Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
DSpace
UBCV
Li, Shumin
Master of Science - MSc
University of British Columbia
The Fraser River plume in the Strait of Georgia, BC, is significantly influenced by the tide. Here we use 17 years of daily MODIS observations of suspended particulate matter to understand the tidal variability of the plume. Our results show a consistent negative correlation between the Fraser River plume area and the tidal elevation with a phase lag at about one hour from two independent methods. The plume area routinely increases/decreases by about 20% during the ebb/flood tides, and a lower river flowrate typically leads to a more dramatic tidal variation in the plume area. A tidal harmonic analysis is performed on the HF-radar derived surface currents, and the difference between the extents of diurnally and semi-diurnally driven river influence suggests two distinct dynamical regions in the horizontal plume structure. A simple analytical model based on the volume conservation and salinity balance equations is built to analyze the mechanism of the tidal variability in the plume size. The observed tidal patterns of the plume area variation are partly reproduced using tidally modulated plume salinity (observed from instrumented ferries) and river flowrate (from numerical model outputs). These new findings will improve our understanding of the short-term dynamics of the Fraser River plume.
Tidal Influence on the Fraser RiverPlumebyShumin LiB.Sc., Xiamen University, 2019A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctral Studies(Oceanography)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)April 2022© Shumin Li 2022The following individuals certify that they have read, and recommend to the Faculty ofGraduate and Postdoctoral Studies for acceptance, the thesis entitled:Tidal Influence on the Fraser River Plumesubmitted by Shumin Li in partial fulfillment of the requirements for the degree of Masterof Science in Oceanography.Examining Committee:Rich Pawlowicz, Professor, Earth, Ocean and Atmospheric Sciences, UBCSupervisorSusan Allen, Professor, Earth, Ocean and Atmospheric Sciences, UBCSupervisory Committee MemberPhil Austin, Associate Professor, Earth, Ocean and Atmospheric Sciences, UBCAdditional ExamineriiAbstractThe Fraser River plume in the Strait of Georgia, BC, is significantly influenced by the tide.Here we use 17 years of daily MODIS observations of suspended particulate matter tounderstand the tidal variability of the plume. Our results show a consistent negative corre-lation between the Fraser River plume area and the tidal elevation with a phase lag at aboutone hour from two independent methods. The plume area routinely increases/decreasesby about 20% during the ebb/flood tides, and a lower river flowrate typically leads to amore dramatic tidal variation in the plume area. A tidal harmonic analysis is performed onthe HF-radar derived surface currents, and the difference between the extents of diurnallyand semi-diurnally driven river influence suggests two distinct dynamical regions in thehorizontal plume structure. A simple analytical model based on the volume conservationand salinity balance equations is built to analyze the mechanism of the tidal variabilityin the plume size. The observed tidal patterns of the plume area variation are partlyreproduced using tidally modulated plume salinity (observed from instrumented ferries)and river flowrate (from numerical model outputs). These new findings will improve ourunderstanding of the short-term dynamics of the Fraser River plume.iiiLay SummaryRiver plumes are the light and fresh water mass coming from a river and floating on theocean. They usually carry a great mount of silt and sediments which makes them to standout in satellite pictures. In this study, satellite images taken above the Strait of Georgiafor the past 17 years are examined to investigate how the tide influences the Fraser Riverplume size. Our results show that the plume area decreases by about 20% as the waterlevel rises up (flood tides) in the Strait, and increases about the same amount as waterlevel goes down (ebb tides). This tide-plume correspondence mainly comes from a tidalvariation on the freshwater input at the Fraser mouth, which pushes more water into theplume during ebb tides, and less water into the plume during flood tides.ivPrefaceThis thesis is original, unpublished, independent work by the author, S. Li, with the adviceof his supervisor, R. Pawlowicz, who will be a co-author of a journal article published outof this study. The SPM images used for this thesis are downloaded and pre-processed usingthe SeaDas software (Sec. 2.1) by research assistant K. Stankov, and all the further imageprocessing procedures (Sec. 2.2) are done by the author. Fig. 1.1 is used with permissionfrom A. Horner-Devine, and Fig. 2.1 is used with permission from R. Pawlowicz.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 River Plumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Strait of Georgia and Fraser River Plume . . . . . . . . . . . . . . . . . . . 41.3 Tide in the Strait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Study Objective and Research Questions . . . . . . . . . . . . . . . . . . . 92 Data and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1 Satellite Imagery of Suspended Particulate Matter (SPM) . . . . . . . . . . 142.2 Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.1 Image Quality Indexing . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.2 Image Processing and Plume Area Calculation . . . . . . . . . . . . 18viTable of Contents2.3 Supplementary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.1 Fraser River Discharge . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.2 Surface Winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.3 HF-radar Derived Surface Currents . . . . . . . . . . . . . . . . . . 222.3.4 Data along Ferry Track . . . . . . . . . . . . . . . . . . . . . . . . . 233 Observational Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1 Subtidal Variability of the Fraser River Plume Area . . . . . . . . . . . . . 313.2 Temporal Biases in Satellite Imagery . . . . . . . . . . . . . . . . . . . . . 333.3 Plume Area Variation under a Tidal Cycle . . . . . . . . . . . . . . . . . . 343.4 Plume Area Variation under Same-day Image Pairs . . . . . . . . . . . . . 363.5 Tidal Influence on the Fraser River Plume Salinity . . . . . . . . . . . . . . 403.6 Tidal Harmonic Analysis on the Surface Currents . . . . . . . . . . . . . . 453.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 A Simple Model of Plume Dynamics . . . . . . . . . . . . . . . . . . . . . 644.1 Analytical Solutions based on the Tidally Modulated Freshwater Input . . 644.2 Base Case Study: Entrainment Flux Estimations and Plume Area Simula-tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.3 Special Case Study: River Flowrate Impact on the Tide-plume Correlationand Entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84AppendixA Simulation of the plume area variation without correction in the phaseof the river flowrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90viiList of Tables3.1 Regression of plume area and river flowrate with different time gaps. . . . . 333.2 Summary of the plume area variation at different stage of the tide. . . . . . 40viiiList of Figures1.1 Schematic river plume dynamical regions . . . . . . . . . . . . . . . . . . . . 101.2 Geographical Map of the Strait of Georgia . . . . . . . . . . . . . . . . . . . 111.3 Fraser River Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.4 Daily and Fortnightly Tidal Patterns . . . . . . . . . . . . . . . . . . . . . . 121.5 Yearly Cycle of Daily Lower Low Tides . . . . . . . . . . . . . . . . . . . . 132.1 Example of MODIS “True Colour” image and derived SPM concentration . 252.2 SPM image quality index rubric . . . . . . . . . . . . . . . . . . . . . . . . . 262.3 Additional image process example 1 . . . . . . . . . . . . . . . . . . . . . . 272.4 Additional image process example 2 . . . . . . . . . . . . . . . . . . . . . . 272.5 Example of image combination . . . . . . . . . . . . . . . . . . . . . . . . . 282.6 Hourly river flowrate at Steveston . . . . . . . . . . . . . . . . . . . . . . . 282.7 Wind Rose Plot at Sand Heads . . . . . . . . . . . . . . . . . . . . . . . . . 292.8 Time series of CODAR data quality . . . . . . . . . . . . . . . . . . . . . . 303.1 Time Series of River Flowrate vs Plume Area . . . . . . . . . . . . . . . . . 483.2 Correlation Between Plume Area and River Discharge . . . . . . . . . . . . 493.3 Bias of SPM images relative to season and wind . . . . . . . . . . . . . . . . 503.4 Illustrative example of the intrinsic bias in SPM images . . . . . . . . . . . 513.5 Moving averages of RAF in a seasonal cycle . . . . . . . . . . . . . . . . . . 523.6 Distribution of RAF over tidal and seasonal cycles . . . . . . . . . . . . . . 533.7 Comparison of plume area vs RAF over a tidal cycle . . . . . . . . . . . . . 543.8 Same-day SPM image pair processing example . . . . . . . . . . . . . . . . 553.9 Tidal/yearly cycles of same-day paired plume area variation . . . . . . . . . 563.10 Comparison of plume area variation from two methods . . . . . . . . . . . . 573.11 Cross-correlations between plume area and the stage of tide . . . . . . . . . 583.12 River flowrate influence on the tide-plume correlations . . . . . . . . . . . . 59ixList of Figures3.13 Salinity threshold example along the ferry track. . . . . . . . . . . . . . . . 603.14 Comparison between absolute and relative salinitiy threshold . . . . . . . . 613.15 Tidal variations of the salinity inside and outside of the plume . . . . . . . 623.16 Aspect ratio distribution for major diurnal and semi-diurnal tides . . . . . . 634.1 Schematic diagram of the Fraser River plume . . . . . . . . . . . . . . . . . 764.2 Tidal cycles of Fraser flowrate from model outputs . . . . . . . . . . . . . . 774.3 Simulated plume area variation under tidal cycles . . . . . . . . . . . . . . . 784.4 River flowrate impact on the entrainments and tide-plume correlations . . . 794.5 River flowrate influence on Sp, So, and weA . . . . . . . . . . . . . . . . . . 80A.1 Simulated plume area variation under tidal cycles without correction in thephase of Q(t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91xList of SymbolsA: Plume areaD: Plume depth at the Fraser River mouth (deepest plume depth)D¯: Average plume depthDT: Time derivative of tidal elevation at Pt. AtkinsonFf : The rate of plume water loss at its front.k: Entrainment coefficientSw: Surface SPM concentrationQ: River flowrate1R: Correlation coefficientRAF: Normalized plume area, defined as the ratio of satellite observed plume area to thearea estimated by the linear regression to the river flowrate.RC: Percentage of plume area change per hour between same-day image pairs.r2: Coefficient of determination (R squared)rrs: Water-leaving reflectanceSewe: salt flux at the bottom of the plumeSf : Ferry-measured plume salinitySmax: Maximum salinity along a ferry trackSmin: Minimum salinity along a ferry trackSo: Ambient ocean salinitySoffset: Salinity offsetSp: Overall plume salinitySref : Reference salinity1In this thesis, adding (t) after a parameter (e.g., Q(t)) refers to the hourly or minute-by-minute-resolution (“minutely”) variation of this parameter, in which tidal variability is important. When anoverline bar is added on top of a parameter (e.g., Q¯), it refers to the daily average of this parameter. In thiscase, it may still show seasonal variations, but no tidal variation is considered. If not particularly specified(e.g., Q), it can refer to either tidal or subtidal variations, or it means that tide is irrelevant. The samenotation is applied to other parameters, e.g., A, weA, Sp, So ...xiList of SymbolsSTabs: Absolute salinity thresholdSTrel: Relative salinity thresholdU: Surface velocity|U|: Depth-averaged surface velocitywe: Upward entrainment velocityweA: Rate of upward entrainment at the bottom of the plumedSfdt : Time derivative of ferry-measured plume salinitydSpdt : Time derivative of overall plume salinityγ: Correction factor to adjust Sf for Spη: Tidal elevation at Pt. Atkinsonρw: Subsurface reflectancexiiList of AbbreviationsBC: British ColumbiaCODAR: Brand name for HF radar systems sold by CODAR Ocean Sensors (MountainView, California)CTD: An oceanography instrument used to measure the electrical conductivity, tempera-ture, and pressure of seawaterFVCOM: Unstructured Grid Finite Volume Community Ocean ModeHF-radar: High-frequency radarl.f.s: left hand sideMODIS: Moderate Resolution Imaging SpectroradiometerM/V: Motor vesselNW: Northwesterly (wind)ONC: Ocean Networks CanadaPST: Pacific Standard TimePt. Atkinson: Point AtkinsonRMSE: Root mean square errorROFI: Region of freshwater influencer.h.s: right hand sideSE: Southeasterly (wind)SoG: Strait of GeorgiaSPM: Suspended particulate matterxiiiAcknowledgementsI would first like to express my greatest gratitude to my supervisor, Professor Rich Pawlow-icz, thank you for your time, patience, and support throughout my master’s journey. Youwitnessed every single step of my progress in research, and provided me with tremendoushelp and encouragements. It is an honour of my life to be a student of yours.I would like to thank my committee member, Professor Susan Allen, for your time,enthusiasm, and helpful suggestions throughout my whole master program. Thank you toProfessor Phil Austin for examining my thesis and providing resource for future applicationsof my work. I would also like to thank Metro Vancouver for funding my master’s research.At last, I would like to thank all my friends in UBC EOAS, I am truly lucky to haveyou all in my life. Thank you for all the good time we share - Connor Henderson, EdMason, Nicole McEwan, Sam Stevens, Becca Beutel, Birgit Rogalla, and Yuanji Sun.xivChapter 1IntroductionRiver plumes are critical links between the land and ocean, and are important to thecoastal environment and local productivity. They are highly dynamic, and their variabilitydepends on multiple intrinsic and extrinsic factors. Among these factors, the high-frequencydependencies (i.e., tidal influence) of the river plumes are important components of theplume dynamics, but they are less understood because of the lack of good observationswith sufficient temporal and spatial resolution. This thesis is aimed at addressing thisproblem, by providing an in-depth analysis on the tidal influence on the Fraser Riverplume.The first chapter of this thesis starts with an overview of background knowledge aboutriver plumes, including their definition, importance, basic structures, and dependencies.Then, local environmental settings of the Fraser River and the Strait of Georgia are intro-duced, with a summary of earlier findings about the Fraser River plume variation underdifferent wind, tide, and river discharge conditions. Important characteristics of the tidein the Strait are described in the third part of this chapter, in particular, tidal patternsin daily, fortnightly, seasonal and decadal cycles are thoroughly discussed. Last, the studyobjectives are proposed and a series of research questions are listed.1.1 River PlumesA river plume, or a region of freshwater influence (ROFI), is the name given to the buoyantwater mass discharged from a river into the coastal ocean. Although the exact definitionof these terms may vary slightly as used by different researchers (and in different stagesof their studies), it is commonly agreed that the river plumes can be highly dynamic,time dependent, and have critical impact on the coastal ecosystem (e.g., Chant, 2012;Warrick and Farnsworth, 2017; Hetland and Hsu, 2013; Horner-Devine, 2009; Hetland,2005). Major river plumes usually carry a great amount of terrigenous sediments andanthropogenic nutrients, which makes them a significant carbon source to some coastal11.1. River Plumesoceans, contribute one-half of all oceanic carbon burial, and dominate the local productivityand environmental quality (Fennel et al., 2011; Hetland and Hsu, 2013; Hetland, 2005;Hedges and Keil, 1995). For example, a large hypoxic area (or called “dead zone”) is foundunderneath the Mississippi River plume, where the bottom oxygen is consumed by thedecomposing organics while the vertical ventilation is prevented by the strong stratification(Rabalais et al., 2002), and toxic dinoflagellate bloom events are found to be associatedwith the variation of Kennebec River plume in the Gulf of Maine (Franks and Anderson,1992).Other than being a critical link between terrestrial and coastal ecosystems, river plumesalso play an important role in social and economic activities. For example, they are habi-tats for many commercial fisheries (Able et al., 1998), provide open water for tourism andrecreation (Chant, 2012), serve as pathways for commercial container ships and passengercruises, and support oil drilling platforms. Because of their importance in ecosystem main-tenance and social activities, a good understanding of the behaviour and variation of riverplumes is crucial to the welfare of marine environment and economic production.However, it is not easy to fully understand the dynamics of river plumes. Their dynam-ics can be fully non-linear and strongly influenced by multiple factors, such as tide, wind,river discharge, ambient currents, coastal bathymetry, earth’s rotation, and internal waves(Chant, 2012; Horner-Devine et al., 2015; O’Donnell, 2010; Hetland and Hsu, 2013; Warrickand Farnsworth, 2017). In the past decades, hundreds of research papers have been dedi-cated to explore the dependence of river plumes worldwide on these intrinsic and extrinsicfactors through analytical solutions (e.g., Yankovsky and Chapman, 1997; Garvine, 1995),observational approaches (e.g., Chen et al., 2017; Warrick et al., 2007; Kastner et al., 2018;Warrick and Farnsworth, 2017), and numerical models (e.g., Chen, 2014; Hetland, 2005;Schiller et al., 2011; Li and Rong, 2012).Although the size, shape and variability of different plume systems are not identical,their horizontal structures can usually be described as being composed of three dynamicalregions: a jet-like near-field plume, a recirculating mid-field plume (bulge), and an along-shore directed far-field plume (see Fig. 1.1) (Chant, 2012; Horner-Devine et al., 2015;Hetland and Hsu, 2013; O’Donnell, 2010). Each of these have very different characteristics.The near-field plume is generally considered as the region where the river water shootsout into the ocean with a speed higher than the intrinsic internal wave propagation speed(Hetland and Hsu, 2013), which usually triggers shear instabilities and vertical mixing. Insome studies, e.g., Horner-Devine et al. (2009), a near-field plume is also referred to as a21.1. River Plumestidal plume, because it can be greatly affected by tide. A tidal pumping mechanism wasfirst proposed by Stommel and Farmer (1952), in which the plume under ebb tide is viewedas a jet with a near rectangular shape while the flood tide draws water back to the estuaryfrom a semi-circular region in the coastal ocean. The asymmetry of this estuarine outflowsuggests a potential pair of “dipole eddies” at the river mouth, and an enhanced exchangerate between the estuary and coastal ocean. Another important mechanism in this regionis related to the initial radial spreading of the plume as it empties into the coastal ocean,which increases