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Oxygen budgets and productivity estimates in the Strait of Georgia from a continuous ferry-based monitoring… Wang, Chuning 2015

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Oxygen Budgets and ProductivityEstimates in the Strait of Georgiafrom a Continuous Ferry-basedMonitoring SystembyChuning WangB.Sc., Ocean University of China, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Oceanography)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)March 2015c© Chuning Wang 2015AbstractThe oxygen budget in the top 50 m of lower Strait of Georgia, British Columbia isinvestigated using high resolution measurements of dissolved oxygen concentration andother oceanographic and meteorological properties from an instrumented ferry. Anbudget equation is established to describe the oxygen balance in the surface Strait ofGeorgia. The budget equation consists of 4 parts, which includes (1) the storage rateterm, which is calculated with the ferry oxygen measurements using a 2-point differen-tial scheme; (2) advective and vertical transport, which is estimated using a box model;(3) air-sea gas transfer, which is estimated using a bulk parametrization of air-sea gasflux; and (4) net community productivity, which is estimated by taking the residualof the budget equation. To further investigate the productivity level in the Strait ofGeorgia, daily community respiration rate is estimated by extracting the diurnal varia-tion signal of oxygen, and gross productivity is estimated by combining net communityproductivity with the community respiration rate. Results suggest that gross produc-tivity in the lower Strait of Georgia varies from 1.4 to 11.8 gC·m−2day−1and averagesat 4.4 gC·m−2day−1, slightly higher than historical measurements.iiPrefaceThis thesis is authored by me, Chuning Wang, and describes original work carried outby me under the supervision of Dr. Richard Pawlowicz. The ferry dataset was collectedas part of the Victoria Experimental Network Under the Sea (VENUS) project, and Iwas directly involved in the process of the calibration of sensors and quality checking ofthe dataset. The analysis and writing of this thesis is carried out by me, but RichardPawlowicz contributed substantially by suggesting specialized analysis techniques, byhelping to interpret the results and by carefully editing the manuscript.Results are unpublished, but are undergoing preparation for submission. Fig 3.7and 4.4 are partly reproduced with permission from Riche (2011).iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 The Strait of Georgia . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Production and biological studies in the southern Strait of Georgia . . 21.3 FerryBox and VENUS project . . . . . . . . . . . . . . . . . . . . . . . 51.4 Research objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Method & Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.1 Gross primary productivity, net primary productivity and netcommunity productivity . . . . . . . . . . . . . . . . . . . . . . 92.1.2 Oxygen budgets in the SoG . . . . . . . . . . . . . . . . . . . . 102.1.3 Diurnal variation in productivity . . . . . . . . . . . . . . . . . . 112.1.4 Depth integrated O2 concentration . . . . . . . . . . . . . . . . 122.1.5 Plume water vs SoG water . . . . . . . . . . . . . . . . . . . . . 172.1.6 Units of productivity . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Observations and data . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.1 Ferry sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.2 CTD sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.3 Wind record & other measurements . . . . . . . . . . . . . . . . 212.2.4 Calibration for O2 sensor . . . . . . . . . . . . . . . . . . . . . . 222.3 O2 concentration in SoG . . . . . . . . . . . . . . . . . . . . . . . . . . 26ivTable of Contents3 Box Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1 Model formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.1 Equation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.2 Parameters & initial condition estimation . . . . . . . . . . . . . 353.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.1 Salinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.2 Volume flux & O2 transport . . . . . . . . . . . . . . . . . . . . 403.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.3.1 Sensitivity to separation depth . . . . . . . . . . . . . . . . . . . 453.3.2 Error estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 Air-sea Gas Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.1 Bulk parametrization of air-sea gas transfer . . . . . . . . . . . . . . . . 514.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.3.1 Bulk parametrization vs other parametrizations . . . . . . . . . 594.3.2 Contribution of bubble plume to gas flux . . . . . . . . . . . . . 634.3.3 High frequency & spatial variation of gas flux . . . . . . . . . . 665 Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.1 Net community productivity . . . . . . . . . . . . . . . . . . . . . . . . 735.2 Respiration rate & gross productivity . . . . . . . . . . . . . . . . . . . 755.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.3.1 Length of day & respiration rate . . . . . . . . . . . . . . . . . . 835.3.2 Seasonal cycle in productivity . . . . . . . . . . . . . . . . . . . 835.3.3 River plume & productivity . . . . . . . . . . . . . . . . . . . . 845.3.4 What triggers the spring bloom? . . . . . . . . . . . . . . . . . . 855.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.5 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.5.1 Ferry-based observations . . . . . . . . . . . . . . . . . . . . . . 915.5.2 14C productivity measurements . . . . . . . . . . . . . . . . . . 915.5.3 Diurnal variation of R . . . . . . . . . . . . . . . . . . . . . . . . 925.5.4 Application of the budget method in other locations . . . . . . . 93Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95AppendicesA Unify Seawater Temperature Measurements from 3 Sensors . . . . 104B Estimate F˜ & S˜p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113C Bubble Enhancement & Stratification . . . . . . . . . . . . . . . . . . . 116vTable of ContentsD Determine the Boundary of Fraser River Plume . . . . . . . . . . . . 120viList of Tables2.1 Climatology of the conversion factor γ. ∗ indicates abnormal extremevalues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Details of STRATOGEM CTD stations. . . . . . . . . . . . . . . . . . . 222.3 Details of JEMS CTD stations. . . . . . . . . . . . . . . . . . . . . . . . 223.1 Details of surface areas and volumes for each basin. . . . . . . . . . . . . 304.1 Different parametrization of transfer velocity given in cm·hr−1 as a func-tion of 10 m wind speed U10 in m·s−1 and Schmidt Number. . . . . . . . 515.1 Comparison of productivity calculated in our study with previous studies(Parsons et al., 1970; Clifford et al., 1989a,b, 1991a,b, 1992; Harrisonet al., 1991; Yin et al., 1997; Riche, 2011). . . . . . . . . . . . . . . . . . 82viiList of Figures1.1 Geography of the Strait of Georgia . . . . . . . . . . . . . . . . . . . . . 31.2 Absolute O2 concentration and O2 saturation level from the FerryBox . 71.3 Normalized and smoothed O2 plotted against daytime . . . . . . . . . . 82.1 An example of the least square fit for the calculation of O2 diurnal variation 132.2 O2 profiles in the top 70 m of SoG . . . . . . . . . . . . . . . . . . . . . 162.3 Raw data of turbidity and O2 from the FerryBox . . . . . . . . . . . . . 202.4 Comparison of O2 measurements from optode 1415, 418, and WinklerTitration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.5 Annual cycle of O2 saturation from 2012 to 2014. . . . . . . . . . . . . . 252.6 Hovmo¨ller diagram of O2 anomaly and track averaged O2 in and out ofFraser River plume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1 Box model schematic diagram . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Total river discharge into the SoG from 1995 to 2014 . . . . . . . . . . . 323.3 Input and output of the box model test run . . . . . . . . . . . . . . . . 383.4 River discharge, Pacific Ocean salinity, and modeled salinities from 1995to 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.5 Comparison of modeled salinities and in-situ measurements . . . . . . . 413.6 Modeled volume fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.7 Advective volume flux plotted against river discharge . . . . . . . . . . . 443.8 O2 concentration, volume fluxes and O2 fluxes in the SoG from May2012 to Oct 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.9 Mean salinity in each box vs. separation depth . . . . . . . . . . . . . . 484.1 Comparison of different air-sea gas flux parametrizations as a functionof wind speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.2 T-S diagram from the ferry measurements of 3 separate days . . . . . . 574.3 Time series of gas flux, effective air-sea concentration difference and windspeed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.4 Comparison of gas flux from Riche (2011) and this study . . . . . . . . . 604.5 Comparison of the range of different air-sea gas flux parametrizationswith respect to wind speed and Schmidt Number. . . . . . . . . . . . . . 624.6 Comparison of different parametrizations to calculate air-sea gas flux inSoG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64viiiList of Figures4.7 Time series of gas flux in and out-of Fraser River plume and the rangeof uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.8 Gas flux and other few characteristics plotted against time and longitudefrom Apr 1 to Apr 8, 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . 694.9 Seawater temperature, salinity and O2 from Apr 1 to Apr 8, 2014 . . . . 714.10 Seawater temperature, salinity and O2 from Jan 1 to Jan 8, 2014 . . . . 725.1 Time series of O2 budgets in the SoG . . . . . . . . . . . . . . . . . . . . 745.2 Time series of net community productivity in and out of river plume . . 765.3 Result of least square fit from Section 2.1.3 . . . . . . . . . . . . . . . . 775.4 Time series of respiration rate and productivity . . . . . . . . . . . . . . 785.5 Time series of gross productivity and range of uncertainties . . . . . . . 805.6 Comparison of productivity estimates from this study and previous studies 815.7 Hovmo¨ller diagram of turbidity plotted against time and along trackdistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.8 Productivity estimates and other characteristics in the SoG from Febru-ary 1st to May 1st, 2013 . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.9 Productivity estimates and other characteristics in the SoG from March1st to May 1st, 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89A.1 Time series of seawater temperature measurements from 3 different in-struments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105A.2 Seawater temperature measurements from 3 different instruments on Feb28, 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106A.3 Seawater temperature measurements from 3 different instruments onMar 03, 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107A.4 Seawater temperature measurements from 3 different instruments on Feb27, 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108A.5 Seawater temperature measurements from 3 different instruments on Sep1, 2013 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109A.6 Comparison of SBE temperature and TURO temperature . . . . . . . . 111A.7 Comparison of SBE temperature and Optode temperature . . . . . . . . 112B.1 Comparison of total river discharge between measurements from (Mor-rison et al., 2012) and regression results in this study . . . . . . . . . . . 114C.1 Bubble enhancement parameter vs. pycnocline depth . . . . . . . . . . . 119D.1 FerryBox salinity measurements from a single track . . . . . . . . . . . . 121D.2 Hovmo¨ller diagram of salinity plotted against time and along track distance122D.3 Time series of salinity in and out of river plume . . . . . . . . . . . . . . 124ixAcknowledgementsFirst I must thank my supervisor, Prof. Richard Pawlowicz, for helping me patientlyboth academically and personally during the period of my study in UBC. The work inthis thesis could not be accomplished without his guidance. Next, I would like to thankmy committee members, Philippe Tortell and Roger Francois, for their good feedbacksand suggestions on my work. Thank you to Susan Allen for examining my thesis, as wellas all the useful suggestions during lab seminars. The FerryBox maintenance group,Akash Sastri, Paul Macoun, Denis Hedji, and Chris Sundstrom also deserve credit fortheir continuous hard work on the ferry sampling system.Thank you to everyone in the Waterhole, as well as my roommate LuDashi, I amgrateful to all of you.Last but not least, special thank-you to my parents and Jing, for their constantsupport across the Pacific Ocean.xChapter 1IntroductionThe purpose of this thesis is to quantify the dissolved oxygen (O2) budgets in the Straitof Georgia, British Columbia, Canada, and use them to estimate primary productiv-ity. To accomplish this goal, the processes that change the O2 budgets in the Straitof Georgia need to be summarized. In any aquatic system, O2 mainly varies with re-spect to the following physical and biological processes: (A) advective and convectivetransports, including river inflow, horizontal advection and deep mixing; (B) gas fluxthrough the air-water interface; (C) biological processes, including autotrophic produc-tion and respiration; and (D) all other processes that could change O2 in seawater, forexample, photochemical oxidation of organic matter, and non-aerobic consumption ofoxygen, which are often assumed to be negligible.By carefully measuring O2 and estimating (A) and (B) in the system, the variationof O2 associated with biological production and respiration can be determined by cal-culating the residual of O2 budgets. This method has been proved effective and widelyused in limnology studies (Hanson et al., 2003; Staehr et al., 2010). In these aquaticsystems, the advective transport can be either neglected or easily estimated, thus theapplication of budget method is relatively easy.In oceanic systems, especially estuaries, the variation of O2 is heavily influencedby the complex dynamics of the system and surrounding environment. As a result,the application of budget method requires a more solid understanding of the systemitself. To introduce the physical and biological environment of the Strait of Georgia,this chapter is organized as follows: Section 1.1 introduces the physical oceanographyof the Strait of Georgia; Section 1.2 describes previous studies on productivity and bi-ological oceanography in the Strait of Georgia; Section 1.3 introduces the observationplatform and the VENUS project.1.1 The Strait of GeorgiaThe Strait of Georgia (hereafter SoG) is a mid-latitude semi-enclosed coastal basinsituated between mainland British Columbia and Vancouver Island (Fig 1.1). It is 220km long, 28 km wide, and oriented in a northwest-southeast direction. The averageand maximum depths are 155 m and 420 m, respectively, and 5% of the total area hasdepth in excess of 360 m (Thomson, 1981). The total volume of the SoG is 1.1× 101211.2. Production and biological studies in the southern Strait of Georgiam3 (Riche, 2011).The Fraser River is the largest point source of fresh water for the SoG, making up50%-80% of the total discharge of fresh water (Pawlowicz et al., 2007; Halverson andPawlowicz, 2008; Halverson, 2009; Halverson and Pawlowicz, 2013). The large quan-tity of freshwater input from the Fraser discharge forms the Fraser River plume. Theplume spreads through SoG surface and carries freshwater into the SoG farther fromthe Fraser River mouth. The river plume is easily visible on satellite imagery during thesummer Freshet, and can be easily distinguished by the lower salinity associated withthe fresh water input (Halverson and Pawlowicz, 2008). Halverson (2009) investigatedthe dynamic of the river plume and its relationship with the Fraser River dischargeusing salinity measurements from an instrumented ferry, and concluded that the plumesalinity decreases quasi-linearly with river discharge. The Fraser River plume changesnot only the salinity, but also the current structure in the SoG. Li et al. (1999, 2000)investigated the estuarine circulation in the SoG using a box model, and concludedthat the volume flux of the estuarine circulation is on the order of 1 × 103 to 1 × 104m3s−1, and varies with respect to the Fraser River discharge.SoG is mainly connected to the Pacific Ocean through the Juan de Fuca Strait(Hereafter JdFS) located south of SoG, between Vancouver Island and WashingtonState. SoG