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A simplified model of interannual water temperature variations in Hecate Strait and Queen Charlotte Sound Ma, Helai 1992

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A SIMPLWIED MODEL OF INTERANNUAL WATER TEMPERATUREVARIATIONS IN HECATE STRAIT AND QUEEN CHARLOTFE SOUNDbyHelai MaB.Sc., Ocean University of Qingdao, 1982M.Sc., Ocean University of Qingdao, 1985A ThESIS SUBMflmD IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIES(Department of Oceanography)We accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1992© Helai Ma, 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.Department of 0 4/VC k,4-pf-I)’The University of British ColumbiaVancouver, CanadaDate OCi. 1, /9?DE-6 (2/88)ABSTRACTThe thermal conditions in the Hecate Strait-Queen Charlotte Soundregion are studied. A coupled upwelling/mixing model was developed tosimulate the interannual variability of temperature in the region; the switchbetween the upwelling and mixing models is controlled by the monthly BakunIndex. A theoretically derived velocity field is applied in the upwelling modelin summer and a simplified upper mixed layer model is used to simulate winterconditions. The temperature variation is integrated by a finite differencescheme. The region is simplified as a two-layer wedge-shaped volume torepresent the Moresby Trough that forms the main passage of cold waterintrusion into Hecate Strait. The model was run for 37 years and hindcasted theinterannual variations of temperature in the Hecate Strait-Queen CharlotteSound region from 1953 through 1989. A comparison was made between themodel results and observed data. The general features of the temperaturevariations are well reproduced by the model results.iiTABLE OF CONTENTSPAGEABSTRACT iiTABLE OF CONTENTS iiiLIST OF TABLES vLIST OF FIGURES viACKNOWLEDGMENTS x1. INTRODUCTION 12. OCEANOGRAPHIC CONDITIONS IN QUEEN CHARLOYI’ESOUND-HECATE STRAIT REGION 42.1.Bathymetry 42.2 General features of the waters in the region 42.3 Bottom cold water intrusion 132.4 Wind forcing 163. THE MODELS 193.1 Hypotheses 193.2 Model geometry 213.3 Bakun Index 213.4 Upwelling model 243.4.1 Formulation of the velocity field 243.4.2 Adjustment of the velocity field 323.4.3 Determination of solar radiation 383.4.4 Formulation of the temperature field 393.4.5 Boundary conditions 403.4.6 Model results 403.5 Mixing/Cooling model 433.5.1 Introduction 43iii3.5.2 Wind forcing 433.5.3 Radiation and effective back radiation 433.5.4 Sensible heat flux 443.5.5 Latent heat flux 443.5.6 Entrainment speed 453.5.7 Mixed layer depth 463.5.8 Mixed layer temperature 463.5.9 Model results 474. COUPLED UPWELLING/MIXING MODEL 494.1 Forcing conditions 494.2 Model results and discussion 535. COMPARISON OF MODEL RESULTS AND OBSERVED DATA 696. CONCLUSIONS 797. BIBLIOGRAPHY 81ivLIST OF TABLESPAGETable 1. Monthly mean solar irradiance at gound level during clear 38weather at Cape St. James (in Cal cm2 day 1)Table 2. Attenuation coefficients for total downward irradiance at 38depths 0 -80 m. (from Ivanoff, 1977)Table 3. Comparison of model results with observed data at x=0 70Table 4. Comparison of model results with observed data at x=100 km 70VList of FiguresPAGEFigure 1 Map of Queen Charlotte Sound-Hecate Strait region. 5The dotted line is the 200 m depth contour and thechain-dotted line is the 2000 m contourFigure 2 Long-term monthly means and standard deviations of 7sea surface temperature at 4 lightstations located in theQueen Charlotte Sound-Hecate Strait region (fromDodimead, 1980)Figure 3 a)Horizontal distribution of temperature at 50 m and 8200m depths in summer from an oceanographic cruise inthe Queen Charlotte Islands region (from Thomson,1989)b) Horizontal distribution of temperature at 50 m and 9200 m depths in winter from an oceanographic cruise inthe Queen Charlotte Islands region (from Thomson,1989)Figure 4 Stations C and E and sections 1-5 in Queen Charlotte 10Sound—Hecate Strait region (from Dodimead, 1980);thick dashed line shows axis described in Fig. 8Figure 5 a) Vertical distribution of temperature at station C in 11summer and winter months. Circled numbers show theyear of samplingb) Vertical distribution of temperature at station E in 12summer and winter months. Circled numbers show theyear of samplingFigure 6 Vertical section of temperature, salinity, density and 14dissolved oxygen at section 2 in Queen Charlotte Sound(from Dodimead, 1980)Figure 7 Annual cycle of temperature at station E in Hecate Strait 15viPAGEFigure 8 Temperature distribution in time and space at the bottom 15along the axis of Hecatè Strait (1954-1955). The axisruns through 5 cross-strait sections from south to northas shown in Fig. 4Figure 9 Grand means and standard deviations of monthly total 18miles of wind resolved along the southeast axis at PrinceRupert, Sandspit, Mclnnes Island and Cape St. James.(from Crean, 1967)Figure 10 Model geometry and coordinate system 20Figure 11 Data grid for Bakun Index. Intersections at which 22upwelling indices are computed are marked with largedotsFigure 12 Monthly Bakun index at 51°N, 131°W for the years 251960 through 1966Figure 13 Velocity profiles for different a1 in upper layer at four 33selected locations. Curves 1,2,3 and 4 correspond to a1 =0.1, 1.1, 2.1 and 3.1, respectivelyFigure 14 Velocity profiles for different a2 in lower layer at four 34selected locations. Curves 1, 2, 3 and 4 correspond to a2=0.05, 1.05, 2.05 and 3.05, respectivelyFigure 15 Velocity profiles for different b at four selected depths. 35Curves 1, 2, 3 and 4 correspond to b=0.01, 1.01, 2.01and 3.01, respectivelyFigure 16 Modeled velocity field for ö=0 36Figure 17 Modeled velocity field for ö=0.2L 37Figure 18 Initial temperature field 41viiPAGEFigure 19 Temperature field after 4 months of upwelling 42Figure 20 Results from mixing model: 48a) change of mixed layer temperatureb) change of mixed layer depthFigure 21 Monthly Bakun Index for 1953-1989 50Figure 22 Daily wind speed at Cape St. James for 1953-1989 51Figure 23 Comparison of wind speeds at Cape St. James and 52WOTAN1 1Figure 24 Daily air temperature at Cape St. James for 1953-1989 54Figure 25 Climate normal of solar radiation at Cape St. James 55Figure 26 Climate normal of vapor pressure at Cape St. James 56Figure 27 Locations of comparison and the layer thickness 58corresponding to each model levelFigure 28 a) Interannual variations of temperature at x=0 duringyears 1953-1963. The vertical solid line shows the startof cooling; d indicates the delay at lower levels; Thedashed line shows a typical example of oppositevariations in the surface and the bottom layers 59b) Interannual variations of temperature at x=0 duringyears 1962-1972 60c) Interannual variations of temperature at x=0 during 61years 1971-1981d) Interannual variations of temperature at x=0 during 62years 1980-1989viiiPAGEFigure 29 a) Interannual variations of temperature at x=100 kmduring years 1953-1963 63b) Interannual variations of temperature at x=100 km 64during years 1962-1972c) Interannual variations of temperature at x=100 km 65during years 197 1-1981d) Interannual variations of temperature at x=100 km 66during years 1980-1989Figure 30 Two-step decrease of temperature due to different 68mechanismsFigure 31 a) Comparison of the model results and the observeddata at x=0 during years 1953-1963. Data from area 1are plotted as crosses; Data from area 2 are plotted ascircles; Those used for statistics (within 10 m of modeldepth in area 1 and 2) are plotted as solid dots 71b) Comparison of the model results and the observeddata at x=0 during years 1962-1972 72c) Comparison of the model results and the observeddata at x=0 during years 197 1-1981 73d) Comparison of the model results and the observeddata at x=0 during years 1980-1989 74Figure 32 a) Comparison of the model results and the observeddata at x=100 km during years 195 3-1963. Data fromarea 3 are plotted as crosses; those used for statistics(data from area 3 within 10 m of the model depth) are 75plotted as solid dotsb) Comparison of the model results and the observeddata at x=100 km during years 1962-1972 76c) Comparison of the model results and the observeddata at x=lOO km during years 1971-1981 77d) Comparison of the model results and the observeddata at x=100 km during years 1980-1989 78ix1. IntroductionThe oceanography of the coastal waters on the British Columbia continentalshelf is influenced by deep-ocean processes as well as by the local effects ofwinds, tides, runoff, heat flux at the sea surface and coastal morphology. Physicaloceanographic conditions on the continental shelves influence other importantoceanic processes; for instance, most of the biological primary productivity of theworld takes place in the relatively fertile surface waters over the shelves. Thebiological phenomena occurring on continental shelves are highly dependent onfluid mechanical processes.Observations