resulting temperature dynam-ics of Lillooet River at the LL site.• Mean, 10th and 90th percentile ASMS wind speeds were used as different model sce-narios to evaluate the sensitivity of the energy budget and temperature dynamics towind.• To understand the accuracy and sensitivity of the stream to the stream shade model andto quantify the effect of longitudinal advection and dispersion on stream temperature,a model instance was run without any surface-atmosphere radiative energy exchange.In this scenario the albedo and water emissivity were set to 1 and 0, respectively; thestream water surface was effectively treated as a perfect ‘thermal mirror’, meaning the33simulated stream temperatures represented only the effects of longitudinal and lateraladvection and longitudinal dispersion.• Model scenarios were run using open-site radiation data to represent stream temperatureunder a ‘no shade’ environment. OSMS air temperature, relative humidity and incomingshortwave and longwave radiation and PAMS wind speeds were used to represent opensite meteorological and radiative fluxes. PAMS wind speeds were used to represent opensite wind speeds due to incomplete OSMS wind speed observations.Table 2.2 summarizes the model scenarios.34Table 2.2: Summary of the stream temperature model scenarios.Scenario Summary Parameters and commentsBaseline Baseline scenario forcomparisonsMean windspeeds from ASMS, corrected UL streamflow and predicted ASMSmeteorological and radiative fluxes.UL Uncorrected Uncorrected UL streamflow Uncorrected UL streamflows as boundary conditions, mean windspeeds fromASMS and predicted ASMS meteorological and radiative fluxes.WS 10th percentile Constant wind speeds using the10th percentile from ASMS10th percentile wind speeds from ASMS with corrected UL streamflows andpredicted ASMS meteorological and radiative fluxes.WS 90th percentile Constant wind speeds using the90th percentile from ASMS90th percentile wind speeds from ASMS with corrected UL streamflows andpredicted ASMS meteorological and radiative fluxes.Advection-only No radiative exchange Incoming shortwave and longwave radiation shut off, meann windspeeds fromASMS, corrected UL streamflow and predicted ASMS meteteorlogical variables.No-RR No heat and flow input from RR No tributary input from RR, mean windspeeds from ASMS, corrected ULstreamflow and predicted ASMS meteorological and radiative fluxes.No-MC No heat and flow input fromMCNo tributary input from MC, mean windspeeds from ASMS, corrected ULstreamflow and predicted ASMS meteorological and radiative fluxes.No-shade Open site radiative fluxes (noaffect of shade model)OSMS radiation data, mean windspeeds from ASMS, corrected UL streamflowand predicted ASMS meteorological data.OS-met Open site meteorological data OSMS meteorlogical data, timeseries wind speeds from PAMS, corrected ULstreamflow and predicted ASMS radiative fluxes.Full-OS Open site meteorological andradiative fluxesOSMS meteorlogical and radiation fluxes, timeseries wind speeds from PAMS andcorrected UL streamflow.a UL = Upper Lillooet, RR = Ryan River, MC = Miller Creek, LL = Lower Lillooet, OS = open-site.35Chapter 3Results3.1 Overview of the study periodAir temperatures in April and May 2022 were slightly below normal at Pemberton Airport(Figure 3.1), shifting to higher than average for July, August and September. Precipitationduring the study period was near-average for June and July, and notably below averagefrom July through December. Streamflow was below average in April and May, reflectingthe below-average air temperatures, shifting to above-average for July and back to near-average for August through October. Thus, the study period was characterized by weatherthat was warmer and drier than average, with near-average streamflow.The mean monthly air temperatures at OSMS during August and September were2.5 and 3.0 oC lower than the 2022 averages at Pemberton Airport, while the monthly totalprecipitation records between the two meteorological stations were relatively similar duringthese months.Continuous records of meteorological variables measured at OSMS throughout themonitoring period are highlighted in Figure 3.4. Three main periods of rainfall occurred inearly August and the start and middle of September. These events coincided with reducedincident shortwave radiation, increased incident longwave radiation, and muted diel air tem-perature cycles. Air temperature and atmospheric vapour pressure show clear diel cyclesthat are superimposed on seasonal cooling trends. The five days that experienced the high-est wind speeds at Pemberton Airport were August 1, August 26, September 3, September7and September 22 (Figure 3.4).36Figure 3.1: Maximum, mean and minimum mean monthly air temperatures (𝑜C) at Pemberton Airportmeteorological station (PAMS) (Station ID: 1086082, elevation: 204 m a.s.l) for the period1985-2021. Monthly air temperatures for 2022 are shown in blue. Air temperatures during thefield season at the open site meteorological stations (OSMS) are shown in red (elevation: 227m a.s.l). Only complete months of data were included for OSMS. Grey polygon represents themonitoring period.Figure 3.2: Monthly mean total precipitation (mm) for the period 1985-2021 (grey) and 2022 (blue) atPemberton Airport meteorological station (PAMS). Monthly total precipitation at the opensite meteorological station (OSMS) during the monitoring period (red). Only complete monthsof data were included for OSMS.37Figure 3.3: Maximum, mean and minimum mean daily discharge (m3s−1) at the Lower Lillooet WSCGauge station (Station ID: 08MG005). 2022 mean daily discharge displayed in blue. Greypolygon represents monitoring period.3.2 Stream boundary conditions3.2.1 Observed stream temperaturesWater temperatures at all four sites (UL, RR, MC and LL) showed strong diel cycles with ageneral cooling trend throughout the monitoring period (Figure 3.6). UL, RR and MC expe-rienced a spell of gradually increasing stream temperature from the beginning to the middleof September, followed by a marked sudden cooling in mid-September. After mid-September– toward the end of the monitoring period – both RR and LL experienced breakdowns intheir diel stream temperature cycles. These irregular patterns exhibited double peaks instream temperature, which on further inspection coincided with low flow periods. This pat-tern could be due to the sensor being in shallow waters, whereby at low daily flows the waterswere shallow enough that they became influenced by air temperatures for a short period.However, these data are not used in any subsequent analysis.As shown in Table 3.1, MC experienced the lowest mean daily water temperatures.The mean daily range was lowest at LL and highest at MC. Daily mean stream temper-atures closely mirrored daily mean air temperatures at OSMS for all sub-reaches (Figure3.7). Although all sub-reaches experienced seasonal cooling trends, MC mean daily streamtemperatures cooled the most throughout the monitoring period.38Figure 3.4: Meteorological variables monitored at the open site meteorological station (OSMS) throughoutthe monitoring period, recorded every 10 minutes. (a) incident shortwave radiation (𝐾 ↓𝑂𝑆),(b) incident longwave radiation (𝐿 ↓𝑂 𝑆), (c) air temperature (𝑇𝑎∶𝑂𝑆), (d) atmospheric vapourpressure (𝑒𝑎∶𝑂𝑆), (e) wind speed (𝑢), (f) barometric pressure (𝑃𝑏) and (f) rainfall.39Figure 3.5: Meteorological variables observed at Pemberton Airport Meteorological stations (PAMS). (a)air temperature (𝑇𝑎∶𝑃𝐴), (b) atmospheric vapour pressure (𝑒𝑎∶𝑃𝐴), and (c) wind speed (𝑢𝑃𝐴).Table 3.1: Mean daily stream temperature statistics for the monitoring period at each sub-reach. Only thedata points that correspond with the observational timings at all four sub-reaches are includedfor comparisons.𝑇𝑤 (𝑜C)Daily statistic UL RR MC LLmin 8.89 9.07 7.40 9.35max 11.77 11.50 10.12 11.44range 2.88 2.43 2.72 2.09mean 10.33 10.18 8.63 10.3440Figure 3.6: Water temperatures (𝑇𝑤) for Upper Lillooet (a), Ryan River (b), Miller Creek (c) and LowerLillooet (d) (oC). Upper Lillooet and Ryan River 𝑇𝑤 are from gauging stations operated byWSC, whereas Miller Creek and Lower Lillooet 𝑇𝑤 are from tidbit water temperature loggers.Red lines for UL are values that were interpolated using the linear regression between 𝑇𝑤 atthe UL PVDD gauge station as a function of 𝑇𝑤 at the UL tidbit temperature logger. Bluelines represent linear interpolation between coinciding periods of no data at the UL tidbittemperature logger and the UL PVDD gauge station. Gaps in the time series represent dataremoved due to suspected dewatering.41Figure 3.7: (a) Maximum, mean and minimum mean daily air temperatures at OSMS (𝑇𝑎∶𝑂𝑆). (b) Meandaily water temperatures at UL, RR, MC and LL (𝑇𝑤).423.2.2 Observed streamflowsContinuous discharge measurements for all sub-reaches are shown in Figure 3.8. All sta-tions exhibited similar diel trends superimposed on a declining seasonal trend despite thecontrasting discharge magnitudes. As seen in panel (a), the effect of the bias correction wasto increase the discharge at UL from the start of the study period through the first week ofSeptember.Figure 3.8: Stream discharge (𝑄) for Upper Lillooet (a), Ryan River (b), Miller Creek (c) and LowerLillooet (d) (m3s-1). Upper Lillooet streamflow from PVDD gauge station, Ryan River andLower Lillooet streamflow from WSC gauge station and Miller Creek streamflow derived fromfrom the model fitting of the stage rating curve produced from the velocity-area streamflowmeasurements. Grey line represents the uncorrected Upper Lillooet streamflows compared tothe bias corrected streamflows in black.433.3 Diel variations in stream temperature and flowThe period from July 29 to August 