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Exchange flow through the Burlington Ship Canal Tedford, Edmund W. 1999

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EXCHANGE FLOW THROUGH THE BURLINGTON SHIP CANAL by EDMUND W. TEDFORD B.A.Sc., University of New Brunswick, 1997  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (CIVIL ENGINEERING)  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA September 1999 © Edmund W. Tedford, 1999  In presenting degree  this  at the  thesis  in  University of  freely available for reference copying  of  department publication  this or of  thesis for by  this  his  or  partial fulfilment  of  British Columbia,  I agree  and study.  Department The University of British Columbia Vancouver, Canada  DE-6 (2/88)  that the  representatives.  may be It  thesis for financial gain shall not  permission.  requirements  I further agree  scholarly purposes her  the  is  that  an  advanced  Library shall make it  permission  for extensive  granted by the understood  be  for  that  allowed without  head  of  my  copying  or  my written  ABSTRACT  The currents in the Burlington Ship Canal were found to be the result of a variety of driving mechanisms. Wind driven upwelling at the western end of Lake Ontario creates a horizontal density gradient through the canal driving baroclinic currents. Wind initiated standing waves and lunar tides in Lake Ontario cause water surface gradients through the canal driving barotropic currents. The barotropic currents are also strongly affected by Helmholtz or Harbour Resonance.  A water balance showed that baroclinic currents contributed moreflowto the harbour than streamflowand waste water treatment plantflow,particularly during periods of intense lake upwelling. The water balance also showed that velocity observations from the Acoustic Doppler Current Profiler were 19% less than predicted by the observed changes in Hamilton Harbour water level. The influence of the side wall boundary is suspected as the source of this difference.  ii  TABLE OF CONTENTS  ABSTRACT  H  TABLE OF CONTENTS  HI  LIST OF TABLES  V  LIST OF FIGURES  V  LIST OF SYMBOLS  VII  ACKNOWLEDGEMENTS  DC  1  INTRODUCTION  1  1.1  Exchange Flow  2  1.2  Objectives  3  2  LITERATURE REVIEW  5  2.1 Baroclinic Current 2.1.1 Upwelling and wind  5 9  2.2 Barotropic current 2.2.1 Standing waves 2.2.2 Tidal Oscillations 2.2.3 Helmholtz Resonance  11 11 13 13  3  17  DATA COLLECTION, PROCESSING AND ANALYSIS  3.1  Data Collection  17  3.2  Data Processing  19  3.3  Spectral Analysis  21  3.4  Filtering  26 iii  4  RESULTS AND DISCUSSION  28  4.1  Water Balance  28  4.2  Thermal Structure  35  4.3  Baroclinic Current  36  4.4  Barotropic Current  42  4.4.1 5  Helmholtz Resonance  46  CONCLUSIONS AND RECOMMENDATIONS  BIBLIOGRAPHY  48 51  APPENDIX A  .....54  APPENDDCB  55  iv  LIST OF T A B L E S  Table 1.1 Exchange Flows Table 3.1 Moored thermistor chains Table 4.1 Summary of water level oscillations observed near the canal Table 5.1 Summary of flow into the harbour (day 10 to 45)  3 19 44 49  LIST OF FIGURES  Figure 1.1 Site location map 2 Figure 2.1 Thermal structure observed in the canal during a two-hour survey of the canal harbour system during the summer of 1988 (Adapted from Spigel, 1988) 6 Figure 2.2 Frictionless two-layer flow in a channel 7 Figure 2.3 The temperature-density relationship expected for the area of study 8 Figure 2.4 Typical temperature profile in a temperate lake during the summer 9 Figure 2.5 First, second and third modes of standing waves (AdaptedfromHenderson, 1966) 12 Figure 2.6 A damped oscillator with periodic forcing (Source: Marion 1970) 13 Figure 2.7 Comparison of theoretical (Q=6) and best-fit (Q=l .7) amplification in Hamilton Harbour (Freeman et al,1974) 16 Figure 3.1a. Plan of the Hamilton Harbour - Lake Ontario system, b. Cross section of the Burlington ship canal 18 Figure 3.2 Depth averaged velocity simultaneously observed by two ADCPs 20 Figure 3.3 a) An example of a two frequency signal b) Spectrum of plotted signal from applying equation (3.9) with two different windowing techniques 26 Figure 3.4 The response function of a low passfilterwith uniform weighting and of a high passfilterwith weighting following a binomial distribution 27 Figure 4.1 Observedflowfor a)Redhill Creek (Water Survey of Canada), b)Spencer Creek (Water Survey of Canada) and c)Grindstone Creek (Halton Region Conservation Authority) 29 Figure 4.2 Cumulative precipitation recorded by the breakwall tipping bucket 30 Figure 4.3 Daily dischargefrommajor municipal treatment plants 31 Figure 4.4 Observed water level and predicted water levels based on the water balances 32 Figure 4.5 Spectrum of observed and predicted Hamilton Harbour water levels 34 Figure 4.6 20°C 16°C and 12°C (8°C in Lake Ontario only) Isotherms in Lake Ontario b) Hamilton Harbour centre and c) Hamilton Harbour east 35 v  Figure 4.7 Sample velocity and temperature difference profiles observed at day 25.9 (25.82 25.98) 36 Figure 4.8 Baroclinic velocity and temperature difference averaged over four hours for the period of record 37 Figure 4.9 Velocity and temperature difference profiles for a period of weak reversed exchange 38 Figure 4.10 a) Westward wind as observed at the west end of the canal b) Water temperatures at a depth of 5m for harbour east (thin line) and Lake Ontario (thick line). 39 Figure 4.11 Temperature observations at a depth of 9m (1959 and 1960 data from Matheson and Anderson 1965) 40 Figure 4.12 Spectrum of baroclinic current for the entire period of record with 90% confidence limits 41 Figure 4.13 Depth averaged velocity observed at the moored ADCP (At=l minute) 42 Figure 4.14 Spectrum of depth averaged velocity observed at the moored ADCP with 90% confidence limits 43 Figure 4.15 a) Wind intensity at the west end of Lake Ontario b) frequency distribution of barotropic current oscillations over time (higher contours represent increased energy)..45 Figure 4.16 a) The spectrum of Lake Ontario and Hamilton Harbour water level oscillations b) Helmholtz amplification and damping in Hamilton Harbour 46  vi  LIST OF SYMBOLS  A  area of Hamilton Harbour (21 km )  ah  amplitude of harbour oscillation  a  amplitude of lake oscillation  acvk  auto covariance for time lag kA  2  w  am and b  sine and cosine Fourier coefficients for frequency m  m  f  frequency (1/period)  g  gravitational acceleration  G  composite Froude number  g'  modified gravitational acceleration  h  total depth of the canal  h;  depth of layer i  i = 1,2  index of top layer and bottom layer  1  longest dimension of basin  L  length of the canal (830 m)  n  number of observation per date window  N  total number of observations  p  spectrum of x in units of x  2  m  P  averaged spectrum  m  Q  dimensionless damping parameter  R  filter  response function (amplitude before/amplitude after)  S  cross sectional area of the canal  t  time  Tim  period of internal seiche  T  period of a standing wave with n nodes  n  Ui  velocity of layer i  w  centralfilterweight  c  Wk  filter  weight k awayfromthe central weight vii  windowing weight m away from the central weight average of time series observed value of time series as time t total depth of flow frequency of forcing sampling interval confidence parameter Chi squared distribution with v degrees of freedom density of layer i natural frequency of a system without damping natural frequency of a system with damping (Helmholtz)  viii  ACKNOWLEDGEMENTS  I would like to sincerely thank Dr. Greg Lawrence and Dr. Roger Pieters who provided guidance and assistance necessary to complete this study. I am thankful to Rich Palowicz for providing answers to many Matlab questions. Many others in the Department of Oceanography patiently guided me through a variety of problems including: Carine Vindeirinho, David Eurin, David Jones, Matt Durham, Joe Tarn and Steve Pond. Lillian Zaremba must be recognized for her help editing and formatting. In addition, I appreciate all the encouragement I have ever received from my family, friends and previous supervisors.  