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Influence of turbidity and aeration on the albedo of mountain streams McMahon, Alexander D. 2016

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Influence of turbidity and aeration on the albedo ofmountain streamsbyAlexander D. McMahonB.Sc., Geography, Appalachian State University, 2014a thesis submitted in partial fulfillmentof the requirements for the degree ofMaster of Scienceinthe faculty of graduate and postdoctoral studies(Geography)The University of British Columbia(Vancouver)August 2016c© Alexander D. McMahon, 2016AbstractStream surface albedo plays a key role in the energy balance of rivers and streams thatare exposed to direct solar radiation. Most physically based models assume that streamalbedo lies between 0.03 and 0.10, based primarily on measurements from low-gradientstreams with low suspended sediment concentrations. Albedo should depend upon solarelevation angle, suspended sediment, aeration, and fraction of direct vs diffuse radiation.However, there is no model available for predicting the dependence of albedo on thesefactors. This study quantified the dependence of albedo of mountain streams on thecontrolling factors in order to improve the representation of albedo in energy balancestudies. Proxy measures for albedo using digital camera imagery were also developedand assessed.Stream surface albedo was measured at nine sites with a variety of gradients and sus-pended sediment characteristics in the southern Coast Mountains of British Columbia,Canada. As expected, albedo of low-gradient, non-whitewater (flatwater) streams in-creased with solar zenith angle, suspended sediment concentration, and proportion ofdiffuse to direct solar radiation, ranging between 0.025 during cloudy periods in clearwater to 0.25 for turbid water at zenith angles of less than 20 degrees. Albedo variedwith discharge in steep reaches or at channel steps and cascades where flow was visiblyaerated, with a range of 0.09 to 0.33. In clear weather, albedo exhibited notable di-urnal variability at flatwater sampling sites. For example, during late summer, surfacealbedo typically fluctuated between 0.08 and 0.15 on a diurnal basis at a flatwater site onthe highly turbid, glacier-fed Lillooet River. Physically based representations of albedoshould be incorporated into energy balance models in order to improve predictions ofstream temperature, especially for future scenarios.iiPrefaceThis thesis is original work completed by the author. Guidance was given by the super-visory committee: Dan Moore, Brett Eaton, and Ian McKendry. A version of this workhas been delivered as a presentation (McMahon, A. & Moore, R.D., Influence of turbidityand aeration on the albedo of mountain streams) on which the author acted as the leadinvestigator, composing and delivering the presentation at the 2016 Canadian Meteoro-logical and Oceanographic Society (CMOS) / Canadian Geophysical Union (CGU) JointAssembly on June 2, 2016 in Fredericton, New Brunswick.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation for the study . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Variability of water surface albedo . . . . . . . . . . . . . . . . . . . . . . 21.3 Albedo representation in energy balance studies . . . . . . . . . . . . . . 41.4 Research objectives and thesis structure . . . . . . . . . . . . . . . . . . 52 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Study area and field sites . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Field methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.1 Suspended sediment . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Streamflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.3 Digital camera imagery . . . . . . . . . . . . . . . . . . . . . . . . 122.2.4 Reach characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.1 Pyranometer calibration . . . . . . . . . . . . . . . . . . . . . . . 122.3.2 Albedo calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.3 Solar position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.4 Digital camera imagery . . . . . . . . . . . . . . . . . . . . . . . . 15iv2.3.5 Statistical modelling . . . . . . . . . . . . . . . . . . . . . . . . . 153 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1 Overview of the study period . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Pyranometer calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Analysis of digital camera images . . . . . . . . . . . . . . . . . . . . . . 223.4 Exploratory analysis of albedo variability . . . . . . . . . . . . . . . . . . 233.4.1 Relation with atmospheric transmissivity . . . . . . . . . . . . . . 243.4.2 Relation with solar elevation angle . . . . . . . . . . . . . . . . . 253.4.3 Relation with suspended sediment . . . . . . . . . . . . . . . . . . 263.4.4 Relation with discharge and aeration . . . . . . . . . . . . . . . . 283.4.5 Recursive partitioning . . . . . . . . . . . . . . . . . . . . . . . . 293.5 Statistical modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.5.1 Model fitting and cross validation . . . . . . . . . . . . . . . . . . 324 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1 Analysis of albedo variability . . . . . . . . . . . . . . . . . . . . . . . . 354.1.1 Solar angle and transmissivity . . . . . . . . . . . . . . . . . . . . 354.1.2 Discharge and aeration . . . . . . . . . . . . . . . . . . . . . . . . 364.1.3 Suspended sediment . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Model performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.2.1 Model selection and testing . . . . . . . . . . . . . . . . . . . . . 384.2.2 Model scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3 Analysis of digital camera images . . . . . . . . . . . . . . . . . . . . . . 395 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.1 Key findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2 Recommendations for future research . . . . . . . . . . . . . . . . . . . . 42Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44vList of TablesTable 1.1 Summary of stream surface albedo representations used by previousriver energy balance studies. . . . . . . . . . . . . . . . . . . . . . . . 4Table 2.1 Stream reaches used in the study. . . . . . . . . . . . . . . . . . . . . 9Table 3.1 Pyranometer calibration results . . . . . . . . . . . . . . . . . . . . . . 21Table 3.2 Summary of albedo values for flatwater and whitewater subsets andrelations with solar elevation angle, stratified by transmissivity . . . . 25Table 3.3 Minumum, mean, and maximum SSC values, mean flatwater albedo,and mean transmissivity observed for each reach . . . . . . . . . . . . 27Table 3.4 Summary of model fitting for the flatwater subset using the categoricalSSC representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Table 3.5 Summary of model fitting for the whitewater subset using the categor-ical SSC representation . . . . . . . . . . . . . . . . . . . . . . . . . . 33Table 3.6 Summary of model fitting for the flatwater subset using the logarithmicSSC representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Table 3.7 Summary of model fitting for the flatwater subset using the logarithmicSSC representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Table 3.8 Cross-validated R2 and RMSE for models selected during the initialstages of model fitting. . . . . . . . . . . . . . . . . . . . . . . . . . . 34viList of FiguresFigure 2.1 Sites used in the study . . . . . . . . . . . . . . . . . . . . . . . . . . 7Figure 2.2 Map of the study area . . . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 2.3 Monitoring set-up used to measure albedo and obtain camera imagery 10Figure 2.4 Sample albedo time series measurement . . . . . . . . . . . . . . . . . 13Figure 3.1 Historical maximum, mean, and minimum monthly air temperaturesand 2015 monthly mean air temperature measured near Pemberton. . 18Figure 3.2 Historical mean monthly total precipitation and 2015 monthly totalprecipitation measured near Pemberton . . . . . . . . . . . . . . . . . 19Figure 3.3 Historical maximum, mean, and minimum daily streamflow and 2015mean flow at the Lillooet River. . . . . . . . . . . . . . . . . . . . . . 20Figure 3.4 Relation between uncalibrated CM3 output voltage and CM6B irradi-ance during calibration. . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 3.5 Relation between measured albedo and the coefficient of variation ofpixel RGB values at Rutherford Creek . . . . . . . . . . . . . . . . . 23Figure 3.6 Albedo as a function of atmospheric transmissivity . . . . . . . . . . 24Figure 3.7 Albedo as a function of solar elevation angle. . . . . . . . . . . . . . . 26Figure 3.8 Albedo as a function of SSC, plotted on log axes . . . . . . . . . . . . 27Figure 3.9 Albedo as a function of SSC, plotted on linear axes . . . . . . . . . . 28Figure 3.10 Albedo as a function of discharge at Rutherford Creek. . . . . . . . . 29Figure 3.11 Regression tree fit to the flatwater subset . . . . . . . . . . . . . . . . 30Figure 3.12 Regression tree fit to the whitewater albedo subset . . . . . . . . . . 31Figure 3.13 Cross-validated predicted albedo values versus observed albedo for theflatwater and whitewater subsets. . . . . . . . . . . . . . . . . . . . . 