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Low frequency residual circulation in Knight Inlet : a fjord of coastal British Columbia Baker, Peter Donald 1992

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LOW FREQUENCY RESIDUAL CIRCULATIONIN KNIGHT INLETA Fjord of Coastal British ColumbiabyPeter Donald BakerDiploma in Electrical Engineering Technology, Ryerson Polytechnical Institute, 1975A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of OceanographyWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAApril, 1992© Peter Baker, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of  OceanographyThe University of British ColumbiaVancouver, CanadaDate ^29 April 92DE-6 (2/88)AbstractMany aspects of the low frequency response of a stratified inlet have not been previouslyobserved due to the lack of simultaneous observations of wind, currents and densitystructure over the entire water column. This thesis describes an experiment that wasspecifically designed to obtain such observations and the statistical analysis of the sub-tidalresponse in Knight Inlet, a stratified, high runoff inlet, during the onset of the freshet.Month long observations of currents, temperature and salinity throughout the watercolumn, both outside and inside the sill, were made during the spring of 1988 and thesummer of 1989. In addition, simultaneous measurements were made of inlet winds andriver runoff data were obtained, giving a complete data set for the analysis of the forcingand the response of the inlet during these time periods.Diurnal and semi-diurnal tidal energy was removed through harmonic analysis and thedominant residual response was found to be due to the wind, with a coherence of greaterthan 0.8 in the near surface and some contributions at depth. A transfer function was thenderived from the cross spectrum and used to estimate the wind driven currents and densityfluctuations throughout the water column. The data records were then dewinded bysubtracting the wind response from the detided records and the remaining residual analyzedwith respect to the vertically nested thermohaline circulations driven by the surfaceestuarine process and deep water renewal. The two circulation cells were found to becoupled through conservation of volume with their characteristics dependent on theavailability of source water for deep water renewal , the river discharge, and wind. Thedynamics of the surface layer was found to be consistent with the work of van derBaaren(1988) who showed that the along inlet balance of forces was between the surfacepressure gradient and the interfacial friction.iiTable Of ContentsAbstract^List of Tables i vList of Figures^Acknowledgements vii1. Introduction ^ 11.1 Coastal Inlets of British Columbia^ 11.2 Knight Inlet 31.3 Thesis Objectives^ 52. Low Frequency Residual Dynamics of Fjords^ 82.1 Definition of the Low Frequency Residual^ 82.2 Energy Sources Driving Inlet Circulation 82.2.1 Estuarine How^ 112.2.2 Density Flows 132.2.3 Wind Driven How 162.2.4 Tidal Forcing^ 202.2.5 Mixing and Diffusion^ 232.3 Previous Observations of the Low Frequency Residual of Inlets^ 263. Experiment Descriptions 353.1 Experiment Design^ 353.1.1 Low Frequency Residual Circulation^ 353.1.2 Verification of Inlet General Circulation Models^ 363.1.3 Modal Response and Dissipation of the Internal Tide 373.2 Instrumentation^ 383.3 Kn88 - Knight Inlet, Spring 1988^ 443.4 Kn89 - Knight Inlet, Summer 1989 493.5 Data Processing^ 533.5.1 Instrument Calibration^ 533.5.2 CTD Bin Averaging 543.5.3 Cyclesonde Outlier Editing 543.5.3 Cyclesonde Time Series Interpolation^ 563.5.4 Current Meter and Anemometer Median Averaging^ 573.5.5 Inter-calibration^ 603.6 Processed Time Series and Spectra^ 644. Analysis and Discussion 804.1 Data Analysis Methodology^ 804.2 29.5 Day Mean Response 844.3 Harmonic Analysis and Computation of the Detided Time Series^ 1034.4 Detided Inlet Response^ 1084.5 Cross Spectra of Wind versus Along Channel Current and Density 1184.6 Wind Driven Response 1314.7 Detided and Dewinded Response^ 1515. Summary and Conclusions 173Bibliography^ 179List of Tables1.1 Charcteristics of some B.C. Fjords 33.1 Kn88/Kn89 Instrument Sampling Strategies 413.2 Basin Salinities at Station 7 for the Kn88 Experiment 484.1 Volume Transport (m3/s) per metre in the Along Channel Direction for 1988 864.2 Volume Transport (m3/s) per metre in the Along Channel Direction for 1989 904.3 Estimated Surface Layer Depth, Layer Densities (as at), and Density Differences (eat) 954.4 Estimated surface Layer Velocities using ICnudsen's Relations 964.5 Tidal Constituents used in Harmonic Analysis 1064.6 Surface and Peak Lag Correlations at depth for Wind and Along Channel Currents 113ivList of Figures1.1 The Coast of British Columbia 21.2 Knight Inlet with Oceanographic Stations 42.1 Energy Paths to the Low Frequency Residual 92.2 Wind Response in Alberni Inlet, Surface Layer Thickness and 2m Along Channel Currents 182.3 Tidal Kinetic Energy calculated from Depth Mean Velocity Squared In Knight Inlet 222.4 Net Current Profiles over the First and Last 25 Hours just Outside the Knight Inlet Sill 282.5 Residual Circulation Profiles from Knight Inlet, July and September 1983 302.6 Layer Velocities for Knight Inlet; 1986 and 1987 343.1 Knight Inlet Profile showing Instrument Moorings 433.2 Kn88 River Runoff and Along Channel Wind for Protection and Tomakstum 453.3 Kn88 Deployment and Mid-Experiment Cruise Ca D Surveys (contours of at) 473.4 ICn89 River Runoff and Wind for Protection (Reconstructed) and Tomakstum 503.5 Kn89 Deployment and Pickup Cruise CID Surveys (contours of at) 523.6 Instrument Preliminary Processing Data Flow 633.7 ICn88 Protection Processed Along Channel Velocity Time Series 653.8 Kn88 Tomakstum Processed Along Channel Velocity Time Series 663.9 Kn88 Protection Processed Density (as at) Time Series 673.10 Kn88 Tomakstum Processed Density (as at) Time Series 683.11 Kn88 Tomakstum Raw Spectra 703.12 ICn88 Protection Raw Spectra 713.13 Kn89 Protection Processed Along Channel Velocity Time Series 733.14 Kn89 Tomakstum Processed Along Channel Velocity Time Series 743.15 Kn89 Protection Processed Density (as at) Time Series 753.16 Kn89 Tomakstum Processed Density (as at) Time Series 763.17 Kn89 Tomakstum Raw Spectra 783.18 Kn89 Protection Raw Spectra 794.1 Residual Analysis Data Flow 834.2 1988 29.5 Day Along Channel Average Velocity (U) and Density (as at) Profiles 854.3 1989 29.5 Day Along Channel Average Velocity (U) and Density (as at) Profiles 884.4 A Three Dimensional Plot of Knight Inlet Sill 914.5 1988 vs 1989 Near Surface Along Channel (U) 29.5 Day Mean Velocity Profiles 934.6 1988 vs 1989 Near Surface Density (as at) Profiles 944.7 Surface Slope(m/m) vs River Discharge for Knight Inlet 994.8 Isobaric Slope Profiles for the 1989 Experiment 1014.9 1988 Along Channel Wind vs Selected Detideid Currents 1094.10 1989 Along Channel Wind vs Selected Detided Currents 1114.11 1988 and 1989 Wind Correlations with Depth 1124.12 1988 Along Channel Wind vs Selected Detided Density (as at) 1164.13 1989 Along Channel Wind vs Selected Detided Density (as at) 1174.14 1988 Protection: Power and Cross Sprectra of Wind vs Along Channel Currents 1224.15 1988 Tomakstum: Power and Cross Sprectra of Wind vs Along Channel Currents 1234.16 1989 Protection: Power and Cross Sprectra of Wind vs Along Channel Currents 1254.17 1989 Tomakstum: Power and Cross Sprectra of Wind vs Along Channel Currents 1264.18 1988 Protection: Power and Cross Sprectra of Wind vs Densities 1274.19 1988 Tomakstum: Power and Cross Sprectra of Wind vs Densities 1284.20 1989 Protection: Power and Cross Sprectra of Wind vs Densities 1294.21 1989 Tomakstum: Power and Cross Sprectra of Wind vs Densities 1304.22 1988 Along Channel Wind vs Selected Wind Driven Currents 1334.23 1989 Along Channel Wind vs Selected Wind Driven Currents 1344.24 1988 Along Channel Wind vs Selected Wind Driven Density Fluctuations (as at) 1364.25 1989 Along Channel Wind vs Selected Wind Driven Density Fluctuations (as at) 137List of Figures(cont'd)4.26 Wind Driven Variance as a Percentage of Total Detided Residual Variance with Depth 1384.27 1988 Protection Wind and Wind Driven Along Channel Velocity Contours 1404.28 1988 Protection Wind and Wind Driven Density Fluctuation Contours 1414.29 1988 Tomakstum Wind and Wind Driven Along Channel Velocity Contours 143430 1988 Tomakstum Wind and Wind Driven Density Fluctuation Contours 144431 1989 Protection Wind and Wind Driven Along Channel Velocity Contours 146432 1989 Protection Wind and Wind Driven Density Fluctuation Contours 147433 1989 Tomakstum Wind and Wind Driven Along Channel Velocity Contours 1494.34 1989 Tomakstum Wind and Wind Driven Density Fluctuation Contours 150435 1988 Along Channel Wind vs Selected Dewinded Currents 152436 1989 Along Channel Wind vs Selected Dewinded Currents 154437 1988 Along Channel Wind vs Selected Dewinded Density (as at) 155438 1989 Along Channel Wind vs Selected Dewinded Density (as at) 156439 1988 River Discharge and Tomakstum Dewinded Along Channel Velocity Contours 1584.40 1988 River Discharge and Tomakstum Dewinded Density Contours 1604.41 1988 River Discharge and Protection Dewinded Along Channel Velocity Contours 1624.42 1988 River Discharge and Protection Dewinded Density Contours 1644.43 1989 River Discharge and Tomakstum Dewinded Along Channel Velocity Contours 1664.44 1989 River Discharge and Tomalcstum Dewinded Density Contours 1674.45 1989 River Discharge and Protection Dewindecl Along Channel Velocity Contours 1694.46 1989 River Discharge and Protection Dewinded Density Contours 171viAcknowledgements"'Did you ever go to a place ... I think it was called Norway?' 'No', saidArthur, 'no I didn't.' 'Pity', said Slartibartfast, 'that was one of mine. Wonan award you know. Lovely crinkly edges.'"-The Hitchhiker's Guide to the Galaxy by Douglas AdamsI'm not sure if this is what first piqued my interest in fjords but the work that this thesisdescribes certainly provided me with plenty of opportunity to explore our own bit ofcrinkly coast. While a lot of long hours and hard work went into completing this project, atthe end of it all I'm still having fun and this is due to the great number of people andorganizations that have lent their support to this research.Foremost I would like to acknowledge the support and patience of my supervisor Dr. StevePond who took a non-physicist under his wing on such a great project. The technical staffat U.B.C. including Denis LaPlante, David Jones, Vivian Lee, Hugh McLean, Pat O'Hara,and Mrigesh Kshatria assisted with the instrumentation and data processing. The officersand crew of the research vessels C.S.S. Tully, C.F.A.V. Endeavour, and C.S.S. Parizeauworked many hours helping us deploy and retrieve moorings. The Institute of OceanSciences and Royal Roads Military College graciously lent us some of their equipment andprovided assistance in its preparation. This research was funded by the National Scienceand Engineering Research Council of Canada under Strategic Grants G1820 and G1821and Operating Grant OGP 0008.301 to Dr. S. Pond.Finally, thanks to snapper@ocgy.ubc.ca for the tireless MIPs and Dr. Susan Allen for thedisk space. Thanks also to my office mates and friends in the Department of Oceanographyfor their infectious energy and enthusiasm. Thanks to Jana, Warren, Anya, Gordon andothers for the great diving, ski trips and hikes.viiChapter 1Introduction1.1 Coastal Inlets of British Columbia:The coast of British Columbia, on the west coast of Canada, is characterised by many inletsand sounds that penetrate deeply into the mountains of the coast range. Heavily glaciatedduring previous ice ages, they exhibit the characteristic 'U' shaped sides, deep basins, andsills of the fjord estuary. Figure 1.1 shows the coast of B. C. and the location of the inletsdiscussed in this thesis. For more information, Thomson(1981) provides a generalintroduction to the oceanography of the B.C. Coast and Pickard and Stanton(1980)compare B.C. fjords to others on the Pacific ocean, including those further north in Alaskaand in the southern hemisphere in Chile and New Zealand.During the fall and winter, the coast receives heavy precipitation in the form of rain at lowerelevations and snow at higher levels. The resulting runoff and melt water leads to astratified water column year round in most inlets. This stratification governs the dynamicsof the inlet circulation, with a surface outflow above the pycnocline that entrains salt wateras it flows seaward and a replenishing inflow below. Tides with ranges of between 4 and 8m, the seasonal availability of replenishment water of sufficient density to penetrate into thedeep basin, and strong winds all modulate this general circulation pattern.Pickard(1961) describes the physical oceanographic features of British Columbia inlets bysuch characteristics as depth profile, bottom sediments, runoff, tides, and estuarinecirculation. Table 1.1 summarizes for comparison the key topographic parameters of someB.C. inlets. The key factors governing their water properties are river runoff which drives13^ 1213°^12° 124°^122°WQueenCharlotteIslandsMIMI 52°QueenCharlotteSoundKnightInletButeInletNorth EastPacific Ocean— 48° N132° W 130°^128°^126°^24°The Coast of British ColumbiaCanada54° N0^100^200Figure 1.1:^The Coast of British Columbia2the estuarine circulation and proximity to the coastal ocean which determines thecharacteristics of the deep basin.Inlet^Leneth^Sill Depth^Max Depth^Ave RunoffIndian Arm 25 km 20m 218m 42 m3/sKnight Inlet^1001cm^Mm^540m^410 m3/sSechelt Inlet 40 km 14 m 300 m 110 m3/sObservatory Inlet^74 km^46 m^530 m^160 m3/sTable 1.1: Characteristics of Some B.C. Fjordsafter Pickard(1961)Pickard(1975) extended the general description to include annual and longer term variabilityof the deep water properties of the southern coastal inlets, noting that there are variations ona one year period at depths to 100 m or more in most inlets.1.2 Knight Inlet:Knight Inlet is on the British Columbia mainland, approximately 300 km north of the cityof Vancouver. It was named by Mr. Broughton, commander of Captain Vancouver'stender Chatham, after Admiral Sir John Knight (1748? - 1831) who was a fellow prisonerduring the American revolution. It is 100 km long from head to mouth, and opens intoQueen Charlotte Strait behind northern Vancouver Island. As shown in Figure 1.2, it iscomposed of a straight near east-west reach from the mouth to Sallie Point, and then makesan abrupt turn into a sinuous reach with a near north-south alignment to the head. Two sillsare present, one at approximately 72 km from the head and with a depth of 68 m and asecond at the mouth with a depth of 64 m. Between them an outer basin exists with amaximum depth of 250 m. The inner basin has its greatest depth (540 m) in the sinuousnorth-south reach just after the bend at Sallie Point. For the purposes of this work the"mouth" of Knight Inlet will be taken as Protection Point in the outer basin and the "sill"will refer to the inner sill. Pickard(1961) classified Knight Inlet as a high runoff inlet and it3p30'107i ow^'53,126°Wp 10'I 1 I 20'40' 30'126°WI '00^50'i , 40'^i 30'MI50'JIMTribunehannelSallie^AdeanePoint I PointIMLullBayOuter—40,Sill^ TornakstumSill^Islan20'I411111---toQueenCharlotteStrait1 40'rotectionPointNOKlinakliniRiver FranklinRiver51°00' NAxe PointMN=I=I40'WI/1..50'WashitaBa00'N..51°Knight Inlet,British ColumbiaKnight Inlet was the site of two experiments. Kn88 which took placein the spring of 1988 and Kn89 which took place in the sununer of1989.Numbered circles show the sites of hydrographic stations used inthe C11) surveys.Crosses show the location of sub-surface moorings consisting of acyclescede and Anderaa anent meters where stafiari depth exceeded200 m.Stars show the location cf both a surface mooring consisting clananemometer and S4 cunent meters positioned from 2 to 12 metres anda sub-surface cyclesonde mooring as described above.Figure 1.2:^Knight Inlet with Oceanographic Stations4is stratified throughout the year. The Klinaldini and Franldin Rivers drain a large area of thecentral coast range and empty into the head of Knight Inlet. These mountains are among thehighest in British Columbia, with Mt. Waddington at 4016 m. As a result the bulk of theprecipitation, which falls during the winter months as snow, creates a large freshet in thelate spring and early summer due to melt water. The Klinaldini, the largest river, has a peakrunoff in June at about 800 m3/sec with a smaller second peak in October due to rainfall.The annual average runoff is about 410 m3/sec with a minimum of about 50 m3/sec.Pickard(1961) describes the summer surface salinity as increasing with distance from thehead. Values ranged from near 0 psu at the river delta to values typical of Queen CharlotteStrait (30 psu) at the mouth. Summer surface temperatures of the fresh water at the head areabout 10° C and range to a mid inlet maximum before falling again to the outside surfacetemperatures at the mouth. Pickard (1975) describes the deep water variability as annualwith maxima of temperature and salinity in the winter. Oxygen levels in the deepest point inthe basin peak in the fall or winter, with values of 3 to 4 m1/1.Tidal action is predominantly semi-diurnal, with a mean range of 4 m and a large range of 6m. A strong spring/neap tide inequality is observed and tends to modulate the inletprocesses at fortnightly frequencies. During the summer sea breezes develop during the daywith weaker land breezes during the night. The up inlet sea breezes tend to be strong due totopographic funnelling from the steep sides of the inlet.1.3 Thesis Objectives:The coastal inlets of British Columbia, including Knight Inlet, have been the object ofmany past studies. Pickard and Rodgers(1959) reported on an early attempt to obtaincurrent meter measurements in Knight inlet, but the limits of available instrumentation5prevented the gathering of large comprehensive data sets and from accurately removingship motion. While on average their results showed a surface outflow with an inflowunderneath consistent with estuarine circulation, the observation period was not longenough to subtract the effects of the wind or investigate the dynamic response of the inletwith respect to the longer period forcing. Farmer(1972), and Farmer and Smith(1978,1980) investigated the dynamics associated with the tidally driven flows over the sill ofKnight Inlet and were primarily interested in the generation and dissipation mechanisms ofthe internal waves. Webb(1985) in his PhD thesis investigated the propagation of theinternal tide around the annular bend in Knight Inlet and as a secondary objective looked atthe subtidal residual and record averages of his data. However, he lacked the necessaryobservations of the wind, and the surface layer above 20 metres to do a comprehensiveanalysis of the residual response.Lacking a comprehensive data set, Freeland(1980) investigated the layer thicknessdynamics of Knight inlet in the light of Long's(1975) model and concluded that the best fitto existing data was the inviscid case, but noted that the concept of a layered model doesnot hold true in the vicinity of the sill where mixing has eroded the pycnoclineconsiderably. The studies of Wetton(1981) and van der Baaren(1988) investigated thesurface layer dynamics using the dynamic height calculated from CTD surveys and anassumed level of no motion to infer the near surface pressure gradient. While their workgives insight into the dynamics of the sub-tidal response of an inlet, the inverse techniquesused suffer inherent uncertainties due to the necessary assumptions and were selectedbecause direct measurements of the response were not available. All previous observationsin inlets either lacked the necessary surface layer measurements or did not constitute asufficiently long time series throughout the water column. They also often lackedsimultaneous observations of the wind and runoff so that a conclusive analysis of the lowfrequency residual could not be performed.6It is the objective of this thesis to first describe experiments that were performed to providea suitable data set for analysis of the low frequency residual and secondly to use statisticalmethods to analyse the low frequency response of an inlet and describe it in terms of theforcing caused by runoff, deep water renewal, and wind. The experiments consisted ofobservations for a period of about a month made throughout the water column of bothvelocity and density fields, both outside and inside the sill. One experiment occurred duringthe spring of 1988 during the onset of the freshet and another during the summer of 1989when the freshet was fully developed. In addition, simultaneous measurements were madeof inlet winds and river runoff data were obtained for both years.The organization of this thesis is as follows; Chapter 2 provides a brief summary of thedynamics important in the low frequency residual response, Chapter 3 describes theexperiments performed and presents a sample of the raw time series and spectra, Chapter 4an analysis of the low frequency residual response of Knight Inlet during theseexperiments, and Chapter 5 contains the summary and conclusions.7Chapter 2Low Frequency Residual Dynamics of Fjords2.1 Definition of the Low Frequency ResidualFor the purposes of this work, the low frequency residual is defined as being that portionof the fjord dynamics with a temporal variability longer than the diurnal tide. Classically,the low frequency residual circulation has been portrayed as estuarine with a surfaceoutflow being driven by river discharge at the head. As the water flows towards the fjordmouth, it entrains salt water thus driving a compensating inflow beneath the surface layer.However the natural case is more complicated, with other forces such as the wind andchanging boundary conditions at the mouth also driving both surface and deep circulationsin the same temporal band. The following section is a summary of the physical processesinvolved in the low frequency residual dynamics of inlet circulation. For a morecomprehensive treatment of the subject of fjord dynamics in general, the reader is directedto Farmer and Freeland(1983) which refers directly to Knight Inlet for many of itsexamples, Burling(1982) which refers to Indian Arm, and Bo Pedersen(1978) whichsummarizes current dynamic theories.2.2 Energy Sources Driving Inlet CirculationIf the water in an inlet is allowed to reach equilibrium it stays at rest unless an energysource is available to do work and move it. However this state is never reached as natureprovides various energy sources to do work and cause motion. The principal energysources are derived from the weather and the tides and their energy paths into the lowfrequency residual circulation are summarized schematically in Figure 2.1.8Deep WaterRenewalForcing Processes^ ResponseWeather^• Sun/Rain^• Estuarine Flow• Wind^— • Wind Driven Flow• Pressure^• Coastal ProcessesTides^• Mixing—O. —01.- • Diffusion iFigure 2.1:^Energy Paths to the Low Frequency Residual9Surface layer flow is established by fresh water input. In British Columbia it is mainlycarried by rivers that empty into the inlet. There is an estuarine circulation with the surfacelayer entraining salt water as it flows out along the inlet and establishing a compensatingflow inwards underneath to maintain salt balance. Winds are topographically confined bythe steep sides of the inlet to the along channel directions. Wind stress forces water motionand builds a surface slope whose pressure gradient balances the applied stress. Howeverwinds are not always persistent and are often highly variable preventing the surface slopefrom coming into a complete balance. Surface outflows can be enhanced, reduced, orreversed by this source. The horizontal pressure gradient established by the surface slopewill be felt throughout the water column until baroclinic compensation can cancel out theeffect in deep water. As this compensation takes some time, there will be some response tothe wind at depth as well. Deep water renewal processes are triggered by the availability ofsalt water at the mouth that is denser than that of the deep basin. Conservation of volumedictates compensating flows above and possibly below the renewal penetration. The resultis that the estuarine circulation and the deep water renewal process may form nested verticalthermohaline structures with the water motion at mid-depths a combination of estuarine saltcompensation flowing inward and volume compensation from deep water renewal flowingoutward.These first three energy sources are coupled to the weather regime. Rain in the winter andearly spring or extended periods of sunny weather can dramatically increase runoff thuschanging the estuarine response. Winds are a function of passing storm fronts or sea/landbreeze regimes set up by persistent good weather. The availability of salt water ofsufficient density to renew the basin deep water is a function of coastal processes thatpromote upwelling and are themselves a function of the winds established by prevailingmeteorological regimes. On the west coast of British Columbia, summers generally bringdominant north westerly winds generated by an Aleutian High. Blowing towards the south10east these winds promote upwelling as the Elcman layer transports water offshore. Theupwelled water being cold and saline is available for renewal of the water in the deep basinsof inlets, such as Knight Inlet, that are closely coupled to the coastal shelf.While semidiumal and diurnal tides have a frequency above the temporal cutoff beingconsidered here, the spring/neap tidal cycle is not and can be expected to modulate theoverall response of the inlet. In addition, inlet topography enhances the non-linearinteraction of the various tidal constituents enhancing components such as the MSf, formedthrough the interaction of the M2 and S2 tidal constituents. Low frequency residualdynamics is coupled to higher frequency phenomena via dissipative mixing. This mixinginfluences the along channel density fields and, through the pressure gradients set up as aresult, generates low frequency motions. The following sections discuss each of theforcing mechanisms introduced above and summarizes the corresponding dynamicaltheory.2.2.1 Estuarine FlowBurling(1982) provides a simple explanation of estuarine circulation extended to fjords.Due to the temperate climate and the storage of winter precipitation as snow at higheraltitudes, the inlets of the British Columbia coast are positive estuaries. Fresh water inputdue to precipitation and runoff is in excess of the evaporation throughout the year. Thisinput of fresh water being more buoyant than the underlying salt water flows out on thesurface. Interfacial shear leads to entrainment of salt water as the upper layer flowsseaward. This progressive entrainment amplifies the surface volume flow and causes ahorizontal pressure force which drives a sub-surface inflow of water to conserve salt andvolume.11The relations that arise from this conservation of volume and salt in a fjord estuary, areoften described as Knudsen's relations and are given as:V. —Vi +R +P-EV.S. V;Siwhere:^V. is the volume flow outward in the surface layerVi is the volume flow inward underneath the surface layerR is the volume flow of fresh water input from riversP is the volume added due to direct precipitationE is the volume loss due to direct evaporationAssuming direct precipitation and evaporation to be negligible in comparison to the riverinput, an assumption true for most B.C. inlets including Knight Inlet, the equations for theflow in the two layers can be derived:U.R Si \H.B H013 k As/^i ^r DO^R S.^= vkv 0 ")^k—AS)HiB HiBwhere:^U. is the flow out in the surface outflow layerUi is the flow in the inflow layerS. is the salinity in the surface outflow layerSi^is the salinity in the inflow layerAS is the salinity difference Si -H. is the depth of the surface outflow layerHi is the depth of the lower inflow layerB^is the breadth of the inletKnudsen's relations assume that the horizontal "diffusion" of salt due to tides andturbulence is small enough to neglect. This is probably a reasonable assumption in fjordestuaries. In the application of these relations practical difficulties do exist however. Forexample the depth of H. and Hi are not well known and noise is present in salinitymeasurements due to wind and tide. Also both U. and Ui are layer averages and so nothingcan be learned about the vertical distribution of velocity within these layers from theapplication of these relations. Note that an increase in river discharge (R) may not bereflected in a larger surface layer velocity (U.). The increase in discharge also lowers thesurface layer salinity stengthening the pycnocline by increasing the salinity difference term12(AS). This response is consistent with the increased stability of the water and a resultingreduced entrainment.2.2.2 Density FlowsExchange of water with the outside is not limited to salt compensation inflow of theestuarine circulation. In the absence of mixing and given time to achieve a steady state, thewater of the deepest part of an inlet basin will be denser than the water above it and thewater column is stabilized by gravity. Over a longer time scale the water properties in thebasin will change. In the limit of no mixing, molecular processes will diffuse salt towardsthe surface where surface flow will carry it seaward. In the more practical case, mixinginduced by wind, interfacial shear and tides produce a much larger 'eddy' diffusion. As aresult of this diffusion, the density in the deep basin is lowered and gravity flows of denserwater from outside the fjord will occur. This inflow will displace the less dense water andlift the isopycnals of the basin, thus raising the potential energy of the water column.Renewal may be to the bottom or to mid-depths depending on the density of the inflowingwater and the density of the water resident in the basin.Density flows are responsible for the oxygen levels that are found in the basin. Bacteria, inthe process of breaking down organic matter from the surface, will slowly consume theavailable oxygen leading to anoxic conditions in the fjord basin if a replenishment sourcewere not available or if downward diffusion is not fast enough. Knight Inlet, as with mostmost inlets on the B.C. coast is renewed with ventilated water from the outside.Pickard(1961) reported that Knight Inlet rarely has an oxygen level below 3 to 4 mill.These values at depths to 500 m or more are higher than in many other B. C. inletssuggesting that some renewal occurs every year in Knight Inlet.13Diffusion is not the only mechanism that controls the renewal of deep basin water.External forcing can change boundary conditions at the mouth and can cause, enhance, orblock these density flows. For example, if the available source water for renewal becomesdenser, it will tend to flow over the sill and penetrate into the basin. Such changes are oftenseasonal and for Knight Inlet, due principally to the upwelling of high salinity water off thewest coast in the summer.Source water must be denser than that in the basin for a density flow to occur. However, ifavailable kinetic energy is sufficient it need not be at or above sill height to penetrate. deYoung and Pond(1988) derived a blocking equation to relate the the blocking height to themean flow and the stratification based on the Bernoulli equation. That is, the kinetic energyof the approaching flow must be at least equal to the energy of the water at the top of the sillin order for penetration to take place. Their blocking equation reduces to:where:^h is the blocking heightu is the velocity of the penetrating flowN is the buoyancy frequency, a function of stratificationEnhanced tidal velocities during spring tides add to the kinetic energy available andtherefore may trigger renewal. However, if the sill is shallow and extended enough, theenhanced tidal velocities of the spring tide may promote mixing that reduces the density ofthe source water and block renewal. The Froude number, the ratio of velocity to the internalwave speed gives a way to parameterize the important factors governing these two effects.If the Froude number is greater than 1, turbulent mixing will occur and blocking will result.If it is less than 1, then the sill depth is great enough or stratification strong enough tosuppress mixing and renewal will be enhanced during spring tides. Knight Inlet has arelatively deep sill, with strong stratification and Farmer and Freeland(1983) calculate the14Froude number at the sill as being much less than 1. Therefore renewal is expected to beenhanced during spring tides. Cases of renewal blocking during spring tides has beenreported by Geyer and Cannon(1982) for Puget Sound, de Young and Pond(1988) forIndian Arm, and Griffin and LeBlond(1990) for renewal in Georgia Strait throughBoundary Pass.Other energy sources can modulate renewal. Strong wind mixing deepens the upper layeras it mixes fresh water down and erodes the pycnocline. If deepened to sill depth, thisprocess can also block renewal. Knight Inlet, with its comparatively deep sills, is unlikelyto experience this type of control. Burling(1982) suggests that external winds may alsocause a response by sloping the surface to balance the wind stress. In order to balancehorizontal pressure gradients, the pycnocline tilts in the opposite direction by a factor ofabout 100 times that of the surface slope and affects the availability of source water at themouth. Klinck et al.