ix  1  INTRODUCTION  Flow in the Burlington Ship Canal in Ontario, Canada has received considerable attention in recent decades. Built in the 1820s for sailing vessels, the Burlington Ship Canal connects Hamilton Harbour (21 km ) to the western end of Lake Ontario (19000 km ). The canal is 2  2  89 m wide by 9.6 m deep and cuts through a sand bar approximately one kilometer wide. The canal is relied upon by Hamilton industry along the south shore of the harbour to pass large ore bearing freighters. The harbour's drainage area includes the city of Hamilton and part of the City of Burlington having a combined population near 500 000 (Spigel, 1988). The municipalities and industries on the harbour have created what one popular writer called 'one of the worst-polluted water bodies in the world' (Gorrie, 1987). In 1985 Hamilton Harbour was indeed designated by the Great Lakes International Joint Commission as one of 42 areas of environmental concern. In the 1960s it was noticed that the harbour's aquatic life had been almost completely eliminated and the harbour has received regular attention ever since. The water quality in the harbour is expected to depend on flow through the canal as it represents the largest source and sink of water. It is this exchange flow through the canal that is the focus of this thesis.  1  Hamilton Harbour Figure 1.1 Site location map 1.1  Exchange Flow  Exchange flow between connected water bodies or basins is caused by: either horizontal water density gradients causing baroclinic current or water surface gradients causing barotropic currents or a combination of the two. Density gradients between the water bodies may arise due to differences in the temperature and salinity of external flow coming into the water bodies or due to differences in the rate of evaporation. Density gradients may also result from the wind, which may cause different pycnocline orientation or atmospheric heat transfer in the two water bodies.  Water surface gradients may be caused by the tides, wind, barometric  pressure gradients or harbour resonance.  Table 1.1 lists a few known exchange flows and  noted driving mechanisms.  2  Table 1.1 Exchange Flows Kinder and Bryden, 1985. Straight of Gibraltar connecting the Atlantic to the Mediteranean The Bosphorus connecting Gregg et al, 1999. the Black Sea to the Mediteranean Several channels connecting Roy, F.E. 1983. Blackbay to Lake Superior Two basins in Amisk Lake, Lawrence et al. 1997. Alberta, Canada.  Tides, evaporation and different incoming flow salinities. Tides, evaporation and different incoming flow salinities. Wind driven oscillations and differential heating. Wind driven oscillations and pycnocline motion.  Previous investigators have identified potential mechanisms drivingflowin the Burlington ship canal. Spigel (1988) hypothesized that wind induced upwelling at the western end of Lake Ontario as important in determining baroclinic current in the canal but did not make any observations to confirm his hypothesis. Palmer and Poulton (1976) recognized Lake Ontario and Hamilton Harbour water level oscillations as sources of barotropic current in the canal. 1.2  Objectives  The objectives of this study are to: interpret observations describing thermal structure, conductivity, water levels,flowin the canal and atmospheric conditions, compare observed behavior with that expectedfromtheory, and identify the mechanisms drivingflowin the canal and characterize their importance. The above objectives should aid in the eventual modeling of the system. 1.3  Scope  An introduction to basic processes in physical limnology and stratified flow along with previously observed features of the system of interest is presented in Chapter 2. The field program and resulting data are described in Chapter 3. The time series analysis tools applied 3  to the data are also discussed in Chapter 3. In Chapter 4 the results of the analyses are presented. Conclusions and recommendations for future work are made in Chapter 5.  4  2  LITERATURE REVIEW  Many investigators have observed exchange flow in the Burlington Ship Canal. Currents driven by both horizontal density gradients and water surface gradients have been observed. In the summer both are considered to be important in determining exchange. In order to ease the interpretation of flow behaviour in the canal it is useful to separate the two types of current, baroclinic and barotropic, as much as possible.  2.1  Baroclinic Current  Spigel's survey (1988) was conducted with the hope of providing a 'broad overview of the processes occurring in the harbour-canal system.' Figure 2.1 shows observations made during one of several single day surveys conducted by Spigel during the summer of 1988. The figure indicates slight tilting of the isotherms in the harbour and steeper tilting in the canal. Because colder water is denser the plot may be interpreted as showing cool (dense) Lake Ontario water moving along the bottom of the canal into the harbour and warm harbour water moving along the top of the canal on to the surface of Lake Ontario. This is not necessarily correct however since it ignores the potential influence of water surface gradients. A more precise interpretation is that the water at the bottom of the canal is moving to the left with respect to the water at the top of the canal. This interpretation may also be incorrect since all of the data  5  A3  A25  A2  Al  AO AM1 AM2 AM3 AM4  Figure 2.1 Thermal structure observed in the canal during a two-hour survey of the canal harbour system during the summer of 1988 (Adapted from Spigel, 1988)  used in the plot was gathered using one instrument over approximately two hours so that the thermal structure shown may never have existed. The changes that may have occurred over the two hours are not so severe as to conceal the broad picture however: that is, cold water does tend to flow beneath warm Hamilton Harbour water through the canal. Spigel's surveys later in the summer show decreases in conductivity (dissolved solids) in the harbour, particularly at depth, indicating the lower conductivity Lake Ontario water must have intruded into the harbour.  6  f  Figure 2.2 Frictionless two-layer flow in a channel  The baroclinic current in a channel such as the ship canal (Hamblin and Lawrence 1990) is often modeled as two homogeneous layers. Figure 2.2 shows a schematic of the simplest model with aflatinterfacefromone end of the canal to the other indicating the assumption of no friction. If the flow is steady it will be characterized by internal controls, where the composite Froude number (G ) equals one, at each end of the channel. G is similar to the 2  2  Froude number for single layer flow:  -4 4-  G2=  +  (21)  where Ui is the average velocity in layer i, hj is the thickness and g' is the modified gravitational acceleration resultingfromthe density difference between the two layers. The modified gravitational acceleration is S ' ^ C ,  (2.2)  where p is the density. If we assume that the water surface is flat such that flow is equal and opposite in both layers, steady and frictionless, then equations (2.1) and (2.2) simplify to  u = -a - u y  2  (2.3)  -f^-(A-A)] A ) 4  Chen and Millero (1986) formulated the equation of state forfreshwater lakes, relating density to temperature and salinity. The relation has been plotted in Figure 2.3 for a range of temperatures using both Lake Ontario (S=0.17 psu) and Hamilton Harbour (S=0.32) salinities. Figure 2.3 shows the maximum density difference due to salinity is of the same order as 1°C temperature difference. Similarly, Dick and Marsalek (1973) found that variations in salinity caused no significant density differences. Therefore the impact of salinity gradients on current will be ignored in this study. The velocity u of equation (2.3), given the above assumptions, is then a function of the temperature difference only. 26  S=0.17 psu S=0.32 psu  24 22 20 18  5  _  1  6  •••X'""--  S.14 E at  12 10 8 6 4  997  997.5  998.5 density (kg/m^)  Figure 2.3 The temperature-density relationship expected for the area of study 8  2.1.1  Upwelling and wind  In the previous section, stratifiedflowin the canal was related to the temperature difference between Lake Ontario and Hamilton Harbour. The temperature difference could be caused by one or more of the following: the wind's differing impact on the two water bodies, the larger thermal load imposed on the harbour by industry and municipal sewage, or the lakes greater depth, which makes it slower to warm. If the latter two causes were responsible then the baroclinic current would be expected to vary with the daily human cycle and gradually with the seasons. Previous investigators (Spigel 1988, Palmer and Poulton 1976, and Fox et al, 1996) have found otherwise, indicating the importance of wind. In order to compare wind and water temperatures around the canal