shear instabilities and also increases the area over which mixing occurs(Horner-Devine et al., 2015).As the inertial momentum from the near-field plume starts to dissipate, a transitionalregion of recirculating water may occur. This recirculating bulge, or mid-field plume, isoften found in numerical models (e.g., Chen, 2014; Hetland, 2005; Nehama and Reason,2015) but has only been observed in the real ocean in a few recent studies under sufficientlylow winds and small ambient currents (e.g., Chen, 2014). When present, the mid-field bulgecan grow continuously in time and accumulate between 25 % and 75 % of the freshwaterdischarge in about 7 days and cause a corresponding reduction in the transport of plumewater to form coastal currents (Fong and Geyer, 2002). However, as wind stress andambient currents become stronger, the bulge formation will be significantly disrupted.The third major dynamical region is the far-field plume. It is the region beyond themid-field in which the plume no longer has the initial momentum of the river discharge.Earth’s rotation, buoyancy, wind stress, and sometimes bottom stress are the primarilygoverning forces (Horner-Devine et al., 2015). The far-field plume may extend hundreds ofkilometers from the river mouth and form a geostrophic coastal current that transports thediluted river water to the right side of the estuary in the northern hemisphere and left sidein the southern hemisphere (Fig. 1.1). The structures, dynamics and propagation speedof this coastal current are determined by the shelf slope and whether or not it is attachedto the bottom (Yankovsky and Chapman, 1997).This prototypical plume structure consisting of three dynamical regions is well studiedand widely recognised, however, it is important to note that the exact shape and dynamicsof a river plume is not steady, and it can vary significantly throughout time by wind,tide and river discharge. For example, the Delaware River plume is bottom attached (far-field plume being predominant) mostly through the year, but in the spring, when the riverdischarge greatly increases, it can form a surface advected plume (all dynamical regions arepresent) at the peak river discharge (Mu¨nchow and Garvine, 1993). Coastal upwelling and31.2. Strait of Georgia and Fraser River Plumedownwelling winds can completely reshape the plume and significantly influence the mixingand dynamics in mid-field and far-field regions (Horner-Devine et al., 2009; Warrick andFarnsworth, 2017; Hetland, 2005; Gan et al., 2009; Fofonova et al., 2015). More importantlyfor this thesis, tide can significantly impact the momentum balance, internal friction andstratification in the near-field plume (McCabe et al., 2009). Fortnightly spring/neap cyclesin the salinity stratification and vertical stability are also found in a few river plume systems(e.g., Simpson, 1997).However, investigations into the role of tide in the dynamics of coastal plumes hasmostly focused on the mixing and entrainment of plume water into sea water in numericalsimulations (e.g., Chen, 2014; Fofonova et al., 2015) and short-term observational stud-ies (e.g., Horner-Devine et al., 2009). For example, in Rijnsburger et al. (2018); Kilcherand Nash (2010), X-band radar images are used to investigate the influence of tide onthe propagation of river plume fronts. Similarly in Kastner et al. (2018), a drifter-basedobservational study is used to characterize the spreading and mixing of the Fraser Riverplume under ebbing tides in winter. These short-term studies nicely observed the tidalevolution of a plume system at the studied time, but the question of the adaptability oftheir conclusions to other times still remains.For a longer period of time, observations of plumes usually rely on moorings (e.g.,Simpson, 1997) or instrumented ferry tracks (e.g., Halverson and Pawlowicz, 2008, 2011),which only focus on a small portion of the plume. These observations are good at providingconsistent records of the some plume properties at a high temporal resolution, but theydon’t treat the plume body as a whole and they can’t directly describe how the plumedevelops in structure and shape.To fully understand the tidal impacts on a plume system, temporal and spatial coverageof the observations are equally important. This requirement is particularly true in the caseof the Fraser River, which is known anecdotally to have very strong tidal and seasonalvariations.1.2 Strait of Georgia and Fraser River PlumeThe Fraser River is the second largest river by discharge on the west coast of North America(Pawlowicz et al., 2017). It drains an area over 230, 000 km2 in the southeast Canada(Kastner et al., 2018) and flows into the Strait of Georgia (hereafter SoG or “the Strait”).The Strait of Georgia is a semi-enclosed, fjord-like coastal basin between mainland British41.2. Strait of Georgia and Fraser River PlumeColumbia and Vancouver Island (Fig. 1.2). It connects to the Pacific Ocean through Juande Fuca Strait in the south and through several narrow but relatively long channels in thenorth. Overall, the Strait is about 220 km long (NW to SE) and 30 km wide, with anaveraged depth of about 150 m and a maximum depth of 420 m (Thomson, 1981). In thevicinity of the plume, the Strait is 100-300 m deep (Fig. 1.2).Before entering the southern Strait, the Fraser River splits into 4 channels, namely theMain Arm (receiving about 75% to 87% of total discharge), the North Arm (carrying mostof the remainder) and two other small channels (Crean et al., 1988; Thomson, 1981). TheMain Arm is the deepest and widest channel, which extends 9 km offshore from Stevestonto Sand Heads Lightstation through a region of mudflats (Fig. 1.2). Since these shallowmudflats are partially uncovered during low tide, Sand Heads is sometimes considered asthe mouth of Fraser River (e.g., in Pawlowicz et al., 2017).As the Fraser River enters the SoG, the buoyant freshwater detaches from the riverchannel and bottom, and forms the Fraser River plume. This fresh and turbid water massis found to have an averaged area of 450 km2(Pawlowicz et al., 2017) and can span acrossthe Strait to its southwest boundary under certain conditions (Halverson and Pawlowicz,2011; Pawlowicz et al., 2017). The plume water contributes 65% to 85% of the particulatematter (Johannessen et al., 2003) and 65% of the fresh water (Halverson et al., 2017) tothe Strait, which consequently affects the local light attenuation, contaminant dispersionand primary productivity (Pawlowicz et al., 2017).Because of the topography surrounding of the Strait, local winds are usually found tobe either southeasterly or northwesterly. These along-shore winds have a significant impacton the plume location and shape. For example, Pawlowicz et al. (2017) show that, underhigh river flowrates, the Fraser River plume has a northern boundary near Sand Headsand a southern boundary all the way towards Georgina Point under strong NW winds.However, under strong SE winds, the southern boundary of the plume can barely reachsouth of Tsawwassen Ferry Terminal and its northern boundary can extend far deeperinto the Strait. Although the wind speed and direction are found to be almost completelyuncorrelated with the overall plume area by Pawlowicz et al. (2017), the mixing, spreadingand thickness of the plume during ebbing tides can be affect by NW/SE winds under lowriver flow conditions (Kastner et al., 2018).Another important factor controlling plume variation comes from the seasonal cycle ofthe Fraser River discharge. Free from any dams along its path, the Fraser River dischargeis a pure reflection of the local weather and seasonal forcing (Halverson and Pawlowicz,51.3. Tide in the Strait2011). It usually has a freshet flow peaking in June (∼ 10,000 m3 s−1) and a typicallylow runoff in fall and winter (∼ 1,000 m3 s−1) with occasional flow pulses after storms(Fig. 1.3). The plume size is then found to be linearly correlated with the river flowrate(Pawlowicz et al., 2017), changing by a factor of 10 between winter and summer. Plumesalinity decreases quasi-linearly with the increasing river discharge at 1.4 psu per 1000m3 s−1, however, the plume freshwater residence time2 is found to be about 1 day, andthe flushing time3 is found to be around 2.2 days, both of which are nearly independent ofriver discharge (Halverson and Pawlowicz, 2011).However, the role of tide in the variation of Fraser River plume is less known. Althoughfreshwater flux at the lower Fraser mouth and the plume salinities are shown to be tidallymodulated through earlier investigations from measurements on regular ferry transects(Halverson and Pawlowicz, 2008), no apparent correlation between plume area and tidalheight was found by Pawlowicz et al. (2017). In theory, as freshwater pulses into the Straitduring ebbing tides, the plume area is expected to expand to accommodate this inflow ofwater. However, a subset of satellite observation with a temporal resolution of about oneimage every five days (i.e., in Pawlowicz et al., 2017) makes it difficult to exhibit thisplume variation in a few hours. In addition, as shown later in this thesis, the coincidenceof linked seasonal cycles of river discharge, cloud coverage and the phase of tide results ina hidden bias in the satellite images (that are captured at about a fixed time in a day),and this bias adds an extra layer of difficulty in showing the tide-plume correlation. Toreveal this subtle impact of tide on the Fraser River plume, a deeper understanding in thenature of tide in the Strait is needed.1.3 Tide in the StraitThe tide progresses as a wave northwestwards along the coastline of the northeasternPacific (Thomson, 1981). As this waves enters the SoG, the raised water is reflected fromthe northern end of the channel. This southward reflected portion of tidal wave is thencombined with the inward portion of the tide to produce a standing wave in the Strait(Thomson, 1981). Thus, unlike a typical coastal Kelvin wave, the entire water level in theStrait moves up and down almost simultaneously with a maximum outflow tidal current at2the average time it takes for a water parcel to exit a system3similar to residence time, but based on a simple bulk estimation of salinity balance between plumeand non-plume waters61.3. Tide in the Straitthe mid-point of an ebbing tide. Because of this concurrent tidal behaviour, the differencein time between identical stages of tide almost never exceeds 30 minutes between any twoplaces within the Strait (Thomson, 1981)4. Thus, it is safe to use the tidal elevation at onerepresentative location to show the stage of tide for the whole Strait5.In this thesis, following earlier studies (e.g., Halverson and Pawlowicz, 2011; Pawlowiczet al., 2017), tidal elevation are derived at Point Atkinson to represent the stage of tide forthe Fraser River plume. Point Atkinson is located 25 km north of Fraser mouth (Fig. 1.2),which is not affected by the river stage (Halverson and Pawlowicz, 2008, 2016; Halversonet al., 2017). What’s more, the tidal record at Point Atkinson is more than 100 yearslong. Based on this well-maintained historical data, the tidal predictions from this site areusually considered to be the most reliable.Tides observed at Pt. Atkinson are mixed semi-diurnal. In a common daily tidal cycleof about 24 h 50 min, two high tides and two low tides are expected (Fig. 1.4a). In orderto describe the time of these maximum/minimum tidal elevation, the relative time afterthe minimum sea level (lower-low tide) of the day is defined as tide lag hours (h). Then,these elevation peaks are named correspondingly as lower-high (h ∼ -7), lower-low (h =0), higher-high (h ∼ 7) and higher-low (h ∼ 13) tides (Fig. 1.4a). The most dramaticelevation change of the day is usually found around the lower-low tide between h = -7 toh = 7, which refers to the big ebb followed by the big flood (namely the “big ebb” cyclehereafter). For the other half of the daily cycle, tidal variation is relatively small, and isthus named the “small ebb” cycle.In a fortnightly cycle (about 14.8 days), the daily tidal range routinely increases anddecreases (Fig. 1.4b). When the daily tidal range is over 3.25 m or the lower-low tide isbelow 1.22 m, it is considered to be a spring tide, otherwise it is under a neap tide6. Duringspring tides, there is a strong diurnal pattern of a dominant “big ebb” followed by a weak“small ebb”. While in the neap tide periods, tidal signals are more semi-diurnal and thedifference between daily “big ebb” and “small ebb” is much smaller.The time in the day when the daily lower-low tide occurs is not random, instead, it4except that the tide gets quite delayed going up the Fraser5excluding the Fraser River channels6spring/neap usually refers to tidal effects arising from the alignment of the sun and moon. However,the largest fortnightly effects in the SoG arise from the height of the moon above the equator, which meansthat it is (in a precise term) a “tropic/equatorial” cycle. Although in this thesis, we still use the term“spring/neap” as a representative of the bi-weekly tidal variation of the “bigger/smaller” daily elevationrange, readers should be aware that this term only refers to the stages in a fortnightly cycle rather thanimplying the relative position of the sun, earth and moon.71.3. Tide in the Straitfollows a unique pattern with a seasonal cycle (Fig. 1.5). For example, daily lower-lowsin January are usually around midnight (20:00 to 2:00) while in June are usually in themiddle of the day (8:00 to 14:00). In a year, all daily low tides are distributed inside adiagonally aligned “band” in Fig. 1.5a, which contains about 2 dozen “strings” which runacross the band. Each “string” contains 13 to 15 “points” of daily lows, which form afortnightly cycle (Fig. 1.5a).Starting with each string (fortnightly cycle), the daily low tide occurs about 38 to 52minutes later than the day before. Within each string, the daily lows always start with arelatively higher elevation (red dots in Fig. 1.5), gradually go lower (green and blue dots)and then increase again. This pattern indicates that a fortnightly cycle usually starts fromneap tide, gradually develops into spring tide and goes back again.The neap-spring-neap pattern in each fortnightly cycle is always observable, but theelevation of the daily lows in spring tides are quite different in different months of the year.For examples, daily low tides with an elevation below 0.5 m (blue dots in Fig. 1.5) canonly be found around noon in summer and around midnight in winter. In spring and fall,such as March and September, the spring tides are never as strong as their winter/summercounterparts. Also, in April and May, spring tide appears early in the fortnightly cycle,while in August it shows up much later, near the end of the cycle.Over a decadal scale, the seasonal shift of daily tidal phase still holds. Inter-annualvariation of the tidal cycle is found to be small, which means that tidal patterns andseasonal variations can be applied to multiple years. Thus, it is safe to use multiple yearsdata of observation without worrying too much about the potential inter-annual variability.Not only does the tide vary in rather predictable ways, but it’s likely that it will alsoaffect the plume in predictable ways that are not random from day to day, but ratherare highly structured in time. Understanding the seasonal cycle of the tidal phase shiftis then also very important to understand the inherent bias from satellite observations,which often occur at fixed times of the day. For example, since the optical images fromthese space based instruments can only be captured during day time, all summer imagesare then taken within the “big ebb” cycles of the day while all winter images are fallen intothe “small tide” periods. Because the river discharge is usually high in summer and low inwinter, satellite observed tidal features around the “big ebb” are then “falsely enhanced”by the summer freshet. More details of this bias and the corrections applied will be furtherdiscussed in Sec. 3.2 and 3.3.81.4. Study Objective and Research Questions1.4 Study Objective and Research QuestionsFraser River plume is important to the local environment and ecosystem in the Strait ofGeorgia. However, the dynamics, especially tidal forcing of this buoyant plume are notfully understood. This study aims to reveal the tidal influence on the Fraser River plume.Specifically, this study aims to answer the following research questions:1. What is the relationship between tidal elevation and the Fraser River plume area inthe Strait of Georgia?2. How does the plume reshape and relocate with a short period of time under flood-ing/ebbing tides?3. What is the general pattern of the Fraser River plume during a tidal day?4. Is the correlation between tide and plume area the same under different river dischargeconditions?5. What is the mechanism of the plume area variation through a tidal cycle?To answer these questions, a 17-year satellite data set of the concentration of suspendedparticulate matters in the Strait of Georgia is carefully examined. Correlations betweenthe tidal stage and the plume area are established, and the mechanism behind this tidalmodulation is investigated. In the following Data and Methods chapter, introduction willbe made to the primary dataset (satellite imagery) and other supplementary datasets. Theimage processing procedure will also be described in detail. The next two chapters willbe focused on the observational results of the tidal variations on multiple aspects of theplume, and a simple quasi-analytical diagnostic model that is constructed to reproducethe tidal variability in the observations. In addition, the consistency of this tide-plumecorrelation will be examined under different river discharge conditions, and the mechanismof this correlation will be investigated by linking to the tidal cycle of the freshwater inputat the river mouth and the tidal variation in the plume salinity. The implication of theresults to the upward entrainment at the bottom of the plume will be discussed in detail.91.4. Study Objective and Research QuestionsFigure 1.1: Schematic representation of the prototypical plume comprising all dynamicalregions. Fig. 2 from Horner-Devine et al. (2015). Reproduced with permission of A.Horner-Devine.101.4. Study Objective and Research QuestionsFigure 1.2: The geographical map of the Strait of Georgia and Fraser River.Figure 1.3: Calculated Fraser River discharge from gauge station at Hope and Chilliwack,2003 - 2019. Thick black curve shows the averaged daily river flowrate.111.4. Study Objective and Research QuestionsFigure 1.4: (a) Daily tidal cycle pattern at Point Atkinson, with h = 0 to be the lower-lowtide of the day. Blue curves are the tidal elevation predicted for each day in 2018, alignedby the time of lower-low tide, while the thick black curve shows the mean value of all bluecurves (b) Fortnightly tidal pattern for years 2003 to 2019, the lowest elevation in eachcycle is aligned at day 7.5.121.4. Study Objective and Research QuestionsFigure 1.5: Distribution of the low-tide time in a day throughout the year. Horizontal axisshows the time in the year when each daily low tide occurs, while the vertical axis showsits time in a day in PST. The corresponding elevation of the low tide is coloured. Upperpanel only shows data from one year (2018) while the lower panel plots data over 17 years(2003 - 2019).13Chapter 2Data and MethodsIn the first part of this chapter, the primary dataset used for this study is described. Theprimary dataset is derived from satellite imagery, but using this source of daily data toinvestigate tidal variations of the Fraser River plume requires some care. In the secondpart of this chapter, the processing and evaluation aspects of this dataset are consideredat length. In addition to this satellite imagery, some supplementary datasets are helpful tounderstand the environment settings of the plume. In the third part of this chapter, thesesupplementary datasets are introduced and described.2.1 Satellite Imagery of Suspended Particulate Matter(SPM)The primary dataset used for this thesis consists of high-resolution (∼ 250 m) images fromthe Moderate Resolution Imaging Spectroradiometer (MODIS) instruments onboard theAqua and Terra spacecrafts. With a wide swath (∼ 2330 km) and broad spectral range(36 spectral bands ranging in wavelength from 0.4 µm to 14.4 µm), MODIS has been usedto provide high quality surface observation images of Earth’s land, ocean and atmospherefor the past two decades (Khlopenkov and Trishchenko, 2008). From year 2003 to 2019,over 10,000 such images covering the southern Strait of Georgia region are available forexamination.With a higher concentration of suspended sediments against the rest of the Strait,Fraser River plume is usually clearly visible in these MODIS images (e.g., Fig. 2.1a).However, it is difficult to define the boundary of the plume region based on true-colourimages. Instead, further processing of these images is required to perform quantitativeanalysis. Commonly, information from band 1 (wavelengths of 620-670 nm, centred at 645nm) is used to assess suspended particulate matter (SPM) concentration (e.g., Chen et al.