(1981) used a two layer numerical model to investigate the interactionof inlet dynamics with a wind driven coastal regime. They found that such forcing canproduce large velocity shears in the fjord thus affecting the eddy diffusion in the basin.de Young and Pond(1988) examined renewal events in Indian Arm and calculated verticaleddy diffusivities based on the change in basin water properties over the time betweenevents. Their results were consistent with those of Gargett and Holloway(1984) thatshowed vertical eddy diffusivity to be dependent function of the buoyancy frequency N,itself a function of the stratification. Gargett and Holloway(1984) proposed that thisrelationship occurred as vertical mixing was principally controlled by internal wave action.However, the exact functions for vertical diffusivity as a function of N varied considerablyfrom that proposed by Gargett and Holloway for energy derived from internal wave fieldsof a single frequency alone. de Young and Pond suggested that the differences may be dueto energy sources other than internal waves contributing to the vertical mixing.152.2.3 Wind Driven FlowOne source of wind predominant in the summer is the diurnal sea/land breeze where solarheating over the land produces an inflow wind during the day and with the more rapidcooling of the land mass at night an outflow wind. The sea breeze is observed to bestronger producing a net up inlet wind flow. Farmer and Freeland(1983) suggest that thisdifference is due to the relative thickness of the air mass in each case, with the sea breezeoccurring over considerable depth but the land breeze restricted to a thinner nocturnalboundary layer heavily influenced by friction. Due to the strength of the pycnocline and thelarge stability found in the surface layer of a high runoff inlet it is unlikely that much of thewind energy would mix down into the deep water, but considerable thickening of thesurface layer might be expected.Wind stress accelerates water movement and, in the inviscid homogeneous case with noboundaries, a steady wind would give a steadily accelerating wind-driven layer. Howeverthis is not the case in fjords where, due to boundaries, a surface pressure gradient builds tocounteract the wind stress and the turbulence generated by shear mixes the momentumdown into the surface layer and gives rise to a larger interfacial friction. Large andPond(1981) give the drag coefficient as observed over the open ocean and thus wind stressmay be calculated from the observed winds as:= paCE,u,„ luwiwhere: -rw is the wind stressPa^is the density of air (1.25 kg/m3)uw is the along channel wind at 10 m above the surfaceCD is the drag coefficient at 10 m and is 1.2 x 10-3 for uw < 12 m/sand varies linearly with ua until 4 x 10-3 for u, =32 m/s, the limit oftheir observations16Direct estimates of the drag coefficient for confined areas such as inlets are limited, but it islikely to behave in a similar fashion. Note that energy input, proportional to -rwluwl,increases as fast as or faster than the cube of the wind speed and that a few extreme windevents may cause a disproportionate amount of mixing especially when stratification isweak in winter.For the case of a steady wind, and the building of a compensating pressure gradientthrough a surface slope, the surface outflow may be reversed until the new balance isachieved. If the wind switches direction to an outflow, the enhanced sea surface slopeadds to that hydraulic head of the fresh water and a strong outflow occurs. Pickard andRodgers (1959) in measuring currents in Knight Inlet observed that the wind appeared toenhance or impede the surface outflow. However winds are rarely steady in an inlet andconstant forcing from the wind is not likely to be the case. Further, studies byWetton(1981) and van der Baaren(1985) indicate that the interfacial friction coefficient isalso modified by wind further implicating the wind's influence on the dynamics of an inlet.Farmer(1972) describes the influence of wind upon the surface layer of Alberni Inlet onVancouver Island. Using cross-spectral analysis, he found that the wind and thelongitudinal current were closely coupled in the diurnal band and used the phase anglesbetween the wind and the current to estimate bulk eddy viscosities for the surface layer (1to 10 cm2/s). He found that strong up inlet winds induce a sudden thickening in the surfacelayer at the inlet head and the disturbance appeared to propagate back down the inlet fromHolm Island to Stamp and Sproat Narrows, suffering an attenuation as it travelled. Thereturn to equilibrium was observed to take several days. He went on to develop a simplefrictional model to explain much of what was observed in the change of surface layerthickness on the basis of measured wind speeds. Figure 2.2 shows the response of17Hohm blandStamp NarrowsSproat NarrowsUP INLETlerDOWN INLETFigure 2.2:^Wind Response in Alberni Inlet, Surface LayerThickness and 2 m Along Channel CurrentsNote Holm Island is closest to the head, Sproat Narrows the closestto the mouth. From Farmer(1972)18both the 2 m current and the surface layer thickness to a strong up inlet wind event inAlberni Inlet.Buckley and Pond (1976), working with data obtained by surface layer drogue tracking inHowe Sound, were able to attribute horizontal surface layer circulation mainly to the effectsof the wind. They found that the time to produce a counter balancing pressure gradient tostrong up inlet winds was in the order of 6 to 7 hours. As it would only take about 1 hourfor sufficient water to flow and produce the necessary surface slope, they surmised that thewind effect must deepen the surface layer as well. In other words, the response timeimportant in the set up process is the baroclinic and not barotropic response time. Weakdensity stratification in the surface layer allowed wind momentum to be rapidly mixeddown to the pycnocline, thus allowing the surface layer to behave as a slab. The strongpycnocline effectively inhibits turbulent mixing as the buoyancy suppression termsdominate over the mechanical production terms. Thus, the interfacial frictional effects donot seem large. (note due to the small size of Howe Sound, say compared with KnightInlet, there is very little salt in the surface layer at the mouth, approximately 4 psu). Whenthe up inlet wind dropped, the pressure gradient due to the surface slope dominated overthe effect of the fresh water input and produced large down inlet surface velocities.Buckley and Pond concluded that the variation due to the wind effects dominated by afactor of 10 over the contributions due to the tide and the river discharge. They also notedthat large lateral shears were present in the surface flows particularly in the top 15 km of theinlet.192.2.4 Tidal ForcingAn inlet mouth is an open boundary allowing the local barotropic tide to drive an exchangeof water between the coastal ocean and the fjord. Knight Inlet is approximately of uniformwidth and extends 72 km inward from the inner sill which has a depth of 68 m. The meantidal range is 4 m and on large tides it is 6 m; the tides are predominantly semi-diurnal. Themagnitudes of the currents produced by this forcing can be calculated from the tidal prismfollowing Burling(1982) as:UT A0( .12)twhere:^UT is the magnitude of the depth averaged tidal currentAo is the inlet's area, the base of the 'tidal prism'h is the height of the 'tidal prism'ao is the cross-sectional area of the inlet moutht^is the time of a half tidal cycle, i.e. to flow in or out, about 6hours or 2.2 x 104 sec for semi-diurnal tidesAt the sill for a 4 m tide, LIT is calculated to be in the order of 19 cm/s. UT is the averagecurrent over the tidal cycle with the peak currents expected to be about 57% larger or about30 cm/s. While the constituent tidal elevations are comparable for both the diurnal andsemidiurnal tides in Knight Inlet, the shorter period of the semidiurnal tides results in afaster current flow.Constrictions at or near the mouth, either a narrowing of the fjord or a sill that reduces thedepth, will lessen a, and therefore increase thr for a fjord with a given surface area. Askinetic energy is proportional to u-r2 , Farmer and Freeland(1983) calculated the along20channel tidal energy from:uT2(x)= (1-511113dx)A dt2where:^A(x) is the local cross sectional areaB(x) is the channel breadthis the tidal heightis the position from the inlet headFor a given inlet size, the kinetic energy of the tidal flow will be larger when the sill is moreconstricted or for a given sill cross sectional area, the inlet area is large. Figure 2.3 showsthe longitudinal distribution of kinetic energy of Knight inlet as determined by Freeland andFarmer. While Knight Inlet's sill is reasonably deep at 68 m, it is one of the larger inlets onthe B.C. coast. It can therefore be expected to be highly energetic near the sill.Sill dynamics are the key generation mechanism for internal waves. The barotropic tideinteracting with the sill tends to lift the density surfaces and generate an internal tide,extracting energy from the barotropic tide and coupling it to the internal response of theinlet. During the spring tide with its higher flow velocities, Freeland and Farmer(1980)found more energy extracted from the barotropic tide and coupled into the internal responsethan during the neap tide. This energy transfer results in a further response at the MSf, thebeat frequency of the M2 and S2 periods in addition to the non-linear interactions mentionedin section 2.2. They argue that because more energy is available during the spring than theneap tides, the low frequency residual circulation will be modulated at the MSf. frequency.Freeland and Farmer(1983) suggest a large MSf component is the signature of an inletwhose mixing is derived from the tide. Thus the higher frequencies and their interactionwith topography are likely to have an effect on the low frequency residual circulation.2110^0 30 40 50 60 70 80 90'640 50 60 70 80 90x km.Figure 2.3: Tidal Kinetic Energy calculated from Depth MeanVelocity Squared in Knight InletAbove: Depth of Knight Inlet as a function of distance from thehead. Below: Depth mean velocity squared, proportional to kineticenergy due to tidal forcing, subject to zero phase change along thechannel. The calculation takes account of cross-sectional area ratherthan the depth alone, but the figure serves to emphasize theimportance of shallow sills, when they are well removed from thehead, as locations for strong tidal mixing. From Farmer andFreeland( 1983)222.2.5 Mixing and DiffusionKnight Inlet is stratified and with a well defined sill geometry. Large tidal velocitiesinteracting with the sill lift the isopycnals and generate an internal tide that propagates awayfrom the sill. If the internal response is large, non-linear terms in the equations of motionmay also be important. Farmer and Smith(1980) observed flow separation, stationary leewaves, and an internal hydraulic jump at the Knight Inlet sill with acoustic observations.Freeland and Farmer(1983) point out that non-linear effects give rise to strong fortnightlycurrents and to tidal harmonics such as the M4 and Mg being present.If the fjord internal structure were two layer, the internal tide would propagate along theinterface in a manner analogous to surface waves and would either dissipate against orreflect from the fjord boundaries. Knight Inlet is not a straight channel and has an almostright angle bend just east of Tomakstum at Sallie Point. The theoretical study ofWebb(1986) and modelling of Stacey and Pond(1992) showed that there is minimalreflection of the internal tide from this bend, with energy propagating along the inlettowards the head. Stacey and Pond(1992) show that the phase change down the inlet is notconstant, however, and undergoes sudden 180 degree changes in phase. This is one of thesignatures of a standing wave indicating that some reflection from the head of the inlet doestake place.A two layer model is an approximation only and the pycnocline is really a sharpening of acontinuous density gradient with depth and the frequency response is restricted by thebuoyancy response at the pycnocline. Therefore, free internal waves are confined to radianfrequencies between the local value of the Coriolis parameter f and the maximum of theBrunt Vaisala. frequency N:23where:N 11-1(-12-d^g2dZi^1-1(Cj-C---.Irt\P CIZN^is the buoyancy frequency (rad/s), a function of fluid stabilityg is the acceleration of gravityP^is the fluid densityz is the depthc^is the speed of soundat^is defined as p(s,t,0) - 1000Pond and Pickard(1983) state that the approximate expression is suitable except in the deepocean. At the low frequency limit, f = 1.13 x 10-4 s-1 for the latitude of Knight Inlet. At thehigh frequency end, Webb(1985) calculated monthly mean N2 profiles based on CID andcyclesonde data and gave a maximum for N of about 0.178 s-1. In Knight Inlet,Pickard(1961) reported internal waves with periods ranging from 1 minute (0.105 s-1) to12 hours (1.405 x 10-4 s-1) corresponding to these limits. Internal tides being forcedKelvin waves are possible despite these limitations and Farmer and Freeland(1983) note thepresence of an internal diurnal tide in Knight Inlet.Freeland and Farmer(1980) calculated the power withdrawn from the barotropic tide inKnight Inlet by using the observed phase difference in the barotropic tide. Because the sillis short compared to the tidal excursion and deep, they estimated that only —3% would belost due to friction with the rest of the energy transferring into the internal processes;internal waves or the non-linear processes documented by Farmer and Smith(1980).Because of the pronounced variation from month to month in the power lost as thestratification changed, they concluded that the energy removed must be coupled into theinternal tide.Stacey (1984) developed a linear model of progressive internal waves to account for energydissipation of the tide over the sill in Observatory Inlet including seasonal variations. Thismodel was applied to Knight Inlet by Stacey(1985) who found that while non-linear sill24processes as documented by Farmer and Smith(1980) are present, these are generally ofless importance than the internal tide as his linear model accurately represented the tides.deYoung and Pond(1989) later estimated the power lost to high frequency internal waves at—2%. Stacey(1985) found that most of the energy removed from the barotropic tide couldbe accounted for in the first two internal modes with the fourth and above internal modescontributing less than the third.The energy partition between the first two modes was found by Stacey(1985) to be highlyvariable and dependent upon the presence of a fresh water surface layer and the densitygradient in the deeper water. The mode 1 energy was correlated with deep water renewalevents with an amplification in the mode 2 response correlated to the freshening of the 5 -10 m surface layer from river runoff in the late spring and early summer. A decrease ininternal energy occurred during the late fall when the stratification of the entire watercolumn was lessened. He concluded that the surface layer may have a major influence onthe circulation in an inlet even when that layer is very thin relative to the total depth of theinlet and is having little apparent influence on the overall velocity field. The presence of thefresh surface layer can have a strong influence on the amount of energy withdrawn fromthe barotropic tide and, because these motions are dissipated internally within the inlet,influence the internal circulation through the resultant mixing.Stacey and Pond(1992) applied a modified form of Dunbar's(1985) XZT model to KnightInlet using data from a cyclesonde near Protection Point to provide boundary conditions.The resultant tidal velocity and density fields compared favourably with the data from threeother cyclesondes positioned along the inlet with the exception of the MS/ densityfluctuations which appeared to be over represented below the surface layer. Thisdiscrepancy was probably due to lack of the mixing of density in the model as such mixingwould tend to reduce this variance. By removing the non-linear terms from the momentum25equations they found that the internal motions could still be well represented, the exceptionsbeing the shallow water constituents, the M4 and MI(3. These results are consistent withthe conclusions of Stacey(1985) and with deYoung and Pond(1989) that little of the totalenergy lost from the barotropic tide is coupled into non-linear or high frequency internalmotions.Webb and Pond(1986b) used cyclesonde data to determine the M2 tide and found by modaldecomposition that only 40% of the power removed from the barotropic tide could beaccounted for at Tomakstum, at least when their observations were made. However this isnot necessarily inconsistent with Stacey(1985) as it is possible that most of the energycould be fed into the internal tide and then be removed while it is close to the sill generationregion. Stacey and Pond(1992) showed with the XZT model that energy flux rises rapidlyto its maximum and then decays a short distance away from the sill. Further, the results ofmodal decomposition are highly dependent upon the modes fitted and, as surface layer datawere not available to Webb and Pond, these results may not be entirely accurate.2.3 Previous Observations of the Low Frequency Residual of InletsEarly attempts to measure inlet circulation directly were restricted by the lack of internallyrecording instrumentation. Measurements had to be done from a ship anchored on station.Costs and the problems of ship movement, made the acquisition of data with sufficientlylong time periods to study the low frequency residual impractical as the energetic highfrequency tidal and wind 'noise' could not be removed from the lower frequencies with anydegree of confidence. Further, the simultaneous acquisition of data from more than onelocation is necessary if a complete analysis of inlet circulation is to be carried out. Withoutthe ability to do direct measurements, Pickard and Trites(1957) attempted to estimate theresidual circulation based on the inlet heat budget.26Pickard and Rodgers(1959) were the first to attempt direct current measurements in KnightInlet. They measured current profiles at the sill and in the neighbourhood of TomalcstumIsland using a combination of Cheasapeake Bay Institute (CBI) drag near the surface andan Ekman Current meter that was lowered to deeper depths. All measurements were donefrom a ship anchored on station, but with only a single anchor.They found that correcting for ship motion was a significant problem particularily at deeperdepths where the motions of the meter relative to the ship were uncertain. They also foundthat wire drag on the CBI drag was significant, and despite an attempt to correct for thisproblem, limited its use to the upper 20 m. Despite these problems, these earlymeasurements were used to describe the mean and the oscillatory currents. An attempt wasmade to explain their features in terms of the estuarine circulation, the winds, and the tides.Twenty five hour averages were used to subtract tidal components. As observations werelabour intensive due to the methods available, only a few days of data were obtained at eachstation.Over the sill and in the absence of significant wind, they found a net outflow in the upperhalf and a net inflow below. They also found the tidal oscillations to be in phase at alldepths. In the presence of an up inlet wind the surface flow reversed, with a net outflowoccurring below the surface layer and the bottom net inflow being maintained. Figure 2.4shows the 25 hour mean current profiles at station 3.5 at the Knight Inlet sill and illustratesthe switch of the dynamics from a two layer to a three layer system. Near TomakstumIsland, both oscillatory and net currents were observed all the way to the bottom with thenet currents showing a three or four layer pattern, rather than the two layer flow previouslythought to exist.27...0.-- UP INLET •--.4-..•. DOWN INLET-40/FIRST 25^•HOURS-.1 ;• 780mSTATION 3 1/2July 6th to 8th, 19562?  0^I 20 CIA/SECC_....."......."'•••.....,..1 ••■ IIN7• •^20tIIIII$60/1I49*NNW •11.1111. MONO•, 7////\LAST 25HOURSFigure 2.4:^Net Current Profiles over the First and Last 25 Hoursjust Outside the Knight Inlet Sill at Station 3.5,6-8 July 1956.From Pickard and Rodgers(1959)28Pickard and Rodgers found significant discrepancies between calculations of net transportand their measurements and suggested these might be due to:1. Ebb flow preferential to mid-channel2. A horizontal eddy with its down-inlet portion in mid-channel3. Interpolation errors due to widely spaced points in the profile4. The mean velocities significantly smaller than the measured mid-channel values5. Artifacts associated with the presence of internal wavesPickard and Rodgers also observed significant cross-channel flow that did not alter 180degrees between the flood and the ebb and had a different direction with depth. Theysuggested that topography might be the cause.Webb(1985) investigated the reflection of energy at the bend in Knight Inlet. In addition heexamined the residual circulation using two months of cyclesonde data from July throughSeptember of 1983. He used harmonic analysis to subtract seven tidal constituents of thethe diurnal and higher frequencies from the observations. This residual was then passedthrough a 24 hour (8 point) running average to smooth the result. A strong MSf component(1 to 5 cm/s) was found, stronger than what could be accounted for by the barotropic tidealone. This result is consistent with the hypothesis of Freeland and Farmer(1980) thatenhanced mixing during spring tides would modify the low frequency residual. In additionto the MSf, there is energy at frequencies between the fortnightly and diurnal bands perhapsassociated with local wind and/or offshore effects. The eight data records from profilingcurrent meters deployed at four stations, Protection Pt., Lull Bay, Tomakstum Island, andAdeane Point (locations are shown in Figure 1.2) during the summer of 1983 wereaveraged over 29.5 days. These residual profiles, shown in Figure 2.5, were found to bereasonably repeatable from month to month. The Protection Point profile showed outflowin the upper part of the water column and an inflow at depth, although the zero crossingwas surprisingly below the pycnocline. At Tomalcstum Island three layer flow is observed29RESIOLAL VELOCITY (CM/SEC)0-5.0^-2.5^0.0^2.5RESIOuRL VELOCITY 1Cm/SEC)-5 0^-2.5^0.0^2. 5^55.0BottomBottom^RES:2U^E'_0:I^CM/SE:-5,0^-2.5 0,0 2.5 502iv Residual longitudinal velocity profiles at Ade,anePoint. Solid line is July 1983, dashed line isSeptember 1983. Positive is up inlet.Residual longitudinal velocity profiles atProtection Point. Solid line is July 1983, dashedline is September 1983. Positive is up inlet.RESIDUAL VELOCITY (CM/SEC)-50 -2.5^0.0^2 5iii Residual longitudinal velocity profile at Lull BayJuly 1983. Positive is up inlet.Residual longitudinal velocity profiles atTomakstum Island. Solid line is July 1983, longdashed line is Tom-S September 1983, shortdashed is Tom-N September 1983. Positive is upinlet.5.0Figure 23:^Residual Circulation Profiles from Knight Inlet, Julyand September 1983.From Webb(1985)30with outflow at the surface and in the deeper water, while at intermediate depths an inflowwas present. At Lull Bay he found an outflow at all depths; this result is not consistent withthe idea of lateral homogeneity, since mass must be conserved. It should be noted thatWebb's data were collected by profiling current meters that due to their sub-surfacemooring arrangement were not able to measure the upper 20 m nor the lower part of thewater column below 190 m. At Tomakstum (depth —340 m) and Adeane (depth —530 m)much of the deep water was not sampled. Further, the surface layer thickness is of order 10m in Knight Inlet and hence essentially missing from the data set. This was not anexperimental oversight but a practical limitation of the current meters available for hisstudy.Wetton(1981) did a short study of the surface layer dynamics of Knight Inlet usingdynamic heights derived from CTD data to estimate the sea surface slope and hence derivethe circulation. In doing so a depth of no motion was assumed. The pressure gradientscalculated show little evidence of a reverse pressure gradient to drive a compensatinginflow, and therefore the depth picked may not have been motionless. The pressuregradient was not found to be balanced by inertial terms and therefore must be balanced byfriction. Wetton suggested that wind may also enter into the balance of forces with the upinlet wind stress acting to modify the pressure gradient so as to increase the surface sloperequired to drive the flow. For one case he estimated the effect of wind to be less than halfthe pressure gradient established by the river runoff.van der Baaren (1988) refined the work of Wetton(1981) and investigated the surface layerdynamics of Knight Inlet using a two layer steady state model derived from integrating the2D momentum equations over each layer. Layer thickness was calculated to achieve thesame potential energy and internal wave speed as observed in CTD data from 1986 and311987. For reference, the vertically integrated momentum equation for the surface layer usedby van der Baaren has the following form:o^0^0au^au^1 ap^1^1ru—dz + rw—dz – – r-- dz – ---ti + —Tv,J ax^J aZ^j-hP aX^P^P-h^-hi^ii^iii^ivwhere:^i and ii:^are the inertial termsiii: is the along channel pressure gradientiv: is the stress due to interfacial frictionv:^is the wind stressSurface slopes were estimated by calculating dynamic heights from the observed densities.By doing a least squares fit through the dynamic heights the isobaric slope was estimated.The Reynold's stress was determined in terms of both wind stress and interfacial stressbetween the upper and lower layers. As all quantities but the coefficient of interfacialfriction are known in the depth integrated equations for the surface layer it could beestimated from the data. Neglecting the wind stress, she found values of order 5 x 10-3 for1987 and 10-2 for 1986 when the runoff was approximately double.van der Baaren found the interface depth was a constant thickness (7 m in 1986 and 3 m in1987) inland of the sill but increased rapidly seaward to the mouth. Her estimates ofsurface layer velocity seem consistent with my observations of average velocity except nearthe mouth, where her results seem to be overly large. Except near the mouth, inertial termsare small compared to the pressure gradient. Therefore the dynamic balance is between thesurface pressure gradient and interfacial friction. At the mouth and sill where the surfacelayer was moving fastest, the two depth integrated inertial terms were almost 5 times largerthan elsewhere; the first term(i) was generally half the second term(ii); their sum is aboutone half of the pressure gradient. However, the two layer model does not accurately depictthe dynamics near the mouth and the velocities calculated from Knudsen's relations are32overly large, probably giving rise to an over estimate of the inertial terms. With no wind,the estimate of the interfacial friction was expected to be low. Wind would increase thepressure gradient and the interfacial stress would then rise to maintain a balance of forces.She found the interfacial friction coefficient increased by about a factor of four when windwas included. A steady state, she concluded, is unlikely to hold unless the wind has beenblowing steadily for some time; thus the interfacial friction is somewhere between hervalues. Figure 2.6 gives van der Baaren's estimates for layer velocities from the interfacedepth for 1986 and 1987. In conclusion she found that the interfacial friction reacts to tides,wind and runoff.3320.0^40.0^60:0^' .2010.0DISTANCE rRom HEAD. IKMI•••5.0r 20.010.0^15.0"5Th 03 ^OS- -TN 7s.c1^10.0^15.0^27:1.0INFLOWING LAYER VELOCITY, (CM/SiESurface layer velocity as a function of distance from the head of for Knight Inlet in 1986 and1987.ii Inflowing layer velocity as a function of inflowing layer thickness for Knight Inlet for 1986.Figure 2.6:^Layer Velocities for Knight Inlet for 1986 and 1987From van der Baaren(1988)34Chapter 3.0Experiment Descriptions3.1 Experiment DesignPrevious data sets of inlet circulation have lacked the detailed observations of the surfacelayer necessary to analyse the low frequency residual response. As a result, newexperiments were designed that would span the entire water column at both the mouth andin the inlet basin. Particular attention was paid to including observations through thesurface layer and the wind forcing. While the key question being investigated was theresidual response, the cost of making such a complex set of measurements dictated thatcare be taken to address other needs as well. These other areas of investigation while notdirectly related to the goals of this thesis were the verification of inlet general circulationmodels and the modal response and dissipation of the internal tide. These later objectivesare discussed briefly here in so much as they impacted the experimental design. I wouldnot like to leave the reader with the impression that the design of these experiments was myown. Steve Pond at the Department of Oceanography, U.B.C. and the supervisor of mywork has amassed a great deal of experience in making observations of this kind, and wasthe chief architect of these experiments. In that the quality of the data is largely due to theinitial experimental design, and that the field program occupied a great deal of my time atU.B.C..it is discussed in detail here.3.1.1 Low Frequency Residual CirculationIn order to fully examine the low frequency (subtidal) residual circulation in a fjord it isnecessary to have high vertical and temporal resolution of both velocity and scalar datathroughout the the water column including the surface layer. Vertical resolution must be35adequate to resolve the anticipated high shears in the surface layer and to gauge the highfrequency responses that are concentrated near the pycnocline. These responses, althoughcontaining relatively high energy levels, will fluctuate over a corresponding smaller verticalscale due to the larger restoring forces in this region. Data are also necessary below thepycnocline, though at a lower spatial and temporal resolution. The dynamics of the surfaceand deep water are intimately tied together through the entrainment and the fact that otherprocesses such as deep water renewal and wind mixing may modulate the response. Datarecords of the relevant forcing must also be obtained for open boundary conditionsincluding the surface meteorology. Observation records must be of sufficient length so thatforcing such as the tides and wind can be analysed and subtracted through statisticalmethods. Previous attempts by Pickard and Rodgers(1959) and Webb(1985) either were ofinsufficient length to subtract interfering signals from other low frequency energy inputs orlacked the direct measurements in the surface layer.3.1.2 Verification of Inlet General Circulation ModelsNumerical models such as those by Dunbar(1985) and Nowak(in prep) have beendeveloped. With further refinement they may be able to predict the water properties,oxygen content, and the movement of contaminants and pollutants in these economicallyand ecologically important bodies of water. In order to refine these models and verify theirusefulness as practical predictive tools, comprehensive data sets of velocity and scalarfields of representative fjords must be collected. Knight Inlet represents a high runoff,highly energetic inlet and one objective of these experiments was to provide data setsadequate for this purpose. Previous data though less comprehensive were gathered byU.B.C. Oceanography for Indian Arm, a low runoff inlet. A similar experiment has alsobeen recently completed in Sechelt Inlet, a small inlet featuring multiple side branches andimportant to the mariculture industry.36For model calculations, the data set must contain the initial conditions for the inlet at thestart of the experiment The density distribution calculated from a CTD survey is requiredas pressure gradients are responsible for establishing the velocity field. The data set mustalso describe the forcing at the mouth where an open boundary couples the local externaloceanographic conditions to the internal dynamics of the inlet. Because wind has beenshown to be important in driving the surface layer dynamics, air temperature and windspeed must be recorded to allow for the inclusion of surface heat flux and wind stress.River runoff establishes a pressure gradient that drives the estuarine circulation and so it toomust be obtained for the duration of the experiment In order for the verification to have areasonable degree of confidence, several key sites must be observed in the interior of theinlet.3.1.3 Modal Response and Dissipation of the Internal TideThe internal response of an inlet is multi-modal. The lack of observations throughout theentire water column, especially in the surface layer and through the pycnocline, hasprevented the definitive determination of the modal composition of the internal response toexternal forcing. While previous work such as that by Stacey(1984, 1985) andWebb(1985) has attempted to resolve this question, limitations in previous current meterdesign and lack of sufficient equipment and ship time haye prevented data being gathered atsufficient resolution and through the entire water column to resolve this questioncompletely. Freeland(1984) speculates that the modal response with the highest energy isthe one with a zero crossing at sill depth. Stacey(1984) observed that modal response inObservatory inlet varied with oceanographic conditions. Considerable work remains to bedone to resolve these questions completely.37Knight Inlet has a near right angle bend at Sallie Point and while the question of whetherthe internal tide was transmitted through or reflected from this bend was answered byWebb(1985), a great deal remains to be explained. For example, the exact nature of thehigh dissipation rate in the straight reach, particularily in the immediate vicinity of the sillstill needs to be explained. Simultaneous measurements outside the sill, just inside the sill,and at the end of the straight reach are necessary to investigate this dissipation and how itaffects the mixing of the surface layer and the more saline water below the pycnocline.3.2 InstrumentationIn order to meet the objectives a great deal of instrumentation of various types had to beemployed. Three stations were picked for investigation; outside the inner sill at ProtectionPoint, just inside the inner sill, and at Tomakstum Island near the end of the straighteast/west reach (see Figure 1.2 for the locations). In 1989 more instrumentation wasavailable and a fourth station at Axe Point in the sinuous north/south reach and nearer thehead of the inlet was also included. Due to the narrowness of the channel and the limitednumber of suitable instruments lateral homogeneity was assumed and a single mooring inthe centre of the channel at each station was used. Each station was composed of a verticalarray of current meters that measured and internally recorded the vector horizontal velocity,and scalar temperature and salinity (through conductivity) fields from which density couldbe calculated to establish a complete picture of the water column. Each experiment lastedapproximately 31 days, the limit of the recording capacity for most of our instrumentationand the minimum required to resolve the longer period monthly tidal constituents byharmonic analysis. All internally recorded data was later retrieved from the instruments atthe end of the experiment and processed on our mainframe and workstations at the U.B.C.Department of Oceanography.38Each station was sampled by a cyclesonde profiling current meter described by van Leer etal.