the nature of isotherm displacement in lakes must be understood. o EPIUMNION  5 10  METALIMNION  E X  t- 15 a LU  O  HYPOLIMNION  20 25 3 0  0  J  5  I  10  1  L  1  15  20  TEMPERATURE  25  30  CO  Figure 2.4 Typical temperature profile in a temperate lake during the summer (Adapted from Wetzel 1983) 9  Figure 2.4 illustrates the typical thermal structure exhibited in temperate lakes during summer stratification. The epilimnion is thermally homogeneous with free vertical circulation. The metalimnion restricts vertical circulation, isolating the hypolimnion from the direct impact of the wind. Mortimer (1952) investigated how different types of wind influence this type of lake stratification. The performance of a two-layer and a three-layer model were investigated. The two-layer model had a uniform layer above and below the thermocline (depth of maximum density gradient). The two-layer model showed that deflections of the thermocline are approximately proportional to the square of the wind speed such that the thermocline tends to rise at the windward end of the lake and fall at the leeward end opposing the slope of the water surface. Watson (1904) found that deflections of the thermocline would oscillate at specific frequencies. The lowest frequency had a period T^, commonly referred to as the period of internal seiching, and given by  21  (2.4)  where hi and h = thickness of the upper and lower layer respectively and 2  1 = length of the basin  Mortimer's observations indicated that the two-layer model could not predict potentially important behavior below the thermocline and consequently adopted a three-layer model. The three-layer model divided the depth below the thermocline into a transition layer above a uniform density layer. This model showed that during light and moderate winds the lower 10  interface would remain horizontal while the upper interface would behave much as it did in the two-layer model. Mortimer also found in his physical model that a slow build up to a strong wind may not cause deflections in the lower interface but if a wind of the same intensity was applied suddenly, it could cause interface deflections.  2.2  Barotropic current  Previous investigators have observed strong currents independent of depth in the Burlington Ship Canal (Dick and Marsalek 1973, Palmer and Poulton 1976 and Fox et al 1996). These barotropic currents are caused by water surface gradients along the axis of the canal. These gradients are a result of water level oscillations in the lake, the harbour or the canal. The oscillations at the canal have been attributed to the following possibilities:  2.2.1  1.  Standing waves  2.  Tidal oscillations  3.  Helmholtz resonance  Standing waves  Standing waves occur in enclosed basins and are the result of the combination of incident waves on a vertical boundary and their reflected waves. Examples of three modes of standing waves in a rectangular basin are shown in Figure 2.5. The period of these oscillations is the same as the incident waves which are assumed to be long low amplitude waves which travel at a speed c=(gy) such that: 1/2  11  21 (2.5)  T = ^ =  where T - period of standing wave with n nodes n  y = the depth of the basin  Y77777777777777.  Figure 2.5 First, second and third modes of standing waves (AdaptedfromHenderson, 1966)  Equation (2.5) is similar to equation (2.4) where the denominator represents the speed of a wave along the interface layer 1 and 2. Equation (2.5) is often only applicable for the lowest modes of standing waves, where cross channel oscillations are negligible.  Wind and/or  barometric pressure changes acting at the surface initiate the waves. Standing waves have been examined in Lake Ontario (Rao and Schwab, 1976) and Hamilton Harbour (Wu et al, 1997).  Palmer and Poulton (1976) found evidence of these oscillations in velocity  measurements from the canal. In Chapter 4 Palmer and Poulton's conclusions regarding standing waves will be extended.  12  2.2.2  Tidal Oscillations  Tidal action has also been observed in the Great Lakes (Hutchinson, 1957). The orbital motion of the moon, and to a lesser extent that of the earth and the sun, influence the surface of large water bodies at regular periods. The most important period is often the semi-diurnal lunar tide of 12.42 hours (Hanson, 1960). Unlike standing waves the tidal signals should have specific phases and amplitudes making them distinguishable from the other more random oscillations. 2.2.3  Helmholtz Resonance  Earlier researchers (Freeman et al, 1974) noted co-oscillations or Helmholtz resonance between Lake Ontario and Hamilton Harbour. Helmholtz resonance occurs where a harbour is connected to another water body subject to surface oscillations.  An analogy with a  common forced and damped particle oscillator is useful in understanding this source of current in the canal.  Figure 2.6 A damped oscillator with periodic forcing (Source: Marion 1970)  13  The equation of motion for this system is rriyX  + bx + kx- Fcos(o)t)  (2.6)  where mi = mass of the particle b = friction coefficient k = spring constant F = the maximum force associated with periodic forcing co = frequency of periodic forcing Each of the above variables are assumed to be represented by the following in a harbour system: mi = pLS ,  the mass of water in the canal  b = (d)Rmi)/Q, the friction factor k = (pgS )/A, restoring force of the changing harbour level 2  per unit displacement of the canal water F = aLSpg,  maximum force of the oscillating lake level on the canal water  where: ah = (xS)/A,  resulting amplitude of harbour oscillation  aL = amplitude of lake oscillations O)R= Helmholtz resonance frequency described in equation (2.8) below. S = cross sectional area of the canal L = length of the canal Q is a dimensionless parameter that decreases as damping increases. The value of Q has been determined for various harbour configurations based on the assumption that damping in the system results from energy loss as the water exits the canal (Miles and Munk, 1961).  Equation (2.6) has been solved for the condition when the system has reached steady state (Marion, 1970) to give an amplification factor:  (2.7) 1-  where  co  0  = (k/mi)  1/2  ,  co  the natural frequency of the system without damping. The damped  natural frequency or Helmholtz resonance frequency is  . 1/2  (2.8) l + l/(20 ). 2  In comparing water level oscillations in the harbour and the lake, Freeman et al. (1974) found Q was approximately 1.7, while according to Miles and Munk's theory it should be 6. Equation (2.7) is plotted for the two values of Q indicating much more damping was observed in the system than expected from the theory.  The two curves also show amplification above the semi-diurnal tidalfrequencyof 0.08 cph and damping above frequencies of about 0.55 cph.  15  0.1  0.2  0.3  0.4 0.5 0.6 frequency (cycles/hour)  Figure 2.7 Comparison of theoretical (Q=6) and best-fit (Q=1.7) amplification in Hamilton Harbour (Freeman et al, 1974)  16  3  DATA C O L L E C T I O N , PROCESSING AND ANALYSIS  To get a comprehensive picture of the harbour-canal system during summer stratification water level, temperature, conductivity, and velocity were measured. Incoming stream flow and municipal discharges were monitored along with atmospheric conditions to characterize external forces on the harbour-canal system.  The data discussed in later chapters was  collected as part of an extensive research project includingfieldwork in the summer of 1996 as described in section 3.1. The processing of continuous datafrommoored sensors, which are particularly relevant to this report, is discussed in section 3.2. Time series analysis used to aid in the interpretation of the data is described in sections 3.3 and 3.4.  3.1  Data Collection  A field program was carried out with instrumentation recording from 4 July to 15 August 1996. Instruments from CCIW, UBC and NOAA were incorporated, so that over $500,000 of field equipment was deployed, as summarized in Fig. 3.1. Instrumentation was placed throughout Hamilton Harbour, in the ship canal, and in the western end of Lake Ontario. One ADCP (Acoustic Doppler Current Profiler) was bottom mounted at the west end of the ship canal and another was mounted on a small vessel equipped with differential GPS.  17  Burlington Ship Canal  Grindstone Creek  Western Lake Ontario  Dundas WWTP  Dundas WWTP  Hamilton WWTP A RedhiJI Creek.  