(2007); Doxaran et al. (2009); Lahet and Stramski (2010); Miller and McKee (2004); Petus142.1. Satellite Imagery of Suspended Particulate Matter (SPM)et al. (2010); Wang et al. (2009)).Then, a threshold of this concentration can be establishedto define the expanse of the plume (e.g., Pawlowicz et al., 2017).The method for calculating SPM concentration is well-articulated in Pawlowicz et al.(2017). In short, first, the high-resolution 250 m L2 QKM files are generated from SeaDAS6.4 software. Then, these L2 files are used to derive SPM concentration from band 1reflectance. The subsurface reflectance ρw is first calculated from water-leaving reflectancerrs:ρw = πRrrs (2.1)where R describes the effects of reflection and refraction by the surface (Morel and Gentili,1996). Then, the surface SPM Sw (grams per cubic metre) can be estimated based on ρwaccording to the following semi-empirical relationship:Sw =Aρρw1− ρw/Cρ +Bρ (2.2)where the parameters Aρ = 258.85, Bρ = 0 g m−3, and Cρ = 0.1641 are the coefficientsspecific to the MODIS high-resolution 645 nm channel, matching in situ calibration samplesdescribed in Nechad et al. (2010).In order to prevent some inappropriately triggered cloud and sea-ice masks onto thecentre of the plume close to the river mouth, a nominal threshold of 0.027 for cloud albedowas increased to 0.4 in SeaDAS processing. However, this threshold increase also results inabnormally high reflectances in regions of known low SPM concentration because of cloudsor other bright targets.In Pawlowicz et al. (2017), 904 images (about 70 images a year) were used for theanalysis. However, to study the influence of a relatively high frequency oceanographicalphenomena (i.e., tidal influence), temporal resolution of the dataset is very important.To increase the number of images available and to the improve temporal resolution, thefollowing improvements are made to image selection procedures:(1) Increase data time spanIn this study, the time span of the satellite data was increased from 13 years (2003- 2015 in Pawlowicz et al., 2017) to 17 years (2003 - 2019). The extra 4 years of dataincreased the number of images by 30 percent.(2) Include images from Terra mission.152.1. Satellite Imagery of Suspended Particulate Matter (SPM)The Terra satellite was launched in December 1999, and it was designed to imagethe earth with its MODIS instrument on a descending orbit that crosses the equator at10:30 am local time. The Aqua satellite was launched in May 2002, it carries an identicalMODIS instrument but follows an ascending orbit that crosses the equator at 1:30 p.m..Both spacecrafts are in orbits with a period of about 100 minutes, inclined at about 98◦,and at an altitude of 705 km.In Pawlowicz et al. (2017), only images from the Aqua mission were used to investigatethe Fraser River plume variation. Ideally, including all Terra images would double thenumber of images available. However, the same processing applied to Terra images doesnot yield a comparable image set. After a careful examination of Terra images from January2016 to January 2019, the number of usable images from Terra is found to be about 6 timessmaller than that from Aqua.The Terra images with the 250-m resolution at the 645 nm frequency are usually as goodas those from Aqua, but some other bands in the 500-m resolution (e.g., 1240 nm, 1640 nm,and 2130 nm) miss significant coverage over the SoG. Some of these frequencies are crucialfor the atmospheric corrections, and are therefore important for deriving correct SPMconcentrations. The reason for this poor performance of Terra observation at these specificfrequencies over the Strait is still unknown. It may relate to a tendency for an descendingsatellite (i.e., Terra) to suffer more sun-glint at the time when it passes over SoG (averagedat 11:22 a.m. in PST). Assuming that this poor quality of Terra observations of the FraserRiver plume would also occur earlier than 2016, and considering the small number of extraimages obtained from the intensive work of the individual image evaluation, no processingof Terra images was carried out for earlier years.(3) Use of Same-day Image PairsAs Aqua and Terra travel along their orbits, the on-board MODIS instrument circlesthe Earth 14 to 15 times a day with a fixed 2330 km swath. This design ensures that most ofthe Earth’s surface can be monitored at least once a day, but also provides the possibilitythat two or more images may be created when a region is located inside the overlap ofconsecutive scan paths of the same satellite (which can happen at mid to high latituderegions). Because the orbital period of the satellite is about 100 minutes, the second imageis usually 100 minutes later than the first one, which provides an opportunity to studythe plume variation over a short period of time. The two-image-a-day feature, which iscalled same-day pairs in this study, is found nearly every other day in the Strait of Georgia(same-day pairs appear in 47.2 % of days). Within all 3300 same-day pairs found in the162.2. Image Processing17 years, 247 of which can be used to investigate the short-term plume variation. Thesesame-day pairs were then carefully examined to reveal the plume variation feature underthe tidal frequency (Sec. 3.4).(4) Additional image processing: cleaning, interpolation, and image com-biningAfter a visual examination of each single SPM image, it is found that at least onethousand flawed images actually contain useful information of the plume, and can befixed by applying individual cleaning and interpolations. After including these previouslydiscarded images, the number of images in our collection is increased to 2466. A step-by-step explanation of this additional image process is described in the following section.2.2 Image ProcessingIn Pawlowicz et al. (2017), a manual evaluation of the image collection resulted in a set of904 images over the 13 years of data used. As described above, multiple procedures werecarried out to increase the number of images available. The dataset used here includes 2466images over 17 years (although this number includes 247 days where 2 different images,spaced about 100 minutes apart). Detailed image processing procedure is described in thefollowing sections.2.2.1 Image Quality IndexingOver 1500 previously discarded SPM images can actually be fixed with proper cleaningand interpolation. Also, even with the previously selected good images, some commonproblems still exist. First, some high reflected cloud patches are recognized as river plume,which needs to be removed (e.g., Fig. 2.2 c1, c4 and c5); second, some regions at thecentre of the plume jet and near the coastline are inappropriately masked and need tobe interpolated (e.g., Fig. 2.2c2, c3); third, high reflectance from other river plumes ormudflats (e.g., Squamish River plume, boundary bay mudflat, water channels among GulfIslands) should be removed (e.g., Fig. 2.2b2, c4). To both include more images into thecollection, and improve the image quality, the following procedures are applied.In the first step, the 11,258 individual SPM images are visually examined, and are eachassigned a quality index (0, 1, 2, or 3). The classification rubric is set up as follows:0: To be discarded172.2. Image ProcessingEmpty files, mostly cloudy images, or almost no useful information from these images.These images should be discarded (Fig. 2.2a1-a5).1: Very good imagesAlmost no missing data in the plume region, plume boundary is clear. In other words,images given with index 1 can be used without further processing, or just need a maskto excluded data outside of Strait of Georgia. (Fig. 2.2 b1-b5)2: To be processedThe plume area is recognizable, but with some common problems (Fig. 2.2c1-c5),which include (1) some gaps in the plume region or on the mudflat, (2) some ab-normally high values outside of plume region (e.g., clouds) and some abnormally lowvalues inside the plume.3: OthersThese images may show some features of the plume, but a significant portion is bad ormissing. These images could still be used in determining the averaged plume structuresunder specific conditions, but the plume areas can not be easily calculated. (Fig.2.2d1-d5)After this visual inspection, 7677 (68.2%) images have index 0, 205 (1.8%) images haveindex 1, 2261 (20.1%) have index 2, and 1114 (9.9%) have index 3. Among all 11,258images, 2466 (145 images per year) with index 1 and 2 can be used for this study.2.2.2 Image Processing and Plume Area CalculationIn this step, all 2466 manually selected images with quality index 1 and 2 are furtherprocessed. The noise in the data are cleaned, and necessary interpolations are made tocalculate the plume areas. For each image, the following steps are applied:1. All negative and zero values in the image are deleted.2. Masks are applied for the SoG, and data outside of the masks are deleted.3. Approximate plume boundaries are manually drawn around the plume in eachimage, and abnormally high values (SPM > 2 g m−3) outside of this contoured regionare deleted.4. Small contours inside the plume regions are manually drawn to delete abnormallylow values (SPM < 2 g m−3 inside the plume.)5. Missing data inside the contoured plume region (especially the near-shore regionsover the mudflat) are interpolated.182.3. Supplementary Data6. Images of the SoG that are separated into different files along the flight track arecombined. (e.g., Fig. 2.5)Plume area is then calculated for each processed image. First, the number of imagepixels are counted in which the SPM concentration is over 2 g m−3, which is a thresholdwell-demonstrated in Pawlowicz et al. (2017) to identify the Fraser River plume boundaryfrom MODIS SPM images. Then, the areas of these highlighted pixels are added to getthe area of the plume.In a common winter scenario (e.g., Fig. 2.3), clouds above the SoG are usually notproperly masked, which results in an overestimation of the plume area. The individualplume mask that is applied to each image helps to reduce these cloud effects. On the otherhand, in summer (e.g., Fig. 2.4), the high-reflectance plume centre is often mistakenlyidentified as clouds and is therefore inappropriately masked. The interpolation inside theplume region helps to solve the underestimation of plume area due to this reason.Satellite data along a swath are broken up into files of a certain size, and sometimesthe break between files happens over the Strait of Georgia. Combining these files helps tocontribute about 40 images into the image collection (e.g., Fig. 2.5).Following the same technique, 247 pairs of same-day images are processed as well. How-ever, it is important to note that the plume area changes between these paired images aresensitive to the manually drawn plume boundary masks. Therefore, the same outer/innerplume masks are applied to both images in order to reduce the inconsistency in some specialcases.2.3 Supplementary DataSome additional observation data and numerical model outputs were also used in this study.These data may serve to reveal the intrinsic bias of the selected image samples, validateand visualize the plume variation, and test the hypotheses made to explain the principlemechanism of the observed phenomena. A brief description of these supplementary datais in the following sections.2.3.1 Fraser River DischargeAs discussed in Sec. 1.1,1.2 and 3.1, river discharge is one of the key factors that affectsthe size, structure and dynamics of a river plume. However, it is not easy to accurately192.3. Supplementary Dataquantify the flowrate at the Fraser River mouth because of the strong tidal modulation andcomplex dynamics in the estuary. For a limited period of time between 1983 to 1993, WaterSurvey of Canada provided model outputs of daily river discharge for the gauging station atPort Mann (ID 08MH126), which is located 35 km upstream of the mouth and just beforethe river splits into different arms (Halverson and Pawlowicz, 2008). This historical recordof Fraser River discharge is usually considered as the best representation of the freshwaterflux in to the Strait.Unfortunately, the daily discharge data from Port Mann is no longer available. Thenearest active station monitoring the Fraser discharge is the gauging station at Hope(08MF005). Hope lies 120 km upstream of the mouth and it does not experience tidalfluctuations. However, unable to include a few important tributaries downstream, dis-charge at Hope is found to be about 17 % less than Port Mann in summer, and nearly 50% less in winter (Pawlowicz et al., 2007). Especially after some high precipitation events(e.g., storms in the BC lower mainland in late falls and early winters), the majority ofthe Fraser discharge at the mouth may come from these downstream tributaries. In thesecases, the Fraser River plume may quickly expand to be several times larger, while nosignificant increase in the flowrate at station Hope is observed.In order to better estimate the river discharge at mouth, a few earlier studies attemptedto estimate the flowrate at Port Mann by combining data from station Hope with someother stations downstream. For example, in Halverson and Pawlowicz (2008), a regres-sion equation was established using data from gauging stations at Hope, Harrison River(08MG013) and Chehalis River (08MG001). However, in Pawlowicz et al. (2017), only theChilliwach River gauge was used to account for downstream inflows. The regression in thesecond example is given by:QPortMann = QHope + 5.61 QChilliwack + 481 m3 s−1 (2.3)(r2 = 0.97, standard error ± 405 m3 s−1, regressed to the historical Port Mann record)where an additional half-day delay was added to Chilliwack River record to account forrunoff effects.Since the Harrison River (used in Halverson and Pawlowicz (2008)) is no longer gauged,in this study, the method given in Pawlowicz et al. (2017) (i.e., Eq. (2.3)) is applied toestimated the river flowrate at the mouth using data from gauging stations at Hope andChilliwack (available online from Water Survey of Canada at https://wateroffice.ec.202.3. Supplementary Datagc.ca/index_e.html). The seasonal pattern of river discharge based on this estimatedFraser flowrate at its mouth can be found in Fig. 1.3.In addition to the daily river discharge, we are also interested in the hourly fluctuationof the Fraser flux, which helps to understand the tidal modulation of the freshwater supplyto the plume. However, there is almost no observation of the hourly discharge along theFraser River. Therefore, in this study, the results from a numerical model are used torepresent the hourly variation of the flowrate at the Fraser mouth.The model used here is obtained from a configuration of the Unstructured Grid FiniteVolume Community Ocean Model (FVCOM), described by Wu et al. (2022), which employsa wet/dry treatment to simulate flooding/drying process in tidal flats (Wu et al., 2022).The model runs under three river flow conditions (low: 1,000 m3 s−1, medium: 5,000m3 s−1, and high: 11,000 m3 s−1) for a one-month period of time with an hourly temporalresolution. From the model outputs at Steveston (Fig. 1.2), time series of depth-averagedeastward velocity is multiplied by the meridional transect area of the Fraser River to derivethe river flowrate at the mouth. Compared to the tidal elevations at Pt. Atkinson fromthe same model, the river flowrate has a good correlation with the time derivative of tidewith a phase lag of about 2 hours (Fig. 2.6a).2.3.2 Surface WindsAnother important factor that affects the plume structure is the surface wind. Consideringboth location and duration, the best meteorological data for the Fraser River plume is fromthe Sand Heads lighthouse station, Environment Canada Climate ID # 1107010, which ispositioned at the end of the jetty extending from Steveston to the edge of the mudflats(Fig. 1.2). Two-minute averaged hourly wind direction and speed data at 11 m can bedownloaded from Environment Canada (https://climate.weather.gc.ca/historical_data/search_historic_data_e.html).Data coverage from Sand Heads is good for the period of time in this study. For all2466 selected SPM images, 2407 (97.6%) have an available, valid wind record ± 1 h fromthe time when these images are taken. As discussed in Sec. 1.2, winds in the Strait aregenerally either northwesterly or southeasterly, aligned with the long axis of the Strait.Southeasterly winds appear more often than the northwesterly winds throughout the year(Fig. 2.7), especially in winter seasons. This wind data will mainly be used in revealingthe bias of SPM images to a preference to the northwesterly wind.212.3. Supplementary Data2.3.3 HF-radar Derived Surface CurrentsHigh-Frequency (HF) radars have been used to monitor the surface currents along coastaloceans in the past decades. In the Strait of Georgia, Ocean Networks Canada (ONC)(https://data.oceannetworks.ca/home) maintains four CODAROcean Sensors Inc. Sea-Sonde units in the southern Strait of Georgia at the Westshore coal port (deployed in Dec2011), Iona outfall (deployed Aug 2012), Georgina Point (deployed May 2016), and PointAtkinson (deployed January 2017) (Fig. 1.2). These direction-finding HF radar systemsare sensitive to currents in the upper 50 cm of the water column, and they operate at anominal frequency of 25 MHz. All stations produce hourly radial current maps by com-bining seven 10-minute averages that are gridded to range bins of 0.5 km and bearing binsof 5◦ (Pawlowicz et al., 2020; Halverson and Pawlowicz, 2016). Total current vectors areproduced by stepping through all points on a regular 1 km× 1 km grid and combining allradial data within a 1 km search radius of each grid point with the vendor’s software.The advantages of CODAR data are that they have a very good spatial and temporalresolution, years of good records can be used, and