5 was selected for further investigation into the timing ofdaily stream temperature maxima and minima because it had the longest period of completestream temperature data at LL during the monitoring period, exhibited marked diel cyclesat all four locations, and contained the least amount of infilled data at UL. An overview ofstream temperature during this period is shown in Figure 3.9. Diel temperature fluctuationswere muted during the evening of August 3, which coincided with a prolonged rainfall eventduring the evening of August 3 until the morning of August 4, during which approximately79 mm of rain was recorded at OSMS.Figure 3.9: Stream temperature (𝑇𝑤) at Upper Lillooet (UL), Ryan River (RR), Miller Creek (MC) andLower Lillooet (LL) between 29 July and 5 August. Timezone in PDT (UTC-7).Figure 3.10 illustrates the timing of each 24-hr stream temperature maximum andminimum between July 29 and August 5. MC consistently had the earliest peak temperature,which peaked around 16:00 on average. UL peaked next, about 3.5 hours later at 19:30,44followed by RR at about 21:00 and LL at about 23:00. Minimum temperatures followed thesame order, but with less variation, with MC reaching a minimum about 8:00, LL at 9:00,RR about 9:40 and LL about 11:15.There was no simple relation between stream temperature and streamflow at anyof the sites (UL, RR, MC, LL), as presented in Figure 3.11. All four sites show similarhysteresis loops for stream temperature as a function of streamflow. For the days withstrong diel variation (July 30 to August 3), there is no clear relation between the peaktemperature for each diel cycle and either the preceding peak discharge or the discharge atthe time of the peak temperature.3.4 Above-stream meteorological conditionsTable 3.2 provides a summary of ASMS field deployment times and air temperatures. Thissection provides an overview of the ASMS data that were collected and the models that wereused to interpolate continuous above-stream meteorological data throughout out the entirefield.Table 3.2: ASMS deployment times, deployment length (hours) and summary statistics for above-streamair temperatures (𝑇𝑎∶𝐴𝑆) during ASMS deployment. All times are relative to PDT (UTC-7)𝑇𝑎∶𝐴𝑆 stats. (𝑜C)Start End Hours Min Mean Max2022-08-16 11:10 2022-08-16 17:40 6.5 23.7 28.1 31.22022-09-02 21:20 2022-09-03 09:00 11.7 11.3 13.5 18.22022-09-03 19:20 2022-09-04 10:20 15.0 13.1 16.4 24.52022-09-06 12:00 2022-09-06 19:00 7.0 16.7 21.2 25.92022-09-08 10:50 2022-09-09 09:10 22.3 6.0 14.0 31.82022-09-23 11:10 2022-09-24 12:50 25.7 8.5 12.6 21.93.4.1 Air temperatureFigure 3.12 illustrates the pairwise relations among OSMS, ASMS and PAMS. Panel (a)highlights that For OSMS temperatures below about 15 oC, there are two clusters of points,one that represents a relatively strong linear relation with higher temperatures at ASMS andother that exhibits a more variable relation with lower temperatures. Panel (c) reveals thatthe two open-site stations could record substantially different temperatures. For example,for a temperature of 20 oC at PAMS, the corresponding temperatures at OSMS varied fromabout 10 to 25 oC.Time series of air temperatures at ASMS and OSMS during ASMS deployment aredisplayed in Figure 3.13. During daylight hours, air temperatures at ASMS were usually45Figure 3.10: (a) Timing of daily maximum water temperature (𝑇𝑤) at Upper Lillooet (UL), Ryan River(RR), Miller Creek (MC) and Lower Lillooet (LL) as red, blue, green and orange, respec-tively. (b) Timing of daily minimum 𝑇𝑤 at UL, RR, MC and LL. Horizontal colored linesrepresent the mean timing of maximum and minimum water temperatures between 29th Julyand 5th August. Horizontal dotted grey lines represent 1-hour intervals. Note that RR watertemperature is recorded hourly. Timezone in PDT (UTC-7).46Figure 3.11: Observed stream temperatures (𝑇𝑤) as a function of streamflow (𝑄) colored by date for UpperLillooet (UL), Ryan River (RR), Miller Creek (MC) and Lower Lillooet (LL).47Figure 3.12: Pairwise relations between air temperatures measured at three weather stations: ASMS ver-sus OSMS (a), ASMS versus Pemberton Airport (b), and OSMS versus Pemberton Airport(c). Dashed line represents a 1:1 relation. Note that 𝑇𝑎∶𝑂𝑆 was recorded every 10 minutesthroughout the entire field season, 𝑇𝑎∶𝐴𝑆 was recorded every 10 minutes throughout fielddeployment visits and 𝑇𝑎∶𝑃𝐴 was recorded every hour throughout the entire field season.lower than at OSMS, while air temperature at ASMS tended to be higher at OSMS duringhours of shade at ASMS. However, during shaded hours that had 𝐿 ↓𝑂𝑆 values above ap-proximately 325 W m-2, the night-time relationship between the air temperatures at bothmeteorological stations was reversed: ASMS air temperatures were usually lower than theOSMS air temperatures during these conditions, for example on August 3rd and September23rd. It was assumed that higher values of 𝐿 ↓𝑂𝑆 in excess of 325 Wm-2 indicated increasedcloud cover.Based on these results, the fitting of models to predict above-stream air temperatureinvolved separate regression models for unshaded, shaded clear, and shaded cloud conditions.Daylight hours were estimated by using the shading calculations that are part of the streamshade model algorithm using the coordinates of ASMS as the POI.Figure 3.13 illustrates the regression models for predicting above-stream air tempera-ture from those at OSMS. The regression models are provided below for the three conditions.Unshaded̂𝑇𝑎∶𝐴𝑆 = −1.51 + 1.01(𝑇𝑎∶𝑂𝑆) (3.1)where 𝑅2 = 0.89, 𝑝 < 0.01 and the residual standard error (RSE) is 1.76 oC.Shaded clear48Figure 3.13: Time series of air temperatures during ASMS deployment comparing air temperatures atASMS (𝑇𝑎∶𝐴𝑆) in blue and OSMS (𝑇𝑎∶𝑂𝑆) in red. Grey lines represent incident longwaveradiation at OSMS (𝐿 ↓𝑂𝑆) and grey polygons represent periods of shade, modelled using theshade model methods in Section 2.3.1). Timezone in PDT (UTC-7).49̂𝑇𝑎∶𝐴𝑆 = 3.21 + 0.86(𝑇𝑎∶𝑂𝑆) (3.2)where 𝑅2 = 0.91, 𝑝 < 0.01, and the RSE is 1.50 oC.Shaded cloudŷ𝑇𝑎∶𝐴𝑆 =⎧{⎨{⎩4.27 + 0.55(𝑇𝑎∶𝑂𝑆), if 𝑇𝑎∶𝑂𝑆 ≤ 18.68−3.52 + 1.04(𝑇𝑎∶𝑂𝑆), if 𝑇𝑎∶𝑂𝑆 > 18.68(3.3)where 𝑅2 = 0.94, 𝑝 < 0.01 and the RSE is 0.49 oC.For reference, both the linear regression for shaded clear (Equation (3.2)) and seg-mented regression for shaded cloudy (Equation (3.3)) conditions performed comparativelybetter than a linear regression model for shaded general (clear and cloudy) (𝑅2 = 0.81,𝑝 < 0.01, 𝑅𝑆𝐸 = 2.20 oC) with 𝐴𝐼𝐶𝑐 values of 839, 659 and 1806, respectively. A linearregression model for shaded cloudy (dashed red line in Figure 3.14d) was run for comparisonto the segmented alternative, which produced the following values, 𝑅2 = 0.85, 𝑝 < 0.01 and𝑅𝑆𝐸 = 1.90 oC. The 𝐴𝐼𝐶𝑐 value for the linear model for shaded cloudy was 839, whichis comparatively worse compared with the 𝐴𝐼𝐶𝑐 value for the segmented model for shadedcloud of 659.Based on the 𝐴𝐼𝐶𝑐 and 𝑅𝑆𝐸 values provided for regression models and their alter-natives, the models listed in the equations above were applied to generate a time series ofpredicted above-stream air temperatures for the entire field season, as shown in Figure 3.15.3.4.2 Atmospheric vapour pressureFigure 3.16 illustrates the pairwise relations for vapour pressure among OSMS, ASMS andPAMS. As seen in panel (a), above-stream vapour pressure was not well correlated withvapour pressure at OSMS, and was often substantially lower. There was a better relationwith vapour pressure at PAMS, with the above-stream vapour pressure often tending to beslightly higher, but with some observations being up to about 0.5 kPa lower that at Pem-berton Airport. Panel (c) reveals that OSMS tended to have higher vapour pressures thanPAMS. Through further inspection it was not possible to relate the nature of the relationsbetween stations with periods of shade and daylight, in contrast with the relationships forair temperature reported in the previous section.Table 3.3 compares model fits for three candidate regression models: one each usingOSMS and PAMS as predictors, and a third using data from both OSMS and PAMS. Al-though model 3 had the lowest 𝐴𝐼𝐶𝑐 value, it was not selected because of concerns over thephysical validity of the negative coefficient for OSMS vapour pressure. Model 2 was applied50Figure 3.14: Relations between above-stream air temperature and air temperature at OSMS. All data areshown in panel (a), with symbol colour indicating sky condition. Panels (b) to (d) presentdata separately by subset, with the fitted regressions shown as red lines. In panel (d), the solidline is the segmented regression used in further analysis and the dashed red line represents asimple linear regression for comparison. Equations for the regressions are shown in Equation(3.1), Equation (3.2) and Equation (3.3).51Figure 3.15: Time series of predicted above-stream air temperature throughout the entire field season asused as input for the stream temperature model.Figure 3.16: Pairwise relations between vapour pressures measured at three weather stations: ASMS versusOSMS (a), ASMS versus Pemberton Airport (b), and OSMS versus Pemberton Airport (c).Dashed line represents a 1:1 relation. The solid red line in panel (b) is the regression relationused in later analysis; the dashed red line in panel (a) is a regression fit for those data. Dashedline represents a 1:1 relation. Note that 𝑒𝑎∶𝑂𝑆 is recorded every 10 minutes throughout theentire field season, 𝑒𝑎∶𝐴𝑆 is recorded every 10 minutes throughout field deployment visits and𝑒𝑎∶𝑃𝐴 is recorded every hour throughout the entire field season. Only the 89 data points whereall observations overlap between all three sites were included in a) and b). All pair-wise datapoints corresponding with OSMS and PAMS are included in d).52Table 3.3: Results of regression model fits for predicting above-stream atmospheric vapour pressure (𝑒𝑎∶𝐴𝑆)using vapour pressure measured at the open-site met station OSMS (𝑒𝑎∶𝑂𝑆)and PembertonAirport atmospheric vapour pressures (𝑒𝑎∶𝑂𝑆) as predictors. Results include corrected Akaike’sinformation criterion (𝐴𝐼𝐶𝑐), residual standard error (RSE), intercept (𝑏0) and the coefficientsfor the predictor variables for all coefficients with 𝑝 < 0.01. Bold indicates the model that wasselected to predict above-stream vapour pressure over the entire study period. Only the 89data points where all observations overlap between all three sites were included to allow directcomparison of 𝐴𝐼𝐶𝑐 values.Model AIC Adj. 