Hamilton Harbour  -2 -4  T  T j  T  T  T  T;  T  T  T,C  T  T  T,C  T  i i t  \  CD  -a  200 400 600 distance from Hamilton H a r b o u r (m)  800  Figure 3.1 a. Plan of the Hamilton Harbour - Lake Ontario system, b. Cross section of the Burlington ship canal. 18  Due to the passage of large draft ore carriers through the ship canal, the bottom mounted ADCP was 4 m from the ship canal walls. The bottom mounted ADCP was also inset 165 m from the west end of the ship canal to diminish the influence of entrance effects on the observed velocity profile. There were 77 moored temperature sensors on 8 chains. Meteorological stations were located at the eastern end of the harbour and the western end of Lake Ontario. Seven conductivity sensors were also installed; however, six of them were not deployed until July 19. Due to logger and sensor failure, data was unavailablefromfour of the temperature instruments. Discharge data from three streams and three waste water treatment plants were also collected.  3.2  Data Processing  Continuous water temperature, water velocity, water level and wind measurements will be used to identity the mechanisms which drive current in the canal. Most of the thermistors and conductivity sensors were calibrated either shortly before and or after deployment as indicated in Appendix A. A summary of moored thermistor locations is provided in Table 3.1 below. Table 3.1 Moored thermistor chains Chain # 1 2 3 4 5 6 7 8  Number of thermistors that functioned 7 9 8 9 10 11 9 10  Location Ship canal west Ship canal north Ship canal east Ship canal south Lake Ontario Hamilton Harbour centre Harbour east Break wall  19  Distance from canal (km) -  3.2 2.7 0.56 0.33  Greatest instrument depth (m) 9 9 9 9 17.5 22 17.5 13  Measurements from the moored ADCP are compared with the boat ADCP in Figure 3.2. The figure shows good agreement between the mean velocity over the depth observed by the instruments, indicating adequate precision. The high frequency blip at time 25.75 is the result of standing waves in the canal (the lowest mode Ti is less than 3 minutes) that are caused by a ship passing through the canal.  _QQ I  I  25.65  .  I  25.7  ,  I  25.75  time (days)  I  25.8  1  Figure 3.2 Depth averaged velocity simultaneously observed by two ADCPs.  The moored ADCP made observations at 0.5 m intervals (17 bins, see Appendix A for a diagram) above the head of the instrument which was 0.4 m above the bottom of the canal. Because of peculiarities associated with ADCP measurements near the instrument and near the water surface the available data does not provide a complete velocity profile. The top bin 20  or measurement is subject to side lobe contamination. Sidelobe contamination is a result of the unpredictable nature of soundwaves reflecting off the surface. The ADCP is also unable to take readings within 0.5m of the head of the instrument. At this distance the reflected soundwaves return to the instrument too soon after they are emitted to be properly interpreted (see Gordon 1996, for a more complete description of ADCP capabilities).  There are  therefore 0.5 m and 1 m gaps at the top and bottom of the profile, respectively. The gap at the top of the profile wasfilledwith the velocity observed in the top good bin. The gap at the bottom wasfilledwith the velocity observed in the bottom bin multiplied by a factor of 0.5. This procedure gave a reasonable water balance in the harbour (see Section 4.1). 3.3  Spectral Analysis  In order to explain the analysis of time series data it willfirstbe assumed that the parameters observed are controlled by deterministic processes. The signal, f(t), describing these parameters may be represented by an infinite series  oo  co  smimt) + ^b  m  m=0  cos(/w/)  where 0 <t <2n  (3.1)  m=0  This series is called the Fourier expansion of the function f(t) and the coefficients a and b m  m  are called the Fourier coefficients of the function with t = time. More practically, the function f{t) may be approximated by the finite series  n n n = £ m sin(/wr) + £ b cos(/wr)  S  a  m  m=0  m=0  21  where 0 <t <2K  (3.2)  with undetermined coefficients a  m  and b . To obtain these coefficients we will find the m  minimum of the integral (3.3)  E = ^-][f(t)-S (t)fdt. n  where E is the mean square of the error of the approximation over the interval between 0 and 2K. Following Karman and Biot (1940) we differentiate equation (3.3) with respect to a specific coefficient a and find m  (3.4)  a =±-)f(t)sm(mt)dt. m  2n \  If f(t) is represented by n points evenly spaced in t  a = - X A sin(—mk) m  for 0 <m <n/2  (3.5)  for 0 <m <n/2  (3.6)  and similarly for the cosine coefficient  9  n  b =-Yf nf m  k  0  9~  cos(— mk) n  where m represents the number of cycles over the interval 0->n associated with the coefficients ^ and b . For example a^ and bio describe an oscillation that occurs 10 times m  22  between time 0 and time n or 10 times over the period of record.  From the Fourier  coefficients the amplitude of the oscillations at a frequency m/(nA) where A equals the time interval between measurements is (3.7) The mean of the time series equals c = b . 0  0  The parameters of concern in this report as mentioned in section 2.2 are expected to be influenced by both deterministic (tidal) and stochastic (meteorological) processes.  The  Fourier transforms alone have been found to be inadequate for describing stochastic processes as stated by Jenkins and Watts (1968): "The basic reason why Fourier analysis breaks down when applied to time series is that it is based on the assumption of fixed amplitudes, frequencies and phases. Time series; on the other hand are characterised by random changes of frequencies, amplitudes and phases. Therefore it is not surprising that Fourier methods need to be adapted to take account of the random nature of a time series." To calculate the spectrum of a stochastic series the Fourier transform of the autocovariance function estimator, acv(k), is instead found. Where the autocavarience,  (3.8)  The autocovariance characterizes the variance associated with lag k. The sample spectrum estimate is found by substituting acv for f in equations (3.5) and (3.6) and then substituting k  k  these into equation (3.7), giving  23  + — y acv cos(—mk)  ^ ^acv sin(—mk)  k  k  n k=0  n  n  k=0  /w = 0->n/2.  (3.9)  Dividing the time series into samples and determining the spectrum for each sample allows an averaged spectrum P to be calculated. Confidence limits may be placed on the averaged m  spectrum by assuming the data follows a Gaussian distribution that is constant over time. Because p is an estimate of the data's variance at frequency m its distribution is most often m  approximated by a Chi squared distribution (x„ ) with u degrees of freedom (Jenkins and 2  Watts 1968, Munk et al 1959).  The 100(l-a)% upper and lower confidence limits are  therefore,  v  v 2  '  (3.10)  2 /2j  The number of degrees of freedom depends on the windowing method used to divide the time series into samples. Two such methods are the triangular window which has u=3N/n and the rectangular window which has u=N/n. The variable N equals the total number of observations in the whole time series while n is the number of observations in one window (Jenkins and Watts, 1968). Where there is limited data rather than computing time it is optimal to overlap the triangular windows by n/2 so that u=3.6(N/n) (Welch, 1978). In this report the triangular windowing technique will be used, but for illustrative purposes the rectangular windowing technique will also be described.  24  The simplest windowing technique (rectangular) is to divide the time series into equally sized blocks and calculate the spectrum using equation (3.9) without any modifications to the data. This is the best method in only one exceptional case: the time series is deterministic with each of the signal's frequencies falling at the centre of a frequency bin (bin=(m±0.5)/(nA)). In a natural time series this is never the case and so instead of generating one peak at the actual frequency, the analysis generates several peaks throughout the spectrum, the largest at the frequency bin bounding the actual frequency.  Modifying each block of data with a windowing function before applying equation (3.8) will alter these false peaks or 'leakage' potentially improving the analysis. The triangular or 'Bartlett' windowing function,  w(m)  = 1 - m - Vytl  for 0 <m <n,  (3.11)  Yin  is perhaps the next simplest after the rectangular window. Figure 3.3 compares the estimated spectrum of a two frequency signal using a triangular and rectangular window.  