exchanges water with Juan de Fuca Strait through a series of narrow chan-nels, the largest of which is the Haro Strait (hereafter HS). HS is characterized bystrong vertical mixing, where the seawater is relatively uniform throughout the watercolumn, thus it becomes an important link of the estuarine circulation of the system(Li et al., 1999, 2000; Riche, 2011). Li et al. (1999) suggests that the volume flux ofestuarine circulation through JdFS is also in the order of 1×103 to 1×104, but slightlylower than that of the SoG basin. The northern SoG is also connected to the PacificOcean through several narrow channels, but the volume transport through these chan-nels only accounts for 7% of the total transport (Thomson, 1994), which is negligiblein most cases (Li et al., 1999; Riche, 2011).1.2 Production and biological studies in the southernStrait of GeorgiaProduction studies in the southern Strait of Georgia can be traced back to the 1960s.In 1967, seven cruises were carried out from February to May to measure productivityin two stations in the SoG. Primary productivity is determined by measuring the netincrease in cellular material using a Coulter Counter. The results are summarized inParsons et al. (1969, 1970), which suggests a primary productivity within the FraserRiver plume between 0.124 to 2.132 gC·m−2day−1, and a total production of 50 gCm−2during the research period. It also suggests that because of the higher light intensityin the Fraser River plume, the photosynthetic production inside Fraser River plume is21.2. Production and biological studies in the southern Strait of Georgia 126oW  125oW  124oW  123oW  122oW   48oN  30’   49oN  30’   50oN  30’   51oN Strait     ofGeorgiaHaro StraitJuan de Fuca StraitVancouver IslandVancouverFraserRiverSJF001SJF002SJF003  Depth [m]5004003002001000 124oW  48’  36’  24’  12’  123oW  54’   49oN   6’  12’  18’ TsawwassenVancouverDukePointS1S2−1S2−2S2−3S3S4−1S4−2S4−3S5Figure 1.1: A map of Strait of Georgia and the surrounding system. The black lineis the route of BC Ferry M.V. Queen of Alberni. The triangles and squares are CTDstations of the STRATOGEM project and JEMS project. The red line in the upperbox is the track from Tsawwassen to Duke Point, and the blue line is the track of thereturn trip.31.2. Production and biological studies in the southern Strait of Georgiahigher.From 1987 to 1991, a series of cruises were conducted along the month of FraserRiver to measure productivity in the SoG. Productivity is determined by measuring14C uptake rate using bottle incubation, and the results are summarized in a series ofreports and studies (Clifford et al., 1989a,b, 1991a,b, 1992; Harrison et al., 1991; Yinet al., 1996, 1997). The productivity measurements in these studies are higher thanthose of Parsons et al. (1969, 1970), and vary between 0 to 5 gC·m−2day−1. The mea-surements from 1987 to 1991 also suggest that productivity is higher outside the FraserRiver plume (Harrison et al., 1991), which is in contrast with the results of Parsonset al. (1969, 1970). Yin et al. (1996) analyzed these measurements and suggests thatthe spring bloom first initiates inside the Fraser River plume and then spreads to theSoG.From 2003 to 2006, a WetLabs ECO Triplet was instrumented onto one of the BCFerries to get high resolution chlorophyll-a fluorescence measurements across the SoG.Although chlorophyll-a biomass is not equivalent to productivity, it is well correlatedwith phytoplankton production and is a good indicator of instantaneous productiv-ity. Using these measurements the relationship between Fraser River plume and thephytoplankton biomass in the SoG is analyzed by Halverson and Pawlowicz (2013).It suggests that although instantaneous near-surface chlorophyll-a is sensitive to thepresence of Fraser River plume, the river plume has little impact on the long-termaveraged biomass.In addition to these direct observations, the dynamic of production and planktonbiomass in the SoG has also been studied with numerical approaches. Li et al. (2000)used a coupled biological-physical box model to investigate the seasonal and interan-nual variability of plankton community in the SoG-JdFS system. Using a specific setof biological parameters, a large spring bloom in the SoG and no spring bloom in JdFSis simulated, which is in agreement with observations. Li et al. (2000) also suggeststhat climate variability, such as Fraser River runoff and shelf salinity, also influencesplankton community through changes in the biological rate parameters. In additionto Li et al. (2000), Collins et al. (2009) used a coupled biophysical model to study therelationship between wind and the timing of spring bloom in the SoG. It is concludedthat strong wind tends to delay the spring bloom by increasing the mixing-layer depth,which is also supported by Yin et al. (1997). In addition to wind speed, Collins et al.(2009) also suggests that the insolation has a secondary effect on the timing of springbloom, while freshwater input is not a significant factor.In addition to the productivity studies stated above, it has also been demonstratedthat some gases in seawater, such as O2, CO2 and dimethylsulfide (DMS), are alsoinfluenced by the process of photosynthesis and respiration and thus can reflect theproductivity in aquatic systems. These studies include the limnology studies as men-41.3. FerryBox and VENUS projecttioned earlier in this chapter (Hanson et al., 2003; Staehr et al., 2010), and also someoceanic studies using combined gas measurements of O2, Ar, CO2 and DMS (Nemceket al., 2008; Tortell et al., 2011, 2012a,b). The work of Nemcek et al. (2008); Tortellet al. (2011, 2012a,b) focus not on the absolute value, but the relative spatial and tem-poral variation of productivity. Since Ar is an inert gas, it only varies with respect tophysical processes in the ocean. By normalizing O2 with the corresponding Ar mea-surements, the contribution of physical processes to the variation of O2 is minimized.Tortell et al. (2012b) conducted these measurements along the BC coast in 2007 and2010, and observed higher ∆O2/Ar ratio and lower partial pressure of CO2 in thesouthern SoG, which suggests that the SoG is a productive area compared to the ad-jacent regions. This work provides an general understanding of the productivity alongthe British Columbia coast, however, it has 2 major limitations: firstly, the ∆O2/Arratio cannot provide any information about absolute productivity in the SoG; secondly,due to the limitation of ship time, this survey could not provide a long-term estimateof productivity.1.3 FerryBox and VENUS projectThe primary dataset used in this work was acquired from the ’FerryBox’, a collection ofsensors sampling seawater aboard the M.V. Queen of Alberni, one of the passenger fer-ries of the BC Ferry Inc. The ferry was instrumented as part of the Victoria Experimen-tal Network Under the Sea (VENUS) project, an ocean observatory operated by OceanNetwork Canada, located in the Salish Sea, the coastal water of British Columbia,Canada. It travels between Tsawwassen and Duke Point (Fig 1.1), making 4 roundtrips during workdays and less during the weekend, departing Tsawwassen at 0515 lo-cal time, and last departing Duke Point at 2245. The track essentially runs along-strait,oriented to the northwest/southeast. A complete transect covers over 60 km and takesmore than two hours. The FerryBox was Installed onto the ferry in May 2012, andis still in operation as this thesis is completed. The ferry goes into annual refits frommiddle October to middle November every year, introducing month-long data gaps intothe dataset. Occasional instrumentation problems caused additional gaps in the datarecord, the longest being for 4 months from May to September 2013. Details on theFerryBox dataset are presented in Section 2.2.1. The FerryBox on Queen of Alberniis only the first stage of the ferry observatory in SoG; in October 2014, as the nextstage of the ferry observation system, a second FerryBox was installed onto anotherpassenger ferry, the Spirit of Vancouver Island, which travels between Tsawwassen andSwartz Bay, and a third one on the Horseshoe Bay to Nanaimo route will be installedin 2015.FerryBox has been widely used and is becoming a common sampling technique inoceanographic studies (Volent et al., 2011; Aiken et al., 2011; Ainsworth, 2008; Franket al., 2010; Kelly-Gerreyn et al., 2006; Grayek et al., 2011; Hydes et al., 2009). It51.4. Research objectivehas several advantages over other sampling techniques, for example, it is cost effec-tive because of the reduced ship time needed for in-situ sampling. In addition, sincemost commercial ferries travel on a daily basis, the FerryBox can provide long-termmeasurements with very high spatial and temporal resolution. On the other hand, theFerryBox also has its limitations: it only samples at a fixed depth on a fixed route,as a result the sampling flexibility is limited; besides, the FerryBox requires frequentmaintenance and calibration to deal with bio-fouling and other issues that might affectthe accuracy of the sensors and the quality of data.In addition to the FerryBox, The VENUS project includes a series of other observa-tory platforms in SoG as well. These platforms include (1) an undersea cabled networkwhich links 3 underwater notes for the deployment of oceanic sensors; (2) a shore-basedHF radar with 2 antennas which measures the surface current in the southern SoG; and(3) ocean gliders that travels across the SoG, as the next phase of the VENUS project.Although data from these platforms is not used in this study, it provides an opportu-nity to cross-check with the FerryBox dataset and can be integrated into future studies.1.4 Research objectiveThe measurements from the FerryBox on board M.V. Queen of Alberni provide anopportunity to investigate the O2-productivity relationship with high spatial and tem-poral resolution and coverage. Fig 1.2 and 1.3 show the 24 months of O2 measurementsfrom the ferry instrument cluster. The two Figures will be explained in detail in Chap-ter 2, for now just consider it as the surface O2 in the SoG. Fig 1.2 shows that in Marchand April surface O2 level is higher and mostly supersaturated, corresponding to higherproductivity during the yearly spring bloom; from December to next February O2 islower and mostly a little less than 100% saturated, corresponding to lower productivityduring winter time. Fig 1.3 shows the variation of O2 within a 24-hour period, andit is observed that O2 is lowest around sunrise and highest around sunset, and variesby around 10% in a diurnal cycle, corresponding to the diurnal cycle of communityphotosynthesis and respiration in surface SoG. These patterns all suggests that thereis a solid relationship between O2 and productivity in the SoG, and the objective ofthis study is to investigate this relationship with the following steps:1. Evaluate and correct measurements from the FerryBox;2. Establish a set of O2 budget equations, and estimate each term in the equationset;3. Use the results from step 2 to estimate productivity in the SoG.61.4. Research objectiveJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 20134710132012 a)4710132013 b)O 2 Concentration [ml/l]4710132014 c)60100140180 2012 d)60100140180 2013 e)O 2 Saturation [%]Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 201560100140180 2014 f)Figure 1.2: Absolute O2 concentration (a, b, c) and O2 saturation level (d, e, f) mea-sured by the FerryBox from May 2012 to Oct 2014. Grey line is the original data, whilethick black line is bin averaged data with a window of 1 day. Data is broken into yearby year segments to highlight the seasonal cycle.71.4. Research objectivePacific Standard Time  Jul Sep Nov 2013 Mar May Jul Sep Nov 14 Mar May Jul Sep3:006:009:0012:0015:0018:0021:00Oˆ2 s−5%−4%−3%−2%−1%01%2%3%4%5%Figure 1.3: Normalized and smoothed O2 (Oˆ2s) plotted against daytime from May 2012to Oct 2014. Black lines are the time of sunrise and sunset. No data is taken whenvessel is in port. Note shifts in schedule related to daylight savings time.8Chapter 2Method & ObservationKnowledge of autotrophic production and respiration are critical for the understandingof carbon cycling in marine systems. Traditional incubation techniques for measuringproductivity and respiration are expensive and time consuming, and are associated witha series of technical issues that lead to increased uncertainties (Williams and Lefevre,2008). Satellite-based methods are being used in the open ocean (Carr et al., 2006),but their application is limited in coastal regions due to the confounding effects ofnon-autotrophic particulate matter, and are also dependent on the local cloud cover-age. Therefore, more advanced methods are required to provide long-term, but alsoaccurate estimates of productivity.Chlorophyll-a fluorescence measurements have also been proved useful for estimat-ing productivity levels (Halverson and Pawlowicz, 2013), but they only identify au-totrophic biomass in seawater, thus the production and respiration of heterotrophicbiomass is neglected. Besides, although autotrophic biomass is highly correlated withthe instantaneous productivity, the interpretation from biomass to productivity stillproduces uncertainties; furthermore, the quality of fluorescence measurement is heav-ily influenced by several confounding factors, such as non-photochemical quenching(Mu¨ller et al., 2001; Cullen and Lewis, 1995), which introduces extra uncertainties intothe calculation. To avoid the problems stated above, we hereby investigate the oxygenbudget method for the estimate of productivity in SoG.2.1 Methods2.1.1 Gross primary productivity, net primary productivity and netcommunity productivityIn order to carry out the analysis, we first describe the relationship between gross pri-mary productivity (PG), net primary productivity (PN ), net community productivity(PNC), and O2 in seawater.Primary productivity (P ) is the rate of incorporation of new organic matter intothe living tissue by phytoplanktons (Miller, 2004). Gross productivity (PG) is the rateof total photosynthetic production of organic compounds in an ecosystem, and netproductivity (PN ) is gross productivity minuses the autotrophic respiration rate (Ra).Net community productivity (PNC) is defined as the difference between PG and the92.1. Methodscommunity respiration rate (R), which is the sum of autotrophic (Ra) and heterotrophic(Rh) respiration rates. To sum up, the relationship of the productivities and respirationrates are described in the following equation set:R = Ra +RhPN = PG −RaPNC = PG −R(2.1)Productivity is linked to oxygen through the process of photosynthesis and res-piration. The organic matter in a phytoplankton (and other organisms in seawater)assemblage approximately follows the Redfield Ratio (Redfield, 1960) in atoms (ormoles):C : N : P = 108 : 16 : 1 (2.2)In addition to carbon, nitrogen and phosphorus, oxygen and hydrogen are alsoimportant components of organic materials. To fully oxidize the organic materials,the organic world is linked to the inorganic environment through the following balanceequation (Redfield, 1960):(CH2O)106(NH3)16(H3PO4) + 138 O2 = 106 CO2 + 16 HNO3 + H3PO4 + 122 H2O(2.3)Eq 2.3 shows that there is a quantitative relationship between the CO2 that is fixedand the O2 that is generated through this process. For every 106 moles of CO2 fixedinto organisms, 138 moles of O2 are produced. Note that Eq 2.3 is a global averagedrelationship and could vary slightly in different locations; in addition, the metabolic ra-tios (photosynthetic quotient and respiratory quotient) in an ecosystem can be slightlydifferent from each other (Oviatt et al., 1986), which also introduces uncertainties intothe carbon/O2 relationship. However, since the range of variation associated with theseuncertainties is small, it is usually neglected and a constant carbon/O2 ratio is usedin this work. Using this relationship, the production/consumption of oxygen can bediscussed in terms of an equivalent amount of carbon, which is illustrated in detail inSection 2.1.6.2.1.2 Oxygen budgets in the SoGThe oxygen budget in the SoG is controlled by both physical and biological processes.The budget terms of O2 in the top 50 m of the SoG can be summarized with 1 equation∂∂t∫ 50m0O2(z)dz = O2adv +O2gasf + PNC (2.4)where the term on the left side is the storage rate term of depth integrated O2.Terms on the right side are advective and vertical transport in the water column, air-sea102.1. Methodsgas flux, and net community productivity, respectively. We choose 50 m as the bottomthe “box” of for budget estimates, as the bottom of the “box” has to be deeper than thatof the euphotic zone. In the budget equation, advection mainly refers to inflow fromthe rivers and outflow through Haro Strait; vertical transport in