𝑅2 RSE 𝑏0 𝑒𝑎∶𝑂𝑆 𝑒𝑎∶𝑃𝐴1 5 0.10 0.24 0.80 0.332 -115 0.77 0.12 0.01 1.003 -166 0.87 0.09 0.18 -0.42 1.33to predict a time series of above-stream vapour pressure for the entire monitoring period, asshown in Figure 3.17.Figure 3.17: Time series of predicted above-stream atmospheric vapour pressure over the entire field season.3.4.3 Wind speedAlthough above-stream wind speeds did reach up to 2.5 m s-1, they were generally muchlower than those at the open sites OSMS and PAMS. Indeed, as seen in Figure 3.18, themajority of observations were below the stall speed of 0.3 m s-1, and were assigned a nominalvalue of 0.15 m s-1. In contrast, relatively few observations at OSMS and PAMS were belowthe stall speed.Figure 3.19 illustrates the pairwise relations for wind speed among OSMS, ASMSand PAMS. As seen in Figure 3.19, there is effectively no correlation between above-streamwind speed and open-site wind speed. Therefore, instead of using a regression model to53Figure 3.18: Histograms of wind speed (𝑢) at (a) ASMS, (b) OSMS and (c) PAMS.produce continuous above-stream wind speed throughout the monitoring period, differentstatic wind speed values were used as input to the stream temperature model. The selectedstatic wind speeds were based on the mean, median and 90th percentile, as presented inTable 3.4.Figure 3.19: Relationships between observed wind speeds at ASMS (𝑢𝐴𝑆) and OSMS (𝑢𝑂𝑆) (a), ASMSand Pemberton Airport (𝑢𝑃𝐴) (b), and OSMS and Pemberton Airport (c). Dashed black linerepresents the 1:1 relationship. All available observations on a pairwise basis are plotted.Table 3.4: Above-stream wind speed statistics (ms−1). Note that wind speeds of 0 ms-1 were replaced withvalues of 0.15 (half the stall speed).Value (ms−1)1 Median 0.1503 Mean 0.5334 90th percentile 1.20054Table 3.5: Summary of Planet Scope satellite imagery (Planet Team, 2017) used for model testing includingthe calendar date, time and solar elevation (𝑆𝜃) and azimuth angles (𝑎𝜃) (𝑜) during imageacquisition. Ground truthing results include the observed and predicted shaded area (km2) as𝑠𝑎 and ̂𝑠𝑎, respectively and the calculated observed and predicted shade fractions as 𝑠𝑜𝑏𝑠 and̂𝑠𝑝𝑟𝑒𝑑, respectively. Δ𝑠𝑡 is the difference in shade fraction between observed and predicted.Date Time (PDT) 𝑆𝜃 (𝑜) 𝑎𝜃 (𝑜) 𝑠𝑎 (km2) ̂𝑠𝑎 (km2) 𝑠𝑜𝑏𝑠 ̂𝑠𝑝𝑟𝑒𝑑 Δ𝑠2019-10-27 12:10 26.0 167.3 0.43 0.44 0.55 0.56 0.012020-10-24 11:23 24.5 155.6 0.38 0.46 0.59 0.72 0.132021-10-31 11:19 22.0 154.8 0.62 0.65 0.81 0.84 0.032022-08-31 11:46 44.7 150.1 0.07 0.07 0.09 0.09 0.002022-09-25 11:13 33.6 146.7 0.10 0.09 0.32 0.29 -0.032022-10-13 11:48 29.7 159.9 0.17 0.19 0.27 0.29 0.022022-10-15 11:44 29.0 160.2 0.15 0.12 0.47 0.41 -0.062022-10-16 11:10 26.7 151.4 0.16 0.16 0.52 0.52 0.002022-10-19 11:46 27.6 160.8 0.26 0.26 0.42 0.42 0.003.5 Shade and view factor modelling3.5.1 ValidationNine PlanetScope satellite image scenes were available and suitable for validating the shademodel (Table 3.5). Image acquisition times were between 11:10 and 12:10. An example ofthe satellite is presented in Figure 3.20 where the modelled shade for October 27, 2019, is inblack and observed shade from satellite imagery that was manually delineated is in red. Asseen in Figure 3.21 and Table 3.5, the model reproduced reach-averaged shade within about± 0.1 for shade fractions from 0.1 to over 0.8.Figure 3.20: Example satellite scene used for model validation with modelled shade in black (shaded)and white (unshaded) and manually delineated observed shading from satellite imagery astransparent red polygon. Grey lines represent 100 m elevation contours. Delineated streamboundary is in blue.Table 3.6 summarizes the level of agreement between the modelled and observedshade at the pixel scale. As shown in Table 3.7, 92% of POIs were classified correctly as55Figure 3.21: Comparison between predicted and observed shade fractions ( ̂𝑠𝑡).either shaded or unshaded across all satellite scenes. The 𝐹1 score and𝑀𝐶𝐶 value were bothclose to one (0.92 and 0.85, respectively), further supporting the robustness of the model.Table 3.6: Confusion matrix of model validation results. Numbers represent the number of gridded 20-mcell centroids (POIs) that were classified as true positive (TP), true negative (TN), false positive(FP) and false negative (FN) when comparing modelled shade to all nine satellite scenes.ObservedPositive NegativePositive 5583 273Predicted Negative 804 62513.5.2 Stream shade and shade fractionFigure 3.22 illustrates the changes in shade patterns through time for August 16, 2022.As the sun rises in the morning, shade is dominantly generated by the forested banks onthe east side. During midday, when the sun’s elevation angle is at its highest, the streamreach experiences little to no shading. As the sun sets in the west, both topographic andriparian features cast shade over the stream due to riparian vegetation close to the westbanks and steep east-facing valley slopes in this section of the Pemberton Valley. Figure3.23 shows stream shade model results for the same day, but at different locations along theLillooet River at 19:00. The UL location (Figure 3.23a) experienced dominantly riparian56Table 3.7: Classification performance statistics from confusion matrix including the accuracy, 𝐹1 − 𝑠𝑐𝑜𝑟𝑒and Matthews correlation coefficient (MCC) and the maximum range of possible values for eachstatistic.Statistic Value RangeAccuracy 0.92 0 to 1𝐹1-score 0.92 0 to 1MCC 0.85 -1 to 1evening shade, while the middle reach location (Figure 3.23b) experienced more dominanttopographic shading alongside riparian shade from the comparatively closer and steepervalley slopes on west side.Figure 3.24 provides a comparison of the mean daily shade fraction by time of daythroughout the monitoring period of CDEM and LiDAR shading compared with the com-bined shade model results. During the hour post-sunrise and pre-sunset, shading based onCDEM and LiDAR both played a fairly even role in shading contributions; however, as theday progressed, LiDAR shading made a more significant contribution to the overall shadingof the stream reach. During midday hours, when the solar elevation angle was at its maxi-mum and the solar azimuth angle was at its most southern position, the CDEM contributedlittle to no shading, while the LiDAR DSM contributed almost entirely to the shade fractionof approximately 0.1.As shown in Figure 3.25, the number of unshaded hours at individual pixels had arange of about 6 hr on a given day. The mean number of unshaded hours at the reach scaledeclined from approximately 8.5 hr in late July to 5.0 hours in early October. The locationof OSMS experienced roughly double the reach-averaged unshaded hours, ranging from 15.2hours at the start of the monitoring period to 11.5 hr at the end. Cell 265 received thegreatest amount of sunlight with an average of 9.7 hours per day, while cell 165 received thelowest amount of sunlight with an average of 4.3 hours per day.3.5.3 Sky view factorAs seen in Figure 3.26, sky view factor ranged from less than 0.6 near the banks to over 0.9mid-channel. The spatial pattern reflects the interacting effects of both channel width andriparian vegetation height. For example, Figure 3.26a shows an upstream segment close toUL with relatively low values of 𝑓𝑣, where the channel is relatively narrow and the steepereast side of the river bank consists of tall dense tree cover with a narrow line of tall trees onthe west banks. The middle course segment in Figure 3.26b has similar stream morphologyand tree cover on the east river banks compared with Figure 3.26a. However, this middlesegment has more sporadic tree cover on the flat west banks, creating large canopy gaps andpatches of higher 𝑓𝑣 close to the right banks. Figure 3.26c shows a downstream segment that57Figure 3.22: Variation of shade patterns through time on August 16, 2022. Modelled shade from LiDARis shown in dark green (Riparian shade), topographic shade from the CDEM is in red, shadecast by both features is in black, and cells with no shade are in white. Also shown is canopyheight (m) calculated by differencing the LiDAR DSM and DTM for a 200-m buffer alongthe delineated Lillooet River water surface polygon. Inset map shows the Lillooet monitoringreach in light blue.58Figure 3.23: Variation of modelled shade patterns for three sections of Lillooet River at 19:00 on August16, 2022. Riparian shade from LiDAR is shown in dark green, topographic shade from theCDEM is in red, shading cast by both features is in black, and cells with no shade are in white.Locations of stream sections are shown on the inset map. Also shown is canopy height (m)calculated by differencing the LiDAR DSM and DTM for a 200-m buffer along the delineatedLillooet River water surface polygon. Inset map shows the Lillooet monitoring reach in lightblue.59Figure 3.24: Diurnal variation of mean reach-wide shade fraction (𝑆𝑡). Total shade is shown as a blackline, while the separate contributions of riparian shade from