they work well both day and nightwithout being restricted by the weather conditions. However, a few drawbacks of thisderived surface current data limit its application to this study.First of all, only after the third station (at Georgina Point) was set up, did the surfacecurrent field start to cover the majority of the plume area, which means that only 3.5 years(mid-2016 to 2019) out of 17 years of satellite observation can be fully examined togetherwith this HF-radar derived surface current field.Secondly, both working range and accuracy of this HF-radar data are found to besensitive to the surface conductivity (i.e., salinity). For example, in Halverson et al. (2017),the working range of HF-radar is found to be negatively and near-linearly correlated withsurface conductivity with a decrease from 37.4 km at 3.5 S m−1 to 19.4 km at 0.9 S m−1. InHalverson et al. (2018), a comparison with drifting buoy velocities finds that the HF-radarderived surface currents in the SoG underestimated the actual surface currents by 0 to5 cm/s with RMSE ranging from 11.3 to 17.2 cm/s, but this underestimation can be ashigh as 30 to 50 cm/s in the Fraser outflow. Fraser River plume is characterized with thelow surface salinity (i.e., low conductivity), which may not be accurately-observed by theHF-radar.What’s more, the percentage of valid HF-radar coverage is relatively low in summer(Fig. 2.8), at which time the majority of the satellite images are taken. This mismatch in222.3. Supplementary Datatime would result in an even smaller subset of data in which both satellite and HF-radarobservation are good in quality.In spite of these disadvantages, HF-radar derived surface currents are still helpful to usin understanding the dynamics of the surface ocean in the Strait. As supplementary data,these surface currents will be used to support the short-term variation of the plume withinsame-day SPM image pairs, reveal the extent of diurnal and semi-diurnal influence of theriver, and help to understand the dynamical structures of the plume.2.3.4 Data along Ferry TrackIn this study, the ferry track data are mainly used to estimate the surface salinity inside andoutside the plume. The data were acquired from sensors on-board the British ColumbiaFerry Services Inc. vessel M/V Queen of New Westminster (2003 to 2006) and Queenof Alberni (2012 onward). Specifically in this study, one year of record is good enoughto evaluate the overall tidal influence on the plume salinity. Therefore, the followingdescription about this ship-board measurements is purely based on the situation in 2018from M/V Queen of Alberni.For the study period, the vessel passes over the Fraser River plume up to eight times perday with the first sailing departing Tsawwassen at 5:15 in the local morning, and the lastsailing departing Duke Point at 22:45 (Fig. 1.2). A complete transect takes about 2 hoursand covers over 60 km across the Strait. Salinity, temperature, chlorophyll-a and dissolvedoxygen, and turbidity data are measured at a 1-minute interval using water samples drawnthrough a 12.7-mm pipe with a length of 1.5 m(Wang et al., 2019). The water intake isknown to be located 2 m below the surface with a variation up to 40 cm depending onthe payload, but some uncertainty about the depth of the actual water being sampledstill remains. For example, Hinatsu et al. (2003) shows that the effective sampling depthfor such system can be shallower than the water intake depth as the surface water beingsubducted underneath the travelling vessel. A similar study on the previous samplingsystem in the SoG (2003 to 2006) also shows the sampled water is from about 1.5-m depthdespite the intake being at 3.5-m depth (Halverson and Pawlowicz, 2011). Although thereis no specific conclusion on the effective water sampling depth for the new system, in thisstudy, the depth of 1 m is considered to be a close estimation to represent the layer ofsurface water being measured.Analysis from earlier ferry datasets suggested that the Fraser River plume could be232.3. Supplementary Dataeasily identified along the Tsawwassen/Nanaimo route from the surface sea salinity (e.g.,Halverson and Pawlowicz, 2008, 2011). However, the best method to automatically identifyplume waters still remains a question. A new relative salinity threshold is developed tomatch with the SPM threshold at 2 g m−3, and further details will be discussed in Sec.3.5.242.3. Supplementary DataFigure 2.1: (a) “True Colour” image generated by merging RGB colour bands from theMODIS instrument for 10 June 2003 during a period of high river flow and southwesterlywinds. (b) SPM derived from band 1 reflectance for the same date. (Fig. 2 from Pawlowiczet al. (2017)). Reproduced with permission from R. Pawlowicz.252.3. Supplementary DataFigure 2.2: Examples of SPM images with different quality indices. (case 0: to be discarded,case 1: very good images, case 2: to be processed, case 3: others). All times are in PST.For geographical information, see Fig. 1.2.262.3. Supplementary DataFigure 2.3: Example 1 of the SPM image before and after processing (a common wintercase). i is the index of the image being processed. For geographical information, see Fig.1.2.Figure 2.4: Example 2 of the SPM image before and after processing (a common summercase). i is the index of the image being processed. For geographical information, see Fig.1.2.272.3. Supplementary DataFigure 2.5: Example of combined SPM images. i is the index of the image being processed.i = 6748 was taken at 13:05 on July 28th, 2014, i = 6479 was taken at 13:10 on the sameday. For geographical information, see Fig. 1.2.Figure 2.6: Example of hourly river flowrate at Steveston from FVCOM model output(blue curve) compared with (a) time derivative of tidal elevation at Pt. Atkinson, and (b)tidal elevation at Pt. Atkinson (red curves). In this example, the model runs under lowriver flow condition (Q¯ = 1000 m3 s−1), and the negative value of the river flowrate meansthat the fresh water discharges from the river into the ocean.282.3. Supplementary DataFigure 2.7: Wind rose for hourly wind speeds measured at the Sand Heads lighthousestation for the years 2003 to 2019. Note that the meteorological convention of usingdirections from which the wind originates is used.292.3. Supplementary DataFigure 2.8: Percentage of good HF-radar (CODAR) data from 2016 to 2020. Bad days(days with an average coverage of less than 50% (i.e., 667 grid points)) are shaded in gray.30Chapter 3Observational ResultsThis chapter consists of 6 sections of observational results and a brief summary. Specifically,the first section examines the subtidal variability in the plume area, and establishes a linearcorrelation between the plume area and the river flowrate. The second section points outa hidden bias in the SPM image collection, which is very important for extracting reliabletidal signals. Aware of this hidden bias, the third section carefully processes the dataand finds a negative correlation between the tidal elevation and the plume area with anone-hour phase lag. Section 4 investigates the plume area changes between the same-dayimage pairs, and derives a very similar correlation between the tide and the plume area. Insection 5, a salinity threshold for the ferry-measured surface salinity is established to bestrepresent the SPM threshold used in the satellite observation, and the tidal variation inthe plume salinity is investigated. In section 6, a tidal harmonic analysis of the HF-radarderived surface currents is made, and the horizontal plume structure is characterized by thedifference in the extent of diurnal/semi-diurnal influence of the river. At last, the primaryfindings of the observational results are summarized.3.1 Subtidal Variability of the Fraser River Plume AreaIn this study, although over one thousand previously discarded “bad-quality” images (byPawlowicz et al. (2017)) are included in our dataset, after a proper processing, the expandedimage collection still shows a consistent correlation between the plume area and the riverflowrate (Fig. 3.1). The only exception is found in August 2016, when an unprecedentedcoccolithophore bloom causes the water across much of the SoG to turn into a bright,almost fluorescent, green colour (Gower and King, 2016). This event affects 17 images(grey dots in Fig. 3.1), and these images are then excluded from further analysis.In the earlier study, Fraser River plume area was found to be linearly correlated withthe river flowrate with the following relationship (Pawlowicz et al., 2017) (black curve inFig. 3.2):313.1. Subtidal Variability of the Fraser River Plume AreaA/km2 = 0.1244QPort Mann(d)/(m3/s) + 1.44 (3.1)(r2 = 0.68, standard error ± 190 km2) where A is the plume surface area (km2) andQPort Mann(d) is the estimated river flowrate at Port Mann based on data from gauging sta-tions at Hope and Chilliwack for the same day when SPM image is taken (more informationabout this calculation is provided in Sec. 2.3.1 ).With the expanded image collection in this study, the relationship is found to be:A/km2 = 0.1342 QPort Mann(d)/(m3/s)− 14.06 (3.2)(r2 = 0.705, standard error ± 196 km2, red curve in Fig. 3.2).The new correlation agrees well with the existing equation with a small improvementin r2 and a very minor increase in the standard error. As discussed in Sec. 2.2.2, withoutcareful image processing and interpolation, summer images (with big plumes) tends tounderestimate the plume ares because of the missing data at the centre of the plume,while winter images (with small plumes) usually overestimates the plume area due tocloud patches that are not properly masked. In this study, every single image is individualexamined and processed, which partly solves the overestimation/underestimation in thewinter/summer images, and results in a regression curve with a steeper slope. Althoughthe intercept from this regression (- 14.06 km2) seems to be near 10 times bigger than thatfrom the previous study (1.44 km2) in magnitude, this difference is actually fairly smallcompared to the range of the plume area (∼ 2000 km2).However, this correlation relationship can be further improved. The observed peak ofthe plume area seems to occur slightly later than the peak of the river flowrate, especiallyafter some high-precipitation events in fall and winters (Fig. 3.1). Theoretically, the plumeneeds time to grow after a massive feeding of freshwater, and the existing plume also needstime to dissipate when the river discharge decreases. This may indicate a better correlationof plume area with an earlier river discharge. After a cross-correlation analysis, the bestcorrelation (maximum r2 and minimum RSME) is found to use the river discharge that is 2to 3 days earlier than the plume image (Table 3.1). This slight mismatch in time is similarto the Fraser River plume freshwater flushing time, which is estimated to be 2.2 days byHalverson and Pawlowicz (2011). Regression curve for the correlation using river flowrate3 days ahead of satellite images is shown in green colour in Fig. 3.2, and this equation willbe used for the further analysis:323.2. Temporal Biases in Satellite ImageryD.A. (days) -6 -5 -4 -3 -2 -1 0 1Slope (km2sm3) 0.130 0.132 0.135 0.136 0.136 0.135 0.134 0.133Y-intercept (km2) -10.4 -19.7 -27.7 -31.1 -29.2 -22.7 -14.1 -6.8r2 0.676 0.698 0.714 0.723 0.720 0.711 0.705 0.697RMSE (km2) 206 198 193 190 191 194 196 199Table 3.1: Properties of linear regression (slope, intercept on the vertical axis, coefficient ofdetermination (r2), and root mean square error (RMSE) in km2). D.A. (days after) standsfor the time gaps between the datasets (river discharge and plume area) for the regression.For example, “D.A. = -3” means that river discharge three days ahead of the time whenSPM images are taken was used for the linear regression.A/km2 = 0.1361 QPort Mann(d− 3 day)/(m3/s)− 31.1 (3.3)3.2 Temporal Biases in Satellite ImageryAs described in the previous chapter, 2466 satellite images are used to derive a time seriesof the Fraser River plume area (Sec. 2.2). However, this image collection is not evenlydistributed and some hidden biases may significantly complicate our analyses.The first intuitively-occurring bias comes from the seasonal cycle of the cloud coverageabove the Strait. Since the plume can only be observed by the satellite under a clear sky,the cloud coverage determines the availability of useful images. Located in a moderateMediterranean climate zone, the Strait of Georgia usually has dry summers and rainywinters, which results in a preference for images to occur during the clear skies in summer.From the image collection, nearly 70 % are between April and September (blue curve inFig. 3.3b). At the same time, Fraser River discharge during its freshet is 6 to 10 timeslarger than it is in winter months, which results in much bigger plumes. Thus, more imagesare seen in summer with a big plume, and less images in winter with a small plume.The second well-known bias of the image collection comes from a preference for north-westerly winds. According to hourly wind records from Sand Heads lighthouse, strong7southeasterly winds (purple curve in Fig. 3.3a) appear more often than strong northwest-erly winds (orange curve) in almost all months. However, the number of useful SPM imagesunder strong northwesterly winds is about 2.5 times larger than those under southeasterly7In this thesis, strong winds refer to winds from any direction with a speed over 4 m/s.333.3. Plume Area Variation under a Tidal Cyclewinds. This bias reflects that winds from northwest tend to bring a clear sky and goodweather to the Strait of Georgia.Another important but less-known bias of the SPM images comes from the relativephase shift of the daily tidal cycles throughout the year. As introduced in Sec. 1.3, thedaily lower-low tide in the Strait is mostly around the middle of the day from April toSeptember, while mostly around midnight in the rest of the year (Fig. 1.5). Since thesatellites scan over the Strait at about the same time in the local day (11:22 for Terra and13:04 for Aqua), it implies that summer images are generally taken in the “big ebb” cycle(tide lag hour, h, from -7 to 7) in any day, while the winter images contribute only tothe “small ebb” cycle (h > 7). Given the fact that summer images usually contain largeplumes, the averaged plume area over a tidal cycle is thus significantly manipulated by thisseasonal cycle of tidal phase relocation.As an illustrative example of this bias, scatter-plots of the plume area and the riverdischarge over a tidal and seasonal cycle are compared in Fig. 3.4a1 and b1. It is clearthat tidal signals of the plume area variation are totally submerged in the strong seasonalcycles. Without removing this seasonal variation of the plume, a simple average of plumearea (or river discharge) over a tidal cycle will lead to a completely false result.More specifically, the river flowrates from Station Hope and Chilliwack, which areboth far away from the river mouth, are known to be not impacted by the stage of tide.However, when this flowrate dateset (corresponding to the times when SPM images aretaken) is averaged across tidal cycles, high flowrate in the spring and summer will onlycontribute to half of the tidal cycle (tide lag hour from -4 h to 8 h), which results in anunrealistic “high river discharge in the flooding tide” (Fig. 3.4b1, b2).3.3 Plume Area Variation under a Tidal CycleIn order to reveal the tidal impact on the Fraser River plume area, the first step is toreduce the bias and seasonal signals from the SPM image collection. Knowing that thelargest effect on the plume size is the river flow (Sec. 3.1), a new variable RAF (normalizedplume area) is defined as an alternative to the plume area itself:RAF =AactualAforecast=Aactual/km20.1361QPort Mann(d− 3 day)/(m3/s)− 31.1 (3.4)343.3. Plume Area Variation under a Tidal Cyclewhere Aactual is the actual plume area observed by the satellite, and Aforecast is theplume area estimated from the regression to the river flowrate (Eq. (3.3) and Table 3.1).QPort Mann is the derived plume flowrate from Station Hope and Chilliwack, and (d−3 day)stands for a cross-correlation with the plume area being delayed by 3 days. Using plumearea with a 3-day delay is to reduce the errors from the remaining big plumes after oc-casional water surges due to high precipitation events (Sec. 3.1). RAF is then a unitlessparameter which averages to about 1. In a tidal cycle, for example, RAF = 1.05 meansthat the the plume area is 5% larger than its daily average at this stage.However, there are still some seasonal signals that remain unexplained. A movingaverage of RAF over a single year with an 1-day step size and a ± 10-day window sizeshows some high anomalies in April and November (Fig. 3.5a). These high values in Aprilmay relate to the relatively higher turbidity from the river input at this time. Since theplume area in this study is defined as the summation area of the image pixels whose SPMconcentrations are above the 2 g m−3 threshold, a higher turbidity in the plume may yield alarger plume extent. Then, in November, high precipitation events in the lower-mainlandmay cause a surge in the Fraser discharge, which results in a rapidly growing plume.Although the river discharge data from Chilliwack was used to better reflect these specialevents, in some cases, the Fraser discharge at its mouth is still considerably underestimated,which inflates the resulting RAF. This remaining seasonal variation may still affect theanalysis of tidal variation.To reduce this secondary seasonal variation, the original RAF is divided by the ratioof its nearest daily moving average to its global mean. The new RAF (Fig. 3.5b) thenshows a moving average that nicely lies around the overall mean of RAF. Additionally,data points that are larger than the 0.99 quantile (RAF = 2.09) and smaller than the0.01 quantile (RAF = 0.23) are considered as outliers and are removed. Hereafter, if notspecifically stressed, RAF refers to this new version in which its remaining seasonal patternis removed. Although the moving variance (standard deviation) also has a clear seasonalcycle with relatively low values from May to September and high values for the rest of theyear, it may imply a more dramatic tidal modulation on the plume area in winter months.In order preserve this information, no further reductions are made to the data variance inwinter months.After removing the seasonal variation of the plume area, tidal signals start to emerge(Fig. 3.6). A clear transition from relatively larger plumes during low tides to relativelysmaller plumes during high tides is found. Averaged across tidal cycles, normalized plume353.4. Plume Area Variation under Same-day Image Pairsarea (RAF) is found to be negatively correlated to the tidal elevation with a small phase lag.More specifically, the biggest plume is usually found about 1 hour later than the lower-lowtide of the day, while the smallest plume is about half an hour later than the higher-hightide of the day (Fig. 3.7b). Unlike the unrealistically dramatic change of plume area ofover 100% from the biased original data (Fig. 3.4a2 and 3.7a), RAF tends to grow 18.5%during the big ebb period (tide lag hour from -7 to 1) followed by a decrease of 18.7% inthe next 7-8 hours of flooding tide. Then, a similar increase of 17.2% and a decrease of22.1% of the plume area occur during the rest of the tidal cycle (Fig. 3.7b, Table. 