34viiAcknowledgmentsThis work was completed as a result of efforts from many people. First and foremost,my thanks go to my supervisor, Dan Moore. Dan’s guidance, immeasurable enthusiasm,and patience were key to the successful completion of the project. I could not ask for abetter supervisor.Funding for this research was provided by operating grants to Professor Dan Moorefrom the Natural Sciences and Engineering Research Council (NSERC) of Canada.Special thanks to Derek van der Kamp, Moritz Ma¨hrlein, Dave Reid, and MarkRichardson, whose technical expertise and guidance was instrumental to the collectionand processing of data during the field season. I’d also like to thank all of people whoprovided field assistance: Eleri Harris, Cameron Hunter, Haven Jerreat-Poole, MoritzMa¨hrlein, Nicholas McMahon, Mark Richardson, and Andras Szeitz.Thanks to my undergraduate supervisor, Professor Baker Perry of Appalachian StateUniversity, whose teaching kindled my interest in the natural sciences. I would not bewhere I am today without his mentorship.Finally, I would like to thank my family, who have always supported and encouragedme throughout my education.viiiChapter 1Introduction1.1 Motivation for the studyWater temperature governs a range of physical, biological, and chemical processes instreams, and plays a crucial role in the overall health of aquatic ecosystems (Coutant,1999; Webb et al., 2008; Symonds and Moussalli, 2011). For example, water temperatureinfluences fish mortality (Thomas et al., 1986), distribution (Hughes, 1998), growth anddevelopmental rates (Shelbourn et al., 1973; Elliott and Hurley, 1997), pollutant uptake(Ficke et al., 2007), reproductive fitness (Fenkes et al., 2016), and competitive interactions(Reeves et al., 1987). In addition, dissolved oxygen solubility decreases at higher tem-peratures, while oxygen requirements for biological processes increase. Dissolved oxygenis a major determinant of aquatic habitat quality during the summer when the oxygenneeds of aquatic organisms are highest and availability is at a minimum (Caissie, 2006).Environmental changes and human activity can modify fluvial thermal regimes (Webbet al., 2008). Forest disturbance associated with wildfire and harvesting in riparian zonesincrease a stream’s exposure to solar radiation, typically resulting in increases in summerwater temperature (Moore et al., 2005). Reduction of streamflow associated with flowregulation and withdrawals increases the sensitivity of stream temperature to surfaceenergy inputs by decreasing stream depth (Sinokrot and Gulliver, 2000). Additionally,dam releases may not be the same as downstream river temperature, providing anothermechanism for altering water temperature (Olden and Naiman, 2010). Climate changecan influence stream temperatures by influencing the timing and magnitude of streamflowas well as the surface energy exchanges (Meisner, 1990; Ficke et al., 2007; Isaak et al.,2010).1Predictive models are often used to assist with designing and evaluating managementoptions to minimize the effects of human activity on stream temperature—for example,for evaluating the sensitivity of stream temperature to flow reductions associated withwithdrawals (Dymond, 1984; Bartholow, 1991). The most rigorous approach to modellingstream temperature is through the use of deterministic models that explicitly simulatesurface energy exchanges, which include short- and longwave radiation and turbulentexchanges of sensible and latent heat (Sinokrot and Stefan, 1993; Caissie, 2006; Hannahet al., 2008). In streams that are exposed to direct sunlight, solar radiation is typicallythe dominant component of the energy balance during the summer (Moore et al., 2005).Stream surface albedo—the fraction of incident solar radiation that is reflected—istypically not measured in stream temperature modelling studies. Some models, likeHeatSource (Boyd and Kasper, 2003), compute albedo using a published function ofsolar incidence angle. Meier et al. (2003) accounted for variability in albedo in terms ofsolar zenith angle and cloud cover according to relations reported by Anderson (1954).Many modelling studies used an assumed fixed albedo. For example, a fixed value of 0.05was assumed by Magnusson et al. (2012) in studies on proglacial channels. A lower fixedvalue of 0.03 was assumed by Caissie et al. (2007) for a pair of low-gradient rivers.The overall objective of this study is to quantify the dependence of the albedo ofmountain streams on the controlling factors to improve the representation of albedo inenergy balance models. Progress in the subject will improve energy balance modelsand ultimately increase confidence in water temperature estimates that drive decisionmaking in riparian and river management. The following section provides a review of thevariability of water surface albedo based on both theory and measurements, and the finalsection summarizes the specific objectives of the study and the structure of the thesis.1.2 Variability of water surface albedoThe Fresnel equations predict that reflectance of a light beam striking a surface increasesat greater incidence angles (between the incident ray and the normal). At high solaraltitudes under clear-sky conditions, albedo of the water surface is typically between0.03 and 0.10 (Oke, 1987). At lower solar altitudes (greater incidence angles), however,values approaching 1.0 have been observed as the sun approaches 0◦ (Nunez et al., 1972).Clouds and haze greatly enhance scattering of solar radiation, increasing the numberof rays travelling at angles other than the solar elevation angle. At low solar elevationangles, this scattering increases the number of rays incident on the water surface at anglesgreater than the solar elevation angle, decreasing the amount of light reflected by the2surface, consequently decreasing albedo. Conversely, scattered light increases albedo athigh solar elevation angles, since a greater number of rays strike the water surface atdecreased angles compared to the solar elevation angle (Katsaros et al., 1985).Increased water surface roughness has a similar effect on reflectance. When the watersurface is roughened and solar altitude is high, there is a higher probability that incidentbeams will be reflected off a sloping rather than horizontal surface, increasing surfacealbedo. At low solar altitudes, a rough water surface decreases albedo since beams wouldbe more likely to encounter a raised slope rather than glancing off the surface (Oke,1987).The relation between albedo, solar elevation angle, and surface roughness has beenquantified for lakes and oceans (e.g. Nunez et al., 1972; Payne, 1972; Katsaros et al., 1985;Jin et al., 2004). Payne (1972) measured ocean surface albedo values ranging between0.03 at high sun angles to 0.45 for solar altitudes below 10◦, although with considerablescatter for low sun angles. Using wind speed as a proxy for surface roughness, theeffect of roughness was most pronounced at low solar angles. The negative albedo-surface roughness relation was most pronounced at solar angles between 17 and 25◦,whereas the positive relation at higher solar elevation angles was relatively small incomparison. Nunez et al. (1972) found that increasing wave height had a modest influenceon albedo, except for solar altitude angles lower than 15◦, when albedo was suppressedwith increasing wave heights. Both studies found that the dependency between solaraltitude and albedo decreases with increasing cloud cover, becoming undetectable duringovercast conditions. Subsequent work has parameterized ocean surface albedo in termsof the driving physical processes with good predictive accuracy. For example, Jin et al.(2004) developed a parameterization of spectral and broadband albedo ocean surfacebased on solar zenith angle, wind speed, and ocean chlorophyll concentration, accountingfor differences between direct and diffuse solar radiation components, achieving a modelstandard error of 0.014.The effects of suspended sediment and aeration on albedo have been examined byfield and laboratory studies focused on the spectral reflectance of lake and ocean surfaces(e.g. Whitlock et al., 1982; Koepke, 1984). In a laboratory study, Han (1997) found thatreflectance increased non-linearly in the visible spectrum as sediment was added, withthe dependence of reflectance on SSC decreasing at higher concentrations. AtSSC = 500 mg/L, reflectance was highest between 600 and 700 nm, with 23% of naturalsunlight being reflected. Whitlock et al. (1982) found in laboratory studies that the re-flectance of dense foam with high aeration, consisting of multiple bubble layers, averagedapproximately 50% in visible wavelengths. Koepke (1984) measured the albedo of foam3patches on the ocean surface. Fresh foam patches measured 1 s after generation had anaverage spectral reflectance of 41%, decaying to 16% after 10 s. The average spectralreflectance of all foam patches was 22%.1.3 Albedo representation in energy balancestudiesTable 1.1 provides a summary of measured stream surface albedo. Leach and Moore(2010) found that mean albedo was 0.05 over pools and glides, and 0.06 over riffles.Evans et al. (1998) reported a mean albedo of 0.07, although there was distinct diurnalvariability in albedo attributed to the solar elevation angle. Monthly daily mean albedovalues ranged between 0.06 in July and 0.08 in November due to