LiDAR and topographic shadingfrom the Canadian DEM (CDEM) are shown as green and red lines, respectively. Verticalgrey lines represent 2-hour intervals. Timezone in PDT (UTC-7).is just upstream of the BC-HWY 99 Bridge, with a higher sinuosity and a wider channel inplaces.As seen in Figure 3.27 mean values of 𝑓𝑣 within the stream cells used in the temper-ature model varied from 0.54 (cell 165) to 0.89 (cell 65). Cell 165 was the 5th narrowest cell,with a mid-cell stream width of 42 m, and had dense forest on both sides of the bank, whilealso recieving the lowest amount of sunlight. Cell 65 was the widest cell with a mid-cellstream width of 245 m, it was located 100 m upstream of a sudden narrowing (at cell 67) ofthe river, and had tree cover along the east banks and low-lying shrub cover along the lowgradient east banks.If only surrounding topography were considered, sky view factors would range from0.81 to 0.96, with a median of 0.92 (Figure 3.28); considering only the riparian zone increasedthe range and reduced the median with values between 0.04 to 0.98 and a median of 0.79.This comparison of sky view factors based only on the riparian zone with that using bothriparian and topographic influences shows that the riparian zone is the dominant influence.60Figure 3.25: Amount of daily modelled sunlight hours for each stream cell in grey, mean number of sunlighthours for the entire stream reach in black and the daily number of sunlight hours at the opensite meteorological station (OSMS) in red. Timezone in PDT (UTC-7).61Figure 3.26: Modelled sky view factor (𝑓𝑣) at each 20-m-grid POI. Delineated stream boundary as bluelines. Inset map provides reference extents for stream reach segments and highlights the largescale topographic features using the CDEM shaded from black (low elevations) to white (highelevations).62Figure 3.27: Longitudinal variation in the mean sky view factor (𝑓𝑣) for each 100-m cell used in the streamtemperature model.Figure 3.28: Boxplot of modelled sky view factor (𝑓𝑣) values for each POI for the normal model (grey) andwhen only taking into account the CDEM (red) and LiDAR (green).633.6 Stream temperature model3.6.1 Surface-atmosphere energy exchangesModelled albedo varied between 0.06 and 0.16 and had a mean of 0.085 throughout theentire monitoring period (Figure 3.29a). Atmospheric emissivity varied between 0.58 and1.00 and was typically higher during night and periods of cloud cover (Figure 3.29b). Asseen in Figure 3.30, reach-averaged longwave losses generally exceeded inputs, except oncloudy days with low solar radiation. Figure 3.31 shows that the cell that acquired greatestamount of sunlight hours per day (Cell 265: average sunlight hours = 9.7, 𝑓𝑣 = 0.83) receivedconsiderably more incident shortwave radiation during peak daylight hours compared withthe cell that acquired the least amount of sunlight hours per day (Cell 165: average sunlighthours = 4.3, 𝑓𝑣 = 0.54). During clear days, cell 165 generally received more incident longwaveradiation at the stream surface compared with cell 265.Figure 3.29: a) Predicted albedo (𝛼) using the FWa-3 categorical SSC model derived by McMahon andMoore (2017). b) Atmospheric emissivity (𝜖𝑎).Both the sensible and latent heat fluxes were dominantly positive through August(Figure 3.32). The sensible heat flux remained positive during the day in September andOctober, but often became negative at night, while the latent heat flux occasionally re-mained negative through the day. The two short periods of negative values of 𝑄𝑒 suggest64Figure 3.30: Reach-averaged radiative exchanges for the Lillooet stream reach including incident long andshortwave radiation (𝐿 ↓𝐴𝑆 and 𝐾 ↓𝐴𝑆, respectively), outgoing long and shortwave radiation(𝐿 ↑𝐴𝑆 and 𝐾 ↑𝐴𝑆, respectively) and net all-wave radiation (𝑄∗).heat loss from evaporation was associated with a coinciding reduction in above-stream airtemperatures and reduced values in Figure 3.32c.3.6.2 Model performance for the full period of recordFigure 3.33 demonstrates that using the bias-corrected streamflow for UL, used as the base-line scenario, resulted in a better simulation of streamflow at the LL site. The baselinescenario had a root-mean-square error of 14.81 m3s-1 and an ME of 12.57) m3s-1 comparedto the UL-uncorrected scenario, which had RMSE = 25.06 m3s-1 and ME = -10.52). Therelationship between observed and modelled streamflow for the UL-uncorrected scenario ex-hibited a clear shift 3.33b. This shift in the relationship was also apparent when examiningthe modelled streamflows above and below each tributary confluence, thus supporting the as-sumption that the source of the erroneous streamflow measurements was the UL streamflowrecord.Modelled stream temperatures for the seven simulation scenarios were similar despitethe differences in inputs (Figure 3.34). There was only 0.2 oC difference between the RMSEvalues comparing observed and modelled stream temperatures at LL from the baseline,UL-uncorrected, WS 10th percentile and WS 90th percentile model scenarios with RMSEvalues of 0.30, 0.29, 0.31 and 0.30 oC respectively and ME values of 0.03, 0.03, 0.03 and0.05 respectively. The advection-only, no-Ryan-River (no-RR) and no-Miller-Creek (no-MC)scenarios had the three worst performances when modelling stream temperatures (RMSE =0.44, 0.41 and 0.37 oC, respectively. ME = -0.07, 0.08 and 0.10 oC).65Figure 3.31: (a) Reach-averaged radiative exchanges for the Lillooet stream reach including incident longand shortwave radiation (𝐿 ↓𝐴𝑆 and 𝐾 ↓𝐴𝑆, respectively), outgoing long and shortwaveradiation (𝐿 ↑𝐴𝑆 and 𝐾 ↑𝐴𝑆, respectively) and net all-wave radiation (𝑄∗). (b) Radiativeexchanges at the cell that experienced the highest average sunlight hours (Cell 265). (C)Radiative exchanges at the cell that experienced the lowest average sunlight hours (Cell 165).Timezone in PDT (UTC-7).66Figure 3.32: Above-stream air temperature ( ̂𝑇𝑎∶𝐴𝑆) (a), reach-averaged sensible (𝑄ℎ) and latent (𝑄𝑒) heatfluxes estimated by the stream temperature model (b) and the difference between abovestream atmospheric vapour pressure ( ̂𝑒𝑎∶𝐴𝑆 ) and reach-averaged above-stream atmosphericvapour pressure ( ̂𝑒𝑤) (c). Baseline model scenario used.67Figure 3.33: Modelled streamflow (?̂?) at Lower Lillooet (LL) using the baseline model scenario (a), whichincludes the bias-corrected UL (Upper Lillooet) streamflows, and the UL uncorrected modelscenario (b).3.6.3 Streamflow simulations for Jul. 29 to Aug. 53.6.3.1 Diel variations in modelled stream temperaturesThe time series of modelled and observed stream temperature values for Jul. 29 to Aug. 5 areshown in Figure 3.35 and the differences between each model scenario and the baseline sce-nario are shown in Figure 3.36. The WS 10th percentile and WS 90th percentile scenarios werenot included in this further analysis. The baseline model scenario generally over-predictedmaximum stream temperatures and under-predicted minimum stream temperatures, thoughto a lesser degree of magnitude. The UL-uncorrected scenario generally tended to produceelevated stream temperatures during the day and reduced stream temperatures near mid-night compared with the baseline model. On a typical day, during peak daylight hours whenthe heating effect of solar radiation was most intense, the advection-only model producedstream temperatures that were typically 0.3-0.4 oC less than the baseline model due to thelack of radiation input. The day that experienced the least difference in modelled streamtemperatures was Aug. 3, which is likely due to the increased cloud cover and decreased in-cident solar radiation associated with rainfall occurring throughout the afternoon. As wouldbe expected, there was little to no difference in modelled stream temperatures during thenight between the baseline and no-advection scenarios. The no-RR scenario produced themost significant elevated stream temperatures compared to the baseline scenario. Theseincreased stream temperatures peaked at around 0.4 oC higher than the baseline model andoccurred throughout the early hours of the morning, coinciding with peak streamflow at68Figure 3.34: Modelled (red) and observed (black) stream temperatures for the seven modelling scenariosat the model cell corresponding to the Lower Lillooet (LL) field. Upper Lillooet (UL) streamtemperatures are shown in grey. Root- mean-square errors (RMSE) only include the periodup to Sept. 21 (grey polygons) and also exclude the first 12 hr to minimize the effect ofincorrectly set initial conditions. UL = Upper Lillooet, LL = Lower Lillooet, WS = windspeeds.69LL. However, between the hours of approximately midday to midnight, the no-RR scenariogenerated lower stream temperatures compared to the baseline model by around 0.2 oC.The differences in modelled stream temperatures between the baseline and no-MC scenariosfollow a similar diel pattern compared to the comparisons between the baseline and no RRmodel scenarios, though with a lower degree of magnitude. The effect of the Lillooet trib-utaries on the longitudinal temperature gradient of the Lillooet River is apparent in Figure3.37 as an abrupt shift just upstream of 20 km downstream.Figure 3.38 shows the timing of daily maximum and minimum stream temperaturesfor the baseline, advection-only, no-RR and no-MC model scenarios compared with theobserved timing at LL. The baseline, advection-only and no-MC scenarios all simulatedmaximum stream temperatures at the same time, which were on average 43 minutes laterthan the observed maximum LL stream temperatures (Figure 3.38a). The average maximumstream temperature for the No RR model occurred 30 minutes after the other model scenariosand 73 minutes after the observed timings. Close to midnight on