(1974). This unique instrument can be programmed to vertically profile through thewater column by inflating or deflating a helium gas bladder to adjust its buoyancy by about1000 grams. As it moves up or down, it samples at fixed time intervals whichapproximately determines the vertical sampling resolution. A pressure sensor is included sothat the depth of each sample is known and to allow data processing to remove the verticalvelocity component due to profiling from the measured current vector. Currents aremeasured by two savonius rotors on either side of the instrument. The rotors are on ahorizontal axis and have opposite direction of rotation. When the two rotor speeds areaveraged the slight angle of attack sensitivities of the rotors effectively cancel. Savoniusrotors normally have a stall speed of about 2.5 cm/s, however when the cyclesonde isprofiling the rotors are biased by its vertical movement of approximately 10 cm/s. Alternateup and down profiles were set for every three hours with a one minute sampling rate andconsequent vertical sampling resolution of about 4 - 10 metres from 15 to 190 metresdepth. The profiling speed changes as the instrument uses up its gas supply. It falls atabout 10 metres per minute and rises at about 4 metres per minute at the start. By the endof the deployment these rates are reversed. Below the surface layer, this sampling strategywas judged adequate to resolve the important higher frequency tidal constituents such as theM4. When not profiling the cyclesonde was set to sample at least every 5 minutes toprovide an inter-comparison record for instrumentation placed either above or below itsprofiling range. The depth limitation is a function of helium gas storage capacity and thenumber of profiles to be performed. Where depths exceeded 190 metres, Anderaa RCM-4and RCM-7 current meters were deployed at 40 metre intervals and sampling at 10 minuteintervals to the bottom of the water column.At two stations, outside the inner sill at Protection Point and in the straight reach inside theinner sill at Tomakstum Island, an additional surface mooring was deployed nearby with39InterOcean S4 electromagnetic current meters through the surface layer at 2, 4, 6, 9, and12 metres. Vertical resolution was concentrated in the surface layer where there are fewprevious observations and none for longer than two to three days. These current meters,described by Lawson et al.(1983), operate by generating a magnetic field in the watersurrounding the instrument and allowing the motion of conductive sea water to generate avoltage by Faraday's Law of Induction. It is then measured and recorded by an internalmicrocomputer that performs true vector averaging of the velocity data based on samplestaken every half second. These instruments are ideal for surface layer work because theyare immune to the errors induced by rotor pumping and directional alignment with surfacewave trains as documented by Kollstad and Hansen(1985) as well as other authors. Inaddition, they have the ability to be programmed for a variety of burst or continuoussampling strategies and sufficient memory capacity to allow reasonable sampling rates inthe region of the highest buoyancy frequency.Storage capacity and power limitations prevented the sampling strategy employed for theseinstruments from resolving the highest frequencies expected in this area, and so alternateinstruments were set to burst sample to provide an estimate of how much energy might bealiased into the other measurements. Additional storage capacity was added to the currentmeters for the 1989 experiment which allowed the sampling intervals to be halved for thisexperiment Sampling rates were set as shown in table 3.1. The 15 metre cyclesonde dataand the 12 metre S4 data provided the ability to inter-compare instrument performance nearthe bottom of the surface layer. Table 3.1 summarizes the instrument sampling strategiesused for both the 1988 and 1989 experiments.Geodyne toroid buoys were located at the top of each surface mooring and equipped with aJ-Tech or Anderaa meteorological station recording air temperature, wind speed, and winddirection at 15 minute sampling intervals at 4 metres above the water's surface.40Depth^Instrument(metres)Mode Kn88Samplin2 RateKn89SamplinE Rate-4 Anemometer Cont 1 sample / 15 min 1 sample! 15 min2 S4 Cont 2 min avg / 10 min 1 min avg /5 min4 S4 Burst 9, 2 min avg / hr 18,1 min avg / hr6 S4 Cont 2 min avg / 10 min 1 min avg /5 min9 S4 Burst 9,2 min avg / hr 18,1 min avg/hr12 S4 Cont 2 min avg / 10 min 1 min avg / 5 min15 190 Cyclesonde Cont — 1 sample / 3 hr — 1 sample /3 hr230 Anderaa Cont 1 sample! 10 min 1 sample! 10 min270 Anderaa Cont 1 sample! 10 min 1 sample! 10 min310 Anderaa Cont 1 sample! 10 min 1 sample! 10 min350 Anderaa Cont (not used) 1 sample! 10 min390 Anderaa Cont (not used) 1 sample / 10 minTable 3.1:^Kn88/Kn89 Instrument Sampling StrategiesAs a significant objective of these experiments was to investigate the estuarine componentof the low frequency residual, the experiments took place in the spring and summer duringthe melt water freshet. Runoff in Knight inlet is principally controlled by the KlinaldiniRiver and can be expected to double when either heavy rainfall or periods of intense hotweather persist and significantly speed snow melting at higher altitudes. Fresh water runoffwas obtained through stream gauges routinely deployed and maintained by Inland Watersof Environment Canada and provided as daily mean discharges in m3/s.Finally, surveys using a Guildline Model 8705 CTD were done at the start and end of eachexperiment. In addition periodic samples of water were taken with a General Oceanicsrosette both to confirm the CTD readings of Salinity with a Guildline AutoSal laboratorysalinometer and to establish dissolved oxygen levels via Winkler titration. Thesedeployment and pickup cruise surveys provided both the initial and final water propertydistribution and were used as an intermediate standard to perform insitu calibration andinter-calibration of the conductivity and temperature sensors of the other instrumentation.Part way through each experiment, additional CTD surveys from small vessels were41performed as an additional check on instrument performance. These surveys took placeover a number of days and in 1989 were only available to 200 metres.Figure 3.1 shows the oceanographic stations used in the CTD surveys and the location ofthe moorings and associated instrumentation used in the Knight 1988 and 1989experiments distributed along the inlet centre line profile. The time base of all datapresented is expressed in decimal Julian Days, where day 1.0 is midnight December 31st,pacific standard time of year previous to the experiment. This definition makes Julian Day1.5 equivalent to 12:00 a.m. pst January 1st of the year in which the experiment startedand a convenient sequential time base for displaying the observations. The reader iscautioned that other definitions of the Julian Day exist, and this particular time base wasadopted as a convenience for processing and analysis. While wind was recorded using thestandard meteorological convention (that is the direction from which the wind is blowing)all wind data presented in this thesis will be rotated to have a directional orientationconsistent with the currents (that is the direction towards which the current is flowing).42AnchorAnchorFigure 3.1:^Knight Inlet Profile showing Instrument MooringsAxe Point(Kn89 only)Sill TomakstumIslanddo^ProtectionStation #^Point310m15-190m 15-190m100 m40 Km^20 Km60 Km2'1'64..f?'„^-FT 4.^ 9Kral 15-190 mm9, 2m Kn139 15-170m 9‘ 12 m* Surface^+ SubsurfaceExperiment Moorings230m0 270mb 310m233m D 200 m270m b310m 00 m350m OD330m  400 mA GeodyneSudace Buoy,equipped withAnemometer• Inter Ocean S4ElectrornagneticVectorAveragingCurrent MeterSteel FloatCyclesondePmftingCurrent Meterb AndemaRCM4 orRCWCurrent Meter^500 m15-170 mKnee Only233m120 Km 100 Km^80 Km3.3 Kn88 - Knight Inlet, Spring 1988The Kn88 experiment took place in the spring from March 22 (Julian Day 82) throughApril 26 (Julian Day 117) when the inlet was in a low runoff condition (— 50 m3/s) tomoderate runoff caused by the beginning of a freshet due spring melting (-180 m3/s). Theaverage runoff throughout the 35 day experiment was 98 m3/s.At both Protection in 1988 and at Tomakstum in 1989, an examination of the wind recordsindicate that the steep sides of the inlet essentially confine the winds to the along channel(either up or down) direction. The anemometer direction sensor failed at the Tomalcstummooring and therefore the vector wind record was reconstructed using the speed fromTomakstum and the direction from Protection as detailed in section 3.5.5. Weather wasdominated by a succession of storm fronts with their associated winds peaking at about 10m/s with a 2.5 to 3 day period and with a trend towards a net outflow during the first halfof the experiment. The meteorological regime then settled into a clear sunny regime with adominant high pressure starting on Julian Day 101 continuing during the second half with afairly steady up inlet wind with a speed of 5 m/s. The wind fields show a small down inletmean wind at Protection and a small up inlet wind at Tomalcstum in the record average.Figure 3.2 shows the composite time series of the river runoff and the hourly averagedalong channel wind as measured at Protection and as estimated (according to the procedureoutlined in section 3.5.5) at Tomakstum during the Kri88 experiment.Three CTD surveys were completed for the Kn88 experiment; a deployment survey at thestart of the experiment on Julian Day 82, a series of mid-experiment surveys near JulianDay 99, and a pickup survey on Julian Day 115. Unfortunately the CTD data loggermalfunctioned during the pickup cruise and those data were not recoverable. Considerable44m3Is^Kn88: River Discharge and Along Channel Winds^ Mean Discharge . 98 rrn/s . .^ .Retection Mean Wind . -21 cm/s f up inletfl P )1down inletV ON(  kI^ Tlmakstum Mpan Wind -41kcm/s up inlet4‘4 I/ VitIllaIli1\frdown inlet,^ .. .85^90^95^100^105^110^115Julian DayFigure 3.2: Kn88 River Runoff and Along Channel Wind forProtection and Tomakstum20010001000cm/s 0-10001000cm/s 0-100045noise from internal tides existed in the CTD records obtained near the sill, but not near thehead.The results of the first two surveys were used to compute contours of density that providesnapshots of the initial and mid-experiment oceanographic conditions in the inlet. Contoursof at computed for the Kn88 deployment cruise and mid-experiment cruise CTD data areshown in Figure 3.3. Some deep water renewal did indeed take place in the spring of 1988shown as the rise of the 24.0 and 24.1 at isopleths. The availability of water of sufficientdensity to penetrate to these levels can be seen just outside the sill in the mid-experimentsurvey, with sufficient density to penetrate into the interior of the basin. With 24.3 sourcewater outside the sill but not quite at sill depth by the middle of the experiment. Strongerflows due to spring tides may complete the energy requirements required for penetration.While CTD data were not available from the pickup cruise, salinity samples were obtainedat standard depths during both the deployment and pickup cruises. These salinity data arecompared with that of the mid-experiment CTD survey in Table 3.2. The increase ofsalinity with time is consistent with renewal continuing through to the end of theexperiment Dissolved oxygen levels obtained by Winkler titration during the deploymentcruise were typical for Knight Inlet, with 3.26 m1/1 at 500 m in the deepest part of thebasin. These values are consistent with those reported by Pickard(1961). Dissolvedoxygen in the deep water at the mouth was 5.10 m1/1.The deployment cruise surface salinities were 21.03 psu at station 11 near the head, 28.83at station 5 near Tomakstum Island, and 30.04 at station 3 near Protection Point. In thissituation, Knight Inlet appears to fit the classical estuarine case with the steady entrainmentof salt water as surface water proceeds to the mouth.46? DIEM0 m24.0• ^24.1^'24.0.. •^ •. .......^•••^•.. •••... 24.0CID^1988 Deployment and Mid-Experiment Ctd Surveys, Contours of Density (as at)Station #Figure 3.3: Kn88 Experiment CTD Surveys, Contours of Density (as at)Density as cft calculated from temperature, conductivity, and depth plotted as along channelcontours. Solid black contours are the deployment cruise isopleths of crt, dotted are the mid-experiment cruise isopleths.Depth(metres'DeploymentpsuMid-ExperimentPSUPick Uppsu50 30.60 30.69 30.7875 30.65 30.78 30.88100 30.75 30.84 31.02150 30.97 31.18200 31.12 31.19 31.34300 31.31 31.39400 31.35 31.38500 31.36 31.38Table 3.2:^Basin salinities at Station 7 from the Kn88ExperimentValues for the deployment and pickup cruises were obtainedby lab salinometer measurements from salinity samples takenat standard depths. Values for the mid-experiment weretaken from the CTD data at the same depths.Data records from the moored instruments were retrieved intact, with the exception of thedirection sensor of the Tomakstum anemometer mentioned previously and the conductivitysensor on the Tomakstum cyclesonde. Unfortunately the S4 current meter deployed at 12m at this location also lacked a conductivity cell and thus an unfortunate 'blind spot' existsat Tomakstum in the density data records from 12 to 190 m.483.4 Kn89 - Knight Inlet, Summer 1989The Knight 1989 experiment took place during the early summer from June 19 (Julian Day170) through July 25 (Julian Day 206) when the inlet was in a high runoff condition fromabout 400 m3/s to 750 m3/s. Average runoff for the period of the 36 day experiment was569 m3/s and the time series shows that the river can very nearly double its discharge andthen drop back within a period of about 5 days. Figure 3.4 shows a composite time seriesof the river runoff and hourly averaged wind as estimated at Protection (according to theprocedure outlined in section 3.5.5) and as measured at Tomakstum for the Kn89experiment.The anemometer at Protection failed during Kn89 due to a faulty power cable; and as aresult the along channel component of the Protection wind was reconstructed from theTomalcstum record based on the relationship of wind speed at the two locations obtainedfrom the Kn88 experiment and as detailed in section 3.5.5. Except for a brief sunny periodfrom Julian Day 174 through 178, weather at the beginning of the experiment was warmbut overcast. The sunny period is characterised by a switch to a net up inlet wind with avelocity of about 5 m/s and the overcast periods by weaker outflow winds. By Julian Day188 clear skies again predominated through Julian Day 196 and the river runoff respondsaccordingly. At the end of the experiment, weather again cooled and the river runoffdecreased. Record averages for both the Tomakstum and estimated Protection alongchannel winds show a net up inlet wind during the experiment. The large variations inrunoff indicate that at least in the early summer, runoff response to changes in the weathercan be quite rapid as the amount of insolation affects the snow melt. Up inlet winds weregenerally stronger than in 1988 indicating the relative strength of the barometric pressuredifferences driving the summer winds.49m3/s^Kn89: River Discharge and Along Channel Winds.Mean Dischttrge . 569.iriA3/s-^^-^,Prptection Mean Wind . 46 cm/s 1 up inlet(' I IN 4 down inlet---Tomakstum Mean. ^Wind . 72 cm/s. -,^t^up inlet;.^V W\4. down inlet.. ..170^175^180^185^190^195^200^205Julian DayFigure 3.4: Kn89 River Runoff and Wind for Protection(Reconstructed) and Tomakstum1 00050001 000cm/s 0-10001 000cm/s 0- 1 00050Densities computed as at from the 1989 deployment and pickup cruise CTD surveys areshown in Figure 3.5. Deep inner basin densities are slightly lower than in 1988, suggestingthat deep water renewal is taking place later in 1989 or that perhaps vertical eddy diffusionwas greater during the previous winter than the 1987/88 winter. Farmer andFreeland(1983) give an example of how strong winter storms and weak stratification cancause deep mixing and thus vertical eddy diffusion may vary from year to year. Water of adensity sufficient to completely renew the deep water is available at the mouth, at or nearsill level. The pickup cruise Cl'D data shown in Figure 3.5 show a rise in the 24.4 isoplethindicating renewal occurred during the 1989 experiment CTD survey data was sparserfrom the mid-experiment cruise in Kn89 and due to instrument limitations was onlyavailable to 200 m. As a result, these data were used only for inter-calibration of themoored instruments temperature and conductivity sensors. Oxygen levels in the deep basinwere slightly higher in 1989 at 3.33 m1/1. Oxygen levels in the renewal source water weresimilar to 1988 at 5.10 m1/1.Surface water is extremely fresh in 1989, with a surface salinity of 0.29 at station 11 nearthe head, 3.38 at station 5, and only 8.17 psu at station 3 near Protection Point during thedeployment cruise. These extremely low surface salinities are the result of the high runoff.While the river discharge has increased, salt entrainment has actually been reduced andsalinity is still extremely low at the mouth. Increased stability will also limit the effects ofwind induced mixing. The strong pycnocline existing along the inlet may effectivelydecouple the wind from the lower layers, as suggested in Buckley and Pond(1976).Due to instrument malfunctions, data records were incomplete for the Protection and Sillcyclesondes for Kn89 with only about 2 weeks of data retrieved from each. In addition,the Tomakstum cyclesonde skipped a number of profiles at the beginning and the end ofthe deployment.5160 Km 20 Km24.124.124.324.3100 Km^80 Km .....24.4^ 24.424.4 24.4• • •^•....^•.• • • ••••120 Km40 KmCTD^1989 Deployment and Pickup Ctd Surveys, Contours of Density (as at)Station IDepthm24.1100 m200 m^300 m400 m^500 mFigure 3.5: Kn89 Experiment CTD Surveys, Contours of Density (as at)Density as at calculated from temperature, conductivity, and depth plotted as along channelcontours. Solid black contours are the deployment cruise isopleths of at, dotted contours are thepickup cruise isopleths.3.5 Data ProcessingThe data records retrieved from the instruments were at various sampling rates and wererecorded in a variety of proprietary formats particular to each instrument type. Further,most of the instruments recorded data as time series at a particular depth whereas thecyclesondes recorded data as a time series of profiles at irregular depths depending on theirspeed of ascent or descent. In order to render all of the observations into a consistent database suitable for statistical analysis the following processing was performed.3.5.1 Instrument CalibrationPre-experiment lab calibrations provided initial processing coefficients for temperature andconductivity records for all instruments, including the CTD, the cyclesondes, and theAnderaa RCM instruments. Previous experience with these instruments has shown thatunless major repairs have been done to the sensors or circuitry of these instruments, theircalibrations are stable for an extended period of time. However, experience with S4 currentmeters was limited and so the calibration coefficients for these instruments were based on aset of extensive pre and post calibrations. In addition, the velocity zeros of theseinstruments were checked before and after deployment. Direction in all instruments issensed relative to local magnetic north. The calibration routines therefore rotate alldirections to be relative to true north by adding the current local value of the magneticdeviation (24 degrees for Knight Inlet).Further adjustments were made to the temperature and conductivity records of theinstruments according to inter-calibration procedures discussed in section 3.5.6. Brieflythese adjustments consisted of adjusting the conductivity records of the instruments so that53they agreed with the CTD measurements made during the deployment, mid-experiment,and pickup cruises and then ensuring that the calculated density increased with instrumentdepth.3.5.2 CTD Bin AveragingThe Guildline Model 8705 CTD logs conductivity, temperature, and pressure data as theinstrument is lowered and then raised again through the water column. Data is collected intobins with a 10 cm vertical resolution and averaged to improve the estimate of the insituvalue. During the cast, extraneous data are rejected. The bin averaged data are thendecimated to provide an estimate for each I m of depth to 50 m and each 5 m of depththereafter by taking the binned value with the depth desired. While data from both up castsand down casts are available, down cast data were preferentially used as the up cast wasfrequently halted to trigger bottle samples at standard depths. Inlet CTD surveys wereperformed at the beginning, during, and at the end of each experiment. These data providedthe initial and final density fields of each experiment and were also used to inter-calibratethe less accurate temperature and conductivity sensors incorporated in the current meters.The inter-calibration will be discussed in section 3.5.6.3.5.3 Cyclesonde Data Outlier EditingCyclesonde data records are stored as a serial synchronous data stream on magnetic tape.In the process of reading these tapes, data dropouts occasionally occur leading to either anincomplete data record, missing data records or both. As a result, all records are scannedand repaired as necessary. Where the number of bits missing is small, the data record canoften be recovered by shifting the data back into data field alignment. Where records do notconform at all to the specified data format, the data records are deleted and the frame54numbers of sequential records checked to ensure that they increment with time. Thisprocedure ensures that garbled data records do not contaminate the final time series and thatthe time base of the observations can be accurately recovered.Data records are then converted to engineering units by applying polynomial calibrationcoefficients to the integer data fields. The cyclesonde's vertical profiling speed asdetermined from the change in pressure with depth is removed from the resulting speed byvector subtraction. These converted files were then scanned for anomalous values detectedby looking for values inconsistent with the physical oceanography of fjords. For example,scalar data were compared with a fit to a local T/S curves and anomalies (usually inconductivity) were interpolated out after individual examination. Velocity data wereobtained by averaging the port and starboard rotor speeds whenever their rotor counts werewithin 5 cm/s, otherwise the lowest value was taken on the assumption that an overspeedcaused by contact bounce from the reed switch contacts in the rotor sensors had occurred.This appears to be the case in only a few percent of the records. Where excessively lowspeeds were found, values interpolated from the previous and next readings weresubstituted on the assumption that the rotor had stalled.Incomplete profiles at the start and the end of each experiment were trimmed from the finaldata records. Conductivity data near the beginning of each set of observations were alsotrimmed when the cell showed signs of an exponential settling to a consistent value in thedeep water. This behaviour is believed due to air being trapped in the conductivity cellduring deployment and preventing accurate readings from being obtained until it diffusesaway in a period with the order of one to two days.553.5.4 Cyclesonde Time Series InterpolationAs a cyclesonde profiles at approximately 5 to 10 m/min and the sampling rate duringprofiling was set at 1 min, profile data were then interpolated to standard depths with 10 mvertical separation. A cyclesonde measures speed by counting rotor revolutions betweensamples and therefore represents the average velocity magnitude over the part of the watercolumn through which the instrument has travelled. Direction is sampled with scalar data(conductivity, temperature, and pressure) by clamping a magnetic compass needle to apotentiometer. Calibration software rotates all directions from relative to local magneticnorth to true north. The rectangular components of velocity were determined using:u V (sine. + sin On_i)2v VII (COS 0 n + COS 0 n-1 )2where:^u is the east-west component with positive flow from east to westv is the north-south component with positive flow from south to northVn is the speed obtained from the rotor counts at sample nen is the true direction recorded as a spot direction recorded at sample nThese velocity components are then sorted into bins at fixed 10 metre depth intervals, anddata in each bin averaged. Time of the velocity time series is adjusted to reflect theaveraging process in each bin. Scalar data were sorted by depth but not averaged. Toprovide data at a fixed depths, a linear interpolation is then applied between data points toprovide a data point at the requested depth.To provide smoother profiles near the surface where changes with depth are larger, thisprocedure was repeated twice, interpolating at 10 metre intervals starting at 20 metres to thebottom and starting at 15 metres and proceeding to 35 m. The data from the interpolatedprofiles were then sorted by depth into a set of times series spanning all profiles. The56sampling interval of these time series was approximately 3 hours, but timing differencesdue to the asymmetry in the instruments rise and fall rates are present. This procedureproduced a data set from the cyclesondes that was consistent in structure with the timeseries produced from the other current meters and allowing a single processing stream to beused in later analysis.3.5.5 Current Meter and Anemometer Median AveragingS4 current meters vector average all velocity data internally based on samples taken every0.5 seconds. As mentioned in section 3.2, two of the instruments on each mooring at 4 and9 m depth were configured to 'burst' mode and recorded 9 two minute velocity averagescentred on the hour in 1988 and 18 one minute averages every hour centred on the hour in1989. The rest of the instruments were set for 'continuous' mode and recorded a 2 minuteaverage every 10 minutes in 1988 and a 1 minute average every 5 minutes in 1989. Theburst mode instruments were used to investigate possible aliasing of high frequency energyinto the other data records, but although a few spikes that may be associated with the highfrequency phenomena can be seen in the record they do not contribute significantly to thetotal energy of the record.Anderaa current meters record a rotor count that represents an average speed between twosampling periods. Direction is a spot reading recorded at each sampling interval. Thereforethe same method of estimating the rectangular components was applied to these instrumentsas the cyclesondes (section 3.5.4) before data were subject to further processing.In order to reduce the raw time series to hourly estimates, velocity data for one hour centredaround the hour were binned, the higher and lower values removed and the remaining datapoints averaged. For example, the averaging bin for the 'continuous' mode data sampled at5710 minute intervals in 1988 included three samples before the hour, the sample on the hourand three samples after the hour for a total of seven samples. The two highest and twolowest values were rejected and the remaining three samples averaged. For the 'continuous'mode data sampled at 5 minute intervals 1989, a total of thirteen samples were binned, thefour highest and lowest rejected and the remaining five samples were averaged. Burst modedata was treated in a similar manner with the averaging window and rejection count alteredappropriately. This procedure effectively removed any contributions from higher frequencyenergy from the resulting time series.Spikes associated with high frequency energy were more noticeable in the unaveraged spotreadings scalar data of the S4 current meters, but still represented relatively smallcontributions to the record. To reduce the scalar time series of the S4 and Anderra currentmeters to hourly