the differences in averagesolar position between months. Neilson et al. (2009) measured albedo on a low gradientreach of the Virgin River, Utah, USA, for turbidities ranging from 2 to 440 nephelometricturbidity units (NTU ). Albedo was less than 0.10 when the river’s turbidity was low, butwas enhanced by 0.03 to 0.07 at higher levels of turbidity. Working on turbid proglacialstreams, Knudson (2012) found that albedo was enhanced by SSC and varied with solarzenith angle. For Lillooet River, albedo ranged from 0.08-0.13, compared to 0.05-0.10measured on two tributary reaches. Chikita et al. (2010) reported a mean albedo of 0.1for a proglacial stream with suspended sediment concentrations typically exceeding200 mg/L, with daily maxima greater than 500 mg/L (Kido et al., 2007).Table 1.1: Summary of stream surface albedo representations used by previousriver energy balance studies. NS indicates values were not specified.Study Location Albedo Channel Gradient SSC / NTUEvans et al. (1998) Staffordshire, UK 0.05 NS; low gradient NS; low SSCHannah et al (2008) Aberdeenshire, UK NS 3-15% NSNeilson et al. (2009) Utah, USA NS 0.12-0.39% 2-440 NTUChikita et al. (2010) Alaska, USA 0.1 2-30% >200 mg/LLeach & Moore (2010) BC, CA 0.05-0.06 2.20% NS; low SSCBenyaha et al. (2011) NB, CA 0.01-0.05 NS; low gradient NSRichards & Moore (2011) BC, CA 0.1-0.4 26% 60-100 mg/LKnudson (2012) BC, CA 0.08-0.10 0.60% 34-831 mg/LKhamis et al. (2015) Cirque de Gavarnie, France NS NS; high gradient NSSome work has found that stream surface albedo can be considerably higher thanthe typical 0.03-0.10 range. Working on a steep proglacial channel, Richards and Moore(2011) found that albedo ranged between 0.10 at low flows up to 0.40 at higher flows asthe water surface became increasingly aerated. Albedo varied nonlinearly with discharge4(a proxy for aeration), with an additional term to account for incoming solar radiation,which represents the combined effects of solar elevation angle and the direct fraction ofsolar radiation. The variable representation of albedo improved the prediction of netradiation at the site: the Nash-Sutcliffe efficiency of the radiation model was 0.81 usingthe variable albedo compared to 0.75 and 0.78 using fixed albedo values of 0.05 and Research objectives and thesis structureThe review of the literature in section 1.2 indicates that stream surface albedo can devi-ate significantly from the typical range of values assumed in many stream temperaturemodelling studies, especially for turbid and/or aerated conditions. Both theory and ob-servations indicate that albedo should depend on (a) angle of incidence, (b) fractionsof direct vs diffuse solar radiation, (c) turbidity and (d) degree of aeration. However,there is currently no quantitative model available for predicting the dependence of streamsurface albedo on these factors. The specific research objectives addressed by the thesisare:1. to quantify the dependence of albedo on suspended sediment, solar position, frac-tions of direct vs diffuse radiation, and aeration for a sample of mountain streamsthat encompass a range of flow regimes, gradients, and channel morphologies;2. to develop a statistical model to predict albedo that could be easily incorporatedinto energy balance models; and3. to develop and assess the viability of proxy measures for albedo using digital cameraimagery.The remainder of the thesis is organized as follows. Chapter 2 describes the studyarea, field methods, and data analysis. Chapter 3 presents the results of the field workand data analysis. Chapter 4 describes how the results of this study address the researchquestions outlined previously. Chapter 5 summarizes the conclusions of the study andidentifies areas where future research is necessary.5Chapter 2Methods2.1 Study area and field sitesResearch focused on nine streams in the southern Coast Mountains of British Columbia,Canada, which encompassed a range of flow regimes and channel morphologies that arerepresentative of a broad range of conditions that occur in mountain streams (Table 2.1;Figure 2.1; Figure 2.2). The study sites spanned a range of gradients between 0.17%and 9.48%, stream discharges between 1 m3s−1 and 400 m3s−1, and suspended sedimentconcentrations from 5 mg/L to 700 mg/L.Sites with minimal topographic and vegetative shading were preferred in order tominimize shadows on the stream surface so that albedo measurements could be takenconsistently in direct lighting conditions during clear weather. In order to sample awide range of sun angles, suspended sediment concentrations and discharges, measure-ments were typically collected from mid-morning until sunset. Monitoring occurred on29 days between May and September 2015 with the goal of sampling each site regularlythroughout the field season. However, sampling during the field season was interruptedby wildfires in the region; access to upper Lillooet River and North Creek was prohibitedduring July and August as the result of the Cougar Creek wildfire in the Lillooet Val-ley. Heavy wildfire smoke throughout the area in early July created air quality concerns,preventing any sampling until smoke had dispersed.6Figure 2.1: Sites used in the study.7Figure 2.2: Map of the study area.8Table 2.1: Stream reaches used in the study. No. Sites = the number of sites onthe reach where measurements were made. VF = sky view factor.* indicates that channel width was estimated from Google Earth. The lowerLillooet reach is located at the BC-99 road crossing. The upper reach islocated at kilometre 15 on the North Lillooet Forest Service road.Site Latitude Longitude No. Sites Channel Type BankfullWidth (m)Gradient (%) VFBirkenhead R. 50.370 -122.727 2 riffle-pool 31.3 2.32 0.67Cayoosh Cr. 50.385 -122.469 2 step-pool 7.6 8.19 0.79Lillooet R. lower 50.317 -122.768 1 riffle-pool 68.4 0.58 0.76Lillooet R. upper 50.542 -123.129 1 riffle-pool 155* 0.24 0.63Miller Cr. 50.356 -122.843 1 riffle-pool 21.9 0.17 0.59North Cr. 50.558 -123.183 3 cascade-pool 10.5* 2.32 0.68Rubble Cr. 49.957 -122.120 3 cascade-pool 17.9 9.48 0.61Rutherford Cr. 50.272 -122.867 3 cascade-pool 37.7 5.81 0.90Soo R. 50.258 -122.864 1 riffle-pool 64.1 0.22 0.872.2 Field methodsIncident and reflected solar radiation, K↓ and K↑ , were measured with a pair of ther-mopile pyranometers mounted on a 2.5 m long pole suspended manually over the watersurface and fixed to a tripod on shore (Figure 2.3). Incident solar radiation was mea-sured with a Kipp & Zonen CM6B pyranometer mounted facing upwards. An integratedlevel on the CM6B ensured that the pyranometer remained level during measurements.Reflected solar radiation was measured with a Kipp & Zonen CM3 pyranometer pointeddownwards and mounted to a gimbal joint to hold it level.Pyranometers recorded voltage values (mV) that were converted to irradiance (Wm−2)using the sensitivity of each device (mV/Wm−2). The pyranometers were scanned every1 s and averaged every 5 s with a Campbell Scientific CR10X data logger. Albedo, α,was calculated as:α = K ↑ /K ↓ (2.1)9Figure 2.3: Monitoring set-up used to measure albedo and obtain camera imagerymounted at the end of the horizontal support pole.Pyranometers were typically held at 0.5 m above the water surface during albedomeasurements. Adjustments to height and orientation were made to keep shadows orrocks out of the pyranometer’s field of view. When sampling at hydraulic jumps, pyra-nometers were positioned higher to prevent spray from swinging the lower pyranometerand compromising the stability of the measurement.Albedo was sampled at several points on the stream surface at sites with visible white-water to compare albedo values at points with varying degrees of aeration. During clearweather, each measurement usually lasted 60 to 120 s. Under variable lighting conditions,albedo values were not steady as incoming solar radiation values shifted, so measurementshad to be longer to ensure that a steady albedo value had been obtained. Pyranome-ters were covered between measurements to zero out irradiance values and protect theinstrumentation. During clear weather with consistent lighting conditions, albedo mea-surements were taken every 30 min. Additional measurements were taken during periodsof variable cloud cover when atmospheric transmissivity changed frequently. Reflectedirradiance was measured during rainy weather early in the study period, but values weresmall enough that they were difficult to distinguish from noise and resulting albedo valueswere unreliable. Therefore, sampling was avoided during periods of rain, when incomingsolar radiation was minimal.102.2.1 Suspended sedimentSuspended sediment samples were collected every 2 h using a DH-48 depth-integratedsampler at the location of each albedo measurement. Samples were processed at a lab-oratory at the UBC Department of Geography. The mass of sediment in each samplewas calculated by weighing 47-mm glass microfiber filters, pumping samples through thefilters, and then drying and re-weighing each filter. Suspended sediment concentration,SSC (mg/L), was then calculated by dividing the sediment mass by the sample volume.2.2.2 StreamflowDischarge was measured at reaches in which albedo measurements were made over aeratedportions of streamflow. Channels where streamflow measurements were recorded tendedto be narrow, relatively steep, irregular, and