Aug. 3, the baseline,advection-only and no-MC scenarios generated maximum stream temperatures at the sametime as the observed stream temperatures, whereas all four scenarios generated maximumstream temperatures at the same time as observed near midnight of Aug. 5.The baseline and no-MC model scenarios both generated minimum stream tempera-tures at the same time, which were on average 54 minutes later than the observed minimumstream temperatures and 10 minutes before the no-RR scenario (3.38b). The advection-onlymodel scenario simulated the greatest difference in the timing of daily minimum streamtemperature, which occurred 40 minutes later than the baseline model and 94 minutes laterthan the observed minimum stream temperatures. During Aug. 5, all four scenarios gener-ated minimum stream temperatures at the same time, which occurred at 14:00 compared toobserved minimum stream temperatures that occurred at 11:20.3.6.3.2 Tributary influencesAdvective heat input via the tributaries tended to cool Lillooet River at night, with RRhaving a greater influence than MC (Figure 3.39a). Tributary inputs had a greater influenceon daily maximum stream temperatures than on daily minima. RR provides the greateststreamflow input into the Lillooet River (Figure 3.39b).Figure 3.40a shows that temperatures downstream of RR were consistently 0.4 to0.5 oC lower than just upstream of the confluence in the hours of the early morning, shortlyafter peak streamflows occur. This pattern follows the same signal as the stream temperaturedifferences when excluding RR from the baseline model scenario. The Lillooet River typicallyexperienced increased stream temperatures of approximately 0.1 to 0.2 oC during afternoonhours, typically just after the lowest streamflows due to the influence of RR.70Figure 3.35: Modelled (red) and observed (black) streamflows (𝑄𝐿𝐿) at LL (top-panel) from Jul. 29 toAug. 5. Modelled and observed stream temperatures (𝑇𝑤) at LL (remaining panels). Observed𝑇𝑤 at UL in grey. Timezone in PDT (UTC-7).71Figure 3.36: Observed and modelled stream temperature for Jul. 29 to Aug. 5. Top panel representsobserved Lower Lillooet (LL) streamflow (𝑄𝐿𝐿) and remaining panels show the differencesbetween each model scenario and the baseline model stream temperatures at LL (Δ𝑇𝑤).Positive values mean that the scenario produces higher stream temperatures than the baselinemodel. Timezone in PDT (UTC-7).72Figure 3.37: Modelled stream temperatures (𝑇𝑤) for each cell as distance downstream from the UpperLillooet (UL) using the baseline scenario.73Figure 3.38: The timing of daily maximum (a) and minimum (b) modelled stream temperatures for thebaseline (red circle), advection-only (green triangle), no-Ryan River (blue plus) and no-MillerCreek (orange cross) scenarios at LL as a function of date. Dashed colored lines representthe corresponding mean times and solid black line represents the mean of observed timings.Note that the stream temperature model calculated stream temperature every 30 minutes.Timezone in PDT (UTC-7).74Figure 3.39: Modelled stream temperature (a) (𝑇𝑤) and discharge (b) (𝑄) above Ryan River (RR) at cell199 (green), between RR and Miller Creek (MC) at cell 201 (blue) and below MC at cell 204(red), with observed Upper Lillooet (UL). Observed 𝑇𝑤 and 𝑄 at Upper Lillooet (UL) in grey.Timezone in PDT (UTC-7).75Figure 3.40b shows the relative influence of MC on Lillooet River temperatures,which experiences similar diel patterns as the stream temperature before and after RR,though at a much lower degree of magnitude. The almost identically modelled, yet slightlyearlier timed, stream temperatures between the cell just downstream of the MC confluence(cell 204) and the cell located at LL field site (cell 237) highlights both the travel time betweenthe two locations and the lack of apparent stream temperature influences from inputs suchas lateral subsurface flows, which were not accounted for in the stream temperature models.Figure 3.40: Differences in modelled stream temperatures ( ̂𝑇 [𝑤]) between cells downstream and upstreamof Ryan River (a) and cells downstream and upstream of Miller Creek (MC). Cell numbersincrease from upstream to downstream. The baseline model scenario was used for calculations.Positive values represent downstream cell conditions that are warmer than the upstream cellconditions. Timezone in PDT (UTC-7).3.6.3.3 Energy exchange scenariosModel performance for the modelled stream temperature of the no-shade, OS-met and full-OS model scenarios generated RMSE values of 0.29 , 0.29 , 0.28 oC and mean bias errors of760.07 , 0.08 , 0.11 oC respectively.The differences between the modelled stream temperatures of the open-site and base-line scenarios were minimal (Figure 3.41). However, Figure 3.42 shows that when using opensite meteorological data, there was a greater magnitude of change from the baseline modelcompared to using open site radiation data. All three open site model scenarios highlightthat using open site conditions to compute surface energy exchanges increases modelled dailystream temperatures between midday to midnight. This is the opposite effect to that of theadvection-only scenario. The smallest difference between the scenarios occurred on Aug. 4,which was characterized by prolonged rainfall and cloud cover.The no-shade, OS-met and OS-full scenarios have a greater effect on the increasedstream temperatures compared with the baseline model with greater distances downstream.In contrast, the difference between the advection-only and baseline scenario modelled streamtemperatures becomes more negative with distance downstream.77Figure 3.41: Modelled stream temperatures at LL during the period 29th July to 5th August (red) com-pared to the observed stream temperatures (𝑇𝑤) at LL (black) and UL (grey). Timezone inPDT (UTC-7).78Figure 3.42: Streamflow at Lower Lillooet (top panel) and the differences between each model scenarioand the baseline model stream temperatures at LL (Δ𝑇𝑤). Positive values indicate that thescenario produces higher stream temperatures than the baseline scenario. Timezone in PDT(UTC-7).79Figure 3.43: The difference in modelled stream temperatures (𝑇𝑤) between the energy exchange scenariosand baseline scenario as distance downstream from Upper Lillooet (UL). Positive values repre-sent where modelled stream temperature are greater than baseline scenario values. Timezonein PDT (UTC-7).80Chapter 4Discussion4.1 Above-stream meteorologyAbove-stream air temperature tended to be lower than open-site air temperature duringthe day, consistent with previous studies (Benyahya et al., 2010; Leach and Moore, 2010;Guenther et al., 2012). This daytime relationship is to be expected due to the cooling ofair as it flows from a warmer land surface over the cooler water surface. This mechanism isconsistent with the simulated sensible heat flux being dominantly positive during daytime.During cloud-free nights, above-stream air temperatures were generally higher than at theopen-sites. This difference is likely due to the greater heat capacity of water compared tosoil, which would result in less nocturnal surface cooling, in conjunction with the effect oflongitudinal heat advection. However, although stream temperatures typically peaked duringnight at the Lillooet River, they mostly remained lower than above-stream air temperatures,resulting in dominantly positive sensible heat fluxes as simulated by HydroCouple. Therefore,the difference between open-site and above-stream air temperatures cannot be explainedby warming of cool air as it flowed from the land over the water surface. An alternativehypothesis is that, under the low-wind conditions typically associated with clear nights,lateral advection was minor, and the difference in air temperatures was driven by the effect ofthe surface boundary conditions on sensible heat flux. That is, the higher surface temperatureover the river would have reduced the sensible heat flux from the air to the surface comparedto that at the open-site, thus resulting in less cooling of the lower atmosphere.In comparison to the situation at Lillooet River, Leach and Moore (2010) found thatopen-site air temperatures were typically 1-3 oC higher and 2-5 oC higher compared to above-stream temperatures during the day and night, respectively, at non-glacier-fed FishtrapCreek, BC. The contrast in daytime-nighttime air temperature relationships between LillooetRiver and Fishtrap Creek is likely due to the contrasting diel stream temperature cyclesbetween stream reaches. Stream temperatures at Fishtrap Creek typically peaked around81midday to early afternoon (Leach and Moore, 2010), whereas at Lillooet River they peakedaround midnight. The depressed nighttime stream temperatures at Fishtrap Creek likelystimulated a more rapid cooling of above-stream air temperature compared with those aboveLillooet River, keeping air temperature above Fishtrap Creek lower than open-site conditionseven at night.During nighttime hours when there was considerable cloud cover, open-site air tem-peratures were generally higher than at the above-stream site. The increased emission oflongwave radiation from significant cloud cover would have suppressed surface cooling atthe open-site, such that the soil surface may have remained warmer than the water surface,where nighttime temperatures were dominated by longitudinal advection, with minimal in-fluence of surface energy exchange. However, measurements of soil surface temperature ormore detailed vertical air temperature profiles would be required to verify this hypothesis.The relations between above-stream and open-site vapour pressures differed betweenthe two land-based stations, although both exhibited substantial