SoG mainly refersto the upwelling from deep SoG as part of the estuarine circulation. The advectionand upwelling term and air-sea gas flux term are calculated separately in Chapter 3and 4; Depth integrated O2 time series is acquired through a combination of ferry-based O2 measurements from the VENUS system and historical CTD O2 profiles fromthe STRATOGEM (Strait of Georgia Ecosystem Monitoring) project (Section 2.2), asdiscussed in detail in Section 2.1.4. Then PNC can be estimated by manipulating theterms in Eq 2.4:PNC = O2stg −O2adv −O2gasf (2.5)where O2stg = ∂∂t∫ 50m0 O2(z)dz is the abbreviation of storage term.2.1.3 Diurnal variation in productivityIn the SoG, productivity shows strong diurnal fluctuation correlated with insolation,which is reflected in the diurnal cycle of O2 in SoG. During daytime, since insolationis positive, productivity occurs and O2 increaes; During nighttime, since insolation islimited, O2 decreases as PG is close to zero so there is only a net consumption of O2.The alternating increases and decreases of O2 within a day is similar to a sinusoidalsignal, which reaches minimum around sunrise and maximum before sunset (Fig 1.3).Twice the amplitude of the sinusoidal signal is approximately the integrated commu-nity respiration over the night, and by assuming a constant respiration rate within a24-hour period, the respiration rate is then estimated by the total respiration over nightdivided by the duration of the night.The amplitude of the sinusoidal function is determined here using a least square fit.The raw oxygen data contains too much ”noise” and signals of other frequencies,thusthe raw data is pre-processed before the actual data fitting with the following steps: (1)To remove variations with periods longer than 1 day, raw O2 time series is normalizedby dividing by the running daily averageOˆ2(t) =O2(t)O2(t− 12 hr : t+ 12 hr)(2.6)(2) To remove high frequency fluctuations and noise, Oˆ2 is smoothed with a runningaverage of 4 hours to obtain Oˆ2s.Oˆ2s is then broken into 24-hr segments, and each segment should be a sinusoidal-likesignal with a period of 24 hours112.1. MethodsOˆ2s = A0 + a1 sin 2piω1t+ b1 cos 2piω1t+ a2 sin 2piω2t+ b2 cos 2piω2t+ = A0 +A1 sin (2piω1t+ θ1) +A2 sin (2piω2t+ θ2) + (2.7)where ω1 = 124 hr−1 is the diurnal frequency; A0 is the average of normalized O2 withina 24 hr period, which should be close to unity; A1 =√a21 + b21 and θ1 = arctan b1/a1are the amplitude and phase of the sinusoidal signal;  contains oscillations of otherfrequencies and measurement noise. A second frequency ω2 = 419 hr−1 is also taken intoconsideration since the data contains a 19/4 hour fluctuation associated with the spatialmovement of the ferry: according to the schedule, the ferry makes 4 round trips withinapproximately 19 hours. The corresponding amplitude and phase are A2 =√a22 + b22and θ2 = arctan b2/a2. Note that the O2 data is normalized in the first step of pre-processing. To convert the normalized amplitude A1 back to the actual amplitude ofdiurnal variation A, A needs to be multiplied by the average O2 level of the correspond-ing day. The absolute amplitude of diurnal variation is then A = A1× O¯2, where O¯2 isthe daily averaged O2.An example of the method presented above is plotted in Fig 2.1. The least squarefit (thin line) is in good agreement with Oˆ2s (dash-dotted line), which proves the fea-sibility of the least square fit method. The diurnal signal is plotted as a thick line,and the large amplitude of diurnal variation also suggests that there is a measurableday-night variation in photosynthesis/respiration, which can be used for productivityestimates as follows.Since there is almost no O2 production during the night, the daily averaged respi-ration rate can be estimated as the loss rate of O2 from sunset to next sunrise, whichis the the range of diurnal variation 2A divided by the duration of night tnR =2Atn(2.8)Here I take tn = 0.5 day to stay consistent with the sinusoidal assumption. Thenthe gross productivity for a particular day can be estimated byPG = PNC +R. (2.9)2.1.4 Depth integrated O2 concentrationA weakness of the ferry is that it only samples at a single depth, while in most cases theintegrated water column O2 is more useful in the analysis of O2 budgets in the upperSoG. The water intake of the system is located 2 m below the waterline, and since122.1. Methods14/04/04 06:00 12:00 18:00 04/05 06:000.90.920.940.960.9811.021.041.061.081.12×A1tn  Oˆ2sLeast Square FitA0 + A1 sin(2piω1t+ θ1)Figure 2.1: An example of the least square fit for the calculation of O2 diurnal variation.The dash-dotted line is the the normalized and smoothed O2 (Oˆ2s), and the thin blackline is the least square fit. The thick line is the diurnal signal, which varies within arange of 2×A1.132.1. Methodsthe body of the ferry itself could mix near surface water and/or push surface waterdownward a little bit, the actual depth that FerryBox samples may be a little shallowerthan 2 m. Analysis by Halverson (2009) for a different ferry design shows that a waterintake depth of 3.8 m approximately corresponds to an actual intake depth of 1.3 to 2m. In this study, because of a lack of synchronous hydrographic measurements alongthe ferry track, it is difficult to verify the actual intake depth. Since the intake depth ofour system is shallower than that of Halverson (2009), the mixing caused by the ferrybody should not be as important; in addition, the variation in payload may changethe intake depth and thus makes it more difficult to do the correction. Based on thesereasons, no correction with respect to intake depth is made, and an effective samplingdepth of 2 m is assumed.The O2 measurements at 2 m are then converted into depth integrated O2 bycomparing with historical O2 profiles from the STRATOGEM project. I assume alinear relationship between 2 m O2 and depth integrated O2∫ D0(O2(z)− β)dz = γD(O2(2m)− β) (2.10)where β is a base O2 level, and γD is the proportion factor. The base O2 level β is theportion of O2 that does not vary with time, or only varies with a temporal scale longerthan a few months. It is usually the O2 concentration at a certain depth where O2concentration is relatively stable both temporally and vertically. After β is determined,γD can be acquired by taking the ratio of depth integrated O2 and 2 m O2γD =∫D0 (O2(z)− β)dzO2(2m)− β(2.11)The calculation of γD can be carried out with two different approaches. Firstly,assuming O2 and biological production both decay exponentially with scale aO2 ≈ β + c1e− za (2.12)The scale a and proportional constant C1 can be acquired by least square fittingwith the O2 profiles. Then γD is calculated by substituting Eq 2.12 into Eq 2.11γD =∫D0 c1e− zadzc1e−2a(2.13)This method is accurate when the assumption of exponentially decaying profilesis met, and can still provide reasonable results even when 2 m O2 measurements aremissing or abnormal. The second approach to calculate depth integration is to discretizethe integration, which givesγD =D∑z=1(O2(z)− β)δzO2(2m)− β(2.14)142.1. MethodsThis method gives a better result when the profile is not strictly exponentially de-caying, but will be biased if the 2 m measurements are missing or abnormal.During the STRATOGEM project, 48 surveys with CTD profiles were carried outin total. From each survey we choose O2 profiles from 3 stations, S2−3, S3, and S4−1(Fig 1.1), and average them to represent the O2 profile of that specific survey. Thenβ can be determined and γD can be calculated with Eq 2.13 or 2.14 accordingly. Asimple way to calculate γD is to assume a constant β and γD, average all 48×3 profilesand apply the equations; however, since the dynamics of O2 near the ocean surface iscomplicated and the vertical distribution of O2 may vary from time to time, a constantconversion factor may not be able to precisely describe the relationship. One reasonableassumption is that β and γD also varies seasonally like other important characteristicsin the SoG. To take the seasonal variation into account, the O2 profiles are dividedby month, and averaged to generate a monthly climatology. Using this climatology, aclimatology for γD is generated accordingly and used in further analysis.The 48 CTD O2 profiles from the surface to a depth of 70 m are plotted in Fig 2.2.Note that O2 concentration drops quickly near surface and reaches a relatively sta-ble state at around 50 m, thus I choose 50 m O2 concentration as the base O2 level,β = O2(50m). To test the assumption of exponentially decaying O2, the monthly av-eraged profiles and the corresponding exponential fits are plotted as black solid anddashed line, respectively. Note that most measurements are made in March and April,for other months there are only a few profiles available. The exponential decayingassumption works well for some months (May to July, October, December); however,for other months, the fitted function is not in good agreement with the profiles. Thisis especially evident in January, which means either the measurements in January arebiased or Eq 2.13 would not be able to give a very accurate estimate γD for this month.To test both Eq 2.13 and 2.14, the conversion factor γD is calculated using the twoequations and the results are listed in Table 2.1. The integration depth D is set tobe 50 m, as 50 m is the separation depth of the top layer and bottom layer in SoG(Section 3.3.1). Eq 2.13 gives a relatively stable γ50, only varying from 15.01 to 17.16 mand lowest in March. Compared to Eq 2.13, Eq 2.14 gives a wider range of γ50. Itis highest in January (24.05 m) and lowest in September (10.07 m). However, the ex-treme high and low values look suspicious. In winter the surface SoG is generally notproductive, thus γ50 should not vary a lot from November to February. Thus I suspectthat the higher value in January is possibly an overestimate due to the limited numberof profiles. This is also true for August and September, when γ50 is significantly lowerand is possibly underestimated. Eq 2.14 also gives lower γ50 value in March, however,since March is usually the time of spring bloom when the surface productivity (andO2) is significantly higher, a lower γ50 value in March is expected. Overall the rangeof variation given by Eq 2.14 is too large to be trusted. To simplify the calculation,the γ50 climatology calculated with Eq 2.13 is averaged to get a single value (16.29 m)152.1. Methods2 4 6 8 10010203040506070JanO2 [ml/l]Depth [m]2 4 6 8 10Feb2 4 6 8 10Mar010203040506070Apr May Jun010203040506070Jul Aug Sep010203040506070Oct Nov DecFigure 2.2: O2 profiles in the top 70 m from the STRATOGEM project (grey lines).Profiles from different months are plotted in different subplots to identify the seasonalvariation. The black solid line in each subplot is the averaged profile of that month.The dashed line in each subplot is the least square fit of an exponentially decayingfunction (Eq 2.12) of the corresponding monthly average. The dotted lines are plottedas identification of the sampling depth of the ferry (2 m).162.1. Methodswith a range of uncertainty of 10%, which is used in the following analysis of this work.γ50[m] Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecEq 2.13 17.01 17.16 15.01 15.75 16.97 15.46 15.60 16.02 16.33 16.31 16.78 17.04Eq 2.14 24.05∗ 16.90 11.70 15.12 14.67 16.52 15.29 10.26∗ 10.07∗ 15.38 14.90 14.22Table 2.1: Climatology of the conversion factor γ. ∗ indicates abnormal extreme values.Another possible issue associated with γD is the in/out-of plume difference. Toinvestigate it, the in and out-of plume γ50 are calculated separately using profiles ofStation S2 − 3 and S4 − 1, respectively. Results show that there is no significant dif-ference of γ50 in and out-of river plume. Therefore, the in/out-of plume difference inγD is usually neglected in the rest of the thesis.2.1.5 Plume water vs SoG waterThe ferry track cuts through the Fraser River plume, a distinctive water mass thatusually has lower salinity associated with fresh water outflow from Fraser River. Othercharacteristics of the plume water can also differ from that of SoG. The plume waterand SoG water can be distinguished with a salinity-based criterion, which is discussedin detail in Appendix D. Using this criterion, data within the plume water can beidentified and discussed separately. When discussing the in/out of plume differences,for each track, data within the river plume is averaged to represent the plume conditionand denoted with subscript P ; for SoG water, data is averaged over a short distancethat is not affected by the river plume (Appendix D), and is denoted with a subscriptof SoG.2.1.6 Units of productivityTo highlight the connection between productivity and O2 in seawater, in this studyO2 is eventually scaled with a carbon based unit: gCm−2. It uses the ratio of carbonand O2 that are generated/consumed during the process of photosynthesis/respirationto convert the partial pressure of O2 in seawater to the equivalent grams of carbon.The Aanderaa Optode on board the ferry only measures percentage saturation of O2in seawater, to convert it into the carbon based unit, the following steps are required:(1) to convert percentage saturation (%) into partial pressure (ml·l−1), the percentagesaturation is multiplied with O2 solubility, which is calculated as a function of salinityand seawater temperature following Weiss (1970); (2) to convert partial pressure todepth integrated concentration (ml·m−2), the results are depth integrated with theconversion factor γ derived in Section 2.1.4; (3) for the conversion from O2 (ml) tocarbon (g), we use the classic relationship of Redfield (1960) in Eq 2.3 to establish theratio172.2. Observations and dataRC/O2 =106× 12138× 32× 1.43× 10−3 = 4.12× 10−4g ·ml−1 (2.15)where 106 and 138 are the moles of carbon and O2 in the relationship, 12 and 32are the atomic weight of carbon and O2, and 1.43 × 10−3 is the density of oxygen ing·ml−1under standard temperature and pressure. Note that since we will be discussingrates, only changes in their values will be important.For other terms in the budget equation such as air-sea gas flux and advective trans-port, the units are converted in a similar manner.2.2 Observations and dataThe datasets used in this work are mainly from three observation platforms: (1) the Fer-ryBox on board the BC Ferry M.V. Queen of Alberni; (2) a series of CTD (conductivity-temperature-depth) casts from 9 stations of the STRATOGEM project and 3 stationsof the JEMS (Joint Effort to Monitor the Strait of Juan de Fuca) project; (3) windspeed and direction record from the Sandheads meteorological station (EnvironmentCanada station #6831). In this section I present the details about these 3 datasets.2.2.1 Ferry samplingThe BC Ferry M.V. Queen of Alberni is a 140 m long double-ended passenger ferrytravelling across the SoG. A double-ended ferry can travel both ways without turningaround at dock. Since the distances of the system water intake to the two bows aredifferent, when the ferry is travelling in different directions, the sampling depths canbe slightly different due to the deflection of water caused by the structure the ferry.This effect appears to be very small and thus is neglected.The FerryBox is located below the main deck, in one of the storage rooms, and isconnected to an opening on the hull through a pipe with a length of approximately 1 mand a diameter of approximately 2 cm. The water intake is located 2 m below the waterline, with a variation of up to 40 cm due to variations in payload (Halverson, 2009).In addition to the oceanographic sensors, a comprehensive meteorological sensor suitelocated on the upper deck is also integrated into the system. The system is poweredby the ferry electricity, and reports data in near real-time via a 3G cellular uplink.The FerryBox consists of 4 sets of oceanic sensors: (1) a Seabird Thermosalino-graph, which measures seawater temperature and salinity; (2) an Aanderaa Optode,which measures dissolved oxygen concentration and seawater temperature; (3) a TURORemote Temperature, which measures seawater temperature at the system water in-take; and (4) a Wetlabs ECO Triplet, which measures turbidity, relative chlorophyll182.2. Observations and datafluorescence, and CDOM fluorescence. Note that there are 3 sensors that measure sea-water temperature; how these measurements are integrated into 1 dataset is presentedin Appendix A. All sensors sample at a depth of 2 m, with a sampling interval of 10 s.The meteorological station consists of 3 sets of sensors: (1) a RM Young Meteoro-logical Station, which measures barometric pressure, air temperature, relative humidity,wind direction and speed; (2) a Kipp and Zonen Pyrogeometer, which measures down-ward atmospheric long wave radiation and net radiation; and (3) a Kipp and ZonenPyranometer, which measures incoming solar radiation. The