3.2).Overall, using RAF as an alternative representation of the plume area decreases the biasintroduced from a series coincidence of tide, river discharge and satellite scanning time.However, the way of deriving this new variable may also introduce some artificial errors anduncertainties. For example, although the negative correlation between the tidal elevationand RAF is generally consistent, the exact curve of mean RAF over a tidal cycle and themagnitude of the plume resizing are slightly sensitive to the method of reducing secondaryseasonal signals and the removal of outliers. To further substantiate the observed tidalvariation is the plume area, a second independent analysis to this problem is applied.3.4 Plume Area Variation under Same-day Image PairsTo reveal the pure plume area variation over a short period of time, an analysis of theplume area change in the same-day image pairs becomes key. As introduced in Sec. 2.1,because of the design of satellite orbit and swath, the SoG is sometimes observed twice aday by the same satellite with a time gap of 1 hour and 40 minutes. This feature providesus with an opportunity to directly study the individual plume behaviour over short timeintervals. From 2013 to 2019, there are 3300 days when two satellite images are available.However, only 247 of such image pairs have fully or near-fully identifiable plume boundariesin both images to estimate the plume area change.The processing procedure of these paired images is similar to the processing of individualSPM images, but requires some more care. Unlike estimating the plume area from a singleimage, the amount of plume area change within each image pair ranges from a few km2 todozens of km2, and it is much more sensitive to the design of plume boundary masks. Insome cases, the individual optimal interpolation may introduce unexpected inconsistencyand exaggerate the difference between the plume area purely from the different plumemasks being applied.363.4. Plume Area Variation under Same-day Image PairsIn order to reduce the error, all 247 image pairs are additionally inspected. As anillustrative example, the same outer mask (magenta curves) and inner mask (cyan curves)are specifically designed for both pre-processed plume images (Fig. 3.8a1, b1). Then, theplume areas are calculated (a2, b2) and the plume contours are compared (red curves forthe first image and blue curves for the second image in a3 and b3).In this example, the river flowrate is ∼ 5100 m3 s−1, and moderate wind comes fromthe northwest. Two images are taken right before and after the lower-low tide of the day.The plume area has a small increase of 21 km2 (3 %), mainly coming from a strong pushof the cross-strait currents from the mouth of the Fraser to the southwest. The northernplume front expands slightly northward as the background southeastward currents fromthe northern Strait ceases. At the same time, in the southeast end of the plume, the frontstarts to disintegrate and retreat back to the plume centre (Fig. 3.8).A time series of the area difference within all image pairs can then be generated. How-ever, the value of the plume area increase/decrease is related to the size of the existingplume at a given time, and the precise time gap between two images could be a few minutesshorter or longer. Therefore, to keep the consistency of the data, a new variable is definedas the percentage of the plume area change per hour (RC):RC =A2 −A1A1(t2 − t1)100% (3.5)where A1 (in km2) and t1 (in hour) are the area and time for the first image in the pair,while A2 and t2 are for the second image. RC that are above the 0.99 quantile or belowthe 0.01 quantile are considered as outliers and are removed.As this rate is displayed over a tidal cycle, a tendency of increased plume area (red lines)during the ebb tides and decreased plume area (blue lines) during the flood tides showsup (Fig. 3.9a), which agrees with the earlier demonstrated negative correlation betweenthe plume area and the tidal elevation in Sec. 3.3. This pattern is found to be consistentthroughout the year from March to September (Fig. 3.9b).Theoretically, RC is an estimate of the time derivative of the plume area variation.Thus, instead of a correlation to the tidal elevation, the plume area change rate (RC) isexpected to be negatively correlated to the time derivative of the tidal elevation (DT, inm h−1):DT =dηdt(3.6)373.4. Plume Area Variation under Same-day Image Pairswhere η is the tidal elevation at Pt. Atkinson. This negative correlation between RC andDT is observed in the results (Fig. 3.10b).In order to directly compare the results from two different approaches, the time deriva-tive of the RAF curve is calculated. This time derivative of averaged RAF (as percentagechange per hour (dRAF/dt× 100%), shown as dashed red curve in Fig. 3.10b) agrees wellwith the pattern of averaged RC (blue curve in the same figure) for the most of the tidalcycle. Even a simplified regional linear representation of the RAF variation (green curves)matches reasonably well with the magnitude of RC. Integrating the RC curve by segments,the accumulative plume area changes for the big flood (-18.8%), small ebb (+18.3), andsmall flood (-23.4%) period are remarkably similar to the overall RAF change for the sameperiods (-18.7%, + 17.2%, and -22.1%, respectively) (Table. 3.2). The only exception is inthe big flood of the day, at which period the accumulative area change from RC (+35.3%)is noticeably higher than that from RAF (+18.7%).Other than the general agreement of the tidal patterns in the plume area variation fromthe two methods, some detailed phase lags observed in the earlier section area reconfirmedin the analysis of the same-day pairs. RC at one hour after the lower-low tide of the day isfound to be positive, which agrees with the short period of continued area increase after thelower-low tide in the pattern of RAF. More specifically, a cross-correlation analysis betweenthe normalized plume area (RAF) and the tidal elevation (η) finds a best correlation of thetwo variables when the phase is shifted by 63 minutes (Fig. 3.11a, c). A similar analysis onRC and DT results in an almost identical phase shift at 62 minutes (Fig. 3.11b,d). Theslope of the regression curve between RAF and η is about −6.58×10−2, which means that asthe water level in the Strait goes up/down by 1 m, the plume area tends to decrease/increaseby about 6.58% (Fig. 3.11a). The slope of the regression between RC and DT gives asimilar but slightly larger rate of about 8% of plume area change per meter of sea levelchange.Furthermore, the same approach and comparisons can be applied to observational dataunder different river flowrate conditions: medium-low flowrate condition (Q¯ < 5000 m3 s−1),and high flowrate condition (Q¯ > 5000 m3 s−1). When Q¯ is relatively low, the satelliteobserved plume area variation (RAF curve) shows a smooth transition throughout the tidalcycle, and nicely reflects the tidal patterns (Fig. 3.12a1). The magnitude of the plumearea change for each tidal segment (big ebb, big flood ...) increases from about 19% onaverage to about 23% (Table 3.2). However, for the high river flowrate condition, there isno significant tidal variation found in the plume area (Fig. 3.12b1, b2).383.4. Plume Area Variation under Same-day Image PairsTo look at the transition of this tide-plume correlation under different river flowrates,we use a series of subsets of plume areas, staring from 0 m3 s−1 < Q¯ < 2000 m3 s−1,incrementing by 100 m3 s−1until approaching 10000 m3 s−1, and then generate a seriesof the correlation coefficients (R) and the slopes of the linear regression between tide (η,DT) and plume area (RAF, RC) of these data subsets, with additional adjustment on thephase lag delays (Fig. 3.12c1). The results show the strongest linear correlation when theriver flowrate is relatively low. Especially for Q¯ < 3000 m3 s−1, the slopes of the linearregression between (RAF and η) and (RC and DT) are found to be consistently at about11 to 13 % m−1, which are over 60% larger than those from a regression of all availableobservations.As the river flow becomes stronger, the magnitudes of the correlation coefficient andthe slope gradually decrease. When river flowrate is above 6000 m3 s−1, both R andthe slope of the regression between RAF and η approach to zero, which means no morecorrelation is found between η and RAF. For the correlation between DT and RC, althoughR never reaches zero, the slope of the regression near-linearly decreases as the river flowrateincreases (Fig. 3.12c2).Comparing these two methods, the analysis based on RAF makes full use of all availableimages. Although an uneven distribution with more data from summer months still exist,the number of winter images is sufficient to capture a relatively smooth transition duringthe small ebb cycle. However, using RAF is an indirect measurement of the plume area,which contains more variance other than the pure area variation. Noise in the time seriesof RAF is relatively large compared to the tidal signals, given a relatively poor correlationcoefficient (R ∼ -0.22, Fig. 3.11a) for the linear regression between RAF and tidal elevation(η) with adjusted phase lags.On the contrary, the analysis of the same-day pairs uses a direct measurement of theplume area change over a short period of time. The correlation between RC andDT is muchstronger (R ∼ -0.41, Fig. 3.11b) than that from the first method. However, the problemwith the uneven data distribution is worse as the available same-day pair observations inwinter (therefore, the small ebb cycle) are sparse. Only 13 image pairs are usable fromNovember to January throughout all 17 years, and consequently, only 18 (7.3 %) samplesfalls in one third (before h = - 3.5 and after h = 13) of the tidal cycle. Especially for theperiod before h = -6 and after h = 16, only 4 of such observations are in use, which meansthe tidal pattern of RC in the early-big-ebb period and the late-small-flood period is notvery reliable. The noticeable mismatch between the two methods for these periods could393.5. Tidal Influence on the Fraser River Plume SalinityBig Ebb Big Flood Small Ebb Small FloodOverall PlumeArea VariationRAF +18.5% -18.7% +17.2% -22.1%RC +35.3% -18.8% +18.3% -23.4%Medium-LowFlowrate ConditionRAF +22.3% -25.2% +19.9% -22.8%RC +41.4% -21.4% +18.7% -23.4%Table 3.2: Summary of the plume area variation under different stage of tide (i.e., the bigebb, big flood, small ebb, and small flood). RAF and RC refer to the results from twoindependent methods based on satellite observed SPM images (Sec. 3.3, 3.4). Results forthe medium-low river flow condition is calculated based on a subset of all observations inwhich daily averaged river flowrate is below 5000 m3 s−1 (Fig. 3.12).also be partly explained by the lack of good observations in the same-day pairs.Overall, these two independent methods complement each other well showing a tidalvariation in plume area of near 20% on average, and consistently show a negative correlationbetween the tidal elevation and Fraser River plume area with a phase lag of about 1 hour.The magnitude of the daily averaged river flowrate has significant influence on the tide-plume correlations, and a relatively low daily river discharge usually leads to a bigger tidalvariation in the plume area. In the next two sections, the tidal variability in the plumesalinity and the extent of river influence on the surface currents will be further investigatedto provide us a deeper understanding in the dynamic features of the tide-plume interactions.3.5 Tidal Influence on the Fraser River Plume SalinityAs a mixture of river water and seawater, the salinity of the plume is a critical parameterthat actively affects its volume and extent. Specifically for this study, the tidal variabilityin the Fraser River plume salinity is important to understanding the dynamics of the plumearea variation over a tidal cycle. As introducted in Sec. 2.3.4, the instrumented ferry thatroutinely crosses the Strait provides a good record of the surface salinity at a relativelyhigh spatial and temporal resolution. However, to estimate the plume salinity using thisdataset, a clear definition of the plume water along the ferry tracks should be established.In other words, a good salinity threshold is needed to define the boundary between theplume waters and non-plume waters.In Halverson and Pawlowicz (2008, 2011), this salinity threshold was defined as Sref −Soffset, where Sref (reference salinity) is the spatial mean of salinity between 45 and 50km away from Tsawwassen Terminal, and Soffset (salinity offset) is a linear function of the403.5. Tidal Influence on the Fraser River Plume Salinityreference salinity. Soffset varied between 0.4 to 1.8 PSU with the highest value when theSref is the biggest. However, in the present, the plume boundary is defined as SPM = 2g m−3 from the satellite imagery. Whether or not this salinity threshold definition used inthis previous work is comparable to the SPM threshold is not clear.To address this problem, 147 satellite images taken in 2018 are carefully examined andcompared with the ferry tracks that are closest in time. Among all good satellite imagesin 2018, 121 of them are paired with a ferry track that is within ± 2 hours from the timewhen the image is taken, and 82 of them see an intersection between the ferry track andthe plume contour at SPM = 2 g m−3. In the other 39 images, the ferry track does notintersect the plume. This occurs either during low river flowrates (when the river turbidityis low and/or the plume is close to the river mouth), or under strong southeasterly windswhen the plume is pushed northwards.For the remaining 82 images, the SPM concentration is interpolated onto the ferrytracks, and a strong negative correlation is found between the SPM concentration andthe surface salinity (Fig. 3.13b). As an illustrative example, such a comparison is madeon July 5th, 2018, when the river flowrate is relatively high (Fig. 3.13). The correlationcoefficient (R) between the SPM and the salinity is found to be about -0.98 (coefficientof determination, r2 ∼ 0.96), and the salinity threshold (STabs ∼ 19.4 g/kg) is derivedbased on this linear regression at SPM = 2 g m−3. As shown in Fig. 3.13c, this salinitythreshold works well in finding the plume boundaries and nicely separates the plume waterfrom the non-plume waters. Additionally, ferry measured surface turbidity is shown on topof the interpolated SPM concentrations to address the good alignment between the ferryand satellited based observations (Fig. 3.13d).From the example above, Sref − STabs ∼ 3.7, which is already bigger than the higherbound of Soffset in Halverson and Pawlowicz (2008, 2011). On average, Sref−STabs from all82 examples in 2018 is about 6.8 g/kg with a standard deviation of 3.2 g/kg. Therefore, thesalinity threshold from Halverson and Pawlowicz (2008, 2011) tends to result in a plumeboundary wider than the satellite observation, and thus, it is not used for this analysis.Instead, a relative salinity threshold (STrel) is found to be better choice (Fig. 3.14):STrel =STabs − SminSmax − Smin (3.7)where STabs is the absolute salinity threshold derived from the regression between SPMconcentration and salinity, Smax is the local maximum of the salinity west of 123.7◦W, and413.5. Tidal Influence on the Fraser River Plume SalinitySmin is the minimum salinity along the ferry track. From the example above, STrel is about0.72, and according to Fig. 3.13c, using a STrel that is 0.1 higher/lower than 0.72 will onlyexclude/include one extra data point in the calculation of the plume salinity. Therefore,as long as the plume has a clear frontal structure, the use of STrel has good flexibility anderror tolerance. To apply this relative salinity threshold from the 82 examples to all ferrytracks in year 2018, an empirical formula for STrel is developed based on the river flowrate(Fig. 3.14a):STrel =6.5× 10−5 Q¯/(m3/s) + 0.30, Q¯ < 6300 m3 s−1.0.71 , Q¯ > 6300 m3 s−1. (3.8)where Q¯ is the daily averaged river flowrate. In year 2018, there are 2052 ferry tracksin total, however, 348 of them either show a salinity range (Smax − Smin) smaller than 5g/kg, or see the plume with a width less than 5 km along the ferry track. Both of theconditions above may indicate that the ferry either does not go into the plume, or it justpasses through the very edge of the plume. Therefore, these 348 data points are excluded.For the remaining 1704 ferry tracks, the ambient ocean salinity (So) and ferry-measuredplume salinity (Sf) are calculated. So is simply taken as an overall average of the salinitiesabove STabs, however, the estimation of Sf requires more care. The plume is usually morefresh at its core and more salty at its edge. When the ferry passes over the plume core,the relatively fresh water accounts for asymptotically O(n−1) of the salinity along the ferrytrack, but it actually only occupies O(n−2) of the plume area. Therefore, a higher weightis given to the “saltier” waters in the plume, and a smaller weight is given the “fresher”plume waters:Sf =∑ni=1 Sf(i)[i2 − (i− 1)2]n2(3.9)where n is the number of salinity data points that are below STabs, and Sf(i) refers to eachindividual data point that is sorted in an ascending order. The equation above assumesthe the horizontal plume salinity distribution is composed of concentric rings, with theouter rings larger and more salty than the inner rings. Based on this formula, Sf is then aweighted average of these salinity records below the given salinity threshold.Then, So and Sf are averaged across tidal cycles to show the tidal influence on theoverall salinity variation inside and outside of the Fraser River plume (Fig. 3.15a1-a4,423.5. Tidal Influence on the Fraser River Plume Salinityb1-b4). Additionally, since there are up to 8 ferry tracks crossing the Strait a day, hourlyplume salinity change can be derived from the 7-a-day consecutive ferry track pairs (Fig.3.15c1-c4). Similar to the concept of the same-day image pairs (RC in Sec. 3.4), calculatingdSf/dt based on the salinity change between consecutive ferry tracks is considered to bea more direct and accurate method rather than a simple derivative of the Sf curve over atidal cycle.Over all river flow conditions, So is consistently around 25.0 g/kg, with a slightly highervalue (26.2 g/kg) and smaller scatter under low flowrate conditions, and a lower value (23.3g/kg) with a relatively larger variance under high flowrate conditions. Tidal influence isfound to be minimal in the variation of So. On the contrary, ferry-measured plume salinity(Sf) is significantly modulated by tide. On average, Sf routinely increases about 2.5 g/kg(15%) from its daily minimum (near the lower-low tide of the day) to its daily maximum(near the higher-high tide) (Fig. 3.15b1). Independently derived dSf/dt over a tidal cyclealso captures the general salinity increase (up to 0.64 g/kg per hour) during the big flood ofthe day (Fig. 3.15c1). This daily variation in Sf is found to be slightly higher in magnitude(∼ 3.2 g/kg) when the river flowrate is relatively low, and slightly lower (∼ 2 g/kg) whenthe river flowrate is high. However, since the daily averaged Sf is also controlled by Q¯ (S¯f= 20.8 g/kg, 16.8 g/kg, 12.8 g/kg at low, medium, and high river flowrate conditions), thepercentage of daily Sf variation is found to be consistently around 15-16% independent ofthe river flowrate.However, the degree to which Sf and dSf/dt represent the salinity variation of the wholeplume is still not clear. As