values the averaging process discussed above was applied. The timevalues of the vector velocity and scalar data sets were then adjusted to account for anyshifts due to instrument timing errors based on the correct time at the beginning and the endof the record, although the worst drift was slightly less than a minute.Anemometers were mounted on the Geodyne surface buoy of the S4 current metermoorings at Protection and Tomakstum in both years. The anemometers record a rotorcount that represents an average speed between two sampling periods and a direction that isa spot reading in a manner similar to the Anderaa current meters. Therefore the samemethod of estimating the rectangular components was applied to these instruments as thecyclesondes and Anderaa current meters (section 3.5.4) before data were subject to furtherprocessing. The sampling interval of these instruments was 15 min.The raw wind records show a considerable fluctuating cross channel component. Thedirection of the wind is taken as a spot reading and may not represent an average wind58direction. Therefore at least some of the cross channel component is likely due to buoymotion induced by wind waves and the dampening characteristics of the instrument'sdirectional vane. In order to reduce this directional noise, the raw wind data were subjectedto the same averaging processing used for the current meters, with the averaging windowexpanded to two hours (9 data points) and the three highest and lowest rejected beforeaveraging.As mentioned in sections 3.3 and 3.4, the direction sensor failed at Tomakstum in 1988and the instrument at Protection totally failed in 1989 due to a faulty power cable. At bothProtection in 1988 and Tomakstum in 1989 the average hourly magnitude of the alongchannel component was close to (within 10% at Protection 1988 and 7% at Tomakstum1989) and well correlated with the hourly average speed (0.98 in both cases) indicating thatthe wind field was essentially confined along channel. Therefore the Tomakstum 1988wind record was reconstructed by using the hourly average speed from the Tomakstum andthe hourly average direction from the Protection wind records. In addition, the speedrecords from both anemometers in 1988 were separated into up and down channel groupsbased on the along channel sense of direction at Protection. The correlation between thespeeds was reasonable (0.74 for the up channel and 0.77 for the down channel) and thedown inlet winds were twice as strong at Protection as at Tomakstum, while up inlet windswere just slightly stronger (1.1 x) at Protection. This relationship was then used to estimatethe along channel component of the wind at Protection from the along channel componentof the hourly averaged wind record at Tomakstum for 1989. If one was to assume that thewind was confined completely along channel and that any cross channel component wasdue strictly to residual vane flop caused by buoy motion, this method of estimation of thealong channel components might be in error by at most the 10% difference noted.However, the examination of the actual topography of Knight Inlet reveals the opening ofTribune channel in the proximity of the Protection mooring and the lowering of the59sidewalls at Glendale Cove near Tomakstum. Therefore the difference between themagnitude of the along channel component and the speed is likely some combination ofdirectional 'noise' and true cross channel variability.Time series from the anemometers, S4s, cyclesondes, and Anderaas were then merged intoseparate vector velocity(uv) and property scalar(ts) time series data bases for each station.Because of the averaging the time for the velocity and scalar samples differ.3.5.6 Inter-calibrationVelocities records were compared as a final check on instrument operation. The 12 metreS4 and 230 metre Anderaa current meters agreed well with the 15 metre and 190 metreinterpolated cyclesonde records, respectively. However conductivity sensor drift and tosome extent temperature sensor shifts required that inter-calibration be performed on thescalar data records from the current meters.Inter-calibration of temperature and conductivity records used the in situ values provided bythe CTD surveys as a secondary calibration standard. The goal of this procedure was toensure that the temperature and conductivity records from the current meters matched theobserved density field at the beginning and end of each experiment and were consistentwith density increasing with depth. A check on the CTD accuracy was made by comparingthe salinities with those obtained by lab salinometer from water samples taken at standarddepths. The mean difference was slightly less than 0.01 psu. The CTD casts nearest in timeto the beginning and end of each instruments data record were then used for inter-calibration procedure listed below:1. Temperature records were compared to the CTD and adjusted if necessary.602. Salinity records were compared to the CTD and an equivalent conductivity offsetcomputed from the salinity difference3. An offset and trend in temperature (if necessary) and conductivity was appliedcontinuously along each instruments calibrated data record.4. The corresponding salinity and density from the corrected temperature andconductivity were recomputed.Adjustments were applied to the calibrated but unprocessed data records so that theunaveraged/uninterpolated data would benefit from this procedure for future use. All datarecords were then reprocessed using the Median Averaging technique described in section3.5.5 for S4 and Anderaa records and the interpolation described in section 3.5.4 forcyclesonde profiles. As a final check on the inter-calibration, composite profiles wereextracted from the adjusted data records and plotted with the nearest CTD profiles to ensurethat the adjustments had been applied correctly.S4 temperature records required little adjustment with only three instruments requiringadjustment in 1988 and one in 1989. More of the conductivity records were adjusted as itwas found that the conductivity electrodes appeared to shift characteristics if mishandled.In 1988 two conductivity records were shifted based on CTD data. However CTD datafrom the surface layer are noisy and the large gradients involved make the exactdetermination of the final adjustment difficult As a result the data records of three others .had to be shifted in order to ensure that the resulting density increased with the depth of theinstrument. In 1989 only one such conductivity shift was necessary due to the more carefulhandling of the instruments, whose electrodes have a soft titanium oxide coating.Cyclesonde temperature records were checked and as is normal for these instruments didnot require adjustment to agree with the cm within ± 0.02° C. In 1988, one cyclesonde61required no adjustment in conductivity, one had a failed conductivity sensor, and onerequired a small adjustment. In 1989 three of the four cyclesondes required adjustment totheir conductivity records.All Anderaa current meters were adjusted to the CTD in both years. In 1988 some of theinstruments had a temperature sensor with limited resolution and hence some of theserecords are of limited value. In 1989 the Anderaa current meters at Axe point showed atrend towards slightly lower salinities in the middle of the record with a subsequent rise atthe end. This characteristic was present in three of the instruments spaced between 230 and310 metres. The Axe cyclesonde record did not show any corresponding change at 190metres and it is assumed, because Axe Point is near the head of Knight Inlet, that these midrecord lower salinities must be an artifact of sensor fouling perhaps caused by the rain ofglacial till input by the river.Figure 3.6 shows the data flow for the preliminary processing of the data acquired by theinstruments deployed during the experiments.62• MooringTimeSeriesDataBaseInterpolate MergeOutlier^InterEditing calibrater) CTD_CWINDAS4sIntercalibrateMedian AvgIntercalibrateMedian AvgCyclesonde0 ACMsCalibrationFigure 3.6:^Instrument Preliminary Processing Data Flow3.6 Processed Time Series and SpectraThe time series produced by the preliminary processing were used in the analysis presentedin Chapter 4. Because data are available over the entire water column only at the Protectionand Tomakstum sites, the data from these stations were the focus of this work and arepresentative subset are presented here to describe their general character. It is theserecords that are truly unique in that they include wind and near surface velocity and scalarvalues from the S4 current meters as well as throughout the rest of the water column. Acomplete presentation of the data from all stations may be found in the data report for theKnFS and Kn89 experiments (currently in preparation), available from the Department ofOceanography at the University of British Columbia.Figures 3.7 and 3.8 present the time series of the along channel velocity from theProtection and Tomakstum moorings of the Kn88 experiment for selected depths. Varioustemporal scales can be seen in the processed time series, including diurnal and semi-diurnaltidal components. However, in the the along channel velocity records of the surface layer(2 to 12 m) it can be seen that a component with an approximately 3 day period contributessignificantly to the variance. When visually compared with the wind record, the majorfeatures are similar. This is the influence of the wind on the surface layer and it decreasesrapidly with depth. Deeper in the water column the tidal periods dominate the variance andthe spring/neap tidal cycle can be clearly seen.Figures 3.9 and 3.10 present the density (as at) time series from the Protection andTomakstum moorings. Tidal fluctuations can be seen in the surface layer along with aresponse to the wind characterised by increased densities coincident with up inlet winds.This is due to the wind reversing or slowing the flow of the surface layer and preventingthe outward flow of fresher water. Down inlet winds restore the lower densities as the64Kn88 Protection Wind and U Velocities (cm/s) at Selected DepthsWind -^ t^up inlet1---fili. II   t^iii ii^, i,^'^I ^._^------ ^iiAriq,1.2^56 ^"Illir^191- ^:^■ ,T ^rl --...4 .1.1111.11..yirii^I...7".h^,i .r rillT^goiTi.......a^,911^I .4t• , i,..  ^IT........ .....'i I I^■^1l-^- IIi^■i^A 's .e^It.-7'12FY III^ .^I,:ii,ry I ,^lir!,,,1r ..,1-i^Ii^iii LAA,.^.^,.,...., 1'111"^..^, I I Illrl ,^t^••I^. ,• e ,L^1m^ ",-71 --6^i iTi^.^•"1"v^"^v'''---4^,I,^,^111^r'r ^'^'''^it-^,1^I^I^.^I^I^.. a.. II1A.„„,„Irtr,..iiiiriAlit..rl t v ■76 m ^4.„Itv•TIV,I,VITTIT• lkilia4- ^t--1'.'4-----^,---,-"v^V'T-- ------ ----4alisiala.11114iiiiii.litiAlliliaiiiiiii.^4^^' ^,^IVIIIIIIIIttlf^..... ^- 0I '^l^I'T,i-1isA.L:.4^Iin M, 'III 'll'IIIII f^1^1 '^'^,IIIIIIIIIIrvil II^,,I,^down inlet85^90^95^100^105^110^115Julian DayFigure 3.7:^Kn88 Protection Processed Along Channel VelocityTime Series65Kn88 Tomakstum Wind and U Velocities (cm/s) at Selected DepthsWind ,si t upinlet ^-:-:fWYiid .1 ^.. ^^WI^- - -Tfp.^-^-^...,^,T,.^4 ^..^ t ^i^hji^1 11111 Vli I in!! ^T.;......i^ i,^1.'7'711111"T^irv•,i^ 4^4- ^I.1■^114....11,0*".Ilif^1 Tr^,^....^.. 1^A v.^rr^ r^r^....4 ^4.^12m f i 1^ i^^ i •^ •^■^2^••^.^• •■•11^ill 111 .^•^a• .•-.•••..,...• • I-,^1^■^• •I^' '^t- % A.-v. - 4+1." K • .4...E., f- -,^.^. 1§15 fr I"i"• 1,14^ 4^4---- -------^'' ' "IWIliri,•rf•I'Y.......4^'•,IIIIIIIIT111/,11,T•latiM•••-■^II. 'IP•F• ••^A••••^4^ i• *.•^',If.^/Sill'••VIVIVIWIVIITY1,1111 ^t^•^v^■^i^t^11111^IliWITWI•4•1••••■■•.•^•^•^•^•^• ^•^I.  ^I ^..;^p•4^'lid m1Y•t, '• • ---- i ^I^rdown inlet70-750250-25250-25250-25250-25250-25250-25250-25250-2585^90^95^100^105^110^115Julian DayFigure 3.8: Kn88 Tomakstum Processed Along Channel VelocityTime Series66Kn88 Protection Wind(cm/s) & Sigma-t(kg/m^3) at Selected DepthsWindi^J.^.'^Ai AI^A ai^. ^li AiiiiiiillI ii imp^- 112 m15 m70 m170 m85^90^95^100^105^110^115Julian DayFigure 3.9: Kn88 Protection Processed Density (at) Time SeriesNote that in the above composite plot, at increases upward and eachdivision is 5 kg/m3. The range for each record is from 20 to 25kg/m3.2520,2525252525201500-150067Kn88 Tomakstum Wind(cm/s) & SIgma-t(kg/m^3) at Selected DepthsWindI^:^iuldli^I,^A kg^-^i VI,,RI PT^im•Fr P I ' 91111 ! I2m.^6 m-^ :#9m230 mf t^t^I310 mi^I .85^90^95^100^105^110^115Julian DayFigure 3.10: Kn88 Tomakstum Processed Density (at) Time SeriesNote that in the above composite plot, ot increases upward and eachdivision is 5 kg/m3. The range for each record is from 20 to 25kg/m3 except for the 2 m record which is 15 to 25 kg/m3.252015, 25252525201500-150068surface outflow is re-established. Response in the density field is more pronounced atTomakstum than Protection, because the vertical density gradient in the surface layer isstronger. The surface layer density exhibits an overall trend towards lower values with timeat both stations consistent with the increase in runoff.The raw spectra computed for the wind, 2 m and 12 m (9 m for Tomakstum 1988 as the 12m instrument stopped recording 5 days before the end of the experiment) detrended anddemeaned velocity time series are presented in Figures 3.11 and 3.12. 'Raw spectra' havenot had any band averaging applied. Note that these spectra are plotted in power preservingform so that the area under the curve is proportional to the total variance. The energy in the2 m spectrum at Tomakstum is dominated by time scales of about 3 days at the samefrequencies as the wind energy. The spectrum is consistent with observations byFarmer(1972) and others. At Protection significant energy also exists at these time scales,but the ratio of the current response to the wind is lower (Note that the scales differ as thetidal peaks are higher at Protection). The stronger response at Tomakstum is probably dueto the stronger vertical density gradient at this station confining the wind driven responsecloser to the surface. The 12 m spectrum at Protection and the 9 m spectrum at Tomakstumstill show some energy at these temporal scales, but now the semidiurnal tides dominate.Diurnal energy is present but it may not entirely be tidal as sea/land breezes also contributeenergy in this temporal scale. At Tomakstum peaks can also be seen at a period of 0.25days corresponding to the M4 constituent. Its relative absence at Protection is probably duethe fact that it is enhanced by the non-linear interactions in the region of the sill, betweenthese two moorings.690Freq(cpd) 0.050.10See 20Freq(cpd)0.05Per (days) 20250105.02.51.00.25^0.500.10Per (days) 2080 x 103 ^Windf4(f)cmSee0 ^Freq(cpd)0.05Per (days) 20400f+(f)cm,10^4.0^2.010 4.0 2.00.25 0.50 1.0 2.5 5.0 100.10^0.25^0.5010^4.0^2.0^1.0^0.40^0.20^0.102.5. 00.401.0^5.0^100.20^0.10.0^0.40^0.20^0.109msec 2Kn88: Tomakstum Raw SpectraFigure 3.11: Kn88 Tomakstum Raw SpectraRaw spectra have not had any band averaging applied. Note thatthese spectra are plotted in power preserving form so that the areaunder the curve is proportional to the total variance.70100.10Kn88: Protection Raw SpectraPer (days) 20 10^4.0^2.0 .0^0.40^0.20^0.10Wind.4\43,4A.44.4 1„f 200 x 103f+(f)cmsee,Freq(cpd)0.05Per (days) 201000^0.10^0.25^0.50^1.0^2.5^5.010 4.0^2.0^1.0^0.40^0.202m0 ^Freq(cpd)0.05Per (days) 2010000.10^0.250.40^0.20^0.1012 m- •Freq(cpd)0.05^0.10 0.25 0.50 1.0 2.5 5.0 10Figure 3.12: Kn88 Protection Raw SpectraRaw spectra have not had any band averaging applied. Note thatthese spectra are plotted in power preserving form so that the areaunder the curve is proportional to the total variance.0.50 1.0 2.5 5.0 1010 4.0 2.0 1.0f+(f)cm'2sec071Selected along channel wind and velocity time series for the Kn89 experiment are shown inFigures 3.13 and 3.14. The character of the wind record is considerably different in 1989,with a prominent fortnightly component instead of the 2 to 3 day disturbances seen in1988. Wind influence can be clearly be seen in the surface layer along with a diurnal andsemidiurnal tides. The cyclesonde at Protection stopped profiling approximately half waythrough the Kn89 experiment resulting in the loss of data at 15 m and below for the secondhalf of the experiment. At Tomakstum, the cyclesonde skipped profiles intermittentlybetween Julian Day 173 and 180 and again after Julian Day 193.The corresponding density time series are shown in Figures 3.15 and 3.16. Lowerdensities in the surface layer are observed at both Protection and Tomakstum than in 1988,due to the higher river discharge during the Kn89 experiment. The stronger densitygradient in the surface layer results in a strong wind response in the density field at bothstations. Here the up inlet/down inlet wind regime is of a longer period than in 1988 andthe switch to an up inlet wind regime brings a corresponding raising of surface layerdensity as in 1988. During down inlet winds, the density suddenly lowers and thenpartially recovers after 2 to 3 days (eg: between Julian Day 179 through 185). If the initiallowering of the surface layer density is caused by the outflow driven by the combinedforcing of runoff and the pressure gradient built by the previous up inlet winds, thisrecovery may be explained by the release of the stored 'fresh' water in the head of the inlet.Once this pool of 'fresh' water has been released a thinner surface layer is reestablished.The raw spectra of the wind and surface currents are shown in Figures 3.17 and 3.18. It isto be noted that the 2m semi-diurnal tidal energy at Protection is twice that of 1988. Thischange in energy is probably due to a change in the modal composition of the internal tidalenergy and not a change in the barotropic tidal response which is primarily controlled bytopography. A larger difference is seen in the 2m spectra for Tomakstum. The 198972Kn89 Protection Wind and U Velocities (cm/s) at Selected DepthsWinci   . I&ri I 11up inleti^I^If-^-iA^ r791^ -,,-^w ' ^ii i1 a^.4..J.ii ii,^II^* 1'^1iI..i^I .,^11,•11 ^ij. , ./1^I,^I ii^II,1^1^!^1^.1.1.iiii^1^1.. .1^rri,f^I l' "III" I^. ^r l^" I^I - II1^rrj ^:^. ^a -4 ^ 1^ :^T7i5 - nii 4. down inlet170^175^180^185^190^195^200^205Julian DayFigure 3.13: Kn89 Protection Processed Along Channel VelocityTime Series73Kn89 Tomakstum Wind and U Velocities (cm/s) at Selected Depths1Wind.^ ....  1^t^up inlet.^v14 vtlevteNiif1:*^ii.^L^.,......^y.^11 . I^I^2 i^1  ^Ilr. ^.^.^.^..i.,1,.^.1^.^.111^VA^,w ^.;i.,^ ..i^'1^  1111.1_^_,.-IIlilit.,^1101,"1^' ^' ' ^' ^'^.'^Twill •.. ■^1^-CFI ---• ul- --vpir.ITIvi, 11. I,.... ^-^-^+.•-MAI--.^ i - • - '4'^•• ,r ■ . '^- ' '4^^i  ^ 4^ 4^ 4^ +^ 4^'^-767.61-! AA-0-0A-et- -1,WAAVAAAMMANYINWA"--  - i'1""v--r.4"."`^i-ild ni^4^ 4^i^4 ^4- ^4^ 4-^-24S5 111 ^ '^^. 4-^• i^•^i^..^..^.^.^.,^. .,^,^• • • A^al L^A ii^i i^• A^i A • a^...• '*TIGri;. • • . .^.^.4 down inlet170^175^180^185^190^195^200^205Julian DayFigure 3.14: Kn89 Tomakstum Processed Along Channel VelocityTime Series7500-750250-25250-25250-25250-25250-25250-25250-25250-2574Kn89 Protection Wind(cm/s) & Sigma-t(kg/m^3) at Selected Depths,^ i^ ^: , .^Wind &^iiiiimi^Ihiallital^ha^ir^1,11,11I^1 1 I^AIL^, I^.^/ 1111.44.—^.^./ IA"' ^. 412M!!!!!!!^ilir"^. ,,.^i^I^+ ^I111^I 1^I 1^'II15 m70 m170 rti•^ :^:i^ !170^175^180^185^190^195^200^205Julian DayFigure 3.15: Kn89 Protection Processed Density (as) Time SeriesNote that in the above composite plot, crt increases upward and eachdivision is 5 kg/m3. The range for each record is from 20 to 25kg/m3 except for the 2 m record which is 5 to 20 kg/m3 and the 6 mrecord which is 10 to 25 kg/m3.2015105, 252015252525251500-150075Kn89 Tomaksturn WInd(cm/s) & Sigma-t(kg/m^3) at Selected DepthsAi I i Mu^iLaitiLa ■ Admi^, , Ir rill gym, w - 1^ WIN "2mi  ^ -1^,^1^l'^A1 ^ .„..^i^o.111.1.i.i..6^TrITIP1! ^•14--'^1^i12'1"11 Till^4^.t^4--.^15m^ •70m .•:190 rrf230n1310 ni_.170^175^180^185^190^195^200^205Julian DayFigure 3.16: Kn89 Tomakstum Processed Density (at) Time SeriesNote that in the above composite plot, cyt increases upward and eachdivision is 5 kg/m3. The range for each record is from 20 to 25kg/m3 except for the 2 m record which is 5 to 20 kg/m3 and the 6 mrecord which is 10 to 20 kg/m3.2015105201510,2525252525252015000-150076semidiurnal energy at 2m is approximately 7.5 times that of 1988. However this peak isconsiderably lower at 12 m suggesting this change is also due to the modal composition ofthe internal tide. The examination of the tidal results is not included in this thesis as thefocus is on the lower frequency residuals. Webb and Pond(1986b) have examined the tidesin Knight inlet before and shown that changes in the modal composition do occur. As thedata from these experiments is more complete (in that they include the near surface) the tidalresults will be examined and the results reported elsewhere.The difference in the character of the wind is clearly seen in the wind spectra with the bulkof the energy at the temporal scales of approximately 15 days as previously noted and at 1day. The energy at this latter time scale appears to be due to the sea/land breeze regime setup during periods of better weather. The wind forcing contributes approximately the sameamount to the total energy of the 2 m velocity in both years. An integration over the windband from the 1 cycle per month to 1 cycle per day gives a ratio of 2 m current speed towind speed of approximately 3.8 and 4.1 percent at Protection and 6.1 and 5.5 percent atTomakstum for the 1988 and 1989 experiments respectively. This is in reasonableagreement with Burling(1982) who gives the wind driven current as approximately thewind speed/30. At 12 m the wind influence appears to be negligible at least at the longerperiods and the semidiurnal tides dominate.7741‘:: i).44S*44PIA IOWA A " " ' 'WindKn89: Protection Raw SpectraPer (days) 20^10^4.0^2.0^1.0^0.40^0.20^0.10250 x 103f+(1)2CMsec0Freq(cpd)0.05^0.10^0.25^0.50^.0^2.5^. 0^10Per (days) 20^10^4.0^2.0^.o^0.40^0.20^0.10....I^■1111111111111111111.•...- Alb111111.- Al MIN*111111■ ...... .... AIL .II. .6.^0.10^0.25^0.50^1.0^2.5^5.0^010^4.0^2.0^1.0^0.40^0.20^0.1012m, AA 1 _ 1 ,Freq(cpd)0.05^0.10^0.25^0.50^1.0^2.5^5.0^10Figure 3.17: Kn89 Protection Raw SpectraRaw spectra have not had any band averaging applied. Note thatthese spectra are plotted in power preserving form so that the areaunder the curve is proportional to the total variance.2000ff(f)an1sec 20Freq(cpd)0.05Per (days) 202500f4(f)cm2sec'078Kn89: Tomakstum Raw Spectra4.0 2.0 1.0 0.4010 0.20 0.10105.01.0 2.50.25 0.500.10105.02.51.00.500.10 0.25• ••Per (days) 20140 x 103Freq(cpd)0.05Per (days) 20300010^4.0^2.0^1.0^0.40^0.20^0 10Windf+(f)cm'2see02msec0Freq(cpd)0.05Per (days) 20 10^4.0^2.0^1.0^0.40^0.20^0.10---;12m,-Ao....iinnelln, na^A 4A^A o c^n CA^1 n^9 c^s n^10400f(f)cm:SeeFreFigure 3.18: Kn89 Tomakstum Raw Spectraunder the curve is proportional to the total variance.Raw spectra have not had any band averaging applied. Note thatthese spectra are plotted in power preserving form so that the area79Chapter 4Analysis and Discussion4.1 Data Analysis MethodologyAs seen in the spectra presented in section 3.6, it appears that wind energy dominates theforcing in the surface layer while the semi-diurnal tides dominate over the rest of the watercolumn. The analysis presented in this chapter examines the major components of the lowfrequency (sub-diurnal) response of an inlet by first examining the monthly mean (29.5day) response and then examining the records using multivariate statistical methods. Thecontributions to the variance that could be statistically attributed to known forcing such asthe tides and the wind were then sequentially removed and the residual response examined.An analysis of the monthly mean response is presented in section 4.2. This method wasused by Webb(1985) to examine cyclesonde data as mean profiles from 20 to 190 m forJuly and September 1983 in Knight Inlet The mean of each time series was calculated over29.5 days as this length is roughly equal to that of the longest tidal constituent (Mm) thatcan be resolved in the time series. It assumes that the wind forcing in this average is alsozero which, as discussed in sections 3.3 and 3.4, is approximately true for bothexperiments. The use of this method allows direct comparison with the vertical structuresof Webb's mean profiles (presented in figure 2.5) and has been expanded to includedensity (as at) as well as along channel currents and near surface data to 2 m. Thestructures were examined for consistency with estuarine circulation forced by river runoffand deep water renewal evidenced in the raising of along channel isopycnals with timeduring each experiment (figures 3.3 and 3.5).80The contributions to the total record energy from the diurnal and higher frequency tidalconstituents seen in the raw spectra (presented in figures 3.11, 3.12, 3.17 and 3.18) aresignificant and dominate much of the water column. In order to best determine the influenceof other forcing, the high energy diurnal and higher frequency tides were removed.Detiding by harmonic analysis is presented in section 4.3 and was accomplished by fittingthe well known astronomical forcing frequencies of the tides, in the least squares sense, tothe record variations and determining an amplitude and relative phase for each constituent.The tidal contributions from the diurnal and higher forcing frequencies were then calculatedfrom these parameters and subtracted from the original record to give the detided residual.Harmonic analysis is a standard method of tidal analysis and prediction. Godin(1972) is anexcellent general reference on tidal analysis and Foreman(1977, 19(79) gives a number ofpractical guidelines in applying harmonic analysis. Section 4.4 discusses the deridedresponse.Anemometer records from the Protection and Tomakstum moorings allowed the detidedresidual records to be dewinded by cross spectral techniques and the method anddiscussion of results is presented in section 4.5. The contributions of the wind to the lowfrequency circulation occurs over a wide range of frequencies beginning with diurnalsea/land breezes, to forcing of periods of 2 to 3 days representing the passage of stormfronts, to lower frequency near fortnightly periods representing changes in the prevailingweather. These contributions are significant and Pickard and Rodgers(1959) reported thatthe wind forcing was sufficient to reverse the direction of flow in the surface layer.Cross spectra of the wind and along channel velocity and the wind and density recordswere used to estimate the wind influence by converting the cospectra and quadrature spectrainto a spectral coherence and phase. The coherence squared represents, for a linear system,the contribution to the variance of one signal (density/current) from the other (wind) as a81function of discrete frequency bands. The coherence was used to estimate the wind drivenresponse in the along channel currents and density records. Farmer(1972) successfullyused this method on surface layer data from Alberni Inlet. A discussion of the wind drivenresponse is presented in section 4.6. Having estimated the influence of the wind throughoutthe water column, the dewinded residual was then determined by subtracting the winddriven response from the detided time series. A discussion of the dewinded residualresponse is presented in section 4.7.Observational time series are only approximately stationary and continuous. For example,the amplitude and phase of a tidal constituent at a given depth is not fixed (Stacey 1985)and varies with the modal composition, in turn a function of the stratification and whichchanges with time. Therefore the statistical methods employed such as harmonic analysiswhich calculate fixed amplitude and phase parameters that best describe the response overthe whole record are inexact and lead to a small amount of the higher frequency 'noise'being left in the residual. Therefore the detided and dewinded time series are presented afterapplication of a post processing low pass spectral filter with a cutoff equal to the period ofthe 01 tidal constituent (0.93 cpd).Figure 4.1 shows the processing data flow used in the analysis of the low frequencyresidual presented in this chapter, with data flowing from the hourly averaged time serieson the left to the monthly mean, detided, wind driven, and dewinded time series on theright. The ovals represent each software routine that operated on the data in turn as it movesfrom left to right in the diagram.82HourlyAveragedWindVelocitiesTidalConstituentAmplitudeand PhaseDewindedU, at.....<Average29.5 DayAstronomicalForcingFrequenciesWind DrivenU, at29.5 DayAverageU, cn^OP"FilteredDetidedU, atFilteredWind DrivenU, at^OPP"FilteredDewindedU, atResidual Analysis Data Flow DiagramFigure 4.1: Residual Analysis Data Flow DiagramData flows from the hourly averaged time series on the left to the monthly mean, detided, wind driven, anddewinded time series on the right. The ovals represent the software routines that operated on the data as itmoves from left to right. Note that a low pass spectral filter (fc = 0.93 cpd) was applied to all processeddata before final presentation.4.2 29.5 Day Mean ResponseFigure 4.2 shows the 29.5 day mean along channel velocity and density (as at) profiles forthe 1988 experiment Surface layer data at Protection and Tomalcstum show a net outflowwith considerable vertical shear. At Tomakstum an inflow just below the surface layer, at12 to 15 m, may be interpreted as at least partial salt replacement forced by entrainment inthe surface outflow. The CTD surveys for 1988 showed evidence of deep water renewaltaking place in the outer basin and the inner basin at mid depths. The mean velocitiescorresponding to a net inflow in the lower third of the water column at Protection (below110 m) are consistent with the renewal process in the outer basin. An inflow at Tomakstumfrom sill depth to 180 m suggests renewal at mid-depths in the inner basin, with returnflows above and beneath the penetration to conserve volume. At the sill mooring (justinside the inner sill), this penetration can also be seen, although spread through more of thewater column. It is possible that more vigorous mixing due to sill dynamics distributes themomentum vertically in this area. At Protection the mid-depths through to the surface allhave outflow, likely due to the fact that in the outer basin the renewal water travels inwardnear the bottom and therefore all volume compensation must be above the penetration.However, the velocity minimum at 35 m may be a manifestation of the salt replacementinflow maximum. These structures correspond well to the concept of nested thermohalinecirculation presented in Chapter 2.0, with estuarine forcing the surface layer and deep waterrenewal the lower part of the water column. However, as noted in the theoreticaldiscussion, linear superposition may be somewhat simplistic. There is also a small localminimum at 12 m at Protection. This is within instrument error, although the larger valuefrom the cyclesonde at 15 m when compared to the 12 m S4 might be due to wave inducedpumping of the cyclesonde rotors.84PrtIISin TomTom22.5 23.5^24.5^23.5^2 .5^23.5^24.50Prt SIII TomDepth(m)-50--100--150--250--15-10-5^0^0^0^5-100-150-200-250-3000Depth(m)-50Kn88: 29.5 Day Average Along Channel Velocities and Sigma-t4-down inlet^ 0 up inlet^20.5^21.5 22.5 23.5 24.5Uavg(crn/s) SIgma-t(kg/mA3)Figure 4.2:^1988 29.5 Day Mean Along Channel Current (U) and Density (as at) ProfilesU profiles are plotted on a scale of 5 cm/s per division with a solid vertical line representing thezero for each station. ot profiles are plotted on a scale of 1 kg/m3 per division with a solid verticalline representing 24.5 kg/m3 for each station. Location of the 24.0 isopycnal is represented with acircle on each profile. Dashed horizontal lines represent the depth of the 12 m S4, and the deepestcyclesonde data; 170 m at Protection, 190 m at the Sill and Tomakstum moorings.By conservation of volume, the vertical integration of these profiles as a net volumetransport should flow out of the inlet and be equal to the mean river discharge for theaveraging period. At both Protection and Tomakstum moorings, where data existed for theentire water column, the profiles were separated into arbitrary layers corresponding to theoutflowing and inflowing portions of the profile and the integrations performed. Thevertical integration interval (dz) for each data point began at a point one half way betweenthe depth of the data and the depth of the next shallowest data and extended to a point halfway between the depth of the data and the depth of the next deepest data. The results arepresented in table 4.1 below as m3/m width.LayerProtectionThickness^VolumeTransport(in)^(m3/s Der mlLayerTomakstumThickness(m)VolumeTransport(m3/sperm)1 105.0 -1.26 1 10.5 -0.552 75.0 0.91 2 7.0 0.043 57.5 -0.764 110.0 1.725 155.0 -4.21Total 180.0 -0.35 Total 340.0 -3.76River -0.04 River -0.04Table 4.1: Volume Transport (m3/s) per metre width in the alongchannel direction for 1988. Note that 'layers' are arbitraryand refer to the thicknesses of inflowing and outflowingwater masses as depicted in figure 4.2. Mean river discharge(98 m3/s) is also shown after being corrected for the channelwidth local to the mooring.The total volume transports were of correct sign but were an order of magnitude greaterthan the mean river discharge, corrected for the surface channel width at each mooring.Because the channel width varies by at most —10 % with depth at both moorings theseresults are a reasonable representation of the total volume transport. Being as conservationof inlet volume must not be violated, one is lead to suspect that cross channel variabilitymay be more important than previously hoped. Figure 2.5 presents Webb's(1985) meanprofiles from two cyclesondes moored across the channel at Tomakstum in September861983. These moorings to the North and South of the channel centre line show differencesin along channel transport at mid-depths and suggest even larger differences above 30 m.Further, despite similar inflows at the bottom of the Protection Mooring for both July andSeptember 1983, the single centre channel mooring at Tomakstum has a mid depth inflowwith a peak of twice the velocity over the two off centre moorings for September.Although the penetration into the inner basin in September 1983 compared to July 1983could be weaker in spite of the penetrations in the outer basin being similar, this resultsupports the evidence from the vertically integrated volume transports that cross channelvariations in flow do exist and may be significant. Although we do not have near surfacedata from the sill mooring, its profile suggests a serious volume imbalance suggesting morecross channel variability near the sill. Webb's(1985) results for Lull Bay just outside theinner sill also show a large volume imbalance is likely there.The relative depths of the 24.0 at isopleth in the mean profiles at the Protection and Sillmoorings indicates a positive potential energy difference exists above sill depth betweenthem. Renewal is likely taking place on a more less continuous basis throughout theexperiment. The lack of a mean density profile between 9 and 230 m at Tomakstum is dueto the failure of the cyclesonde conductivity cell during the deployment. The mean densityprofile at the Protection and Sill moorings were used to compute an estimated buoyancyperiod profile, expressed in minutes/radian. Values were comparable to those presented inFarmer and Freeland(1983) for the spring, with deep water values of 3 to 10minutes/radian and near surface values of about 0.5 minutes/rad.The 29.5 day mean along channel velocity and density (as at) profiles for the 1989experiment are shown in Figure 4.3. Because only 2 weeks of data were available from theProtection and Sill cyclesondes, averages were computed over a 14.7 day period for these87Kn89: 29.5 Day Average Along Channel Velocities and Sigma-t-400-300-200-100down inlet^up inlet0^0^0_ ....FirI IISIII on--I—iIA xieI ItII.IIiItI1I:. 