boulder filled with cascade-pool or step-poolmorphologies, and were appropriate for salt dilution gauging in place of the standardvelocity-area method. Dry salt injection was used since flow was adequately turbulentto facilitate rapid solute dissolution and mixing (Hudson and Fraser, 2005; Richardson,2015). Salt was injected hourly or more frequently if stream discharge changed rapidly.Temperature-corrected electrical conductivity, ECT , was monitored with a pair of WTWCond 3310 conductivity meters and WTW Tetracon conductivity probes downstreamof the injection point. The meters were staggered by 5 to 10 m in order to verify thatcomplete solute mixing had occurred. Background ECT (ECBG) was measured priorto injection, and the changes in ECT were monitored as the injected salt wave movedpast the probes until ECT had returned to the background level. The temperature-corrected calibration factor CFT (kg m−3/(µS · cm−1) was calculated at the end of eachmonitoring day using the procedure described by Richardson (2015), in which a knownmass of salt was added to a measured volume of streamwater, and then samples of thissolution were added incrementally to another measured volume of streamwater, with ECTmeasured after each addition. CFT was calculated as the slope of the linear regressionline between the calculated mass concentration of salt and ECT . Following calibration,stream discharge, Q (m3s−1), was calculated as:Q =MCFT · A (2.2)where M is the mass of the salt injected (kg), and A is the area under the time series of(ECT - ECBG) during the salt wave passage (µS · cm−1 · s).112.2.3 Digital camera imageryVideo of the water surface was recorded during each albedo measurement using a water-proof GoPro HDHERO2 digital camera. The camera was mounted facing downwards onthe pole mount and was run continuously for the duration of each measurement (Figure2.3). Video collected was used to provide imagery to refer to while processing and ver-ifying albedo data as well as for the development of a proxy for pyranometer-measuredalbedo.2.2.4 Reach characteristicsSurveys were conducted in June and August 2016 to determine the view factor, averagebankfull channel width, and channel gradient of each site using a LTI Impulse 200 laserrangefinder and handheld clinometer. Average bankfull width was calculated as the av-erage width of two transects of each stream and was obtained with horizontal rangefindermeasurements. Gradient was determined by obtaining horizontal and vertical distancemeasurements with the rangefinder. The sky view factor (VF) was calculated from zenithangles measured at each site in eight directions (N, NE, E, etc.):V F =∑8i=1[1− (cosZ)2]8(2.3)where Z is the angle between the zenith and the horizon (defined by topography or forestcanopy) in each direction, measured with a clinometer.2.3 Data analysis2.3.1 Pyranometer calibrationUsing the manufacturer’s calibration sensitivities for each pyranometer, irradiance valuesfrom the CM3 pyranometer were typically 91 to 95% of the values recorded by the CM6B.There was no offset between pyranometers when both were covered and zeroed. Thisproportional offset was compensated for by calibrating the voltages reported by the CM3pyranometer with those reported by the CM6B. At the conclusion of each trip to the field,pyranometers were run side by side for several hours. A linear model with no interceptwas fitted between the CM3 raw voltage output and the CM6B irradiance. The recordedCM3 voltage was then multiplied by the model’s slope to calculate the calibrated CM3irradiance.122.3.2 Albedo calculationFollowing pyranometer calibration, albedo values were extracted from the pyranometertime series. A five-point moving window, corresponding to 25 seconds of measurementtime, was used to calculate smoothed means and standard deviations of K↓, time ofmeasurement, and albedo (Figure 2.4). Stable measurements were isolated by removingperiods between measurements, unstable measurements, and the leading and trailingedge of each measurement by removing points where K↓ within each window exceededa set standard deviation and slope. Albedo, measurement time, and K↓ were calculatedas the mean of the values for each measurement period. Further manual processingwas performed in order to determine whether measured albedo values were physicallyreasonable by comparing them to field notes and the digital camera imagery. Unstablealbedo measurements that were not removed by the filter were also discarded from thedataset. Lighting conditions and an estimate of the amount of surface aeration for eachalbedo measurement (i.e. minimal aeration versus highly aerated) were appended to thedataset from field notes.Figure 2.4: Sample albedo time series measurement. Hollow circles are centroidsof each 5-point window within the measurement. The black triangle denotesthe position of the mean K↓ within the measurement.132.3.3 Solar positionAlbedo should vary with solar zenith angle (which, for a horizontal water surface, is alsothe angle of incidence) and with the fractions of direct and diffuse solar radiation. Forsimplicity, the atmospheric transmissivity, τ , was used as an index of these fractions (i.e.,higher transmissivity indicates a higher fraction of direct radiation). Solar zenith angle,θ, was calculated following Iqbal (1983):θ = cos−1[sin(δ) · sin(φ) + cos(δ) · cos(ω)] (2.4)where δ is solar declination, φ is latitude at the measurement location, and ω is the hourangle. The declination was calculated based on a seven term Fourier expansion:δ = 0.0069− 0.3999cos(γ) + 0.0703sin(γ)− 0.0068cos(2γ) + 0.0009sin(2γ)− 0.0027cos(3γ) + 0.0015sin(3γ) (2.5)where γ is the day angle, 2pi(d - 1)/365, where d is the calendar day (d = 1 on Jan. 1).Hour angle was calculated as:ω = 0.2618(Lt − 12) (2.6)where Lt is local area time, calculated as:Lt = Td −DST + 4(λstandard − λ)/60 + Et (2.7)where λ is longitude, Td is the local clock time, λstandard is a standard parallel of longitude(120◦W for the region), and Et is the equation of time, calculated with a five term Fourierexpansion:Et = 229.18[0.000075 + 0.001868cos(γ)− 0.032077sin(γ)− 0.014615cos(2γ)− 0.04089sin(2γ)]/60 (2.8)Transmissivity was calculated as:τ = K ↓ /[K0cos(i)] (2.9)where K0 is the solar constant, taken here to be 1367 Wm−1, and i is the solar incidence14angle, approximated here by the solar zenith angle. To simplify interpretation, furtheranalysis was performed using the solar elevation angle, h, which is the complement ofsolar zenith angle.2.3.4 Digital camera imageryStill frames from the digital camera imagery were used to develop a proxy measure foraeration. Still frames were extracted from the digital camera video recorded betweenJune and September at Rutherford Creek. One video frame was extracted per albedomeasurement taken at each site. Each frame was converted into a 3-dimensional matrixrepresenting the image’s red, green, and blue components, where the number of columnsand rows in each matrix channel was equal to the image’s height and width in pixels.The coefficient of variation (CV ) of the pixels in each colour channel was calculated andaveraged between all three colours as a measure of the total variability within the image.Nonlinear regression was used to fit a model relating albedo to CV to assess its value asa proxy.2.3.5 Statistical modellingAlbedo measurements were stratified into a ”whitewater” set for measurements that tookplace over visibly aerated flow and a separate ”flatwater” subset for the rest. A separatesubset was created for measurements taking place at a hydraulic jump on RutherfordCreek to look explicitly into the relation between albedo and discharge. Discharge mea-surements were also made on Cayoosh Creek and North Creek, but neither stream hadan adequate number of discharge measurements associated with albedo at a specific lo-cation on the stream to perform a valid statistical analysis. Since albedo measurementswere not always taken at the same time as discharge and suspended sediment, Q andSSC values were assigned to each albedo measurement using cubic spline interpolationthrough the time series of those variables for each day. Splines were generated accordingto Forsythe et al. (1977); in this approach end conditions were determined by fitting anexact cubic through the four points on each end of the data, thus minimizing the splineenergy subject to constraints imposed by the end conditionsAlbedo was plotted individually against solar elevation angle, transmissivity, sus-pended sediment concentration, and discharge to determine the forms of the relation.Predictors were transformed if, during the initial stages of model fitting, it appearednecessary to linearize the relationship and to improve predictive ability. A categoricalrepresentation of SSC was used in which low concentrations were assigned a value of 0,15and higher concentrations were assigned a value of 1. The split between low and highconcentrations was defined at 30 mg/L for the flatwater subset and at 15 mg/L for thewhitewater subset. Additionally, sinh was used in order to linearize the relationship be-tween solar altitude and albedo. Transformed variables were used to fit models for albedousing multiple regression separately for the flatwater and whitewater subsets. A set ofcandidate models was constructed for every possible combination of selected