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The effect of discharge variability on the heat budget and tributary mixing dynamics of a proglacial… Knudson, Justin M. 2012

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The effect of discharge variability on the heat budget and tributary mixing dynamics of a proglacial river  by Justin M. Knudson B.Sc., Montana State University, 2008  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  Master of Science in THE FACULTY OF GRADUATE STUDIES (Geography)  The University Of British Columbia (Vancouver) September 2012 © Justin M. Knudson, 2012  Abstract A distinctive characteristic of proglacial streams is unsteady streamflow associated with diurnal ice melt. The role of discharge variability on downstream temperatures is not well understood. This study addressed the influence of diurnal discharge fluctuations on temperature by quantifying longitudinal heat advection and unsteady flow effects in a heat budget model for a proglacial stream in the Coast Mountains of British Columbia, Canada. Given advection has not been quantified in previous modeling studies, the dominant role of advection over surface heat fluxes found here was surprising. Advection was expected to have a considerable cooling effect due to the flow contributions from cold meltwater. This effect was confirmed while discharge generally increased; however, advection also exhibited a diurnal warming phase of similar magnitude and duration as the cooling phase, while flow generally decreased. The role of discharge variability on transverse mixing dynamics found in previous studies has been inconsistent. Here, transverse mixing lengths tended to be longer with greater tributary flow relative to the main channel. These findings need to be confirmed with further research.  ii  Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iii  List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  v  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vi  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ix  1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Motivation for the study . . . . . . . . . . . . . . . . 1.1.1 Characteristics of alpine glacial catchments . . 1.1.2 Stream temperature response to climate change 1.2 Processes influencing stream temperature . . . . . . . 1.2.1 Vertical energy exchanges . . . . . . . . . . . 1.2.2 Surface-subsurface interactions . . . . . . . . 1.2.3 Longitudinal advection/dispersion . . . . . . . 1.2.4 Unsteady flow . . . . . . . . . . . . . . . . . 1.2.5 Tributary mixing . . . . . . . . . . . . . . . . 1.3 Research objectives and thesis structure . . . . . . . .  . . . . . . . . . . .  . . . . . . . . . . .  . . . . . . . . . . .  . . . . . . . . . . .  . . . . . . . . . . .  . . . . . . . . . . .  1 1 2 5 7 7 8 8 9 9 11  2  Methods . . . . . . . . . . . . . . . . . . . . . . . 2.1 Study area . . . . . . . . . . . . . . . . . . . 2.2 Data collection . . . . . . . . . . . . . . . . 2.2.1 Stream temperature . . . . . . . . . . 2.2.2 Meteorological data . . . . . . . . . 2.2.3 Parameters for modelling net radiation 2.2.4 Streamflow . . . . . . . . . . . . . . 2.2.5 Electrical conductivity . . . . . . . .  . . . . . . . .  . . . . . . . .  . . . . . . . .  . . . . . . . .  . . . . . . . .  . . . . . . . .  13 13 16 16 16 17 18 18  iii  . . . . . . . .  . . . . . . . .  . . . . . . . .  . . . . . . . .  . . . . . . . .  2.3  Analysis and modelling . . . . . . . . 2.3.1 Transverse mixing . . . . . . 2.3.2 Reach-scale heat budget model 2.3.3 Net radiation model . . . . . . 2.3.4 Convective heat exchanges . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  . . . . .  19 19 22 24 27  3  Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Overview of the field season . . . . . . . . . . . . . 3.2 Longitudinal variations in water temperature . . . . . 3.3 Transverse mixing . . . . . . . . . . . . . . . . . . . 3.3.1 Observed transverse mixing in Lillooet River 3.3.2 Modelled transverse mixing . . . . . . . . . 3.3.3 Effect of stream discharge . . . . . . . . . . 3.4 Surface-atmosphere energy exchanges . . . . . . . . 3.4.1 Radiative exchanges . . . . . . . . . . . . . 3.4.2 Net surface-atmosphere energy exchange . . 3.5 Reach-scale heat budgets . . . . . . . . . . . . . . . 3.5.1 Clear-sky period . . . . . . . . . . . . . . . 3.5.2 Cloudy periods . . . . . . . . . . . . . . . . 3.5.3 Precipitation event . . . . . . . . . . . . . . 3.5.4 Landslide event . . . . . . . . . . . . . . . . 3.5.5 Spatial variation . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . .  29 29 36 39 39 44 45 47 47 53 54 55 57 63 66 66  4  Discussion . . . . . . . . . . . . . . . . . . 4.1 Reach-scale heat budget considerations 4.1.1 Longitudinal heat advection . . 4.1.2 Unsteady flow effects . . . . . . 4.1.3 Surface energy exchanges . . . 4.2 Transverse mixing . . . . . . . . . . . .  . . . . . .  . . . . . .  . . . . . .  . . . . . .  . . . . . .  . . . . . .  . . . . . .  72 72 72 75 75 76  5  Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Key findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Future research recommendations . . . . . . . . . . . . . . . . .  78 78 80  Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  82  A Supporting methods . . . . . . . . . . . . . . . . . . . . . . . . . . . A.0.1 Shade function, gt . . . . . . . . . . . . . . . . . . . . . A.0.2 Sky view factor, fsky . . . . . . . . . . . . . . . . . . . .  90 90 92  iv  . . . . .  . . . . .  . . . . . .  . . . . .  . . . . . .  . . . . .  . . . . . .  . . . . .  . . . . . .  . . . . .  . . . . . .  . . . . .  . . . . . .  . . . . . .  List of Tables Table 2.1  Instrument specifications . . . . . . . . . . . . . . . . . . . .  Table 3.1  Daily summary statistics of water temperature at each sub-reach from July 24 to October 15, 2010. sd = standard deviation. . . Transverse mixing length statistics for the given degree of mixing (Pm ) at 10% increments. s.d. = standard deviation . . . . . Predicted transverse mixing lengths using Rutherfords (1994) models for given channel form and tracer input location. Predicted ranges reflect given transverse dispersion coefficient ranges. Mean observed Lz80 was 3036 m. . . . . . . . . . . . . . . . . Transverse mixing distances and dispersion coefficients at times of the given Qratio statistic. . . . . . . . . . . . . . . . . . . . Summary of parameters used in the heat budget model for each reach: upper Lillooet River (UL), lower Lillooet River (LL), and Ryan River (RR). . . . . . . . . . . . . . . . . . . . . . . Heat budget model performance for given site and time period (month/day). MBE is mean bias error, RMSE is root mean squared error, NRMSE is RMSE normalized by the range of observed values and expressed as a percentage, and Em is the Nash-Sutcliffe model efficiency. . . . . . . . . . . . . . . . .  Table 3.2 Table 3.3  Table 3.4 Table 3.5  Table 3.6  v  19  32 39  44 46  52  61  List of Figures Figure 2.1 Figure 2.2  Figure 2.3  Figure 3.1  Figure 3.2  Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6  Figure 3.7 Figure 3.8  The study area with the Lillooet River catchment delineated from the lower extent of the monitoring area. . . . . . . . . . The monitoring area included 27.6 km of Lillooet R., one major tributary (Ryan R.), and one minor tributary (Miller Ck.). Stream reaches were upper Lillooet R. (UL), lower Lillooet R. (LL), and Ryan River (RR). . . . . . . . . . . . . . . . . . . Longitudinal bank temperature profiles on 13 Aug at 17:50 along Lillooet River downstream of the tributary confluence. . Historical mean monthly air temperature from 1969-2006 and 2010 measured at PACS. Mean monthly air temperature for August and September, 2010, measured on-site (OSMS), is shown with solid black points. . . . . . . . . . . . . . . . . . Monthly total precipitation for 2010 and mean monthly total precipitation for 1969-2006. Data were missing for May and June, 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discharge for 2010 measured near LL with historical maximum, mean, and minimum daily discharge from 1914-2010. . From top to bottom: incident solar radiation, air temperature, vapor pressure, and wind speed measured at OSMS. . . . . . Instantaneous water temperature at (top to bottom) UL, LL, RR, and MC. . . . . . . . . . . . . . . . . . . . . . . . . . . Maximum, mean, and minimum daily air temperature at OSMS (top) and daily mean water temperature at UL, LL, RR, and MC (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . Daily water temperature ranges at each reach. . . . . . . . . . Longitudinal temperature gradients in Lillooet River on July 25 showing the end of the cooling phase (blue) in the morning followed by the warming phase (red). . . . . . . . . . . . . . vi  14  15 21  30  31 32 33 34  35 36  37  Figure 3.9  Figure 3.10  Figure 3.11 Figure 3.12  Figure 3.13  Figure 3.14 Figure 3.15 Figure 3.16  Figure 3.17 Figure 3.18 Figure 3.19  Figure 3.20 Figure 3.21 Figure 3.22 Figure 3.23  Figure 3.24  Longitudinal temperature gradients in Lillooet River showing the end of the warming phase (red) late on July 25 followed by the cooling phase (blue) through the morning of July 26. . . . Time-series of left (blue) and right (red) bank water temperature along Lillooet River at four downstream locations from the Ryan River confluence. Temperature difference (black) between the banks at each location is shown on the bottom of each panel with axis on right. . . . . . . . . . . . . . . . . . Mean transverse mixing lengths for the percent of lateral mixing at 10% increments. . . . . . . . . . . . . . . . . . . . . . Longitudinal bank temperature profiles on 13 Aug at 17:50 along Lillooet River downstream of the tributary confluence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrical conductivity (EC) was surveyed by eight lateral transects approximately 250 m apart, extending downstream of the Ryan River confluence 2.1 km. . . . . . . . . . . . . . . . . . Observed and modelled mean transverse mixing lengths for given degree of mixing. . . . . . . . . . . . . . . . . . . . . Transverse mixing lengths at the 80% mixing level for given ratios of tributary to mainstem discharge. . . . . . . . . . . . Measured albedo (top) and suspended sediment concentration (bottom) for Lillooet River, Ryan River, and Miller Creek on August 25, 2011, with calculated solar zenith angle (center). . Atmospheric emissivity (εa ) was calculated over the monitoring period. . . . . . . . . . . . . . . . . . . . . . . . . . . . Shading function gt for each reach, August 14-17. . . . . . . Radiative exchanges averaged over the upper Lillooet River reach (UL): incident and outgoing shortwave (K) and longwave (L) radiation (top), net all-wave radiation (Q∗ ) (bottom). Net all-wave radiation (Q∗ ) for upper Lillooet River (UL), lower Lillooet River (LL), and Ryan River (RR). . . . . . . . . . . Latent and sensible heat flux at UL. . . . . . . . . . . . . . . Net surface heat exchange (H) with net radiation, latent heat, and sensible heat flux components at UL. . . . . . . . . . . . Heat budget (top), discharge (center), and water temperature (bottom) during clear-sky conditions, July 24 to July 27, 2010 at UL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Predicted (gray) and observed (black) temporal stream temperature change and their difference (red) at UL. . . . . . . . . .  vii  38  40 41  42  43 45 47  49 50 51  52 53 53 54  56 57  Figure 3.25 Heat budget (top), discharge (center), and water temperature (bottom) from July 30 to Aug. 2, 2010 at UL. Conditions were clear on July 30, switching to overcast July 31, and partlycloudy Aug. 1. . . . . . . . . . . . . . . . . . . . . . . . . . Figure 3.26 Heat budget (top), discharge (center), and water temperature (bottom) from Aug. 3 to Aug. 6, 2010 at UL. Aug. 4 was consistently overcast while Aug. 3 and Aug. 5 were partlycloudy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 3.27 Heat budget (top), discharge (center), and water temperature (bottom) for the partly cloudy-overcast period from Sept. 5 to Sept. 8, 2010 at UL. . . . . . . . . . . . . . . . . . . . . . . Figure 3.28 Heat budget (top), discharge (center), and water temperature (bottom) for Sept. 18 to Sept. 21, 2010 at UL. A 30 mm rain event occured Sept. 19 - 20. . . . . . . . . . . . . . . . . . . Figure 3.29 Heat budget (top), discharge (center), and water temperature (bottom) for Aug. 5-8, 2010 at UL. An outburst flood occured on Aug. 7 from the release of a lake created from a landslide on Aug. 6 in a tributary catchment of Lillooet River. . . . . . Figure 3.30 Heat budget for UL (top) and LL (bottom) during mostly clear skies from Aug. 14-17. . . . . . . . . . . . . . . . . . . . . . Figure 3.31 Heat budget (top), discharge (center), and water temperature (bottom) during mostly clear skies from Aug. 14-17 at UL. . . Figure 3.32 Heat budget (top), discharge (center), and water temperature (bottom) during mostly clear skies from Aug. 14-17 at LL. . .  viii  58  59  60  64  65 68 69 70  Acknowledgements This work could not have been completed without the help from many people. Above all, my gratitude goes out to my supervisor, Dan Moore, for his guidance, attentiveness, patience, funny stories, and never-ending support. Many thanks go to Jason Leach for being my go-to problem solver, Joe Shea for weather station training, and Jennifer Guay and Dave Hutchinson for data support. Assistance with field work was provided by Matthew Chuang, Luisa Muenter, Eli Heyman, Pascal Szeftel, Jason Leach, Peggy Donnelly, Marc Edwards, and Saskia Hoevelmann. I appreciate the help from Brett Eaton, Ian McKendry, and the many colleagues, faculty, and staff of the Geography Department. Last but certainly not least, I am forever grateful to my loving family and friends for their enduring encouragement.  ix  Chapter 1  Introduction This chapter introduces the topic of study, highlights additional research needed, and outlines the objectives of this research.  1.1  Motivation for the study  Stream temperature is an important fundamental control on the general well-being of lotic ecosystems through its influence on water quality and a range of physical, chemical and biological processes (Milner and Petts, 1994; Beschta, 1997; Coutant, 1977; Gu and Li, 2002; Smith and Lavis, 1975; Gooseff et al., 2005; Cadbury et al., 2008). For example, dissolved oxygen concentration decreases with warmer temperatures; furthermore, oxygen consumption increases with the higher biological activity associated with warmer temperatures (Caissie, 2006). Stream temperature impacts the mortality, stress, and energy reserves of salmonids, even over diel time scales (Thomas et al., 1986), and specific temperature ranges are required at each life stage (Coutant, 1977; Lee and Rinne, 1980; Burgner, 1991; Nelitz et al., 2007). Salmonids have been observed congregating at local thermal refugia within rivers that would otherwise exceed their lethal temperature, such as at cooler tributary junctions (Torgersen et al., 1999; Ebersole et al., 2003). Although glacial-fed streams have often been viewed as having harsh, unstable habitat conditions and low biodiversity, a growing body of research is showing that glacial contributions to stream flow can create diverse habitat which benefits many  1  plant and animal species, including important fisheries and invertebrate communities (Milner et al., 2001, 2009; Moore et al., 2009). Glacial meltwater benefits aquatic ecosystems by augmenting streamflow and moderating stream temperature during hot, dry weather when non-glacial streams are often stressed. Such benefits can outweigh the negative effects of instability and higher turbidity, especially where lakes allow suspended sediment to settle (Moore et al., 2009). Stream temperature can be affected by environmental changes, such as forest harvesting or water management (Moore et al., 2005a; Caissie, 2006). The province of British Columbia, Canada recently passed legislation to protect thermal habitat for cool water species which requires the designation of temperaturesensitive streams to guide in forest harvesting restrictions (Nelitz et al., 2007). There is additional concern about the influence of climate change on stream temperature and aquatic habitat. Hydrological regimes influenced by meltwater have shown particular sensitivity to climatic warming (Moore and Demuth, 2001). Glacial systems exhibit complex spatiotemporal interactions between climate, glacier mass balance, meltwater generation and transport, and stream temperature. A better understanding of these systems is needed in order to properly assess potential impacts of climate change and other environmental disturbances on stream temperature.  