of currents on continental shelves have shown that the nature ofthe flow in different regions, such as off the northeast and off the northwest coastof the United States, can be quite different. Major variations in flow patternsappear to be due in part to differences in the shelf width, to the nature of the localand nearby coastal winds, and to the strength and character of offshore currents.It appears that a primary driving mechanism for the velocity field on manycontinental shelves is the along-shore component of wind stress. The wind stresstypically produces energetic fluctuations of the shelf velocity field on the two-toten-day time scales that characterize the variability of atmospheric storms andsynoptic scale wind events. In addition, on longer time scales, the seasonalvariability of the wind field may induce a corresponding seasonal variability inthe shelf current (Allen, 1980).Studies of the oceanography of the Queen Charlotte Sound-Hecate Straitregion have revealed the general features of the currents (Crawford, et.al.1985,1988), the surface temperature and salinity distributions, as well as theseasonal variability of temperature, salinity and dissolved oxygen content of thedeep water masses (Dodimead, 1980).1The physical processes and driving mechanisms in the Queen CharlotteSound-Hecate Strait region, to the extent that they are understood at the present,appear to be due mainly to the nature of local and nearby coastal winds and thespecific topographic condition of the strait. In particular, an important process isthe northwest-wind-induced upwelling which gives rise to an outward drift ofsurface water from the Strait and the Sound and an intrusion of cold water at thebottom.As part of the OPEN program, which reflects the joint efforts of physical andbiological oceanographers, fisheries scientists and geneticists to enhance researchin fisheries oceanography, an effort was made to model the processes whichcontrol bottom water conditions in the Queen Charlotte Sound—Hecate Straitregion. In this thesis, a simple two-layer upwelling model is developed to studythe summer water conditions and their interannual variations. The model isdriven by inputting surface wind (in the form of a Bakun Index). The temperaturefield and its variation with time and space are deduced from the velocity field.The relationship between the temperature and wind stress and that betweentemperature distribution and topography are also investigated. To close theannual cycle of variation, a cooling/mixing model was developed to model thewinter conditions. Time scales considered range from a few days to a fewmonths. The model is tested against the annual cycle of the temperature variationin the Queen Charlotte Sound- Hecate Strait region revealed by the historicaldata. Then a coupled model is used to hindcast the thermal conditions in theregion over the past four decades.In Chapter 2, a brief review is given of the bathymetry of Queen CharlotteSound—Hecate Strait region, the oceanographic conditions in the region and thespecific phenomena of interest.Chapter 3 describes the development of a 2-layer numerical upwelling modelof summer conditions and a mixing/cooling model for simulating winter2conditions. The basic physical assumptions and the related processes, such asradiation, mixing and entrainment are discussed. The velocity field is derivedanalytically for the upwelling modeL and the temperature field is solvednumerically in both models.Chapter 4 shows the results from the composite model of upwelling andmixing. A long time series of temperature distribution is obtained from thehindcast of the model.In Chapter 5 a comparison is made between the modeled results andhistorical data. Statistics are given from the comparison.Finally, a conclusion is given in Chapter 6 discussing the validity and futureuse of the model.32. Oceanographic Conditions in Queen Charlotte Sound-HecateStrait Region2.1 BathymetryHecate Strait is a relatively wide area between the British Columbia coastand the Queen Charlotte Islands (Fig. 1). The length of the strait is about 220 km.It is 130 km wide in the south with a water depth of about 300 m and 60 km widein the north with water depths of 20-80 m. The axis of the Strait is a narrow longsubmarine valley along the southeast-to-northwest direction. The northwest sideof the Strait is a broad platform of glacial sands and gravels less than 100 m deep,adjacent to the flat coastal plain or strand flat of east Graham Island. Hecate Straitconnects with Dixon Entrance at its northern end and joins Queen CharlotteSound in the south.Queen Charlotte Sound is a broad area between Vancouver Island and theQueen Charlotte Islands with the mainland of British Columbia on the east (Fig.1). It has a considerably more complex topography than Hecate Strait. Threebroad troughs (Moresby Trough, Mitchells Trough and Goose Island Trough) inthe Sound area, separated by two wide shallow banks, form the major topographicfeatures and have important influence on the oceanography of the area. Thenorthern trough (Moresby Trough) is the most irregular one and trends 270 kmnorthward to form the deep channel of Hecate Strait. To the west, the Soundconnects with the Northeast Pacific; it is therefore one of the main passages foroceanic water flowing into Hecate Strait.2.2 General features of the waters in the regionLong-term records of daily observations show that the sea surfacetemperature variations at the northern coastal lightstations in Queen Charlotte4zC135° W 1330 WFigure 11voIs.Mclnnes Is.‘ 4 7MiheUS Tughri Cha-1otteSounGoose ISl2fldN.-.....?\ç.iiI IS II II II II IMap of Queen Charlotte Sound-Hecate Strait region. The dottedline is the 200 m depth contour arid the chain-dotted line is the2000 m contour.0IL,If)BRiTISHCOLUMBIADi±on Entranced:Bonilla Is.HecatS tai::.MoresbyTrough0C1)If)z051310 W 1290 W1270 W5Sound and Hecate Strait region are clearly dominated by the annual heating cyclewith maximum water temperature typically in the 10-13 °C range in August andminimum temperature in the 4-8 °C ranges in February to March (Fig. 2).The horizontal distributions of monthly mean temperatures at 50 m and200 m depths in September 1983 and January 1984 are shown in Fig. 3a, 3b.They represent the temperature patterns in summer and winter respectively. Insummer, the isotherms at 50 m approximately parallel the coast. The lower layershows evidence for a strong eddy and associated frontal system off the southerncoast of Moresby Island, although the information is incomplete and does notdescribe well conditions over most of Hecate Strait. In winter, the temperature at50 m depth decreases gradually from 8.8 °C in the south (Q.C.S) to 6.8 °C in thenorth (northern H.S.). At 200 m depth, the temperature is nearly uniform andthere is a marked northward warm water intrusion from the Queen CharlotteSound (Thomson, 1989) , but again, data coverage in Hecate Strait is poor.The vertical distribution of temperature at selected locations in QueenCharlotte Sound ( station C, Fig. 4) and Hecate Strait (station E , Fig. 4) areshown in Fig. 5 (a and b) in summer and late winter respectively (Dodimead1980). In summer, the distinctive features of the temperature structure are the thinmixed or near-mixed surface layer and the marked thermocline. In the absence ofsurface mixing, the thermocline will extend to near the surface. The thermoclineextends from near-surface to about 75-100 m depth in Queen Charlotte Sound atstation C (Fig. 5a) and to about 100-125 m in Hecate Strait at station E. Thestrength of the thermocline is dependent upon the degree of surface heating andmixing and is about 6 to 8 °C.During late winter (January-March), the cooling, mixing and conductiveprocesses started in October continue. The main features are the near-isothermalconditions to depths of 150-200 m and the relatively large temperature inversionscommon at depth, particularly at station C and E.655Figure2Long-termmonthlymeansandstandarddeviationsofseasurfacetemperatureat4lightstationslocatedintheQueenCharlotteSound-HecateStraitregion(fromDodirnead,1980).505545I. w I 4 w 0. LU50—.1554550LU I- 4 LU 0. LU I-.554550 45\),‘74•0o:E9.I xN!000 64630xx)’’\I3306_\\K‘Cx )C‘C‘C‘CSEPTEMBER1983TEMPERATURE(°C)at50m/\‘CSEPTEMBER1983‘C(\(‘____TEMPERATURE‘\\\\-(°C)at200mIIIU4WFigure3a)Horizontal distributionof temperatureat50mand200mdepthsinsummerfromanoceanographiccruiseintheQueenCharlotteIslandsregion(fromThomson,1989)54-p•6i.0C6IITGU6flIw.UCCI.050006Iz5gzso3266.0C6Nt4U66.0r,Iw.6i.U(S.45Z5fl61.1.U(6.96)7CL.0.1000611Z56Z15004WtXJANUARY1984TEMPERATURE(°C)at200mFigure3b)Horizontaldistributionoftemperatureat50mand200mdepthsinwinterfromanoceanographiccruiseintheQueenCharlotteIslandsregion(fromThomson,1989)•c::s,L;xxcxFC 1K.4KSituC•WlitIS71C.10Z000iqw.VSLuC:6.13iSkflSX.SLUCi.QO‘KKSL:ZSSJK) YYHiJANUARY1984TEMPERATURE(°C)at50mCI12N4situCSMJOUSiI1IN.VSt_U(6ZSZ]‘?IA.VStUC76101C.I.