introduced in Sec. 2.3.4, the ferry draws water at an intakedepth of 2 m below its surface. However, because of the subduction of the surface waterunderneath the travelling vessel, the effective sampling depth is usually estimated at abouthalf of this intake depth (e.g., in Halverson and Pawlowicz (2011)). For the purpose of thisstudy, Sf is then roughly considered as the plume salinity at a depth of about 1 m.In Halverson and Pawlowicz (2011), the Fraser River plume is approximated as a linearlystratified layer, which assumes the plume salinity linearly increases from the surface to itsbase (D¯ for the overall plume depth) (e.g., Fig. 4.1). Following the same approach, thevertical dependence of the plume salinity can then be established based on the salinity attwo known depths (Sf at z ∼ 1 m and So at z = D¯):S(z)− SoSf − So =z − D¯z0 − D¯ (3.10)433.5. Tidal Influence on the Fraser River Plume Salinitywhere S(z) is the plume salinity at a certain depth (z), D¯ is the average plume depth, andz0 = 1 m is the effective sampling depth of the ferry. The equation above can be rearrangedas:S(z) = So − So − SfD¯ − z0 D¯ +So − SfD¯ − z0 z (3.11)and then, the overall plume salinity (Sp) can be estimated as:Sp =1D¯∫ D¯0S(z)dz = So − D¯2(D¯ − z0)(So − Sf) (3.12)For convenience purposes, a correction factor γ is used to replace D¯/[2(D¯− z0)], wherez0 = 1 m. Based on its definition, γ is a function of the average plume depth D¯. In a recentstudy by Kastner et al. (2018), Fraser River plume depth (defined as the depth of the 21psu isohaline) is found to be 2-4 m at the Fraser River mouth, which agrees with an earlierestimation of the plume depth at 3 m by Cordes et al. (1980) from CTD measurements.Both of these studies were carried out in winters, when the river flowrate is relatively low.On the other hand, in Halverson and Pawlowicz (2011), the plume depth is estimated to be7 m, and a high degree of salinity variability can reach as deep as 10 m from CTD profilesnear the river mouth. Although the exact value of D¯ is still unknown, it is reasonable toassume that D¯ varies between 2 m and 10 m, which corresponds to a γ ranging from 0.55to 1.Additionally, the magnitude of the time derivative of the plume salinity may also beoverestimated by the ferry. Since the plume water is strongly stratified, the freshwaterspread at the surface can rapidly change the surface salinity. However, the salinity atthe bottom of the plume may not change as quickly and vigorously as the surface plume.Therefore, taking dSo/dt = 0 ,the hourly plume salinity change in tidal cycles can becorrected by γ:dSpdt= γdSfdt(3.13)However, it is important to keep in mind that, in practice, the stratification of the plumesalinity may not be fully linear, and the plume depth may also vary from the river mouthto the plume front. Therefore, although γ = D¯/[2(D¯ − z0)] is a reasonable estimation, itmay still need to be adjusted according the specific situations when it is applied.443.6. Tidal Harmonic Analysis on the Surface Currents3.6 Tidal Harmonic Analysis on the Surface CurrentsTidal modulation of the surface currents in the southern Strait is important to understand-ing the dynamical structure of the Fraser River plume. As introduced in Sec. 2.3.3, HFradar derived surface currents can be used for this analysis. In this study, data from year2018 is found to have the best spatial and temporal coverage, and a tidal harmonic analysisis performed on a 366-day hourly velocity field from Jan 1st, 2018 to Jan 2nd, 2019.In this procedure, least-squares fits are made to sinusoidal variations at a numberof known frequencies which are related to the orbital dynamics of the earth/moon/sunsystem. Each sinusoidal variation with its unique frequency is called a “constituent”.These constituents can then be plotted in terms of elliptical shapes that describe the cyclicrotation of velocity vectors at a particular location, with associated semi-major and semi-minor axes amplitudes which describe the degree to which tidal currents rotate or oscillateback and forth in a single direction given by the ellipse inclination.In the SoG, tidal currents are found to be along the Strait in most regions. However,near the Fraser mouth, the sinusoidal river flux across the Strait acts on top of the existingtidal currents, which results in more rounded tidal ellipses (Halverson and Pawlowicz,2016). In this study, an aspect ratio, defined as the ratio of semi-minor axes to the semi-major axes, is used to represent the river influence on the surface tidal currents. Basedon the results from major diurnal tidal constituents (K1, O1, P1, and S1) and major semi-diurnal constituents (M2, S2, N2, and K2), diurnal tides generally show a much bigger riverinfluence from the Sand Heads all the way across the Strait to the other side, while in thesemi-diurnal frequencies, the region with high aspect ratios barely extends past the middleof the Strait (Fig. 3.16).Therefore, the horizontal structure of the Fraser River plume can be characterized astwo distinct dynamical regions: a semi-diurnally modulated “inner plume” which quicklyresponds to the freshwater input from the river mouth, and a diurnally controlled “outerplume” through which the stronger once-a-day river jet passes.Recall from Sec. 3.5, the daily drop/jump in Sf around the big ebb/flood of the dayis the most dominant feature in the tidal variation (Fig. 3.15). Halverson and Pawlowicz(2008) also find that the ratio of K1/M2 to be 2.89 in the plume salinity but only 0.94 inelevation. However, when the time series of Sf is separated into subsets, this big diurnalfeature of the plume salinity variation is only found when the river flowrate is relativelylow (Fig. 3.15b1, c1). When Q¯ is greater than 2400 m3 s−1, Sf during the small ebb cycle453.7. Summaryshows a variation at a similar magnitude as the big ebb cycle (Fig. 3.15b2, c2).This phenomenon can be partly explained by the proposed plume structure with dif-ferent regions of diurnal/semi-diurnal influence. When the river flowrate is relatively low,the plume area is smaller. Since the ferry follows about the same route, as the plume sizedecreases, it is more likely for the ferry to see the feature of the “outer plume”, which ismore diurnally driven. When the river flowrate is higher (the plume size is bigger), the“inner plume” is a more significant part of the ferry track, and its semi-diurnal feature isthen reflected in the observed salinity variation. In short, the diurnal effect of the strongerriver jet (during the “big ebb”) is more important to the plume section (which the ferrycrosses over) when the daily river discharge is relatively low.3.7 SummaryIn this chapter, observational data have been carefully examined to investigate the tidalinfluence on multiple aspects of the Fraser River plume, from the plume area to the plumesalinity and surface currents. First of all, the plume area is found to be negatively correlatedto the tidal elevation in the Strait, with near 20% of area increase from low to high water.The daily maximum of the plume area is usually found to be about 1 hour later than thelower-low tide. River discharge has a significant influence on the tide-plume correlations.When the daily averaged river flowrate is relatively low (commonly in fall and winter),the plume area variation is larger over a tidal cycle, with a stronger correlation and asteeper slope in the regression to the tidal elevation. These findings are consistent in twoindependent methods of the satellite observation, one uses a normalized plume area (RAF)to reduce bias and seasonal signals, and the other uses the plume area change betweensame-day captured image pairs. To the best of the author’s knowledge, this is the firsttime that the plume area variation has been measured over a tidal cycle.With a near 20% of area loss twice a day, nearly half of the plume water is mixed intothe ambient ocean within a full tidal cycle. At this rate, salt, nutrients and sediments areactively exchanged between the river water and the ocean water. Periodical resizing of theregion of high SPM concentration could also affect the local light attenuation, and subse-quently, the local primary productivity. Especially when the river flowrate is relatively low(winter months), tidal influence is the dominant factor in the short-term plume variation,and tides control the mixing of the surface water out of the Fraser River mouth.The plume salinity is found to vary 15-16% during tidal cycles. Although seasonal vari-463.7. Summaryations in the plume salinity have been investigated previously (Halverson and Pawlowicz,2011), my results show the variability in tidal frequencies, which also indicates a vibrantexchange of salt between the plume water and seawater within short time intervals. Tidallymodulated entrainments may play an important part in the dynamics of the plume body.Unlike open-ocean plumes, the Fraser River plume is located in the semi-enclosed Straitof Georgia, which limits the development of the mid-field and far-field plumes that havebeen the subject of much previous work (e.g., Horner-Devine et al., 2015; Hetland andHsu, 2013; Chant, 2012). Therefore, the conventional dynamical scheme for the horizontalstructure of a plume may not apply in this area. However, tidal harmonic analysis on thesurface currents in the Strait reveals a significant difference in the extent of diurnal/semi-diurnal driven river influence. This may offer us a new perspective in dividing the FraserRiver plume into two distinct dynamical regions: a diurnally driven “outer plume” thatis largely affected by the “big ebb” of the day, and a semi-diurnally driven “inner plume”where the “big ebb” and “small ebb” are equally important.These new findings provide us a deeper understanding of the behaviour of Fraser Riverplume under tidal periods. However, the reason for this tidal modulation on the plumearea is still not clear, and the dynamics of the tidal influence on the seawater entrainmentin the Fraser River plume is still not known. In the next chapter, a simple semi-analyticaldiagnostic model is developed to further investigate the dynamics of the tidal influence onthe Fraser River plume.473.7. SummaryFigure 3.1: A time series of the Fraser River flowrate vs Fraser River plume area from 2003to 2019. Red dots are the plume areas calculated from images aquired from Aqua mission,while blue dots are from Terra mission. Abnormally big plumes (grey dots in August 2016)are due to a rare coccolithophore bloom, and are excluded from further analysis.483.7. SummaryFigure 3.2: Linear regression (solid curve and equation in red) of the plume area andthe Fraser River flowrate based on expanded image collection (scattered as blued dots).As a comparison, a similar equation from Pawlowicz et al. (2017) based on a smallerimage collection is shown as dashed black curve, its equation is written in black colourunderneath the curve. Based on a cross-correlation analysis of the two time series, a 3-daylag of plume area to the river flowrate is found to give the best regression result. Thiscorrelation relationship is then shown in green dashed curve and green equation in thefigure.493.7. SummaryFigure 3.3: (a) Percentage of recorded wind data at each month under different windconditions from Sand Heads, 2003 - 2019. (b) Monthly distribution of the number ofselected SPM images under different wind conditions.503.7. SummaryFigure 3.4: (a1) Scatter plot of the Fraser River plume area over tidal and seasonal cycles.Referential tide peaks (Tidal lag hour = -7 for lower-high tide, 0 for lower-low tide, 7 forhigher-high tide, 13 for higher-low tide) are labelled with thin black lines. Dots right of orabove the dashed grey lines are the duplicated data points to better visualize the wintertransition of plume area over tidal cycles. The corresponding horizontal and vertical tick-labels for these duplicates points are marked with braces. (a2) mean plume area over atidal cycle (green curve) with standard error of mean as error bars (duplicated data to theright of the dashed grey line in (a1) are excluded, while duplicated data above the dashedgrey line are included and were averaged using grey curves with grey error bars). (b1) and(b2) are the same as (a1) and (a2), but for the river flowrate data. Note that the flowrateis upstream of tidal influence.513.7. SummaryFigure 3.5: (a) moving averages of RAF in a seasonal cycle with a 1-day step size and a± 10-day window size. (b) similar to (a), but the original RAF is divided by the ratio ofits nearest daily moving average to its global mean to further reduce seasonal signals inthe data. Data points that fall below the 0.01 percentile and above the 0.99 percentile areexcluded from further analysis.523.7. SummaryFigure 3.6: Regional medians of RAF values are plotted onto a grid stepped by 10 days inthe horizontal axis (seasonal cycle) and 0.5 hours in the vertical axis(tidal cycle). Colourof the dots shows the median value of the data points within ± the step size of eachgrid point, and the size of the dots represent the number of data points being averaged.Blue/red colour means that the plume area is smaller/larger than its daily average.533.7. SummaryFigure 3.7: (a) Strongly biased result of the plume area over a tidal cycle (same informationas in Fig. 3.4 (a2)). (b) Corrected result from RAF over a tidal cycle. Standard error ofmean is added as error bar on both subplots. Referential tidal elevation curve of the dayis added at the bottom.543.7. SummaryFigure 3.8: Example of image processing and data comparison for the same-day imagepairs. Upper panels (a1 to a3) are for the first image of the pair (12:20 PST), while thelower panels (b1 to b3) are for the second image (13:35 PST), both images are taken inthe same day on July 15th, 2018. Left panels (a1 and b1) are for the original SPM imagebefore processing. Magenta contours are manually drawn to define the approximate outerboundary of the plume region, while the inner cyan contours are used for cleaning theabnormally low-reflectance small patches inside the plume. Note that the same outer andinner mask contours were applied to both images in this paired group. Middle panels (a2and b2) show the images after cleaning and interpolation, together with information ofplume area, wind and river flowrate (Q). Wind direction is defined as angle of the origin ofthe wind clockwise from the north. Right panels (a3 and b3) show a comparison betweenplume boundaries (red for the first image while blue for the second). HF-radar derivedsurface currents are added underneath the plume contours (surface currents at 12:00 PSTare used for (a3) and at 14:00 are used for (b3)). Relative lag hours in a tidal cycle forthe paired plume image are shown at the lower-left corner of the plots. Legend for themagnitude of surface current vectors is added on (a3) and the ruler for the length scale isadded on (b3).553.7. SummaryFigure 3.9: Distribution of the plume area resizing rate (RC) within a tidal cycle (a) and ina tide-year 2-D distribution (b). In (a), daily tidal cycles are plotted in grey curves, witha mean tidal elevation in thick dashed black line. Short thick lines with colours in blueto red are for the percentage of area change per hour (RC) between each grouped SPMimage pairs. Same concept for (b), in which all 3300 potential same-day pairs are drawn inthin grey lines showing the start and end times for each pair, and 247 good pairs are usedto calculate the area change rate and were plotted in thick lines with colour ranging fromdark blue to dark red. Referential tidal peaks are added on (b), as in Fig. 3.4, 3.4 and 3.6563.7. SummaryFigure 3.10: Comparison of the plume area variation from the mean RAF among all SPMimages (a) and the change rate (RC) from same-day image pairs (b) in a tidal cycle. (a)is the same as shown in Fig. 3.7, with a approximated regional linear regression (greenlines) on top of the pattern of RAF variation within a tidal cycle. For (b), RC in a tidalcycle is drawn in a blue curve with black errorbars showing the standard error of mean.Calculated percentage of hourly RAF variation (1RAFdRAFdt 100%, i.e., the time derivative ofthe red and green curves divided by value from (a)) are shown in (b) with the same colouras in (a). Instead of a referential tidal elevation shown in (a), the time derivative of tidalelevation (DT, m/h) is used as a reference to RC.573.7. SummaryFigure 3.11: (c) Cross-correlations between the normalized plume area (RAF) and tidalelevation at Pt. Atkinson (η), and (a) the linear regression at the minimum correlationcoefficient (phase shift at - 63 minutes). Same concept in subplot (d) and (b) for thecross-correlation between the plume area change rate (RC) and the time derivative of tidalelevation (DT), with a best correlation at phase shift = - 62 minutes.583.7. SummaryFigure 3.12: (a1) and (a2) are similar to Fig. 3.10, but for the medium-low river flowcondition (Q¯ < 5000 m3 s−1). (b1) and (b2) apply the same approach for high riverflow condition (Q¯ > 5000 m3 s−1). In (b1) and (b2), hourly RAF with less than 10 validSPM images and hourly RC with less than 3 valid same-day pairs are not shown. (c1)Correlation coefficients (left axis) and slopes (right axis) for the linear regression betweentidal elevation (η) and normalized plume area (RAF) for continuous subsets of the SPMimages with incremented river flowrate. (c2) correlation parameters for DT and RC.593.7. SummaryFigure 3.13: (a) SPM image at 13:20, July 5th, 2018 (PST), and its nearest ferry trackin time (departed from Duke Point Terminal at 11:50 (PST) and arrived at TsawwassenTerminal at 13:40 (PST)). White square boxes are drawn to show the intersection pointsbetween the ferry track and the plume boundary in the SPM image. (b) linear correlationbetween the satellite observed SPM concentration and the salinity measured along the ferrytrack with a correlation coefficient of -0.98. An absolute salinity threshold (STabs ∼ 19.4g/kg) is calculated at SPM = 2 g m−3. (c) salinity along the ferry track, with the calculatedsalinity threshold (STabs), ambient ocean salinity (So), and the weighted ferry-measuredplume salinity (Sf). Plume boundaries are shown as thin black lines at the intersectionsbetween STabs and the along-track salinities. (d) interpolated SPM concentration from theSPM image onto the ferry track (black curve with square markers). Intersections to theSPM = 2 g m−3 threshold is shown in thin black vertical lines (same locations at the whitesquare boxes in (a)). To show the good match between satellite-based SPM concentrationand the surface turbidity measured by the ferry, a yellow curve with triangle markers areadded in this plot to show the ferry-measured turbidity values.603.7. SummaryFigure 3.14: (a) relative salinity threshold (STrel, according to Eq. (3.7)) for the examined82 examples in 2018 against river flowrate. A segmented linear correlation of STrel is shownas a thick red curve. (b) absolute salinity threshold (STabs).613.7. SummaryFigure 3.15: (a1-a4) tidal variations of the ambient ocean salinity (So) for four river flowconditions: all, low (Q¯ < 2400 m3 s−1), medium (2400 m3 s−1 < Q¯ < 5000 m3 s−1), andhigh (Q¯ > 5000 m3 s−1). (b1-b4) for ferry-measured plume salinity (Sf). (c1-c4) for thetime derivative of Sf (dSf/dt), calculated based on the Sf change rate between consecutiveferry tracks. Standard error of means are used as error bars on top of the hourly averagesalinities.623.7. SummaryFigure 