scatter. As seen in Figure3.16c, vapour pressures at OSMS were generally greater than at PAMS, which could be dueto irrigation and increased evapotranspiration occurring in the agricultural fields surroundingOSMS. This influence of irrigation is also likely reflected in the fact that the relation betweenvapour pressures at the above-stream site and PAMS was stronger than that for OSMS. Therelation between above-stream and PAMS vapour pressures had 𝑅2 = 0.77 and a tendencyfor above-stream vapour pressures to be slightly higher than or notably lower than at theopen-site. Guenther et al. (2012) and Leach and Moore (2010) both similarly found thatabove-stream vapour pressure was consistently higher than that at an open-site location.For Lillooet River, higher vapour pressures at the above-stream site cannot be attributedto moisture inputs to the lower atmosphere via evaporation from the river surface becausepredicted above-stream vapour pressures for Lillooet River were dominantly higher thanthose at the stream surface, resulting in a positive latent heat flux (i.e., condensation), evenduring the day. It may be that the slightly higher above-stream vapour pressures apparentin 3.16b is an artifact of differences in instrument accuracy/precision between the sites.While previous literature found that wind speeds above a stream surface at siteswith significant riparian vegetation were generally lower compared to open-site observations(Benyahya et al., 2010; Leach and Moore, 2010; Guenther et al., 2012), this study wasunable to identify any robust relationship between open-site and above-stream wind speeds.The above-stream meteorological station was deployed from a highway bridge that had largesupporting columns either side of the stream’s centreline. These supporting structures mayhave sheltered ASMS from wind directions perpendicular to the stream channel, creatingthe lack of relation between meteorological sites. This is further supported by the highfrequency of ASMS wind speeds that fell below the stall speed relative to OSMS and PAMS.82However, this site had less shelter from riparian forest than most of the reach, and thus maynot have been representative in any case. In future studies, it would be useful to deploy anabove-stream meteorological station at different locations along the study reach with differentdensities of canopy cover. However, in the absence of structures crossing the stream, such astation would need to be deployed on a boom extended over the stream from a bank. Forwider channels, like Lillooet River, it may be difficult to extend a boom a significant distancebeyond the river bank, so that it would not be possible to sample across-stream variability.4.2 Assessment of stream shade modelThe satellite validation of the stream shading model showed that it provided accurate sim-ulations of reach-scale total stream shade, with a maximum error of 0.13 and with seven ofnine estimates of fractions being within ± 0.03 of the values derived from satellite imagery.Further, the high values of the MCC and 𝐹1 scores provided evidence of accurate shadeprediction at the point scale; these indices account for the potential inflation of statisticsthat can occur from highly skewed presence or absence classifications that could be apparentat the stream surface, especially during peak shaded hours (skewed to shaded conditions)and during periods where the sun casts the least shadows (skewed to unshaded conditions).Relative to previous shade models based on LiDAR imagery (e.g., Loicq et al., 2018; Hyatt,2022), the advantage of the model developed for this study is that it accounts for contri-butions of both topography and riparian vegetation to shading. While the contributions oftopography were less important than those of riparian vegetation for the study reach dueits dominantly north-south orientation, topography could be more important for reachesorientated east-west.The major drawback of the shade model developed in this study is that it doesnot account for canopy overhang, which can provide a significant influence on overall shadein narrower streams (Li et al., 2012). However, the model accuracy results support theassumption that shade cast by overhang was minor for a stream as wide as Lillooet River.However, to allow the model to be applied to a broader range of stream types, it should beextended to account for overhang.Where LiDAR data are not available, it may be possible to use a DEM of tree heightsestimated using structure from motion (SfM) from drone-based photogrammetry in place ofa LiDAR DSM. For example, Dugdale et al. (2019) found similar stream temperature modelperformances when using LiDAR based shading rather than SfM shading. However, thatstudy did not account for topographic shade using either approach.The broad application potential of the model developed for this study is enhancedby the recent push for open-science and continued proliferation of accessible LiDAR data.83A major advantage of the approach is that no field measurements are required, comparedto the use of hemispherical photography or photogrammetry. However, a limitation of theuse of PlanetScope imagery for model evaluation was that the imagery was only availablenear mid-day, and provided no basis for assessing performance over a broad range of solarazimuth and elevation angles. Therefore, further work should include field surveys of shade– e.g., using the ground-based photogrammetry approach developed by li_modeled_2012 ordrone-based photography – to evaluate the shade model for a broader range of stream andriparian vegetation types and a broader range of solar positions.Some initial testing suggested that accuracy could be improved by reducing theazimuth interval used to compute horizon angles, but at the cost of increased processingtime. Similarly, greater POI resolution (i.e., smaller grid spacing) would also be likely toimprove model performance at the reach scale by increasing the sample size for averaging,but would also increase processing time. Another potential source of error is that the LiDARand satellite image acquisition were from different years: 2016 for LiDAR and 2019 to 2022for PlanetScope imagery. This difference in acquisition dates is likely to make a negligibledifference for Lillooet River given that the riparian forest was mostly mature and would notbe expected to exhibit significant growth over a six-year period. However, this may not bethe case in other situations.The LiDAR-only shade model formulated by Hyatt (2022) highlighted reach scalesummer sunlight exposure of at least 8 hours in a forested stream reach that had bankwidths wider than 60 m. These results were somewhat similar to those in this study, wherereach-scale mean sunlight hours ranged from 5.0 to 8.5 hours from late July to early October.Interestingly, when comparing modelled energy fluxes of the cells with the highest and lowestsunlight hours, the cell with the lowest number of sunlight hours generally experienced morepositive net longwave radiation. This is likely due to the considerably lower average sky viewfactor of the cell with less daily sunlight, meaning the increased obstruction from riparianvegetation are more likely to trap and re-emit incident longwave radiation.4.3 Consistency of streamflow dataAs seen in Figures 2.6 and 3.33b, there was an inconsistency between the sum of the ULand tributary flows and streamflow at LL. It is believed that the streamflow record at ULis the source of the shifting bias for several reasons. First, Miller Creek’s contribution toflow is minor relative to UL and RR, and cannot account for the bias. Second, both the LLand RR stations are operated by WSC, with several measurements made each year to ensurean up-to-date rating curve. In contrast, the UL station is operated by a contractor with aprimary focus on the water level record as a basis for flood warning, and fewer streamflow84measurements are conducted each year to update the rating curve. Further, the UL site islocated at the boundary where the Lillooet River transitions from braided to a straightersingle channel. Pulses of sediment produced from the 2010 Meager Creek debris flow aremoving through the reach and would be expected to influence the rating curve, and are alikely cause of the apparent bias trend. However, further investigation of the reach-scalewater balance, including more frequent streamflow measurements at UL, and surveys of thechannel bed could help substantiate these conclusions.4.4 Observed stream temperature dynamicsThe timing of daily maximum stream temperature was correlated with catchment size, withthe earliest peak at Miller Creek (typically about 4 pm) and the latest at Lillooet River (closeto midnight). This difference in timing is consistent with expected differences in the timerequired for each day’s meltwater pulse to travel from the glaciers to the monitoring location(travel time should increase with catchment area). Stream discharge tended to peak laterthan stream temperature, producing hysteresis loops between the stream temperature anddischarge at all four monitoring sites, as seen in Figure 3.11. From a Lagrangian perspective,one can infer that the daily maximum temperature experienced at downstream sites resultedfrom heating of water parcels that originated during the rising limb of the diel cycle of glacierdischarge. By the time glacier discharge peaked, either the cumulative energy inputs by aparcel had declined from the diel peak, and/or the increase in water volume associated withthe higher discharges made them less sensitive to energy inputs. Similar phase differencesbetween stream temperature and discharge cycles were observed in other glacially fed streams(Chikita