variablesand their interactions.Candidate models were initially evaluated on the basis of coefficient values. Modelswith coefficients that were not physically reasonable were immediately removed fromconsideration. The predictive ability of remaining models was compared with the AkaikeInformation Criterion (AIC ) for the model fitted to the entire subset. A modified versionof the metric, AICc, was used, since the number of observations was relatively smallcompared to the number of predictor variables, and since AICc imposes a greater penaltyfor extra predictors (Symonds and Moussalli, 2011). Candidate models with ∆AICc ofless than 2 for each subset were evaluated further using leave-one-out cross validation.Models were cross-validated on a stream-by-stream basis to avoid overfitting and toproduce a more rigorous test of the model’s predictive ability when applied to new sites.Recursive partitioning was used to categorize variability in the dataset and identifyinteractions between predictor variables. The resultant regression trees classified subsetsof the albedo dataset based on how predictor variables reduced variance in each sub-set of albedo. Regression trees were pruned using a complexity parameter (cp) of 0.04.Results of recursive partitioning were used to draw inferences regarding the relative im-portance of each predictor variable and the structure of the relationship between albedoand predictors.16Chapter 3Results3.1 Overview of the study periodMonthly mean air temperatures measured near Pemberton, BC, from 1969-2014 and dur-ing 2015 are displayed in Figure 3.1. The majority of the study period was characterizedby air temperatures well above monthly averages. The mean monthly air temperaturewas 3.7 ◦C above normal during May and June and 2.4 ◦C above average in July. Tem-peratures toward the end of the field season were closer to long-term averages. The meanmonthly air temperature was 1.0 ◦C above average in August and 0.4 ◦C below averagein September.Historical monthly mean total precipitation from 1969-2014 and 2015 monthly totalprecipitation are displayed in Figure 3.2. Monthly precipitation was below the long termaverage during much of the spring of 2015 and for the majority of the field season. Lessthan half of average precipitation fell during April, May, and July 2015. May 2015 wasparticularly dry; 9.6% of monthly average precipitation occurred. In contrast, Augustand September 2015 were wet months, receiving 263% and 176% of average total monthlyprecipitation respectively.17Figure 3.1: Historical maximum, mean, and minimum monthly air temperaturesand 2015 monthly mean air temperature measured near Pemberton. The2015 field season is highlighted in blue. Data from 1969 - 1984 are sourcedfrom Environment Canada station 1086083 (Pemberton BCFS), with years1984 - 2015 sourced from a nearby station, 1086082 (Pemberton AirportCS).18Figure 3.2: Historical mean monthly total precipitation and 2015 monthly totalprecipitation measured near Pemberton. Data from 1969 1984 are sourcedfrom Environment Canada station 1086083 (Pemberton BCFS), with years1984 - 2015 sourced from station 1086082 (Pemberton Airport CS).19Peak summer flow on the Lillooet River occurred during the beginning of the 2015field season (Figure 3.3). Peak summer flows occurred during late May and early June,well before the mid-July average. The early peak is likely attributable to meltwatergeneration resulting from higher than average air temperatures during the late springand early summer. Rainfall was below average during the same period, minimizingprecipitation contributions to streamflow. Daily mean streamflow was above average formuch of July, and returned to near-normal conditions in late July and August as moreprecipitation fell and temperatures returned to long-term averages.Figure 3.3: Historical maximum, mean, and minimum daily streamflow and 2015mean flow at the Lillooet River 3 km northwest of the Lower Lillooet reach(Water Survey of Canada station 08MG005 Lillooet River near Pemberton)3.2 Pyranometer calibrationThe relation between CM6B irradiance and CM3 output voltage used to calculate CM3irradiance is shown in Figure 3.4. Prior to calibration, percent difference between dailyCM3 and CM6B irradiance during parallel runs differed from between 4.7% and 18.7%.Following calibration, percent difference between pyranometers was 0.7% to 14.0% (Ta-ble 3.4). Standard error of the estimate was between 4.3 and 18.7 Wm−2. The largestdifferences in irradiance following calibration occurred on days when shading from clouds20or buildings covered pyranometers during the calibration procedure, creating periods inwhich one pyranometer would be shaded while the other was exposed to direct solar radia-tion. On July 21 and August 3, shadows from nearby buildings covered the pyranometersafter several hours of recording in direct solar radiation.Table 3.1: Pyranometer calibration results. Percent differences are between CM3and CM6B irradiance. Se = standard error of the estimate.calibration date % difference calibrated slope (Wm−2/mV) Se (Wm−2)31 May -0.67 55.32 7.218 June -0.94 56.75 4.2521 July -4.33 57.2 9.733 August -14.0 56.15 13.9124 August -1.09 56.07 12.7321 September -5.6 56.48 18.66Figure 3.4: Relation between uncalibrated CM3 output voltage and CM6B irradi-ance during calibration. Red lines are the regression lines for each relationused to convert the CM3 voltage to irradianceThe period of time in which the pyranometers were not exposed to identical lightconditions was removed, producing the discontinuities in panels 3.4c and 3.4d (Figure3.4). Percent difference following calibration was 4.3% on July 21 and 14.0% on August213. Calibration on September 21 occurred during a period of variable clouds that inducedscatter in the relation as shadows moved over the pyranometers, again subjecting themto non-identical irradiances (Figure 3.4f). On days when shading was minimal, calibratedCM3 and CM6B irradiance differed by 1.1% or less.Variability in the slope of the regression line was minimal despite differences in lightconditions during calibration and relatively large differences in calibrated values on Au-gust 3 and September 21. Regression slopes ranged between 55.3 and 57.2 Wm−2/mV.The percent difference between the maximum and minimum vales was 3.3%. Addition-ally, no trend in the slope of the regression was evident over the course of the monitoringseason, indicating that the calibration process produced consistent calibrated irradiancevalues and that any systematic drift was minimal.3.3 Analysis of digital camera imagesDigital images were captured at Rutherford Creek during trips to the site between Juneand September at three locations along the stream surface that encompassed a gradientof visible aeration (Figure 3.5, panels a - c). Measurements at location (a) were made overslow moving flow upstream of a rock step. Measurements at (b) and (c) were downstreamof the rock step, where (c) was immediately in the lee of the boulder over layers of foamon the water surface, and b) was approximately 2 m downstream.Linear regressions fitted between albedo and CV for each subset were not significant.Plotted together, the albedo-CV relation appears consistent with a logistic curve, al-though with considerable scatter. Model residuals had a standard deviation of 0.041 andNash-Sutcliffe efficiency of 0.28.22Figure 3.5: Upper panel shows the relation between measured albedo and the co-efficient of variation of pixel RGB values at Rutherford Creek based on mea-surements at three locations denoted a, b and c. The lower panels providean example image for each site.3.4 Exploratory analysis of albedo variabilityIn this section, the relation between albedo and several hypothesized controlling variables(atmospheric emissivity, solar elevation angle, suspended sediment concentration anddischarge) are examined. Sections 3.4.1 to 3.4.4, below, present exploratory analysesusing bivariate graphs with stratification, and section 3.4.5 examines the potentiallyinteracting effect of all candidate predictor variables using recursive partitioning. Theresults of these exploratory analyses are then used to define the form of a formal predictivemodel in section Relation with atmospheric transmissivityThe relation between albedo and atmospheric transmissivity is displayed in Figure 3.6.Albedo exhibited a slight positive correlation with transmissivity for both subsets. Ashift in the mean and variance of albedo is apparent at around τ = 0.6. Mean albedowas decreased by 0.03 within the flatwater subset and 0.02 within the whitewater subsetwhen τ < 0.6. Standard deviation from the mean within each subset decreased 0.006 forflatwater and 0.009 for whitewater over the range of measurements.Compared to a subjective classification of the dominant insolation condition (directvs diffuse), defining diffuse as dominant for τ < 0.6 and direct for τ ≥ 0.6 matchedobserved lighting conditions for 97% of albedo measurements. Since sampling typicallytook place during fair weather, the majority of albedo measurements were taken in directlighting conditions in both subsets. A total of 66 of 212 flatwater measurements and 17of 91 whitewater measurements were measured when τ > 0.6.Figure 3.6: Albedo as a function of atmospheric transmissivity for flatwater (leftpanel) and whitewater (right panel) sites. Solid black lines are regressionlines for each subset. Vertical dotted lines at τ = 0.6 indicate an inferredsplit between light conditions dominated by diffuse (τ < 0.6) and directinsolation (τ ≥ 0.6), respectively.243.4.2 Relation with solar elevation angleStream surface albedo exhibited a broad range of variability associated with solar eleva-tion angle (Table 3.2; Figure 3.7). Flatwater measurements ranged from 0.036 to 0.246 indirect light conditions, with a mean of 0.057. Albedo was enhanced by aeration at pointson the stream with visible whitewater, and more scatter was present in the relation.Albedo ranged from 0.09 to 0.329 in direct light, with a mean of 0.189. Albedo exhibiteda negative response with solar elevation angle in direct light, particularly for elevationangles below 25◦ during flatwater measurements. Albedo decreased within both subsetsduring diffuse lighting conditions when the response to solar elevation was suppressed.Differences in albedo during direct and diffuse lighting conditions were most pronouncedat low solar elevation angles.Flatwater albedo in diffuse light ranged from 0.025 to 0.175 in flatwater and from0.124 to 0.188 in whitewater. The slopes of the relation between albedo and solar eleva-tion were significant for all subsets other than whitewater albedo measurements in diffuselight, which consists of 17 measurements. Measurements over whitewater exhibited morescatter than flatwater measurements. More scatter was inherent in the relation for di-rect lighting conditions compared to diffuse lighting conditions within both subsets, asevidenced by higher standard deviations.Table 3.2: Summary of albedo values for flatwater and whitewater subsets andrelations with solar elevation angle, stratified by transmissivity. Slope refersto the slope of the relation between albedo and solar elevation angle, n isthe number of points in each subset, and p is the significance level for theregression.τ Min Mean Max Std. Dev. Slope p nFlatwater ≥ 0.6 0.036 0.088 0.246 0.033 -0.002 2e-16 212< 0.6 0.025 0.057 0.175 0.027 -0.0009 0.0003 66Whitewater ≥ 0.6 0.091 0.210 0.329 0.049 -0.003 1.07e-9 98< 0.6 0.124 0.188 0.253 0.040 -0.0003 0.645 1725Figure 3.7: Albedo as a function of solar elevation angle. Solid and dashed lines arebest-fit regressions for direct- and diffuse-dominated conditions, respectively.3.4.3 Relation with suspended sedimentSuspended sediment concentrations and associated flatwater albedo and transmissivityvalues for each reach are listed in Table 3.3. Minimum and maximum concentrationsmeasured during the field season were 0.83 mg/L, measured at Cayoosh Creek, and746 mg/L, measured on the Lower Lillooet River. The sites had mean albedo values of0.05 and 0.10 respectively. The albedo-SSC relation is shown on log-axes for the completeflatwater and whitewater subsets in Figure 3.8. The relation is plotted with linear x-axesin Figure 3.9. Albedo had a strong positive relation with SSC at low concentrationsthat flattened at higher concentrations. Transmissivity had a weak influence on therelation for the flatwater subset. The slope of the relation for flatwater was 0.026 formeasurements in direct light, compared to 0.020 for diffuse conditions. The differencewas greater for the whitewater measurements. Slopes of the regression were 0.047 and0.026 for direct and diffuse conditions respectively. However, the slope of the regressionwas not significant for diffuse measurements in either the flatwater or the whitewatersubset.26Table 3.3: Minumum, mean, and maximum SSC values, mean flatwater albedo,and mean transmissivity observed for each reach. Albedo measurements overaerated flow were excluded from the calculation of mean albedo.Reach min SSC mean SSC max SSC mean α mean τ(mg/L) (mg/L) (mg/L)Birkenhead R. 2.37 15.1 182 0.050 0.491Cayoosh Cr. 0.83 2.50 7.23 0.054 0.727Lillooet R. lower 173 405 747 0.099 0.713Lillooet R upper 208 375 677 0.114 0.710Miller Cr. 13.1 26.2 41.7 0.047 0.335North Cr. 24.9 35.4 43.2 0.062 0.611Rubble Cr. 1.63 117 650 0.087 0.628Rutherford Cr. 3.25 22.8 40.1 0.088 0.693Soo R. 15.7 75.5 166 0.105 0.692Figure 3.8: The relation between albedo and SSC. Note that the x-axis is plottedon a logarithmic scale. Solid black regression lines are for τ ≥ 0.6.27Figure 3.9: The relation between albedo and SSC. Note that the x-axis is on alinear scale and truncated at SSC = 250 mg/L. Vertical lines are positionedat 30 mg/L for the left panel and 15 mg/L on right panel to highlightdifferences in the form of the relation at low and high SSC.3.4.4 Relation with discharge and aerationAlbedo exhibited a weak positive relation with discharge at the hydraulic jump on Ruther-ford Creek (Figure 3.10), although the slope of the regression was not significant(slope = 0.018, p = 0.127). The relation was stratified by solar elevation angle (h) andSSC to assess potential confounding effects. Both high and low SSC measurements werepresent across the range of measured flows. However, a majority of measurements takenduring high flows (Q > 2.4 m3s−1) were taken at low solar elevation angles (h < 40◦).The influence of atmospheric transmissivity was minimal, since only 2 of the 54 albedomeasurements at the hydraulic jump were measured during diffuse lighting conditions.28Figure 3.10: Albedo as a function of discharge at Rutherford Creek, stratified bytransmissivity and suspended sediment concentration.3.4.5 Recursive partitioningRegression tree fits to the flatwater and whitewater albedo subsets are displayed inFigures 3.11 and 3.12. For both subsets, SSC was the strongest predictor of albedo.Initial splits occurred at SSC = 30.9 mg/L for flatwater measurements and at SSC =15.4 mg/L for whitewater measurements. For flatwater, subsequent splits were made ath = 37.52◦ and τ = 0.52. For whitewater, the subsequent split occurred at SSC = 1.61mg/L. No additional splits occurred for whitewater measurements with values of SSCgreater than 15.44 mg/L using cp = 0.4.29Figure 3.11: Regression tree fit to the flatwater subset. Mean albedo values forthe final classes are indicated on the end of each leaf. Variable names inthe figure correspond to predictor variables as follows: flatSSC mgl = SSC(mg/L), flatAlt = h (degrees), flatTr = τ .30Figure 3.12: Regression tree fit to the whitewater albedo subset. Variable namesin the figure correspond to predictor variables as follows: whiteSSC mgl= SSC (mg/L), whiteAlt = h (degrees), whiteTr = τ .313.5 Statistical modelling3.5.1 Model fitting and cross validationTables 3.4 and 3.5 summarize results of the model fitting using the categorical SSCrepresentation. For both flatwater and whitewater subsets, many models, including thosewith the lowest ∆AICc values, did not have physically reasonable coefficients. Withinthe flatwater subset, the two models with the highest predictive ability had SSC termswith a negative coefficient for both models, which is not physically realistic. Of theflatwater models with physically reasonable coefficients, models 3 and 4 had the greatestpredictive ability. Both explained 60% of the variance prior to cross-validation. Models 5and 6 were the only candidate models within the whitewater subset that had physicallyreasonable coefficients. Model 6 had the highest predictive ability, accounting for 43% ofthe variance in albedo.The model fitting process was repeated using ln SSC (Table 3.6; Table 3.7). Model11 has the lowest AICc value of all models within the flatwater subset, and accountsfor 62% of variance in albedo. Additionally, all coefficients are physically reasonablefor the model. There was also support for model 10, as evidenced by ∆AICc of 1.875and plausible coefficients. Within the whitewater subset, only models 12 and 13 hadreasonable coefficients.Model R2 and RMSE following the cross-validation process are displayed in Table3.8. Within the flatwater subset, models using ln SSC had higher predictive ability thanmodels that included categorical SSC. However, differences in predictive ability in theflatwater candidate models using the same SSC representation were small. Cross vali-dated R2 and RMSE each differ by less than 0.001 between the two flatwater categoricalSSC models. The difference was slightly larger for the flatwater ln SSC models; R2 dif-fered by 0.005. Whitewater models had higher predictive ability using categorical SSCthan with ln SSC. Residual distributions varied little between models built for the samesubset of albedo and using the same SSC representation, so models were selected on thebasis of predictive ability. Since models 3 and 4 were nearly identical in their predictiveability, model 3 was selected for its simplicity. Observed versus predicted values of albedousing the selected models are displayed in Figure 3.13.32Table 3.4: Summary of model fitting for the flatwater subset. SSC is representedcategorically with a threshold at SSC = 30 mg/L. Bold values indicate modelswhere ∆AICc < 2 compared to the strongest model with physically reasonablecoefficients. Se = standard error of the estimate. Only models with physicallyreasonable coefficients are displayed in this table and in Tables 3.5-3.7.