11i^1.I1^t^I^ir^i^1^j ij ! 11Ir:iIrI:ssrI!•11Ir;iIIrr:;.I:r.;.:!1i^1ie18.5^18.5^20.5^22.5^24.5Prti 411 ft xeI- -0Depth(m)0Depth(m)-100-200-300-400-20 -10^0^-10^0^05^20.5^22.5^24.5^24.5^24.5^24.5Uavg(cm/s) SIgma-t(kg/m^3)Figure 4.3:^1989 29.5 Day Mean Along Channel Current (U) and Density (as ad ProfilesU profiles are plotted on a scale of 5 cm/s per division with a solid vertical line representing thezero for each station. of profiles are plotted on a scale of 1 kg/m3 per division with a solid verticalline representing 24.5 kg/m3 for each station. Location of the 24.0 isopycnal is represented with acircle on each profile. Dashed horizontal lines represent the depth of the 12 m S4, and the deepestcyclesonde data; 170 m at the Protection and Sill moorings, 190 m at the Tomakstum and Axemoorings.instruments. Fortunately the mean wind velocity over this period at Protection andTomakstum was quite small.At Protection, a surface outflow and some compensating inflow underneath are present aswell as deep inflow consistent with the evidence of deep water renewal from the CTDsurveys presented in Chapter 3.0. As with the 1988 experiment, the inflow just below thesurface may be interpreted as providing at least a partial salt balance for entrainment despitethe significantly lower surface salinities in 1989. The peak inflow velocities at about 100 mcorrespond to the higher density water being available for renewal at this depth during the1989 experiment In 1988 the peak inflow velocities at Protection were deeper (-150 m)and weaker. The positive velocities at the bottom of the Tomakstum mooring indicate thatthe renewal in the inner basin was deeper than in 1988 but evidence from the Axe mooringsuggests this penetration did not extend to the deepest part of the basin and is consistentwith the movement in the 24.4 isopycnal presented in figure 3.5. As deep basin densities(below 200 m) are lower and source water in the outer basin higher in density than in 1988,deep water renewal is expected. However observed mean penetration velocities of deepwater are smaller than than in 1988.While an inflow just below the surface layer is present at Protection, an inflow does notseem to be present at Tomakstum although a minimum in the outflowing velocity doesoccur. As the salinity of the surface layer remained much fresher along the whole length ofthe channel from the mouth to the sill in 1989 compared with 1988, less entrainment wastaking place. Less entrainment would require a somewhat smaller salt compensation flow.Mixing caused by the shear with volume compensation from the deep water renewal mightexplain the presence of this minimum or perhaps the compensating salt water inflow isbeing advected seaward by the outward flow of water at mid-depths in response to deepwater renewal.89At the Sill mooring, a disturbing result is the net outflow at virtually all depths. Thisbehaviour is inconsistent with conservation of volume and may be due to topographicsteering causing cross inlet variability in this region. The location of the Sill mooring waschanged for the 1989 experiment placing it shallower and closer to the sill. The sill bottomtopography is presented as a three dimensional plot in figure 4.4. It can be seen that thepath presenting the smallest energy barrier for renewal water at or deeper than sill depth isoff to the south side of the channel. This assymetry might explain the lack of inflow seenwhen the mooring was moved closer to the sill in 1989. Also the east-west reach realignsslightly at the sill and inertial effects may carry shallower inflows to the north side of thechannel again missing the mooring. Webb(1985) presents a similar mean profile from acyclesonde mooring at Lull Bay, just on the outside of the sill, with outflow at all depths.Volume transports were calculated at Protection and Tomalcstum by vertically integratingthe mean profiles as for the 1988 data. The results are shown in table 4.2. As with 1988,LayerProtectionThickness(m)VolumeTransport(m3/sperm)LayerTomakstumThickness(m)VolumeTransport(m3/sperm)1 7.5 -0.50 1 165.0 -5.052 10.0 +0.13 2 175.0 +1.513 57.5 -1.944 105.0 1.74Total 180.0 -0.57 Total 340.0 -3.54River -0.24 River -0.25Table 4.2: Volume Transport (m3/s) per metre width in the alongchannel direction for 1989. Note that 'layers' are arbitraryand refer to the thicknesses of inflowing and outflowingwater masses as depicted in figure 4.3. Mean river discharge(569 m3/s) is also shown after being corrected for thechannel width local to the mooring.90Depth(m)Cross Channel(km)0.5^1.0^2.02.54^6Along Channelacni)Figure 4.4:^A Three Dimensional Plot of the Knight Inlet SillThis plot represents the bottom topography of the inner sill ofKnight Inlet as digitized from chart number 3578 of the CanadianHydrographic Service. The view is from the inner basin towards thesill with the south shore on the left and the north shore on the right.Location of the 1989 Sill mooring is shown in 180 m of water. The1988 mooring was also centre channel in 340 m of water closer tothe viewer.91they show a net outflow but larger by an order of magnitude than the average rivertransport. These results confirm the need to look more closely at the assumption of lateralhomogeneity in inlets.The mean density profiles for 1989 are also shown in Figure 4.3. Again a potential energydifference exists between the Protection and Sill moorings, above sill height. Thereforesufficient energy is present to drive a penetrating density flow throughout the experiment.Also of note though, is a similar difference between the Sill mooring and the Tomakstumand Axe moorings. The density profile at Protection is characterised by a noticeably largervertical gradient with depth from about 40 m to 150 m caused by the very dense water (as >24.7) in the outer basin. Buoyancy period estimates were calculated for all moorings andwere consistent over all depths, with the exception of Protection where the larger verticaldensity gradient mentioned above gave a corresponding shorter period. Deep water periodswere in from 5 to 10 min/rad, in the same order as for 1988. Surface layer periods weremuch shorter than in 1988, extending to approximately 0.12 min/rad.To allow closer inspection of the surface layer response, Figure 4.5 shows the 29.5 day(14.7 day at Protection in 1989) near surface mean velocities to 35 metres at both theProtection and Tomakstum moorings where S4 current meters were placed through thesurface layer starting at a depth of 2 m. Figure 4.6 shows the 29.5 day (14.7 day atProtection in 1989) near surface mean density profiles. Note that although the runoff wason average 5.7 larger in 1989 compared to 1988, the surface layer volume transport did notincrease substantially. However the vertical velocity shear is much larger. The surfacesalinity was extremely low along the entire length of Knight Inlet in 1989 and the increasedstability of the surface layer would suppress entrainment, thus preventing the volumeamplification that might otherwise be expected.92—1111"0 up inletProtection Tomakstumdown inlet down inlet088- _Co.....„.K n89 *-- ---..^1I^+ –I;---:::-'45s- –..– – —......_ ..\•At_ ___ _; I;4kI;I /. e...I1;;1;;1 /;;^i! 1i 0. •o up inlet0...... K n88^!K n89rI---- --i^s 4%•-r-r + 1–^" ^11r^ +^i1::!.i...._.IIii!I^1I^i J,i1-25-35Depth( m)-2-4-6-9-12-15Depth(m)-2-4-8-9-12-15-25-35Kn88/89: 29.5 Day Average Along Channel Near Surface Velocities-1 0 -5 25 -20 -15 -10 -15 25Uavg(cm/s)^Uavg(cm/s)Figure 4.5:^1988 vs 1989 Near Surface Along Channel (U) 29.5 Day Mean Velocity ProfilesDashed horizontal lines show the level of the observations; S4 electromagnetic current meters to 12m and cyclesonde profiling current meters below.Protection Tomakstum15 151010 20 20 2525Sigma-t(kg/mA3) Sigma-t(kg/m^3)Kn813189: 29.5 Day Average Near Surface Density-30-25-20-35Figure 4.6:^1988 vs 1989 Near Surface 29.5 Day Density (as at) ProfilesDashed horizontal lines show the level of the observations; S4 electromagnetic current meters to 12m and cyclesonde profiling current meters below.Depth(m) o-2-4-9-12-15-20-25-30-35Depth(m) 0-2-4-8-9-12-15^i I^1 1^Ii I^Kne8 . .....Kip89 ----....^ I^I^-......^ r—L I^*---.....^1i r -tk—r --1^1—I ^1—F-t1---------r— ------- ---T---- -------1I— ------- ----1---------r ----- -1------Experiment^Protection^TomakstumDepth Inflow Outflow Aat^Depth Inflow Outflow Aat(110^at^at^(m)^at -at 1988 12 23.7 23.2 0.5 10 23.3 21.8 1.51989 8 22.7 16.6 6.1 6 22.4 14.8 7.6Table 4.3 summarizes the outflowing surface layer depth, layer densities, and densitydifferences estimated from the data presented in figures 4.5 and 4.6. The depth of thesurface outflowing layer was estimated from the velocity profile as the depth of the firstzero crossing or, where a near surface velocity minimum existed, the depth of the upperTable 4.3: Estimated Surface Layer Depth, Layer Densities (as at), andDensity Differences (Aat) across the surface outflow andnear surface inflow layers. at is expressed in units of kg/m3.inflexion point of the minimum. The average density of the outflowing surface layer wasestimated as the average density of the 4 m record as the volume transport is greatest in theupper part of the surface layer. The average density of the inflowing layer was estimated tobe the average of the record from just below the surface layer. The average change indensity between the upper and lower layers was then calculated. The reason for the deeperdepths of the surface layer for 1988 is not certain, but may be caused by wind mixing asthe surface layer density is considerably higher during this experiment leading to smallvalues of Aat and resulting restoring buoyancy forces.The conservation of salt equation given in section 2.2.1, VcSo = Vi Si is approximated byVocrto = \fiat; in an estuarine situation where density is controlled by salinity. Therefore theratio of the salt compensation inflow to the estuarine outflow should be:V. ao= tV. a.For 1988 the inflow volume flux should be approximately 98% of the outflow at Protectionand 94% of the outflow at Tomakstum. For 1989 the inflow volume should be95Experiment^Protectionati^R Depth U0 UavgAat (m3/s)_(m) (cm/s)(cm/s) TomakstumR Depth U0 UavgAat (m3/s)_(m) (cm/s)(anis)1988 47.4 98 12 16 4.0 15.5 98 10 6 6.01989 3.72 569 8 11 7.0 2.95 569 6 11 14.9approximately 73% of the outflow at Protection and 66% of the outflow at Tomalcstum.Clearly the volume flux of the inflow layer just below the outflowing surface layer (whenthere is one) is insufficient to provide the salt balance in itself. One may surmise thatvolume compensations due to other inflows such as deep water renewal may be advectingthe salt compensation inflow out of the inlet and that this layer is really much thicker thanwould first appear.The volume flow out of the inlet can be calculated using Knudsen's relations (given insection 2.2.1). Again substituting at for salinity, the volume flow out of the inlet becomes afunction of river discharge and the ratio of the inflowing layer density to the densitydifference:^V^= R°^AS^Au,Using the inflowing layer density, layer thickness and density differences given in table4.3, the mean river discharge over the length of each experiment given in sections 33 and3.4, and an approximate channel width of 2.5 km an estimate of the surface layer velocitycan be therefore calculated by dividing the volume flow by the layer thickness and thechannel width. The velocity estimates (U0) from Knudsen's Relations and the observedaverage velocities vertically integrated over the surface layer (Uavg) are shown in table 4.4.Table 4.4: Estimated Surface Layer Velocities using Knudsen'srelations (U0) versus the observed integrated surface layervelocity (U.,g). A linear profile was assumed from 2 m tothe surface for the integration. The value used for R is theaverage river discharge during the experiment, the densityand layer thicknesses are from table 4.3, and an approximatechannel width of 2.5 km was used. Aat for Protection isquite uncertain and could be larger if the surface layerthickness were increased to lower the estimate of u0.96At Tomakstum the velocities obtained from ICnudsen's relations appear to give a reasonableestimate of the vertically integrated surface layer velocity, however at Protection this doesnot appear to be the case. In both years a deceleration of the surface layer was observedfrom Tomakstum to Protection possibly due to the vertical transfer of momentum due to themixing processes over the sill. These same processes make it difficult to estimate thethickness of the surface layer and likely contribute to the error. For example if the surfacelayer depth at Protection in 1988 were taken as 25 m and the value of Aot adjustedaccordingly, the estimated and average velocities would be in reasonable agreement. Theaverage velocity profile still shows outflow at this depth and perhaps the interpretation thatthis outflow is completely due to volume compensation due to deep water renewal isincorrect. The observed deceleration from Tomasktum to Protection is consistent with thethickening of the surface layer, perhaps due to vertical momentum redistribution as a resultof sill processes. For 1989 the depth would have to be 12 m. While this seems unlikelylooking at the average velocity profile, it is perhaps illustrative of the types of problems thatcan arise in approximating a continuous system as two layers.In both years the volume flux out and the density of the inflowing layer are approximatelythe same, while the ratio of the 1989 to 1988 density difference (12 at Protection and 5 atTomakstum) increases to the same order as ratio of the 1988 to 1989 record average riverdischarge(5.8). This result indicates that the balance in Knudsen's relations comes not froman increased surface volume flux with discharge, but from a change in the entrainmentleading to the larger density differences observed with increased runoff.Wetton(1981) used dynamic height calculations to estimate the surface slope and showedthat it increased with runoff. van der Baaren(1988) also estimated surface slopes in thesame way during high runoff in 1986 and 1987. Pond and Pickard(1983) provide a general97introduction to the calculation of dynamic heights through the numerical integration ofspecific gravity anomaly with pressure. Of course Wetton and van der Baaren had toassume that the pressure gradient was zero at some fairly deep level (200 m for Wetton and100 m for van der Baaren). While it might not have been zero, as we have seen that thevelocity is not zero at depth, it will be small compared with the surface pressure gradient.Therefore any pressure gradient that existed at the level of no motion would be much lessthan the surface slope and the error in the surface slope estimation will be small. van derBaaren's programs were recovered from tape archive and used to estimate the surfaceslopes for both experiments using data from the 1988 deployment and 1989 deploymentand pickup cruise CTD surveys. Dynamic height profiles for casts taken inside the innerbasin (stations 4 through 11) were calculated at 1 m intervals to 50 m and at 5 m intervalsthereafter, from 1 m to the level of no motion . The level of no motion was taken as 180 mfor the 1988 experiment and 170 m for 1989 experiment and was selected from theTomakstum 29.5 day mean velocity profile presented in figures 4.2 and 4.3 by estimatingthe depth of the deepest zero crossing.Following van der Baaren(1988) surface slope was then estimated by applying a linear leastsquares fit through the dynamic heights at 1 m, the shallowest level available. A compositeplot of all calculated surface slopes (including those of Wetton and van der Baaren) versusriver discharge is presented in figure 4.7. Although this plot is noisy, there is a clearrelation between increasing river discharge and increasing surface slope. The three isobaricsurface slopes calculated for the 1988 and 1989 experiments are consistent with those ofWetton, while somewhat under those of van der Baaren. However, a CTD survey of aninlet that is about 100 km long requires a great deal of time and CTD casts were not takenduring the same phase of the tide. As the typical slope of say 10-6 corresponds to about a10 cm rise over 100 km noise in these results is hardly surprising. Three of Wetton'ssurface slope estimations had pressure gradients of reverse sign sloping back towards the98- Surface Slope (m/m)2.5 10-6 ^2.0 10-6-5.0 10-7(2)•Knight Inlet Surface Slope vs River Dischargeá,^,T ^ .1^i ^ .1^ 1. ^t^11ii^i^ 1^1 Ii 1I^I ^iI i 1i i^f!i^i^i Q^1200^400^600^800^1000^1200Figure 4.7:^Surface Slope (m/m) vs River Discharge for Knight Inlet^River Discharge (mA3/s)Note that surface slopes has been multiplied by -1 so that slopes above zero on the y axis arenumerically negative. This plot incorporates the results of Wetton(1981) [open circles], van derBaaren(1988) [dots], and those from the 1988 deployment and 1989 deployment and pickupcruises [solid squares]. The level of no motion used were 200 m, 100 m, 180 m and 170 mrespectively.head of the inlet and driving surface flow back towards the river mouth. Because thesethree slopes were based on data from cruises in November, December and January, strongoutflow winds in conjunction with the low river discharge may be responsible. Winds andthe difficulty in estimating a level of no motion without velocity data contribute to the noiseobserved in the relationship between surface slope and river discharge.Following Wetton(1981) and van der Baaren(1988) I also estimated the isobaric slopeprofiles by repeating the least squares fit at each level through to the level of no motion.Unlike those of Wetton and van der Baaren whose isobaric profiles with only oneexception do not cross zero, the profiles calculated for the 1988 and 1989 data set showzero crossings in the pressure gradient consistent with the character of the mean velocityprofiles. The 1989 pickup cruise isobaric slope profile resembles a detided (see section 4.3for method) velocity profile from the Tomakstum mooring from a few days earlier, beforethe cyclesonde stopped profiling. The 1989 isobaric slope profiles and the velocity profileare presented in figure 4.8.The reason for the difference between these results and those of Wetton and van der Baarenis not certain, but may simply be due to offset errors arising from selecting a level of nomotion where small velocities are present The 1988 and 1989 data sets suggest thatselecting a level of no motion is difficult without velocity data. Also, the correlation in theleast squares fit while high at the surface (0.7 to 0.8) falls off rapidly as slopes areestimated through the interior of the fluid. Except near the surface where the slopes arelarge, dynamic height calculations are noisy and that noise could easily mask the characterof the internal pressure gradients.The balance of forces for the surface layer in Knight Inlet was shown by van derBaaren(1988) to be between the surface pressure gradient and the interfacial friction except100LDay 199.5Kn89: isobaric Profiles and Representative Tomakstum U Velocity ProfileDepth(m) 0Day 168Deployment CruiseDay 206Pickup Cruisedown inlet-12 -12-12--100 ^ -100 -100 ^-150-150-^ -150^rLNM^-17043e-7^-4e-7^-2e-7^ -6e-7^-4e-7^-2e-7^-50 -40 -30 -20 -10 0^10Isobaric Slope (m/m)^Isobaric Slope (m/m)^Detided U (cm/s)Figure 4.8:^Isobaric Slope Profiles for the 1989 ExperimentIsobaric slope profiles as estimated from the 1989 deployment and pickup cruises and a representativevelocity profile from Tomakstum. Slopes are in m/m. The level of no motion used was 170 m. These twoisobaric slope profiles clearly show reverse pressure gradients driving inflows at some depth. Note themaximum slope at the surface is off scale on these profiles. The pickup cruise isobaric slope profileresembles the detided velocity profile at Tomakstum from a few days earlier.up inletperhaps seaward of the sill where inertial terms were larger. It appears that, compared withthe observed 29.5 day mean velocities from the 1988 and 1989 data sets, the estimates ofsurface velocity calculated using ICnudsen's relations shown in table 4.4 and those of vander Baaren shown in figure 2.6, were high outside the sill. In fact there is a smalldeceleration in the surface layer from Tomakstum to Protection in both years, consistentwith a thickening of the surface layer due to increased mixing and the resultant loss ofmomentum. Therefore it is likely that the balance between the surface pressure gradient andinterfacial friction holds true all along the inlet.Referring again to figure 4.5, a much larger vertical velocity shear can be seen across thesurface layer during the 1989 experiment suggesting that greater turbulent friction isbalancing the larger pressure gradient associated with the increased runoff. van derBaaren(1988) estimated coefficients of interfacial friction in Knight Inlet for the late springof two years, 1986 and 1987. The runoff during 1986 was much higher and her calculatedfrictional coefficients were an order of magnitude higher for 1986 than 1987. She alsostates that these coefficients are not static values, and likely vary with and on the sametemporal scales as the tides and the wind.1024.3 Harmonic Analysis and Computation of the Delided Time SeriesDetiding was accomplished through harmonic analysis, the least squares fit of well knownastronomical tidal forcing frequencies to the fluctuations of each data record. Thisprocedure estimates a fixed amplitude and relative phase representing the contributions ofeach tidal constituent to the data record. Once the amplitude and relative phase of theconstituents has been determined, the tide can be reconstructed and subtracted from theoriginal data record to create a detided residual time series.The harmonic analysis program used solves an over determined system expressed as alinear matrix equation[A] [X] = CD]where:^[A]^is the coefficient matrix to be determined[X]^is the matrix of orthogonal tidal constituents[D]^is the matrix of observational records[D] is a matrix of observational records and for the purpose of this analysis consisted ofeither vector velocity (u, v) or scalar (t, s, ot) time series from a single depth. [X] is amatrix of orthogonal constituents for each tidal forcing frequency expanded as sine andcosine terms and computed along the same time base as the observational data in matrix[D]. The mean and the trend were also included as zero order and first order polynomials.[A] is the relative amplitudes of the sine and cosine components of each constituent and isdetermined by the following process. First, for the solution of [A], the equation isrearranged to the form:[A] = [X]-1 [ID]Second, the inverse matrix form of [X] is computed and the problem is reduced todecomposing the equation to find the triangular form of matrix [A]. Third, the solution to103[A] can obtained through back substitution. As each vector velocity component or scalarproperty time series at each depth held simultaneous observations, the manipulations toobtain a triangular matrix need only be performed once and then a back substitution madeinto each of u and v or temperature, salinity and at to determine the coefficients for each.The amplitudes of the cosine and sine components of each trigonometric constituent wherethen converted to an amplitude and relative phase to describe the constituent contributions.For the purposes of tidal prediction and comparison to other observations, phase is usuallyexpressed relative to Greenwich Mean Time. However, since only relative phases wererequired for detiding, the phase calculated was left relative to Julian Day 1.0, midnight(PST) January 1 of the year of each experiment.The method of singular value decomposition is recommended by Press et al.(1988) forreducing [A] to triangular form as it produces the best fits in the presence of 'noise', in thiscase fluctuations not attributable to the tidal constituents alone. It also has an advantage inthat this method was chosen for analysis in general inlet circulation models underdevelopment by others and procedural compatibility was desirable for future work. As thelower frequency monthly and fortnightly tidal constituents fall well inside the bandwidth ofthe low frequency residual as defined in this work, only the diurnal and higher frequencytidal constituents were subtracted from the data record as part of the detiding procedure.However the mean, trend and lower frequency monthly and fortnightly tidal constituentswere included in the analysis as including them considerably improved the fit of the higherfrequency constituents to the data records.The selection of the astronomical tidal constituents to include in the harmonic analysisrequires care as harmonic analysis does not conserve variance. The high frequency limitwas determined from the Nyquist frequency, one over twice the sampling rate of the data.For example, as the processed time series had a sampling rate of at least every 3 hours, the104M4 quadiurnal harmonic was included. The lower limit is determined by the ability toresolve a full cycle of the constituent over the data record and therefore all trigonometricconstituents included in the analysis must have a frequency greater than one over the recordlength. For example, the observational records were generally for greater than 30 days, andtherefore the lunar monthly constituent Mm was included. The exception was the 1989Protection cyclesonde mooring where premature instrument failure allowed only the lunarsolar fortnightly constituent MS/, to be resolved.Between these limits, care must also be taken in specifying the constituents so that theirfrequencies are far enough apart that they can be clearly distinguished by the fittingprocedure. If two constituents fit the data equally well, ambiguities may lead to computedcoefficients with large magnitudes that are delicately and unstably balanced to cancel out.To determine if two tidal constituents were too close in the frequency domain, the Rayleighcriterion specified by Foreman (1977, 1979) was applied. This states that the record lengthmust be greater than the reciprocal of the difference between the two frequencies to beresolved. For example, applying this criterion to the principal lunar M, and principal solarS2 constituents, a record length of greater than 14.9 days is required. And so both of thesewere included. Applying this criterion to the MS/ and Mf a record length of 182 days isrequired. In the latter case, the MS/ was included over the Mf because a strong non-linearinteraction between the M, and S2 was reported by Freeland and Farmer(1983) in KnightInlet. Similarly the Qi, P1, and K2 constituents were left out of the analysis. For both1988 and 1989, with the exception of data from the 1989 Protection and Sill cyclesondetime series, the constituents chosen for analysis are given in Table 4.5. In the two casescited above the Mm was not included.105# Name Description Period Frequency(hours) (cud)1 Zo - Mean, zero order polynomial2 Z1 - Trend, 1st order polynomial3 M. - Lunar Monthly 661.3 0.03634 MSf - Lunar Solar Fortnightly 354.4 0.06775 O - Principal Lunar Diurnal 25.82 0.9306 K1 - Luni -Solar Diurnal 23.93 1.0037 N2 - Large Lunar Elliptic 12.66 1.9008 M2 - Principal Lunar 12.42 1.9329 S2 - Principal Solar 12.00 2.00010 MK3 - Lunar Solar Tridiumal 8.18 2.9311 M4 - Quadiumal Harmonic 6.12 3.92Table 4.5:^Tidal Constituents used in Harmonic AnalysisOnce the contributions of each constituent to the data had been computed, thoseconstituents with periods equal to the 01 and shorter were reconstructed from thedetermined amplitude and phase, and subtracted from the original time series to form thedetided residual. The mean, trend and low frequency (M. and MSf) trigonometricconstituents were left in, as these have frequencies in the same band as the desired residualand subtracting them would also subtract some of the response from other forcing at thesefrequencies. In effect the detiding procedure, has the same effect as a low pass filter for theobservations, selectively removing only diurnal and higher frequency tidal energy.Close inspection of the spectrum of a time series before and after detiding revealed that thetidal constituents are significantly reduced by this process but not totally eliminated. It islikely that the tidal response is not strictly invariant over the length of the observationalrecord. Stacey(1985) noted a change in the modal response of the tide with stratification inKnight Inlet which implies that the constituent parameters may be continuous functions ofriver runoff and wind mixing. Other non-tidal high frequency variance also remains in therecord although it has little energy. For the purposes of presentation only, a low passspectral filter with a half power cutoff equal to 0.9 times the absolute cutoff frequency anda discretized cosine taper was used to remove remaining higher frequency fluctuations. For106the purposes of displaying the data records in the following sections, the absolute cutoffwas set to equal to the lowest tidal frequency (01) removed.Note that cyclesonde data are slightly irregular in time since the instrument alternatelyprofiles up and then down through the water column and each profile takes approximatelyone half hour. In order to apply a filter or do spectral analysis, data equally spaced in timewere required whereas the harmonic analysis can be and was done using the original data.As the data needed adjustment over only a small fraction (s 1/5) of the sampling interval,linear interpolation was used to grid the detided data onto a regular sampling interval.Being as the bulk of the higher frequency variance has been removed by the detidingprocedure, the interpolation should have little effect, if any, on the lower frequencies. Thecyclesonde at Tomakstum in 1989 failed to profile at regular intervals, especially at the startand the end of the data records. In order to allow these data records to be subject to thesame spectral analysis and filters as the others, the detided records for this instrument werelinearly interpolated at 3 hour intervals between existing data points and there is a bit moreuncertainty in these results.Note that further processing and analysis utilized the unfiltered detided data so as to not toadversely affect the analysis of contributions at frequencies near the filter cutoff. Forconsistency in presentation, where wind and detided data are presented together, the wind. data were subjected to the same low pass filter.1074.4 Detided Inlet ResponseThe results of the detiding process for the along channel currents at selected depths areshown in Figures 4.9 and 4.10. Note that depths selected for display are representative ofthe surface layer and those deeper depths where peaks in correlation of wind (shown inFigure 4.11) to velocity were found. Because the tidal fluctuations have been removed, itwas necessary to change the velocity scales with depth in order to adequately portray theresponse.Figure 4.9 shows that the 1988 2 to 12 m along channel currents at Protection closelyresemble the wind with a decrease in this response with depth. At 12 m the current stillappears positively correlated with the wind, but with a larger lag and about half the peakvalues of the 2 m current. At 25 m the wind driven current is smaller still and appears to beof opposite phase with the wind for the last two thirds of the record, while at 150 m thewind response appears larger than that observed at 120 m but with what appears to be amore complex phase relationship than that observed at shallower depths. The peak lagcorrelation at 150 m is negative while at 120 m it is positive. There clearly appears to bewind influence throughout the water column at the Protection mooring in 1988. In contrast,the wind response at Tomakstum is more confined to the surface layer, with much lessresponse at 12 m, probably due to the greater stratification on the inside of the sill andbuoyancy forces suppressing the vertical transfer of momentum. Correlations at depth aresmall but fluctuations with the same character as the wind's lower frequencies dominate thealong channel currents as deep as 270 m.108!Wind 1^;1 ;1111^ai^il I^•^.ihroir 1RIMIBMMFitkrriMllifIIIIIIIIL!NIIIIIIMMIllifiniraplimmarim.._ 4....l'_ 1; KILMil illr i^.1 =111:- .._^;v ir^•7 ._._....V._.