•01000A,ZSZ:$0I\4O34WDC.Figure 4 Stations C and E and sections 1-5 in Queen Charlotte Sound—Hecate Strait region (from Dodimead, 1980); thick dashed lineshows the axis described in Fig 7.100—504)I00O2000_50U,a,0)EI00Hw0150200Figure 5 a) Vertical distribution of temperature at station C in summer andwinter months.Circled numbers show the year of sampling.TEMPERATURE (°C)9 10 II5 6 7 8 911Figure 5 b) Vertical distribution of temperature at station E in summer andwinter months.Circled numbers show the year of sampling.5 6TEMPERATURE (°C)7 8 9 10 II (2 (3 14VVEII—0U0050100150200U,1...0)uJ0506 7 8 S I0STA. E‘JANUARY---FEBRUARYMARCH50100150200122.3 Bottom cold water intrusionOne of the most interesting features of bottom water in Hecate Straitrevealed by the historical data is that the lowest temperature of the year occurs insummer and the highest temperature in winter. This feature is just the opposite tothe seasonal variation of surface water. Similar features were also observed offsouthern Vancouver Island (Freeland and Denman, 1982).Fig. 6 is a vertical section (section 2, Fig. 4) of water properties in QueenCharlotte Sound on June 22, 1955. It shows strong evidence of upwelling over thecontinental shelf off the Queen Charlotte Sound in summer. Deep cold water of5.5 °C (high salinity, —34 %o and low oxygen, —1.5 mi/I ) upwelled from 275 m toabout 200 m depth and was believed to intrude into Hecate Strait along theMoresby Trough. In 1961, at station E, the decrease of bottom temperature startedin April and reached the lowest vaiuein August (Fig. 7). During this period, the6°C isotherm rose about 80 meters, reflecting the progress of the cold waterintrusion. This event happened earlier in the southern part of the Strait and later inthe northern part, indicating that the event propagated northward from thesouthern opening of the Strait--Queen Charlotte Sound.Fig. 8 shows the temperature distribution in time and space at the bottomalong the axis of the strait during 1954-1955; the axis runs through 5 cross-straitsections from the south to the north (thick dashed line in Fig. 4 ). Cold waterreached section 3 about ninety days earlier than it reached section 5. Consideringthe distance between section 3 and section 5 (111 km), this corresponds to apropagating speed of 1.4 cm/s. I argue that advection due to upwelling isresponsible for the observed temperature changes. If we assume the speed of 1.4cm/s is the same as the rate of bottom water intrusion, and the lower portion ofsection 4 is a triangle of 60 km wide and 100 meters high, an estimated fluxthrough this section based on this speed will be1.4 x 0.01 x 60 x 1000 x 100/2=42, 000m3 / s If we chose an upwelling index1330wI.tIa‘Si00fli‘aIxI-a‘Si0Figure 6 Vertical section of temperature, salinity and dissolved oxygen at section2 in Queen Charlotte Sound (from Dodimead, 1980)14STA. Esection numberFigure 8 Temperature distribution in time and space at bottom along the axis ofHecate Strait (1954-1955). The axis runs through 5 cross-strait sectionsfrom south to north as shown in Fig. 4Figure 7 Annual cycle of temperature at station E in Hecate Strait.InIA0)No,SepAuçJunMayAptMarFebI 2 3 4515of 31 (unit=m/sec/100 meters of coastline) as the mean value over 90 days andthe width of the southern opening of the strait as 120 km, we calculated anoffshore transport of about 31/100 x 120 x 1000 = 37,000m is, which is ingood agreement with the estimated influx.The above estimation indicate that the bottom cold water intrusion isclosely related to wind-induced upwelling at the mouth of the strait. Therefore anupwelling model is considered to be reasonable to represent this event.The bottom water began to warm up from September in 1954. It is shownthat the bottom warming was slower than the cooling and, obviously, due to adifferent mechanism.2.4 Wind forcingThe prevailing winds in Queen Charlotte Sound—Hecate Strait region arecontrolled by the locations and intensity of two semi-permanent atmosphericpressure systems. The Aleutian Low centered in the Gulf of Alaska predominatesin winter and produces strong south-to-southeasterly winds along the coast ; theNorth Pacific High predominates in summer and is responsible for generallynorth-to-northwesterly wind along the coast (Thomson, 1989).Westward migrating synoptic-scale atmospheric systems (high and low) areresponsible for modification of the prevailing winds over periods of days toweeks. The weather in Queen Charlotte Islands is famous for frequent and intensestorms with their attendant fronts and strong southwesterly winds.Synoptic winds are modified in near-coast areas by the mountainous terrainand within about 50 km offshore tend to blow parallel to the coast. Strongestwinds occur in December through February and weakest winds in July andAugust. Late September to early October usually marks the time of an abruptincrease in mean wind speeds.16Fig. 9 shows the grand mean and standard deviation of monthly total milesof wind resolved along the southeast axis at Prince Rupert, 1954-1962, Sandspit,1955-1964, Mclnnes Island, 1955-1963, and Cape St. James, 1955-1963 (Crean,1967). A marked feature of this figure is that in the northern part of Hecate Strait,say, Prince Rupert, the prevailing wind around the year is southeasterly, while inthe southern part of the Strait, such as at Cape St. James, northwesterly windsprevail in summer and southeasterly winds prevail in winter. This divergentdistribution of wind may give rise to the specific flow features of the water inHecate Strait.17SECzSEU0U,UJ-J2NW6,000SE4,0002,0000NW2,000Figure 9 Grand means and standard deviations of monthly total miles ofwind resolved along the southeast axis at Prince Rupert, Sandspit,Mclnnes Island and Cape St. James. (from Crean, 1967)SE183. The Models3.1 The hypothesesTwo hypotheses were made based on the topography of the area and theexisting oceanographic conditions.First, the geography and hydrography of Hecate Strait are modeled in termsof a wedge (Fig. 10), simulating Moresby Trough, containing a two-layer liquid.The northern end is open in the upper layer, allowing flow connection with DixonEntrance.Second, the thermal history of the waters is assumed to be controlled by theadvection of upwelled waters at depth during summer and vertical mixing duringthe winter.The complex geometry and hydrography of Hecate Strait are thus idealizedenoughto be accessible to simple modeling. We assume that the thermal behavioris controlled by mean seasonal upwelling and vertical mixing, and that all highfrequency motions (tides, inertial oscillations, storm response) are filtered out.The model will hold only for slow variations, on time scales of half-a -month andlarger; it is the seasonal and interannual behavior that are modeled here. The gyrearound the Goose Island Bank is not considered in this model.Flow in the model wedge is assumed to be forced by the Ekman divergenceof surface waters, as characterized by the Bakun Index (Bakun, 1973). Underupwelling conditions, flow is out (seaward through southern opening) at the top.A vertical distribution is assumed and the rest of the flow field follows fromcontinuity. Provision is made for influx through the shallow end of the wedge,representing flow into Hecate Strait from Dixon Entrance.The model is presented in two sections: the advective part is calculatedfirst, followed by the vertical mixing and br stratification component. In fact, thetwo sections describe two different models. One is a two-dimensional upwelling19Fig. 10 Model Geometry and Coordinate Systemzy2=(L(D1-.Do)z+LH1DO-HI(DI-D2)x)/2H1Lyl=(-L(D1-Do)z-LHID0+H1(D1-D2)x)/2H1LUpper LayerHoLower LayerH(x)Ho(x -L)/L20model which takes into account the wind forcing in terms of the Bakun Index andsolar radiation; the other is a one-dimensional upper ocean mixed layer modelwhich is controlled by wind stress, turbulent transfer of heat at the air-seainterface and entrainment which occuring at the bottom of mixed layer. Theswitch between the two models is controlled by Bakun Index. i.e. a positiveBakun Index in a month switches the model to an upwelling regime and anegative Index switches the model to vertical mixing.3.2 The model geometryAs explained above, the geometry of the region is simplified as a two-layerwedge-shaped water volume with Queen Charlotte Sound at the wide mouth andthe northern part of the Hecate Strait being the narrow end of the wedge. Thewater depth decreases from the mouth to the end. The wedge is 250 km long witha water depth of 320 m at the seaward mouth and 42 m at the northern end. Thesurface width is about 120 km at the mouth and 30 km at the end (Fig. 10).3.3 Bakun IndexThe Bakun Index is widely used as an upwelling index in the NortheastPacific. It is in fact the offshore transport of mass in the Ekman layer, which isconsidered an indication of the amount of water upwelled through the bottom ofthe Ekman layer to replace that driven