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Refinement of tracer dilution methods for discharge measurements in steep mountain streams Richardson, Mark E. 2015

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Refinement of tracer dilution methods for discharge measurements insteep mountain streamsbyMark E. RichardsonB.Sc., Civil and Environmental Engineering, Case Western Reserve University, U.S.A, 2012B.A., Computer Science, Case Western Reserve University, U.S.A., 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Geography)The University of British Columbia(Vancouver)September 2015c© Mark E. Richardson, 2015AbstractTracer dilution methods using salt and Rhodamine WT (RWT) are commonly used to measuredischarge in steep mountain streams. This research addressed knowledge gaps associated with dilu-tion methods using original field data collected on nine streams in southwest British Columbia anddischarge measurements conducted by Northwest Hydraulic Consultants. Laboratory experimentswere conducted to evaluate the uncertainties associated with different procedures for calibrating therelation between salt concentration and electrical conductivity (EC) for dry salt injection, and toevaluate the effects of RWT decay due to sorption and photolysis.For salt dilution, calibration should be conducted at the in-situ stream temperature for greatestaccuracy. The calibration factor varied linearly with background EC for water samples with EC lessthan 1000 µS/cm. For higher background EC, factors plotted below the fitted relation, likely due todifferences in the relative ionic abundances.Minimum mixing lengths ranged between 6.5 and 24.5 stream wetted widths, but determiningthe mixing length can be confounded by surface-subsurface water fluxes. Probes need to be placedon opposite sides of the stream to verify adequate mixing, because probes located at different lo-cations on the same of the stream sometimes suggested complete mixing had occurred when it infact had not. For probes located downstream of complete mixing, breakthrough curves (BTCs) forprobes located in the main current differed significantly from probes in zones with recirculatingflow, even though they yielded discharge values within ± 10%.The peak of the BTC is a function of the mass of tracer injected, reach length, channel cross-sectional area, and the integral of a non-dimensional BTC, A∗. The distribution of A∗ derived fromanalysis of 175 BTCs can be used, in conjunction with estimates of channel geometry and desiredincreases in EC, to estimate dosing requirements to avoid under- or over-dosing a stream reach.The calibration factor for RWT varied with turbidity, indicating that calibration is essentialfor each discharge measurement. Laboratory and field experiments focused on RWT decay wereconfounded by other factors, so no firm conclusions could be drawn.iiPrefaceThis thesis is original work completed by the author. Guidance was given by the supervisory com-mittee: Dan Moore, Brett Eaton, and Andre´ Zimmermann.A version of work in sections 3.1, 3.3, and 3.5.1 has been presented as a poster: “Advancementsin tracer dilution gauging: quantifying uncertainties in streamflow data” (Richardson, M., Moore,R.D. and Zimmermann, A.). The author acted as lead investigator and presented the poster at theAGU-GAC-MAC-CGU Joint Assembly meeting on May 4, 2015, in Montreal, Quebec and at theCanadian Water Resources Association (CWRA) meeting on June 3, 2015, in Winnipeg, Manitoba.A version of the results in section 3.1 has been presented with the title “Derivation, uncertainty,and variance of the calibration factor used in salt dilution flow measurements” (Sentlinger, G.,Zimmermann, A., Richardson, M. and Fraser, J.). The author provided data and analysis results forthe presentation material. The presentation was given at the American Water Association (AWRA)meeting on November 4, 2014, in Tysons Corner, U.S.A., and at the International Conference onForests and Water in a Changing Environment (IUFRO) meeting on July 7, 2015, in Kelowna,British Columbia.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation for the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.1 Salt dilution gauging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Rhodamine WT dye dilution gauging . . . . . . . . . . . . . . . . . . . . 81.3 Research objectives and thesis structure . . . . . . . . . . . . . . . . . . . . . . . 92 Study sites and methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1 Study sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1.1 Field sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1.2 Water sample sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Field methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.1 Stream gauging for salt dilution . . . . . . . . . . . . . . . . . . . . . . . 142.2.2 Measurement probe setup . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.3 Surveying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.4 Stream gauging for Rhodamine WT dye dilution . . . . . . . . . . . . . . 192.3 Laboratory methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20iv2.3.1 Laboratory calibrations for salt dilution . . . . . . . . . . . . . . . . . . . 202.3.2 Laboratory calibrations and laboratory experiment for Rhodamine WT dyedilution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4.1 Uncertainty analysis of discharge measurements . . . . . . . . . . . . . . 242.4.2 Mixing lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.3 Relationships for dosing guidelines . . . . . . . . . . . . . . . . . . . . . 273 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1 Calibration factors for salt dilution via dry slug injection . . . . . . . . . . . . . . 293.2 Mixing characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3 Measurement location and discharge variability . . . . . . . . . . . . . . . . . . . 333.4 Dosage guidelines: relations between A* and reach characteristics . . . . . . . . . 343.5 Rhodamine WT dilution gauging . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.5.1 Laboratory calibrations and experiment for Rhodamine WT . . . . . . . . 433.5.2 Stream gauging with Rhodamine WT . . . . . . . . . . . . . . . . . . . . 454 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.1 Calibration factors for salt dilution via dry slug injection . . . . . . . . . . . . . . 484.1.1 Experiments 1 through 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.1.2 Experiment 5 - province-wide CFT analysis . . . . . . . . . . . . . . . . . 494.1.3 Guidelines for determining CFT uncertainty . . . . . . . . . . . . . . . . . 504.2 Mixing characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.3 Measurement location and discharge variability . . . . . . . . . . . . . . . . . . . 544.4 Dosage guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.4.1 Relations between A* and reach characteristics . . . . . . . . . . . . . . . 564.4.2 Using A∗ for dosage guidelines . . . . . . . . . . . . . . . . . . . . . . . . 584.5 Rhodamine WT dilution gauging . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.5.1 Laboratory calibrations and experiment for Rhodamine WT . . . . . . . . 614.5.2 Stream gauging with Rhodamine WT . . . . . . . . . . . . . . . . . . . . 625 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.1 Summary of key results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70vList of TablesTable 1.1 Salt dilution dosage guidelines from various sources. . . . . . . . . . . . . . . 7Table 2.1 Streams used in study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Table 2.2 Laboratory experiments for salt dilution calibration procedure . . . . . . . . . . 21Table 2.3 Instruments and materials used for laboratory calibrations for salt dilution . . . 21Table 2.4 Example calibration results using the distilled water correction used in this study 22Table 3.1 Results from laboratory experiments for salt dilution calibration procedure . . . 29Table 3.2 Statistical tests for laboratory experiments for salt dilution calibration procedure 30Table 3.3 Cation and anion analyses results for selected water samples . . . . . . . . . . 31Table 3.4 Multiple linear regression for CFT vs. ECBG for triple calibrations . . . . . . . 32Table 3.5 Mixing lengths determined from discharge measurements at multiple locations 34Table 3.6 Discharge measurements for Carnation Creek Trib C . . . . . . . . . . . . . . . 34Table 3.7 Discharge measurements for injections focusing on measurement location vari-ability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Table 3.8 Measurement location variability of A∗ . . . . . . . . . . . . . . . . . . . . . . 39Table 3.9 Results for each set (n = 7) of Rhodamine WT calibrations . . . . . . . . . . . . 43Table 3.10 Statistical tests for comparisons between turbidity levels and between probes forRhodamine WT calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Table 3.11 CFR values used for field discharge measurements . . . . . . . . . . . . . . . . 46Table 3.12 Signal/noise observations for the RWT discharge measurements . . . . . . . . . 46Table 3.13 Discharge measurements for RWT and salt dilution gauging at Mosquito Creek,North Vancouver, BC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Table 4.1 Values of dCFT for different calibration conditions, using an example CFT valueof 0.48 L · cm ·µS−1 ·m−3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Table 4.2 Values for determining A∗ from example BTC in Figure 4.2 . . . . . . . . . . . 60Table 4.3 Example salt dosage calculation using A∗ . . . . . . . . . . . . . . . . . . . . . 60viList of FiguresFigure 1.1 An example breakthrough curve (BTC) for a slug injection salt dilution dis-charge measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 2.1 Streams used in study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.2 Field sites and water sample sites . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 2.3 Examples of experimental setups at Rutherford Creek and Pemberton Creek . . 18Figure 2.4 Rhodamine WT laboratory experiment setup . . . . . . . . . . . . . . . . . . 24Figure 2.5 Discharge measurement uncertainty breakdown for a a typical low uncertaintymeasurement and a typical high uncertainty measurement. . . . . . . . . . . . 25Figure 3.1 Relation between CFT and background ECT for salt dilution calibrations con-ducted in the laboratory and field . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 3.2 Relation between CFT and background ECT for salt dilution calibrations con-ducted with three probes concurrently . . . . . . . . . . . . . . . . . . . . . . 32Figure 3.3 Stage-discharge relation for Bridge Glacier West Creek (data from Moyer, 2015) 35Figure 3.4 BTCs for discharge measurements focused on measurement location variability 36Figure 3.5 Plots of all non-dimensional BTCs . . . . . . . . . . . . . . . . . . . . . . . . 38Figure 3.6 Boxplot of A∗ values for all injections (field study streams and NHC streams)and for each field study stream. . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 3.7 Histograms of A∗ values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.8 Variability of A∗ with discharge, for all injections from all field study streams(n = 121) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 3.9 Variability of A∗ with ratio of reach length to wetted width, for all injectionsfrom all field study streams (n = 121) . . . . . . . . . . . . . . . . . . . . . . 41Figure 3.10 Variability of A∗ with discharge, for a constant reach length, at Pemberton Creek 42Figure 3.11 Variability of A∗ with reach length, for constant discharge, at Carnation CreekTrib C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42viiFigure 3.12 Time series plots of turbidity and Rhodamine WT for laboratory experiment . . 44Figure 3.13 Rhodamine WT decay at different silt concentrations . . . . . . . . . . . . . . 45Figure 4.1 Example BTC from Bridge Glacier South Creek . . . . . . . . . . . . . . . . 55Figure 4.2 Example BTC transformation to determine A∗ . . . . . . . . . . . . . . . . . . 59viiiAcknowledgementsThis work is the result of efforts by many people. First, thanks go to my supervisor Dan Moore.Dan’s enthusiam, ideas, and passion for this project were without bounds, and kept me focused andexcited.The guidance and ideas from Andre´ Zimmermann during and after my internship at North-west Hydraulic Consultants were invaluable to the success of this thesis. Thanks also go to BrettEaton for showing me the streams of North Vancouver and for guidance in fluvial geomorphology.I learned an immense amount from my discussions with Frank van der Have, Dave Hutchinson,Robin Pike and Gabe Sentlinger.Funding for this research project was provided by operating grants to Professor Dan Moorefrom Natural Sciences and Engineering Research Councel (NSERC) and by Northwest HydraulicConsultants and Mitacs as part of a Mitacs Accelerate Internship.Special thanks go to the many enthusiastic individuals who provided field assistance and goodcompany: Kevin Akaoka, Tim Argast, Brett Eaton, Luke Gould, Greg Grzybowski, Eleri Harris,Cameron Hunter, Michele Koppes, Jason Leach, Alex McMahon, Dan Moore, Alexis Moyer, TobiasMu¨ller, Elli Papangelakis, Robin Pike, Colin Sutherland, Charlotte Trowbridge, David West, andAndre´ Zimmermann.Many of the field and laboratory experiments would not have been possible without the equip-ment and water samples provided by Jane Bachman (Environmental Dynamics, Inc.), Frank vander Have and Christoph Langley (Hoskin Scientific), Dave Hutchinson (Water Survey of Canada),Robin Pike (Ministry of Environment), Gabe Sentlinger (Fathom Scientific), and Northwest Hy-draulic Consultants.I would like to thank Professor Stephen Hauck at Case Western Reserve University and Profes-sor Daniel Bain at University of Pittsburgh for introducing me to the wonderful world of environ-mental science and fluvial systems.Lastly, I would like to thank my parents, sister and brother who have supported me throughoutmy education, and are always keen to learn about my thesis work.ixChapter 1Introduction1.1 Motivation for the studyIn the last decade, there has been increasing attention within both the operational and research com-munities to quantifying the uncertainties in stream flow data (e.g. Liu et al., 2009; Westerberg et al.,2011; McMillan et al., 2012). Hydrologists need a clear understanding of the uncertainty associatedwith the data they are using for integration into rating curve development, hydrological model cali-bration, and hydrologic analyses. The uncertainty associated with a discharge time series combinesthe uncertainties in the discharge measurement, in the measurement of stage, and in the rating curve.This study focuses on discharge measurement uncertainty. Field discharge measurements may beprone to high uncertainty, and factors that affect uncertainty include field conditions, practitionerexperience, and the method used for discharge measurement.The velocity-area method via current metering or via acoustic doppler current profiling is themost commonly used method for discharge measurement. There is a vast body of literature explor-ing the accuracy of, and the uncertainties associated with, the velocity-area method (e.g. Herschy,1975; Pelletier, 1988; Oberg and Mueller, 2007). However, this method may be impractical orsubject to great uncertainties for steep stream reachs due to complex channel geometries.An alternative discharge measurement method is dilution gauging via stream tracers (domi-nantly salt or Rhodamine dye). This method can be a powerful tool for measuring stream dischargeor exploring solute dynamics, especially in steep, rough streams that cannot be gauged accuratelyusing the velocity-area method (Moore, 2005). Dilution gauging has been growing in use due toincreasing need to monitor discharge in steep mountain streams. For example, flow measurementsin these streams are vital for planning and managing run-of-river hydro-electric projects that aretypically sited on steep streams, and for scientific studies that focus on the hydrology of headwaterstreams (e.g. Gomi et al., 2002; Ward et al., 2013; Kelleher et al., 2013).1The advantage of dilution gauging over the velocity-area method for steep streams warrantsfurther research into the uncertainty of dilution gauging. The method has been shown to be accurateto within ± 4-7% (Day, 1977) and is applicable to a wide range of stream sizes, from small first-order streams (Q = 0.007 m3/s) to large rivers (Q = 400 m3/s) (Gonalez-Pinzon et al., 2013).Despite decades of experience with tracer injection, there are many uncertainties involved in themethod. Furthermore, there are no standard operating procedures (SOPs) for