____;..1^!i4 i rib,^i^_^....I tau Irairm• -iv -12 m ' 1Ii -^All.^m.....■^_ ...-----.,---■25m+t^i1+-^-4.^. .1;- .^•^v v^,+___ __I___$20 t^. t... Alb. _v^-^•-40 1^; 11_ I.^• 1tiWincli^I^;t^ ;i1_m•^•^11111111111•Na• ; •^V V- -1'.^.I^tI ■ii^i1 ,1i1^111141E11111 11111M11111111 -^1• _11.‘ ,P,PrIlI 2^;tA^.,^Ar1^i1_-_..f _4.1tV^7 ; V1 4 m ;r^I.....V4 ...11t111- .tr 12 mlt^; t t,1^.t ,+----1^1tt1135 m:I^:A ._ _ ____! _ ^_ _,i^11 ; Ir180^riltt^,,t,tt—^-,Nomper270 nii^IVIIIIR'volly^v-I^!I— + -11IU (cm/s)750-75025-2525-2512.5-12.512.5-12.56.25-6.256.250-6.25U (c111/8)750-75025-2525-2512.5-12.512.5-12.56.250-6.256.25-6.251988 Filtered Wind and Detided Along Channel VelocitiesProtection^Tomakstum85^90^95^100 105 110 115^85^90^95^100 105 110 115Julian Day^Julian DayFigure 4.9:^1988 Along Channel Wind vs Selected Detided CurrentsNote both wind and detided currents have been filtered with a spectral filter with a cutoff frequency with aperiod of 0.929 days. Depths shown are representative of the surface layer and of those depths wheresignificant correlations with the wind were found.Figure 4.10 shows that the 1989 2 and 4 m along channel current at Protection and to alesser extent at Tomakstum also resemble the wind. At 12 m the current appears to benegatively correlated with the wind at both moorings. Stratification is stronger in 1989 thanin 1988 and is confining the direct wind response nearer to the surface. Unfortunately theProtection cyclesonde failed half way through the experiment and the dominant forcingfrequencies of the wind (10 to 15 days) are much lower, making it difficult to place a lot offaith in the correlations at depths greater than 12 m. At Tomakstum the cyclesonde onlyintermittently profiled at the beginning and end of the experiment and occasionally skippedprofiles during the rest of the deployment To allow the data records to be used in furtheranalysis and to be filtered with the same spectral filter, a linear interpolation between datapoints in the detided records were used as a basis to estimate values for the missing datapoints. The 15,70 and 120 m filtered time series suggest a much stronger wind response atdepth in the inner basin than in 1988. At 15 m the currents appear to be negativelycorrelated with the wind and at 70 and 120 m positively correlated. At 310 m a strongnegative correlation appears. However, one must be careful about inferring that thesecorrelations are all due to baroclinic response to the wind. The frequencies of the wind arenear fortnightly and it is likely that some of the motion may be due to the fortnightly tidesor deep water renewal modulated by the spring/neap tidal cycle.Figure 4.11 shows the lagged cross correlations of the wind and along channel currents forboth experiments. These values were plotted using the sign of the correlation coefficient(R) but with a magnitude of R2, the coefficient of determination. Roughly this valueestimates the intensity of association between two variables that appear correlated and canbe interpreted as the percentage of the energy in the along channel currents that might beexplained by the energy in the wind.110U (cm/s)7500-750250-25250-2512.50-1250-12.50-12.56.250-6.258.250-6.25NMIiInd^1.. 1"1"---.A- di1L.• 7111111111.A____I___Ir1....^...i ^1-....I --4-- 4-.^1i^1.I1'Nmsr--+Pog• — —0 M— —11st^is 1i^1M 1iIi^11^--1--1 0 m 1ki.Ind-t- ---4.--.^i^1z1^---1-i^11...^...i1 t4 ^_V 1^,--P-Ir--4-----m^11 1^1-^-I- - - --1- --- 1- ^_M^/^11 1r• 1^1- -I--1^1M^I 1 1^1---+---4--- ---1--^---1----r-0 m g^i i_3 0 m i^:r 1 i^1U (CM(8)7500-750250-2525-2512.5-12.512.50-12.56.25-6.258.25-6.251989 Filtered Wind and Detided Along Channel VelocitiesProtection^Tomakstum175 180 185 190 195 200^175 180 185 190 195 200Julian Day^Julian DayFigure 4.10: 1989 Along Channel Wind vs Selected Detided CurrentsNote both wind and detided currents have been filtered with a spectral filter with a cutoff frequency with aperiod of 0.929 days. Note that prior to filtering, where the cyclesonde failed to profile continuously, alinear interpolation between the detided samples was used to provide an estimate of a continuous timeseries. Depths shown are representative of the surface layer and of those depths where significantcorrelations with the wind were found.;0I^;^;^t^1t^I50^;^tL^r^+^ ...:^...;^1.-;^; I:^i,i ;^.i^i,i oo r^ 4.1^.I   .:-.1I 1^',', I,......^ i)rt^i^It150-- ------------t-^; ,^.•t J /^!/^!^!!^1.i^! 1. ,200-4------------i-----4 ------ -s^•^.^..^.^;i^i ;^t1^t .s.^.^t.^. t;^i^,1^1)^;^! i300- -1 ---- --- ----- 'r-----r-a^;^ I.^aIII .^I4i...... j I^I'^I-1.0^-0.5 -0.25 0 0.25 0.5 1.0, r ............. 1' 14116111114111611-r^+----1— 1 ^40 "11 1 iC..^I—I-^ i;i---r— --..,Prt It1—I ----- — — I—^1........ ..........■....= ... —Tom--r- ------^--t1 ----- 4---------- ------------r-I^1t^I I ,.-0.5 -0.25 0 0.25 0.5-1.0050100150200250300Wind/Along Channel Velocity Lag Correlations With Depth1988^1989Depth (m)^ Depth (m)— RsqFigure 4.11: 1988 and 1989 Wind Correlations with DepthPeak correlations are indicated with circles for Protection and squares for Tomakstum. Correlation wasplotted as R2 (with the sign of R) as it gives an estimate of the contribution of the wind driven currentenergy to the total current energy at that depth. Table 4.6 gives the lags associated with the surface layercorrelations and the peak lag correlations at depth.=MS^RsqTable 4.6 gives the lags associated with wind and along channel velocities for the surfacelayer and for the peaks in the correlation profiles at depth as highlighted by the circles andsquares on figure 4.11.Depth(m) PrtR2,Lag(h)1988TomR2, Lag(h)PrtR2, Lag(h)1989TomR2. Lag(h)2 0.81,^7 0.72,^4 0.83,^1 0.71,^24 0.81, 7 0.56, 5 0.66, 1 0.15, 06 0.76, 8 0.37, 6 0.07, 0 -0.24, 309 0.72, 8 0.17, 10 -0.35, 30 -0.26, 3012 0.50, 9 0.03, 11 -0.56, 14 -0.27, 2515 -0.29, 39 -0.10, 63 -0.52, 15 -0.64, 4525 -0.52, 3335 -0.37, 350 0.26, 4870 0.55, 6380 -0.45, 0120 0.55, 39 0.69, 72140 -0.35, 39150 -0.37, 69180 0.10, 81270 -0.10, 81310 -0.72, 63Table 4.6:^Surface and Peak Lag Correlations at depth (as R2with the sign of R) for the Wind and AlongChannel CurrentsThrough the surface layer the lag times appear to describe the time scales associated withthe vertical transfer of momentum. For example, in 1988 the peak correlation at 9 m isweaker in the inner basin at Tomakstum and the peak correlation occurs at a greater time lag(10 hours) than at Protection (8 hours) although at 2 m the situation is reversed with asmaller lag time in the peak correlation at Tomalcstum. In 1989 the lower density of thesurface layer results in a rapid (1 to 2 hours) vertical transfer of momentum at bothmoorings, although the time taken for this transfer at Tomakstum is higher. It appears thatthe stratification is suppressing vertical momentum transfer as shallow as 4 m in the innerbasin in 1989.113At depth, peak correlations occurred with the current lagging the wind with temporal scalesof 40 to 80 hours. As the speed of a mode 1 internal wave based on the densities and layerthickness given in table 4.3 at Tomalcstum is about 0.4 m/s (1988) and 1 m/s (1989). Itwould take about 83 hours in 1988 or 33 hours in 1989 for a baroclinic wave to travel theapproximately 60 km up to the head and return. To balance the pressure gradientsassociated with the surface slope built to balance the wind stress, the isopycnals at depthnear the head would have to be depressed. This baroclinic adjustment would require aninternal wave to reach the head and return. If these peaks in the lag correlation are due tothe wind these temporal scales support the work of Buckley and Pond(1976) who foundthat the baroclinic adjustment controlled the wind response in Howe Sound.Wetton(1981) raises the possibility of quarter wave internal resonance for wind forcing in achannel open at one end. The period required for a mode 1 wave to traverse a 100 km longinlet would be about 69 hours in 1988 and 28 hours in 1989. A standing wave in a channelwith a length equal to one quarter wave length, requires a forcing period of 11.5 days in1988 and 4.6 days in 1989. As these are within the temporal scales of the wind forcing forthe 1988 and 1989 experiments, perhaps some of the wind response at depth is due tointernal seiches. As the pressure gradient response to the wind forcing will vary from being180 degrees out of phase at frequencies much lower than resonance to being in phase at theresonant frequency this process may account for some of the apparent change in the phasewith frequency noticed in the deeper along channel velocity time series.At 80 m at Protection in 1989 a reasonably strong anticorrelation with the wind is found ata lag of 0 hours. However, the time scales of the wind record in 1989 are longer than in1988, from 10 to 15 days and the shortness of the along channel current record due toinstrument failure makes the interpretation of the correlations difficult. Also, the time scales114of the wind are close to the time scales associated with the spring/neap tidal cycle in 1989and the possible fortnightly tidal modulation of deep water renewal in the inner and outerbasins also makes an interpretation of the correlations difficult.Figures 4.12 and 4.13 present the detided density (as at) time series at Protection andTomakstum for the 1988 and 1989 experiments. As noticed earlier there are largefluctuations in the surface layer density field that resemble the wind. With up inlet winds, acorresponding raising of the isopycnals occurs as estuarine outflow is retarded or reversed.With down inlet winds, a lowering of density is observed consistent with the re-establishment of the estuarine outflow. In 1989, where winds are of a much longer periodthe up inlet winds at Tomakstum starting at day 186 are followed by an increase in the 2 mdensity for a period of about 4 days followed by a sudden drop despite continuing upchannel winds. This result may be explained by the fact that the surface pressure gradientmust come into balance with the wind at some point if the forcing is steady. At this time theestuarine outflow will re-assert itself with the fresher water lowering the observed densityagain. The time scale of this adjustment (4 days or 96 hours) also suggests that the windresponse is controlled by the baroclinic and not bamtropic adjustment. The densityfluctuations are larger at Tomakstum than at Protection in both years because of thestronger pycnocline on the inside of the sill. The 2 m detided near surface density recordsshow a trend to decreasing density with time consistent with the increase in river dischargetowards the end of each experiment.In order to improve the analysis further, a cross spectral analysis between the wind and thealong channel currents is presented in section 4.5. The coherence spectra may be used toestimate the contributions of the wind to the current in each frequency band and calculatethe wind driven flow and the phase spectra will allow the investigation of mechanismscontrolling the wind response in the along channel currents at depth.1151988 Filtered Wind and Detided Densities (as Sigma t)ProtectionU (cm/s);^i_ 3 3IWind;t;s,ttI!iii1i1^i1I^;I^1m ;:;; 4 m t;^i,1"------jr411t1...,'---1I ,II I„,...-4.—„,....._..„),^ii^Ii^6 111 3 .1f••■/—•,---s-----1I ^;3^i33^Itp112 mlt^1I6-1--------4--------4—HI;,- It^;t Ir tt 26 rnit^1i^1 t .Ittt1i150 nii^t:--- I ..;ii^■1t^i33 3! 3^!90^95^100 105 110 115Julian DayTomakstumU (cm/s)t 33 1^3Wind;Imi L1IIA^I3 1.1I^;1 •IiIIlia^vIlvir-ig 1 i^T=,^I^1^1. ; 1 ;1;1;. ,i^1^1^•iitikAatiodLH iA^AL lat,..;i:4 m ,11aly^.:^tr•i^;.311.11.11111111111I^1I 1^itt119 m 1Ii'30m.iI3I11I^i11^!1tt3II:v70^rri..11i1I:11^i.14.^;r13t1 i. iI40 160 ^105 ^110 1115Julian Day20, 25252525252520sigma-T(kg/mA3) 8520sigma-T(kg/m"3) 85Figure 4.12: 1988 Wind vs Selected Detided Density (as at)Note in the above composite plot, at increases upward and each division is 5 kg/m3. Both wind anddensities have been filtered with a spectral filter with a cutoff frequency with a period of 0.929 days. AtTomakstum the 12 m S4 was not equipped with a conductivity cell and the conductivity sensor of thecyclesonde failed.2520, 2252252150015001500-1500ProtectionU (cm/s)TomakstumU (cm/s)1989 Filtered Wind and Detided Densities (as Sigma t)Julian DayFigure 4.13: 1989 Wind vs Selected Detided Density (as at)Note in the above composite plot, at increases upward and each division is 5 kg/m3. Both wind anddensities have been filtered with a spectral filter with a cutoff frequency with a period of 0.929 days.Thewind influence on the density field is larger than in 1988 and more confined to the surface layer due to thestronger pycnocline.Julian Day20sigma-T(kg/m"3)1500150015105,2015102015,252525202015105, 2015102015,25252520sigma-T(kg/mA3)Mil '*J 1arldle.r4II1aPripirpomme1I^1, rirmA 1 -1W. rillir - - r17a.1 it1i1i12 r i25i 1111111 1 11150m 1t!;.1175 180 185 190 195 200Wi d^i.,_^i 1 r1^1t^1+----i---t^t1t tiitI-ti^1i 1- I - - - 1 - -t AII^1i I---I----^1I^1: 1- - -^-^1 r1^1^111^t--+–^-4^-1 111 1111111^111119^1----r---%--.,-----t-----/-1;^  1^;1^11^tt230m^il^t1 I1 tt^1II270m^Ii^1 -^ 11 r1t^it t+----4----I^I175 180 185 190 195 200150015004.5 Cross Spectra of Wind versus Along Channel Current and DensityThe lag correlations presented earlier indicated that the dominant forcing in the surface layerwas wind, and that considerable effects were discernible at other depths in the watercolumn. Further, the raw spectra of the along channel currents presented in section 3.6,showed energy in the same bands as the wind spectra. A cross spectrum presented in theform of coherence and phase spectra can provide information similar to the correlationspresented in the previous section, but as a function of discrete frequency bands rather thanas a single number representing all of the variance in the two records.The original data records were not sampled at the same rates at all depths and the data at 15m through 190 m was not sampled on a strictly repeated sampling interval. Cyclesondesprofile through a given depth starting alternately from either the top or the bottom of theirprofiling range making the sampling interval at a specific depth vary by as much as 40minutes in the worst case. As the detided observations have had all diurnal and higherfrequency removed, all data was gridded by linear interpolation to a fixed sampling intervalof 3 hours. This places the Nyquist folding frequency at 4 cycles per day and above anysignificant remaining energy in the detided residual data records. It also has the advantageof placing all of the spectral estimates on the same frequency scale.The frequency spectra.of the wind, current, and density were computed by demeaning anddetrending the time series and by applying the fast fourier transform algorithm. Thisprocedure determines a series of discrete fourier coefficients, ak and bk, that represent theamplitude of two sinusoids in quadrature at each specific frequency in the discrete fourierseries that represents the original data.118The discrete fourier series representing the transformed data can be expressed as follows:X( t)^(ak cos(2r fkt) + bk sin(2x fk t))where: fk = 1/(2N At), represents the discrete frequencies in the transformN = total number of samples in a time seriesAt = the sampling interval of the data record. Note the frequency rangeover which the transform is performed is between the limits:f(1) = 1/(N At), one cycle in the record lengthf(N) = 1/(2 At), the Nyquist Frequency, one cycle in 2 samplesFrom the coefficients in the discrete fourier series, the power can be estimated at eachdiscrete frequency as follows:p(fl) = 1/2 [ak2 bk2]Because the sampling function is a discrete boxcar whose frequency domain representationis a sinc function, the spectrum is the convolution of the original signal's spectrum and thisfunction. If the original data contains a single sinusoid at precisely one of the discretefourier frequencies, it will be correctly represented as a single spectral line. If the originaldata contains the representation of a single sinusoid at a frequency other than a fourierfrequency, energy is spread amongst the nearest discrete fourier frequencies. Observationaldata contains many characteristic frequencies and therefore to improve the accuracy of thefft power estimation, band averaging is routinely applied. All power spectra presented inthis section have been averaged using a Daniel window spanning seven discrete fourierfrequencies.The cross spectrum can be computed from the discrete fourier coefficients for any two timeseries that are coincident on the same time domain, X(t) and X'(t). It consists of twoorthogonal spectra the co-spectrum Co(fk), and the quadrature spectrum Q(fk). The co-spectrum Co(f) is defined as that part of the two spectra that are in phase, while thequadrature spectrum Q(fk) is defined as the part of the two spectra that are out of phase by11990 degrees. These spectra are computed from fourier coefficients of the two time series, akbk and ak' bk', as follows:Co(fk) = 1/2 [akaks + bkbk]Q(fk) = "2 fakbk ak'bklAn alternative and often more useful representation of the cross spectrum for analysis arethe coherence C(fk) and phase spectra F(fk). These are computed from the co andquadrature spectra as follows:/^CO2^(22c2 VI) P(f,^)F(11)Arc tanIS - (2( fk ))co (ç))Calculation of the coherence and phase spectra must be made over bands of discretefrequencies, for without it the coherence is identically 1 as any discrete sinusoid iscoherent with any other of the same frequency. Through experimentation it was found thataveraging over seven discrete fourier frequencies produced reasonable estimates ofcoherence and phase through the wind band while maintaining as much spectral resolutionas possible. The coherence squared can be interpreted as that fraction of variance of onesignal that is related to the other in each frequency band regardless of phase. The phasegives the amount by which the fluctuations in one time series leads or lags the other foreach discrete frequency band.Figures 4.14 through 4.17 show representative band averaged power, coherence squaredand phase spectra of the wind and along channel currents at each mooring. The powerspectra of the wind are scaled and plotted with the 2 m power spectrum with a grey line for120reference. As with the raw spectra presented earlier, the vertical axis is plotted as fc13(f) sothat the area under the curve is proportional to the total variance of the original record on asemi-logarithmic plot. Note that while there is more energy in the wind at Protection than atTomalcstum, there is more energy in the 2 m current at the peak frequencies of the wind forTomakstum in 1988. A comparison of the power spectra to 12 and 15 m suggests that thestronger stratification at Tomakstum is confining the direct effects of the wind more closelyto the surface.In 1988 the along channel velocities are generally highly coherent with the wind (wherecoherence squared is > 0.5) in the low frequency end of the spectrum with periodsgenerally greater than 2 and less than 7 days. At Protection there is clearly wind energy to150 m near the bottom of the mooring, while there is considerably less at 25 m particularilyat the frequencies corresponding to the peak of the wind energy. At Tomakstum the deepcurrents are not very coherent, at least at the dominant 2 to 3 day period of the wind.The 1988 phase spectra for the near surface are consistent with the lag times of the peakcorrelations presented earlier in section 4.5. At 25 m depth and greater at Protection, thephase of the energy at the frequencies close to the peak of the wind energy is close to being180 degrees out of phase with the surface currents (and thus slightly more than 180 degreeswith respect to the wind). At Tomakstum, a similar phase reversal can be found butshallower at 15 m. Below approximately 50 m the coherence squared falls below 0.5 andthe phase spectra become more difficult to interpret. Except in the near surface, the phase isa function of frequency and it appears that the contribution of the wind to the variance ofthe deeper records is more complex than can be determined with a simple lag correlation.This phase variation may explain some of the higher correlations found at depth in section4.5. At the high frequency end of the spectra, the coherence squared is generally low and12111ii-irp1^.i..._ILL112 m1....._A1 1111211I 111 i^glilliii•^.IiiiI EMI 1' mII IINIFIMALA 1lui1,^,,iiiiii.1 M,_,.......1l__,...4i LAIrillAlIL 11,150 m11. al Al30 20 1075^ 2 1.7,5.1._._1___.1.....1_._....—I--iiiiiiii. It;__j _1imairmniminar1 iii IKM! ;ulimuriamouiviNM_ ' illifit4'5111irralliMelMRVairilliffilI wail.PMrzrammin11111111111117211075 32^1.7.5:1--1--1no1-1----12 m114mI1It11111111111!I 1m1mpg11111i1...t....11;;__Jr__id 1 11m; ilorivIr 1;;1; _.....,, _....]... 1 ,%...ral 1-0cm2,S9C2 30 20 1075 32 1.7.5deg+380+1800-180+1900-180+1800-180+1900-180+1800-180+1900-180380M(t)-18I-1001000500, 100500,100500,1050,100,1051.00.50, 1.00.50, 1.00.50, 1.00.50, 1.00.50, 1.00.51988 Protection Cross Spectra of Wind vs Along Channel Currents at Selected DepthsSpectra30 20 1075 3 2 1.7,5 .3Coherence Squared30 20 1075 32 1 .7 .5 _3Phase30 20 1075 32 1 .7 .5 .3Period (Days)^Period (Days)^Period (Days)Figure 4.14: 1988 Protection: Power and Cross Spectra of Wind vs Along Channel Currents atSelected DepthsNote the grayed power spectra at 2 m is the wind power spectra for reference. All spectra have beenaveraged over 7 adjacent discrete frequencies and have been computed from the unfiltered detided timeseries. Positive phases denote that the currents are lagging the wind, negative phases denote that thecurrents are leading the wind.30 20 1075 32^1.7.5.3t—r-tiI11t•1^11 Iii- i12^.A I. HA I1— -r—1^i÷---1 --1 --11 1 I1 1^11 LI L .a ,,i1MA 1. m1 11MAIM"I1i 3t111111LI^•I i. IL,11 1i^1I 1IllikAIL /LA^1.1I iI^1 270 m1 i i Itt -"IA^1^, 1^;i /ariligi t^4I 1—4--1;---MOMOOWOEIMENUMWilliNMJINNIiiigiii11111111111111011IEL111111111101111111111111imprAmilirltrill' OHMICantiNMI IIIiillinWinFaM11111111111111N111IIIMENA1......,,erii.=1 141! i r,30 20 1075 32 1 .7 .5 .3s1 r11di^1.1r^I1 I1r1ra m 'ti1L :t1t^ti1 114 miL^.tI:ttItt1i tI^rt tr-^I1 1nom......!tI1^It 1t^11ttI1IIttI tt^tt 1It^tt It^1t ttCM2 SOC2 30 20 1075 3 2 1.7.5 .3d eg+MO+1800-180+1800-180+1800-180+1800-180+1800-180+1800-180-380t4)(t)—W-2002501000, 100500,20100,1050,100,1001.00.50, 1.00.50, 1.00.50, 1.00.50, 1.00.50, 1.00.51988 Tomakstum Cross Spectra of Wind vs Along Channel Currents at Selected DepthsSpectra30 20 1075 32 1 .7 .5 .3Coherence Squared30 20 1075 32 11.5  .3Phase30 20 1075 32 1.7.5.3Period (Days)^Period (Days) Period (Days)Figure 4.15: 1988 Tomakstum: Power and Cross Spectra of Wind vs Along Channel Currents atSelected DepthsNote the grayed power spectra at 2 m is the wind power spectra for reference. All spectra have beenaveraged over 7 adjacent discrete frequencies and have been computed from the unfiltered detided timeseries. Positive phases denote that the currents are lagging the wind, negative phases denote that thecurrents are leading the wind.unstable with a corresponding phases that have large variations. Priestley(1981) states thatextremely large variations in the phase may occur when coherence is low.For 1989 the highly coherent part of the signal is also in the lower end of the spectrum, butgenerally with periods about 1.5 to 30 days. The broader band of the 1989 coherencesquared spectra is due to the shift in the wind regime noted earlier. As will be shown laterin Figure 4.26, the energy coherent with the wind is more confined to the surface in 1989probably due to the stronger stratification, with significant wind energy penetrating deeperto perhaps 20 m at Protection. The near surface velocity phases appear to be consistentlyleading the wind in 1989. This result is somewhat contrary to expectations and was alsofound in the lower frequencies of the wind response in Alberni Inlet by Fanner(1972). Heproposed that offshore disturbances may propagate as surface gravity waves in advance ofthe wind.Figures 4.18 through 4.21 show representative band averaged power and cross spectra ofthe wind and density fluctuations (as at) at each mooring. In general much less of thevariance in the density field is coherent with the wind at the peak frequencies of the windforcing. The density field appears to respond more to the lower frequencies in the windenergy, probably due to the periods of net up and down inlet wind stress reversing the flowof the surface layer and affecting the density field. In 1988 at Protection and Tomakstumthe phase spectra of the 2 m density field is at —90 degrees indicating the wind drivendensity is fluctuating in quadrature with the velocity. Thus the near surface density isresponding to the time rate of change of the velocity. This response can be taken asevidence that a pressure gradient does build to balance the wind stress. In 1989 the winddriven density is close to being in phase with the velocities indicating the strongerstratification is inhibiting mixing and the fluctuations in surface density are likely the resultof the surface layer behaving as a 'slab' flow.12410 7 5 3 2^1 .7 .5 .330 20 1075 32^1.7.5.3Figure 4.16: 1989 Protection: Power and Cross Spectra of Wind vs Along Channel Currents atSelected DepthsNote the grayed power spectra at 2 m is the wind power spectra for reference. All spectra have beenaveraged over 7 adjacent discrete frequencies and have been computed from the unfiltered detided timeseries. Positive phases denote that the currents are lagging the wind, negative phases denote that thecurrents are leading the wind.1909 Protection Cross Spectra of Wind vs Near Surface Along Channel CurrentsSpectra10 7 5i^- --1i1t--+loyindr1;i11 2 mIfIt1ttttI 4m;;1;I1I1I 6 mi1i1 t t1t1;;1tttI 9 m1I; 1ti1;tt112 mI1 ;t t; 1i; ;11Period (Days)Phase.i,.... :^.,iiIiii.1111,111111111111ffl:11111111111111i1111111111,4111111 111111111111:MII1-M11111111111111111111111111111awand1-1.11111111111....),___1 -111 MNiLMIII^II30 20 1075 32 1.7.5.3Period (Days)Coherence Squared30 20 1075 32 17.5 .330 20f40(t)..11- 200100032^1 .7 .5 .3.^.^.0.50, 1.00.50, 1.00.50, 1.00.50, 1.0•^I^I1 2m' 42d eg+380+1800-180+1800-180+1800-180+180-180+1800-180-3800.5ii I^3020 1075 32 1.7.5 .3Period (Days)1000, 100500,100500,50250,50250cm2 sea1 .7 .5 ..330 20 1075 32V^I30 20 1075 32 1Figure 4.17: 1989 Tomakstum: Power and Cross Spectra of Wind vs Along Channel Currents atSelected DepthsNote the grayed power spectra at 2 m is the wind power spectra for reference. All spectra have beenaveraged over 7 adjacent discrete frequencies and have been computed from the unfiltered detided timeseries. Positive phases denote that the currents are lagging the wind, negative phases denote that thecurrents are leading the wind.1989 Tomakstum Cross Spectra of Wind vs Near Surface Along Channel CurrentsSpectras7-,1r --.1I",....1,I1— I--g 2 m1....4...._11La.;1IIIII• 111 illbandihiit 18 m1II11I1tttt&di_.... lellantion; i I;i III IiII M.1111111 I; I 12 m1: 1 11It;tttIPeriod (Days)Coherence Squared30 20 1075 32 17.5  _31—r--1^i111r1 2 mg1 14 m1 1.^... - --1-1 6 m1a9 m2 m—r ---Period (Days)Phase1075 32 17.5  _31,111111111----maimplal:AgraIlumemi----1-----NIUMEN1littlilliallionair NMIMillilignillIIIIIIIIIIIIINIMMIMIIIfilarlirdamNEIII --------Iii30 20 1075 32Period (Days)+1800-1800cm2SeC2 30 20 10 7 5 3 2 1 .7 .5 ..330202501000, 100500,100so0,500,501.00.50, 1.00.50, 1.00.50, 1.00.50, 1.00.5deg+360+1800-180+1800-180+180-180+1800-180-36030 20 10 7 5 32^1.7.5.3Coherence Squared Phase30 20 1075 32 1 .7.5 _330 20 1075 32^1.7.5.3Figure 4.18: 1988 Protection: Power and Cross Spectra of Wind vs Densities at Selected DepthsNote the grayed power spectra at 2 m is the wind power spectra for reference. All spectra have beenaveraged over 7 adjacent discrete frequencies and have been computed from the unfiltered detided timeseries. Positive phases denote that the densities are lagging the wind, negative phases denote that thedensities are leading the wind.1988 Protection Cross Spectra of Wind vs Selected Densities (as at)Spectra-iithllIhrit-liIIIIIIIII.i.m---;1; 11111 2oolliallilligirir;;t; 111 0NMI1;;--i—t;1 oiiPeriod (Days)ls^If 1$1.1••=i14111 L1111111111ammo11111111111111111111111111111111111111M11110111+1800-180-380+1800-180d eg+380+1800-180+1800-180+180-180+1800-180114)(f).i.3.‘(5/0 005cm220.0250,0.050.0250,0.010.0050,0.0020.0010,0.0010.00050,0.0010.000530 20 1075 32 1 .7 .5 .3Period (Days)30 20 1075 32 1 .7 .5 .3Period (Days)deg+180-180+1800-180+1800-180+180-180-3801^II^^30 20 10 7 5 3 2^.1988 Tomakstum Cross Spectra of Wind vs Near Surface Densities (as 01)Spectra^Coherence Squared^Phase2° 10 7 5^1^-330 20 1075f(f)W 2x100,0.020,0 . 100,0.200.010.050.101--1t--f– –II–.2— —m–..^4pill1.pmorn1,, ,[,1II ,".....^.--r A Iill,---r–t---I-- vi:........t..... ..m.... .....,iiPILE111IMPAIIIIMIIi^ill_ .^ .._t1_.....1.....,a---112111111111 ,SIVEMINP111113111111111111111,11111111111111111111iRir==111•1111•11■11710••■ iie I;II ,I- - --- 4---- ,---1------I111111111111111111130 20 1075 32 1.7.5 .3cm 2 /sec 20.12Period (Days)^Period (Days) Period (Days)1988 Tomakstum: Power and Cross Spectra of Wind vs Densities at Selected DepthsNote the grayed power spectra at 2 m is the wind power spectra for reference. All spectra have beenaveraged over 7 adjacent discrete frequencies and have been computed from the unfiltered detided timeseries. Positive phases denote that the densities are lagging the wind, negative phases denote that thedensities are leading the wind.Figure 4.19:10 7 5 32^1.7.5.3 30 201,7.5 ..330 20 1075 321 2mI1 4 m," P1. _^., 9mAai2 mALA A30 20 1075 32 1 .7 .5 .3Period (Days)1075 32^1.7.5.31111111111M110111111211I1,IilIiinM xiIIIMMIIIIMilI WirlarariaIIIIIIIIIit11111111A1=am12 m I Ii 1 11.11111Mallinellt I tI■I11130 20 1075 32 1.7.5.3Period (Days)iitI1 wild11ttti1 2 m1tII1i1 4 m11s i 1 6 mt t1 1 .._^.ittItI1i--r —+1*--1=3"==it1t--ttI 9 m1tIrt1 1Ii II;i---{ttII ^r2 m11 -^ItI1111t1 ,...,ANIiti ! 