offshore. The indices are based oncalculations of offshore Ekman surface wind transport from surface atmosphericpressure data. Indices for 1945-1972 were provided by the National Oceanic andAtmospheric Administration (NOAA) on monthly bases. Now NOAA providesboth alongshore and offshore transport of 6-hourly, daily, weekly and monthlyvalues for the years from 1973 through present for the locations along the eastcoast of North Pacific on a three degree grid (Fig. 11, Bakun, 1973)21Figure 11 Data grid for Balcun Index. Intersections at which upwelling indicesare computed are marked with large dots.3 1G JO?322The upwelling index, defined as mass transport in tons per 100 meters ofcoastline per second is defined asw=—fwhere: t is the wind stress;f is the Coriolis parameter.The layer in which appreciable transport occurs is referred to as the Ekmanlayer and extends from the surface to depths not exceeding 50 to 100 meters.The surface wind stress is calculated from the geostrophic wind-4-->TPaCd V Vwhere: Pa is the density of the air;Cd is an empirical drag coefficient;-4-4V is the estimated wind vector near the sea surface with magnitude V . Itstwo components are computed from surface pressure maps,i aiU =— —fPaR 9o- 1 dPVg— fPa0S((P)92Lwhere: P is the atmospheric pressure;R is the radius of the earth;Ug is the northward component of the wind velocity;Vg is the eastward component of the wind velocity;.p is the latitude;2 is the longitude.23NOAA calculates a coastal upwelling index using wind stress obtained forlocations near the west coast of North America. A negative value of the indexindicates accumulation of wind-transported surface water at the coast resulting indownwelling. A positive index value is an indicator of how much water isupwelled from below the Ekman layer to replace the water driven off shore (Fig.12). Both upwelling and downwelling occur as distinct events at various times ofthe year. In the Queen Charlotte Sound- Hecate Strait region, upwellingpredominates during the summer months (May through September) anddownwelling dominates during the winter months (October through March).3.4 Upwelling modelWhen the Bakun Index in a month is positive, the model switches to anupwelling state, a velocity field is derived from equation of continuity andboundary conditions. The velocity field is driven only by wind forcing in terms ofthe Bakun Index. It is a two-layer flow and the flow directions in the two layersare opposite. The water in the upper layer of the wedge is driven out of the regionby Ekman transport, cold deep sea water comes into the region from below tocompensate for the water flow out in the upper layer. Two differently simplifiedheat equations are used to calculate the temperature changes in the upper andlower layers respectively. In the lower layer, temperature changes due only to theintrusion of cold water at the bottom, while in the upper layer, both solar radiationand advection of cold water from bottom contribute to the temperature changes.3.4.1 The formulation of velocity fieldThe wedge-shaped area makes it easier to simplify the equation ofcontinuity from three dimensions to two and reduces the number of boundaryconditions. A coordinate system is chosen with the origin at the deep end of the24UPELL INC INDEX PT 51N 131N BY MONTHPIO4TH INDEX RHOIiRLY —300 —200 —100 0 100 200 300 £00 5006681 -65 -26682 —25 116883 —48 -354_*___6661 —32 —276685 —9 -1322 6-—1 —166868 34 226889 4 76818 -43 -36811 —48 18.58j2 - -5618) —1 -6)82 —84 —486)23 —55 —426184 27 326125 —5 -8616187 --96168 9 -36189 28—- 29E112 5 I____6)11 — 2861)8 565281 —6282 —4 326203 —1 12V6281 —39 -L5225 23 28.SZ?6 5-jr____________________ — — — V6207 24 65266 iS 36209 2 S6216 -21 196211 -64 -6.Zi-ll3zS____________________636) 6 726362 —165 -l3 VV V6303 15 25 V6384 3 95305 —4 —7630 48 3 — — 4538 26 18 V5305 28 6 IVV6369 —78 -575316 —151 —11)35311 1—64 —s612 —123 —65 —-6481 —44 Z86482 29 635183 22 ?S6484 46 5)5405 19 162 —13648’ —0 —166468 9 —36409 18 2)6418 —58 —176411 —24 346582 14 526583 2 156581 —3 25585 33 29-10—6ssoe is 46509 69 7265)2 —112 —786511 —29 29V—12 4’568) -69 -6682 —9 276683 —87 —756664 17 226505 5 2JS8 —12 —266687 47 31ssee II 26609 —41 —386618 —11 266611 —18 486612 —76 —28Figure 12 Monthly Bakun index at 51°N, 131°W for the years 1960 through1966.25wedge on the interface between the two layers. The x-axis is directed horizontallytoward the shallow end of the wedge, the y-axis is perpendicular to the axis of thewedge along the interface; the z-axis points upward from the origin (Fig. 10). Thesimplified equation of continuity is obtained by integrating the equation from oneside of the wedge to the other with respect to y.In the upper layer, the laterally integrated volume continuity is expressedas:-_U1D+--W = 0, (1)where U1 and W1 are the horizontal and vertical velocity components respectively,andD=y2—y=H1L{L(D1 —D0)z+HL—(D —D2)H1xjis the width of the wedge; Subscripts 1 refer to the upper layer, 2 to the lowerlayer.At the interface, z = 0, the horizontal flow changes sign and the verticalvelocity is continuous:U1=0 1 (2)at the interface, z = 0W1—W J (3)At the sea surface, z = H1, the vertical velocity vanishes,W = 0 at the sea surface, z—Hj (4)At the deep end of the wedge, the horizontal transport out of the upper layeris controlled by the Bakun Index:26DBff Udydz =—at deep - end, x =0 (5)oy’where B is the Bakun Index at 51°N, 131°W.At the shallow end, the horizontal transport (T) into the upper layer fromthe Dixon Entrance is expressed as:H, y2f$ U1dydz = — T at shallow — end, x = L (6)o y,In the lower layer, the laterally integrated volume continuity is expressedsimilarly as:(7)We have similar boundary conditions at the interface:U=O 1 (8)at the interface, z = 0W2=W1 j L (9)and at the sea bottom the velocity is perpendicular to the bottom, i.e.= W2 at sea bottom, z = H(X) (10)Assume the vertical dependence of velocity in both layers is exponentialand consider (2) and (8), we define:e 1U1(XZ)=U1(X)ea,Hl—l(11)27e —1U2(XZ)=U2(X)eaH(,,—l(12)where H(X) = H0 (x — L) / LAssume that the horizontal dependence of transport is also exponential, i.e.— 1 B D — 1IHISY2U (x,z)dydz=e”8>- f$U(0,z)ddz=—j 1e’5 —1Jo Ioylwe also haveH1 y2$ $Ui(x,z)dydz=$1Ui(x,z)D(x,z)dz0 y1from which we find:H1—-----Deb 1 = u1(x) $[L(D1—D0)z+HL—(D1—D2)H1xj(e —l)dz100 ‘— 1 I—I1L(e”— 1)— u(x)H1L(ec2huhl [LP — (D1 — D2)H1XQOHI jwhere P =$d[(D10)z+DHi](e —1)dzd=11i(e—1)dzBDiHiL(eb+S_ — 1)(e’”’ — 1)hence, u1(x)=—— 1){LP”— (D1 — D2)H1xQh128BDiHiL(eb(S_— 1)(e’ —1)U1(XZ)___lOO(eb(L+o) l)[LP’ —(D1_D2)HxQ1 jTo obtain the vertical velocity, we first integrate (1) from z to H1 withrespect to z,W1(x,H )D(x,H1—W1 (x, z)D(x,z)= —j’ —U1Ddz = UDdzusing (4) we getW1(x,z)= 1 aJHIUDdiau1(x)[LPZ —(D1—D2)HxQJD(x,z)D(x,z) c9x Z D ax H1L(e’’ —1)— BD1[AZ( -D2)E1HQ” —A1A0b(E +l)—A10(D_D2)E1HQIII—- lOOD(e — l)Awhere A10 LP’1— (D1 — D2 )H0xQA1 = LP” — (D1 — D2)H0xQE1 (x) = — 1At the interface, z = 0 , the vertical velocity is reduced toBbD1Le’3’W1(x,O)=— l)[LD0— (D1 — D2 )x]Similarly in the lower layer; at any cross wedge section, the transport in thelower layer is the residual of transport in the upper layer from the transport atx=L:29o Y2——H1y2$ fu(x,z)dydz._e1’j•fUi(0,z)dydz+T- —1= D —100 1 e’5’—1Again, sinceo y2 0f fU(x,z)dydz= fU2(x,z)D(x,z)dzIi() yI H(X)= u2 (x) $ [(D1 — D0 )Lz +D0H1L— (D1 — D2 )Hix](ea2z — 1)dzHiL(ea2hI— 1) H(s)= u2(x)H1L(e2hl—[LR— (D1 — D2 )H1xS Iwhere R =f’{(D1_Do)z+D0H1I(ea2z —1)dzdSI =$(eaz —1)dzCwe fmd then that— D1HLB(e’’ — l)(e3 e”3)u2 (x)— l00(e — 1)[LR — (D1 — D2)H1xS ID1HLB(e — l)(eb +Sx) — e”3)U2 (x, z) = lOO(ebS)— 1)[LR — (D1 — D2)H1xS]30To find the vertical velocity in the lower layer, we integrate (7) from z to 0with respect to z,W2(x,O)D(x,O)—W2(x,z)D(x,z)= —1°2Ddz2d u(x)[LR —(D1—D2)H1xSjdx— i)BD1 IA2ob(E1+ 1) + A20 (D1 — D2 )H1(e”3— ebS )s— lOO(e—1)1— A2 (eb) — ebS ){(D1 — D2)H01x— HOL{(DI — D0 )H(X) + H1D0j}(ea211 — i)A2L20— A2 (D1 — D2 )HlLS (e’6— e1’8)}where A20 = LR — (D1 — D2 )H1xSA2 =LR —(D1 —D2)H1xS°Finally we getD1B 1A2b(E+1)___________________I 20W2(XZ)=lOO(eb(L+3)—1) 4A2OAZb(EI + 1) + A20 (D1 — D2 )H1(e3— ebS )sA22031A2(e3— ebS ){(D1 — D2)H01x— HOL[(DI — D0 )H() + H1D0]}(e” — i)A0L3.4.2 Adjustment of velocity fieldThe velocity field is controlled by parameters a1 and b in the upper layerand a2 and b in the lower layer; a1 and a2 determine the vertical dependence of thevelocity in the upper and lower layers respectively. By choosing a large a1 we canget strong surface intensification in the upper layer (Fig. 13) while small a2 resultsin strong bottom intensification in the lower layer (Fig. 14). By changing b we canadjust the amount of intruding water in the lower layer that will reach the end ofthe wedge. We note that the horizontal transport from Dixon Entrance, defmed asT above (equation (6)), may be expressed asT’( e—1— 100 e6 — 1The parameter ö determines the value of T; as seen in (13), x=L+ö wouldbe the location where the upper layer transport vanishes. Figures 13-15 showvelocity profiles in the upper and lower layers for various values of a1 and a2, andalong the axis of the wedge for various value of b. A two dimensional “vectordiagram” of the flow field is shown in Fig 16 for a =0.1/H1,a2 = -1/Ho, b =0.01/L, and ö = 0, corresponding to no inflow from the north end, and 6= 0.2L,(Fig. 17) which corresponds to T/(BD1/100)=0.165. Therefore we can determinehow far the bottom water can intrude before it upwells into the upper layer. If weA2r’2032010-20-30-40-50010-20D40-500-10-20O40-50010-20o-40-50-0-10-20-30-40-500-10-20-30-40-500-10-20-30-40-500-10-20-30-40-50Figure 13 Velocity profiles for different a1 in upper layer at four selected locations.Curves 1,2,3 and 4 correspond to a = 0.1, 1.1,2.1 and 3.1-4 -3 -2 -1 0 0.0 0.1 0.2 0.3 0.4 0.5x5k x = 62.50.0 0.1 0.2 0.3 0.4 0.5-4 -3 -2 -1x = 125 km0.0 0.1 0.2 0.3 0.4 0.5-4 -3 -2 -1 0x = 187.5 km-4 -.3 -2U (cm/s)x = 187.5 km-1 0 0.0 0.1 0.2 0.3 0.4 0.5W (1 E-3 cm/s)33Figure 14 Velocity profiles for different a2 in lower layer at four selected locations.Curves 1,2,3 and 4 correspond to a2=0.05, 1.05, 2.O5and 3.05.0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 1.2x = 62.5 km-50-100-150-200-250-300-50-100-150-200o -250-300-50--100-150.