meteorological sensorssample at a height of 18 m, also with a sampling interval of 10 s. GPS data is acquiredby a Thrane and Thrane Sailor navigational sensor. Because data from each devicedoes not have common timestamps, the raw GPS data is integrated onto each deviceusing linear interpolation.The ferry data is characterized by a series of gaps associated with the ferry schedule,instrument failures, quality checks and scheduled maintenance (Fig 1.2). The annualrefit of the Ferry creates a one month long gap from middle October to middle Novem-ber every year; another long gap was caused by an instrument failure from July toNovember 2013, when the water intake for the FerryBox was blocked and all water sideproperties were influenced. Water intake blockage also happened a few other times,causing week-long gaps in the dataset. Some shorter term gaps are mainly caused bythe settings of the system: when the velocity of the ferry falls below a certain threshold,the system automatically shuts down and stops recording to save hard drive storageand transmit the data, which creates hours-long gaps in the dataset (Fig 1.3).The FerryBox is regularly maintained by the VENUS FerryBox maintenance team.The purpose of maintenance is to check the system condition, clean the instruments,and make adjustments to improve the performance of the system. Before July 2013, themaintenance was carried with an interval of approximately 2 months; After July 2014,the maintenance was carried out more frequently, with an interval of approximately 2-3weeks. When seawater flows through the FerryBox, suspended material and biomasscould accumulate in the system, which causes the readings to drift; therefore, frequentcleaning is important to the reliability of FerryBox dataset. Fig 2.3 shows the rawdata of turbidity and O2 from the FerryBox, with the date of instrument maintenancemarked as black dash lines. Note the great differences in turbidity and O2 after certainmaintenances (e.g., August 3, 2012, July 18 & August 1, 2014), which suggests thereadings have been greatly biased before cleaning. To get quality assured data fromthe FerryBox, it is suggested that the system has to be cleaned at least every otherweek, especially during the spring bloom and the following summer freshet; in addi-tion, corrections are also required to compensate this bias, which is described in thefollowing paragraph.The data is transmitted back to the VENUS server and distributed to other users192.2. Observations and dataMay Jul Sep Nov 2013 Mar May Jul Sep Nov 14 Mar May Jul Sep020406080100Turbidity [NTU]May Jul Sep Nov 2013 Mar May Jul Sep Nov 14 Mar May Jul Sep051015O 2 [ml/l]Figure 2.3: Raw data of turbidity (upper panel) and O2 (lower panel) from the Ferry-Box. Black dash lines identify the date of instrument cleaning.202.2. Observations and datathrough a FTP based network. To correct for bio-fouling and other possible instrumentissues, a pre-process procedure is carried out by the author of this thesis, which includesthe following steps: (1) since the Optode does not have a salinity sensor, salinity com-pensation for O2 concentration calculation is made with salinity measurements fromthe Thermosalinograph; (2) for turbidity, relative chlorophyll fluorescence, CDOM fluo-rescence and O2, a linearly increasing correction term is added to the raw data betweencleaning visits to compensate for bio-fouling; (3) for O2, the first 20 measurements atthe beginning of a day are removed to avoid potential bias from unflushed water thatresides in the system at night; and (4) for solar radiation, some bad measurements areremoved due to the potential influence of shade of the ferry structure at noon. Ananalysis of chlorophyll quenching was also carried out following Halverson (2009), butthe results are not used for correction because of the large uncertainties of the analysis.2.2.2 CTD samplingDuring Apr 2002 to Jun 2005, 48 cruises were made to sample 9 stations in the south-ern and central regions of SoG as part of the STRATOGEM (The Strait of GeorgiaEcosystem Project) project (Fig 1.1) (Pawlowicz et al., 2007; Riche and Pawlowicz,2014). The CTD profiles used in this study are mainly from this dataset. During thetime of spring bloom, cruises were held weekly or biweekly; during the rest of the year,cruises were mostly held every month. Details of the nine stations are listed in Ta-ble 2.2. Profiles with a range of parameters were taken, but in this study only salinityand O2 profiles are used.Another long-term observational project is the JEMS (Joint Effort to Monitor theStrait of Juan de Fuca) project, which includes 3 stations located near the southernend of Haro Strait. Details of the 3 stations are listed in Table 2.3. Cruises were heldmonthly from August 1999 to March 2012. Similar to the STRATOGEM project, arange of oceanographic variables were measured, but only salinity profiles are used inthis study.2.2.3 Wind record & other measurementsThe key variable for the calculation of air-sea gas exchange is the wind speed above theocean surface. A R.M. YOUNG Marine Wind Monitor (Model 05106) is attached tothe meteorology station as part of the FerryBox unit, however, the wind measurementsare contaminated by the high speed and the superstructure of the ferry. To avoid theseuncertainties, an alternative dataset is needed. Pawlowicz (2014b) shows that the windalong the ferry track is mostly uniform. Hence, dataset of hourly wind speed and di-rection from meteorology station Sandheads (Lat: 49.11 ◦N, Lon: 123.30 ◦W, StationID: 1107010) is acquired to better represent wind speed along the ferry track. The sta-tion provides meteorological measurements including air temperature (◦C), wind speed212.2. Observations and dataStation# Latitude[◦N ]Longitude[◦W ]Max Sam-pling Depth[m]Bin Size [m]S1 48.92 123.25 137 1S21 48.98 123.49 127 1S22 49.03 123.42 294 1S23 49.08 123.35 150 1S3 49.13 123.56 238 1S41 49.25 123.75 390 1S42 49.23 123.58 330 1S43 49.25 123.38 229 1S5 49.36 123.85 373 1Table 2.2: Details of STRATOGEM CTD stations.Station# Latitude[◦N ]Longitude[◦W ]Max Sam-pling Depth[m]Bin Size [m]SJF000 48.42 123.03 172 0.5SJF001 48.33 123.03 138 0.5SJF002 48.25 123.03 147 0.5Table 2.3: Details of JEMS CTD stations.(km·h−1) and direction (◦) at a height of 11 m, with very few (≈ 1%) missing datafrom May 2012 to Jul 2014. No quality check is applied to the measurements, here weassume all archived data from Sandheads station is quality controlled.Another set of wind records used in this study is the along coast wind speed, whichis measured by the Buoy Station La Perouse Bank (Station Number C46146) from 1980to 2014, provided by the U.S. National Data Buoy Center.In Chapter 3, Fraser River and Englishman River discharge is required as part ofthe model input. The discharge data from 1980 to 2014 is obtained from the Environ-ment Canada data archive. For the Fraser River, the discharge is measured at Hope(water station 08MF005); For the Englishman River, the discharge is measured nearParksville (water station 08HB002).2.2.4 Calibration for O2 sensorThe O2 sensors used in this study are Aanderaa Oxygen Optodes (Model 3835, se-ries number 1415 & 1416), which were alternately mounted onto the FerryBox systemduring the 30 months of research period. Optode 3835 is one of the very first genera-222.2. Observations and datation Aanderaa Optode designed to measure shallow water O2 saturation and seawatertemperature, with an accuracy of ±5% for O2 saturation and ±0.05◦C for seawatertemperature. Although there is no quality test for this specific model, the long-termstability and quality performance of the Aanderaa Optode family has been proved re-liable at low sampling frequency (Takeshita et al., 2013), however, the optode tendsto give lower values than expected, especially when it is sampling at high frequency asthe sensing ’foil’ ages (Tengberg and Hovdenes, 2014).One way to deal with this problem is to let the optode go through a ’Burn-in’ stagebefore it is calibrated, but this procedure has only been carried out since 2012 andis not likely to be applied on the old models like 3835. The 2 optodes used in thisstudy were both purchased in 2010 and have not been calibrated since then; also, theFerryBox samples at a relatively high frequency (every 10 s). Thus it is reasonable tobelieve that both of the optodes should have this drift problem by now.To assess this drift and correct the data collected with the 2 optodes, a field tripon board the ferry was carried out on Dec 05, 2014. During this trip, another optode(series number 418, calibrated in advance) was placed inline alongside the resident in-strument (series number 1415), and the two instruments were run in tandem for anhour shortly after the ferry left Tsawwassen (1515, local time). In the mean time, watersamples were collected and analyzed using Winkler Titration for direct O2 concentra-tion measurements along the same ferry track.The measurements from the 2 optodes 418 & 1415 are plotted in Fig 2.4 for com-parison along with the Winkler measurements. Note that from 1520 to 1540, readingsfrom optode 418 is higher than that of Winkler Titration, suggesting that the optode isgoing through an adjustment period during the first 25 minutes. After 1545, readingsfrom optode 418 is in good agreement with that of Winkler Titration, thus only dataafter 1545 is used for the comparison. The 2 sets of measurements from optode 1415and 418 are well correlated, which confirms the stability of both instruments. However,there is a steady difference between them, suggesting that the measurements of optode1415 contain an offset.The next step is to determine how fast the offset developed during the 2 years ofmeasurements. Tengberg and Hovdenes (2014) suggests that even without the ’Burn-in’ treatment, the offset can reach a steady level after 1 year of measurements with asampling interval of 5 seconds. For the optodes used in this work, although the datais only recorded every 10 seconds, the actual sampling interval is only 1 second. Thus,the offset of the optodes used in this work should be stable after 2-3 months of mea-surements. To evaluate how the offset was developed over time, the annual cycle of O2saturation from 2012 to 2014 is plotted in Fig 2.5. No evident inter-annual offset isobserved from the 3 years of measurements, therefore, it is reasonable to believe thatthe offset is relatively stable during the entire period.232.2. Observations and data14/12/05 15:20 15:30 15:40 15:50 16:00 16:107580859095100105110115Local TimeO 2 Saturation [%]  1415418Winkler1415+17%Figure 2.4: O2 saturation measurements from optode 1415 (solid) and 418 (solid). TheWinkler measurements are also converted to % saturation and plotted in circles. Thethick solid line is the 1415 measurements plus 17%, which is the ’correction’ for O2saturation applied in this study.To correct for this offset, a correction constant, 17%, is added to the measurementsof the optodes. After the correction is made, the 1415 measurements are in very goodagreement with those of 418 (Fig 2.4, thick line). Note that although the comparison isonly carried out for 1415, the same correction is also applied to the 1416 measurementsin further analysis of this study. This is somewhat problematic, however, since bothof the optodes were purchased at the same time, and also due to the lack of similarcomparison for optode 1416, I assume that the offsets of both optodes are at a similarlevel. To make a more comprehensive correction, a multi-point calibration for bothoptodes on board the ferry is needed, which is in preparation and will be carried outby the VENUS maintenance team in early 2015.242.2. Observations and dataJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan8090100110120130140150O 2 Saturation [%]  201220132014Figure 2.5: Annual cycle of O2 saturation from 2012 to 2014.252.3. O2 concentration in SoG2.3 O2 concentration in SoGThe absolute O2 concentration and O2 saturation level from May 2012 to Oct 2014 areplotted in Fig 1.2. The total duration of measurement is 30 months, but since fromJul to Dec 2013 most of the data is contaminated due to instrument failures, there areonly approximately 24 months of data available for the analysis.During the 30 months of observation, O2 varies from 4.6 to 12.9 ml·l−1and has astrong seasonal signal. Daily averaged O2 is lower in winter at around 7 ml·l−1, andstarts to increase in March, peaks at around 9 ml·l−1in late March (2013) or earlyApril (2014), and drops slowly to winter level during the rest of the year, with a fewfluctuations possibly correlated with secondary bloom events. In 2012 a second peak inthe early October is also picked up, which is not seen due to a lack of data in October inthe other 2 years. Daily averaged O2 saturation level shows the same seasonal pattern,lower in winter at around 100% and rising to as high as 148% in spring.Beside seasonal variation, diurnal O2 cycle is also very important for the analysisof respiration rate. The width of the grey areas in Fig 1.2 is a first glance of the am-plitude of diurnal cycle, but note that it also includes the spatial along-track variation,the amplitude of which is larger than that of diurnal variation for much of the time.To analyze the amplitude of diurnal circle, the normalized and smoothed O2, Oˆ2s (Sec-tion 2.1.3) is plotted against time of day, in Fig 1.3. Normalized O2 is lowest in theearly morning, around 4:30 to 8:00, corresponding to the time of sunrise. As solar radi-ation increases, O2 starts to increase, and peaks around 18:00 to 20:00, correspondingto the time of sunset. After sunset O2 drops back to the lower level during nighttime.The range of variation is approximately 5-10% of the average O2 level. This diurnalfluctuation pattern is in good agreement with a sinusoidal signal, which supports theassumption and method presented in Section 2.1.3.As the ferry travels across SoG back and forth, the FerryBox also picks up the spa-tial variation in oxygen along the track. To analyze this spatial variation, O2 anomalyfor each track is calculated and the Hovmo¨ller diagrams for each year are plotted inFig 2.6. The O2 anomaly in the Hovmo¨ller diagrams is defined as the O2 level sub-tracted by the average O2 level of that specific track. The plots below each Hovmo¨llerdiagram are comparisons of O2 in (O2p) and out of (O2SoG) Fraser River plume, asdefined in Section 2.1.5. Overall, O2p is higher than O2SoG by 0.19 ml·l−1. O2p andO2SoG both vary seasonally, peak during the spring bloom and stay at a lower level inwinter. At the early stage of the spring bloom (middle Mar 2013, early Apr 2014), O2pis higher than O2SoG for a few days, the maximum difference is 2.11 ml·l−1in Apr 2014;As bloom spreads across the Strait the spatial difference becomes less evident. As timeproceeds into May, O2SoG starts to be greater than O2p, which lasts for 1 to 2 monthsdepending on the year. For example, in late May 2014, O2SoG is greater than O2p byas much as 1.47 ml·l−1. During some specific time of a year, i.e., spring bloom, O2262.3. O2 concentration in SoGchanges greatly near the boundary of river plume, which is an indication of differentphysical and ecological dynamics in and out of river plume.272.3. O2 concentration in SoGDistance from Tsawwassen [km]2012 a)  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 20131020304050O 2 Anomaly [ml/l]−2−10122013 c)10203040502014 e)10203040506810  b)In PlumeOut of Plume6810d)Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 20156810O 2 [ml/l] f)Figure 2.6: a, c, e): Hovmo¨ller diagram of O2 anomaly along each ferry track. b, d, f)track averaged O2 in (black) and out of (grey) Fraser River plume. Black lines in a), c),and e) are the boundary of Fraser River Plume determined from salinity measurements(Appendix D).28Chapter 3Box ModelIn Eq 2.4, the storage term and air-sea exchange can be estimated through in-situmeasurements directly; on the other hand, due to lack of direct measurements of theflow rate in the Strait of Georgia, it is almost impossible to get a long time series of thevolume flux with high temporal and spatial resolution. Thus, an alternative approachis needed.One option is to estimate the outflow as a function of freshwater inflow, as describedin Riche and Pawlowicz (2014). Here we attempt a slightly more sophisticated proce-dure, by estimating the volume flux through the upper layer of the Strait of Georgiausing a box model to simulate the salinity budget and volume fluxes in the Georgia-Haro-Fuca system. The primary objective is to understand the relationship betweenseasonal to interannual variability of the estuarine circulation and the surrounding en-vironment, i.e., Fraser River runoff and Pacific water intrusion. This box model is notthe first attempt to estimate the volume flux - several studies, including a series