tracer dilution gaugingfor discharge measurements, leading to the emergence of a range of different methodologies basedon individual practitioner knowledge and experience. In contrast, SOPs have been developed forthe velocity-area method of discharge measurement by different government agencies (e.g. Letvaket al., 1998; Turnipseed and Sauer, 2010).Salt tracers and dye tracers are the most common conservative (non-reactive) tracers used inhydrology studies. Salt tracers tend to be more widely used for discharge measurements than dyetracers, but questions and concerns have been raised in the scientific literature and in the water re-sources industry, such as the magnitude of measurement uncertainty (Moore, 2005; Sentlinger et al.,20141), the reliability of tracer experiments for developing relations between stream flow and flowresistance (e.g. Lee and Ferguson, 2002; Comiti et al., 2007), and the quantity of salt to inject duringan experiment (Kite, 1993; Hudson and Fraser, 2002; Moore, 2005). Dye tracer injection methods,while more expensive than salt tracer methods, have the ability to measure higher discharges be-cause dye concentrations are detectable at much lower concentrations than salt. However, manypractitioners are hesitant to use dye tracers due to the potential for non-conservative behaviour andsignificant mass loss in the stream channel (Bencala et al., 1983; Clow and Fleming, 2008). Tracerdye is susceptible to in-channel loss due to sorption onto sediment suspended in the water and on thechannel bed and photolysis from sunlight, so it may not be an appropriate method for highly turbidstreams or for exposed streams on sunny days. Nevertheless, some practitioners have adopted dyemethods exclusively, but the range of applicable scenarios is not widely known.For a tracer dilution measurement, tracer material is injected into a stream and its concentrationis monitored at a downstream location. The primary assumption of dilution gauging is that thetracer is completely mixed across the stream channel at the location of measurement. The streamreach distance required for complete mixing is the mixing length (xm). The major processes thatgovern tracer transport and mixing are the bulk transfer of tracer material via advection downstream,transverse dispersion across the stream channel via turbulence, vertical mixing through the watercolumn, and longitudinal dispersion that causes some material to travel downstream more quickly(Moore, 2005).There are two injection techniques for discharge measurement via tracer dilution. Constant-rate1Sentlinger, G., Zimmermann, A., Pike, R., Hutchinson, D., Hudson, R., Richardson, M., and Moore, R. Salt dilutionstandard operating procedure protocol working group meeting. April 29, 2014. Environment Canada, Vancouver, BC.2injection involves injecting a continuous supply of tracer material into the stream for the duration ofthe measurement, while slug injection involves a near-instantaneous injection of a specified amountof salt. Constant-rate injection tends to be more accurate, because complete mixing at the measure-ment location can easily be verified, the method only requires measurements at the stream waterbackground tracer concentration and at the steady state tracer concentration, and long tracer res-idence times in the measurement reach do not affect the discharge measurement. However, sluginjection may be more appropriate at higher flows since less tracer material is needed. Also, spe-cialized equipment is needed for constant-rate injection; therefore, slug injection may be preferreddue to equipment availability, costs, and/or site accessibility.Slug injection will be the focus of this thesis due to its potential to measure a much wider rangeof discharges with significantly less tracer material and specialized equipment. For slug injection,the tracer can be injected in two ways. For slug injection via salt-in-solution, the salt is pre-mixedwith stream water, and a known volume of this primary/injection solution is injected into the stream.For slug injection, a known mass of salt is injected directly into the stream, either as dry salt or as abrine comprising the known mass of salt and an arbitrary volume of water.The record of tracer concentration with time at the measurement location is called a tracer break-through curve (BTC) (Figure 1.1). For salt tracers, the temperature-corrected electrical conductivity(ECT ) of the stream water is measured, as the difference between ECT (t) (the ECT measured at timet (µS · cm−1)), and ECBG (the background ECT of the stream water (µS · cm−1)) is linearly relatedto the concentration of the injected salt. For dye tracers, the fluorescence of the stream water ismeasured.The discharge (Q) of a stream can be determined from the integral of the BTC (approximatedas a summation of discrete measurements) and the initial mass of injected salt, as follows:Q=MCFT ·Dtåni=1[ECT (t)−ECBG](1.1)where M is the volume of salt injected (g), CFT is a calibration constant relating salt concentrationto ECT (g · cm ·µS−1 ·m−3), Dt is the time interval between successive measurements (s), and n isthe number of ECT measurements. To determine the calibration constantCFT , a solution of salt andwater (known as the secondary solution) is added to a sample of stream water in increments. Theresulting ECT and salt concentration ([NaCl]) after each addition of secondary solution is recorded.[NaCl] is plotted as a function of the ECT , and the slope of the line, CFT , is determined by linearregression.3Figure 1.1: An example breakthrough curve (BTC) for a slug injection salt dilution dischargemeasurement.The objective of this study was to contribute to our understanding of the uncertainties and limita-tions of, and best practices for, tracer dilution gauging by slug injection. Progress in this subject willsave time and money for practitioners, promote consistency between different flow measurements,and improve confidence in the results of hydrological studies. The remainder of this chapter consistsof a literature review identifying key knowledge gaps, followed by specific research objectives toaddress these knowledge gaps.1.2 Literature review1.2.1 Salt dilution gaugingIn this section, the current state of knowledge of salt dilution gauging is reviewed with particularattention to three topics: (1) the calibration procedure, (2) determination of mixing length, and (3)estimation of appropriate mass of salt to inject.Calibration procedure. The calibration procedure relating ECT and [NaCl] is a primary sourceof uncertainty in discharge measurements. The practitioner must decide how many additions of4secondary solution are sufficient to characterize the relation between [NaCl] and ECT . Differentpractitioners are known to use one, four, or more additions of secondary solution. Moore (2003)suggested to add secondary solution until the ECT measured in the calibration tank exceeds themaximum ECT recorded during the dilution measurement, in order to accurately characterize therange of ECT values measured during passage of the breakthrough curve.For the salt-in-solution method, the practitioner can use a volume of the primary/injection solu-tion to determine the relation between ECT and the relative concentration of injection solution in thestream water. Salt-in-solution is advantageous since it is only based on measurements of volume,which can be accurately measured in the field. However, since the secondary solution is based onthe injection solution, the calibration procedure must be performed for each measurement. Also,if the salt concentration is unknown in the injection solution, and there is an error during the cali-bration procedure, the discharge measurement is invalid since one cannot simply re-calibrate with adifferent solution of differing salt concentration.For the dry injection method, a calibration solution must be created with a known mass of saltmixed with water. Mass measurements are difficult in the field, and practitioners may bring pre-weighed salt to add to stream water for the secondary solution, or they may pre-mix a secondary so-lution. Practitioners may use stream water, distilled water, or tap water for this calibration solution.However, if the water used to generate the calibration solution differs from the background ECT forthe gauged stream, the calibration factor will be biased. For example, when using distilled water,the effective background concentration decreases with each addition of calibration solution due todilution of the stream water with low-conductivity distilled water. The dry injection calibration pro-cedure can be advantageous since the secondary solution is not dependent on the concentration ofthe injection solution, and a practitioner can use a standard secondary solution (e.g. 2.0 g salt in 1.0L water) for every calibration.A. Zimmermann (pers. comm., October 19, 2014) and G. Sentlinger (pers. comm., October27, 2014) have each developed a correction procedure to account for differences in ECT betweendistilled water used for the secondary solution and the stream water. However, a correction proce-5dure for calibration is not included as an SOP from any agency. An adequate correction procedurewill allow practitioners to pre-mix a secondary solution before heading into the field, and to use onesecondary solution for multiple tracer injections at different stream sites.Mixing length determination. One of the most critical factors governing the accuracy of streamgauging by slug injection is the requirement that the tracer be fully mixed across the stream at themeasurement location. A range of models have been proposed to determine mixing lengths basedon hydraulic and geometric parameters of the stream (e.g. Glover, 1964), and the application of one-dimensional diffusion models (e.g. Fischer, 1966; Yotsukura and Cobb, 1972; Ward, 1973). Manyof these early models proposed that the mixing length must be much longer for tracer injectionsfrom the side of the channel, xs, versus injections from the centre of the channel, xc. Glover (1964)and Fischer (1966) suggested that xs = 4 · xc, while Ward (1973) suggested that xs = (25=7) · xc.Day (1977) studied mixing lengths on five mountain streams in New Zealand. The streamswere described as steep (slope = 0.018 - 0.027 m/m), with large relative roughness values, andstream widths ranging from 2.7 m to 11.4 m. Based on results from 41 dilution gaugings, Dayrecommended that the mixing length (xm) should equal or exceed 25 wetted stream widths (w)to ensure complete mixing. He also determined that centre versus side injection does not have asignificant effect on the mixing length. Day’s (1977) protocol remains the de-facto standard whenestimating an adequate mixing length for a stream reach. However, the mixing characteristics ofthe stream will be dependent on its geomorphic properties as well as the flow level, suggestingthat a universal mixing length (xm = 25 ·w) may not be accurate for all streams and all flow levels.Furthermore, in some streams it may be impossible to find a suitable stream reach that is longenough to accomodate Day’s standard (e.g. due to tributary inflow, safety/accessibility).An adequate mixing length is typically confirmed by comparing discharge measurements fromtwo different measurement locations for the same tracer injection. If the measurements agree withinsome specified tolerance (based on the estimated uncertainty of the calculated discharges), then themixing length is considered adequate. Ideally, the measurement locations are on opposite sides ofthe stream. With this method, however, it can be difficult to determine the mixing length, often due6to surface-subsurface water fluxes. For example, Zellweger et al. (1989) found that, for a gravel-bedstream, measured discharge increased as the measurement location moved downstream, becausethe tracer needed a longer stream reach to fully mix with sub-channel bed flow. Clow and Fleming(2008) also found a steady increase in discharge measurement moving downstream, and attributed itto either surface-subsurface water fluxes or tracer loss. The measurement discrepancy arising frommixing length ambiguity poses a major issue for accurate stream flow measurements.Tracer dosage for injection. The quantity of tracer to inject during an experiment is a balancingact, as there must be enough injected to ensure an adequate response for accurate measurements(Moore, 2005) while minimizing the potential for deleterious ecological impacts (Wood and Dykes,2002). The minimum dosage necessary is dependent on the stability of the measurement reading,the precision of the measurement probe, the desired increase in tracer concentration, and the mixingcharacteristics of the stream. For example, a stream with less longitudinal dispersion induces a moreconcentrated salt wave with a higher peak concentration, and requires less injection volume (Moore,2005). Multiple suggestions for minimum mass for injection have arisen in the literature and frompersonal communication (Table 1.1). Moore (2005) also suggested conducting trial injections witha small volume or mass, and then increasing the volume or mass as necessary.Table 1.1: Salt dilution dosage guidelines from various sources.Literature Suggestion for peak ECT (ECpeak) and/or injection amountKite (1993) ECpeak > 1:5 ·ECBGHudson and Fraser (2002) ECpeak > 6:0 ·ECBGMoore (2005) ECpeak > 2:0 ·ECBG to 3:0 ·ECBG for streamswith ECBG < 50 mS/cmECpeak > 1:5 ·ECBG for streamswith ECBG > 50 mS/cmA. Zimmermann (pers. comm., July 31, 2015) ECpeak > ECBG+30 mS/cm1 kg of salt per m3/s of stream flow, or0.5 kg of salt per m3/s of stream flow for well-mixedchannel with minimal in-channel storageB. Bowden (pers. comm., August 5, 2015) Consider BTC as square pulse at easily measureableconcentration. Injection mass is based on thisconcentration and expected stream discharge71.2.2 Rhodamine WT dye dilution gaugingRhodamine WT (RWT) is the most commonly used dye for measuring discharge via tracer dilution.In-channel tracer loss is a major concern for Rhodamine WT, due to its ability to sorb to organicand inorganic material in suspension or in the bed, and photolysis. Tracer loss (via decay or otherprocesses) would cause an overestimate of discharge, since the tracer would be more diluted in thestream water. Also, light scattering by suspended sediment may affect the measured fluorescence.Smart and Laidlaw (1977) looked at tracer properties for seven different fluorescent dyes, in-cluding RWT, in a series of laboratory experiments. Notable findings from that study relating toRWT decay are as follows: (1) suspended sediment raised measured fluorescence and reduced ef-fective dye fluorescence due to light absorption and scattering by the sediment, (2) sorption effectswere not found to be an issue for sediment concentrations below 1000 mg/L, unless the sedimentwas very fine and/or contained organic matter, and above 1000 mg/L adsorption became a poten-tial issue, (3) dye losses did not scale proportionally with the amount of dye, and therefore thepercentage loss in dye was relatively higher for low concentrations than for high concentrations.Researchers conducting field studies with RWT have reported effects from sediment sorptionand photolysis. Duerk (1983) did not find significant dye loss from any source when they gaugedtwo concrete-lined storm sewers during a series of rain events. Bencala et al. (1983) found (1) tracerloss due to interaction with the gravel stream bed (the stream water had low suspended sedimentconcentration), (2) no interaction between salt and RWT in a laboratory experiment, and (3) evi-dence of RWT sorption to suspended sediment in a laboratory experiment. Dierberg and DeBusk(2005) found tracer loss due to sediment adsorption and photolysis. However, it is important tonote that the field and laboratory experiments performed by Bencala et al. (1983) and Dierberg andDeBusk (2005) were over much longer time scales (multiple hours to multiple days) than are thecase for dilution gauging injections (typically under an hour for the tracer to flush out of the streamreach). Kilpatrick and Cobb (1985) suggested that significant RWT decay from photolysis occurswhen exposed to direct sunlight for several hours.These studies have confirmed that (1) RWT decay due to sediment sorption and photolysis is a8possible issue, and (2) suspended sediment affects the measured fluorescence. However, no studiesknown to the author have focused specifically on the effect that RWT decay or suspended sedimentconcentration has on a dilution discharge measurement.1.3 Research objectives and thesis structureThe review in Section 1.2 has identified a number of knowledge gaps in the current protocols fortracer dilution gauging