-200o -250-300-50—-100-150-200o -250-300-50-100-150-200-250-300-50-100-150-200-250-300-50-100-150-200-250-300-50-100-150-200-250-3000.0 0.2 0.4 0.6 0.8 1.0x = 125 km0.0 0.2 0.4 0.6 0.8 1.0x = 62.5 kr0.2 0.4 0.6 0.8 1.0 1.2x = 125 km0.2 0.4 0.6 0.8 1.0 1.2x = 187.5 km x = 187.5k0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.81.0 1.2U (cm/s) W (1E-3 cmls)n34VelocityProfileforDifferentb1.0z=Om1.0z=lOOmz=200m1.0z=300m0.50.50.50.5n-p.0.00.00.0Eo°:-0.5-0.5-1.0-1.0________________-1.5________________-1.5________________-1.5_______________C”-1.5_________o050100150200250050100150200250050100150200250050100150200250__________________________________0________________..1.2z=Om1.2z=lOOm1.2z=200m1.2z=300mCD1C)1.01.01.01.00.80.80.80.820.40.4U0.60.620.630.4CD40.20.20.20.23%)__________0.0__________________0.0_________________0.0_________________0.0_________________050100150200250050100150200250050100150200250050100150200250Distance(km)Distance(km)Distance(km)Distance(km)VelocityField(delta=O)0••—4—-4-.•—4._4......4-.4—4.._._.._—4—4—.—4—4—4—.--4—.4—4—4—.—4—..-.__4.—4—.———.—..—8—-.——._._.—_.—_.__..—_——.—.——.8-.‘.......‘.S%——.-—.-——•.-••%.‘—50..•.///_/1I•---—,.,_.A•---———F.AA__....—100-------——__•4---——————.—.-A_.-4.——————.—.—.—.—•_8————-.—.—.—.__•—•_____.__..A-150——__...4———-.—.—.—_.....-40—-.-.-.-——.—200_.4—-.--.—84.4.4----A.-250-.———.—‘.4-8----—3.3E-3cm/s_8_k__.4.t-300——s1—’1.6cm/sII050100150200250Distance(km)Figure16Modeledvelocityfieldforö=0.VelocityField(delta=O.2L)04444—4-4--.-4—4—‘—4—4—.-4—4—4-4-4—.-__4-_4__4-_4-_.___-———..........-..N.-\‘••••,•IIIII///,11•/////__A--—,—.—._AA•---—‘--—————.._A_...A-——————.A._.--.————_AA-———-.—.__..b————-.-—I_-———_A4A——-—.—.—._-.—4—-....A..--.--—.—..-_4--.e—--4--4—4-4—__42.4E-3cm/s1.5cm/sIII-IDistance(km)Figure17Modeledvelocityfieldfor6=0.2L.L)—J4—-50-100-150-200-250-300—————-.-.——-.—-.—-4-.—-4—4—4—-4-.4—4—4050100150200250choose a smaller b, we can get stronger current near the northern end of thewedge. (Fig. 15)3.4.3 Determination of Solar Radiation in the Upper layerThe amount of solar energy which reaches the sea surface is affected bymany factors, such as the elevation of the Sun, the cloudiness of the sky, themolecular scattering and absorption and scattering by aerosols, etc., in addition,the amount of solar energy absorbed by the ocean depends upon the opticalproperty of the sea water, the penetration angle and the sea surface roughness andso on.(Ivanoff, 1977)In this thesis, a simple formula of the penetrating component of solarradiation is used as followsI(z,t)=I0(t)e (13)where I (t) is a time series of monthly mean solar irradiation at ground level atCape St. James (51°20’N, 130°30’) for clear weather (Table 1); y is theattenuation coefficient which varies with depth (Table 2).Table 1 Monthly mean solar irradiance at ground level during clear weather atCape St. James (Cal cm-2 day-’) obtained from Atmospheric EnvironmentService(AES)Imonth Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.I Io(t) 159 270 438 608 729 780 742 628 474 318 190 131Table 2 Attenuation coefficients for total downward irradiance atdepths 0-80 m ( from Ivanoff, 1977)depth(m) 0 - 5 5 - 10 10 - 20 20 -40 40- 60 60 - 80‘y (rn-’) 0.26 0.04 0.04 0.04 0.04 0.0438As most of the solar energy reaching sea surface is absorbed in the upperlayer, the radiation term is only considered in the upper layer of the model.3.4.4 Formulation of Temperature FieldDifferent simplifications of the heat equation are used in the upper layer andlower layers during the upwelling period.In the upper layer, both the advection term and radiation term are included inthe heat equation:a, aT, 1 ai—+U1- W—=— — (16)at az azIn the lower layer, no radiation is considered. The change of temperature isdue only to the advection of cold water:aT,____aT=0 (17)at ax azwhere: T1 is the temperature in the upper layer;T2 is the temperature in the lower layer;Cp is the specific heat of water;Pw is the density of the water.U1 is the horizontal velocity component in the upper layer;U2 is the horizontal velocity component in the lower layer;Wi is the vertical velocity component in the upper layer;W2 is the vertical velocity component in the lower layer;These equations are discretized by using the finite difference method. Acentered differencing scheme is applied for the spatial derivatives and the leapfrog method is used to advance the solution in time. The grid for the scheme is396.25 km in the horizontal by 70 cm in the vertical. The time step is chosen as 600seconds. U and W1 (i=1,2) are calculated once a month at each grid pointaccording to the previously derived formulae during upwelling months.3.4.5 Boundary conditionsBoundary conditions for the velocity field have been given in theformulation of velocity field. For the temperature field, a non-diffusive conditionis applied at the bottom of the wedge and air temperature is used as the surfaceboundary condition. At the seaward opening of the wedge, a time dependentboundary condition is applied to reflect the seasonal variation of the water cominginto the region. Information is obtained from the thermal conditions at the oceanstations on line P (Tabata and Peart, 1985).3.4.6 Modeled resultsThe upwelling model is run separately for several months withal=0.l,a2=1,b=0.05. The model starts from a presumed stratified ocean (Fig. 18).The velocity field is turned on at t=0. Cold water starts to come into the straitfrom the seaward opening at the bottom. Water in the surface layer moves out ofthe strait due to Ekman transport. At the same time, solar radiation works on thesea surface and cause surface temperature to rise. The calculated result showsclearly cold water upwelling and surface warming (Fig. 19)It can be seen from Fig 19 that after 4 months of upwelling the 7°Cisotherm rose from 200m to about 130 m and the surface temperature increasedfrom 7.8 °C to 11.0 °C. Upwelling was more significant in lowering thetemperature along the sloping bottom, but was not strong enough to upwell coldwater to the surface. Therefore on most of the study region the surface watertemperature increased during an upwelling period with a reducing rate from theseaward opening to the narrow end. This is consistent with the historical data.40InitialTemperatureFieldforUpwelJingI..J-50-100I--150-200-250-300IIIII050100150200250Distance(km)Figure18Initialtemperaturefield.