1.1.1  Characteristics of alpine glacial catchments  As stream thermal fluxes are dependent on channel geometry and riparian microclimate, it is important to understand the common progression of channel morphology and vegetation characteristics following glacier retreat and, therefore, displayed spatially downstream of the glacier margin. Shortly after ice retreat (near the glacier margin), the stream sediment budget is generally transport-limited, and the lack of colonized vegetation creates a highly unstable, braided channel network (Milner and Petts, 1994; Sidle and Milner, 1989). However, confined valleys are typical of headwater areas and commonly support only a single channel until the valley broadens and allows lateral expansion into a braided channel network (Uehlinger et al., 2003). Thermal heterogeneity in confined streams is dominated by longitudinal temperature gradients, but a braided stream network exhibits significant lateral thermal heterogeneity as well (Malard et al., 2001; Uehlinger et al.,  2  2003). With increasing time since glacier retreat, coinciding with increasing distance downstream and lower elevation, bars and banks are strengthened by encroaching vegetation. The channel network then narrows and progresses into a wandering dominant channel which is laterally-mobile, of irregular sinuosity, and may have a set of relatively stable secondary channels (Milner and Petts, 1994). Eventually the stream evolves toward an equilibrium between sediment supply and transport, larger trees provide greater bank and bar stability, fallen trees create deep pools, and a single, stable meandering channel of higher sinuosity forms (Sidle and Milner, 1989; Milner and Petts, 1994). The general progression is thus a continuum from a braided channel network to a single meandering channel, but this can be disrupted by variable valley confinement, tributary confluences, and the presence of lakes (Milner and Petts, 1994; Uehlinger et al., 2003). Stream temperature is also controlled in part by streamflow, and glacial cover in a catchment has a strong influence on climate-streamflow relations (Moore et al., 2009). Glaciers of southwestern British Columbia have generally retreated since the mid-nineteenth century, with occasional periods of minor advance (Osborn and Luckman, 1988; Moore and Demuth, 2001). Streamflow responded through two apparent long-term phases: (1) glacier volume was lost mostly through thinning and meltwater generation increased, and (2) meltwater generation eventually declined when more ice area was lost (Moore and Demuth, 2001). Most glacial streams in southern BC are in the second phase (Fleming and Clarke, 2003; Stahl and Moore, 2006). Given that stream temperature is typically negatively correlated with discharge, streamflow declines associated with glacier retreat should have a general long-term warming influence on stream temperature. Moore (2006) linked lower glacier coverage to higher median monthly stream temperature, with an average increase of 1.2 °C for July and August per 10% decrease in glacier cover. Net mass balance and glacial streamflow respond to decadal-scale climatic variability. A shift from the cold to warm phase of the Pacific Decadal Oscillation (PDO) in 1976 initiated a persistent period of more negative net mass balance and more rapid terminal retreat at Place Glacier of the southern Coast Mountains, BC. However, after accounting for the effects of winter mass balance and monthly air temperature in a multiple regression analysis, Moore and Demuth (2001) found that mean August discharge at Place Glacier declined after this PDO shift. This is 3  consistent with the idea that for given hydroclimatological conditions, inter-annual discharge should generally decrease with further glacier retreat due to the lower glacier surface area available to generate meltwater. Glacial streams are generally characterized by low winter flow when precipitation is mostly stored as snow. From spring to mid-summer, streamflow is enhanced by snowmelt runoff (hereafter, the nival freshet), which typically terminates early to mid-summer in North America (Milner and Petts, 1994; Fleming, 2005; Moore et al., 2009). The annual hydrograph for glacial streams differs from snowmeltdominated streams by having an extended period of enhanced flow beyond the nival freshet charged by the continuous supply of glacial meltwater (Milner and Petts, 1994; Fleming, 2005; Moore et al., 2009). Annual peak flow is likely to occur later as the proportion of ice-to-snowmelt increases (Milner and Petts, 1994). The prolonged meltwater contribution moderates downstream temperature at a time when non-glacial streams are often thermally stressed (Milner et al., 2001; Moore et al., 2009), which has been explained by higher thermal capacities from higher flow volumes and a higher cool meltwater component of total flow (Brown et al., 2005; Cadbury et al., 2008). For warmer summers, or for summers following lower winter glacier mass balance, streamflow tends to be higher, peak earlier in the season, and have greater diurnal variation. This was explained by earlier ablation and a larger exposed area of lower-albedo ice, which enhances meltwater production and transport relative to higher-albedo snow (Moore and Demuth, 2001). On a seasonal scale, given the negative correlation of winter mass balance to late-summer meltwater contribution and the general negative relation between streamflow and water temperature, a lower winter mass balance should relate to higher streamflow, which in turn should relate to lower summer stream temperature. In southwest BC, glacial influences are typically most distinct in August, after the majority of non-glacial snow has melted and before the cooler and more rainy weather of autumn (Moore and Demuth, 2001). Streamflow generally declines in autumn due to decreasing meltwater contributions, but is often punctuated by rain events. These relations show that temperature variability in proglacial streams depends on the timing and magnitude of meltwater discharge, which in turn depends on seasonal mass balance and climate history. Within the seasonal melt period is a daily melt pattern, resulting in a character4  istic diurnal pulse in streamflow (Milner and Petts, 1994; Smith et al., 2001; Brown et al., 2003, 2005). Near the glacier terminus, the wave peak tends to occur late in the afternoon, reflecting the lag time required for the transport of meltwater to the stream channel (Milner and Petts, 1994). The diurnal peak occurs relatively earlier and fluctuations are greater following winters of lower mass balance or during periods of warmer weather (Fountain, 1996; Moore and Demuth, 2001). Stream temperature likewise shows marked diurnal variation; however, interactions between flow and temperature in glacial streams have not been well studied (Uehlinger et al., 2003). Stream temperature near the glacier terminus is usually near 0 °C with little variability (Milner and Petts, 1994; Uehlinger et al., 2003; Cadbury et al., 2008; Moore et al., 2009). With increasing downstream distance, temperatures are generally higher and exhibit greater diurnal variability, trends which have been described by atmospheric heating (primarily through solar radiation) trumping the cooling effects of meltwater (Milner and Petts, 1994; Malard et al., 2001; Cadbury et al., 2008; Moore et al., 2009). Evidence for this was higher air-water temperature correlations with increasing distance below a glacier (Cadbury et al., 2008). Higher flows during warmer weather have been linked to lower longitudinal thermal gradients and lower diurnal variability, resulting from the apparent cooling effect of meltwater. The cooling effect has been inferred in a qualitative manner to be caused by higher thermal capacity (from higher water volume) and a higher fraction of meltwater to other, warmer water sources (e.g. tributaries and groundwater) (Cadbury et al., 2008). Such trends do suggest that meltwater promotes lower temperature and attenuates variability, but they do not improve our understanding of heat exchange processes related to discharge variability. The specific influences of diurnal meltwater fluctuations on stream temperature remain uncharacterized, at least from a deterministic, quantitative standpoint.  1.1.2  Stream temperature response to climate change  There is increasing concern about the effects of climate change on stream temperature (Caissie, 2006; Moore et al., 2009). Glacial-fed streams may be particularly vulnerable due to the additional linkages between climate, glacier mass balance, glacier retreat, meltwater generation and streamflow, and stream temper-  5  ature. For any hydrological regime, expected effects of climatic warming include increased incident longwave radiation, increased sensible heat flux from the atmosphere, and warmer groundwater discharge (Meisner et al., 1988; Milner et al., 2009). In glacierized catchments, continued climatic warming and glacier retreat should continue to cause a decrease in meltwater generation. Given the moderating effect of meltwater, streamflow declines associated with glacier retreat should generate higher stream temperatures (Moore et al., 2009). In addition, lower flow volume (heat capacity) would cause greater temperature response to heat exchanges through the water surface and bed, and exposure time of water parcels to surface energy exchanges would increase with ice retreat and stream lengthening. Estimating stream temperature response to climatic variability has been the focus of several studies, although physical processes have largely been ignored. Most previous studies have used correlations between stream and air temperature, in conjunction with projected air temperatures from general circulation models, to predict stream temperature response to climatic warming (Eaton and Scheller, 1996; Mohseni et al., 2003). In glacial systems, however, the air-water temperature correlation is often poor due to meltwater generation also being positively correlated with air temperature. Furthermore, empirical models are not suited to extrapolation beyond the range of data used to fit them, and the model is not transferable to different locations (Johnson, 2003). Even within the same stream, for example, the air-water temperature correlation can change markedly between reaches (Brown et al., 2005). Understanding the physical processes controlling temperature variability is fundamental for prediction of ecological response to environmental changes (Brown et al., 2005). Statistical models are insufficient for understanding physical processes as they do not imply causative effects (Johnson, 2003; Brown et al., 2005). Process-based heat budget models satisfy these limitations of statistical models and are more robust for determining causation.  6  1.2 1.2.1  Processes influencing stream temperature Vertical energy exchanges  Energy exchanged in the vertical dimension of the water column, that is, through the water surface and stream bed, will be referred to as vertical heat flux. In decreasing order of their general influence, surface fluxes include solar radiation, incident/outgoing longwave radiation, latent heat flux, and sensible heat flux (Caissie, 2006; Morin and Couillard, 1990; Sinokrot and Stefan, 1993). Solar radiation typically dominates vertical heat flux during clear weather, except in highly shaded environments, and is highly sensitive to cloud cover (Brown, 1969; Webb and Zhang, 1997a; Evans et al., 1998; Johnson, 2003; Caissie, 2006; Hannah et al., 2008). Incident longwave radiation depends on air temperature and atmospheric emissivity, which varies with cloud cover, water vapor content and air temperature. Latent and sensible heat fluxes (convective fluxes) are usually secondary terms for cold and cool streams and are a function of wind speed (Evans et al., 1998). Bed heat conduction is often relatively important in shallow streams but is typically negligible in larger, deeper streams (Brown, 1969; Cadbury et al., 2008; Evans et al., 1998; Hannah et al., 2004; Poole and Berman, 2001; Webb and Zhang, 1997b, 1999; Sinokrot and Stefan, 1993). Fluid frictional heating/dissipation can be important during winter (Webb and Zhang, 1997b) or for steep (>5%) streams under low solar radiation conditions (Meier et al., 2003; Moore et al., 2005a). Shading and stream surface albedo are important controls on net shortwave radiation (Leach and Moore, 2010; Richards and Moore, 2011; Webb and Zhang, 1997b; Johnson, 2003; Hannah et al., 2008). Characterizing shade is, therefore, critical in reach-scale heat budget analysis. Stream shading has been estimated by a variety of methods, but perhaps the most rigorous and accurate method employs hemispherical sky/vegetation photographs taken along the reach (Leach and Moore, 2010). However, this approach can be logistically problematic for longer reaches or deeper rivers. Albedo varies with several parameters, including solar angle, suspended sediment concentration (SSC), water surface roughness, water surface foam, aeration of the water, and the diffuse fraction of global radiation (Nunez et al., 1972; Payne, 1972; Whitlock et al., 1982; Han, 1997; Jin et al., 2004;  7  Richards and Moore, 2011). Evans et al. (1998) found surface albedo was highest in the morning and evening and was lowest near midday. Previous heat budget analyses have typically ignored albedo variation and assumed a constant value not based on site-specific measurements, usually between 0.05 and 0.1 (Richards and Moore, 2011). Glacier-fed streams have high SSC levels during summer and likely have higher albedo than assumed in most studies. Field measurements of stream albedo should be made for process-based modeling, especially for streams having higher turbidity.  1.2.2  Surface-subsurface interactions  Groundwater and hyporheic discharge are potentially important heat sources. Their influences are dependent on relative flow contribution and temperature. Groundwater advective flux has been shown to be an important control on temperature in small streams (Story et al., 2003; Leach and Moore, 2010). In larger-order streams, the reach-scale effect is relatively minor (Poole and Berman, 2001). Hyporheic heat exchange is a type of advective energy exchange associated with water exchange between stream bed sediment and the water column. In a small proglacial stream (up to 10 m3 s−1 ) surface and hyporheic water differed by 12.1 °C over a distance of only 80 cm, suggesting hyporheic flux to be an important control (Malard et al., 2001). Burkholder et al. (2008) calculated the overall cooling effect from hyporheic discharge to be negligible at the reach-scale in a larger river, but pointed out that local hyporheic discharges can create a spatial mosaic of temperature variability. Groundwater and hyporheic advective fluxes can be important in smaller streams but their relative influence should diminish with higher stream flow.  1.2.3  Longitudinal advection/dispersion  The focus of nearly all previous energy budget studies has been on vertical energy exchanges, with some attention to hydrological processes such as groundwatersurface water interactions. Longitudinal dispersion may be important to consider in cases involving localized injections of heat (such as power plant cooling water), but it has typically been excluded for situations where localized injections do not occur (Chikita et al., 2009; Hockey et al., 1982). No known studies have  8  specifically investigated longitudinal heat advection as a component in the energy balance of glacial-fed streams. Some modelling studies have implicitly included advection by employing a Lagrangian frame of reference (Hockey et al., 1982; Chikita et al., 2009). Some studies have included the effects of longitudinal heat advection within a numerical model, but did not quantify their magnitude (Sinokrot and Stefan, 1993; Meier et al., 2003). The influence of longitudinal heat advection on stream temperature in relation to other heat fluxes is thus poorly known over a range of hydrological regimes.  1.2.4  Unsteady flow  The influences from changes in within-reach heat storage and advective flux divergence should be considered when modelling stream temperature over unsteady flow conditions. The former effect is associated with heat capacity changes. The latter effect is associated with wave celerity, which differs from stream flow velocity, and longitudinal heat advection changes with passage of the diurnal discharge wave. These influences, which collectively will be referred to as unsteady flow effects, have been implicitly calculated in numerical modeling studies but have not been explicitly quantified as components of a reach-scale heat budget (Chaudhry et al., 1983; Meier et al., 2003).  1.2.5  Tributary mixing  Stream temperature is influenced by advective inflows such as tributaries. These inflows can be especially important in glaciated catchments where tributary sources often differ substantially in temperature, such as a proglacial stream joining a lakefed or groundwater-fed stream. Temperatures in the mixing zone are variable in time and all three spatial dimensions. Longitudinal mixing is rapid and only a concern when pulse injections of a tracer are involved (such as power plant thermal effluent) (Rutherford, 1994). Vertical mixing can be important for tracer sources which enter the water column heterogeneously in the vertical dimension, such as where tributary beds are discordant (Biron et al., 2004). The motion of turbulent eddies arising from bed friction is dominantly vertical, causing vertical mixing to be much more rapid than transverse mixing, which is the slowest of the three and  9  therefore often of most concern (Rutherford, 1994). The laterally unmixed zone can provide a diversity of habitat conditions, such as thermal refugia for salmonids (Kaya et al., 1977; Berman and Quinn, 1991). Research has shown considerable variation in the river length required for complete transverse mixing (Lz ) to occur (Lane et al., 2008; Mackay, 1972). Mixing lengths are commonly between 100 and 300 multiples of channel width (Gaudet and Roy, 1995; Rutherford, 1994; Fischer, 1979), although mixing lengths have often been much lower (Day, 1977; Biron et al., 2004; Lane et al., 2008; Rutherford, 1994). There can be considerable variation in Lz within a site due to changing conditions. For example, Lane et al. (2008) reported a range in Lz between 8 and 400 channel widths and ascribed the variation to changes in flow dynamics between the two tributaries, with bed discordance as an additional control. In addition to protecting critical thermal habitat, understanding the drivers of transverse mixing variability also finds important application in pollution transport studies. Transverse mixing occurs by a complex array of interacting processes. The fundamental processes acting in all directions are advection and diffusion. Molecular (Fickian) diffusion is relatively negligible on its own, but transverse turbulent diffusion is considerable and commonly occurs when turbulent eddies, formed by bed friction, undergo rotation and move along the transverse axis. This results in increased transverse tracer gradients and more rapid diffusion (Rutherford, 1994). Transverse dispersion is the dominant transverse mixing mechanism. It is caused by vertical variation in transverse velocity of secondary currents, a condition commonly generated by helical secondary currents and lateral movement of the thalweg. Helical secondary currents are common at river bends, in which water moves in opposite lateral directions at the surface and at the bed, increasing local tracer gradients and diffusion rates and greatly enhances transverse mixing rates (Henderson, 1966; Rutherford, 1994). Lateral movement of the thalweg can occur from bathymetric non-uniformities. Bed friction from lateral movement of the thalweg causes vertical variation in transverse velocity in the same manner bed friction of the primary current creates vertical variation in longitudinal velocity. However, transverse mixing from lateral thalweg movement is of far less magnitude than that of helical currents (Rutherford, 1994). Transverse mixing is largely controlled by dispersion processes, but stream flow may also be an important factor influencing 10  transverse mixing. There have been conflicting findings on the influence of discharge variability on transverse mixing dynamics. Higher transverse mixing rates (kz ) have been related to both lower (Gaudet and Roy, 1995; Biron et al., 2004) and higher total discharge (Chu and Babarutsi, 1988). The influence of fractional discharge (smaller tributary flow/larger tributary flow) on kz has also been ambiguous. Lane et al. (2008) and Biron et al. (2004) reported more rapid mixing with higher fractional discharge, but Gaudet and Roy (1995) found that mixing rates were not affected by fractional discharge changes. These findings may have been confounded by other factors known to influence tributary mixing, such as tributary bed discordance, junction angle, and sinuosity (Gaudet and Roy, 1995; Best, 1988; Boxall and Guymer, 2003). In a laboratory flume experiment, Mosley (1976) found that opposing helical flow structures formed at a confluence and maintained flow separation between the waters of the two channels. The strength of flow separation increased with fractional discharge approaching unity. Rhoads and Kenworthy (1995) confirmed the occurrence of flow separation downstream of a natural junction when momentum ratio was less than one but found a single helical flow cell (such as at a bend) when the momentum ratio exceeded one. Best (1988) also illustrated the formation of mutual flow deflection and flow separation of confluent channels, although flow separation strengthened with increasing fractional discharge (even beyond one). The downstream persistence of flow separation and its influence on mixing dynamics have not been determined, but flow separation suggests that lateral secondary currents (such as at bends) would be limited to half the channel width, thus limiting kz , until flow separation structures break down. Flow separation potentially has important implications for explaining the effects of stream flow variability on tributary mixing.  