1II^•1075 3 2 1.7.5 .3Period (Days)30 2014)(t)4x104cm2 h10022.50(30 20•^1deg+380+1800-180+1800-180+1900-180+1800-180+1800-180-3800, 5.02.50,2.01.00,1.00.50,0.50.251.00.50, 1.00.50, 1.00.50, 1.00.50, 1.00.51989 Protection Cross Spectra of Wind vs Near Surface Densities (as at)Spectra Coherence Squared^PhaseFigure 4.20:^1989 Protection: Power and Cross Spectra of Wind vs Densities at Selected DepthsNote the grayed power spectra at 2 m is the wind power spectra for reference. All spectra have beenaveraged over 7 adjacent discrete frequencies and have been computed from the unfiltered detided timeseries. Positive phases denote that the densities are lagging the wind, negative phases denote that thedensities are leading the wind.----- - --2 1114 m11 a1 11 a1118 m1i1i19 m1i130 20 1075 32 1 .7 .5 .3Period (Days)IMINIUMIIiiiiiiiiiIImanimunnaINS11111111111INN1111111110NalOM•Ertrunt"11____•wil.a.a...rmalurommumwas111112111111111MillPPM R , A ■ MP• FIMPPI711111114.MIMI. TIM.P. WPM.....0. riarlin- -I-4--1,30 20 1075 32 1 .7 .5 .3Period (Days)i— —1ItIttI1 2 onitt1—tItI 11t14 ir1 tt[AI1; t; ti----r—1111--i-- -t1-1tI 9m;1:---4I1t1rIi1_; ttI1i;;tI12mi1s 1IPeriod (Days)( 251230 20 1075 32 1.7.5.3dog+380+1800-180+1800-180+1800-180+1800-180+1800-180-380to(f)^5.0cm2Isec22.50, 5.02.50,2.01,00,1.00.50,0.50.251.00.50, 1.00.50, 1.00.50, 1.00.50, 1.00.51989 Tomakatum Cross Spectra of Wind vs Near Surface Densities (as at)Spectra^Coherence Squared^Phase30 20 1075 32 1.7.5 .3^30 20 10 7 5 3 2 1,7.5 .3^30 20 10 7 5 32 1.7.5.3Figure 4.21:^1989 Tomakstum: Power and Cross Spectra of Wind vs Densities at Selected DepthsNote the grayed power spectra at 2 m is the wind power spectra for reference. All spectra have beenaveraged over 7 adjacent discrete frequencies and have been computed from the unfiltered detided timeseries. Positive phases denote that the densities are lagging the wind, negative phases denote that thedensities are leading the wind.4.6 Wind Driven ResponseThe evidence from the cross spectra presented in section 4.5 suggest that the wind responsemay be estimated using the coherence from the cross spectra of the wind versus the alongchannel currents and density fluctuations. As the coherence spectrum can be interpreted asthat fraction of fluctuations of one signal that are related to the other, it can serve as a basisto calculate the contribution of the wind to the fluctuations in the along channel currents ordensity records. Farmer(1972) used this technique to remove the variance due to the windsfrom the near surface along channel currents in Alberni Inlet. The spectral transfer functionhe used is defined as:T(fk )sw^P(fk )u C2 (fk U^P(favwhere: T(fk)w->uRfk)uC2(fk)wuRfk)wis the amplitude transfer function describing the contributionof the wind to the along channel current or scalar property.is the power spectrum of the along channel current or scalarproperty time series.is the coherence squared between the wind and the alongchannel current or scalar property.is the power spectrum of the wind.Hence in this application, the fourier series representing the wind driven component of adata record can be estimated by multiplying the fourier series representing the along channelcurrent or density fluctuations by the coherence from the cross spectrum. The time seriesrepresenting the wind driven component can then be computed by applying an inverse -fourier transform to the discrete fourier series. Because the mean and the trend wereremoved before the calculation of the fourier series, all of the mean and the trend are left outof the wind driven component as determined by this method. The estimation of the winddriven component of a data record uses the coefficients of the discrete fourier transform of131the original current or density data record complete with its phase information intact andhence the phase spectrum is not used in the calculation.The fourier transform and its inverse preserve only a time base relative to the start of thedata record, and therefore the original time base of the data record was recreated byapplying a time offset equal to the time of the first sample in the original detided time series.To remove high frequency noise, the same cosine tapered spectral filter with a cutofffrequency equal to 0.929 cpd used in the presentation of the detided data was appliedbefore plotting the wind driven time series.The wind driven velocity and density time series at selected depths for 1988 and 1989 areshown in figures 4.22 through 4.25. The depths chosen for display correspond to those ofthe detided time series presented in figures 4.9, 4.10, 4.12 and 4.13. As the cyclesonde atProtection in 1989 stopped profiling approximately half way through the experiment thewind driven currents were calculated using a shorter 14 day time series. The cyclesonde atTomakstum in 1989 profiled only intermittently at the beginning and the end of theexperiment while profiling continuously in the middle of the record. Therefore a linearinterpolation was made between data points in the detided (but not filtered) time series andthe interpolated data subject to the same spectral processing as the others.In both years the 2 m wind driven currents shown in figures 4.22 and 4.23 closelyresemble the 2 m detided currents and clearly have approximately the same amplitudes. In1988, it is clear that a good proportion of the variance at Protection is due to the wind atmost depths however this is much less true at Tomakstum, where the down inlet flow at1321988 Filtered Wind and Wind Driven Along Channel VelocitiesProtection^ TornakatumI Wind;L .^;^-I A htIt^;ii---1-40-miiii■1^1+-Act--1^1I I-10------+-----ErainviurvalINIIIIIMMINIIIarAvarraupermrieIMIIIMVAIMW.IMWEIIIIVARDINA i a 111=11,1" I11 Vill r — —L_,^Y ‘11111^1125^Ill : ;^ip20+----1----;1^-w^hae, rAmrp.Hiv^• IN MI.^•II1I vVe0-1 1 1 —1..A1^1.^AWino:1i^-"ma,iadasall1– – II^I•1^v^Ir^•I110111WHIMIAT1Wria.1111111M1111111MIIINHI111611111111111111111111ISFAIK11111111111111111111d1111ur•v•morm___.....__I15 m ii i^1iI 35 m I-i I^rI- t80mii+ -- -------_J^.---1^iI_I^-.II 1——I—e 7-0 nt.-i ---11I ..1I^1.cm/s7500-75025-25250-2512.5-12.5t•-Lo.)^ 12.50-12.56.25-8.256.250-8.25cm/s7500-75025-25250-2512.5-12.512.50-12.58.256.256.250-6.2585^90^95^100 105 110 115^85^90^95^100 105 110 115Julian Day^ Julian DayFigure 4.22: 1988 Along Channel Wind vs Selected Wind Driven CurrentsNote both wind and wind driven currents have been filtered with a spectral filter with a cutoff frequencywith a period of 0.929 days. Depths shown correspond to those chosen for the detided times seriespresented in figure 4.9..Wqu:11rI; I--I- ---- I^;.^I^..^1 I---r-----r - -;1.^-- I --^--- -^---^I^-.I^t-+-- -12 irn■^i^i1^;rt^' --1^;r---+;^;r^1 ;4^-Ir12 tm^l^s-^ 1—.......^__.„/"...).^1 I . _^—;50m^1^;r^---+^-I^--i i^!rI^;r -1----80 im^I^i1 tr^rr ;1^ji^i^I+.01.- - ^- -1 - I1^1 I1 j.1401m!^t^;Ir1r !:^Iwind :Eillikill111111111111riiitii111111111111^i: f!he. AlIT ^•11at' m1--r-11s•■■• II* ANALt.....--.. VW'15 ;In i;------------- — - -----I1----1t1201 mi1rr.-%--L. __....,---8--- 1,...__ _...1..._r; r t II31C1 m ri 1 ricm/s7500-750250-25250-2512.50-12.512.50-12.58.250-6.258.250-8.25cm/s7500-75025-25250-2512.5-12.512.50-12.56.25-6.256.250-8.251989 Filtered Wind and Wind Driven Along Channel VelocitiesProtection^Tomsk stum175 180 185 190 195 200^175 180 185 190 195 200Julian Day^Julian DayFigure 4.23: 1989 Along Channel Wind vs Selected Wind Driven CurrentsNote both wind and wind driven currents have been filtered with a spectral filter with a cutoff frequencywith a period of 0.929 days. Note that where the cyclesonde failed to profile continuously, a linearinterpolation between detided samples was used to provide a continuous time series. Depths showncorrespond to those chosen for the detided times series presented in figure 4.10.270 m in particular (seen in figure 4.9) does not appear to be wind related. In 1989 themagnitude of the wind driven current below the surface at Protection is less than in 1988but the record is short. The reverse is true at Tomakstum, where considerable motion in thedeep basin (120 and 310 m) seems to be attributed to the wind. Perhaps it is the baroclinicresponse to the surface setup caused by the longer period wind forcing in 1989 or it may beassociated with deep water renewal with a period similar to the wind.The near surface wind driven density field in figures 4.24 and 4.25 appears to follow thefluctuations in the detided data, but clearly not all of these fluctuations can be attributed tothe wind. The density fluctuations are also a function of river runoff and whatever mixingprocesses (particularily those in the vicinity of the sill) that water being returned up inletmay have been subject to. The wind driven fluctuations at depth shown in figures 4.28,4.30, 4.32, and 4.34 are also small. In the basin the horizontal gradients of density areknown to be small and even large flows due to baroclinic compensation for surface setupwould not result in a large change in density.Figure 4.26 shows the portion of the detided variance (as percentage) that may be attributedto the wind. It was calculated by finding the variance of the wind driven time series for alldepths and dividing by the variance of the corresponding detided time series. At Protection,from 35 to 50 % of the detidecl along channel velocity variance is attributed to the windbelow 100 m in 1988, while this value drops to approximately 20 % in 1989. AtTomakstum in 1988 below 100 m these contributions are also small, but surprisingly theyseem larger in 1989. Correspondingly large values (35 % at Protection and as high as 80 %at Tomakstum) in the density field for 1989 seem anomalously high. The broad peakreaching 80% at Tomakstum occurs from 120 to 190 m and may not be due to the wind.The longer periods of the wind forcing in 1989 are close to that of the fortnightly tides andthe separation of the wind driven component from the deep water renewal is difficult.1351988 Filtered Wind and Wind Driven Densities (as at)Protection^ TomakatumU cm/s^ U cm/s^1 ^I^Windt^ii1A^h^,^.1;--r---i1A Ali1—+I1 1 f ! r'l '^' ,,,--T.-,, ,,Imi a4 m 1ItImilIII—I^r1tt I^—1 .90^95^100 105 110 115Julian Day1WindiI^tig 11A^I^11i1A ANA AOI111--it41 V 1 r 1,t11Iv 1^v11II 2 m...• • Alb ad&• -I^-+ ^; 4 m1wI^•I. . .^It1I^...---1 ..^—II 9m91,^vormin_I41nior...-...^_. . . I . . . . . .t .1 u m1.J._ ..._._._.I1—III1--If30 m tII1Ii111/0--m-----41r—t1 ----1t---111— -, i 15.02.50-2.5, 2.50-2.5, 2.5-2.5, 2.50-2.5, 2.5-2.5, 2.5ot (kg/1773)+15000-1500^5.02.5-2.5, 2.50-2.5, 2.50 --2.5, 2.50-2.5, 2.5-2.5, 2.50" (kg/m3) 90^95^100 105 110 115Julian Day+1500-1500Figure 4.24: 1988 Wind vs Selected Wind Driven Density Fluctuations (as at)Note in the above composite plot, at increases upward and each division is 5 kg/m3. Both wind anddensities have been filtered with a spectral filter with a cutoff frequency with a period of 0.929 days. AtTomakstum the 12 m S4 was not equipped with a conductivity cell and the conductivity sensor of thecyclesonde failed. Depths shown correspond to those chosen for the detided times series presented infigure 4.12.1989 Altered Wind and Wind Driven Denisities (as at)5.02.50-2.5, 2.50-2.5, 2.50-2.5, 2.50-2.5, 2.50--2.5. 2.50cm (IV m3)Protectionliaki^11 Mug1I II- -I-- -^-II^I;I111..Pi4A/111111111111./11111 iYYi-VIr111111E1M,MIMIwiry ,r _ -rah. 4,I^1I 1V12m^1^iI t:s^r it25m t1^I I- 1^5C m1^IL^irIF^ 1I2+ --r!I^11 t175 180 185 190 195 200U cm/s+15000-1500^5.02.50-2.5, 2.50-2.5, 2.5-2.5, 2.50-2.5, 2.50-2.5, 2.50ot WO)TomaketumI^iVilid^11elkall^:1^i "I1v...1I^I2n 1........,__.yr4 Ft^Ailliralkil.,, rrAK•414111111121, 11111111111yr"AL:^-• 46111111NA,.IlekiiiiiiMINI,^I230m, i1.. I^1, ,s^1270! m -r-,-I^I: 1,^I, .1;5 180 185 190 195 200U cm/s+1500-1500Julian Day^ Julian DayFigure 4.25: 1989 Wind vs Selected Wind Driven Density Fluctuations (as at)Note in the above composite plot, ot increases upward and each division is 5 kg/m3. Both wind anddensities have been filtered with a spectral filter with a cutoff frequency with a period of 0.929 days.Thewind influence on the density field is larger than in 1988 and more confined to the surface layer due to thestronger pycnocline. Depths shown correspond to those chosen for the detided times series presented infigure 4.13.Protection (U)... -11;)f (1989198$Depth(m) 030025020015010050Tomskstum (U) Protection (at) Tomakstum (at)Depth(m) 030025020010015050-5100-15o-2025300-0-0-Depth(m) 0Depth(n) 050100150200250300-1988 1991^4-Wind Driven Variance as a Percentage of Total Detided Residual Variance with Depth50 100 %0 50 100 %0 50 100 %0 50 100Figure 4.26: Wind Driven Variance as a Percentage of Total Detided Residual Variance with DepthSolid lines are values for 1988, speckled for 1989. Note that no density information was available fromthe cyclesonde at Tomakstum in 1988 due to a failure in its conductivity cell.However, if the wind is enhancing deep water renewal by helping complete the energyrequirements to overcome sill blocking, a large part of the observed density change mightbe attributed to the wind.Figures 4.27 and 4.28 show the wind driven along channel velocities and density (as at)fluctuations contoured on axes of depth versus time for Protection during the 1988experiment. The along channel wind driven velocity shown in figure 4.27 clearly reflectsthe character of the wind in the near surface during the periodic 2 to 3 day wind forcingfrom the beginning to about Julian Day 102. Velocities as large as 5 cm/s can be attributedto the wind as deep as 20 to 25 m during this time. During the second half of the recordafter Julian Day 102, the wind forcing is steadier and is generally up inlet. The near surfacelayer currents clearly are a reflection of the wind whenever there is a substantial change inthe wind however from Day 107 through 109 there is only a small up inlet current despitepersisting strong up inlet winds. Perhaps this change is due to the fact that a surfacepressure gradient has built up to balance (or nearly balance) the wind stress. During thesecond half of the record the penetration by the wind is clearly more limited with winddriven velocities of greater than 5 cm/s no deeper than 12 to 15 m. A possible explanationis that the net up inlet winds have retarded the flow of fresher water along the surfacelowering the density and buoyancy forces are suppressing the vertical exchange ofmomentum. Also on Day 105 a sharp increase in river discharge occurs, possiblyenhancing the suppression during this time.At depth the wind response is weaker, but velocities as high as 2.5 cm/s exist throughoutthe water column particularily during the period of periodic forcing at the beginning of therecord. The response is often three layer to up inlet winds and but occasionally appears tobe single layer or nearly so (very weak return flows at mid depth if any) during periods ofstrong down inlet winds such as occur at Julian Days 86 and 88. Persisting down inlet13985 90 95 100 105 110 11585^90^95^160^165^110 115-20 +30 10+20 -20+10-20 +5 -100 -595-30 +30 -10 +10^Contours of V^to 25 m^(0, 5, 10,^cm/s)100Depth(m) 0510 -15-20-25.-20 +10^+590 105 110 115cm/s5000-50-1000VWind \A!^1988 Protection Wind and Wind Driven Along Channel CurrentJulian DaysFigure 4.27: 1988 Protection Wind and Wind Driven Along ChannelVelocity Contours vs Depth and TimeWind, wind driven velocity in the near surface and wind drivenvelocity over the entire water column. Note that the contours are at 0and +-5, 10, 20, and 30 cm/s in the near surface plot and at 0, +-2.5, 5, 10,20 and 30 cm/s in the plot of the entire water column.Light shading depicts positive velocities (inflow), dark shadingnegative velocities (outflow).140Depth(m) 0-0.1 +0.2+0.1••:. :**1-0.2 +0.05-0.1+0.1 +0.2 -0.2 +0.20.05 +0.1 +0.1+0.2-; -0.0595^1005-10152025- P14 105 110 1151988 Protection Wind and Wind Driven Density (as at)es^90^95^100^105^110^115, .. !Wind e_I 1,1^11^. 1Figure 4.28: 1988 Protection Wind and Wind Driven DensityFluctuations (as at) Contours vs Depth and TimeWind, wind driven density in the near surface and wind drivendensity over the entire water column. Note that the contours are at 0and +-0.05, 0.1, and 0.2 kg/m3 in the near surface plot and at 0, +-0.01, 0.02, 0.05, 0.01, and 0.2 kg/m3 in the plot of the entire watercolumn. Light shading depicts density increases, dark shadingdensity decreasing.cm/s5000-500-1000141winds such as those seen from Day 96 to Day 101 seem to generate a 3 or perhaps 4 layerresponse. There is clearly much less wind response in the second half of the record atdepth, perhaps because of the stronger stratification perhaps too because a surface pressuregradient has built to balance the wind stress and little baroclinic compensation is beingdriven as a result.Figure 4.28 shows that the strongest density response is in the surface layer as expected,but that the response increases in depth from 10 to 12 m at the beginning of the record to 12to 20 m during the second half of the record. This is likely due to the thickening of thesurface layer due to the net up inlet wind stress. Smaller changes are seen at depth perhapsdue to the tilting of the isopycnals due to baroclinic compensation.Figures 4.29 through 4.30 show the wind driven along channel velocities and density (asat) fluctuations contoured on axes of depth versus time for Tomakstum during the 1988experiment. Figure 4.29 shows that while wind response is present at Tomakstum, it ismuch more confined to the near surface with the depth of the 5 cm/s contours rarely greaterthan 10 m. Stratification is stronger at Tomakstum likely due to the fact that it is on theinside of the sill and well away from its associated mixing processes. At depth, in contrastto Protection, there are only weak flows (<2.5 cm/s) although the shape of the zerovelocity contours might suggest that there are similar vertical structures in response to thewind as observed at Protection. Figure 430 shows the wind driven density contoured overthe first 9 m. The 12 m S4 lacked a conductivity cell in 1988 and the cyclesondeconductivity cell failed. Here, due to the stronger stratification, the wind driven response ismuch greater than at Protection as noted in the discussion of the time series presented infigure 4.24. However the structure of the wind response in the near surface is similar tothat at Protection.14285 90 95 100 105 110 11585 90 95 100 105 115110Windcm's500-500-10 +30 -20+20-10+20-20^-10^-30 +30 -20 +201988 Tornaketum Wind and Wind Driven Along Channel CurrentJulian DaysFigure 4.29: 1988 Tomakstum Wind and Wind Driven Along ChannelVelocity Contours vs Depth and TimeWind, wind driven velocity in the near surface and wind drivenvelocity over the entire water column. Note that the contours are at 0and +-5, 10, 20, and 30 cm/s in the near surface plot and at 0, +-2.5,5, 10,20 and 30 cm/s in the plot of the entire water column.Light shading depicts positive velocities (inflow), dark shadingnegative velocities (outflow).143*0.6-0.4 +0.6 -0.2+0.2-0.4+0.4 +0.2 +0.6-0.2 -0.6-0.6 +0.6 -0.6^-1-0.6100Julian Day85 105 1101988 Tomakstum Wind and Near Surface Wind Driven Density (as ot)cm/s 85^90^95^100^105^110^115. •. i1.^1iWild il• -,!Figure 4.30: 1988 Tomakstum Wind and Wind Driven DensityFluctuations (as ot) Contours vs Depth and TimeWind, wind driven density in the near surface to 9 m. The 12 m S4lacked a conductivity cell and the cyclesonde conductivity cell failed.Note that the contours are at 0 and +-0.2, 0.4, and 0.6 kg/m3 in thenear surface plot. Light shading depicts density increases, darkshading density decreasing.500-500114Figures 4.31 through 4.32 show the wind driven along channel velocities and density (ascrt) fluctuations contoured on axes of depth versus time for Protection during the 1989experiment. The river discharge is much larger during the 1989 experiment than during the1988 experiment and low surface salinities noted in section 3.4 result in a pronouncedpycnocline even at Protection. The wind forcing is a bit stronger in magnitude than in 1988and of much longer periods. The wind driven velocity shown in figure 4.31, shows thewind response essentially confined to the near surface (above 25 m) consistent with theobservations from 1988 that showed the wind response at Tomakstum much more confinedto the surface than at Protection where stratification was weaker. Strong changes in thewind such as the one that occurs at about Julian Day 177 indicate some response (3 layer)as deep as 160 m. Unfortunately the cyclesonde record is short due to an instrumentmalfunction and whether this is typical over the entire record is not certain. Much of thedeeper response however seems to be above sill depth and might be due to baroclinicresponse to the surface slope setup in the inner basin.During the period of approximately constant up inlet winds from Julian Day 187 through196, surface wind driven currents are strong (>30 cm/s) and then appear to taper off (to 20cm/s). Unfortunately the winds are not completely steady and a small drop in the magnitudeof the up inlet wind forcing at about Day 194 is coincident with near zero outflow, likelydue to the surface surface slope adjusting to rebalance with the lower wind stress. Theapproximate steady down inlet winds from Julian Day 177 through 187 shows a nearlysteady decline in the surface wind driven current from approximately 30 cm/s at the start toabout 5 cm/s at the end. This decline may be the surface slope coming into balance with thewind stress but the wind also decreases after day 183. Unfortunately no period of preciselysteady winds is likely to occur in nature to allow a better interpretation of this behaviour.145195185 190175 180 200Cohtours of (0, 2.5,1,5, 10, 20, 30) cfri,s185^190Julian DayInstrument Malfunction1.95 200-30 +30+10 +30 -5^+30^+20^+10 +20 -30 -20 +10-30 -20Depth(m) 0510152025/61989 Protection Wind and Wind Driven Along Channel Current175^180^185^190^195^200•^ ._...._._._____......_.....r._....._- -- ---; ----"-- -- -- -.1-- - ---- -^_, r _I,Figure 431: 1989 Protection Wind and Wind Driven Along ChannelVelocity Contours vs Depth and TimeWind, wind driven velocity in the near surface and wind drivenvelocity over the entire water column. Note that the contours are at 0and +-5, 10, 20, and 30 cm/s in the near surface plot and at 0, +-23, 5, 10,20 and 30 cm/s in the plot of the entire water column.The lack of data below 12 m in the latter half of a record is due thefailure of the cyclesonde to profile during this period. Light shadingdepicts positive velocities (inflow), dark shading negative velocities(outflow).cmis1000-100014610152025195180 185 190 200180 185175175Depth(rn) 0^^0 1^•^1^ I ,1Coptours of (0.01, (p.02, 0.05, 0.1, ap,0.5, 1,2) Kg/m32550-+,01111--r-- Instrument Malfunction100--.0115Cr0190Julian Day195 2001989 Protection Wind and Wind Driven Density (as at)200,^1------- - -------------------r^4.7.^ r^_.1,-1 • _______.-1.0 +0.5^+1 .0^-2.0^-1.0 +0.2^+0.5^+2.0^-1.0 +0.5^-0.5cm/s1000-1000Depth(m) 05.175 180 185 190 195VIL JOOLQ.. Contours of (04, 0.5, 1,2) Kg/m3;Instrumeni Malfunction0Figure 4.32: 1989 Protection Wind and Wind Driven DensityFluctuations (as at) Contours vs Depth and TimeWind, wind driven density in the near surface and wind drivendensity over the entire water column. Note that the contours are at 0and +-0.2, 0.5, 1.0, and 2.0 kg/m3 in the near surface plot and at 0and +- 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0, and 2.0 kg/m3 for theplot of the entire water column. The lack of data below 12 m in thelatter half of a record is due the failure of the cyclesonde to profileduring this period. Light shading depicts density increases, darkshading density decreasing.147Figure 4.32 shows the wind driven density fluctuations. Due to the strong stratification, thesignal is large with fluctuation s in excess of 2 kg/m3 in the near surface. What signal thereis in the deeper water seems to be mainly confined to above sill depth indicating it may bedue to the tilting of the isopycnals along the entire inlet and not just in the outer basin.Figures 4.33 and 4.34 show the wind driven along channel velocities and density (as at)fluctuations contoured on axes of depth versus time for Tomakstum during the 1989experiment Figure 433 shows the wind driven velocity is confined to the near surface in asimilar manner to Protection, perhaps to a slightly greater extent. The deeper depths exhibitmuch less vertical structure as seen by the more random meandering of the zero velocitycontours. An interesting exception are the inflows and outflows near sill depth at JulianDays 180, 186, 195 and 201. These movements might be wind related, perhaps part of thebaroclinic adjustment to the longer period wind forcing in 1989. Wind effects might alsoenhance or retard the deep water renewal process by helping to complete energyrequirements to overcome sill blocking. However these flows are in close antiphase withthe spring/neap tidal cycle (peak spring tides occur near Days 185 and 201) and separationof the wind effects from the fortnightly modulation of deep water renewal is not possiblewithout a longer observational period.Figure 4.34 shows similar and stronger density fluctuations with the wind in the nearsurface at Tomakstum in 1989 as at Protection. However there is even less wind responsein the density fluctuations at depth, although some does appear as deep as 50 m. This typeof response was expected in the inner basin but unfortunately we do not have a densityrecord from the previous year at Tomakstum for comparison.148175^180^185^190^195^200es.cm/s+1000+5000500175^180^185^190^195^2001989 Tomakstum Wind and Wind Driven Along Channel Currents175^180^185^190^195^200Julian DayFigure 4.33: 1989 Tomakstum Wind and Wind Driven Along ChannelVelocity Contours vs Depth and TimeWind, wind driven velocity in the near surface and wind drivenvelocity over the entire water column. Note that the contours are at 0and +-5, 10, 20, and 30 cm/s in the near surface plot and at 0, +-2.5,5, 10,20 and 30 cm/s in the plot of the entire water column.Light shading depicts positive velocities (inflow), dark shadingnegative velocities (outflow).149175 180 185 190 195 200+2_0^+2.0-1.0 +1.0 +1.0 +1.0-1.0 -1. 0 -1.0 +0.2175^180^185 195190 200 1 Wind100-150-200,-250-300-Depth(m) 0,^2550.-1-0.01criVs+1000+5000-500Depth(m) 05101520251989 Tomakstum Wind and Wind Driven Densities (as at)175^180^185^190^195^200Julian DayFigure 4.34: 1989 Tomakstum Wind and Wind Driven DensityFluctuations (as at) Contours vs Depth and TimeWind, wind driven density in the near surface and wind drivendensity over the entire water column. Note that the contours are at 0and +-0.2, 0.5, 1.0, and 2.0 kg/m3 in the near surface plot and at 0and +- 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0, and 2.0 kg/m3 for theplot of the entire water column. Light shading depicts densityincreases, dark shading density decreasing.1504.7 Detided and Dewinded ResponseThe dewinded residual was calculated by subtracting the wind driven component asdetermined in section 4.6 from the detided residual time series. Given time it is assumedthat a surface pressure gradient will build to balance the wind stress and as a result all of therecord mean and the trend were preserved in the dewinded residual. Although thistechnique reduces the variance due to the wind dramatically, it probably does not eliminateall of the energy due to the fact that the original time series are neither continuous orstationary causing errors in the spectral estimates. To remove high frequency noise, thesame cosine tapered spectral filter with a cutoff frequency equal to 0.929 cpd used in thepresentation of the detided data was applied before plotting the dewinded residual timeseries.The results of the dewinding process for the 1988 and 1989 moorings are shown in figures435 through 4.38. These are time series plotted at the same depths and scales as thedetided and wind driven time series and against the filtered wind time series for reference.Figure 4.35 clearly shows a mean outflow at 2 m during the 1988 experiment with theTomakstum mooring showing a continuous outflow over the entire record length butProtection dropping to a near zero outflow in the second half of the record. Both recordsshow a trend of decreasing outflow with time despite the river discharge increasing ataround Day 105. A sudden decrease in outflow at Protection and Tomakstum at Day 102appears to be correlated with the wind. It is worth noting that the runoff and the wind arecoupled, at least at the lower frequencies below a period of 7 to 10 days, through theprevailing meteorology and have a correlation of 0.7 for 1988 and 0.6 for 1989 with a lagof 2 to 3 days. As a result, the dewinding process may also be removing part of theestuarine velocity response at these lower frequencies. At 12 m at Protection and 15 m atTomakstum the two negative peaks (stronger outflows) do occur, one around Julian Day1511988 Filtered Wind and Dewinded Along Channel VelocitiesProtection^ TomakstumWind^1i 11111UtiartIMMEWVagvarama-sliI^1t it:tt1-...........w2 m I^1^-1---4"---1---1--r1tihimi-......maiiiIMPIIIIIIIIIIIIMINUNIMININE^Te m:^1t tAulli20^1irirl,V111.511P1111P.^6. 'A. Am...a.... "11WIPENIMMIIt150^11i1tIti Win.^t1^I11^I11moll 451111M1111111 1^111^2 m1 I^4 m11I-- -I- .--1^.I115 m ts i^1I 3i m:t^1-r--0801---4 'tI1^;-^•I ;t i^i-1111....Nrirr'woirraeligillt!....1.1111111WOPPw..... 1I1270!cm/s7500-750250-25250-2512.50-12.512.50(.1;^ -12.58.250-6.258.250-6.25cm/s750-750250-25250-2512.50-12.512.50-12.56.250-6.256.250-6.2585^90^95^100 105 110 115^85^90^95^100 105 110 115Julian Day^Julian DayFigure 4.35: 1988 Along Channel Wind vs Selected Dewinded CurrentsNote both wind and dewinded currents have been filtered with a spectral filter with a cutoff frequency witha period of 0.929 days. Depths shown correspond to those chosen for the detided times series presented infigure 4.9.95 and another at Day 110. These increases are coincident with the spring tides and may beattributed to the volume compensation for the deep water renewal that is enhanced by theadditional available kinetic energy. The presence of these effects at 12 metres, well into thesurface layer, is surprising. At Protection inflow is initially seen at 150 m and then at 120m towards the end of the record, likely the signature of the renewal process in the outerbasin. At 180 m at Tomakstum, an inflow is seen towards the end of the record, and anincreasing return flow is present at 270 m. This may be the signature of the deep waterrenewal process in the inner basin and a compensating volume flow underneath.Figure 436 show the dewinded velocity time series for the 1989 experiment. The nearsurface flow at 2 m is outward over the entire record and and with a larger velocity than in1988, as noted earlier. The river runoff has peaks at around Julian Day 176 and 195. Slightincreases in surface outflow can be seen at Tomakstum several days afterward although thesignal is very small. It would take approximately 2.7 days for water to travel the 60 kmfrom the head to the Tomakstum mooring at 25 cm/s.Figure 4.37 and 4.38 show the dewinded density time series for the two experiments.Despite having subjected the records to the dewinding process approximately 50 to 80percent of the derided variance remains in the 2 m records. In 1988 a trend towardsdecreasing densities with time is present, but as a sharp increase in river runoff does notoccur until Julian Day 105 the estuarine signal may at least be partially obscured by thethickening of the surface layer caused by the net up inlet wind stress. In 1989 decreases inthe 2 m density are roughly coincident (when the lag of 2.7 days for along inlet transport istaken into account) with the sharp increases in river discharge at days 175 and 192. The153Wi d"nonBM/MIMI;----4– tI-^-- -.------.. -^•.- ..---.....n,....^...: _p i..^•-•12 II i-tI50i— --- -: -- -- -1It.1 1I^1I 1^–r ^-I-I!;____ .....140It1!Mild-- hiliiii Jr___.^._- --I- -- - ----- -- ...... L.__^1^!!!!! 1 ._I^1s ; :^11aIli2;m^1.I^_I;t4:m^;■- ^-.4 15 IraI^;....--......–.....s^;-t^-1"---,...........70 1 m^1 I^;i------ 1"-----4-----t------- 1--------4------L .4-^-;■_-.4111arirs.120! M^II i^1---i-----+--- -----1-----1-^-^...... _........^..^...