∆AICc Adj. R2 Se b0 sin h SSC τ sin h · SSC sin h · τ SSC · τ1 16.724 0.574 0.022 0.121 -0.119 0.026 0.0432 18.716 0.572 0.022 0.119 -0.115 0.030 0.043 -0.0063 0.000 0.600 0.021 0.043 -0.009 0.026 0.173 -0.1824 1.915 0.599 0.021 0.045 -0.012 0.020 0.174 0.008 -0.185Table 3.5: Summary of model fitting for the whitewater subset using the categoricalrepresentation of SSC with a threshold of SSC = 15 mg/L.∆AICc Adj. R2 Se b0 sin h SSC τ sin h · SSC sin h · τ SSC · τ5 0.663 0.419 0.036 0.218 -0.117 0.049 0.0586 0.000 0.428 0.036 0.256 -0.119 0.001 0.006 0.069Table 3.6: Summary of model fitting for the flatwater subset using ln SSC as apredictor variable.∆AICc Adj. R2 Se b0 sin h ln SSC τ sin h · ln SSC sin h · τ ln SSC · τ7 23.545 0.581 0.022 0.156 -0.114 0.007 0.0428 16.647 0.592 0.022 0.187 -0.158 0.018 0.041 -0.0159 13.227 0.597 0.022 0.092 -0.025 0.007 0.148 -0.14810 1.875 0.615 0.021 0.154 -0.165 0.010 0.096 -0.017 0.01411 0.000 0.619 0.021 0.117 -0.106 0.009 0.150 -0.014 -0.086 0.01233Table 3.7: Summary of model fitting for the whitewater subset using ln SSC as apredictor variable.∆AICc Adj. R2 Se b0 sin h ln SSC τ sin h · ln SSC sin h · τ ln SSC · τ12 1.686 0.352 0.038 0.299 -0.121 0.013 0.07313 0.000 0.368 0.038 0.264 -0.115 0.002 0.125 0.017Table 3.8: Cross-validated R2 and RMSE for models selected during the initialstages of model fitting. FW and WW indicate whether the model is forflatwater or whitewater conditions. Bold indicates final selected models.Model R2 RMSE3 FW sin + SSC + τ + (sin h · τ ) 0.597 0.0234 FW sin h + SSC + τ + (sin h · SSC ) + (sin h · τ) 0.597 0.0245 WW sin h + SSC + τ 0.413 0.0616 WW sin h + SSC + τ + (SSC · τ ) 0.422 0.06110 FW sin h + ln SSC + τ + (sin h · ln SSC ) + (ln SSC · τ) 0.615 0.02311 FW sin h + ln SSC + τ + (sin h · ln SSC ) + (sin h · τ ) + (ln SSC · τ ) 0.620 0.02312 WW sin h + ln SSC + τ 0.360 0.06413 WW sin h + ln SSC + τ + (ln SSC · τ ) 0.373 0.065Figure 3.13: Cross-validated predicted albedo values versus observed albedo forthe flatwater and whitewater subsets. The left-hand panel shows resultswith SSC represented as a binary variable (low/high) and the right-handpanel shows results with ln SSC as a predictor variable34Chapter 4Discussion4.1 Analysis of albedo variability4.1.1 Solar angle and transmissivityAlbedo exhibited large diurnal swings in magnitude during clear sky conditions. Dif-ferences between maximum and minimum albedo values observed in direct lighting con-ditions averaged by reach were 0.12 for both flatwater and whitewater locations. Themaximum flatwater albedo value measured on the lower Lillooet reach was 0.25, measuredat a solar elevation angle of 13.9◦. Measured values of albedo at given solar elevationangles were similar to those reported in ocean and lake surface. For example, Payne(1972) reported a diurnal pattern in albedo that was similar in magnitude to those inthis study, including comparable values at low solar elevation angles.The latitude and high relief of the study area restricted the range of angles thatdirect solar radiation could be measured from. Horizon angles throughout the studyarea averaged 25◦ in the west and southwest directions, and were consistently above 10◦,imposing a lower limit on the range of elevation angles. The highest elevation anglepossible for the sites (at solar noon on the summer solstice) is 63.1◦, and the highestelevation angle during an albedo measurement was 62.8◦. As a result of these limits,some patterns of variability were not observed that may affect streams at lower latitudesor in lowland regions. For example, albedo values approaching unity have been observedon calm surfaces as the sun approaches 0◦ at sunrise or sunsetThe interaction between transmissivity and solar elevation angle matched the ex-pected pattern of variability described by Katsaros et al. (1985) and Oke (1987) for flat-water conditions. Diffuse lighting conditions (low transmissivity) were associated with35reduced surface albedo across the range of calculated solar elevation angles. The largestreduction of albedo during diffuse light conditions occurred at low elevation angles whenthe sun was near the horizon. However, diffuse lighting conditions appeared to haveminimal influence on whitewater albedo at high elevation angles. The apparent lack ofresponse may reflect the fact that aeration would create a broad range of incidence an-gles, even for direct solar radiation, in contrast to flatwater. However, the apparent lackof response could also result from suspended sediment bias. SSC measurements corre-sponding to whitewater albedo measurements taken at solar elevations greater than 45◦in direct light conditions averaged 22 mg/L, whereas average SSC for whitewater albedoin the same conditions was 81 mg/L. The suppressed response of albedo to solar altitudeunder diffuse lighting conditions also explains the reduction in variance in albedo, sincevalues are reduced the most at low solar elevation angles. Diffuse lighting conditionsshould create the greatest reduction in albedo at low solar elevation angles when albedovalues are highest during clear-sky conditions, which would reduce the amount of variancein the relation between albedo and elevation angle.4.1.2 Discharge and aerationA primary objective of this study was to quantify the influence of aeration on streamsurface albedo. At Rutherford Creek, albedo measurements were taken at three locationsthat encompassed a range of visible levels of aeration. Average albedo values at the threesites were 0.09, 0.13, and 0.22, respectively. Subsequent albedo measurements taken atcalm and aerated portions of the stream surface several metres apart from each other onRutherford Creek and Rubble Creek differed by 0.14, on average. These findings indi-cate that, controlling for the effects of solar elevation angle and transmissivity, aerationsignificantly enhances albedo.The relation between albedo and discharge was weak. The weak response of streamsurface albedo to aeration with increasing flow can likely be attributed in part to theheight of the pyranometers above the stream surface during measurements as well asthe range of flow conditions experienced at Rutherford Creek during the field season.Measured flows during sampling campaigns on Rutherford Creek only ranged between1.8 and 3.1 m3s−1, reflecting the diversion of flow around the sampling reach for a run-of-river hydroelectric facility. Albedo measurements at the hydraulic jump were takenat a height of approximately 0.5 m in order to minimize the pyranometer’s view ofboulders and to consistently view aerated portions of the surface, as opposed to viewinga combination of visibly aerated and calm portions of the water surface that wouldvary with discharge. In contrast, Richards and Moore (2011) measured albedo over36a broader range of flows, ranging from approximately 0.5 to 7.0 m3s−1. Furthermore,their downward-facing pyranometer was at a greater height above the surface than inthe current study (1 m at low flow), so it sampled a larger area with varying degrees ofaeration, which in turn varied with discharge, contributing to a stronger relation betweenalbedo and discharge.Reflectance increases in visible wavelengths as the thickness of foam increases (Whit-lock et al., 1982), suggesting that increasingly thick layers of foam should increase albedoafter the entirety of the pyranometer’s field of view is covered by whitewater. Despitewhitewater covering almost all of the pyranometer’s field of view during whitewater mea-surements at Rutherford Creek, the highest albedo value measured was 0.32, which isbelow the maximum value of 0.4 measured by Richards and Moore (2011), and 0.5 mea-sured by Whitlock et al. (1982), suggesting that albedo could continue to increase withaeration at higher discharges at the hydraulic jump. Highly aerated flow over cascades,where albedo values were likely to be higher than 0.32, were present at Rubble Creek;however, the most vigorously aerated portions of flow were inaccessible and thus werenot sampled.One issue that is difficult to address is the location-specific relation between aerationand discharge. For instance, the rate at which flow becomes visibly aerated with increas-ing discharge may differ between riffles and hydraulic jumps downstream of rock steps.Additionally, stream surface albedo varies widely on a fine spatial scale in channels withcomplex morphologies. Therefore, it may be most effective to determine the relationshipbetween albedo and aeration in terms of areal increases to visible whitewater at higherflows to account for aeration effects.4.1.3 Suspended sedimentStream surface albedo varied with suspended sediment concentration (Table 3.3). Albedoin streams with low suspended sediment concentrations (SSC < 50 mg/L) averaged 0.06,which is comparable with the values found in studies on low-gradient streams with lowSSC (e.g Evans et al., 1998; Leach and Moore, 2010). Other studies have reportedaverage daily albedo values as low as 0.03 (Caissie et al., 2007; Benyahya et al., 2012),which were lower than almost all clear-sky albedo values measured in this study. Onlythree measured albedo values in this study were less than 0.03; all three were measuredunder overcast conditions.Measured albedo values for streams with higher suspended sediment concentrationwere similar to values found in past work from high-turbidity settings. Mean albedovalues for streams with SSC greater than 50 mg/L averaged 0.10, which is consistent37with the values reported by Chikita et al. (2010) on a highly