for stream discharge measurements. The overall objective of this study wasto improve current field and analysis techniques for tracer dilution gauging, as we move towards thedevelopment of standard operating procedures to measure stream discharge. The specific researchquestions addressed by the thesis are:1. For salt dilution gauging via injection of dry salt, what are the uncertainties associated withthe range of calibration procedures currently in use, and what is the most accurate and robustapproach to calibrating the relation between salt concentration and electrical conductivity?To what extent does the calibration factor vary with background water chemistry? How muchuncertainty would be involved in using a standard value if it is not possible to conduct acalibration in the field?2. For Rhodamine WT dilution gauging via injection of dry Rhodamine WT, to what extent doesthe calibration factor vary with suspended sediment concentration (turbidity level)? Howmuch uncertainty would be involved in using a standard value if it is not possible to conducta calibration in the field, and how does this compare to the uncertainty for a standard valuefor salt calibration?3. Can mixing lengths be predicted from geomorphic properties of the stream channel? Whatfactors influence our ability to determine an adequate mixing length for a stream reach?4. How sensitive is the discharge measurement to location along or across the stream channel?5. For salt dilution gauging, can dosage guidelines be developed based on geomorphic and/or ge-ometric properties of the stream channel and desired increases of peak ECT over background9ECT ?6. For gauging with Rhodamine WT, what are the effects of tracer decay (from sorption andphotolysis) on the calibration procedure and discharge measurement?The remainder of this thesis is organised as follows. Chapter 2 describes the study sites andthe field, laboratory, and data analysis methods. Chapter 3 presents results of the field experiments,laboratory experiments, and data analysis. Chapter 4 discusses the results in the context of the re-search objectives defined above. Chapter 5 summarizes the main conclusions of this study, presentsrecommendations for SOPs, and identifies areas where further research is required.10Chapter 2Study sites and methodology2.1 Study sites2.1.1 Field sitesThe study focused on streams that are appropriate for stream gauging via tracer dilution. Thesestreams are small to intermediate size (typical discharges less than 10 m3/s) with gradients exceeding2% and channel morphologies ranging from riffle-pool to cascade (Table 2.1, Figure 2.1). Studystreams were located in the southern Coast Mountains and Vancouver Island (Figure 2.2).11Table 2.1: Streams used in studyStream General location Coordinates Channel type Average Average channel Discharge Average flow No.(approximate) slope width (m3/s) velocity reaches(%) (m) (m/s)Bridge Glacier Lilloet Icefield, 50◦49’ 50” N Step-pool 5.7-22 6-8* 0.78-3.58 0.30-1.08 5South Creek 123◦29’ 50” WBridge Glacier Lilloet Icefield, 50◦49’ 47” N Step-pool 9.5 10-12* 4.58-10.8 0.73-1.02 1West Creek 123◦33’ 19” WCarnation Creek Southwest 48◦55’ 05” N Riffle-pool 1.9 3.9 0.010-0.188 0.06-0.36 1Tributary C Vancouver Island 124◦59’ 02” WCarnation Creek Southwest, 48◦55’ 05” N Step-pool 8.6 2.1 0.009-0.010 0.07-0.08 1Tributary L Vancouver Island 124◦59’ 02” WCayoosh Creek Pemberton 50◦23’ 05” Step-pool 10.7 6.1 4.50-4.96 0.86-0.89 1122◦28’ 10”Mosquito Creek North Vancouver 49◦21’ 10” N Step-pool 10** 5-7* 0.261-0.319 0.23-0.28 1123◦05’ 6.5”Pemberton Creek Pemberton 50◦19’ 19” N Cascade-pool 4.1 8.9 1.10-3.93 0.45-0.75 1122◦48’ 44” WPlace Creek Pemberton 50◦27’ 57” N Step-pool 18 7.1 0.542-1.03 N/A 1122◦38’ 31” W (steep)Rutherford Creek Between Whistler 50◦16’ 19” N Cascade-pool 3.4 7.7 1.77-3.04 0.41-0.48 2and Pemberton 122◦52’ 13” W* indicates estimates made from field photographs** indicates estimate made from Google Earth12(a) Place Creek (b) Rutherford Creek (c) Pemberton Creek(d) Carnation Tributary C (e) Carnation Tributary L (f) Mosquito Creek(g) Bridge Glacier South Creek (h) Bridge Glacier West Creek (i) Cayoosh CreekFigure 2.1: Streams used in study2.1.2 Water sample sitesWater samples were collected at field sites listed in Table 2.1, at Northwest Hydraulic Consultants(NHC) project sites, at Environmental Dynamics Inc. project sites, and at Water Survey of Canadahydrometric gauging stations (Figure 2.2). The intention was to collect a diverse set of water sam-ples from different areas of British Columbia and Yukon with a range of background water chemistryand electrical conductivity. Samples were collected in 1-L plastic sample containers and transported13to NHC. They were stored in a refrigerator to keep them near in-situ temperature until they werecalibrated.2.2 Field methods2.2.1 Stream gauging for salt dilutionTracer injections were performed to determine stream discharges as well as study the mixing dy-namics of the streams. The dry mass slug injection method (Hudson and Fraser, 2005) and thesalt-in-solution slug injection method (Moore, 2005) were used. Dry injection was used for higherflows when more salt was needed and rapid dissolution of the salt could be ensured. Slug injectionwith salt-in-solution was used for lower flows. In general, these methods are the preferred mea-surement techniques for the study streams, as the stream reaches are high-gradient and turbulent,facilitating rapid mixing of solutes.Dry mass injection is performed by injecting a known mass of salt upstream and measuring thechange in temperature-corrected electrical conductivity (ECT ) at a point downstream of the injectionpoint. Prior to injection, the background ECT (ECBG) of the ambient streamwater is measured. Afterinjection, ECT is measured as the salt wave travels downstream, until the ECT returns to its stable,background level.A calibration procedure relating mass concentration of the salt to the ECT of the water wasperformed either on-site or later in the laboratory with a collected stream water sample. First, thebackground ECT of the streamwater is measured. Then, a salt solution (typically 2 g of salt in 1L of streamwater, known as the secondary solution) is added in either 5 or 10 mL increments, andthe new ECT is recorded after each secondary solution addition followed by stirring to ensure it isfully mixed into the stream water sample. The stream water sample with the additional secondarysolution is known as the calibration solution. Secondary solution additions are continued until theECT of the calibration solution exceeds the maximum ECT observed during the injection. Thesalt concentration of the calibration solution is plotted as a function of the ECT of the calibrationsolution, and the slope of the line is determined by linear regression. The slope of this relation is14Figure 2.2: Field sites and water sample sites: fieldwork and water sample acquired (blue dots)and water sample only (red dots). Five additional water sample sites were in Yukon, butthe exact locations are unknown.15referred to as temperature-corrected calibration factor, CFT (g · cm ·µS−1 ·m−3).After calibration, the stream discharge, Q (m3=s), can be calculated asQ=MCFT ·A (2.1)where M is the mass (g) of salt injected into the stream, and A is the area under the plot of ECT -ECBG versus time (µS · s · cm−1). The value of A is typically determined as follows:A= Dt ·nåi=1[ECT (t)−ECBG] (2.2)For salt-in-solution injection, a primary solution is made with salt and stream water. A typicalconcentration for the primary solution is 1 kg of salt in 6 L of water, or about 160 g/L, which issufficiently below the solubility to ensure complete dissolution of the salt (Moore, pers. comm.).A sample of primary solution, typically 50 or 100 mL, is removed and set aside for calibration. Ameasured volume of primary solution is injected into the stream at the injection point, and ECT ismonitored in the same way as dry injection.The primary solution set aside for calibration is diluted in a secondary solution by mixing asmall volume of primary solution (typically 5 or 10 mL) with a sample (typically 1.0 L) of purestream water. This secondary solution is incrementally added to a streamwater sample and changesin ECT are recorded in the same manner as the dry injection method.After calibration, the stream discharge can be calculated asQ=VkT ·A (2.3)where V is the volume (L) of primary solution injected into the stream, and kT is the slope of thecalibration line (L · cm ·µS−1 ·m−3).Electrical conductivity was measured using two instrument setups. The first setup is a WTWMulti 340i handheld meter connected to a Cambell Scientific CR510 data logger. The data logger isset up to measure ECT at 1-s intervals, and record a 5-s average of these measurements. The WTW16meter is accurate to ± 0:1 µS/cm for ECT readings below 200 µS/cm, and accurate to ± 1 µS/cmfor readings above 200 µS/cm. The second setup is a high-resolution electrical conductivity sensor(H-RECS) connected to a QiQuac storage device, developed by Aquarius Research & Development.The QiQuac measures ECT at 1-s intervals and records a 6-s average of these measurements. TheH-RECS is accurate to 0:01 µS/cm.The electrical conductivity (EC) of water increases with temperature. All measurement probescompensate for this by applying a nonlinear correction to the measured electrical conductivitybased on the measured temperature. This results in the temperature-corrected electrical conduc-tivity (ECT ), which is the equivalent EC value at 25 ◦C.2.2.2 Measurement probe setupThe ECT measurement probes were set up in three arrangements, depending on whether the goalwas to measure discharge, to study mixing lengths, or to study variability of breakthrough curvesand discharge measurements with measurement location (Figure 2.3). To assess whether the saltwas completely mixed at the downstream end of the reach, two probes were set up on opposite sidesof the stream, and staggered downstream by 5 to 10 m. When access to both sides of the stream wasnot possible, the probes were staggered on the same side of the stream. Complete tracer mixing inthe stream channel was assumed if the two measurements agreed within a reasonable tolerance.To study mixing lengths, complete mixing was first verified by comparing discharges deter-mined from two probes placed as described earlier. These first two probes were typically locatedat least 25 wetted widths downstream, the recommendation of minimum reach length from Day(1977). Additional probes were installed upstream in a longitudinal pattern.To study variability associated with measurement location, complete mixing was first verifiedby comparing discharges determined from two probes placed as described earlier. In subsequentmeasurements, probes were placed downstream of the point of complete mixing in different areas ofthe stream. Figure 2.3d shows an example probe setup for measurement location variability, whereprobes were placed in a slow-moving side pool (Probe 3), in a backwater eddy behind an obstruction17(Probe 2), in a flow constriction (Probe 1), or in turbulent whitewater (Probe 4). In some scenarios,the probes were placed in close proximity to minimize the effects of longitudinal dispersion ofthe tracer as much as possible. In other scenarios, some probes were placed significantly furtherdownstream (up to 54 wetted widths) to observe the effects of extending the reach length.(a) Discharge measurement setup (b) Mixing length setup(c) Microscale variations setup (d) Microscale variations setup, close up on measurementlocationsFigure 2.3: Examples of experimental setups at Rutherford Creek (a, b, c) and PembertonCreek (d). For reference for Rutherford Creek, the distance from the injection point tothe location where complete mixing was verified was 140 m and the mean wetted widthwas 7.7 m. For reference for Pemberton Creek, the mean wetted width was 10.0 m.182.2.3 SurveyingChannels were surveyed to determine reach length, reach gradient, average wetted channel width,and a classification of channel morphology. Reach length was measured with a surveyor’s tape or aLTI TruPulse 360R rangefinder (specified accuracy from manufacturer for distance measurementsis ± 30 cm). Reach gradient was calculated using reach length measurements and vertical distancemeasurements with the rangefinder. Average wetted channel width was measured with a surveyor’stape when the stream was small enough to wade across safely; otherwise, a rangefinder was used.Width measurements were taken at three to five locations along the stream reach and averaged.Distances were measured to the nearest 0.1 m. Channel morphologies were determined by visualobservation in the field and from photographs. These observations were matched to specific mor-phologies detailed in the BC Channel Assessment Procedure Field Guidebook (British Columbia,1996). The morphologies in Table 2.1 refer to the classifications in the Field Guidebook.2.2.4 Stream gauging for Rhodamine WT dye dilutionStream gauging with Rhodamine WT dye follows the same principles as salt dilution gauging. Aknown mass of RWT was injected upstream and the change in dye concentration was measureddownstream of the injection point. The fluorescence probe provided output in millivolts (mV). Acalibration procedure, analogous to salt dilution calibration, was performed to relate RhodamineWT concentration (g/L) to measurements in mV.After calibration, the stream discharge Q (m3=s) can be calculated asQ=MCFR ·A (2.4)where M is the mass (g) of Rhodamine WT dye injected into the stream, CFR is the slope ofthe calibration line (g ·L−1 ·mV−1), and A is the area under the plot of RWT (t) - RWTBG versustime (mV · s), where RWT (t) is the measurement reading from the fluorometer at time t (mV), andRWTBG is the measurement reading from the fluorometer for the ambient stream water (mV) .Discharge measurements with RWT were performed at Mosquito Creek in North Vancouver,19BC. Two dye probes were placed downstream of complete mixing (215 m from injection point), andtwo additional probes were placed much further downstream (520 m from injection) to observe anyeffects of sorption to suspended sediment or the stream channel. Each dye probe had a conductivityprobe installed in close proximity. For each injection, dye was injected into the stream, followed bya salt injection approximately three minutes later. This procedure allowed for comparison betweenthe two tracer dilution techniques. Laboratory experiments have shown that salt and RWT do notinteract (Bencala et al., 1983), allowing for concurrent tracer measurements.For Rhodamine gauging, Sommer TQ-Tracer fluorescent tracer devices were used. These de-vices record measurements at 1-s intervals, and are accurate to ±0.1 mV. The instrument setup forthe salt dilution was the same setup as described in Section Laboratory methods2.3.1 Laboratory calibrations for salt dilutionLaboratory calibrations to determine the temperature-corrected calibration factor (CFT ) for salt di-lution gauging were performed at Northwest Hydraulic Consultants (NHC) in North Vancouver,British Columbia. The calibration procedure is the same as described in Section 2.2.1 above.Five comparative experiments, in conjunction with data provided by NHC, were performedto observe CFT variation due to equipment, calibration procedure, the technician performing thecalibration, and the environment in which the calibration was performed (Table 2.2). Table 2.3 liststhe equipment and materials used for laboratory calibrations.The environmental setup and procedures were intended to be as controlled as possible to min-imize experimental and human error. Volumetric flasks, mason jars, and probes were rinsed withdistilled water and stream water prior to calibration. Stream water and standard calibration solu-tions were mixed vigorously before each calibration. At each addition of standard solution into thecalibration stream water, the water was mixed until the ECT reading stabilized. When calibratingat in-situ stream temperature, the calibration stream water and standard solution were placed in anice-water bath to keep water temperature low (5-10 ◦C).20Table 2.2: Laboratory experiments for salt dilution calibration procedureExperiment Methods compared Method (a) Method (b)1 (a) Autopipette vs. Autopipette used to inject secondary Glass pipette used to inject secondary(b) Glass pipette solution into stream water sample solution into stream water sample2 (a) One secondary solution vs. One secondary solution used for all New secondary solution used for each(b) Multiple secondary solutions calibrations calibration3 (a) Stream water vs. Stream water mixed with NaCl used for Distilled water mixed with NaCl used(b) Distilled