The  rectangular window shows substantially more leakage and was therefore not used to generate spectral estimates in this report.  25  •  0.2 0.1  ;  ...  /)..  If n  0.05 —•  i  rectangular triangular  i  0.15  0  i  l  I  1 '  A  s\\  Y  !y\.7T~~~~  r—  1  i  frequency  Figure 3.3 a) An example of a two frequency signal b) Spectrum of plotted signal from applying equation (3.9) with two different windowing techniques.  3.4 Filtering Another tool used in time series analysis is a filter. High frequencies are filtered out of a stochastic time series by using a sliding average to smooth the data (low pass filter). Similarly, to filter out low frequencies the smoothed time series is subtracted from the original series (high pass filter). A variety of weighting techniques have been adopted in the sliding average to minimize the unwanted interference caused by filtering. The effect of a given filter on the spectrum, commonly referred to as the response function, is given by Panofsky and Brier (1958) as, *a) = w +22> cos(2*^A) c  t  k=\  where f = frequency wc = central weight 26  (3.12)  Wk = k* weight away from the center Equation 3.12 applies only to low passfilterswith weighting coefficients that are symmetric about the centre. A high passfilter'sresponse function is simply one minus the response function of the respective low passfilter.Figure 3.4 shows some typical response functions. 03  o  if  o  low pass filter high pass filter  « 0.8 =3  E 0.6 ra cn  c  3 0.4 CD  |  0.2  -a =3 CL  E  0 0  0.1  0.2 0.3 0.4 frequency (cycles/hour)  0.5  0.6  Figure 3.4 The response function of a low passfilterwith uniform weighting and of a high passfilterwith weighting following a binomial distribution.  The response function of the filter using a uniform average, the low passfilter,shows unwanted distortion throughout the spectrum. The response function of the high pass filter, the onlyfilterused in this study, is shown to distort only the spectrum of oscillations with periods greater than 7 hours (f = 0.14). This filter is used to decrease the peaks in the spectrum associated with less frequent oscillations consequently decreasing their unwanted leakage to the rest of the spectrum. 27  4 RESULTS AND DISCUSSION  This chapter describes and discusses the observations made during the summer of 1996 with regard to mass balance in the harbour and mechanisms drivingflowin the canal. The available flows into and out of the Harbour are examined in section 4.1. In section 2.1 the conditions required for stratifiedflowwere introduced and are studied in section 4.2 and 4.3. Section 4.4 covers water level oscillations and their impact on flow in the canal.  4.1  Water Balance  In order to carry out a water balance for Hamilton Harbour the inputs and outputs of expected significance will first be identified.  Canalflow:The depth averagedflowobserved at the ADCP is assumed to describe the input and output through the canal. Testing this assumption is perhaps the most important reason for carrying out the water balance.  Stream flow: The harbour watershed has several streams totalling a drainage area of approximately 494 km . 2  Three of the streams, encompassing a drainage area of 312.5km ,  were gauged during the period of study.  2  Figure 4.1 shows the discharge for the three 28  streams. Redhill Creek, to the south of the harbour and flowing through the city of Hamilton, has the smallest area with the largest and flashiestflowstypical of a basin with a large proportion of impervious area. Spencer Creek to west is the only stream known to be controlled and hasflowtypical of such a stream. Grindstone Creek to the north on the other hand exhibits a more natural hydrograph. Theflowsfrom these streams are summed and prorated for the water balance to represent runoff from the entire harbour basin. Redhill Creek 60.9 km 20  I  1  A  I  -I  1  T  1  1  2  r  Grindstone Creek 82.6 km 1  1  r—  2  I  45 time (July days)  Figure 4.1 Observedflowfor a)Redhill Creek (Water Survey of Canada), b)Spencer Creek (Water Survey of Canada) and c)Grindstone Creek (Halton Region Conservation Authority)  Direct Evaporation and Precipitation: A precise estimate of evaporation may only be made after a heat balance for the harbour has been carried out, this is unfortunately beyond the scope of this report. Viessman and Lewis (1996) give typical rates of annual evaporation for 29  small lakes and reservoirs in the region (25 inches) as well as the annual proportion of pan evaporation in the region for July (15%) giving a rate of 3.1 mm/day. Precipitation is estimated from a tipping bucket located on the breakwall just outside the entrance to the canal and is plotted in Figure 4.2.  0.12 |  1  1  1  1  10  15  20  1  1  1  1  1  25  30  35  40  45  1  0.1  -  0.08 f  0.06 \  50  time (days)  Figure 4.2 Cumulative precipitation recorded by the breakwall tipping bucket.  Municipal discharges: Figure 4.3 shows the daily rate of discharge from the three major waste water treatment plants. These flows consist primarily of water pumped out of Lake Ontario as well as some storm water runoff. The minimumflowobserved for each plant is assumed to represent only the water pumpedfromthe lake such that the total input of lake water through the municipal systems is taken to be 3.8 m /s or 15.3 mm/day over the entire harbour (21.5 3  30  km ). The remaining portion of the flow through the municipal systems is assumed to be 2  storm water, which has already been accounted for in prorating the three streams as mentioned above. This assumption is expected to be adequate because the ignored treatment plant discharge of 0.64 m /s (average over the period of record) is reasonably less than the 3  additionalflowof 0.71 m /s (average) associated with prorating the stream discharges. 3  WWTPflows- Dundas, Skyway and Woodward 4.5 |  1  1  1  1  1  1  1  1  1  1  Dundas  ,1  0  i 5  i  10  i 15  i  20  i 25 July days  1  1  1  1  1  30  35  40  45  50  Figure 4.3 Daily discharge from major municipal treatment plants.  Figure 4.4 shows the harbour water level according to several water balances and the observed water levels at the breakwall in the harbour. The predicted water levels are based on the accumulatedflowobserved by the ADCP plus a variety of adjustments yet to be defined. All of the water level estimates include an added portion of flow at the top of the velocity 31  profile filling the gap in the data due to side lobe contamination (See section 3.2 for a description of the ADCP measurement bins). The depth of this portion of flow varies as the depth of Hamilton Harbour varies and its velocity is set equal to that observed in the top bin. With this extra top portion 8.5 m of the approximate 9.5 m flow depth are accounted for leaving lm at the bottom of the canal with unknown current.  The lowest water balance plotted in Figure 4.4 includes only the adjustment to the top. The second lowest also includes stream flow, direct precipitation, evaporation and treatment plant discharges as outlined above. The third and fourthfromthe bottom include 0.5 m and 0.75 m respectively of additional flow depth with velocity equal to that observed in the bottom bin.  0.3 -  ;  i  :  :  I  j  j  i  i  I  I  10  15  20  25  30  35  40  *  \, I  45  1  50  time (July days)  Figure 4.4 Observed water level and predicted water levels based on the water balances. 32  Several unsuccessful attempts were made to improve these estimates particularly with respect to the gradual downward divergence of the predicted water levels after about day 33 and the rapid downward divergence on days 15 and 19. Figure 4.5 shows the spectrum of water levels predicted using the above water balance (0.75 m of additionalflowdepth at the bottom) and that of the observed harbour levels. Both data sets were averaged to the same 15 minute time steps andfilteredusing the high passfilterdescribed in section 3.4.  