of fullresolution 3D model has been carried out for this purpose (Masson and Cummins, 2004;Crean et al., 1988; Foreman et al., 1995; Foreman and Thomson, 1997; Hibler et al.,2008). Here we choose the box model over the more sophisticated 3D model becauseof its low demand for computational power; since the ferry system is still operationalas this thesis is written, data is updated constantly and the advective term needs tobe continuously recalculated; in addition, the box model is easy to tune, which makesit a perfect tool to match in-situ measurements and understand the system.This chapter is organized as follows. In section 3.1, the setting of box model andrelated in-situ measurements are described. In section 3.2, results of the model arepresented and compared with in-situ measurements and other studies. In section 3.3,the results are summarized and discussed in more detail.3.1 Model formulation3.1.1 Equation setupThe box model we used is adapted from a earlier version developed by Li et al. (1999).A schematic diagram of the box model is shown in Fig 3.1. The system is divided into3 basins - the Strait of Georgia (SoG) Basin, Haro Strait (HS) Basin, and Juan de FucaStrait (JdFS) Basin. Each basin is divided into 2 boxes, an upper box characterized293.1. Model formulation𝐹�  𝐹�  𝑄𝑔 − 𝐹�  𝑄𝑔 − 𝐹�  𝑄𝑔 − 𝐹�  𝑄𝑔 − 𝐹�  𝐹�  𝑄ℎ − 𝐹�  𝐹�  𝑄ℎ − 𝐹�  𝑄ℎ − 𝐹�  𝑄ℎ − 𝐹�  𝑄ℎ − 𝐹�  Figure 3.1: Box model schematic diagram. The system is divided into 3 basins: SoG,Hs, and JdFS, each of which consists of an upper and a lower box. Boxes with dashedline are boundary conditions. Volume fluxes between two boxes are denoted as thinarrows, while vertical mixings are denoted as thick arrows.Ag 4000 km2 Vgu 225 km3 Vhl 47 km3Ah 500 km2 Vgl 375 km3 Vju 112.5 km3Aj 2000 km2 Vhu 28 km3 Vjl 187.5 km3Table 3.1: Details of surface areas and volumes for each basin.by the water mass from sea surface to the depth of 50 m, and a deep box from 50 mto the bottom. The system is driven by fresh water runoff from Fraser River and othersmall rivers that flow into SoG, which is balanced by water exchange between PacificOcean and the western end of the Juan de Fuca Strait. Water exchange through theair-sea interface and other small channels is neglected in this study.For each basin the upper box and lower box are linked by a mutual interface, theareas of which are denoted as Ag, Ah, and Aj . The subscripts g, h, and f representthe SoG, HS, and JdFS. Accordingly the volumes of each box are denoted as Vgu, Vgl,Vhu, Vhl, Vju, and Vjl. The subscripts u and l represent the upper and lower boxes.A rough estimate of the areas and volumes based on Thomson (1981); Davenne andMasson (2001) are shown in Table 3.1.The salinities in each box are denoted by S˜gu, S˜gl, S˜hu, S˜hl, S˜ju, and S˜jl, the volume303.1. Model formulationflux between SoG and HS upper boxes by Q˜g, and that between HS and JdFS upperboxes by Q˜h. River discharge, which is the primary forcing of the estuarine circulation,is denoted by F˜ .Although Fraser River is the primary freshwater source and comprises more thanhalf of the total discharge, simply scaling the measured Fraser River discharge (as inPawlowicz et al. (2007)) may not produce the best short-term estimates of the inflow.Occasional intense rain fall and/or winter storms can bring additional freshwater intoother rivers, which is sometimes a large portion of the total inflow, especially duringwinter when Fraser River discharge is near its minimum. To include both snow-meltcontrolled rivers like Fraser River and rain/storm controlled rivers, we choose dischargemeasurements from 2 separate stations, Fraser River at Hope and Englishman Rivernear Parksville, and use a linear functionF˜ = a× F˜Fraser + b× F˜Eng + c (3.1)to represent the total freshwater discharge (Collins et al., 2009). The coefficients a, b,and c are acquired using linear regression based on a long-term monthly river dischargemeasurements for the entire drainage basin given by Morrison et al. (2012). The re-gression gives a = 1.11, b = 18.80, and c = 1651.7 (Appendix B).Total river discharge varies seasonally (Fig 3.2). Two-thirds of the runoff comesfrom snow-melt, which begins in April and increases to a maximum in late May andearly June. The early summer maximum varies every year, from approximately 8000m3s−1 (2010) to more than 14000 m3s−1 (2012). After the summer discharge max-imum, river discharge drops to around 2500 m3s−1 in winter, with occasional spikesfrom rain fall or storms, and reaches a minimum in January. Interannual variation isalso observed, but at present this variability cannot be linked to any other phenomena.The salt budget in the system is balanced by high salinity deep water inflow fromthe Pacific Ocean into JdFS. From late spring to early fall, wind-driven upwellingbrings high salinity water to the lower JdFS; From late fall to early spring, wind-drivendownwelling transports high salinity water downwards and lowers the salinity on shelf.Hence Pacific salinity can be defined as a function of along coast wind speed, which isacquired from the National Data Buoy Center. Details of the calculation are illustratedin Appendix B.Vertical mixing between upper and lower boxes is represented by vertical mixingvelocities, ωg, ωh, and ωj , and accordingly the volume flux rates ωgAg, ωhAh, ωjAj .Li et al. (1999) suggests that vertical mixing velocities in SoG and JdFS are relativelyconsistent, and in HS it is influenced by spring-neap tidal cycle:ωh =12ωmh f × (S˜hl − S˜hu)(1 + sin2pitT/24) (3.2)313.1.Modelformulation1995 96 97 98 99 00 01 02 03 04 050200040006000800010000120001400016000Total River Discharge into SoG [m3/s]2005 06 07 08 09 10 11 12 13 140200040006000800010000120001400016000Total River Discharge into SoG [m3/s]YearFigure 3.2: Daily averaged total river discharge into the SoG from 1995 to 2014.323.1. Model formulationwhere ωmh is the maximum mixing velocity at spring tides, T = 1 yr is the period of 24spring-neap tidal cycles. The effect of stratification is represented by (Li et al., 1999)f =∆S˜cS˜hl − S˜hu(3.3)when S˜hl − S˜hu ≥ ∆S˜c andf = 1 (3.4)when S˜hl − S˜hu < ∆S˜c. This expression means when the stratification is strong(S˜hl − S˜hu ≥ ∆S˜c), vertical movement will be suppressed and mixing will be dampedaccordingly.The estuarine flow, Qg and Qh, is estimated using a parametrization derived byStommel (1961). If the densities of 2 water masses are ρ1 and ρ2, the density gradientbetween 2 water masses will drive a gravitational flow from the higher density end tothe lower density end:Q = c(ρ1 − ρ2) (3.5)where Q is the volume flux of gravitational flow, and c a constant of proportionality. Ifwe take surface water in SoG, HS, and JdFS as 3 separate water masses, and assumedensity in the system is mainly a linear function of salinity, we getQg = cg(ρhu − ρgu) = cgβρ0(S˜hu − S˜gu) (3.6)Qh = ch(ρju − ρhu) = chβρ0(S˜ju − S˜hu) (3.7)where Qg and Qf are the volume fluxes of primary and secondary estuarine flow re-spectively, β the saline contraction coefficient, ρ0 a reference density. Based on Fig 3.1the salt budgets in each box can be written asVgudS˜gudt= (Qg − F )S˜gl −QgS˜gu + ωgAg(S˜gl − S˜gu) (3.8)VgldS˜gldt= (Qg − F )(S˜hl − S˜gl)− ωgAg(S˜gl − S˜gu) (3.9)VhudS˜hudt= QgS˜gu − (Qg − F )S˜hu + (Qh − F )S˜hl −QhS˜hu + ωhAh(S˜hl − S˜hu) (3.10)333.1. Model formulationVhldS˜hldt= (Qg − F )(S˜hu − S˜hl)− (Qh − F )(S˜jl − S˜hl)− ωhAh(S˜hl − S˜hu) (3.11)VjudS˜judt= Qh(S˜hu − S˜ju) + ωfAf (S˜jl − S˜ju) (3.12)VjldS˜jldt= (Qh − F )(S˜p − S˜jl)− ωfAf (S˜jl − S˜ju) +1trVjl(S˜p − S˜jl) (3.13)Note Qg represents the total volume flux between SoG upper box and HS upperbox and Qh represents that between HS upper box and JdFS upper box. tr is ameasure of the response time taken for the deep JdFS water to equilibrate its salinityto the Pacific salinity. Transfer through air-sea interface is zero in the case of salt flux.Nondimensionalizing salinities by S0, we obtaindSgudt=1ts{(qg − F1)Sgl − qgSgu +R2(Sgl − Sgu)} (3.14)dSgldt=λdts{(qg − F1)(Shl − Sgl)−R2(Sgl − Sgu)} (3.15)dShudt=1tsλhg{qgSgu− (qg−F1)Shu+(R3qh−F1)Shl− qhShu+R4(Shl−Shu)} (3.16)dShldt=λdtsλhg{(qg − F1)(Shu − Shl)− (R3qh − F1)(Sjl − Shl)−R4(Shl − Shu)} (3.17)dSjudt=λhjtsλhg{R3qh(Shu − Sju) +R5(Sjl − Sju)} (3.18)dSjldt=λhjλdtsλhg{(R3qh − F1)(Sp − Sjl)−R5(Sjl − Sju)}+R6(Sp − Sjl) (3.19)whereλd = hu/hl = 1/3, λhg = Vh/Vg = 1/8, λhj = Vh/Vj = 1/4, (3.20)F1(t) =F (t)cgρ0βS0, (3.21)R2 =ωgAgcgρ0βS0, (3.22)343.1. Model formulationR3 =chcg, (3.23)R4 =ωhAhcgρ0βS0=12Rm4 f × (Shl − Shu)(1 + sin2pitT/24), Rm4 =ωmh Ahcgρ0βS0, (3.24)R5 =ωfAfcgρ0βS0, (3.25)R6 =tstr, (3.26)ts =Vgucgρ0βS0. (3.27)Sgu, Sgl, Shu, Shl, Sju, Sjl are nondimensionalized salinities. Nondimensionalizedvolume fluxes are accordingly given byqg = Shu − Sgu, qh = Sju − Shu. (3.28)3.1.2 Parameters & initial condition estimationFive nondimensional numbers need to be determined to solve the equation system 3.14to 3.19. ωmh = 1× 10−3 m·s−1, ωj = 2.5× 10−5 m·s−1, S0 = 33.5 g·kg−1, and tr = 20.4days are directly adopted from Li et al. (1999). ωg, on the other hand, is set to be7.5 × 10−6 m·s−1 (3 times as large as that from Li et al. (1999)) to match up within-situ measurements of the lower SoG box. For cgρ0βS0, Li et al. (1999) used a valueof 106 m3s−1, which is a reasonable estimate as the output is in reasonable agreementwith in-situ measurements; however, to improve the performance of the model we usea nonlinear data fitting method for the estimate of cgρ0βS0.The determination of cgρ0βS0 is a data fitting problem for a set of sophisticatedODEs. Unfortunately, for most ODE systems, analytical solutions are not applicable,so that conventional data-fitting methodology is not directly available. To simplifythe problem, we only use Eq 3.14, assuming dSgu/dt is a nonlinear function of Sgu(t),Sgl(t), Shu(t), and F (t), and Cgρ0βS0 is the unknown parameter that needs to bedetermined. Then this fitting problem for a 6-ODE system is transferred into thatof one nonlinear multivariate equation, which can be easily solved with MATLAB(R2011b). Using in-situ salinity measurements from the STRATOGEM project andJEMS project, and river discharge measurements from Environment Canada database,we get cgρ0βS0 = 0.83 × 106 m3s−1. This estimate is slightly smaller than that fromLi et al. (1999), which means the same salinity difference will give a smaller volumeflux Qg from Eq 3.6; On the other hand, the river discharge we used for our modelis larger that that of Li et al. (1999) by more than 1500 m3s−1, which will create a353.2. Resultslarger salinity gradient and increase the estuarine flux. Overall our model will result insimilar but slightly higher volume flux in the system compared to that of Li et al. (1999).The ratio of cf and cg, R3 =chcgis on the order of 1. Trial and error process showsthat R3 = 3 gives the best fit with in-situ measurements.Based on the reasons listed above, the nondimensional parameters are given asR2 = 0.036, R3 = 3, Rm4 = 0.602, R5 = 0.0602, R6 = 0.154, (3.29)and the nondimensional time scalets =Vgucgρ0βS0= 2.70× 105 s = 3.13 days. (3.30)There are a few ways to determine the initial condition for the box model. A rea-sonable setup is to start with a homogeneous salinity distribution, and let the modelrun for a few years until the differences between two periodic cycles is smaller thansome predefined threshold. However, it requires that the forcing term for the model isperiodic, which is not applicable in our case since we are using in-situ measurements,which are not exactly periodic. Although theoretically we can still let the model run fora reasonably long time and assume it reaches equilibrium, here to save computationalpower and time, we use a different approach.Instead of using homogeneous initial condition, we conduct a ’test run’ to gen-erate a set of initial values that represent the ’most likely’ salinities in each box.It is carried out with the following steps: (1) calculate daily averaged climatologyof river discharge using in-situ measurements from 1995 to 2014; (2) assume a ho-mogeneous initial condition, i.e., S˜gu = S˜gl = S˜hu = S˜hl = S˜ju = S˜jl = S˜0. (3),run the model using the above initial condition and river discharge until the outputat the beginning of the year satisfies the condition that the mean-square deviation,δ = [∑i=gu,gl,hu,hl,ju,jl(Syri −Syr−1i )2] · 6−1, is smaller than 10−6. Then Syri , the outputof a steady state, is considered as the ’most likely’ salinities and thus the initial condi-tion of the actual model.3.2 Results3.2.1 SalinityEq 3.14- 3.19 are solved numerically using a fourth-order Runge-Kutta method. Sev-eral time steps (0.5, 1, 2, 4 days) are chosen to test the performance of the model, andresults show that the model is convergent with a time step equal to or smaller than 2days. It is also shown that a temporal resolution greater than 1 day will not evidently363.2. Resultsenhance the performance of the model, thus a time step of 1 day is used for this work.First the test run is carried out to determine initial values, the results of which areshown in Fig 3.3. The model reached equilibrium in 4 years of model time. The upperlayer in SoG is diluted by river discharge: S˜gu is smallest among all 6 boxes, and reachesa minimum of 27.6 g·kg−1 in July, one month after maximum discharge. Then it risesslowly, reaches a maximum of 29.21 g·kg−1 in next March. The decrease from Marchto July is more rapid due to a sharp increase in river discharge from snow-melt. S˜huand S˜ju have similar seasonal pattern, with a maximum salinity of 31.2 g·kg−1 and 31.9g·kg−1 in March and a minimum of 30.1 g·kg−1 and 31.3 g·kg−1 in July, respectively.Along with seasonal variation, strong tidal mixing in HS also leads to a spring-neapcycle in salinity, the amplitude of which is about 0.2 g·kg−1. Note that this spring/neapcycle does not appear in the SoG surface box. Compared with the upper layer, theseasonal fluctuation of salinity in lower layer is much smaller - S˜gl averages 30.4 g·kg−1,with a seasonal variation of about 0.09 g·kg−1; S˜hl averages 31.6 g·kg−1, with a sea-sonal fluctuation of about 0.3 g·kg−1 and a spring-neap fluctuation of 0.15 g·kg−1. S˜hlis both influenced by fresh water input and Pacific water intrusion, leading to a maxi-mum salinity in July. Salinity in deep JdFS, S˜jl is mainly influenced by Pacific Ocean,with a maximum of 33.4 g·kg−1 in July and a minimum of 32.8 g·kg−1 from Decemberto next May.The equilibrium state gives an initial condition of Sgu0 = 29.0, Sgl0 = 30.4,Shu0 = 30.8, Shl0 = 31.6, Sju0 = 31.6, and Sjl0 = 32.8 g·kg−1at day 1 of a year.Using this initial condition, the second run is carried out with daily total river dis-charge, and the results are shown in Fig 3.4. Salinities in the upper layer are heavilyinfluenced by river runoff, reach minimum salinities in July every year, 1 month aftermaximum runoff. Total river runoff varies from year to year, which is related to theamounts of snow deposition in the mountains of British Columbia and precipitationalong the river path. Annual maximum discharge varies in a range of 0.83 × 104 to1.48× 104 m3s−1, with an average of 1.14× 104 m3s−1. Maximum discharge exceeded1.1 × 104 m3s−1 in 9 out of 18 years, and the minimum salinities in upper layers areaccordingly smaller; Annual minimum salinity in the upper SoG varies between 26.8g·kg−1 and 28.1 g·kg−1; Minimum S˜gu is found in year 1997, which corresponds to theyear of second largest river discharge. S˜hu and S˜ju have similar seasonal cycle becauseof the influence of river discharge, but increase towards the open ocean as the freshwa-ter mixes with the salt water from the Pacific Ocean. S˜hu also has a spring-neap cycle,similar to the spring-neap cycle in the test run. S˜gl averages 30.4 g·kg−1, with a smallvariation of about 0.2 g·kg−1. Annual S˜hl cycle is influenced by both river flow andPacific water intrusion, with a minimum in July corresponding to river discharge anda maximum in September corresponding to Pacific water intrusion. S˜jl varies from aminimum of 32.7 g·kg−1 to a maximum of 33.6 g·kg−1, highly correlated with Pacificsalinity.373.2. Results012 x 104River Discharge [m3/s]Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec Jan3333.534Pacific Salinity [g/kg]Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec Jan272829303132333435Salinity [g/kg]  Sgu Sgl Shu Shl Sju SjlFigure 3.3: Upper panel: Total river discharge climatology generated by daily dis-charge measurements from Jan 1995 to Jan 2012 (solid) and Pacific Salinity climatology(dashed); Lower panel: salinities in each box at year 4 in the test run.383.2.Results1995 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 1426272829303132333435Salinity [g/kg]  Sgu Sgl Shu Shl Sju Sjl050001000015000River Discharge [m3/s]1995 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 143334Pacific Salinity [g/kg]Figure 3.4: Upper panel: Total river discharge from Jan 1995 to Mar 2004 (solid) and Pacific salinity (dashed); Lower panel:Modeled salinities in each box from Jan 1995 to Mar 2014.393.2. ResultsThese model predictions of salinities are in reasonable agreement with observations(Fig 3.5). STRATOGEM and JEMS salinity profiles are averaged over the top 50 m torepresent the upper layer, and 50 m to 200 m or the maximum sampling depth if thewater is shallower than 200 m to represent the lower layer. Note that the averaging isweighted by hypsography. Modeled salinities are denoted as solid lines, while in-situmeasurements are denoted as circles, squares and triangles. Upper panel is the com-parison for SoG upper layer (solid line and circles) and lower layer (dashed line andtriangles). S˜gu is in good agreement with in-situ measurements, except at the end of2003 when modeled salinity is lower than in-situ measurements by less than 0.5.For the SoG lower layer, the in-situ measurements averages 30.4, smaller than thatof S˜gl by 0.02. Averaged S˜gl in our model is smaller than that of Li et al. (1999) byabout 0.6, which mostly due to the increased vertical mixing parameter in our model.Lower panel is a comparison in HS upper layer (solid line, circles, triangles, andsquares). Modeled salinity in JdFS upper layer is also plotted (dashed line) as a ref-erence since the 3 stations are located close to the HS and JdFS boundary. It maybe more appropriate to define an weight coefficient for each station and generate anaveraged time series, but since the choices must also be subjective, we choose to plotall 3 stations separately to show the spatial variation as well as the temporal variation.The model predictions are in reasonable agreement with observation, considering theHS is a small basin with strong tidal mixing and interaction with the other 2 basins.Overall, the modelled salinities are good estimates of the reality in the 2 basins, thusit is reasonable to assume that the volume fluxes calculated from the salinities are ac-cordingly reliable.3.2.2 Volume flux & O2 transportNet O2 transport in the SoG upper layer is the sum of river input, advective transportand deep water entrainment, which can be written asO2adv = −QgO2gu + (Qg − F )O2gl + FO2f (3.31)where O2adv is the total net advective input of O2 into the upper SoG layer; Qg is theadvective volume flux from SoG upper layer to HS upper layer; Qg − F is deep waterentrainment; F is the volume flux of total river discharge; O2gu, O2gl, and O2f areO2 concentrations in SoG upper layer, SoG lower layer, and river flow into the SoG,respectively. The volume fluxes Qg, Qg − F , and F are shown in Fig 3.6. For Qg,the spring-neap cycle, which has a range of about 0.5-1×104 m3s−1 is removed usinga low-pass filter with a window of 15 days. River discharge F , as stated before, variesboth seasonally and interannually, ranges from 0.225× 104 m3s−1 to 1.48× 104 m3s−1;Qg is highly correlated with F , ranges from 3.77×104 m3s−1 to 7.35×104 m3s−1. Since403.2.ResultsJan Jul 2003 Jul 04 Jul 05 Jul 062627282930313233Salinity [g/kg]Box Model VS STRATOGEM (upper) & JEMS (lower)  Sgu Model Sgl Model Sgu STRATOGEM Sgl STRATOGEM2000 01 02 03 04 05 06 07 08 09 10 112929.53030.53131.53232.533Salinity [g/kg]  Shu Model Sju Model Shu JEMS000 Shu JEMS001 Shu JEMS002Figure 3.5: Modeled salinities (solid and dashed lines) and in-situ measurements (circles, triangles, and squares). Upperpanel: Modeled and measured salinities in SoG upper layer (solid line, circles) and lower layer (dashed line, triangles). Lowerpanel: Modeled and measured salinities in HS upper layer (solid line). Three stations, JEMS000, JEMS001, and JEMS002are denoted as circles, squares, and triangles respectively. The dashed line is modeled salinity in JdFS upper layer.413.2. ResultsQg is about an order of magnitude greater than F , entrainment Qg − F is similar toQg but the amplitude is slightly smaller.The modelled volume flux is in good agreement with Li et al. (1999), and I alsocompared it with an independent estimate from a more recent study. The lower panelof Fig 3.6 shows the volume flux Qg from this study (hereafter the forward model) andthe values esitmated using an inverse box model developed by Riche (2011) (hereafterthe inverse model) based on STRATOGEM measurements. Overall, the two modeledvolume fluxes are of comparable magnitude, having similar seasonal cycle over the 4 yrsmodeling time; The inverse model gives slightly lower estimates but the disagreementis well within the stated uncertainty of the inverse model.Previous studies show that the estuarine circulation, which is driven by fresh waterinflow from rivers often appears in the form Q = αF 1/n, in the case of SoG the 2constants were estimated to be α = 2.68×103 and n = 3 (Riche and Pawlowicz, 2014).To further investigate the relationship, we plot the advective volume flux Qg from boththe forward model and inverse model against total river discharge F in Fig 3.7. Thefitted power law relationship is plotted in dashed line, while the forward and inversemodel are plotted in squares and triangles respectively. To analyze the relationshipmore objectively, only days when both of the models have outputs are used. Overall,both models have good agreement with the theoretical relationship. Although Qg fromthe forward model is slightly larger and above the theoretical curve, considering thatthe river discharges used in the 2 models are calculated differently, the difference hereis acceptable.To complete Eq 3.31, O2 concentrations in the rivers and SoG upper and lowerlayers are needed as well. The FerryBox gives consistent O2 measurements since May2012, but it only takes measurements at 2 m, which cannot represent the mean O2level throughout the water column; as an alternative approach, we use the STRATO-GEM O2 profiles to generate a monthly O2 climatology for the upper and lower boxes.Each survey of the STRATOGEM project contains 9 O2 profiles, which are averagedto generate one profile. Using all 48 surveys from Apr 2002 to Jun 2005, a climatologyof O2 profiles is generated, and then averaged vertically from 0 to 50 m and 50 to 200m, weighted by hypsography to represent O2gu and O2gl respectively.O2 concentration in Fraser River is acquired from historical chemistry measurementsat Hope, conducted monthly or biweekly from Nov 1998 to Dec 2006. Because of theturbulent nature of the river, the O2 measurements are equivalent to depth-integratedvalues. The time series is also monthly averaged to generate a monthly climatology,O2f , as that of O2gu and O2gl. Generally O2 in rivers is at about 100% saturationof the temperature of the water, hence, for the other rivers flow into SoG, as long asthe water temperature is similar to that of Fraser River, the differences in O2 level areneglected.423.2. Results1995 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14012345678x 104Volume Flux [m3 /s]  Qg F Qg−FJan Apr Jul Oct 2003 Apr Jul Oct 04 Apr Jul Oct 05 Apr Jul Oct 0602468x 104Volume Flux [m3 /s]Figure 3.6: Upper panel: Advective volume flux between SoG and HS upper layer Qg(solid line), Fraser River discharge F (dashed line), and deep water entrainment Qg−F(dash-dotted line). The predefined spring-neap tidal variation in Qg is removed usinga low-pass filter. Lower panel: Comparison of Qg between the forward model (solidline) and the inverse model of Riche (2011) (circles).433.2. Results0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 1100001234567x 104F [m3/s]Q g [m3 /s]  ForwardInverseQg=α F1/nFigure 3.7: Advective volume flux Qg from the forward model (squares) and the inversemodel (triangles), plotted with respect to total river discharge. The dashed line rep-resents the theoretical relationship between total river discharge and advective volumeflux (α = 2.68× 103, n = 3) (Riche and Pawlowicz, 2014).443.3. DiscussionFig 3.8 shows the results from May 2012 to Apr 2014, corresponding to the timewhen the FerryBox measurements are available. The 3 panels from the top to the bot-tom show O2 concentration, volume flux, and O2 flux respectively. O2 is always highestin the Fraser River. It peaks in January and varies seasonally from 6.78 ml·l−1 to 9.91ml·l−1; in SoG upper and lower layer, O2 concentrations also vary seasonally from 4.55ml·l−1 to 6.58 ml·l−1 and from 3.11 ml·l−1 to 4.88 ml·l−1 respectively, but unlike inthe Fraser River they peak in April instead of January. This is because in SoG the O2peak is caused by the strong spring bloom near the surface and a renewal process atdepth, while in Fraser River it is caused by the variation in solubility due to seasonaltemperature fluctuation. The volume fluxes, as stated before, vary both seasonally andinterannually. The total advective flux O2adv, which is plotted in grey line, is the sumof the 3 separate terms in Eq 3.31, is relatively stable through the 2 years span, rangesfrom −0.77 gC·m−2day−1 to −0.40 gC·m−2day−1. Negative values mean that the netflux always transport O2 out of the surface SoG. The estuarine outflow is the largestterm, but is partially compensated by river inflow and upwelling.3.3 Discussion3.3.1 Sensitivity to separation depthThe separation depth hu =50 m, which is the depth that separates the surface out flowfrom the deep inflow, is adopted from Li et al. (1999) and was also used by Pawlowiczet al. (2007). The choice of 50 m as separation depth is consistent with that of thebudget equation itself (Eq 2.4). In this section, we show that the estimated volumetransport is not sensitive to separation depth, thus the choice of separation depth canbe arbitrary to some extent in this work.In previous studies, Riche (2011) used 30 m as the separation depth in the inversemodel, while in other box models (Li et al., 1999, 2000; Pawlowicz et al., 2007) hu isset as 50 m. The choice of hu differs because of the basic natures of different types ofmodel. In an inverse model, the accuracy relies mostly on the accuracy of the in-situmeasurements, which in this case is the vertically averaged salinity in SoG. Because theupper layer is much thinner in SoG, hu has to be chosen carefully to avoid includingtoo much water from the lower layer, which can dramatically change the averages; thelower layer average is not as sensitive to hu due to the great thickness. Hence, in aninverse model, the separation depth should be shallower. On the other hand, for aforward model as we used here, it is a very different situation.A forward model should be stable so that there won’t be sharp increases or decreasesthat will cause the model to break. In the case of our box model, the 6 governing equa-tions should be evenly weighted so that no equation has a particularly large or small453.3. DiscussionMay Jul Sep Nov 2013 Mar May Jul Sep Nov 14 Mar May Jul Sep24681012DO Concentration [ml/l]  O2gu O2gl O2fMay Jul Sep Nov 2013 Mar May Jul Sep Nov 14 Mar May Jul Sep02468 x 104Volume Flux [m3 /s]  Qg Qg−F FMay Jul Sep Nov 2013 Mar May Jul Sep Nov 14 Mar May Jul Sep−1012345DO Flux [gCm−2 day−1 ]  QgO2gu (Qg−F)O2gl FO2f O2advFigure 3.8: Upper panel: monthly O2 climatology in SoG upper layer (circle-dashedline), lower layer (square-dashed line), and Fraser River (triangle-dashed line). Middlepanel: Volume fluxes Qg (solid), F (dashed), and Qg − F (dash-dotted). Lower panel:O2 fluxes QgO2gu (solid black), (Qg−F )O2gl (dashed), FO2f (dash-dotted), and O2adv(gray). O2 fluxes are converted into gC·m−2day−1 to link with productivity.463.3. Discussioncoefficient over the others. A small hu will reduce the upper-lower depth ratio λd, whichis an important coefficient in Eq 3.15, 3.17 and 3.19, and thus causes instability andleads to other problems. One solution is to reduce the time step, but it will increasecomputational cost and time; instead we can increase hu within a reasonable range andthus increases λd.The influence of hu on model stability is tested by carrying out a series of testruns with different separation depths. Results show that when the separation depth issmaller than 23 m, the model collapses after a few steps by giving negative salinities.Fig 3.9 shows annual mean salinity in each box with respect to different separationdepths in a series of test runs. When separation depth is greater than 30 m, meansalinities vary gradually with separation depth; when separation depth is smaller than30 m, the salinity increases in all boxes are much sharper except the lower JdFS.Since Sgu and Shu both increase with separation depth, Qg, which is proportional toSgu − Shu, turns out to be not very sensitive to separation depth. Analysis shows thatQg only increases by 1% as separation depth increases from 30 to 100 m. Based onthe analysis above, it is reasonable to assume 30 to 100 m is a safe range of separationdepth. However, it is important that the analysis above is based on the test run, andthe actual river flow varies within a wider range. Hence to prevent further breakdownin the other runs, we choose 50 m over 30 m as the separation depth, and no breakdownhas occurred in any of the model run we have conducted so far.3.3.2 Error estimatesBefore we start this section we first make a couple of assumptions that will rule outsome of the errors: First of all, a few predefined functions and parameters, includingvertical mixing parameters (ωg, ωmh , ωf ), and response time (Tr), are assumed to besteady over at least a few decades. Fluctuations of these parameters are neglectedbecause there are not enough in-situ measurements to give a reliable understanding ofthe possible variations of these parameters. Secondly, systematic and random errors inin-situ measurements are neglected because of the difficulty in detecting such errors.With these 2 assumptions, other errors can be discussed accordingly.For most of the analysis in Section 3.2, spring-neap tidal fluctuation is removedfrom the model output. This is because the spring-neap tide in the box model is apredefined function, and does not replicate either the phase or amplitude of the actualspring-neap tide. The real spring-neap tide is much more complicated, but since alltidal signals are periodic, it is safe to assume that the long term net contribution ofspring-neap tide can be neglected by averaging. Spring-neap tide contributes to thevolume flux of estuarine circulation in a different way: it controls the vertical mixingin HS, without which the mixing in HS will be damped and model results biased; Thuswe use a pseudo-tidal signal to simulate this process and remove it later to reduce theerrors. Since the spring-neap tidal cycle in HS is not fully investigated at present, it473.3. Discussion20 30 40 50 60 70 80 90 10028293031323334Separation Depth [m]Salinity [g/kg]  Sgu Sgl Shu Shl Sju SjlFigure 3.9: Mean salinity in each box with respect to the separation depth in the testrun. The model is not convergent with a separation depth smaller than 23 m. In theupper boxes, salinity mostly increases with separation depth while in the lower boxessalinity decreases with separation depth with one exception from 23 m to 30 m.483.3. Discussionis possible that the mixing parameter of HS R4 is biased; however, its influence onthe long-term average transport should be minimal due to the periodic nature of tidaltransport. Sensitivity tests show that when the mixing parameter R4 is doubled, theamplitude of spring-neap variation in Qg and Qf increases by approximately 80%, whilethe long-term transport only varies by approximately 5%. Although the spring-neaptidal flux does not have great contribution to the long-term transport, it might beable to explain the wide range of salinity in HS upper layer, where the vertical mixingassociated with spring-neap tide is strongest (Fig 3.5); On the other hand, the ferrymeasured O2 sometimes shows periodic variations with a period of a couple of weeks,which may be or may be not linked to tidal transport. Another possible explanation forthe biweekly signal in O2 is that it is the period of a full bloom cycle, but no evidencesupports either of the hypothesis. Without further investigation of the tidal transport inthe system, the direct influence of spring-neap tide on O2 transport will remain hidden.49Chapter 4Air-sea Gas FluxAir-sea gas exchange is critical in the study of gas budgets and the biogeochemicalcycling of climate and weather. A major component of the greenhouse gases, CO2is of particular interest for atmospheric sciences, and the absorption of excess atmo-spheric CO2 through air-sea exchange is a significant contributor to the mitigation ofthe greenhouse effect (Olsen et al., 2005; McGillis and Wanninkhof, 2006; Wanninkhofet al., 2009; Mørk et al., 2014). Other studies focus on the air-sea flux of dimethyl-sulfide (DMS), due to its importance for climate and atmospheric radiative transfer(Miller et al., 2009; Bell et al., 2013; Fairall et al., 