-c4-,cici) UTemperatureFieldafter4MonthsofUpwellingIIIIII0501001502002500-50-100-150-200-250-300Distance(km)Figure19Temperaturefieldafter4monthsofupwelling.3.5 Mixing/Cooling model3.5.1 IntroductionThe mixing model is applied in the months when the Bakun Index isnegative.During mixing/cooling period, a simplified Niller-Kraus one-dimensionalupper mixed layer model is applied (Niller and Kraus, 1977). In this model,turbulent heat transfer at the air-sea interface generated by wind stirring andentrainment of cold water from the bottom of the mixed layer are considered.Wind stress plays a most important role in the process. No advection/convectionis taken into account and the effect of topography is ignored. Therefore a uniformthickness mixed layer is formed over the whole region. Only the deepening of themixed layer depth and the mixed layer temperature are simulated. The oppositeprocess of creation of a mixed layer due to turbulent tidal mixing at the bottom isnot included in this model, over most of which depths are too large for this effectto be important.3.5.2 Wind forcingDaily wind speed at Cape St. James is used in the calculation ofentrainment speed, sensible and latent heat transport. In considering the elevationof the station, a factor of 0.85 was used to convert the wind speed at 89 metershigh to 10 meters above sea level after a simple comparison of the mean windspeed at Cape St. James and at 7 meters above the sea surface from a buoy nearCape St. James.3.5.3 Radiation and effective back radiation.In calculating the heat flux at the air-sea interface, daily solar radiation isobtained from the monthly mean radiation normal at Cape St. James by linear43interpolation.The effective back radiation is calculated at each time step as (Rosemaryand Walker, 1990):Hb = —EaT (0.39— 0.05e/2)(1 — 0.83C) (18)where E is the emmisivity;c is the Stefan-Boltzman constant;Tj is water temperature in the upper mixed layer;ea is the vapor pressure at the sea surface;C is the cloud coverage in tenths for the region.3.5.4 Sensible heat fluxSimilarly, the turbulent flux of sensible heat is calculated at each time stepfrom (Pickard and Emery, 1990):H3 =—L88V(T1Ta) (19)where V is the daily mean wind speed;Ta is the daily mean air temperature interpolated from climate normal.3.5.5 Latent heat fluxThe latent heat flux is calculated at the same time as sensible heat from(Pickard and Emery, 1990):He =1.4(e —ea)V(2494—2.2T)103 (20)where es is the saturated vapor pressure;The latent heat flux is calculated at each time step.443.5.6 Entrainment speedFrom Stigebrandt (1981) the entrainment speed is obtained from:We = gifa(T1_T2)[pmdb0v—Z ( 10 bHs”e) + 0] (21)where T2 is the water temperature below the mixed layer;Pa is the air density;Pw is the water density;g is the acceleration due to gravity;m is a constant;Cjo is the drag coefficient;c, is the heat capacity of sea water;‘y is the attenuation coefficient of radiation;H is the mixed layer depth;a is the coefficient of expansion;I is the incident solar radiation at the sea surface.The above equation suggests that the entrainment speed is determined fromthe contribution of wind stress; the turbulent heat flux at the air-sea interfacewhich is the combined effect of incident solar radiation, effective back radiation,latent heat flux and sensible heat flux, and penetrating solar radiation whichdecreases with the increase of the attenuation coefficient. The buoyancy flux dueto salinity changes is neglected. The first term in the bracket is proportional to thecube of wind speed and is always positive. It shows that the stronger the wind, thelarger the entrainment speed. The second term in the bracket represents thebalance between the four heat fluxes at the air-sea surface. All the fluxes into theupper layer are positive and those out of the layer are negative. In summer, whenthe incident radiation is strong, the inward flux is larger than the outward flux,45and the thermocline is strengthened. The increased stratification preventsentrainment from developing. In winter, when the influx is less than the outfiux,the entrainment speed is increased, therefore the mixing becomes stronger. Thethird term in the bracket is the contribution from the penetrating part of solarradiation. It is inversely propotional to the attenuation coefficient whichrepresents the optical properties of the sea water. Therefore the clearer the water(the smaller ‘y), the stronger the entrainment speed. Apart from the second term inthe bracket, the contribution of the other two terms is inversely proportional to themixed layer depth. i.e. the deeper the mixed layer depth, the weaker theentrainment speed. This results in a reduced deepening rate of the mixed layer asit gets thicker.3.5.7 Mixed layer depthThe deepening of the mixed layer depth is determined by the entrainmentspeed as:tAWe (22)at1 We>Owhere0 We03.5.8 Mixed layer temperatureThe mixed layer temperature is determined by the following equation:=_[pc1(Hb+Hs+He)+(Tl_T2)We+ (23)The change of the mixed layer temperature is controlled by the balance of46turbulent heat flux at the sea surface, the entrainment of cold water from below,and absorption of penetrating solar radiation. It also shows that the deeper themixed layer depth, the slower the bulk temperature changes.-3.5.9 Model resultsThe above equations are discretized and integrated with time. As a test themodel was run separately for the winter months. It started from t=tO with aninitial mixed layer depth of H0, which is assumed to be the same as the diurnalthermocline depth, and with an initial mixed layer temperature T0 , which isobtained by mixing the stratified upper layer of depth H0 to uniform. Theintegration is performed at each horizontal grid point and leads to a uniformupper mixed layer on the surface of the region. It should be pointed out that sincethis model does not take into account tidal mixing on the bottom,which may beimportant in shallow areas, the result of the model deviates more in the shallowwaters.The mixing/cooling model was run for four months using data fromOctober 1954 to January 1955. Calculation shows that, after 120 days of mixing,the mixed layer deepens from 5 meters to about 300 meters. The mixed layertemperature decreased from 8.2°C to 6.6 °C. (Fig. 20).47a)aEa)H000a-0o00CFigure 20 Results from the mixing modela) change of the mixed layer temperatureb) change of the mixed layer depthQcoLC)0 20 40 60 80 100 120Day V0 20 40 60 80 100 120Day484 Coupled upwelling-mixing modelIt is assumed that upwelling and mixing are two distinct processes. Whenthe Bakun Index is positive, upwelling is the dominant process in the area. Noturbulent mixing is considered during the upwelling period. When the BakunIndex is negative, the current in the area is assumed weak, turbulent mixingbecomes the dominant process in the change of temperature and the mixingmodel is used. These two processes do not exist simultaneously.4.1 Forcing conditionsIn the upwelling period wind stress, as parameterized by the Bakun Index,and solar radiation are the only forcing terms to the model. Air temperature isused as a boundary condition at the sea surface. The wind drives the velocity fieldand the water in the wedge moves following the conservation of mass. Figure 21shows the time series of monthly mean Bakun Index for the period 1953-1989.Only the positive values which imply upwelling are used to derive the velocityfield.During the cooling period, wind forcing at the sea surface, solar radiationand the turbulent heat flux at the air-sea interface are considered. Figure 22 showsthe daily wind speed at Cape St. James. Since the station on Cape St. James is 89meters high above the sea level, an attempt has been made to convert these valuesto wind speed at 10 meters above the sea surface. A simple factor of 0.8 waschosen after a comparison between the mean wind speed at Cape St. James (6.95m/sec) and mean over-the-ocean winds (5.63 m/sec) measured by WOTANanemometers on a surface buoy near Cape St. James. The average was applied tothe period from June 4, 1982 to September 15, 1982. This is the only sea surfacewind data we obtained in the area near Cape St. James. Figure 23 shows thecomparison between the two time series. The mean speed is shown by a dashed49BakunIndexat51N,131W00-0 C 0 I00.cJ‘.0I.‘.00000-‘.0C?________________________IIIIIIIIIIIIIIIIIIIIIIIIIIIIII11111III1953195619591962196519681971197419771980198319861989WindSpeedatCapeSt.JamesT1cJQ0 c\j.L’)0 0 0 co(p (PCRC-) (DC)E-ci (pC)(P C,,C)-I.C1Q0•19601980199000IIIi1L1hL t1970 yearWindSpeedatCapeSt.James‘•10 C’.’LI,o C,, 0 o0__________________________________01.0500100015002000250010:004/6/1982hoursCD CDWindSpeedatStationWOTAN11I’-)U)CD C,,0CDE0 Z0500100015002000250010:154/6/1982hoursline on each panel.Figure 24 shows the daily air temperature at Cape St. James obtained fromthe Canadian Climate Center. It was used to calculate the sensible heat fluxduring the mixing period and as a boundary condition for the upwelling period.Monthly mean values of solar radiation and vapor pressure were obtainedfrom the Canadian Climate Normals compiled by the Atmospheric EnvironmentService (AES). They are shown in Figure 25 and Figure 26 respectively. Thismeans that the same values were used for each year of modeling. To obtain asmooth shift from one month to the next, these monthly mean values wereinterpolated linearly into daily values and are updated daily during theintegration.Cloud coverage is always a uncertain parameter to handle. A simpleconstant coverage of 0.15 is used in the model.Because the longest time series of the above forcing parameters that meetthe requirement of the model were obtained from Cape St. James, they were usedas representative for the whole modeled area. Except for the wind data, thedeviations from the sea level value due to the station elevation are ignored.4.2 Modeled results and discussionRunning the upwelling and mixing model consecutively, temperature goesthrough a cooling-warming-cooling cycle. At the end of the cooling period, themodel switches to upwelling. The end state of cooling period becomes the initialstate of the upwelling model. A new thermocline starts from the surface on thestart of the upwelling model. At the end of upwelling period, the model switchesback to the cooling regime again. The end state of upwelling period becomes theinitial state for the next cooling period. A new mixed layer starts from thesurface. The consecutive execution of the two models generate a complete annualcycle of temperature in the study region.53DailyAir TemperatureatCapeSt.James1960197019801990Yearsuif•1iiUO!11?!p1?.II0SciCat/cm2/day100200300400500CD‘-1Cl)0-‘0D0-o>CDCDCDr-4-VCDCl)zo-.IDCD_&C,C!)ci)-,C’)ci)00I.