The frequencies  dominating the spectrum will be discussed later but for now the differences between the two spectrums are of interest. The distributions of the two spectrums are shown to be very similar. However, the intensity of the water level oscillations associated with the water balance are uniformly less such that multiplying the observed velocities by a factor of 1.23 gives an almost perfect match. All other assumptions being reasonable this implies the velocities observed at 4m from the wall of the canal are approximately 19% less than the average velocities across the canal. This could be the source of the discrepancies in Figure 4.4 as, since the ADCP is much closer to one end of the canal, the dynamics of the side boundary layer will be different according to which direction theflowis going. The ADCP is at the harbour end of the canal, which may be observing more of the side boundary layer and therefore lower velocities when the flow is entering at the far end. This would tend to overestimate the predicted loss of water from Hamilton Harbour, which seems to be occurring on days 15 and 19 and after day 33 no matter how the gaps in the velocity profile are filled in.  Multiplying the ADCP measurements by 1.23 does not however aid in matching the lines shown in Figure 4.4. It makes their change over the period 23% greater consequently making  33  the match slightly worse. This is because multiplying by 1.23 only corrects the amplitude of oscillations, overlooking any positive or negative bias.  water balance observed harbour levels  j  0  0.5  1  frequency (cycles/hour)  L  1.5  2  Figure 4.5 Spectrum of observed and predicted Hamilton Harbour water levels.  For any later analysis using the ADCP measurements there is 0.5 m offlowadded to the top and bottom of the profile each withflowequal to that observed in the top and bottom bins respectively. The factor of 1.23 has not been applied so that all of theflowdiscussed may be as much as 19% less than the average across the canal.  34  4.2  Thermal Structure  The isotherms in Figure 4.6 illustrate the thermal structure of the water bodies at each end of the canal. The isotherms show relatively cooler water in Lake Ontario until about day 30 and then by about day 38 warm water in Lake Ontario. The centre of Hamilton Harbour shows cooling, which is much more gradual, throughout most of June (< day 32) associated with isotherms in Lake Ontario,  5  10  15  20  25  30  35  40  45  time (July days)  Figure 4.6 20°C 16°C and 12°C (8°C in Lake Ontario only) Isotherms in Lake Ontario b) Hamilton Harbour centre and c) Hamilton Harbour east.  exchange through the canal and then gradual heating. The east-end of the Harbour, near the canal, shows the same trends as the centre with oscillations superimposed on the isotherms. The amplitude of these oscillations is the least at the shallowest isotherm (20°C) indicating  35  internal seiching rather than diurnal heating. The period of the oscillations is slightly less than 24 hours which is comparable to the fundamental mode as predicted by equation (2.4) and assuming hi=7.5m, h=5.5m, Ti=22°C, T =13°C and l=8km (the longest dimension of the 2  2  harbour) which gives a period of 20 hours. It is expected that the thermal conditions at harbour east and Lake Ontario will control baroclinic current in the canal.  4.3  Baroclinic Current  Figure 4.7 is a plot of a 4 hour average of a velocity profile on a typical day (time =25.9) with strong baroclinic current and also a plot of a 4 hour average of the water temperature difference between harbour east and Lake Ontario for the same period. The velocity profile shows lake water entering the harbour underneath harbour water entering the lake.  velocity (cm/s) and temperature (C°)  Figure 4.7 Sample velocity and temperature difference profiles observed at day 25.9 (25.82 25.98). 36  The temperature gradient between the two water bodies varies between 8°C and 15°C through a depth of 10m. Conditions below 10m, the approximate depth of the canal, are not expected to influence flow through the canal.  In order to compare baroclinic current and temperature (density) gradients the two profiles will be parameterised as the baroclinic velocity and the temperature difference as proposed in section 2.1 such thatfromequation (2.3) and Figure 2.3: baroclinic velocity =f (temperature difference).  25  30 time(day9)  Figure 4.8 Baroclinic velocity and temperature difference averaged over four hours for the period of record. The baroclinic velocity is calculated by subtracting the average of the bottom three velocity measurements from the average of the top three measurements and dividing by two giving a baroclinic velocity of 16.7 cm/s for the profile in Figure 4.7. This procedure is an attempt to 37  get an average of the top and bottom layer velocities independent of the mean velocity (barotropic forcing). The temperature difference is simply taken as the temperature observed at a depth of 5m at harbour east minus the temperature observed at a depth of 5m in Lake Ontario giving a temperature difference of 14.5°C for the plotted profile.  The velocity in Figure 4.8 traces the temperature difference very well with a few exceptions. There are a few brief periods, particularly around days 38 and 42, where the comparison is not very good. On these days the parameters are not so useful as the density gradient as described by the temperature difference at 5m is too weak to drive the observed velocity difference between the top and bottom of the canal.  -4  -2  0  2  4  6  8  temperature (C°) and velocity (cm/s)  Figure 4.9 Velocity and temperature difference profiles for a period of weak reversed exchange. 38  Figure 4.9 shows profiles similar to those in Figure 4.7 except for a period with much weaker as well as reversed exchange during day 38. Through this period above 5m the water is warmer in the harbour than the lake, approximately the same at 5m, and then below 5m the harbour is cooler than the lake. The assumption that there are homogeneous water bodies at each end of the canal and the two layer conceptual model introduced are probably inappropriate during periods of weak baroclinic current.  The baroclinic current as indicated in Figure 4.8 varies considerably as a result of changes in the temperature difference. The changes in\the temperature difference occur as the thermal structures of the two water bodies are affected by the wind. The temperature at a depth of 5m is plotted for harbour east and Lake Ontario in Figure 4.10b.  time (days)  Figure 4.10 a) Westward wind as observed at the west end of the canal b) Water temperatures at a depth of 5m for harbour east (thin line) and Lake Ontario (thick line). 39  Lake Ontario is shown to exhibit much more dramatic temperature fluctuations at this depth and so is considered to be more important in controlling baroclinic exchange. In section 2.1 deflections of the thermocline were related to wind speed squared which is plotted in Figure 4.10a. The wind speed plotted represents the eastward (negative) and westward (positive) components of the wind squared and then averaged over 6 hours.  The temperature plotted in Figure 4.10 is from the west-end of Lake Ontario and so is expected to show cooling during an eastward wind and warming during a westward wind. This is found to be the case throughout most of the record, with eastward winds causing upwelling through most of July ending on about day 29 when the largest westward wind  T  4 -20 1  '  0  —'  i  20 40 time (July days)  '  1  60  Figure 4.11 Temperature observations at a depth of 9m (1959 and 1960 data from Matheson and Anderson 1965). 40  occurs. Prolonged westerlies (eastward wind) may be necessary for baroclinic exchange of the magnitude observed during 1996 however Figure 4.11 compares water temperatures observed at the west-end of Lake Ontario for the years 1959, 1960 and 1996 indicating 1996 was not an unusual year in terms of upwelling.  The spectrum of baroclinic velocity averaged over 15 minutes is plotted in Figure 4.12, with very few notable features. An overwhelming proportion of the energy is in the first mode indicating the dominating period is at least as long as the period of record. The 20-24 hour period observed in the isotherms of Figure 4.6c does not show up as a significant peak either  i  I 0  1  i 1  !  i  i  2  1  3  1—:  !  i i 5 6 frequency (cycles/day) i  4  r  1  7  i  i  8  i  9  1 10  Figure 4.12 Spectrum of baroclinic current for the entire period of record with 90% confidence limits.  41  because it is drowned out by the leakage associated with the less periodic larger variance in Lake Ontario temperature or the harbour east oscillation may only occur at too great a depth to effect flow in the canal. The spectrum of barotropic current, flow associated with water level oscillations in the two water bodies, will be discussed below and will be shown to have dramatically different spectrum.  