2011). Although the air-sea O2 fluxis not as thoroughly investigated as these gases, it is critical for estimating O2 budgetsin coastal regions, where O2 concentration varies seasonally between over-saturatedand under-saturated conditions. Hence, it will be necessary for this thesis that wesummarize and compare different methods for the calculation of air-sea gas fluxes andfind the most appropriate one for SoG.Recent studies of air-sea gas exchange mainly focus on 2 separate approaches:For environmental applications, a series of studies has been carried out using directmeasurements of air-sea gas exchange rates to form simple empirical parametrizations(Wanninkhof, 1992; McGillis et al., 2001; Nightingale et al., 2000). These parametriza-tions link gas transfer to wind speed, but the accuracy is not known because of theuncertainties in the form of the relationship between gas transfer and wind speed, andthe question of whether wind speed alone can adequately quantify air-sea gas exchange.For example, most of the experiments failed to take the sea state into consideration, aswell as other variables like seawater temperature, salinity, air temperature, air pressure,humidity, etc. Topography may also have some influence on gas transfer in coastal ar-eas, since it affects fetch and hence sea state. To include the contribution of the factorsabove, the traditional parametrization approach is modified to combine with theoriesof basic physics such as turbulence and molecular diffusive activity (Liu et al., 1979;Fairall et al., 1996a,b, 2000, 2003, 2011; Hare et al., 2004; Liss, 1983; Woolf, 2005).This approach, which is also based on parametrization, with most of the parametersredefined and estimated using even more sophisticated and elegant parametrizations,is called bulk parametrization.This chapter is organized as follows. In section 4.1, the basic theories and settingsof bulk parametrization are described. In section 4.2, air-sea gas flux on the ferry trackis calculated and the results are presented. In section 4.3, the influences of stratificationon gas flux is discussed in more detail.504.1. Bulk parametrization of air-sea gas transferLiss and Merlivat [1986] Vt = 0.17 · U · (Sc/600)−2/3, U ≤ 3.6 m·s−1Vt = (U − 3.4) · 2.8 · (Sc/600)−0.5, 3.6 < U ≤ 13 m·s−1Vt = (U − 8.4) · 5.9 · (Sc/600)−0.5, U > 13 m·s−1Nightingale et al. [2000] Vt = (0.333 · U + 0.222 · U2) · (Sc/600)−0.5Wanninkhof [1992] Vt = 0.31 · U2 · (Sc/660)−0.5Wanninkhof and McGillis [1999] Vt = 0.0283 · U3 · (Sc/660)−0.5Table 4.1: Different parametrization of transfer velocity given in cm·hr−1 as a functionof 10 m wind speed U10 in m·s−1 and Schmidt Number.4.1 Bulk parametrization of air-sea gas transferThe gas flux Ft through the air-sea interface is most commonly described with a bulkrelationshipFt = Vt∆X (4.1)where Vt is the transfer velocity and ∆X the effective air-sea concentration difference.In the empirical approach, Vt is usually parametrized as a polynomial function of windspeed combined with a power function of normalized Schmidt NumberVt =N∑n=1αnUn10 × (Sc/Scref )k (4.2)where U10 is the wind speed at 10 m, and Sc is Schmidt Number defined as the ratioof viscosity (ν) and diffusivity (D) of a specific gas in seawater Sc = νD . αn and kare constants that are determined by data fitting. N is the maximum power, whichis usually no more than 3; Scref is a reference Schmidt Number, which is usually 600or 660, the Schmidt Number for CO2 in 20 ◦C water with salinity of 0 and 30 g·kg−1,respectively. If the wind speed measurements are taken at a height other than 10 m(as is often the case), these measurements are converted to those at 10 m by assuminga logarithmic wind profile from the sea surface. Sarmiento and Gruber (2006) summa-rized fittings from 4 different studies, which are listed in table 4.1.These parametrizations work well for estimating total air-sea gas transfer over globalscales. For the study of smaller scales, the environment may be much more compli-cated. Taking the SoG as an example, river discharge creates strong stratification nearthe sea surface and damps the bubble entrainment; human activities, such as sewagedischarge, change the chemical environments of seawater and may enhance or reducethe air-sea exchange rate for some specific gases. To quantify these small scale phe-nomena associated with gas fluxes, the parametrization needs to be broken down into514.1. Bulk parametrization of air-sea gas transfersmaller pieces as well.The bulk parametrization process begins by breaking the transfer velocity into 2termsVt = k + kb (4.3)where k is the basic gas transfer rate from molecular and turbulence diffusion, and kbis the transfer rate enhancement from bubble entrainment. Both are in m·s−1. Gastransfer resistance comes from diffusion through gradients on both air side and waterside of the air-sea interface, thus k can be written as the reciprocal of 4 different typesof bulk resistancek =1R=1Rwm +Rwt + α(Ram +Rat)(4.4)the subscripts w, a, m, t represents water side, air side, molecular sublayer and tur-bulence sublayer, respectively. α is the gas solubility in ml·l−1, which is a functionof seawater temperature Tw in ◦C and salinity S in g·kg−1. In some cases a chemicalenhancement factor  is added into the equationk =1R=1Rwm +Rwt + α(Ram +Rat)(4.5)to account for the reaction between some gases and water, but since oxygen is not anactive gas in seawater, here we take  = 1.Each of the resistance terms can be further broken downRwm =hwSc1/2wu∗w(4.6)Rwt =ln zw/δwu∗wκ(4.7)Ram =haSc1/2au∗a(4.8)Rat =C−1/2d − 5 + (lnScw)/(2κ)u∗a(4.9)wherehw = ΛR1/4rw /φ, ha = ΛR1/4ra /φ (4.10)Details of Eq 4.6 to 4.9 are discussed in Fairall et al. (2000). Since air and waterside resistance are calculated separately, most parameters are estimated for both airand water side accordingly. u∗w and u∗a are water/air side friction velocities, and zw is524.1. Bulk parametrization of air-sea gas transfera reference depth of the water side, here we use the ferry intake depth (2 m). Scw andSca are water/air side Schmidt numbers. Scw is the same as Sc defined above, whileSca is the ratio of viscosity and diffusivity on the air side. κ is the Von Ka´rma´n constant(0.4). Cd = Cd(U∗a, S) is the drag coefficient on the air side, where S =√U210 +W2gis the wind gustiness, Wg is a predefined minimum wind gustiness. Λ is a combina-tion of coefficients and has been determined empirically. Rra is the air side roughnessReynolds number, which is a function of u∗a, roughness depth Z0a, and the kinematicviscosity of air νa. Rrw is the water side roughness Reynolds number, which is set asa constant as surface shape has very little influence on turbulence effect in water. φis an empirical function of the normalized height/depth, here we take it as a constantand combine it with Λ.The bubble enhancement kb, is the additional flux resulting from the transport ofair bubbles to greater depth where they can dissolve. Increased bubble entrainment canbypass the limited exchange rate of the molecular sublayer bottleneck and exchangegases with the deep water directly. Bubble entrainment is mainly caused by wavebreaking in strong winds, therefore it is also parametrized as a function of wind speedin a series of studies (Woolf and Thorpe, 1991; Woolf, 1997, 2005; Woolf et al., 2007;Asher et al., 1996; Asher and Wanninkhof, 1998; Goddijn-Murphy et al., 2011; Zhang,2012). Here we offer one from Woolf (1997)kb = V α−1[1 + (eαDn)−1/f ]−f (4.11)where e = 1.4 × 104 s1/2m−1, f = 1.2, D is the molecular diffusivity in m2s−1for aspecific gas dissolved in seawater, andV = 6.25× 10−3WB m · s−1 (4.12)where WB is the ocean surface whitecap coverage estimated in Monahan (1993)WB = 1.44× 10−11ν−1(U10 − 1.62× 102ν1/3)3 (4.13)with ν is the kinematic viscosity of seawater in m2s−1.So far all the parameters and constants for the calculation of Vt have been intro-duced. One modification that has been made in a recent study by Fairall et al. (2011)is to integrate the bubble enhancement directly into the water side resistance insteadof writing it as in Eq 4.3. The modified Vt becomesVt =1[(Rwm +Rwt)−1 + kb]−1 + α(Ram +Rat)(4.14)The transfer velocity Vt is then solved with Eqs 4.3 to 4.14.Finally, the effective air-sea concentration difference ∆X is534.2. Results∆X = Xwr − αXar(1 + ∆) (4.15)where Xwr and Xar are the bulk concentration of gas in water and air, respectively,and ∆ is a bubble associated enhancement of the gas concentration (Woolf, 1997)∆ ≈ (U10/Ui)2 × 100% (4.16)where Ui is a empirical reference wind speed for a specific gas. Using Eq 4.14 and 4.15,gas flux through the air-sea interface is then calculated with Eq 4.1. Combined withthe cool skin correction in Fairall et al. (1996b), the air-sea gas flux for a specific gasis described as a function of 15 variablesFt = ft(Xwr, Zw, Xar, Ur, Zr, Ta, Zt, H, Zh, Pa, Tw, S,Rs, Rl, Rn) (4.17)where Zw is the depth of DO concentration measurements; Ur, Ta, H are wind speed,air temperature, and relative humidity measured at height Zr, Zt, Zh, respectively;Pa is air pressure; Rs, Rl, Rn are insolation, downwelling longwave radiation, and netshortwave radiation into the water, respectively. Since this study only focuses on O2,here we use CO2 and CO2ar to denote bulk concentration of O2 in seawater and air,Xwr and Xar, respectively. The last 4 inputs are only required for the so-called coolskin correction, which is optional in practice.4.2 ResultsThe analysis is carried out with MATLAB (R2011b), combined with the Air-Sea Tool-box for MATLAB (Pawlowicz et al., 2001). Results show that among all the vari-ables in Eq 4.17, wind speed is the primary factor that controls gas transfer veloc-ity, which is consistent with expectations. To compare bulk parametrization withother parametrizations, O2 transfer velocities calculated from each parametrization asa function of wind speed is shown in Fig 4.1, upper panel. The 2 solid lines are bulkparametrizations without (kb = 0, lower) and with (kb > 0, upper) bubble enhance-ment; dashed lines are 4 other parametrizations summarized in table 4.1. Grey barsare the wind speed histogram from station Sandheads. At very low wind speed, bulkparametrization gives a slightly higher Vt than other parametrizations. As wind speedgets higher, different parametrizations start to diverge quickly. Bulk parametrizationwithout bubble enhancement is the lowest among all 6 parametrizations, with Vt of 32.8cm·hr−1at 20 m·s−1 wind speed. The highest transfer velocity comes from Wanninkhofand McGillis (1999), where Vt is 176.4 cm·hr−1at 20 m·s−1 wind speed, almost twiceas the second highest, Wanninkhof (1992) (96.60 cm·hr−1). Bulk parametrization withbubble enhancement is the third highest, where Vt is 81.1 cm·hr−1at 20 m·s−1 windspeed. Nightingale et al. (2000) & Liss and Merlivat (1986) give smaller transfer veloc-ities than bulk parametrization, but still higher than the bulk parametrization without544.2. Resultsbubble enhancement.The wind histogram shows that wind speed in SoG mainly falls in the interval be-tween 0 m·s−1to 12 m·s−1. Despite of a spike at 2 m·s−1, wind speed generally showsa log-normal distribution, with an average wind speed around 5 m·s−1. Fig 4.1 lowerpanel is the wind record from Sandheads station in 2013. Wind speed does not showmuch seasonal variation, however, high frequency fluctuations are observed throughoutthe year, the amplitude of which is higher in winter, possibly related to winter storms.As another important factor of air-sea gas flux, CO2satr controls the direction ofair-sea gas flux. CO2satr is mainly a function of S and Ts. As shown in Fig 4.2, CO2satrdecreases as Ts or S increases, ranging from 4.7 to 10.2 ml·l−1 from S = 35 g·kg−1,Ts = 25 ◦C to S = 0 g·kg−1, Ts = 0 ◦C. In SoG, CO2satr varies both seasonally anddiurnally due to the variation of Ts and S. To investigate this, in-situ measurementsof S and Ts from 3 different days, Jan 1st, May 1st, and Aug 1st, 2014 are plotted incrosses, circles, and triangles in Fig 4.2 to represent winter, spring, and summer days,respectively. In winter, since the Fraser River discharge is minimal, the variation ofTs and S is not large, and CO2satr only varies by less than 0.5 ml·l−1. In spring, theFraser River brings large quantities of cold and fresh water, and the saturation levelinside the plume can be higher than that out of the plume by 2 ml·l−1. In summer thedifference in CO2satr is not as large but can still exceed 1 ml·l−1.The next step of the analysis is to calculate the gas flux Ft following Eq 4.1. Sincethis section mainly focuses on long term variation, the spatial and short term fluctua-tions of all variables are filtered out through spatial average following Section 2.1.5.Fig 4.3 shows the track averaged Ft in (grey crosses) and out of (black dots) plumeas discussed above. The effective air-sea concentration difference ∆X and wind speedU from the same period are plotted in middle and lower panel, as these are the 2primary factors that control Ft. Ft varies below and above zero and shows strong sea-sonal variation, consistently around -0.5 to 0 gC·m−2day−1in winter but with peakswell above zero during the spring bloom due to higher ∆X during the same period oftime. In summer Ft is slightly above zero, but lower than that during spring bloom.High wind conditions (U > 15 m·s−1) occurred 10 times during the 30 month periodand are marked in triangles. Note that high wind events tend to be related to extremegas flux events, as the transfer velocity increases quickly at high wind speed. Ft insideriver plume varies from -7.5 to 9.3 gC·m−2day−1, reaches minimum on Dec 19, 2012,which corresponds to a high wind speed event of 15.1 m·s−1; maximum Ft inside plumeis found on Apr 29, 2013, which also corresponds to a high wind speed event of 14.7m·s−1. Ft out of river plume ranges from -4.8 to 5.7 gC·m−2day−1, varies similarly asthat inside river plume, but the range of variation is smaller. During spring and sum-mer time, O2 is generally more saturated out of plume, which sometimes causes greatdiscrepancy in ∆X and thus gas flux. The average in and out-of plume Ft difference554.2. Results0 2 4 6 8 10 12 14 16 18 20020406080100120140160180200Fairall et al. [2011]  With Bubble EnhancementFairall et al. [2011] Without Bubble EnhancementLiss & Merlivat [1986]Nightingale [2000]Wanninkhof [1992]Wanninkhof & McGillis [1999]Schmidt # = 1087Wind Speed [m/s]Air−sea Transfer Velocity [cm/hr]2013 Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec05101520Wind Speed [m/s]Figure 4.1: Upper panel: Air-sea gas transfer velocity Vt as a function of windspeed, calculated with bulk parametrization (solid) and other parametrization (dashed).Schmidt Number is 1087, which is a typical Schmidt Number of O2 for SoG. Greybars are the wind speed histogram from meteorology station Sandheads. Lower panel:hourly wind speed record in 2013 from Sandheads station.564.2. ResultsTemperature [°C]Salinity [g/kg]10 9.59 8.5 87.5 76.565.550 5 10 15 20 2505101520253035Figure 4.2: T-S diagram from the ferry measurements of 3 separate days. Contourlines are O2 solubility in ml·l−1as a function of S and Ts. Crosses, circles, and trianglesare S and Ts measurements from the ferry on Jan 1st, May 1st, and Aug 1st, 2014,respectively.574.2.ResultsJul Oct 2013 Apr Jul Oct 14 Apr Jul−10−50510Gas Flux [gCm−2day−1]  PlumeOut of Plume−4−20246∆ X [ml/l]Jul Oct 2013 Apr Jul Oct 14 Apr Jul05101520Wind Speed [m/s]Figure 4.3: Upper panel: O2 flux through air-sea interface from May 2012 to July 2014. The ferry measurements are averagedspatially over every track, both inside Fraser River plume and out of Fraser River plume. Positive indicates a net flux fromthe ocean to the atmosphere. High wind conditions are marked with black triangles. Middle panel: O2 saturation level in% saturation from the same period. Symbols as in the upper panel. Lower panel: Wind speed at Sandheads from the sameperiod. Symbols as in the upper panel. The dashed line is the high wind condition threshold, U10 = 15 m·s−1.584.3. Discussionfrom April to August is 0.18 gC·m−2day−1.To provide some context for my results, the gas flux calculated in this Chapteris compared with another estimate from Riche (2011) and the results are shown inFig 4.4. The estimate of Riche (2011) is based on the measurements of STRATOGEMproject, which also includes O2 measurements from an instrumented ferry. In Riche(2011), gas flux varies from -0.95 to 1.42 gC·m−2day−1, lower in winter around -0.7 to 0gC·m−2day−1, and peaks in March or April around 0.7 to 1.5 with respect to differentyears. During summer, gas flux is relatively constant at around 0.5 gC·m−2day−1, andin autumn it quickly drops from the summer condition to the winter condition.The air-sea gas flux from Riche (2011) is in good agreement with our calculation.In our estimate, Ft varies from -0.78 to 1.23 gC·m−2day−1, lower