(ci)DC’)C’)ci)a00>Ed)jFigure 26 Vapor pressure normal at Cape St. JamesC)‘-a)0>-0za)C/)C)-,C-,>%Vt.-CILC-ct10•1. 9056The model was run from January 1951 to December 1989. To eliminate theeffect of assumed initial conditions, output from the first two years of integrationwere dropped. Plotted results start on January 1, 1953.Results from the coupled model of upwelling and cooling at the twolocations of the wedge (Fig. 27) at four selected levels are shown in Figure 28 (ad) and Fig. 29 (a-d) respectively. The first location is at the seaward opening ofthe wedge (x=0) through where the cold deep sea water is expected to come. Thesecond location is 100 km northward from the first one (x=100 1cm). The fourselected levels are 7m, lO5m, 203m and 3Olm.The same features observed by Dodimead (1980) of opposite variations inthe top and bottom waters are shown in the model results. A typical year isindicated by a vertical dashed line in Fig. 28a.The modeled temperature fields show a clear annual cycle in the upperlayer, i.e. high temperature occurs in summer and lower temperature in winter, aswe would expect from the boundary conditions. In the bottom layer an annualcycle shows up when both summer upwelling and winter mixing are strong. Astrong upwelling brings enough cold water into the lower layer of the wedgetherefore the bottom water becomes cold. A strong fall/winter mixing bringswarm surface water down to the lower layer, causing the temperature there toincrease.If the winter mixing is not strong enough, then the water column is notcompletely mixed, the bottom water will stay cold for years until a strong mixingevent happens. For instance, following the summer of 1962, cold water of 5.5 °Cstayed at 300m depth at x=0 for four years until a strong mixing occurred in thewinter of 1965/1966 (Fig. 28b). Similar events also happened during 1966-1968,1975-1978, etc. If the upwelling is not strong enough, the cold water canonly reach a lower level, and water in a higher level will keep warm. For exampleduring 1983- 1985 the water temperature at x=0 at 203m depth stayed above 7.557330mFigure 27 Locations of comparison and the layer thickness corresponding to eachmodeled levelOm42m1 SOm250m580II><D4—’a)2a)00>DC”a)4-’Ca) Interannual variation of Temperature at X=O during 1953-1963.The vertical solid line shows the start of cooling; d indicates the delayat lower levels; The dashed line shows a typical example of oppositevariations in the surface and the bottom layers0 (0 0 co (0 0000 co N- (0 10E EE t.o0 0c’JFigure 2860C)59InterannualVariationofTemperatureatX=O10196219631964196519661967196819691970197119721973__________________________________________________________________I105m1962196319641965196619671968196919701971197219732O3m7196219631964196519661967196819691970197119721973301m196219631964196519661967196819691970197119721973InterannualVariationofTemperatureatX=O18 14J/P\7Z\]JAP\,f\7rn10C)6197119721973197419751976197719781979198019811982I____________________________________________________________________105m, 1%f_p 0_197119721973197419751976197719781979198019811982C)8.0203m76.0___________________________________________III1IIIIIIC19711972197319741975197619771978197919801981198270301mo005.0________________________________________IIIPIIIIIII197119721973197419751976197719781979198019811982InterannuatVariationofTemperatureatX=O7m15___________________________________19801981198219831984198519861987198819891990CD I:105m19801981198219831984198519861987198819891990C203m70________________________________________________________19801981198219831984198519861987198819891990301m19801981198219831984198519861987198819891990TjInterannualVariationofTemperatureatX=100kmt)7mCD1953195419551956195719581959196019611962196319641105m6IJJT1IIIIIo___________________________________195319541955195619571958195919601961196219631964CD203m6II I.195319541955195619571958195919601961196219631964_4.1__________________________________301m‘.03.93.7195319541955195619571958195919601961196219631964CInterannualVariationofTemperatureatX=100km196219631964196519661967196819691970197119721973105m196219631964196519661967196819691970197119721973203m7196219631964196519661967196819691970197119721973301m196219631964196519661967196819691970197119721973InterannuatVariationofTemperatureatX=100km18 147m10 6: 197119721973191741975197619771978197919801981198210105m8(31o197119721973197419751976197719781979198019811982CD8203m7 6II5._________________________________________1971197219731974197519761977197819791980198119824.3_4.1___________________________________________I.____________________________________________301m3.9.I.3.7IIIIIIIIII197119721973197419751976197719781979198019811982InterannualVariationofTemperatureatX=100km7m19801981198219831984198519861987198819891990105mt.19801981198219831984198519861987198819891990CD CD203m\LrL198019811982198319841985198619871988198919904.3.4.1___________________________________________301m_3.9.003.7—C19801981198219831984198519861987198819891990°C (Fig. 28d). The difference between the annual cycle at the surface and that inthe lower layer is that the former depends on the alternation of heating from solarradiation in summer and wind cooling and mixing in winter, whereas the latterowes its existence to cold water upwelling in the summer and mixing andwarming in the winter.There is a delay for the lower layer to warm up because of surface mixingand for the cold water to reach higher layers due to upwelling. An interestingphenomenon shown in Fig. 28 and Fig. 29 is that when surface layer temperaturebegins to decrease, the temperature in the layer just below it often shows a sharpincrease, indicating warm surface water has been mixed down to that level. Afterthis sharp increase, the temperature in the lower layer begins to decrease in thesame manner as surface water. Similar features are shown in even lower layers,too, though the time of sharp increase occurs even later than in the upper layer.Such is the case in the fall of 1959, where delays of 40 days, 85 days and 140days are shown at level 2, 3 and 4 in Fig. 28a after cooling in level 1.During strong upwelling years, the decrease of temperature in the lowerlayer shows a two-step process (Fig 30). The first decrease in temperature is dueto the winter surface cooling, while the second drop of temperature reflects thecold water intrusion from below.Cold water of 5.5 °C rose to a higher level at the location 2 than at location1, reflecting that it climbs along the slope of the Moresby Trough from south tonorth, the same feature as shown in Fig. 8.67?O]niFigure 30 Two-step decrease of temperature due to different mechanisms.685. Comparison of model results and observed data- Corresponding to the above two locations, observed data from the nearbyareas were obtained for comparison with the modeled results. In order to havemore data points for comparison, observed data from three areas were extractedfrom the MEDS (Marine Environmental Data Services Branch of the Departmentof Fisheries and Ocean) data for the years 1953-197 1 and from lOS CTD data forthe period 1971-1989 (Figure 27). Observed data from area 1, which is on themain axis of Moresby Trough, are used to compare with the modeled results atx=O. Data from area 3 are compared with the modeled results at x=100 km. Area2 is not on the main axis of Moresby Trough, but there were numerousobservations during 1953-1968 (this area covers station A and C of Dodimead,1980); data from this area were also used to compare with modeled results at x=0.In comparing the modeled results with the MEDS data, the wedge isdivided into four layers ranging from 0-42m, 43-150m, 151-250m and 251-330mrespectively (Fig. 27). All the observed data falling into these four layers wereused to compare with the modeled results at the four corresponding levels (7m,105m, 203m and 3Olm).For CTD data, because of the denser sampling interval, only data fromwithin 10 meters above and below the four corresponding levels were extractedfor comparison.All the extracted data were plotted on the corresponding panels as symbols(Fig. 31 a-d, Fig. 32 a-d).To evaluate quantitatively the modeled results, part of the extracted datawere used to calculate the closeness of modeled results and observed data. Onlythe points within 10 meters from the selected levels were used in the statistics forx=0 and x=lOO km. A deviation of ±0.8 °C is defined as good and ±1.5 °C isregarded as fair. The percentage of good and fair points at four selected levels are69shown in Table 3 and Table 4 for location 1 and 2 respectively. Those points arealso plotted on the corresponding panels as big dots (Fig 31 a-d, Fig. 32 a-d).