turbid proglacial riverwhere SSC typically exceeded 200 mg/L. Measurements from Lillooet River were nearlyidentical to those found in previous work by Knudson (2012) on the same river. Nielsonet al. (2009) also reported an increase of 0.03 to 0.07 in albedo with turbidity. Averageflatwater albedo measured in this study with corresponding SSC > 50 mg/L was 0.04higher than measurements with SSC < 50 mg/L.Albedo increased sharply with SSC at low concentrations and flattened at high con-centrations for both flatwater and whitewater conditions. This nonlinear dependence ofalbedo on SSC is not surprising; a similar relation was observed by Han (1997) withinvisible wavelengths in a laboratory setting. The strong positive relation between albedoand SSC visibly began to flatten as sediment concentrations approached 30 mg/L in flat-water and 15 mg/L in whitewater. Consistent with these visual observations, primarysplits in the recursive partitioning analysis were at 30.91 mg/L for flatwater and15.44 mg/L for whitewater.The saturation effect in the relation may be explained by enhancement of albedo bybackscatter that would decrease at higher concentrations of suspended sediment (Nunezet al., 1972; Katsaros et al., 1985), since backscatter has been reported to be higher inclear water than highly turbid water (Jerlov, 1968).4.2 Model performance4.2.1 Model selection and testingModels fit for flatwater albedo had greater predictive ability than those for whitewaterconditions. The weaker predictive ability of the whitewater models reflects the increasedscatter in the relation brought on by aeration that was not accounted for by any terms inthe model. Surface roughness at low solar elevation angles at aerated locations may havealso contributed to scatter (Oke, 1987), particularly at hydraulic jumps where albedotended to be largest in magnitude.The majority of the models considered during the initial stages of model fitting didnot have reasonable coefficients and were thus rejected. Considering the cross-validationperformance and the physical reasonableness of the model coefficients, three models arerecommended. Two flatwater models, models 3 and 11, were selected, using each repre-sentation of SSC (categorical and continuous), as well as one whitewater model (model6) using the categorical SSC representation. For flatwater, model 3 (continuous SSC )slightly outperformed model 11 (categorical SSC ). However, the categorical representa-38tion is useful because the model can be used even in the absence of suspended sedimentdata for streams that can visibly be classed as turbid. Model 6 had greater predictiveability using a categorical SSC term than model 13, which used continuous SSC as apredictor. Moreover, model 6 requires less input data.4.2.2 Model scalingThe models developed here address variability in albedo with respect to the governingphysical processes, but are based on measurements from isolated points on the watersurface. As demonstrated at Rubble Creek, Cayoosh Creek, and Rutherford Creek, thevalue of albedo can vary widely on a scale of metres. Measurements from a single pointor several points on the stream surface do not necessarily represent the entire streamsurface, since variability in albedo is continuous both temporally and spatially across thestream surface.Spatial variability could be addressed to some extent by sampling albedo at a greaternumber of points along the stream surface and calculating an average value for the reachin question. Temporal variability due to solar elevation angle is already accounted forby the model. However, stream surface shading derived from vegetation, topography,streambanks, and cloud cover varies both spatially and temporally, influencing the frac-tions of direct and diffuse solar radiation (and thus the albedo). Future work shouldexplore methods of upscaling albedo measurements to represent the full stream surfaceand investigate the effectiveness of point measures compared to a more complete whole-surface representation of albedo.4.3 Analysis of digital camera imagesThe magnitude of scatter in the relation between albedo and the coefficient of variationwithin the photographs was comparable in proportion to the measured albedo values,limiting the utility of the relation as a predictor of albedo. However, the form of therelation between albedo and CV is reasonable. The fit of the observations to a logisticfunction supports the assertion that albedo increases with CV as the surface becomesmore visibly aerated, and that the relation should flatten at high amounts of aeration asimages become increasingly white as they are saturated with light-coloured pixels.39Much of the noise in the relation may be inherent to the changing appearance ofthe water surface from moment to moment. Flow crossing beneath the camera may nothave the same appearance and CV from second to second, particularly over rock- or log-steps or cascades where localized water velocity is high. Further, solar elevation angle,atmospheric transmissivity, and SSC influence albedo independently from aeration, thusrepresenting additional confounding influences and sources of scatter.40Chapter 5Conclusion5.1 Key findingsDue to its dependence on the incidence angle for direct solar radiation, albedo exhibiteda strong diurnal cycle in clear weather conditions that is consistent with patterns ofvariability reported in ocean and lake studies (Nunez et al., 1972; Payne, 1972; Oke,1987). Albedo values measured in conditions dominated by direct radiation ranged from0.04 to 0.25 in flatwater and 0.09 to 0.33 in whitewater, so characterizing stream albedousing individual albedo measurements may not be appropriate, especially in streams thatare exposed to direct solar radiation at a range of solar elevation angles. Albedo tendedto decrease with increasing diffuse radiation, especially at low solar angles, consistentwith optical theory (Katsaros et al., 1985; Oke, 1987).Albedo was enhanced at sites with visible whitewater: at Rutherford Creek, albedoaveraged 0.09 over calm surfaces and 0.22 over aerated surfaces. The observed weakresponse of albedo to increasing discharge and aeration was potentially limited by thenarrow range of flows that were sampled during the field season. Also, it is likely thatalbedo exhibits a stronger response to discharge when averaged over larger areas of thestream surface, as found by Richards and Moore (2011).Albedo increased sharply with SSC at low concentrations and then levelled out athigher concentrations. Recursive partitioning analysis of the albedo-SSC relation sug-gested thresholds of 30 mg/L in flatwater and 15 mg/L over flatwater. Compared to lowSSC conditions, average values of albedo were enhanced by 0.04 for SSC ≥ 30 mg/Lover flatwater, and by 0.06 for SSC ≥ 15 mg/L over whitewater.Predictive models were fit separately for flatwater and whitewater using regressionanalysis, with candidate predictors including the sine of the solar elevation angle, trans-41missivity and suspended sediment concentration, and their interactions. Candidate mod-els were tested through cross-validation between study reaches, and models with phys-ically unrealistic coefficients were rejected. For flatwater, use of ln SSC as a predictoryielded the highest predictive capability; predictive ability decreased slightly using a cat-egorical representation of SSC. However, the model incorporating SSC as a categoricalvariable (low/high) offers the advantage of allowing the user to make predictions in theabsence of suspended sediment data. For whitewater, the categorical SSC representationyielded superior predictive ability compared to the inclusion of ln SSC into the model.The coefficient of variation of digital camera images was tested as a proxy for albedoin relation to aeration. The albedo-CV relation approximated a logistic curve, suggest-ing that the positive relation between albedo and CV flattens as images become morevisibly white as light-coloured pixels saturate the image at high flows. Unfortunately,the magnitude of scatter in the relation is comparable to the range of measured albedovalues, limiting the utility of the relation as a predictor.5.2 Recommendations for future researchThis study has quantified the dependence of albedo on the controlling physical processesfor mountain streams encompassing a broad range of conditions and developed statisticalmodels to predict stream surface albedo. The statistical models were tested through crossvalidation, but should be evaluated over a broader range of conditions. In particular, therange of solar elevation angles sampled was limited by the high relief of the study sites andby the latitude and dates of sampling. Therefore, the predictive models should be furthertested at sites that experience both lower and higher solar elevation angles than sampledhere. In this study, only suspended sediment concentration was considered, whereas theeffect of suspended sediment on albedo could also be influenced by mineralogy or particlesize distribution.Stream surface albedo varies both spatially and temporally across the stream surface.Measurements of albedo, including those in this study, have been measured at isolatedpoints over the stream surface that may not be representative of the overall albedo of thestream surface. 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