in winter and peaksin April. Compared to Riche (2011), Ft shows less inter-annual variation, the largestof which is approximately 0.8 gC·m−2day−1; in Riche (2011), the inter-annual varia-tion can be as large as approximately 1.3 gC·m−2day−1. Data from autumn is mostlymissing because of the absence of ferry service, however, it is reasonable to assume atransition phase from summer condition to winter condition in autumn, similar to thatin the upper panel.4.3 Discussion4.3.1 Bulk parametrization vs other parametrizationsThere is an on-going debate about which parametrization, including bulk parametriza-tion and the other parametrizations that has been used in a variety of studies, is the bestone for the calculation of air-sea gas flux. The differences among these parametrizationsmainly come from the different methodologies to get them: Some of them are acquiredby field experiments, i.e., Nightingale et al. (2000); Wanninkhof (1992); Wanninkhofand McGillis (1999); Some are based on laboratory experiments, i.e., Liss and Mer-livat (1986); Other parametrizations, like the bulk parametrization, use a theoreticalapproach to derive gas flux from basic physical processes. Each of the methodologieshas advantages and disadvantages. Field experiments give direct measurement of gasflux and thus should be the most accurate, however, they are tied to specific locations,and the lack of measurements at very high wind speed casts questions of the accuracyat high wind speed. Laboratory experiments can cover a larger range of wind speedand thus may be more accurate at high wind speed, however, the complex sea state,environment and their influences on gas flux cannot be simulated. This is the majorlimitation of lab experiments. Theoretical approaches can take account in the complexsea state with an appropriate choice of parameters, but their accuracy needs to betested by comparing with other approaches.594.3.Discussion−1−0.500.511.5Riche2011 [gCm−2 day−1 ]Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan−1.5−1−0.500.51F t [gCm−2 day−1 ]Figure 4.4: Comparison of air-sea gas flux in SoG from Riche (2011) (top) and this work (bottom). Both signals are filteredwith a window of 30 days.604.3. DiscussionHere we try to verify bulk parametrization by extending the analysis in Fig 4.1.As shown in Table 4.1, most parametrizations treat gas transfer rate Vt as a functionof wind speed U and water side Schmidt Number Scw; In Fig 4.1, we only show therelationship between Vt and U at a specific Scw; In this section, we will discuss theinfluence of Scw as well.Scw varies with respect to seawater temperature T and salinity S, both of which,in SoG, have a strong seasonal cycle, thus Scw also varies seasonally. And since Vtis inversely proportional to Sc2/3w or Sc1/2w , at a fixed wind speed, Vt can vary with arange corresponding to the range of Scw.Using the T and S measurements from theFerryBox, Scw is calculated and plotted in Fig 4.5, lower panel. Scw shows strongseasonal variation as expected, and varies within a range of approximately 500 to 1300.In Fig 4.5 upper panel, similar to Fig 4.1, the 4 parametrizations in Table 4.1 are plot-ted against wind speed, but for each parametrization there are 2 lines representing theupper and lower limits, corresponding to the the lowest Schmidt Number Scw = 500and highest Schmidt Number Scw = 1300, respectively. To compare these parametriza-tions with bulk parametrization, we calculate Vt using bulk parametrization and plotit against wind speed on the same graph. Here we use the subscripts F , N , LM , W ,and WM to represent the parametrization of Fairall et al. (2011), Nightingale et al.(2000), Liss and Merlivat (1986), Wanninkhof (1992), and Wanninkhof and McGillis(1999), respectively.In Fig 4.5 upper panel, when wind speed is greater than 8 m·s−1, VtF mainly fallsinto the area of VtN , showing great agreement between these 2 parametrizations. How-ever, when wind speed falls below 8 m·s−1, all Vts except VtF converge quickly to zeroand the range of variation also decreases quickly, and this is more evident when windspeed falls below 4 m·s−1. On the other hand, VtF still varies within a reasonable rangeeven under very low wind speed. This variation, caused by the influence of sea stateand environment other than surface wind, is a major advantage of bulk parametrizationover other parametrizations, which as well as diffusive processes, are forced to convergeto zero as a condition of regression.Generally speaking, at very low wind speed VtF is higher than the others by ap-proximately 3 to 5 cm·hr−1. This is because even at lower wind speed, gas exchangethrough the air-sea interface still happens because of some certain processes, for exam-ple, diffusion and convection. Since low wind speed condition (<4 m·s−1) is commonin SoG (Fig 4.1), the choice of different parametrization could make a great differencein long-term averaged net gas flux. To make a direct comparison, we calculated gasflux outside Fraser River plume using 4 parametrizations in Table 4.1, and comparedeach of them with bulk parametrization in Fig 4.6. Overall, FtN is in better agreementwith FtF than the other parametrizations, which is in agreement with Fig 4.5, and theabsolute value of FtF tends to be larger when Ft is close to zero, which corresponds tothe higher transfer rate VtF at low wind speed condition. Since Ft is mostly positive614.3. Discussion0 2 4 6 8 10 12 14 16 18 20020406080100120140160180200Wind Speed [m/s]Air−sea Transfer Velocity [cm/hr]  Fairall et al. [2011]Liss & Merlivat [1986]Nightingale [2000]Wanninkhof [1992]Wanninkhof & McGillis [1999]Sep 2013 May Sep 14 May Sep400600800100012001400ScwFigure 4.5: Upper panel: Air-sea gas transfer velocity Vt as a function of wind speedUr. Lower panel: Scw time series calculated with the FerryBox measurements. The 2lines of a specific parametrization is the range of variation with respect to the range ofScw in the lower panel. The black circles are Vt calculated with bulk parametrization.624.3. Discussionduring the 30 months of observation, the average net gas flux calculated with bulkparametrization tends to be more positive as well. Results show that averaged FtFis higher by 0.085, 0.216, 0.049 and 0.223 gC·m−2day−1compared to FtN , FtLM , FtWand FtWM , respectively, approximately 12% to 57% of the averaged FtF itself (0.394gC·m−2day−1).Although the different parametrizations give different results, it is still hard todecide which one is ‘best’. However, the analysis in this section shows that bulkparametrization 1) is in good agreement with at least one of the other parametrizationsthat have been widely used, and 2) shows some new features and advantages over theother parametrizations at low wind speed. Therefore, here we choose bulk parametriza-tion for the estimate of air-sea gas flux in SoG.A more comprehensive way to use all 5 parametrizations is to use one of them asa ‘primary’ choice, and then use all 5 of them to estimate the range of uncertaintiesassociated with different parametrizations. The range of uncertainties should coverall the possible values comes from different parametrizations, and thus is defined asfollow: each time the gas flux is calculated, we use all 5 parametrizations, and choosethe lowest value and highest value as the range of uncertainty. As we calculate throughthe 30 months of research period, a time series of uncertainties is also generated, andthe uncertainties can be considered as a possible range of variation in gas flux. Fol-lowing these steps, the range of uncertainties is calculated and plotted in Fig 4.7. Theupper/lower panel corresponds to gas flux in/out-of river plume, respectively. Blackdashed lines are gas flux calculated using bulk parametrization, and the shaded areasare the corresponding uncertainties. A low-pass filter is applied to remove oscillationswith a period shorter than 2 weeks. The range of uncertainties is positively correlatedwith the absolute value of gas flux. In spring and summer, the absolute gas flux ishigh, and the range of uncertainty is correspondingly higher, reaching a maximum of1.3 gC·m−2day−1, in April 2013; note that this is the filtered value, the actual max-imum can be even higher. In winter, since the absolute value of gas flux is smaller,the range of uncertainty is also lower. This range of uncertainties is also used in laterchapters, as an important segment of the error estimate of the budget equation.Another advantage of bulk parametrization over other parametrizations is that sincethe bubble enhancement is a separate module in the algorithm, it is much easier toadjust the magnitude of bubble enhancement. This gives us the flexibility to analyzethe contribution of bubble to the total gas flux, which is discussed using a simpleconceptual model in the next section.4.3.2 Contribution of bubble plume to gas fluxA quick glance at Fig 4.1 gives a general idea of the contribution of bubble enhancementto gas flux. Bubble enhancement makes a great contribution to the total flux whenwind speed is greater than 10 m·s−1, at a wind speed of 15 m·s−1, bubble enhancement634.3. Discussion−10 −5 0 5−10−505Bulk ParametrizationNightingale [2000]a)Ft [gCm−2day−1]−10 −5 0 5−10−505Bulk ParametrizationLiss & Merlivat [1986]b)−10 −5 0 5−10−505Bulk ParametrizationWanninkhof [1992]c)−10 −5 0 5−10−505Bulk ParametrizationWanninkhof & McGillis [1999]d)Figure 4.6: Comparison of different parametrizations to calculate air-sea gas flux in SoGbetween bulk parametrization and a) Nightingale et al. (2000), b) Liss and Merlivat(1986), c) Wanninkhof (1992), and d) Wanninkhof and McGillis (1999).644.3. DiscussionJul Oct 2013 Apr Jul Oct 14 Apr Jul−2−10123                                                    F t [gCm−2 day−1 ]Jul Oct 2013 Apr Jul Oct 14 Apr Jul−2−10123Figure 4.7: Gas flux in (upper panel) and out of (lower panel) river plume, low-passfiltered with a window of 2 weeks. The black dashed lines are gas flux calculated withbulk parametrization, and the shaded areas are the range of uncertainties determinedby 5 different parametrizations.654.3. Discussioncontributes to approximately 50% of the total flux. However, histogram shows thatwind speed higher than 10 m·s−1only occurs around 5% of the 1 year record in 2013.Thus, bubble enhancement does not contribute greatly to gas flux on a large temporalscale. A rough estimate based on Fig 4.1 shows that on average bubble enhancementonly contributes to 21% of the net gas flux in the SoG.It also should be noted that there are some uncertainties associated with the processof bubble enhancement. First of all, the hourly wind speed records from buoy stationsare not exactly averaged wind speed through the whole hour. ’Hourly wind speed’ isacquired by averaging observation over a short period of time (usually 2 minutes), andthe variation between the end of each measurement and the beginning of next one isneglected. Note that bubble enhancement does not increase linearly with wind speed(Eq 4.13), thus how bubble associated gas flux varies with the wind histogram within1 hour is a complex issue depending on different conditions over the ocean surface.Another problem with bubble enhancement is the effect of stratification. Bub-ble populations are recurrently introduced into the ocean surface by wind-generated,large-scale breaking waves. The effect of bubble entrainment depends on 2 impor-tant factors: 1) wind speed, which determines how many bubbles can be introducedinto seawater and 2) stratification, which influences the depth of bubble entrainment.Strong stratification suppresses vertical exchange below and above pycnocline, thus theentrainment depths of bubbles are limited, and bubble enhancement should be corre-spondingly smaller. A rough estimate shows that strong stratification can suppressbubble enhancement by 19% to 50% (Appendix C). Thus the uncertainty due to bub-ble processes is 4-11% of the net gas flux.4.3.3 High frequency & spatial variation of gas fluxThe seasonal variation of gas flux is relatively stable and does not show much changefrom year to year. In contrary, short term variations are usually more complicatedand are associated with more unpredictable factors. For example, during the suddenspring bloom, the sharp increase in production can greatly increase O2 concentrationand thus gas flux in a specific location, which is hard to predict as the timing of springbloom varies from year to year. Sufficient measurements and knowledge are requiredto understand these fluctuations and the mechanism behind them. Now, with the highresolution measurements from the FerryBox, the short term fluctuations are investi-gated and discussed in this section.The high frequency variation discussed in this section is confined to frequencieswith periods from a few hours to a few days, which mainly include 2 components: (1)Diurnal fluctuation with a period of 24 hours; (2) Fluctuation related to Fraser Riverdischarge with a period of a few days. In addition, since the ferry takes approximately5 hours to finish a round trip, the spatial variation is also reflected in the time series as664.3. Discussionfluctuations with a period of 5 hours. These signals are controlled by different factorsbut also interact with each other, which makes them difficult to identify and isolate.Here we choose 2 representative data pieces - the first 7 days in Jan & Apr, 2014, toillustrate how these factors change air-sea gas flux within a short period of time.As discussed above, the time of spring bloom is a special period of time, as theenvironment in SoG starts to change rapidly with the initiation of the bloom. Toinvestigate how the gas flux varies both temporally and spatially during this specialperiod of time, gas flux Ft (a), ∆X (b), along with 4 other variables (chlorophyll flu-orescence (c), seawater Ts (d), S (e) and turbidity (f)) from the first week in Apr areplotted against time and longitude in Fig 4.3.3. Green lines below every subplot arethe track averaged time series corresponding to the data plotted above, with the rangeof variation plotted in green bars. Wind speed from Sandheads is also plotted in (b) asan indicator of transfer velocity. Chlorophyll is plotted as an indicator for productivity,which is an important source for O2 during the spring bloom; Seawater temperatureand salinity are plotted as an indicator of gas solubility; Turbidity is plotted as anindicator for the river discharge, as the Fraser River carries a large quantity of mudand other sediment materials into the SoG as discharge increases.During the first week in April, turbidity is higher at the east end and in the middleof the track, but decreases sharply around 123.6 ◦W, corresponding to the boundaryof Fraser River plume. Properties inside and outside the plume show great differencesalong the track. ∆X and gas flux show strong temporal and spatial correlation withchlorophyll fluorescence: From Apr 1 to Apr 3, higher chlorophyll fluorescence is ob-served outside the river plume, while after Apr 3 it shifted east towards the plume; ∆Xand gas flux vary accordingly, higher outside the plume from Apr 1 to 3 and shiftedafter Apr 3. On Apr 7, a rise in seawater temperature inside the river plume leads toa decrease in gas solubility, which is reflected as higher ∆X inside the river plume.The length of green bars in (a) is the difference between maximum and minimumgas flux of each track, which mainly quantifies the differences in gas flux in and out-ofriver plume; Similarly, the length of green bars in the other subplots also denotes thein/out-of plume changes of each variable. Here we denote ∆Ftr and ∆Chltr for thealong track differences of gas flux and chlorophyll fluorescence, where the subscript trrepresents the difference for each track. ∆Ftr is small at the beginning of the week,increases through the first 3 days, peaks to greater than 4 gC·m−2day−1on Apr 3 and4, which is a combined effort of higher wind speed and ∆Chltr; after Apr 4 ∆Ftr dropsa lower level due to lower wind speed, but still higher than that before Apr 3. ∆Chltrpeaks on Apr 7, which has positive contribution to ∆Ftr; However, it is not able tocompensate the negative contribution of decreased wind speed to gas flux.A closer look at Fig 4.3.3 suggests that the amplitude of diurnal fluctuation is notas significant as that of in/out-of plume variation during the spring bloom. The di-674.3. Discussion01/Apr/14 02 03 04 05 06 07 08123.2123.4123.6123.8684.3. DiscussionFigure 4.8: Gas flux (a), ∆X (b), chlorophyll fluorescence (c), Ts (d), S (e) andturbidity(f) plotted against time and longitude from Apr 1 to Apr 8, 2014. Greenline below each subplot is the corresponding track averaged data, with the range ofvariation for each track plotted as green bars. the blue line in (b) is wind speed fromSandheads.69

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