4.4  Barotropic Current  The barotropic current in the canal is characterized by the mean velocity observed at the moored ADCP. The mean velocity assumed to represent the average velocity across the canal is plotted in Figure 4.13. The barotropic current is shown to continuously oscillate about zero  80 60 -  -40 -60 h  i|  10  \  20 30 time (July days)  !  -  40  Figure 4.13 Depth averaged velocity observed at the moored ADCP (At=l minute). 42  at varying degrees of intensity. The maximum velocity observed is 89 cm/s (out of the harbour) and the minimum is -63.23 cm/s (into the harbour).  The spectrum of the mean velocity is shown in Figure 4.14 using 6 minute averages of the 1 minute observations shown in Figure 4.13.  Because of gaps, only data after day 10 is  considered in the following spectral analyses. The spectrum was created using equation (3.9) with 80 hour overlapping triangular data windows.  The 90% confidence limits are also  plotted. Several significant peaks occur in the spectrum and are tabulated below.  0  0\5  2 frequency (cycles/hour) 1  1^5  2^5  ~3  Figure 4.14 Spectrum of depth averaged velocity observed at the moored ADCP with 90% confidence limits. 43  Hamblin (1974) examined tides by analyzing water level oscillations around the whole of Lake Ontario. The semidiurnal lunar tide (12.48 hours) was found to be the most important with the highest tidal oscillation for the lake observed at Burlington All of the modes of oscillation observed by Hamblin (1982) appear to drive current in the canal. Hamblin found some evidence of afifthmode (1.6 hours) but had difficulty discerning it from the fourth mode. The fifth mode is expected to be most apparent at the east end of Lake Ontario and is not recognizable in the calculated spectrum shown in Figure 4.14.  Table 4.1 Summary of water level oscillations observed near the canal Previous studies Current study Frequency (cph) Period (hours) Period (hours) 0.080  12.5  12.48**  M tidal oscillation  0.20  5.0  5.06*  First mode of Lake Ontario  0.31  3.2  3.21*  Second mode  2.32*  Third mode  1.68  1.7*  Fourth mode  0.70(80% conf.) 1.43  1.4*  Sixth mode  0.41(80% conf.) 2.42 0.59  2  0.79  1.26  1.26*  Eighth mode  0.93  1.08  1.05*  Ninth mode  0.39***  First mode of Hamilton Harbour  *Hamblin 1982, **Hamblin 1974, ***Wu et al 1996  The first mode of Hamilton Harbour (0.39 hours) does not show up in the calculated spectrum. It may be drowned in the leakage of the Lake Ontario spectrum, regardless, it is 44  apparently of far less importance in causing barotropic current. Palmer and Poulton (1976) who observed current at only two depths in the canal found evidence of the same oscillations observed in this study excepting the tides.  Figure 4.15 compares wind intensity with the distribution of barotropic oscillations over time with varying degrees of success. The most intense barotropic event occurs on about day 20 (see Figure 4.13) which corresponds with the most intense wind event. The current during this time is primarily composed of oscillations with periods between 1 and 2 hours. Increased barotropic activity on days 16 and 32 are however accompanied by light winds perhaps indicating the importance of meteorological phenomena elsewhere on Lake Ontario.  0^150 "To  I  I  }ioo CD <D  8" 50  1  1  1  40  45  1  c  0  15  20  20  25  30  35  25 30 35 time (July days)  Figure 4.15 a) Wind intensity at the west end of Lake Ontario b) frequency distribution of barotropic current oscillations over time (higher contours represent increased energy). 45  4.4.1 Helmholtz Resonance To investigate the influence Helmholtz Resonance on barotropic current the water level oscillations at the pier outside the east end of the canal (Lake Ontario) are compared with those at the breakwall outside the west end of the canal (Hamilton Harbour). The spectrum of the two water level measurements is plotted in Figure 4.16a. and the harbour spectrum divided by the lake spectrum is plotted in Figure 4.16b. The lake measurements were made with afloatin a stilling well at 15 minute intervals and the harbour measurements were made with a pressure sensor at 2.5 minute intervals and were then averaged to the same time step as the Lake Ontario measurements. Both time series were thenfilteredusing the high pass filter described in section 3.4.  frequency (cycles/hour) Figure 4.16 a) The spectrum of Lake Ontario and Hamilton Harbour water level oscillations b) Helmholtz amplification and damping in Hamilton Harbour. 46  Tidal oscillations are shown to be equivalent in the two water bodies, thefirstthree Lake Ontario modes are amplified while higher modes are damped out. Despite damping the fourth eighth and ninth mode of Lake Ontario oscillations may cause the most intense barotropic event (seefigures4.13 and 4.15b). Freeman et al. (1974) similarly observed amplification and damping as plotted in Figure 4.16b. The ideal Helmholtz amplification curvefromFigure 2.7 is also shown.  The deviations in Figure 4.16 may be associated with imperfections in the applied method of spectral analysis. Performing the comparison using only the significant peaks in Lake Ontario spectrum would also improve the match between the ideal and the observed amplification curve.  47  5 CONCLUSIONS AND RECOMMENDATIONS Afieldprogram from July 4 to August 15, 1996 collected data during stratified conditions at the Burlington Ship Canal. The purpose of this study was to identify the factors influencing flow in the canal by interpreting observations made during thefieldstudy and determine the applicability of theory regarding internal and surface hydraulics.  A water balance was also carried out to compare the quantities associated with various sources of flow and test the ADCP measurements. Flow in the canal was found to be the most important of these sources followed by municipal waste water and then stream flow. The water balance showed ADCP observations were 19% lower than those expected by Hamilton Harbour water level oscillations. The source of the discrepancy is unknown but may be the result of side wall boundary effects.  Temperature and wind observations showed intense upwelling in Lake Ontario during July when westerly winds prevailed. The upwelling was similar in intensity to those observed in 1959 and 1960 and may therefore be considered fairly typical. The lake upwelling was accompanied by cooling throughout most of the harbour's hypolimnion. Hamilton Harbour showed regular temperature oscillations at a frequency near that calculated for thefirstmode of internal seiche. Observations from the ADCP indicated that density currents in the canal were primarily the result of upwelling in Lake Ontario. During the three week period of 48  intense upwelling Lake Ontario water was flowing through the canal at an average of approximately 65 m /s. 3  Barotropic currents in the canal were caused by tides and standing waves in Lake Ontario. The harbour exhibited Helmholtz Resonance, amplifying some oscillations and damping out others. The peak barotropic velocity, 89 cm/s, occurred during the most intense wind event. However, increases in the amplitude of velocity oscillations were not generally associated with increases in wind activity indicating the importance of other factors such as weather elsewhere on the lake. Table 5.1 Summary of flow into the harbour (day 10 to 45) Flows (m /s)* maximum minimum 19.0 0.78 prorated stream flow 5.45 4.02 waste water treatment plants 97.7 0 baroclinic exchange *taken from Figures 4.1, 4.3 and 4.8 3  Source  mean 2.7 4.88 32.2  Considering the flows indicated in Table 5.1 and their extremes the water quality in the harbour is expected to be highly variable through a typical summer and to depend strongly on Lake Ontario upwelling. Allowing for the difficulty of predicting Lake Ontario upwelling it may be necessary to install one or two thermistors to monitor flow in the canal and predict changes in harbour water quality. The problem of the fate of intruding lake water however should be addressed before exchange flow can be related to water quality at the surface of the harbour.  49  The variability of exchange flow should also be considered in any future data collection project. To get a representative picture of typical summer conditions data collection should include periods of upwelling and downwelling at the western end of Lake Ontario. This would require afieldprogram of perhaps several weeks between mid June and mid September.  