- Table 3 comparison of model results with observed data at x=0layer 1 layer 2 layer 3 layer 4No. dots 919 398 208 78%good 33.6 71.1 61.5 75.6% fair 24.3 19.1 27.4 23.1Table 4 comparison of model results with observed data at x=100 kmlayer 1 layer 2 layer 3No. dots 432 230 64% good 47.5 89.5 29.7%fair 22.5 5.2 62.5700Itx0U)cii0600Figure 31 a) Comparison of modeled results and the observed data at x=0 duringyears 1953-1963. Data from area 1 are plotted as crosses; Data fromarea 2 are plotted as circles; Those used for statistics (within 10 m ofmodel depth in area 1 and 2) are plotted as solid dots—cDo)aDr--cD‘- YENE0EC)0C%J71ComparisonatX=O7m_________________________196219631964196519661967196819691970197119721973105m196219631964196519661967196819691970197119721973Cj•J203mliii________________________________196219631964196519661967196819691970197119721973301m;__________________________________________________196219631964196519661967196819691970197119721973ComparisonatX=O18 147m6197119721973197419751976197719781979198019811982105m8J°6197119721973197419751976197719781979198019811982CD C’, cz C’,8.0203m7.0_____60LdfljCD 0 C’) CD197119721973197419751976197719781979198019811982CD7.0301m6.0:II C5.0___________________________________________________________197119721973197419751976197719781979198019811982ijcIooo00C CD CD C,, CD 0 0 CD CDComparisonatX=O198019’81198219831984198519861987198819891990-J207m15 10•105m8.58.0203m6.5-6.0- 8301m6 5.19801981198219831984198519861987198819’891990198019811982198319841985198619871988198919903 0-‘k••,..1801981198219831984198519861987198819891990EQC11><C0Cl)0E0()coLO1f)0)1CD0)LI)I!)LI)0)cv)LI)0)CD0)cr,Co0)C’]CD0)CD0)10CD0)0)0)- 0 CD OCoCO‘- ‘-E ELI)0Figure 32EC)cC’ja) Comparison of modeled results and the observed data at x=100 kmduring years 1953-1963. Data from area 3 are plotted as crosses; thoseused for statistics (data from area 3 within 10 m of the model depth)are plotted as solid dots.75T1ComparisonatX=100km147m10i(_)6196219631964196519661967196819691970197119721973Cl)10’CD6,-J____o105mJ-____196219631964196519661967196819691970197119721973Cl)Cl)____________________________________________________________________8:_iLL±Lji203m7CD605Cl) CD196219631964196519661967196819691970197119721973CD4.3’4.1’_____________________________________________301mII3.7196219631964196519661967196819691970197119721973ijComparisonatX=100km18 147m10• 6197119721973197419751976197719781979198019811982-1)-•_0101056N’”m8197119721973197419751976197719781979198019811982C..,203m7 6C197119721973197419751976197719781979198019811982CD4.3301mI, C3.7197119721973197419751976197719781979198019811982ComparisonatX=100km7m119801981198219831984198519861987198819891990ez.C’,C,,0000105mCD_______________________________________________________________________19801981198219831984198519861987198819891990C’,I-.203mCD 0 C________________________________________________C.,,II1IIIIIICD19801981198219831984198519861987198819891990CD4.34.1_________________________________________________________301m3.7IIII198019811982198319841985198619871988198919906. ConclusionsInterannual variations of temperature in Hecate Strait-Queen CharlotteSound region have been studied using a composite upwellinglmixing model. Thedominant processes of summer upwelling and winter mixing have beeninvestigated by different models separately, which were then coupled to model theannual cycle of temperature field. The switch between the two models depends onthe sign of monthly Bakun Indices. The studied area is simplified as a wedge-shaped water volume. In the two-dimensional upwelling model, a velocity fieldwas derived analytically from the off-shore transport in terms of the Bakun Indexand the equation of continuity. This velocity drives cold water into the bottom ofthe wedge and moves warm water out of the wedge in the surface layer. In themixing model, a one-dimensional upper mixed layer model was developed. Thecoupled model starts from a uniformly stratified ocean, either an upwelling or amixing regime is chosen by examining the sign of the Bakun Index in the startingmonth. The end state of the former regime becomes the initial state of the latterregime. The model was run for 37 years and reproduced profiles of interannualvariations of temperature in the region for the period 1953-1989.The model reproduced a clearer annual cycle in the surface layer than thatin the lower layers, but a comparison of modeled result with observed data showthat in the lower layers, modeled results are closer to the observations. Themodeled results also show the relative importance of mixing and upwelling in thevariation of temperature in the lower layers. Weak winter mixing results in longercold water residence on the bottom (1962-1966 at 300 m depth); strong upwellingsends cold water to higher levels (1957, 1962, 1972, etc.).A comparison was made between modeled results and observed data. Twomeasures, good and fair, were used to evaluate the deviation of modeled resultsfrom the observed data. It is shown that, in the lower layers, 69.4% and 59.6% ofthe compared points are in good agreement with the modeled results at x=O and79x=100 km respectively, while in the surface layer, 33.6% and 47.5% are good atx=0 and x=100 km respectively.The model assumes upwelling and mixing are two distinct processes andnever happen simultaneously. This may cause some deviation from the realnature, because mixing effects also exist during upwelling months, although it isnot as important as upwelling.The forcing parameters, such as, wind speed, solar radiation and airtemperature, etc. are all from Cape St. James, a station with elevation of 89meters, not as required at the sea surface or at 10 meter above sea level. Exceptfor wind speed, all parameters were used without converting to the requiredheight. This is another source of error.Although the model has the above limitations, it explains well the twoimportant processes happening in the region. The main features of temperaturevariations of the surface and bottom temperature in the region have beenrepresented clearly. The model hindcasted the last 37 years of temperatureprofiles with reasonable accuracy. This result may improve our understanding ofthe dynamics of Hecate Strait- Queen Charlotte Sound region and contribute tothe implementation of “reconstruction of the oceanographic conditions” within theregion. It may also provide background physical oceanographic knowledge to thefisheries researchers involved in the OPEN project and may lead to a betterunderstanding of variations in the habitat of ground fish.80BibliographyAllen, J.S. 1980: Models of Wind-driven Currents on the Continental Shelf. Ann.Rev. Fluid Mech. 12: 389-433.Bakun, A., 1973: Coastal Upwelling Indices, West Coast of North America,1946-1971. NOAA Tech. Rep. NMFS SSRF 671.Crawford, W.R. , W.S. Huggett, M.J. Woodward and P.E. Daniel, 1985: SummerCirculation of the Waters in Queen Charlotte Sound. Atmosphere-Ocean, 23:393-413.Crawford, W.R. , W.S. Huggett and M.J. Woodward, 1988: Water Transportthrough Hecate Strait, British Columbia, Atmosphere-Ocean, 26: 301-320.Crean, P.B., 1967: Physical Oceanography of Dixon Entrance, British Columbia.Fish. Res. Board Can. Ottawa . Bulletin 156. 66pp.Dodimead, A.J., 1980: A General Review of the Oceanography of the QueenCharlotte Sound-Hecate Strait-Dixon Entrance Region. Canadian ManuscriptReport of Fisheries and Aquatic Sciences. No. 1574.Freeland, H.J. and K.L. Denman, 1982: A topographically Controlled UpwellingCenter off Southern Vancouver Island. J. Marine Res. 40: 1069-1093.Ivanoff, A., 1977: Oceanic Absorption of Solar Energy. Modeling and Predictionof the Upper Layers of the Ocean. Pergamon Press, 325pp.Niiler, P.P. and E.B. Kraus, 1977: One-Dimensional Models of the Upper Ocean.Modelling and Prediction of the Upper Layers of the Ocean. Pergamon Press,325pp.Pickard, G.L. and W.J. Emery, 1990: Descriptive Physical Oceanography.Pergamon Press. 320pp.81Rosemary, D. Mey and Nan D. Walker, 1990: Surface Heat Fluxes and MarineBoundary La3ier Modification in the Aguthao Retroflection Region. I. Geophys.Res. 95:C9 15,997-16,015.Stigebrandt, A., 1981: Cross Thermocline Flow on Continental Shelves and theLocations of Shelf Fronts. Ecohydrodynamics, Elsevier Scientific PublishingCompany.Tabata, S. and J.L. Peart, 1985: Statistics of Oceanographic Data Based onHydrographic/STD Casts Made at Station 1 through 6 along Line P DuringJanuary 1959 through June 1981. Canadian Data Report of Hydrography andOcean Sciences. No. 38.Thomson, R.E., 1989: The Queen Charlotte Islands Physical Oceanography. TheOuter Shores. Queen Charlotte City, B. C.82

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