1.3  Research objectives and thesis structure  Attention has recently been drawn to stream temperature dynamics in glacierized catchments because of their sensitivity to climatic variability (Hannah et al., 2007; Cadbury et al., 2008; Moore et al., 2009). The role of meltwater flux on stream temperature dynamics remains a key gap in our understanding of the thermal regime  11  of glacial streams. Higher heat capacity and greater relative discharge contribution from cold meltwater have been qualitatively used to explain the apparent cooling effect of advected glacial meltwater (Cadbury et al., 2008; Brown et al., 2005), and our understanding of the influence of meltwater flux on temperature thus remains mainly theoretical. The need to further investigate and understand stream temperature responses to hydrological fluxes in glacier-fed streams has been directly expressed (Uehlinger et al., 2003; Brown et al., 2005; Cadbury et al., 2008; Moore et al., 2009). This study will address the role of diurnally varying discharge on stream temperature changes by specifically quantifying longitudinal heat advection and the effects of unsteady streamflow as components in a reach-scale heat budget model. The effects of these components have not previously been specified quantitatively in deterministic heat budget models (Mohseni and Stefan, 1999; Sinokrot and Stefan, 1993; Hockey et al., 1982), and particularly not for glacial streams Chikita et al. (2009). This study will also be unique by applying the heat budget to a reach considerably farther downstream than previous glacial stream temperature studies to investigate potential influences of the added length and travel time. Tributary mixing dynamics are highly complex, particularly in natural settings such as river confluences, as they depend on relationships and interactions between several different flow mechanisms and physical factors. There have been conflicting findings on relationships between discharge variability and transverse mixing. However, some studies were based on only a small number of observations (Biron et al., 2004; Lane et al., 2008). This study aims to elucidate the influence of variable streamflow on transverse mixing lengths below the confluence of two glacialfed tributaries. This setting should provide a wide range of flows and fractional discharge values to attain a high number of observations to meet this objective. The remainder of the thesis is organized as follows. Chapter 2 describes the study area, field measurements and monitoring, and the methods of data analysis. Chapter 3 presents collected data and the results of data analysis. Chapter 4 discusses the results in the context of the research objectives stated above. Chapter 5 summarizes the key findings from the study, draws conclusions, and identifies topics for further research.  12  Chapter 2  Methods 2.1  Study area  The Lillooet River lies within the Pacific Ranges physiographic region of the southern Coast Mountains of British Columbia, Canada. The upper Lillooet River flows nearby the town of Pemberton, B.C., about 150 km north of Vancouver, B.C, and drains approximately 3150 km2 before flowing into Lillooet Lake 90 km downstream (Prent and Hickin, 2001). The upper basin is characterized by rugged topography, with local relief up to 2800 m and alpine summits reaching elevations of 3000 m (Mathews and Pratt, 1986; Friele et al., 2005). The river originates at the Lillooet Icefield and flows into Silt Lake (1.4 km long) 2.5 km downstream (Figure 2.1). The 55 km stretch from Silt Lake to Railroad Creek has mostly a natural braided channel morphology with some reaches confined by valley walls. Much of the remaining 35 km stretch to Lillooet Lake (a large fjord-like lake) has been straightened and confined by dike networks, resulting in substantial reduction of the original sinuosity, and can be classified as wandering to meandering (Friele et al., 2005; Desloges and Church, 1987). This study focused on this lower reach. At the inlet to Lillooet Lake, glacier coverage of the Lillooet River catchment has been estimated at about 15% (Prent and Hickin, 2001; Friele et al., 2005). Snow and ice meltwater account for the long freshet from approximately May to September. Lillooet River discharge varies considerably on a diurnal cycle during the melt season, with a typical range from 7 to 35% of the daily mean discharge 13  UTM zone 10 U 5630000  Lillooet Glacier  5620000  Silt  Lake  l  !  et  C  5600000 5590000 5580000  Ry elev. (m)  5570000  an  0  er  250  500 km  > >  River  >> > >> > > >> > >> >  Miller Creek  2900  125  R ai lr C k o ad  Ri v  r  k  5610000  M ea g e  Value  2600 2100 1600  5560000 5550000  Vancouver  oo  L il  British Columbia  1100 600  440000  water temp. logger  Lillooet Lake  Ryan R. basin  Monitoring Area  Miller Ck. basin glacier  100 0  >  10  20  460000  40 km  480000  500000  520000  540000  Figure 2.1: The study area with the Lillooet River catchment delineated from the lower extent of the monitoring area. (Prent and Hickin, 2001). The Meager Creek area of the upper Lillooet River basin has a long history of large landslide events caused by failure of the weak hydrothermally altered volcanic rock making up the Mount Meager volcanic complex. Four slides in the twentieth century alone were in excess of 1×106 m3 , one of which produced a debris flow that reached the mouth of Meager Creek and caused flood surges along Lillooet River (Friele et al., 2005).  14  500000  504000  Q1  UL  >  512000  516000  520000  Open Site Met Station  R  ve  r  L  5588000  ya  Ri  R ivr o et tRiv e Lilillo lo oe  n  >  Water Temperature Logger Q1-3 Stream Gaging Station  er  Miller Ck  >  RR  1  500000  2  >> > > > >>> >> >> > >>  Q3  UTM zone 10 U 0  5580000  Q2  Pemberton  4 km  504000  > >  508000  512000  WSC Gage  > > > > !  LL  5576000  5576000  5580000  5584000  Stream Reach  5584000  UL  5588000  5592000  !  5592000  >  508000  > >  516000  520000  Figure 2.2: The monitoring area included 27.6 km of Lillooet R., one major tributary (Ryan R.), and one minor tributary (Miller Ck.). Stream reaches were upper Lillooet R. (UL), lower Lillooet R. (LL), and Ryan River (RR).  15  2.2  Data collection  On-site monitoring and manual data collection were carried out between July and October, 2010, with some supplementary data collected in August, 2011. The monitoring area spanned 27.6 km of Lillooet River, from a bridge 5 km downstream of the Railroad Creek confluence (upper bridge) to the Highway 99 bridge 13 km upstream from Lillooet Lake (lower bridge), (Figure 2.1). At the lower bridge, the Lillooet catchment is approximately 2120 km2 and 19% glacierized. Two tributaries were monitored just upstream of their junctions to Lillooet River. Ryan River joins Lillooet R. 8.0 km upstream from the lower bridge and has a catchment area of 413.4 km2 with 18% glacier cover. Miller Creek joins Lillooet River 475 m below the Ryan River junction and has a catchment area of 73.1 km2 with 22% glacier cover. Upstream extents of both tributaries were at bridge crossings on Pemberton Meadows Road.  2.2.1  Stream temperature  Water temperature (Tw ) was sampled at 5-min intervals using Onset TidbiT v2 data loggers anchored to the stream bed (please refer to Table 2.1 for all instrument specifications). It was assumed that the flow was turbulent enough to cause negligible vertical temperature differences. Sampling locations for Tw are shown in Figure 2.2. Sampling was most concentrated along both banks of Lillooet River below the Ryan River confluence to facilitate the investigation of transverse mixing of unsteady flows. Other sampling locations were at points which defined upper and lower bounds of stream reaches intended for heat budget modelling.  2.2.2  Meteorological data  Meteorological data were collected at an automated weather station installed 30 m from the Lillooet River in an open field. Incident shortwave and longwave radiation were measured with a Kipp & Zonen CM6B pyranometer and a Kipp & Zonen CGR3 pyrgeometer, respectively. Ambient air temperature and relative humidity were measured with a Rotronic HC-S3 sensor outfitted with a multi-plated shield to reflect solar radiation while allowing easy air passage. Wind speed was measured with an R.M. Young 5103-10 anemometer. Instruments were scanned every 1 s and 16  averages were recorded every 1 min with a Campbell Scientific CR10X datalogger.  2.2.3  Parameters for modelling net radiation  To calculate stream albedo, incident and reflected solar radiation were measured manually over the course of the day on Aug 25, 2011. Incident solar radiation was measured using a Kipp & Zonen CM6B pyranometer mounted on a tripod on shore. A second Kipp & Zonen CM6B pyranometer was mounted on a 2.5-m-long pole using a specially designed gimbel joint that kept the instrument level while being held inverted. Measurements were made at a height of 0.25 m above the stream to limit the pyranometer’s view of non-water surfaces while also limiting the effect of the instrument’s shadow. The pyranometers were scanned every 1 s and means were recorded every 10 s with a Campbell Scientific CR10X datalogger. The 10 s means were then averaged over the duration of each manual measurent, which ranged from 3-5 min. A water sample was collected with a DH-48 sampler at the location of each albedo measurement. These samples were taken to a laboratory in the U.B.C. Department of Geography to determine suspended sediment concentrations (SSC) by filtering the sample through a pre-weighed 0.45 micron filter, then drying and weighing the filter. A hemispherical photograph at the Open Site Meteorological Station (OSMS) was used to determine the site’s view factor for use in modelling the longwave radiation incident at the stream surface (details in Appendix) following Oke (1987) and Leach and Moore (2010). A Nikon Coolpix 4500 4.0 mega pixel digital camera was fitted with a Nikon ”fisheye” FC-E8 lens, mounted on a tripod with lens facing upward, levelled at the same height and location as the pyrgeometer, and oriented north to capture hemispherical images of the sky and horizon. The images were analysed using Gap Light Analyser (Frazer et al., 1999). For modelling stream shading and calculating view factors for the stream surface, riparian tree heights were measured at several riparian access areas using a clinometer and tape. Trees were selected for measuring based on the intent to represent the spatial average over the monitoring area. Subsequent to the monitoring period was it realized that the stream surface area beneath vegetation overhanging the stream may be important to consider in the reach-scale view factor calculation  17  and the solar shading function. The estimate of vertical distance from the water surface to vegetation overhanging the stream was based on field observations and on-site photographs. Reach-averaged lateral vegetation overhang, longitudinal vegetation presence, plan-view channel orientation, and channel width were determined for each reach using Geoeye-1 satellite images (0.41 m panchromatic resolution).  2.2.4  Streamflow  Streamflow was gauged at the upper boundaries of the upstream Lillooet River reach (UL) and the Ryan River reach (RR) to provide discharge and hydraulic geometry data (Figure 2.2). Data for the downstream boundary of the lower Lillooet River reach (LL) were provided by The Water Survey of Canada from the Lillooet River Near Pemberton gauging station (station number 08MG005). Stream flow was calculated by the standard velocity-area method. Water velocity and depth were measured at locations across the stream at each gauging site by suspending a Price-type current meter from a bridge with a winch and crane. Stage was recorded every 5 min in slackwater areas near the flow measurement sites using a Van Essen Diver pressure transducer anchored to the stream bed, and barometric pressure was accounted for with measurements of a second Diver on shore. Mean depth, width, and water velocity were computed for each flow measurement, which were later used to produce hydraulic geometry vs. discharge rating curves for each flow measurement site.  2.2.5  Electrical conductivity  Electrical conductivity (EC) was surveyed from an inflatable boat with an outboard motor on Aug 15, 2010 to provide a second method to determine transverse mixing for comparison with the estimates based on water temperature. EC measurements were taken with a WTW TetraCon 325 conductivity probe at five locations across the river channel: near each bank, center, left-center, and right-center. The survey began near the confluence of the Lillooet and Ryan rivers, and eight transverse routes were repeated at roughly 250 m intervals downstream. The longitudinal extent, which was approximately 2km, was limited by accessibility constraints.  18  Table 2.1: Instrument specifications. Parameter  Sensor  Range  Accuracy  Tw stage (cm) Ta RH u K↓ L↓ EC  Onset TidbiT v2 Van Essen Diver DI243 Rotronic HC-S3 Rotronic HC-S3 RM Young 05103 Kipp & Zonen CM6B Kipp & Zonen CGR3 WTW TetraCon 325  -20 to 70 °C 2900 cm -30 to +60 °C 0 to 100% 0 to 100 ms−1 300 to 2800 ηm 4500 to 42000 ηm 1µS/cm to 500 mS/cm  ± 0.2 °C ± 0.1% ± 0.2 °C ± 1.5% @ 23 °C ± 0.3 ms−1 < 5% < 5% ± 1.5%  2.3 2.3.1  Analysis and modelling Transverse mixing  Lateral mixing was investigated downstream of the confluences of Ryan River and Miller Creek primarily by using temperature differences between the left and right banks of Lillooet River. Whereas mixing studies commonly have utilized chemical tracers and visual indicators (Day, 1977; Gaudet and Roy, 1995; Rathbun and Rostad, 2004; Lane et al., 2008), water temperature can be used when the waters being mixed differ sufficiently in temperature (Mackay, 1972). Because mixing was hypothesized to be most rapid near the confluence, temperature loggers were concentrated toward the confluences with Ryan River and Miller Creek in order to provide higher resolution of the degree of mixing. Longitudinal temperature profiles (in the x direction) at a 10 m resolution were computed for each bank of Lillooet River by linear interpolation between logger stations. At any x location and any time t, the degree to which the waters had mixed was indicated by the temperature difference between the banks relative to the initial bank temperature difference. The deposition of suspended sediment in Lillooet River caused several temperature loggers to become buried at various times during the monitoring period. Even slight burial compromised the measurements. The period from August 12 - 20 had the highest spatial resolution of valid water temperature data below the 19  Ryan-Lillooet confluence and will henceforth be referred to as the mixing study period. A subset of data from this period was selected in which initial temperature differences between the merging rivers (∆Ti ) were ≥ 1°C. Application of this criterion resulted in removal of about half the data but was necessary to minimize the effect of instrument accuracy (temperature logger accuracy = 0.2 °C) in determining longitudinal distances for transverse mixing completeness (Pm ) of 80% and lower. The transverse mixing completeness was defined as a percentage of the initial bank temperature difference at the confluence: Pm = 1 −  ∆Tx ∆Ti  × 100%  (2.1)  where Pm is the percent completeness of transverse mixing, ∆Tx is the bank temperature difference at longitudinal distance x downstream of the confluence, and ∆Ti is the initial bank temperature difference at the confluence. The distance for a particular Pm will be referred to as the transverse mixing length,Lz , with an extension for Pm (e.g. Lz80 for Pm = 80). Figure 2.3 illustrates the method used to estimate mixing lengths for August 13, 2010, at 17:50. At this time, ∆Ti was 1.07 °C (gray line), ∆Tx was 0.63°C where ∆Ti decreased by 40% at 780 m (gray dotted line), and ∆Tx was 0.21°C where ∆Ti decreased by 80% at 2550 m (black dotted line). Rutherford (1994) integrated results from several published studies to derive empirical methods for estimating Lz and the transverse dispersion coefficient (kz ). Rutherford’s methods will be used here as a check on Lz estimated by the method described above and to make estimates of Lz beyond the limits of instrument measurement accuracy. The transverse dispersion coefficient kz , which represents the rate of lateral mixing, has been found to range considerably between different rivers within reaches of similar channel morphology. However, when kz was scaled by mean depth and mean shear velocity for gently meandering reaches, a general range was found so that 0.3 <  kz < 0.9 H ·U ∗  (2.2)  where kz is the transverse dispersion coefficient (m2 s−1 ), H is mean depth (m) and  20  14  Lillooet R. left bank Lillooet R. right bank initial difference difference at 40% mixed difference at 80% mixed  T w (°C)  12  13  ●  ●  ●  ●  ●  ●●  ●  9  10  11  ●  0  2000  4000  6000  8000  Distance downstream from confluence (m)  Figure 2.3: Longitudinal bank temperature profiles on 13 Aug at 17:50 along Lillooet River downstream of the tributary confluence. U ∗ is mean shear velocity (ms−1 ), defined as U∗ =  g·R·s ≈  g·H ·s  (2.3)  where g is gravitaional acceleration (ms−2 ), s is longitudinal channel slope (dimensionless), and R is hydraulic radius (m) (Rutherford, 1994). For shallow channels, the hydraulic radius is approximately equal to the mean depth (Dingman, 2002; Rutherford, 1994). Using mean H and U ∗ from Lillooet River over the mixing 21  study period, 0.21 < kz < 0.64.  (2.4)  Rutherford presented curves for different transverse locations of tracer input showing how Pm increases with non-dimensional distance downstream. Mixing lengths were extracted from these curves to compare with estimates from Lillooet River. Non-dimensional distance was defined by Rutherford (1994) as x∗ =  Lz · kz v · b2  (2.5)  where x∗ is non-dimensional distance, Lz is transverse mixing distance for a certain Pm (m), v is mean velocity (ms−1 ), and b is mean channel width (m).  