3.16: Distribution of the aspect ratio (defined as the ratio of the absolute valuesof the semi-major axes to the semi-minor axis of the tidal ellipses) between major diurnalconstituents (K1, O1, P1, and S1) and major semi-diurnal constituents (M2, S2, N2, andK2) in the Strait.63Chapter 4A Simple Model of PlumeDynamicsObservational results of the Fraser River plume show a variety of interesting tidal featuresfrom the plume area and salinity to the surface currents. However, the mechanism ofthe tidal forcing on the plume area is still unclear. To explain and reproduce the plumearea variation over a tidal cycle, a simple semi-analytical diagnostic model is constructedin the following sections, and its applicability under various river flowrate conditions isinvestigated.4.1 Analytical Solutions based on the Tidally ModulatedFreshwater InputConsidering the Fraser River plume as a reservoir of freshwater in the Strait of Georgia, itsvolume is mainly controlled by the water inputs, outputs, and the fraction of freshwaterin the system. From Sec. 3.5, the plume salinity is found to increase about 15-16% duringthe daily big flood. If the amount of freshwater is conserved in the plume system, a highersalinity will lead to a lower fraction of freshwater, which means a bigger volume of theplume. However, on the contrary, the plume area is found to decrease during flood tides.Therefore, the salinity variation alone is not able to explain the observed tidal modulationon the plume area. The volume flux of the water input/output to the plume must be animportant factor.The volume flux of a plume system generally consists three main parts: the rate offreshwater input (from the river discharge), seawater entrainment (at the bottom of theplume), and the plume water exit (by mixing into the rest of the Strait at the plume front):dVpdt= Q+ weA− Ff (4.1)644.1. Analytical Solutions based on the Tidally Modulated Freshwater Inputwhere Q is the river flowrate, weA is the upward entrainment rate, and Ff is the rate ofplume water loss at the front. A schematic diagram (Fig. 4.1) of the plume shows therelationship between these factors. From earlier introduced model outputs at Steveston(Sec. 2.3.1, Wu et al. (2022)), the fluctuation of the river flowrate is clearly modulated bytide (Fig. 2.6), with a strong correlation to the time derivative of the tidal elevation (DT)8.Note that the numerical model which is the source of this information is run in a barotropicmode, and it does not take account of the salt-wedge induced friction and salinity variationat the river mouth. Therefore, this estimated hourly (or “minutely”, after interpolation)river flowrate theoretically reflects the rate of freshwater input into the Strait.In a tidal cycle, although the derived river flowrate seems to be negatively correlatedto the tidal elevation (Fig. 4.2), a comparison in the time series shows that the flowrateis actually better correlated to the time derivative of the tide elevation (DT) with a smallphase delay (Fig. 2.6). This correlation with DT means that the maximum daily outflowoccurs shortly after the middle of the big ebb, at which time the southward tidal currentin the Strait is about the strongest. This alignment of the maximum outflow aroundthe midebb is also found in McCabe et al. (2009), in which the model simulated surfaceelevation and velocity at the Columbia River mouth are compared.Under the low flowrate condition, the river water empties into the plume at a muchhigher rate during ebb tides than the daily average rate, while during flood tides, the plumewater is drawn back into the river channel. In Horner-Devine et al. (2009), the estuarydischarge for the ebb tides at the Columbia River mouth is found to be more than 4 timesthe averaged river discharge, which is similar to the model results shown here (about sixtimes of the mean daily flowrate, Fig. 4.2a). For the medium flowrate condition, riverwater rarely goes upstream, but the freshwater flux can be as low as zero after the middleof the big flood. When the river flowrate is high, tidal impact on the flowrate variation ismuch smaller, the river water discharges into the plume at a high and stable rate.Theoretically, in a short period of time, the bigger the river flowrate, the more fresh-water is injected into the plume, therefore, the faster the plume grows. When the riverflowrate is higher/lower than its daily average, the plume size tends to increase/decrease.8Note that in Sec. 2.3.1, the hourly river flowrate is derived from the depth-averaged eastward velocityand meridional river transect area, the positive values are for the flux upstream (estward) into the riverchannel. This hourly flowrate nicely shows a positive correlation to DT with a phase delay of about 2-3hours in Fig. 2.6. However, in our model set-up, the freshwater input (Q) enlarges the plume size, whichis an overall positive term. Thus, hereafter, we switch the sign of the flowrate data as shown in Sec. 2.3.1,with the positive values in Q to be the flowrate from the river to the plume.654.1. Analytical Solutions based on the Tidally Modulated Freshwater InputFrom the earlier sections, an increasing/decreasing plume area under ebbing/flooding tidesis found, and the rates of the plume area resizing is also negatively correlated to DT witha small phase delay, both of which agree with the pattern of the river flowrate in a tidalcycle.The overall agreement between the tidal cycle of the plume area variation and the riverflowrate variation at the mouth yields a qualitative explanation of the mechanism of theplume resizing resulting from the tidal fluctuation on the freshwater input. Furthermore,we can quantitatively simulate this tidally modulated plume area variation.First, the plume needs to be idealized. In Halverson and Pawlowicz (2011), the FraserRiver plume was simplified as a cylinder-shaped single-layer slab water with a uniformthickness. However, the plume water is usually fresher near the river mouth and saltier atits peripheral. Therefore, it is reasonable to assume that the plume depth is thicker at itscentre and thinner at its edge. This assumption agrees well with the field observation ofthe Fraser River plume depth by Kastner et al. (2018), in which the plume depth is definedas the depth of the 21 psu isohaline, and this depth is found to decrease almost linearlyaway from the river mouth. Therefore, in this study, the plume is re-constructed to be anupside-down semi-cone with the deepest point (D) at the river mouth and the shallowestline at the plume front (Fig. 4.1). The plume volume (Vp) is then characterized by thesurface area (A) and its depth at the river mouth (D):Vp =13AD (4.2)As described by Eq. (4.1), the plume gains its volume from both the freshwater inputby the Fraser River and the entrainment of seawater at the base of the plume, while itloses its volume as the plume water is entrained out of its front. At the same time, theupward entrainment of seawater brings salt into the plume, while the exiting plume waterat its front takes salt away from the system. A salinity budget can then be established as:d(ρpSpVp)dt= ρoweASo − ρpFfSp (4.3)where Sp and So are the salinity for the plume water and ambient ocean water, ρp andρo are their densities. Ignoring the very small difference in the density between the plumewater and seawater, the density terms can then be dropped from Eq. (4.3). Next, Eq.(4.1) and (4.3) are combined to eliminate the loss terms associated with Ff (the right-mostterm for both equations). Finally, the l.h.s term in Eq. (4.3) is expanded using the product664.1. Analytical Solutions based on the Tidally Modulated Freshwater Inputrule, and Eq. (4.2) is substituted to replace Vp. The balance of the plume salinity can thenbe expressed as:dSpdt= − 3QADSp +3weD(So − Sp) (4.4)Rearranging the equation above, the following formula is derived to calculate the rateof upward entrainment (weA):weA =DA3(So − Sp)dSpdt︸ ︷︷ ︸term1+QSpSo − Sp︸ ︷︷ ︸term2(4.5)In this case, weA is determined by two terms, both of which vary with the tide. Interm 2, tidal variability is dominated by Q since its daily tidal variation (∼ ± 75% onaverage) is much bigger than that of Sp (∼ ± γ×8%, where γ is slightly less than 1, seeSec. 3.5). In term 1, tidal variation brings a ∼ ± 10% variability to A around A¯. However,dSp/dt averages to 0 and changes sign throughout a tidal cycle, which leads to a dailyoscillation from about - |term 1|max to + |term 1|max. It is clear that dSp/dt dominatesthe tidal variation in the term 1, and the tidal variabilities in A and Sp are insignificant tothis term. Specifically for this analytical solution, we aim to reproduce the tidal variationin A simply based the tidal variation in Q and Sp (dSp/dt), therefore, A in the r.h.s. ofEq. (4.5) is replaced by A¯ in further calculations.Theoretically, during the ebb tides, Q is bigger than its daily average, which increasesthe magnitude of term 2. At the same time, the plume salinity tends to decrease as morefreshwater is injected into the system, which leads to a negative dSp/dt and a consequentdecrease in the term 1. From this reasoning, tidal variations in the weA are expected tobe reduced as its two components work counter to each other.Defined as the rate at which plume waters leave through the front, Ff is theoreticallyproportional to the plume front length (i.e., Ff ∝√A). According the earlier reasoning,tidal variation of A is usually much smaller than that of Q, and it is also a less significantpart in weA. Therefore, the variation of Ff over a tidal cycle is also expected to bereasonably small compared to Q and weA. In this study, Ff is assumed to be a constantthroughout the tidal cycle, and its value is determined by the sum of Q¯ and weA. Then,the plume area change rate can be easily estimated from Eq. (4.1) and (4.2):674.2. Base Case Study: Entrainment Flux Estimations and Plume Area Simulations1A¯dA(t)dt=1V¯dVp(t)dt=3(Q(t) + weA(t)− Ff)A¯D(4.6)where Q(t)9 is the hourly river flowrate at the Fraser mouth, and weA(t) is the derivedupward entrainment variation over a tidal cycle from Eq. (4.5). This plume area changerate from Eq. (4.6) is essentially the same as the RC calculated from the same-day SPMimage pairs. Furthermore, an integral of this equation yields the plume area variation overa tidal cycle to be:A(t) = A0 +3D∫ tt0(Q(t) + weA(t))− 3Ff(t− t0)D(4.7)where t0 is the start time of a tidal cycle at tide lag hour = -7.5 h, and A0 ∼ A¯ is the initialplume area at t0, which can be estimated according to Q¯ using Eq. (3.3). Since a typicaltidal cycle in this study starts at the lower-high tide of the day, at which time the plumearea is relatively small compared to its daily average, A0 is usually a few percent smallerthan A¯. In theory, dividing A(t) from the Eq. (4.7) by A¯ should result in a comparabletime series in tidal cycles as calculated RAF in Sec. 3.3.4.2 Base Case Study: Entrainment Flux Estimations andPlume Area SimulationsIn the first case study, we aim to reproduce the averaged plume area variation during thetidal cycle. For all SPM images in use, the median river flowrate (Q¯) on the days whenthese images are taken is around 3,500 m3 s−1, which corresponds to a median plume area(A¯) of 432 km2 (Eq. (3.3)).To estimate the plume area variation using Eq. (4.6) and (4.7), the only term that isnot determined is the plume depth at the Fraser mouth (D). This depth D may affect ourmodel in two aspects. First, D determines the plume volume (Vp). At a fixed rate of volumeinput, the larger the exiting Vp is, the smaller percentage of variation it shows. Second, Ddetermines the correction factor γ for the estimation of Sp and dSp/dt (γ = D¯/[2(D¯−z0)]9As indicated in the List of Symbols, adding (t) after a parameter refers to the hourly or minute-by-minute-resolution (“minutely”) variation of this parameter, in which tidal variability is important. Whenan overline bar is added on top of a parameter (e.g., Q¯), it refers to the daily average of this parameter.In this case, it may still show seasonal variations, but no tidal variation is considered. The same notationapplies to we, A, weA, Sp, and So.684.2. Base Case Study: Entrainment Flux Estimations and Plume Area Simulationsfrom Sec. 3.5, where z0 = 1 m and D¯ = D/3 for our “semi-cone” plume model), whichsubsequently affects the both term 1 and term 2 in weA (Eq. (4.5)). For term 1, whenD is smaller, γ is larger, and then the magnitude of dSp/dt variation is larger. For bothterms, γ also affects the value of Sp, however, in terms of the tidal variation, this affect isconsidered to be relatively small.As far as the scope of the equations, the value of D could affect our model results insophisticated ways, and a correct estimation of D is important. In practice, the actual“plume depth” could be as large as 18 m in high-flow periods due to hydraulic controlsand salt wedge dynamics (MacDonald and Geyer, 2004), but such depths may not providea good model for the rest of the plume under a linear variation model. After a carefulinvestigation, we find that D from 10 to 14 m gives good simulation in the tidal variationof the plume area.The other difficulty is to match the phase difference between the model and observa-tional results. Using the original hourly river flowrate from the numerical model output,our plume area simulation always shows a delay in the phase (see Appx. A, Fig. A.1).After a series of careful investigations, we find a consistent match in phase between themodel and the observation when shifting the hourly river flowrate ahead by 80 minutes ina tidal cycle.This 80 minutes of phase difference may come from two parts. First, the barotropicnumerical model (FVCOM) does not simulate the salt wedge in the lower parts of theriver, and hence may overestimate the effects of friction on the phase of tide at the rivermouth. Earlier observational studies show that the phase of tide at Steveston is only 5minutes later than that from Pt. Atkinson (Thomson, 1981), however, the tidal elevationoutput at Steveston from FVCOM results in an averaged delay of 55 minutes to that atPt. Atkinson. This mismatch means that, in practice, the actual tidal phase of the riverflowrate at Steveston should be about 50 minutes earlier than that from the FVCOM modeloutput.Secondly, as introduced in Sec. 1.2, the main arm of the Fraser River extends 9 kmoffshore from Steveston to Sand Heads through a region of mudflats. Since the shallowmudflats are partly uncovered during the low tide, Sand Heads may be a better representa-tive of the “Fraser mouth” than Steveston. Although the tidal fluctuation of the freshwaterdischarge at Sand Heads is hard to derive, its phase against tide can be estimated by ex-trapolation. Investigations of the surface velocity along the lower Fraser from the FVCOMmodel (not shown in this thesis) suggest that the tidal phase of surface currents increases694.2. Base Case Study: Entrainment Flux Estimations and Plume Area Simulationsroughly linearly upstream by about 3 minutes per kilometer. Similar increase of the phasedelay upstream along the river channel is also found in Thomson (1981), which shows a rateranging from 1.8 to 6.2 minutes per km from Steveston to New Westminster, dependingon whether tides are in their spring or neap phases. Extrapolating this would suggest thatthe phase of flow at Sand Heads is about 30 minutes earlier than that at Steveston.After the correction of the phase of Q(t) by shifting it 80 minutes early in a tidal cycle,the result from our analytical simulation matches well with the RAF and RC curves (Fig.4.2). In this case, daily averaged weA is around 1.49 × 104 m3 s−1(Eq. (4.5)), and Ff isaround 1.79 × 104 m3 s−1. The Fraser River plume area increases 14.1% during the bigebb of the day, and the daily maximum of the plume area is about 1.5 hours later thanthe daily lower-low tide. Although the exact shape of the curve and the magnitude of thetidal variation are not perfectly reproduced, the phase and the general structure of plumearea resizing match reasonably well with the observational results in Sec. 3.3 and 3.4 (Fig.4.3c, d).However, there still remain some tidal features unexplained by our model, especiallyduring the end of the flooding tides (tide lag hour 5-11, and 15-17). Two possible reasonsmay account for this mismatch. First, the tidal variation in the plume salinity (i.e., Sp,dSp/dt) that we use in the model may not be smooth and accurate enough. For example,in Fig. 4.3a and b, we see a strange drop in weA from h = 9-11 in the tidal cycle. This dropmainly comes from a drop at the same time from the term 1 in the model (blue curve in Fig.4.3a), which originally comes from a relatively low dSf/dt value at h = 10 (Fig. 3.15c1).Second, our model does not include the drop-off effects of SPM in the plume. In particular,during flood tides, the salinity of the plume water at the edge may still below the threshold(be considered as plume waters), but the suspended particles have been rapidly sinkingdown to the deeper ocean, which results in a faster decrease in the satellite observed plumearea.The daily averaged entrainment flux estimated from this study (weA ∼ 1.49 × 104m3 s−1) is slightly smaller than the results from Halverson and Pawlowicz (2011), in whichweA ranges from 1.7 × 104 m3 s−1 to 2.7 × 104 m3 s−1. This difference may result fromthe methods used to estimate the plume area. In Halverson and Pawlowicz (2011), theplume area is characterized to be a function of Q1/2: A = αQ1/2, where α is 11.1 ±0.5 km2 (m3 s−1)1/2. From this rough estimation, plume area at Q = 3500 m3 s−1 is about657 km2, which is over 50% bigger than the area that we use for this case (432 km2). In Sec.3.1, the plume area is shown to be actually linearly correlated to the the river flowrate, and704.2. Base Case Study: Entrainment Flux Estimations and Plume Area Simulationsa similar linear correlation is found in Pawlowicz et al. (2017). Therefore, we argue thatthe weA in Halverson and Pawlowicz (2011) is overestimated because of incorrect plumearea estimation. Dividing weA by the plume area, the estimated entrainment velocity(we ∼ 2.9 m d−1) then falls nicely in the range proposed by Halverson and Pawlowicz(2011) (2.2 m d−1 to 4.5 m d−1).Over a tidal cycle, variations in both term 1 (dominated by dSp/dt) and term 2 (dom-inated by Q(t)) of weA (Eq. (4.5)) are significantly modulated by tide (Fig. 4.3). Theseterms vary at similar amplitudes but work in opposition to each other. Therefore, the tidalvariation of weA turns out be smaller than the variation of either of its components. How-ever, there still remains a great deal of tidal variability in weA: it is generally bigger duringebb tides and smaller during flood tides, with a maximum daily entrainment flux about 4.7times as big as its daily minimum. In Cordes et al. (1980), an entrainment coefficient k isestimated at the Fraser mouth under different stage of tides. This entrainment coefficientis defined as the ratio of upward entrainment velocity to the depth-averaged plume velocity(k = we/|U|), and the entrainment velocity is estimated by the horizonal divergence of thesurface velocity field measured by drogued drifters (we = h∇ ·U). The daily maximumentrainment coefficient at the big ebb (k ∼ 4.9 × 10−4) is found to be about 4 times asbig as its daily minimum at the small flood (k ∼ 1.3× 10−4), which is consistent with ourresults.Assuming k is a constant in space over the whole plume, then we (and weA) mustbe positively correlated to