water secondary solution for secondary solution4 (a) In-situ temperature vs. Calibrations performed at near in-situ Calibrations performed at room(b) Room temperature temperature (ice bath) temperature5 Comparing calibration results of various stream waters collected throughout British Columbia and YukonTable 2.3: Instruments and materials used for laboratory calibrations for salt dilutionEquipment/Materials Desciption/Information InstrumentprecisionSifto Hy-Grade Food Grade SaltCole-Parmer Symmetry 0.00005%(120g x 0.0001g) mass scaleWTW Cond 3310 cell constant = 0.475 cm−1 0.5%Portable Conductivity MeterTetracon 325 Conductivity Cell 0.5%Thermo-Scientific Finnpipette 0.8%F2 adjustable autopipette10 mL glass pipette 0.2%Glass volumetric flask (500 mL) 0.0003%Glass volumetric flask (1000 mL) 0.0004%Two mason jars For holding secondary solution and calibration solutionPortable cooler and ice For ice bath set-up in Experiments 4, 5PC software for salt gauging calibration Developed in-house at NHCDistilled water Used for secondary solution in Experiments 3, 4, 5Stream water Used for secondary solution in Experiments 1, 2, 3(Seymour Creek, North Vancouver, BC)Stream water Water to be calibrated in Experiments 1, 2, 3(Seymour Creek)Stream water Water to be calibrated in Experiment 5(streams throughout BC)21For Experiments 3 and 5, distilled water was mixed with salt to use for the secondary solution.Since the ECBG of distilled water was different than ECBG of the stream water to be calibrated, adistilled water correction must be applied. The effective ECBG of the calibration stream water assecondary solution is added, ECBG;e f f , can be calculated as follows (Zimmerman, pers. comm.):ECBG;e f f =ECBG;S ·VS+VD ·ECBG;DVT(2.5)where ECBG;S is the ECBG of the stream water sample, VS is the volume of the stream water sample,VD is the volume of secondary solution added, ECBG;D is the ECBG of the distilled water, and VTis the total volume of the stream water sample and secondary solution added. Table 2.4 showsthe results from an example calibration procedure, with and without the distilled water correction.The difference in CFT values will increase as the difference of ECBG;S and ECBG;D increases. Thecorrection from Equation 2.5 can be used with any secondary solution water (e.g. distilled water,tap water), as this would only change the value of ECBG;D.Table 2.4: Example calibration results using the distilled water correction used in this study.The concentration of the secondary solution was 1.99 g/L, the volume of stream water tobe calibrated was 0.5 L, and the ECT of the distilled water used for the secondary solutionwas 2.0 µS · cm−1.Secondary Salt concentration ECBG;S ECBG;e f f ECT measured ECT correctedsolution of calibration (µS · cm−1) (µS · cm−1) (µS · cm−1) (µS · cm−1)added (L) water (mg/L)0 0.0 84.7 84.7 84.7 84.70.005 19.7 84.7 83.9 124.9 125.70.010 39.0 84.7 83.1 163.8 165.40.015 58.0 84.7 82.3 202 204.40.020 76.5 84.7 81.5 239 242.2Resulting CFT 0.496 0.486(g · cm ·µS−1 ·m−3)For Experiments 1-4, seven calibrations were performed for each method. The mean and stan-dard deviation were determined for each method. A two-sided T-test for means and an F-test forvariances were conducted to compare the two methods for each experiment. For Experiment 5,22many water samples were calibrated with one measurement probe. In addition, some water sampleswere calibrated with three probes concurrently to observe differences in probes. All measurementprobes used were calibrated with a 0.01 mol/L KCl conductivity standard solution prior to streamwater calibration.Selected water samples from Experiment 5 were analyzed at the Ministry of Environment An-alytical Laboratory. Samples were chosen based on unique characteristics such as low or highbackground ECT and low or high CFT value. The Analytical Laboratory performed cation analysisby ICP/OES Spectrometer and anion analysic by ion chromatography.2.3.2 Laboratory calibrations and laboratory experiment for Rhodamine WT dyedilutionLaboratory calibrations for Rhodamine WT dye were performed to observe differences in CFR dueto suspended sediment concentration. Two TQ-Tracer devices were used for calibration at a low andhigh turbidity level. The turbidity sensor used was an Analite NEP395 Turbidity Probe, accurateto ± 0.1 NTU for turbidity measurements up to 400 NTU. Stream water from Seymour Creek(North Vancouver, BC) was used for the low turbidity calibration water (turbidity = 2.0±1.0 NTU).Silt was added to the stream water to obtain a high turbidity calibration water (turbidity = 250 ±50 NTU). At each addition of Rhodamine WT secondary solution, the measured fluorescence wasrecorded after 10 s of stirring of the calibration solution due to initial instability of the measurementsignal. Before each addition of secondary solution, the turbidity of the calibration solution wasmeasured and recorded. Seven calibrations were performed for each combination of probe (WSCAand WSCB) and turbidity level (low and high) for a total of four combinations. F-tests for varianceswere conducted to compare the variation of CFR values between probes or between turbidity levels,and a two factor analysis of variance (ANOVA) was conducted to determine if there was a significantdifference in average CFR value between probe and between turbidity level.For the laboratory experiment, low turbidity stream water (Seymour River, turbidity < 10 NTU,volume = 19.5 L) in a large bucket was continuously mixed with a paint mixer connected to a drillpress (Figure 2.4). Silt (from natural sources) and Rhodamine WT dye and were added throughout23the experiment to observe changes in both turbidity level and Rhodamine WT concentration. Theexperimental setup was covered with black bags to minimize light disturbance. Two RWT probesand the turbidity probe were installed securely in the water, with ample space between the measuringcells and the edges of the container.Figure 2.4: Rhodamine WT laboratory experiment setup2.4 Data analysisData analysis was performed using the R programming language Version 3.1.3, in the RStudio IDEVersion 0.98.1103 (R Core Team, 2015). Basic data organization and editing were done in MicrosoftExcel 2013 and LibreOffice Calc.2.4.1 Uncertainty analysis of discharge measurementsThe uncertainty in stream discharge determined from dilution gauging has three components: themass (or volume) or salt injected, the area under the breakthrough curve, and the calibration factor.Figure 2.5 shows a breakdown of the uncertainty associated with two example discharge measure-24ments.Figure 2.5: Discharge measurement uncertainty breakdown for a a typical low uncertaintymeasurement and a typical high uncertainty measurement.If the salt is weighed before injection, the uncertainty of mass injected, dmass, is the resolution ofthe mass scale (typically 0.1 g). For some injections, unweighed boxes with nominal salt masses (1.0kg or 1.8 kg) were injected. In this case, multiple boxes of salt were weighed, and the uncertaintywas taken as two times the standard deviation of the measured mass.The uncertainty associated with the area under the breakthrough curve, dA, is determined bydA = 2 ·n ·s (2.6)where n is the number of ECT measurements during the experiment, and s is the measure of the25stability of the ECT reading. If the recorded ECT is completely stable, then s is the resolution ofthe probe (typically 0.01, 0.1 or 1 µS/cm, depending on the equipment and range of ECT values, seesection 2.2.1). Each measurement point has two sources of uncertainty: the measurement itself andthe background ECT subtracted from the measurement, thus the multiplication by two.The uncertainty in CFT , dCFT , is based on the variability of the CFT values measured in thisstudy. Two different values of dCFT were used in this study, depending on how the calibrationprocedure was performed. If the stream water was calibrated by the author, then the value of dCFTwas based on the repeatability of the calibration (i.e. how much theCFT varies between calibrationsof the same stream water and same environmental conditions). Therefore, it was taken as two timesthe standard deviation of the seven calibrations performed for Experiment 1(a), described in Section2.3.1. If the calibration was not performed and the CFT was estimated, then the value of dCFT wasassigned a value of two times the standard error of the residuals of the relation between CFT andECBG from Experiment 5 (Section 2.3.1).The total uncertainty in a discharge measurement can be expressed either in terms of a maximumprobable error (usually at a 95% confidence level) or a maximum possible error. These are calculatedusing the fractional error for each term. The maximum probable fractional error is calculated asddpQ=sdmassM2+dAA2+dCFTCFT2(2.7)whereas the maximum possible fractional error is calculated asddmQ=dmassM+dAA+dCFTCFT(2.8)The values of ddp and ddm can be multiplied by the discharge (Q) to obtain the errors in units ofdischarge (m3/s).262.4.2 Mixing lengthsThe maximum probable and maximum possible errors are used as tolerance ranges for each mea-surement. For individual discharge measurements, if the discharge measured upstream agreed withthe furthest downstream discharge measurement, within the tolerance range, then it was deemedthat complete mixing had occurred at the location of the upstream probe.2.4.3 Relationships for dosing guidelinesAs defined earlier, the equation to determine discharge from a dry salt injection isQ=MCFT ·A (2.9)The area under the breakthrough curve, A, can be represented in non-dimensional form asA∗ = Dt ·nåi=1fi (2.10)where f is the normalized difference between ECT and ECBG, computed asf =ECT −ECBGECpeak−ECBG (2.11)and Dt is one timestep of a non-dimensional time, t , computed ast =tth(2.12)where th (s) is the harmonic mean travel time of the tracer pulse. Combining Equations (2.9) and(2.10) and re-arranging yields the following relation:M = Q ·CFT ·A∗ · th · (ECpeak−ECBG) (2.13)Since th is equal to the reach length, L (m), divided by the mean velocity, v¯ (m/s), and Q dividedby v¯ is equal to the mean cross sectional area of the stream channel, Ac, Equation 2.13 becomes27M = Ac ·L ·A∗ ·CFT · (ECpeak−ECBG) (2.14)This relation indicates that the appropriate mass of salt to inject can be estimated given estimatesor measurements of L, Ac, CFT and A∗, and a desired change in ECT from background to peakis specified. The derived relation in Equation 2.14 is algebraically equivalent to the RWT dosagesuggestion reported by Kilpatrick (1970) that relates the volumetric RWT dosage to the desired peakRWT concentration.To determine A∗, each BTC must be transformed with t and f . For this study, 121 dischargemeasurements from the field studies and 54 discharge measurements from fieldwork performed byNorthwest Hydraulic Consultants (NHC) were analyzed to determine A∗. The distribution of valuesof A∗ was used to determine recommended values for use in salt dosing calculations.28Chapter 3Results3.1 Calibration factors for salt dilution via dry slug injectionSummaries of the means and standard deviations for the first four experiments are provided in Table3.1. As shown in Table 3.2, there are statistically significant differences in the mean CFT betweenthe use of an autopipette versus a glass pipette (Experiment 1), using one secondary solution versusa new secondary solution for each calibration (Experiment 2), and calibrating at room versus in-situ temperature (Experiment 4). The percent differences between the (b) method and the preferred(a) method were 0.5%, 0.3% and 1.3% for Experiments 1, 2, and 4, respectively. There were nosignificant differences among the variances for any of the experiments.Table 3.1: Results from laboratory experiments for salt dilution calibration procedureExperiment Method Sample size Mean CFT Standard deviation of CFT Coefficient of[(mg/L) / (mS/cm)] [(mg/L) / (mS/cm)] variationExperiment 1 (a) Autopipette 7 0.4750 0.001604 0.33%(b) Glass pipette 7 0.4774 0.001386 0.29%Experiment 2 (a) One secondary solution 7 0.4750 0.001604 0.33%(b) Multiple secondary solutions 7 0.4765 0.000717 0.15%Experiment 3 (a) Stream water secondary solution 7 0.4750 0.001604 0.33%(b) Distilled water secondary solution 7 0.4748 0.000687 0.14%Experiment 4 (a) In-situ temperature calibration 7 0.4811 0.000927 0.19%(b) Room temperature calibration 7 0.4748 0.000687 0.14%In Figure 3.1, theCFT values of the water samples are plotted in black and blue for the province-29Table 3.2: Statistical tests for laboratory experiments for salt dilution calibration procedure.There are six degrees of freedom for all tests.Experiment Description T-test for means (two-sided) F-test for variancesp-value p-value1 (a) Autopipette vs. 0.011 0.732(b) Glass pipette2 (a) One secondary solution vs. 0.048 0.07(b) Multiple secondary solutions3 (a) Stream water vs. 0.732 0.058(b) Distilled water4 (a) In-situ temperature vs. < 0.001 0.485(b) Room temperatureFigure 3.1: Relation between CFT and background ECT for salt dilution calibrations con-ducted in the laboratory and field. The black line is the best-fit linear relation for labcalibrations (not including the five EDI Yukon samples calibrations).30wide CFT analysis (Experiment 5). The data points in blue are five water samples from Yukoncollected by Environmental Dynamics, Inc., which display markedly different ECBG and ionic com-position. It is unknown how these Yukon samples were collected, or where they were collected in theprovince. These five Yukon samples will be referred to as the “EDI Yukon” samples. The red datapoints are calibrations that were performed by NHC field technicians in the past three years. The“all calibrations” and “lab calibrations without Yukon samples” both exhibit a significant positiverelation between ECBG and CFT . The EDI Yukon water samples had CFT values that deviated fromthe relation between CFT and ECBG for the British Columbia and other Yukon samples, plottingsubstantially below the best-fit line.The Ministry of Environment Analytical Laboratory results are displayed in Table 3.3. The EDIYukon samples and the Eagle River sample contained markedly higher concentrations of severalcations, particularly boron and calcium, and one anion, sulfate. The EDI Yukon samples and theDuke River sample contained high concentrations of potassium.Table 3.3: Cation and anion analyses results for selected water samplesSample ID B Ca K Mg Na P F Cl NO2 Br NO3 PO4 SO4mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/LIndian River 0.025 42.62 1.57 12.94 4.94 0.02 < 0.01 0.53 < 0.01 < 0.01 < 0.01 < 0.01 241.00Porc Border 0.032 38.97 0.38 19.82 1.25 < 0.01 < 0.01 0.41 < 0.01 < 0.01 < 0.01 < 0.01 93.50Duke River 0.107 77.10 3.11 16.94 6.35 < 0.01 < 0.01 0.59 < 0.01 < 0.01 < 0.01 < 0.01 157.00Bridge South Creek < 0.002 2.84 0.46 0.18 0.25 < 0.01 < 0.01 0.28 < 0.01 < 0.01 < 0.01 < 0.01 1.14Bridge West Creek < 0.002 1.24 0.24 0.19 0.36 < 0.01 < 0.01 0.28 < 0.01 < 0.01 < 0.01 < 0.01 0.36Eagle River 0.083 77.65 0.79 25.80 16.52 < 0.01 < 0.01 0.65 < 0.01 < 0.01 1.00 < 0.01 347.00St. Mary’s Creek < 0.002 13.77 1.02 3.58 2.40 < 0.01 < 0.01 1.17 < 0.01 < 0.01 1.29 < 0.01 14.14Duck River < 0.002 24.30 1.16 10.70 0.88 < 0.01 < 0.01 0.43 < 0.01 < 0.01 < 0.01 < 0.01 7.95EDI Yukon sample #2 0.341 400.35 6.39 61.34 34.94 < 0.01 < 0.01 0.97 < 0.01 < 0.01 < 0.01 < 0.01 920.60EDI Yukon sample #4 0.315 270.55 12.71 43.48 16.45 < 0.01 < 0.01 0.65 < 0.01 < 0.01 < 0.01 < 0.01 691.00Tamihi West Trib < 0.002 3.03 0.58 0.72 0.84 0.01 < 0.01 0.58 < 0.01 < 0.01 1.06 < 0.01 2.72Gallant Creek < 0.002 9.53 0.78 1.46 7.40 0.02 < 0.01 7.39 < 0.01 < 0.01 < 0.01 < 0.01 36.23The water samples that were calibrated with three probes concurrently are displayed in Figure3.2. Testing for main effects (difference in intercept), the intercepts are not significantly differentfrom each other. Testing for main effects and interaction (difference in intercept and slope), theintercepts and slopes are not significantly different from each other (Table 3.4).31Table 3.4: Multiple linear regression for CFT vs. ECBG for triple calibrationsMain effects assuming a common slope Estimate Std. Error T statistic p-valueIntercept (WTW Black) 4.90E-01 1.15E-03 426.621 <2e-16Slope 8.20E-06 3.17E-06 2.591 0.0135Intercept (WTW Green) -2.36E-04 1.36E-03 -0.174 0.8632Intercept (WTW Red 2) -2.52E-03 1.36E-03 -1.855 0.0714Main effects and interaction Estimate Std. Error T statistic p-valueIntercept (WTW Black) 4.90E-01 1.48E-03 330.67 <2e-16Slope (WTW Black) 9.34E-06 5.59E-06 1.67 0.104Intercept (WTW Green) -4.63E-04 2.09E-03 -0.221 0.826Intercept (WTW Red 2) -1.62E-03 2.09E-03 -0.773 0.444Slope (WTW Green) 1.15E-06 7.92E-06 0.145 0.886Slope (WTW Red 2) -4.52E-06 7.89E-06 -0.573 0.571Figure 3.2: Relation between CFT and background ECT for salt dilution calibrations con-ducted with three probes concurrently. Solid lines are linear regression relations foreach probe.323.2 Mixing characteristicsTable 3.5 displays channel characteristics, discharges, and mixing lengths for different streamreaches. “Mixing length from same-side probes” indicates that two measurement probes on the sameside of the stream measured similar discharges, while “mixing length from opposite-side probes”indicates that two measurement probes on opposite sides of the stream measured similar discharges.