2.3.2  Reach-scale heat budget model  The heat budget model (Eq. 2.6) was applied to three stream reaches within the study area: the Lillooet River in the upstream end of the study area (UL), the Lillooet River in the downstream end of the study area (LL), and Ryan River near the Lillooet River confluence (RR). Due to accessibility constraints, the reaches were not of equal length. A summary of reach properties is provided in Table 3.5. For unsteady flow, the Eulerian heat budget for a laterally well-mixed stream with no tributaries or groundwater discharge can be expressed as follows (Chaudhry et al., 1983; Meier et al., 2003): ∂T ∂ (AT ) ∂ (QT ) ∂ AE + − ∂t ∂x ∂x ∂x  =  Q∗ + Qh + Qe + Qb ρCp  (2.6)  where A is the cross-sectional area of the stream (m2 ), E is the longitudinal dispersion coefficient, Qh and Qe are the sensible and latent heat fluxes (Wm−2 ), Qb is heat conduction from the bed (Wm−2 ), ρ is the density of water (kg m−3 ), and Cp is the specific heat capacity of water (J kg K−1 ). Cp was assigned a constant 4191 J kg K−1 , which is the specific heat capacity of water at 10 °C (Dingman, 2002) (water temperatures of the proglacial streams of this study were typically between 8 °C and 12 °C.) Because longitudinal dispersion is typically a second-order term for streams 22  without point sources of heat (Gu et al., 1998; Sinokrot and Stefan, 1993), it will not be considered here. In addition, the bed heat flux can be considered a secondorder influence for larger streams (Gu et al., 1998). Given these simplifications, and expanding the derivatives using the product rule, the governing equation can be expressed as: ∂T Q∗ + Qh + Qe ∂T T ∂A ∂Q = −v − + ∂t ρCp D ∂ x A ∂t ∂x  (2.7)  The first term on the right-hand side represents the temperature change associated with exchange of energy across the water surface. The specification of net radiation, sensible, and latent heat fluxes are described in the next two sections. The second and third terms on the right-hand side represent the effects of advection and unsteady flow, respectively. Cross-sectional area, depth, width and velocity were computed from stream gauging data. Continuous time series of these quantities were derived by fitting power-law relations to predict them from recorded discharge. Derivatives were estimated using finite differences. Heat advection occurs where a thermal gradient is present between the upper and lower bounds of a reach. The advection term is preceeded by a minus sign to maintain the standard thermal gradient calculation, which was used to estimate the space derivative of water temperature: ∆T Tds − Tus ∂T ≈ = ∂x ∆x L  (2.8)  where the middle term is the reach-averaged thermal gradient (°C/m), T is water temperature with subscripts ds and us the downstream and upstream ends of the reach, and L is reach length (m). Therefore, when the upstream water temperature is less than the downstream water temperature and the thermal gradient is positive, heat advection has a cooling effect; heat advection has a warming effect when the thermal gradient is negative. The time derivative of cross-sectional area was estimated as ∂ A ∆A Ai+1 − Ai−1 ≈ = ∂t ∆t ti+1 − ti−1 23  (2.9)  where the subscript i denotes the time step of the heat budget model calculation. The space derivative of discharge is difficult to determine without having multiple gauging sites with no intervening tributaries, which was not feasible in this study. However, an order-of-magnitude estimate was computed as follows, based on the assumption that the wave celerity can be approximated by the mean velocity of flow: ∂Q 1 ∂Q ≈ ∂x v ∂t  2.3.3  (2.10)  Net radiation model  Incident shortwave and longwave radiation measurements made at the Open Site Meteorological Station (OSMS) were used in conjunction with measured riparian vegetation dimensions to develop a reach-scale net radiation model for each stream reach. The general approach was adapted from Moore et al. (2005b). Net radiation Q∗ can be expressed as Q∗ = K ∗ + L ∗  (2.11)  where K ∗ is net short wave radiation (Wm−2 ) and L∗ is net long wave radiation (Wm−2 ). The remaining portion of this section explains the calculation of K ∗ and L∗ . Net short wave radiation Net short wave radiation K ∗ is computed as: K ∗ = K↓(1 − α)  (2.12)  where K↓ is incident short wave radiation (Wm−2 ) and α is stream surface albedo. Incident shortwave radiation K↓ was calculated over a reach as K↓ = gt Kd + fv Ks  (2.13)  where gt is the fraction of the stream surface that is not shaded by riparian vege24  tation at time t, Kd is direct solar radiation (Wm−2 ), Ks is diffuse solar radiation (Wm−2 ), and fv is the sky view-factor. Global solar radiation, which included both direct and diffuse components, was measured at OSMS as a surrogate for incident solar radiation above the riparian foliage canopy. Neither component was specifically measured on site. Therefore, the components were partitioned by calculating the diffuse fraction according to the procedure presented by Erbs et al. (1982) and as used by Leach and Moore (2010) for computing insolation at a stream surface. The procedures for estimating gt and fv are described in detail in the Appendix. Stream surface albedo measurements have typically ranged between 0.05 and 0.1 for low-gradient and valley-bottom streams (Evans et al., 1998; ?; Leach and Moore, 2010), but the albedo of water is known to vary with factors such as the incidence angle of direct solar radiation, the ratio of diffuse to global solar radiation, suspended sediment concentration, and aeration (Han, 1997; Richards and Moore, 2011). In this study, albedo was specified based on measurements at Lillooet and Ryan rivers. In addition, the data were used to investigate the dependence of albedo on solar zenith angle and SSC.  Net longwave radiation Longwave radiation emitted by the sensor was included in the longwave radiation measurement (Lmeas ) at OSMS and required post-processing to remove. The Kipp&Zonen CGR3 manual (Kipp and Zonen, 2009) provided an equation to calculate the sensor temperature: Tsens = ( a + b[ln(v)] + c[ln(v)]3 )−1  (2.14)  where Tsens is the temperature of the CGR3 sensor (K), v is sensor output voltage (µv), a = 1.03 × 10−3 , b = 2.39 × 10−4 , and c = 1.57 × 10−7 . The sensor was considered a black-body and assumed to have an emissivity of 1. The incident longwave radiation at OSMS was then calculated as 4 L↓OSMS = Lmeas − σ Tsens  where σ is the Stefan-Boltzmann constant (5.67 × 10−8 Wm−2 K−4 ). 25  (2.15)  Measured incident longwave radiation at the open site meteorological station was used to calculate atmospheric emissivity (εa ). This method of estimating εa implicitly accounts for the presence of clouds and was valid during day and night. The incident longwave radiation at OSMS can be expressed as follows: L↓OSMS = [εa fOSMS + ε f (1 − fOSMS )]σ (Ta + 273.2)4  (2.16)  where fOSMS is the sky view factor at OSMS, ε f is emissivity of foliage, and Ta is air temperature (°C). The emissivity of deciduous trees is between 0.97 - 0.98 (Oke, 1987). For this study ε f was assumed constant at 0.97, and the foliage temperature was assumed equal to the air temperature measured at OSMS. Given values for fOSMS and ε f , the atmospheric emissivity can be computed by solving Eq. 2.16 for εa . Hemispherical sky photos at OSMS were analysed with Gap Light Analyser software (Frazer et al., 1999) to calculate fOSMS by the method presented by Moore et al. (2005b): fOSMS =  1 π  2π 0  π/2 0  g∗ (θ , ψ) cos θ sin θ dθ dψ  (2.17)  where θ and ψ are solar zenith and aziumuth angles, respectively, and g∗ (θ , ψ) is the canopy gap fraction at the hemispherical image position θ , ψ. The image was overlaid with a 5◦ zenith by 5◦ azimuth grid and gap fractions were computed for each grid square. The double integral was approximated by summing all gap fractions. The longwave radiation reaching the stream surface can be expressed as L↓ = [εa fv + ε f (1 − fv )]σ (Ta + 273.2)4  (2.18)  where fv is the sky view factor for a particular reach (Eq. A.15). The longwave radiation emitted by the stream surface can be calculated as L↑ = εw σ (Tw + 273.2)4  (2.19)  where εw is the emissivity of the stream and Tw is the stream temperature measured at the nearest Tidbit logger (°C). The stream emissivity was assumed to be 0.95, 26  which is the mean of the water emissivity range provided by Oke (1987). Net longwave radiation was then calculated as L∗ = εw L↓ − L↑  (2.20)  where εw represents the fraction of incoming longwave radiation absorbed by the stream.  2.3.4  Convective heat exchanges  The latent heat flux was estimated using a Penman-type equation presented by Moore et al. (2005b) which was adapted from Webb and Zhang (1997a): Qe = 285.9 (0.132 + 0.413u)(ea − ew )  (2.21)  where u is measured wind speed (m s−1 ), ea and ew are vapor pressures of the ambient air and the hypothetical thin layer of air above the water surface, repectively (kPa), and the constants account for the latent heat of vaporization, the specific weight of water, various unit conversions, and empirical constants of the Penman equation. The actual vapour pressure of the ambient air above the stream (ea ) was calculated as ea = e∗  RH 100  (2.22)  where RH is relative humidity measured at OSMS and e∗ is saturation vapor pressure (kPa), which was calculated as a function of air temperature from an empirical relation presented by Dingman (2002): e∗ = 0.611 · exp  17.3 · T T + 273  (2.23)  where T is air temperature (°C). For hydrologic computations, this relation is sufficiently accurate compared to the true relation between e∗ and air temperature represented in the more complex Goff-Gratch Equation (Dingman, 2002). In calculating ea , T in Eq.2.23 was the ambient air temperature recorded at OSMS.  27  The hypothetical thin layer of air immediately above the water surface was assumed to have a temperature equal to the water temperature and to be saturated with water vapor. Therefore, the vapour pressure within this boundary (ew ) was calculated directly from Eq. 2.23 with T equal to the water temperature measured at the nearest Tidbit logger. Following Moore et al. (2005b), sensible heat flux (Qh ) was calculated as Ta − Tw ea − ew  Qh = Qe γ  (2.24)  where γ is the psychrometric constant (kPa/°C). The psychrometric constant is not a true constant, but varies with atmospheric pressure according to Brunt (1952): γ=  Ca · P rM · λ  (2.25)  where Ca is the specific heat of moist air = 1.013 kJ kg−1 °C−1 , P is atmospheric pressure (kPa), rM is the ratio of the molecular weight of water vapor to the molecular weight of dry air = 0.622, and λ is the latent heat of vaporization = 2.45 MJ kg−1 . Following Allen et al. (1998), atmospheric pressure was calculated as a function of air temperature and elevation: P = P0  Ta − Γ · z Ta  g/(Γ·R)  (2.26)  where P is atmospheric pressure (kPa), P0 is standard atmospheric pressure = 101.3 kPa, Ta is air temperature (K), Γ is the moist lapse rate = 0.0065 K m−1 , z is the site elevation = 220 m, and R is the specific gas constant = 287 J kg−1 K−1 .  28  Chapter 3  Results 3.1  Overview of the field season  Figure 3.1 shows mean monthly air temperatures from 1969-2006 near Pemberton, BC. Also shown are mean monthly air temperatures for 2010 from PACS and August/September 2010 from the open site meteorological station (OSMS). Mean monthly air temperatures at PACS for the 2010 field season were about 1 °C above normal in July, close to historical averages in August and September, and slightly above average in October. Air temperature at OSMS was about 1.5 °C lower than at PACS in August and September, which was expected given its higher elevation, closer proximity to Lillooet Glacier, and its location adjacent to the river. Precipitation preceding the study period (January to April) was cumulatively below normal (Figure 3.2). Precipitation in July was well below normal and August saw only about half the normal precipitation. Precipitation in September was roughly double the normal amount, while less than half the historic average fell in October. Maximum, mean, and minimum mean daily discharge from 1914-2010, along with 2010 mean daily discharge at the Lillooet River WSC gauging station, are shown in Figure 3.3. Flow in early July peaked above average. This peak was not associated with a rain event detectable at PACS and was likely the result of higher than normal air temperature in July and high rates of meltwater generation. Flow was near the long-term mean in late July and early August, after which flow de29  30  ●  20  ● ● ●  1969−2006 Max. 1969−2006 Mean 1969−2006 Min. 2010 2010 Open Site  ●  ● ●  10  ● ●  ● ●  0  ● ●  ●  ●  ●  ● ●  ●  ●  ●  ●  ●  ●  ● ● ● ● ● ●  ●  ● ●  ●  ●  ● ●  ●  ● ● ● ●  ● ●  ● ● ● ●  ● ● ● ●  ●  −10  Mean Monthly Air Temperature ( °C )  ●  Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec  Figure 3.1: Historical mean monthly air temperature from 1969-2006 and 2010 measured at PACS. Mean monthly air temperature for August and September, 2010, measured on-site (OSMS), is shown with solid black points. clined more rapidly than the long-term mean until the rain events of late September through November. Incident solar radiation, air temperature, vapor pressure, and wind speed measured at OSMS from late July to mid-October are shown in Figure 3.4. Late July and mid-August had periods of about one week of daily maximum air temperatures over 30 °C. After mid-August, temperatures in general declined gradually. Incident solar radiation in July and August commonly exceeded 800 Wm−2 and gradually declined through September and October. Vapour pressure generally declined after a broad peak in early August, but late September and October had periods of several days in which vapour pressure was elevated. Wind speed, measured as oneminute averages, was typically less than 1 ms−1 with spikes between 1 and 2 ms−1 . There was no discernible seasonal pattern of wind speed, except for a lull in early 30  200 150 100 0  50  Precipitation (mm)  1969−2006 2010  Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec  Figure 3.2: Monthly total precipitation for 2010 and mean monthly total precipitation for 1969-2006. Data were missing for May and June, 2010 . October. Water temperatures at the four reaches (UL = upstream Lillooet River, LL = lower Lillooet River, RR = Ryan River, and MC = Miller Creek) ranged between 5 °C and 13 °C, varied on a diurnal cycle, and generally decreased gradually after mid-August (Figure 3.5). Daily mean water temperature is shown for each reach in Figure 3.6 (bottom panel). The temperature pattern at each reach generally followed the pattern of daily mean air temperature (top panel), but with lower magnitudes. Average daily statistics for each site are displayed in Table 3.1. Mean daily temperatures were highest at LL and lowest at MC. Daily variability (expressed as standard deviations) was highest at MC and UL, and LL had the least variability.  31  1500 1000 500 0  Mean Daily Discharge ( m3s−1)  Maximum Minimum Mean 2010  Jan  Mar  May  Jul  Sep  Nov  Jan  Figure 3.3: Discharge for 2010 measured near LL with historical maximum, mean, and minimum daily discharge from 1914-2010.  Table 3.1: Daily summary statistics of water temperature at each sub-reach from July 24 to October 15, 2010. sd = standard deviation.  daily stat. mean sd maximum minimum range  Water temperature (°C) UL LL RR MC 9.70 9.99 9.44 7.79 1.12 0.83 0.87 1.14 11.39 11.36 10.94 9.67 8.07 8.76 8.20 6.31 3.32 2.60 2.74 3.36  32  600 200 0.0  0.5  1.0  1.5  2.0 0  5  10  15  20  25 0 5  15  25  35 0  K ↓ (Wm−2) T a (°C) e a (mb) w (m/s)  Aug  Sep  Oct  Figure 3.4: From top to bottom: incident solar radiation, air temperature, vapor pressure, and wind speed measured at OSMS.  33  6  8  10  12  14  Upper Lillooet  6 14  Ryan  6  8  10  12  T w (°C)  8  10  12  14  Lower Lillooet  6  8  10  12  14  Miller  Aug  Sep  Oct  Figure 3.5: Instantaneous water temperature at (top to bottom) UL, LL, RR, and MC.  34  20 0  5 10  T a (°C)  30  Max. Mean Min.  9 8 6  7  T w (°C)  10  11  Upper Lower Ryan Miller  Aug  Sep  Oct  Figure 3.6: Maximum, mean, and minimum daily air temperature at OSMS (top) and daily mean water temperature at UL, LL, RR, and MC (bottom).  35  3 0  1  2  T w Range (°C)  4  5  Upper Lillooet Lower Lillooet Ryan Miller  Aug  Sep  Figure 3.7: Daily water temperature ranges at each reach.  3.2  Longitudinal variations in water temperature  Figure 3.8 shows temperature profiles for Lillooet River at two-hour time intervals from 07:00 - 21:00 on July 25 (all times reported are in Pacific Standard Time). The upper two stations are the upper and lower boundaries of reach UL. The furthest downstream station is the lower boundary of reach LL (the logger at the upper boundary of LL was not yet installed). The 07:00 and 09:00 profiles represent the end of the cooling phase at the uppermost site and the remaining profiles were during the following warming phase. By 11:00, UL had entered a warming phase 36  13 10  ● ●●  8  9  T w (°C)  11  12  July 25 07:00 to 21:00  ●  7  ●  6  ●  0  5000  10000  15000  20000  07:00 09:00 11:00 13:00 25000  15:00 17:00 19:00 21:00 30000  Distance downstream (m)  Figure 3.8: Longitudinal temperature gradients in Lillooet River on July 25 showing the end of the cooling phase (blue) in the morning followed by the warming phase (red).  while LL still experienced cooling. Longitudinal temperature gradients at 11:00 were negative at UL and positive at LL; as a result, longitudinal heat advection was having a warming effect at UL and cooling effect at LL. A rather uniform longitudinal temperature gradient existed throughout the entire study segment of Lillooet River from 13:00 to 19:00. UL warmed slightly between 19:00 and 21:00 while considerable warming still occurred downstream. 37  13  July 25 19:00 to July 26 09:00 ●●  ●  10  ●  ● ●●  ●  ●  19:00, July 25 21:00 23:00  7  8  9  T w (°C)  11  12  ●  ●  6  ●  0  5000  10000  15000  20000  01:00, July 26 03:00 05:00 07:00 09:00 25000  30000  Distance downstream (m)  Figure 3.9: Longitudinal temperature gradients in Lillooet River showing the end of the warming phase (red) late on July 25 followed by the cooling phase (blue) through the morning of July 26.  38  Table 3.2: Transverse mixing length statistics for the given degree of mixing (Pm ) at 10% increments. s.d. = standard deviation Pm 10 20 30 40 50 60 70 80 90  mean (m) 473 529 602 740 1110 1717 2332 3036 4456  s.d. (m) 105 126 193 319 464 460 421 343 835  min, max (m) n/a, 820 n/a, 1170 n/a, 1570 400, 1980 430, 2490 460, 3010 500, 3510 2150, 4560 2970, n/a  By 23:00, UL had entered a cooling phase while the lower section of Lillooet River was still warming, reflecting the passage of a temperature wave along the study segment (Figure 3.9). By 01:00 on July 26, UL had a positive thermal gradient and was thus subjected to advective cooling while LL was still warming, still had a negative thermal gradient and experienced advective warming. The entire study segment was cooling from 03:00 to 09:00 (July 26). However, the longitudinal temperature gradient was non-uniform during the cooling phase.  