et al., 2010; Carrivick et al., 2012; Baker et al., 2018). Chikita et al. (2010) wasable to relate stream temperature to discharge by grouping days into categories based onmaximum daily discharge, and found that positive relationships between stream temperaturewas more strongly associated with shortwave radiation and air temperature on days withsmaller peak flows. However, Figure 3.11 indicates that, for Lillooet River, there is noconsistent relation between maximum discharge and maximum water temperature for eachdiel cycle. This difference likely occurs because Chikita et al. (2010) monitored a relativelyshort reach (about 1 km in length) with short travel times relative to Lillooet River, whereobserved temperature dynamics reflect an integration of energy inputs and routing effectsover longer distances and travel times.4.5 Model performanceModelled stream temperatures agreed well with observed values, producing an RMSE valueof 0.30 oC using the baseline model scenario. This performance compares well with results85of other applications of process-based reach-scale stream temperature models in glacially fedstream reaches (Chikita et al., 2010; Carrivick et al., 2012; Somers et al., 2016; Baker et al.,2018). Of this literature, only Baker et al. (2018) and Chikita et al. (2010) had marginallylower RMSE values than this study; however, the former study reach had no tributaries,the latter study reach had no riparian vegetation, and both were shorter (≤ 2 km) than thestudy reach at Lillooet River. The performance of the Lillooet River model was better thanachieved in other applications of the HydroCouple modelling framework. For example, Leachet al. (2021) reported RMSE values of 1.16 oC when modelling temperature in a 1.4-km-longreach downstream of a lake and Buahin et al. (2019) reported RMSE values of 0.44-0.70 oCfor a 13.6-km-long urbanized stream reach.An important consideration when assessing the performance of a reach-scale modelis the fact that much of the downstream temperature signal results from the advection of theupstream boundary condition. This point does not seem to have been addressed in previousapplications of reach-scale temperature models. In this study, the model was run with allsurface energy inputs set to 0, such that the upstream boundary condition was modified onlythrough longitudinal advection and dispersion. This “thermal mirror” simulation achieved aRMSE of 0.44 oC, consistent with the dominant influence of longitudinal advection. Whilethe scenarios with energy inputs did outperform the thermal mirror scenario, this exerciseconfirms that one must be careful when interpreting the performance of reach-scale models.It is recommended that future studies include a thermal mirror scenario and use that as abenchmark for assessing model performance.The baseline model relatively consistently predicted diel maximum and minimumstream temperatures on average 43 and 54 minutes later than observed, respectively. As nocalibrations were performed to tune the model, differences in the diel timing of stream tem-perature are likely due to the assumptions made when calculating stream geometry, whichwould influence downstream routing. Stream geometry measurement locations were onlysituated at two sites, near UL and near LL, and thus did not account for any significantlongitudinal stream geometry variations. Although channel morphology does not changedramatically along the Lillooet River reach, varying channel geometry could influence thechannel routing component and potentially explain the timing of modelled stream temper-atures. The high accuracy indicated by the stream shade validation suggests that errorsin predicting shade are unlikely to be the cause of the shifted modelled baseline streamtemperatures. Given the relatively high flow magnitudes, the channel morphology and thealluvial sediments, hyporheic exchange is likely to have been negligible. Bed heat conductionwould tend to delay the timing of maximum discharge, so that the timing error cannot beattributed to not including that process in the model.864.6 Model sensitivityThe relative lack of modelled stream temperature sensitivity to different model scenarioswas highlighted by the similar RMSE values, ranging from 0.29 oC for the uncorrected ULflow scenario to 0.44 oC for the advection-only scenario. The similar values of RMSE andME between scenarios with baseline (corrected) and uncorrected streamflow at UL suggestedthat the uncertainty in UL streamflow likely made minimal difference to the modelled streamtemperatures.Although including surface energy exchanges improved model performance comparedto the advection-only scenario, there were relatively small differences among the scenarioswith varying above-stream meteorology and radiative inputs. Further, excluding the effectof tributary inflows did not substantially degrade model performance at LL. This relativelack of sensitivity to surface energy inputs and tributary inflow highlights the dominantcontrol that advection from upstream boundary conditions has on the thermal regime of thisglacially fed stream reach. A previous study that used a site-specific Eulerian energy balanceanalysis at the UL and LL sites also concluded that advection dominated in comparison tosurface heat fluxes (Knudson, 2012). The results in this study further substantiate theseconclusions while providing a more detailed breakdown of the driving mechanisms of streamtemperature dynamics within the Lillooet River study reach.Despite Ryan River providing a significant contribution to the overall streamflow atLL and clearly affecting the longitudinal thermal gradient of the Lillooet stream reach, thoseeffects were not great enough in magnitude to significantly influence the performance of themodel when the tributary influence was removed. The similar diel cycles and stream tem-peratures of RR compared with Lillooet River likely acted as a limiting factor on the impactthis tributary had on the stream reach. Despite the MC tributary experiencing the loweststream temperatures, it evidently did not have large enough flows to contribute a significantvolume of water to Lillooet River to have a considerable effect on stream temperatures. Ifthe diel cycles of the tributaries contrasted more substantially than those of Lillooet River,they would likely have had a greater influence.The tributaries of Lillooet River together tended to have a damping effect on dielstream temperatures. During the early hours of the morning, when Lillooet River temper-atures were at their highest, the combined effect of the tributaries acted to cool LillooetRiver by around 0.5 oC during clear sunny days. RR alone produced a cooling of 0.4-0.45 oCduring this time. In contrast, during the early afternoon, when Lillooet stream temperatureswere lowest, the tributaries acted to warm Lillooet River by approximately 0.1 oC.The model scenario with the poorest performance was the advection-only model.This scenario was the only to yield a negative ME, which is to be expected from the under-87prediction of stream temperatures due to a lack of radiation exchange. The warming effectof incident solar radiation being received at the stream surface became more pronouncedfurther downstream from UL, which is to be expected as the stream surface became moreexposed to incident shortwave radiation for a longer period. Net radiation at the stream sur-face influenced stream temperatures in two ways: firstly, by providing a maximum warmingeffect of 0.3-0.4 oC during the early afternoon; secondly, by advancing the timing of simu-lated minimum stream temperatures by 40 minutes compared to the advection-only scenario.Even though the advection-only model scenario produced the least accurate RMSE values,the fact that they were still reasonable and similar to values reported in other reach-scalestudies further demonstrates the significance of advection from upstream boundary condi-tions.4.7 Implications for understanding the scale-dependenceof stream temperature dynamicsLeach et al. (2023) provided a conceptual model of the variation of the importance of differentenergy exchange processes when moving from headwaters to larger downstream reaches.However, that model was specifically focused on forested landscapes in the mid-latitudes.This study has emphasized major contrasts in the thermal dynamics of glacier-fed streamsbetween smaller streams located closer to the glacier and a downstream, valley-bottom river,and thus provides a basis for extending the Leach et al. (2023) conceptual model to otherlandscape settings. Whereas the Leach et al. (2023) model posits that solar radiation inputsshould increase with increasing stream width in forested landscapes, the pattern may bemore complex in glacier-fed catchments, with high solar radiation in the headwaters andreduced solar radiation in downstream reaches with riparian forest. Considering even largerspatial scales, solar radiation may again increase at spatial scales greater than Lillooet Riverdue to increasing channel width and the resulting reduction in riparian shade. Further, thisstudy revealed the significance of longitudinal advection, which is not included in the Leachet al. (2023) model.88Chapter 5Conclusions5.1 Summary of key findingsThis research has demonstrated that a reach-scale process-based stream temperature modelcan generate accurate predictions of downstream discharge and temperature without cali-bration. The model achieved a RMSE value of 0.30 oC, which is competitive with or betterthan the performance documented in other applications of similar models, most of whichwere focused on smaller streams and shorter reaches with less flow contribution from trib-utaries. In