“NA” indicates that there were probes on only one side of the stream. Note that some streams havedifferent mixing lengths based on discharge.The mixing lengths summarized in Table 3.5 range from 2.5 to ∼25 wetted widths. However,the lack of a clear relation between discharge and stage for Bridge Glacier West Creek (Figure 3.3)suggests that the tracer was not sufficiently mixed at the measurement location to yield accuratedischarge measurements. For Rutherford Creek reach 1, there was a lack of agreement betweenthe two probes, indicating that the mixing length was at least as long as the distance between theinjection point and the downstream probe.Table 3.6 summarizes results from a reach-length case study of Carnation Creek Trib C. In all sixexperiments, the calculated discharge steadily increased as a function of reach length, particularlydownstream of probe 4. The relative increase in discharge decreased with increasing flow levels.3.3 Measurement location and discharge variabilityFive streams were studied specifically for discharge variability in relation to probe location (Table3.7, Figure 3.4). A measure of the uncertainty related to probe location, eQ, was computed asfollows:eQ =Qmax−Qmin0:5 · (Qmax+Qmin) (3.1)where Qmax and Qmin are the maximum and minimum discharges among probes, respectively. Someprobes were placed in areas of significant upstream flow in a side pool (Carnation Creek Trib C), inareas of turbulent whitewater (Mosquito Creek), in near-stagnant pools behind boulders (Pemberton33Table 3.5: Mixing lengths determined from discharge measurements at multiple locationsCreek Reach Reach Reach Discharge Mixing length from Mixing length from Length/widthslope width (m3/s) same-side probes opposite-side probes ratio(%) (m) (m) (m) (m/m)Bridge South Creek 1 5.7 6-8 0.818-0.859 57.1 NA 9.5Bridge South Creek 2 7.5 6-8 0.778-0.822 14.2 NA 2.4Bridge South Creek 3 7 6-8 1.20-1.21 147.1 NA 24.5Bridge West Creek 1 9.5 10-12 4.58-5.44 146.5 NA 14.7Carnation Creek Trib C 1 1.9 1.5 0.0096-0.0549 35.9 35.9 23.9Carnation Creek Trib C 1 1.9 3.9 0.146-0.188 74.3 74.3 19.1Carnation Creek Trib L 1 8.6 1.5 0.0087-0.0095 29.6 29.6 19.7Pemberton Creek 1 4.1 9-11 1.26-2.28 58.3 58.3 6.5Pemberton Creek 1 4.1 9-11 2.28-3.29 78 78 8.7Pemberton Creek 1 4.1 9-11 3.30-3.93 107.9 NA 12Place Creek 1 17.7 7.1 0.523-1.04 45.8 45.8 6.5Rutherford Creek 1 4.8 12.0 2.56-3.04* > 105* > 105 > 8.8*Rutherford Creek 1 4.8 12.0 4.38-5.14* > 127.1* > 127.1 > 10.6*Rutherford Creek 2 3.4 7.7 1.97-3.04 142 142 18.4* indicates well-mixed reach length was not established from multiple probe agreementTable 3.6: Discharge measurements (m3/s) for Carnation Creek Trib C. Reach length (m) foreach probe is in parentheses. From visual field observation, the wetted width was between1.5 m and 2.0 m for Injections 1 through 5, and unknown for Injection 6.Injection Probe 1 Probe 2 Probe 3 Probe 4 Probe 5 Probe 6 Probe 7(34.9) (36.9) (49.2) (90.7) (120.2) (133.2) (153.7)1 0.01 0.012 0.01 0.014 0.025 0.029 0.0342 0.011 0.017 0.011 0.022 0.041 0.048 0.0573 0.022 0.026 0.021 0.025 0.029 0.032 0.0334 0.04 0.046 0.042 0.041 0.053 0.056 0.0615 0.052 0.057 0.053 0.052 0.063 0.068 0.0716 NA NA NA 0.735 0.768 0.809 0.865Creek), or in fast-flowing narrow chutes of water (Pemberton Creek). Despite obvious differencesin BTC shape (Figure 3.4), all measured discharges were in reasonable agreement for each injection(<± 10 %).34Figure 3.3: Stage-discharge relation for Bridge Glacier West Creek (data from Moyer, 2015).Rating curve and errors bands are not provided due to lack of relation between stage anddischarge.Table 3.7: Discharge measurements for injections focusing on measurement location variabil-ity. The value of eQ is a measure of the percent error in measured discharge for oneinjection.Stream Injection Number 0.5 ·(Qmax + Qmin) Qmax - Qmin eQ Notes onof probes (m3/s) (m3/s) (±%) probe locationCarnation Trib C 1 3 0.0109 0.0016 7.1 narrow stream (w = 2 m)2 3 0.0238 0.0045 9.5 narrow stream (w = 2 m)3 3 0.0400 0.0035 4.4 narrow stream (w = 2 m)4 3 0.0515 0.0074 7.2 narrow stream (w = 2 m)Carnation Trib L 1 3 0.0094 0.0006 3.1 narrow stream (w = 1.5 m)2 3 0.0090 0.0008 4.3 narrow stream (w = 1.5 m)Mosquito Creek 1 5 0.349 0.020 2.9 distributed across stream channel2 5 0.267 0.009 1.8 distributed across stream channel3 5 0.303 0.032 5.3 distributed across stream channelPemberton Creek 1 2 2.24 0.07 1.5 both sides of stream2 3 2.30 0.18 3.9 both sides of stream3 3 2.17 0.13 3.0 both sides of stream4 3 2.16 0.16 3.6 both sides of stream5 3 2.14 0.11 2.7 both sides of stream6 3 2.19 0.23 5.4 both sides of stream7 3 2.09 0.08 1.8 both sides of stream8 3 2.04 0.34 8.4 both sides of stream35Figure 3.4: BTCs for discharge measurements focused on measurement location variability.One sample injection for each stream. Different colours are the BTCs for different probesfor the same injection: (a) Carnation Creek Trib C Injection 3 (Q = 0.040 m3/s ± 4.4%;(b) Carnation Creek Trib L Injection 2 (Q = 0.0090 m3/s ± 4.3%; (c) Mosquito CreekInjection 1 (Q = 0.349 m3/s ± 2.9%; (d) Pemberton Creek Injection 5 (Q = 2.14 m3/s ±2.7%.363.4 Dosage guidelines: relations between A* and reachcharacteristicsValues of A∗ ranged from 0.25 to 0.93, with an average value of 0.55 (Figures 3.6 and 3.7). Thespread of A∗ values is less for the field study streams compared to the NHC streams, although theaverage values are similar. The spread of A∗ values decreases when looking at specific streams.Carnation Creek Trib L had high A∗ values relative to all other streams. Based on the nondimen-sional BTCs (Figure 3.5), there are two observed trends: (1) the tails of the non-dimensional BTCswere longer (or “shallower”) for larger A∗ values; and (2) the non-dimensional first arrival times(t0) were earlier for larger A∗ values.When looking at all streams, there is a positive trend between A∗ values and discharge (Figure3.8), and a negative trend between A∗ and reach length (Figure 3.9). The Pemberton Creek mea-surements for a long reach length (xm = 53·w, seen as outlier dots on Figure 3.6) had much lowerA∗ values than compared to the other Pemberton Creek measurements.A series of measurements at Pemberton Creek were taken for a wide range of discharges ata constant reach length (Figure 3.10). A weak positive relation was observed between A∗ anddischarge (p = 0.053). A series of measurements at Carnation Creek Trib C were taken at differentreach lengths for a constant discharge (Figure 3.11). The spread of these A∗ values is low, althoughthere is a significant negative relation between A∗ and reach length (p < 0.001), as was also observedfor the long reach length experiments at Pemberton Creek.Table 3.8 shows variability of A∗ based on measurement location. Carnation Creek Trib L hadsimilar A∗ values for all three probes, and the stream was significantly narrower than the otherstreams (wetted width = 1 m). The highest and lowest A∗ values occurred in all areas of the stream(e.g. slow side-pool, main water column), indicating that there is no systematic relation betweenA∗ value and measurement location across different streams. However, for each stream, the highestand lowest values of A∗ occurred at the same measurement location for all injections, indicating thatthe measurement location variability is dependent on the stream but consistent between differentinjections.37Figure 3.5: Plots of all non-dimensional BTCs: (a) BTCs with A∗ values between 0.24 and0.49 (n = 51), (b) BTCs with A∗ values between 0.49 and 0.62 (n = 67), and (c) BTCswith A∗ values between 0.62 and 0.94 (n = 51).38Figure 3.6: Boxplot of A∗ values for all injections (field study streams and NHC streams) andfor each field study stream.Table 3.8: Measurement location variability of A∗. Highest/lowest A∗ is the highest/lowest av-erage A∗ value from one probe for all injections at that stream. In the location description,the value in brackets is a visual estimate of the ratio of the local velocity near the probe tothe maximum local velocity across the channel.Stream Number Highest A∗ Lowest A∗ Location description Location descriptionof probes of highest A∗ of lowest A∗Bridge Glacier 4 0.45 0.36 Fast flowing water [speed 4/5] Directly underneathWest Creek water chute [speed 3/5]Carnation Creek 3 0.77 0.75 Slow pool [speed 1/5] Directly underneathTrib L water chute (speed 3/5)Mosquito Creek 5 0.46 0.32 Fast flowing water [speed 4/5] Steady flow in mainwater column [speed 3/5]Pemberton Creek 3 0.64 0.59 Steady flow in main Slow side-pool [speed 1/5]water column [speed 3/5]39Figure 3.7: Histograms of A∗ values: (a) Field study streams (n = 121); (b) NHC streams (n =54).40Figure 3.8: Variability of A∗ with discharge, for all injections from all field study streams (n =121). The black line is a linear regression fit to provide visual reference.Figure 3.9: Variability of A∗ with ratio of reach length to wetted width, for all injections fromall field study streams (n = 121). The black line is a linear regression fit to provide visualreference.41Figure 3.10: Variability of A∗ with discharge, for a constant reach length, at Pemberton Creek.There was no significant linear relation found.Figure 3.11: Variability of A∗ with reach length, for constant discharge, at Carnation CreekTrib C. Black line is linear regression relation for all injections (p < 0.001).423.5 Rhodamine WT dilution gauging3.5.1 Laboratory calibrations and experiment for Rhodamine WTSummaries of the means, standard deviations, and coefficients of variation for each calibrationcondition are provided in Table 3.9. As shown in Table 3.10, there were no significant differences inCFR variance between probes or between turbidity levels. The probe used did not have a significanteffect on CFR value, but the level of turbidity did have a significant effect.Table 3.9: Results for each set (n = 7) of Rhodamine WT calibrationsProbe Turbidity Mean CFR Standard deviation Coefficient of[(g/L)] / mV] of CFR [(g/L)] / mV] VariationWSCA low 6.82E-05 0.30E-05 4.3%WSCA high 7.48E-05 0.35E-05 4.6%WSCB low 6.71E-05 0.22E-05 3.3%WSCB high 7.58E-05 0.30E-05 4.0%Table 3.10: Statistical tests for comparisons between turbidity levels and between probes forRhodamine WT calibrationsF-tests for variances (6 degrees of freedom for each test)Turbidity level Probe p-valueLow vs. high turbidity WSCA 0.49Low vs. high turbidity WSCB 0.72Low turbidity WSCA vs. WSCB 0.69High turbidity WSCA vs. WSCB 0.46Two factor analysis of varianceFactor Degrees of freedom F-value p-valueProbe (WSCA and WSCB) 1 0.165 0.688Turbidity (low and high) 1 53.7 < 0.001Residuals 25Figure 3.12 shows results from the full laboratory experiment. Both RWT probes exhibitedsimilar behavior, and only one probe’s data are presented here. RWT and turbidity measurements43were averaged over 60-s intervals for visual clarity. The background fluorescence of the samplestream water was approximately 67 mV.Figure 3.12: Time series plots of turbidity (top) and Rhodamine WT (bottom) for laboratoryexperiment. Blue vertical lines indicate addition of RWT and/or silt to the water sample.Figure 3.13 highlights three 15-min intervals of the full experiment. RWT concentration wasmeasured at 1-s intervals. Over the 15 minutes, approximately 10%, 5%, and 5% of the RWT waslost due to decay for the no silt, low silt, and high silt measurements, respectively. Although thehigh silt content and no silt content trials had similar decay rates, the initial RWT concentrationduring the high silt content measurements was double the initial RWT concentration during the nosilt content measurement, resulting in half the proportional decay rate. It was observed during theexperiment that the measurements became noisier at higher suspended sediment concentrations.44Figure 3.13: Rhodamine WT decay at different silt concentrations. The y axis shows the ratioof RWT concentration to the initial concentration.3.5.2 Stream gauging with Rhodamine WTCalibrations of the stream water for all eight probes (four RWT, four salt) were performed off-site ina laboratory setting. Despite using the same calibration approach as discussed in Section 2.3.2, theRWT calibrations were not consistent (Table 3.11). DifferentCFR values were obtained for multiplecalibrations of the same probe. For HoskinB, WSCA, WSCB, the average of two calibration CFRvalues were used for calculating discharge. For HoskinA, the CFR value of the first calibration wasused due to its similarity to HoskinB CFR values and due to similar peak/background ratios duringthe gaugings.Table 3.12 shows signal:noise observations for the RWT discharge measurements. The Hoskinprobes (downstream) behaved in a similar fashion, while the WSC probes (upstream) did not.Discharge measurement results are shown in Table 3.13. Measurement uncertainties were de-termined as per the method described in Section 2.4.1. CFR uncertainty was taken as the differenceof the two measuredCFR values divided by two. The relatively high uncertainty associated with theRhodamine WT discharge measurements are due to (1) CFR uncertainty for all measurements, and45Table 3.11: CFR values used for field discharge measurementsProbe Calibration CFR CFR used r2 Number offor measurement calibration pointsHoskinA 1 0.56E-4 0.56E-4 0.999 32 1.46E-4 0.978 7HoskinB 1 0.45E-4 0.41E-4 0.937 62 0.37E-4 0.998 6WSCA 1 1.07E-4 1.21E-4 0.977 82 1.34E-4 0.998 5WSCB 1 1.25E-4 1.36E-4 0.991 62 1.46E-4 0.986 6Table 3.12: Signal/noise observations for the RWT discharge measurementsProbe Location Injection Mass injected Background uncertainty Peak:background ratio(g) (± mV) (mV:mV)WSCA Upstream 1 1.4893 0.3 150:852 2.1439 0.3 190:853 1.9986 0.3 185:85WSCB Upstream 1 1.4893 0.7 135:1002 2.1439 0.7 155:953 1.9986 0.7 150:95HoskinA Downstream 1 1.4893 1.5 220:1202 2.1439 1.5 290:1203 1.9986 1.5 280:120HoskinB Downstream 1 1.4893 1.5 225:1252 2.1439 1.5 280:1253 1.9986 1.5 275:125(2) an unstable background RWT measurement in relation to the peak to background ratio for somemeasurements and probes (Tables 3.12 and 3.13). The WSCB and HoskinA probes consistently mea-sured markedly different discharges than the other six probes (even if they were within tolerancebounds for measurement agreement for some injections).46Table 3.13: Discharge measurements for RWT and salt dilution gauging at Mosquito Creek,North Vancouver, BCInjection Probe Type Location Discharge Discharge uncertainty Measurement agreement?