3.3 3.3.1  Transverse mixing Observed transverse mixing in Lillooet River  This section focuses on the period from August 12 - 20, 2010. Figure 3.10 shows time-series of left and right bank water temperatures, interpolated linearly from observed temperatures, at four locations downstream of the Ryan River confluence, along with the temperature difference between the banks. The temperature difference near the confluence ranged from 0 °C to 1.8 °C. The difference between left and right banks decreased downstream and was near zero most of the time at 6 km downstream of the confluence. Transverse mixing progressed most rapidly immediately below the confluence 39  14 10 14  0  2  8  n  12  150 m downstream  10 10 14  0  2  8  n  ∆T w (°C)  2 0  14  4 km downstream  12  T w (°C)  8  n  12  2 km downstream  10  0  2  8  n  12  6 km downstream  Aug 13  Aug 15  Aug 17  Aug 19  Figure 3.10: Time-series of left (blue) and right (red) bank water temperature along Lillooet River at four downstream locations from the Ryan River confluence. Temperature difference (black) between the banks at each location is shown on the bottom of each panel with axis on right.  40  80  ●  ●  60  ●  ●  40  Percent Mixing  ●  ●  20  ●  ●  ●  1000  2000  3000  4000  Mixing Length L z (m)  Figure 3.11: Mean transverse mixing lengths for the percent of lateral mixing at 10% increments. and was continually less rapid downstream. An example for a specific time is shown in Figure 3.12. Roughly half the initial temperature difference between the left and right banks was closed within a distance of 1 km from the confluence. The mixing length at that time for Pm = 80% was 2.55 km, which was over three times that for Pm = 40% at 0.78 km. This behaviour is also illustrated in Figure 3.11. For example, the mean value of Lz80 (3036 m) was more than four times that of Lz40 (740 m). Table 3.2 summarizes the values of Figure 3.11 with additional statistics.  41  14  Lillooet R. left bank Lillooet R. right bank initial difference difference at 40% mixed difference at 80% mixed  T w (°C)  12  13  ●  ●  ●  ●  ●  ●●  ●  9  10  11  ●  0  2000  4000  6000  8000  Distance downstream from confluence (m)  Figure 3.12: Longitudinal bank temperature profiles on 13 Aug at 17:50 along Lillooet River downstream of the tributary confluence. Electrical conductivity (EC) measurements confirmed the general pattern of lateral mixing. Figure 3.13 presents results from the first of two watercraft surveys that measured EC across Lillooet River downstream of Ryan River junction on Aug. 26, 2010 between 12:25 and 16:45. Surveys extended only to 2.1 km below the confluence due to logistical constraints. EC above the confluence was nearly uniform at 44 µ S/cm. Just below the confluence, EC on the right bank (the side of the junction) dropped to 23 µ S/cm. After 2.1 km, right bank EC was 35 µ  42  ●  60  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  ●  40  EC ( µS/cm)  ●  left bank left center center right center right bank left − right bank  ● ●  20  ● ●  ● ●  0  ●  ●  ●  0  500  1000  1500  2000  Distance downstream (m)  Figure 3.13: Electrical conductivity (EC) was surveyed by eight lateral transects approximately 250 m apart, extending downstream of the Ryan River confluence 2.1 km. S/cm and the left bank remained near 44 µ S/cm, which was a 40% closure of the EC difference near the junction. This was similar to the upper range of Lz40 of 2.0 km observed over the mixing study period using temperature differences. The second survey was conducted immediately after the first survey with nearly identical results.  43  Table 3.3: Predicted transverse mixing lengths using Rutherfords (1994) models for given channel form and tracer input location. Predicted ranges reflect given transverse dispersion coefficient ranges. Mean observed Lz80 was 3036 m. Channel form Gently meandering Gently meandering Gently meandering Sharp bends/constrictions  3.3.2  Input location bank 1/3 1/2 bank  Predicted Lz80 (m) 3970 to 11900 3080 to 9250 980 to 2940 1205 to 3565  Modelled transverse mixing  Transverse mixing lengths calculated from the model presented by Rutherford (1994) (Section 2.3.1) for various channel morphology and tracer input locations are given in Table 3.3. Mean observed Lz80 was 3036 m, less than the range predicted by the model for bank source tracer input in gently meandering channels. Considering the momentum of a tributary, however, the effective input location across the receiving channel’s width may be some distance from the bank. Mean observed Lz80 was within the range predicted by Rutherford’s model for tracer input between one-third and one-half the width of the receiving channel in gently meandering channels. Though Lillooet River can be characterized as mostly gently meandering, there are some sharp bends below the confluence. Mean observed Lz80 was within the range predicted by Rutherford’s model for bank source tracer input in channels having sharp bends. Instrument accuracy limitations prevented determining transverse mixing lengths higher than the 80% mixing level. Complete transverse mixing lengths were therefore estimated for comparison to other studies, which often report this metric. Mean observed Lz80 was used to calculate the mean transverse dispersion coefˆ = ficient (kz ), which was used to estimate Lz at the 98% mixing level. Mean Lz98 ˆ ranged from 3870 m to 8300 5420 m (69 multiples of average river width) and Lz98 m (49 to 105 river widths). Figure 3.14 compares Lz predictions from Rutherford’s model (calibrated at Pm = 80%) to observed values for a range of mixing completeness levels. Near the con-  44  100  ● ●  80  ●  ●  ●  60  ●  ●  40  Percent Mixing  ●●  ●  ●  ●  ●  20  ●  ●  ●  ● ● ●  ●  measured modelled  0  ●  0  2000  4000  6000  8000  Mixing Length L z (m)  Figure 3.14: Observed and modelled mean transverse mixing lengths for given degree of mixing. fluence, observed transverse mixing was more rapid than modelled. Where mixing neared completion downstream, observed mixing was less rapid than modelled.  3.3.3  Effect of stream discharge  Variation in Lz was in part explained by the fraction of tributary to mainstem streamflow (Qratio ), calculated as  45  Table 3.4: Transverse mixing distances and dispersion coefficients at times of the given Qratio statistic. Statistic instantaneous min instantaneous max mean daily min mean daily max  Lz80 (m) 2580 3760 2710 3480  Qratio 0.46 0.94 0.57 0.86  Qratio =  Lz98(m) 4670 6809 4900 6300  kz 0.98 0.67 0.94 0.73  Qtributary Qmainstem  (3.1)  where Qtributary and Qmainstem refer to discharge in Ryan River and Lillooet River, respectively (m3 s−1 ). Miller Creek’s flow was negligible in comparison to the other rivers and not considered in Eq. 3.1. Lz tended to increase with increasing Qratio . Figure 3.15 shows this relation for Pm = 80%. The best-fit line for this plot took the form ˆ = 1481 + 2237 · Qratio Lz80  (3.2)  ˆ is the predicted value. The fitted relation has R2 = 0.43 and p < 0.001. where Lz80 The relation between Ryan River flow and Lz was not as strong (R2 = 0.27), and there was no significant relation between Lillooet River flow and Lz . As shown in Table 3.4, Qratio increased 51% on average over the course of a day, from an average daily minimum of 0.57 to a maximum of 0.86. Lz80 correspondingly increased by 28%, on average, between daily minimum and maximum Qratio . For modelled Lz98 , the increase was 29% between daily minimum and maximum Qratio . Estimated kz correspondingly decreased by 22%.  46  5000 4500  ● ●  ● ●● ● ● ●  ●  ● ●● ●● ●● ●● ●●  3500  ●● ●● ● ● ● ●● ● ● ● ●● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ●● ● ●● ● ●● ● ●● ● ● ● ●● ● ●● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ●●●● ● ● ●● ● ● ●● ● ●●●● ● ●●● ● ● ● ● ●● ● ●● ●● ●●●●● ● ● ●● ●● ● ●●●● ● ●● ● ●● ●● ● ●● ● ●● ● ● ●● ● ●● ●● ● ● ●● ●● ● ● ● ●● ● ●●● ●● ● ● ●●● ●●● ● ● ● ● ●● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ●●● ●●● ● ● ●●● ● ●● ●● ●●● ● ●●●● ● ● ●● ● ● ● ●●● ●●●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●●● ●●● ● ● ● ● ●● ●● ● ● ●●●●● ● ●● ●● ● ●● ● ● ●● ● ●● ● ● ● ● ●● ● ● ● ● ●●● ● ●●● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ●● ● ● ● ●●● ●● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ●● ● ● ●● ● ●● ●●● ● ●● ● ●● ● ● ●● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ●● ●●●● ● ●● ●●● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● ● ●●●● ●● ● ●● ●●●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●● ●● ● ● ●● ● ●●●●●● ●● ●● ●● ● ● ●● ● ● ● ●● ●● ● ●● ● ●● ● ●● ●● ● ●● ● ● ●●●● ● ● ●● ● ●● ●● ● ● ● ● ●● ●● ●●● ●● ●●● ●● ● ● ●● ●● ●●● ● ● ● ●● ●● ● ● ●● ● ●●● ● ● ● ●●● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●● ●● ● ● ●● ● ● ● ●●●● ● ● ● ● ●●●● ● ●● ●● ● ● ●● ● ● ●● ●●● ●● ● ● ● ● ●●● ● ●● ●● ●●● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ●●● ● ● ● ● ● ● ●  2000  2500  3000  L z80 (m)  4000  ●● ●  0.4  0.5  0.6  0.7  0.8  0.9  1.0  1.1  Q Ryan Q Lillooet  Figure 3.15: Transverse mixing lengths at the 80% mixing level for given ratios of tributary to mainstem discharge.  3.4 3.4.1  Surface-atmosphere energy exchanges Radiative exchanges  The material in this section first focuses on the quantification of key factors that control the radiation budget, including albedo, sky view factor, shading factor and atmospheric emissivity. The calculated net radiation for each reach are then presented. 47  Albedo Measured albedo varied with solar zenith angle θ (0◦ overhead to 90◦ at the horizon), although there was scatter in the relation, especially for Lillooet River (Figure 3.16). At a given time (and θ ), albedo was highest for Lillooet River, followed by Ryan River and Miller Creek (Figure 3.16). Albedo measurements were not possible for θ above 75◦ , due to shading from banks, or below 40◦ , as this was the lower limit of θ for this time and latitude. The effect of the upper θ limit on energy balance calculations should be minor since the streams were largely in shade under those conditions. Suspended sediment concentration (SSC) was highest in Lillooet River, followed by Ryan River and Miller Creek, with medians of 831, 71, and 34 mg L−1 , respectively (Figure 3.16). A regression of albedo as a function of zenith angle, SSC, and their interaction was fitted over all observations, and took the form αˆ = aθ + bSSC + c(θ · SSC)  (3.3)  where αˆ is the predicted albedo, θ is solar zenith angle, SSC is suspended sediment concentration (mg L−1 ), and the coefficients are a = 0.00116, b = not significant at α = 0.05, and c = 1.04×10−6 , with p-values = 0.00015, 0.416, 0.0385, respectively (R2 = 0.83, p << 0.0001, standard error of the estimate = 0.008). The means (and medians) of albedo measurements were 0.10 and 0.08 for Lillooet River and Ryan River, respectively. These values were used as constants in calculating net shortwave radiation, as described below. Sky view factor and atmospheric emissivity The Upper Lillooet reach had the highest percentage of riparian canopy presence of the three reaches and the lowest sky-view factor ( fv ) (Table 3.5). The Lower Lillooet reach had less canopy presence and a wider channel, and thus a higher fv , than UL. The Ryan River reach had the lowest riparian canopy presence and the lowest channel width, and thus the highest fv of the three reaches. View factors were assumed constant through the study period, which should be reasonable given that the study period began after spring leaf-out and before leaf-fall in the autumn. 48  ●  Lillooet Ryan Miller  ● ● ●  ●  0.08  ●●  ●● ●  0.04  Albedo Albedo  0.12  ● ●  60  65  ● ●  ● ● ●  55  ● ●  50  ● ●  ● ● ● ●  45  Zenith Angle  70  ● ●  ●  1000  ●● ●●  ●●●  ●●●  ●●  100  ●● ●  10  SSC (mg/L)  ● ●●  ●  40  ●  07:00  09:00  11:00  13:00  15:00  17:00  19:00  Figure 3.16: Measured albedo (top) and suspended sediment concentration (bottom) for Lillooet River, Ryan River, and Miller Creek on August 25, 2011, with calculated solar zenith angle (center).  49  1.00 0.90 0.70  0.80  εa  Aug 01  Aug 15  Sep 01  Figure 3.17: Atmospheric emissivity (εa ) was calculated over the monitoring period.  Atmospheric emissivity, computed using (Eq. 2.16), varied between 0.69 and 1 over the study period and had a mean of 0.90 (Figure 3.17). Values of εa were typically lower during the day than at night, which may be expected from cloud formation. Shade function, gt Table 3.5 summarizes mean gt over the study period for each reach (means include zero values during night or complete shade). Each site reached similar maxima near 0.95 but their non-zero minima and daily patterns differed (Figure 3.18). Net radiation, Q∗ Figure 3.19 shows the components of net shortwave and longwave radiation with resulting net all-wave radiation for UL. Figure 3.20 shows Q∗ for each reach. RR consistently had the highest daytime values and UL the lowest. On average, Q∗ at RR was 20% higher than at UL, while LL received 12% more net radiation than UL.  50  1.0 0.8 0.6 0.4 0.2 0.2  0.4  gt  0.6  0.8  1.0 0.0  UL  0.2  0.4  0.6  0.8  1.0 0.0  LL  0.0  RR 14Aug  15Aug  16Aug  17Aug  Figure 3.18: Shading function gt for each reach, August 14-17.  51  Table 3.5: Summary of parameters used in the heat budget model for each reach: upper Lillooet River (UL), lower Lillooet River (LL), and Ryan River (RR). item reach length (m) channel width (m) orientation (◦ ) canopy presence (%) canopy height (m) albedo, α sky view-factor, fv shade function, gt (mean)  UL 1767 61.6 322 78.2 28.5 0.10 0.666 0.51  LL 2757 78.7 298.3 49.9 28.5 0.10 0.818 0.71  RR 2079 45.1 303.5 21.6 28.5 0.08 0.861 0.82  L↓ L↑  0 800  Q*  0  400  Radiation ( Wm−2 )  400  800  K↓ K↑  08/01  08/15  09/01  Figure 3.19: Radiative exchanges averaged over the upper Lillooet River reach (UL): incident and outgoing shortwave (K) and longwave (L) radiation (top), net all-wave radiation (Q∗ ) (bottom).  52  800 400 0  Q * ( Wm−2 )  UL LL RR  08/01  08/15  09/01  0  50 100  Qe Qh  −100  Heat Flux ( Wm−2 )  Figure 3.20: Net all-wave radiation (Q∗ ) for upper Lillooet River (UL), lower Lillooet River (LL), and Ryan River (RR).  Aug 01  Aug 15  Sep 01  Figure 3.21: Latent and sensible heat flux at UL.  3.4.2  Net surface-atmosphere energy exchange  Latent heat flux (Qe ) was 7% of Q∗ at UL, on average, and ranged between -80 Wm−2 and 61 Wm−2 (Figure 3.21). Negative values indicate heat loss by evaporation and positive values indicate heat gain by condensation. Sensible heat flux (Qh ) was typically higher than Qe and ranged from -20 Wm−2 to 127 Wm−2 . Qh was 15% of Q∗ at UL, on average. In Figure 3.22, sensible and latent heat flux are plotted with net radiation at UL, the sum of which 53  1000 200  600  Qe Qh  0  Heat Flux ( Wm−2 )  H Q*  Aug 01  Aug 15  Sep 01  Figure 3.22: Net surface heat exchange (H) with net radiation, latent heat, and sensible heat flux components at UL.  is the total energy flux across the water surface, which will be referred to as vertical energy flux.  3.5  Reach-scale heat budgets  Eq. 2.7 provided the model used to predict rates of change of stream temperature with time for each site. The terms on the right-hand side of Eq. 2.7 represent the contributions to temperature change associated with vertical energy exchange across the surface, longitudinal heat advection, heat storage change with streamflow, and effects of flow divergence. For brevity, these terms may be referred to as vertical, advection, δ A/δt, and δ Q/δ x terms, respectively. The latter two can be grouped to represent the effects of unsteady flow. This section provides heat budget model results for UL, which had the longest period of record, for clear-sky, partly cloudy, mostly cloudy, and rainy periods. The landslide event was also modelled. Weather conditions were categorized according to the shortwave radiation record at OSMS and the precipitation record at PACS. The following section focuses on heat budget calculations for UL to illustrate the contrast between upstream and downstream (LL) sites.  54  3.5.1  Clear-sky period  Figure 3.23 shows UL heat budget model results (top panel) for the clear-sky period July 24 to July 27 along with discharge and water temperature. Vertical heat flux was mostly in phase with advection, and both terms had relatively smooth arching patterns during this clear-sky period. The vertical and advection terms were out of phase with the unsteady flow terms δ A/δt and δ Q/δ x. Daytime positive vertical heat flux had a magnitude of about half that of advection. At night, vertical heat flux was near zero and advective cooling reached slightly greater magnitudes than advective warming during the day. Heat advection also had a greater magnitude than the unsteady flow terms and was thus the dominant control on stream temperature dynamics. The unsteady flow terms were opposite in phase with each other due to the different directions of their relations with the temporal rate of discharge (Q) change, thus offsetting their individual effects (Figure 3.23). The positive phase of the δ Q/δ x term had a similar magnitude to the positive phase of the vertical term (but differed in timing). At any time, however, the magnitude of the δ Q/δ x term was only slightly greater than that of the δ A/δt term of opposite sign. The result was a combined influence near zero (green line), although during rising flow the combined terms had a slight warming influence and a slight cooling influence during decreasing flow. Discharge (middle panel of Figure 3.23) displayed a mirror-like phase relation with advection. Daily maximum discharge during this period occurred near the time of minimum heat advection (and minimum δ T /δt), and daily minimum discharge occurred near the time of maximum advection (and maximum δ T /δt). The sign of the advection term depends on the longitudinal temperature gradient, which alternated diurnally and varied spatiotemporally in the Lillooet River study reach. Positive longitudinal temperature gradients (cooler upstream) typically occured during nighttime cooling phases and negative thermal gradients (warmer upstream) during daytime warming phases. There was a lag time in temperature gradient shifts between UL and LL, which related to their timing of advection phases. The heat budget model performed quite well over this period at UL (Nash-  55  predicted observed  −0.5  0.0  0.5  1.0  dQ/dx component dA/dt component dQ/dx+dA/dt components  180 170 11 9 7  T w ( °C )  13  150  160  Q (m3s−1)  190  200  dT/dt ( °C hr−1 )  vertical component advection component  24Jul  25Jul  26Jul  27Jul  Figure 3.23: Heat budget (top), discharge (center), and water temperature (bottom) during clear-sky conditions, July 24 to July 27, 2010 at UL.  56  0.5 0 −1  −0.5  dT/dt ( °C hr−1 )  1  predicted observed predicted−observed  24Jul  25Jul  26Jul  27Jul  Figure 3.24: Predicted (gray) and observed (black) temporal stream temperature change and their difference (red) at UL.  