place of calibration, substantial effort was invested in developing approachesfor estimating radiative exchange, above-stream meteorology and channel morphology. Thestudy benefitted from existing stream gauges and temperature monitoring at two sites onLillooet River and the two tributaries to the study reach. The study has added to thecurrently limited literature focused on comparing above-stream air temperature, humidityand wind speed to measurements at a land-based weather station. While some differencesbetween above-stream and open-site conditions were similar to previous studies, there werealso some differences that could be attributed to differences in the thermal regime of glacier-fed Lillooet River compared to the non-glacier-fed streams monitored in previous studies.In particular, the timing of peak water temperatures near midnight reduced above-streamair temperature cooling during cloud-free nights, resulting in above-stream air temperaturesbeing greater than those at open sites. This relationship had not been identified in previousliterature. A lack of strong correlation between open-site and above-stream vapour pressuresand differences between two open-site locations highlighted the importance and complexitiesof accurately representing above-stream microclimate in a glacially fed and variably forestedstream reach.An important contribution of this study was the development of a new model to pre-dict shade contributions from both riparian vegetation and surrounding topography. Themodel provided accurate predictions at both individual points on the stream surface and89for reach-scale averages when evaluated using shade interpreted from high-resolution Plan-etScope imagery. Shade model performance could be improved further by using smallerazimuth bands and a higher resolution computational grid, although both would increaseprocessing time.Longitudinal advection from upstream boundary conditions dominated stream tem-perature variations at the lower Lillooet River monitoring site. Indeed, a scenario in whichall surface energy inputs were set to 0 generated a RMSE of 0.44 oC, whereas the best-performing scenario generated RMSE = 0.29 oC.Tributaries to the study reach provided a combined cooling effect of approximately0.5 oC around midnight to early morning when daily maxima occurred and a warming effectof approximately 0.2 oC during typical summer days. Although Miller Creek was consid-erably cooler and experienced the largest contrasts in the timings of typical diel streamtemperature cycles, the Ryan River had a more significant impact on the longitudinal tem-perature gradient of the Lillooet River due to significantly higher flow inputs. A scenarioin which Ryan River’s contributions were excluded produced a RMSE of 0.41 oC, whileexcluding Miller Creek was associated with RMSE = 0.37 oC.The model was not overly sensitive to uncertainties in streamflow at the UpperLillooet River gauging station, which appeared to have a time-varying bias, likely associatedwith the effect of a sediment pulse originating from the 2010 Meager Creek debris flow onchannel morphology and hence on the rating curve. Scenarios using uncorrected and bias-corrected flows for Upper Lillooet generated similar values of RMSE of 0.29 and 0.30 oC,respectively.Overall, the lack of sensitivity to surface energy inputs and tributary contributionsis related to the dominance of the effect of advection of the upstream boundary condition.This point does not appear to have been considered in previous applications of reach-scalemodels, which based the evaluation of model performance purely on goodness-of-fit statisticsbetween simulated and observed downstream temperatures, and did not consider using anadvection-only scenario as a benchmark for comparison.5.2 Future recommendations and researchGiven the significance of riparian vegetation for stream shading and resulting energy budgetsin smaller streams (Rutherford et al., 2004; Loicq et al., 2018), the stream shade modelshould be further developed to incorporate shading from overhanging vegetation to make itapplicable for a wider range of stream morphologies and environments. Such a model wouldneed to utilize crown detection algorithms that could delineate canopy boundaries abovethe stream surface. Future work should evaluate the shade model over a broader range of90sites and solar azimuths and horizon angles. Because imagery such as PlanetScope maynot sample a broad range of solar positions, studies should also include field work usingphotogrammetric approaches such as that developed by Li et al. (2012) and/or drone-basedphotography.A growing body of research has focused on how afforestation could potentially mit-igate the ecological effects of increasing stream temperatures from future climate changescenarios (LeBlanc and Brown, 2000; Webb and Crisp, 2006; Brown et al., 2010; Bowleret al., 2012; Dugdale et al., 2019). However, the results of this study, along with others(e.g. Bowler et al., 2012), highlight that some streams may not be as thermally sensitiveto riparian canopy change as others. If further refinement and rigorous assessment of thestream shade model prove successful, then future work involving virtual experiments thatsimulate afforestation through the editing of elevation data could provide valuable informa-tion on the resulting relative changes in shading and view factor dynamics and their ultimateinfluence on stream temperature. This work could provide useful insight for forest manage-ment practices and be used as a tool to guide investment in riparian afforestation for streamrestoration. Such a study could also highlight regions within a catchment that are alreadyconsistently shading the stream surface due to mountain topography throughout the day,enabling afforestation efforts to be focused elsewhere throughout the riparian zone.Stream orientation can play a role in determining stream reach shading patterns(Loicq et al., 2018). Future work that investigates the shading results posed by multiple shiftsin stream reach orientation could help substantiate claims that mountain topography couldplay a more significant role on stream surface energy exchanges under different topographicalsettings. For example, rotating the Lillooet stream reach by approximately 90 degrees anti-clockwise would provide a roughly consistent west-to-east facing stream reach with steepvalley slopes on the south side that are likely to play a more significant role on shading atthe stream surface.Further work is required to develop approaches for estimating above-stream meteo-rology from land-based weather stations. Deploying multiple meteorological stations abovethe stream surface longitudinally throughout the stream reach could help further elucidatethe drivers of varying microclimate through variable land-use change. Making above-streamobservations at multiple sites with varying riparian canopy density and at nearby open siteswould help deepen our understanding of how such relationships change in both space andtime. Above-stream stations could be deployed at the same time for more direct comparisonsalong the stream’s length. However, ASMS deployment locations may be limited for widerstreams because equipment set up close to the stream surface would be dependent on theavailability of surrounding features such as bridges or large trees to deploy them from inorder to sample locations away from the stream banks.91ReferencesArendt A, Walsh J, Harrison W. 2009. Changes of Glaciers and Climate in NorthwesternNorth America during the Late Twentieth Century. Journal of Climate 22 (15): 4117–4134 DOI: 10.1175/2009JCLI2784.1Arismendi I, Johnson SL, Dunham JB, Haggerty R, Hockman-Wert D. 2012. 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Hydraulic geometry were available for Lower Lillooet River from stream-flow measurements made by WSC from 2000-2002 and between 2004-2023, and were providedby Hutchinson (2023). For Upper Lillooet River, hydraulic geometry and cross-sectional databased on streamflow measurements were available by NHC just downstream of their gaugingstation at the Upper Lillooet Forest Service Road Bridge (Zimmermann, 2023).Stream side slopeTo compute bank slope, a regression model was fit between stage and stream width, and theregression equations are presented in Figure A.1. To account for the fact that a given changein width results from the slope on both sides, the bank slope was computed as double theregression slope. An average between the two regression slopes was taken to represent theassumed symmetrical side slopes for the entire monitoring reach, calculated at 0.365 m/m.Bottom widthBottom width was estimated by plotting the river’s cross-section from ADCP flow measure-ments taken along the Upper Lillooet and provided by Zimmermann (2023) (Figure A.2).Based on the cross-sectional area, the bottom width was estimated as the distance betweenthe points at which the depth reached 6 m on either side (red line), which was estimated as12.5 m.102Figure A.1: Stage as a function of width using the stream geometry measurements provided by Hutchinson(2023) at the two monitoring locations. Regression line presented in red.Figure A.2: Stream cross-section observed during 2023 high flows using ADCP measurements near theUpper Lillooet FSR Bridge and provided by Zimmermann (2023). Red line represents thebottom width, blue line represents stream water surface.103
Thesis/Dissertation
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Geography
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Moore, R. Daniel
Process-based modelling of stream temperature dynamics in a glacially fed river system
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