(m3/s) (%) (with WTWred and WTWyellow)1 WTWred Salt Upstream 1.06 9.0 YesWTWyellow Salt Upstream 1.07 4.6 YesWSCA RWT Upstream 1.05 15.5 YesWSCB RWT Upstream 1.97 43.0 YesWTWblack Salt Downstream 1.13 3.4 YesWTWgreen Salt Downstream 1.10 6.5 YesHoskinA RWT Downstream 0.76 37.5 YesHoskinB RWT Downstream 1.08 30.4 Yes2 WTWred Salt Upstream 0.93 3.4 YesWTWyellow Salt Upstream 0.93 4.7 YesWSCA RWT Upstream 0.92 15.3 YesWSCB RWT Upstream 1.23 34.5 YesWTWblack Salt Downstream 0.96 6.4 YesWTWgreen Salt Downstream 0.95 6.6 YesHoskinA RWT Downstream 0.66 28.1 NoHoskinB RWT Downstream 0.94 19.6 Yes3 WTWred Salt Upstream 0.88 3.1 YesWTWyellow Salt Upstream 0.88 3.1 YesWSCA RWT Upstream 0.88 13.5 YesWSCB RWT Upstream 1.43 15.2 NoWTWblack Salt Downstream 0.93 5.8 YesWTWgreen Salt Downstream 0.92 5.9 YesHoskinA RWT Downstream 0.63 28.3 NoHoskinB RWT Downstream 0.86 20.3 Yes47Chapter 4Discussion4.1 Calibration factors for salt dilution via dry slug injection4.1.1 Experiments 1 through 4Although the mean CFT values differed significantly between methods for Experiment 1, the dif-ference is small (0.5%) and of the same order of magnitude as the uncertainty associated with theequipment used for calibration. The variances are similar between methods. These results indicatethat using an autopipette versus a glass pipette has little effect on the uncertainty of the calibration,and ultimately the choice in equipment should be based on user preference.As was the case for Experiment 1, the differences in mean CFT values between methods forExperiment 2 are statistically significant (at a = 0.05) but small (0.3%). The variance in CFT ofusing a new secondary solution for each calibration is smaller than using one secondary solutionfor all calibrations. These results suggest that mixing a new secondary solution for each calibrationwill minimize CFT variability. However, if time constraints do not allow mixing a new solution foreach calibration, the resulting error should be under 1% based on the experimental results.In Experiment 3, there was no significant difference among CFT values, which suggests thatthe distilled water correction (Equation 2.5) adequately accounts for the differences in ionic com-position of the stream water and distilled water. However, the background ECT of the stream water48was low (37 µS · cm−1), and thus the correction was minor. More calibration tests for Experiment 3should be performed with high ECBG stream water, as the correction would have a larger influenceon the derived CFT .The variance of using distilled water for the calibration solution is smaller than using streamwater for the calibration solution. These results suggest that using distilled water for the secondarysolution will minimize CFT variability. However, the errors from using distilled water or streamwater for the secondary solution should both be under 1% based on the experimental results, aslong as the distilled-water correction is applied. Therefore, the choice in secondary solution solventshould be based on user preference.For Experiment 4, the 1.3 % difference in meanCFT values between the methods is statisticallysignificant. This difference is likely due to inaccuracies of the nonlinear correction applied to theelectrical conductivity based on temperature. The correction method is known to be most inaccurateas the water temperature drops below 3 ◦C and approaches 0 ◦C (Moore et al., 2008). Therefore,the calibration procedure should be performed at in-situ water temperature when possible. In thefield, the calibration container should rest directly in the stream to ensure the temperature is similarto that of stream water, as recommended by Moore (2005).4.1.2 Experiment 5 - province-wide CFT analysisAlthough the regressions are significant, the relative change in CFT is small over a large range ofECBG. For example, the CFT changes by approximately 1.5% over a range of 500 mS/cm for thelab calibrations. Theoretically, higher concentrations of ions impede their mobility, resulting ina weaker positive relation between EC and concentration as more ions are present in the solution(Hem, 1982; Moore et al., 2008). Therefore, one would expect an increase inCFT with an increase inEC (and ECT ), which agrees with calibrations in this study (disregarding the EDI Yukon samples).The value ofCFT will vary depending on the chemical species present in the stream water (Hem,1982; Moore et al., 2008). Therefore, one would expect different values of CFT depending on therelative proportions of different ions in the water. The low CFT values of the EDI Yukon samples49may be due to significantly higher concentrations of several cations (boron, calcium, and potassium)and/or one anion (sulfate). However, water from Eagle River in Yukon, with a relatively high ECBG,also contained high concentrations of many of these ions without exhibiting a characteristically lowCFT . Potassium (K) was not present in Eagle River water in notable quantities, but was presentin high concentrations in the EDI Yukon water samples. The Duke River water, also from Yukon,contained high concentrations of potassium, but its CFT was not markedly low in comparison toother water samples’ CFT values. The relatively large concentration of potassium ions could beaffecting the calibrations of the EDI Yukon samples, but there is not enough information to drawfirm conclusions.For the triple calibrations, the differences among probes are statistically insignificant. The threeprobes had very similar calibration constants (0.469, 0.470 and 0.469 for Red, Green and Blue,respectively). The “NHC WTW Red 2” (Red) probe produced systematically lower CFT valuesthan the other two probes. Based on the linear regressions, the Red probe produced CFT values thatwere approximately 0.4% to 1.0% lower. At least among similar devices, this study shows that oneshould expect similar CFT values, assuming the probes are properly calibrated. However, given thesystematic difference shown by the Red probe, and that there are many electrical conductivity metersavailable for use, one should always use the same device to measure the discharge and calibrate thestream water. It would be beneficial to replicate these concurrent calibrations with more devices(especially non-WTW devices).4.1.3 Guidelines for determining CFT uncertaintyAs discussed in Section 2.4.1, dCFT should vary based on the calibration conditions for each dilutionmeasurement. Table 4.1 presents a framework to determine the value of dCFT . Adequate calibrationconditions would involve an experienced user, fair weather conditions, adequate equipment (glass-ware, properly calibrated ECT measurement probe, etc.), and calibrating at in-situ stream tempera-ture. Non-adequate conditions could involve an inexperienced user, wet weather conditions (e.g. ifrainwater is splashing into the calibration container, diluting the salt concentration), non-adequate50equipment (plasticware, damaged equipment, etc.), and calibrating at air temperature. Extra careshould be taken to calibrate stream waters with very high ECBG values, as the EDI Yukon samplescalibrated in this study had the highest ECBG values and did not follow the same trends observedfrom the other stream water samples.Table 4.1: Values of dCFT for different calibration conditions, using an example CFT valueof 0.48 L · cm ·µS−1 ·m−3. The value of SD is the standard deviation of the calibrationsperformed in Experiment 1(a), the value of SEall is the residual standard error of the linearrelation between CFT and ECBG for all calibrations (from this study and from NHC fieldcalibrations), and the value of SElab is the residual standard error of the linear relationbetween CFT and ECBG for the laboratory calibrations from Experiment 5 (disregardingthe EDI Yukon water samples’ CFT values).Calibration condition Uncertainty method Value used in dCFT fordCFT determination CFT = 0.48(L · cm ·µS−1 ·m−3) L · cm ·µS−1 ·m−3Calibration performed in Based on repeatability of calibration. SD = 0.001604 0.7%adequate conditions dCFT = 2·SDCalibration performed in Based on variability of CFT values SEall = 0.009746 4.1%non-adequate conditions from all available calibration data (n = 434).dCFT = 2·SEallCFT is estimated, no Based on relation between CFT and SElab = 0.005037 2.1%calibration performed ECBG from Experiment 5 (n = 116).dCFT = 2·SElab4.2 Mixing characteristicsDay (1977) found that using a reach length xm equal to or exceeding 25 wetted widths (w) wassufficient for complete tracer mixing from 41 dilution gaugings across five mountain streams. Hefound that the typical minimum adequate mixing length ranged from xm = 8·w to xm = 25·w. Withthe exception of Bridge South Creek Reach 2, the mixing lengths in this study generally agreed withDay (1977), with xm ranging between 6.5·w and 24.5·w. In both studies, it is apparent that mixinglengths are reach-dependent as expected.In this study, it was observed that it can be problematic to use two probes on the same side of thestream to confirm adequate mixing. The experiments at Rutherford Creek Reach 1 had same-side51probe agreement, but disagreement in the opposite-side probe measurement. Two probes on thesame side of the injection location yielded a discharge of 2.60 ± 0.05 m3/s, while one probe on theopposite side of the injection location measured a discharge of 20.9 m3/s. This extreme discrepancywas seen during all injections, and all probes were approximately the same distance downstream ofthe injection point (xm = 104±1 m). Using only the same-side probes, this measurement would betaken as adequate, when it is obvious that complete mixing has not occurred across the entire streamchannel. Another example of this “same-side error” was seen at Bridge Glacier West Creek. Thedischarges yielded from the four probes were in agreement, but there was a poor relation betweenstage and discharge (Figure 3.3), indicating that the measurements were not accurate, likely due toincomplete mixing across the stream channel.This “same-side error” may confound any of the results in Table 3.5 that only have same-sidemeasurement confirmation. For example, it seems highly improbable that xm of Bridge South CreekReach 2 is equal to 2.4 w. The same-side error suggests that (1) opposite side probes are necessaryto confirm adequate mixing, and (2) at least one opposite side probe is needed to confidently studymixing lengths as in this study. Day (1977) did not comment on his methodology for measurementlocation.It was observed at Carnation Creek Trib C that determining adequate mixing length and verify-ing discharge measurements can be confounded by stream-subsurface water fluxes. A steadily in-creasing discharge with increasing reach length indicates that the stream was gaining water throughthe reach, diluting the tracer, and causing a higher discharge measurement downstream (Table 3.6).This phenomenon has been reported by others (e.g. Zellweger et al., 1989; Clow and Fleming,2008). The bottom portion of Trib C (location of Probe 4 and further downstream) flows acrossthe floodplain of the main stem of Carnation Creek. Groundwater could be discharging into TribC from Carnation Creek’s floodplain aquifer. In addition, some of the injections were performedduring a rain event, and surface and near-surface runoff likely entered the stream throughout themeasurement reach. Clow and Fleming (2008) used constant-rate injection to confirm completemixing, and found a steady increase in discharge moving downstream. However, they could not52distinguish whether it was due to surface-subsurface water fluxes or RWT decay.In some scenarios, stream-subsurface water fluxes make it almost impossible to determine thecorrect discharge and adequate mixing length, since probes at different mixing lengths, but down-stream of complete mixing, can yield different discharges. It may be most difficult to reconcile thisissue in small streams, where the stream is too narrow to space two probes an adequate distanceapart on opposite stream sides. For larger streams, the mixing length may be able to be reconciledmore easily, as probes on the same side as the injection point generally underestimate the discharge(higher tracer concentration), while probes on the opposite side generally overestimate the discharge(lower tracer concentration), if xm is too short. This situation was seen at Rutherford Creek Reach1 (discussed above). In these scenarios, the discharge measurements from either stream side shouldconverge as the probes are moved downstream, until the discharge measurements agree, and ade-quate mixing can be assumed.These discussions lead to spatial considerations. It is useful to understand the water flux ten-dencies between the stream reach of interest and the surrounding area. For example, at CarnationCreek Trib C, it would be advisable to choose a stream reach further upstream of the CarnationCreek floodplain. Losing reaches and gaining reaches will affect the discharge measurement differ-ently. If the stream is losing water downstream of complete mixing, it would lose equal amounts ofwater and tracer, with no effect on the measured discharge. However, if the stream is losing waterprior to complete mixing, it would likely affect the measurement. Therefore, a losing reach wouldaccumulate measurement error only in the mixing reach, while a gaining reach would accumulatemeasurement error throughout the entire measurement reach (mixing reach and downstream of themixing reach). In both cases, it is best to measure the discharge at the minimum xm that guaran-tees complete mixing to minimize the effects of lateral water fluxes (e.g. groundwater recharge anddischarge).In contrast to Trib C, a long reach length was not an issue at Pemberton Creek. Measurements atlengths xm = 12·w and xm = 54·w agreed. Lateral channel inputs of water were likely more insignif-icant at this stream due to the following: (1) the area was dry at the time; (2) Pemberton Creek is a53glacier-fed stream, and receives most of its water from a point source upstream, especially duringdry conditions; (3) Pemberton Creek is a steeper, valley-incised stream, and is likely not influencedby the near vicinity of other streams; (4) the drainage area for Pemberton Creek is significantlylarger than the drainage area for Trib L, and therefore the effect of lateral water fluxes per unit ofstream length will be smaller in comparison to the total flow.Based on the preceding reach-length discussion, the discharge measurement is dependent on thespecific measurement reach. Therefore, if one is comparing discharges over time (e.g. generating arating curve), one should try to use a given measurement reach consistently (i.e. the same injectionpoint and measurement point for all injections). However, stream-subsurface water fluxes and theadequate mixing length will vary based on discharge, so using the same measurement reach will notcompletely resolve these issues.The potential issues associated with “same-side” measurement error and stream-subsurface wa-ter fluxes may be impossible to reconcile in some situations, but being aware and knowledgeable ofthem will aid in attributing uncertainty levels and confidence to discharge measurements.4.3 Measurement location and discharge variabilityUnder favorable conditions (e.g. steady ECBG, confident calibration procedure), the uncertainty(ddp or ddm) in discharge measurement may be low (< 5%). The uncertainty in Q for many of theexperiments in Table 3.7 is larger than 5%. It is common to attribute a measurement discrepancybetween probes to inadequate mixing (i.e. xm is too short), but this study shows that the discrep-ancy can also be due to measurement location even if the tracer is well-mixed at the measurementlocation.There was no discernible relation between measurement location and discharge (e.g. if allprobes in fast-flowing water had closer measurement agreement than probes in slow-flowing pools).Probes that were located in fast-moving chutes of water generally had the smoothest BTCs (e.g. inFigure 3.4: Carnation Creek Trib C, blue BTC; Mosquito Creek; yellow BTC). Smooth BTCs arepreferred because they indicate that the tracer is arriving at the measurement location in a continu-54ous flow of tracer material. However, a smooth BTC does not confirm that the tracer is well-mixedthroughout the stream channel. For example, Figure 4.1 shows a smooth BTC from Bridge GlacierSouth Creek, but it is highly unlikely that complete mixing had occurred at the measurement loca-tion (xw = 2.4·w).Figure 4.1: Example BTC from Bridge Glacier South Creek. Despite the smooth shape, it ishighly unlikely that adequate mixing had occured across the stream channel, consideringthe reach length was only 2.4 wetted widths.Abrupt changes in ECT indicate that the tracer is arriving in discontinuous “pockets” of tracermaterial, which is not reflective of a well-mixed water column. Examples of choppy BTCs in Figure3.4 that exhibit abrupt changes include the green BTC at Pemberton Creek and the green BTC atCarnation Creek Trib L. The probes that recorded choppy BTCs were generally located in areas ofslow moving water (side-pools, behind obstructions). The choppiness also suggests that the streamreach is not long enough to allow for adequate mixing. In the case of Pemberton Creek, both thegreen BTC probe and the blue BTC probe were in slow side-pools, but the green BTC probe wason the opposite side of injection. Although the measurements agreed well in this case, the tracerwas likely not completely well mixed across the entire stream channel. BTC choppiness may alsobe due to probe placement in areas of aerated water, as air bubbles will cause a downward spike in55ECT reading (e.g. in Figure 3.4: Mosquito Creek, purple BTC). Moore (pers. comm.) has observedchoppy BTCs in areas with groundwater discharge through the bed.From these results, it is advised to place the measurement probes in areas of fast-flowing, non-aerated water when possible. For determining discharge, measurement location may substantiallylower the precision of the measurement, even at a location downstream of complete mixing. Quali-titatively, these experiments have shown that measurement location can have a significant effect onthe shape of the BTC, and may confound other findings that use BTC shape to quantify residencetimes of solutes and transient storage parameters (e.g. Szeftel et al., 2011; Jimnez and Wohl, 2013;Gonalez-Pinzon et al., 2013). Studies using tracer dilution should always provide a photograph anddetailed description