Sutcliffe model efficiency (Em ) = 0.96, Table 3.6). Figure 3.24 highlights the difference (red) between predicted and observed values in time. The model tended to over-predict, with a mean bias error (MBE ) of 0.04 °C/hr. The largest errors occurred on the rising and falling limbs of δ T /δt each day, in which over-predictions reached up to 0.26 °C/hr on either limb. Advection alone closed the heat budget on the rising limb overnight until advection began to level off in the morning. At that time, the model began over-predicting by a combination of advection and vertical heat flux. The combined unstready flow terms were near zero. This error persisted until around 11:00, when the heat budget was closed by all components. Overprediction occurred again in the evening when vertical flux was near zero. At this time, advection was greater than observed δ T /δt and the combined unsteady terms were slightly positive. The error lessened as δ T /δt approached the daily minimum and the heat budget was again closed by advection alone.  3.5.2  Cloudy periods  The heat budget components were sensitive to changes in atmospheric conditions (Figure 3.25). Daytime cloud cover can be identified in periods when the verti57  predicted observed  −0.5  0.0  0.5  1.0  dQ/dx component dA/dt component dQ/dx+dA/dt components  180 170 11 9 7  T w ( °C )  13  150  160  Q (m3s−1)  190  200  dT/dt ( °C hr−1 )  vertical component advection component  30Jul  31Jul  01Aug  02Aug  Figure 3.25: Heat budget (top), discharge (center), and water temperature (bottom) from July 30 to Aug. 2, 2010 at UL. Conditions were clear on July 30, switching to overcast July 31, and partly-cloudy Aug. 1.  58  predicted observed  −0.5  0.0  0.5  1.0  dQ/dx component dA/dt component dQ/dx+dA/dt components  180 170 11 9 7  T w ( °C )  13  150  160  Q (m3s−1)  190  200  dT/dt ( °C hr−1 )  vertical component advection component  03Aug  04Aug  05Aug  06Aug  Figure 3.26: Heat budget (top), discharge (center), and water temperature (bottom) from Aug. 3 to Aug. 6, 2010 at UL. Aug. 4 was consistently overcast while Aug. 3 and Aug. 5 were partly-cloudy.  59  predicted observed  −0.5  0.0  0.5  1.0  dQ/dx component dA/dt component dQ/dx+dA/dt components  100 90 11 9 7  T w ( °C )  13  70  80  Q (m3s−1)  110  120−1.0  dT/dt ( °C hr−1 )  vertical component advection component  05Sep  06Sep  07Sep  08Sep  Figure 3.27: Heat budget (top), discharge (center), and water temperature (bottom) for the partly cloudy-overcast period from Sept. 5 to Sept. 8, 2010 at UL.  60  Table 3.6: Heat budget model performance for given site and time period (month/day). MBE is mean bias error, RMSE is root mean squared error, NRMSE is RMSE normalized by the range of observed values and expressed as a percentage, and Em is the Nash-Sutcliffe model efficiency. site UL UL UL UL UL UL LL UL  dates 7/24-7/27 7/30-8/02 8/03-8/06 8/05-8/08 9/05-9/08 9/18-9/21 8/14-8/17 8/14-8/17  conditions clear clear to cloudy partly cloudy (landslide) mostly cloudy rain clear clear  MBE 0.0381 0.0690 0.0784 0.0863 -0.0284 0.0195 0.022 0.079  RMSE 0.096 0.111 0.110 0.195 0.157 0.096 0.053 0.150  NRMSE (%) 6.8 7.5 8.6 7.1 10.9 11.3 6.9 13.2  Em 0.961 0.926 0.892 0.695 0.673 0.600 0.876 0.833  cal component does not display a smooth arch such as it did in Figure 3.23 for clear conditions. Partly-cloudy conditions were associated with irregular patterns (spikes and dips) in the vertical component of the heat budget, as incident solar radiation fluctuated from the passing shade of clouds, (e.g., on August 1). During those partial-cloud periods, the advection component also displayed an irregular pattern, which contrasted to the smooth arch during clear conditions. The irregular advection pattern typically transitioned into a smooth arch the night following partly-cloudy daytime conditions (Figure 3.26). Similar to clear conditions, advection during partly-cloudy conditions was generally in phase with, and of greater magnitude than, the vertical component. Advective warming and cooling rates during partly-cloudy conditions had magnitudes similar to those during clear skies although, at times, advective warming rates actually reached higher values and advective cooling did not reach values as low as those seen during clear weather. The timing of the response of heat advection to cloud cover changes was inconsistent at times. An immediate response occurred on July 31, when clear conditions suddenly became overcast (Figure 3.25). Advection dropped simultaneously with the vertical term (it interestingly rebounded shortly after, despite the vertical term remaining low). A delayed response occurred on August 5, when a major dip in advection was not coincident  61  with a dip in the vertical component (Figure 3.26). The most recent dip in vertical heat exchange had occurred several hours prior. The heat budget model performed well in predicting these temperature responses, in spite of the apparent inconsistency in the timing relation between irregularities in the advection and vertical components. With increasing cloud cover, the vertical and advection components decreased. On September 6, the vertical component remained low during heavy overcast conditions (Figure 3.27). Advective warming was greatly subdued, and there were periods of several hours in which advection was negligible. There was still a considerable period of advective cooling, although shorter and lower magnitude than during clearer conditions, with similar onset timing in late evening, but ending in the early, rather than late, morning hours. This shortened advective cooling phase was associated with warmer absolute nighttime water temperatures (bottom panel of Figure 3.27). Thus, in general for a variety of conditions, the magnitudes of advective warming and cooling, and also the cooling phase timespan, related with the magnitude of the daytime vertical component. Similar to clear conditions, during partly-cloudy conditions, the advection term generally increased (decreased) while discharge decreased (increased) (Figures 3.25 and 3.26), but this association was not as apparent when cloud cover was heavy (Figure 3.27), and did not exist during the rain event (Figure 3.28. Overcast conditions were associated with a substantial decline in streamflow, displaying irregularities and a less well defined diurnal meltwater wave (center panel of Figure 3.27). With the vertical and advective components having low magnitudes, the relative influence from unsteady flow had more importance than during clearer conditions, noticeably during rapid flow changes within the hydrograph irregularities. However, the combined unsteady flow effect was still minor. Predicted temperature changes were generally less accurate with greater cloud cover (Table 3.6). The model performed well during partly-cloudy conditions (Em = 0.89), although less well than during clear conditions (Em = 0.96), despite rapid fluctuations in vertical and advective heat exchanges. It tended to over-predict more than during clear conditions, (MBE = 0.078, 0.038 °C/hr, respectively). Model performance was poorer in the afternoon and evening as flows increased than at other times, when flows were decreasing (Figure 3.26). Advection alone was often 62  greater than observed dT /dt while the other terms were near zero. Advection alone closed the heat budget over much of the night-time cooling phase (other terms were near zero); at other times, closure was more or less met by advection and vertical components. Predicting the irregularities in temperature changes was particularly inaccurate under heavy overcast conditions (Em = 0.67). Predictions tended to be, however, only slightly under-estimated on average, with MBE = -0.028 °C/hr. Although the patterns of the heat budget components varied with weather conditions, the advection component remained the dominant component throughout the conditions encountered. During partly-cloudy to light overcast conditions, advection was in-phase with the vertical term and out of phase with discharge, which was consistent with clear conditions. With heavy overcast conditions, advection displayed different phase timing and much lower magnitudes in both warming and cooling influences, even having several-hour periods of negligible effect. These results showed that the heat budget was quite sensitive to changes in atmospheric conditions, often responding in an irregular manner and at times in a manner that was difficult for the model to predict.  3.5.3  Precipitation event  A significant rain event of over 30 mm occured September 19 - 20, resulting in a two-fold discharge increase (Figure 3.28). Water temperature during the event was moderated compared to clear sky conditions, with less diurnal variation. There was a less well defined advection trough following the positive vertical flux on September 19 than on the previous overcast day, limiting cooling. During elevated flow on September 20, warming was much lower than usual. The advection term displayed an extremely sporadic pattern during elevated flow, often switching between having a warming or cooling influence, and advection alone nearly closed the heat budget. The unsteady flow terms reached much higher magnitudes (negative and positive) within the rising and falling limbs of the storm hydrograph than seen during the typical diurnal flow patterns of clearer weather. Model closure over the rain event was similar to the cloudy period, despite the storm flow (Em = 0.60), and predictions were slightly high (MBE = 0.02 °C/hr). The greater positive magnitude of the combined unsteady flow components within  63  predicted observed  −0.5  0.0  0.5  1.0  dQ/dx component dA/dt component dQ/dx+dA/dt components  140 120 11 9 7  T w ( °C )  13  80  100  Q (m3s−1)  160  180  −1.0  dT/dt ( °C hr−1 )  vertical component advection component  18Sep  19Sep  20Sep  21Sep  Figure 3.28: Heat budget (top), discharge (center), and water temperature (bottom) for Sept. 18 to Sept. 21, 2010 at UL. A 30 mm rain event occured Sept. 19 - 20.  64  3 1 0 −1 200 150 11 9 7  T w ( °C )  13  50  100  Q (m3s−1)  250  300 −3  −2  dT/dt ( °C hr−1 )  2  vertical component advection component dQ/dx component dA/dt component dQ/dx+dA/dt components predicted observed  05Aug  06Aug  07Aug  08Aug  Figure 3.29: Heat budget (top), discharge (center), and water temperature (bottom) for Aug. 5-8, 2010 at UL. An outburst flood occured on Aug. 7 from the release of a lake created from a landslide on Aug. 6 in a tributary catchment of Lillooet River.  the rising limb of the storm hydrograph created additional over-prediction (Figure 3.28).  65  3.5.4  Landslide event  August 5 showed a typical δ T /δt (top) and temperature (bottom) pattern for cloudy weather (Figure 3.29). Discharge declined sharply at 08:00 on August 6, several hours after a landslide dammed the upstream tributary of Meager Creek and partially dammed Lillooet River (Figure 3.29). The landslide dam on Meager Creek was breached early on August 7 and the flood water from the draining lake reached UL around 03:00, creating a discharge spike from 160 to 290 m3 /s in about 2 hours. Water temperature over the event was irregular (bottom plot). August 6 showed an irregular δ T /δt pattern similar to that observed during the September 19 - 20 rain event despite the sudden drop in discharge, with advection alone basically closing the heat budget. However, δ T /δt increased suddenly on August 7 to 1.92 °C/hr, over twice the maximum warming rate observed during clear-skies (0.74 °C/hr). This was precisely the same time that discharge surged. The magnitude of the unsteady flow terms increased drastically during the drop and spike in discharge, and their combined influence was of a similar magnitude to the vertical term. The spike in δ T /δt and discharge was short-lived. Both returned to typical cloudy-sky patterns within hours. The model provided reasonably good fits throughout this extreme event (Em = 0.70), better than during the September 19 - 20 rain event (Em = 0.60), and predictions tended to be high (MBE = 0.086 °C/hr). Advection alone did a reasonable job of closing the heat budget over this event. When the flood arrived on August 7, advection spiked to the highest values observed over the entire study period (2.46 °C/hr), although this slightly over-estimated the observed warming rate. When the flood receded, advection plummeted to the lowest value over the study period (1.04 °C/hr), which slightly under-estimated the observed cooling rate. The fit was relatively good and made only slightly poorer with the addition of the unsteady flow terms over the sudden temperature spike associated with advection from the lake water.  3.5.5  Spatial variation  Modelled heat budgets differed between UL and LL, as shown in Figure 3.30 during a mostly clear-sky period from August 14 - 17. The two sites are compared for  66  this period because LL did not have complete data for the July 24 - 27 clear-sky period. The fit at UL for August 14-17 was not as good as for July 24 - 27 in regard to magnitude during the warming phase; however, the cooling phase predictions were accurate and the predicted timing of warming/cooling phase shifts were similar to observed. In addition, relations in timing and magnitude between heat budget terms were similar to the clear-sky period for UL. Model performance was reasonably good at both sites: Em for August 14-17 at UL was 0.83 and at LL was 0.88 (Table 3.6). Warming and cooling rates reached considerably higher magnitudes and diurnal phase shifts occured earlier at UL than LL over this period. The observed maximum warming rate at UL was 78% higher than at LL (0.71 °C/hr and 0.40 °C/hr, respectively) while maximum cooling at UL was 13% higher than at LL (-0.42 °C/hr and -0.37 °C/hr, respectively). Warming began at UL each day near 09:30 and at LL near 11:30. Cooling began at UL each day near 19:00 and at LL near 23:30. Therefore, the duration of observed warming (and cooling) at LL was 12 hours and at UL was only 9.5 hours. The greater warming rates at UL compensated for the shorter warming phase and resulted in similar diurnal maximum temperature to LL. The cooling rates at UL were only slightly greater than at LL, but these rates, along with longer cooling phase duration at UL, resulted in lower diurnal minimum temperature than at LL. Vertical heat flux timing was nearly identical between the two sites, but the magnitude at LL was slightly greater than at UL, consistent with LL having less shade (gt ). The timing of heat advection, as well as magnitude, differed substantially between the sites. Advective warming began at UL near 09:30 each day, which was the same time as observed overall warming and slightly after the onset of positive vertical fluxes. At LL, advective warming began near 14:00 each day, about 5.5 hours after the onset of positive vertical heat flux and about 2.5 hours after observed warming began. Like at UL, advective cooling at LL began concurrently with the start of observed cooling after the vertical term declined. However, advective cooling at LL began 4.5 hours later than at UL. Thus, durations of advective warming at each site were about 9.5 hours and durations of advective cooling at each site were about 14.5 hours over this clear-sky period, but advection phase shift timing at LL lagged UL by about 4.5 hours. 67  dQ/dx component dA/dt component dQ/dx+dA/dt components  predicted observed  0.5 0.0 0.5 0.0 −1.0  −0.5  dT/dt ( °C hr−1 )  1.0  −1.0  −0.5  dT/dt ( °C hr−1 )  1.0  vertical component advection component  14Aug  15Aug  16Aug  17Aug  Figure 3.30: Heat budget for UL (top) and LL (bottom) during mostly clear skies from Aug. 14-17.  68  predicted observed  −0.5  0.0  0.5  1.0  dQ/dx component dA/dt component dQ/dx+dA/dt components  160 150 11 9 7  T w ( °C )  13  130  140  Q (m3s−1)  170  180  dT/dt ( °C hr−1 )  vertical component advection component  14Aug  15Aug  16Aug  17Aug  Figure 3.31: Heat budget (top), discharge (center), and water temperature (bottom) during mostly clear skies from Aug. 14-17 at UL.  69  predicted observed  −0.5  0.0  0.5  1.0  dQ/dx component dA/dt component dQ/dx+dA/dt components  270 260 11 9 7  T w ( °C )  13  250  Q (m3s−1)  280  −1.0  dT/dt ( °C hr−1 )  vertical component advection component  14Aug  15Aug  16Aug  17Aug  Figure 3.32: Heat budget (top), discharge (center), and water temperature (bottom) during mostly clear skies from Aug. 14-17 at LL.  70  Discharge had a mirror-like phase relation with advection at both sites (Figure 3.31 and 3.32): peak advection occurred within discharge troughs and minimum advection occured within discharge peaks. This was true despite the considerable difference in timing of advection variations between UL and LL, and further suggests a general relation between discharge and advection variability. At both sites, as discharge waned, advective heat flux increased, reaching its maximum at nearly the same time as the discharge minimum. As discharge increased, advective heat flux tended to decline or remain negative, reaching its lowest values near the time of maximum discharge. Peak diurnal discharge lagged peak vertical flux by about 12 hours at UL and 18 hours at LL. At UL, discharge peaked around 02:00 and was decreasing when vertical and advective warming began. At LL, high flows extended from about 05:00 to 12:00 – halfway through the vertical flux warming phase – and advective warming did not begin until flows began decreasing.  71  Chapter 4  Discussion This chapter discusses the results presented in the previous chapter in relation to the research objectives outlined in Chapter 1. It begins with the heat budget model and the roles of longitudinal heat advection and unsteady streamflow in governing temporal changes in temperature. Physical processes are discussed and inferences are made into the underlying causes of spatiotemporal stream temperature variability and the relation of the diurnal meltwater wave to heat advection. Then, tributary mixing and transverse mixing lengths are discussed with reference to the findings of other mixing studies. Inferences are made regarding potential physical processes governing the somewhat surprising relation found between relative discharge and transverse mixing lengths. Conclusions and suggestions for future research are presented in the next chapter.  