The water balance indicated lower velocities near the ADCP than expected across the canal. An ADCP mounted on the side of the wall of the canal to give a horizontal velocity profile would eliminate this uncertainty and perhaps describe the effects of the side walls on the flow.  Finally, confidently quantifying the contribution of barotropic current to exchange flow without monitoring the flux of a conservative substance through the canal is not possible under stratified conditions. A total dissolved solidfluxthrough the canal should therefore be carried out to determine the contribution of barotropic current to exchange flow. 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Transactions of the Royal Society of London. B. 236:355-404. Munk, W.H., Snodgrass, F.E., and Tucker, M.J. 1959. "Spectra of low frequency ocean waves". Bulletin, Scripps Institution of Oceanography. 7:283-362.  Palmer, M.D., & Poulton, D.J. 1976 "Hamilton Harbour: Periodicities of the physiochemical process" Limnology and Oceanography. 21:118-127 Panofsky, H. A. and Brier, G.W. 1958. Some Applications of Statistics to Meteorlogy.  Penn. State Univ. Press, pp. 148-151.  52  Rao, D.B. and Schwab, D.J. 1976. "Two dimensional normal modes in enclosed basins on a rotating Earth: application to Lake Ontario and Superior". Transactions of the Royal Society of London. A. 281:63-96.  Roy, F.E. 1983. Spring exchange flows, Black Bay, Lake Superior. National Water Research Institute, Canada Centre for Inland Waters. Engineering services No. 547. Spigel, R.H. 1989. Some aspects on the physical limnology of Hamilton  Harbour.  Environ. Can. NWRI Contribution No. 89-08 Viessman W. and Lewis G.L. 1996. Introduction to Hydrology. Harper Collins, pp 8285. Watson, E.R. 1904. "Movements of the waters of Loch Ness as indicated by temperature observations". Geographical Journal. 24:430-437. Welch, P.D. 1978. "The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms", pp. 17-20. In: Childers, D.G. (ed), Modern Spectrum Analysis. IEEE Press. Wetzel, R.G. 1983. Limnology. Saunders College Publishing, pp 75. Wu, J., Tsanis, I.K. and Chiocchio, F. 1996. "Observed currents and Water Levels in Hamilton Harbour". Journal of Great Lakes Research. 22(2):224-240.  53  APPENDIX A  Surface  0.5 m 1  observation contaminated by side lobe contamination 16 good observations (bins) each covering 0.5 m in depth  ~  ~  ~5~  ~6~  -9.5 m  W  IT rT  IF 14~ l5~  W 0.5 m  no observation due to blank after transmit  0.4 m  instrument height  Bottom  Figure A. 1  Diagram of ADCP observation bins and data gaps  54  APPENDIX B  Legend Location: where the instrument was moored as indicated in Figure 3.1a (TChain #) or Figure 3.1b (Burlington ship canal west, north, east or south).  The bracketed  abbreviations will be used in future reference such that thermistors BSCW4 is located at a depth of 4m at the west end of the ship canal. Res.: The resolution of the instrument as logged. Acc Spec: Manufacturers specified accuracy. Max Dev w/o cai: The absolute maximum temperature error observed during calibration without the application of a calibration adjustment. Max Dev w cai: The absolute maximum temperature error observed during calibration with the application of a calibration adjustment. Temp Range: The range of the temperature observed during deployment.  55  Wadar  Paroscientific pressure sensor Stowaway  CCIW  UBC  UBC  4424  Res.  XL-100 CCIW  Inst.  s  o  Acc. Spec.  XL-105 CCIW  6777 0.002  Serial No.  OS-200 UBC  4432 0.01  Ship canal west (BSCW)  TR-1000  CCIW  4013 0.08  0.05  UBC  XL-105  CCIW  6781 0.002  3608  XL-100  UBC  100  4016 0.08  i—»  is)  00  o  •—i  o  0.05  TR-1000  UBC  ©  0.001  ADCP Current meter  0.05  Max Dev. w/o cal  -.1 +.12 +/- .005 0.006 (0.05)  Max. Dev. w cal  7-25C  Temp Range (degrees C)  Logger failed  15-24  17-25 -.01 +.21 -.015 +.009 (0.17)  +/- 0.003  +/- 0.02  (0.04)  (0.046)  -0.02 (0.1) (0.14) 0.03  8-24  6-24  6-23  6-22  56  B  o  LH  ON  1  » rt  9.5m  1  o  ON  to  1  rt xji -a n  oo  1  to  s 3 n s NO  Res.  0.001  Acc. Spec.  0.054  CCIW  -.05 +.175  Max Dev. w/o cai  (0.042)  Max. Dev. w cai  7-25  7-25  (0.13)  (0.13)  247-L  CCIW  4423  (0.25)  247-L  CCIW  (0.12)  XL-105  ON  Ul U)  (0.04)  (0.04)  (0.034)  5-23  5-23  5-24  Failed  15-25  Temp Range (degrees C)  (0.15)  (0.04)  (0.15)  6-25  247-L  (0.04) (0.2)  5-25  CCIW  247-L  247-L  (0.04)  5-24  O o  CCIW  o ©  o o O  o o  247-L  o o  (0.15)  (0.04)  +  O o o  to o © ON UI  1  Inst. CCIW oo 4^  Ul  00  Ul  Ul  00  Ship canal north (BSCN) Stowaway UBC VO  3610  Wadar CCIW o  CCIW  ©  Serial No. Pvc#4  247-L  CCIW  ON  o oo ON  VO  S7  ON ON  Ul  to ON  VO  TR-1000  XL-105  Wadar  Paroscientific pressure sensor Stowaway  CCIW  UBC  CCIW  UBC  UBC  4234  LIZ  6782  4420  Pvc#3  CCIW  4023  Max Dev. cai  Max. Dev. cai w  Temp Range (degrees C)  10-26  w/o  -.03 +0.19  Acc. Spec.  0.25  7-25  Res.  0.054  -0.008 +0.007  7-25  0.001  -0.005 +0.023  (0.022)  0.01  -0.02  (0.1)  -0.2  (0.035)  (0.026)  5-24  5-24  5-25  6-25  Failed  6-25 0.05  0.08  (0.09)  O  (0.038)  +/- 0.004 0.002  0.01  (0.14)  0.001  0.08  0.05  (0.15)  0.002  o to  100  OS-200  CCIW  4629  XL-100  6780  o to  Serial  XL-100  CCIW  »  Inst.  XL-105  ~o oo  UBC  ;+ i  >—»  o o  to  No.  4^  TR-1000  So  o to  o to  Ship canal east (BSCE)  ui 00  1287  as VO  Serial  Gnome  Wadar  Gnome  Gnome  Gnome  Stowaway  UBC  UBC  UBC  UBC  UBC  UBC  UBC  3612  Inst.  Gnome UBC  No.  Gnome  UBC  Acc. Spec. 0/+.22  w/o  Max Dev. cal  0.25  +0.002  +0.06  +0.005  0.054  0.054  0.001  0.001  VI  o to  +0.045  Temp Range (degrees C) Max. Dev. w cal  5-23  5-24  5-24  5-24  6-25  9-25  12-25  17-25  +0.005  -0.01  + +/- 0.007  59  U)  to  u>  Ship canal south tBSCS)  Wadar  to i—'  00 LAY OS  oo  to ON  00 NO  Inst. 1291 0.25  0.25  Acc. Spec.  -0.02  (0.17)  +.08/+.28  +.08/+.33  -0.025/+.2  Max Dev. w/o cal  +/- 0.003  +/- 0.004  (0.038)  -0.75/+0.15  +/-0.1  Max. Dev. w cal  10-15  10-16  18-30  18-28  Temp Range (degrees C)  4428 4630  Res.  3609 0.25  -0.02  0.002  •  Serial No.  3605 0.08  o to  10-18  11-21  12-23  15-25  17-25  4012 0.08  o to  4008  0.05  ©  o  Harbour east (HHE) TChain 7 Stowaway  CCI  Stowaway  XL-100 CCI  Stowaway  XL-100  0.01  0.05  o 6779  CCI  o to  TR-1000  XL-105  0.01  o  6775  10.0  0.002  o to  TR-1000  CCI  17.5  XL-105  S o S o  12.5  S o n  60  S n <  S  <  UJ UJ 00  b  Breakwall (BWL) TChain 8  Res.  Stowaway UBC  UBC  3158  73157  73156  Serial No.  Stowaway UBC  Inst.  Stowaway 1088  1238  2034 0.08  to  XL-100  5424  1993 0.08  SACM3 UBC  CCIW  10.0 XL-200  1094  13.0  5423  SACM3  XL-100  SACM3  o  CCIW  o  UBC  0.25  0.25  Acc. Spec.  -0.1/+0.16  -0.17/+0.08  Max Dev. w/o cal  +/-0.1  +/-0.1  Max. Dev. w cal  17-25  18-26  Temp Range (degrees C)  17-25  0.25  failed  13-22  failed  7-19  9-20  +/- 0.04  7-19  7-19  +/- 0.04  0.05 -0.11 +0.06 t  to  o k>  XL-200  +^  LAI  13.0  ©  61  o k> to  o  to '©  GO  bo 4^ ON  Lo  00  Max Dev.  Res.  Seria!  Temp Range (degrees C)  Acc. Spec.  19-26  Max. Dev. cai  0.05  19-26  w  0.002 0.05  100  (10)  -0.05/+0.18  w/o cai  6764 0.002  No. CCIW 6767  Inst. TR-1000 CCIW  Harbour Centre (HHC) TChain 6  TR-1000 0029  19-25  19-26  UBC 73159  +/- 0.11  Stow UBC 0.08  1  15-24  4007  (0.05)  CCIW  (0.15)  XL-100  (0.05) 0.08  (0.016)  3482  (0.09)  +/- 0.005  CCIW  0.01  XL-100  0.002  (0.019)  4429 6850  (0.09)  +/- 0.01  CCIW UBC  +/-0.1  XL-105 TR-1000  0.01 0.002  4632 6783  0.002  CCIW UBC  6776  XL-105 TR-1000  UBC  1  to 0.05  i  Ul  to  o  to  o  to  1  oi  17.5  TR-1000  0.05  o  +/- 0.005  o  +0.03  to  0.05  12.5  to  0.25  Stow  o  0.25  3.75  o  to to Ul  o  6a  Ul  o to  Ul  to to  12.5 TR-1000  XL-105  CCIW  CCIW  CCIW  4633  6768  4426  Max Dev. w/o cai -0.23/+0.  -0.15/+0, (0.1)  ax. Dev. cai -0.14  emp Range legrees C)  - 0.004  U l  U l  ON  ON  ON  to  to  to  to  to  to  U J  U J  1  b  O  b b  (0.1) (0.15) 0.02 (0.08)  (0.09)  63  ;f  U l  XC.  Serial No. 73151 U l U l  les.  UBC 73152 U l U l  o  Inst. Stowaway UBC 73153  Ul  to  ©  U l U l  l>  o  C« o  b  Lake Ontario (LOnt) TChain 5  Stowaway UBC 4421  to  pec.  Stowaway CCIW 4431  o to  XL-105 CCIW  o to  XL-105 4018  o  CCIW  ©  XL-100  p  6778  to  UBC  b  TR-1000  b  XL-105  17.5  U l  to  o  o to  o  H U l  rb  -o  o to  b  ^ U l U l u i  o to  * g  —i  H-»  o  b  •p  b  o o  'p  b  o  o  o  ^-*\ o  b oo o  o o  fid bo  to  U J  o  o  bo 'o  U l  U l  to •o  00  ON U J  U J  oo o  i—»  U l  


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