of measurement location in relation to area of the channel (e.g. same/oppositeside of injection, behind an obstruction), reach length, reach width, and speed of the water column(e.g. in a back-eddy, in aerated fast-flowing water).4.4 Dosage guidelines4.4.1 Relations between A* and reach characteristicsThe relations between A∗ and the non-dimensional BTC tail (longer tail leads to larger A∗ values)and between A∗ and non-dimensional first arrival time (earlier arrival time leads to larger A∗ values)can be attributed to the mixing and transport characteristics of the stream reach. The three physicalprocesses that affect the BTC shape are advection, dispersion, and the amount of transient storage inthe stream reach. A stream dominated by advection with minimal dispersion and transient storagewould cause the tracer to quickly flush out of the measurement reach, resulting in a short durationBTC and a short BTC tail. A short BTC tail compared to a long BTC tail would correspond toa relatively smaller harmonic mean travel time (th), and the transformation by th will “collapse”the nondimensional BTC less, resulting in a later t0. Conversely, a stream with significant transientstorage would result in a long duration BTC and a long BTC tail. A long BTC tail would correspondto a larger th, and the nondimensional BTC will be more collapsed, resulting in an earlier t0. A longtail will remain long after transformation, leading to more area under the nondimensional BTC (A∗)56when compared to a short-tailed BTC.The high A∗ values for Carnation Creek Trib L were due to the long tail of the BTCs for thisstream, indicating a large amount of transient storage and/or dispersion throughout the measurementreach. Most tracer pulses from other streams were around 10 minutes long, while the pulses at Trib Llasted 20 minutes. The transient storage at Trib L was visible at the field site, as the reach containedmultiple pools connected by small trickles of water, with a high bed roughness relative to the sizeof the wetted channel. The mean water velocity (v¯ = 0.07 m/s) and discharge (Q = 0.009 m3/s )measured at Trib L were lower than any other stream studied. Similar velocities (v¯ = 0.10 to 0.23m/s) and discharges (Q = 0.010 m3/s to 0.040 m3/s) were also measured at Carnation Creek Trib Cfor a series of injections during a rain event. For four injections, a decrease in A∗ occurred in relationto an increase in discharge. The active stream channel visibly changed from many pools connectedby small trickles of water at low flow, to a faster-flowing, uniform flow of water at higher flows.From these observations of the two Carnation Creek watershed streams, A∗ seems highly dependenton the amount of transient storage in a stream reach. A longer tracer pulse coinciding with a streamwith more transient storage will result in a higher A∗ compared to a shorter tracer pulse.Presumably, transient storage will change with discharge depending on the stream. In somestreams, a higher discharge will cause areas of storage to connect with the main stream flow, re-sulting in less transient storage and a lower A∗. In other streams, a higher discharge will activatenew areas of the channel that will pool with water, resulting in more transient storage and a lowerA∗. Pemberton Creek was the only stream studied with a large range of discharges measured for aconstant reach length (Figure 3.10). The lack of relation between A∗ and discharge suggests that theimpact of transient storage stayed constant at this stream.As shown in Figures 3.9 and 3.11, A∗ tends to decrease as the reach length is extended. Thisrelation is most apparent when looking at the long reach length experiments at Pemberton Creek.For these three measurements, the peak ECT at the downstream location was half the value at theupstream location, and th at the downstream location was four times the value at the upstreamlocation, resulting in the value of A∗ at the downstream location equal to half the value at the57upstream location. Since the peak ECT and th do not scale proportionally as the measurementlocation is moved downstream, A∗ will vary with reach length.Measurement location can have a large effect on A∗. For example, A∗ values from MosquitoCreek ranged from 0.32 to 0.46, even though all five probes were within 8 m of each other (for ameasurement reach of 140 m). For a narrow stream (e.g. Trib L), measurement location seems tohave less of an effect on A∗ variability.The limited metadata associated with the NHC data set (e.g. no visual observation, no reachwidth or slope information, no confirmation of adequate mixing length, unknown accuracy of data)makes it difficult to integrate these results into the discussion of the field study experiments. How-ever, certain observations can be discussed. Despite the uncertainties regarding the NHC dataset,the distribution of A∗ values is comparable to the field study. There were measurements at markedlyhigher flow levels (Q = 20, 34 and 40 m3/s), and the resulting A∗ values (0.41, 0.47, 0.58, 0.48,0.53) were close to the average A∗ value (0.55), suggesting that typical values of A∗ remain similarat higher discharges.One NHC stream at very low flow (Q = 0.003 m3/s) had high A∗ values (0.69-0.84), similar tothe low flow measurements at Carnation Creek Trib L and Trib C. The tracer pulse was also verylong, indicating a large amount of transient storage. In contrast, some of the other NHC data withthe largest A∗ values (0.92, 0.89) had short tracer pulses (5-15 minutes). This may be due to a shortmixing length (possibly even too short for adequate mixing), as we have seen that A∗ and reachlength are inversely related.4.4.2 Using A∗ for dosage guidelinesThe variability of A∗ has been explored using BTCs from 21 streams (8 field study streams and 13streams in the NHC dataset). The average A∗ value (0.55) can be used as a first-order approximationto estimate the amount of salt to inject into a stream using Equation 2.14. The remaining variables inthe equation are either estimated or calculated (Ac, CFT , and L) or specified by the practitioner (thedesired peak ECT over background ECT ). Figure 4.2 and Table 4.2 show the process for determining58A∗ for an example BTC from a discharge measurement. Table 4.3 shows an example salt dosagecalculation.Figure 4.2: Example BTC transformation to determine A∗: (a) Original BTC, (b) non-dimensional BTC transformed by (ECpeak−ECBG) and th. The value of A∗ is the areaunder the curve in (b). In this example, (ECpeak−ECBG) = 12.3 µS · cm−1, and th = 839s.59Table 4.2: Values for determining A∗ from example BTC in Figure 4.2Term Description ValueA Area under BTC (µS · s · cm−1) 3860ECpeak−ECBG (µS · cm−1) 12.3th Harmonic mean travel time (s) 836A∗ Area under non-dimensional BTC (dimensionless) 0.38Table 4.3: Example salt dosage calculation using A∗Desired ECpeak - ECBG (µS · cm−1) 30Mean channel width (m) 10.0Mean water depth (m) 1.0Reach length (m) 200CFT (g · cm ·µS−1 ·m−3) 0.48A∗ (dimensionless) 0.55Salt dosage for injection (kg) 15.8The uncertainty of the salt dose will be based on the uncertainty of A∗, which may be takenas two times the standard deviation of all computed A∗ values (0.13). The uncertainty of A∗ (±0.26) is approximately half (50%) the mean value of A∗ (0.55). The A∗ uncertainty suggests that theestimate of the salt dose may be incorrect by up to 50% for a 95% confidence level. If the streamis underdosed by 50%, then the peak ECT over background ECT will be half of the desired value.For example, if the resulting peak ECT over background ECT is 15 mS/cm instead of 30 mS/cm,the discharge may still be computed, but with a higher uncertainty. If the stream is overdosedby 50%, the peak ECT over background ECT will be 150% of the desired value, which will onlyimprove (decrease) the uncertainty associated with the computed discharge. Also, compared tothe wide range of dosage guidelines suggested by others in Table 1.1, a 50% uncertainty in doseis reasonable. However, the dose uncertainty will increase based on the uncertainty in estimatingother parameters in Equation 2.14, such as the mean depth and wetted width.For practitioners, the ease of calculating A∗ leads to the ability to generate a database of A∗values for different field sites. This database can be used to better estimate the amount of salt60needed for injection, which is especially useful for (a) measuring discharge at flow levels previouslyunmeasured, and (b) measuring discharge at new streams or stream reaches. A value of A∗ can bemore accurately estimated if previous injection data from that stream can be used, as A∗ has lowerin-stream variability compared to between-stream variability. The results of this study promote thefollowing best practices to minimize A∗ variability between streams and for a single stream: (1) Theminimum adequate reach length should be used, as A∗ has been shown to decrease with reach length;(2) Similar measurement locations should be used for different injections (e.g. always measure infast-flowing, non-turbulent water), as A∗ can vary significantly based on measurement location.4.5 Rhodamine WT dilution gauging4.5.1 Laboratory calibrations and experiment for Rhodamine WTThe significant difference in CFR values for both probes between turbidity levels indicates that theamount of suspended sediment in the water affects the RWT measurement (10% and 13% differencefor each probe). These differences are much higher than observed in salt calibrations, as discussedin Section 4.1.1. This effect was also observed during the lab experiment, when adding silt atapproximately 16:13 resulted in a small but noticeable increase in measured fluorescence (Figure3.12). These observations agree with Smart’s and Laidlaw’s (1977) results that the presence ofsuspended sediment raises apparent fluorescence.BecauseCFR apparently varies across streams and probes, it is necessary to perform a calibrationfor each gauging. Future work should explore any relationships between RhodamineCFR value andstream water turbidity and/or water chemistry (similar to the salt CFT value analysis in this thesis).These relationships may provide a basis for estimating the Rhodamine CFR factor in cases whereit is not feasible to complete the calibration in the field (e.g., due to time constraints or equipmentfailure).As shown in Figure 3.12, there was a continuous decline in RWT concentration over time, evenwith no suspended sediment present. The decay is likely due to RWT degradation from the lightemitted from the measurement probe, as noted by others (Gooseff, pers. comm.). This photolytic61decay would not be an issue in the field, as the RWT would not be recirculated through the mea-surement probe.There was no discernible relationship between suspended sediment concentration and rate ofRWT decay (Figure 3.13). Surprisingly, the decay rate decreased with the addition of silt. The siltmay effectively shield the RWT from photolytic decay during measurements. The decay of RWTdue to light emission from the measurement probe and the silt additions confound any conclusionsthat may be made from this experiment about the effect of silt on RWT decay rates.The “no silt content” and “low silt content” segments of the experiment had suspended sedi-ment concentrations well below 1000 mg/L (approximately 0 mg/L and 200 mg/L, respectively).The “high silt content” segment of the experiment had a suspended sediment concentration of ap-proximately 1200 mg/L. Smart and Laidlaw (1977) found that sorption can be an issue at sedimentconcentrations above 1000 mg/L or if the sediment is extremely fine or contains significant organicmatter. However, in this study, there was no notable increase in RWT decay when the suspendedsediment concentration exceeded 1000 mg/L.Since the signal becomes less stable, or noisier, with higher suspended sediment concentrations,highly turbid waters may warrant a higher dosage of RWT for injection, to obtain an adequatesignal:noise ratio in the discharge measurement. Also, a noisier signal could make it difficult toobtain a strong linear relation between measurement reading (in mV) and concentration during thecalibration procedure. The instability of the measurement signal affected the laboratory calibrationsas one can see with the high coefficients of variation in Table 3.9, which were an order of magnitudehigher than the coefficients of variation from the salt calibrations (Table 3.1). A five-point (or more)calibration procedure should always be used to minimize any effects of signal instability.4.5.2 Stream gauging with Rhodamine WTThe discharges yielded by WSCA and HoskinB probes agreed well with those computed from saltdilution for all injections. The downstream probes yielded a small increase in discharge compared tothe upstream probes, likely due to minor tracer loss into the streambed (for both salt and Rhodamine62WT) or due to diffuse discharge of groundwater into the stream channel. This similar behavior intracer loss between both salt and RWT indicates that RWT loss due to sorption or photolysis waslikely not a factor in these measurements. If decay was an issue, an increase in discharge fromthe Rhodamine measurements relative to the salt measurements would have occurred for the down-stream probes. If there was an active degradation process, it may be hidden in the large uncertaintiesfor the RWT measurements.The RWT measurement uncertainties (13.5%-43.0%) were markedly and consistently higherthan the salt measurement uncertainties (3.1%-9.0%) for all measurements, due to the instability ofthe RWT measurement signal and large uncertainty associated with the CFR values. The measure-ment discrepancies from HoskinA compared to HoskinB, WSCA, and the conductivity probes maybe attributed to the inability to conduct a confident, consistent calibration (Table 3.11). Both Hoskinprobes had similar background uncertainty and peak/background ratios; the only difference was theCFR values. The source of measurement error is unknown for WSCB.Duerk (1983) did not detect RWT loss in constant-rate injections in a concrete storm sewer anda concrete-lined open channel. However, sorption onto the streambed is more likely an issue fornatural stream channels (versus concrete channels) due to the water and RWT filtering in and outof the streambed. Regardless, sorption with the stream bed was not apparent at the injections atMosquito Creek for this study.Bencala et al. (1983) and Dierberg and DeBusk (2005) measured decay due to gravel bed in-teractions, suspended sediment adsorption, and photolysis, but their experiments were on the timescale of hours to days, much longer than a typical slug injection measurement. The results fromthis study at Mosquito Creek suggest that RWT degradation may be insignificant for low turbiditystreams for the duration of a typical slug injection measurement (i.e. under an hour).Additional measurements should be performed in high turbidity streams, where sorption maybe a larger concern. Many streams and rivers in B.C. have high turbidity from glacial meltwater, soa greater understanding of when Rhodamine is a viable measurement technique is invaluable, espe-cially considering previous studies have identified significant decay processes at longer timescales63and at high suspended sediment concentrations. Smart and Laidlaw (1977) observed that dye lossesdue to sorption are independent of dye concentration. Therefore, if sorption is a concern, a higherdosage would minimize the relative loss of RWT for a discharge measurement.The relatively highCFR uncertainty (compared to saltCFT uncertainty) and the relation betweenCFR and turbidity level raise concerns for using RWT for automatic gauging setups. In automaticgauging setups, theCFR would not be determined for each injection, and would have to be estimated.Turbidity levels will vary based on flow level, especially during storm events when the turbidity willbe much higher than normal levels. Therefore, using one CFR value for different flow levels wouldbe inaccurate. This CFR variability is in contrast to salt CFT variability, where we have seen thatCFT remains relatively constant over a large range of background ECT values.64Chapter 5ConclusionsThe first section of this chapter summarizes the important findings of this study in relation to theresearch objectives outlined in Section 1.3. The first section also integrates these results with sug-gestions for best practices. The final section discusses areas where further study would be beneficialfor improving tracer dilution stream gauging.5.1 Summary of key resultsCalibration procedure of salt tracer dilution. The first four experiments revealed the following.There were minor (< 1%) and statistically insignificant differences in the precisions