4.1 4.1.1  Reach-scale heat budget considerations Longitudinal heat advection  A main objective of this study was to quantify the influence of longitudinal heat advection. Longitudinal heat advection was found to be the dominant control of stream temperature changes under all weather conditions. This was unexpected, given that Caissie et al. (2007) assumed longitudinal heat advection was negligible and other modelling studies did not specifically quantify it (Hockey et al., 1982;  72  Chaudhry et al., 1983; Sinokrot and Stefan, 1993; Meier et al., 2003; Chikita et al., 2009). While advection has been included in a number of numerical models, its influence has not specifically been quantified in the reach-scale heat budget using field observations. The results here demonstrate that longitudinal heat advection must be included in deterministic models. Previous studies for glacierized catchments have pointed to the cooling effects of glacial meltwater to help explain the fact that observed stream temperatures in glacier-fed streams tend to be lower than in streams without contributions from glacier runoff (Brown et al., 2005; Cadbury et al., 2008). Here, heat advection was found to have not only a cooling effect, but also an equally substantial warming effect. The cooling effect was expected, given previous findings of warmer water with downstream distance from the glacier terminus. Given these previous findings, the warming influence from advection, and especially the substantial magnitude, was surprising. The warming influence from advection found here may be in part a function of the distance of the stream reach from the glacier terminus. Most previous proglacial stream temperature research was conducted within a few kilometers of the glacier terminus, whereas the reaches of this study were over 50 km from the glacier. The additional travel time and exposure to vertical heat sources for the sites studied here, in combination with the diurnal fluctuations in streamflow, account for the observed magnitude and variations in longitudinal heat advection, as explained in more detail below. Under clear-sky conditions, advection warming/cooling phases were related to the falling/rising limbs of the diurnal discharge wave, respectively. This relation can be explained by changes in heat capacity within the diurnal meltwater wave. At UL, streamflow was in a state of decline from approximately 03:00 to 18:00 (Figure 3.31). When discharge decreases through time at a given location, discharge must be lower at a point upstream. When positive vertical heat flux became available near 09:00, the lower heat capacity upstream, due to lower water volume, allowed greater warming and higher temperature than at the downstream boundary. Thus at UL, positive heat advection commenced at a similar time as positive vertical heat flux (there was a slight lag) with the key requirement that discharge was in a decreasing phase. The onset of advective warming at LL did not occur until discharge began decreasing at 13:00 (Figure 3.32), which strongly suggests a cause 73  and effect relation. Hence, advective warming commenced at both UL and LL when two conditions apparently allowed it: (1) discharge was declining while at the same time (2) there was positive vertical heat exchange. The timing of the cooling phase of advection was also related to discharge at both reaches. At each reach, advective cooling began shortly after discharge began increasing. This lag time was similar at each reach (about 2 hours) and may be an artefact of the complex relations between thermal history and travel time within the system, or perhaps simply due to the thermal ”memory” associated with water’s high heat capacity. Advective cooling during increasing flow can be explained by spatially varying thermal capacities similar, but opposite, to advective warming. With increasing flow, heat capacity was greater upstream and temperature response to earlier vertical heating was lower than downstream. The cooler upstream temperature thus made and advective cooling effect. The relation of advection to discharge (explained above) was supported by the consistency of the relation between both reaches, despite differences between the two reaches in timing relations between advection, vertical heat flux, and discharge phases. Longitudinal heat advection patterns in a non-glacial stream were markedly different than Lillooet River. Fishtrap Creek is a non-glacial stream in the interior of British Columbia and was analyzed for clear weather in August, for which streamflow was approaching steady-state conditions (Leach, 2012). Advection was minimal at night and became negative (a cooling influence) during parts of the daytime, with magnitudes of only about half that of the vertical term. There was no significant warming effect from advection, as opposed to Lillooet River. In addition, the advective cooling phase at Lillooet River occurred largely at night and displayed a more consistent, arch-shaped pattern, and advection magnitudes of warming and cooling phases were typically twice that of the vertical component. With streamflow variability being a key difference between these streams in August, the notion that the advection patterns found in Lillooet River are mainly due to diurnal discharge variability is supported by the different advection patterns between these streams.  74  4.1.2  Unsteady flow effects  The stream temperature response to the effects of the combined unsteady flow components were relatively minor in contrast to the other terms of the energy balance 3.23. The unsteady flow terms were dependent on the rate of discharge change. At UL, streamflow typically increased more rapidly than it decreased, and the unsteady flow effect was relatively greater with the arrival of the meltwater wave than during decreasing flow. However, even during increasing flow the effects were relatively negligible in contrast to advection and the vertical term. At times of rapid streamflow change, such as with irregular meltwater generation associated with variable cloud cover, the heavy rain event, and the dam breach associated with the landslide event, the combined unsteady components were of the same order of magnitude as the other heat budget components (vertical and advective fluxes).  4.1.3  Surface energy exchanges  Characterizing reach-scale net radiation is a challenge in energy balance studies and important to estimate accurately, as it is typically the dominant component of the vertical energy exchanges. Here, a simple geometric relation between solar position and average stream reach characteristics, such as geographical orientation, riparian canopy height and occurrence, and channel geometry, was used to determine the amount of shade casted upon the stream surface at each time step. This approach apparently worked well during clear conditions, according to the good heat budget model performance. Stream surface albedo was found to vary between the Lillooet River and its tributaries as a function of suspended sediment concentration (SSC) and also with solar zenith angle. The measured albedos were approximately double the values of 0.03 to 0.05 that are often assumed in modelling studies (Caissie et al., 2007; Benyahya et al., 2011) or have been measured over low-turbidity streams (Evans et al., 1998; Leach and Moore, 2010), but are consistent with the values reported by Chikita et al. (2009) for a highly turbid proglacial river in Alaska. The values are also similar to those reported by Richards and Moore (2011) for a proglacial stream at lower flows, when aeration was relatively low. These results suggest that stream temperature models applied to proglacial rivers should use albedos that are  75  appropriate for turbid water.  4.2  Transverse mixing  There was considerable variability found in transverse mixing lengths (Lz ). The ˆ ) in multiples of channel width was from 49 range of complete mixing lengths (Lz98 to 105, with a mean of 69. This mean was lower than the 100 to 300 channel widths that have been previously reported (Rutherford, 1994). Although the studied reach of Lillooet River mostly had gentle meanders, there were some sharper bends, which could explain the relatively more rapid mixing. However, some studies have found much shorter mixing lengths (e.g. Day, 1977; Lane et al., 2008). The variability in mixing lengths observed in this study was partially explained by the influence of the discharge ratio between the tributary and mainstem (Qr ). Previous studies have found conflicting relations between Lz and flow, both total and relative tributary flow. Lane et al. (2008) found Lz was lower during higher Qr , but Gaudet and Roy (1995) found no relation between Lz and Qr . This study found Lz to be positively related to Qr . This relation was somewhat unexpected. It is well established that faster transverse mixing rates (shorter Lz ) result from tracer being input further toward the center of the receiving channel’s width (Rutherford, 1994). For the case of increasing Qr , the higher flow of the tributary would carry greater momentum, forcing tributary water further out into the main channel and essentially making the initial mixing location (analogous to the tracer input location) further toward the center of the channel. Rutherford’s model, however, was not developed specifically for river confluences and may not represent the effects of mixing dynamics occurring at river junctions. The positive Lz - Qr relation may be in part explained by flow mechanisms occurring at the confluence. In a flume experiment of confluent channels, Mosley (1976) found that sediment from each channel was separately transported downstream in the merged channel. This was caused by streamflow separation of water from the two channels, which was maintained by the action of two helical flow cells, one from each channel, which rotated in opposite directions. The strength of the two opposing helical flow cells was greatest when Qr was nearest unity, and at  76  low or high Qr the flow cells did not form. It could be inferred that flow separation caused by opposing helical flow cells would limit transverse mixing rates. It was not determined how far downstream the helical flow cells persisted. Such opposing helical flow cells, if they do in fact have a considerable downstream persistence, could help explain the relationship observed in this study of longer Lz with higher Qr . The absence of these flow cells in tracer experiments could explain the apparent inconsistency (explained above) that tracer mixing was more rapid when put in closer to the center-width. The existence and persistence of near- field flow mechanisms at natural river junctions, such as opposing helical flow cells, and impacts on local and downstream transverse mixing rates needs further attention.  77  Chapter 5  Conclusions This chapter summarizes the key findings in relation to the research objectives and provides recommendations for future research.  5.1  Key findings  A main objective of this study was to quantify the influences of longitudinal heat advection and unsteady flow on stream temperature changes. Longitudinal heat advection was the dominant stream temperature control under all weather conditions. This was unexpected, given it has been assumed negligible (Caissie et al., 2007) and has not been specifically quantified in other modeling studies (Hockey et al., 1982; Chaudhry et al., 1983; Sinokrot and Stefan, 1993; Meier et al., 2003; Chikita et al., 2009). Given previous findings of cooler water upstream in glacialfed streams (Cadbury et al., 2008; Brown et al., 2005), the cooling effect from longitudinal heat advection was expected; however, it was surprising that the warming influence was equally important in both magnitude and duration. The timing of cooling/warming advective phases was explained by timing relations between longitudinal temperature gradient shifts and the passage of the diurnal meltwater wave. This explanation was supported by the fact that advective flux patterns in a steadyflow, non-glacial stream are markedly different from those in Lillooet River. These findings demonstrate that longitudinal heat advection must be included in deterministic models for glacier-fed streams where unsteady flow conditions dominate.  78  The influences of the individual heat budget terms representing unsteady flow conditions were considerable. However, their combined effect was mostly negligible, with the exception of periods in which discharge changed rapidly, such as during the rain and landslide events. At times, variable cloud cover caused rapid flow changes which made the combined effect of the unsteady flow terms a similar magnitude to vertical or advective fluxes. The thermal effects of unsteady flow should be considered in modelling studies in which flow changes are rapid, such as the case of hydro-peaking releases from dams (Toffolon et al., 2010). Solar radiation dominated vertical heat fluxes during clear weather conditions. Field measurements demonstrated that albedo depends on both solar zenith angle and suspended sediment concentration. Albedo values were generally in the range 0.08 to 0.1, similar to values observed at other turbid glacier-fed streams (Chikita et al., 2009; Richards and Moore, 2011) and approximately double those measured over low-turbidity streams (Evans et al., 1998; Leach and Moore, 2010). This study confirms that a surface albedo of 0.03 to 0.05, which is typically assumed in many previous studies (e.g. Caissie et al., 2007; Benyahya et al., 2011; Magnusson et al., 2012) is inappropriate for turbid proglacial streams. Transverse mixing length (Lz ) at the confluence showed considerable variability. The tributary to mainstem discharge ratio (Qr ) was positively related to Lz and explained approximately half of the variation. This result disagrees with previous studies that found more rapid transverse mixing with higher Qr (Biron et al., 2004; Lane et al., 2008) and no relation between Lz and Qr (Gaudet and Roy, 1995). This also contrasts with tracer studies which have found longer Lz with tracer input closer to the bank (Rutherford, 1994). Higher Qr , which is associated with longer Lz , would force the tributary water further from the mainstem bank. These apparent inconsistencies are not necessarily surprising, given the multitude of factors and processes involved in mixing at and downstream of natural river confluences. The well-documented opposing helical flow cells, which can form at confluences and limit transverse mixing by separating the flows from each channel, could help explain the positive Qr - Lz relationship found in this study, as these structures strengthen with increasing Qr approaching unity (Mosley, 1976; Best, 1988). Below-confluence (total) discharge had no significant relation to Lz , which is inconsistent with previous studies that found more rapid mixing with lower total 79  discharge (Gaudet and Roy, 1995; Biron et al., 2004) and with higher total discharge (Chu and Babarutsi, 1988).  5.2  Future research recommendations  Given the importance of stream albedo in controlling the absorption of solar radiation, a study should be conducted to measure albedo for a broader range of sky conditions, solar zenith angles and suspended sediment concentrations. The results of such a study could be used to develop an improved parameterization of stream surface albedo to be incorporated into physically based models. This study illustrated the importance of including longitudinal heat advection, in addition to vertical heat flux, in process-based temperature models for glacierfed streams. The diurnal phase relations between vertical flux, advective flux, and streamflow shown here were for two reaches over 50 km from the glacier margin and may not represent the patterns elsewhere along the river. Future work should investigate these phase relationships in a more spatially distributed sequence of study reaches downstream of the glacier margin. The phase timing relation between meltwater flux and advective heat flux was similar at both reaches. Considering that the absolute times differed between the sites, there would appear to be a causative effect of the passage of the meltwater wave on heat advection. Such inferred processes can be supported if similar patterns are found in other catchments. Therefore, similar work should be conducted in other glacier-fed streams. The influence of longitudinal heat advection should be investigated for other hydrological regimes as well. It would be useful to combine field investigations with numerical modelling. This study suggests that, with further climatic warming, glacier retreat, and streamflow decline, longitudinal heat advection (cooling and warming phases) should decline in magnitude due to lower diurnal discharge (heat capacity) variability. Stream temperature responses to climate change should be addressed by coupling the stream heat budget with models representing the additional process linkages between climate, glacier mass balance, glacier retreat, and meltwater generation. The positive relation found between relative tributary flow and transverse mixing distance needs to be confirmed with further experiments in natural and labo-  80  ratory confluences. The underlying processes controlling transverse mixing, and their variation with discharge, need further investigation. The role of near-field flow structures, such as opposing helical flow cells, on transverse mixing dynamics is an area for further research. This would be best-approached in a laboratory setting to isolate the effect of flow structures, and their evolution with relative discharge, from the many other potential factors encountered in natural channels.  81  Bibliography Allen, R., Pereira, L., Raes, D., Smith, M., et al. 1998. Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. FAO, Rome, 300:6541. Benyahya, L., Caissie, D., Satish, M., and El-Jabi, N. 2011. Long-wave radiation and heat flux estimates within a small tributary in Catamaran Brook (New Brunswick, Canada). Hydrological Processes, 26(4):475–484. Berman, C. and Quinn, T. 1991. Behavioural thermoregulation and homing by spring chinook salmon, Oncorhynchus tshawytscha (Walbaum), in the Yakima River. Journal of Fish Biology, 39(3):301–312. Beschta, R. 1997. Riparian shade and stream temperature: an alternative perspective. Rangelands, 19(2):25–28. Best, J. 1988. Sediment transport and bed morphology at river channel confluences. Sedimentology, 35(3):481–498. Biron, P., Han, S., et al. 2004. Three-dimensional numerical modeling of mixing at river confluences. Journal of Hydraulic Engineering, 130:243. Boxall, J. and Guymer, I. 2003. Analysis and prediction of transverse mixing coefficients in natural channels. Journal of Hydraulic Engineering, 129:129. Brown, G. 1969. Predicting temperatures of small streams. Water Resources Research, 5(1):68–75. Brown, L., Hannah, D., and Milner, A. 2003. Alpine stream habitat classification: an alternative approach incorporating the role of dynamic water source contributions. Arctic, Antarctic, and Alpine Research, 35(3):313–322. Brown, L., Hannah, D., and Milner, A. 2005. Spatial and temporal water column and streambed temperature dynamics within an alpine catchment: implications for benthic communities. Hydrological Processes, 19(8):1585–1610. 