-..../1Ii^I,_^I^I - 1cm/s7500-75025-25250-2512.5-12.512.50-12.58.25-8.258.250-8.25cm/s7500-75025025250-2512.50-12.512.50-12.58.250-8.258.250-8.251989 Filtered Wind and Dewinded Along Channel VelocitiesProtection^ Tomakstum175 180 185 190 195 200^175 180 185 190 195 200Julian Day^Julian DayFigure 4.36: 1989 Along Channel Wind vs Selected Dewinded CurrentsNote both wind and dewinded currents have been filtered with a spectral filter with a cutoff frequency witha period of 0.929 days. Note that where the cyclesonde failed to profile continuously, a linear interpolationbetween detided samples was used to provide a continuous time series. Depths shown correspond to thosechosen for the detided times series presented in figure 4.10.-1500-1500 254m250U cm/s+1500U cm/s+15002m20,2525I^; I^II 1 It^1t7o m^I I120ot (IV m3) 85t III I Mii^t^11 9 m^1 r1^I^_J ii II I^I^I I30m^t^ii 90^95^100 105 110 115Julian Day25251988 Filtered Wind and Dewinded Densities (as at)Protection^Tomaketum2520, 252525252520ot (kg/ M3)I4^i I^IiIiir -I-t^1t iiIIIIIIII^II II^I--I^II2m''-'''-'t.-s--'4"-''''■-■••'+-'-"--1'-'-'I IIt^r— --1--------..----1,--1-1i1^rt^4m 1^r t^I1 1i ^I12m 1 :r:t 11%../■^ I 1^I^1 ^I1 I25m t^1II^It 1t^Ig 1 1 1120g ^tt 11^ml ^g1^11 11^1150 ^I^  t 11^tml 1i^1t^it 11^1tt 1 I^I1AC^90^95^100 105^110^115Julian DayFigure 4.37: 1988 Wind vs Selected Dewinded Density (as at)Note in the above composite plot, at increases upward and each division is 5 kg/m3. Both wind anddensities have been filtered with a spectral filter with a cutoff frequency with a period of 0.929 days. AtTomakstum the 12 m S4 was not equipped with a conductivity cell and the conductivity sensor of thecyclesonde failed. Depths shown correspond to those chosen for the detided times series presented infigure 4.12.+150001500 20...21YOul___ iI^11 ;;t-r----4--------+---1---tt^,r;;1 t;1 I ; 1 ;;2 tt i11Iittttiti tI ^at -.1 r —11tt i t ;t12 m I14 1 I 1251m1 1 i I it150 mt1;t 11 r. 1 ,175 180 185 190 195 200Julian DayWindWillii^'^1I^;1 Aiiii"iii^■;y i^"-maw11:. 4* A • 16L 44 114 ;;Y L^ilir 1^;^Ili 1PI ;I I1Si&.......^—1; i8 n111119 i.ii1.n.^..Aromorted200111111111, 11 i2301 m 1^!IIii270; mI' ------ r.----•1^!1– ----- + ------ 1----;^;1i----4--115,2525ot (kg/ in') ot (kg/ m3) 175 180 185 190 195 200Julian Day+150001500201105,15, 2515, 25251105,15,251989 Filtered Wind and Dewinded DenisItles (as at)Protection^U cm/s^ Tomakstum U cm/sFigure 4.38: 1989 Wind vs Selected Dewinded Density (as at)Note in the above composite plot, at increases upward and each division is 5 kg/m3. Both wind anddensities have been filtered with a spectral filter with a cutoff frequency with a period of 0.929 days.Thewind influence on the density field is larger than in 1988 and more confined to the surface layer due to thestronger pycnocline. Depths shown correspond to those chosen for the detided times series presented infigure 4.13.mean river discharge and its variations are much larger in 1989 perhaps making theestuarine signal much easier to detect.Figures 4.39 and 4.40 present the dewinded velocity and density data contoured againstdepth and time for the 1988 Tomakstum mooring. Figure 4.39 shows that a constantoutflow is present in the near surface and extends to approximately 5 or 6 m and sometimesdeeper. An inflow just below the outflow appears centred at about 15 m except for twoshort periods centred on Julian Days 95 and 110. This surface outflow with an inflowimmediately below is certainly suggestive of classical estuarine circulation, with fresherwater flowing seaward on the surface and an inflow of salt water underneath to compensatefor the entrainment of salt water as the surface flow moves seaward. These depths confirmthat the thickness of the surface layer as estimated in section 4.2 (10 m) from the 29.5 daymean velocity was reasonable. Given the trend towards decreasing density with time evenat 10 m perhaps the estimate of the density of the inflowing layer water is also reasonablewhen figure 4.40 is consulted. The velocity of the surface layer at Tomakstum in 1988 asestimated from Knudsen's relations agreed with the 29.5 day mean observations (6.0 cm/s)also suggesting these estimates were representative of the record mean values. There doesnot appear to be any clear signal of the river discharge in the surface outflow and this isconsistent with the results we obtained from our analysis of the 29.5 day mean circulationpresented in section 4.2.At depth from 70 m (approximately sill depth) to 150 m a band of inflow occurs withstronger inflow centred on Days 95 and 110. These stronger flows are approximately inphase with the spring tides and probably show the enhancement of the deep water renewalprocess by the added kinetic energy of these tides. Given a deep water buoyancy period atProtection of 5 minutes/radian (from section 4.2) and a spring to neap M2 tidal variation ofapproximately 12.5 cm/s peak and by applying the blocking formula (h = u / N) of157-5-10-5 -5-10 -10-10 -5 -10-5-10Depth(m) 05-1015.20-25.30-1988 River Discharge and Tomakstum Dewinded Along Channel Current85^90^95^100^105^110^115-- --------.■I!- _I85^90^95^100^105^110^115Jullan DaysFigure 4.39: 1988 River Discharge and Tomakstum Dewinded AlongChannel Velocity Contours vs Depth and TimeRiver discharge, dewinded velocity in the near surface anddewinded velocity over the entire water column. Note that thecontours are at 0 and +-5, 10, 20, and 30 cm/s in the near surfaceplot and at 0, +- 2.5, 5, 10, 20 and 30 cm/s in the plot of the entirewater column. Light shading depicts positive velocities (inflow),dark shading negative velocities (outflow).m3/s2001000158de Young and Pond(1988) from section 2.2.2, it appears that the added kinetic energy ofthe peak spring tides may be sufficient to lift renewal water by as much as 38 m.There appear to be flows back towards the sill both above and below the penetration. Theseare likely displacements due to the penetration of the new water. The enhancement of deepwater renewal on the spring tides also provides a possible explanation for the interruptionof the inflow of salt water seen in the estuarine circulation. Due to the enhanced inflow ofrenewal water during the spring tides and conservation of volume, the salt inflow may beadvected seaward (and hence appear as an outflow). The concept of two vertically nestedthermohaline cells presented in section 2.0 provides a reasonable interpretation of theseobservations with conservation of volume serving as a coupling mechanism between them.Figure 4.40 shows the river discharge and dewinded density at Tomakstum to 9 m.Unfortunately the 12 m S4 lacked a conductivity cell and the cycle-sonde conductivity cellfailed during this deployment. The trend over the record is towards decreasing salinity inthe surface layer, but while this is not inconsistent with increased river discharge, the trendtowards lower density appears in advance of the increase of runoff on Day 105. One is leftto conclude that the lowering of the density of the surface water is therefore due to thewind. At the beginning of the record a steady decrease in the 22.5 contour may be due towind mixing from the oscillatory winds during the first half of the record. Due to thevertical exchange of salt, mixing should also raise the density near the surface. There is noevidence of this in the observations, however the upper record is at a depth of 2 m isperhaps too deep to show this effect. During the second half of the record, strong up inletwinds may thicken the upper layer as they retard surface outflow and build a surface slopewhose pressure gradient balances the wind forcing. Perhaps the added fresh water from theriver also is playing a part in this effect towards the end of the record.1591988 Runoff and Tomakstum Dewinded Near Surface Density (as at)85^90^95^100^105^110^115m3ls2001000Depth(m) 2- -----___.r. -^.. . - ........ .;- t*--1Z------..1 - '"`""•""•`-.1- 1Julian DayFigure 4.40: 1988 River Discharge and Tomakstum Dewinded Density(as at) Contours vs Depth and TimeRiver discharge, dewinded density in the near surface to 9 m. The12 m S4 lacked a conductivity cell and the conductivity cell on thecyclesonde failed. The 22.5 contour drawn with a heavier line forreference.160Figures 4.41 and 4.42 present the dewinded velocity and density data contoured againstdepth and time for the 1988 Protection mooring. Figure 4.41 shows that the surfaceoutflow does not persist for the entire dewinded record at Protection. This result issomewhat puzzling, particularily as the dewinding process appeared to be reasonablysuccessful at Tomakstum. Surface velocities are larger at Tomakstum than at Protection andperhaps the sudden change in the wind regime is not handled as well by the technique used.To the north of Protection Point, Tribune Channel connects Knight Inlet to other sources offresh water such as Kingcome Inlet. One might speculate that fresher water entering viaTribune Channel is flowing towards the head of Knight Inlet, with the 'surface" layer ofKnight Inlet being more dense, sinking below. However, there is a general outflow on thesurface and an inflow underneath between 15 and 50 m. As at Tomakstum, this inflowappears to disappear periodically likely also due to return flows from penetration of waterdue to deep renewal in the outer and inner basins.The depth of the surface layer estimated from the 29.5 day mean velocity in section 4.2 was12 m. This appears to be an underestimate based on these results and perhaps 25 m wouldbe a better layer thickness estimate. The velocity of the surface layer estimated fromKnudsen's relations for a surface layer thickness of 12 m was 16 cm/s considerably largerthe observed 29.5 day mean of 4.0 cm/s. Correcting the surface layer thickness for theobserved 25 m and using the dewinded density of the inflowing water (as at) of 23.9 (fromfigure 4.42) would give a surface layer velocity estimate of 5.4 cm/s, close to thatobserved in the 29.5 day mean. It appears that the major difficulty with using Knudsen'srelations for such estimates is in determining an appropriate surface layer thickness to use.At Protection the mixing due to sill processes likely breaks down the initial stratificationallowing the wind to mix the surface of the water column more easily. The surface layerthickness can then be expected to vary with time and such difficulties are understandableparticularily when data from a single CTD cast are used for the estimate.161m3/s2001988 River Discharge and Protection Dewinded Along Channel Current85^90^95^100^105^110^115ir"--14^1..4r ...4ri rDepth(m) 02550100150Julian Days85 90 95 100 105 110 115Figure 4.41: 1988 River Discharge and Protection Dewinded AlongChannel Velocity Contours vs Depth and TimeRiver discharge, dewinded velocity in the near surface anddewinded velocity over the entire water column. Note that thecontours are at 0 and +-5, 10, 20, and 30 cm/s in the near surfaceplot and at 0, +- 2.5, 5, 10, 20 and 30 cm/s in the plot of the entirewater column. Light shading depicts positive velocities (inflow),dark shading negative velocities (outflow).162At 170 m, there appears to be strong inflows centred on Julian Day 87 and 100 roughlycoincident with the neap tides. Not much movement is observed towards the inner sill onDay 95 but movement is seen from 100 to 150 m centred on Day 110. Perhaps the latter isthe movement towards the sill caused by the deep water renewal in the inner basin,although the lack of a strong flow on Day 95 is somewhat disappointing. If thesemovements on the spring tides can be explained by renewal of the inner basin, then perhapsthe stronger inflows on the neap tides are penetrations over the outer sill into the outer basinas part of the deep water renewal there. The outer sill is shallow and extended and it islikely that the enhanced mixing due to the energy of the spring tides inhibits and notenhances deep water renewal in the outer basin as found in Indian Arm by de Young andPond(1988) and Puget Sound by Geyer and Cannon(1982). It seems that Knight Inlet has,at least during part of the year, two distinct partitions in its deep water exchange cycle withthe outer basin receiving deep water on the neap tides and the inner basin on the springtides.Figure 4.42 shows the dewinded density at Protection in 1988. As with Tomakstum, thereis a trend towards a lower density with time in the near surface. However the timing of thedecrease suggests that as with the Tomakstum record that it is mostly due secondary windeffects and not due to the direct effects of increased river discharge at the end of theexperiment. At depth the rising of the 24.0 and greater isopycnals indicate that renewal istaking place in the outer basin and that greater potential energy is available in the deep waterto drive renewal into the inner basin. This increase in energy towards the end of the recordis consistent with the larger flow noted on the spring tide in the velocity record forProtection and the evidence of deep water renewal occurring deeper with time in thedewinded record at Tomakstum.16311511010095 105908511:,.j i^ 111=11=1111111111menes=g 4-1988 Runoff and Protection Dewinded Density (as at)90^95^100^105^110^115I 1..•3.0^'4 .....„_,,—.........e;—.;. - •-------"".1L.■'"""'''mow23_.4. :23.9 23.9 23.924024 a 24.024.024.1 24.124.1;' 4 11i 24.2■ 24.g1124.2; I24.3!ii1 1,24.2 I1;1 1, 1I 11_ 185^95^100^165^110^115Julian DayFigure 4.42: 1988 River Discharge and Protection Dewinded Density(as at) Contours vs Depth and TimeRiver discharge, dewinded density in the near surface and dewindeddensity over the entire water column. The 23.5 contour is drawnwith a heavier line on both density contour plots for reference.m3is200100Depth(m) 051015202585Depth(m)25510150-164Figures 4.43 through 4.44 present the dewinded velocity and density data contouredagainst depth and time for the 1989 Tomakstum mooring. Figure 4.37 shows near surfaceoutflow for the entire record length to a depth of 5 to 7 m. Just underneath this outflow to adepth of perhaps 15 m (23 m at Julian Day 179) is an inflow again suggestive of classicalestuarine circulation and a salt water inflow to compensate for the entrainment of salt water.While the surface layer thickness of 6 m used in the estimates of surface layer velocity insection 4.2 looks reasonable, the estimate of 11 cm/s from Knudsen's relations and theobserved 14.9 cm/s 29.5 day mean are not in close agreement. An inspection of thedewinded density field near 15 m reveals a strong density gradient in this error and perhapsthe original estimate of the inflowing layer density (as at) of 22.4 is slightly too large. Forexample decreasing the inflowing density to 19.8 produces an estimate for U0 fromKnudsen's relations of 15 cm/s and this is certainly reasonable when looking at thedewinded densities in figure 4.44. It appears that when stratification is strong producinglarge density gradients in the near surface deciding on the 'correct' density to represent theinflowing layer is not particularily straight forward.Between Days 190 and 198 there is a deep outflow although there are two occurrences ofvelocity zeros, one at day 191 and one at day 197. From 15 m to 150 m there is generallyoutflow, sometimes stronger than 5 cm/s. These stronger outflows are coincident with thespring tides at Julian Day 172, 185, and 201. The first centred at Day 175 and 70 m depthhas only a small volume inflow at 250 to 300 m and perhaps the bulk of the deep waterrenewal is occurring below the deepest Anderaa at 310 m or cross channel effects are takingthe bulk of the inflow to one side of the mooring. At Day 185 another region of outflowoccurs at 50 to 100 m and again only a small inflow at 250 to 300 m. At the end of therecord another mid depth outflow occurs paired with and preceded by a much largervolume of inflow at depth. If the deep water renewal was initially occurring deeper than the165m3/s800175^180^185^190^195175 180 185 190 195 2004001989 River Discharge and Tomaketum Dewinded along Channel CurrentsJulian DayFigure 4.43: 1989 River Discharge and Tomakstum Dewinded AlongChannel Velocity Contours vs Depth and TimeRiver discharge, dewinded velocity in the near surface anddewinded velocity over the entire water column. Note that thecontours are at 0 and *5, 10, 20, and 30 cm/s in the near surfaceplot and at 0, * 2.5, 5, 10, 20 and 30 cm/s in the plot of the entirewater column. Light shading depicts positive velocities (inflow),dark shading negative velocities (outflow).1661989 River Discharge and Tomakstum Dewinded Density (as at)180 185 190 195 200400"FigreiliTsFtia-rge--01^1523;^5Depth(m) 0510152025Depth(m) 02550100 -150-200-250-300175^180^185^190^195^200--- 1--- - • .--. - ..;.-,... , ...--....", 222424.224 2424 224.224.3 24.3 24.3175^180^185^190^195^200Julian DayFigure 4.44: 1989 River Discharge and Tomakstum Dewinded Density(as °t) Contours vs Depth and TimeRiver discharge, dewinded density in the near surface and dewindeddensity over the entire water column. The 22.0 contour is drawnwith a heavier line on both density contour plots for reference.167310 m Anderaa (the actual depth at the Tomakstum mooring was 340 m), then as renewalcontinued the depth of the penetration might be expected rise as the density of the innerbasin increased, thus explaining why the large outflow seen at Day 175 has almost nocorresponding inflow while the more modest outflow at the end of the record has a largercorresponding inflow. It may be that renewal is happening on a continuous basis during the1989 experiment due the high potential energy of the water available at the depth of theinner sill as shown in figure 3.5. The spring tides would then be simply enhancing the flowat these times and accounting for the general outflow over most of the record at 15 to 150m.Figure 4.44 shows the dewinded density for Tomakstum. The depth of the 15.0 isopycnalappears to be correlated with the river runoff, becoming shallower with lower dischargeand becoming deeper again when the river runoff increases at the end of the experiment.The depth of the 22.0 through 23.5 isopycnals however appear to decrease over time,indicating that the water below about 10 m is becoming more dense. If deep water renewalis occurring one would expect that all of the isopycnals would lift as the deep inflowsdisplace deep water and lift it towards the surface raising the potential energy of the basin.However both the 24.0 and 24.3 isopycnals are almost flat, perhaps due to an error in theinter-calibration of the cyclesonde which profiled only intermittently during the start of therecord making conductivity adjustments difficult This picture is however consistent withthe density contours from the deployment and pickup cruise surveys presented in figure3.4. Most of the renewal appears to occur deeper than the Tomakstum 310 m Anderaa. Themaximum depth at this mooring site was 340 m while the deepest part of the inner basin isslightly over 500 m.Figures 4.45 through 4.46 present the dewinded velocity and density data contouredagainst depth and time for the 1989 Protection mooring. The second part of the record is1681989 River Discharge and Protection Dewinded Along Channel Currentrn3/s^175^180^185^190^195^200-10^-10 -5^-10^-10^-10^-10^-10^-10 -20^-20 -10,Alier''' 41...it.i.o. a ;.A.0 0^i 0^0AIra -2 .5. 4.5 Contours ot (0,;2.5,5, 10, 20) enhisInstrurneni Malfunction ---1-11.,_ 0 _ :,...,- 0 ....-2. --I +^ ....175^180^185^190^195 200- - -, ,,,Is,*)^',. ...4°`•-•lisir.IOWc".4.1 r.^....— •■•-.;,—.,..M...,.—^Nt•^'!-"• 5-0^000%^.0^p .25^+2.5•It2-5.0 1 ■I ;1 ;I■, ;0 ;+ I+2 5 ;.^•^. ;.^•:. 2 '^..I4.--.----- InstrUMeni MEW UnCtiOn —"---0/1.+ • • :• •.:•;1-5.0;•: ;I 1.^• ;. . ;2 5 i.&a;,.: 5t;I;175^180^185^190^195^200Julian DayFigure 4.45: 1989 River Discharge and Protection Dewinded AlongChannel Velocity Contours vs Depth and TimeRiver discharge, dewinded velocity in the near surface anddewinded velocity over the entire water column. Note that thecontours are at 0 and +-5, 10, 20, and 30 cm/s in the near surfaceplot and at 0, +- 2.5, 5, 10, 20 and 30 cm/s in the plot of the entirewater column. Light shading depicts positive velocities (inflow),dark shading negative velocities (outflow).Depth(m) 0510152025Depth(m) 02550100150169missing below 12 m due to the failure of the cyclesonde to profile during the last half or theexperiment. Figure 4.45 shows a continuous near surface outflow between 5 an 10 m atProtection. The thickness of the outflow does vary and might possibly be correlated withthe river discharge, with increased discharge giving rise to a thicker surface layer. Areexamination of the Tomalcstum record reveals that it also exhibits some of this behaviour,although any such relationship is obscured in the 1988 data perhaps due to the weakerestuarine forcing and the greater mixing due to weaker stratification. Underneath between10 and 20 m there is generally inflow. Again this structure is consistent with what wewould expect from estuarine circulation. The estimates of the surface outflow calculatedwith ICnudsen's relations would almost match the 29.5 day mean observations (7 cm/s) if10 m instead of 8 m had been taken as the surface layer depth in section 4.2.At around 100 m there is enhanced flow towards the head of the inlet coincident with boththe spring and the neap tides and it is not inconsistent with the analysis from the 1988 dataof renewal of the outer basin occurring or being enhanced on the neap tide while renewal ofthe inner basin occurs or is enhanced on the spring tide. During the neap tide at aroundJulian Day 180 the inflows appears confined above 120 m and there is some return volumecompensation underneath. If this water were penetrating into the outer basin after somerenewal had already taken place this behaviour would be expected. Between 25 and 70 mthere is an outflow that is likely volume compensation due to deep water renewal.Figure 4.46 shows the depth of the 15.0 isopycnal may be a function of river runoff asdiscussed for Tomakstum. The 23.0, 24.8, and 24.85 isopycnals appear to rise with timeconsistent with rise in the potential energy of the water column due to renewal. Howeverthe lack of movement by the intermediate contours is puzzling. The fall in the 24.0isopycnal is also pu771ing but appears to agree with the C'TD data. One would expect thatthe volume compensation outflows occurring at these depths would slowly raise these170175^180^185^190^195^2001111101111111161 11 11111- -- .......^.... -. In-Pls80040024.5450.-100-24.724.824.524.74.824.851Depth(m)232523 3=-212424.3instrument; Malfunction150-./N24.851989 Runoff and Protection Dewinded Density (as at)-4-1— Instrument MalfunctionDepth(m) 0510152025175^180^185^190^195^200175^180^185^190^195^200Julian DayFigure 4.46: 1989 River Discharge and Protection Dewinded Density(as at) Contours vs Depth and TimeRiver discharge, dewinded density in the near surface and dewindeddensity over the entire water column. The 22.0 contour is drawnwith a heavier line on both density contour plots for reference.171isopycnals with time as the inner basin water is renewed. Perhaps from sill depth to thebottom of the estuarine circulation vertical shear is mixing some of the surface water downinto the deeper water lowering its density as it flows seaward.172Chapter 5Summary and ConclusionsThe analysis presented in Chapter 4.0 attempts to describe the low frequency residualresponse of a high runoff inlet in terms of the longer period forcing of river runoff, deepwater renewal, and wind. Month long observations taken throughout the water columnboth inside and outside the inner sill of Knight Inlet during the onset of the freshet in 1988and 1989 were analysed. Both the 29.5 day mean and the detided and dewinded recordsshow vertical structures consistent with two vertically nested thermohaline circulation cells,an estuarine outflow at the surface with an inflow of salt water directly underneath and deepwater renewal with flow back towards the inlet mouth both above and below thepenetration. These two structures are coupled through conservation of volume and possiblythrough vertical mixing induced by shear, sill processes, and the wind.5.1 Estuarine CirculationThe estimated velocity of the surface outflow from Knudsen's relations agreed well withthe observed 29.5 day mean velocity vertically integrated over the surface layer providing arepresentative depth for the surface layer and the density of the inflowing salt water couldbe determined. Outside the sill, mixing initially from sill processes and then enhanced bythe wind, makes the determination of the depth of the surface layer difficult. Inside the sill,at least during high runoff conditions, strong density gradients in the region of the saltwater inflow requires careful determination of the the density of the inflowing salt water.The detided and dewinded records show that in simplifying an estuarine system to a twolayer representation care must be taken to understand that the depth of the surface layer andthe densities of the two layers vary with time. It appears that wind forcing is one of the key173contributors to this variance with wind mixing deepening the surface layer by eroding thepycnocline and by the surface setup in response to longer period forcing.Values for the surface layer velocity determined from Knudsen's relations by van derBaaren(1988) appear reasonable when compared with the observations with the exceptionof those outside the sill. Also the along inlet surface slopes of Wetton(1981), van derBaaren(1988) and myself determined using dynamic height calculations are consistent withthe corresponding river discharge. Therefore van der Baaren's conclusion that the balanceof forces along the inlet is between the the surface pressure gradient and the interfacialfriction appears to be valid. My 29.5 day observations show a deceleration in the surfaceoutflow from inside to outside the sill. This observation is consistent with the thickening ofthe surface layer and the vertical exchange of momentum by mixing. It is likely that thehigher velocities outside the inner sill estimated by van der Baaren using Knudsen'srelations are in error due to the difficulty in estimating surface layer thickness from a singleCTD cast. Therefore it is likely that the inertial terms do not play a major role in the balanceof forces there and that the balance remains between the surface pressure gradient and theinterfacial friction all along the inlet.Isobaric slopes determined from dynamic height calculations using CTD survey data andusing a level of no motion determined from the 29.5 day mean observations show a surfaceslope in the order of 10 cm/100 km driving the estuarine outflow and small reversepressure gradients just underneath the surface, consistent with the inflow of salt waterbeing driven by entrainment.The 29.5 day mean velocity and density profiles suggest that the primary signature of theestuarine forcing is in the density and not the velocity fields. With the river dischargeduring the 1989 experiment an average of 5.7 times the river discharge during the 1988174experiment, the change in the 29.5 day mean density differences between the surface waterand the water below the velocity minimum at the Tomakstum mooring was 6.6. Whilegreater surface velocities were observed at both Tomakstum and Protection during 1989,greater shear in the surface layer itself prevented the volume transport from beingsubstantially different. This behavior is consistent with the higher density gradient in 1989reducing the entrainment of salt through the increased stability in the water column. Thisresult supports the interfacial friction coefficients calculated by van der Baaren(1988) whichshowed an order of magnitude difference between a low runoff and high runoff regime.The dewinded velocity time series show no clear correlation between the runoff and surfacelayer transport during either experiment. If the balance of forces is between the along inletpressure gradient and the interfacial friction as proposed by van der Baaren this result is notsurprising. In both experiments river discharge increased towards the end of the record andthe near surface isopycnals deepen with time. However the timing of the variations suggestthat secondary effects of the wind such as mixing and the deepening of the surface layer bysetup certainly contribute to a large part in this observation. However, during the 1989experiment when stratification is high and wind mixing suppressed, a fluctuation followingthe variability in the runoff signature is visible close to the surface. Many of the isopycnalsjust below the first instruments rising in what appears to be a response to the deep waterrenewal of the inner basin.5.2 Deep Water RenewalThe 1988 deployment and mid-experiment and the 1989 deployment and pickup CTDsurveys reveal that water of sufficient potential energy to displace inner basin water at leastat some depths is present outside the inner sill in both years. The inner basin densities areslightly lower and densities outside the inner sill higher during the 1989 experiment. The175movement of the isopycncals between the two cruises suggest that deep water renewal istaking place in both years, with replenishment at deeper depths in 1989. The 29.5 daymean velocity profiles suggest that deep water renewal is indeed taking place and that returnflows due to volume compensation are taking place both above and below the penetrations.An examination of the dewinded residual shows that deep water renewal in the inner basinof Knight Inlet appears to be triggered or enhanced by the additional kinetic energy of thespring tides. This is consistent with the blocking equation of deYoung and Pond and thecontrol of the renewal process for well stratified inlets with deep sills (i.e. with a Froudenumber < 1). Inflow movements during the neap tides at Protection during both yearssuggest that the outer sill which is shallow and extended inhibits renewal on the springtides. The outer sill, having larger tidal velocities and a lower internal wave speed fromreduced stratification (i.e. with a Froude number > 1) has enhanced mixing during thespring tides which reduces the density of the water available for penetration into the outerbasin. Thus deep water renewal in the outer basin is favoured during the lower velocityneap tides. The renewal of the deep water of Knight Inlet is a two step process, with theouter basin renewing on the neap tides and the inner basin renewing once the outer basinhas filled with suitable source water, most likely on the spring tides.The dewinded velocity also shows inflow just below the surface layer more or lesscontinuously. Interruptions tend to be synchronous with the enhanced inward flows ofdeep water renewal on the spring tides suggesting that when the inflow disappears it isactually being advected out of the inlet by the volume compensation due to the deeperpenetrations. This behaviour illustrates the coupling that exists between the two verticallynested circulation cells. It is likely that mixing due to vertical shear, sill processes, and evenwind also serve to couple these two circulation cells.1765.3 WindThe influence of the wind dominates over all other processes in the surface layer of astratified water column. At depth the wind response is a function of stratification and it cancontribute to significant motion throughout the water column when stratification is weakerduring modest runoff. The influence of other mixing processes that break downstratification, such as those in the vicinity of the sill, can cause a major change in windresponse. During 1988 at Protection, this wind response has a multi-layered structure butthe exact nature of the structure changes with time indicating changes in phase response.Wind driven currents greater than 2.5 cm/s were observed at the bottom of the watercolumn. In 1989, an extremely sharp pycnocline effectively limits the direct influence of thewind to the surface layer and the vertical structure of the wind response at depth is muchless defined. The baroclinic response to wind setup is consistent with Buckley andPond(1976) who proposed that response time to wind stress in a stratified water column isdominated by the baroclinic adjustment and not the barotropic adjustment of sea surfaceslope alone.At Tomakstum in 1989 there is a large contribution by the wind to the detided densityvariance between 150 and 200 m. It is likely that the wind is aiding the deep water renewalprocess through the tilting of the isopycnals. However the time scales of the 1989 windforcing and the deep water renewal are similar and the certainty of the analysis could beimproved by longer recordsvan der Baaren(1988) found that interfacial friction was a function of wind. 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