associated withthe following variations in calibration procedure: (1) the use of glass pipettes versus autopipettes,(2) mixing a new secondary solution for each calibration versus using the same secondary solutionfor each calibration, and (3) using distilled water in the secondary solution (with the appropriate dis-tilled water correction) versus using stream water in the secondary solution. Therefore, the choice ofmethodology for these different calibration approaches should be based on user preference. Despitethe temperature compensation applied by the probes, calibrating at air temperature in the laboratoryyielded significantly different values of CFT from calibrating at the stream temperature. Therefore,calibration should be performed at in-situ temperature whenever possible.For the water sampleCFT analysis from samples from British Columbia and Yukon, a significant65positive linear relation between CFT and ECBG was found for the water samples with ECBG < 600µS · cm−1. The water samples with ECBG > 1000 µS · cm−1 did not follow this trend, likely dueto differences in the relative concentrations of various cations and anions. The high ECBG watersamples imply that (a) a confident estimation of CFT based on a linear relation with ECBG may notbe possible for water samples with high ECBG, and/or (b) regional relations betweenCFT and ECBGmay be more applicable (e.g. separate relations for British Columbia and Yukon) versus a universalrelation.Also, it was found that different probes can behave differently when calibrating the same streamwater, and therefore the discharge measurement and calibration procedure should always be per-formed with the same probe. Table 4.1 can guide users when determining the uncertainty associatedwith the CFT value.Mixing lengths. The minimum adequate mixing length was found to lie between 6.5 and 24.5wetted widths for the study reaches, in general agreement with Day’s (1977) recommendation of25 wetted widths. Mixing length was reach dependent. Placing probes on opposite sides of thestream is required to verify with confidence that adequate mixing has occurred, as probes on thesame side of the stream may yield similar discharges even if the tracer is not well mixed acrossthe stream channel. If placement on both sides of the stream is not possible, then the measurementreach length should be at least 25 wetted widths downstream of the injection point to ensure thetracer is fully mixed across the stream channel at the measurement location. In channels withoutgood lateral mixing (e.g. shallow gradient channels), using an adequate mixing length may notbe feasible or possible. However, in these cases, the velocity-area method will likely be the moreappropriate discharge measurement method.Surface and subsurface discharge into the channel can confound the determination of xm andresult in ambiguous discharge measurements, as seen in this study and reported by others (Zellwegeret al., 1989; Clow and Fleming, 2008). Therefore, the shortest possible mixing reach should be usedwhen possible to minimize effects of lateral water inputs. Lateral water fluxes will likely be a largerissue for smaller streams since they will have a larger relative impact on the total flow. One could66take point measurements of ECT along the stream reach to help diagnose the existence of significantlateral inputs, since varying values of ECT suggests inflow from a different water source (Mooreet al., 2008).Discharge measurement variability due to measurement location. The choice in measure-ment location can significantly affect the discharge measurement, even downstream of adequatemixing. Differences in derived discharge were as high as 9% between different probe locationsfor the same measurement. Generally, it is best to be consistent in measurement location (e.g. al-ways place probes in areas of fast-moving water). Aerated areas and side pools tend to producechoppy BTCs, indicating that the tracer is arriving in clumps (i.e. not adequately mixed). Probes infast-moving chutes of water resulted in the smoothest BTCs, which suggests (but does not confirm)that the tracer is well-mixed across the channel. Therefore, it is advised to place probes in fast-moving (non-aerated) water when possible. The practitioner should provide detailed descriptionsand/or photographs of the measurement locations to assist in documenting factors that influence theaccuracy of a measurement.Dosage guidelines. Using Equation 2.14, the dosage can be estimated based on estimates ofchannel geometry, desired peak tracer concentration over background tracer concentration, and thenondimensional area under the BTC, A∗. Analyzing 165 BTCs, a first-order estimate of A∗ wasfound to be equal to 0.55, with a standard deviation equal to 0.13. Using two times the standarddeviation as a measure of A∗ uncertainty, the uncertainty is approximately ± 50%, suggesting thatusing this dosage approach may underdose or overdose the stream by up to 50%.The variability of A∗ decreased when focusing on a specific stream reach. The value of A∗ alsoseems to be dependent on reach length, the amount of in-stream storage in the stream reach, andmeasurement location. Therefore, a more accurate estimate of A∗ can be used, based on previousinjections from a stream reach.The practitioner can generate a database of A∗ values, with detailed descriptions of measurementlocation, measurement reach length, and other experiment conditions. He/She can use this databaseto choose a value of A∗ to use to determine injection dosage. For example, if a practitioner is67continuously returning to a stream reach for discharge measurements, he/she may use an A∗ valuespecific to that stream reach. As this database is populated, between-stream trends may becomeapparent, such as a relation between A∗ and channel morphology, which can assist the practitionerin choosing an A∗ value for measuring discharge at new field sites.Rhodamine WT dilution gauging. The CFR value from Rhodamine WT calibrations variedsignificantly as a function of the water’s turbidity level, indicating that calibration is required foreach discharge measurement (moreso than saltCFT determination). Also, the variability of repeatedcalibrations for RWT was an order of magnitude higher than for salt. It is recommended that at leastfive points be used in the calibration procedure to minimize problems associated with instability ofthe measurement signal. Due to these uncertainties associated with the calibration procedure, auto-matic gauging with RWT (using an estimated CFR value) may not be accurate. The laboratory andfield experiments focused on RWT decay due to sorption and photolysis were confounded by otherfactors, and no conclusions can be made on the effect of decay on the measurement. Regardlessof decay, measurement uncertainties were consistently and markedly higher for the RWT probes(13.5%-43.0%) than for the salt probes (3.1%-9.0%) for the field measurements.5.2 Future researchThis study has explored many aspects of tracer dilution stream gauging and the potential uncertain-ties involved. Future research should focus on a full integration of all aspects of this streamflowmeasurement technique into a standard operating procedure (SOP). This SOP should document arange of practices with associated uncertainties to allow flexibility under varying field conditions.An SOP will prove to be an invaluable asset to practitioners and scientists as we strive to quantifyand minimize measurement uncertainty.For the salt calibration procedure, additional work should be done with high ECBG (greater than1000 µS · cm−1) water samples. It will be useful to know how well the distilled water correctionworks when using distilled water in the secondary solution for these high ECBG samples. Also,additional data in this range will help us understand the relation betweenCFT and ECBG, and which68specific ions may have the greatest effect on CFT variability. Lastly, more controlled, concurrentcalibrations with different brands of conductivity probes are warranted to better understand thevariability between measurement devices. Sentlinger and Zimmermann (pers. comm.) have alreadydone significant work in CFT uncertainty, independent of the work presented in this thesis and incollaboration with the author of this thesis.A more detailed study focusing specifically on mixing lengths may reveal stronger relationsbetween reach morphology and adequate mixing lengths. These relations can be valuable, as thisstudy has shown the presence of measurement error arising from mixing length ambiguity. A betterestimate of minimum adequate mixing length will help minimize effects of lateral water fluxes.To improve upon the dosage guidelines introduced in this study, a first step would be for usersto test the guidelines in the field. The user can estimate dosage based on estimates of A∗, reachgeometry, and a desired peak ECT over background ECT , and observe how close the actual peakECT over background ECT is to the target value. Further exploration of non-dimensional BTCsand their associated non-dimensional area under the curve of the BTCs (A∗) can refine and buildupon the dosage guidelines. Specifically, the variability of A∗ in relation to stream morphology andflow level (within stream and between streams) will guide higher accuracy dosage guidelines. Theecological impact of stream tracers is a major concern for this technique, and a consistent, standarddosage guideline can help ensure that toxicity threshholds are not exceeded.This study attempted to quantify Rhodamine WT decay due to sorption and photolysis. Previousstudies (e.g. Smart and Laidlaw, 1977; Duerk, 1983; Dierberg and DeBusk, 2005) reported variouslevels of RWT decay, but many of the results were limited to laboratory experiments or during fieldexperiments over long time periods (significantly longer than a dilution gauging tracer pulse). Futureresearch on RWT should focus on the effect of water chemistry and/or turbidity on the calibrationfactor (similar to the salt calibration study described in this thesis), and on field experiments on highturbidty streams.69ReferencesBencala, K. E., Rathbun, R. E., Jackman, A. P., Kennedy, V. C., Zellweger, G. W., and Avanzino,R. J. 1983. Rhodamine WT dye losses in a mountain stream environment. Journal of theAmerican Water Resources Association, 19(6):943–950.Clow, D. W. and Fleming, A. C. 2008. Tracer gauge: An automated dye dilution gauging systemfor ice-affected streams. Water Resources Research, 44(12). W12441.Comiti, F., Mao, L., Wilcox, A., Wohl, E. E., and Lenzi, M. A. 2007. Field-derived relationshipsfor flow velocity and resistance in high-gradient streams. Journal of Hydrology, 340(12):48 – 62.Day, T. J. 1977. Observed mixing lengths in mountain streams. Journal of Hydrology,35(1):125–136.Dierberg, F. E. and DeBusk, T. A. 2005. An evaluation of two tracers in surface-flow wetlands:Rhodamine-WT and lithium. Wetlands, 25(1):8–25.Duerk, M. D. 1983. Automatic dilution gaging of rapidly varying flow. Water ResourcesInvestigations Report 83-4088, United States Geological Survey, Washington, DC, U.S.A.Fischer, H. B. 1966. Longitudinal dispersion in laboratory and natural channels. Technical ReportKH-R-12, California Institute of Technology.Glover, R. 1964. Dispersion of dissolved or suspended materials in flowing streams. ProfessionalPaper 433B, United States Geological Survey, Washington, DC, U.S.A.Gomi, T., Sidle, R. C., and Richardson, J. S. 2002. Understanding processes and downstreamlinkages of headwater systems. BioScience, 52(10):905–916.Gonalez-Pinzon, R., Haggerty, R., and Dentz, M. 2013. Scaling and predicting solute transportprocesses in streams. Water Resources Research, 49(7):4071–4088.Hem, J. 1982. Conductance: a collective measure of dissolved ions. In Minear, R. and Keith, L.,editors, Water Analysis: Vol. 1. Inorganic Species, pages 137–161. Academic Press, New York.Herschy, R. 1975. The Accuracy of Existing and New Methods of River Gauging. University ofReading, Reading, UK.70Hudson, R. and Fraser, J. 2002. Alternative methods of flow rating in small coastal streams. Forestresearch extension note EN-014, British Columbia Forest Service, Vancouver Forest Region,Nanaimo, BC.Hudson, R. and Fraser, J. 2005. Introduction to salt dilution gauging for streamflow measurementpart 4: The mass balance (or dry injection) method. Streamline Watershed ManagementBulletin, 9(1):6–12.Jimnez, M. A. and Wohl, E. 2013. Solute transport modeling using morphological parameters ofsteppool reaches. Water Resources Research, 49(3):1345–1359.Kelleher, C., Wagener, T., McGlynn, B., Ward, A. S., Gooseff, M. N., and Payn, R. A. 2013.Identifiability of transient storage model parameters along a mountain stream. Water ResourcesResearch, 49(9):5290–5306.Kilpatrick, F. A. 1970. Dosage requirements for slug injections of Rhodamine BA and WT dyes.Professional Paper 700-B, United States Geological Survey, Washington, D.C., U.S.A.Kilpatrick, F. A. and Cobb, E. D. 1985. Measurement of discharge using tracers. Techniques ofWater-Resources Investigations A16, United States Geological Survey, Washington, DC, U.S.A.Kite, G. 1993. Computerized streamflow measurement using slug injection. HydrologicalProcesses, 7(2):227–233.Lee, A. J. and Ferguson, R. I. 2002. Velocity and flow resistance in step-pool streams.Geomorphology, 46(1):59–71.Letvak, D., Richards, R., and staff, R. I. B. 1998. Manual of standard operating procedures forhydrometric surveys in british columbia. Manual 1.0, Ministry of Environment, lands and Parks,Victoria, BC.Liu, Y., Freer, J., Beven, K., and Matgen, P. 2009. Towards a limits of acceptability approach to thecalibration of hydrological models: Extending observation error. Journal of Hydrology,367(12):93–103.McMillan, H., Krueger, T., and Freer, J. 2012. Benchmarking observational uncertainties forhydrology: rainfall, river discharge and water quality. Hydrological Processes,26(26):4078–4111.Moore, R. D. 2003. Introduction to salt dilution gauging for streamflow measurement: part 1.Streamline Watershed Management Bulletin, 7(4):20–23.Moore, R. D. 2005. Introduction to salt dilution gauging for streamflow measurement part 3: sluginjection using salt in solution. Streamline Watershed Management Bulletin, 8(2):1–6.Moore, R. D., Richards, G., and Story, A. 2008. Electrical conductivity as an indicator of waterchemistry and hydrologic process. Streamline Watershed Management Bulletin, 11(2):1–6.71Oberg, K. and Mueller, D. S. 2007. Validation of streamflow measurements made with acousticdoppler current profilers. Journal of Hydraulic Engineering, 133(12):1421–1432.Pelletier, P. M. 1988. Uncertainties in the single determination of river discharge: a literaturereview. Canadian Journal of Civil Engineering, 15(5):834–850.R Core Team, R. 2015. R: A Language and Environment for Statistical Computing. R Foundationfor Statistical Computing, Vienna, Austria.Smart, P. L. and Laidlaw, I. M. S. 1977. An evaluation of some fluorescent dyes for water tracing.Water Resources Research, 13(1):15–33.Szeftel, P., Moore, R. D., and Weiler, M. 2011. Influence of distributed flow losses and gains onthe estimation of transient storage parameters from stream tracer experiments. Journal ofHydrology, 396(3):277–291.Turnipseed, D. P. and Sauer, V. B. 2010. Discharge measurements at gauging stations. Techniquesand Methods 3-A8, United States Department of the Interior and United States GeologicalSurvey, Washington, D.C., U.S.A.Ward, A. S., Gooseff, M. N., Voltz, T. J., Fitzgerald, M., Singha, K., and Zarnetske, J. P. 2013.How does rapidly changing discharge during storm events affect transient storage and channelwater balance in a headwater mountain stream? Water Resources Research, 49(9):5473–5486.Ward, P. R. B. 1973. Prediction of mixing lengths for river flow gaging. ASCE Journal of theHydraulics Division, 99(7):1069–1081.Westerberg, I., Guerrero, J., Seibert, J., Beven, K. J., and Halldin, S. 2011. Stage-dischargeuncertainty derived with a non-stationary rating curve in the Choluteca River, Honduras.Hydrological Processes, 25(4):603–613.Wood, P. and Dykes, A. 2002. The use of salt dilution gauging techniques: ecologicalconsiderations and insights. Water Research, 36(12):3054 – 3062.Yotsukura, N. and Cobb, E. D. 1972. Tranverse diffusion of solutes in natural streams.Professional Paper 582-C, United States Geological Survey, Washington, D.C., U.S.A.Zellweger, G. W., Avanzino, R. J., and Bencala, K. E. 1989. Comparison of tracier-dilution andcurrent-meter discharge measurements in a small gravel-bed stream, little lost man creek,californation. Water-Resources Investigations Report 89-4150, United States Geological Survey,Menlo Park, CA, U.S.A.72


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