82  Brunt, D. 1952. Physical and dynamical meteorology. Cambridge University Press. Burgner, R. 1991. Life history of sockeye salmon (Oncorhynchus nerka). Pacific salmon life histories, pages 3–117. Burkholder, B., Grant, G., Haggerty, R., Khangaonkar, T., and Wampler, P. 2008. Influence of hyporheic flow and geomorphology on temperature of a large, gravel-bed river, Clackamas River, Oregon, USA. Hydrological Processes, 22(7):941–953. Cadbury, S., Hannah, D., Milner, A., Pearson, C., and Brown, L. 2008. Stream temperature dynamics within a New Zealand glacierized river basin. River Research and Applications, 24(1):68–89. Caissie, D. 2006. The thermal regime of rivers: a review. Freshwater Biology, 51(8):1389–1406. Caissie, D., Satish, M., and El-Jabi, N. 2007. Predicting water temperatures using a deterministic model: Application on Miramichi River catchments (New Brunswick, Canada). Journal of Hydrology, 336(3):303–315. Chaudhry, M., Cass, D., and Edinger, J. 1983. Modeling of unsteady-flow water temperatures. Journal of Hydraulic Engineering, 109:657–669. Chikita, K., Kaminaga, R., Kudo, I., Wada, T., and Kim, Y. 2009. Parameters determining water temperature of a proglacial stream: the Phelan Creek and the Gulkana Glacier, Alaska. River Research and Applications, 26(8):995–1004. Chu, V. and Babarutsi, S. 1988. Confinement and bed-friction effects in shallow turbulent mixing layers. Journal of Hydraulic Engineering, 114:1257. Coutant, C. 1977. Compilation of temperature preference data. Journal of the Fisheries Board of Canada, 34(5):739–745. Day, T. 1977. Observed mixing lengths in mountain streams. Journal of Hydrology, 35(1-2):125–136. Desloges, J. and Church, M. 1987. Channel and floodplain facies of a wandering gravel bed river. In: Recent developments in fluvial sedimentology. Society of Economic Paleontologists and Mineralogists, vol. 39. Dingman, S. 2002. Physical Hydrology, 2nd Edition, volume 575. Prentice Hall Upper Saddle River, New Jersey, USA. 83  Eaton, J. and Scheller, R. 1996. Effects of climate warming on fish thermal habitat in streams of the United States. Limnology and Oceanography, pages 1109–1115. Ebersole, J., Liss, W., and Frissell, C. 2003. Cold water patches in warm streams: physicochemical characteristics and the influence of shading. Journal of the American Water Resources Association, 39(2):355–368. Erbs, D., Klein, S., and Duffie, J. 1982. Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation. Solar Energy, 28(4):293–302. Evans, E., McGregor, G., and Petts, G. 1998. River energy budgets with special reference to river bed processes. Hydrological Processes, 12(4):575–595. Fischer, H. 1979. Mixing in inland and coastal waters. Academic Press Inc. San Diego, California. Fleming, S. 2005. Comparative analysis of glacial and nival streamflow regimes with implications for lotic habitat quantity and fish species richness. River Research and Applications, 21(4):363–379. Fleming, S. and Clarke, G. 2003. Glacial control of water resource and related environmental responses to climatic warming: empirical analysis using historical streamflow data from northwestern Canada. Canadian Water Resources Journal, 28(1):69–86. Fountain, A. 1996. Effect of snow and firn hydrology on the physical and chemical characteristics of glacial runoff. Hydrological Processes, 10(4):509–521. Frazer, G., Canham, C., and Lertzman, K. 1999. Gap Light Analyzer (GLA): Imaging software to extract canopy structure and gap light transmission indices from true-colour fisheye photographs, users manual and program documentation. Friele, P., Clague, J., Simpson, K., and Stasiuk, M. 2005. Impact of a Quaternary volcano on Holocene sedimentation in Lillooet River valley, British Columbia. Sedimentary Geology, 176(3):305–322. Gaudet, J. and Roy, A. 1995. Effect of bed morphology on flow mixing length at river confluences. Nature, 373:138–139.  84  Gooseff, M., Strzepek, K., and Chapra, S. 2005. Modeling the potential effects of climate change on water temperature downstream of a shallow reservoir, lower Madison River, MT. Climatic Change, 68(3):331–353. Gu, R. and Li, Y. 2002. River temperature sensitivity to hydraulic and meteorological parameters. Journal of Environmental Management, 66(1):43–56. Gu, R., Montgomery, S., and Al Austin, T. 1998. Quantifying the effects of stream discharge on summer river temperature. Hydrological Sciences Journal, 43(6):885–904. Han, L. 1997. Spectral reflectance with varying suspended sediment concentrations in clear and algae-laden waters. Photogrammetric Engineering and Remote Sensing, 63(6):701–705. Hannah, D., Brown, L., Milner, A., Gurnell, A., McGregor, G., Petts, G., Smith, B., and Snook, D. 2007. Integrating climate–hydrology–ecology for alpine river systems. Aquatic Conservation: Marine and Freshwater Ecosystems, 17(6):636–656. Hannah, D., Malcolm, I., Soulsby, C., and Youngson, A. 2004. Heat exchanges and temperatures within a salmon spawning stream in the Cairngorms, Scotland: seasonal and sub-seasonal dynamics. River Research and Applications, 20(6):635–652. Hannah, D., Malcolm, I., Soulsby, C., and Youngson, A. 2008. A comparison of forest and moorland stream microclimate, heat exchanges and thermal dynamics. Hydrological processes, 22(7):919–940. Henderson, F. 1966. Open Channel Flow. Macmillan, New York. Hockey, J., Owens, I., and Tapper, N. 1982. Empirical and theoretical models to isolate the effect of discharge on summer water temperatures in the hurunui river. Journal of Hydrology (New Zealand), 21(1):1–12. Jin, Z., Charlock, T., Smith Jr, W., and Rutledge, K. 2004. A parameterization of ocean surface albedo. Geophys. Res. Lett, 31(22):L22301. Johnson, S. 2003. Stream temperature: scaling of observations and issues for modelling. Hydrological Processes, 17(2):497–499. Kaya, C., Kaeding, L., and Burkhalter, D. 1977. Use of a cold-water refuge by rainbow and brown trout in a geothermally heated stream. The Progressive fish-culturist, 39(1):37–39. 85  Kipp and Zonen 2009. Instruction Sheet - CGR3 Pyrgeometer. Lane, S., Parsons, D., Best, J., Orfeo, O., Kostaschuk, R., and Hardy, R. 2008. Causes of rapid mixing at a junction of two large rivers: R´ıo Paran´a and R´ıo Paraguay, Argentina. Journal of Geophysical Research, 113. Leach, J. 2012. personal communication. Leach, J. and Moore, R. 2010. Above-stream microclimate and stream surface energy exchanges in a wildfire-disturbed riparian zone. Hydrological Processes, 24(17):2369–2381. Lee, R. and Rinne, J. 1980. Critical thermal maxima of five trout species in the southwestern United States. Transactions of the American Fisheries Society, 109(6):632–635. Mackay, J. 1972. Application of water temperatures to the problem of lateral mixing in the Great Bear-Mackenzie river system. Canadian Journal of Earth Sciences, 9(7):913–917. Magnusson, J., Jonas, T., and Kirchner, J. 2012. Temperature dynamics of a proglacial stream: Identifying dominant energy balance components and inferring spatially integrated hydraulic geometry. Water Resources Research, 48(6):W06510. Malard, F., Mangin, A., Uehlinger, U., and Ward, J. 2001. Thermal heterogeneity in the hyporheic zone of a glacial floodplain. Canadian Journal of Fisheries and Aquatic Sciences, 58(7):1319–1335. Mathews, W. and Pratt, J. 1986. Physiographic map of the Canadian Cordillera. Geological Survey of Canada, Department of Energy, Mines, and Resources. Meier, W., Bonjour, C., W¨uest, A., and Reichert, P. 2003. Modeling the effect of water diversion on the temperature of mountain streams. Journal of Environmental Engineering, 129. Meisner, J., Rosenfeld, J., and Regier, H. 1988. The role of groundwater in the impact of climate warming on stream salmonines. Fisheries, 13(3):2–8. Milner, A., Brittain, J., Castella, E., and Petts, G. 2001. Trends of macroinvertebrate community structure in glacier-fed rivers in relation to environmental conditions: a synthesis. Freshwater Biology, 46(12):1833–1847. Milner, A., Brown, L., and Hannah, D. 2009. Hydroecological response of river systems to shrinking glaciers. Hydrological Processes, 23(1):62–77. 86  Milner, A. and Petts, G. 1994. Glacial rivers: physical habitat and ecology. Freshwater Biology, 32(2):295–307. Mohseni, O. and Stefan, H. 1999. Stream temperature/air temperature relationship: a physical interpretation. Journal of Hydrology, 218(3-4):128–141. Mohseni, O., Stefan, H., and Eaton, J. 2003. Global warming and potential changes in fish habitat in US streams. Climatic Change, 59(3):389–409. Moore, R. 2006. Stream temperature patterns in British Columbia, Canada, based on routine spot measurements. Canadian Water Resources Journal, 31(1):41–56. Moore, R. and Demuth, M. 2001. Mass balance and streamflow variability at Place Glacier, Canada, in relation to recent climate fluctuations. Hydrological Processes, 15(18):3473–3486. Moore, R., Fleming, S., Menounos, B., Wheate, R., Fountain, A., Stahl, K., Holm, K., and Jakob, M. 2009. Glacier change in western north america: influences on hydrology, geomorphic hazards and water quality. Hydrological Processes, 23(1):42–61. Moore, R., Spittlehouse, D., and Story, A. 2005a. Riparian microclimate and stream temperature response to forest harvesting: a review. JAWRA Journal of the American Water Resources Association, 41(4):813–834. Moore, R., Sutherland, P., Gomi, T., and Dhakal, A. 2005b. Thermal regime of a headwater stream within a clear-cut, coastal british columbia, canada. Hydrological Processes, 19(13):2591–2608. Morin, G. and Couillard, D. 1990. Predicting river temperatures with a hydrological model. Encyclopedia of Fluid Mechanics: Surface and groundwater flow phenomena, 10:171–209. Mosley, M. 1976. An experimental study of channel confluences. Journal Of Geology, pages 535–562. Nelitz, M., MacIsaac, E., and Peterman, R. 2007. A science-based approach for identifying temperature-sensitive streams for rainbow trout. North American Journal of Fisheries Management, 27(2):405–424. Nunez, M., Davies, J., and Robinson, P. 1972. Surface albedo at a tower site in lake ontario. Boundary-Layer Meteorology, 3(1):77–86. 87  Oke, T. 1987. Boundary Layer Climates, 2nd Edition. Methuen and Co. Ltd., London. Osborn, G. and Luckman, B. 1988. Holocene glacier fluctuations in the Canadian Cordillera (Alberta and British Columbia). Quaternary Science Reviews, 7(2):115–128. Payne, R. 1972. Albedo of the sea surface. Journal of Atmospheric Sciences, 29:959–970. Poole, G. and Berman, C. 2001. An ecological perspective on in-stream temperature: natural heat dynamics and mechanisms of human-causedthermal degradation. Environmental Management, 27(6):787–802. Prent, M. and Hickin, E. 2001. Annual regime of bedforms, roughness and flow resistance, lillooet river, british columbia, bc. Geomorphology, 41(4):369–390. Rathbun, R. and Rostad, C. 2004. Lateral mixing in the Mississippi River below the confluence with the Ohio River. Water Resources Research, 40(5). Rhoads, B. and Kenworthy, S. 1995. Flow structure at an asymmetrical stream confluence. Geomorphology, 11(4):273–293. Richards, J. and Moore, R. 2011. Discharge dependence of stream albedo in a steep proglacial channel. Hydrological Processes. Rutherford, J. 1994. River Mixing. John Wiley and Sons Ltd. Chichester, England. Sidle, R. and Milner, A. 1989. Stream development in Glacier Bay National Park, Alaska, USA. Arctic and Alpine Research, pages 350–363. Sinokrot, B. and Stefan, H. 1993. Stream temperature dynamics: Measurements and modeling. Water Resources Research, 29:2299–2312. Smith, B., Hannah, D., Gurnell, A., and Petts, G. 2001. A hydrogeomorphological context for ecological research on alpine glacial rivers. Freshwater Biology, 46(12):1579–1596. Smith, K. and Lavis, M. 1975. Environmental influences on the temperature of a small upland stream. Oikos, pages 228–236. Stahl, K. and Moore, R. 2006. Influence of watershed glacier coverage on summer streamflow in British Columbia, Canada. Water Resources Research, 42(W06201):1–5. 88  Story, A., Moore, R., and Macdonald, J. 2003. Stream temperatures in two shaded reaches below cutblocks and logging roads: downstream cooling linked to subsurface hydrology. Canadian Journal of Forest Research, 33(8):1383–1396. Thomas, R., Gharrett, J., Carls, M., Rice, S., Moles, A., and Korn, S. 1986. Effects of fluctuating temperature on mortality, stress, and energy reserves of juvenile coho salmon. Transactions of the American Fisheries Society, 115(1):52–59. Toffolon, M., Siviglia, A., and Zolezzi, G. 2010. Thermal wave dynamics in rivers affected by hydropeaking. Water Resources Research, 46(8):W08536. Torgersen, C., Price, D., Li, H., and McIntosh, B. 1999. Multiscale thermal refugia and stream habitat associations of chinook salmon in northeastern Oregon. Ecological Applications, 9(1):301–319. Uehlinger, U., Malard, F., and Ward, J. 2003. Thermal patterns in the surface waters of a glacial river corridor (Val Roseg, Switzerland). Freshwater Biology, 48(2):284–300. Webb, B. and Zhang, Y. 1997a. Spatial and seasonal variability in the components of the river heat budget. Hydrological Processes, 11(1):79–101. Webb, B. and Zhang, Y. 1997b. Spatial and seasonal variability in the components of the river heat budget. Hydrological Processes, 11(1):79–101. Webb, B. and Zhang, Y. 1999. Water temperatures and heat budgets in Dorset chalk water courses. Hydrological Processes, 13(3):309–321. Whitlock, C., Bartlett, D., and Gurganus, E. 1982. Sea foam reflectance and influence on optimum wavelength for remote sensing of ocean aerosols. Geophysical Research Letters, 9(6):719–722.  89  Appendix A  Supporting methods A.0.1  Shade function, gt  The fraction of the stream reach surface not being shaded from direct solar radiation by riparian vegetation and topography is represented by gt , which is a function of time t, stream width, stream orientation and riparian canopy height and overhang (li2012). To simplify calculations, the reach was treated as a straight symmetrical corridor of infinite length with undercut vertical walls representing riparian vegetation that overhangs the stream. Parameters used in calculating gt which were variable for each reach were reach-averaged plan-view channel orientation, channel width, and longitudinal occurrence of vegetation on each bank. Parameters used in calculating gt which were assumed constant over all reaches were vegetation height, lateral extent of vegetation overhanging the stream, and height from stream surface to vegetation overhang. Where present, riparian vegetation was assumed to be opaque to solar radiation. The shading potential of the banks was considered separately from that of the riparian vegetation. For the bank on the side in which the solar azimuth comes from, the length of shade extending on the stream surface along the line of solar azimuth from the vegetation edge (not the bank) was sazi = Y f / tan β  90  (A.1)  where Y f is height of foliage above stream surface and β is solar angle (angle from ground to sun). The length of shade from the bank and perpendicular to the bank was s = sazi (cos ω) + z f  (A.2)  where ω is the acute plan-view angle between the solar azimuth line and the crosssectional line, z f is the additional lateral length of shade from foliage overhanging the stream. Since the corridor is straight and y f is constant, s is the same along the bank and solving gt can be simplified to a one-dimensional approach across the channel. The percent longitudinal occurence of riparian vegetation was estimated as Pf =  1 l  n  ∑ xf  (A.3)  i=0  where n is the number tree stands along the bank, x f is the longitudinal length of a stand, and l is reach length, can then be used as a coefficient for Eq. A.2 so that s¯ = Pf [ sazi (cos ω) + z f ]  (A.4)  where s¯ is reach-averaged perpendicular length of shade from the bank on the shady side of the stream. Pf is unique for each bank and is selected based on solar position. For the side of the stream opposite the solar azimuth direction, stream surface shade would only stem from overhanging vegetation. The calculation of the shade length is similar to that of the shady side, except the length of sun (not shade) is first found, which is subtracted from the overhang distance. The length of shade under the overhang (s2 ), on the stream surface, perpendicular to the bank, and compensated for the reach by Pf is s¯2 = Pf [z f − (y f / tan β · cos ω)]  (A.5)  where y f is the vertical distance between the stream surface and overhanging vegetation.  91  The average riparian canopy gap function over a reach is then gt = (w¯ − s¯ − s¯2 )/w¯  (A.6)  where w¯ is reach-averaged channel width.  A.0.2  Sky view factor, fsky  Calculation of sky view-factor fsky was based on the same assumptions as used to compute the canopy gap fraction. However, directionality in respect to solar position is not relevant for calculating fsky , which can be treated as a constant for each reach over the study period. The longitudinal structure of a reach was simplified to two cases: (1) trees on both banks and (2) no trees on either bank. Case 1: Trees on both banks The riparian corridor is again assumed infinitely long and symmetrical, with opaque vertical walls of trees on either bank which overhang the stream. With longitudinal uniformity in Case 1, the problem can be approached from a cross-sectional view broken into three segments: (i) under the left bank overhanging vegetation, (ii) open sky, and (iii) under the right bank overhanging vegetation. For symmetrical corridors, the sky view factors for segment (i) and segment (iii) are identical. Segment i or iii: under overhang For any z location across the stream under the overhang, the sky view factor φz is φz = cos β1 − cos β2  (A.7)  where β1 and β2 are the angles from z to the edge of the nearby overhang and the top edge of the far wall, respectively. The sky view factor φz can be integrated across segment (i) to calculate the segment’s average sky view factor φˆi : φ¯i =  1 c − zo  c zo  (cos β1 − cos β2 ) dz  Eq. A.8 is solved as  92  (A.8)  1 φ¯i = c  [(d − zo )2 + h2 ]1/2 − [(d − c)2 + h2 ]1/2 −[(c − zo )2 + y2 ]1/2 + y  (A.9)  where c is the lateral position of riparian overhang (the near corridor wall), d is lateral position to far corridor wall, h is corridor wall height above the stream surface, y is overhang height above the stream surface, and zo is the lateral length where β1 = β2 , calculated as zo =  (h · c) − (y · d) h−y  (A.10)  For zo < 0, which is typical for wide channels, zo can be dropped from Eq. A.8. Segment ii: between corridor walls For any z location across the stream between the overhanging vegetation on either bank, the sky view factor φx12 is φx12 = 0.5 (cos θ1 + cos θ2 )  (A.11)  where θ1 and θ2 are the angles from z to the top edge of either corridor wall. The sky view factor φx12 can be integrated across section (2) to calculate the the segment’s average sky view factor φ1¯ 2: d  φ12 =  1 d −c  φ12 =  1 [ (d − c)2 + h2 ]1/2 − h d −c  c  0.5(cos θ1 + cos θ2 ) dz  (A.12)  Eq. A.12 is solved as (A.13)  Segments 1 and 2 for Case 1 were combined over the average channel width as φ1 =  2(c − b) φ11 + (d − c) φ12 2(c − b) + d − c 93  (A.14)  Case 2: No vegetation on either bank The view factor for Case 2 (φ2 ) was calculated using the same form as Eq. A.13 for the open segment of Case 1 but substituting channel width for (d − c) and bank height for h. Case 1 and 2 Finally, the overall average view factor for a reach ( fv ) was found by combining Case 1 and Case 2 according to the tree presence along each bank of the reach: fv = (Pf ) φ1 + (1 − Pf ) φ2  (A.15)  where Pf is the average longitudinal tree presence of both banks. View factors vary with seasonal vegetation structure. View factors were assumed constant through the study period since vegetation changes were negligible until late October.  94  

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