the depth-averaged surface velocity |U|. In other words, thenear-field plume, in which the surface velocity is the strongest, must have a much biggerentrainment velocity than the plume region that is far away from the river mouth. Thiseffect is shown by Kastner et al. (2018), in which paired-drifter separations are analyzed toestimate the salt flux (Sewe) at the bottom of the Fraser River plume across the isohalinewith Se = 21. Sewe is the biggest at the river mouth (Sand Heads), and gradually decreasesas the drifters move away. The value of Sewe drops to near zero at 4 to 12 km away fromthe river mouth.Halverson and Pawlowicz (2011) also argues that the entrainment in the plume pre-dominantly occurs in the near-field plume and the estuarine salt-wedge, given the fact thatthe entrainment velocity estimated for the whole plume is at least one order of magnitudesmaller than the results from some earlier observations around the Fraser mouth (e.g.,Cordes et al., 1980; MacDonald and Geyer, 2004). Here in this thesis, the results agreewith the discussions in Halverson and Pawlowicz (2011), and we can provide two more714.3. Special Case Study: River Flowrate Impact on the Tide-plume Correlation and Entrainmentpieces of evidence to show this dominance in the near-field mixing: (1) tidal variationsin weA are strongly semi-diurnal, which agrees with the dynamical feature of the “innerplume” (see Sec. 3.6). If the entrainment mainly occurs at the outer plume, more diurnalfeatures in the weA variation are expected, (2) the plume area only varies up to 20% over atidal cycle, but the maximum daily weA is about 4 to 5 times as big as its daily minimum.If the we is constant in both space and time, a much smaller daily variation in weA wouldbe expected.4.3 Special Case Study: River Flowrate Impact on theTide-plume Correlation and EntrainmentIn the second case study, further investigations are made on the tide-plume correlationunder different river flow conditions: medium-low flowrate (Q¯ < 5000 m3 s−1) and highflowrate (Q¯ > 5000 m3 s−1). For the medium-low river flowrate condition, median Q¯ from1685 relevant SPM images is found to be about 2750 m3 s−1, which corresponds to a plumearea (A¯) of 343 km2. For the higher river flowrate condition, median Q¯ for the remaining781 images is about 6700 m3 s−1, and A¯ is 880 km2.As discussed in Sec. 3.4, the magnitude of the daily averaged river flowrate (Q¯) hassignificant influence on the tide-plume correlation, and the magnitude of the tidal variationin the plume area. From our analytical model, this feature is nicely reproduced (Fig. 4.4).For the low flowrate condition, Q(t) is interpolated from two cases (1000 m3 s−1 and 5000m3 s−1, i.e., blue and green curves in Fig. 4.2) on to 2750 m3 s−1, with the same phasecorrection of 80 minutes. D = 12 m is again found to provide the best simulation to theobservation.For this “best simulation” result, the plume area variation matches even better withthe observation than it does in the base case. Especially for the period from h = -7 to h= 6, the analytical simulation (green curve) is almost overlapped on top of the observedRAF curve (red curve in Fig. 4.4b1). The magnitude of the plume area increase at thethe big ebb increases from 14.1% in the base case simulation to 18.9%. On the contrary,when Q¯ is relatively high, simulated plume area variation is always small. Although noneof the D value can reproduce the exact shape of RAF for this case, both observation andanalytical simulations agree that the plume area is less affected by tide when the riverdischarge is high.724.3. Special Case Study: River Flowrate Impact on the Tide-plume Correlation and EntrainmentThe reason for this stronger tide-plume correlation under low river flows may come fromthe following factors: (1), when Q¯ is smaller, the tidal fluctuation on the river discharge isstronger, which results in a more dynamical plume, (2) the existing plume size is smaller,which reacts faster to the sinusoidal river input, (3) the river turbidity is lower and themixing is stronger, which makes it easier for the surface SPM concentration to drop belowthe plume threshold, (4) when the river turbidity is lower, SPM = 2g m−3 may only capturethe near-field plume and fail to capture the whole plume, which exaggerates the dynamicalnature of the plume.In the low flowrate condition, the mismatch between the model and the observationsfor the period of small ebb and small flood is still significant. In this case, the potentialeffect of the low dSp/dt at h = 10 is less severe as it was in the earlier section, which leftthe drop-off effect of SPM to be a more important factor.As discussed in Sec. 3.6, the Fraser River plume is horizontally characterized as asemi-diurnally modulated inner plume, and a diurnally driven outer plume. Assume thatthe suspended particles fall down from the plume body into the deeper ocean at a nearconstant speed. During the big flood of the day, plume water is pushed far away into theStrait, and its area rapidly grows nearly 20% in a few hours. In the next few hours whenthe river flowrate eases, the sediment carried by the plume continues to either drop downinto the deeper ocean, or to be entrained out of the system at the front.Since the Fraser River discharge at the small ebb is usually weaker than it is at the bigebb, it mainly replenishes the SPM to the inner plume region. Therefore, from h = 6 to8 in the tidal cycle, although the rate of the volume gain in plume is already bigger thanthe rate of volume loss (plume area increases in the model), the suspended particles keepdropping down at the boundary region of the plume, which makes the plume “visually”decrease in size. Similarly in the small flood, the plume area decreases faster in RAF curvethan the model simulation, which could also be partly due to the speed of the suspendedparticle drop-off at the plume edges faster than the rate of entrainment from the plume tothe ambient ocean.Other than influencing the tide-plume correlation, weA is also found to be a function ofQ¯ (Halverson and Pawlowicz, 2011). At a subtidal frequency, daily plume salinity variationis no longer considered to be an important part, thus, term 1 in Eq. (4.5) can be droppedout. Tidal variations in Q, So, and Sp can also be ignored. Therefore, after averaging, Eq.(4.5) can be written as:734.3. Special Case Study: River Flowrate Impact on the Tide-plume Correlation and EntrainmentweA =Q¯S¯pS¯o − S¯p (4.8)Both S¯p and S¯o are function of Q¯ (Fig. 4.5a). Substitute these linear regressions intoEq. (4.8), the weA can be estimated by any given Q¯:weA =Q¯(α1Q¯+ β1)(α2 − α1)Q¯+ (β2 − β1) (4.9)where α1 = −7.96× 10−4 k skgm3 , α2 = −3.4× 10−4 k skgm3 , β1 = 23.37 g/kg, and β2 = 26.46g/kg. These parameters are simply the slopes and intercepts of the linear regressionsbetween Sp,So and Q¯ (Fig. 4.5b). Since the daily averaged plume area (A¯) is also afunction of Q¯ (using Eq. (3.3), but ignoring the small constant term and the 3-day phasedelay), subtidal variation in the entrainment velocity (we) can be expressed as:we =weAA¯∼ weA0.1361 km2sm3Q¯=α1Q¯+ β10.1361 km2sm3[(α2 − α1)Q¯ + (β2 − β1)]× 86400 sday(4.10)For weA, our results show a fast increase when Q¯ is relatively low, and it stays at anear-constant level (∼ 1.8×104 m3 s−1) when Q¯ is high (Fig. 4.5b). This pattern is similarto the results in Halverson and Pawlowicz (2011), but the magnitude of our weA estimationis 25% to 60% smaller. As discussed in Sec. 4.2, this difference mainly comes from thedifferent ways in estimating the plume area at a given river flow condition.Tidal fluctuations in the short-term weA variation are found to be relatively indepen-dent of the rate of river discharge. From the 3 case studies carried out in this study, thedaily minimum of weA is found to be 0.3 to 0.5 times weA, and the daily maximum is foundto be 1.8 to 2 times weA. The ratios of the daily maximum/minimum weA to its dailyaverage are then used as the upper/lower bounds of the tidal fluctuation, and these boundsare applied to the 1704 ferry track records in year 2018. The lower bound works very wellin holding the lower-reach of the weA scatter points based on each individual track, andthe upper bound also does a fairly good job in limiting most of the higher points (Fig.4.5b).Considering we alone, the analysis shows a higher value (∼ 4 m d−1) with stronger tidalvariation (± 2 m d−1) when the Q¯ is relatively low, and a lower value (∼ 1 m d−1) withweaker tidal variation (± 0.5 m d−1) when Q¯ is relatively high. The lower entrainment744.3. Special Case Study: River Flowrate Impact on the Tide-plume Correlation and Entrainmentvelocity during high river discharge may due to the stronger stratification in the surfaceocean.To sum up, the river flowrate has a significant influence on the tide-plume correlationand the amplitude of daily plume area fluctuation. In addition, it also controls the rate ofupward entrainment in the plume. Therefore, for any future studies on the tidal influenceon the Fraser River plume, it is important to specify the river flowrate condition on whichthe study is based on, and carefully discuss the potential differences under high/low riverdischarges.754.3. Special Case Study: River Flowrate Impact on the Tide-plume Correlation and EntrainmentFigure 4.1: Schematic diagram of the Fraser River plume of surface area (A) and thicknessat the river mouth (D). The average plume depth (D¯) is one third of D. Q is the riverflowrate, weA is the upward entrainment rate of the bottom SoG water, and Ff is thevolume flux lost at the plume front. Sf is the ferry-measured plume salinity (effectivesampling depth at about 1 m), and Sp is the overall plume salinity estimated from Sf , So,and D¯ (Eq. (3.12)). With respect to the salt budget, weA brings in ambient ocean waterwith salinity of So, Q brings fresh water, and Ff exports plume water at salinity Sp.764.3. Special Case Study: River Flowrate Impact on the Tide-plume Correlation and EntrainmentFigure 4.2: (a) River flowrate in a tidal cycle from numerical model outputs at Stevestonfor different river flow conditions. (b) tidal cycle of the time derivative of tidal elevation(DT) at Pt. Atkinson. (c) tidal cycle of the tidal elevation (η) at Pt. Atkinson. Note thatthe daily averaged flowrates are not slightly smaller to the given conditions (1000, 5000,and 11000 m3 s−1), because the main arm (at Steveston) receives about 75% to 87% of thetotal discharge.774.3. Special Case Study: River Flowrate Impact on the Tide-plume Correlation and EntrainmentFigure 4.3: (a) tidal variation for weA and its components (term 1 and term 2) from Eq.(4.5). (b) tidal variation for Q, weA, Q+ weA(net volume gain), and Ff (net volume loss).(c) and (d) are similar to Fig. 3.10, with the analytical solution of the plume area variation(in light green curves, at D = 12 m) based on Eq. (4.6) and (4.7) on top of the satelliteobservations. A series of sensitivity plots using D = 10, 11, 13, 14 m are added as dashedpurple curves in (c). Note that in this case, the phase of the hourly river flowrate (Q(t))is corrected by shifting 80 minutes advance in the tidal cycle.784.3. Special Case Study: River Flowrate Impact on the Tide-plume Correlation and EntrainmentFigure 4.4: (a1) and (a2) are similar to Fig. 4.3b, but for the medium-low river flowcondition (Q¯ < 5000 m3 s−1) and high river flow condition (Q¯ < 5000 m3 s−1). (b1), (b2)are similar to Fig. 4.3c, and (c1), (c2) are similar to Fig. 4.3d. In (b2) and (c2), hourlyRAF with less than 10 valid SPM images and hourly RC with less than 3 valid same-daypairs are not shown. Solid green curves in (b1) and (c1) show the best model simulationof the plume area variation at D = 12 m. Dashed purple curves in (b1), (b2) and (c2)provide a series of sensitivity plots for the results from a different choice of D. Specificallyin (b2) and (c2), since none of the results match with the observation, all model simulationsare shown in dashed purple curves. The phase of Q(t) is corrected by shifting 80 minutesadvance in a tidal cycle, same as used in Fig. 4.3.794.3. Special Case Study: River Flowrate Impact on the Tide-plume Correlation and EntrainmentFigure 4.5: (a) linear correlations between river flowrate with plume salinity (Sp) andambient ocean salinity (So). (b) Entrainment flux (weA) as a function of river discharge,theoretical fit is derived in Eq. (4.9). (c) Entrainment velocity (we) as a function of riverdischarge, theoretical fit is derived in Eq. (4.10).80Chapter 5ConclusionsTidal influence on the Fraser River plume was investigated using two independent methodsapplied to a 17-year satellite observation dataset. The results consistently show a negativecorrelation between the tidal elevation and the plume area with a phase lag of about onehour. The plume size on average increases up to 20% during ebb tides, and decreases bya similar magnitude during flood tides. A simple analytical model based on the volumeconservation and salinity balance equations was built to analyze the dynamics of the tidalinfluence on the Fraser River plume. Using a tidally modulated river flux and plume salinitywith a correction in phase by shifting the time series 80 minutes in advance, the observedtidal variation in the plume area is partly reproduced. Tidal fluctuations in both thefreshwater input and the plume salinity are important to the rapid plume resizing in tidalcycles. The rate of upward entrainment at the bottom of the plume and its tidal variationsare found to be consistent with earlier studies. In addition, the horizontal structure ofthe plume is characterized by a semi-diurnally dominated inner plume and a diurnallycontrolled outer plume based on a tidal harmonic analysis on the surface currents in thesouthern Strait. This horizontal plume structure helps to explain some subtle variabilities inthe plume salinity, and the mismatch between analytical simulation and observation at theflood tides. Lastly, river flowrate is found to be important in the tide-plume correlations.Stronger correlations and bigger amplitudes (23%) are seen in the daily tidal cycles of theplume area when the river flowrate is medium to low, while a significant correlation cannot be established when the river flowrate is higher than 6000 m3 s−1.For the first time, the magnitude of the tidal variation in a river plume area is quan-titatively investigated. This 20% of the daily variation in the Fraser River plume extentcan be used to characterize some high-frequency variability of the surface nutrients andproductivity in the southern Strait. For monitoring purposes, this result can also be usedto separate the tidal and non-tidal variations of the plume. The results can also be usedto evaluate and improve numerical models (e.g., SalishSeaCast (Soontiens et al., 2016,https://salishsea.eos.ubc.ca/nemo/)), which sometimes do not accurately represent81Chapter 5. Conclusionsthe surface currents in the plume. Such currents are important in tracking, e.g., debris andoil spills. In particular, a similar tidal harmonic analysis in Sec. 3.5 can be applied to themodel derived surface currents to see if the model can correctly represent the difference inthe diurnal and semi-diurnal extents of the plume. Furthermore, a salinity threshold canbe developed to define the boundary the Fraser River plume in the model outputs, andinvestigate the tidal variation on the plume volume, salinity, bottom entrainments, and theriver flux.This study fills in the missing gap of knowledge in the tidal variation of the Fraser Riverplume, and the same technique can be applied to other plume systems worldwide. As longas the plume contains sufficient amount of SPM, a threshold for the plume boundary canbe easily established by a linear correlation between the SPM concentration and the surfacesalinity. Then, tidal variability in the plume area can then be characterized.One important thing to be aware of for such analysis on the tidal variation is the bias inthe highly aliased sampling scheme. In the case of SoG, more satellite images are taken insummer time when the sky is clear and the plume is big. At the same time, the lower-lowtide also occurs in the middle of the day. Without careful debias, it will result in a falsebig plume during the “big ebb cycle” of the day. Not only for satellite observations, butfor any observation of tidal variability, if the sampling time is at a fixed time of the day,care should be taken to investigate the potential biases.In this study, we also show that analyzing the plume variation through the same-dayimage pairs is a useful and powerful technique. For research on the short-term behaviour ofa dynamic water mass (i.e., the river plume), comparing these same-day images is usually agood start. In recent days, other than Aqua and Terra missions, satellites like Suomi NPPand NOAA-20 with a Visible Infrared Imaging Radiometer Suite (VIIRS) instrument, andthe high-resolution Sentinel-2 products can also be used to expand the data collection andprovide more same-day observations. Although the subtle differences between the imagesfrom different satellites should be carefully calibrated, observations can be dramaticallyimproved through the inter-comparison of these satellite images.However, there is still room for improvement to this study. First of all, SPM = 2g m−3 may not be a threshold that clearly separates the plume water from the ambientocean in all conditions. In some special cases, especially when the river flowrate andturbidity are relatively low, SPM = 1 to 1.5 g m−3 might be a better choice. Furtherinvestigations are needed to develop a better SPM threshold that is time dependent andcan effectively capture the plume under all possible conditions.82Chapter 5. ConclusionsSecond, the use of the correction factor γ to adjust the ferry-measured salinity torepresent the overall plume salinity may need further justification. A sufficient number ofCTD profiles throughout the plume area is needed to measure the spatial distribution ofthe plume depth and the surface stratification to provide a better estimation of γ.In addition, the tidal variation of the ferry-measured plume salinity and its time deriva-tives are not smooth, which may indicate a degree of non-tidal variation in the results. Toimprove the estimation of the tidal variability in the plume salinity, more advanced timeseries analysis tools should be applied. For example, the Lomb–Scargle periodogram can beused for this analysis, and the magnitude of diurnal/semi-diurnal influences in the plumesalinity for different river flowrate conditions can be quantitatively characterized.Other than the level of river discharge, wind direction and speed may also influencethe tide-plume correlation. Theoretically, stronger winds tend to trigger stronger surfacemixing, and wind-driven currents may actively change the plume shape and positions, bothof which may directly or indirectly increase the short-term variability in the plume size.At last, in this study, we recognize that the mixing and entrainment of the plumeprimarily occurs in the near-field plume and the estuarine salt wedge, however, it is stillnot known which portion is more important. To quantitatively analyze the percentage ofsalt-wedge entrainment to the whole plume entrainment, a long-term high-resolution timeseries of the river salinity is crucial. 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Tidal influence on the Fraser River plume
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